kar
1 1
=
1) 12”
Sn == — 23 Sf}:
n 1
OH IN) OD)
at) — 2 Gh nr =D Y Ie
toen oral
and proves the following theorem :
ag) Da a jb seo Cage Ef thw
Theorem C: The conditions lim. — vr» = Oand liam. Sana? =s
no I Tl 1
e ea Tim. sn =s, and tak
are each necessary for the existence of lim. s, =s, and taken toge-
noo
ther they are sufficient.
(A)
The mean-valuesjs, differ from Cusarò's or Hörper's mean-values,
but in a second paper’) Kienast has shown the equivalence of his
mean-values with those of Cresarò-HöLDeR.
Remark 2.
iva}
We have tacitly assumed that Sa,w" converges if —1 @ il;
J 8
1
This is however superfluous for our purpose as the condition
4 (p (p 5 : 5 KS
lim. ny? Ali Zi — 0 implies the convergence of > az” pro-
nzo l
vided |a|’< 1.
. (p) (p) ain
Indeed from dian. n (ae = An = 0 we infer the absolute
n= @
; > (p) (p) n .
convergence of ,(#) = > [An — Anje” provided |«| < 1.
|
Further we have by (17):
pi, =#.y, (#) He (le) @);
therefore the absolute convergence of (a), which implies the abso-
lute convergence of gy’; (a), implies also the absolute convergence of
gr—1(w). Repeating the argument we infer the absolute convergence
a
of p‚(#)= = a,2" provided |z|< 1.
1
Be) Proceedings of the Cambridge Phil. Soc., vol. 19 (1918), p. 129.
3) Proceedings of the Cambridge Phil. Soe., vol. 20 (1920), p. 74.
Chemistry. — “Hydrogenation of Paraffin by the Bureaus’ Method”.
By Prof. H. 1. Waterman and J. N. J. Perquin. (Communicated
by Prof. J. BörsSEKEN).
(Communicated at the meeting of February 24, 1923).
In a previous communication on the hydrogenation by Brrarus’
method of mineral oils or allied products, different experiments were
discussed, which were carried ont with heavy Borneo-asphalt-oil,
distillation residue (pitch) of this oil, and with asphalt obtained by,
distillation of Mexican crude oil’).
The experiments in question, comprising both cracking- and ber-
ginisation experiments, were executed in a vertical immovable auto-
clave.
That we have now chosen another material, technically perhaps
of less importance for this purpose, is owing to the peculiar advan-
tages which commercial paraffin offers for such experiments over
other materials, as asphalt. Paraffin is much more easily analysed
than asphalt, and this holds also for the products prepared out of
paraffin, when they are compared with the corresponding substances
formed in the treatment of asphalt. Thus paraffin yields products
that are less strongly coloured than Mexican asphalt. For these
experiments we had an autoclave at our disposal which could be
shaken continuously *).
The way of procedure was for the rest quite analogous to the
earlier experiments; the arrangement of the apparatus is represented
in fig. 1. The capacity of the autoclave was about 2500 em”, the
heating took place by means of gas, in such way that the tempe-
rature could be regulated accurately to a few degrees.
The paraffin had a Sp. Gr. (15°/15°) of 0,913, the solidifying point
(SHUKOFF method) was 50,6°, the bromine-value, (addition) determined
by Mc. [rarer’s method *), was 0,5.
1) Congrés international des combustibles liquides, Paris, 9—15 Octobre 1922;
Chimie et Industrie, numéro spécial, Mai 1923, p. 200.
3) Apparatus supplied by AnpreAs Horer, chief instrument-maker at the
laboratory of Prof. Dr. Franz FrscHer, Kaiser Wilhelm Institut für Kohlenfor-
schung, Milheim—Ruhr.
3) Journ. Am. Chem. Soc. 16, 275 (1894), 21, 1084 (1899), Journ. Soc. Chem.
Ind. 19, 320 (1900); H. Beckurrs, Die Methoden der Massanalyse, Braunschweig
1913, p. 480.
a
227
Practically the bromine value of the paraffin may, therefore, be
neglected. The bromine-value determined according to Mc. Iuminey’s
method, is obtained by subtracting the substituted bromine from the
Fig. 1.
430°
42o
2 Koo |.
5 ©
re Pes ©
0 2.
H I
> 38° oO
0 a,
Í —— DUUR IN MN
STe
hd Go 12e 180 24o
Overdruk = Pressure Duur in min, = Time in minutes
Fig. 2.
228
total amount of the absorbed bromine. The remaining quantity gives
a measure of the degree of unsaturation, and is expressed in percent-
ages of weight of the weighed quantity.
In every experiment 300 gr. of paraffin was taken, an equal
weight of stones being put in the autoclave to promote a thorough
mixing; the temperature was always 435°. Some of the results
obtained are recorded in the table, and in fig. 2 an illustration is
given of the variation of the pressure in the course of experiments
33 and 34. Though in experiment 33 the typical pressure curve
according to Beraius given in our preceding communication is not
obtained, probably on account of the high temperature, the difference
from the cracking-pressure curves is nevertheless very striking. In
all the other experiments recorded in the table the pressure curves
obtained are analogous to those of 33 and 34. The oils obtained
by the Beraivs’ process were coloured from yellow to red, and
perfectly transparent, a small quantity of “carbon” was deposited on
the bottom. The oils obtained in cracking were very dark of colour
and pretty well opaque. Here too separation of some carbon is found.
The small quantity of carbon which is deposited on the bottom,
when the weight of carbon which had already been deposited on
the stones is added, is so small, both in the cracking and in the
Bereius’ method, that practically the paraffin may be assumed to
have been entirely converted into oil and gas in both processes.
In this we leave out of consideration experiments 35, 37, and 40,
where the duration of the processes was still so short that the
reaction produet had remained partially solid. Hence the product
obtained had to be melted out in these experiments.
It appears from the experiments made that,
1. observations can be obtained which can be perfectly reproduced
(compare 35 and 37, and 46 and 48).
2. if the duration of the experiments is long enongh, the paraffin
is practically quite converted into liquid oil and gas, both in the
cracking and in the Berarus’ process.
3. the yield of gasoline does not differ much in the two processes.
4. there is a great difference in the nature of the residues left in
the distillation of the oil obtained according to Enarer. Its specific
gravity is always smaller in the Berginisation experiments than in
the corresponding cracking experiments, which is a confirmation of
corresponding experiments made by Berxeus.
5. lt appears from the final pressure, also in connection with the
gas analysis (percentage of hydrogen), that actually considerable
quantities of hydrogen are absorbed in the berginisation.
EN
COMPARISON OF BERGINISATION AND CRACKING AT + 435° C,
] on
= £ = L Distillation of the obtained oil
= 2s v5 5 NEE = according to ENGLER CLES:
<= —
= 0 ia an ore v 5 es u ApS
8 |fe2 | See | #5 | 28) Ss lsd.) 55 Br d
S$ | 3ge sE fe | 83 | fe |< E | 2 | Weight % of the distilled oil. Sp. Gr.
= fe ES 5 = Be BS 58 = E ER 6 Sp. G. Quantity |compar-| Hydrogen
Cec bee, = wis w ~ H 5 E _
5 Bar | 5 a Ss w SES 5 3 © to to || residue residue in Litres | ed with) percentage.
at el nee A Sie E EE Sn Sn IE Loss?) | 15°/15°.
Z v me sl Le 220° | 300° [> 3009 air
= |
chy) 60 60 40 ORS 37.5 2601)| 16.4 | 24.9 | 41.0 | 56.3 Peal 0.846 — 0.24 85.8
37 E 60 60 40 108.5} 37.5 | 272')| 16.1 | 22.8 | 37.9 | 59.0 Boll 0.854 — 0.20 89.5
©
36 3S 60 120 40 107 | 3) 272 19.0 | 36.6 | 56.6 | 38.7 4.7 0.835 — 0.37 74.6
33 5 60 180 40 117 30 256 20885 bleh Wwe |p 22 5c! Ono) 0.852 — 0.56 56.9
-
U
46 JA 15 240 40 118 | 28 250 | 21.0 | 58.9 | 79.6 | 14.8 5.6 0.836 63 0.63 47.5
48 15 240 40 120 | 28 240 PAD KOOR MORZAN STE 7.0 0.838 62.5 0.63 46.5
40 80 60 Oa SOB sal) es EZLN 21565923). 0F | 39s ONO] 0.9 0.854 — 0.99 —
45 2 10 120 0 5 51.51< 4 BOR STORIONI KOI NRR 20 4.3 0.855 — 0.80 —
ES 2
34 S 60 180 Of i Om dome P20 A18 ROOM eK ZO EON PND 6.0 0.900 — 1K) Pas)
O 8
49 15 240 0 1E 12 1.5) 238 | 23.9 | 56.8 | 76.9 | 16.2 6.9 0.902 29 0.94 3.7
') The product obtained was still solid and had to be melted out, which gave rise to extra losses of weight.
2) Belongs to the lowest fraction.
230
6. The bromine value caused by addition of the oils obtained
by berginisation is lower than that of the corresponding cracking
experiments. It is, however, very risky to draw general conclusions
from this bromine value, for dissolved unsaturated gases can have
a great influence on the halogen value.
The example given here proves convincingly that a determination
of the yield of oil and gas from a solid substance does not suffice
to enable us to form a correct opinion on the process of Brr@ius.
A comparative cracking experiment is required for this. Possible
results refer only to the procedure followed, in this case to the
periodic process, the temperature at the experimenting etc.
It is self-evident that in practice processes that proceed continu-
ously, will be preferred. It may, however, be considered to be an
established fact that when Bereivs’ method of procedure is followed,
important quantities of hydrogen added from the outside, are che-
mically bound. After the scientific researches of SABATIER C.S. CON-
cerning the hydrogenation of hydro carbonic vapours with catalyst and
the technical hardening of fatty oils (NorMANN and others), this fact,
combined with the absence of express addition of catalyst, may be
considered as the third great discovery in the region of hydrogenation.
Delft, Laboratory of Chemical Technology
of the Technical- University.
Palaeontology. — “Contributions to our Knowledge of the Palae-
ontology of the Netherlands. 1. Otoliths of Teleostet from the
Oligocene and the Miocene of the Peel-district and of Winters-
wyk.” By O. Posrnumus. (Communicated by Prof. J. C. Scnourr).
(Communicated at the meeting of February 24, 1923).
As regards the fish-fauna of the tertiary deposits in the Nether-
lands the occurrence has been reported of a number of Selachii in
the Oligocene of South-Limburg >), and of the Miocene of East-Gelder-
land *) and Overijssel *). No remains had as yet been found of Teleostei.
We are in a position to form an idea of the fish-fauna in the
North Sea of Miocene time, from a number of otoliths occurring in
material obtained from borings, undertaken by the Government
(Institute for the Geol. Exploration of the Netherlands) on the Southern
Peelhurst, notably from boring 20 (Helden) of the Middle-Miocene
(75.4—80.4 m.), from boring 21 (Swalmen) of the Upper-Oligocene
(100—160 m.), and of the Middle-Miocene (75—100 m.); likewise
in material originating from boring 22 (Liessel) also of Middle-
Miocene date (LOO—190 m.).
Moreover the test-boring U near Winterswijk, placed at my
disposition some otoliths from the Septarian clay, and from the Middle-
Miocene, laid bare in the bed of Slingerbeek near Winterswijk.
The following specimens have been found‘):
Oligocene.
Middle-Oligocene (Septaria clay), Winterswijk.
Otolithus (Seopelus) pulcher, Prochazka.
1) W. C. H. Sraring De bodem van Nederland, Ze deel, Haarlem, 1860, p. 282.
2) Ibid, p. 209, 210.
3) T. C. Winkuer. Catalogue systématique du Musée Teyler, 6me livr. 1867,
p. 624.
*) They will before long be figured and described in a more detailed memoir.
232
Upper-Oligocene, Swalmen.
Otolithus (Dentex) nobilis, Koken.
55 (Percidarum) limburgensis, nov. spec.
i (Trachinus) mutabilis, Koken.
Ms (Trigla) Schuberti, nov. spec.
i. (Scopelus) austriacus, Koken.
A (Scopelus) pulcher, Prochazka.
5 (Gonostoma ?) parvulus, Koken.
he (Gonostoma?) angustus, nov. spec.
5 (Fierasfer) nuntius, Koken.
ce (Gadus) elegans, Koken.
a (Merlangus) cognatus, Koken.
Miocene.
Middle-Miocene, Swalmen.
Otolithus (Pereidarum) frequens, Koken.
a (Trachinus) mutabilis, Koken.
* (Trigla) rhombiens, Schubert.
" (Gobius) aff. elegans, Prochazka.
33 (Ophidiidarum) semiglobosus, nov. spec.
5 (Ophidiidarum) swalmensis, nov. spec.
S (Gonostoma?) parvulus, Koken.
en (Solea) approximatus, Koken.
a (Rhombus) rhenanus, Koken.
a (incertae sedis) peelensis,. nov. spec.
Middle-Miocene, Helden.
Otolithus (Serranus) Noetlingi, Koken.
55 (Centropristis) integer, Schubert.
is, (Dentex) nobilis, Koken.
re Percidarum) acuminatus, nov. spec.
En Trigla) Schuberti, nov. spec.
on ‘Sciaenidarum) Staringi, nov. spec.
7 Gonostoma) aff. gracilis, Prochazka.
os (Clupea) testis, Koken.
ee Clupea) Priemi, nov. spec.
% (Gadus) elegans, Koken.
bs (Phycis) elongatus, nov. spec.
5 (incertae sedis) Mariae, Schubert.
n (incertae sedis) peelensis, nov. spec.
233
Middle-Miocene, Liessel.
Otolithus (Dentex) nobilis, Koken.
(Percidarum) frequens, Koken.
(Percidarum) Liesselensis, nov. spec.
(Scopelus) austriacus, Koken.
(Scopelus) pulcher, Prochazka.
(Gonostoma?) parvulus, Koken.
je (Clupea) testis, Koken.
(Fierasfer) nuntius, Koken.
(Gadus) elegans, Koken.
(Merluccius) emarginatus, Koken.
(Phyeis) elongatus, nov. spec.
(Hymenocephalus) globosus, nov. spec.
5 (Hymenocephalus) medius, nov. spec.
=; (Hymenocephalus) ovalis, nov. spec.
ns (Hymenocephalus) Brinki, nov. spec.
(Hymenocephalus) dubius, nov. spec.
(Maerurus) pusillus, nov. spec.
(Maerurus) ellipticus, Schubert.
(Maerurus) debilis, nov. spec.
Middle-Miocene, Winterswijk.
Otolithus (Gadus) elegans, Koken.
The fauna of the Upper-Oligoeene ot Swalmen is characterised
by the absence of littoral forms; the fishes that occur, inhabit the
deeper fand more open parts of the sea, as e.g. Dentex, especially
in the upper water-layers, or the Scopelidae, especially at greater
depth. {The depth may have been somewhere about 400 m. at a
moderate distance from the shore. This tallies with the known data,
as the Upper-Oligocene is represented in erosion-rests as far as the
line Liege —Aachen—Cologne.
From Middle-Miocene data are known from localities on the
Southern Peelhurst, lying in one line, that is about straight and
runs about $.E.—N.W. In the South-most of these three localities,
near Swalmen, the genera Rhombus, Solea and Gobius are conspi-
cuous. They are all littoral forms, and not met with in the material
of Helden, about 20 km. farther, where, however, Clupea, Serranus,
and Dentex oceur; these fishes we also find naar Liessel, about 18 km.
farther in Noord-Brabant, where, however, Macruridae and Scopelideae
predominate in the material. Judging from the remains of fishes
Swalmen is not far from the ancient coastline; in the vicinity of
234
Helden the fauna resembles closely that of a moderately deep sea,
while the remains of Macruridae, occurring in the material of
Liessen, originate from deep-sea forms, so that here we have to
assume a greater depth of about 1000 m. This conclusion is in
accordance with the results of the inquiries of the Government Institute
for the Geological Exploration of the Netherlands: the boundary-line
between the continental and the marine Miocene runs about via
Swalmen; the lignite formation occurs near Melick-Herkenbosch and
Vlodrop, while in the profile of boring 21 the lowermost layers
of the Miocene are marine, and the upper layers display a limnie
facies. It seems to me that a closer inspection of material from the
Groote Slenk, southwest of the Peelhurst, would be very interesting.
The tertiary fauna of this region differs from the recent fauna of
the North-Sea: on the one side forms occur that inhabit greater
depths than those living in the North Sea at the present day, such
as Scopelidae and Macruridae, which occasionally occur at high
latitudes in the Atlantie Ocean; on the other side the tertiary fauna
comprises genera such as Dentex, Centropristis and Serranus, now
living at lower latitudes. In my judgment the occurrence of the
latter points to a change of environment, which is to be aseribed
either directly to a change of climate, or to other conditions, e.g. an
altered direction of the oceanic currents.
In conclusion I wish tot express my warm thanks to Prof. Dr.
J. H. Bonnema for kindly placing at my disposal the material in
the Geological-Mineralogical Institute of the State University of
Groningen.
/
Palaeontology. — “Contributions to vur Knowledge of the Palae-
ontology of the Netherlands”. Il. ““On the Fauna of the Phos-
phatic Deposits in Twente. (Lower Oligocene)” By O. Posrnumus.
(Communicated by Prof. J. F. van BEeMMELEN).
(Communicated at the meeting of March 24, 1923).
In examining a collection of fossils, derived from the phosphatic-
nodulus-bearing deposits of the localities Ootmarsum and Rossum
(between Oldenzaal and Denekamp) I came upon the following
formations :
Coeloma balticum Scarier, Zeitschrift der deutschen Geol. Ges.
Bd. 31, 1879, p. 604, Pl. XVIII; one specimen.
Myliobates toliapicus 1 Acassiz, Recherches sur des Poissons
fossiles, vol. 3, 1843, p. 321, tab. 47, fig. 15—20; loose toothplates.
Carcharodon angustidens a. Agassiz, Recherches etc., vol. 3,
1843, p. 255, tab. fig. 20—25, tab. 30, fig. 3: teeth.
Notidanus primigenius L. Acassiz, Recherches ete., vol. 3, 1843,
p. 218, tab. 27, fig. 4—8, 13—17; teeth.
Oxyrhina Desori (L. AGassiz) Sismonpa, Memoria della Reale.
Accademia delle Science de Torino, 2d series, t. X, 1849, p. 44,
tab. II, fig. 7—16; teeth.
Owvyrhina Desori L. Sismonpa mut. flandrica, M. Lerican, Mé-
moires du Musée Royal d’histoire naturelle de Belgique, T. 5, p.
280, fig. 87; vertebrae.
Odontaspis cuspidata L. Agassiz, Recherches etc. vol. 3, 1843,
p. 294, tab. 37, fig. 43—49; teeth.
Otodus obliquus L. AGassiz, Recherches ete., vol. 3, 1843, p.
267, tab. 31, tab. 36, fig. 22—27; teeth.
Lamna spec., vertebrae.
Phyllodus polyodus L. Agassiz, Recherches ete., vol. 2, 1843,
p. 240, tab. 69a, fig. 6, 7;
And in addition some fragments of bone, presumably from Cetacea.
The phosphatic deposits are disposed in the profile as follows *):
“Underlying the Middle-Oligocene Septarian clay are..... pale-
green, very fine glauconite sands, probably referable to Lower-
Oligocene, but seeming to belong to the Middle-Oligocene. At the
basis of these sands a very typical conglomerate layer of loosened
phosphorite nodules and shark’s teeth appears, as may be found
e.g. in the eocene quarries at the southern base of Lonnekerberg
in the neighbourhood of Rossum, between Oldenzaal and Denekamp,
and in the hills north of Ootmarsum”. The phosphatic deposits
1) Eindverslag van de Ryksopsporing van Delfstoffen. Amsterdam, 1918, p. 114.
16
Proceedings Royal Acad. Amsterdam. Vol. XX VI.
236
therefore may be estimated to be of Lower-Oligocene date; at all
events they must have been formed at the commencement of the
Oligocene transgression.
These formations are best compared with the Oligocene phosphatic
deposits of the North-German Plain, of which those from Helmstedt
have become familiar to us through the researches of Von KoENEN
and H. B. Grinitz'). It appears that all the fossils found in Twente,
except Oxyrphina Desori, are also to be found near Helmstedt,
which proves that the two deposits are equivalent.
This induces me to put forward some remarks about the forma-
tion of phosphatic nodules. Most authors advocate the view that
the more or less rounded shape of these bodies is to be attributed
to transportation, which view is adhered to by recent observers,
as shown by the “Eindrapport” from which we just now quoted a
passage. We contend that the nodules, in many cases, are not
rounded, but more or less irregular, nay, as STARING?) observes,
they often seem to be made up of two or more rounded nodules.
The shark’s teeth are in many cases enclosed in an approximately
rounded phosphatic nodule: the portion that is sticking out, however,
is not worn off at all, which fact clashes with the presumable
genesis. H. B. Gwinrrz assumed the transport of the nodules to have
taken place in the Recent Tertiary and based this view on the
fact of their presence in the layers of Myliobates and of Lamna
cuspidata, which he had examined, and which up to that time had
been recognized only in the Pliocene. Now, this cannot apply to
the Overijsel phosphatic deposits, in which these remains have also
been met with, because the younger deposits of the Oligocene also
occur here. The palaeontologieal argument that the rounded shape
is attributable to rolling cannot be sustained. We are bound to
assume that after the formations of the phosphate-concretions, the
position of the deposits remained unaltered, which conception has
been supported already by Dr. W. P. A. Jonker *) on other grounds.
I wish to conclude by gratefully acknowledging my indebtedness
to Mr. J. Berninx, Director of the Museum ‘Natura Docet’ at
Denekamp, for granting me access to the fossils collected by him.
1) H. B. Geintrz, Die sogenannten Koproliethenlager von Helmstedt, Biidden-
stedt und Schleweke bei Harzburg. Abhandlungen der Naturwiss. Geselschaft , Isis”
in Dresden. 1883, p. 3— 14.
H. B. Gerrrz, Ueber neue Funde in den Phosphatlagern von Helmstedt, Biid-
denstedt und Schleweke. Isis, 1883, p. 37—46.
2) W. H. C. Srarina, De bodem van Nederland. 2e deel. Haarlem, 1860, p. 195.
3) W. P. A. Jonker, Het ontstaan van phosphorieten. Handelingen van het 17e
Natuur- en Geneeskundig Congres, 1920, p. 94— 96.
Mathematics. — ‘An application of the theory of integral equa-
tions on the determination of the elastic curve of a beam,
elastically supported on its whole length’. By Prof. C. B.
Brezeno. (Communicated by Prof. J. C. Kiurver).
(Communicated at the meeting of March 24, 1923).
In his well-known treatise ,,Vorlesungen iiber Technische Mecha-
nik” (Vol. III, § 48) Fépr1 describes a construction, by which the
elastic curve of a beam, elastically supported on his whole length,
might been approximated.
If in the differential equation of this elastic curve
Ely" +ky=q
(Hl = coefficient of stiffness of the beam, / — coefficient of stiffness of
the supporting ground, g = specific continuous loading) the function 4
where known, it would be possible to refind this function by
integrating four times the expression fe
This integration would graphically correspond to the construction
of the elastic curve of a beam, which carries only well-known forces.
It is obvious, therefore, first to make a supposition about the
elastic curve — in such a way, of course, that the reaction-forces
of the supporting ground will be in equilibrium with the external
forces of the beam —, then to integrate graphically the expression
ua and finally to controll, if the before-mentioned accordance
takes place.
„Im allgemeinen — such is the opinion of FérpL — wird man
zunächst eine starke Abweichung in der Gestalt beider Kurven
finden. Dann ändert man die zuerst gezeichnete Belastungsfläche
so ab, dasz sich die Lastverteilung jetzt der Gestalt der gefundenen
elastischen Linie nähert und wiederholt das Verfahren für diese zweite
Annahme. Die Uebereinstimmung zwischen Belastungsfläche und
zugehöriger elastischen Linie wird jetzt besser werden und nach
mehrmaliger Wiederholung findet man mit hinreichender Genauig-
keit die wirkliche Druckverteilung.”
16*
238
Certainly it will be possible, — under favourable conditions —
to find in this way technical sufficient accordance between the
supposed curve and the one, derivated from it; but generally the
convergency of the described process is uncertain.
In the following paper a convergent process will be given.
2. The equation
Ely" +ky=g
is transformed in
gj + kel y = q'
k q
if —=k*, 6
TNT,
Putting y"" =p (2) it becomes:
gp (a) + xf ple) det = q' + Av? + Ba? + Cz + D
0
or, using the well-known relation
f ple) da* Le p (s) ds
*(e— s)°
yy
ple) +k
0
p(s) ds =q' + Az' + Ba? + Cr + D.
A, B, C and D are constants of integration, which enable us to
satisfy the following conditions:
lee oy 0, Dr ie — ())
Bett Ot ORL 1
The former conditions imply, as is seen from the relation
> Ab Sede (Cia JD
fn
that the coefficients A and B are zero. The coefficients C and D
are determinated by the latter conditions.
3. According to VorLrerrA the solution of the integralequation
ae
ag y (s)ds = q' + Ce + D
239
may be written as:
p (7) =p, (@) + kp, (@) + kK? py (e) + RPG (we) +...
where
f, (#2) =q + Ca + D
n= gas
0
pn (x) == TT (p= fn—1 (s) ds,
0
This solution however can only graphically be used, if the
coefficients C and D are known. Nevertheless this coefficients depend
on the second and first integral of y (x) in a point which is different
from zero. Therefore we cannot find them a priori.
4. To meet this difficulty, we introduce the function
Xe) =g + Cor + Ds
C, and D, being two constants, determinated by:
| %e (©) dx = 0
0
l
ue 2 de = 0.
0
By choosing C, and D, in this manner, we reach that 1°. C, and
D, can easily be graphically found, and 2°. that the function
g(a) = — [Oo ats as
0
satisfies at the point «—/ the conditions
p‚' == 0, Q," == 0,
or the conditions
l l x
fu mar =0, fte fn mae=e
0 0 0
240
x l l
For:
l x
p', (omi fte fr (z) dx = a ® Xo (z) dx = 0.
0 0 0 0
If we should deduce the function vp, («) from g, (a), in the manner
which Vorrrrra indicates, the second and third derivates of ~, (2)
would not be zero at the point «—/. Therefore we define the
function
x oe dg
Xi (x) ZT | ($= ho (s) ds se C, © +D,|
0
C, and D, being constants determinated by
l
lie (@) dx = 0
0
l
fue ndi A0
0
In this way, the second and third derivates of x, (v) take at the
points «=O and «e=! the prescribed values; on the other hand
fore-fold integration of x, (~) gives rise to a function, the second
and third derivates of which are at the point « = /also equal to zero.
This being stated, we are lead to define the series of functions
x, (7) =q + Cor + D,
% (x) = — [Jar Xo (s) ds =i C, x ar D, |
ta wo = [fs
(w — He
Xn (@) = == 7 B TT) 1 (3) ds + Cu 4D, |
where the coefficients Ci and Di are bound by the conditions
l
[u@d=o
0
l
fue). ar=0
0
Mn drt Ce D,|
241
and to put
= ITB) Se 12 9a(@) a2 ee0e (9) dos
This function satisfies formally the equation
x
' («—s)'
p(x) +k nn (s) ds =q' + Ca D
. !
and the expression y, which follows from it:
DCE DEN OEE
Os Fran ke a k
=— x, (z) — Ky, (2) — ky, (2)...
satisfies formally the conditions, imposed at the ends « = 0 ande = /.
For, substituting the expression g in the integral equation we
obtain — provided that it be allowed to integrate term by term the
series, which occurs under the sign of integration:
Cx + D,— k(C, «+ D,) —k? (C, a+ D)—....=Ca+D.
If the series, which appears in the first member of this equation,
converges, there can be disposed of the constants C and D in such
a manner, that the equation becomes an identity.
Of course it would now be necessary to examine the convergency
of the described process of iteration.
For this investigation however we refer to the paper of Mr. J.
Droste, which follows this. We will state here only, that conver-_
»]4
gency is sure, if a7 < 500, and go on to demonstrate in which
manner the process can be graphically performed.
5. At the first place the system of forces, which loads the beam,
is substituted by another load, changing linearly, (q, — ae + B), and
which is statically equivalent with the first.
This substitute load causes a sinking down of the beam, determi-
nated by
arg
Ip Dean
This y, can be considered as the first approximation of the
required y, and can be brought in relation with the expression
C,z + D,, which is defined in N°. 3.
Indeed, «x + 3 satisfies the equations
242
l l
JG + B) dx =fgde
0
l l
J Gea fiers
0
on the contrary Cr + D, is defined by
l 1 i
fice | D,) de = — ide = (de
0 0
0
l l l
[ce + D,). 2 da= feae Aven
0 0 0
It follows, that aa + 8B=— E/(C,x + D,), so that:
az+B , Cat D,
ET ek
The load which really charges the beam differs from the substitute
load by:
Van
ng 4=g ler Hp) =H + Cr + D)= Ely, (2).
By adding this load (which is in equilibrium) to the load q,, we
would regain the real conditions of loading.
However, if we add the load g, the beam gets a deflexion y,,
determinated by:
Ely” = ET?, (2)
Hence:
na fReoden (es Gide Acct Bi Cee
The second and third derivates of y, being zero for «= 0, it
follows that 4, =0, B, =0.
Choosing C, and D, so that:
we identify y, and — x, (2).
243
At the same time, the forces, defined by Zy,, are in equilibrium.
If the elastic ground were loaded with 4, it would obtain the
the deflexion y,. In this case the beam and the ground would have
the same shape. However the load on the ground can only arise
from the beam. The deflexion y on the ground therefore involves
necessarily a reaction-load —y, on the beam.
This latter load gives rise to another deflexion y, of the beam,
defined by:
EIy,"" = — ky, =k YX, ()
Hence
x
disse | (Sn, (s) ds + Cr zin Dl
0
3!
If we require again that the load £y,, which follows from y,,
is in equilibrium, we find that:
IST k' X, (x).
From this, we deduce y, = — k?x,(x) and so on. Therefore, the
terms of the series:
C,«+ D
ae En > —X, (w) — kX, (2) — kX, (©)
represent elastic curves of a beam, which is loaded in a well-
defined manner.
6. Fig. 1 illustrates the described construction in the case:
7/= 200 em., 6 = breath of the beam = 25 em., J = 5000 ecm‘,
E = 100000 kg/em?; EI = 5 X 10° kg.em’, £= 5 kg/em?,
k=—=bk=125 kg/em*. The load diagram has a parabolic form; the
specific load at the ends of the beam is '/, of its value at the
middle. The total load is 15000 kg. The scale of length in horizontal
direction is n= 5 (l em — means 5 cm <—=).
t
The deflexion are 25 times enlarged; 1 cm. fn Wee em].
The linear load q,, which is statically equivalent to the given
load q, will give a sinking down to the beam, which is:
15000 KG
UTERO GA
This sinking down is represented in figure 1a by 25 < 0,6 cm.
= 15 cm.; and gives rise to the straight line y,. This line also
244
represents, when the scale is altered, the load q,; in this case 1 em.
| eee nes 15000 kg. Si k
en as Le N 7 bh
must be interprete 200 X 15 em g/em (say m, kg/cm)
Yo
On this scale the parabolic load q has been drawn in fig. 1a,
so that the load q—q., — Which determines the elastic curve y, —
is represented in fig. 1a by the hatched area.
In the well-known manner the elastic curve y,, which corresponds
to the load g—q,, is constructed (see figures 16 and 1c with the
corresponding pole figures 1 and 2).
To determine the situation of the pole in the second pole figure,
we make the following remarks.
In figure 1a 1 cm. <—— represents 2 cm. ——; 1 cm. | represents
m, kg/em. Therefore 1 cm? of fig. la represents nm, kg.
Assuming now that in the first pole figure 1 cm. (whether ——~
or ) will represent m, em? of figure Îa (in the drawing m, is
supposed to be 5) and that the first pole distance has a length of
H, em (in the drawing 10 em), we see that 7, represents m,m,n/, kg.
Hence | cm. | in fig. 15 represents m,m,n’?H, kg. cm. Consequently
245
: ; ‘ : emmen
the unity of area in fig. 15 means in the next integration Ke
units.
. m,m,m,n'H, H,
The second pole distance H, therefore represents TE
units, if we suppose that 1 cm. of this distance represents m, cm?
(in the drawing 10cm’) of the area in fig. 16.
From all this it follows finally that 1 em. | in fig. 1¢ represents
4
m,m,m,n‘ HH,
EI
em.
Now the elastic curves y, and y, must been drawn on the same
scale; hence:
m,m,m,n‘ H, H
EI
1 EI
H.
a mnd 7
25 m, m, m, n* H,
Ssi:
= 12,8 em.
The elastic curve y, once found, the drawing process is to be
repeated so many times, that the last approximations may be neglected.
By adding the different curves yy, y,.... we obtain the elastic
curve y. The final result can be controlled as follows. We load the
beam at the one side by the well-known external forces, at the
other side by the continuous load ky, which follows from the elastic
curve y. Then we construct the elastic curve y. If the result y were
exact, the curves y and y must be identical. Fig. 1/,9, 4 shows, that
a difference between the curves y and y cannot be observed.
7. Considering fig. 1, it appears that the ordinates of the curves
y, and y, are proportional. If the factor of proportionality is called
— wu, so that y, = — uy‚, it is easily seen that the ordinates of the
curve y, can be written as — uy, and so on.
The ordinates y,,y,,...Yn at any point can therefore been looked
upon as terms of a geometrical series and the curve y can be
obtained by adding y, to the sum of all the following approximations.
Not only when the factor of proportionality u is <1, but also
when « >1, it may occur that the described drawing process is
useful to find the elastic curve.
Supposing that the load — ky, gives rise to the deflexion — uyn
there can be found a factor rv, such that the function vyn
246
satisfies the equation ly" + ky——ky,. Using the relation
— EI py," = — ky,, we find the condition:
kin
== = kvyn == TT kun
lu
whence:
SU
y= ——
a+ 1
We therefore can obtain the deflexion y of the beam by
—="
adding oy yn to the sum of the curves y,, 7, .-- Yn, or by adding
—u 1
(1 de | Un Dn yn to the sum y, + y, +... + Yn-t-
u
Thus we can stop the drawing of curves, as soon as two conse-
cutive ones y, and vj are found, the ordinates of which are
proportional.
Though — generally — the above mentioned proportionality only
appears exactly after an infinite number of iterations, it nevertheless
will be approximately observed tolerably soon. Neglecting in such
a case that part of the last found loading diagram which troubles
the proportionality between its ordinates and those of the foregoing
diagram, we can use the preceding remark, provided that 1° the
neglected load diagram be insignificant, and 2" it gives no rise to
following load diagrams which grow larger and larger.
kis
The second condition is satisfied when EIS 14600.
The justification of this latter statement can be given most
naturally by the aid of the deductions, given by Mr. Droste. We
therefore refer to his paper.
Mathematics. — “An application of the theory of integral equations
on the determination of the elastic curve of a beam, elastically
supported on its whole length’. By Dr. J. Droste. (Communi-
cated by Prof. J. C. Kruiver).
(Communicated at the meeting of March 24, 1923).
1. Under the same title and at the same time a paper’) of Mr.
BirzrNo appears in these Proceedings. The question, suggested, in N°. 4
of that paper as to the validity of the process of iteration used in
it, will be answered here.
For that purpose we observe that the function of a, satisfying the
differential equation
4
y
— Ay=g (a br EEA leo el 1
mee ane (x) . (1)
and the conditions at the ends of the interval, is a meromorphic
function of 2. We might find it by means of the method of the
variation of constants and then expand it in ascending powers of 2;
the radius of convergence R of the power series that stands after
the first term (containing At as a factor) might easily be calculated
then. After this it will be necessary to investigate wether it agrees
or not for 42=' with the series of paper I; it is only in the first
case that the latter series will be valid for #<{ R. For the sake of
this investigation, however, and also in order to get an idea of the
proportionality of the functions %, («) (vid. I, 7), we prefer to use
the method based upon the theory of the integral equation of
FREDHOLM.
2. We construct a function of x, satisfying in the interval (0, /)
both the equation
4
d'y
det
and the conditions y" = y'"= 0 at the ends, and being continuous
as well as its first three derivates everywhere in (0,/) with the only
exception of a saltus of the third derivate at the point 5:
d°y | +0
ke = (j)
da |: =o
TAN Ot YS Soe te ER bd A. (2)
1) Referred to in the sequel as “paper I”.
248
This function we call K(w,§, 4); it represents the deflexion of
the beam, loaded by a load 1, which is concentrated at the point §.
Putting 4 = — gf the function
1
zE 15 {sinh OQ (a—§) — sin 0 (x—§)}
(the upper sign for «<6§, the lower for «2 §) will satisfy all
conditions excepted those at the ends.
Assuming
1
USS Se 40° \sinh @ (a—8) — sin 9 (a—§)} +
Q
+A cosh 9 (w«—}) + Bsinhole— tl) + Ceose(w—$l) + Dein ole — 3),
we may determine A, B, C and D in such a way that K(w, &, 4)
satisfies the conditions at the ends. This gives
1
— Acosh} ol + Bsinh } ol + C cos } ol —D sin } ol — i }sinh OS +-sin 0§},
Q
1 2 2
— Asinh} ol+ Beosh 4 el—C sin 4 ol —D cos } ol = 40’ fcosh 08+ cos QS},
— Acosh 4 el—B sinh } ol + C cos Hol + Dsin} ol =
1
~ { sink @ (I—&) + sin 0 (/—8)},
40
— Asinh } el—B cosh $ pl —C sin } gl 4 D cos } ol =
Sap {cosh @ (J—§) + cos @ (I—S)}.
Adding the first and the third of these equations and also the
second and the fourth we get two equations containing only A and C.
Subtracting the third from the first and the fourth from the second
we get two equations containing only B and D. In this way we
obtain
1
— Acosh} ol + C cos} el= Dn {sinh 4 ol cosh e(§—4 ol) + sin $ ol cos e(E—41)},
Q
1
— Asinh}el— Csint ol= i {cosh 4 ol cosh 9 (§—4 1) + cos } gl cos p (541) },
] .
Bsinh } ol — Dsin} ol = Te {cosh 4 ol sinh o(S—} l) + cos 4 ol sin 0 (E—$ D},
1
Bosh } ol — Dain} Ql = re { sinh 4 ol sinh 9 (§—4 1) — sin } gl sin o(S—}))},
249
From these equations A, B, C and D are easily solved; putting
A, (e) = cosh } yl sin } ol + sinh 4 ol cos 4 ol,
A, (9) = cosh 4 ol sin § ol — sinh } gl cos 4 ol,
we get
— 40° A, (9)} Acosho (etl) + C cos 9 (v—}$ l)} =
= (cosh } ol cos ol + sinh } ol sin } el) cosh 9 (a —} 1) cosh 9 (S—
+ cosh 9 (x—t4 l) cos g (S—} /) + cos 9 (a—} L) cosh (5 —} 1)
+ (cosh 4 ol cos 4 ol —sinh $ ol sin 4 ol) cos v (w—} 1) cos 9 (E—4 J),
— 40° A, (0)} Bsinh 0 (rtl) + Dsing (e—-$)}=
= (cosh 4 ol cos $ pl —sinh } gl sin 4 ol) sinh 9 (x —} 1) sinh ol E — $1)
+ sinh 9 (c—3 l) sino (§—} ) + sin 0 (a—} lL) sinh gp (§—3 l)
+ (cosh } ol cos $ ol + sinh 4 ol sin } gl) sin 0 (a—} 1) sing (S—$ U).
We now have calculated the function A (z,8,2); it appears to be
a function with the denominator 407 A, (e) A, (©). The values of À
equating to zero this denominator are the characteristic numbers of
the problem; as A (a, &,A) is symmetrical with respect to « and &
that numbers will be all real. From this it follows that the cor-
responding values of @ have an argument that is a multiple of
+; it is easily proved to be an even multiple so that the values
of o wil be real or purely imaginary and the corresponding values
of 4 negative or zero. For that purpose we first write 1—cosh olcos ol
for 24, (0) A,(e) and then substitute in it ed =a@+478; equating
the real part to zero we get
cosh a cosh B cos a cos B 4+- sinh a sinh B sin a sin B == 1,
which is not satisfied by B= + a +0, for substituting 8 = + a@ in
it we get sinh? a — sin? a, which is impossible for a 4 0. Therefore
the values of @ are real or purely imaginary and the characteristic
numbers are negative, except one which is zero.
If @ be a root of A, (e)—0, also zg will be a root (and con-
sequently — e and — 10); the same is true with respect to the
roots of A, (ge) =90. We now call the positive roots of the equation
toh p = — tg p,
in the order of their magnitude p,,p,,.... and the positive roots
of the equation
toh p = tg p,
ordered in the same way q,,q,,... Then the characteristic numbers
will be
2 pn\* Zn
Gil i ) ff 2) os Il Pes)
250
3. We will also calculate the characteristic functions. If p represents
one of the numbers p, and g one of the numbers qg, we have to
calculate the following limits:
2p\* 2q\4
lim of K (x, §, A), lim \ — ( 2 | K (a, §, 2), lim je’ (7)
20 peer ty U e>2g/l l
ay
1
To none of the limits the term = FS | sinh @ (a —&) — sin g(x —§)}
Q
ACS ZN
contributes.
For the first of the limits we find immediately
lim o* K (x, §, 2) = ze 41) (§ — 4 4).
20 l ip
To the second only the term A cosh y (we — 4 l) + Ccoso (ae — $2)
contributes. First we have
jel ces = i) 1
CE) —49° A, (eye — Leosh p cos p
and the numerator of the fraction we have found for
A coshe (a—t l) + Cos e (a—} l)
changes for gp = *?/; into
5 E
cosh 2 p G- :) (os poop + sinh psinp) cosh 2p G i) + cos 2»( | -1)
a
+ cos 20( — :)
From cosh p sin p + sinh p cos p=0 we have
ie E
cosh 20( | — 1)+ (cosh p cosp—sinh p sinp) cos 2p G- 1) |
, 4 cosh p
cosh p cos p — sinh p sin p = ———
cos p
, cos p
cosh p cos p + sinh p sin p = ;
cosh p
and consequently the numerator becomes
x coshp x cos p Ë )
Nen 2 } h2p| ——3 2p| ——
jou zl P :) ae cos of i i) = 5 cosh (| 1 ) tom (| 4
In this way we find
9 4
lim Je" -(7) | Hua, E,a)=
o—>2p/l l
251
i cosh ‘ 2»(F :) cos (5 - 1) cosh 2»(7-
= =
= a
l cosh p cos p cosh p cos p
| rs
tol
ee
isc)
S
a”
io
3
EN
| On
nh
S74
In the same way
AD
lim Je" =
prol! v3
sinh 2g aa sin 2g LA Ni 29 Jen t sin 2q Sia 4
1 AK at Lars l iy)
RE Ss: A= —
l sinh q sin g sinh q sin q
Putting
i cosh 2 Dn € — :) cos 2p,, (G- i)
(U) = —,7 2, (es) = = ’
Po (# Vl Pale) vl | cosh py r COS Pn
x x
3 | sinh 2 (| = :) sin 2qn GC — i) |
= — (¢4—} eK Ge) j= aa 9
Beem tO TM enk qn i sin Qn
(SR)
the functions @, (x), W, (w) mn = 0,1, 2...) will be the orthogonal
/ 8
and normal characteristic numbers; ‘iby: satisfy equation (2), 2 being
replaced by the corresponding characteristic number.
Now drawing graphs of the functions y= tgv, y= tghe and
y= tgha in one figure, it is easily seen that p, is an angle in
the 2n-'® quadrant, and gq, an angle in the (22 + 1)-*" quadrant.
For no p, and gq, converge to the middlepoints of the intervals.
From this it follows that cos p, and simp, converge to +42 and
it is easily seen that the absolute value of ~, (2) and w, (7) remains
less than a number which is independent from w and n. Now as
Fie eee
no NN no N
the two series occurring in
OB tw OW OL nn)
À n=1 A == (7Pnji)*
AA (77 m(é
EN)
n=1 4 = (CAI)
will be uniformly convergent and the right hand side therefore will
be equal to K (a, &, 4).
NASI
iY
Proceedings Royal Acad. Amsterdam. Vol. XX VI
252
4. We now suppose y to be the required solution of (1), viz. that
solution for which y" = y'" =O in the points «=0 and «=/ and
which is continuous in (0,/) as well as its first three derivates ;
as to y'” it may have a saltus in a finite number of points aj,
which will be the case if q' (x) has in the points a; discontinuities
for which g' (a; +0) and q(ai —0) exist. The points a; and the
value € divide the interval (0,7) into a number of subintervals; in
the interior of each of them we have
d ’ 1 À ' " wl 2
EE [y"" K(e, &, 4) —y K' (w, &,4) + y' K" (a, 8,2) —y K" (a, §, a =
ax
= y'" K (w, &, a) — y K'" (@, &, a):
Integrating the equation over the subintervals, adding the results
and regarding that y" = y" = K" (a, §, 4) = K'" (#,§,4)=0 forz=0
and «—/ and that y,y',y",y", K,K', K", K"' are continuous every-
where except A’” in & we find
l
— y (5) = fis" (x) K (w, 5,2) — y (@) K'" (a, 5, A)} de
0
Replacing y'" by q'—ay from (1) and &'" by —aK from (2)
we get
l
y (§) = | K (, &, a) q (2) de
0
or interchanging rv and § and observing the symmetry of K (2, &, a)
with respect to w and &
l
ole 4b K (a, &. 2) q'(8 a8.
0
If the beam is not loaded by q(x), but by N loads Q;, concen-
trated in the points §;, we have
N
ye) = E UK 5D
where Q';= Q;/EI. If the beam bears both the load q(x) and the
loads Q; we have
l
N
vk EDI OEH E OKE ED. EE
0
From (4) it follows that y is a meromorphic function of à with
the poles 0, — (2?,/))* and — (?9,/)*. This is easily seen from sub-
253
stituting (3) in (4) and integrating term by term, which is permitted,
the series (3) being uniformly convergent.
Expanding y in a series of ascending powers of 2 (the first term
will in general contain A) the expansion will generally be con-
vergent for |A <(??1/)*; only if the term with the denominator
A + (#?4)))* cancels, the expansion will be valid for larger values of
2. In case the Q;’s are zero this occurs if g(x) be orthogonal to
g, (x). We thus see that if the expansion of paper 1 be exact and
if not by chance
{
{a (x) p‚ (we) da = 0
0
it converges only if
4
ray a) gh ea beh ai, CO)
From (4) we deduce a formula which will be of use further on.
Supposing the beam to bear only a load p(x) pro unit of length
and to be in equilibrium, we will have
l |
[eta = ferme =0
0
a
or which is the same
1 i
fe (2) po @ de = fp (2) ap, (@) dx = 0.
0 0
Now from (4), in which q' (x) is to be replaced by p(x)/HJ and
in which Q'; =0, we have
l
y (2) = | Tea, EA Me ae.
where K(x, &, 2) arises from K (a, §, 4) by omitting in (3) the term
with the denominator 4. Putting 2=0 K (w, 8,2) changes into
K(o, 8) = = Ge) 5 Peelen (5)
n=1 (?Pn/,)* n=1 (4m 1,)°
tees ee 0)
and we get
l
ye) = Fy [Kop Oa Perea e549)
0
254
This represents the deflection of the beam under the conditions
that the beam be in equilibrium and that the ground be absent;
it is such that
l l
fr@a= PNY) - ET ve (C3)
0 0
since ‘K(x, §) is orthogonal with respect to v(x) and y,(x). By the
conditions (8) the deflection is perfectly determined and (7) repre-
sents it.
5. We shall now prove that the series deduced from (4) agrees
for 2=k’ with the series of paper |. Representing the iterations
of K(x, &) by K,(a, §), Kw, §).... we get for |a| < (/;)*
K (a, §, 4) = K (« B) —1 K, (@, &) +2° K, (2,8 .-.,
l ! l
[Kt §, Aa) q' (§) ds = [Ke 5) q' (8) dE —À fr, (zE) (E)dE+.--,
0 ° 0
as is proved in the theory of integral equations. From this it follows
that (4) for |A| < (%1//)* takes the form
ve) = ye) +9, (©) +9, (@) + ---s- - + &
where
l
l
1 Le
pe = = |. (a) | @, (8) 9 (8) dE + w, (w) f he (&) 9 (8) dB +
0 0
N N
+H) = AH) +H) F Gv (8)|
l
Ms 1 N
n= ap [KIO op, >, WK 8,
0
l
k
0
255
k .
el) = pr ij K (x, 8) yn © dE,
0
Each of the functions y,(2), except v,(w), satisties (8). We shall
now prove the terms yv, 4, ¥,,--- to be the same as the corresponding
quantities of I, 5, from which it will follow that the series
Yo ty, +.-.-- agrees with the series of I, 4. Indeed in the first
place y,(z) is a linear function of 2; the function /y,(x) represents -
the linear load ax + 8, which is defined in I, 5 and is statically
equivalent to the given load. For we have
l
N
kfm (x) , (x) dz =o, BAD d5 + EQ, 6),
0 0 ai
1
N
fn Ondern fwd + = WE,
0
0
or substituting in it the expressions found for the functions ¢, («)
and 1p, (0)
fis (a) jie fr dE + = Q:
Senin = fea ja} > = DE
which proves the proposition.
Omitting from (9) the deflexion y,, the remaining terms represent
the remaining deflexion. This becomes y, for £=O and so y,
represents the deflexion which the beam, if not supported by the
ground, gets under the influence of the load that remains after
subtraction of «2+ 8 from the given load. As besides y, («) satisfies
(8), it is identical with the quantity y, of I, 5.
The reaction of the ground, arising from the deflexion y,, represents
a load — fy, of the beam; by this load the beam, if not supported
by the ground, would get a deflexion, which we may calculate
from (7) viz.
l
k
— gf Kende
0
256
This represents the deflexion y, (a); it is seen to be the same as
the quantity y, of I,5. In the same way we continue and so we
may prove that (9) agrees term by term with the series of paper I.
7. In case the expansion do not converge, it may happen that
the method of graphical integration, communicated in paper I,
remains still valid (vid I, 7); this depends on the approximate
proportionality of the functions y, (x) for large values of n. We
shall prove this now; more exactly: we shall prove
ek)
no Un (2)
where u is independent from w.
Now K,(x,§) is represented by the absolutely and uniformly
convergent series
Palen en Wm lize (Ss).
m=1 he
where the quantities 4,, represent the numbers (2i/))* and (2%/;)* in
the order of their magnitude and the functions w,,(#) are the
corresponding normal orthogonal functions. Putting
l
fm Gd > ROA an
RE
0
we get the absolutely and uniformly convergent series
ES =P, ©
Yn (x) =(— nt zn (n == 1 2, OE x)
n=
° m
Supposing / to be the smallest value of m for which P,, 4 0, we
can write
k'yn—1 À Eh ei
Un (@) = = j = |p, Wh (a) AF (* : y = ( nal En Um (x).
Ant m=1 Ah+m
The series in ate right hand member of this equation has an
absolute value which is less than the sum of the series
25 hi Py Wm (2) |,
m=1 Antm
a quantity which is independent from n. From this and from
: 2 h n
ie || == || ==0)
n=> AH
we get
257
Qn
h
lim ———— y,, («) = Ph, wp (x
Bee ea yet! («) (7)
In this way we find
chan.
Yn+i (£)
n k Kyr k'
l date! @) lim ( i =
n—>o Yn (a) an ro ri An?
mn dale)
rr!
which proves the proposition; we see that
k'
u a ae
Now, if in drawing the successive deflexions y,,7,,¥;,.... it is
found that y,41:y, is sufficiently independent from z, it will be
permitted occasionally to consider
— Yn
Yn == HUF. ty—i+— k'
es
ie A
to be the deflexion y. For we have
DL A entra (2) Yn
u SAE nn de 5 + x
gesl m= À
1 an m 1 ——,
at Ge =f Fi
ze = == Wn = -(— ay" i S En = oR (— J
m=h 4m + m m=h Je 1 ien
Ah
= on m\z ra — kN! 1 2
== mn Ee) —— | i
mah Am == k m=h Am An =F ke Am (Ah Se k')
and as
EN Wm (a ;)
= Dy
Sn ien hm ar K
we get
— — Nt 1 hp
nn Yl —— 55 Pm Wm (& ca RIO
7 il m=h+ ( ) (5 Ne ) Jan + k Am (An SF k') \
Since m=h gives zero. If k' Angi, the series has zero as a limit
for n — oo, which is easily seen by writing it in the form
= Ni (0 À n—1 1 À
Yn -Y=— ( ) = ‘Pe Wm (a) ( zt) | seh h
Jr m=hA--1 Devs Jin ae k An On HE k
258
since the absolute values of the series occurring in the right hand
member is less than the sum of the convergent series
Ee | Bm Wm (a) |
m=h+1 Am =F k'
It thus appears that we may consider yn to be the required
deflexion 4, supposed n be large enough and & <2. If g is,
after h, the first value of m such that Pm #0, the condition Z'<.
must been satisfied if we wish to replace y by yp for large values of n.
Chemistry. — “The Phenomenon of Electrical Supertension.’ IL. *)
By Prof. A. Smrrs. (Communicated by Prof. P. Zeeman.)
(Communicated at the meeting of February 24, 1923.)
In my book ‘Die Theorie der Allotropie’’*), and also in the
preceding communications I have treated the electrical supertension
only very briefly. Therefore I will discuss this important phenomenon
somewhat more at length here.
We imagine the case that a palladium or platinum electrode is
made cathode. For the explanation of the phenomenon that will now
2H 46 Pa
Fig. 1.
appear, we shall make use of the /#, X-diagram, in which the ex-
perimental electric potential of the electrodes is plotted as function
) These Proc. Vol. XXI No. 3, p. 375 (1918); Vol. XXI, No. 8, p. 1106 (1919).
®) JOHANN AMBROSIUS BARTH, Leipzig. 1921.
English edition Lonamans, GREEN and Co. London 1922.
French edition GaAuTHIER VILLARS. Paris. 1928.
260
of the concentration; on the assumption that the pressure (1 atm.),
temperature, and total ion-concentration (metal ions + hydrogen
ions) are constant. In the foregoing figure 1 hydrogen is taken for
one electrode, and palladium for the other, but instead of the
latter platinum might, of course, have been chosen just as well.
Line bh indicates the potentials of the series of electrolytes that
can coexist with different palladium phases. These phases of the
palladium are different, because palladium dissolves the hydrogen
in quantities which increase with the hydrogen-ion concentration
of the electrolyte.
Line bf indicates the potentials of the different palladium phases
containing hydrogen’), which coexist with the different electrolytes.
In our Z,X-figure the potential of the metal-phase can be read on
the H-axis, but it is clear that on this axis also the potential of the
electrolyte can be read, when we reverse the sign.
The line ag represents the potentials of the different electrolytes
coexisting with the gaseous hydrogen phases. These hydrogen phases
consist of pure hydrogen, and lie, therefore, on the hydrogen axis.
Accordingly the portion ak of the hydrogen axis gives the potentials
of the hydrogen phases coexisting with the different electrolytes.
The point of intersection c of the lines bh and ag represents the
electrolyte which can coexist at the same time with the palladium
phase (e) and with the hydrogen phase (d), so that it also shows
the potential of this three-phase equilibrium. The situation of this
point of intersection follows from the solubility products of hydrogen
and palladium : *)
Lp, = Gy =AV* ==
Era (GO LO mt:
At the three-phase equilibrium
(Or, = (9) ra
from which follows:
(Pa) Bs
ay Ze
lii(Hs)sisaput == 4, then) (2a) — 102x142.
From this it is seen that the point e lies very much on one side,
and that when a palladium electrode was immersed in a 1-N sulphuric
102 x —14.2
1) This line indicates the gross hydrogen concentrations, and gives, therefore,
no information about the state in which the hydrogen is.
2) Compare with regard to the smallness of these products the remarks in
“The Theory of Allotropy” in the chapter: “Small concentrations” p. 172.
261
acid solution, and the palladium was and remained in inner
equilibrium, this metal would dissolve a little, till the palladium
concentration of 10? '4? was reached, while a corresponding in-
appreciable quantity of hydrogen would have been generated. In
this it is assumed that both platinum and hydrogen continue to be
in inner equilibrium, for the value used for Ly, agrees with the value
for hydrogen in inner equilibrium, and we shall for the moment
assume the value used for Lp, also to agree with the condition of
inner equilibrium of Pd. Pd is, however, an inert metal, so that
the solubility product of this metal will in reality have decreased
through the slight attack, and the dissolving will have already stopped,
before the palladium ion concentration 10? —15-2 has been reached *).
For the sake of simplicity we shall, however, assume here that
no disturbance of the Pd takes place, and that the three-phase
equilibrium is established, in which the Pd-phase e coexists with the
electrolyte c and with the hydrogen phase d at a pressure of one
atmosphere. When now the Pd-electrode is made cathode, or in
other words, when electrons are added to the Pd, hydrogen and
palladium ions in the ratio of 1 : 10°*—'42 or practically only
hydrogen ions will be separated at this electrode. It will now depend
on the velocity with which the inner equilibrium
2H + 26¢2 He,
sets in, if the hydrogen formed will coexist in a state of internal
equilibrium or in a state of formation. In this condition the solubi-
lityproduct of the hydrogen is greater, and the point that now
denotes the coexisting hydrogen phase, will lie on a potential curve
that lies at more negative values, and is represented by ag in fig. 2.
We must, however, not forget that this line could only be realised
when the state of formation of the hydrogen discussed just now could
coexist unchanged in electro-motive equilibrium with a series of solutions.
This is, however, not the case; only one point can be realised on
this curve, and this is the point indicating the liquid layer that
coexists with the hydrogen phase d', which is in a state of formation,
and with the palladium phase e’. The heterogeneous equilibrium
between the metal boundary layer and the hydrogen boundary layer,
just as that with the liquid boundary layer, having been immediately
established, the palladium boundary layer will also contain too many
hydrogen ions and electrons, which means that also the hydrogen
dissolved in this metal boundary layer, will be in a state of formation.
1) The potential + 0.82 V., from which the solubility product Lpa = 10?* —822
has been calculated, is most probably already a potential of a disturbed state of
the metal palladium.
262
We may, of course, also start from the Pd, and say that only
in the Pd-electrode to which electrons are added, and in which
hydrogen ions dissolve, hydrogen is formed in a state of formation, and
that afterwards gaseous hydrogen occurs in a state of formation, but this
only implies a difference so far as the first moments are concerned,
for when once electrolytic generation of hydrogen has set in, this
oH 3E Fl
Fig. 2.
will occur in a state of formation at the same time in the gas
phase and in the metal phase.
It should be pointed out here that when we have a homogeneous
phase, as the solid solution of hydrogen in palladium, the electrical
potential of these two components with respeet to the coexisting
electrolyte must be the same. This applies also to the solid solutions
lying on the line be, but in the solid solution lying on this line
there is equilibrium between hydrogen molecules, hydrogen ions,
and electrons, whereas this is not the case in the Pd-boundary layer
which coexists with hydrogen in a state of formation.
This is, therefore, the reason that the Pd-phase e' coexisting with
the hydrogen phase a', does not lie on the prolongation of the line be.
The hydrogen dissolved in the Pd-phase e' is in the state of
formation, and consequently this phase is richer in hydrogen ions
and electrons than when the hydrogen is in inner equilibrium. The
263
potential of the dissolved hydrogen in e' is more strongly negative,
and the same must, therefore, hold for the Pd. lt is now, however,
the question in what way the potential of the palladium has under-
gone this change.
It is clear that the Pd must have become richer in Pd-ions and
electrons. We have already seen that this phase has become richer
in electrons through addition of hydrogen in a state of formation,
so that only the question is still to be answered how the
concentration of the Pd-ions can have been increased. This must
have taken place through the reaction
2Hs + Pds — Pds + 2Hs
in which, therefore, hydrogen ions have ceded their charge to
Pd-atoms. We, therefore, come to the conclusion that the palladium
boundary layer, which coexists with hydrogen in a state of formation,
will possess too many hydrogen ions, palladinm ions and electrons,
or in other words, that it will contain both hydrogen and palladium
in a state of formation.
If palladium could coexist in the same state of formation with a 1.N.
solution of a palladium salt, the electric potential would, of course,
possess a more strongly negative value than corresponds to point 6 in
fig. 2. This more strongly negative potential is indicated by 0’.
And when, therefore, the same state of formation of Pd could continue
to exist also in contact with the whole series of solutions, the line
b'e would indicate the solid solutions which can coexist with the
electrolytes lying on the line 6'c’. The new three-phase equilibrium
that is found when Pd is made cathode at a definite density of current,
and in which hydrogen escapes in a state of formation, is denoted
by the points d'c'e’. The line a'c'g' rising very little throughout
the greater part of the concentration region, it is clear that the
value of the negative potential in this new three-phase equilibrium
would be equally great when the point c’ lay on the prolongation
of the line be, and the point e on the prolongation of the line be,
but as we demonstrated above, the points c’ and € belong to other
lines than those that are mentioned here. It follows from these
considerations that in the ease of electrolytic generation of hydrogen
the state of formation of the hydrogen in the coexisting hydrogen and
palladium phases are very closely related. This makes it clear that
the cathode metal can exert influence on the degree of super-tension.
The state of formation is a state of non-equilibrium, and the differ-
ent cathode metals will, to a different degree, accelerate the con-
version of this state of non-equilibrium in the direction of the inner
264
equilibrium. This is the reason why the so-called super-tension of
hydrogen is different, when different metal cathodes are used.
It is self-evident that when the state of formation of the hydrogen
does not vanish too quickly, the hydrogen must possess an abnormally
high conductivity for electricity immediately after the escape. This
phenomenon was, indeed, found long ago‘), but it was tried to
explain it in another way; it is, however, probable that this phe-
nomenon is for the greater part to be attributed to the state
of formation.
The activity of the hydrogen dissolved in the metal phase, is in
perfect harmony with the considerations given here. As regards the
temperory variations of the super-tension, they will have to be
explained by the slow change in constitution of the coexisting
phases. The heterogeneous equilibrium between the boundary layers
is established with great velocity, but the composition of the phases
changes slowly, and this must be the reason that the three-phase
equilibrium metal-electrolyte-hydrogen changes slowly.
In conclusion I will still point out that analogous considerations,
of course, apply to oxygen and other non-metals. As is discussed
in “The Theory of Allotropy” p. 160 et seq, the extension of
this theory to non-metals, necessitated the assumption that the atoms
of all elements can split off and receive electrons.*) The difference
between the solubilities of the positive and the negative ions in
elements with pronounced metal- resp. metalloid character, is so
great that for the explanation of the electro-motive behaviour as a
rule only the positive or the negative ions need be taken into
account. But as was also already stated the supposition mentioned
must very certainly be used when the positive charges of non-metals
with regard to electrolytes, and likewise the small electric conducti-
vity of non-metals in electrically neutral condition, is to be explained.
Further the said supposition is also required to make clear the
formation of compounds between metals. ’)
When we now return to the non-metals and choose oxygen as
example, we have to consider the two following reactions:
ONZ 20" + 2v, 9
and
0, + 27,0220"
As v, = 2, the latter reaction may be written:
On 40 = 20",
1) Becker. Jahrb. der Radioaktivität. 9, 52 (1912).
4) Theory of Allotropy p. 160.
265
The latter equation is sufficient to explain the electric super-
tension of the oxygen. It was stated *) that in the case of anodic
polarisation of an unattackable electrode or an inert metal the sepa-
rated oxygen must relatively contain too few electrons and too few
negative oxygen ions, so that oxygen in a state of formation or in other
words oxygen in super-tension would have to possess an abnormally
small electric conductivitly immediately after its formation, at least
when no other phenomena neutralise this effect.
When we have an inert metal, i.e. a metal that can be easily
disturbed, and we make this anode, polarisation will take place.
If the disturbance of the metal goes so far that oxygen is separated,
then, the metal boundary layer being poor in ions and electrons,
also the coexisting oxygen phase will be abnormally poor in elec-
trons. Besides the other substances coexisting in the liquid, the metal
boundary layer will also contain oxygen dissolved, and it is evident
that the state of this oxygen, dissolved in the metal, will depend on
the state of the oxygen in the coexisting oxygen layer.
Laboratory for General and Inorganic
Chemistry of the University.
Amsterdam, Februari 1923.
1) Theory of Allotropy p. 164.
Chemistry. — “The Influence of Intensive Drying on Internal
Conversion”. 1. By Prof. A. Smrrs. (Communicated by
Prof. P. ZrrMAN).
(Communicated at the meeting of March 24, 1923).
In December 1921 a communication was published in the 100th
volume of the Z. f. physik. Chemie under the same title as is given
above. In manuscript this communication was at first more extensive,
for it also contained a possible explanation of the great influence
found by Baker of intensive drying on the chemical reactivity of
gases, and besides a discussion of the sa-ammoniae problem’). The
reason why for the present | withheld this part was as follows.
[ was at the time still in doubt whether in intensive drying it
should be assumed that a fixation or a shifting of the inner
equilibrium takes place. The results of Baker’s researches *) published
then spoke greatly in favour of a shifting, but at first this assumption
seemed open to objections, because it is then necessary to assume that
the slightest trace of moisture can give rise to a great displacement
of the inner equilibrium.
Afterwards, when Baker had published*) a new series of experi-
ments, it seemed nevertheless the most probable conclusion that here
a shifting of the inner equilibrium takes place, which from a
thermodynamic standpoint means that very much work is required
to withdraw the last traces of water from a system.
Accordingly I showed in the English and in the French edition
of the Theory of Allotropy, in which I devoted a chapter to Bakrr’s
experiments, that in my opinion intensive drying gives rise to a
displacement of the internal equilibrium. Since then my own investi-
gation, which L carried out with some of my pupils, has confirmed
this supposition. A
The explanation of the influence of intensive drying on reactivity,
which I left unpublished so far, is exceedingly simple, for we
1) Also the influence of intensive drying on the properties of Sal ammoniac,
becomes explicable, when this substance is assumed to contain two kinds of
molecules, one of which is dissociable, and the other is not.
3) Trans. Chem. Soc. 51, 2339 (1903).
8) Trans. Chem. Soc. 121, 568 (1922).
267
have only to apply the theory of allotropy, i.e. we have to
assume that every phase of these substances contains at least two
different kinds of molecules, which are of course in inner equili-
brium in the case of unary behaviour, to which we add the supo-
sition that at least one of these kinds of molecules is chemically
inactive. This is very well possible, since the mechanism of the
transformation into another type of molecule will be an intirely
different one from that of chemical action with other substances.
To represent the case as simply as possible we can then assume
that there are only two different kinds of molecules, one of which
is active, the other inactive. When for ammonia we denote them
by NH,a and NH,?, we have in each phase in the case of unary
behaviour, the following inner equilibrium:
NH, 2 NH,g
HL
My supposition was this that on intensive drving this inner
equilibrium is shifted towards the inactive side, and in this case,
completely, so that in the ammonia remains that only contains the
inactive kind of molecules.
I will just mention here that I emphatically pointed out before
that the expression “different kinds of molecules” should be taken
in its widest sense. It should comprise not only the isomer and
polymer molecules, but also the electrically charged dissociation products,
ions -++ electrons, and if stands to reason that in many cases the
difference between the different kinds of molecules lies in a difference
in the atomic structure.
It is particularly the more recent views of atomic structure that
have brought to light that between the different atoms very subtle
differences are possible, which are e.g. in connection with a change
of the quanta values of the valency-electron-paths, and this leads to
kinds of molecules with more subtle differences than those which
are assumed to exist between the ordinary isomers. The fact, however,
remains that also these different kinds of molecules may be ranged
under this category when the sense in which the idea “‘isomery”’ is
taken, is very wide.
During my investigation there appeared a publication by Bary
and Duncan’), in which they communicate among other things that
the rapidity at which gaseous ammonia, withdrawn from an iron
cylindre with liquid ammonia, is decomposed by a platinum spiral
heated at a definite temperature, is dependent on the velocity of
evaporation of the liquid ammonia. On rapid evaporation ammonia gas
1) J. Chem. Soc. 121 en 122, 1008 (1922).
18
Proceedings Royal Acad. Amsterdam. Vol. X XVI.
268
was obtained of much smaller velocity of decomposition than on slow
evaporation. BaLy and Duncan expressed the opinion that this difference
is probably caused by this, that on rapid evaporation there is formed
a gas phase rich in the kind of molecules that preponderate in the
liquid phase, whereas on slow evaporation there has been a possi-
bility for the conversion of this kind of molecules into another, of
which the gas phase chiefly consists in ordinary circumstances.
One kind of molecules, which chiefly occurs in liquid ammonia,
would then be the inactive kind, and the other kind of molecules,
of which the ordinary ammonia gas chiefly consists, the active one.
They further pointed out that the existence of inactive and active
kinds of molecules probably accounts for the chemical inactivity of
the gas dried by Baker.
So we see that in this paper Bary and Duncan already express
the supposition at which I had also arrived, though 1 did not publish
it because my investigation was not yet sufficiently advanced. Baty-
Duncan’s results, however, are not very convincing, as BRISCOE ')
observed, because they can also be explained in another way. He
says: “It is known, that ordinary commercial ammonia, dried over
lime, contains about | percent of water’), and that rapid, irreversible
destillation, such as may occur by free discharge of gas from a cylinder
of liquid, is a very effective means of separating the constituents even
of a constant boiling mixture’), so that the gas thus obtained may well
be considerably drier than that in real equilibrium with the cylinder
liquid. Baty has found that the addition of water vapour to ordinary
ammonia increases its reactivity, drying certainly decreases its reac-
tivity, and so the greater dryness of the “inactive” form would
appear to be capable of explaining the whole of the observations,
including the “recovery” of the gas in cylinders on standing (by
acquisition of the equillibrium content of water vapour) identity of
slowly released cylinder gas with laboratory preparations dried by
lime, recovery of inactive gas in the experimental tube, when the
wire is heated at 200° (release of absorbed water from the wire or
walls) and the increase in reactivity of “inactive”
increase of temperature of the wire’.
These remarks of Brrscor’s, which are very true in my opinion,
deprive Baty’s published experiments for the present of all their
ammonia with
1) Annual Reports of the Progress of Chemistry vol. 19 1922, p. 37.
2) Briscoe refers here to Wurre T. 121, 1688 (1922), but this must be a mistake
for Wurrtre has not found this.
3) Mutuken J. Amer. Chem. Soc. 44, 2389 (1922).
269
cogency as a proof of the existence of an active and an inactive
kind of molecules in ammonia.
I wanted to test my supposition in another way and took, accord-
ingly, an entirely different course.
After having convinced myself that the pure P,O, which I prepared
by Baker’s method, had really the same properties as that of Baker’),
I began with some of my pupils an investigation of the influence of
intensive drying on the point of transition, the melting-point, the
vapour tension of the solid and liquid state, and the electrical resistance
of the liquid phase of a great number of substances, and among them
those substances, of which Baker found that the chemical activity
disappeared by intensive drying, occupy a very particular place on
account of the great importance of this phenomenon. Of this latter
group first of all NH,, HCl, CO, and O, were taken in hand.
In a following communication our results and the particulars of
the experiments will be discussed.
Laboratory of General and Inorg.
Chemistry. of the University.
Amsterdam, March 20% 1923.
') | became acquainted with this method through a private communication by
Prof BAKER before it was published, which saved me a great deal of trouble
and time. [ will avail myself of this apportunity to express my cordial thanks to
Prof. Baker for his kindness.
Se
Chemistry. — “The System Sulphur Trivaide” 1. By Prof. A. Smits.
(Communicated by Prof. P. Zeeman).
(Communicated at the meeting of March 24, 1923).
For some years the examination of sulphur trioxide has been on
my programme, because I surmised that this substance would yield
suitable material to test the theory of allotropy. As, however, other
investigations had to go first, this examination could not be taken
in hand until a short time ago.
In the meantime Brertnoup') Le Branc with Rürrr*) published
each a treatise on vapour tensions and melting-points of this sub-
stance. Though these two papers will be discussed more at length
later on, I will make here already a few remarks, and more parti-
cularly in connection with the latter publication.
The results published there prove with the greatest clearness
that SO, is really a substance which not only can be used as a test
of the above-mentioned theory, but which is so eminently fit for it
that in this respect it is unequalled by any other. For the results
obtained show that both the liquid and the solid phases of the SO,
can behave as phases of more than one component, which without
any doubt must be attributed to the complexity of this phase.
This complexity is owing to the occurrence of different kinds of
molecules in the same phase, which molecular-species are in
internal equilibrium with each other in the case of unary behaviour.
I emphatically pointed out on an earlier occasion that the term
“different kinds of molecules” should be taken in as wide a sense
as possible*). By them we should understand not only the isomer
and the polymer molecules, but also the electrically charged disso-
ciation products, ions + electrons, and it is self-evident, that in
many cases the difference between molecular-species mentioned
here lies in a difference between the atoms. It is in particular the
more recent views on the atomic structure, that bring to light, that
there are very subtle differences possible between the different atoms,
which e.g. are in connection with a change of the quanta-values of
the valency-electron-paths, and this leads to kinds of molecules with
1) Helvetica Chem. Acta 5, 513 (1922).
4) Ber. d. Sachs. Akad. v. Wiss. Leipzig 74, 106 (1922).
8) The theory of Allotropy p. 2.
271
more subtle differences than those, which are assumed between the
ordinary isomers. Nevertheless when the idea of “isomery” is taken
in a wider sense, also these different kinds of molecules may be
classed under this category.
We cannot say as yet what kinds of molecules occur in the diffe-
rent phases of the pure SO,. The molecular size in the vapour
phase agrees about with SO,, but it is very well possible that there
occur isomer molecules of SO, at the same time, and it is also
possible that there is also a polymer kind of molecules present in
small concentration. The kinds of molecules that occur in the gas
phase, will also be present in the liquid phase, hence according to
the theory of allotropy also in the solid phase, though in a different
proportion, when the idea molecular of conception is taken in a
wide sense *). Up to now we have been completely in the dark as
far as the internal state of solid SO, is concerned. The measurements
of the surface tension can, indeed, extend our knowledge concerning
the complexity of the liquid phase somewhat, but we still lack means
to decide whether a unary solid phase is a mixed crystal in internal
equilibrium or not.
Contrary to Lr Branc’s opinion it is not possible to conclude to
the molecular size of a substance in the solid state in a solvent
from the found mol. weight of this substance. ?)
With a view to supplementing our methods of research with those
that make use of RénTGEN rays in the hope of learning something
more in the end about the more delicate inner state of equili-
brium in the solid phase, I instituted a department for the RÖNTGEN
investigation of the solid substance in my laboratory some years
ago. Though the way which I had decided to follow, leads to the
typical allotropic substances, it seemed desirable first to examine
some simple. but nevertheless very interesting, substances, in which
results were to be expected which might be of great importance
for getting a clearer insight into the nature of the chemical bond.
Accordingly Messrs J. M. Bisvowr and A. Karssen bave studied
Li, LiH, NaClO,, NaBrO,, in which it was possible to determine
the structure and the binding of the particles on definite suppo-
sitions.*) Now the investigation of Hgl, has been taken in hand,
though we know that by means of this investigation we shall not
be able to decide whether the solid phase in a mixed crystal.
1) Cf. “The Theory of Allotropy” p. 220.
3) Loc. cit.
8) Partly published in These Proc. 28, 644, 1365 (1921); 25, 27 (1922); Zeit-
sehr. f. Physik. 14, 291 (1923).
272
The investigation by means of RÖNTGEN rays is by no means so
powerful as it is often supposed to be. Thanks to the researches of
Baknuis RoozeBoom and his pupils we have got to understand the
bebaviour of the mixed erystal phases in binary systems to a great
extent, but what does the RONTGEN investigation teach us about these
mixed crystals ?
Let us e.g. take the simple system KCI,KBr, a system of which
we know that the solid components are homogeneously mixable in
all proportions, and let us now suppose an arbitrary mixed crystal
from this continuous series to be given to a RénTGEN analyst. If this
investigator is under the impression that he has to do with a solid
phase of a simple substance, he will interpret the intensities found
in the usual way, and will find them in very good agreement with
the image of the system that was supposed by him to be mono-
componential. For the intensities can only serve as a test of an
already assumed model, and as there are still so many factors that
are not sufficiently accurately known in the interpretation of these
intensities, and because besides there are nearly always some para-
meters that have to be chosen so as to suit, a good agreement
can be found, even when the supposition is erroneous.
Partly in consequence of these circumstances, partly in conse-
quence of the impossibility to give already now a sharp image of
the complexity, as this has also been assumed by me for the solid
phase, the ROnTGEN investigation, in its present stage of development,
cannot serve as yet for a further elaboration of the theory of
allotropy, and it will, no doubt, be still some years before the
RöNrceN research will be able to throw new light on the inner
equilibria, which have already been found in the solid state.
All the same we have started the RöNrGeN study of the interesting
Hgl,, because we wished in any case to ascertain if any changes occur
in the ROnTGeN spectrum of these compounds in the temperature
interval of 130—255°, and, if so, what changes, hoping that some
conclusions may be drawn from this with some probability.
I have thought it necessary to publish the above discussion, because
a great many mistaken ideas still prevail in this region.
When we now return to Le Branc's investigation, I will remark
that he found, among other things, that on cooling of the supercooled
liquid below 13.9° solidification suddenly sets in,‘ on which the
vapour tension appeared to have risen, also after the temporary rise
of temperature had disappeared. Hence at the same temperature
the solid phase formed presented a higher pressure than the super-
cooled liquid, and Le Branc thought this phenomenon comparable
273
with the action of oxygen on phosphorus, in which ozone and a
phosphoro-oxygen compound was formed.
This, statement shows very clearly the insuperable difficulty with
which one is confronted, when with phenomena which so clearly
point to the complex character of the phases, one yet continues to
occupy the old standpoint.
I will not treat the phenomena found in the examination of SO,
more at length here, but leave the discussion of them to the
following communication.
Amsterdam, March 1923.
Laboratory of General and Inorganic
Chemistry of the University.
Geology. -— “Geological data derived from the region of the
“Bird's head” of New-Guinea’. By Prof. L. Rurren.
(Communicated at the meeting of March 24, 1923).
The great northwestern Peninsula of New-Guinea is one of the
least known parts of the Indian Archipelago. In recent times some
data concerning it have been published by R. D. M. VerBeeK in
his “Molukken Verslag’’’), and C. E. A. Wicnmann, when journeying
from the east coast to Horna, discovered a folded coal-bearing for-
mation”) which proved to be of tertiary age *).
In the last few years (between 1917 and 1921), however, explo-
rations were made on a large scale in Northern New-Guinea and
also in the “Birds head” for oil and coal, by the officers of the
Mining Department in the Dutch East Indies. The results of these
explorations have not been published as yet*), but some years ago
I received from the Director of the Mining Department in the Dutch
East-Indies a rather large collection of limestones and marls for
examination. The study of this collection has been finished, but there
would be little sense in expatiating on it here, a fortiori as a
description will probably be published elsewhere. I] may be of
interest though, to summarize the obtained results.
Although we are not quite sure that all the rocks we examined,
are of tertiary age, this may yet be assumed for the great majority.
Now, when observing on the subjoined sketch-map the localities
of ‘“Bird’s head” from which the examined rocks are derived, we
realize at once that tertiary deposits have a wide distrbution in the
north-west part of New-Guinea. However, eocene rocks seem to be
scarce among the tertiary deposits, which is quite in keeping with
what we know about the other parts of New-Guinea. They were
found only in two regions: in the first place between the island
of Rumberpon and Horna, where, in two localities, Nummulites-
Alveolina limestone and Alveolina-Lacazina limestone have been
1) Jaarboek Mijnwezen Ned. Indié 1908. Wetensch. Gedeelte.
2) Nova Guinea. IV. 1917.
3) Nova Guinea. VI. 2. 1914.
4) [.C.0.-Commissie, The history and present state of scientific research in the
Dutch East Indies. Geology. p. 28. 1923.
275
collected, as well as oligomiocene limestones; while Lacazina-lime-
stones have been found near the Campong Horna; in the second
Warmands.
Www
BES
NW N-CGuinea.
a Eoceen
o Oud Neogeen.
MU Jong Neogeen.
NW Jndifforende Gesteenten,
maart lertrarr.
a JMlarune Ârkose.
m Marmer
« Oude. Schuler un
lertrarr
Eoceen = Eocene.
Oud Neogeen = Older Neogene.
Jong Neogeen j . = Younger Neogene.
Indifferente Gesteenten, meest tertiair = Indifferent Rocks, mostly tertiary.
Marine Arkose = Marine Arcose.
Marmer = Marble.
Oude Schist-materiaal in Tertiair © = Old Schist-material in Tertiary.
place in the northwestern part of the “Bird's head”, where Laca-
zina-limestones have been collected, at one locality. From this it is
evident that eocene is only sparingly distributed; moreover it should
be observed that the rocks of the two localities, where Lacazina
alone is found, cannot on that account be referred to the eocene
with absolute certainty, however probable this may be. From the
region between Rumberpon (Amberpon) and Horna rocks have been
described by me formerly that pointed to the boundary strata
between eogene and neogene ‘).
On the contrary limestones of littoral facies from the older neogene
have been found in a large number of localities, characterized by
the occurrence of Lepidocyclina, Miogypsina and Cyeloelypeus.
Similar limestones from the region between Rumberpon and Horna
and from the Andai-river near Menokwari, have been previously
described. They now appear to occur to the west of Rumberpon
in a broad zone, running north-south, and to extend farther south
1) Nova Guinea. VI. 2. 1914,
276
than Andai, while they can be recognized in a zone running all
along the north coast of “the Bird's head” as far as the island of
Batanta. I] will be seen at a glance that we have to do here
with a comparativily narrow zone of older-neogene, which follows
the east coast and the north coast of the “Bird’s head”. It may be
that older-neogene still occurs also in the more western and southern
region of “Bird's head”, but it is remarkable that among the numerous
rocks from those regions that were examined by me, there was not
a single one that could positively be referred to the older neogene.
We shall see lower down that this is partly due to the facies of
the discovered rocks being indifferent, to our having to do either
with non-fossiliferous rocks or with rocks that have been deposited
in a deeper sea, in which the fossils, so characteristic of the littoral
older neogene, cannot be expected to occur. But beyond these also
rocks occur repeatedly in the southern part of the “Bird's head’, that
are of littoral facies, in which e.g. Lithothamnium, Operculina and
Amphistegina, the companions of Lepidocyclina in the older neogene
etc, occur, but in which the Foraminifera, which are characteristic
of the older neogene, are lacking. In such cases we no doubt have
to do with younger neogene which indeed is often borne out by the
habitus of the rocks. As an instance we point to the basin of the
Aer Beraur and of the Aer Klasaman, in which a series of rocks
occur that are referable to the younger neogene. Another region of
probably young-neogene rocks, partly with true littoral habitus, is
situated North of lake Amaru. Between lake Amaru and the Aer
Beraur a number of rocks have been found: globigerina marls, fine
grained lime sandstones and the like, which are completely indif-
ferent, so that nothing can be said about their age. The same
applies to some rocks from the region south of lake Amaru. A long
list of rock samples, collected in a west-east zone far north of lake
Amaru, are undoubtedly referable to the neogene, but their fossils
and their facies are not typical enough to say whether they belong
to the older or to the younger neogene. In some rocks, however,
doubtful Lepidocyclina were recognized; the others have been
classed under the ‘indifferent rocks’. Lastly among the rocks from
the basin of the Aer Sebjar there are some littoral limestones, in
which no “older” forms are to be found, so that here also we have
probably to do with younger neogene. On the other hand, a number
of very fine grained lime sandstones and globigerina limes, collected
east of Muturi-river have to be classed under the ‘indifferent rocks’.
They may be of older-neogene age, because in the adjacent region
towards the east (west of Rumberpon) a few transition rocks were
277
found among true littoral Lepidoeyelina-limes and Globigerina-limes.
Lastly presumably young-neogene rocks are to be found to the
North and West of Menokwari. Here Globigerina marls and loose
limesands, occur, which indeed do not include typical fossils, but
which on account of their quite young habitus are most likely to
be reckoned to the younger neogene. This in fact agrees with the
circumstance that some limestones in this region are of littoral
facies but do not contain Lepidocyclina, Cyclocly peus or Miogy psina.
Before this a description was published of limestones from the island
of Manaswari, near Menakwari, that were considered to be younger-
neogene *).
Between the localities of old-neogene limes south of Menokwari
and those west of Rumberpon are situated the high Arfak Moun-
tains, which according to VerBewk *) and WicHMANN °) are composed
of granular eruptive rocks, schists and slates. From the region of the
Arfak mountains I received three rocks most likely tertiary and built
up of detritus from the Arfak Mountains. They are coarse-grained
arcoses of marine origin, which together with Corals also contain
a very few Globigerina. The minerals represented here are much
quartz, orthoclase, perthite and less plagioclase and biotite: apparently
we have to do here with the detritus of acid granites.
Coarse-grained detritus of old rocks occurs also frequently in the
northern part of “the Bird’s head” in the rocks of tertiary age —
notably in the old-neogene rocks. This goes to show that below,
and perhaps also at the surface, there must evist a mountain range of
older rocks. The localities marked on the map by an o are those
where in the limestones transported fragments of quartzite and
phyllite oecur. A rock from the basin of the Aer Sebjar contained
grains of perthite and orthoclase, which remind us of the detritus
rocks of the Arfak mountains.
The future reports of the Mining Department will undoubtedly
contain interesting information on these ‘‘older rocks” in the‘ Bird’s
head’.
1) Nova Guinea. VI. 2. p. 29. 42.
*) Nova Guinea IV. p. 97.
3) Tijdschr. Kon. Ned. Aardr. Gen. (2). 21. 1904.
Mathematics. — “A theorem concerning power-series in an infinite
number of variables, with an application to Dirrcnuer’s *)
series” By H. D. KroosrerMaN. (Communicated by Prof.
J. C. Kiuyver.)
(Communicated at the meeting of March 24, 1923).
$ 1. An important relation between the theory of DiricHLer’s
series and the theory of power-series in an infinite number of variables
(for abbreviation we shall write: power-series in an i. n. of v.) has
been discovered by H. Bour’). Let
5 2 An 5
AE) Elek os. EO EN ot ern oe (U
n=1 N°
. . 4 1 1
be an ordinary Dinicuer’s series. Puts, = —, dige ee Mn
1 gs 3 3s
1 ? ;
= ne … (where p,, is the m-th prime-number, and let » = pe pi says
m
where pn, Pno»--+ Pn, Are the different primes which divide 7.
Then the series (1) can formally be written as a power-series in an
i.n. of v., thus:
n
r
0
INE Ganon otame cad) 25 Gy GE OS os o ==
A= ny Pa ar
c+ DB fete + TE Cagtata+ DE Cae, Wa tae, +...
aijn: a,8—1,2,... ,8,/7—1,2,...
a 8, in terms of (preferably as simple as possible) analytic
properties of the function represented by (1). Let B be the abscissa
of absolute convergence of (1), and D the lower limit of all numbers
a, such that /(s) is regular and bounded for 6 >«. The absolute-
convergence-problem will be solved, if the difference B— D is
known. Bonr proves that B= D for any Diricuiet’s series that
can be formally represented in one of the following forms:
1) A more detailed proof of the theorem will be published elsewhere.
2) Göttinger Nachrichten, 1913.
279
al
os
II
m=1 zl (pl):
or
al
AO s —2
= ;
m=l l=1 (pl, )s
or, what comes to the same thing, for any DiricHLer’s series for
which the connected power-series in an i.n. of v. has one of the
forms
Blan, em JEG (Gp) to vee oren Bt)
or a
IPN Goo bos ng NE 10 SE OUCH) vg eer (3)
where Q, (#,) (2 = 1, 2,....) is a power-series in «2, without a con-
stant term. The equality 4 — D is a consequence of the theorem:
< Gai td.) ). then
b. it is absolutely convergent for |z,|< OG, where @ is an
If: a. The series is bounded *) for |x,
arbitrary positive number in the interval 0O<4< 145).
Now, if we consider the power-series (2) and (3), we see that
the variables z, occur to some extent separated from one another.
This led Boar to the conjecture, that the equality b= D would
hold for any Diricuier’s series, for which the variables in the con-
nected power-series in an i.n. of v. do not occur too much mixed up.
Confirmation of this conjecture is the purpose of the present com-
1) According to Hitpert (Wesen und Ziele einer Analysis der unendlich vielen
unabhängigen Variabeln, Palermo Rendiconti, vol. 27, p. 67) a power-series in an
i. n. of v. is defined to be bounded if:
1°. The power-series Pi (2%, %,...%m) (Abschnitte), that may be obtained from
the power-series inan i.n. of v. by putting am 1 = %m+2 =...=0, are, for all
values of m, absolutely convergent in the region |zj\< Gj, |a2| < Go, |am| < Gn.
20, There exists a number K, independent of m, such that, for every m, the
inequality
| Pm (ei, oem) SK
holds in the region |2,| < Gi, |xol < Go,.... |am| < Gm.
*) It is well known, that b follows from a for-any power-series in a finite
number of variables. Originally Hinperr had assumed this also, as being self-evident,
for an i. n. of v. But Bonr showed that this could not be true by constructing an
example to the contrary.
280
munication. In fact it can be proved that B= D holds for any
Diricaiet’s series that can formally be written in the form
f (s) =p De m
mi Il (pl ye
where p is an arbitrary (non-constant) ') integral function. As a
consequence of the relation, already mentioned above several times,
the following theorem concerning power-series in an i. n. of v. is
equivalent to this statement.
Theorem. If p is an integral function and Q,(«,) (n=1,2,...) a
formal’) power-series in 2,, without a constant term, and if the
power-series in an i. n.of v. P(w,,2,,...-&m,-+-)J=(Q,(#,) + Q,(@)
H.H Qn(am) + ....) is bounded for |z| < G,(n=1, 2,....),
then it is absolutely convergent for |2,,) << OG,, if0<0<1.
In the following pages an outline of the proof of this theorem
will be given.
§2. For the sake of simplicity we take G, = G, =....=G,=
SiGe 1 butinaiG <1.
Because the given power-series in an i.n. of v. is bounded, there
exists a number A, not depending on m, such that
(Qi) + Qs) ew 41 Qa (an) SE 2).
The first part of the proof of the theorem of § 1 discusses the
power-series Q,, (a) (n= 1,2,....). It is proved that it follows from
(4) that all these power-series possess a certain region of conver-
gence. Further research shows that two cases may occur:
1*. The functions Q, (#,) are all regular for |2,/ 1, all
regular in their resp. circles |2,|< 1.
For any function f(e), regular for jz <1, and for which /(0)=0,
we now define a number 7 as follows: r is the radius of the largest
circle, of which all points represent numbers assumed by f(z) in
the circle KES 1. Let rv, (n =1, 2,...) be the corresponding quantity
on
for Q, («‚). Then we first prove, that the series > 7, converges.
ul
For this purpose we consider (4), valid for all sets of values of
Hy, %,,.-.. Xm, Satisfying [onl < Gar ANA ten) vand ar fortzor2, for
all satisfying |,|< 1. Because p(y) is an integral function, it is
possible to choose a number £ so large, that the maximum value of
(y)|, on the circle \yl—= L, is > K. Now suppose that, for some
value of m, r,+r,+....+7, > L. Then the maximum value of
lp (y)| on the cirele |yl=r, Ar, +... rm would be > K.
Now if we let the variables z, (u — 1, 2,....m) describe their resp.
cireles a, < 1, then Q, (w,) assumes all values satisfying |Q, (#,)| =7n.
Hence y= Q, (@) + Q, (v,) +... + Qn (wm) assumes all values
satisfying jy) =r, +r, +... + rn Therefore it would be possible
to find a set of values w',,2',,.....2', such that
PSs («',) iQ) + --- + Qn (en) = (1, + SS ae) ea
where (7, +7, -+....—+7,)e represents that point of the circle
y= Fr, +... Hr where |g (y)| assumes its maximum value.
Therefore we should have
| p (Q, («',) ofr Q, (z') in Pd Qn ('n)) | => K,
contradictory to (4). Therefore the supposition r,+7,+...+7, >L
can not be true. Since ZL is independent of m, this proves the
a
convergence of > rr
n=
We now apply the following theorem of Bour *):
Let the function f(z) = = a, 2" (f (0) = 0) be regular for |z| <1.
nl
Let M(o) be the maximum value of | f()| on the circle |z|=o0
(O k Mo), where £ is a number which depends on g only (X is
1) Not yet published.
282
therefore the same for all functions satisfying the assumptions of
the theorem).
Hence, if M,„(e) is the maximum value of |Q, (w‚)| on the circle
en "9 (1,2). wenhaven 1, Dik M, (v). Since we have
proved that st r, is convergent, it now follows that the series © M,(e)
n=1 n=1
converges also (for g <1). From this fact the theorem of $1 can
be easily deduced.
For let Q, (an) = > i. a (n=1,2,...). Then
p=1
M,(e) (n= 1, 2,
(n) | < 1
es 5 bn 2, Jes ).
If o=6G (where @ is the constant of § 1), then it follows
1+0
that, if O0< 9 <1, (we take for example e = + |
Hence the series
oo ao
= = | alr)| OP,
n=1p=1 P
is also convergent. This proves a fortiori the convergence of the
given power-series in an i. n. of v. for w‚ <0=0G(n=1,2..,).
It cannot be denied that the assumption, that ~ is an integral funetion,
is somewhat unaesthetic. However, the author has not succeeded
in dealing with the more general problem, where p is an arbitrary
(purely formal) power-series. In any case the method described does
not give the required result in the more general case.
Copenhagen, November 1922.
Chemistry. — ‘“/n-, mono- and divariant equilibria.” XXII. By
Prof. F. A. H. SCHREINEMAKERS.
(Communicated at the meeting of March 24, 1923).
Equilibria of n components in n +1 phases, when the quantity
of one of the components approaches to zero. The injluence
of a new substance on an invariant equilibrium. (Continuation).
We write the isovolumetrical reaction of an equilibrium #(«=0):
Fla Fo OD. HO SOR) SO Savy=o. . WW
and the isentropical reaction :
eee te ee OREN (WEL OSR (VA >10.. (2)
Consequently in reaction (1) are formed on addition of heat and
in reaction (2) on increase of volume those phases, which have a
negative reaction-coefficient. We have, therefore:
= (ax) y = — a, &, —A, 2, — en = (ue) = — , 2, — py, 2, —
When we subtract both reaction-equations (1) and (2) from one
another, after having multiplied the first one with u, and the
second one with 2, then we find the reaction:
(#4, — 4,4) EH dn A) P+. >. =O. … (3)
wherein the change of entropy is u, 2 (A H)y
and the change of volume is —A, > (u Vr).
As (3) represents the reaction, which may occur in the equilibrium
(F,)= FE, + F,+..., we have
dP\ ssw, 2 (AA)y i
Ely Nae Alas (fe VOTERS ee 2)
Pal LTP NO TENS
Herein 5 indicates the direction of curve (#,) in the invariant
C 1
point. In the same way we find:
ne
dl DEN (LV) en NUTR A, = (UV)
As we are able to deduce from (1) and (2) also the direction of
temperature and pressure of the different monovariant curves, the
P,T-diagram is, therefore, quantitatively defined.
Now we add to the equilibrium a new substance X, which occurs
19
Proceedings Royal Acad. Amsterdam. Vol. XXVI.
284
in the phases PF, F,... with the concentrations x,2,... In accor-
dance with. (13) and (15 ) (XXII) we now have:
> (AH
— WV (dT) = 4,2, FA, +... = (As)
= (uV
aT Je …(dP): = — uti at. =E(ue)H. . (8)
V IP
iv) EG (5) —«u,(55) — 4 « (©)
RT dP), dP),
A fe (5) dm & ESD)
RT IT RENT
It follows from (8) and (9):
dT ro {Re dT OAD dT
(%),= > (wa) (oP), eli a
from (7) and (10) it follows:
dP fay Zk GME Ede dP
- are. Ly aH
(5). = (An); ee) = (Ax)y @)
and from (7) and (8):
= (u yer (F By, + Bs +... (13)
SS (H)y dT ANN 4-Ajyay t+...
From (7) we see that we are able to express (d7’), with the aid
of the isovolumetrical reaction (1); it is apparent from (9) that,
however, we cannot express (d7’), with the aid of the isentropical
reaction (2) only, but that we must know also the directions of the
monovariant curves (Ff) (fF)... of the equilibrium # («= 0).
It appears from (8) that we are able to express (d/), with the
aid of the isentropical reaction (2); we see, however, from (10) that
we cannot define (dP), with the aid of the isovolumetrical reaction
only but that we must know for this also again the directions of
the curves (Pf) (F,)...
The direction of the monovariant curve # can be defined, as is
apparent from (13), with the aid of the isovolumetrical and isen-
tropical reaction; it follows from (11) and (12) that it can also be
defined with the aid of the directions of the curves (Ff) (F,)....
and one of both reactions.
When we add a new substance X which occurs in one of the
phases only, f.i. in F, than we must put in (7)—(13) 2,=0 #,—0...
As now & (Ax)y=— 4, x,, it follows from (12):
dP _(dP 14
==), ne EN
285
which follows of course immediately from (11). Consequently curve
FE and (F,) have the same tangent in the invariant point. It follows
from (7) and (8) that they go also in the same direction of tempe-
rature and pressure, starting from this point. When viz. 2, is
positive, then it follows from reaction (1) that curve (F) goes
towards higher temperatures, starting from the invariant point. As
it follows, however, from (7) that (d7), is then positive also, con-
sequently curve ZE goes also towards higher 7. When 4, is negative,
then the curves (#,) and F go both towards lower 7. It follows
from (2) and (8) that both curves have also the same direction of
pressure.
In accordance with previous papers (Communication XXII) we,
therefore, find: when the new substance occurs in the phase F,
only, then curve # coincides with curve (4).
When the new substance occurs in the phases #, and F, only,
then (12) passes into:
dP jk dP VEN er
I= ir teer 1005)
AD) pee Ka Na) a. RA aT)
; = x A
wherein K=—. Hence it follows:
Zi
(PD — 2s dP aN ae in
(a wap lar), Gr) «00
: 4 HEN dP
For fixing the ideas we assume that | —, | is greater than | —, |.
aE dT),
Now we distinguish two cases.
1. 2, and 2, have the same sign. The following is apparent from
iP
(15) and (16). When A changes from O tot oo then =) increases
dd
fr (5 to
om ae
discontinuous.
2. 4, and 2, have opposite sign. When K changes from 0 to oo, then
dl
dP . : . ie
( | without becoming maximum, minimum or
2
dP ; ee :
( =| decreases without becoming maximum or minimum from
C x
BPN. }
a till — oo, then it proceeds discontinuously towards + oo and
C 1
} dP
afterwards it decreases to | — |.
dT),
When À, and 4, are both positive, then, in accordance with
reaction (1) both curves (#,) and (F,) go towards higher tempera-
{Sj
286
tures starting from the invariant point; when 2, and 2, are both
negative, then both curves go towards lower 7’; when A, and 2, have
opposite sign, then both curves go, starting from the invariant point
in Opposite direction of temperature.
It follows from all this that the tangent to curve F is situated
within the angle, which is formed by the curves (Ff) and (F,). [Of
course we mean that angle wich is smaller than 180°]. As in the
case of A =O (consequently «,—0) curve EF coincides with (/,)
and in the case of K—o (consequently #, == 0) curve F coincides
with (/’,) consequently the property follows, which we have deduced
already in the previous communication also, viz:
Curve £ is situated between the curves (F,) and (/) or in other
words: in the region (H, F).
Yet also we find, however:
Curve HE is situated nearer curve (/,) in proportion as the con-
centration of the new substance in the phase /’, is larger with
respect to that in /,; curve U is situated nearer to curve (Ff) in
proportion as the concentration of the new substance in the phase
F, is greater with respect to that in F’.
When the new substance occurs only in the phases F, F, and
F,, then we find, in accordance with previous papers that curve #
is situated in the region (£, #, F,).
When one of the curves, fi. (/’,) is between the other two (/’,) and
(F,) then curve MW is situated also between (/’,) and (/,). When,
however, none of the three curves is situated between the other
two, then curve # may go, starting from the invariant point in
every arbitrary direction.
Now we consider the binary equilibrium
E(@@=0)=F+L1,4+1,46
we represent the composition, the entropy and the volume of
F by y 1—y H and V
Ley Ay and 7,
L, „ 4. 1—y, H, and V,
G ,, y, 1—y, A, and V,
When we add a new substance Y, then we call its concentration
in those phases xa, a, and «,
In order to deduce the isovolumetrical and isentropical reaction
we take two arbitrary reactions; for this we choose:
287
eine ee aE i) (AMR. 50 a 12)
(LDL, AF HIG AVE Vi. jee eae (is)
Herein is:
AH=(1+a)H,—H—aH, A: H'= H+ bH,—(14 6)4d,
AV =(1 + a) V, — V—al, A vVi=V4 6bV,—(1 +5) V,
In (17) and (18) a and 6 may be as well positive as negative.
It follows from (17) and (18) for the isovolumetrical reaction:
(AVLAV’) F —(1+a) AV'L, + [aAV'— (148) AV] L,+0AV.G=0
Tia EY AA AUING AUT Naa aa a (19)
and for the isentropical reaction :
— (AH+AH') F+(1+a)AH'. L,— [aA H'—(1 +4548] L,— bd. G=0
0 LEENA Ee GVM ope (20)
We now add to this equilibrium H («= 0) a new substance X,
which occurs in the two liquids LZ, and ZL, only. With the aid of
(19) and (20) it then follows from (7) and (8):
M. (dT), = — (la) AV'. #, + [aA V' — (1b) AV] a, . (21)
M .(dP), = — (1+a) AH’, «, + |aQH'— (1408) AA) a, . (22)
wherein :
Mis (EEA VEE ASTER
It follows from (21) and (22): when we add to the equilibrium
E(e=0) a new substance which occurs only in the two liquids,
then the temperature as well as the pressure may be increased or
decreased.
We now shall assume that the four phases are situated with
respect to one another, as on the line Y Z in fig. 1. Then we have:
VN Ph > Ys.
It follows from (17) and (18) for the determination of a and 6:
ytay,=—(1+a)y, (1 + 6)y, =y + by,
pee je 23)
Yas Ya Vs
so that a and 6 are positive. Further we assume that Hand L, and
also that L, and L, are not situated very close to one another, so
that a is neither very small nor very large. When F and L, and
also L, and G are not situated very close to one another, then also
b is not very small and not very large.
As now AV’ is positive and very large with respect to AV, M
is positive.
Further we may distinguish the following cases.
AH>0 DOVE
ahH'- (1+)AH>0
AH>0 AVZ0
GA (th BA Fee
AH>0 AVA
ahA'—(1+s)AH<0
a)
b)
¢)
In each of the three cases,
ficient of w, negative and of
(dT), Z 0 when
We >
288
ATi) wei | (24)
aAVv'—(14+d)AV>0
A50 Am Vassr0 | (25)
aQ vV'i—(1+b5)AV>0
IN 151 << MV) LV (26)
ak WEE HA
mentioned above, is in (21) the coef-
xv, positive; consequently we have:
(hay A We
EA
(27)
As AV’ is very large with respect to AV it follows from this
approximately with the aid of (23):
wv N=
(4T)z 20 when -2.
2 (28)
vm yyy
In the case, mentioned sub 6 in (22) the coefficients of a, and wz,
are negative, so that (dP), is also negative; consequently the pressure
is lowered.
In order to examine more in detail the sign of (dP), we write
for (22)
MNP) =
aya
wherein:
EGET
l+a
x, | N (29)
a
eae
EREA
a
AH! H
N=aÂAH'!—(l+4+b)AAH
When we put herein the value of a from (23) then we may write
for (29):
AH! =)
(GP). — |= Lr ln a
—1 Uae
1 A = AH y U vy ( )
a
When we consider the three cases a, 6 and c mentioned above,
then we may write for (30):
x, Hae
a) anas tte. (31)
%, YY
b) (iP), =—| Zr. (32)
vy Vn
c) um. rate. (33)
x, yn"
289
wherein 1, AK, 1+ K and 1—K are positive. In each of the three
formula’s L and K have different values.
In order to apply the above we take the figs. 1 and 2, wherein
XY is a side of the components-triangle XYZ. The points FL, L,
and G represent the four phases of the invariant binary equilibrium
E(j«=0)=F+L,+ L,+ G. When we add a new substance
X then the ternary equilibrium H= F+ L, + L, + G arises. The
liquids ZL, and ZL, then proceed along the curves L,q,7, and
L,q,7,; as the new substance is not volatile, G follows a part of
the line XZ. When we add only a little of the new substance, then
the liquids are represented by the points g, and q, in the immediate
pf
AT>o
a) dpèo
6) ap 0 as is also indicated
in the figure. It follows from (31)—(33):
in case a is (dP), 20
” ” De (dP), cv <0
” ” ” (dP), <0
as is also indicated in fig. 1.
In fig. 2 is:
a, < vy OF apa
Y—4Ys Yrs wv, Vn
It follows from (28): (d7’), <0. From (31)—(38) it follows:
(35)
290
in case a is (dP), <0
ed AE dn
” ” c ” (dP), 2 < 0
as is indicated also in fig. 2.
In fig. 1 the pressure may as well increase as decrease in the
case a; it is apparent from (31) that (dP), shall be positieve for
large values of w,:w,. As L, (and consequently also q,) is the liquid
which contains the most of the solid substance # we shall call L,
(and consequently also q,) the concentrated and ZL, the diluted solution.
We, therefore, find the following:
when the threephases-triangle solid-liquid-liquid turns its concen-
trated solution towards the side of the components-triangle (fig. 1)
then the temperature increases and the pressure generally decreases ;
only when the concentration of the new substance in the diluted
liquid (consequently z,) is much larger than in the concentrated
liquid consequently «,), then in the case a the pressure may incre-
ase also.
In fig. 2 in the case c the pressure may as: well increase as
decrease; it appears from (33) that (dP), shall be positive for small
values of 2,:2,.
Consequently we find the following:
when the threephases-triangle solid-liquid-liquid turns its concen-
trated solution away from the side of the components-triangle (fig. 2)
then the temperature decreases and generally the pressure also.
Only when the concentration of the new substance is much larger
in the concentrated solution (w,) than in the diluted solution (,),
then in the case c the pressure may also increase.
We may obtain the previous results also by using the P, 7-dia-
gram of the equilibrium H(«=0). We may deduce this in the
following way. ;
The direction of temperature of the equilibrium (G) = F + L, + L,
is defined by the sign of the coefficient of the phase Gin the isovo-
lumetrical reaction (19). As 64V may be as well positive as negative,
curve (G) may go, starting from the invariant point 7, as well
towards higher as towards lower temperatures.
The direction of pressure of the equilibrium (G) is defined by
the sign of the coefficient of G in the isentropical reaction (20). As
—b4H is negative in each of the cases a, 6 and ec, curve (G)
proceeds, starting from the invariant point 4, towards higher pressures,
As further, in accordance with (17):
291
TENE aL H
ar) AV
and AV is very small, curve (G) is ascending, starting from point 2
fast vertically. In figs 3 and 4 this curve is drawn vertically up-
wards; the double arrow indicates that starting from 7, it may run
either towards the right or to the left. ,
As the coefficient —(l + a)4V’ of the phase /, is negative in
each of the cases a, 6 ande, in accordance with (19) curve (L,) = F
+ L, 4 G is going starting from point 7 towards lower pressures
(figs 3 and 4).
In the cases a and 6 the coefticient (1 + a) 4 H’ of phase L, is
positive in equation (20) so that curve (L,) is going, starting from
2, towards lower pressures (fig. 3). In the case c is(1 + a) A H'
negative and curve (L,) is going, therefore, starting from 7, towards
higher pressures (tig. 4). This is in accordance also with that which
follows from (18) viz.
dP fe! A H'
Ce) ny
Consequently we have defined the direction of the curves (G) and
(Z,); fig. 3 is true for the cases a and hb, fig. 4 for the case c.
With the aid of (19) and (20) we should be able to determine
also the position of the curves (/’) and (Z,) and then we could
prove that the four curves are situated with respect to one another
as in figs 3 and +. [Compare f. i. Communication XIII]. As we know,
however, the situation of the curves (G) and (L,) we can find the
position: of curves (F) and(Z,) much more easily by using the rule
for the position of the four monovariant curves of a binary equili-
brium [Compare Communication [| fig. 2].
In accordance with this rule we must meet, when we go, starting
(Z)
>
&
292
from curve (G) in the direction of the hands of a clock towards
curve (Z,) firstly curve (F) and afterwards curve (Z,). As further
(G) and (#) must form a bundle and their prolongations must be
situated between (£,) and (L,) and as the angle between two suc-
ceeding curves, must be always smaller than 180°, hence follows
for the curves (#’) and (Z,) a situation as in the figures 3 and 4.
In fig. 3 curve (Z,) is drawn horizontally; starting from 2 it
may run either upwards or downwards; this has been indicated
by the double little arrow. When it goes upwards, starting from 27,
then its prolongation must yet always be situated above curve (Z,).
It appears from the coefficient of the phase Z, in reaction (20) that
curve (Z,) must go in case a starting from 2 upwards and in case
bh, starting from 7 downwards. This has also been indicated in fig. 3.
As we know the P, 7-diagram of the equilibrium H(#=0) we
can easily determine the situation of curve Z. It follows viz. from
our general considerations in the beginning of this communication,
that curve / must be situated between the curves (L,) and (Z,).
For «,:2,=0 curve Z coincides with (/.,) for #,:x,=0 with
curve (L,). When w,:«, changes from oo towards 0 than curve U
moves in the direction of the hands of a clock from (Z,) towards (Z,).
Firstly we now take the case a, so that we must imagine in
fig. 3 curve (L,) to be drawn upwards starting from 7. When we
do change now w,:2, from ao to 0, then it follows from the diffe-
rent positions which curve E may obtain, that the following cases
may occur:
((T);>0 and (dP),>0
(dT),>0 and (dP),<0
(T);<0 and (dP),<0
In case 6 we must image in fig. 3 curve (Z,) to be drawn down-
wards starting from 7. When we do change x,:x, from oo to 0,
then it follows from the situation of curve ME:
(aly, ande (EP) 0
(AT), <0 and (dP),<0
In case c fig. 4 is true. When wv, :w, changes again from oo to
0, then it follows from the position of curve L:
(dT), >0 and (dP),<0
(AT), <0 and (dP),<0
(AT), <0 and (dP),>0
We see that those deductions are in accordance with the previous
ones and with the figs 1 and 2.
293
Our previous considerations are all valid in the supposition that
the four phases /'L,L, and G are situated with respect to one
another as is indicated in the figs 1—4. When the four phases are
situated otherwise with respect to one another, the reader my deduce
all in similar way.
We now shall assume that the new substance is volatile, so that
it occurs in the phases 4,4, and G with the concentrations
Ti Edle
We find with the aid of (7) and (19):
M (dT), =— (la) AV'e, + [AAV, —(14B)AV]e, HbAV.e, (36)
and with the aid of (8) and (20):
M (AP), = — (la) AH'z, + [aAH' —(14-b)AH]e, + bAH-e, (87)
wherein
M=(AH.AV'—AH'.AV):RT
so that the direction of temperature and pressure of curve F are
defined by (36) and (37).
As AV is very small in comparison with AV’ we may neglect
in (36) the terms with OV as long as x, is not very large, then
it follows with approximation :
<<
(AT), 20 voor SZ... GB
Cn ann
Only for very great values of w, in comparison with x, and a,
the term b64V..2, in (36) will be of great importance and will be
approximately
RNN Ie
In (37) AH is not small in comparison with AH’ and the term
bAH.z, will assert its influence already with values of 2, which
are not too small.
Consequently, in general the influence of the new substance on
(aT), and (dP), will be larger in proportion as the new substance
is more volatile and it will assert its influence sooner on (dP),
than on (dT).
RAE Vi Tees! (falar
= ( ) (39)
We may also deduce anything about the position of curve ZE
with the aid of the general considerations at the beginning of this
communication. Hence it follows viz that curve /# must be situated
either between the curves (L,) and (L,) or between (L,) and (G) or
between (Z,) and (G). As in the figs 3 and 4 the prolongation of
each of those curves is situated between both the other curves,
curve Z may go, therefore, starting from point 7 in every direction.
294
Consequently the temperature may as well increase as decrease,
and the pressure may increase or decrease as well at rising as at
falling temperature, dependent on the position of curve £.
It follows from (12):
when w, is extremely small with respect to w, and x, then curve
/ is situated between (G) and (L,);
when wv, is extremely small with respect to 2, and w, then curve
His situated between (G) and (L,);
when w, is extremely small with respect to v, and rv, then curve
FE is situated between (L,) and (L,);
when w, is extremely large with respect to w, and a, then curve
E is situated in the vicinity of L);
when a, is extremely large with respect to 2, and z, then curve
4 is situated in the vicinity of (L,);
when w, is extremely large with respect to «, and w, then curve
les
=
Eis situated in the vicinity of (G).
In each of those cases we can see at once from the figs 3 and +
which signs (dT), and (dP), may have.
When fi. x, is very small with respect to x, and x, then curve
FE is situated between (L,) and (G); when now fig. 4 is valid then
the pressure shall, therefore, always increase and the temperature
shall decrease. In the special case only, when w, is still also extremely
large with respect to w, and when at the same time AV > 0 [then
curve (CG) proceeds, starting from 7, a little to the left | then the
temperature may fall a little.
When we add a new substance which is not volatile, but which
forms mixed crystals with the solid substance #, then we have in
figs. 3 and 4 the curves (#) (Z,) and (L,). It appears from the
position of those curves with respect to one another that the previous
considerations are also valid in this case.
When we wish to calculate (dT), then, as is apparent from (19)
we have to substitute in (36) b4V x, by(AV+AV") a. When we
neglect again the terms with AV then we find:
M (dT), = [a —(1+a) 2, Hao, A V'
or:
(40)
(T= Ela Os
H en
In the figs 5 and 6 YZ represents a side of the components-
triangle, FL, L, and G the four phases of the invariant binary
equilibrium Z(r 0). When we add a new substance then the
ternary equilibrium H= F+ L, + L, + G arises. The solid sub-
295
stance F’ and the liquids ZL, and L, then proceed along the curves
Fqr, L,q,7, and L,q,7,. When we add only little of the new
substance, then the 3 phases are represented by the points q q, and
gq, Which we must imagine in the immediate vicinity of the side YZ.
When we put ¢= 2 (y,—y,) —(y—y,)", + (y—y,)", and when we
consider x and y as running coordinates, then ¢= 0 represents the
equation of the straight line which goes in fig. 5 and 6 through
g, and g,
When the point g is situated on the line q,q, then ¢=0; the
sign of (dT), is then determined by the terms which have been
neglected in (40).
When q is situated at the right side of the line q,g, (viz. when
we go from g, towards q,) as in fig. 5, then ¢>>0; when q is
situated at the left side of the line q,q,, as in fig. 6, then ¢< 0.
Hence it follows, therefore, that in fig. 5 the temperature increases
and in fig. 6 the temperature decreases, as is also indicated in both
figures.
Fig. 5. Fig. 6.
Consequently we find the following:
when we add to the invariant binary equilibrium # (v= 0) =
=F+L,+ L, + G a substance which is not volatile and which
forms mixed crystals with the solid substance #, then
the temperature rises, when the threephases-triangle solid-liquid
liquid turns its concentrated liquid towards the side of the com-
ponents-triangle (fig. 5)
the temperature falls when the threephases-triangle turns its con-
centrated solution away from this side (fig. 6).
Comparing fig. 1 with fig. 5 and fig. 2 with fig. 6, the reader
will see that for the change of temperature the same rules are true,
independent of the fact whether the new substance forms mixed
crystals with F or not.
296
Finally we could still treat the general case that the new sub-
stance forms not only mixed crystals with / but that it is volatile also.
It follows from figs. 3 and 4, in connection with the theories
discussed in the beginning of this communication that curve / can
go in all directions, starting from point 7.
In order to define (¢d7’), we must still include in (86) the term
(AV-+AV"),; then we get again (40) approximately unless a, is
extremely large.
Consequently in this case also the figs. 5 and 6 remain valid,
unless the threephases-triangle gq, q, becomes very narrow and the
concentration of the new substance in the vapour is extremely
large.
(To be continued).
Leiden, /norg. Chem. Lab.
Anatomy. — “The Development of the Shoulder-blade in Man”.
By O. H. Duxstra. (Communicated by Prof. L. Bork).
(Communicated at the meeting of March 24, 1923).
Unlike the development of the clavicula that of the scapula has
received comparatively little attention. The textbooks of anatomy
(CUNNINGHAM, GEGENBAUER, RAUBER— Korpsen, Merker, Porrter—Cuarpy,
Tersrur) contain only general notions such as the information that the
ossification of the shoulder-blade begins in the vicinity of the collum
scapulae at the end of the second or in the beginning of the third
month. Poirier and CHARPY speak of an incipient ossification between
the 40% and 50‘ day. BARDELEBEN reports a periostal ossification (such
as occurs with the bones of the cranial vault) beside and under
the spina scapulae at the end of the 10% week.
Bryce alone enters into more details in Quains’s Elements of Anatomy.
According to his description the rudiment of the shoulder-blade is
in the 6t® week entirely cartilaginous, proc. acromialis and proc.
coracoïdeus are present, but the spina scapulae is wanting. (Nevertheless
Bryce reproduces the diagram of Lewis’), in which a spina is really
indicated). In the 8" week ossification begins with a centre near
the collum scapulae, developing into a triangular plate, at whose upper
margin the spina appears in the 3'¢ month as a low ridge. At birth
coracoid and acromion, margo vertebralis and the margin of the spina
are still made up of cartilage. This description by Bryce agrees fairly
well with the one we find in Broman’s textbook of Embryology and
in that of Keren and Marr, in which BarpreN deals with this subject.
Broman, like Brycn, states that no spina is to be found at the cartila-
ginous scapula. Nonetheless he reproduces the figure of Lewis, in which
there is indeed a spina. KoOLLMANN, SCHENCK, Minot, Parker do not
speak of the first development of the shoulder-blade and only dwell
on stadia of advanced ossification. In Herrwie’s Entwickelungsgeschichte
Braus and also Hertwie himself report a separate centre of ossification
in the spina scapulae; according to the latter the spina in the neonatus
still consists of cartilage sometimes; according to Körriker (quoted
by Bape, Arch. f. mikr. Anat. LV) this is even always the case.
1) Am. Journ. Anat. Vol. 1. 1901—’02.
298
The most detailed report concerning the development of the shoulder-
blade is that by Bryce and Broman. From their figures it is evident
that they derive their data from Lewis, who published in the American
Journal of Anatomy (Vol. 1 1901—’02) a minute description of the
development of the arm in man. Broadly stated his data agree with
those of Bryce, mentioned above. They differ, however, as to the spina
scapulae. According to Lewis the spina probably takes origin in the
upper margin of the scapula. This margo superior thickens and then
splits into a medial and a lateral lip. The medial lip is the future
margo superior, the lateral one is the first beginning of the spina scapulae.
Haen *) deseribes a shoulder-blade of an embryo 17 mm. in length.
The spina scapulae is absent, the proc. coracoideus is large, the proc.
acromialis small. The latter statement cannot be reconciled with Lewis’s
communication, which, on the contrary, speaks of a relatively large
proc. acromialis.
This review of the literature would not be complete without
mentioning the interesting study by RurHerrorD*) who entered into
many details of the development of the shoulder-blade. Like Luwis he
constructed wax models of the skeleton of the shoulder-girdle, and
La. found that the spina scapulae originates in very early ossi-
fication of derivates of cartilage cells, situated between M. supra- and
infraspinatus.
From this review it is clear that our knowledge of the modus of
development of the shoulder-blade in man is still limited. The
shape in the initial stages of development is described differently.
Contlieting views are held as to the genesis of the spina and from
the contents of this paper it will be seen that these are not the
only points of controversy.
With a view to trace the development of the shoulder-blade in
man, I constructed wax models of various stages of development.
Fig. 1 represents the wax model of the shoulder-blade of the youngest
embryo, 16 mm. in length. The scapula is drawn from the lateral
side and from above.
The reconstruction shows:
1°. that the shoulder-blade lies in a sagittal plane, so that the
lower half is in contact with the three upper ribs. Processus acro-
mialis and clavicula are not in contact as yet.
2°. that the processus coracoideus is large; the processus acro-
mialis is relatively small. The joint-cavity rests chiefly on the
processus coracoideus. j
1) Arch. f. Anat. u. Entwickel. Gesch. 1900.
3) Journal of Anatomy and Physiology 1914.
299
3°. There is no indication of a spina scapulae. The margo superior
is neither thickened nor split into two labia.
Fig. 1. Fig. 2.
4°. The margo superior is straight, so there is no incisura scapulae.
5°. For the rest the shape of the scapula fairly well agrees with
that of an adult shoulder-blade. In reconstructing the scapulae of two
monkey embryos (viz. Macacus cynomolgus 17 mm. in length, and
Semnopithecus maurus) it became evident that, also in these primates,
the embryonic shoulder-blade already in its first beginning resembles
that of the adult. Here also a spina was absent.
6°. Close beneath the angulus superior we observe a well-defined
fovea where a foramen is found in older stages of development. To
this we shall revert when discussing the following stage.
This stage is illustrated in fig. 2. It concerns the shonlder-blade
of an embryo, 25 mm. in length. Also in this stage any indication
of a spina scapulae or of a thickening of the margo superior is
lacking. Nevertheless when compared with the first stage some
modifications can be recognized.
1*. The shoulder-blade does not lie any more in a sagittal plane,
but makes an angle with it, as is also the case with the adult. The
joint-cavity lies at the level of the first rib. Acromion and clavicula
have joined.
20
Proceedings Royal Acad. Amsterdam. Vol. XXVI.
300
2°. The processus coracoideus las comparatively decreased, the
processus acromialis, on the other hand, has increased. It appears,
then, that the processus coracoideus, which is phylogenetically the
oldest part, is most strongly developed in the youngest stage, where-
as the processus acromialis, which is phylogenetically younger, comes
more to the fore in the older stages. The joint-cavity now lies for
the greater part on the planum scapulae.
3°. The margo vertebralis consists of a shorter upper portion and
a longer lower portion. They are at an obtuse angle to each other.
4°. The portion of the scapula from which afterwards the fossa
supraspinata develops, makes an angle with the future subspinal
portion. This deviation of the upper part, which also occurs in the
adult shoulder-blade (since fossa supra- and infraspinata do not lie in
one and the same plane), had not yet taken place in the 16 mm. embryo.
5°. In the cranial part of tbe shoulder blade a foramen oceurs
under the angulus superior, which extends at the costal plane of
the scapula as a groove along the margo superior in the direction
of the joint-cavity. In fig. 3 we give a cross-section of this foramen,
which is filled with connective tissue.
The existence of this foramen is no doubt surprising; yet it was
not entirely unknown, as already RurnerrorD has described it (1. ¢.).
However, according to this author it proceeds in a groove, which
reaches as far as the margo vertebralis. Now, in all the serial sections
in whieh I also met with a groove as well as with the foramen, it
proceeded along the margo superior in the direction of the joint-cavity.
RurnerrorD explains this foramen as follows. He considers the
part of the scapula, cranial to the foramen (resp. groove), as a
separate piece of cartilage, which he terms praescapula, and which,
according to his account, is connected by a strand of mesenchyma
tissne with the sternal half of the clavicula. In this way he believes
an inner shoulder-girdle to have developed, while he supposes the
acromion-clavicula to build up the outer girdle. He adduces various
arguments to prove this; however, they are weak. In my judgment
the hypothesis is of no value, because a connection of the so-called
praescapula with the sternal balf of the clavicula does not occur.
At all events in my preparations I never found a cell-strand like
the one described by RuTHErForD.
This foramen is not present in all cases. Its development also
differs with various individuals, as shown by the following data. I could
establish its presence either as a true foramen, or as a deep groove in
human embryos of the length of 16, 17.5, 18, 19.6, 21, 22, 25
(see fig. 3), 26, 27, 56, and 90 mm. On the other hand I did not
301
recognize it in embryos of 12, 18, 18, 24, 26, 40, 120 mm. From
this it follows that it is not infrequently absent. In some embryos the
portion of the planum scapulae cranial to the foramen, i.e. RoTHERFORD’s
praescapula, made an angle with the rest of the planum, a fact that lends
support to Ruraerrorb’s view, viz that it is really a separate piece
Fig. 3. Homo 25 mm. transverse. Sc = Scapula;
Acr = Processus acromialis.
of cartilage. The foramen which, in young embryos, is situated
rather closely to the margo superior, as observable in fig. 3, migrates
in older embryos towards the margo vertebralis. Consequently Rurur-
FoRD’s praescapula is relatively enlarged.
Now it is an interesting fact that this foramen does not occur in
any other mammal, neither in reptiles, nor in amphibians. At least
1 never detected any. The following embryos I have examined for
the occurrence of this foramen.
* Semnopithecus maurus 20 mm. (C. R.)
Macacus cynomolgus 17 mm. (C. R.)
Cercopithecus 2 stages.
Sus scrofa N.T. (Keibel) 83—85, N.T. 88, N.T. 88, N.T. 91,
24 mm. (C. R.) 26 mm. (C. R.) In the last two embryos two
foramina were recognized in the fossa infraspinata. It is not quite
impossible that these foramina are analoga of the foramen in the
human shoulder-blade.
Bos taurus 21 mm. (C. R.)
Ovis aries 19.5, 20.5, 21.5, 22.5, 23, 23.5, 26, 27, 29, 35,
45 mm. (C. R.)
20%
302
Canis familiaris 12, 12, 22, st mm. (C. R.)
Sciurus vulgaris 12, 30 mm. (C. R.)
Mus decumanus 11.5, 12, 13, Dn 13.2, 14.5, 16, 18, 20, 22 mm. (C. KR)
Lepus cuniculus 17, 20 mm. (C. R.)
Spermophillus citillus 15 mm. (C. R.)
Rousettus amplexicaudatus 7.5, 10.5, 11, 11, 11.5, 12, 12, 14.5,
ily, 1d ikke) Tame (Ole)
Talpa europea 8.5, 9, 9, 10, 12, 13, 16.5, 20 mm. (C. R).
Perameles obesula 50 mm. (C. R.)
Perameles spec. 38 mm. (C. R.)
Dasyurus viverrinus 19.6, 33, 36, 40, 53, 63 mm. (C. R.)
Sminthopsis erassicaudatus 13, 25 mm. (C. R.)
Phascalogale pennicillata 37 mm. (C. R.)
Trichosurus vulpecula 32 mm. (C. R.)
Didelphys cancrivora, 4 embryos of 25 mm. length.
Lacerta agilis N. T. (Keibel) 117, 118, 120, 123, 123, 124,
125, 126.
Calotes iubatus, length of the head 5'/, mm., 7 mm.
Lagysoma 27.5 mm.
Hemidactylus fren. length of the head 4.5 mm.
Salamandra mac. 11, 13, 15, 16, 16, 24 mm.
Pipa Americana, 12 mm.
Rana . 2 embryos.
So far as I am able to judge foramina in adult shoulder-blades
occur only with Homo and with various Edentata, in which they
are always formed by bridging of the Incisura scapulae, and with
Delphinus delphis. In the latter the character of the foramen is not
known. RurnerrorD (1. ¢.) has described it.
A conceivable connection, that might exist between the praesca-
pula of RurHerForD and the attachment of the clavicula (not only
the sternal half of the clavicula, as RurHerrorp supposed) to the
margo superior scapulae, as it occurs in reptiles, echidna and orni-
thorynchus, could not be ascertained, since a connection of the
praescapula of RuruerForD to the acromial part of the clavicula
could not be detected either.
It appears, then, that the foramen, present in the majority of
human embryos in the cranial part of the shoulder-blade, does not
occur in other vertebrates, (except in Delphinus delphis, which,
however, is of such a pronounced specificity that this foramen cannot
be looked upon as a homologue of that of man). Neither did I find
any attachment of the praescapula of Rurnerrorp to any other
303
skeletal bone. The significance of this foramen is unknown as yet.
As to the ossification of the seapula my experience proved it not
to be so simple as is represented in the literature.
The earliest ossification I observed in an embryo of 40 mm. I
constructed a wax model (fig. 4) of the scapula of this embryo.
4 LAN SHA
Dor AA
B es
"5 i
0) Hi 4 fee:
Aar + Hy
4 LY \ | :
MW \
AN
= {iy
Fig. 4. Fig. 5. Homo 40 mm. Transversal.
Cor = Processus coracoideus; Hu = Humerus;
Acr = Processus acromialis; Sc — Scapula.
Like the preceding model this also is viewed from above and
from the dorso-lateral side. What this reconstructed model shows
us may follow here:
The joint-cavity, lying at the level of the first rib, is now
located almost entirely on the planum scapulae (as with the adult
scapula). Of the spina not a trace is visible as yet, the margo supe-
rior is not thickened. To the basis of the processus acromialis an
area of closely packed mesenchyma is attached, which extends
between the muscular tissue and separates the rudiment of Muse.
supra-, and infraspinatus.
This area of mesenchyma is cut in a cross section as represented
in fig. 5. Behind the root of the processus acromialis begins a peri-
chondrial ossification, which continues into this condensed mesen-
chyma. This ossification is the first formation of the spina. We see,
304
therefore, that it is formed by a perichondrial ossification, for although
no ossifying perichondrium is visible here, the fact that the bone is
formed from the surrounding mesenchyma co-ossifying with carti-
lage, established the character of the ossification. In fig. 5 we givea
cross section of this first stage of the spina.
I have not been able to recognize two centres of ossification in
the cartilaginous scapula, described by RamBaup and ReNaLr (quoted
by Porrier'), which, according to these authors, arise between the
40% and 50 day and fuse in the third month.
In the scapula of an older embryo (56 mm. in length) this peri-
chondrial ossification appears to be largely extended. The margo
anterior scapulae is almost reached. The cartilage of the planum
WAY Nd
Ast
Fig. 6. Homo 56 mM. Transversal. Hu — Humerus; Cl = Clavicula;
Cor = Processus coracoideus; Acr = Processus acromialis;
Sp = Spina scapulae; Sc = Scapula.
scapulae, however, has been distinctly calcified over a considerable
area already. The marked enlargement of the spina scapulae is shown
in fig. 6. Besides the spina this figure also shows part of the foramen
described above. The spina is formed by a growth of bone between
1) Poirier et Carey, Traité d’Anatomie humaine.
305
M. supra- and infraspinatus, between acromion and planum scapulae.
It cannot be denied, however. that in the mesenchyma, in which
this bone develops, very young cartilage-cells are noticeable here
and there. These cells, however, have no intermediate matter as yet;
they are little differentiated and it is difficult to distinguish them
from the mesenchyma-cells. So it is evident that besides bone-cells
also cartilage-cells develop in the mesenchyma.
In an embryo of 90 mm. enchondrial as well as perichondrial
ossification takes place, the boundary between the two being no
Pl. Se.
Fig. 7. Homo 90 mm. Margo Fig. 8. Homo 90 mm. Scapula trans-
anterior scapulae transversal. versal Acr. = Processus acromialis
J.c. = Joint-eavily. Pl. Sc. = Planum
scapulae.
longer perceivable. The peculiar character of the perichondrial ossi-
fication along the margo anterior is remarkable. In the place of
the formation of compact bone, which in other cases occurs with
perichondrial ossification e.g. that of the long bones, we see here a
bony framework encircled by mesenchyma. Fig. 7 shows a cross
section through the margo anterior.
The study of this object (embryo of 90 mm.) shows remarkable
pecularities of the growth of the spina scapulae. In the mesenchyma
between M. supra- and infraspinatus a distinet cartilage is now
recognizable. It is quite independent of the other mass of cartilage
306
of the scapula. [t is younger than the remaining part of the shoulder-
blade; nevertheless it has already calcified to some degree and
forms bone of the spina.
The cartilage has been cut in three different cross sections, as
represented in the figures 8, 9 and 10. Fig. 8 illustrates a section
through the scapula above the place of attachment of the processus
acromialis. In the mesenchyma, which extends from the processus
acromialis towards the margo vertebralis, lies the cartilage which
is already partly calcified. In fig. 9 we give a section at a lower
level.
The processus acromialis attaches itself at this level to the planum
scapulae. Here also we observe the cartilage of the spine, independ-
ent of the remaining cartilage of the shoulder-blade. Fig. 10 shows
a section through the scapula at the level of the lowest place of
Fig. 9. Homo 90 m.m. Scapula trans-
versal. Aer. = Processus acromialis. Pl. Sc.
Pl. Sc. = Planum scapulae. Fig. 10. 90 m.m. Scapula
transversal. C.= cartilage of
the spine. Pl. Sc. = Planum
scapulae.
attachment of the spina. The young cartilage, which forms the spina,
has here been cut over a large area. The cartilage will be seen to
307
be partly calcified, while bone has been formed, uniting with this
calcified area.
So while the first beginning of the spina is formed by perichon-
drial bone in the mesenchyma between M. supra-, and infraspinatus,
its further development is effected by chondrial bone, which origin-
ates in the younger cartilage. This cartilage has been generated
between the afore-said muscles by the same mesenchyma.
A peculiar feature is still to be observed at the shoulder-blade of
the embryo of 90 mm. Bone is developed at the margo superior as
well enchondrially as perichondrially. In the mesenchyma that forms
the perichondrial bone, and into which this bone extends over some
distance, there are two cartilaginous nuclei, made up of the same
young tissue from which the cartilage of the spina has been built
up. Fig. 11 shows in cross section these nuclei, which are not in
contact with the remaining cartilage of the shoulder-blade. These
cartilage-islets appear to be already calcified and ossified here and
there. It is impossible to draw a boundary-line between the bone
formed in this process and the perichondrial bone of the scapula.
This ossifying process, in which (besides the enchondrial ossification
of the scapula) both perichondrial and chondrial ossification of
a cartilage nucleus, situated outside the perichondrial bone, are
present, agrees completely with the formation of the spina scapulae.
This is striking, since the spina scapulae and the definitive
margo superior are the two parts of the shoulder-blade, which are
missing in the first rudiment of the cartilaginous scapula. This
deficiency vertebral of the place destined for the future incisure, is
indeed accounted for by the fact that the margo superior in young
embryos is still straight and displays no incisure. The missing parts
are apparently supplied by the perichondrial bone that reaches far
into the mesenchyma, together with the bone formed by the afore-
said cartilage-nuclei. At the shoulder-blade of an embryo of 120 mm:
in length, in which the ossification had considerably advanced, the
incisure was indeed present.
Of course, the question arises, how the cartilage of the spina as
well as the cartilage nuclei are further developing. In both places
the cartilage is soon transformed completely into bone. In an embryo
of 120 mm. only a very few remnants of the cartilage of the spina
were still left. The rest had been ossified.
After this the development of the shoulder-blade proceeds in the
way described in the text-books of embryology.
Now let us review once more the current opinions of the develop-
ment of the spina scapulae. It will be seen, then, that however
308
divergent they may be, most of them cannot be deemed incorrect,
when we bear in mind that they concern different stages.
Fig. 11.
Homo 90 m.m.
Margo superior scapulae
transversal.
Rurnerrorp’s view of the very early ossi-
fication of cartilaginous cells is no doubt correct,
but holds good only for young stadia. Neither
is the conception of Hertwie and Braus about
a separate centre of ossification quite incorrect,
since there is a stage in which an _ in-
dependent cartilage is forming bone.BaRDELEBEN’s
record about an ossification under and beside
the spina cannot altogether be disqualified
either, but it only applies to a brief stage of
development. However, ossification like that
of the bones of the cranial vault does not
occur in the development of the shoulder-blade.
In the neonatus a few cartilage may possibly
sometimes be found at the spina (Bryce), but
it is certain that the spina scapulae in the
new-born child does not consist of cartilage.
(K6LLIkER and HeErtwicg advocate the opposite
view). Lewis’s conception, however, (doubling
of the margo superior) is altogether wrong. The diagram borrowed
from Lewis by Broman, Bryce and BARDEEN represents a faulty recon-
struction of the shoulder-blade.
Zoology. — “Secondary ser-characters and testis of the ten-spined
Stickleback (Gasterosteus pungitius LJ)” By Dr. G. J. van
Oorpr. (Communicated by Prof. J. Boeke).
(Communicated at the meeting of March 24, 1923)
It is generally known that the sex-glands strongly influence the
so-called secondary sex-characters. This is apparent from the marked
somatic and psychic differences, which e.g. Mammals or Birds,
castrated at an early age, show, when compared with normal
animals.
At present it is generally accepted that in Vertebrates this effect,
resulting from the gonads, takes place by internal secretion, that is
by the influence of certain substances, which pass into the blood
(“hormones’’). As the correlation between the secondary sex-characters
and the gonads generally is most distinct in male Vertebrates, |
will speak only of the formation of these hormones in the testis
for convenience’ sake.
Recently it has been especially attempted to ascertain, by which
part of the male gonad these hormones are formed. The numerous
investigators, treating this subject, chiefly hold the two following,
contradictory opinions.
According to Stimve (1922) and others these hormones are exclu-
sively formed by the sexual cells, whereas Bouin and Ancer (1903),
Sremacnh (1920), Lipscnürz (1919), Bascom (1923), their collaborators
and others are of opinion that these hormones originate in the
interstitial cells (Luypie’s cells), situated in the interstitium of the
male gonad. According to Stimve these cells are only thropic ele-
ments for the sperm cells. Consequently no value must be attached
to the name ,,Puberty Gland’, which name was given to the col-
lective Leypia’s cells by Sremacn and Lirscnürz.
Up till now the investigators, when treating the subject above
mentioned, have chiefly examined Mammals, Birds and Amphibia.
For that reason I resolved to trace the changes in the testis at the
appearance of the secondary sex-characters in a Fish, and so I
chose the ten-spined Stickleback (Gasterosteus pungitius L.),
which was easy to obtain.
During breeding time, in spring, the males of this species possess
310
a number of secondary sex-characters (ef. Tirscnack 1922), of which
the following are distinetly perceptible.
In spring a very distinet black pigmentation (red in the three-
spined species) can be observed at the throat and at the abdomen,
which soon spreads over the rest of the body, so that the animals
become dark-black, except for their pectoral spines. Outside
breeding-time it is difficult to distinguish the males from the females:
then both show dark spots on a pale green ground. Individual
colour-differences occur.
Every male makes a nest, in which the eggs are deposited. The
material of which the nest consists (parts of waterplants ete.) is
collected by the male and fastened by means of a secretion, formed
by the kidney-tubules and Wolffian Duets (Trrscnack 1922, COURRIER
19226, both in Gasterosteus aculeatus 1..). This peculiar secretion
occurs exclusively in the male during breeding time ; for that reason
in spring the kidney strongly increases in size, the kidney-tubules
and the Wolffian Ducts get a larger diameter and exercise a different
function.
The male guards his nest and drives off all intruders fiercely. When
the eges have been deposited in the nest, they are at once fertilized.
During the development of the eggs, the male takes care that they
are constantly provided with oxygen by conducting fresh water to
the nest with his pectoral fins. Sometimes, when eggs drop out of
the nest, they are again collected by the male and taken back to
the nest in his mouth. Whether the young are guarded by the male,
after they have left the nest, in nature, is not known to me: care
must be taken to separate the young, living in prison, from their
father and the other inhabitants of the aquarium, as the young
will otherwise be eaten.
The aim of my investigation, begun in September 1922, was to
trace the changes, occurring in the testes of the Stickleback at the
appearance of the secondary sex-characters. So it was my intention
to catch a number of Sticklebacks at fixed times during the winter
and the sueceeding spring and to examine their sex-glands. At that
time [ thought that nothing was known as yet about the relation
between the secondary sex-characters and the testis of the Stickle-
back, but it soon appeared to me that Courrier had already investi-
gated the three-spined Stickleback (Gasterosteus aculeatus L.) and
had published some papers, regarding this point (1922a, 19226).
I therefore changed my original plan and resolved to trace what
influence a rather high temperature, about the temperature of
311
ditehwater in spring (12°—20°C.), would have on the appearance of
the secondary sex-characters and what changes would take place
in the testes of these animals simultaneously. The sex-glands of
control-animals, caught in nature, could serve at the same time to
verify the results of Courrier. In this paper I will only communi-
cate the results, obtained in animals, kept in a temperature of
12°—20° C. during last winter.
In September and October 1922 I caught a large number of
specimens of (rasterosteus pungitius L. at Rotterdam. They were
kept in an aquarium of which the water was often renewed, and
they were copiously fed with Chironomus-larvae.
All the testes of the Sticklebacks, killed in autumn, contained a
more or less large number of spermatozoa. The number of sperma-
togonia is always small, the number of spermatocytes and sperma-
tids varies in the different specimens. In all cases, examined by me,
small groups of interstitial cells (Luypie’s cells) were present, close
to the hilus or there where three or more tubules come together.
In a few testes, in which the interstitium is somewhat wider, these
cells are also situated between the seminiferous tubules. They were
absent in none of the cases examined.
In one specimen (n°. 6), a rather dark-coloured male, not showing
the black pigmentation of males during breeding time, however, the
interstitium is much wider than in the other males, caught at the
same time. The number of interstitial cells is also larger in this
specimen, while in the seminiferous tubules spermatozoa are almost
exclusively found.
Oblong connective tissue-nuclei are observed everywhere in the
interstitium of the testes of animals, caught in autumn, blood-vessels
are present, but they are not numerous; they are narrow and contain
few blood-cells.
This testis-structure is shown by animals, caught in September and
the beginning of October, and which were kept in an aquarium of
which the water then agreed in temperature with ditehwater.
The testes of Sticklebacks, kept for two, three and even four
months, i.e. till the end of January 1923, in a temperature of
12°—20° C., all increase in size and show the following structure.
The spermatogenesis is very intensive. In all testes this process
takes place from the exterior to the interior, i.e. the spermatozoa
are situated as a rule more in the centre, the spermatogonia and
spermatocytes more at the periphery of the gonad. The interstitium
of such animals does not change; it remains narrow, the number
312
of Leypie’s cells is generally small and they are especially present
near the hilus and there where three or more seminiferous tubules
come together.
Till the end of January it was difficult to distinguish the males
from the females. In the last days of January, however, one of my
specimens showed at throat and abdomen a faint black pigmentation,
which soon increased strongly. Besides, this animal became very
agressive and in the beginning of February he began to collect
material for the nest. On the 14% or 15 of February the eggs were
laid in the completed nest; (I cannot give the exact date, as the
female was not seen in this nest). On the 16 of February this
male was killed.
The nuptial colours successively developed in the other males,
which soon began to prepare their nests. After the eggs had been
deposited in them, they were carefully guarded by the males, which
constantly conducted fresh water to the nests. 3
On comparing the testes of animals killed in the end of Decem-
ber or in January with the testes of these males, we see that the
latter have greatly changed.
The spermatogenesis has totally come to an end. The seminiferous
tubules are entirely filled with a large number of spermatozoa.
Moreover, at the periphery of the tubules small groups of sperma-
tozoa are to be seen, the heads of which are directed to the wall
and the tails to the centre of the tubules. The number of sperma-
togonia and spermatocytes has strongly decreased.
The interstitium is no longer narrow but is enlarged; the number
of Lrypre’s cells has strongly increased ; the blood-vessels have become
more numerous and larger.
So we see that the high temperature of the water in winter
favours the spermatogenesis and that consequently after four months
a testis originates of which the seminiferous tubules practically
contain spermatozoa exclusively. Then the secondary sex-characters
distinctly develop, the interstitium is enlarged and the cells of
LeypiG and the blood-vessels increase in number.
So I have observed a coincidence of the occurrence of the second-
ary sex-characters and the termination of the spermatogenesis, while
simultaneously an enlargement of the interstitium with increase in
number of the Leypie’s cells and of the bloodvessels takes place.
This does not prove, however, that a correlation exists between
these phenomena.
According to Courrier (1922a, 19226) it does. This investigator
observed in the three-spined Stickleback that after the spermato-
313
genesis the interstitium increases considerably in size. In it a strong
augmentation of the number of Luypia’s cells and of the blood-
vessels has taken place. According to Courrier the testes of Stickle-
backs, caught in winter, only contain a few interstitial cells here
and there. The spermatogenesis, which is very intensive in spring
till the end of March, has no influence on the development of the
secondary sex-characters. The latter occur not earlier than at the end
of April, simultaneously with the strong development of the inter-
stitial cells. As he, moreover, observes the same granules in the
cells of LeypiG and in the bloodvessels, situated close to them, he
assumes that the hormones which influence the development of the
sex-characters are formed in the interstitial cells and pass from the
‘latter into the blood. In my opinion it might be that the granules,
observed by Courrier, are transmitted by the blood to the inter-
stitial cells.
Courrier has also kept his fishes in water of 17° C. (19224 and
19226, p. 137) during a part of the winter. After two months and
a half the structure of the seminiferous tubules of these animals
resembles that of animals during breeding time i.e. they are entirely
filled with spermatozoa and contain only a few spermatogonia,
spermatocytes and cells of Serrorr. Changes in the interstitium have
not occurred. Consequently, the secondary sex-characters have not
developed in these animals. Courrier thinks, however (1922, in a
note), on the ground of experiments, which were in progress at that
time, that the interstitium would increase in size, when exposed
longer to a high temperature and that consequently the sex-characters
would also develop in these animals.
I think I am justified to conclude from my investigations, de-
scribed above, that the correlation of interstitial cells and secondary
sex-characters is not so easy to establish.
In the first place all testes of Gasterostevs possess a more or less
large number of interstitial cells. These evidently do not cause the
development of the secondary sex-characters. Here I must especially
point to the male above described (N°. 6) of which the testes
contain a wide interstitium with many Lerpie’s cells and of which
the seminiforous tubules are entirely filled with spermatozoa. The
secondary sex-characters had not developed in this animal, however.
Among the testes of control-animals, caught in nature in winter,
I also found some-of which the tubules almost exclusively contained
spermatozoa and of which the interstitium with numerous interstitial
cells is rather strongly developed. These animals, however, did not
show sex-characters either.
314
In a very recent paper Cnrampy (C. R. Soe. de Biologie, Séance
du 17 Février 1923) communicates that he has obtained Sticklebacks
(aculeatus) with nuptial colours last winter and that in the testes
of these animals he had not observed a well-developed interstitial
tissue. As he has not found any interstitial cells in the testes of
various species of fishes with distinct secondary sex-characters,
Cuamry is of opinion that these cells have no influence on the
development of those sex-characters and that the formation of the
hormones responsible for the development of these characters would
take place by means of the sexual cells.
Finally, I will once more call attention to the fact that the testes,
examined by me, in which the spermatogenesis has almost come
to an end, possess a more strongly developed interstitium than testes,
in which the spermatogenesis is still in full swing. Possibly this
fact points to a correlation between spermatogenesis and interstitial
cells. Whether the sex-hormones are formed in the seminiferous
tubules as well, | cannot decide at this moment. Later on, when
I have more material at my disposal, I hope to recur to this
subject in a more detailed paper.
Zoblogical Laboratory of the Veterinary College.
Utrecht, March 1923.
REFERENCES.
Bascom, K. F. 1923. The interstitial cells of the gonads of cattle, with especial
reference to their embryonic development and significance. Amer. Journal
Anat., vol. 31.
Bouin, P. et AnceL, P. 1903 Recherches sur les cellules interstitielles du testi-
cule des Mammifères. Arch. de Zoöl. expér. et génér., 4de Série, T. 1.
SN CHAMPY, CH. 1928. Observations sur les caractéres sexuels chez les Poissons.
G. R. Soc. de Biol., T. 88, pag. 414.
| Courrier, R. 1922a. Sur l’indépendence de la glande séminale et des caractères
sexuels secondaires chez les Poissons. Etude expérimentale. C. R. Acad. des
Sciences, T. 174, pag. 70.
“Courrier, R. 19225. Etude préliminaire du déterminisme des caractères sexuels
secondaires chez les Poissons. Arch. d'Anat., d'Hist. et d'Embryologie, T. 2.
Lipscutirz, A. 1919. Die Pubertätsdrüse und ihre Wirkungen. Bern, Verlag von
E. BrrcHer.
STEINACH, E. 1920. Kiinstliche und natürliche Zwitterdrüsen und ihre analogen
Wirkungen. Archiv f. Entw. Mech., Bd. 46.
Streve, H. 1921. Entwickelung, Bau und Bedeutung der Keimdrüsenzwischenzellen.
Ergebnisse der Anat. und Entwickelungsgeschichte, Bd. 23.
\TitscHack, E. 1922. Die sekundären Geschlechtsmerkmale von Gasterosteus acu-
leatus L. Zool. Jahrb. Abt. f. allg. Zoologie und Physiologie, Bd. 39.
KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.
PROCEEDINGS
VOLUME XXVI
Nes, 5 and 6.
President: Prof. F. A. F. C. WENT.
Secretary: Prof. L. BOLK.
(Translated from: “Verslag van de gewone vergaderingen der Wis- en
Natuurkundige Afdeeling,” Vol. XXXII).
CONTENTS.
J. C. KLUYVER: “On EULER’s Constant”, p. 316.
J. P. WIBAUT and J. J. DIEKMANN: “Researches on the Addition of Water to Ethylene and Propylene”.
(Communicated by Prof. A. F. HOLLEMAN), p. 321.
W. H. JULIUS and M. MINNAERT: “The relation between the widening and the mutual influence of
dispersion lines in the spectrum of the sun's limb”, p. 329.
J. P. BANNIER: “Cytological investigations on Apogamy in some elementary species of Erophila
verna”. (Communicated by Prof. F. A. F. C. WENT), p. 349.
F. W. ‘I’. HUNGER: “On the nature and origin of the cocos-pearl”. (Communicated by Prof. G. VAN
ITERSON Jr.), p. 357.
TH. VALETON: “The genus Coptosapelta KORTH”. (Rubiaceae). (Communicated by Prof. J. W. MOLL),
p. 361.
D. TOLLENAAR: “Dark Growth-responses”. (Communicated by Prof. A. H. BLAAUW), p. 378.
JAN DE VRIES: “Representation of a Tetrahedral Complex on the Points of Space”, p. 390.
A. SMITS: “The Electromotive Behaviour of Magnesium’. Il. (Communicated by Prof. P. ZEEMAN),
p. 395.
D. S. FERNANDES: “A method of simultaneously studying the absorption of Og and the SEE
of COs in respiration”. (Communicated by Prof. F. A. F. C. WENT), p. 408.
H. J. HAMBURGER: “A new form of correlation between organs”, p. 420.
J. P. WIBAUT and Miss ELISABETH DINGEMANSE: “The Synthesis of some Pyridylpyrroles”. (Com-
municated by Prof. P. VAN ROMBURGH), p. 426.
G. M. KRAAY and L. K. WOLFF: “The splitting of lipoids by Bacteria’. (First communication).
(Communicated by Prof. C. EYKMAN), p. 436.
\ J. B. ZWAARDEMAKER: “The Presence of Cardio-regulative Nerves in Petromyzon fluviatilis”.
(Communicated by Prof. H. ZWAARDEMAKER), p. 438.
W OD. COHEN: “The light Oxidation of Alcohol (III). The Photo-Catalytic Influence of some Series
of Ketones on the light Oxidation of Ethyl Alcohol”. (Communicated by Prof. J. BOESEKEN), p. 443.
M. }. BELINFANTE: “On Power Series of the Form: x?0— xP1 + xP2—..” (Communicated by Prof.
L. E. J. BROUWER), p. 456.
F. F. HAZELHOFF and Miss HELEEN WIERSMA: “On Subjective Rhythmisation', (Communicated by
Prof. E. D. WIERSMA), p. 462.
R. BRINKMAN and A. V. SZENT-GYORGYI: “Researches on the chemical causes of normal and patho-
logical Haemolysis”. (Communicated by Prof. H. J. HAMBURGER), p. 470.
L. HAMBURGER: “Nitrogen fixation by means of the cyanide-process and atomic structure”. (Com-
municated by Prof. P. EHRENFEST), p. 480.
F. D'HERELLE: “Culture du bactériophage sans intervention de bactéries vivantes”. (Présenté par
Mr. le Prof. W. EINTHOVEN), p. 486.
V. VAN STRAELEN: “Description de Crustacés décapodes nouveaux des terrains tertiaires de Borneo”.
(Présenté par Mr. le Prof. H. A. BROUWER), p. 489.
C. WINKLER: “A partial foetus removed from a child”, p. 493.
Erratum, p. 496.
Proceedings Royal Acad. Amsterdam. Vol. XX VI.
Mathematics. — “On Eurer's Constant’. By Prof. J. C. Kivyver.
(Communicated at the meeting of May 26, 1923).
In calculating the value of HEurer’s constant C the summation
formula or any other asymptotic series is used, and one term at
least in the expansion is always a transcendental quantity. It would
be preferable to represent Cas a convergent expression containing
rational terms only, because such a representation of the number C
perhaps eventually will furnish the means to establish its irrationality.
As yet Vacca’s series *)
ne of Mees!
Sach \ api a Ng en
A Cdn 1 Sere ab ener
is the only result in the desired direction, and as a second | will
add the proof that C—4 can be expanded in a convergent continued
fraction
44
Wp
1 1
ALL dels aoe
a. Yate
the quantities a, being throughout positive and rational.
Following Stie_tses’ method *) for converting an integral into a
continued fraction, I consider the integral
1
J (z) aha NO == i . Brul’
de
supposing z >>0. Expanding the integrand in powers of —, term-by-
2
term integration gives the divergent series
the coefficients of which are determined by the equation
1) Q. J. Math, London, vol. XLI, p. 363.
2) Recherches sur les fractions continues. Oeuvres completes, II, p. 402.
317
ao 0
2 * p2h+1 Bi
= h ee 1 = peewee
ch =| uh f (u) du = Em | n= TE)
0 0
Hence cj, directly deduced from the Bernoullian number Bj,
is a positive and rational quantity.
In order to evaluate the integral J(z), we write
ao
Sekt
udz
emu Le ArVu 1 e—6rVu He 2m | +
oe 4
du g—2mrV u
El
0
0
and substituting in the remainder w= v’, we find
co oo
du e—2mnV u dv ve rv 1
de welig = 4 :
utz eu] vitz etl 2n°mz
0
Hence we have
a du k=0 a k=o il
J (2) =| in € rk =| due tru > SE)
k=1 ut hz
0 0 :
Utz Jel
zu"
and, putting u=-——, we get
4x?
a k=c0 9 n° v 1 1
MEN rl >>, ee == | el 2'dy Lee es
kar v?* HAL x? ev—] v 2
ao oo ;
ev ex1—_V 2) Sti 1
=f dv | — — dv =
| | v ev—1 | +f v 2Vz
, 7 ;
=: I” l
= — 5, (V2) + log (V2) —
’
2V2
a result from which we deduce at once J/(1) = C—}.
Now according to Stirites’ theory the integral J (z) can be
converted formally in a continued fraction
il
vz
Bebe Alte
tp ole lt ot...
le, lage” le, lave
the quantities a, depending on the coéfficients c,,c,,c,,... of the
Zs
318
divergent series. Following the general method we consider the
determinants
| CG, @& Ch EC ON ann Cn A
c, Cs C, lots anions Cn+1 C, cy Cy wa cece Cn
Vanin ACH Che | Aan |E; CF G7 foe peas Cutt |»
| €n CnHl “n42+-. . C2n—1 Cn—1 Cn Cn4i+ +++ €2n—2
then we shall have
WZ : Dn ZE ab: k= Bice
: @. ars Gh : : Ak Are
These general formulae give no insight in the numerical values
Se ges Ars Bin
of the quantities az, remembering however that cj, = es
242
obvions that they are rational and depending on the Bernoullian
numbers only. Moreover they are positive, for considering the
determinant
[Cp Cp pte ++. Sp tin
lep Cp42 Cp+3 see Gptm4+i
D= lep+2 Cp+3 Cp+4 sees Cptm+2)5
| - á 5 A 5 . 5 e
|
le Opm Sptm+i1 &p+-m-+2 - «Cp
with arbitrary indices p and m, we get
1 2 m 2
UNI
2
oe lu, w.... Us
D= 7 Si rn In, 2 oe ae
0 0 . . . Bo, ©
2 m
Luin lee Um
Hence D and in particular every determinant 27 is positive, there-
fore the same conclusion holds for az. By direct calculation we get
for the very first quantities a, rather irregular numerical values.
We shall find
252 no 24072
5 ee
= 12, Sn WT én cea 2480
a, 6" Fase TR Te RET REEN.
but these results give no indication about the possible convergence of
319
the continued fraction. In order to prove this convergence for z > 0,
we change f(%) into
]
J () EE e2tVu__ eV u
and applying StieLrJes’ method to the new integral
ih r' An Tav N ] hae
= ——— — 2) - — AEN Nanda tand LOG) ag
© =f dee iW A ps OV ah ap
we obtain the continued fraction
1 | 1 | 1 | 1 1 |
se SRR la de See
la’,z la’, la',z a, la 62
ith a’ - d a! ne N both the series Sa and
WIEN Aon =S And Aon = =—_,. NOW Doth the series 209; anc
ae an an 2n+1 ae 1
oo
Ed's evidently, diverge, hence we infer that for z >>0 the new
0
continued fraction necessarily converges, and by the way we may
1
note for z =o the rather remarkable result
JT
bean:
Comparing the functions f(u) and g(w) we have
eh.
9 («)
and accordingly everywhere in the range of integration
LO on,
gu) =
therefore, again using SrieLTJES’ argument, we conclude to the
inequalities
5 (a, Ha, +a',+.-.4-@'2n41) < (4,+4,+4,+..-+42 n41) <<
AGS a,+a,+...-+ Aoi)»
en
Ed
otherwise written
ls) CO 1
(rte oe ae
1
<16(1 +5 eed +59).
320
Consequently the lower limit of asz4, must be zero, and that
CnH1
Cn
agrees with the fact that tends to infinity, for StieLTsEs shewed
that in that case no upper limit can be assigned to :
Un An4+4
oo
The principal conclusion, however, is that the series > dar
0
diverges, that therefore the continued fraction
EN
2
la,2
el ERE
dd dje ee
| la,z la, la,z
8 6
converges except when z is real and negative, and that it is equal
to the integral J(z). Thus then, putting z— 1, we have proved that
C — } can be expanded in the continued fraction
| eS ae
+ = SS 1 Sere
la, la, la, fe la, |
the quantities a, being rational and positive, whilst those of odd
index have the lower limit zero. More or less we are inclined to
believe that a fraction satisfying these conditions cannot represent
a rational number, and so the expansion of C — } again suggests
the conjecture that C must be irrational.
The result obtained is of no. practical value; that after some
reductions we have
6| 79| 2410) | 262445
5 * lag a Ape es ELSES
C eee
“ea
is of small service in the evaluation of the constant, and though
numerator and denominator of any convergent can be expressed in
the Bernoullian numbers, in approximating the constant C other
methods are to be preferred.
Chemistry. — ‘Researches on the Addition of Water to Ethylene
and Propylene”. (Preliminary Communication). By Dr. J. P.
Wipaur and J. J. DieKMANN. (Communicated by Prof. A. F.
HorLeMAN).
(Communicated at the meeting of March 24, 1923).
About two years ago experiments were carried out by one of
us purposing to study the possibility of a direct addition of water
to ethylene and propylene. The continuation of this investigation
has been rendered possible by a liberal support granted me from
the HooGrewerrr-fund. [ gladly avail myself of this opportunity to
express my great indebtedness to the Board of Management of. the
Hoocewerrr-fund for this help.
Though these investigations have not yet been completed, it seems
desirable to me in connection with a short notice in the ,,Cbhemiker
Zeitung’ of Jan. 2ed 1923 (N°. 47, p. 7), in which H. W. Krrver
describes similar researches, to publish a preliminary communication
on the results obtained by us.
J. P. Wieavr.
§ 1. The Action of Water-vapour on Ethylene and Propylene
in the Presence of Catalysts.
Since the investigations by [PATIEW, SENDERENS and SABATIER it has
been known that at high temperature and in the gaseous condition
ethyl-alcohol and some of its homologues can be decomposed in two
ways:
C HOH GH HO ns .ughe alike . covedhp
H
©, A. OH =>, CH,C==0 + Ho esrueb. oidavel (iD:
Both reactions are typical catalytic reactions, which only proceed
readily in the presence of certain contact-substances. Anhydrous
aluminiumsulphate and aluminiumoxide are typical catalysts that
split off water (reaction I). Metals like copper and iron, especially
in finely divided condition, are typical catalysts for the splitting
off of hydrogen (reaction II).
The range of temperature, in which particularly the first reaction
322
takes place, lies between 300—400°, dependent on the nature of
the catalysing substance; when the temperature is raised to about
400° and higher, the formation of aldehyde becomes prominent even
in the presence of substances like aluminium oxide and other catalysts
that split off water.
It is well known that reaction (II) is reversible — aldehydes
can be smoothly reduced with molecular hydrogen over nickel —
but nothing is known about the reversibility of reaction (1).
In the extensive literature on the splitting up of alcohols into
olefine and water, the question whether direct addition of water to
the double bond in ethylene and propylene is actually possible, has
never been examined. We have carried out a number of experiments
to answer this question. A mixture of ethylene and water-vapour
was led over different contact-substances at a temperature between
300° and 400°C. On use of aluminiumhydroxyde or of aluminium
sulphate as catalysts, the reaction product contained acetaldehyde.
We have proved the presence of acetaldehyde by the usual reactions
(reduction of an ammoniacal solution of silver hydroxide); Scurrr’s
reaction; reaction with nitro-prussidsodinm and piperidine aceording
to Lewin) and also isolated as p-nitrophenylhydrazone. The quantities
of acetaldehyde are very small; by far the greater part of the ethylene
remains unchanged during the experiment. The quantity of acetal-
dehyde amounted to from 0,2 to 0,4 °/, at 350°—360°, calculated
to the quantity of ethylene.
The presence of alcohol could not be verified ').
In our opinion the formation of acetaldehyde must be explained
in this way that primarily ethylaleohol is formed through addition
of water to ethylene, and then acetaldehyde through splitting up of
hydrogen. If this second reaction proceeds much more rapidly than
the addition of water to the double bond, no alcohol will be found
in the reaction product. As at 350°—360° ethyl-alcohol is almost
quantitatively decomposed into ethylene and water (at this temperature,
however, a little hydrogen is also formed) it is clear that only
at a lower temperature the inverse reaction can take place in a
considerable degree. We have, however, not succeeded in finding
a catalyst that causes the addition of water to ethylene below 300°.
We have proved by means of a separate experiment that no acetal-
dehyde is’ formed from mixtures of dry ethylene with about 10°/,
of air at 360° over aluminiumoxide. It, therefore, appears from
1) The analytical particulars will be given later. as also the full description of
the arrangement of the experiments,
323
this that the formation of acetaldehyde is not the consequence of
an oxidation of ethylene, e.g. according to the scheme
H
C,H, + O >CH,—CH, — CH,C=O
DOE
Hence the formation of acetaldehyde cannot have been caused by
the possible presence of small quantities of air in the ethylene used.
We are, therefore, of opinion that we are justified in concluding
that a primary addition of water to. the double bond has taken
place, and that the reaction:
C,H,OH 2 C,H, + H,O
may accordingly be considered as a reversible reaction.
We have obtained perfectly analogous results with mixtures of
propylene and water-vapour. At 350° and in the presence of alumi-
niumbydroxide acetone was then formed in a quantity of from
0,2 to 0,3 °/, of the propylene. In our opinion the primary
formation of isopropylalcohol by addition of water to propylene,
must be assumed in this case. Afterwards the isopropylalcohol
is transformed to acetone through the splitting off of hydrogen.
Hence the direct addition of water proceeds analogously to the
addition of hydriodie acid, in which likewise the isopropyl compound
appears. Accordingly the rule of Markonikow remains valid also in
this case.
On the ground of these results it is probable that the addition
of water to propylene and ethylene can take place under high
pressure at temperatures far below 300°. We have, however, made
no experiments in this direction.
§ 2. The Hydration of Ethylene and Propylene by
Means of Acids.
The syntheses of ethyl- and isopropylaleohol from ethylene and
propylene by the formation of alkyl-sulphurie acid, and subsequent
hydrolysis, by M. Berrarvor *) are among the classic syntheses of
organic chemistry. Berrarror investigated the absorption of these
olefines by pure sulphuric acid of 98—99°/, H,SO, at ordinary
temperature. Afterwards the absorption of ethylene by sulphuric acid
has been repeatedly studied. Particularly in the last few years several
technical chemists have made experiments to absorb the ethylene from
') BerTHELoT: Chimie organique fondée sur la synthèse, p. 115. c.f. Ann. de
Chimie et de Physique. (7), 4, 101 (1895). Bull. Soc. Chim. XI, 13. (1869).
324
coal-distillation gases by means of hot strong sulphuric acid (of
96 °/), and to obtain ethvlaleohol after dilution and distillation
of the sulphuric acid *).
With regard to the action of sulphuric acid on propylene, a process
of CaRLETON-Erus ®) has become known. In this process the waste
gases formed in the preparation of light hydrocarbons from heavy
petroleum-distillates (cracking-process of Burton) are passed through
sulphuric acid of 87°/,; the propylene present in these is said
to be transformed into isopropylsulphuric acid. After dilution and
distillation of the sulphuric acid isopropylalcohol is obtained.
Systematic researches on the behaviour of ethylene and propylene
towards acids of different concentrations have not been published.
On the other hand there are many instances known, in which
the addition of water to a double bond takes place under the
influence of diluted acids. Geraniol absorbs two molecules of
water when treated with 5°/, sulphuric acid. Burrerow *) found
that isobutylene and heptylene were very slowly hydrated to the
corresponding alcohols by means of diluted sulphurie acid and
nitric acid at the ordinary temperature.
It seemed interesting to us to examine how ethylene and propy-
lene would behave towards acids of different concentrations. If
ethylsulphurie acid can be obtained through the action of ethylene
on diluted sulphuric acid at high temperature, there would be a
possibility that afterwards the ethylsulphurie acid should be hydro-
lized :
(1) C,H, + H,S0, > C,H,HSO,
(2) C,H,HSO, +-H,0 > ©,H,OH + H,0
If the two reactions proceeded rapidly enough, the experiment
might be arranged so that the alcohol formed is immediately
distilled off from the reaction liquid.
Such a course of the reaction would then be practically an
addition of water to ethylene, in which the question whether we
have to do here with a direct addition or which an intermediary
') PRITZSCHE. Chemische Industrie 20, 266 (1897) and 21, 27 (1898); Tau and
BERTELSMANN, Glück Auf 57, 189 (1921); Bury en OLLANDER: ,,Byproduct devel-
opment in the [ron and Steel Industry”; Paper read before the Cleveland Institution
of Engineers, 15 December 1919; cf. Tipman, Journ. Soc. Chem Ind. 40, 86 T
(1921); pe Lorsy. Compt. Rend. Ac. d. Sc. Paris 170, 50 (1920); DAMIENS, DE
Lorsy en Pierre, Eng. Pat. 180988 (1922).
2) Cf. Chemical and Metallurgical Engineering. Vol. 23, 1230 (1920).
*) Lieb. Ann. 180, 245 (1876).
325
formation of ethylsulphuric acid, can be left undecided for the
present.
We have devised an apparatus, in which an ascending stream of
gas came into intimate contact with the descending acid. ‘This
washing apparatus, which is placed vertically was electrically heated
by means of a coil of nichrome-wire so as to make it possible
to keep the reaction temperature constant within narrow limits.
The ethylene, which is led through the heated, diluted sulphuric
acid will withdraw water-vapour from the liquid, for so far as it
is not absorbed, which would cause the acid to become more con-
centrated in the course of the experiment. To prevent this we
have added water-vapour to it at the same time with the ethylene ;
the partial tension of the water-vapour in the introduced gas-mixture
was about the same as the water-vapour tension of the used sul-
phurie acid at the temperature of the experiment. In this way the
concentration of the sulphurie acid was kept about constant during
the experiment.
At the top of the apparatus there escaped, therefore, water-vapour,
not absorbed ethylene, and alcohol vapour, if any was formed.
It actually appeared possible to obtain alcohol from ethylene in
this way. A mixture of ethylene and steam was washed with
sulphuric acid of 65°/, H,SO, at a temperature of 150°—160°.
After 5 litres of ethylene had been passed through in 5 hours’ time,
the distillate contained 0,21 gr. of alcohol’), i.e. a conversion of
about 2 °/,.
Then the sulphuric acid used was strongly diluted and distilled
out, and in this way 0,08 gr. of alcohol more was obtained. Hence
a little ethylsulphuric acid was still present in the sulphuric acid
after the experiment. This renders it probable that the ethylsulphuric
acid is formed as an intermediate product, and that accordingly
the formation of alcohol is the result of two successive reactions,
as given above. ,
In a second similar experiment 4°/, of the ethylene that was
passed through, was converted into ethylalcohol.
With a mixture of sulphuric acid and water containing 55°/, H,SO,
only 0.01 gramme of ethylalcohol was found in the distillate, when
5 litres of ethylene mixed with steam had been passed through at 140°.
With sulphuric acid of 70°/, no alcohol was found in the dis-
tillate, when three litres of ethylene had been passed through. After
1 The analysis took place by oxidizing the reaction liquid with chromic acid, in
consequence of which the alcohol present was oxidized to acetaldehyde. This
latter was determined colorimetrically.
326
dilution and distillation the sulphurie acid yielded, however, 0.32
gr. of alcohol, which was, therefore, present as ethylsulphuric acid.
This corresponds with a conversion of 5 °/,.
In these experiments most of the ethylene passed unchanged
through the sulphuric acid; only a slight carbonisation took place.
Though in principle it, therefore, appears possible to convert ethylene
in this way into ethylaleohol, the yield was so small that: no
practical significance can be assigned to these experiments.
These researches are being continued with other acids and with
salts, as aluminiumsulphate and others.
§ 3. Propylene and Sulphuric Acid.
It is well known from Berrneror’s investigations that propylene
is very rapidly absorbed at the ordinary temperature by sulpburic
acid of 98—99°/,. We have first of all made some preliminary
experiments on the action of sulphuric acid of different concen-
trations on propylene.
In a Hempet’s gas-pipette 100 ec propylene was placed together
with the sulphuric acid to be examined.
Sulphurie acid of 96°/, at once absorbs the propylene, also sul-
phurie acid of 90°/, acts very rapidly on it; with acid of 85 °/,
the propylene is absorbed after 20 minutes’ shaking, about an hour
being required for this with acid of 80°/,. Also sulphuric acid of
75 °/, still absorbs propylene, but very slowly.
We have further investigated the action of propylene on sulphuric
acid of 96°/, at 0°, in which we carefully guarded against rise of
temperature both during the absorption of the gas, and during the
pouring out of the reaction product on ice. We have only succeeded
in obtaining a small quantity of isopropylaleohol from the reaction
product.
Through the action of the sulpburic acid the bulk of the pro-
pylene was changed into an oily liquid, which was unsaturated,
and boiled within wide limits. It is, therefore, probable tbat
higher unsaturated hydro-carbons are formed by the condensing
action of the sulphuric acid. Bertne.or too states that such
condensation products are formed, when rise of temperature takes
place during the experiment. In our experiments with sulphuric
acid of 96 °/, at O° the bulk of the propylene was always
transformed into condensed and resinous products in spite of all
our precautions. With sulphuric acid of 85°/, the absorption of
propylene takes place very slowly at 10°. On further treatment
327
of the reaction product, chiefly condensation products were again
obtained.
We then examined the absorption of propylene by more diluted
sulphuric acid at higher temperature. The experiments were arranged
in the same way as was already described for ethylene. The mixture
of propylene and steam was brought in contact in counter-current
with sulphurie acid of definite concentration and definite temperature
in the vertical washing-apparatus; 7.5 litres of propylene mixed
with steam were passed in 4 hours through sulphurie acid of 55 °/,
H,SO, at 140°. The distillate contained 0.25 gr. isopropyl alcohol,
After dilution with water a distillate was obtained from the acid
in which 0.27 gr. of isopropylaleohol ') was present. There was,
therefore, evidently still isopropylsulphuric acid present in the acid.
In all 2.6°/, of the total quantity of propylene was, accordingly,
obtained as isopropyl alcohol.
A much greater part of the propylene was, however, decomposed.
Separation of carbon took place and formation of sulphur-dioxide.
After the experiment 5,3 litres of the 7,5 litres of propylene was
found back. Hence 9°/, of the consumed quantity of propylene was
changed into isopropyl alcohol.
An experiment with sulphuric acid of 45°/, H,SO, and at
125 —130° proceeded in the same way; 6 litres of propylene
were passed through, 5 litres of them were obtained after the
experiment. The yield of isopropyl! alcohol amounted to 0,2 gramme
in the distillate and 0.1 gramme in the acid liquid, together 0,30.
gr. Le. 10°/, of the consumed propylene. Here too a large part of
the consumed propylene was carbonised.
It therefore, appears from these experiments that the bydration of
propylene by hot diluted sulphuric acid is possible. The reaction
velocity, however, is small, which renders the yield small. Besides
the sulphuric acid has a decomposing action on the propylene. If
on the other hand the experiment is made with concentrated sul-
phurie acid at low temperature, the propylene is quickly attacked,
but chiefly transformed into condensation products.
We have tried therefore the action of other acids. We first
investigated the action of benzene sulphonic acid. 6 litres of pro-
pylene with steam were passed through a concentrated solution
of benzene sulphonic acid; in the aqueous distillate of this expe-
riment we found 0,25 gr. isopropyl alcohol or about 1'/,°/, of the
propylene. Hence in this case too the reaction proceeds slowly.
1) The analysis took place by oxidation to acetone, and colorimetric deter-
mination of this substance.
328
The result of the experiments on the action of acids on ethylene
and propylene can, therefore, be summarized as follows: It is pos-
sible to obtain ethyl alcohol, resp. isopropyl! aleohol by one opera-
tion from ethylene and propylene by means of mixtures of sulphuric
acid and water at 130—150°. In this reactions the alkylsulphuric
acids are probably formed as intermediate products.
The yield of alcohols is, however, very small, and particularly
with propylene, the hydro-carbon is decomposed in another way
during the experiment. These investigations are being continued.
Physics. — “The relation between the widening and the mutual
mfluence of dispersion lines in the spectrum of the sun’s limb.”
By Prof. W. H. Junius and Dr. M. Minnaekrr.
(Communicated at the meeting of April 28, 1923).
Introduction.
The hypothesis that the darkness of Fraunhofer lines is mainly
an effect of anomalous dispersion enables one to explain, at any
rate qualitatively, a great many characteristics of the solar spectrum.
It thus appears possible to formulate a theoretical connection —
which has then of course to be verified quantitatively — between
numerous phenomena that are less easily seen as inter-dependent if
we consider them from the point of view of the unmodified classical
absorption theory introduced by Krircnnorr. Such phenomena are
e.g.: the general displacement of the solar lines towards the red,
differing greatly in amount from line to line; the limb-centre dis-
placements and their dependence on intensity and wave-lenght; the
widening and the change of intensity of the lines as the limb is
approached; the apparent mutual repulsion of neighbouring Fraun-
hofer lines, generally greater at the limb than in the centre of the
disk; the systematically curved shape of the lines of the spot-
spectrum if the slit cuts the spot in a direction passing through the
centre of the disk; the gradual increase of the distance between
the components of the bright calcium lines H, and K, as the limb
is approached; and varjous particulars of a more local character.
We shall endeavour to express mathematically the connection
which, according to the dispersion theory, should exist between a
few of the above-mentioned phenomena, and then to investigate how
far these quantitative relations agree with the results of measure-
ments made on solar lines.
It is evident that the absolute magnitude of the influence exercised
by anomalous dispersion in the solar gases on the aspect of Fraun-
hofer lines cannot be calculated directly so long as the refracting
and scattering power of the sun is not otherwise known. Neither
can this power be safely computed starting from line displacements
only. It must be remembered, however, that a similar uncertainty
prevails regarding the values given for temperatures, pressures,
radial velocities, intensities of magnetic or electric fields, or grades
of dissociation in the sun in so far as such values are derived from
330
spectral phenomena; in fact, such statements are always based on
the doubtful assumption that the observed spectral phenomena are
entirely due to the causes mentioned. There is, of course, no
objection to introducing this assumption, — provided its hypothetical
character be always kept in mind.
With equal justification we may assume that Fraunhofer lines
are mainly “dispersion lines”; the essential point will then be to
examine whether the deductions from this hypothesis result in an
adequate theory, covering a substantial proportion of observational
data. In this paper we confine ourselves to showing that the dis-
persion theory of the solar spectrum connects quantitatively two at
first sight independent groups of observed phenomena, namely the
well-established general widening of the Fraunhofer lines at the
limb, and the increase, also at the limb, of the mutual influence of
neighbouring lines. This relation proves to be independent of the
unknown laws that govern the weakening of any given kind of
light on its way through the solar gases; it enables us to indicate
an upper limit of the mutual influence that may be expected, thus
lending fresh support to our fundamental hypothesis. It will be
shown, indeed, that the average value of the mutual influence as
deduced from the dispersion theory is perfectly consistent with the
actual observations.
The dispersion lines which, according to our hypothesis, envelop
the exceedingly narrow‘) true absorption lines of the solar spectrum
arise from two dimming processes, viz.: irregular refraction and
molecular scattering. For although light of any wave-length is sub-
ject to refraction and scattering on its long way through selectively
absorbing gases, it is well known that these causes of darkening
specially affect waves in the immediate vicinity of absorption lines. As
the two processes weaken the transmitted light according to different
laws, we shall treat them separately.
[. ON THE WEAKENING OF LIGHT IN PASSING THROUGH
EXTENSIVE MASSES OF GAS.
$ 1. Spreading of light by irregular ray-curving in a mixture
of gases.
Suppose we have in a given space a mixture of gases which, if
they were each of them alone to fill the space, would show the
absolute refractive indices 7,, n,.... ni... then, according to ex-
1) Our assumption that real absorption is restricted to very small ranges of
wave-lengths is in harmony with views recently derived from the quantum theory
by N. Bour (Zeitschr. f. Physik 13, 162, 1923).
331
periments of Biot and Araco (confirmed by modern observations),
the refracting power of the mixture equals the sum of the refracting
powers of the constituents:
- n—1= 2 (n;—1).
The condition is implied that the gases do not act on each other.
We shall assume this law to be valid also in those spectral regions
where one of the constituents causes anomalous dispersion, although
no very accurate direct measurements concerning such cases are as
yet available. (The exceedingly narrow regions of true absorption
are not considered here).
If the gaseous mass is very extensive and of unequal optical
density, with irregular gradients in all directions, it will make every
beam of light spread out like a bunch of feathers. According to
ORNSTEIN and Zwrnicke') the rate of this kind of scattering is
determined by ‘the average square of the spreading per unit of
length” = to any short path / corresponds an angle « depending on
the average value of the irregular density gradients, and proportional
to n—1 of the mixture. The weakening of the transmitted light
will therefore be a function of
Se FG =1) ED en ie an)
that has the property of increasing and decreasing with this quantity.
A characteristic difference between scattering by irregular refraction,
and molecular scattering, is, that in the latter process a considerable
part of each beam passes straight, and a small part of it disperses
in all directions, whereas in refractional scattering every beam itself
widens like a plume.
§ 2. Scattering of light by the molecules of a gaseous mixture.
If a beam of light of intensity /, has travelled a distance z
through a medium containing iV scattering particles per cube cm,
its intensity has diminished to / = /,e—"*, where, according to
Ray.rieH, A has the value
32 2? (v—1)?
ERE ZK
In this expression v is explicitly stated to represent the refractive
index of the medium as modified by the scattering particles against
the unmodified medium’). Denoting the absolute index of the latter
h
1) ORNSTEIN and ZERNICKE, These Proceedings, Vol. 21, p. 115 (1917).
4) RAyreiGH, Phil. Mag. 47, 375, 1899. — Scientific Papers IV, 400.
22
Proceedings Royal Acad. Amsterdam. Vol. XXVI.
332
by n, the absolute index of the modified medium by n', we have
n' 2
32 n° | —-—1
n 3227 (n'—n)? 322° (n'—n)?
SENS dear Ed me 3 At
.
hi
because for thin gases we may put n?= 1.
We shall take for granted that this expression for A remains
valid in those regions of the spectrum where the scattering particles
produce anomalous dispersion. It is precisely in those regions that
h will assume considerable values.
Now suppose there be a mixture consisting of N,, N,,...Nj,...
scattering particles of the kinds 1,2,...7,... For each kind the
mixture of the remaining kinds forms the “unmodified medium”,
whilst the ‘modified medium” is the same in all cases, viz. the
complete mixture. We are concerned, therefore, with a single quantity
n' and several values m1), %2),..-7@,... Of n, if ng denotes the
absolute refractive index of the mixture without the constituent 2.
The scattering-coefficient 2 of the complete mixture will be the
sum of the scattering-coefficients peculiar to the separate constituents,
each in its proper medium:
sant s (n'—n()”
3 13 N;
This expression may be simplified because the above-mentioned
law of Bror and AraGo requires, that
n'—1 = (no)—l) + (n;—1)
n; representing the absolute refractive index which the gas 7 would
show if it were alone in the given space. We, therefore, have
n'—nq) = nj—1, and may write:
32 2* _ (nj—1)?
— = DE °
B Ni
A beam of light, having travelled a long way through such a
mixture of gases, will emerge with a loss of intensity expressible
as a certain function of h which has the property of increasing
and decreasing with 4. In regions of the spectrum sufficiently small
to permit of neglecting the change of 2* in them, we see that now
(n;—1)?
Fait ae Market cana aie
v
is the variable quantity determining the loss of light. (Compare this
expression (2) with the corresponding one (1) which applies to
refractional scattering).
kh, + hd...
=
333
§ 3. How anomalous refraction and anomalous scattering act in
producing dispersion lines.
It appears from the above remarks that the distribution of the
intensity in a dispersion line is determined by two darkening laws
which, it is true, depend on local circumstances (dimensions and
shape of the source of light, condition of the medium, etc), and
to that extent are unknown, but which we do know will change
with wave-length in accordance with the functions (1) and (2). We
shall first deal with the share which irregular refraction, and there-
after with the share which molecular scattering has in the formation
of dispersion lines.
A. Imaginary pure refraction Lines.
Imagine a selectively absorbing gaseous mixture, lacking the
faculty of molecular scattering, but with many irregular gradients
of density; let a beam of white light travel through that medium,
and attention be confined to a small part of the spectrum where
only one characteristic frequency, i.e. one ideally sharp absorption
line, is in evidence.
If the said line were absent, the mixture would, in this narrow
range of wave-lenghts, show a refracting power n,—1 varying only
very slowly with A, but to this will now be added the anomalous
refracting power n,—1 of the constituent producing the absorption
line, thus determining the resultant refracting power:
n— 1 =(n, — 1)+ (n, — 1).
The term (n,—-1) will, as a rule, preserve the same (generally
positive) sign throughout the region considered, whereas (n,—1) is
negative on the violet side of the line, positive on the red side.
Light on the violet side of a line will be called V-light, on the red
side f-light. All effects of refraction in a gaseous mixture are,
therefore, on an average greater for R-light than for V-light, because
they depend on (n—1)? or on the absolute value of n—41, i.e. on
| (n‚—1) == (n,—1) |.
Fig. la shows the course of n,—1 and n,—1 each separately ;
Fig. 2a gives n—1 = (n,—1) + (n,—1); in Fig. 3a is represented
the course of /n—1) = |(n,—1)-+ (n,—1)| which determines the
distribution of the light in our “refraction line”.
The sharp absorption line will thus be enveloped in an asymme-
tric refraction line, whose “centre of gravity” is displaced towards
the red if m,—1 has the positive sign.
(The general displacement of the Fraunhofer lines towards the
22*
334
red, which increases on approaching the sun’s limb, may be con-
sidered in connection with these inferences).
Let us now imagine our small spectral region to contain two
neighbouring sharp absorption lines, then we have
n—l = (n,—1) + (n,—1) + (n,—1),
where n,—1 is again assumed to be nearly constant, and the other
two terms are strongly variable with A. In the region between the
lines, (n,—1) and (n,—1) have opposite signs (cf. Fig. 1,6, where
the three terms are represented separately). The resultant »—1 = / (A)
Fig la Fig 16
ek
= 0
Fig 2a | Fig 26
2(n,-1)
Fig 3a | Fig 36
| |Z(n-1)|
|
0 :
Fig 4a Fig 4b
expe)
0 - ~ - - — —- =
Fig. la—4b.
shows a point of inflexion there (Fig. 2,5); and, owing to the
opposite signs of (n, —1) and (n,—1), the modulus |(m, —1)H(n,—1)+
+(n,—1)| is smaller than |(m,—1)-+ (n,—1)| in the left section,
and smaller than \(n,—1) + (m,—1)) in the right section of the
interval (ef. Fig. 3,5), so that on the two sides of the refraction
lines that face each other the weakening of the light is less than
it would be if the lines stood wide apart. The “centres of gravity”
_ of two neighbouring refraction lines are, therefore, a little more
335
distant from each other than their cores, i.e. the true absorption
lines: we observe an apparent repulsion.
In Fig. 3 we see, moreover, that on the violet side of each line
there appears a point where n—1=0. (If n,—1 were negative,
such a point would be found on the red side of the line). Light of
the corresponding wave-length would not be weakened by irregular
refraction and should, therefore, show an intensity in the spectrum,
surpassing the average intensity of regions clear from lines. JEWELL’)
seems indeed to have observed casually such phenomena in the
solar spectrum. It is not surprising, however, that similar places of
greater brillancy are not very conspicuous there; for we can scarcely
doubt that in the sun the proportion of the components of the
mixture varies with depth, so that the values of 2 for which
n—1i =O will not be the same on the entire paths of the beams.
Moreover, the Fraunhofer lines are partly due to molecular scat-
tering, and it will presently be shown that this process does not
involve the appearance of such narrow regions of greater brillancy
in the spectrum (at least not in the central parts of the solar disk).
Both circumstances tend to obliterate the brighter places near refrac-
tion lines.
B. Imaginary pure scattering-lines.
Now suppose the density of a gaseous mixture to be so uniform,
that rays of light pass through it in straight lines, then the true
absorption lines will yet be enveloped into dispersion lines, because
for kinds of light belonging to the nearest environment of the
distinctive frequenties the coefficient of molecular scattering has
greater values. Let us analyse, indeed, how
32 n° _ (nj—1)?
3 A Ni
varies with 2 in a narrow spectral region containing a single absorp-
tion line of the constitnent 7. All terms of the sum but one may
there be treated as constants, so that
Sarma (ri 1):
344 N;
This quantity varies with 2 in the manner represented in Fig. 4,0;
the curve is symmetrical with respect to the absorption line, provided
that the dispersion curve associated with the line has the regular
D= Sl
1) Jewett, Astroph. Journ. III, 99, 1896. Cf. also: ABBor, The Sun, p. 115,
where analogous observations of EVERSHED are mentioned in addition.
336
shape, and that the change of 2* in the small region may be
neglected. The distribution of the light in the scattering line will
then also be symmetrical; this we may infer without knowing the
exact form of the law of darkening’).
In contrast to what characterizes pure refraction lines, the sym-
metry of pure scattering lines is not disturbed by the addition of a
similar cause of weakening that is constant in the region considered.
(The above expressions (1) and (2) explain this difference).
Anomalous molecular scattering, or diffusion of light, cannot
therefore have any share in the production of the general displace-
ments of the solar lines towards the red’).
Let us now consider the case that our small spectral region
contains two absorption lines. The scattering coefficient will then
take the form
EN [es | |
N; Nk
; 3220? 2
for we may replace the factor Or by the constant quantity p.
Fig. 46 represents / as a function of 4. To this will correspond a
darkening curve whose ordinates grow and decline with h. We see
that in the interval between the absorption lines the superposition
of their individual scattering effects must produce a greater increase
of the darkening than outside the pair; so the centres of gravity
of the two diffusion-lines will be a little less distant from each other
than the absorption lines proper (apparent attraction).
Summarizing the above qualitative results with a view to their
application in the spectroscopy of celestial bodies, we may state:
1. The general but very unequal displacements of the Fraunhofer-
lines towards the red can be explained by the properties of refraction
lines, but not by those of diffusion lines. This also applies to the
limb-centre displacements.
2. The mutual influence of neighbouring Fraunhofer lines, which
increases, as a rule, from the centre towards the limb of the solar
disk, may be the result of either scattering process; but irregular
refraction causes apparent repulsion, molecular diffusion of light
gives apparent attraction.
1) The Jaw of darkening through molecular scattering in the sun has been amply
studied by J. SPIJKERBOER in a dissertation, published in Utrecht, 1917; cf also
Arch. néerl. IIT A, 5, p. 1—115, 1918.
8) To this point our attention has first been drawn in a conversation with
EINSTEIN.
337
Il. THE RELATION BETWEEN WIDTH AND MUTUAL INFLUENCE IN
DISPERSION LINES AND IN FRAUNHOFER LINES.
In this chapter formulae will be deduced expressing the connection
between mutual influence and width of dispersion lines. If Fraunhofer
lines are in the main dispersion lines, it will thus be possible, starting
from data concerning the widening of the lines in the spectrum of
the sun’s limb, to derive values for the probable increase of the
mutual influence in passing from the centre to the limb. We may
then compare these theoretical results with the data obtained from
observations regarding limb-centre displacements of Fraunhofer lines.
The respective shares which irregular refraction and molecular
scattering may have in the production of the lines will again be
treated separately.
§ 1. Refraction lines in the spectrum of the centre of the solar disk.
The distribution of the luminosity in a refraction line depends on
the values of |n—1|/— f(/). We owe to Roscupestwensky !) the most
accurate measurements concerning the form of this function. He
found that in region of the two yellow sodium lines SELLMEIER’s formula:
an a,’
=1= Ns AEEA NE (dl
: PLR wae ee Ne,
represents the observations almost exactly. We shall suppose this
formula to be applicable to the cases we are considering.
If the difference between 2, and 2, is rather considerable and if
we only pay attention to the surroundings of one of the lines, we
may unite the latter two terms of (1) into a single, nearly constant
refracting power (n,—1), and moreover put À + A4,—24. The
; fn One : C
expression thus simplifies itself, if we write / for —, to:
k
valde Sia Bae DA ee (2)
D=
The intensity at any place in the spectrum depends on the absolute
value |n—1|. On either side of the absorption line we mark the
values of 4 where n—1 — + H (ef. Fig. 5), H being provisionally
an arbitrary constant. These places in the spectrum will be called
the ‘“‘H-boundaries” of the dispersion line; their distance (to be
1) RoscHDESTWENSKY, Anomale Dispersion im Natriumdampf. Ann. d. Phys.
39, 307, 1912.
338
indicated by 5) is the “H-width” of the line. So B signifies the
width an observer would assign to the line if he estimated its
Fig. 5a—6b.
boundaries to be situated at the wave-lengths where the relative
intensity has the value corresponding to H. (By “relative intensity”
we understand the proportion between the intensity at the selected
point of the dispersion line and the intensity in the surrounding
continuous spectrum).
Suppose the ““H-boundaries” of the line to be situated at ap and
Ay, then we obtain from equation (2);
k k
pa Ay, = .
AEs H—(n,—1) Be om A+ (n,— — Dj ED
Re 4
Sc) eh gmeriae Os is
or, inversely, expressing H in B,
Hee Ey erm
We may leave the negative value of the radical out of account.
Now proceeding to the case of two neighbouring equally strong
lines, we prefer to indicate the places in the spectrum by the
quantity
(SA
(ef. Fig. 5,5) in which 2 represents the wave-length corresponding
to the point halfway between the two absorption lines, so that this
339
middle-point becomes the zero in our scale of l-valnes. If the
distance between the lines is 2A, we have in the new notation:
1, =A for the line on the red side, /, —— A for the line on the
violet side, and we get, in analogy with (2), the relation
n—1l= Ke + ‘ lln N nk ses et clas (8)
Eh TE :
For each of the lines we may again define two ‘/7-boundaries”,
to be found by taking (6) equal to + H, wherein H has the value
fixed by the relation (5).
We consider the red-facing line of the pair. Its H-boundaries
Ir and /y are found by substituting in (6) H for n—1, /r or ly
for 7. We thus obtain, according as the + sign or the — sign is
chosen:
k ee
BELT + H— (n,—!) 1 We H—(n,—))7? b Seana Raton B
or Sy+Ty. (0)
Similarly it follows, that the violet-facing component of our pair
has for its H-boundaries
Ue OF TENOR 1595p OP Ta TR (a)
§ 2. Refraction lines in the spectrum of the limb of the solar disk.
Seen in the light of the dispersion theory, the widening of the
Fraunhofer lines in the spectrum of the limb is due to the fact,
that near the limb smaller values + H’ of n—1 are already suffi-
cient for producing the same relative darkening, which in the central
parts of the disk is only produced by the greater values + H.
The H’-width, shown by the line at the limb, will be called B’.
As a counterpart of (5) we now obtain the relation
se al 1)? 8
gn Rat Mee 12h either (8)
and, in the case of two limb-lines, as counterparts of (7) and (7a):
k k:
WENO we BOS pc 1
Ror’; EG a EH RAR
or Sy LT’ (9)
IR or LIS RET ER OF STE Jeg, (9a)
$ 3. Theoretical possibility of a general solution of our problem.
In principle, the formulae (5), (7), (8), and (9) embody a rather
complete answer to the question how, on the basis of the dispersion
340
theory, the widening of the lines near the limb and the increase
of their mutual influence must be connected. Indeed, if the distribu-
tion of the relative intensity were established both for an isolated
refraction line of the centre type and for the corresponding limb
line, it would now be possible to plot the curve giving the distribu-
tion of the light in a set of two neighbouring equal lines, and to
examine how the asymmetry in it increases when passing from the
centre to the limb of the disk. It would only be necessary to sub-
stitute for B and B’ the values corresponding to relative intensities
0,9, 0,8, 0,7 ete., and then to calculate from (7) and (9) where the
places of equal intensity ought to be found in the pair. *)
For the present, however, the intensity curves are not sufficiently
known; the observers of the solar spectrum provide us with the
“visual widths” and the wave-lengths of the “centres of gravity”
of the lines, quantities by no means free from subjectivity.
Nevertheless we can draw from such observations some useful
inferences concerning our problem.
§ 4. Limitation to what may be derived from already existing
data.
The average widening in the limb-spectrum of lines whose widths
lie between 0,07 and 0,16 A was found by FaBry and Buisson *)
to be 0,01 A. Although we do not know the exact value of the
relative intensity at the places where their interference method made
them estimate the “boundaries” of the line, there was yet in this
way assigned a definite width to each line. (We have some reason
to think that in the ordinary visual estimates of the width of a
dark line the relative intensity at the borders is about 0,8. This
statement reposes on extrapolation of an empirical formula by which,
in an earlier investigation, we were able to represent the visual
boundaries of bright lines on the photographie plate. Cf. Ann. d.
Phys., 71, 59, 1923).
Whilst under the influence of a neighbouring line these boundaries
shift asymmetrically, the central parts of the dispersion line, with
1) If limb- and centre-lines have been photographed on one and the same plate
(the centre spectra with shorter exposition so as to make the intensity of clear
spaces equal in both centre and limbspectra) it is even possible to use the
transparency values of the single lines directly for computing, by means of our
formulae, the course of the transparency in pairs of lines occuring on the same
plate. It is unnecessary then, first to translate the degrees of blackening into
original intensities.
2) FABRY and Buisson, CG. R. 148, 1741, (1909); Astroph. Journ. 31, 97, (1910).
341
their greater darkness remain almost stationary. The point midway
between the boundaries will, therefore, by its position depict all
asymmetrical distortions of the dispersion line somewhat exaggerated
in comparison with the “centre of gravity” instinctively used by
the observer to identify the place of the line. If, therefore, we
calculate the displacements of that midway point, we are sure to
find upper limits for the displacements which, according to the
dispersion theory, may be expected as the result of measurements.
$ 5. The difference in mutual influence of refraction lines at the
limb and in the centre of the disk.
It is easily seen that the midway point Mp between the H-
boundaries of the red-facing displaced refraction line is determined
by the absciss
ly =|, ((r+lv)='/,\Sr+Sv+Tr+Tyv) in the centre-spectrum,
and by (10)
Uy="/,Urtly='/,(Srt+tSv+T'r-+T'y) in the limb-spectrum,
so that the amount of its displacement, when passing from centre
to limb, is:
Uu—ly="/, (S'r + S'y—Sae—Sy + T'r+ T'y-Tr—Ty)- (11)
This expression contains side by side all the various systematic
displacements of Fraunhofer lines which the dispersion theory fore-
sees as consequences of irregular ray-curving. The first two terms
give the general displacement of limb-lines against arc-lines; the
third and fourth the general displacement of centre-lines against
arc-lines*); the fifth and sixth term show the apparent repulsion
of neighbouring lines in the limb-spectrum; the seventh and eighth
the apparent repulsion in the centre-spectrum.
At present we are especially interested in the increase which the
apparent repulsions must undergo when passing from the centre to
the limb, because we are in possession of a good many observational
data concerning this phenomenon ’).
For each component of a pair the said increase is represented by :
TE lo! RL)
which expression, after substituting the quantities determined by
(9), (8), (7) and (5), becomes
1) Here are, of course, not included those displacements which the core-lines or
true absorption lines may perhaps be subjected to as a result of radial velocities,
pressure, or fields of force. Such displacements will simply have to be added to
the phenomena we are considering.
8) Cf.: W. H. Junius, Mutual Influence etc., Astroph. Journ. 54, 92, 1921, and
W. H. Junius and M. Minnaert, Ann. d Phys. 71, 50, Kayser-Festheft, 1923.
342
B : Ny 1 A? |
2 de (n,—1)?B? (n,—1)B Egt |
E Be Wipers we |
I A?
a AE (4,--1)'B* | (n,— DB TB
Ft Bt |
(12)
1 4 ABN)
Hey Gree n —1)B |? B
ele _ 2 |
pil a) >
Ee
n,—1)B 13%:
Ve en ef |
In order to estimate the numerical value of this expression we
base ourselves on the result of observations of FaBry and Buisson,
who found the widening at the limb to be approximately 0,010 A
with lines varying from 0,07 to 0,16 A in width (mean width 0,11 A).
The mean width of those other lines, taken from the observational
materiai of Mount Wilson and Kodaikanal concerning limb-centre
displacements, for which the existence of mutual influence has been
stated *) by us in the above mentioned papers, amounts to 0,09 A.
Taking these data into consideration, we have calculated the value
of the expression (12) after substituting 6 — 0,100 A, B=B=O0010 A,
(n,—1)B
and, in succession, mp — tropes A tan du Om ihe Mesut
2A
have then been plotted as ordinates against abscisses B (which,
therefore, represent distances of the lines expressed in their width
as unit). We so obtained the full drawn curves of Fig. 7 (p. 346).
They represent (for a refraction line) by how many thousandth parts
of an Ängström unit the middle point M'j between the boundaries
of a limb-line is shifted in excess of the middle point My between
the boundaries of the corresponding centre-line, in consequence of
the presence of an equally strong neighbouring line, if this is situated
at a distance equal to 3, 2, 1 times the estimated width of the
lines. [t will be seen that the repulsion is already perceptible at a
1) W. H. Juus, Astroph. Journ. 54, 92, (1921); W. H. Junius and M. Minnaert,
Ann. d. Phys. 71, 50, Kayser-Festheft, 1923.
343
rather great distance, and increases slowly to 0,004 A maximum.
Obviously the value of nm, has only little influence on the result.
As B' differs little from B, the radical quantities of (12) can be
developed into rapidly converging series. It will then appear that as
a first approximation the repulsion is proportional to the absolute
value of the widening at the limb, ie. to B'—B, Accordingly, our
curves are also valid for lines differing in width from those here
considered, provided their widening at the limb has the value found
by Fasry and Buisson. They are therefore applicable to the case
of lines having the average type of those for which mutual influence
has been observed.
§ 6. Diffusion-lines in the spectrum of the centre of the solar disk.
The distribution of the intensity in a pure molecular scattering
line (in the absence of irregular gradients of optical density) depends
on the manner in which the scattering coefficient (cf. p. 335):
322" (nj;—1)?
PN
varies with À in the surrounding small part of the spectrum. And
because even the variation of A‘ may be neglected there, the distri-
bution is entirely governed by the nature of
(ie) ERE
NET MAO
a function, obviously symmetrical with respect to the position of
the absorption line. On either side of the latter we may again
2
mark a wave-length where (omitting the index 7) ae equals a
certain — provisionally arbitrary — quantity L*. By these places
in the spectrum we define the ‘‘Z-boundaries’, and by their distance
the “L-width” of the diffusion line (Cf. Fig. 6, on p. 338).
We now introduce the dispersion formula (2) of p. 337 and
confine our attention to the case that there is only one single ab-
sorption line, so that we may write
k
ape
h=C+
n—1 = (13)
Our two L-boundaries will be found by substituting in this
equation n—1=+ LVN and À=dr or =Ay, which leads to
k - k
ARA pai, == ale na Aerin (412-5
R 1 LYN en | 1 LVN ( )
and makes the L-width of the diffusion line equal to
from which follows
Lan ns Pulte iaie Wi
In case we are dealing with two neighbouring lines of equal
+2
k
strength (na is: equal value of Fr) at distance 2A from each
other, it is convenient to indicate all places in the spectrum (like
we did on p. 338) by a new system of abscisses:
l=1—iy ee ee en. (10)
Am representing the wave-length of the point midway between the
absorption lines, where we place the zero of our scale of /-values.
The abscisses of the two absorption lines are now — A and + 4.
According to the equation = +h; of p. 335, and considering
the smallness of the selected spectral region, the distribution of the
(n,—1) rm (n,—1)?
light in it will entirely depend on the quantity
N, NS
as a function of 4 or of /. Applying (13) and (16) we find
(n,—1)* (Ae k,* k,” hk hk”
7 = = AT () 3 AT, ES = T P a5 7 (17)
N, Ne). NOAR Naa) CLA NUE
The ZL-boundaries of each of the components of the pair are
k
. Let us
iN
obtained by making (17) equal to L’ or, after (15), to
consider the red-facing component. Its L-boundaries are situated at
=/p and /=/y, and can be deduced from (17). According as the
+ or the — sign is taken, we obtain
B 44?
lr votives DAE el nod ars vnd a (USE
The two negative values of the same radical quantities represent
lr and ly of the violet-facing component of the pair.
§ 7. Diffusion lines in the spectrum of the limb of the solar disk.
(n—1)*
At the limb a smaller value £/* of — Fai will suffice to bring
about the same degree of darkening that ZL? gave in the centre.
The ‘Z'-boundaries’” determine a width B' through the relation
2k
EEA in analogy with (15). We thus find for the borders
345
of the components of our pair of limb-lines
nisi A sier os MOLEN
§ 8. The difference in mutual influence of diffusion lines at the
limb and in the centre of the disk.
In conformity with our procedure with the refraction lines, we
are now going to determine also in the case of pure diffusion lines
an upper limit for the apparent displacements which the components
of a pair impart to each other. We therefore consider the point
My, midway between the L-boundaries of one of the lines, defined
by the absciss
lu ='/, lr + ly)
and will only have to compute how much this value differs from
+ A. But we are especially interested in the difference between the
apparent displacements of a component in the limb-speetrum and of
the same line in the centre-spectrum, i.e. in the quantity
Uum lu=!/, UR + lv —lr—lyp).
for which we find, after substituting (18) and (19),
ee: ee Vi ABE
UM — = — == = = ==: ==
Mg | B: sl B ait B B dT B 5
a sare AA =a
Soa ld a BR
(20)
The numerical value of this expression has been calculated for
four different widths of the lines, namely B — 0,050, 0,070, 0,100
and 0,200 A. We took B’ always to be = B+0,010 A, and
2
selected a number of distances A so as to have values of Be (as
abscisses) suitably situated for plotting curves.
The dotted curves in Fig. 7 show the result. All ordinates should
be imagined negatwe, because in this case there proves to be an
apparent attraction of the components. We notice that the effect is
346
less than 0,001 A so long as the distance exceeds twice the width
of a line. On closer approach the lines rapidly grow very asym-
0010 A
|
\
L \
n ee Ie EEn Zn
| B=q200 A AFSTOOTING BIJ
BREKINGSLIJNEN
| _--- AANTREKKING BIJ
| VERSTROOIINGSLIJNEN
|
4 :
| \ B-qroo A
iy
1 fi
dt
4 i if
LN 1 a
| | | B-g070 A 4
Mise 0005 A
i]
i
ki i
Bret) _ eh
sat, -
0
(B-0,050 A
5 &
\
2A=1B =2B
metric; at distances smaller than about 1,5 times the width, the
second term of (20) becomes imaginary and the formula impracticable.
$ 9. Comparison of the theory with the results of observations on
Fraunhofer lines.
In the foregoing we have supposed, for simplicity’s sake, that
the width of the true absorption lines could be neglected; but there
are, of course, reasons for assigning a finite width to these cores
of the Fraunhofer lines. Especially as far as very strong lines of
the solar spectrum are concerned (which were not considered in
the above), it would have been necessary, therefore, to base the
calculations on a still closer approximation to the shape of the
347
dispersion curve. There is still another reason why strong lines
— many of which lose their “wings” near the limb — require
separate treatment, namely because for such lines, according as the
limb is approached, it is indispensable to make due allowance for
the spherical shape of the source of light when the consequences
of diffusion, and particularly of irregular ray-curving, are inquired
into. Indeed, looking almost tangentially towards the source, we are
no longer allowed to assume that the darkness of the line increases
2
4 at 7 ; 5 a
with — and with h, particularly not if n—1 has great values. Such
l
considerations suggest that in a further development of the theory
it will be necessary to reckon with a different set of conditions and
circumstances for different lines, especially very near the limb, where
the Fraunhofer spectrum passes gradually into the chromospheric
spectrum.
The sharply differentiated structure visible in the chromosphere
at times of excellent seeing indicates that, at least at a level only
slightly outside the apparent edge of the disk, the gaseous medium
must be highly transparent along the path of the nearly tangential
rays, even for waves belonging to the very Fraunhofer lines. This
proves that in those layers molecular scattering is unable to make
the medium appear “foggy”, in other words: that anomalous irregular
refraction plays a greater part there in determining the distribution
of the light, than anomalous molecular scattering.
We infer that probably with most Fraunhofer lines, also with the
weaker ones, the darkness will depend to a greater extent on
refraction than on molecular scattering — though it appears possible
that the proportion between the respective influences differs from
line to line.
All this has to be taken in consideration when comparing our
theoretical results with observational data. Fig. 7 shows the upper
limits of the effects of mutual influence to be expected in the cases
we discussed, if the lines were pure refraction- or pure diffusion-
lines. In Fraunhofer lines the two processes are probably intermingled
and the respective displacements opposed; but refraction is likely
to have the advantage.
We therefore may expect, e.g., if the distance between certain
Fraunhofer lines lies between 1,5 and 3 times their width, that
their mutual repulsion at the limb will exceed their repulsion in
the centre by an amount certainly not greater than 0,002 A.
Now, according to the above-mentioned observations of Mount
Wilson and Kokaikanal, the examined effect has the average value
23
Proceedings Royal Acad. Amsterdam. Vol. X XVI.
348
0,00175 A, for pairs of lines whose average distance amounts to
1,7 times their mean width.’) This harmonizes, as regards order
of magnitude, with the computed value.
In the publication just referred to we have shown that the mutual
repulsions which two equal, symmetrical lines seem to exercise on
each other as a mere consequence of systematic (photographical or
psychological) errors of measurement, only become appreciable when
the distance between the lines sinks below 1,5 times their width,
and that, therefore, only a fraction of the mutual influence observed
with Fraunhofer lines, can be ascribed to such errors.
The theoretical anticipation here advanced thus proves to be
consistent with the observational material till now available; but
for the present our conclusion cannot go beyond this, because the
quantities involved in this investigation are near the limit of preci-
sion attainable with existing means for measurement in the solar
spectrum.
Utrecht, April 1923. Heliophysical Institute.
') Cf. our article „Kritisches zu Deutungen des Sonnenspektrums”, Ann. d.
Phys. 71, p. 50, 1923.
Botany. — “Cytological investigations on Apogamy in some elemen-
tary species of Erophila verna”’. By J. P. Bannter. (Commu-
nicated by Prof. F. A. F. C. Went).
(Communicated at the meeting of March 24, 1923).
After Jorpas, in 1823 *), made his well-known communications
concerning the constancy of the elementary species, and in particular
those of Hrophila verna, this highly polymorphie species became not
merely the classic type of absolute constancy of the elementary
species, but also the subject of much experimental research. The
best known work on this subject is that of Rosen on the formation
of new sub-species by cross-fertilization. According to this writer
the hybrids do not conform to the laws of Menper, but, after having
formed a very heterogeneous F, remain constant in the F, and
following generations *). The explanation of this can only be found by
cytological research, accompanied by repeated efforts at hybridization.
The investigations, the principal results of which so far obtained
are given here below, were prompted by similar attempts at hybri-
dization, carried out by Dr. J. P. Lorsy between two elementary
species found near Bennebroek, and further cultivated constant by
him, which, as they could not be identified with absolute certainty
with any previously described sub-species, were christened Hrophila
eochleoides and Erophila violaceo-petiolata. These experiments, however,
were unsuccessful in so far as no hybrids resulted from a cross-
fertilization, but all the offspring were like the mother plant, and
remained constant in following generations.
One plant only, at first regarded as a hybrid, was a very fine
intermediary between the two aforesaid sub-species, but further
cytological examination proved that it could not be a hybrid result
of the applied cross-fertilization. The following generations of this
1) Arexis JoRDAN. Remarques sur le fait de l'existence en société, a l'état
sauvage, des espèces végétales affines et sur autres faits relatifs à la question de
espèce. Bull. Ass. franc. Avance. des Sciences Lyon 1873.
5) Ferix Rosen. Die Entstehung der elementaren Arten von Erophila verna.
Beitr. z. Biol. d. Pfl. 1911. Bnd. X, p. 379—421.
23%
350
plant were perfectly constant. They all possessed quite the habitus
of the intermediary form. That the plant in question cannot be a
true hybrid, but had probably arisen from a seed of another ele-
mentary species which cannot be discussed here, was however,
only demonstrated with certainty by the examination of the
generative nuclei.
My thanks are due to Dr. Lorsy who, in the spring of 1921,
gave me part of his material for the purpose of repeating the ex-
periment of cross-fertilization, further cultivation of the plants, and
cytological examination to ascertain the cause of the constancy.
My own experiments in cross-fertilization also yielded only plants
which were the same as the mother plant. The cultures of E. coch-
leoides and of E. violaceo-petiolata, as well as those of the inter-
mediate form which was first taken to be a hybrid, but which,
since it appears that this is not the case, I will now term Zrophila
confertifolia on account of its extremely close roset of leaves, remained
perfectly constant in the years 1922 and 19237). The results of the
attempts at eross-fertilization soon suggested to Dr. Lorsy the possi-
bility of apomixy. This would not agree with the results obtained
by Rosen, but if correct it might explain why his Hrophila’s remained
constant in the F,.
The following notes upon the results | obtained will prove that
the supposition of apomixy was correct and that apogamy ’) played
a part in the affair.
As regards the methods, it must be remarked that the best pre-
parations were obtained by fixing with chloroform-alcohol-acetie acid
after Carnoy. The sections, after being imbedded into paraffin, were
made with a ReinsoLnp-Ginray microtome to a thickness of 5 u.
The colouring was done with HeIDENHAIN's haematoxylin.
Like all elementary Mrophila species hitherto described, which
were found together at the same place, the sub-species here treated
exhibit, besides points of great difference, also a great similarity, which
a very close systematic relation suggests. K. cochleoides is the smallest
of the three, possesses short spatulate leaves, slightly narrower
towards the base and only in the older stadia showing a shallow
denticulation. The stalks are strong but not of great length. On
the other hand £. confertifolia possesses longer and softer stalks
1) Although the plants have not yet flowered, the constancy can be proved with
a fair degree of constancy from the young rosets.
3) ,Apogamy”’ is employed here in the definition of STRASBURGER, i.e. develop-
ment of an unfertilazed diploide ovule; according to WINKLER this is a question
of somatic parthenogenesis.
351
and its very close roset has larger leaves with a fairly broad base
and which exhibit several deep dentata, while in /. violaceo-petio-
lata all three characteristics are much more pronounced. Also the
flower differs in form in the three subspecies.
The cytological examination in the first place brought to light
that the nuclei are extremely small; in young cells in rest they are
but 24—34 u.
Fig. 1—4. 1 Vegetative equatorial-plate before the division of Erophila cochleoides.
2 Idem of E. confertifolia. 3 Vegetative prophase of EF. violacea-petiolata ;
4 Segmentation of the chromosomes in a vegetative cell of HL. violaceo-petiolata
n. = nucleolus (in all the figures). Magnification 1-2-3: 2200 X; id. 4: 1100 X.
Vegetative cell-divisions were studied in stem-tips, of which a
cross-section is usually found in the sections through the entire
inflorescence. No abnormalities are seen in the vegetative divisions
of E. cochleoides and of EL. confertifolia. HE. cochleoides possesses 12
(Fig. 1), EF. confertifolia 24 chromosomes (Fig. 2). They lie typi-
cally in pairs, a feature which recurs in all the divisions and in
352
nearly all the stages studied. The chromosome pairs differ appreci-
ably in size. The vegetative cells of /. violaceo-petiolata exhibit a
peculiarity which seems to belong only to this subspecies and occurs
but very rarely in the vegetable kingdom. The normal number of
chromosomes (diploid) is here 12 (Fig. 3). This number, however,
was very seldom found. In almost every case the numbers found
were higher and invariably different, up to 100 and probably still
higher. Only in distinetly early prophases could the number 12 be
found with certainty, and in very late telophases, shortly before the
period of rest commences, this number is again nearly reached. In
this last stage the counting is a matter of great difficulty, as the
nuclei are very small and the outline of the chromosomes indistinct.
Finally there is a third stage in which the normal number occurs,
namely, the stage of splitting and seperation of the chromosomes.
Occasionally, however, the number 12 was clearly seen. In all other
stages of division the chromosomes divide up into numerous chro-
matie particles (Fig. 4). The longer the time is between the division
stage and the resting stage, the larger is this number. How the
transition from these stages and the metaphasic division-stage is
accomplished could not be investigated.
The formation of the embryosac takes place in all three elemen-
tary species mainly in the same way. One large right-angled sub-
epidermal cell immediately becomes an embryosac-mother-cell, without
first forming a tapetal-cell. The embryosac grows considerably in
size and the nucleus passes through a lengthy synapsis-stage. Finally
it divides into two daughter-nuclei which do not divide again directly,
but round off and like normal mitotic nuclei pass over into a res-
ting-stage. A cell-wall is formed, and for a short time the two
daughter-cells lie undivided. Then only does a second division take
place in the two cells. Frequently the micropylar cell degenerates
during this division; in other cases this takes place with the new-
formed products from it. This division of the micropylar daughter-
cell very often takes place in a transverse direction, whereas that
of the chalazal daughter-cell always takes about the same direction
as the first division of the embryosac-mother-cell. One of the four
grand-daughter- or tetrad-cells, that is situated nearest to the chalaza,
increases and becomes primary embryosac-cell. The other three tetrad-
cells have usually degenerated by now and meet closely over the
embryosac-cell.
The development of the primary embryosac-cell to an embryosac
probably takes place according to the normal plan; stages with 2
and 4 nuclei are frequently met with. The nuclei lying near the
353
micropyle in the latter stage form the egg-cell, synergidae and
one of the polar nuclei. It was not possible to ascertain whether
the division of the group lying towards the chalaza takes place in
the normal way, as the antipodal cells degenerate very early, per-
haps even during their formation. So much is certain, however, that
one or more antipodal cells and a lower polar-nucleus are always
formed, and the two polar nuclei speedily fuse together.
The formation of pollen did not exhibit any special features in
the cases under examination, but very typical tetrads are formed
from the pollen-mother-cells. It was immediately seen, however, that
the pollengrains which were formed were largely sterile. No division
of the nucleus of a pollengrain was clearly observed, and artificial
cultures of pollen were unsuccessful, although a considerable quan-
tity of pollen was usually found on the ripe stigmas. From here
the pollentubes penetrated to any depth only in a very few stigmas.
In one single case did the pollentube reach the cavity of the ovule.
Although in this way the chance of fecundation was augmented
here, the ends of the pollentubes were not found in this embryosac
any more then in any of the other preparations. A male nucleus
was never in a single case to be found in this embryosac; the egg-
cell invariably remains lying alone and after some time begins to
enlarge of itself. Finally it begins to divide, after which the first
embryo- and suspensor-cells are formed. The further development
of the young embryo is quite normal.
While this points to apogamy, it is only proved with absolute
certainty from the behaviour of the nuclei in the embry osac-mother-
cells. These commence to divide. like in so many other apogamous
plants, according to the heterotypical scheme. Many synapsis- and
Spireme-stages are observed. Instead of real gemini of chromosomes
which totally or for the greater part fuse together, merely pseudo-
diakinese-pairs are observed. The chromosomes approach each other,
but remain at some distance from each other. After this the division
has a homoiotypical character. Fig. 5 represents a telophase-stage
of the division of the embryosac-mother-cell of K. cochleoides. In the
uppermost micropylar daughter-céll the chromosomes are present in
diploid number (12). The same number can also be counted in the
chalazal daughter-nucleus, though less distinctly. The knife of the
microtome had touched this nucleus, so that a few ends of chromo-
somes are to be found in the adjoining section. The figure shows
which fragments in the two cross-sections belong to each other. The
telophase-stage of FE. confertifolia, which possesses vegetatively 24
chromosomes, is a still clearer and stronger proof of the apogamy,
3504
as is shown in Fig. 6. Here there are 24 chromosomes in both
nuclei; they can be best counted in the micropylar nucleus. The
fact, that the chromosomes after the division still lie so clearly in
Fig. 5—9. 5. Daughter nuclei of the embryosac-mother-cell of ZE. cochleoides,
on the left the chalazal nucleus, on the right the micropylar nucleus ;
al—a?, cl—c? ete. fragments belonging to the same chromosome. 6. Idem
of B. confertifolia. '7. Endosperm nucleus of 2. violaceo-petiolata. 8 One
of the three sections through a pollen-mother-cell of E. violaceo-petiolata.
9. Formation of the tetrad nuclei in a reducing-division in a pollen-mother-
cell of ZE. cochleoides. Magnification 5-6-8: 2200 X; id. 7: 1450 X; id 9%:
1100 X.
355
pairs, points to a very strong affinity which cannot be broken by
the individual splitting.
In the division of the embryosac-mother-cell and the pollen-mother-
cell of the E. violaceo-petiolata we have the same phenomenon again
as was also seen in vegetative cells, namely the segmentation of
the chromosomes. It is remarkable, however, that here the chro-
matic particles lie in pairs, as we find all the chromosomes in the
two other subspecies in pseudo-gemini. Here too very large num-
bers were found; approximately 50, 64, 70 and even as high as
130 or 140 were found. Fig. 8 represents such a stadium taken
from a_pollen-mother-cell, which had been cut into three sections,
only one of which is shown here. Nevertheless about 60 chromo-
some particles can be counted. As the embryosac-mother-cell has
exactly the same appearance and as here too the same phenomenon
is seen directly after the division, it was impossible to find a pair
of daughter nuclei with the diploid number to prove apogamy.
Here, however, some very distinct endosperm-divisions lend assistance.
As it was established that the polar-nuclei unite with each other in
this apogamous plant also, the endosperm-nuclei must possess twice
as many chromosomes as the embryosac-nuclei. Thus, to demonstrate
apogamy this number would have to be 24, and that this is actu-
ally the case is shown by fig. 7, which illustrates a cross-section
through the middle of one spindle, looking in the direction of one
of the poles. The ends of the 24 chromosomes can be clearly
distinguished, while the attraction of some chromosomes by the
poles can also be observed.
Whereas in the divisions of the embryosac-mother-cell there is no
reduction of the number of chromosomes, even though it has passed
from the heterotypic phase to the homoiotypic very shortly before
the division, the reducing division in the pollen-mother-cells occurs
normally. During this division no peculiarity was observed in
any of the cases examined other than the segmentation above-men-
tioned in B. violaceo-peticlata. Fig. 9 represents 2 sections of the
tetrad nuclei of a pollen-mother-cell of E. cochleoides, all of which
form the reduced number of chromosomes.
As has been said, however, the great majority of the pollen-grains
produced from them are sterile. But even if there be fertile ones
among them, they are not productive.
Thus the most important conclusion arrived at was that apogamy
occurs in these three elementary species of Hrophila, which explains
the failure of the attempts at cross-fertilization. The experiments of
Rosen have shown that not all subspecies are apogamous, or at
356
least they are not obligatory apogamous. The constancy of his new
forms in the F, might find their explanation in apogamy. The
intermediate hybrid formation in the F, and the singular appearance
of the F, on the other band, are not explained, and in respect to
this a special theory would have to be applied to explain the sudden
occurrence of apogamy.
Utrecht, March 1923. Botanical Laboratory.
Botany. — “On the nature and origin of the cocos-pearl”. By
Dr. F. W. T. Huneer. (Communicated by Prof. G. van
IrERSON JR.).
(Communicated at the meeting of March 24, 1923).
In the endosperm cavity of the seed of Cocos nucifera a
local calcareous formation is sometimes found to occur, to which
the name of ‘cocos-pearl” has been given, and which must be
looked upon as a highly remarkable and very rare phenomenon *).
Such a cocoa-pearl has usually the form of a pear, or egg, some-
times it is almost spherical and has a smooth surface, as a rule of
a milky-white colour. Its chemical composition corresponds somewhat
to that of the oyster-pearl, from which it differs, however, in appear-
ance by the lack of the pearly sheen.
Rumenius was the first to describe this caleareous formation as
“calappites’ *), and for more than a century after him nothing was
heard of this phenomenon, till at the Meeting of the Boston Society
of Natural History on the Ist. of February 1860 ®), Mr. Frep. T. Busa
presented a specimen of this cocos-pearl for chemical and micro-
scopical examination. The research was entrusted to Dr. Bacon, who
submitted his report on the subject at the Meeting of the same
Society on 16th. May 1860 “).
In 1866 Dr. Rieper, Ex-Resident of Menado, reported having found
a pearl in a cocoanut he opened’). This was the first report by an
eye-witness who had actually seen this phenomenon, apart from the
many stories told by natives about it.
Contrary to the statement of Bus to the effect that cocos-pearls
“are said to be found free within the cavity of the cocoa-nut”,
SkeaT’) reported in 1900 that they are “usually, if not always,
found in the open eye or orifice at the base of the coeoa-nut”’.
1) F. W. T. Hunger, Cocos nucifera, 2nd Ed. pp. 243—250, Pl. LXVII (1920).
*, E. Rumpuius, Herbarium Amboinense, Vol. I, pp. 21—23 (1741).
Idem, D'Amboinsche Rariteitkamer, pp. 291- 292 (1741).
3) Proceedings of the Boston Soc. of Nat. Hist., Vol. VII, pp. 229 (1861).
4) Idem, Vol. VII, pp. 290—293 (1861).
5) Nature, Vol. XXXVI, pp. 157 (1887).
6) W. W. Skrar, Malay Magic, being an introduction to the folk-lore and
popular religion on the Malay Peninsula, pp. 196 (1900).
358
No other data regarding this remarkable phenomenon exist, and
at the present day we are still completely in the dark as to the
nature and origin of such a cocos-pearl.
On my last voyage to the Hast Indies for purposes of study, 1
resolved to endeavour to find out something further about the cocos-
pearl and if possible solve the problem of its formation. At the
same time I realised the utter futility of going to look for cocos-
pearls in the Tropics on account of their extremely rare occurrence.
In proof of this it may be mentioned that on a cocoa-nut estate,
where approximately 3 million nuts have been opened annually for
years, no such pearl has ever been found, although stories about
them have led to their existence being suspected.
| therefore directed my research to gathering as many authentic
data as possible.
On one of my voyages | met a native of British India who pos-
sessed a very fine cocos-pearl. According to his own account he had
seen with his own eyes this specimen inside an opened cocoa-nut
which had been brought to him from Madras. He assured me solemnly
that his pearl had been attached to the kernel of the cocoa-nut and
exactly at the place where, in germination, the cotyledon forms a
haustorium.
Later on I also met with an Arab on whose cocoa-nut plantation
in South Borneo a cocoa-nut had been gathered which, on being
opened, proved to contain a pearl attached to the inside of it. He
had dislodged the pearl from the kernel of the nut with his own
hand. In this case also the pearl had been attached at exactly the
same place as in the case first-mentioned.
These two corroborative declarations of eye-witnesses, who had
both seen a cocos-pearl still attached inside an opened cocoa-nut,
furnished me with a preliminary guiding-thread and led me to sup-
pose that the spot which they indicated would probably be the
normal point of attachment of such a cocos-pearl.
The normal germination process of the cocoa-nut begins by an
enlargement of the embryo, whereby the cotyledon commences to
grow inwards to an absorbing organ (haustorium), and thereby
comes to protrude outside the endosperm and into the central cavity.
Simultaneously with this, the plumule grows out and, breaking
through the membranous operculum of the germinating pore, it
pushes its way out through the hard shell.
Proceeding from the provisional determination of the place of
359
attachment of the cocos-pearl, the following hypothesis could now
be formed. Given that the germination, being in progress, is stopped
by some cause or other, thus preventing the further development
of the haustorium, it is conceivable that the haustorium in this state
might become encrusted by the influence of the cocoa-nut milk, and
that from this the completely petrified cocos-pearl would gradually
be formed.
It was now essential to find the reason for any such check in
the process of germination and the accompanying solidification of
the haustorium, and I wish now to submit the following remarks
on this head.
At the side where “the cocoa-nut has been attached to the stalk,
three thin spots so-called germinating pores, or ‘eyes’, can be seen
in the hard inner shell of the fruit. As a rule one of these holes,
the so-called “‘porus pervius’’, is closed by a membrane, whereas
the two other, the so-called ‘‘pori caeci’, are furnished with a hard
tegument. In germination, the plumule pushes its way out through
the porus pervius.
By way of exception there may be, instead of three, two germi-
nating pores, viz. one porus pervius and one porus caecus, and
only very rarely will there be only a porus pervius with both pori
caeci entirely absent. Nevertheless a cocoa-nut of this description can
germinate in the usual way.
It is a different case, however, when there is not even a porus
pervius, the base of the inner shell showing no germinating pore at
all, as occurs in extremely rare cases.
Such a cocoa-nut is known in the Malay language as a ‘“kelapa
boeta’’, or “klapa& boentet” in Javanese, which signifies a “blind
cocoa-nut”’.
As remarked above a cocoa-nut without germinating pores is a
very great rarity, for which reason they are regarded by the Mahom-
medans as sacred. The “kelapa boeta” is a talisman (tjimat) par
excellence, and consequently it is very difficult to obtain a specimen.
This meeting with the kelapa boeta furnished me with an instance
of the way in which a normal germination is rendered impossible
by nature, and I did my utmost to procure some specimens.
I finally succeeded in collecting eight unopened “blind” cocoa-nuts
from the Kast Indian Archipelago. Two of them came from South
Borneo, one from Halmaheira, one from Ceram, one from the North
of New Guinea, one from South New Guinea, one from the Arde
Islands and one from the Tanimber Islands, all of which I have
collected personally from these several places.
360
Most of the specimens were very old nuts; some, according to
their owners, had been preserved for scores of years as family
heirlooms.
The first four ‘“boetas” which I opened produced nothing, but in
the fifth I found a really beautiful pearl still attached to the kernel;
the two next produced negative results again, and the eighth speci-
men I have kept unopened.
The nut which had contained the pearl, as shown in Fig. 1, had
been purchased from an old native at Ritabel (Larat), one of the
Tanimber Islands in the Moluceas, who informed me that it had
been gathered but a short time before. This proved to have been
the case, because the endosperm in it was quite normal, whereas
in the other nuts the kernel was either very much dried up or had
even partly become a mass of brown powder.
The pearl was attached without the least trace of a stalk, being
merely embedded in the endosperm (Fig. 2), and was quite easy to
remove from the kernel. It lay exactly at the base of the nut, just
under the spot where the germinating pores ought to have been,
and thus agreed completely with the indications as given above.
This discovery, in my opinion, warrants the inference that the
cocos-pearl actually represents a calcified haustorium, which has
been retained in the nut after the primary germination was checked,
owing to the plumnle not being able to get through the shell on
account of the porus pervius being lacking. As the inner shell of
the kelapa boeta remains hermetically closed, the newly formed
haustorium becomes encrusted under the influence of the cocoa-nut
milk with calcium-salts, although it still remains unexplained why
the cocos-pearl consists almost entirely of calcium carbonate, while
neither the cocos-kernel nor the cocoa-nut milk contains any calcium
carbonates.
The belief that a Kelapa boeta invariably contains a cocos-pearl
was sufficiently disproved by my experience that of seven specimens
only one such formation was found in a “blind” cocoa-nut. On the
other hand, it is probable, in my opinion, that it will be principally
(or exclusively?) the kélapa boeta that contains the cocos-pearl.
The nature and origin of the cocos-pearl as a calcareous plant
germ might botanically be considered as analogous to a phe-
nomenon seen in human and animal pathology in the petrifaction
or mummification of the embryo, and termed Lithopaedion or
Lithoterion respectively.
Amsterdam, March 1923.
F. W. T. HUNGER: “On the nature and origin of the cocos-pearl’’.
Fig. 3.
Cocos-pearl from fig. 2.
nat. size.
Fig. 1. Kelapa boeta Basis of a blind cocoanut, without
germinating pores. :
3
nat. size.
Fig. 2. Kelapa boeta Endosperm cavity with a
cocos-pearl insite. 3/5 nat. size.
Botany. — „The genus Coptosapelta Kortn”. (Rubiaceae). By Dr.
Tu. VALETON. (Communicated by Prof. J. W. Morr).
(Communicated at the meeting of April 28, 1923).
§ 1 In my paper on Lindeniopsis, a new sub-genus of Coptosa-
pelta Kortn. (Proceedings of the Academy of Sciences of May 30,
1908) I gave a synopsis of the few species of the genus, known at
that time. At my further study of the Rubiaceae of the Malay
Archipelago and of New-Guinea, I again found a number of species
not described at all or not in the right genus, in consequence of
which this number has increased to 11. Besides it appeared from
the research, that the existing diagnosis, already revised by me,
could no more be applied to all species. For this reason I want to
subject the chief characteristics of the genus of systematical interest
to an investigation and subsequently to summarize the species known
at the present time.
§ 2. Historical review. The genus was constituted by
Kortuais (1851) on some fruiting branches of a liane, gathered by his
colleague Dr. Minter on the sandy plains near Karrau (Southern
and Eastern division of Borneo). He found them to belong to anew
genus in the group of the Cinchoneae DecANDOLLE, of which there
are but a few genera known in the Duteh Indies.
As chief characteristics he considered the liane-like habit, the
fruit splitting up in two cells, each of them splitting up again and
the peltate seeds provided with a fringed wing, a combination of
characteristics, not yet found in any genus. In naming the genus
he apparently referred to the seeds. At least | think to recognise
the words zonmtw, in the meaning of ,,Chopping” or „Hewing”
(because of the notched wings) and szreaty shield. The significance
of the connecting syllabe sa” is not clear to me. Probably the
name originally ran: Coptospelta, a bad word-formation. As a
specific name he used flavescens”, alluding to the yellowish tint
the leaves get on drying.
Korrnars’s specimen is lacking in the Dutch and Dutch-Indian
Herbaria. It is not apparent either, that Mique, knew it (1856). It
was however known to Hooker, when describing in 1876 a second
species of the same genus, C. Grijithii Hook f. in Icones plantarum
362
tab. 1089, in which he quoted Korruats’s original and Borneo,
Sumatra and Malacca as its native places. A short description of the
species was afterwards given by Hooker in Hook. Flora indica ILI
(1885) especially to distinguish this species from C. Grijithi. A little
more detailed was Kine in Kine and GaMmBLe, Flora of the Mal.
Peninsula (1903).
The species however had not escaped the attention of either
Warrien or Biome. The former published it in 1828 mistakenly as
Stylocoryne macrophylla (= Webera macrophylla Roxs.), the latter
took it for a new species of the same genus and gave a brief
diagnosis of it in Brome, Bijdragen (1826), as Stylocoryne tomen-
tosa, while Mique, gave a somewhat fuller description of the same
species, gathered by ZorLLINGER in Tjikoja in Java (number and date
unknown), in 1856 in Fl. Ind. bat.. as Stylocoryne ovata Miquer.
A third species of this genus, in order of time of discovery, is the
Coptosapelta Hammii (subgenus Lindeniopsis) 1 previously discussed.
It was gathered by Ham in Billiton in 1907. At about the same
time a fourth species was collected in the Philippine Islands and,
by E. D. Merrit, described as Randia olaciformis and classed with
the right genus by Ermer in 1912 (in Philippine Leaflets). A fifth
species, already gathered by H. O. Forges in British New-Guinea in
1885—86, was described by Wernuam in 1917 (in Journ. of Botany).
He classed it however with the genus Tarenna Garrrn. (= Styloco-
ryne Wicut et Arnorr). Besides | found two Borneo species unde-
- seribed in the Herbaria at Leyden and Berlin and three of New-
Guinea, while finally an eleventh species was discovered, gathered
bij the army surgeon JaNnowsky at the ‘“Geelvinkbaai’ in 1910.
$ 3. Habit. Except the deviating species C. Hammii, above
mentioned, a half-climbing shrub, all Coptosapelta-species hitherto
known are lianes. To all of them the excellent description by
Eimer of C. olaciformis (Phil. Leaflets V. p. 1856) is mainly appli-
cable: “A looping treeclimber; stem two inches thick, very irregular,
heavylooping, numerously branched toward the top and forming
hanging masses; leaves coriaceous, descending, curved upon the
upper deeper green surface, apex recurved; inflorescence from the
longer samewhat drooping branches, erect.
Of the species, gathered in German New-Guinea by LEDERMANN,
is twice given “Liane mit beindickem Stamm’, once “Liane mit
armdickem Stamm”. For C. Grijithii from Malacca as well as for
the oldest species C. flavescens is given Liane’, to which Kune’s
native collector adds: ”A handsome creeper, 30— 50 ft. high”. The
363
two species from Borneo first described here, were probably of a
similar habit. Of Janowsky’s species is only said: ”10 Meters high”;
the piece of branch or stem, about as thick-as a finger, gathered
by him, shows a soft whitish strongly-lobed wood-cylinder with
large vessels.
§ 4. Stem and buds. The rod-shaped twigs, as occurring in the
herbaria, are nearly cylindrical (only in some species e.g. C. montana
the utmost twigs are square), the nodes swollen and provided with
an annular groove. As a rule only the flowering lateral and terminal
branches are gathered, consequently but a few terminal buds, all
of young specimens of C. flavescens and C. montana are present. These
are wanting bud scales; they are formed by the two youngest
leaflets, pressed together with the flat upper-surfaces, and are enclo-
sed by the two rather small stipules only at the base. With the
young growing twigs these very young leaflets are lanceolate and
they consist more than half of a broad ” Vorlduferspitze’ rounded
at the tip and certainly dark-green when alive (see RaciBorskt in
Flora 1900), reminding us of Dvoscorea-species. Where there are
axillary-buds, they are but a couple of mms. long, ovate, covered
with long and dense hair.
§ 5. /ndument. All species have a coat consisting of single
short appressed hairs, and long hairs lying flat but free at the top;
the latter are soft, straight, colourless or rarely (in sieco) yellowish,
usually thinly spread; on the young twigs and leaves, the inflore-
scences and generally also the petioles, they are closer together,
forming a soft, thin “tomentum”.
On the full-grown leaves they are almost or totally absent in
C. olaciformis, fuscescens and maluensis, where the twigs also grow
bare in course of time. C. Grijithii, C. Beccarii and a hairy type
of C. flavescens have a soft hairy covering, consisting of long curved
hairs not close together.
$ 6. Leaves: 1. Shape: In most species hitherto known, the almost
exact elliptical shape of the lamina is characteristic for the average-
leaf; i. e. a symmetry of the two halves with respect to the trans-
verse as well as the longitudinal diameter of the leaf, apart from
the frequently lengthened tip and wedge-shaped base.
Hooker (1882) and Kine (1903) refer to it in their descriptions of
C. Grigithii and C. flavescens, Merritn of C. olaciformis, WeRNHAM
of C. hameliaeblasta.
24
Proceedings Royal Acad. Amsterdam. Vol. XXVI.
364
Of course the elliptical shape is not constant with any individual,
but often passes into the ovate form or becomes oblong (in this case
the symmetry is preserved), the leaf-base varies between rounded and
wedge-shaped. Young plants of C. flavescens have lanceolate leaves.
The few known leaves of C. Janowskii (a mountain-species) are likewise
lanceolate and provided with a long dropping-point. C.-montana (a
mountain-species from Borneo) has on several twigs elliptical and
Oval leaves with rounded base, and lanceolate, acuminate leaves.
C. Hammiu (the xerophilous species above-mentioned) has the tip
ending in a very short bard mucro. For the rest the leaves of all
species have a clearly marked acumen, sometimes very short.
2. The consistency of the leaf of old plants and twigs is thin-
leathery, the colour of the upper-surface is glossy dark-green, of the
lower surface lighter green with dark-green veins, in a dry condi-
tion hard and in herbaria as a rule brittle. Of young plants (see
above) they are much thinner, in sicco almost membranous (in
vivo herbaceous). C. Janowskii (see above) has likewise thin ones.
When drying the leaves always change their colour to yellow or
yellow-green, more or less mixed with sepia-brown, the upper-surface
is as a rule dark-brown or olive-brown 153—155 (Code des couleurs
de KrincKsieK et Varerre). For C. olaciformis 183 —188 or 193, or
paler 217 ; for C. Hammii 202—217, for C. flavescens the colour of
the upper-surface frequently 114, of the lower-surface 153.
3. With respect to the diagnosis of the genus as well as the
species the nervature of the leaves, though showing common char-
acteristics for all species, is of some importance. The nervature of
the leaves is penniform, and the secondary or lateral veins never
start from the median nerve opposite to each other at the same
level, their number being as a rule rather small, 2 or 3 or 4 on
each side. In many species the secondary veins next to the tip do
not start above the middle of the median nerve, so that the upper
half of the leaf is mainly supplied by tertiary veins. Besides they
start at unequal distances from each other and are closest to each
other at the leaf-base, the /owest two (or sometimes one) starting
close to or even from the leaf-base; in consequence of this they
resemble triplinerved and trinerved leaves (/icus, Cinnamonum,
Viburnum). There often starts from the leaf-base on one or both
sides a secondary vein so thin, that it may be counted among the
tertiary veins and may easily be overlooked; yet it follows in its
course the stronger veins. After starting from the midrib these
go upward in a wide curve till close to the edge, next about
parallel with the edge towards the apex. The two foremost veins
365
end in the apex (acrodromous veins of ErriNGHAUSEN), the next run
some way between the edge and the first pair and all or most of
them end in the tertiary net without uniting.
The secondary veins thus run parallel to the margin for a great
length and most of the basal veins partly embrace the higher ones.
A definition answering exactly to this nervature, | do not find in
ErrincHausen. It forms a mixture of the common camptodromous,
(bogenläufige) with the acrodromous (= spitzenläufige) nervature ;
the term amplexidromous might be applied (see e.g. the figures of
Thibaudia species (acrodromous) in v. E.’s work, besides Nectandra
and other Lauraceae). The species with larger leaves C. flavescens,
olaciformis, Beccarii have a somewhat greater number of veins
(11—12), while the basal veins sometimes curve inward and unite
with the preceding: schlingenläutige (brochidodromous) nervature.
The number of secondary veins of the deviating species C. Hammit
amounts to 12; in the rather small leaves they are more crowded
and fairly equally divided over the length of the leaf, joining with
a curve. This is an instance of regular brochidodromous nervature,
but the leaf-base is pointed and the veins are ascendent and embrace
each other upward from the base, so that the character of the
genus is not quite lost. The tertiary nervature is always clearly
visible and equally spread over the whole leaf; the horizontal
connecting veins are usually prominent and form a delicate lattice-
like reticulation. Leaf-impressions made with carbon-paper usually
show only this net-work.
4. Regarded biologically the leaves of Coptosapelta jlavescens
belong according to HanscirG (Phyllobiology, 1903, pag. 293) to the
Myrtus- or Lawraceae-type with which he also classes the Cofjea-
species together with numerous other Rubiaceae, among which
Crossopteryz, an african genus closely allied to Coptosapelta.
According to him these types are xerophilous. They belong to
the periodically dry and moist regions along the Mediterranean
from Spain to Palestine and also to tropical regions with similar
climatological properties. As their characteristics he gives: Strongly
cutinized epidermis, rectilinear polygonal or sometimes undulated
epidermis-cells, stomata sunk, very glossy lamina usually bare, some-
times grey- or white velvety, simple, narrow and entire or round,
elliptical, oval and oblong, leathery and stiff’, as protection against
strong insolation, excessive evaporation, adhesion of water, winter-
temperature, etc. Without doubt many of these properties belong
to C. jlavescens, occurring in the secondary woods of the first zone,
a.0. in bamboo-woods between 200 and 500 meters, but only on
24%
366
adult old plants, the leaves of which are indeed rather like those
of Coffea arabica. Also the tomentose leaves of C. Beceari and
C. Griffithii belong to this type. On the other hand C. Janowskii
and C. montana are both mountain-plants with narrower leaves and
a long dropping-point, instances of Hanseire’s “jicus-type of the rain-
woods’. To this type the young plants of the above-mentioned
species also approach, in which the’ xerophilous habit does not
much come to the fore.
Here it is not only the danger of too strong evaporation, brought
along by the succession of the monsoons, but no less the risk of
the damage, caused by strong rainfall which prevails.
Among the remaining species, of which C. maluensis does not
grow higher than 200 meters above the sea-level, while the others
occur at different levels in the mountains, various transitions between
Hanseire’s Myrtus- and Ficus-type are found.
An instance of real xerophilous habit is only given bij C. Hammii
(Lindeniopsis) which as I previously mentioned should be classed
with Scaimprr’s “Hartlaub formation”.
§ 7. Stipules. The usual shape of the stipules is that of a
small triangular scale, which has often been lost with the full-grown
twigs in the herbaria. At the back-side and along the edges it is
covered with hairs, turned to the front, often longer than the stipule
and sometimes covering it entirely. The variations in shape are
usually due to differences in the ratio of width and length, which
depends on the width of the node. Sometimes however they may
be of use in the determination of the species. This is for instance
the case with C. flavescens and C. olaciformis, which show a great
resemblance on superficial contemplation of leaves and flowers and
were considered identical by Merrit.
Here, in numerous specimens examined by us, the stipules are
quite sufficient to distinguish between the two species. C. flavescens
has linear-lanceolate ones, rather abruptly passing into the broad
base. They vary in length between 4 and 8 mms. and strike the
eye in the herbaria because, at least in the dry specimens, the
back-side is absolutely bare and the broad hairy edges show clearly.
C. olaciformis has smaller stipules, usually only 2 mms., slightly
longer than broad, in old condition hairless and swollen at the
base. This description has been taken from a specimen, distributed
by Merrit himself from Luzon (Ph. pl. 396) and classified as
C. flavescens. It is also applicable to Ermer’s original specimen (see
below § 11. Synonymy and relationships).
367
§ 8. Inflorescence. In all species the inflorescence consists of
axillary compound cymes or corymbs, starting from the leaf-axils
near the top of the twigs. At the top they are closer together and
often (by the reduction of the floral leaves) are combined to large
terminal decussated panicles or thyrsi. Such terminal panicles also
occur in other genera of the group of Cinchoneae, viz. on Cinchona
and Ferdinandusa.
In the descriptions of the genus (Hooknr—Scuumann— VALETON in
Ie. bog.) there is wrongly spoken of ”thyrsi penduli”. Undoubtedly
the panicles are erect in all cases (see Ermers’ description above,
§ 3), but the ends of the long branching twigs are drooping and
proper flowering-branches start sideways from these. In good her-
baria it may sometimes be observed how the flowering-branches
form an almost right angle with the leaf-twigs.
The extension and relative length of the axis determine the cha-
racter of the inflorescences with respect to the species. First of all
two types may be distinguished.
The simplest case is C. Janowskit, a New-Guinea-Mountain-liane,
where the axilary inflorescences have been reduced to single flowers
and the terminal thyrsus to a simple closed raceme. The pedicels
are rather long and about midway provided with two bracts. It is
highly probable that on more luxuriant branches these bracts are
fertile, forming forked cymes (dichasia). C. montana likewise has
isolated flowers (uniflorous cymes) in the axils of poor flowering-
branches and at the top a raceme of 5 flowers. A more luxuriant
terminal twig, consisting of 6 internodia, has in the lower axils
long-stalked closed racemes, bearing 5 flowers, in the following
three-flowered cymes, while the top again forms a closed raceme
with linear bracts. The twig of C. Hammii also ends in a raceme
of 5—7 flowers, but with very short internodes and pedicels, so
that the flowers, provided with long corollatubes, are close together
and take the shape of an umbel.
In the second type both the axillary and the terminal inflores-
cences are compound, and the latter have the shape of corymbi or
depressed (almost umbelliform) thyrsi in consequence of the decrease
of length towards the apex of the internodes and peduncles; the
axillary ones too are more or less corymbiform. Especially the
relative length of the peduncles of the partial inflorescences, the
number and density of the flowers, the number of internodes of the
terminal panicles, determine the character of these species.
C. olaciformis deviates most of the rest on account of the slight
extension of the corymbi and the small number of flowers. The
368
axillary inflorescences are sbort-peduncled cymes with only 3—5
flowers, many times shorter than the leaves. The terminal thyrsi
consist of but 2—3 internodes and cymes with few flowers and short
peduncles, and are also shorter than the higher leaves.
In the remaining species of this second type both the axillary and
the terminal inflorescences are multiflorous much branched, corym-
bous, with moderately long or very long stalks, while the terminal
panicles may consist of 5 internodes.
§ 9. Flower and Seed. The calya is now cup-shaped, only
superficially emarginate with 4—5 very short pointed teeth, now
divided into nearly free sepals down to or almost down to the base, in
which case the limb is not sharply separated from the ovary; in a
third more frequent case cleft to the middle or a little farther. To
characterise the genus it is therefore of no value, but of great value to
determine the species. For all species mention should be made of
the “intestinal gland papillae’, (Darmdriisen papillen: Sour-
REDER), which are placed at the inside alternate with the lobes or
teeth, and resemble those which the Rubiaceae always bear at the
inside of the stipules and are sure to occur on their calyces more
frequently than appears from literature
The corolla which is contorted in aestivation, but without
externally visible torsion, is trumpet-shaped and reminds us of species
of Randia and Tarenna, having a quinquepartite limb and as in the
case of Manda the relative lengths of tube and limb, though not
always constant in the same individual, is when the average is
considered, a means of distinguishing the species.
The following average rations were found: Tube many times as
long as the lobes (Lindenia-type), 3—6 cms. long: C. Hammii.
Tube twice as long as the lobes: C. Janowski. Tube about the
same length as the lobes or a little shorter: most of the species.
Tube about half the length of the lobes: C. Grijfithii, C. fuscescens
and C. lutescens. A peculiarity is, that the tube which is usnally
cylindrical and equally wide along its whole length, shows a sudden
inflation above the middle in two species, C. Grijithit and C.
Janowsktt, which for the rest are farthest apart on account of the
length of the corolla tube.
The internal hairy covering of the corolla tube is also of some
interest. Only in 3 species C. Hammi, C. olaciformis, C. flavescens,
the interior of the corolla tube and the filaments are glabrous. In
the other species, where the filaments are covered in front with
long furry hairs directed downwards, this hairy covering continues
369
as projecting ridges along the inside of the tube, down to the middle
or till close to the base. Between these ridges the inside is covered
with soft crisp hair; the descriptions of the genus however are
wrong, where they say: “Haux barbata” for the hairy covering of
the faux (regarded as orifice of the tube) is lacking everywhere.
When the limb is still closed, the corolla is externally entirely
covered with thiek-velvety or short silky hair.
The stamina have thin filiform filaments, which, as already
observed, are congenitally attached to the corolla-tube, forming
protuding ridges; the part projecting from the corolla is short and
filiform, in some species hairless, in most of them covered with
furry hair in front; the anthers are very narrow lanceolate and
have a linear connective, coherent with the filament near the base
at the backside; the long linear anthercells diverge more or less at
the base, so that the base of the anther is retuse, or arrow-shaped
as with C. flavescens, while the tip ends in a tapering point; the
backside is covered with appressed hair, except in C. Hammit, where
also the free filaments are almost lacking. The anthers hang more
or less versatile from the corolla during the flowering and are
curved up or contorted.
The pistil is highly characteristic for this genus. The stigma is
wedge-shaped or cylindrical (in Lindeniopsis club-shaped) not divided
into lobes, and proportionately long. The style is straight and smooth
and compressed sideways, and about as long as the corolla-tube, so
that the stigma overtops the corolla far. The papillary surface I
generally found covered with pollen.
The ovary, covered with an annular disk, is regular, bilocular
as in the whole group of Cinchoneae. Around a fleshy, cylindrica!
axis, nearly filling the two ovary-cells, are the numerous anatro-
pous, flat, peltate, erect, imbricate ovules.
The fruit is globular or more or less oblong, compressed at
right angles with the septum and has in a ripe condition a though,
horny or thin parchment-like envelope, surrounded by a thin dry
outer-integument. In very old fruits the outerlayer crumbles down
and the horny valves come quite into view; in this respect there
is some analogy with Bikkia (Condamineae). The splitting into
valves is not perfectly regular. It begins with the separation of septum
and axis, (loculicide dehiscence) at the top of the capsule, but next
the septum itself splits, so that 4 cocci are formed open at the top
and at the sides and connected at the base. This latter splitting
however may fail to occur. During the splitting the fleshy placenta
shrivels up, causing the numerous seeds to get gradually loose.
370
The seeds are flat, round or oblong with the hilum about in the
middle (peltate) and surrounded by a membranous fringe-like notched
wing, about as broad as the seed. For the distinction of species
only differences in size are to be considered (except in Lindenvopsis
where the edge of the wing is not fringed); C. olaciformis and C.
maluensis have the smallest seeds; C. Grijithii the largest, as far
as we know.
As to the process of pollination it may only be surmised. The
contorted movable projecting anthers and the long protruding stigma
point at the probability of wind-pollination, but the prominent flowers
scenting of elder and orange-blossom may point at a connection
with insects. The possibility of self- and inter-pollination is corro-
borated by the great mass of flowers and by the fact that (at least
in the herbarium) the anthers are already open in the buds.
§ 10. The station: About the character of the locality in which
the various species are found we only know as follows:
C. flavescens was gathered by Korrnars on the barren sands along
the river Karrau in Borneo; by Kine’s collector in bamboo-woods
in Malacea 100—200 metres above the sea-level, by various collect-
ors in Western Java at the foot of the mountains, on various spots
in light secondary wood.
C. maluensis at 40—100 meters above the sea-level in passable
primeval forest, about 20—25 meters, high; the ground covered with
foliage („Galerie wald’’ Scuimprr), with occasional low wood, mostly
consisting of Pandanus and low feather-leaved palms (Camp Malu);
idem with many tree-ferns and bamboo and Selaginella a metre
high, as undergrowth (April-flusz): LEDERMANN.
C. fuscescens in “Buschwald” changing into mountain-wood up to
1500 metres above the sea-level, few large trees, many epiphytes
and moss, many glades, ground often overgrown. On steep rocky
slopes (Felsspitze): LEDERMANN.
C. lutescens in dense wood on hills, about 25 metres high, rather
mossy; in the underwood many dwarf-fan-palms and lianes, Frey-
cinetia, Araceae, Agathis, Pandanus: LEDERMANN.
§ 11. Relationships and synonymy. On account of the structure
of ovary and fruit Coptasapelta belongs to the very natural tribe of
Cinchoneae Hooker (Genera plant. II p. 11) among which 44 genera
are reckoned. This tribe is divided into two subtribes:
I. Mucinchoneae with a valvate aestivation.
Il. Hillieae with an imbricate or twisted aestivation.
371
To the latter tribe Coptasapelta belongs, which genus in Genera
plant. was placed among the former, a mistake already corrected
by Kine and by SCHUMANN.
The latter places (Pflanzenfam. IV, 4 p. 42 and 48) Coptasapelta
immediately beside Crossopterya, an African genus, I could not
examine, to which only one species or group of species belongs,
living on the barren Campos of Abyssinia — till lower Guinea. On
comparing the detailed description Oriver gives of this genus, |
found, that nearly all more or less important characteristics given
by O. are also applicable to Coptosapelta; only two are lacking,
viz. Stigma clavatum bilobum and tubuscorollae graci-
lis, limbus parvus. The important characteristic of the length
of the stigma however is present. Lindeniopsis however has a stigma
clavatum and a tubuscorollae gracilis, so that only the bilobular
stigma forms an important difference. This points to a close relation
between these two genera, especially between Crossopteryx and Lin-
deniopsis, on account of the shrubby, xerophilous habit.
The leaf-nervature of Crossopteryx is not fully deseribed, but the
leaves have the same shape; they are larger than with most Copto-
sapelta-species, but equal to those of C. flavescens. The close rela-
tionship of the two genera cannot be doubted. I could not find
any striking points of similarity with other genera of the tribe of
Cinchoneae, of which but a small number of species occur in the
old world. The most characteristic peculiarity, the structure of the
stigma does not occur in any other genus of this tribe.
Remarkable however is the resemblance of pistil and corolla in
species of two genera, belonging to the bacciferous Rubiaceae with
many ovules, viz. Tarenna GAERTN. (syn. Stylocoryne, syn. Webera),
which has given rise to a peculiar synonymy.
The name Stylocoryna, given in 1797 by CAvaNILLEs to a species
from the Liu-tchiu-Archipelago, is formed from the words orvdos:
pillar and xogvry: club, briefly denoting the structure of the pistil
of Coptosapelta, as described above. Hooker referred this species to
the genus Randia Linn., so that the characteristic generic name
was lost. In 1834 Wienr brought it up again in the form of
Stylocoryne (independent of Cavanilles?) for a plant from Ceylon
new to him, viz. St. corymbosa Wiant, which again showed this
peculiar shape of pistil. Neither could this name be kept, as the
same species had previously been diagnosed by GARRTNER (in 1788)
as Tarenna zeylanica, wich latter name of course enjoys the pre-
ference. The first generic name however had been accepted by
various authors (RoxBuren, BLUME, a.o.) and Brumm was the first to
372
apply it to Coptosapelta flavescens Kortu, discovered by v. Hasse.
and himself in Java. He called it Stylocoryna tomentosa, while
likewise Warricn, Mique. and later Merri. and WerRNHAM classed
species of Coptosapelta either with Stylocoryne or with Randia (see
above p. 2).
Whether the great similarity in floral structure between two genera,
belonging to different principal divisions of the family, also points
to a natural relation, is still an open question.
§ 12. New description of the genus. Calya cup-shaped,
quinquepartite, quinquelobate or quinquedentate, perennial, with
axillar glands.
Corolla, contorted in the bud, trumpet-shaped, tube varying in
length, outside velvety or covered with sulky hair, inside bare or
provided with furry ridges descending from the filaments, between
those thinvelvety, straight or inflated above the middle, throat not
bearded, lobes linear-oblong, obtuse.
Stamina 5, inserted on the throat, filaments filiform, short, the
front furry or bare, anthers thin, linear-lanceolate, tapering at the
top, at the base twice-pointed, obtuse or arrow-shaped, near the
base dorsifix, on the backside provided with two rows of hairs
directed upwards (in Lindeniopsis bare).
Dise small, annular.
Ovary bilocular, style anceps, hairless, stigma entire, cylindrical
or club-shaped, long, far overtopping the corolla (in one species
square with hairy angles); placentas coherent to the septum, ovules
numerous, ascendent, imbricate.
Capsule more or less globular or oblong, bilocular, at the top
loculicide bivalvular, later on quadripartite.
Seeds small, peltate, imbricate; membranous, winged all round
with fringy notched (in Lindeniopsis undulate) wing; endosperm
fleshy, germ straight, root straight, directed downwards.
Lianes or Shrubs (Lindeniopsis). Twigs velvety or bare, round
or more or less square. Leaves opposite, thin-leathery, elliptical,
lanceolate or oval, usually tapering with a rather abrupt acumen;
usnally hairy on the underside. Leaf-nervature more or less acrodro-
mous. Stipules small, interpetiolar, triangular.
Flowers small or middle-sized, white or light yellow, in axillary
closed racemes or trichotomous, branched cymes, united at the twig
tops to many-flowered panicles.
373
§ 13. Conspectus of the Species.
I. Subgenus Lindeniopsis. Shrub. Seeds with a slightly crenate and undulated
wing. Calyx-lobes longer than the ovary. Corolla tube long. Anthers hairless.
1. C. Hammii, Var. 1909.
Leaves elliptical with short, acute, hard point; secondary veins 5—7 on each
side, arcuately anastomosing (brochidodromous). Corolla hairless inside. Twigs
sharply squared. Stipulae very small. Plant grey velvety all over, later on bare.
Fruit oblong, length up to 30 mms.
Distribution. Hitherto endemic in Billiton on sandy barren soil.
Il. Subgenus Hu-Coptosapelta. Lianes Seeds with fringed wing. Calyx-lobes
not longer than the ovary. Corolla tube not more than twice as long as the lobes.
Backs of the anthers covered with long hair.
2. C. olaciformis (MERRILL), EtmeR 1913. Randia olaciformis, Merr. 1908.
C. flavescens, Mrrr. (non KorrH.) 1909.
Inside of corolla tube and filaments glabrous. Corolla lobes slightly longer than
the tube. Inflorescences corymbose united to panicles at the tops of the twigs;
cymes short-peduncled and few flowered. Flowers very small. Stipules small,
triangular, no hairy edges. Leaves elliptical or oval, shortly acuminate, smaller
than 100 mm. number of secondary veins 4—5 on each side, hairless when full-
grown, colour in sicco pale greenish grey or olive grey. Width of fruit at most
6 mm., broader than long, calyx consisting of free oval lobes.
Distribution. Hitherto endemic in the Philippines, in the following places:
Mindanao, lake Lanao, camp. Keithly, Mrs. CrrMeNs n. 1220, 1907 (type);
Mindanao, prov. of Agusan, in mt. Urdaneta, 700 M. above sea-level KLMER
n. 18355 ?; Luzon, San Antonio, prov. Laguna, mt. Ramos Bur. of Science,
Manila, n. 396! .
3. C. flavescens, KortH. 1851. Stylocoryna tomentosa Bl, Bijdr. 1826;
Stylocoryne ovata, Mig. 1856; Stylocoryne (Webera) macrophylla, WALL non
Roxs.; Coptosapelta macrophylla, K. Scuum.
Inside of corolla tube and filaments glabrous. Inflorescences corymbose long-
peduncled and dense flowered, united at the twig-tops to large thyrsus-shaped
panicles. Leaves elliptical or oval or oblong. shortly acuminate, base as a rule
broad, rounded, length 80—125 mm., number of secundary veins 4—5 on each
side, colour in sicco usually olive-brown, undersurface of leaves, especially along
the veins thinly covered with accumbent or crisp hair. Young twigs and in-
florescences coated with dense, soft hair. Fruit obovate, sepals free, oval, erect.
Stipules linear-lanceolate with broad base, hairy edges.
Distribution: Malay peninsula, Burma, Western Java, Sumatra: Palem-
bang, (Pretorius), 1837, in Herb. L B; Borneo S.E. Division, on sandy plains
on the river Karrau (KORTHALS).
4. C. hameliaeblasta (Wernn.) VAL. nova comb. Tarenna hameliaeblasta
1) Fhis species being rather widely spread, differs rather in habit according to
the place where it is found. For instance the specimens from the Malay peninsula
(Kies collector 10384 and 10393) have stronger flowering-twigs and considerably
greater leaves and flowers than the specimens from Java and Sumatra. The latter
are again distinguished from the Javanese form by smaller, narrower leaves, in
sicco coloured darker brown, covered with crisp hair on their undersides. Similar
leaves also occur in a specimen from Malacca (MainGAy, 908).
Kl | D) AN WAN yl Ne
> Oi ) a PN x
ISOs
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BEN D
A vand, SS En: < AN
SEL Ms) ‘i if id A ONREIN |
Banse LANDING Wb | Ae
Kah TAN WS bas
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iy
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376
Wernu. Inside of the upper part of the corolla tube and the filaments densely
hairy, the former not inflated. Corolla lobes about as long as the thin corolla tube.
Axillary cymes longpeduncled and dense-flowered; terminal thyrsi many-flowered.
Corolla tube (in sicco) covered with appressed whitish hairs. Calyx lobes about
as long as the ovary, erect, curved outward. Leaves oblong or elliptical, with very
short acumen. Secondary veins 3—4 on each side, sometimes with an additional
thin basal vein; veins erect. Stipules very small, triangular, the edges covered
with dense hair. Colour of the leaves in sicco yellow-olive-green. Stalks and
inflorescences hirsute, leaf-veins at the backside with remote procumbent hairs.
Distribution: British New-Guinea, Sogeri-region, 950 —1400 metres above
sea level. (FORBES).
5. C maluensis, VAL. n. sp.
Upper part of the corolla tube not inflated, hairy as are the filaments. Corolla
lobes a little shorter or of equal length as the corolla tube. Axillary inflorescences
with long stalks; terminal thyrsi with abundance of flowers. Flowers the smallest
of the genus. Outside of corolla covered with short appressed hair. Calyx-limb
divided for half its length, lobes oval, erect. Leaves usually broad, elliptical with
3—4 rarely 2 secondary veins on each side (together 5—7), acrodromous. Fruit
crowned by the very small calyx-lobes. Underside of leaves with a very thin
hairy covering near the edge, for the rest bare. Stipules pointed, with thin
indument.
Distribution: North-East New-Guinea, at 190—200 metres above sea level,
in primeval wood. (LEDERMANN).
6. C. Beccarii, Val. n.sp.
Upper part of corolla tube not inflated and at the inside covered with long and
dense hairs, as are the filaments. Corolla grey velvety externally, lobes about as
long as the corolla tube. Axillary inflorescences long-peduncled, thyrsus-shaped.
Terminal thyrsi with abundance of flowers. Leaves broadly oblong, ending in a
caudate acumen, large, with 3—4 secondary veins on each side. Petiole fairly
long; underside of leaf covered with crisp soft hair.
Distribution: Borneo (BEccaRi 2271).
7. C. fuscescens VAL n.sp. Upper part of the corolla tube not inflated, inside
covered with dense hairs, as are the filaments. Corolla lobes twice as long as the
tube. Axillary cymes long-stalked and repeatedly remotely branched; terminal
thyrsi many-flowered, spreading. Outside of corolla tube covered with short silky
hairs, lobes hairless. Calyx small, lobes detached nearly to the base. Leaves
elliptical, glabrous. Usually 3 secondary veins, or in a single specimen 2, on each
side. Stipules very small, obtuse, triangular, hairy,
Distribution: Nord-East New-Guinea in mountain woods 600 —1500 metres
above sea level, in the Kani and Torricelli mountains (ScHLEcHTER) on the
Felsspitze at 1500 metres (LEDERMANN).
8. C. lutescens, VAL. n. sp.
Flowers as in C. fuscescens, but a little larger. Leaves with 2 secondary veins
on each side, in sicco greenish-ochreous-yellow.
Distribution: North-East New-Guinea, on the Etappenberg at 850 m. in
dense high wood (LEDERMANN).
9. C. Griffithii, Hooker. f.
Upper part of corolla tube inflated, inside covered with long dense hairs, as are
he filaments, lobes more than twice the length of the short wide tube. Axillary
ane
cymes rather many flowered; terminal thyrsi densely. Outside of corolla grey velvety
all over. Calyx-hmb wide by cup-shaped, divided for half its length into broad
lobes. Leaves elliptical, at the underside crisp hairs. Secondary veins 3—4 on
each side.
Distribution. Gathered in numerous places in the Mal. peninsula, in the
low lands.
10. C. Janowskii, VAL, n. sp.
Upper half of the corolla tube inflated, inside covered with long, dense hair,
as are the filaments Corolla lobes half the length of the tube. Axillary flower-
stalks with 1-3-5 flowers. Terminal inflorescences simple racemose. Flowers the
largest in the genus. Outside of corolla-tube thin-velvety, lobes hairless. Calyx
large, cup shaped, not incised, with short broad acute teeth. Leaves lanceolate,
long-acuminate.
Distribution: Northern New-Guinea. Jabi mountains.
11. C. montana, Korra. mse., in Herb. L. B.
Flowers unknown. Fruits in the leaf axils isolated or in peduncled cymes of
3-5-flowers, forming simple closed racemes at the twig-tops.
Calyx-lobes persistent on the fruit, only connected at the base, linear-subulate.
Leaves lanceolate or elliptical, rather firm, with long tapering points and acute, obtuse
or rounded base. Secondary veins 2-3 on each side. Stipules small, triangular,
having long hairs. Stems, inflorescences and under sides of leaf-nerves thin-velvety,
in sicco ochreous yellow. Fruit obovate oblong.
Distribution. S.E. Borneo. Summit of the Sakoembang, 1000 metres above
sea level.
EXPLANATION OF THE FIGURES.
Fig. 1 Coptosapelta montana; Leaf of an old plant.
Fig. 2 af flavescens, flowering plant.
Fig. 3 or an very young plant.
Fig. 4 +3 montana; young fruiting plant.
Fig. 5 5 hameliaeblasta.
Fig. 6 5 olaciformis.
Fig. 7 = Fig. 1.
Fig. 8 and Fig. 9 Coptosapelta fuscescens.
Fig. 10 zi flavescens, flowering plant
Fig. 11 = Fig. 6.
Fig. 12 er lutescens.
Fig. 13 and Fig. 14 ,, maluensis.
Fig. 15 3 Hammii.
The figures have been obtained by carbon-impressions according to the method
of Eimer D. Merrity. Fig. 4 is not retouched, only retraced with ink.
The others have all been worked up by the designer with the aid of the
original print and of the leaf; the tertiary vein system is consequently a little too
promineut !
Botany. — „Dark growth-responses”’. By D. Torvenaar. (Commu-
nicated by Prof. A. H. Braauw).
(Communicated at the meeting of April 28, 1923).
In our previous report on the light- and dark-adaptation of Phy-
comyces nitens (Proc. Vol. XXIV Nos. 1, 2 and 3, 1921) the existence
of the so-called ,,dark-growth-response’ was already proved in a
great number of experiments. By dark-growth-response we under-
stand the occurrence of a growth-response, when a sporangiophore
of Phycomyces nitens adapted to light (by a four-sided illumination
for hours at a stretch) is placed in the dark. It seemed worth while
considering in how far this dark-growth-response of Phycomyces-nitens
(the negative after-images of the human eye probably being in reality
comparable) occurs in other organs.
In this communication the results are mentioned concerning the
dark-growth-responses of the sporangiophore of Phycomyces nitens,
the hypocotyledons of Helianthus globosus, the coleoptiles of Avena
sativa, the roots of Avena sativa and the roots of Sinapis alba.
If possible the results have been compared with the light-growth-
responses hitherto known.
Method and accuracy of the results.
In all experiments the preceding illumination was four-sided; the
temperature being kept constant by means of the oil-thermostat,
described in ,,Licht- und Wachstum 1”. In this way the temperature
could be kept constant to 0.02° C. with moderate illuminations. It
should be particularly kept in view, that the growth was as a rule
only considered sufficiently constant, when it did not oscillate above
10°/,, i. 0. w. with an average rate of growth of 100 no rates
higher than 105 or lower than 95 occurred. This enables us to
ascertain responses of growth more than 5°/, above or below the
average; responses of growth therefore of an acceleration or retar-
dation of 10°/, we can ascertain with some certainty.
We mention this in order to give the illustrations and reviews
the value due to them, which could not be judged of without the
full data — which we omit here with a view to space, but all of
which will appear in the ‘“Mededeelingen der Landbouw-hoogeschool”
this year.
379
As long as on account of insufficient constancy of the outward
circumstances or through inward causes, the growth already greatly
oscillates before the change in light-conditions, it may be easily
understood that a response of growth due to this one factor cannot
be accurately ascertained.
As responses of growth of more than 50°/, are but rare, they
are not demonstrable when the growth shows such variations
beforehand. With the data in literature however this repeatedly
occurs. We repeat, that for our reactions we only used organs,
showing as a rule no oscillations of growth greater than 10 °/,.
The figures subjoined all represent the response of individuals,
approaching the average type as closely as possible. Only in the
case of Phycomyces nitens a schematical figure of the process of
reaction was given.
Just as in most of the previous curves published by Braauw such
figures, in which the reaction-type of a definite experimental series
is composed, are mainly based on the so-called cardinal points, to
be found in the reactions of all individuals. These cardinal points are:
1. the average-point of time, at which the response of growth
begins ;
2. the average-time, at which the reaction reaches its first climax
(either maximum or minimum of growth);
3. the average-rate of growth at that moment in percents of
the original rate of growth; and next again the average time, at
which eventually another maximum or minimum occurs and the
average-rate of growth at that moment.
Dark- and light-growth-responses of Phycomyces nitens.
The light-growth-responses are known from the results of BLaauw,
published in “Licht u. Wachstum III’ (Med. d. Landb. Hoogesch.
1918) p. 108. The cardinal points for some intensities follow :
TABLE I.
; Maximum of response
: À : Hise Ee = Final rate of
Light-intensity | after beginning | after beginning | in °%o of the
of exposure rate of growth growth
of exposure in dark
1/8 MK. 8 Min. 9!/, Min. 141 0/9 102 %
1 n 51/, „ 9 ” 148 0 103 0/5
are Sl» 82 „ 152 % 111 %
64, PS 8 jn 174 9% 112 %
25
Proceedings Royal Acad. Amsterdam. Vol. XX YI.
380
At a temperature of about 17° C. some sporangiophores adapted
to exposures to 1/512, 1/64, 8 and 64 M.K., were darkened, the
growth-measuring being continued. The responses of growth, con-
sisting in a retardation of growth were very characteristic.
The cardinal points, computed from sets of 5—6 experiments are
given in the subjoined table.
TABLE II.
Pp ie En Minimum of growth
Adapted to | after beginning | after beginning | in %o of the
of darkening | of darkening See
1/512 MK. | 10% Min. 12! Min. 89 %
1/64, 64; 1200 85 %
8 Dn 6 De 11 À 61 %
64 7 4} i 10 . 13 6
The reaction at 64 MK was observed in a great number of
observations (19). From the results obtained a maximum after about
17 min. could be derived with a rate of growth of about 984°/, of
the rate of growth in light; after that the oscillations get more and
more indistinct and after 1*/,—2 hours the equilibrium for the
growth has externally been reached. The rate of growth appears to
have become 93°/, of the rate of growth in light, with a mean
error of about 1 °/,.
From comparison of the above reports the contrary reactions,
brought about by making light and dark, are clearly perceptible.
(See the figure).
The dark- and light-growth-responses of hypocotyledons
of Helianthus globosus.
The light-growth-response of these organs is sufficiently known
from “L.u.W. II”. It consists in a retardation of growth, making
its first influence felt, when exposed to 1 MK after 8 min.; the
minimum of 74°/, of the rate of growth in light appears after
27 —38 minutes, after which the growth reverts to its previous rate,
at least in a slight number of observations it is after 3 hours not
perceptibly different from the rate before exposure.
381
<5 20--— 49 60-80" 00MIN.
0 20 AO: ©. 60 80 100 MIN.
EXPLANATION OF THE FIGURES.
These figures have been arranged in twos, in such a way, that above the
process of growth has been represented when the organ after having been in dark,
was permanently exposed to light (7) below the organ made dark (J) after having
been exposed for hours. The height. of the dotted space represents the rate of
growth. In the case of Phycomyces the two growth-curves have been plotted
according to the average progress of a number of individuals; the cardinal points
are indicated by X For all the other organs the curves have been composed of
the figures found for one of the individuals. The curve for the coleoptile of Avena
sativa has been plotted after an individual reaction after KONINGSBERGER.
How these curves have been plotted will be further discussed and explained in
the more detailed publication.
25*
382
AVENA SATIVA (WORTEL)
0 RRT
HELIANTHUS GLOBOSUS (HYPOCOTYL)
7 En
0 DE DRE EE
383
At 64 MK the first reaction already appears after about 34 min.,
the minimum amounting to 39°/,, after 20—25 min., while after
that the rate of growth gradually reverts to its initial value.
Finally at 512 MK the reaction-period is 34 minutes, the minimum,
now 21°/,, appears after about half an hour and continues for a
long time. Even some hours after the beginning of the exposure the
rate of growth remains considerably below the rate in dark. Compare
the figures subjoined.
What reaction takes place, when we darken after these hypoco-
tyledons have been mainly adapted to a constant illumination for
5—7 hours?
The results of these experiments, made at about 20°C. have been
briefly summarized in the subjoined table.
TABLE III.
| Maximum of response | i
Beginning of Second
Adapted to response after | After beginning in & of tne
; rate of grow i
darkening Oene a ie Em maximum after
1 MK. 7's Min. 18's Min. 128 % 40 Min.
64 84: „ Kera 137 2% pe
SIZE oe, 8% „ 18 Fe 15 18e —
After about an hour and a half the growth had become settled
again. As to the rate, putting together all data of 1,64 and 512 MK
and comparing the rate of growth in light to the rate 1—2 hours
after darkening, we find of the 14 results: a retardation of growth
in 7, an acceleration in 6 and an unaltered rate in one, while an
average acceleration of growth of 5 + 21°), may be computed.
Therefore the chances for the existence of a lasting acceleration of
growth may be called slight.
On comparing the light- and dark-responses to each other (see
figure!), we are again struck by the reverse process, though there
is no perfect symmetry. In both cases the reaction is more marked
for higher intensities (lower minima, resp. higher maxima).
Upon the whole the dark-response is not so strong as the light.
response. The reaction-period is longer, the change in growth less
intense, the external equilibrium of growth sooner restored.
384
The light- and dark-growth-response of coleoptiles
of Avena sativa.
By means of the experiments of Vor, Simrp and KONINGSBERGER
a light-growth-response has been ascertained. On application of 90
MK on 3 sides KONINGSBERGER finds a minimum of about 55°/, 85—40
minutes after the beginning of the exposure — next a maximum
after about 65—70 minutes (about 80 "/, of the rate of growth in
dark) — while after 90 minutes a second minimum occurs amounting
to about 65—70°/, of the rate of growth in dark. The latter how-
ever continues oscillating irregularly for hours together. In the figure
the curve of the light-growth-response is taken from an individual
of table 9 from KONINGSBERGER’s dissertation.
What reaction oceurs, if we darken after the rate of growth has
been in the main adapted to light for some hours?
With Helianthus and Phycomyces darkening appeared to cause
less intense changes of growth, than “Light”. If this should be the
case with the coleoptiles of Avena sativa, there would be danger
of this reaction finding no expression at all or but indistinctly, on
account of the irregular growth of Avena, in consequence of occurring
nutations.
We have therefore tried to eliminate or restrict these impeding
movements. Not only were a great number of Oat-races observed
in this respect, but also conditions of more or less moist and hot
cultivation were tried. In this way we have succeeded in finding
an Oat-race called “Zwarte President” which when cultivated in a
very dry soil but very rarely nutates inconveniently. As long as the
coleoptiles secrete little or no drops of moisture, the growth was
extraordinarily constant and frequently remained within the limits
fixed by us: no more than 10°/, variation of growth. The tempe-
rature at which the plants grew was about 22°C. In order to give
a good idea of the results, obtained for this object, we decided to
give the whole of its individual responses of growth in this commu-
nication. Our preceding illumination was 4-sided with 64 MK..
which intensity deviates but little from that used by the above-
mentioned investigators. The rate of growth has been given in microns
per minute. *)
N°. 1. Exposed beforehand for 44 hours at 21°,9 C. to 64 MK:
1) The small figures denote the time of observation, by which the beginning
of darkening is again put at the full hour (60).
385
45 124 50 124 55 124 park! 0 125 5 124 10 124 15 124 20 13 25
16 30 13 35 12 40 104 45 9 50 10 55 105 1 hour 104 1.05 104 1 10
N°. 2. Exposed beforehand for 4 hours at 21°,9 C. to 64 MK.
51 20 54 20 57 20 park! 0 19 3 19 6 19 9 20 12 19 15 18 18
NSR 2 2 RANT SN SO RIMS ese Oil eere AIS "50 1953
18 56 18 1 hour 18 1.03 18 1.06.
N°. 3. Evposed beforehand for 4 hours at 22°,2 C. to 64 MK.:
ESAT END NR KOMO ANG RIN OPI DEN ANS 29: 18 29
zi Dn GL DG Lr WM BO) Die Why so DEL Shy Py ce DB) EEDE
Di5sAo i st 2081 hour 26, 1.03.25) 1.06 25 1209" 25 1212:
N°. 4. Exposed beforehand for 8 hours at 21°,9 C. to 64 MK.:
50 9 55 8 Dark! 0959 10 11 15 11 20 12 25 11 30 104 35 10
40 94 45 10 50 10 55 94 1 hour 94 1.05.
N°. 5. Exposed beforehand for 6 hours at 22°,0 C. to 64 MK.:
40 9 45 9 50 9 55 9 Dark! 084 59 10 11 15°12} 20 14 25 12
Bom 35110) 40) 10) 45° 110'50'92 559 1 hour 971.059 9M1 101915 91:20.
N°. 6. Exposed beforehand for 4 hours at 21°,1 C. to 64 MK:
45 26 48 24 51 25 54 25 57 25 Dark! 0 24 3 24 6 25 9 25 12
25 15 28 19 30 21 33 24 86 27 36 30 36 33 29 36 24 39 24 42 26
AAS 4825-51 20 542051) 20, de hour 2671.03 Aid 1,10;
The occurring dark-growth-responses in the above cases yield the
following averages for the cardinal points:
Mene Lespouse A minimum in the rate of
in % of the growth (except in No. 5)
rate of growth | after beginning of darkening
First response |
after beginning | After beginning
of darkening | of darkening in light
16 Min. + 23% Min. | 133 % + 42 Min.
In some cases there is apparently a slight secondary maximum
after 50—60 Min. (Nos. 2, 3, 4 and 6). Little may be concluded
from these experiments with respect to the final rate of growth. It
does not seem to deviate much from the rate in light.
The above shows a distinct response of growth, again contrary
to the light-growth-response. Again it is less intense than the light-
growth-response; the former gives a slighter change of growth: the
undulatory movement is less vehement (undulation of shorter duration
with slighter amplitude).
386
In the averages KoNINGSBERGER's tables (4) of the light- and dark-
growth-response a maximum occurring after darkening may indeed
be found on pages 51, 52 and 53. It occurs after about 20—30 min.,
(circa 25 minutes), but also in connection with further experiments
KONINGSBERGER does not consider these reactions as dark-growth-
responses.
In the cases, in which Voer observed the dark-growth-response,
it lies averagely after 21—24 min., (averagely 22} min.), which is
in accordance with our results. Simre finds his maximum averagely
after 30$—35! min. (averagely 33 min.). But we should bear in
mind, that this investigator did not change the exposure to 320 MK.
to dark, but to a slighter illumination with .17.7 M.K. (pag. 699
and (following).
Accordingly in our experiments both after a previous exposure
of 6 and 8 hours, and of 4 and 43 hours, we found a dark-growth-
response with the coleoptiles of Avena, contrary to the light-response
of this organ.
The Light- and Dark-growth-responses of the root of Sinapis alba.
This organ being much less sensitive to light, | deemed it desirable
to apply stronger illuminations, viz. of 3500 M.K. In spite of the
insertion of a cooler with running water into the circuit, a gradual
rise of temperature from 0°.5—1°.0 C. in the course of an hour
could not be prevented. On darkening, a fall of temperature could
be prevented by again putting the heating into operation. Then
oscillations above 0°.05—0°.1 C. did not oceur.
The roots were subjected to 4-sided illumination at 21°.5—22°.8C.
for 3—5 hours. First the light-growth-response was determined,
yielding the following averages :
Ta, Minimum of growth oe Rate of growth
EN after some hours in
in % of the rate |lightin ofthe rate
First response
after making |
after light of growth in dark jof growth in dark
31 Min. | 391s Min. | 19 % 88 %
We observe a distinct response of growth. The retardation of
growth is permanent in all cases also after the new external equi-
librium of growth has been attained.
387
A subsequent darkening caused the following reaction :
Fired response Maximum of response Rate of growth in
after in % of the rate |dark in% oftherate
alter darkening | of growth in light | of growth in light
30! Min. | 35!s Min. | 124 2% 113 2
Here too the contrast between light- and dark-response is found.
Both are fairly equally marked.
Meanwhile I have observed the dark-growth-response with an
illuminating-power of 512 M.K. | found as an average of 7 experi-
ments:
Birseeres pause Maximum of response Rate of growth in
after in % of the rate |darkin % ofthe rate
after darkening | of growth in light | of growth in light
27 Min. | 36! Min. | MI 26 105 %
Here we already approach the limit of the reactions still percept-
ible, which also appeared from the fact, that a few plants no more
gave a perceptible dark-growth-response. On subjecting these plants
to an illumination of 512 M.K., there did not occur a light-growth-
response either.
The sensitiveness to light, found by Braauw (“L. u. W. III”) for
Sinapis alba was greater. At the time there was even found a marked
response at 64 M.K. with a minimum of 81 °/, and arate of growth
after 2 hours of 91 °/,, an equally strong response, as the one found
by us for 3500 M.K. To what causes this may be owing (older
seed? other Sinapis alba race?) should be further investigated into
and may become an indication for the deeper cause for sensitiveness
to light.
The behaviour of the tap root of Avena Sativa, with
respect to light and dark.
Braauw did not find a perceptible response with illuminating-
powers of 64—500 M.K. I exposed to 3500 M.K. Even then no
reaction occurred, or so slight a reaction, that it might as well be
attributed to the slight rise of temperature.
After a 3 hours exposure at a constant temperature of 20}°—
224° C. followed darkening. In not a single case there was a marked
388
response, i.e. the oscillations of growth remained of the size also
occurring in constant circumstances (smaller than 10°/,). With a
reservation as to the existence of such an exceedingly slight reac-
tion, we may observe, that the lack of a light-growth-response goes
together with the lack of a dark-growth-response.
SUMMARY.
1. With the organs observed the occurrence of a lght-growth-
response went together with a dark-growth-response, in the main con-
trary to the former.
2. The lack of a light-growth-response (Avena-root) goes together
with the lack of a dark-growth-response. This going together seems
to hold good also individually (Sinapis-root 500 MK.).
3. With Phycomyces, Avena coleoptile and Helianthus-hypocotyledon
the dark-growth-response is less intensive than the light-qrowth-response :
the waves have smaller amplitude and are of shorter duration so
that externally a constant rate of growth is sooner attained.
It remains to be investigated into, whether the inward equilibrium
is likewise sooner restored than the externally observable light-
growth-response. Equilibrium in the inward processes indeed does
not coincide with the appearance of a constant rate of growth to
be judged by the observer (7).
With regard to the word ‘dark-growth-response’, used for con-
venience, sake, it should be borne in mind, that dark as such does
not cause the response: dark itself is not a stimulus, but the modifi-
cation in energy-supply, either when suddenly occurring (light-growth-
response), or suddenly ceasing \dark-growth-response), respect. increasing
or decreasing.
It may be easily understood, that stoppage of energy-supply causes
a slighter and shorter reaction in an organ, i.e. it sooner settles
down than when energy is supplied.
LITERATURE.
l and 2. Braauw, A. H. Licht u. Waclistum I en II (Zeitschrift f. Bot. 1914,
6 und 1915, 7).
3. BLAAUW, A. H. Licht u. Wachstum III (Med. d. Landb. Hoogesch. 1918, 15).
4. KONINGSBERGER, V. J. Tropismus u. Wachstum (Dissertatie. Utrecht, 1922).
5. Srerp, H. Ein Beitrag zur Kerntniss des Einflusses des Lichts auf das Wach-
stum der Koleoptile von Avena sativa (Zeitschr. f. Bot. 1918, 10).
6. Siere, H. Untersuchungen über die durch Licht und Dunkel hervorgerufen
Wachstumsreaktionen bei der Koleoptile von Avena sativa (Eb. 1921, 13).
389
7. ToLLeNAAR, D. and Braauw, A. H. Light and Darkadaptation of a plant
cell (Proc. Vol XXIV. Nos. 1, 2 and 3, 1921)
8. Voer, E. Ueber den Einflusz des Lichtes auf das Wachstum der Koleoptile
von Avena sativa. (Zeitschrift f. Bot. 1915, 7).
9. Wepvers, Tu. „De werking van licht en zwaartekracht op Pellia epiphylla”.
(Verslagen Kon. Akad. v. Wet. Deel XXX, 1922).
Laboratory for Plant-physiological Research.
Wageningen, April 1923.
Mathematics. — ‘Representation of a Tetrahedral Complex on the
Points of Space.” By Prof. Jan pr Vries.
(Communicated at the meeting of April 28, 1923).
1. Let there be given a pencil of quadratic surfaces which has
a twisted curve g‘ as base curve. The polar planes of a point P
with respect to these surfaces pass through a straight line p, which
we shall call the polar line of P. Through P there pass two
bisecants of o°; the straight line p joins the points of these bisecants
which are harmonically separated from P by of. If P lies in the
vertex of one of the four cones belonging to the pencil, the polar
line becomes indefinite; any straight line of the plane wx = O; On On
may be considered in this case as a polar line.
The complex of rays 7’ of the polar lines p is represented on
the space of points {P}. The side 0, O; is represented in any of
the points of the opposite side 0, On. If a straight line r is to
belong to 7, its polar lines 7’ and r" with respect to the surfaces
«° and 8? of the pencil, must cut each other. If the straight line r
describes a plane pencil, 7’ and r" describe two projective plane
pencils; the plane pencil (7) contains accordingly two rays for which
r’ and r" cut each other. The complex 7’ is therefore quadratic ')
and has four cardinal points 0; and four cardinal planes w;; hence
it is tetrahedral.
A point P of of is the image of the straight line p which touches
o‘ at P. The scroll of the tangents of of is therefore represented
in the points of o*.
2. If P describes a straight line 7, the polar planes of P with
respect to a’ and 3? describe two projective pencils round the polar
lines r’ and r". The polar line p describes accordingly a quadratic
scroll (p)?; the conjugated scroll consists of the polar lines of r
with respect to the quadratic surfaces through o*. The points of
intersection of 7 with the cardinal planes , are the images of four
1) If the pencil is defined by Zas? =O and Lbhyx,* = 0, the polar planes of
4 4
the point y have axs and byys for coordinates. The coordinates of p are in this
case Py = (d3b4—A, bs) yz yy etc. If we put a) a3 by by + dada bj bs = Cg,04, T is
represented by Cj2,34 Pia P34 + Cass14 Pag Pis + C1524 Pan Pas = 0.
391
rays p, which pass through the cardinal points Oz. 7’ contains
evidently * scrolls (p)’.
If r is a ray of 7, r’ andr" cut each other, so that the projective
pencils of polar planes produce a quadratic cone which has the
point 7’7" as vertex. From this follows that the complex cones of
T are represented by the point ranges (P) lying on complex rays.
3. The rays of 7’ which lie in a plane p (and which accordingly
envelop the complex conic p*), are represented by the points P of
a twisted curve which passes through the cardinal points O;. For
the intersection of the planes p and wj is a tangent of ~’ and is
represented in Q,. As wj can only contain the images points QO),
On, On, the image of the system of the tangents of p?° is a twisted
cubic g* circumscribed to the tetrahedron O, O, O, O,.
4. The complex 7’ cuts a linear complex A in a congruence (2,2)
which has singular points in O,, singular planes in w,;. For O, is
the vertex of a plane pencil belonging to both complexes, hence to
(2,2). The polar lines p’ and p" of the rays of this plane pencil
with respect to a and g* form two projective plane pencils in w;
and these produce a conic cireumseribed to QO; On On. The image of
the congruence (2,2) is therefore a quadratic surface $2* cireum-
scribed to O, O, O, O,.
As A does not generally contain any of the sides O0, $2? will
not generally contain any of these sides either. ’)
The o* surfages £2? are the images of o* congruences (2,2)
contained in 7. To these belong a‘ axial (2,2) defined by the a‘
axial linear complexes.
5. The rays of 7’ belonging to two complexes 4, and 4,, form
a scroll (p)* of the fourth order; this scroll belongs of course at
the same time to all complexes 4 of the pencil defined by 4, and
A,, hence also to both axial complexes of this pencil. Their axes
are director lines of (p)* and moreover double director lines, for
the complex cone of a point lying on one of these axes,:is cut
twice by the other axis.
=0, (2° has for equation
1) If A is defined by 2d Pay
Be Cae! y,, = 0.
Inversely the surface Ev, y, =9 is the image of the (2,2), which is defined
6
by the complex s/e Dmn =O.
6 Ck/
392
The scroll (p)* is represented by the twisted curve o* which is
the intersection of the two surfaces {2° that are the images of the
congruences defined by A, and 4.
If, the axes 7, and 7, of two axial complexes cut each other, the
congruence (2,2) which these complexes have in common with 7,
degenerates into the system of the complex rays p through the point
R=r,r, and the complex rays in the plane e=7,7,. In connection
with this the image surfaces (2* defined by 7,7, cut each other in
the twisted curve o° representing the complex rays in ov, and in
the polar line + of FR (the image of the complex cone of &);
evidently 7 is one of the bisecants of 9’.
If o° is an arbitrary twisted cubic cireumseribed to O,O,0,0,,
there pass oo° surfaces 2* through e* of which any two have also
in common a biseeant of o*; evidently they represent two axial
complexes of which the axes cut each other, so that the corresponding
(2,2) splits again up into a complex cone and a complex conic; the
latter is represented by o°.
6. A conic (P)? has four points in common with the surface (2?
belonging to an axial complex 4; it is accordingly the image of a
rational scroll (p)'. Any ray s of 7’ lying in the plane of (P)’,
contains two points of (/)*; the image S of s carries therefore two
rays of (p)*. Hence the curve (S)*, representing the rays s, is the
double curve of (p)*.
If (P)* passes through O,, it is the image of a eubie scroll (p)°
of which the double director line passes through O,; for the points
of intersection of (/)* with w, are the images of two rays p through O,.
If (P)? passes through O, and through Q,, it is the image of a
quadratic scroll (p)*. Inversely a seroll (p)* has two rays in common
with an axial complex; its image cuts accordingly the corresponding
surface 2* outside Ox in two points. Hence this image is either
a straight line ($ 2) or a conic through two cardinal points O.
7. The points P of a plane p represent the rays of a congruence
|p|. The polar planes « and 3 of P with respect to two quadratic
surfaces «? and 3? of the given pencil form two projective sheaves
of planes ronnd the poles of p. Their intersections with a plane w
form two projective fields of rays, hence pp contains three rays
p= ag.
The planes « through a point Q form a pencil; one plane of
the corresponding pencil (8) passes through Q, hence Q carries one
ray p.
393
The field of points [P] is therefore the image of a congruence
(1,3). This consists of the chords of a twisted cubic 6* which passes
through the points O; for the range of points (P) in wx is the
image of the generatrices p of a quadratic cone which has O, for
vertex.
8. If the twisted cubic (P)* passes through three cardinal points,
it is the image of a cubic scroll (p)*. For an arbitrary surface ®*
representing an axial complex cuts (/)* in three more points; on
the axis of this complex there rest therefore three lines of the
scroll. One pencil (#*) can be passed through (/)'; for through any
four points of ¢P)* aw! ? can be passed, each of which contains
seven points of (/)*. The corresponding complexes A form also a
pencil; the axes of both axial complexes belonging to this pencil,
cut all rays of the seroll and are therefore the director lines of the
cubic scroll (p)°.
If (P)* passes through two cardinal points, it is the image of a
scroll of the fourth order. In this case one #* passes through (P)*:
the seroll belongs to the congruence (2,2) which the corresponding
complex A has in common with 7’; as it is rational, it has a
double cubic.
9. A surface | P|" is the image of a congruence with sheaf degree
n, for its intersections with a ray ¢ of 7’ are the images of n rays
through the vertex of the complex cone represented by ¢ The jield
degree of the congruence is generally 3 for each point of inter-
section of |P] with the cubic g? representing the rays ¢ lying in
a plane g, is the image of a ray of the congruence in gy. If { P|”
passes sj times through O,, the field degree is evidently 3n— sg.
A twisted curve (P)" is the image of a scroll of the Dre.
for the image surface [P|’ of an axial complex cuts (P)" in 2n
points, which are the images of as many rays ¢ cutting the axis
of the complex.
10. If the base of a pencil of quadratic surfaces consists of a
cubic 9’ and one of its chords, the polar lines of the points of
space form a quadratic complex which is represented in the same
way as the tetrahedral complex.
We can always represent this pencil by
a(w,*— 2, «,) + B(2,’—a«, ,) = 0.
The polar planes of the point y relative to the cones « — 0 and
394
B=0O have for coordinates y,,—2y,,¥,,0 and 0, y,,—2y,,y,. The
polar line of y is therefore represented by
Nie as peed Ts, Lg Cire War en
vet At, UI We vts yd
Hence
4P as” = Pis Pas
This complex has QO, and O, as cardinal points, w, and w, as
cardinal planes.
The complex cone of « touches 0,0, at O,, O,O, at O,. The
polar line of y lies in the plane § if the equation
$1 (2447s YY as) + Esala + Es Vaate + §, Cya uit) =O
is satisfied by all values of «, and «,. From this follows that the
complex rays in § are represented by the points of the cubic which
is defined by the cones
25u HE Ea so 2E HEI = Sia
(The chord O,O, does not belong to the image).
The congruence (2,2) which the complex has in common with
the axial complex with directrix a, — 0, 6, =O, has for image the
quadratic surface the equation of which is
(a,b) viva + [4(a,b,) + (a,b) Yas — (a,b) Hiv, + (0,6) Yao +
+ (a,b) 9,7 + a,b) ys” = 9,
where (ab) = azbi—aibr.
Chemistry. — “The Electromotive Behaviour of Magnesium’. 11°).
By Prof. A. Smits. (Communicated by Prof. P. Zrrman).
(Communicated at the meeting of March 24, 1923).
Introduction. The fact that the rest potentials of magnesium and
aluminium in aqueous solutions of their salts are too small negative
has been the subject of frequent comment.
An apparently succesful explanation was that which assumed the
presence of a film of oxide on the metal. This was however due
to a not sufficiently careful examination of the consequences of such
a premise.
This is especially true in the case of aluminium where it had
been supposed, that the etched or even the polished metal was
coated with a not porous film of oxide of molecular. thickness.
Now a number of different investigations have proved with cer-
tainty that if an etched or polished aluminium electrode is immersed
in mereury above which there is an aqueous solution of the alu-
minium salt, the aluminium immediately shows the potential of the
mercury layer, whilst there was no indication of the penetration of
a film of oxide *).
It follows from these investigations that either a film of oxide
does not hinder the passage of the electrons or there is no film at all.
If the electrons only were going through an oxide layer we should
expect the behaveour of a gas electrode. This is not in accordance
with the fact. Consequently if the oxide film existed it would be
penetrable for ions, but it is then manifest that we are dealing with
a metal-electrode.
Now it is possible that under certain circumstances the liquid in
the liquid bounding layer is saturated with respect to the hydroxide
of the metal. This could easily be proved by the fact, that in the
formula
OTS ede
1) The considerations applied here are explicated in the book “Theory of Allo-
tropy”. Longmans, Green and Co. 1922.
The first Communication appeared These Proc. Vol. XXII, 876 (1920).
2) See Zeitschr. f. Electr. Chem. 27, 523 (1921) and 28 (1922).
26
Proceedings Royal Acad. Amsterdam Vol. XXVI.
396
Lm (OH),
OH)’
0.058, Ly (OH'y
(My) can be substituted by so that
en, Brie AND
5 y 08 Lm (OH), ~ (4)
or
0.058 Ti Ken
EZ AO SEE CLM of 18 EGT KN
Y °8 Lm (OH), (Hr) Ge
From which it appears, that the electrode will behave as an
oxygen or hydrogen one, but that the electromotive forces will show
a constant difference.
These considerations however are no help to us, for expression (1)
which always holds good, requires the potential of the metal to be
very negative, because the concentration of the metal ions in a
saturated solution of Mg(OH), or Al(OH), is very small. The exact
converse is observed.
Ten years ago KistiAkowsky ') calculated the normal potentials
neglecting the temperature coefficient in the formula of GiBBs-HELM-
HonTz and found with Mn, Fe, Co, Cu and Cd differences between
the calculated and experimentally found normal potentials of
10—60 m.V.; with Ni, Sn, Pb and Hg differences of 140—190
m.V.; with Ag he found diverences of 310 m.V., and with TI of
360 m.V., whilst the difference with Al was 460 m.V. and with Mg
900 m.V.
As Kisriakowsky found the electromotive force which the caleu-
lated for Mg and Al so much higher than that found experimentally,
he simply assumed that at the two electrodes in the galvanic cell
metal-electrolyte-lydrogen, the reactions
Ms > My + 26,
and
26, + 2Hr > H,,
do not take place as in other cases, but the following:
M, + 2 0H, > M (OH), + 26
and
291-980 >20H +H.
It should be noticed that the remarkable assumption is made there,
1) Z. f. phys. Chem. 70, 206 (1910).
397
that a reaction which takes place at the hydrogen electrode is
reversed when Mg is replaced by zinc.
Kistiakowsky, however, rightly comes to the following conclusion :
“Hieraus fogt unmittelbar, dass die Mg bzw. Al. Electroden die
Eigenschaften von Gaselektrode besitzen mussen, d.h. ihr Ey, von
der Metallionen-konzentration unabhängig, dafür aber von der H°
und OH’-Konzentration abhängig sein muss; ausserdem muss es,
wie bei Pt, von den reduzierenden Eigenschaften des Elektrolyten
abhangen.”
In this Kistakowsky, however, quite overlooked that the behaviour
of an hydrogen electrode will also be found with any other metal,
if tbe boundary liquid consists of a saturated solution of the metal
hydroxide.
Kistiakowsky, instead of measuring the Mg and H, potentials
in the same solution by changing the Mg concentration, dipped his
Mg electrode, besides in a solution of MgSO, and in a solution of
MgCl,, in different other solutions, not containing Mg, and then
obtained results, of course, from which no conclusions at all can
be drawn. In his opinion, however, his results proved that the Mg-
potential is independent of the Mgconcentration.
Beck!) was the first to demonstrate in his Thesis for the
Doctorate the invalidity of Kistiakowsky’s views; he has also shown
experimentally that Mg never behaves as a hydrogen electrode. All
the same electromotive behaviour of Mg in MgSO,-solutions of
slight (Hy) was not yet cleared up, for it appeared to him that the
difference in potential between the Mg and H electrodes in these
solutions of small H’-concentration increases with the Mg-concen-
tration. *)
Breek found that the Mg electrode does not behave as a
hydrogen electrode, but the Mg does not behave as a normal metal
electrode either, for it was found that the Mg-electrode becomes
more negative when the MgSO,-concentration increases. It further
appeared that on increase of the H'-concentration the Mg-potential
becomes more negative, and that it reaches a maximum negative
value for every MgSO,-concentration at a definite H'-concentration.
This maximum negative value varied with the MgSO,-concentration,
at least qualitatively, in a normal way.
1) Rec. tray. chim. 41, 353 (1922).
*) All the measurements were carried out by Beck in an atmosphere of very
pure hydrogen, with vigorous stirring of the liquid, the Mg-electrode being at
rest. If was found, that this way of stirring is much better than stirring by the
electrode it self.
26*
398
The maximum negative potentials are however no equilibrium
potentials, that follows already from this, that the potential of Mg
activated by amalgation in a solution of 1 gr. mol of MgSO, per
litre, is more negative, i.e. — 1.856 Volt. instead of —1.790 Volt,
which value will also lie still below the real normal potential of
equilibrium of Mg, as will be shown below.
Magnesium.
After this introduction we shall examine the metals Mg more
closely. ; |
The difficulties which are usually encountered in the study of
the electromotive behaviour of magnesium and aluminium are owing
to the fact that extraordinary phenomena appear when the usual
methods of determining the equilibrium potential are applied to
these strongly basic metals.
For example, suppose that the Mg potential is — 1.86 Volt. Since
the Me electrode develops hydrogen, this means that the above
potential corresponds to the potential of the three phase equilibrium,
magnesium (inner equilibrium) — hydrogen (by inner equilibrium)
and the surrounded liquid layer.
The liberation of gaseous hydrogen takes place because hydrogen
ions from outside diffuse into the surrounding liquid layer and com-
bine with the electrons.
The above assumption holds for -Fe and Zn because it can be
shown by calculation that the surrounding liquid layer can coexist
with metal and hydrogen, the two latter in inner equilibrium.
If however we take now strongly basic metals, we can see that
the quotient — would be so large, that the electrolyte would
(2H")
become inconsistent.
The question now arises: “Can the above negative potential (—1.86
Volt) be the potential of magnesium and unary hydrogen (that is
to say hydrogen in inner equilibrium) with respect to the surround-
ing liquid layer containing say 1 gr. ion Mg per litre.”
0.058
Applying the formula KE = — log. ta 2.8) and sub-
stituting for E the value — 1.86 we can calculate that
Lise — (Mg) (0, )* = 108% 16.
If we consider that for hydrogen in inner equilibrium
1) The Theory of Allotropy p. 128.
399
L, = (i jr = 102% 48
ITT
it will be seen, that for the surrounding liquid layer which is in
electromotive equilibrium with magnesium and hydrogen the
following formula holds good :
MEL) Ee gren
(A, Ly
It is evident that this ratio is not realizable.
If we chose (Mey) = 1 then CH) = 10°*32 and since (a (OH, =
= 10—-" we have (OH) = 1018.
If we take (Mgy) = 10+ then (HY) == 10-25 Ge (OH) = 1010,
From the above figures it is seen that if magnesium is in such a
state that the solubility product is 10°"
with unary hydrogen and liquid because the surrounding liquid
it can never coexist
layer, required for this coexistence, cannot exist.
A graphical representation of the above statement in Z,X diagram
(fig. 1), is given by the point C. C lies so near one axis that any
stable aqueous solution lies to the right of it. If we assume that the
Fig. 1.
solution into which the Mg electrode is dipped has the composition
X then there are two limiting possibilities for the coexistence of
400
Fig. 3.
401
Meg, hydrogen and electrolyte. Between these limits the observable
cases lie.
One limit is indicated in fig. 2. Here the hydrogen is in inner
equilibrium but that of the Mg is displaced to such an extent that
the potential line of this metal has the position a, ¢,.
At the other limit the Mg remains in inner equilibrium but the
liberating hydrogen is in a state of formation so that its potential
line has the position 6,c, in fig. 3.
In the latter case the observed potential of the three phase equi-
librium ac,e will practically correspond with the equilibrium poten-
tial of Mg’). The observed cases lie between these limits.
The above remarks concerning Mg with a potential of —1.86 V.
also apply to Mg with a potential of —1.3 Volt. In this case
2x —26 (Mey) Ly. 2x 22
lee 110 and then —— = —"== 10 ‚so that if (Me)
Mg (Hy le > L
=1,(H)=10-* or (OH’) = 10°.
Consequently when Mg of a potential of — 1.3 V. was liberating
hydrogen in inner equilibrium from a solution of a Mg salt in
which (Mgy) =1, then OH’ in the surrounding liquid layer would
be 10°. This is practically also an impossibility.
From the above it follows that the hydrogen which coexists with
magnesium and the surrounding liquid must be in such a condition
that the value of 1, is much greater than that corresponding to
the inner .equilibrium.
This statement arouses a suspicion to the precipitations of Mg-
hydroxide in the surrounding liquid layer, but if this occurred the
coexisting hydroged would be formed in a stronger state of formation
than even in the case that the surrounding liquid is no longer
saturated with respect to Mg(O8),.
The solubility produet of Mg(OH), is about 10°” since the value
we choose for Mg, is immaterial we will assume (Mg) — 1. In
this case (OH) = dom
If the Mg-electrode has the value Liv; = 10°* 73 we have already
calculated that (Hy) = 10 anon (OH) = 10° which is quite im-
possible for the solubility produet of Mg(OH), requires here (OH’) =
1) Here it must be remarked, that if hydrogen is being liberated the composi-
tion of the bounding liquid layer will always lie more to the lef than that of
the liquid outside.
402
It is therefor evident that the apparent svlubility product of
hydrogen shows large deviations, from the value which would be
expected when the hydrogen is in inner equilibrium. We will now
calculate what the value of the solubility product of hydrogen must
be in this case.
In the pee we have manifestly employed a value for Ly, which
2x13.25 ,. A grt a ee
is 10 times too small. The value of Li, for the hydrogen
2
which is being liberated, in the case under considerations, is therefore
10°*—** instead of 10°%—**. In other words this hydrogen has
become so much more basic, that in respect to its electromotive
behaveour it somewhat resembles zinc.
If the OH-ion concentration in the surrounding liquid layer is
lower than 10-°” then no precipitation of Mg(OH), will take place.
If (OH) = 10 °° then 10 and electromotively the
heden is beginning to resemble manganese.
From the above considerations it follows that an approximation
to the equilibrium potential of magnesium would only be possible
if the hydrogen could appear in a stronger state of formation, for,
as already has been demonstrated, an increase in the solubility
produet of magnesium will always be accompanied by an increase
in the solubility product for the hydrogen which is being liberated.
This is not necessary the case with less basic metals. It is clear
that the foregoing conclusions will also hold for aluminium and
we will now examine the conditions under which we can measure
the most active potentials of these metals.
According to the theory of capillarity the change between two
liquid phases or between a liquid and a gaseous phase is really an
extremely sharp change in continuity. In the above case however
we are dealing with random arrangements of particles in each phase.
When we come to consider a metal and an electrolyte one has a
definite structure and the other has not.
We are however sure, that in this case also in the bounding
layer there will be a very sharp transition, though with a discon-
tinuity, and that consequently the coexisting phases will only show
quantitative differences with respect to compositions.
Now we make the assumption, that the parts, present in the
metal bounding layer, in concentrations depending in the depth of
the layer, in general will exert influence in the rapidity, with
which the inner equilibrium is establishing in the bounding layer.
Oxygen, nitric acid, nitrates, etc., are already known to exert a
retarding influence on the establishment of internal equilibrium in
403
metals and the electromotive behaveour of Mg and Al now shows
that their oxids and hydroxides may exert a similiar influence.
In a solution of MgSO,, to which no acid is added, some Mg(OH),
is in solution. If we dip a Mg-electrode into this solution then,
besides other parts, present in the electrolyte, also Mg(OH), will
solve in the metal bounding layer. This does not mean to say, that
the Mg will lose any of its characterisiic properties such as the
power to precipitate mercury from a solution but this small quantity
of Mg(OH), seems to exert a retarding influence on the velocity
with which the internal metallic equilibrium is established.
A Me-electrode under the above conditions dissolves slowly, evolu-
ting hydrogen, and shows too low a potential owing to the disturbance
of the inner equilibrium. Addition of sulphuric acid however decreases
hydrolysis, and with this the Mg(OH), concentration in the metallic
surface and induces a change in the direction of the inner equili-
brium of the metal, such that the potential becomes more strongly
negative.
This effect of adding acid is however twofold. On the one hand
the concentration of the negative catalyst in the metal Mg(OH), is
decreased, on the other hand direct attack at the metal is increased.
This attack in cases where it is rapid, such as the one under con-
siderations, always gives rise to disturbances and it might be expected,
that the potential would first become more negative and finally
would fall a little.
This was found to be the case by the author and the GRUYTER
and also by Beck.
Beck's table XII p. 42 shows this quite plainly.
This table sbows in addition that the differences between the Mg
and the hydrogen potentials are not constant and that, whilst the
hydrogen potential is becoming decreasingly negative, the magnesinm
potential changes in the opposite direction.
This means that Mg does not behave as a hydrogen electrode,
which would be the case if the magnesium surface was unchanged
and moreover was surrounded by a liquid layer saturated with
respect to the Me(OH),.
It is probable that this was the case with some solutions when
the H-ion concentration was very low, merely with the vigorous
stirring employed in these experiments. The certain conclusion from
Brck’s experiments is that, whether the surrounding liquid layer
was saturated with respect to Mg(OH), or not, the state of the Mg
bounding layer was changing with the hydrogen concentration.
By increasing the hydrogen concentration the magnesium bounding
404
layer became more basic that is to say the normal inner equilibrium
tended to be established.
Another phenomenon showed by Beck which has not yet been
considered is that the potential of Mg in MgSO, solutions alone
becomes more negative as the concentration increases.
Up to the present it has always been observed that a metal dipped
into dilute solutions of the corresponding sulphates or chlorides were
more early disturbed than in concentrated solutions of the same salts.
This was particularly the case with sulphates but also with chlori-
des; the phenomenon was namely with chlorides also very distinct,
though not so strong as in the case of sulphates.
This was always ascribed to the strong catalytic effect of Cl ions
and the less one of the SO,. Brck’s measurements now show us
that with magnesium not in inner equilibrium, SO, ions has also
a powerful effect.
Although the highest potential shown in the last table (—1.816 V)
is that of an active state of magnesium and the coexisting hydrogen
must have been in a strong state of formation (strong overvoltage)
yet this potential of Mg does not correspond with the inner equili-
brium, for Mg containing small quantition of mercury shows a still
higher negative voltage. This value was a maximum for 2 at
24°/, Hg.
Now Beck found that the compound between Mg and Hg richest
in the latter is Hg,Hg and that the electrolytes in equilibrium with
the various amalgams are practically free from mercury.
The influence therefore of the small quantity of mercury, under
discussion on the Mg electrode can only he an activating one for
the EK—X fig. on the Mg side must be as follows (fig. 4). From
this will be seen that if the influence of small quantition of mercury
has not an activating one, then the potential of the amalgamated
magnesium would have been less negative than that of the pure metal.
Thus activating by small quantities of mercury causes the true
inner equilibrium to be approached more closely.
Magnesium which has been activated by mercury showed a poten-
tial of —-1.856 Volts when placed in a solution containing 1 gr.
mol. of MgSO, per liter.
Even this potential is below the equilibrium value owing to the
disturbing effect, due to corrosion, but it is probable this is near
the true equilibrium potential.
It is evident, that the potential of pure magnesium in true inner
equilibrium must be more negative than that of the not disturbed
amalgam, containing 2 at °/, Hg., because the E—X diagram
405
(fig. 4) shows us, that such potential is rendered less negative by
increasing mercury content.
Fig. 4.
Finally we must consider a remarkable phenomenon to which
brief reference has already been made.
If we add a little HgCl, in an aqueous solution of MgSO, or of
MgCl, in which there is a magnesium electrode, there is an im-
modiate fine deposit of metallic mercury on the electrode whose
potential becomes /ess negative.
As follows from the formula
Mg, 2 Mg; + 29,
me + wh and 2 4, + Her Her
The precipitations of mercury proves that mercury ions penetrate
the surrounding liquid layer and that these on arrival combine with
electrons, thereby disturbing the heterogenous equilibrium with the
result that electrons and magnesium ions enter the solution.
It must also be observed that in consequence of the hydrolysis
in the magnesium salt solution to which no acid has been added
the magnesium electrode will contain dissolved Mg(OH), and will
consequenty behave inertly, so that by sending ions and electrons
into solution, the potential of magnesium will be altered in the
direction of that of the noble metals.
The experiment mentioned here is very important; it shows in
the first place that the magnesium electrode notwithstanding its non
406
equilibrium state and the dissolved Mg(OH), has still retained its
metallic properties. Still its properties have altered, for the precipitated
mercury is not able to activate it at once. An apparent explanation,
namely that the precipitated mercury does not dissolve in the
magnesium, is not correct.
For if we remove the magnesium electrode covered with fine
mercury, prepared as above, wash it with distilled water and than
dip it into pure MgSO, solution, the potential is at first less
negative, but it becomes increasingly negative, so that after a few
minutes it is stronger than that which attained before the negative
electrode was coated with mercury.
This is shown in the following table
Mg-potential in relation to a
Solution 1-N-calomel electrode
0,1 gr. mol. MgSO, p. liter | — 1.902 V.
to 150 ccm. of the above men-
tioned solution is added 5 ccm. of |
a saturated solution of HgCl, | — 1.740 V.
|
The magnesium electrode was then washed with distilled water and dipped
into a pure solution of MgSO4.
0.1 gr. mol. MgSO, p. Liter | — 1.898 V.
— 1.956 V. after 5 minutes
The above data show that the magnesium eleetrode, though its
surface is strongly disturbed by corrosion, has dissolved some mercury.
When we consider the great change brought about in a magnesium
electrode by corrosion it is no wonder that its other properties,
such as the power of dissolving mercury, are modified.
The explanation of the results in the above table now is clear.
The activating influence exerted by the small quantity of dissolved
mercury is not sufficient to decrease the retardation, exercised by
the Me(OH), in such a way, that the electrode becomes insensible
to the corrosive action of water and sublimate. When this solution
has been substituted by one of pure MgSO, the influence of the
sublimate disappears and that of the small quantity of mereury
becomes manifest.
It might be supposed at first sight that in the experiment under
consideration solid Mg(OH), depositing on the magnesium electrode
might diminish tbe contact between the magnesium and the mercury,
407
the fact is however that the contact between the magnesium and
the electrolyte is so good that mercury is separated over the whole
surface in a finely divided state, even whilst hydrogen is being
given off.
At the same time it is clear, that if we wish to get a magnesium
into as highly an active state as possible, it is desirable to make
its surface as poor as possible in Mg(OH), by first immersing it in
an acid solution and then amalgamating it.
Magnesium, activated in this way, contains more dissolved mercury
and even remains active in normal KOH, giving the high negative
potential of —1.97 volts in relation to the hydrogen electrode on
account of the low Mg-ionic concentration.
In a solution containing 1 gr. mol. MgSO, per liter this electrode
gave a potential of —1.85 V. in relation to the hydrogen electrode.
Amalgamation experiments have also been studied in detail for
Al and will be the subject of a next paper.
Amsterdam, Febr. 1923.
Laboratory for General and anorganic
Chemistry of the University.
Botany. — “A method of simultaneously studying the absorption
of O, and the discharge of CO, in respiration.” By D. 8.
Fernanpes. (Communicated by Prof. F. A. F. C. Went.)
(Communicated at the meeting of May 26, 1923).
Before entering into details, writer will briefly indicate, how the
apparatus works and what precautions should be taken, illustrated
by a simple diagram. (fig. |).
Fig. 1.
From p, a rubber sucking- and forcing pump, the air is pumped
as the arrows indicate. The air enters the respiratory vessel v at
the top, leaves it at the bottom and is dried in the wash-flask de
which contains concentrated sulfuric acid. From d, passing through
409
the glass cock &, (k, is then closed) it reaches the absorptiontubes
b,, 6, and 6,, containing baryta-water. On its way back the air
passes through the wash-flask d,, containing sulfuric acid like d,
and the control-baryta-tube e, after which it returns to p and
recommences its circular course.
In a subsequent observation 4, is closed and 4, opened, causing
the CO, absorption to take place in the tubes b,, b, and b,. The 6
absorption-tubes are fixed to a copper frame with clips. In order
to enable us to take more than two observations, without bringing
too many tubes in the glass vessel filled with water, which serves
as a thermostat, we should have two of these frames at our disposal.
If one has served its purpose, the connecting parts 1 and 2 are
turned up and rise above the water, where they may be loosened.
The whole frame with the 6 baryta-tubes is raised out of the vessel
and the other (the tubes of which are meanwhile cleaned and filled
each with 100 c.c. baryta-water) is put in. This exchange of frames
is brought about in less than a minute, but before taking further
observations with the newly-inserted baryta-tubes, we should wait
(according to the temperature in the thermostat) 10—15 mins. that
the tubes and their contents may adopt the temperature of the
thermostat. The apparatus works ventilating during this time in the
following way: Cock k, is closed, while #, and #, are opened. If
next the pump is set working, the air, leaving the vessel, can only
pass through 4#,, while at k, air is sucked in, after having first
been rid of CO, by means of wash-flasks containing strong KOH-
solutions (not represented in the fig.). There is another advantage
in the ventilating action of the apparatus. When in experiments of
long duration the observations are stopped in the evening, the
apparatus can continue to work ventilating the whole night. Conse-
quently the objects are not subject to oscillations of temperature
aud the next morning the experiment may at once be continued by
opening &, and closing &, and &,. In experiments, lasting 10—12
hours, it saves a great deal of time, to put the plants into the
apparatus the previous night, so that early in the morning the ex-
periments can begin at once. After the ventilation during the night
all CO, has been driven from the apparatus which may be demon-
strated by blind experiments.
When the outer-air is shut from the apparatus, and the pump is
set working, there is immediately produced an effective pressure on
the vessel, while the manometer m,, indicates a reduction of pressure.
If next k, is opened, the air pressed in the vessel is blown off. On
subsequent gradual closure of this cock, the pressure in the vessel
410
= 1. In the manometer m, the liquid is equally high in both limbs,
whereas m, indicates a greater negative pressure than before. The
broken equilibrium, generated by the action of the sucking-and
forcing pump in the closed system is apparently shifted by the
opening and closing of 4, in such a way, that in the respiratory-
vessel (accordingly on the plants) no effective pressure can arise.
As soon as there disappears O, from the closed system through
respiration, m, will indicate it at once. When however an equal
quantity. of O, is added at the same time, m, will remain at zero
and the atmospheric pressure is preserved in the vessel. At O the
oxygen, electrolytically produced in Z, enters the vessel. With the
aid of the resistance w the O,-development can be increased from
a minimum to a definite maximum. The intensity of the electrolytic
process may be thus regulated, that the O,-production keeps pace
with the O,-consumption.
By inereasing or reducing the resistance this equilibrium is soon
found and the manometer m, indicates whether this condition is
preserved. [t may happen (for instance by rise or fall of the respi-
ration-intensity), that for a moment there is a somewhat greater or
smaller supply of O, to the apparatus. In this case the height of
the manometer 7,, indicating as slight a difference as 0.1 cc.‚ may
at once be restored by means of the resistance, so that irregularities
in the O, supply, amounting to more than 0,1 ce. need not occur.
The hydrogen simultaneously produced by the electrolysis in Z
is collected in the burette du. After necessary corrections (in height
of barometer, temperature, water-vapour tension and pressure of
the water-column in the burette) the quantity of hydrogen received,
divided by 2, denotes the volume O,, brought into the apparatus
during the observation.
The manometer m, renders some other services. When a solution
of kalium-jodide (with some soluble amylum) is used, m, is a
sensitive test for the existence of spores of ozon. In the presence
of this gas for instance the germ-plants of Pisum sativum do not
develop normally, so that it is desirable to prevent ozon from
entering the respiratory-apparatus.
Finally we have in the manometer m, a suitable test whether
the desired temperature has been completely adopted by the whole
apparatus as well as by the objects. If the observations are started
before the whole has attained the desired temperature, the fluid
will at onee rise in the open limb of m,, which signifies, that
extension still takes place, while in consequence of the respiration
(O, absorption) an immediate decrease of volume should appear.
411
For determining the period of preheating therefore m, is of practical
interest.
The watervapour carried along from the vessel is combined in
d, so that dry air enters the baryta-tubes. The watervapour taken
from the lye is absorbed in d,. By measuring the increase of volume
in d, it may be found, how much water disappears from the lye
and the titration standard may be corrected accordingly. This eva-
poration from the baryta-tubes is very slight and amounted to cirea
2 ce. in experiments lasting 8 days, so that the correction may be
left out without scruple.
The manometer m, is filled with mercury and serves to indicate
the pressure, to be surmounted by the sucking and forcing pump,
needed to drive the air throngh the various liquids. A drop of
paraffine-oil on the mercury in the closed limb, prevents the origin-
ating of damaging mercury-vapours.
On the rubber-pump p taps a flat hammer /, moved vertically
by an electro-motor (not represented in the figure). This hammer
may be mounted higher or lower in order to regulate the capacity
of the pump and consequently the size of the bubbles. The speed
of the motor may be increased or decreased by means of a resistance,
with which the regulation of the number of bubbles is possible.
Size and number of bubbles are of course material to a good CO,-
absorption.
For an equable distribution of the air, entering the vessel, the
ebonite plates on which the plants lie, are brought into a slow
rotary movement by an axis. Accumulation of CO, in the vessel
(see further on) is excluded in this way.
The suction of the air into and from the vessel, causes the liquid
in m, to move up and down, which is not to be prevented. At an
effective regulation of the pump this movement may be kept so
slight, that it is no impediment. Indeed the motor may be stopped
at any moment, to Convince oneself whether the manometer is really
at zero.
The whole apparatus is fixed to the inside of a copper frame
and fits exactly in a glass vessel (contents about 45 L.), serving as
a water-thermostat. Electrical heating enables us to keep the tempe-
rature of the water constant to 0.03° C. The oscillations of tempe-
rature in the apparatus itself are slighter than those in the thermostat,
so that corrections relating to this, may be omitted.
If the apparatus is immersed in the water of the thermostat, it
may be easily tested with respect to air-tightness. For this purpose
air is pumped into the apparatus through £, and one watches whether
27
Proceedings Royal Acad. Amsterdam. Vol. XXVI.
412
any bubbles rise from the water. When the connections are made
with vacuum rubber-tube and glass to glass, leakages do not oceur.
IT.
Descriptions of the parts.
a. Sucking- and foreing-pump (tig. 2).
An air-tight pump, working for a long period without failing and
having a sufficient capacity, is easily constructed.
"The glass tubes 7 and w are connected by a piece of strong
rubber-tube p (about 15 ems. long and 2*/, ems. wide). Each of the
tubes 7 and « is provided with a valve, consisting of a piece of
vacuum-tube (1 em. long) 1, to which the end of a piece of valve-
tube 2 (about 3 ems. long) is glued on with solution. The other
end of the valve-tube is tightly tied with a string at 3; in the
valve-tube a straight lengthwise cut 4 is made, the two edges of
which meet, when the pump does not work. To prevent these edges
from sticking together afterwards, they have been rubbed in with
taleum powder. The glass tubes / and v fit in the rubber-tube p,
while the vacuumpieces 1 must also fit perfectly. How the pump
works, when the hammer A taps on it, is clear from the fig. 2.
b. The respiratory-vessel (fig. 3).
As in Kuyprr’s research’) here too is made use of a copper
cylinder 1. The experimental objects are on the ebonite plates ¢,
fixed to an axis a,. In each of the plates ¢ 25 round holes are
made in such a way, that germinating seeds of Pisum sativum
cannot fall through. On the plates ¢, moist cotton-wool is put, on
which the roots rest, in consequence of which there cannot occur
a deficiency of water. The axis a, is enlarged at the top, provided
1) Kuyper J: Recueil des Travaux Botaniques Néerlandais. Vol. VII. 1910, pag. 1.
413
with 4 teeth ¢a, just fitting into the four teeth ta, belonging to a
simular enlargement at the base of the axis a,. This steel axis a,
passes through a copper case / (soldered to the cover), in which it
| th
vil
ie B
H
i
—
¢ 2
i i
H H
H H
Á ;
H H
) i
A
H Y
A
| |
| |
2
my, H f
i /
H 4
H
| |
H : / vu
i f x Ú
Amite ss, J 4 f
H 4
/ men t
i Lp
4
a | il D
i A
Za
je
A
4,
be
Fig. 3.
fits exactly, but may be easily rotated. Round & there is a glass
cylinder g, closed at the bottom by the india-rubber-ring 7. The
axis a, is at the top tightly clasped in a copper tube &,, at the
bottom of which the hollow metal cylinder c is fastened, and at
the top the grooved wheel sv. By the oil in g the axis is closed
27*
414
off air-tight and leakage is impossible, because there never arise
great differences Gf pressure in the vessel. In the middle of the
loose part 6 there is a cavity, in which a, can rotate freely. When
sn is slowly rotated by a motor, a, will transmit this movement
by means of the teeth fa, and ta to a,, which causes the circulating
air to be equably distributed over the whole vessel, in consequence
of which the germplants are constantly surrounded by fresh air.
The necessity of ventilation in a cylindrical respiratory vessel (dia-
meter 15 cms., height 20 cms.) was immediately apparent from one
of the many test experiments. At a constant temperature of 20° C.
the O,-absorption caused in 50 mins. a height of 4 ems. on ‘the
manometer m,. Next a quicker circulation of 10 mins. duration
followed, causing an equal rise of the manometer as before in
50 mins. No other explanation of this could be found, but the
occurrence of a CO,-accumulation in the vessel. This was supposed
to be due to the fact, that the air entering at v/ passed by the
easiest route through the vessel to the exit vu, taking with it only
part of the CO,. When in consequence of a more rapid circulation
part of the accumulated CO, disappeared, this explained a sudden
greater rise of the manometer. As soon as the rotary movement of
the respiring objects, prevented all CO,-accumulation in the vessel,
there was indeed no abnormal rise of the manometer to be noticed.
It needs no argument, that not only with a view to oxygen-supply
and measurement, but also for other reasons, the CO, due to re-
spiration, should be directly removed. With a CO,-accumulation in
the vessel, a volumetric determination of the vanished quantity of
QO, is no more possible. Besides in this case part of the plants gets
into an atmosphere full of CO, and deficiency of O, will soon cause
intramolecular respiration.
It seems to me, that in the respiratory apparatus after the model
given by Prrerrer and Dermer and used e.g. by Kuyper, little or no
attention has been paid to the error which may be committed,
when in a respiratory vessel as described in this paper, no perfect
ventilation is provided for.
The loose bottom 6 is provided with a marginal groove, containing
a rubber-ring. The handle be bears in its middle a screw s, which,
when turned up, presses on ve and by doing so presses the lower
edge of the vessel tightly in the groove with rubber-ring.
In the cover of the vessel is, besides the aperture o to admit
oxygen, also a pierced rubber-cork through which a thermometer
th passes.
c. Fig. 4 gives a representation of the drying-tubes and the
415
controltube. Cock 1 serves for filling, coek 2 for emptying and
cleaning.
d. The absorption-tubes are fastened to a copper frame (fig. 5).
As with a view to preversing a constant temperature
; the size of the thermostat cannot be chosen at will,
straight absorption-tubes (length 25 ems., width 3 ems.)
si are more suitable than Perrenkorgr or WINKLER-tubes.
When baryta-water is chosen for combining with CO,
(21 grammes of bariumhydroxyde + 3 grammes of barium-
chloride in 1 L. of water), the absorption is only complete,
when the air passes through 3 of those tubes (each
containing 100 ee. lye). Each frame of 6 tubes therefore
can only serve for two observations. The tubes end at
the base in thin open pieces, which may be plugged
by rubber stoppers. At the top they are closed by rubber-
corks 3 ems. thick. In each cork there are three holes,
Fig. 4. two of which serve for the inlet- and exhaust-tubes,
while the third, which serves for filling can be plugged by a little
massive glass bar. The tubes are connected with vaeuum-rubber
416
tube, just as all other connections in the apparatus are made. There
was no sign of any CO, diffusion inward from the water of the
thermostat through the rubber-connections and corks, nor of an
Q,-absorption through the rubber. Blind experiments, lasting 24 hours
gave no measurable change of titration standard of the lye at tempe-
ratures between 20° and 30°C., while the manometer m, remained
at zero throughout that time.
e. The oxygen-supply and measurement.
In order to prevent ozon-formation, a 10°/, natronsolution is to
be preferred to diluted sulfurie acid for the electrolysis,
In fig. 6 C is a glass eylinder with natron-lye in which the
platina-eleetrodes p, and p, are placed. By means of thin platina-
wire these electrodes are fastened by melting in the glass-tubes 1
and 2 respectively. The tubes 1 and 2 pass through caoutchouc-
‚Fig. 6.
417
corks, fitting exactly in the wider tubes w and z (open at the
bottom) and are filled with some mercury. By means of a resistance
we the intensity of the current can thus be regulated, that the
amount of the electrolysis can reach the desired extent. Thus it is
possible to keep the oxygen-development, occurring in the tube z
at the electrode p,, in balance with the O,-consumption of the
respiration. As a resistance (we) a glass basin with water, in which
the electrodes w, and z,, is quite satisfactory for this purpose. By
moving w,, which is fastened to a stand, along a sloping board,
not only the distance w,—z, is made smaller or larger, but this
electrode also goes more or less deep in the water.
The O, formed in z is in open connection with the manometer
m, and the respiratory-vessel. The tube z really is likewise a mano-
meter, in which the lye will be equally high as in c, when the
quantity of O, developed is equal to the quantity disappearing in
the apparatus; m, however, as already mentioned, is necessary to
control the ozon-formation.
For receiving the hydrogen, formed at the electrode p, in the
tube ww, the burette bu serves, which gives accurate readings to
0.1 ce. This burette ends at the top in a bent glass tube 3, provided
with a glass cock & At the bottom the burette has a narrow
aperture, while not far from this a lateral tube has been fitted on,
forming a connection with the tube w. When the burette is placed
in such a way, that the bottom aperture lies just below the water-
level in the thermostat, it is impossible, that while water is flowing
out, air is ascending in the burette at the same time. Filling the
burette with water from the thermostat is done by closing 4,
opening & and sucking at the tube 3. When after filling & is closed
and &, open, the only reason why water should flow from the burette,
is the formation of hydrogen in w, which rises in the full burette
as bubbles. The formation of the first hydrogen-bubbles in the burette
requires a little effective pressure, which is shown by the fall of
the fluid in the tube w. This effective pressure, which remains
constant during the emptying of the burette, should exist before the
observations begin, lest the first reading should give a too small
figure. This error is prevented, when some minutes before the
experiment commences — when the apparatus still works ventilating —
the electrolysis is made to take place, till the first bubbles vise in
the burette. In case that, during one and the same observation, the
burette is filled several times, the sucking up of the water should
occur very slowly and equally, lest the hydrogen, which is in the
connective-tube between 4, and the burette, should be sucked in
418
with it. If the water is sucked cautiously into the burette, the
effective pressure once made is preserved in 2.
Another error arises, when the burette is exposed to oscillations
of temperature in the laboratory. In that case not only in w, but
also in z and m, falls and rises occur, which are not due to ab-
sorption of oxygen. This may be prevented by keeping the burette
likewise at a constant temperature, which may be attained as follows.
By means of a metal sucking- and forcing-pump zp (likewise
fastened to the copper frame, to which the whole apparatus is
fastened) water from the thermostat is pumped up with great
rapidity into a wide glass cylinder wa, which contains the burette.
The water enters wa at the bottom and is led back to the thermo-
stat at the top through the tube af. Even at high temperature (50°,
55° C.), the temperature in the burette is kept equal to that of the
water in the thermostat in this way.
f. The regulation of the temperature principally corresponds to
the one deseribed by Rurerrs') and Conen Stuart’) and is an
imitation of apparatus, used in the van r Horr-laboratory at Utrecht.
The heating-apparatus » (fig. 7) consists of a copper case, sur-
mounted by a metal tube, rising above water. In v is paraffine-oil,
electrically heated by a nickel-chrome-wire, wrapped round a piece
of mica.
Thermoregulator 7, stirring-apparatus 7 and v, are close together
in an open glass cylinder c, resting on legs in the centre of the
thermostat g. To prevent all influence of vibration in the height of
the mereury, the thermoregulator is hung from the ceiling on a
steel spiral-spring, according to the method Morr.
The method described above gives no new principle, with respect
to the CO,-determination. We have chosen the simple and always
trustworthy baryta-method, which need not be further described
here. On account of the insertion into a closed system, the various
parts were subjected to some alterations in shape, which however
have nothing to do with the principle of the baryta-method.
The problem of oxygen-supply, ever yielding many difficulties,
could be satisfactorily solved. Compared with the methods’) already
existing, the following advantages and simplifications are achieved:
1) Rutgers, A. A. L., Recueil des Travaux Botaniques Néerlandais. Vol. IX,
1912, pag. |.
2) CoHEN Sruart, Recueil des Travaux Botaniques Néerlandais. Vol. XIX,
Livraison 2. 1922.
3) Cf. Krom: “The respiration exchange of animals and man. LoNemans,
Green and Co., London 1916”.
419
a. the decrease of pressure and oxygen-content in the apparatus
is reduced to a minimum.
6. the place of the consumed QO, is at once taken by pure O,,
without first passing a stop-valve, and may directly be controled.
c. an oxygen-bomb or other reservoir may be omitted.
The apparatus has been constructed by Mr. P. A. pr Bourne,
amanuensis at the Botanical Laboratory at Utrecht. I am greatly
indebted to him, not only for the way, in which he performed his
task, but also for introducing some clever improvements.
Utrecht, May 1923. Botanical Laboratory.
Physiology. — “A new form of correlation between organs.” By
Prof. H. J. HAMBURGER.
(Communicated at the meeting of May 26, 1923).
Thus far we were acquainted with two forms of cooperation
between organs. As to the eldest known form, here the central
hervous system plays an important role. If any one pricks my
finger unexpectedly with a needle, | immediately withdraw my
arm; a cooperation has taken place between the skin of the finger
and the museles of the arm, and well by means of the spinal chord.
Here we have to deal with a reflex.
Some years ago we got acquainted with a second form of corre-
lation between organs; this one is not effected by means of nerves,
but here the bloodeurrent is the mediator of the cooperation. For
instance, the glandula thyroidea produces substances, which are
carried through the body by the bloodeurrent and influence the
metabolism and growth of distant organs.
That nerves here don’t play an essential role appears from the
fact, that the glandula thyroidea still exerts its influence, even when
it is detached from its nerves and transplanted to another part of
the body.
Now, in the last years experiments, performed in our laboratory,
have clearly demonstrated a third new form) of correlation between
organs. The starting point of these researches, carried out by
Dr. R. Brinkman, Miss E. van Dam and Dr. L. JeNDRASSIK, was the
following experiment of O. Loew: in Graz. The vagus nerve of an
isolated frog’s heart, which is filled with a salt solution, is for some
time stimulated so that the heart stops its beat. Then the content
of the heart is removed and transferred into another frog’s heart,
which was isolated in the same way. Then the well-known pharma-
1) See my lecture at the opening of the Biological Buildings of Me. Gill’s
University in Montreal (Canada) in September 1922. See also: H. J. HAMBURGER.
The increasing significance of permeability problems for the biological and
medical sciences; the Charles E. Dohme Memorial Lectures. First Course, 10, 11,
12 October 1922, delivered in Baltimore; printed in: Bulletin of the Johns
Hopkins Hospital, June 1923.
421
cologist saw, that the second heart often showed slower contractions.
Experiments with the sympathetic nerve gave analogous results.
Now the purpose of our experiments was in the first place to
eontrol the results of Lonwi’s researches under more physiological
conditions.
In the vena cava of a frog A a glass tube is inserted and in
this way a suitable saltsolution is conducted through the heart. A
similar small tube is introduced into the aorta. Then we see, that
the saltsolution will leave the heart in a rhythmical manner. If
then the fluid, leaving the heart, is led to the vena cava of another
frog B, the fluid will run through the heart B, and after leaving
it by the aorta of this second frog, it may be taken up again by
the vena cava of the first frog A. Thus we obtain a circulation of
saltsolution through both frog’s hearts. This method of socalled
“crossing circulation” was first introduced by Prof. J.C. HEMMETER.
Now, if the sympathetic of the first frog A be stimulated electric-
ally, causing acceleration of the heart beat of this frog, it can be
observed that already after a few seconds, the heart rate of the
second frog B is also quickened, although the sympathetic of this
animal has not been stimulated. How to account for the acceleration
of the second heart? Evidently in no other way than by assuming
that in the first heart A, in virtue of permeability of course, sub-
stances were liberated which had a similar effect upon the second
heart as if this had been directly stimulated. I shall presently come
back to the probable nature of these substances.
How it is possible that substances, liberated by a physiological
action of an organ, here the heart of the frog A, may also stimulate
the same organ of the second animal B, [ shall not discuss here.
It is sufficient to say, that there is an analogy between this case
and the secretion of saliva. If we allow a salt solution to percolate
through the salivary gland, as J. Demoor has demonstrated some
years ago, no saliva is secreted. However it does occur if a small
quantity of saliva is added to the saltsolution. The product formed
during the activity of the salivary gland is, it seems, a stimulus
again to further secretion of saliva. The substances, formed in the
stomach during conversion of protein, excite gastric secretion. It is
therefore not strange that the substances, liberated in the first heart
during stimulation of the sympathetic, should have a stimulating
action on the second heart.
Dr. BRINKMAN and Miss van Dam made yet another experiment
that in a still more convincing and striking manner demonstrates,
that the transmission of stimuli can take place by means of fluids,
422
in other words that there exists a humoral transmission’), I say
“in a still more convincing manner’, for by the just mentioned
experiment the remark could be made, that with the movement of
the second heart hydrodynamic influences might have played a rôle.
For this reason for the second organ not the heart of the frog B
was taken, but the stomach of this animal.
It is well known that stimulation of the sympathetic nerve is
followed not only by an acceleration of the heart beat, but also it
slows, even inhibits the spontaneous movements of the stomach.
Now the question arose: if the fluid of the stimulated heart of
frog A is transferred into the arteria gastrica of the frog B, will it
then cause the spontaneous movements of the stomach of this last
frog to grow slower, even to stop? This proved to be the case, as
the experiments of Dr. BRINKMAN and Miss van Dam showed us.
In other words, on sympathetic stimulaiton of the first heart sub-
stances were liberated which influenced the movements of the stomach
in an inhibitive way.
Analogical phenomena as occur in stimulating the sympathetic
nerve could be observed by stimulation of the vagus nerve.
As it is well known, stimulation of this nerve affects the rate of
the heart beat and also influences the strength of the contractions
of the stomach, but in an antagonistic sense. Stimulation of the
vagus slows the heart, but causes the contractions of the stomach
to become more powerful, contrary to what happens when the
sympathetic nerve is stimulated. Now the experiment was repeated
by crossing the circulation of the beart of the first frog with that
of the stomach of the second frog; in other words, the salt solution
coming from the heart of the first frog, is conducted to the stomach-
circulation of the second frog. On stimulating the vagus of the first
frog, the heart slows its beat and when the solution has passed
through this heart and reached the stomach of the second frog,
this organ shows typical vagal contractions, though the vagus of
frog B has not been stimulated electrically. From this we may
infer that stimulation of the vagus of the first frog sets free in its
heart vagus-substances, which may cause the stomach of the second
frog to contract, as if its own vagus nerve had been directly
stimulated.
We are therefore in presence of two kinds of substances liberated
by the vagus and sympathetic nerve respectively, which may be
called vagus- and sympathetic substances.
IR. BRINKMAN und Frl. E. v. Dam, Pfliiger’s Archiv. Bd. 196, S. 166, 1922.
423
That really such substances exist, could be directly proved by the
fact that the salt solution, leaving the heart after stimulation of the
vagus, contains substances, which lower the surface-tension of the
original salt solution, socalled capillary-active substances. On the
other hand we find that the surface-tension of the salt solution,
coming from the heart after the sympathetic nerve has been stimulated,
is slightly increased"). Further it appeared that the vagus- and
sympathicus-substances were able to neutralize each other in capillary-
active sense, i. 0. w. they were able to neutralize each other’s
influence on the surface-tension.
I shall not euter here into further particulars. It is an established
fact now, that as an effeet of stimulation of the vagus nerve, a
liberation of vagus-substances takes place, and that on stimulating
the sympathetic nerve, sympathetic-substances are set free. However
the nature of these substances has not yet been determined ; perhaps,
at least with the vagus-stimulation, we have to do with cholin-
compounds, which cooperate with the potassium.
As for the method to determine the surface-tension of very small quantities of
fluids, we refer to two articles, which appeared last year?). There it is shown
that a very simple apparatus will do for this purpose. By means of a torsion
balance, well-known to the clinicians, the force is determined which is necessary
to pull off a small platina-ring from the surface of the fluid which is to be
examined.
The experiments discussed here, give rise to many questions. So
the clinician will think of the bearing of these results on the nature
of vagotonia and sympathicotonia and will ask himself under whieh
conditions an excess of vagus- and sympathicus-substances will exist
in the circulation and influence different organs; and also he will
put himself the question how it will be possible to make this surplus
harmless for the body.
The physiologist will ask himself whether the latent period and
the after-effect in vagus-stimulation can be explained by the time,
which is necessary for the liberating and the disappearing of the
vagus-substances; further he wants to know whether the vagus-
substances are specific for one and the same animal. And what will
be of interest both for the physiologist and the clinician is the
question: can we observe the same phenomena, seen in the frog,
1) See the article of Dr. BRINKMAN and Miss van Dam, in the Journal of
Physiol., still to appear.
2) R. BRINKMAN und Fr]. E. van Dam. Münch. Med. Wochenschr. 1921. S. 1550.
R. BRINKMAN, Arch. Néerl. d. Physiol. VII 1922, p. 258.
R. BRINKMAN und Frl. E. van Dam VIII, 1923, p. 29.
424
also in warmblooded animals? With this question Dr. L. JENDRASSIK
has occupied himself very recently. The results obtained untill yet,
can be summarized in a few words. If the surviving heart of a
rabbit is perfused with a suitable salt solution, and we stimulate
the vagus nerve, then the liquid, leaving the stimulated heart is
able to accelerate in a high degree the contractions of an isolated
piece of gut, taken from the same animal.
I cannot enter into these researches on this place. Dr. JENDRASSIK
will describe them in a short time in the Biochemische Zeitschrift.
Here we will only point out that the experiments proved, that on
stimulation of the vagus nerve not only in the heart of coldblooded
animals but also in those of warmblooded animals substances are
produced, which are able to influence other organs in the very same
way, as if the vagus of those organs were stimulated by an electrical
current. Here the gut proved to be the most suitable object for the
researches.
Further I might draw the attention of the readers to three remark-
able facts. In the first place it appeared that an extract of the
atrium of a rabbit’s heart in saltsolution was also able to accelerate
the contractions of the isolated piece of gut. This experiment was
made in considering that it would be very probable, that the atrium
still contained vagus-substances, which were formed there during
the life of the animal. Secondly it appeared that if atropine, which,
as is well known, inhibits the influence of vagus-stimulation, was
added to the active extract, this was turned into an unactive one,
i.o.w. then it had no more influence on ihe movements of the gut.
In the third place it was found, that the extract of the ventricle-
muscle of the heart has a sympathetic effect on the movements of
the gut instead of a vagus-influence.
The experiments on warmblooded animals described above, were
all performed in a room of body temperature.
Sau WM ALR:
Thus far we have been acquainted with only two forms of correlation
between organs, one, the eldest, established through interference of
the central nervous system in cases where a quick response is
needed (reflexes). The second form comes into play where slow
processes are concerned; it may be exemplified by the intluence of
the glandula thyroidea on metabolism and growth. For the formation
of hormons the influence of the nervous system is not needed,
neither for the transport by the bloodeurrent. In the third new form
425
of correlation the action is neither quick nor slow; it is to be seen
at work where functions, holding the medium between these two,
are concerned. The essential thing here is, that by nervous stimula-
tion substances are set free, which are conducted to other parts of
the body.
There is much evidence to lead to the belief that the three forms may finally by
reduced to one, but I cannot enter into this here. | have spoken about this possibility
already in one of my Herrer-Lrorures, delivered in New-York in October 1922.
It may be of importance to lay stress on the fact that the forma-
tion of vagus- and sympathicus-substances is not only postulated,
but that it is proved directly in a physico-chemical way.
There is no doubt that an analogous correlation between organs
as described here for heart and stomach and for heart and gut will
be established also between other organs’). We face here a wide
field of new researches; we are only in the beginning.
May 1923. The Physiological Laboratory of the
University of Groningen.
1) So it appeared very recently in our laboratory, that when stimulating the nervus
vagus and the nervus sympathicus of the heart, substances are set free, which
influence the Jwmen of the small urteries of another animal. (Note after the
correction).
Chemistry. — “The Synthesis of some Pyridylpyrroles.” By Dr.
J. P. Wisaur and Miss ErisaBETH DINGEMANSE. (Communicated
by Prof. P. van ROMBURGH.)
(Communicated at the meeting of March 24, 1923.)
In the course of the researches on the structure of the natural
alkaloids, several of these vegetable bases have been prepared by
synthesis. In other groups of vegetable substances, investigators have
not only succeeded in building up the substances occurring in nature,
but also closely allied bodies were obtained synthetically. In the
group of the sugars, e.g., a number of monoses have been obtained
which do not oceur in the vegetable kingdom, but which are
isomeric with or closely related to the sugars found in nature. Our
knowledge of the chemical and biochemical properties of the monoses
dias been greatly improved by these synthetic researches. It seems
not devoid of interest to try and build up an isomer of a natural
alkaloid, in order to examine afterwards in what respect the iso-
meric substance is distinguished from the natural alkaloid, especially
with regard of physiological and biochemical properties.
Keeping this end in view we will try to build up an isomer of
nicotine.
‚In his synthesis of nicotine Picrer started from g-amino-pyridine;
this substance was heated with mucic acid, through which N (g-
pyridyl)-pyrrole (I) was obtained. At high temperature N (3-pyridyl)
pyrrole undergoes an isomerisation, in which C (s-pyridyl)-pyrrole
(II) is formed:
CH CH = CH CH ore, a
HCS eK | i EL No 20 nen
| oi. \ch=cH erase nd
HC N/CH HC NY CH H
N N
IT.
Pictrt and Cr&pinux') give the above structure to this C (8-pyridyl)
1) Ber. d. deutsch. chem. Ges. 28, 1904 (1895).
427
pyrrole, in which it is, therefore, assumed that the pyridine nucleus
is united at the «C atom of the pyrrole nucleus.
In how far this assumption is justified, will be discussed after-
avards. The preparation of these substances did not offer any special
difficulty; on the other hand, the conversion of C (pyridyl) pyrrole
(Il) into the methyl derivative, nicotyrine (III), was difficult to realize:
a en a OGL.
HZ \ nee He HEA von ba
aa CH De HC JCH ENG
XN CH, Ng CH,
UI Iv.
When it is tried to methylate the pyrrol derivative at the nitrogen
atom by treating the potassium-compound with methyl-iodide, there
is also a molecule of methyl iodide combined with the nitrogen
atom of the pyridine nucleus, so that the iodine methylate of nicot-
yrine is formed, from which afterwards methyl iodide must be
split off.
Prerer and Rotscny') have obtained but very little of the nicot-
yrine by this method. For the continuation of his experiments Picrer
has, therefore, made use of a nicotyrine preparation which was
prepared by oxidation from nicotine (IV) by Brav’s method.
A similar procedure is of course impossible in our case. In the
end Picrer and Rorscuy have succeeded in reducing nicotyrine to
nicotine by an indirect way through making use of iodine and
bromine substitution products.
Hence if this synthesis is repeated, starting from «-amino-pyridine,
an isomer of the nicotine can be built up, in which the pyridine
nucleus is substituted at the «-place.
As a-amino-pyridine is at present an easily accessible substance,
it seemed not impossible to obtain sufficient quantities of all the
intermediate products, so that it may also be expected that it will
be possible to prepare so much of the final product that its properties
can be properly studied.
§ 2. The preparation of N-(a-pyridy!)-pyrrole.
For the preparation of N-(@-pyridyl)-pyrrole we have heated 25 gr.
of a-amino-pyridine with 28 gr. of mucie acid. First the salt of
1) Ber. d. deutsch. chem. Ges. 37, 1225 (1904).
28
Proceedings Royal Acad. Amsterdam. Vol. XXVI.
428
mucie acid with 2 mol. @-amino-pyridine is formed. At a tempera-
ture of about 140° this salt begins to decompose: with separation
of water and carbon dioxide the pyrrole derivative is formed while
1 mol. amino pyridine is split off. Hence a distillate is obtained
which contains besides water, the required pyrrole derivative and
amino pyridine. We have subjected the reaction product to fractio-
nated distillation at 15 m.m. pressure. The first fraction of 104—
130° is chiefly «-amino pyridine: At 140—145° distills a liquid, of
a slight yellow colour, which solidifies to a white crystalline mass
on being cooled in ice. The melting-point of these erystalls is
Went.
This substance is N-a(pyridyl)-pyrrole, to which the following
structure formula (V) applies.
CH
Ho7\ cH
v HC =CH
He Jo nt |
NZ Nuc = CH
nb
The freshly distilled N-(«-pyridyl)-pyrrole is a colourless liquid,
which, however, assumes a dark colour after some time. The boiling-
point at 760 mm. lies at 260—261°.
This substance is sparingly soluble in cold water, volatile with
water vapour, and readily soluble in all organic solvents. A pine-
chip moistened with hydroehloric acid is coloured red-violet by
the vapour of N-(@-pyridyl)-pyrrole; with a hydrochlorie acid
solution of dimethylaminobenzaldehyde there arises a red-violet
colour, which later on changes into a dirty green. These colour
reactions are considered as characteristic of pyrrol derivatives. By
potassium permanganate this compound is rapidly oxidized already
at the ordinary temperature.
The values of 19.58°/, N and 19.34°/, N were found for the
nitrogen percentage of this preparation, the calculated percentage
for C,H‚N, being 19.44". We have prepared a picrate of this
substance which melts at 143°. We obtained the iodine methylate
of the N (a-pyridyl)-pyrrole by heating it in'a sealed tube at 100°
with the calculated quantity of methyl iodide. The reaction product
was recrystallised from aleohol: yellowish white prisms, melting-
point 141°—142°.
The isomeric N (s-pyridyl)-pyrrole prepared by Picrer and
Crépreux has been described by these investigators as a liquid with
429
a boiling-point of 250.5—251° at 730 mm., which does not solidify
at —10°.
The yield of N (e@-pyridyl) pyrrole was in our experiments from
7 to 8 gr. out of 25 gr. of «-aminopyridine.
We found, however, that there is formed another substance
besides this pyrrole derivative in the reaction between mucic acid
and amino pyridine. During the distillation of the reaction product
a liquid went over at 170°— 190° and 15 mm., which erystallized
at room temperature. After reerystallisation from aleohol this
substance had a melting-point of 95°, and appeared to be «-'-
dipyridyl amine. The formation of this compound during the heating
of the mucic acid salt of amino pyridine seems to be analogous to
the formation of diphenylamine from aniline and hydrochloric aniline.
. We have actually obtained «-e-dipyridy! amine by heating
equivalent quantities of e-amino pyridine and the bydrochloric acid
salt of this base in a sealed tube for two hours at 300°. We hope
to return to this reaction on another occasion.
§ 3. The conversion of N(a-pyridy!)-pyrrole ito two isomeric
C (a-pyridyl)-pyrroles.
It was found long ago by Ciamician') and his collaborators that
the N-derivatives of pyrrole can be transformed into C-derivatives by
the action of high temperatures.
CramicraN and Magnacui’) heated N-acetyl pyrrole in a sealed
tube at 250—280° and found that part of the starting material was
changed into pyrryl methyl ketone:
HC—CH HCS CH
(hy fe
HC CH = HC €.COCH;
a NVA
N. COCH, NH
That the acetyl rest actually oecupies the «-position in the pyrrole
nucleus, results from the observation that the bromation product of
this pyrryl methyl ketone yields the imide of di-bromomaleic acid by
oxidation with nitric acid *). Also some other pyrrole derivatives, in
which an acylrest is combined with the nitrogen atom, were trans-
formed into «-pyrrylketones on heating.
It was found later by Picrer and his collaborators that N-methyl
pyrrole, N-phenyl-pyrrole, and similar substituted derivatives of
1) Cf. Cramrcran. Ber. d. deutsch. chem, Ges. 37, 4200 (1904).
2) Ibid. 18, 1828 (1885).
3) Cramician and SiLBeR. ibid. 20, 2594 (1887).
28*
430
pyrrole can be transformed into C-derivatives by distillation throngh
a red-hot tube.
In all these intra-molecular arrangements only one C-derivative
was found, whereas it would be theoretically possible that two
isomeric pyrroles would be formed, since the hydrocarbon rest
might be united at the «- or at the g-carbon atom of the pyrrole
nucleus.
From N-methyl! pyrrole the «-C-methyl pyrrole was obtained by
Picter. The structure of «-C-methyl pyrrole had already been deter-
mined by Zanetti, by converting this substanee into the dioxime of
levulie aldehyde.
Picter and Créprikux assume on grounds of analogy that in the
C-phenyl pyrrole which they obtained from N-phenyl-pyrrole, the
phenylgroup is united at the «carbon atom of the pyrrole nucleus,
and that the same thing holds for the C-pyridyl pyrrole (ID), which
they obtained from N-(pyridyl)- pyrrole (I). A direct experimental
evidence, for this view was not given.
As regards Prcrer and Crépirox’ B-pyridyl-e-pyrrole, the structure
which these investigators assign to it, is undoubtedly supported by
the fact that they have obtained nicotyrine (III) from this g-pyridyl
pyrrole, as the structural formula ([V) of nicotine has been made
very probable by Pinner’s researches.
We found however that two isomeric C-pyridyl-pyroles are formed
in the transformation of N(a@-pyridyl) pyrrole, one of which melts
at 93° and the other at 132—132.5°. This reaction must be
represented by the following scheme:
CH
HCZ\CH HC—CH
shit be ™
CH aad N Sn
HCZ\CH ay NH
(0) EN SCH
HON ZON \ da
HC HC/Z\ CH
ere
~ HO\/C————C—_CH
N oll Cae
HC CH
Ww
NH
To which of our isomers formula VI applies and to which
formula VII should be assigned, has not yet been established. It
431
will not be very easy to decide this point. In former researches it
has been tacitly understood that in the transformation of a N-deri-
vative of pyrrole in a C-derivative, it is always the «-compound
that is formed. In consequence of our observations the validity of
these conclusion has become doubtful.
We shall now give a short description of our experiments on
these reactions.
In the first place we have determined the most favourable
temperature for the transformation of N(e-pyridyl) pyrrole into
the C(a-prridyl) pyrroles, as in Picter’s papers the reaction tempe-
rature is only vaguely indicated as “heated to redness” or ‘faintly
red-hot”. The best procedure appeared to be as follows:
25 gr. of N(a-pyridyl)pyrrole are distilled through a glass tube
filled with pieces of pumice, which is heated at 670°—690° C. in
an electrical oven. Part of the substance is decomposed, which
shows itself in the formation of dense white vapours. The distillate
consists of a black liquid, which soon solidifies at room temperature.
This reaction product was distilled with steam, in which a white
erystalline substance passed over, which was filtered off. This
substance appeared to be very sparingly soluble in cold water. The
erude product melted at 84°; after recrystallisation from a mixture
of benzene and ligroine the melting-point is 90°. The yield of this
substance was about 12 gr. The aqueous distillate contained
only very little unchanged N(e-pyridyl) pyrrole. A second substance
remained behind in the distillation flask, which is not volatile with
water-vapour, and which after recrystallisation from hot water melts
at 132—132.5°.
Properties of the pyrridyl-pyrrole melting at 90°.
This substance is obtained from benzene, to which some ligroine
has been added, in hard, very shiny, colourless octobedrical crystals.
We found 19,41 °/, for the nitrogen content; 19,44°/, was calculated
for C,H,N,.
This substance is readily soluble in alcohol, ether, chloroform
acetone and benzene; less easily in hot water and ligroine, very
little in petroleum ether. These solutions exhibit a blue fluorescence,
except the aqueous and alcoholic solution. A solution of 3-pyridyl
a-pyrrole also shows fluorescence according to Picret and Cripievx.
Our pyrrole derivative does not give a colour reaction with a
pine-chip moistened with hydrochloric acid; with a hydrochloric acid
432
solution of dimethyl-aminobenzaldehyde there appears, however, a
red-violet colour.
Metallic potassium acts on this substance: a potassium compound
is formed, as is to be expected. For this purpose we dissolved the
substance in toluene, and let the potassium act at the boiling tem-
perature of the solution. At first the action proceeds pretty rapidly,
but it soon slows down, so that the heating must be prolonged.
The potassium compound was deposited as an insoluble yellow-
brown powder.
In order to ascertain the structure of the C-(«-pyridyl)-pyrrole,
we have oxidized two grammes of this substance with potassium
permanganate in sulphuric acid solution. The oxidation takes place
very readily at the ordinary temperature. Out of the reaction product
we have isolated the characteristic violet copper salt of picolinic
acid, and from this salt we freed the picolinic acid itself by addition
of sulphuretted hydrogen. The picolinic acid thus obtained was
sublimated in order to purify it. The sublimated preparation melted
at 134°.2, while we found 136°.8 for the melting-point of picolinie
acid obtained by oxidation of picoline. The melting-point of the
mixture of these two preparations was 132.5°—133°. The nitrogen
percentage of our preparation that melted at 134.2, was 11.25 °/,
(calculated for picolinie acid 11.38 °/,). In spite of the slightly too
low melting-point there is no doubt of the identity of our prepara-
tion; the characteristically crystallizing platinum salt had exactly
the same appearance as the platinum salt of the picolinie acid
prepared from picoline. It appears from this that in the pyrrole
derivative melting at 90° the pyrrole nucleus is united to the «-C-atom
of the pyridine nucleus.
We have prepared a picrate from this pyridyl pyrrole, which
was obtained after reerystallisation from alcohol as fine, yellow
needles of the melting-point 227—228°.
We have prepared the iodine methylate of the pyridyl! pyrrole
melting at 90° by heating this pyrrole derivative in methyl alcoholic
solution with an excess of methyl iodide at 100° for three hours.
After evaporation of the solvent and of the superfluous methyl iodide
the reaction product was recrystallized from methyl alcohol; in this
way yellow-brown hard prism-shaped crystals were obtained, which
melt at 148°. We found 9,6°/, for the nitrogen content, and 44.7 °/.
for the iodine content. The calculated values for CHN, J are
N: 9,73 °/,; J: 44,37 °/,. This substance has, therefore, been formed
bv the addition of one molecule of methyl iodide; the group
CHA is combined with the nitrogen atom of the pyridine nucleus.
433
Properties of the pyridyl-pyrrole melting at 132° 5.
This substance, which as we already remarked, is not volatile
with water vapour, and is separated in this way from the isomer
melting at 90°, crystallizes from alcohol or benzene in leaves joined
to rosettes; from hot water long needles are obtained.
This base is readily soluble in alcohol, ether, acetone, chloroform,
and benzene; not so easily in ligroine and hot water, very little soluble
in low-boiling petroleum ether. As far as the solubility properties
are concerned, there is, therefore, a close agreement with the isomer
melting at 90°. The ethereal solution shows a blue fluorescence.
We found 19,34°/, and 19,62 °/, for the nitrogen content (calculated
for C,H,N,: 19,44°/, N). This base does not give a colour reaction
with a pine-chip moistened with hydrochloric acid; with a hydro-
chlorie acid solution of dimethylamino-benzaldehyde there appears,
however, a cherry-red colour, which has changed into blueviolet
after a day.
That this substance, too, possesses a pyrrole nucleus, appears again
from the behaviour towards metallic potassium. The base was
dissolved in toluene and the calculated quantity of potassium was
added. The potassium dissolves with vigorous generation of hydrogen;
the reaction is much more rapid than with the isomer of melting-
point of 90°. The potassium compound is deposited as a white powder.
We have oxidized the pyridyl pyrrole of melting-point 182.5 in
the same way with potassium permanganate in an acid solution, as
we already described for the isomer of melting-point of 90°. From
the pyridyl pyrrole melting at 132°.5 we likewise obtained picolinic
acid, which melted at 136°.8 after sublimation, and was identical
with the picolinie acid from picoline.
It results from these experiments that the two substances that
are formed from N-(«-pyridyl)-pyrrole, are two isomeric C-(a-pyridyl)-
pyrroles, which are distinguished in this that the pyrrole-nucleus in
one substance is substituted at the «-place, and in the other substance
at the @-place, as is expressed in formulae (VI) and (VII).
We may also mention that in this reaction chiefly the isomer
melting at 90° is formed; the quantity of the isomer melting at
132°.5 is small.
§ 4. The methylation of the C-(a-pyridyl)-pyrole of melting-point 90°.
The next step in the synthesis of a substance isomeric with nicotine
is that the hydrogen atom of the imide group of the pyrrole-nucleus
is replaced by the methyl rest.
434
The difficulties experienced by Picrer and Crépimux when they
endeavoured to realize the reaction, were already pointed out in
the introduction. We met with the same difficulties in our case.
The potassium compound of the pyridyl pyrrole melting at 90° was
heated with an excess of methyl iodide in a sealed tube at 100° for
three hours. The reaction product was freed from superfluous excess
of methyl iodide and solved in water. On evaporation of the aqueous
solution crystals were separated, while potassium iodide was present
in the mother liquor. These crystals were purified by recrystallisation
from a small quantity of water. Yellow-brown crystals were obtained,
inelting at 186°. Analysis gave 8.95 for the nitrogen percentage,
and 42,55 for the iodine percentage. Calculated for C,,H,,N,1:
Nitrogen 9,34 °/,, iodine 42.30 °/,.
This substance is, therefore, the iodine methylate of C (a-pyridy!)-
N-methyl-pyrrole: (CHI) N—C,H, .C,H,N . CH,.
Just as in Prerer and CRÉPiROX’ experiments not only was the
nitrogen atom of the pyrrole nucleus methylated, but also a molecule
of methyl iodide had combined with the nitrogen atom of the
pyridine-nucleus.
This iodine methylate is easily soluble in water, sparingly in
alcohol, very little soluble in the other usual organic solvents.
In order to split off the group CH,I out of this compound, we
have followed the method which Pricrer and Rorscuy') already
applied, i.e. heating with quick lime.
The jodine-methylate was mixed with quick lime, and slowly
heated in a retort. Soon a liquid distilled over, which was received
in ether, in order to separate it from a little of the unchanged
methyl iodide compound, which had also been distilled over in a
small quantity. After evaporation of the ethereal solution there was
left a light yellow liquid; we have converted this base into the
picrate, which melted at 143° after a double recrystallisation from
alcohol, We found 18.19 for the nitrogen percentage of this sub-
stance, while 18.09 °/, of nitrogen is calculated for the monopicrate
of C (a-pyridyl)-N-methyl-pyrrole,
We have, accordingly, very probably obtained the required methyl
derivative, which must, therefore, be an isomer of nicotyrine.
[t seems, however, possible to carry out the methylation of the
C («-pyridyl) pyrrole in such a way that the C(a-pyridyl) N-
methyl-pyrrole is obtained without the necessity of following the
indirect way over the iodine methylate.
jmke:
435
It had, indeed, already appeared that the addition of methyl
iodide to the pyridyl pyrrole of melting point 90° only takes place
at a higher temperature, whereas Picrer and CrÉPimux’ pyridyl
pyrrole combines with methyl iodide already at the ordinary tem-
perature.
For this reason we have heated a mixture of pyridyl pyrrole
potassium with methyl iodide in molecular quantities in a sealed
tube at 50°. The reaction mixture was a solid mass, in which pyridyl]
pyrrole potassium and the above mentioned methyl iodide compound
of C-(pyridyl)-N-methyl-pyrrole were present. It was, however,
possible to extract by means of ether a little of a yellow oil from
this reaction mixture. This liquid was received in alcohol, and
picric acid was added; a picrate crystallized out, which melted
at 142° when it had been recrystallized out of alcohol, and appeared
to be identical with the picrate of the C (a-pyridylj-N-methyl-
pyrrole described above, as appeared from the melting point of the
mixture of both preparations.
We shall first of all set ourselves the task of preparing a larger
quantity of this C(a-pyridyl)-N-methyl-pyrrole, and examining its
properties closely. We shall further try to determine the structure
of the two isomeric pyridyl pyrroles more exactly.
A full communication of this investigation will appear in the
Recueil des Travaux chimiques des Pays Bas.
Organie-chemical Laboratory of the University.
Amsterdam, March 1923.
Bacteriology. — ‘The splitting of lipoids by Bacteria.” (First
communication.) By G. M. Kraay and L. K. Worrr.
(Communicated by Prof. C. Eykman.)
(Communicated at the meeting of June 30, 1923).
The splitting of fats by bacteria has often been investigated and
the behaviour of the lipases has properly been recorded. However
no literature dealing with the splitting of lipoides by bacteria is
known to us. Also in general physiological chemistry little infor-
mation is given concerning the splitting of lipoids (lecithin) by
enzymes, apart from the beautiful researches by DerrzeNNe and
Fourngau about the splitting of lecithin by serpent venom. In many
respects we thought it of interest to investigate the action of bacteria
on lipoids, the formation of strong blood poisons being possible, as
DELBZENNE and FourNeav found as the result of the action of serpent
venom on lecithin. We first tried to find out whether some fat-
splitting bacteria are able to split lecithin and further if there exist
among the non-fat-splitters some that will split lecithin.
Considering our working method this; we mostly used plates with
lecithin agar obtained by shaking up a small quantity of lecithin
and ordinary nutrient agar (about 0.5 gram per 100 gr.) at about
50° C. If the lecithin is affected an area is formed all around the
streeks of inoculation.
It appears on microscopical examination that this area contains
per surface unit more grains than are to by found anywhere else
in the culture medium. Plates with yolk of egg cannot be used;
the fat contents of yolk of egg cannot be used; the fat contents of
yolk of egg makes one unable to distinguish lecithin-splitters from
fat-splitters. Our results are summarized in the following table.
Our conclusions based upon this table are: there exists fat-splitting
bacteria unable to affect lecithin; lecithin-splitting bacteria unable
to act upon fat, bacteria unable to act upon both fat and lecithin,
and bacteria able to act upon both. (See table on p. 437).
The latter bacillus, a very strong lecithin splitter, but quite
unable to split fat has been isolated by us from brackish water;
this bacillus resembles much the bac. piscium pyogenes described
by MATZUSCHITA.
437
Splitting of
fat lecithin
bact. typhi == | ae
ne coli en | Ke
, dysenteriae Shiga Ze | ae
» prodigiosus a ai
» pyocyaneus + H
» fluor. liquef. al a
» proteus‘) an ga
staphylocc. pyogenes ai. =
spir. El Tor. EEn ap
Dunbar | = aL
» Cholerae En ee
Bac. piscium pyogenes ? | — | =.
We have not yet resolved the question, how the lecithin is broken
down; we can only say that as a result of the splitting by the
here above mentioned bacteria no hemolysines are formed. We
could not find a link between hemolysis by bacteria and lipolysis
or lipoidolysis; we found a staphylocc. which had lost its hemolytic
property but not its lipolytic character and on the other hand one
of our colistrains behaved hemolytic but was inactive on fat or
lecithin, our bac. piscium pyogenes splitted lecithin but had no
hemolytic action.
No fatty acids could be titrated in broth containing splitted lecithin
(B. piscium prog.). This result is in agreement with observations
on the non-hemolytic action of the splitted lecithin, because if
lecithin is splitted in such a manner that (unsaturated) fatty acids
are formed, a hemolytic action must take place.
We still want to mention that the power of splitting of the
bacteria in the table, has been tried on cholesterol and lanoline,
the latter was affected only by a staph. pyog., the former only by
B. pyocyaneus.
June 1923. Laboratory of hygiene of the University
of Amsterdam.
1) One of our proteus strains affected fat.
Physiology. — “The Presence of Cardio-regulative Nerves in Petro-
myzon fluviatilis’. By J. B. Zwaarpumaker. (Communicated
by Prof. H. ZWAARDEMAKER.)
(Communicated at the meeting of March 24, 1923).
In the 2rd edition of his “Physiologie des Kreislaufs” TiGeRSTEDT *)
remarks that inhibitory cardiac nerves are present in nearly all
vertebrates. Only among the ecyclostomata some exceptions are
known, Greenn?) found that in Myxine electrical stimulation, starting
from the brain, the spinal cord or the vagi did not affect the
frequency of the heart-beat. Cartson *) corroborated this finding and
tried to extend the investigation to another group of cyclostomata,
viz. the petromyzonta. At first he could work only on the larval
form, in which cardio-regulative nerves appeared to be absent.
Afterwards he examined adult animals *). When, in these experiments,
he applied an electrical stimulus to the medulla oblongata on the
level of the vagus nucleus, he noted a brief standstill, which was
followed by an accelerated rhythm. From this he concludes that
“the central nervous system is connected with the heart by ordinary
augmentor and probably also by inhibitory nerves” (l.c. p. 231).
In the continuing volume of his ‘‘Vergleichende Anatomie der
Myxinoiden” Jouwannes Méii.er makes mention of a connection
between. N. sympathicus and cardiac nerves °). He also adds some
remarks about the N. vagus, for which | think it better to refer to
„the original work (le. p. 59 sqq.)
The first experiments which I made myself to ascertain whether in
petromyzon fluviatilis any influence is exerted by the central
nervous system upon the hearts action, yielded a negative
result, which was in accordance with GREENE and with the first
set of experiments performed by Cartson*). However, | have
been in a position to extend my research. In order to preclude
1) R. Treersrepr, Die Physiologie des Kreislaufs II p. 319.
2) Cu. W. GREENE, Amer. Journ. of Physiol. VI p. 318 1901.
8) A. J. Carson, Zeitschr. f. allg. Physiol. IV p. 259 1904.
*) A. J. GARLSON, Amer. Journ. of Physiol. XVI p. 250 1906.
5) J. Mürrer, Fortsetzung der vergleichenden Anatomie der Myxinoiden p. 57,
Berlin 1838.
6) J. B. ZWAARDEMAKER, Physiologendag Amsterdam Dec. 1922.
439
movements of the animal I eurarized it beforehand. Paralysis
of the skeletal muscles can, in fishes, be effected only with
very large doses'). For my animals | used 4 mgr. tubo curari of
which, 2 mgr., injected intraperitoneally, was sufficient to paralyze
a 220 gr-rat. after 7 minutes. This also plays an influence upon
the vagus-function *), but this inconvenience could readily be obviated
by the technique followed, because the synapses of the vagus are
restored sooner than the motor innervation.
After the injection the animal was let alone until no “Stellreflexe”
were distinguishable any longer. Also the gills are completely
motionless then. At that juncture the cerebrum is severed from the
rest of the nervous system by an incision posteriorly along the eyes.
After this the cerebrum and the spinal cord are laid bare down to
the second gill-hole. Now a straight glass cannula is inserted into
the Vena cava dextra, through which the animal, in ventral position,
is perfused during some time with Rinewr’s fluid, containing 6'/, er.
NaCl, 200 mgr. NaHCO,, 200 mgr. CaCl,, 200 mgr. KC) *). The
surplus of curari is hereby gradually washed out. Through a window
in the cartilagenous pericardium‘) the atrium is fixed to a lever
beneath the animal. Now two thin platinum electrodes are fixed,
so as to be well visible, at the level where stimulation produces
the effect aimed at. With strongly curarized animals it sometimes
takes rather a long time before any effect can be distinguished. At
that moment, however, the animal is perfectly quiet, and the
experimenter can be sure that only the movements of the heart are
registered. In subsequent periods of the perfusion also the contraction
of the gills can be distinguished. The electrodes are connected with
the secondary coil of an inductorium of Dusois-Reymonp, provided
with a Nerer-hammer. An accumulator is connected up in the
hg. J. Scuirrer, Arch. f. Anat. u. Physiol. p. 453, 1868.
b. J. Sremer, ibid 1875.
c. Bout, Mon. Ber. d. Kg]. Preuss. Akad. d. Wissensch. Noy. 1875.
d. J. Steiner, Das americanische Pfeilgift Curare p. 56.
c. and d. After R. Borum’s article in Handbuch der experimentellen Phar-
macologie II 1. Hälfte p. 183.
*) R. Borum, |. c. p. 202.
8) J. B. ZWAARDEMAKER, Diss. Utrecht 1922.
*) When the pericardium is being opened it all at once changes colour. Originally
the heart is seen to loom vaguely through the transparent cartilaginous tissue
with a bluish tint; after the opening the pericardium shows its own milkwhite
colour, while the atrium now appears to lie at tbe bottom of the cavity. Apparently
in the pericardium a negative pressure obtains, which of course is lost at the
opening, so that the atrium partly collapses.
440
primary circuit. The Pfeilsignal, which was used sometimes (e.g. in
the first figure), could not be placed in shunt, so it came in the
primary circuit. The obtained coil-distances (C. d.) are smaller than
when no signal is connected up. On stimulation we note a considerable
acceleration shortly after the stimulus has been set up. If the
stimulus continues a short time only (in fig. 1 5 seconds) the
acceleration will be seen to disappear soon and to be substituted
by a retardation ; in case the latter increases, the heart is brought
to a standstill. After cessation of the negative chronotropic effect,
Frome
Accelerans-vagus effect.
Petromyzon fluviatilis. Perfused with Rincer’s mixture. Stimulation
for 5 seconds of medulla oblongata of the level of the exit of the
N. vagus. C. d. 100.
The tracings from above downward: record of atrium movement
- , stimulus signal
5 „ time line 10 sec.
a new rhythm appears, more rapid than the original. A little later
it gives way to the old rhythm. In fig. 1 the rhythm prior to the
stimulation is + 45 beats per minute, after the standstill the
frequency amounts to 55. The action of side-currents upon the
heartmuscle need not be taken into consideration in these experi-
ments, because the effect appears only when. a sharply defined area
in the medulla oblongata is stimulated and the effect is destroyed
again by a slight displacement of the electrodes. Besides this a great
influence is exerted by summation. A stimulus, for instance, that
produces no effect after 5 seconds, causes a distinct standstill after
a longer period.
441
When instead of presenting a short stimulus, the current is sent
through permanently, at first a marked quickening of the rhythm
will be noted, attended with a marked positive inotropic effect.
This is apparently an accelerans effect.
tig. 2.
Petromyzon fluviatilis.
Fatigue of accelerans and vagus through permanent stimulation from
medulla oblongata. The stimulus starts at the first elevations.
C. d. 143. This continues as far as the stroke. Time 10 see.
When breaking the current during this period a standstill will
rapidly ensue, which will disappear again directly after fresh stimu-
lation. When, however, the current passes continuously, a slower
rhythm will appear after some time spontaneously an fig. 2 + 30
seconds), while at the same time the height of the contractions
diminishes gradually. It is the transition to a distinct vagus-effect.
When this rhythm has also continued for some time (in fig. 2 about
1 min.), it will change into a rhythm that is only slightly quicker
than the normal, or does not differ from it at all, and will persist
unaltered after the breaking of the current.
When perfusing the animal with a potassium-free uranium-con;
taining, instead of a potassium-containing fluid we shall see that the
phenomena are practically the same in the K-, and in the U-condition.
First we see an acceleration, then a retardation, which in some
cases is followed again by an acceleration. This, however, is never
so pronounced as at the beginning of the stimulation.
What has been said above goes to show that:
1. in Petromyzon fluviatilis cardio-regulative nerves are present.
2. with the technique employed after the removal of curari the
excitability of the cardiac nerves returns sooner than that of the
motor nerves.
3. in the curarized animal the latent period of the accelerans is
shorter than that of the vagus.
442
4. with long-continued stimulation the accelerans-effect is notice-
able before the vagus-effect.
5. with brief stimulation the vagus effect appears only after cessation
of the stimulation.
6. after cessation of the vagus-action an acceleration will some-
times follow, which is perhaps due to a longer after-effect of the
accelerans-stimulation.
Chemistry. — “The Light Oxidation of Alcohol (UI). The Photo-
Catalytic Influence of some Series of Ketones on the light
Oxidation of Ethyl Alcohol’. By W. D. Conen. (Communicated
by Prof. J. BöesEKEN).
(Communicated at the meeting of May 26, 1923).
Introduction. A first communication on this subject appeared
in these proceedings) already several years ago; a continuation of
this was published by BörsrKeN*). In this paper the theoretical
grounds on which these researches are founded, are set forth in
extenso*), and we may, therefore, refer to this treatise for a study
of them.
It was now my purpose to examine what relation exists between
the configuration of a ketone and its photo-catalytic influence on
the oxidation of a definite alcohol, and for this reason I studied the
influence of some series of ketones on the velocity of oxidation of
ethyl alcohol, to be able, if possible to arrive at a conclusion with
regard to the constitutive requirements which a ketone must satisfy
to be able to act as a photo-catalyst under the circumstances specified
later, which at the same time establishes its photo-chémical attackability.
This question has, indeed, already been mentioned more than once
before“), but the comparatively small regularity in the observed
phenomena rendered an extension of the research in this direction
very desirable.
The light-thermostat. In the reaction :
Light + Ketone + Alcohol + Oxygen = Ketone + Aldehyde + Water
a certain quantity of oxygen disappears, and the rapidity with which
the oxygen is absorbed, is under for the rest fixed circumstances,
a measure for the photo-catalytic activity of the examined ketone.
The light thermostat (fig. 1) consists of a copper trough, provided
with two windows placed opposite each other in the longitudinal
walls, which make a continual observation of the reaction vessel
1) BOESEKEN and CoHEN, These Proc. XVIII, p. 1640.
2) BOESEKEN, Rec. 40, 433 (1921).
5) Ibid, 437.
4) CoHeN, Rec. 39, 258 (1920). Chem. Weekblad 13, 902 (1916).
29
Proceedings Royal Acad. Amsterdam. Vol. XXVI.
444
possible, and a window in the bottom for the illumination. The
thermostat rests on an iron framework, which has become an entirely
445
closed space by a cover of incombustible material. This space is
divided in two by a vertical partition. On the left there are found
two gas-burners connected with a thermo-regulator, and on the right
there is adjusted a Heraeus quartz lamp. To work this the wall in
the lefthand side of the framework is made like a door (drawn
halfopen in the figure); in the front partition at the place of the
incandescent body there is a ventilator which works by suction
and serves to cool the lamp. The water in the thermostat can further
be cooled by means of a cooling spiral, through which water flows
under constant pressure, a screw stirrer ensuring thorough mixing
in the trough; besides the windows, the vertical walls are insulated
with felt. Ventilator and stirring apparatus are worked by separate
regulatable motors. The temperature of the thermostat can be kept
constant at 35 + 1/,,,°, which temperature has been chosen, because
at this temperature the thermostat can be regulated most accurately.
As reaction vessel I, at first, used the before described stirring-
apparatus) (fig. 2); it possesses the drawback, however, that the
surface of illumination is small, the accuracy of the measurement
being seriously impaired by the rapid contamination of the mercury
in the mercury feal. Therefore I tried to modify the reaction
o
vessel in such a way that also without intensive mixing of gas and
liquid, an aleoholie liquid could be obtained, which remains saturated
with oxygen, or contains at least such an excess of oxygen that
there can be no question of measuring a velocity of diffusion instead
of a velocity of reaction.
This is possible when the thickness of the liquid layer is taken very
small (about 1 mm.). According to fig. 8 a reaction vessel is then obtained,
whieh chiefly consists of a flask with a perfectly flat bottom; the
dimensions being such that 5 ce. of liquid give a_ thickness of
layer of 5 mm. The neck is narrow and possesses a ground piece
to which a bent capillary tube with tap can be attached. Near the
bottom there is further a side tube with tap, through which the
whole apparatus can be filled with oxygen. Besides there is a filling
body in the flask, to make the gas-volume as small as_ possible
in proportion to the surface of illumination; this considerably
enhances the accuracy of the measurement. For definite purposes
this filling body has been made to a second reaction vessel within
the former; then an apparatus is obtained as is shown in fig. 4.
By the aid of a narrow tube the reaction vessel is connected
with the micromanometer. The lefthand leg of this has a capacity
1) These Proc. XVIII, p. 1642.
29%
446
of 1,5 ce. and is divided into 150 parts. Each space between two
dividing lines represents, therefore, a capacity of 0.01 cc. The
adjustment is obtained by moving the flask up and down by
means of a hoisting apparatus, the position of the meniscus in the two
Fig. 5.
A
1
|
Rigas:
Fig 2.
Ee
447
legs of the manometer being verified by a mirror behind it, on
which horizontal lines are drawn at distances of 1.mm. When the
apparatus has been properly cleaned and filled with distilled mercury,
an accuracy of adjustment can be attained of 1 or 2 hundredths,
which as well as the influence of the temperature lies within the limits
of the error of observation. The calibration error of the apparatus
was so small that it could be neglected.
After having been weighted with a copper ring, the reaction
vessel is placed on a glass table, which itself rests on the bottom
plate of the thermostat. The table can be put in a horizontal position
by means of three adjusting screws, through which the thin liquid
layer entirely covers the bottom surface of the reaction vessel.
After being lit the incandescent body of the lamp is always
placed in a horizontal position; the lamp burns ata terminal voltage
of 110 Volts and a series resistance of about 20 2 constant at 2,7
Amp./40 Volt. Lamp and reaction vessel are always at the same
distance from each other; in my experiments the distance from the
bottom side of the reaction vessel to the window was 20 mm., and
from the upper side of the lamp to the window 25 mm.; taking
into account the thickness of the glass, the mutual distance from
lamp to object was about 50 mm.
The measurements.
a. The preparations. They were prepared for the greater part by
myself or under my supervision, and purified as carefully as possible.
As the way of preparing is known for all of them, we may refer
for this to the records of the literature published on this subject. When
it was possible, at least two preparations of different origin were
examined, or the preparation was again recrystallized or distilled
after the measurement; the values found were not considered as
definitive until they were perfectly constant and reproducible; save
for a single exception this was always the case.
6. As solvent, resp. liquid that is to be oxidized, was used absolute
ethylalcohol, not because its being absolute was quite indispensable
for the success of the reaction — for water is formed during the
reaction — but in order to start always from a solution of
constant proporties. In my, earlier investigations I had come to the
conclusion that water would be a strong anti-catalyst, at least for
the photo-chemical reduction’). At the time | did not yet know
the photo-catalytie alcohol oxidation by molecular oxygen, nor that
1) Cowen Rec. 39, 244 (1920).
448
this reaction and the keton reduction were primarily the same, and
that it is, therefore, illogical to assume that water would be an
anti-catalyst in the ketone reduction. It has really appeared in a
new investigation, that there would be no question at least of a
considerable anti-catalytic action of water, but that the error made
before, which has, unfortunately, already been adopted in the hand-
books *), must be attributed to a wrong interpretation of the
experiments made at the time.
It seems to me of use to discuss this a little more at length. if it were only
to point out how easily certain phenomena are overlooked in the study of a
reaction. For at first | made my experiments on the photochemical ketone reduc-
tion in such a way that I illuminated the 96°/, alcoholic solution in a thin layer
in open flasks, but did not observe then anything of the crystallisation of
the sparingly soluble pinacone already described by Cramicran®). This succeeded
however without any difficulty when | used absolute alcohol — as CrAMICIAN
also did —, and besides worked in closed apparatus, hence with exclusion of
oxygen. I then drew the very plausible conclusion, which proved erroneous after-
wards, that water would be a strong anti-catalyst, and quite overlooked the
interesting photo-catalytie alcohol oxidation in which — the results of this paper
are a convincing proof of this — aldehyde does appear, but no pinacone3), and
which was not discovered until a few years later.
c. In order to be able always to have a great excess of oxygen
at our disposal, the reaction vessel after addition of 5 ec. of the
solution to be examined, is filled with oxygen which is saturated
with alcohol vapour in a washing bottle. Under these circumstances
the solution always remains more than sufficiently saturated with
oxygen; it is, however, without influence on the result of the
measurements, if the gas in the reaction vessel is air or oxygen;
for the sake of safety oxygen was, however, always taken.
The measurements, the results of which are combined in the
following table, extend chiefly over the following series of ketones:
a. benzophenon and its hydration products in the nucleus,
b. acetophenon and some alkyl-, and also phenyl substitution pro-
duets in the CH,-group,
c. the phenyl substitution products of acetone,
d. the simplest aliphatic, aromatic, and fat aromatic «-g-diketones,
e. some a-p-y-triketones.
The figures over the horizontal division line indicate the molar
1) HouBeN— Weyn. Die Methoden der organischen Chemie 2te Aufl. (1922),
Band Il pag. 983.
„ °) Cramrcian and SinBer, Ber. 33 2911 (1900); 34 1530 (1901); 44 1288 (1911).
3) BöesEKEN and Couen, l.c.
449
concentration of the ketone, the values under it representing the
oxygen absorption, expressed in ec. per hour. They are the mean
of a great many mutually concordant observations.
1 3/4 Mo We Vy Nhe | '/30 | Ves
(saturated)
10.30 |12.00| 12.00) 11.90) 9.00 | 5.60 | 3.65 | 2.28
1. Benzophenon.
1 Yo Wy Ve
(saturated)
5.15 5.00 | 2.82 | 1.12
2. Phenylcyclohexylketone.
3. Dicyclohexylketone. Inactive in all concentrations.
2 1 YB Wy
4, Phenyl n. hexylketone. —
1.00 | 0.97 0.68 | 0.22
5. Di-n hexylketone. Inactive in all concentrations.
2 11, 1 “Ja Vy
6. Acetophenon. |
1.30 | 1.40 | 1.42 | 1.03 | 0.22
7. Propiophenon.
1.10 | 1.11 | 0.92 | 0.20
y/ U | Ms
(saturated)
5.05 | 4.85 | 2.35
8 Phenylbenzylketone.
AAG “ea
9. Diphenylacetophenon. Kea turated),
3.13 | 0.78
eee rpucnylacetophenon(e-Denepinacoline). Inactive.
11. Acetone. Inactive in all concentrations.
12. Monophenylacetone.
0.50 | 0.48 | 0.35
15.
16.
17.
18.
19.
20.
Symm Diphenylacetone
(dibenzylketone).
1.76 | 1.75 | 0.85
1 iy
Asymm. Diphenylacetone. LEED
0.03 0.01
ay
Triphenylacetone 1.1.2. eee
0.05
Z l/o
Symm Tetraphenyl- (saturated)
acetone !).
0.17
2 1 If,
Phenylfurylketone.
0.07 | 0.10 | 0.10
Diacetyl.
4 3 2 1, 1 | 3/4 Vg Vy an at i 7
16.00 | 15.30 | 15.30) 15.10 | 14.90| 14.10} 10.60| 6.40 | 2.60 | 0.64 | 0.16
Ig 1/,
(saturated)
Benzil.
3.20 1.44 | 0.52
Acetylbenzoyl 2).
4 3 l/o 3 2 11/ 1 3/4 Vo 1, Is "6
8.60 | 11.70 | 12.90 | 12.60 | 12.80) 13.10) 10.80) 8.50 | 6.05 | 4.15 | 2.08
1) Prof. STAUDINGER, Zürich, had the kindness to send me a small quantity of
this preparation.
*) By illuminating an alcoholic solution of acetylbenzoyl in a sealed tube the
corresponding photoreduction product can be very easily obtained. The substance
consists of very fine colourless crystal needles, sparingly soluble in alcohol, and
is perfectly stable at the air in dry condition. For the rest the compound is quite
comparable with the corresponding reduction product of diacetyl (Comp. Chem.
451
Remark. After some time’s illumi-
fae dead nation the absorption, which was
21. Furil. NESS | constant at first, descends to 0; in
2.80 this the ketone itself is attacked with
decoloration of the liquid
; 2 1 Vy Vig
22. Benzfuril.
5.80 | 6.30 | 6.20 | 2.20
0.01 | 0.006 | 0.004
23. Terephtalophenon. (saturated)
2.80 | 3.55 | 3.45
0.1 0.01
24. Isophtalophenon. (saturated),
2.80 1.48
0.02 0.01
25. Phenanthrenequinone. GEEN Remark. Behaves like furil.
10.50 | 6.25
0.004
26. Anthraquinone. SCALE)
0.67
27. Camphorquinone. The activity varies with the origin of the preparations.
Some five varied at 14, mol. from 0.19—0.43. With still lower concentrations,
and also with very small ones the activity is practically not perceptible
28. Fluorenone. In all concentrations — also very small ones — inactive.
2 1 Yo
29. «-Hydrindon.
9.19 0.17 | 0.07
Weekbl. 13, 594 (1916); it melts amidst decomposition at 116°—124°. It is still
uncertain whether the structure formula is:
CsHs CeHs CH; CH;
EE 5 or HO dieses
ts tog 2s cao
CH, CH, Cos Cal
452
30. @-Hydrindon. Is useless as a photocatalyst, as this substance itself is very
readily attacked by oxygen in alcoholic solution.
1 "he
31. Indanedion 1.2. He ee —
| 0.92 0.39
32. Pentanetriketone. Inactive.
33. Diphenyltriketone. Inactive.
34, Alloxane. Exceedingly slight activity.
These data allow us to draw the following conclusions :
a. The velocities of activation are independent of the concentration
of the ketone (printed in bold type in the tables) within compara-
tively wide limits, quite corresponding to the reduction velocities
found before). This phenomenon does not, indeed, manifest itself
in all the examined cases, but it should not be forgotten that the
circumstances of the experiment necessitate a certain degree of
activity and solubility of the ketone to reach the maximum velocity
of activation.
Clear examples in which the oxygen absorption remains constant
within wide limits, are benzophenon, diacetyl, and benzoyl! acetyl
(compare the graphical representations in fig. 5 and 6). We some-
(imes see the activity diminish again in very high ketone concen-
trations (20) or in the neighbourhood of the point of saturation (1),
which must then be attributed to mutual disturbances of the ketone
molecules’). The diminution of activity in lower concentrations must
simply be accounted for by the absence of a sufficient quantity of
activable ketone molecules, in which part of the available light is
left unused. That really in the concentration region of the maximum
activation all the photo-active light is absorbed by a layer only
1 mm. thick, | have been able to prove very clearly by means of
the reaction vessel according to fig. 4, which can, therefore, be
perfectly compared with the ‘mantle tubes” described formerly for
the photo-chemical reduction. When e.g. an alcoholic (or a benzolic)
solution of benzophenon in a concentration necessary for the maxi-
mum activation is brought into the outer reaction vessel, a benzo-
phenon solution in the inner reaction vessel appears to absorb no
trace of oxygen; the absorption begins, however, to become imme-
diately perceptible, as soon as the ketone concentration in the outer
-) Conen, Rec. 39, 253 (1920).
2) Ibid.’p. 273.
453
vessel descends below the critical. In the region of maximum acti-
vation all the photo active light is, therefore, arrested by a layer
of 1 mm., and this takes place independent of the solvent used.
These phenomena are in perfect harmony with what was found
before in the ketone reduction. Corresponding experiments with
diacetyl and benzoyl acetyl! lead to perfectly the same results.
IT
ee \ [. benzophenon
Sis \ If. phenyleyclohexyl ketone; Fig. 5.
s 4 \ Ill. phenyl. n. hexyl ketone /
a 7 \
sé \ UL ee y
2 + — \
ao DATE \ IV. acetoph
20 \ phenon
5 4 TESS \ 5 » Fig. 6.
Ss, . \ V. acetylbenzoyl \
DN
is 4 DN 1 WI. diacetyl
5 1} AT FEET en : DNS
it Vy 7 =
conc. in mol.
Fig. 5.
| |
‘oe |
|
sj = 7 LE =
i se
a \
gen s See:
$ tz} ad : 3 \ N
Ss , ya \ |
ay \
S 3 EN
So \
2 |
© ‘| \
En |
ol Pra 5 Ore sai \
| i \
L SS.
4 3 =z 7 6
conc. in mol.
Fig. 6. :
b. For the photo-activity of the mono-ketones the “aromatic”,
character
influence
has been
is in general
decisive '), constitutive factors being of
by the side of it. Thus the photo-activity of benzophenon
reduced to about half its value, when one of the nuclei
1) Conen, Chem. Weekbl. 13, 902 (1916).
454
has been hydrated (2) (fig. 5), and it has quite disappeared in the
dieyelohexyl ketone (3). That for the rest the cyclohexyl nucleus
weakens the activity of the phenyl nucleus less than a purely
aliphatic group, is proved by the much smaller activity of phenyl
n. hexyl ketone (4) (fig. 5), which may be put on a line with the
activity of acetophenon and propiophenon (6,7) (fig. 6). On intro-
duction of C,H,-groups into the CH,-group of acetophenon, the
activity at first greatly increases (8,9), suddenly becoming 0 in
triphenyl acetone. It is, indeed, known that g-benzpinacoline lacks
all the ketone characteristics. In the phenyl substitution products of
acetone (quite inactive in themselves, just as di-n-hexyl keton (5, 11)),
the introduction of only one phenyl group appears to make the
compound photo-active (12). Of the higher phenyl! substitution pro-
ducts, the molecules built symmetrically show the greatest activity
(compare 13 and 16 with 14 and 15).
c. The photo-activity of the «-8-di ketones is a much more general
property, and bound neither to the specifically aliphatic or aromatic
character, nor in particular to the more or less symmetrical struc-
ture of the molecule. The introduction of a second C=O group
has mostly a greatly strengthening influence on the photo-activity
(compare 18 and 20 with 11 and 6), in which possible disturbing
influences issuing from the rest of the molecule, are thrown into
the background. In this connection it is e.g. interesting to point
out that phenanthrene quinone (25), which is to be considered as
a particularly ortho-substituted benzil, far exceeds all the examined
ketones with regard to its relative activity, whereas fluorenon (28),
which may be compared with it, is perfectly inactive. The opposite
case presents itself in the comparison of benzil (19) with regard to
benzophenon (1), where the di-ketone compared with the mono-
ketone is less active. It may, however, be possible that in conse-
quence of the slight solubility of benzil in alcohol the maximum
activation concentration cannot be reached.
Of great importance is also the activity of the a--di-ketones,
which carry one or two furane-nuclei (21 and 22), which furnishes
a new proof of the great resemblance in properties of the furane
and benzol. derivatives.
d. Thus we see that the phenyl and furyl groups do not exert a
disturbing influence on each other in the «-g-di-ketone ; this influence
is, however, evidently particularly strong in the corresponding
mono-ketone, phenyl furyl ketone (17), which presents a very small
activity. Here the above-mentioned influence of the symmetry of
the molecule on the photo-activity of the mono-ketone is very
455
pronounced. This influence of the symmetry was already observed
more than once in the photo-chemical reduction of the substitution
products of benzophenon, but it had not been recognized as such *).
To give a further support to this view it has been tried to make
di-furyl ketone, as this compound would have to possess an activity
equivalent to benzophenon. Unfortunately all attempts to obtain this
substance have failed so far’), but in this connection attention may
already be drawn to the much greater activity of terephtalophenon
compared with isophtalophenon (23 and 24).
e. A somewhat separate place among the «-g-diketones occupies
camphorquinone, the activity of which is unexpectedly slight,
and moreover not reproducible. The greater or smaller purity of
the preparations seems to be of great influence.
jf. a-Hydrindon (29) and indane dion 1.2. (81), considered as
internal condensation products of resp. propiophenon (7) and acetyl
benzoyl (20), present a greatly diminished activity. 3-Hydrindon
cannot be used as object of comparison with mono-phenyl acetone
on account of its great oxidisibility.
g. The photo-activity of the examined «-p-y-tri-ketones is zero, or
so small as to be negligible (32, 33, 34)*). This phenomenon must,
without any doubt, be attributed to the paralysis of the middle
C=O group caused by the solvent‘), through which the compound
has practically quite lost its favourable properties of double «-g-di-
ketone. °)
Laboratory of Organic Chemistry
of the Technical University.
Delft, April 1923.
1) Compare. Conen, Rec. 39, 258 (1920).
2) FREUNDLER, Bl. (3) 17, 612 (1897).
3) Compare for the photo-chemical reduction of alloxane Ciamician and Silber,
Ber. 36, 1581 (1903).
4) At first pentane tri-ketone and di-phenyl tri-ketone dissolve in absolute
alcohol with a dark yellow colour, after standing some time the colour of the
solution changes into light yellow, in which very probably alcohol addition
„OH „OH
products CH,—CO—C< t——-CO—CH, and (C,H;—CO—C< —W\CO—(G,H,
NOCHE \ OCH;
which are analogous to the hydrate, are formed.
5) Comp. SacuHs, Ber. 34, 3052 (1901); 35, 3311 (1902); Von PrcHMmANN, Ber.
23, 3380 (1890); WieLAND, Ber. 37, 1531 (1904); Brurz. Ber. 45, 3662 (1912).
Mathematics. — “On Power Series of the Form: «Po — «Pi 4 wPs—..”
By M. J. BELINFANTE. (Communicated by Prof. L. B. J. BROUWER.)
(Communicated at the meeting of April 28, 1923).
Introduction.
It is a well-known theorem of Frosenius that if a, is summable
of order 1, (te if lim. © gei zE et Sn
n= n
wo
Ha, +... + an) then lim. 2 a, «"=s, provided «a approaches 1
1
== |S, where silk
by real values from below (which we denote by «— 1).’)
Under the same conditions we have: ?)
oo
lim. E a, an
mm Pal
= 8
provided p, ay)
1
Put p, = 2” and a, =(—1)"t', then we have:
KJ Se St hie Sp
lim, ans ==
n= 0 n
ao
while > a, an = « — a2? + a4 —a*+... oscillates between limits
1
at least as wide as 0,498 and 0,502, if «—+1').
Thus we are led to the question: what is the connexion between
the exponent-series pp, pi, Ps, Ps ----- and the existence or non-
existence of
lim. (ao ar + aPa—...)
Td |
1) Bromwicu, Theory of infinite series, p. 312.
*) BromwicH, op. cit., p. 388.
3) Bromwicn, op. cit., p. 498 example 30.
457
Harpy‘) has investigated several particular exponent-series with
particular methods that cannot be applied to other exponent-series,
for instance the series of Fisonacctr:
lo Ao Gy Saw
The only general result Harpy could reach was the non-existence
of a limit if:
Pate CRT) OPEN ve ey Cl)
but Harpy’s example quoted above (where p, = 2’), shows the non-
existence of a limit notwithstanding the condition (2) is not satisfied.
In the present paper another condition is given ($ 2), with the
aid of a theorem of Lirti.nwoop which is treated in $ 1.
el
LirrLewoop has proved the following theorem: *)
a
oo
Theorem 1. lf |na„l <<, and lim. Sa, 2°=s, then Sa, con-
=> 1 1
verges to s.
For our purpose we want the following extension which has also
been enunciated by LirrLewoop: *)
Theorem 2. If the mean-values*) of order k-—1 of = a, are limited
00
and lim. Za, a" = s, then Za, ts summable of order k.
tet dl
LirrLewoop states that the proof of theorem 2 follows the lines
of his proof of theorem 1. The latter being rather long and tedious,
it seems not without interest to show that theorem 2 is an immediate
consequence of theorem 1.
Adopting the notation of our article “On a Generalisation of
TauBur’s Theorem concerning Power Series” *), we have the follow-
5 5 k) :
ing relations between the mean-values A.’ and the functions Gk:
1) Quarterly Journal, vol. 38, p. 269, 1907.
8) Proceedings of the London Mathematical Society Ser. 2, Vol. 9, p. 434—448,
1911.
3) Proc. of the Lond. Math. Soc. l.c., p. 448.
*) For definitions of the mean-values of order p we refer to BRomwicu, op.
cit., § 122, 123 and Lanpav, Darstellung und Begründung einiger neuerer Er-
gebnisse der Funktionentheorie, § 5.
5) Proceedings Vol. XXVI (p. 216—225).
458
ao
p= = [An — Aloe.
1
Pe (2) = 2a, 22
1
9, (2) Ha). D= @)
ne in
With the aid of (2) we have proved !) that lin . Bane" = s implies
Lap ll
lim. P, (2) =s.
Tp Ì
Now, if moreover:
k k)
ln. LA; jee AS] LC,
ao 4
we have by theorem 1 that D[A®— AW | converges to s, i.e. :
1
; k
lim. AN ls
nz
or: La, is summable of order &.
Since
(k—1) (k—1)
2
ienie An
n
k-1
4h Ai zie A
n=
we infer from |A%—| << c: | A®| 1 + oy , then
rn cL,
fe) = a—er+er— .... does not tend to a limit as x1).
Proof: We show that the series of coefficients of f(x) (which
consists of the terms 1, (7,—7,—1) zeros, —1, (7,—7,—1) zeros, 1,
and so on...) is „ot summable of the first order, i.e. that o, does
not tend to a limit as no. Then it is impossible that f(w) should
tend to a limit as «—1, for this implies by theorem 3 the existence
of lim. on °).
n=
We show that 6, does not tend to a limit ifm — oo, by calculating
two positive numbers y and 7 so that:
Oe — Gi OM GD tide
We have:
sds, 4... Hsn na, + (n—l)a, +. + [n—(n—1)]a,
D= == — a Ss
: n n
Beedle Nl ate ee le ee tT
rap = rap
Ty — Tg +73 — ee — Top Tap — Tp + 12p-2 — ---— 1
=1 + —— --— Py Ees see ee
"2p Top
ie r, 5 4
Since 1 <4, < 2 it follows that. m4: 2 7, k, and
ry
r4i— 12 (k,—1)r,. Substituting this in the expression for Ora,
we have:
6, < ae (Ai—1) T2p—1 +- (ki—1) T2p—-3 H see + (arl) m1
ADT Tap
zi kil rapt + rop—a Hs. HM
We ka Pap
- 1 1
Seep Sal RE Ps et eo Tr en
: | ET el
1
ie
jn ke
ey a! A
pe ko 1
atl E
1) We suppose 7) = 1.
8) The condition |s,\ ky 1 1 a i
Ek gint te
1
il kept?
>
EK ko 1
1 1
hid kapt? il kip
Or Fae pa > —1 =F Se
2p+1 2p ka ] ko 1
hes =
tee
„hl 2 Let ke
mam ko 1 ka k2p 1
een 2 ES
2
Ls is
kid 2 2 — 1
Put ——. —1=c, then it follows from k, > 1 + 4 >—
he cas ib 2k,
ks
that c > 0. Hence we have:
e+ 1 | 1
2 UE
2
Orap si Oron ZC = ;
Since k, > 1 the second term
is possible to calculate whatever
m so that:
Oren tt
— Onde if
tends to zero as poe; hence it
be y between O and c an integer
Pp > m.
461
Remark 1.
a! : / r
Of course it is sufficient that the relation 1 <4, gees ke
n
is only satisfied provided n> some finite number g, since the
addition of a finite number of terms does not influence the
existence or non-existence of a limit.
Thus the function #—#? + a}? + x'—x'? +... does not tend
to a limit as «—1 since
22
(yo
9 3 3
3 Vul a,
SEZ = ifm >5 and 1 7 >1+ a(t 2) :
9
ba ei a
5 Tn ] ers
3
Remark 2.
Strictly spoken we have proved theorem 2 only if the Hörper-
mean-values are limited. Now the existence of a “Hölder-limit” of
order / implies the existence of a “Cesaró-limit” of order 4 and
vice-versa’); hence if we prove that the Hörper mean-values of
order p are limited provided the Crsaró mean-values of the same
order are limited, then our theorem is proved for both classes of
mean-values.
Now we have (see lanpau l.c.):
(k ï + (k)
EI =S JI lms 5 TC ) . . . . . . (1)
(k) th Hú zat tl
where H,” is the nth Hörper mean-value and C, is the nt
Crsaró mean-value of order &, and:
a pl wi + a2 +...+ a, 1
Ta ee ERE fal
n P
From (2) we deduce that | z;| <{e implies | 7} (e;) | of meas- [beginning of|beginning of||accented stimulus is per-
3 ured |non-accented|accented and ceived sooner than the
O |2-rhythm.|and accented|non-accented non-accented
stimulus. | stimulus. Hal) SEE
B. 20 221 241 0,020
H. 20 249 264 0,015
Ho. 20 272 287 0,015
R. 25 284 292 0,007
W. 10 167 174 0,014
Il. Rising 2-rhythm (~ —).
Timein !/5 sec. between :
E Number On an average the
> of meas-| beginning of | beginning of ||@¢cented stimulus is per-
a ured jaccented and|non-accented|| Ceived sooner than the
O |2-rhythm./non accented/and accented non-accented
stimulus. | stimulus. U ISES
B. 25 330 sis | 0,012
Ho. | 40 571 537 | 0,020
R. 40 470 444 0,013
W. 40 554 516 0,019
Ill. Falling 3-rhythm (+ ~ ~).
Time in '/9, sec. between: On an average the
accented stimulus is
8 Number perceived sooner than the
o beginning | beginning Been
5 ES: 2nd non-ac- |accented and See
a ured Ist and 2nd
5 3-rhythm. cented and Ist non- non-accented Ist non-ac- | 2nd non-ac-
accented accented fini cented cented
stimulus. stimulus, in sec.: in sec.:
B. 30 355 416 413 0,028 0,052
H. 10 141 168 145 0,068 0,044
Ho. 10 99 114 113 0,040 0,036
W. 20 267 272 271 0,004 0,006
466
IV. 3-rhythm. Amphibrachic (— — ~).
Time in !/y5 sec. between: On an average the
accented stimulus is per-
: ani ceived sooner than:
3 Banter ogeinning beginning | beginning
3 of ri an a a Ist non-ac- jaccented and
ure cented an
rs} 3-rhythm Ist non- cents and gal non ist non ac- | 2nd non ac-
i accented accented
accented sidan as cented cented
ches stimulus. stimulus, Eer Tees
40 488 469 505 0,017 0,018
H. 30 312 348 390 0,029 0,027
W. 40 460 450 494 0,018 0,026
| |
»
In all these cases, in which “subjective rhythmisation” readily
manifested itself, and in which the observer reported his experience
as accurately as could be, it is evident that
1°. the observer perceives the accented stimulus sooner than the
non-accented
2°. that the perception by accented stimulus lasts
longer, as is shown directly by readings from the curves, so that
special measurements in this respect we considered superfluous.
That the observer perceives the accented stimulus with greater
aroused the
intensity is not expressed in the above curves, the deflection of the
being the same at every time. That this is a fact,
made manifest by introspection. As shown by the
following curve this is also easily demonstrable by another method
of recording, viz. by using a tambour instead of a copper layer
for the accompanying taps of the observer. Owing to the slowness
of the recording pointer these curves do not indicate small time-
differences accurately; for the
were taken from electrically registered curves only.
electromagnet
however, is
this reason measurements of time
AAN A {\ Kanten ‘ Kone
Fig. 2.
Falling 2-rhythm — —
In summary, then, the results of our curves illustrating the
perceptions, lead to the following conclusions :
467
1. The subjective accented stimulus is perceived sooner.
2. It is perceived with greater intensity.
3. It is of longer duration.
Psychologically these three characteristics are easy to understand
and may be explained upon the basis that a keener attention is
given to one stimulus than to another, for we know that our per-
ceptions are aroused sooner, that they become more intense, and
that their after-effect lasts longer, according as our attention is more
closely concentrated upon the stimulus.
This, in our judgment, is the nature of ‘subjective rbythmisation”’:
we attend more keenly to one stimulus than the other.
Some points still require further elucidation. First of all the
so-called “Jnnerliche zusamimenfassung”’, the running-together of the
impressions to form groups, which generally start with the subjective
accented stimulus. This is also a temporal grouping, in such a sense
that the elements of the group seem to follow each other at a
quicker rate, while at every time there is a longer pause between
two groups (MrumanN(2)). We believe this grouping to be of a
secondary nature and to result from the fact that the after-effect
of the subjective accented stimulus is prolonged. This causes the
pause between the termination of the accented stimulus and the
beginning of the non-accented stimulus to be shorter than in the
opposite case. This also accounts for the fact that rhythmisation
always occurs in the sense of a falling rhythm, the shorter pause
then falling within the group, or rather in consequence of the short
pause it seems to us as if the stimuli by which it is bounded,
belong together; conversely the long pause causes a separation
between two groups. Another question that arises concerns the
cause of subjective rhythmisation: why do we attend to one
stimulus more keenly than to the other, and why is this alternation
regular ?
Our capacity of receiving outside impressions is limited. Of a
large number of simultaneous stimuli to which we are exposed, we
perceive only a part. Some attain a high state of consciousness,
others are driven into the background of consciousness. When the
stimuli are weak and affect us only for a short time, the quantity
need not be large for a selection.
Experiment: two, three or more lines or points, perfectly equal inter se, are
presented to the observer for a very brief period of time. When the lines or
Points are not very clear, and the exposure is short enough, only a few will be
perceived well, the others appear to us much less distinct, or we do not see
them at all.
468
In so short a period of time we cannot divide our attention
among several weak stimuli so as to perceive all of them with the
same distinetness. Now when such weak stimuli are presented in
rapid succession, we may expect the same; also when they follow
each other at short intervals, we cannot perceive all of them and
we must make a selection. In our experimentation we also observed
that it is exactly series of weak and obscure stimuli that are best
adapted to subjective rhythmisation.
Now, why is this accentuation regular ?
A periodically recurring stimulus is easy to perceive; we are
beforehand predisposed to the impression, as we know when it is
coming. When for instance of a series of stimuli we clearly apprehend
the first and the third, we are better prepared for the fifth and the
seventh. We may change this accommodation at will every moment
so that we apprehend a 3- instead of a 2-rhythm, or we may sub-
stitute a rising for a falling rhythm.
The foregoing offers an explanation for other familiar features of
subjective rhythmisation.
The quicker the rate of succesion of stimuli the larger will be
the groups in which they are included. We endeavour to apprehend
well as many stimuli as is possible, the slower the movement the
larger will be the number of stimuli we perceive distinctly. When
the rate of succession increases a 2-vhythm is changed into a 3-rhythim,
a 3-rhythm becomes a 4-rhythm, ete.
It is also evident that the rate of the movement must not exceed
certain bounds. When the pauses between two stimuli are too long,
all our attention may be directed to every separate stimulus, the
perception of every stimulus attains its maximal intensity, so that no
rhythmisation will occur. When the pauses are too short, we cannot
single out any stimulus, they run together into a vague entity.
It is also clear now that a sensation of relaxation (a pleasurable
relief) is aroused when, after being constrained to intently follow
a series of stimuli, we perceive them rhythmically, because of the
much smaller demand upon our attention.
In experimenting it will be noted that the observer’s aptitude for
the rhythmic perception of a series of stimuli is ever increasing.
Ultimately a certain rhythm will stick to him, it has so to say
become an obsession.
It is just the same with special series of regular stimuli, which
continually affect us in every-day life, such as the ticking of a
clock, in which every one recognizes a rhythm, without being able
to break away from it.
469
SUMMARY.
Rhythmical perception of a series of perfectly equal stimuli,
following each other in regular succession, is aroused by the
different. degree of attention given to the various stimuli.
This divided attention is a necessary result of the fact that of a
large quantity of stimuli operating upon us, only a limited number
can be attended to (constriction of consciousness).
At the outset we can divide our attention at will, in the long
run we may be constrained to do so.
The primary characteristies of subjective rhythmisation are based
upon the fact that one stimulus is perceived after a shorter interval,
with greater intensity and for a longer period of time than the
other. The formation of groups results from it.
Subjective rhythmical perception can be aroused not only by
visual-, and auditory-, but also by tactual impressions of stimuli
that satisfy certain conditions.
REFERENCES.
1. Botton, THappreus L., Rhythm. Amer. Journ. of Psychology, Vol. VI.
No. 2, 1894.
2. Mpumann, Ernst. Untersuchungen zur Psychol. und Aesthetik des Rhythmus.
Phil. Stud. 10. 1894.
3. Korrka, Kurt. Experimental Untersuchungen zur Lehre vom Rhythmus,
Zeitschr. f. Psychol. und Physiol. der Sinnesorgane. 1. Abt. Ztschr. f. Psychol.
Bd. 52, 1909.
4. Foret, O.L. Le Rythme. Etude psychologique. Journ. f. Psychol. und Neurol.
Bd. 26 H, 2 1920.
5. Bücrer, Karu. Arbeit und Rhythmus. Leipzig 1899.
6. Werner, Heinz. Rhythmik, eine Mehrwertige Gestaltenverkettung. Ztschr. f.
Psychol. Bd. LXXXII 1919.
Physiology. — ‘‘Researches on the chemical causes of normal and
pathological Haemolysis”. By R. BRINKMAN and A. v. Szent-
Grökrerr. (Communicated by Prof. H. J. HAMBURGER),
(Communicated at the meetings of February 23 and April 26, 1923).
I. Zsolation of the haemolytic substances of normal human blood.
It has been known for a long time that it is possible to isolate
from normal blood by means of fat-extraction methods groups of
substances, which possess strongly haemolytic properties. The study
of these substances must be important for the explanation of normal and
pathological haemolysis, but a definite result revealing their structure
and manner of action has not yet been obtained. Nocucni'), when
extracting these substances supposed them to be soaps, but he only
examined them in regard to immunological phenomena and his
views were not supported by later investigators’). Others were
thinking of substances with a phosphatid structure, but could not
give sufficiently conclusive proofs’).
A more exact investigation of the chemical constitution and the
physico-chemical form, in which they exist in the blood, is wanted
to be able to determine the physio-pathological significance of these
substances. We have started from the idea, that it must be desi-
rable to isolate these substances in a form as pure as possible, to
be able to determine their chemical and physico-chemical properties.
The first condition to be fulfilled was complete extraction of the
haemolytic substances. Afterwards the extracts were fractioned under
the guidance of their more and more increasing activity. This
activity was tested by dispersing the extracts in isotonic neutral
phosphate mixture at 37°‘).
The determination of the haemolyties was carried out in the
following way :
The human blood obtained by venapunction was defibrinated and sharply
centrifugalized at once The corpuscles were imbibed in fat-free filterpapers and
1) Noaucut, Biochem. Zeitschr. VI, 327, (1907)
2) See LANDSTEINER. Handbuch Kotie-Wassermann II, 1291, (1913)
3) BRINKMAN, |. c.
4) See for the method Brinxman Arch. néerl. de Physiol. VI, 451, (1922).
471
dried at 37°, Afterwards the red corpuscles were extracted for one hour by petrol-
ether at room temperature; in this way neutral fat and most of cholesterin are
extracted without any loss of haemolytics. The following quantitative extraction
of haemolytics was made in a specially constructed small apparatus for “boiling-
point extraction”, with always freshly destilled fluid, adaptable for small quantities.
As extraction-liquid acetone was chosen in analogy to the use of this liquid in
phosphatid chemistry. In order to extract the haemolytics completely with acetone
a preceeding treatment with alcohol-vapour for half an hour was necessary; the
than following acetone-extraction dissolves all haemolyties in two hours.
To complete purification the acetone-extract was concentrated to a small volume and
allowed to stand for one night in ice. In this way most of the dissolved substances are
precipitated but no haemolytics are found in the precipitate. The remaining strongly
active fraction has the following properties: it can be dissolved in all typical
lipoid-dissolving liquids, if the reaction is slightly acid, but in an alkaline medium
the haemolytics are insoluble is petro] ether. The examined substances are not
precipitated by cadmium, but they are precipitated quantitatively in aquous solution
by barium and in acetone solution completely by an ammoniacal solution of acetate
of lead, in the presence of not less than 30°/, of water
So we see, that the investigated haemolyties show the typical
reactions of the higher fatty acids. The said precipetate contained no
phosphorus, so that phosphatides can be excluded definitely, and the
haemolytics, which can be extracted from normal blood must be
identified with higher fatty acids resp. their soaps.
The solubilty of the Pb and Ba salts indicated, that a mixture of
fatty acids must be present, containing no or one and also more
than one double linkage. Further experiments must determine the
constitution and procentual concentration of these substances.
Separation of the fraction of the fatty acids and of phosphatids
can only be obtained by careful quantitative methods of working ;
it is probable, that complete separation was not got by former
investigators.
In addition to these results we have examined once more the
haemolytic action of pure lecithin. If was found that a praeparation
of lecithin purified by the newest methods showed no haemolytic
properties; the haemolytic action of common trade lecithin must be
ascribed to impurities, and this also is the case if this substance is
somewhat purified by the usual acetone-precipitation.
With the knowledge, that the haemolyties of lipoid blood extract
are higher fatty acids it is possible to isolate them in a simpler
way. This may be done by the following method: the dried blood,
sucked in filterpaper (5 ce. of blood) is treated with absolute alcohol
for one hour in the boiling-point extraction apparatus. The extract
472
is concentrated to 5 ec. and than 5 ec. of a solution is added,
which contains 0,2 n.Na,CO, and 0,2 n. NaOH (in water). After
five minutes the mixture is thoroughly shaken with 5 ce. of petrol
ether; in this way neutral fats and cholesterin are eliminated
completely and phosphatids for the greater part. The remaining
alcoholic extract is acidulated with 0.5 ee. of HCl conc. and shaken
with 2 <5 ce. of petrol ether; afterwards 1 cc. of benzo] is added
to the alcoholic extract, and this is once more shaken with 5 ce. of
petrol ether. The three petrol ether fractions thus obtained contain
practically all normal haemoly ties.
If this extract is dried and the residue emulgated in neutral
isotonic phosphate mixture, then the amount of fatty acids obtained
from 1 ce. of blood and emulgated in 1 ce. of phosphate solution
may be diluted to '/,, and is still capable to haemolyse 1 °/, of
blood corpuscles completely in half an hour at 37°.
CONCLUSION.
lt is possible by means of lipoid extraction to isolate from normal
blood substances wich are strongly haemolytic. These substances
solely consist of higher fatty acids. A simple method is indicated
for their quantitative extraction.
Il. The form in which strongly haemolytic fatty acids are
contained in normal blood.
In the previous communication it was stated, that a rather large
quantity of intensively haemolytic higher fatty acids can be isolated
from normal blood. It will be obvious that in normal blood this
action must be completely on or nearly completely prevented; the
mechanism of this inactivation is not definitely known. In this
relation the formation of a protein-fatty acid compound was generally
supposed, but we did not know if these combinations could exist
in the blood plasma and if their haemolytic character has disappeared
in this way. The knowledge of this inactivation must be important
for the analysis of normal and pathological haemolysis, because
insufficiency of the inactivation-mechanism must be dangerous to
the corpuscles.
In order to investigate in which way the fatty acids are bound
in the blood, we have made use of the high degree of capillary
activity of these compounds; and this in the first place because this
473
surface activity is a property to which combining power and hae-
molytie action are intimately related, and secondly because the
surface tension of small a amounts of blood can be measured accu-
rately and easily by the torsion balance method’).
The surface-tension of a neutral highly diluted solution of fatty
acids is much lower than the statie surface tension of blood or
serum. This fact already indicates that the fatty acids of blood
cannot occur in the free state but must be bound somewhere. The
minutest trace of free fatty acid must reveal itself immediately by
a marked decrease of static surface tension, but the capillary-
activity of the protein-fatty acid compounds also is, as far as we
know, so intensive, the a decrease of surface tension plasma-air
should be observed if an added fatty acid was bound as protein-
compound.
The possible combination of protein and fatty acids may supposed
to be primarely chemical or adsorptive; the last form would be
probable by the intensive surface activity of these substances.
In the following table it is shown how the surface tension serum-
air changes when small quantities of a diluted neutral emulsion of
fatty acids are added.
Surface tension of fresh human serum. . . . . . . . . . 52 Dynec.M.
Os 001eNroleicfacidinpneutralfemulsions Se 3) 39) 5 eee. 52 ;
+ 0.002 N 7 pn 5 ö 2S (se ee We oe 4
+ 0.003 N _ 5 5 5 nr VAREND 2 i
+ 0.004 N a . 5 si DE we me DL i
+ 0.005 N 5 5 En 5 En ok en en AT: 5
+ 0.006 N 5 En 5 5 EE oe oe OL »
+ 0.007 N 5 En 5 7 SR rnc, OA BOA 7
+ 0.008 N 7 5 . el Amparo ot re ow ihe) se 7
+ 0.009 N 5 pe Fy 5 ede te ya ee MEEO 5
+ 0.010 N i ij pe) : DP ie bs ve cael Rote eee 30 55
It is seen, that 0,004 N. oleic acid may be added to serum
without change of surface tension; when more acid is given, a
gradual decrease of surface tension takes place till the value of
+ 40 dynes/em. has been reached. A further lowering is only
to be seen, if large amounts of fatty acid are added. We will not
delay upon the explanation of the gradual decrease of tension, but
try to investigate the mechanism by which the plasma can preserve
its original tension. Any marked lowering of this tension must be
considered abnormal.
The constancy of surface tension indicates that the researched
') BRINKMAN and VAN Dam. Münch. med Woch. 1550 (1921).
474
fatty acid compound can not lower the surface tension of water
to less that 52 dynes/em. By this observation the hypothesis of
inactivation of fatty acids by protein solely is proved to be in-
sufficient. Therefore we had to think of other possible compounds
und found a sufficient explanation for constancy in the formation
of calcium soaps. The existence of this proces of inactivation was
found in the following way:
A. If the Calcium of serum or blood is precipitated by addition
of oxalate of ammonia, the surface tension can not be held eon-
stant if small quantities of oleic acid are added. This is to be seen
in the next table.
Surface tension of fresh human oxalate plasma. . . .. . . . 49 d. cM.
=-*05001 Nioleicacid: injneutraltemulsion’ >... IA AE SUN AT
+ 0.002 N ; 5 é A gy toy RET sie Ally hile a
J5 000 Np tee . FP Be is | nr oe ae
+ 0.004 N 5 F, = = Bo ete eat eel GREEN AO NNS
+ 0.005N „ >) HY Ë DEE Mo CET gg NN
The same results are obtained, when NaF! plasma is used.
B. A salt-solution containing the same amount of Ca as Plasma
can maintain its tension above 50 dynes on addition of a neutral
emulsion of oleic acid at 37°, to the same extent as plasma can.
This holds for a solution of CaCl,.6 Aq. 0,05 °/, as well as for
a solution composed of NaCl 0,7 °/,, NaHCO, 0,2 °/, KCI 0,02 °/,,
CaCl,.6 aq. 0.05 °/, and H,CO, till [H-] =0,4.10—7 is reached.
The following table gives the surface tension of the said salt
solution if small amounts of oleic acid were added very gradually.
Surface tension of the balanced salt-solution. . . . . . . . . 74d. ¢.M.
-- 0.0001 N oleicacid in neutral emulsion. . . . . . . «= « «{s54i uF
+ 10 X 0.0001 N , » Ps HR ter en idaho ete) MOSER
+ 10 X 0.0001N, „ y A ehhh hae loans tek ego
+ 10x 0.0001 N, > 5 Se Ree Art ree dte a RO
O5 0.0001. N>, °, > RENEE CED
EENS *5<10.0001' N's > Kete MC) EAA ES oO ae
If the surface tension of the saline shall not be lowered unter
the plasma tension, it is necessary to add the oleic acid very gradu-
ally, and to leave the mixture for a half hour at 37° after each
addition; only in this way it is possible to obtain a form of Oleate
of Ca, whose capillary activity is low enough. But this condition
is fulfilled in vivo.
The question now arose, wether this mechanism of inactivation
would be equally important for the normal fatty acids of the blood
as it proved to be for oleic acid. It is certain, that about one third
part of the blood-calcium is present in the colloidal state; when we
475
consider the insolubility of Ca soaps it is possible, that the indiffusible
part of the plasma Ca will consist wholly or partially of soaps. It
is easily to be shown, that complete precipitation of the blood Ca
is followed by a marked decrease of surface tension.
Surface tension of one ce. of freshly taken human serum is 53
dynes/em; when 0,3 cem. of a saturated solution of oxalate of
ammonium is added, it decreases to 50, 48, 46 dynes/em. The action
of NaF! is similar.
Further if at little acid is added to the plasma, the fatty acids
must be liberated from the eventually existing Ca soap compound.
This proved to be the case; the amount of HCI necessary to lower
the surface tension of serum from 52 to 45 dynes is exactly
equivalent to the potential alkalinity of that serum. So it is probable
that in normal blood also a great deal of the fatty acids are circu-
lating in the form of Ca compounds. Direct chemical analysis will
have to bring further evidence.
Till now we only examined the inactivation of oleic acid; the
saturated fatty acids appear to be bound in the same way, but the
physiologically important highly unsaturated linolenic acid give Ca
salts, which lower the surface tension of the balanced salt solution
to 38 Dynes. In accordance with this the blood or plasma it is not
capable to maintain its surface tension if a small amount of isotonic
neutral emulsion of linolenic acid is added, contrary to what occurs
when oleic acid is given. This is seen from the following experiment.
Surface tension of fresh human serum. . . . . . . . . 53 dynes p. cm.
= OsO0leNelinolenicsacidvemulsiony, 0. 4 EE Ave one 3
+ 0.002 N “9 r fy ee eet) Se eer AO
+ 0.003 N 7 5 5 AN Ach eS AD hel «os de ten ek nl SON 5
-+ 0.004 N rs “ 5 Dr EEEN rade Gean 5
+ 0.005 N 5 “5 Dn NP oe ENP TEs p59 ho ed El a Dn
Although linolenic acid also is in plasma subject to considerable
capillary inactivation, this process is not so complete, that the surface
tension can be maintained absolutely constant. This fact must be
explained by the capillary activity and solubility of the linolenate
of Ca.
By these circumstances the higher unsaturated fatty acids circula-
ting in the blood must have a great biological importance, because
their Ca inactivation is failing. Therefore these acids must be bound
by plasma colloids or corpuscles with decrease of interfacial tension.
If now the inactivation of fatty acids extracted from corpuscles is
compared in serum and in salt solution with the process described,
it appears that these substances have the same properties as saturated
31
Proceedings Royal Acad. Amsterdam. Vol. XXVI.
476
acids, and oleic acid have, but that a very small fraction is present
which acts in the plasma as would do linolenic acid. Addition of
fatty acids extracted from blood lowers the surface tension of serum
from 53 dynes to 49,5 dynes; when more extract is added, the
tension remains as constant as if oleic acid were added. The extracted -
fatty acids lower the surface tension of the serum to that of total
blood, for corpuscles also can decrease the surface tension of serum
to 50 dynes. So the tension of blood is not decreased by extracted
fatty acids. If it may be concluded, that a small fraction of highly
unsaturated fatty accids is absorbed normally to the corpuscles, this
must be verified by further investigation.
In a following communication we will describe the influence
which the investigated mechanisms of inactivation have on normal
and pathological haemolysis.
SUMMARY.
By- means of determination of surface tension of blood and
serum it was shown, that the normal fatty acids of the blood or
also those added on purpose are bound in the form of Calcium
soaps, by which mechanism their capillary activity is decreased
considerably. It is very probable, that this formation of a Calcium
compound is the cause of disappearance of haemolytic properties of
stearic acid, palmitinie acid and oleic acid in serum. The inactivation
by means of Ca is not present in the case of linolenic acid; by
this circumstance the haemolytic character of this substance of serum
will be much greater.
Ill. Experimental anaemia caused by injections of linolenic acid.
In a previous communication it was pointed out, that higher fatty
acids in the blood generally are circulating as Ca compounds, and
thus have lost their marked capillary activity. It was stated however,
that the Ca soaps of the higher unsaturated fatty acids i.e. of
linolenic acid, do not loose their capillary activity, and that by this
reason we have to expect much greater haemolytic action in vivo
of this substance.
It was shown, that linolenic acid is an intravital haemolytic
substance, of great activity and that there is no direct inhibition of
the action of linolenic acid in the plasma. It was known fora long
time, that injection of the saturated fatty acid or of oleic acid can
not cause a distinct intravital haemolysis, probably by the mechanism
of Ca inactivation, described formerly. In the case of linolenic acid
477
the injection is followed by marked haemolytic symptoms, as appeared
from the following experiments.
Intravenous injection. A rabbit of 3620 gr. is injected in the
auricular vein 0.250 gr. of linolenic acid dispersed in 10 cem. of
isotonic phosphate mixture. After 10 minutes the surface tension of
the blood, which otherwise is 54,5—55,5 dynes/em is decreased to
50 dynes and the serum is coloured lightly reddish. If now the
surface tension is measured with regular intervals, it is seen, that
the surface tension can not rise to the normal value but always
has a value of 50 dynes approximately. The haemoglobinaemia is
increasing more and more. After twenty minutes a strong haemoglo-
binuria is observed, and the rabbit makes a very sick impression.
One hour after injection the animal dies with symptoms of utmost
anaemia and dyspnoe.
_ In this way we could prove by several experiments, that a rabbit
is killed by intravenous injection of + 100 mg. of linolenic acid per
Kg. under symptoms of very strong haemolysis. If smaller quantities
of linolenic acid are given intravenously, the rabbit is not killed at’
once, but a chronic haemolysis with severe anaemia, urobilinuria,
ete. sets on. When the linolenic acid is given intravenously, there
is always a certain chance, that a little too large dosis of linolenic
acid will lead to a direct mortal haemolysis.
A severe chronic haemolytic anaemia is produced by the subcu-
taneous, or better intramuscular injection of the acid. In this case
the greater part of the injected substance seems to be inactivated
and the following discase develops itself.
A rabbit of 3450 gr. in good state of health. Number of red cells
5,400,000. Haemoglobin 60 (Sahli). The form of the red cells in
plasma is purely biconcave; a very small degree of anisocytosis, no
polychromatophilia, absence of normoblasts. The serum is colourless
and does not contain bilirubin. No uroblin or urobilinogen in the
urin. The surface tension of the blood is 55,4 dynes at 19°.
The rabbit is injected every day with 200 mgr. of linolenic acid
intramuscularly. After the first injection the surface tension of the
blood decreases to 51—52 dynes, and remains so during all the
experiment. 2—3 days after beginning of the treatment an intensive
urobilinuria sets on and does not disappear during the course of
injections. The blood picture shows from the third day a more and
more increasing anisocytosis and polychromatophilia, while the
number of irregularly shaped cells and sphaeric cells is rising. After
five days the number of red corpuscles was lowered to 2.500.000 ;
after that the first regeneration showed itself with numerous normo-
31*
478
blasts, and strong anisocytosis and polychromatophilia. The number
of red cells at this time was 3.700.000, the haemoglobincontent 55.
So the index had increased distinctly and this increase remains very
marked during the course of injections.
Twelve days after the first injection the number of red cells had
decreased again till 2.900.000 (Haemoglobin (45), and the second
period of regeneration began. Now the blood picture demonstrated the
typical symptoms as they are found in distinct pernicious anaemia.
Kspecially macrocytosis, poikilocytosis, strongly disshaped corpuscles,
polyehromatophilie megalocyts and normoblasts were striking. Bili-
rubinaemia could only be traced in the rabbit in cases of strong
acute haemolyses. In the more chronic forms this phenomenon is
not observed, urobilinuria being very marked however.
The rabbit is emaciated and makes a sick impression. If the
injections are stopped in the beginning, the anaemia may be cured;
if the treatment is continued, the typical pernicious symptoms will
last.
So there is no doubt, that intramuscular injection of linolenic
acid causes a chronic haemolytic anaemia in a short time, the red
picture of which is showing all typical marks of pernicious anaemia.
The picture of white cells has not yet been researched till now. We
shall have to make a more exact analysis of this anaemia by linolenic
acid, but it may be stated already, that linolenic acid is a very
severe haemolytic substance. As it was found in the previous com-
munications, we must ascribe this intravital action to the fact, that
the Ca soaps of higher unsaturated fatty acids are capillary active
and haemolytic, contrary to the Ca soaps of palmitinie acid and
oleic acid.
Now this acid, forming an important percentage of the phos-
phatid fatty acids, it is practically certain, that the formerly used
praeparation of trade-lecithin could effect the described haemolytic
action by the rather large content of linolenic acid. Linolenic acid
is a substance, which is found in the biochemistry of fat and phos-
phatid metabolism and it is probable, that this acid is circulating
in normal blood.
In fact we were able to demonstrate by means of specific extraction,
that in the 0,6—0,7 mgr. of fatty acids, which are found in one ccm.
of normal human blood there is always present a small fraction
consisting of higher unsatured fatty acids.
It appeared further, that all other fatty acids of the blood are
inactivated by serum, in regard to capillary active and haemolytic
action, but this small fraction of higher unsaturated fatty acids can
479
not be inactivated completely, so that we must ascribe a great
importance as a physiologically haemolytic substance to the normal
circulating linolenic acid. We will try, to determine the concen-
tration of linolenic acids in the severe human anaemias.
SUMMARY.
Intramuscular injection of 200 mg. of linolenic acid per day in the
rabbit is followed in a short time by chronic haemolytic anaemia.
The blood picture shows a striking resemblance to that in pernicious
anaemia.
Intravenous injection of == 100 mgr. of linolinic acid pro Kg.
causes a letal haemolysis.
Chemistry. — “Nitrogen fixation by means of the cyanide-process
and atomic structure.’ By Dr. LL. HAMBURGER. (Communicated
by Prof. P. Exrenrest).
(Communicated at the meeting of June 30, 1923).
a. Introduction. It is known that the reaction
MCO, +4C+N,=M (CN), + 3 CO
forms the foundation for the nitrogen fixation by the so called
cyanide process. For this conversion the temperature at which the
capture of the nitrogen takes place with practically appreciable
velocity appears to be very divergent, according as another M is
chosen for the metal. H. Lunpen *) has also included rubidium and
ceasium in his researches, and is of opinion that there is a relation
between the boiling-points and atomic weights of the metals in
question and the ‘“cyanizing-temperature’. Itis, however, not possible
to derive a quantitative relation on this foundation.
b. Stages of the cyanizingreaction. In order to arrive at a clear
insight the fact should be considered that according to J. E. Bucner ®),
two stages before all should be distinguished in the course of the
reaction :
I MCO,+2C=M-+43CO
HT. M+2C+N,=M(CN),.
Of these reactions I bears an exceedingly endothermal character,
Il on the other hand, is strongly exothermal, IT takes place pract-
ically momentarily (either with addition of a catalyst or without).
Whether a practically appreciable reaction-velocity will appear,
will therefore depend on I. The strongly endothermal character of
1*), however, causes the temperature to remain pretty well constant,
when the reaction sets in, till the reaction of MCO, has been com-
pleted. The quantities of energy required for this are so great, that,
especially at comparable conditions, factors like energy-quantities,
1) Cf. Ta. Tuorsett. Zeitschr. f. angew. Chem. 33, 251 (1920).
4) J. E. Buenen. Jl. of Ind. and Eng. Chem. 9, 233 (1917).
3) In consequence of which the total reaction [ + II is also still endothermal
in a high degree.
481
required for division, dilution, solution, melting and evaporation
remain of subordinate importance '). Hence notwithstanding the
complicated character, we have to do with:
1. comparatively characteristic reaction temperatures ;
2. with the decisive influence of metal-formations.
We can now divide I again into the following more elementary
processes :
a. MCO, = MO + CO, CO MEEO
b. MO =M +0 d. C+ CO, = 2 CO
in which c and d follow the same reaction equation for all metal
cyanide-syntheses, whereas 6 is first of all the reaction which claims
the lion’s share of the energy-supply.
ce. The primary reaction. From W. Kosser’s ®) point of view the
course of / means only this, that under the influence of the supplied
energy in the metal oxide the oxygen cedes again the negative elec-
tron taken from the metal. In our case this view entails the diffi-
culty that this restitution would have to take place more easily
with metal atoms with relatively great affinity to the returning
electron than to more electro-positive elements. In reality, however,
the reaction appears to set in more easily with increasing electro-
positivity of the elements.
It is, however, not necessary to assume that in every metal-
metalloid compound one or more of the metal-electrons has quite
‘gone over to the metalloid. In many cases it may be more a question
of partial transition, i.e. conditions will be found in which only
partial separation (“Lockerung”’, dislocation) of the metal- (valency-)
electron with regard to the metal atom must be assumed. In con-
nection with the spectral interpretations by Bonr this may also be
expressed thus, that the electron in question will on an average be
at the disposal. both of the oxygen atom and of the metal atom in
a characteristic “abnormal” path.
The decreasing reaction temperature with the increasing electro-
positivity of the metal leads us further to the assumption that pri-
1) In the same way the dependence of the reaction-energy on the temperature
may be neglected within a wide margin. The possibility of all these approximations
stamps the cyanizing-reaction as one of the few chemical conversions, which like
the rare ideal photo-chemical reactions are able to give experimentally demon:
strable indications in favour of the theories which at the same time bear a funda-
mental and idealizing character [cf. e. g. F. Wetcaert, Zeitschr. f. Phys. 14,
383 (1923)].
3) W, Kosser, Ann, d. Phys. 49, 229 (1919).
482
marily the electron does not entirely return to the metal atom, but
that inversely a complete separation of the valency-electron from
the metal rest should be taken into account. It is this process that
we shall subject to a fuller examination in what follows, and which
we shall briefly denote by the expression of “primary reaction’. ')
Hence we come to realize the possibility of the conclusion that
the dissociation of the metal oxide does not take place by the
direct process of splitting up MO—M-+ O, but that with increase
of energy first an activation sets in, manifesting itself as formation
of ions. From this activated condition the further course of the
reaction takes place.
Thus we are led to place ourselves on the basis of these theories
of reaction-velocities which have appeared to possess remarkable
validity, at least in definite cases; particularly we come to the
“activation” basis given as of general validity first by Sv. ARRHENIUS”)
and later among others by J. Prerrin*) in his “Lumière et Matière”.
d. Ionisation Potential.
It is known that the ionisation potential of the vapour is a decisive
quantity for the detaching of an electron from a free metal atom.
Where there is reason to assume that the primary reaction takes
place in the gasphase‘) we will first of all try, in connection with
the view about the primary reaction given under c, in how far
the ionisation potential can also govern the cyanizing-reaction. For
7
this purpose we will calculate the values of the quantity 7 according
to the table below, in which V represents the ionisation. potential
1) A possible addition of the separated electron to the oxygen rest should be
considered as a second stage. From J. FRrancx’s researches on the collisions of slow
electrons in electro-positive and noble gases we know that negative electrons are
seized by oxygen, but are on the contrary under certain conditions relinquished
by the electro-positive atom. In the same way a partially bound electron, which
gets free through “critical” energy supply with small velocity [thus the lower limit
of energy supply required to bring about the primary reaction may be indicated
for brevity], may be bound to the oxygen atom. We leave this out of account in
the next close examination of the primary reaction.
2) Sv. Anruenius. Zeitschr. f. Phys. Chem. 4, 226 (1889).
8) J. Perrin. Ann. d. Phys. 11. 5 (1919).
4) All the metal carbonates or oxides of the alkalies and earth-alkalies are
greatly or appreciably volatile at the indicated reaction temperatures. In the
dissociable carbonates the evaporation is promoted by the formation of oxydes in
molecular distribution (formation “in statu nascendi’’ and transportation by the
gas current). The parallelism between the cyanizing temperature and volatility of
the carbonates resp. oxydes is striking.
483
of the free alkali-resp. earth alkali atoms, and 7’ the cyanizing-
reaction-temperature.') It is seen from the fourth row of the table
that the same order of magnitude is found everywhere for —.
If
Ou Metal Li. |Na.| K. |Rb.|Ce.| Mg. lee Sr. | Ba.
2 | Reaction-temp. in °K(T) 1370/1200) 1100 | 970 | 870 |2100?|1900) 1670/1320
3 | Ionisation-potent. in volts (V) [5.4 |5.1 (4.3 |4.2 13.9 |7.6 (6.1 5.7 |5.2
4 = 108 4.2 4.2 |4.0 |4.2 4.3 |3.2? |3.2 /3.4 3.9
5 | Excitation potential V’ in Volts |1.84/2.09/1.60 |1.55/1.38/2.70 |1.88/1.79/1.56
V- Vv’ ae
6 ro 103 202002: omm 22850 203) 2202032
Considering the widely divergent circumstances the agreement
may even be called remarkable, the more so as a perfectly sharply
defined reaction temperature cannot be expected on theoretical
ground either.
e. Dislocation potential.
The ionisation potential determines the energy required to detach
an “outer” electron of a metal atom entirely from a normal path.
As under c we arrived at the view that in the compound the
electron in question is present in an abnormal path, the conclusion
is obvious that not V, but a smaller quantity V— VV’ can give a
measure for the critical supply of energy, in which V’ is a quantity
which determines the difference of energy between the electron in
the abnormal path of the compound and the electron in the free
metal atom, that is in the normal path. We shall call this quantity
briefly dislocation potential, the electron in the abnormal path will
be called dislocated electron.
The separation of the dislocated electron from the metal rest must,
in our opinion, require a quantity of energy that is proportional to
‘) The value of the reaction temperature of CaO is taken from a communication
by P. Scrräprer (Schweiz. Chem. 1919, Heft 29 (30), the values of the ionisation-
potential are derived from a summary given bij J. Franck (Phys. Zeitschr. 22,
413 (21). The values of 7 taken for Mg and Ca will be discussed elsewhere,
among others because reduction- and cyanizing-temperature (resp. the temp. of
the formation of metal cyanamid) differ considerably for (the compounds of) these
elements.
484
e (V—V’) (in which e represents the charge of the electron), and
which is derived from the available thermal energy of the medium.
Putting the latter in approximation proportional to T, we find:
e(V—V)) =f,
so that the following relation is found:
vV—V’
7 must be constant for all cyanizing reactions.
f. Excitation potential.
With the analogous structure of the “outer electron shells” of
the homologous elements it is probable that in the metal oxide the
dislocated electron as a rule and on an average will be in a cor-
responding abnormal path. With the available date we can, however,
not say which. When we, however, compare the values of the excitation
tension V" of the different elements, which quantity is decisive for the
energy-supply required to transfer an “outer” electron in the metal
atom from the normal into the first abnormal path (Row 5 of the table)
with the ionisation potential (row 3), the analogous course of these
values with increasing electro-positivity of the elements, is striking.
When we, therefore, introduce the quantity V—V" instead of V—V'
we should, reasoning in the same line, obtain practicable results
not only for these cases in which the abnormal path of the valency
electron in the compound would be identical with the first abnormal
path, but also when the position of the dislocated electron would
be identical with another abnormal path. A considerable difference
between V" and V' is, however, unlikely, because then the value
of the quantity V—V" would no longer be in accordance with the
considerable energy-supply required if the primary reaction is to
take place *).
… V—V"
In row 6 the valnes are recorded of the quantity na
It is seen that the difference between the alkalies and the earth
alkalies is smaller than in row 4. Considerations for a further cor-
rection wil be given elsewhere.
g. In eonclusion we will remark that with the aid of Rurnrr-
FoRD-Bour’s atomic model we have endeavoured in the above to
1) This is the more cogent as moreover at the complete addition of the “‘outer”
electron to the oxygen rest energy is liberated. We have not considered this more
closely, because this increase of energy with regard to the oxygen rest may be
put equal for all the metal oxydes considerated, and can therefore not give
occasion to characteristic differences. [See also “note at the correction’).
485
give an example of the view that at least in definite cases, ioni-
sation- and dislocation-potentials are not only decisive with regard
to the possibility of reaction, but also with regard to reaction
velocity and reaction temperature.
Prrrin sees photo-chemical action in every chemical action. Our
insight into the structure of the atom makes us realize that the
fundamental feature is the displacement of the electrons in it. This
displacement may be brought about by radiation, but also in various
other ways. Accordingly it is not justifiable to assign merely a part
to light in the explanation of chemical action; other forms of energy
also make their influence felt. In connection with the conception of
an interaction between the different forms of energy, the possibility
might, however be considered of a derivation, even though it be a
critical energy supply
formal one, of the relation constant from
reaction temperare
the laws of radiation, in which case the directing lines given by
R. C. Totuman') and E. K. Rrprar, °) should be taken into account.
This will be treated elsewhere.
Dordrecht, June 26" 1923.
Note at the correction. From recent determinations of the electron-
affinity of some electronegative elements as well as from known
electro-chemical date may be deduced — as will be shown elsewhere
— that the addition potential of an electron to an atom of oxygen
can at most be about 2 volt. This value confirms the assumptions
given sub / and justifies the neglect of the addition potential of
the valency-electron to the oxygen, the value of which in our cases
(as a rule) can only be little.
July, 4%, ’23.
)
R. CG. Totman. Journ. Amer. Chem. Soc. 42, 2506 (1921).
2) E
. K. Rear. Phil. Mag. 42, 156 (1921).
Bactériologie. — Culture du bactériophage sans intervention de
bactéries vivantes”’, par F. p’ HERELLR.
(Présenté par Mr. le Prof. W. Einrroven dans la séance du 26 mai 1923).
On sait que l'activité des différentes souches du Bactériophage
est essentiellement variable, cette activité se mesure par l’intensité
de l’action destructrive vis-a-vis des bactéries sensibles. Un Bactério-
phage au maximum d’activité, introduit a unité dans une émulsion
bactérienne, provoque la dissolution totale des bacteries présentes ;
le milieu est, l’action terminée, aussi limpide que du bouillon filtré
et reste tel indéfiniment. Ces souches au maximum d’activité sont
rares dans la Nature, c'est pourtant exclusivement a de telles souches
qu'il faut s’addresser pour étudier et comprendre le mécanisme
intime du phénomene de bactériophagie qui, avec des souches moins
actives, est déformé ou masqué par des phénomènes secondaires
liés à la résistance des bactéries.
En possession d'une souche du Bactériophage possédant une activité
maxima vis-a-vis d'un Staphylocoque blanc, j'ai tenté la culture de
ce Bactériophage aux depens d'une émulsion de la bactérie sensible,
non plus vivante comme dans toutes les expériences jusqu’ici reali-
sées, mais morte.
Le Staphylocoque sensible est cultivé sur bouillon gélosé; apres
24 heures d’incubation la surface de la gélose est lavée avec une
petite quantité d’eau salée A 9 p. 1000: on obtient une émulsion
épaisse qui, répartie dans des tubes qui sont scellés, est maintenue
pendant une heure dans un bain-marie règlé a 58—60°C. La ste-
rilité est vérifiée par ensemencements.
Cette émulsion épaisse est répartie dans des tubes renferinant 10
e.e. d'ean distillée sterilisée, salée a Ip. 1000, de manière a obtenir
une opacité correspondant environ a 200 millions de Staphylocoques
tués par c.c. Tel est le milieu employé pour la culture du Bacté-
riophage.
Un tube de ce milieu est ensemencé avec 10-2 cc. d'une émul-
sion en bouillon du Staphylocoque vivant, dissoute sous l'action du
Bactériophage en expérience puis filtrée. Le tube est placé à l’étuve
a 37° pendant 24 heures. 10 ?c.c. de la première emulsion est alors
introduit dans un second tube, renfermant 10 c.c. de Pémulsion
487
du Staphylocoque tué par la chaleur. Les passages successifs étan
ensuite continués de même manière.
Au dixième passage, le taux, facilement calculable, de la dilution
du ecentième de e.c. du liquide renfermant le Bactériophage, intro-
duit dans le premier tube de la série, est de 10-30. Si le Bactério-
phage se trouve encore dans ce dixième tube, on peut être certain
quil y a eu culture car, du liquide introduit dans le premier tube,
il ne pourrait rester dans ce dixieme tube qu'une fraction d’un
électron, par suite des dilutions successives. D’autre part on ne peut
admettre que le Bacteriophage soit constitué par des corpuscules ne
représentant qu'une fraction d'un électron.
Or, après incubation, 137 c.c. de l’émulsion du dizième passage,
introduit dans uns émulsion en bouillon du Staphylocoque vivant
provoque une bactériolyse totale: preuve que le Bactériophage s'est
maintenue a travers les passages. Il n’a done pu se multiplier qu’aux
dépens des bactéries mortes.
Je suis arrivé actuellement au vingt-troisième passage (dilution
du liquide primitif 10~®): apres 24 heures d’incubation l'activité
de lémulsion est la même qu’au dizième passage. c'est a dire que
10-7 ee. introduit dans une émulsion en bouillon de la bacterie
vivants provoque la bactériolyse.
Je me suis naturellement assuré que l'émulsion seule du Staphy-
loeoque tué par la chaleur, de même d’ailleurs que vivant, ne
possède aucune propriété bactériolytique.
Le Bactériophage se cultive done indubitablement aux dépens de
bactéries mortes. Contrairement a ce qui se produit lorsqu il se
cultive aux dépens de bactéries vivantes, les bactéries mortes ne
sont pas dissoutes.
Les caracteres du Bactériophage qui s'est développé dans une
émulsion de bacteries mortes sont fort différents de ceux qu’il pré-
sente quand il se développe aux dépens de bactéries vivantes: dans
ce dernier cas le Bactériophage présente une résistance al’action de
la chaleur et des antiseptiques, analogue a celle des spores bacté-
riennes; cultivé aux dépens de bactéries mortes il est au contraire
tres sensible: il est tué par une exposition de quinze minutes a une
température de 56°C. de méme que par un séjour de dix heures
dans l'eau renfermant 20 p. 100 d’alcool ou d’acétone; il ne résiste
pas plus longtemps dans l'eau saturée d’éther ou renferment des
traces d’iode. De plus il ne traverse plus les bougies de porcelaine,
non pas a cause de ses dimentions (l’examen de préparation colorée
ne montre ancun corpuscule visible), mais, vraisemblablement, por-
cequ’il est adsorbé par le filtre, ce qui se produit d’ailleurs pour
488
d'autres ultravirus. Par contre, la virulence ne semble pas atteinte
car, mis en présence de bactéries vivantes, il provoque leur disso-
lution d'une maniére très active: il réeupere alors ses propriétés de
résistance a la chaleur et aux antiseptiques et il traverse les bougies
de porcelaine, même serrées.
Ces différences de résistance confirment ce que des expériences
antérieures semblaient déja indiquer; le Bactériophage présente deux
formes: une forme végétative et une forme de résistance. Toutes
deux coexistent dans les cultures aux dépens de la bactérie vivante :
les formes de résistance ne pouvant vraisemblablement se produire
que dans les bactéries vivantes. Dans les cultures en présence de
bactéries mortes, seules existent les formes végétatives qui, des lors,
se reproduisent uniquement par scissiparité.
J'ai effectué des expériences complementaires qui montrent que
la culture du Bactériophage peut également s’effectuer dans des
macérations du Staphylocoque tué centrifugées, c'est à dire dans
un liquide de macération débarassé des corps microbiens: la forme
vegetative se cultive done, non pas dans la bactérie tuée, mais dans
le milieu, aux dépens des produits bactériens solubles.
Par des expériences antérieures, j'ai montré que le Bacteriophage
est un être autondme, possédant des caractéres propres, indépendants
de la bactérie qui subit son action, se qui donnait la preuve, qu'il
se multiplie en milieu hétérogene. Ce fait implique le pouvoir
d’assimilation chimique, caractere fondamental qui suffit pour carac-
tériser la nature vivante de l'être qui le possède. Les présentes
expériences ne font que confirmer la nature vivante du Bactériophage.
Nombre d’auteurs ont voulu expliquer le phénomène de bactério-
phagie et la reproduction du principe actif en cours d'action, comme
un phénomène lié au métabolisme microbien. Cette explication,
déjà contredite par le fait de l'autonomie du Bacteriophage, tombe
définitivement devaut le fait de la culture dans de l'eau salée ne
renfermant que des bactéries mortes, ou méme leurs seuls produits
solubles, car une bactérie morte, ou ses produits solubles, ne sont
plus qu'un assemblage de substances chimiques inertes, incapables
d’aucun acte de métabolisme *).
(Institut d’ Hygiene tropicale de Université de Leyde).
1) Je tiens naturellement à la disposition des expérimentateurs la souche du
Bactériophage avec laquelle j'ai realisé ces expériences.
Géologie. — „Description de Crustacés décapodes nouveaux des ter-
rains tertiaires de Borneo”, par V. VAN STRAELEN.
(Présenté par Mr. le Prof. H. A. Brouwer dans la séance du 26 mai 1923).
Les Crustacés décapodes déerits dans cette note, ont été recueillis
par M. le Dr. G. L. L. KeMMERLING, au cours d'un voyage d’explo-
ration effectué en 1912, dans le bassin du fleuve Barito, au S. E.
de Vile Borneo’). Ces fossiles, conservés au Musée géologique de la
Technische Hoogeschool a Delft, m’ont été obligeamment communiqués
par M. le Professeur G. A. F. Morenoraarr, directeur de ce Musée.
Famille : RANINIDAE Dana 1852.
Genre : Ranina Lamarck 1818.
Sous-genre: LOPHORANINA Fabiani 1910.
Ranina (Lophoranina) Kemmerlingi nov. sp. (Fig. 1, 2a, b.).
= Ranina sp, in G. L. L. Kemmerling (le. p. 740, pas fig.)
AS Les restes assez fragmentaires de cette
A , ima ;
TB EN NS espece se réduisent a la partie droite de
la région postérieure du céphalothorax
| et d'un article d'un péréiopode droit, pro-
bablement le troisième.
Les crêtes du céphalothorax, caracte-
ristiques du sous-genre, sont disposées
transversalement. Elles sont onduleuses,
irrégulieres, ne présentant aucun paral-
lélisme et concaves vers l’avant, tout au
2 Fig. 1. moins dans la moitié postérieure du
anina sp. (schéma). — Ws „x A
Papen ae) céphalothorax. Ces ecrêtes sont garnies
grandeur naturelle.
Céphalothorax indiquant en ©! vant par un grand nombre de tuber-
grisé, la région a laquelle appar- CUles subépineux. Le bord du eéphalo-
tient le fragment décrit sous le thorax, souligné par un sillon, est granu-
nom. de R. KEMMERLINGI. leux ainsi que l'article, probablement un
carpopodite, du péréiopode encore conserve.
) G. L. L. KeMMeRLING. Topografische en Geologische Beschrijving van het
Stroomgebied van de Barito, in Hoofdzaak wat de Doesoenlanden betreft (Tijd-
schrift van het Koninklijk Nederlandsch Aardrijkskundig Genootschap, 2de ser,
Deel XXXII, p. p. 575-641 & p.p. 717—774, carte et nombreuses figures dans
le texte, Leiden 1915).
490
C’est une espece de grande taille, dont les dimensions devaient
atteindre celles que présentent souvent des formes actuelles, telles
que Ranina serrata Lamarck des mers du Japon. Les autres repré-
AY
Fig. 2b.
Ranina (Lophoranina) Kemmerlingi nov. sp. — Face dorsale.
Qa. Fragment du céphalothorax. — Grandeur naturelle.
2b. Crétes du céphalothorax. — X 3.
sentants fossiles du genre Ranina, dont l'espèce de Borneo se rap-
proche le plus par les caractères de son ornementation, sont:
Ranina laevifrons Birrner, du Lutétien du Vicentin,
R. Bittneri Lorerexrtney, du Bartonien du Vicentin et de la Hongrie,
R. Reuss: H. Woopwarp, du Bartonien de la Hongrie,
R. Marestiana Kounic, du Priabonien du Vicentin,
R. porifera H. Woopwarp, de l’Oligocene inférieur de Vile
Trinidad.
R. Kemmerlingi se distingue :
de R. laevifrons par ses tubercules arrondis a peine spiniformes,
de R. Bittneri par ses tubercules moins serrés et dépourvus de
ponctuation,
de R. Reussi par ses erétes plus nombreuses, plus serrées et
ses tubercules moins distants,
de Rk. Marestiana par ses crêtes plus serrées et garnies de tuber-
cules plus espacés mais plus volumineux, :
de R. porifera par Vabsence de ponctuation en avant des tuber-
cules des crêtes.
Type. Musée géologique de la Technische Hoogeschool à Delft,
échantillon No 6561 et 6562, empreinte et contre empreinte.
Gisement. Etage y de R. D. M. VurBerK, probablement Oligocene.
Localité. Vallée du fleuve Barito (Borneo).
Famille: CaLAPPIDAE Dana 1852.
Genre: CALAPPILIA A. Minne Epwarps 1873.
Calappilia borneoensis nov. sp. (Fig. 3).
491
Les marnes calcariferes avee débris de végétaux de l'étage p de
R. D. M. VerBreK, renferment parfois de nombreux débris appar-
tenant a un Brachyoure de petite taille. Ces restes toujours incom-
plets, sont a rapporter au genre Calappilia A. Mine Epwarps.
La région frontale est étroite et se prolonge en avant par un
faible rostre, les orbites semblent avoir été larges et peu profondes.
Les sillons limitant une région gastro-cardiaque étroite sont peu
profonds, les régions branchiales sont relativement
étendues. La surface du eéphalothorax est ornée
de petits tubercules arrondis, d’autant plus saillants
qu’ils sont plus rapprochés des bords, leur nombre
augmentant dans les régions postérieures du cépha-
lothorax. L’espace compris entre les tubercules est
occupé par de fines granulations. Les bords latéraux
borneoensis yencontrent le bord postérieur sous un angle a peu
nov. sp. Face
dorsale. X 2.
Reconstitution : ;
a l'aide de frag- Les fragments de céphalothorax sont accompagnés
pres droit et se prolongent postérieurement, par une
épine. La face sternale n'est pas connue.
ments prove. de débris de péréiopodes, trop morcelés pour qu’on
nant de 5 indi- puisse les décrire. Tout ce qu il est possible de voir
vidus. est que comparativement au corps de l’animal, ces
péréiopodes étaient extr@mement développés. Jusqu’ a présent, on
ne possède pas d'autres renseignements sur les appendices du genre
Calappilia.
Ces caractères sont suffisants pour distinguer cette forme, de toutes
les espèces de Calappilia décrites jusqu'à ce jour. Le genre a été
rencontré depuis |’Kocene moyen jusqu’ a l’Oligocène moyen. On en
connait les espèces suivantes:
Calappilia incisa Birrner, du Lutétien du Vicentin,
C. dacica Birryer, du Bartonien de la Hongrie,
C. verrucosa J. Bornm, de Eocene supérieur de Java,
. perlata Noetrine, du Tongrien du Samland,
vicetina Fagranr, du Tongrien du Vicentin,
WAN
serdentata A. Mitne Epwarps et
C. varucosa A. Murre Epwarps, du Rupélien de Biarritz.
L’espéce de Borneo se distingue de toutes les Calappilia sauf de
C. varucosa A. Miune Epwarps, par l’absence de nombreux tuber-
cules spiniformes sur les bords latéraux du céphalothorax. Son
ornementation la rapproche également de cette espèce de Biarritz,
32
Proceedings Royal Acad. Amsterdam. Vol. XXVI,
492
elle s'en écarte cependant par ses tubercules plus saillants et moins
également répartis sur toute la surface du céphalothorax. D’autre
part, elle se distingue de C. verrucosa J. Boram par son céphalo-
thorax plus circulaire et quasiment hémisphérique.
Type. Musée géologique de la Technische Hoogeschool a Delft,
échantillon No. 6563.
Cotypes. Echantillous No. 6564, 6565, 6566, 6567.
Gisement. Etage 8 de R. D. M. VerBeeK = étage marneux (Mergel-
etage) = Kocene, probablement Lutétien.
Localité. 2 Kilometres a l’Ouest de Kampong Lemoe (Borneo).
Neurology. — “A partial foetus removed from a child.” By Prot.
C. WINKLER.
(Communicated at the meeting of June 30, 1923).
A few months ago a child of nearly three months, was brought
in my clinic, having a fluctuating tumour in the neck and a not
very intensive internal hydrocephalus.
Apparently it suffered from spina bifida, as the transverse proces-
sus of the 2d and 3d cervical vertebrae stood far apart and the
processus spinosi were missing. The examination of the tumour made
it probable that a myelo-cysto-cele might be found in it.
For the rest this healthy child had normal breathing, responded
to pin-pricks with mimic facial expressions and spontaneously moved
its four extremities.
The tumour, filled up with liquor, was opened by Dr. Warrer.
He found in the middle of the fluid a strongly vaseulated stalk,
nearly 1 c.M. in diameter, connecting the deep tissues in the mid-
line with the external wall of the tumour-cyst. After underbinding
the stalk in the depth, he removed stalk and cystic tumour. In a
week the child recovered. As | saw it again, six weeks after the
operation, it appeared to bea rather normal child of circa five months
of age.
The removed specimen was given to me.
A section made through the middle of the stalk proved, that it
was a spinal cord surrounded by an intensely vasculated membrane
(fig. 1a). In this spinal cord the columna posterior had
disappeared and the dorsal wall of the central canal was } |
open. The form of the central canal was as this figure shows.
The lateral, the anterior column and the grey matter were easily
recognisable. In the lateral column the area of LissavEr, the spino-cere-
bellar tracts and the surroundings of the grey substance are myeli-
nisated. In the anterior funiculi was seen a strongly marrowed
commissura anterior, and the tecto-spinal path has also gained
marrow. Both, not medullated, pyramidal tracts are recognisable.
The substantia Rolando is strongly developed. The anterior horns
contain atrophic large cells.
494
From this cord, ventral and dorsal medullated rootlets take
origin.
Examining sections through the central end of the stalk (fig. 16),
the central canal widens. The lateral part of the medulla disappears
and only a ventral rest of nervous tissue remains lined by the
Fig. 1. Wall of the tumor and stalk.
ependyma of the central canal, now irregularly shaped and wound
in an irregular way. The membrana vascularis also divides in two
membranes, leaving a hole between them.
Examining sections through the stalk, towards its
entrance in the skin (fig. 1c), the central canal soon
closes dorsally. Its shape changes into another form,
then it ends into many branches, one of which may be
followed, lying excentrically, to the end.
At that moment the nervous tissue is represented by a. strongly
medullated fibres of the medullar columns 6. medullated posterior
roots with well developed spinal ganglia (fig. 1c).
At the moment that the stalk reaches the skin, there is found,
ventrally from what seems to me to be the caudal end of the spinal
cord, a tube, which soon appears to be the intestinal tube.
Sectioning the wall of the tumour, caudally from the entrance
of the stalk, it appears to contain the caudal end of an imperfectly
developed, partly atrophied, foetus.
495
In foto 2 is seen, that cutis and subeutaneous tissue with hair-
follicles and sudorifie glands is separated from the new tissue by
a system of lacunae, filled up with blood and bordered by endo-
Fig. 2. Foto from a section through the wall of the tumour (see fig. 1d.)
thelium-cells. Most striking however is the deeper part. A trans-
verse section of a tube is found there, whose internal surface is
irregularly wound.
It is formed by a single layer of cylindric epithelium, placed
upon a membrana basilaris and bordered towards the lumen of the
496
tube by a transparent band with small transverse lines — a hem
of cell-cilia. The loose connecting tissue, building the basilar mem-
brane upon which the epithelium-cells repose, is surrounded by a
transversal and by a longitudinal muscle-layer. I consider this tube
to be the intestinal tube.
Dorsally from this tube are found the large vessels, aorta and
vena abdominalis. In the foto (fig. I Jd) the section touches the left
femur; at the right side the trochanter femoris is found. Also both
ureters and more caudalward the bladder is seen.
In this way it appears that the wall of the tumour contains the
caudal end of an insufficiently developed foetus, connected to the
well developed child by a stalk, containing the caudal end of a
medulla spinalis.
I presume a double monstrum, a duplicitas posterior is here
present. The single head of this monstrum was followed by a double
caudal part of the body. The one half of the body developed
normally.
The other half atrophied. A relatively well developed medulla
remained in the stalk, the caudal end of the foetus was found in
the wall of the fluctuating tumour.
Hence this female child carried its atrophied twin-sister at her back.
The superfluous atrophic foetus was removed and it is not impossible,
that the remaining child may grow up normally.
ERRATU M.
On p. 310 of this volume line 13 from the top to omit the words
and Wolffian Ducts and to read: by the kidney-tubules (TrrscHack
1922, a. s. o.).
: es 4
‘
4 4) i
AL J Ae IN
Oke S xi ;
pa Sr
’ Ee yy ®
‘ iN
i
\
.
KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.
RROGEEDINGS
VOLUME XXVI
Nes, 7 and 8.
President: Prof. F. A. F. C. WENT,
Secretary: Prof. L. BOLK. [
(Translated from: "Verslag van de gewone vergaderingen der Wis- en
Natuurkundige Afdeeling," Vol. XXXII).
CONTENTS.
H. W. J. DIK and P. ZEEMAN: “A Relation between the Spectra of lonized Potassium and Argon”.
(Second Communication), p. 498.
W. TUYN and H. KAMERLINGH ONNES: “Further Experiments with liquid Helium. S. On the Electric
Resistance of Pure Metals, etc. XII]. Measurements concerning the Electric Resistance of Indium
in the Temperature Field of Liquid Helium”, p. 504
W. F. GISOLF: “On the occurrence of diamond as an accessory mineral in olivine and anorthite
bearing bombs, occurring in basaltic lava, ejected by the volcano Gunung Ruang (Sangir-
Archipelago north of Celebes)”. (Communicated by Prof. EUG. DUBOIS), p. 510.
G. SCHAAKE: “The Complex of the Conics which cut Five Given Straight Lines”. (Communicated
by Prof. HENDRIK DE VRIES), p. 513.
G. SCHAAKE: “On the Plane Pencils Containing Three Straight Lines of a given Algebraical
Congruence of Rays”. (Communicated by Prof. HENDRIK DE VRIES), p. 522.
G. BREIT: “Transients of Magnetic Field in Supra-conductors’. (Communicated by Prof. H. A.
LORENTZ), p. 529.
J. R. KATZ: “Further Researches on the Antagonism between Citrate and Calcium Salt in Biochemical
Processes, Examined by the Aid of Substituted Citrates”. (First communication). (Communicated
by Prof. A. F. HOLLEMAN), p. 542.
J. R. KATZ: “Researches on the Nature of the So-Called Adsorptive Power of Finely-Divided Carbon.
I. The Binding of Water by Animal Carbon”. (Communicated by Prof. A. F. HOLLEMAN), p. 548.
J. LIFSCHITZ: “Volta-Luminescence”. (Communicated by Prof. F. M. JAEGER), p. 561.
H. ZWAARDEMAKER, W_ E. RINGER and E. SMITS: “Is Caesium Radio-active ?”, p. 575.
]. M. BURGERS: “On the resistance experienced by a fluid in turbulent motion”. (Communicated by
Prof. P. EHRENFEST), p. 582.
FERNAND MEUNIER: “Sur quelques nouveaux insectes des lignites oligocénes (Aquitanien) de Rott,
Siebengebirge (Rhénanie)”’, p. 605.
H. R. WOLTJER: “Magnetic Researches. XXII. On the determination of the magnetisation at very
low temperatures and on the susceptibility of gadolinium sulphate in the region of temperatures
obtainable with liquid hydrogen”. (Communicated by Prof. H. KAMERLINGH ONNES), p. 613.
H. R. WOLTJER and H. KAMERLINGH ONNES: “Further experiments with liquid helium. T. Magnetic
researches. XXIII. On the magnetisation of gadolinium sulphate at temperatures obtainable
with liquid helium”, p. 626.
W. F. EINTHOVEN: “The string galvanometer in wireless telegraphy”. (Communicated by Prof. W.
EINTHOVEN), p. 635.
L. BOLK: “The Menarche in Dutch Women and its precipitated appearance in the youngest
generation”, p. 650.
Proceedings Royal Acad. Amsterdam. Vol. XXVI.
Physics. — “A Relation between the Spectra of lonized Potassium
and Argon.” (Second Communication). By H.W. J. Dik and
Prof. P. ZEEMAN.
(Communicated at the meeting of June 30, 1923).
The observations of the spectrum of potassium vapour under the
influence of the discharge without electrodes have now been com-
pleted. These measurements go up to 2 2342,3 A. They, too, have
been made with a quartz spectrograph. We begin Table IV with
3514.0, so that Table I of our first communication’) and Table IV
for a small part overlap. The values of Table IV are more accurate,
and have been obtained by direct comparison with the standard
iron lines.
TABLE IV. Potassium lines on discharge without electrodes.
Intensity.
A y Remarks.
EV S |McL| D
— 1 9 3514.0 28458
— — 9 | 3490.8 28647
1 1 10 3480.9 28728
1 1 10 | 3476.4 28765
— 1 9 3468.3 | 28833
— —|—- 3 3457.4 28923
-- — — 2 3447.8 29003
2 — 3447.5 arc-line
i 3 — 3446.5 are-line
6 3 20 3439.9 - 29070
1 2 15 3433.2 29128
eae) 2 3427.0 | 29180
1) These Proceedings, Vol. XXV, p. 67.
499
TABLE IV (Continued).
Intensity.
A y Remarks.
EV | S |McL| D |
|
ale 3421.9 29223
AEN ay 3421.0 29231
Ee Id 3417.0 29266
Dell 2 15 3404.2 29376
ZA 9 | 3302.6 29476
6 | 4 15 3384.6 29545
6 | 4 | 15 3380.3 | 29583
1 3 | 15 3373.5 | 29643
Brea G7 (| 3363.9 29721
20
1s <8" ( 3362.5 29739
2 | 2 3358.6 29774
be | 2 BaZ 29796
Gn „615 3345.0 29895
et 2 3338.0 29958
DE 3336. 1 29975
Syl aes NE 3326.4
aS | 3324.7
Ne eis 3322.2 | 30101
Beld e5 | 15 | 3311.9 | 30194
ti 232 Inis 3301.2 | 30292
ONIN S | 5 | 15 3289.8 30397
==) eset ee 3285 5 30437
ea ca 10. 3278.6 | 30501
A | 3261.9 30657
EE 834g | 3258.6 30688
SIA ENE 3253.9 30732
B ee re 3244.5
a ol OE 3241.2 30853
EEE 3237.8 30885
500
TABLE IV (Continued).
Intensity.
ï A y Remarks.
EV | 'S |McL| D
—|—| = 1 3226.9 30989
1 1 1 8 3224.2 31016
|Z 0 | 10 3220.2 | 31054
== 1} - 3 3218.5 | 31071
i A= | eS 3217.5
—|- 0} — 3213.0
1 A \ =d ie 3209 0 31162
—|— Al = 3205.6
t | 3] = | ie 3201.8 | 31232
Dia) 2 CEO 3190.0 | 31348
zal zel | 10 3187.7 31371
— | — 2 3 3171.8 | 31528
1 1 4 | 9 3169.6 31550
1 1 3 6 3157.0 31676
== 2) = 3148.6
=| =| = 1 3145.1 31795
Sk SS 3142.7 31820
Ge Bl sie TGs 3128.8 31961
== 5 3109.7 | 32157
Belk gb | = IE 3104.9 | 32208
1 1 6 4 3102.9 32228
1 1 2 8 3074.7 32524
lol) ==) Ss ee 3067.3
Gl Si & zo 3061.7 32661
it |) 2 0 | 10 3056.5 32717
lh Se 2015 3051.9 32767
= |= DAs 3047.0 32819
1 1 Sow) 3030.4 32999
DZ AS 3023.5 33074
Intensity.
EVe ies) |eMcle) | 3D)
4 3 a} |] 16)
1 1 2 9
— | — 2 Bl
ES 1 —_ —
— | — 1 4
=5 i == 1
— = — 1
| 1 210
== ENE 8
— | — 1 4
— | — 2 8
= aie 1
le 1
= ea 3
Sid 1
—}|—}]— 2
1 1 2 10
— | — -- 4
se de £ 1
— 3 2
1 1 in
— | — 2 3
zi seh
1 1 3 10
— ~ — 5
SE 9
=e) a 5
= prs 5 =
le 3
501
TABLE IV (Continued).
35711
Remarks.
502
TABLE IV (Continued).
Intensity.
EV) |S!) Meck D>
1 1 — —
— | — 1 5
— — — 1
= — 1 —
— = 1
= 1 2 9
1 1 4 5
= = 1 =
l 1 3 9
1) — 3 3
— — 1 1
| 1 4 10
= = 0 =
1 1 2 1
== = 3
de ON 1 e
—;|;-|]—- 3
Ei Di
2 1 4 | 10
— | — |= 1
= 1 = | =
== |W 3 5
— = — 5
2 = 2 =,
ee ee 1
— 1 3 8
aay IN ee Sy
— | — 2 1
35998
36022
36187
36450
36547
37175
37555
37636
37950
38259
38874
39043
39215
39339
39425
39927
40234
40434
40771
40834
Remarks.
503
TABLE IV (Continued).
Intensity.
A y Remarks
EV | S | McL D
— | — 4 1 2447.2 40864
1 1 2 7 2440.0 40984
—}|— 4 1 2436.7 41039
—|—}]— 2 2431.1 41134
—|/-|]—- 1 2415.4 41401
—-|-|;-— 1 2414.4 41417
= — 3 = 2410.4
— — — 1 2404.5 41588
— | — 3 | = 2402.0
S| 3 — 2393.4
nd tl es 1 2389.1 41857
1 1} — 2 2379.2 42031
— 4 | — 2376.3
— 5 2 2369.6 42202
— 2 — 2365.8
— 1 |= 2362.6
1 1}; —}]— 2358.9
1 1 SR 2350.3
=| — 4 | — 2348.3
1; —|—]|]— 2344.7
1 1 3 1 2342.3 42693
The constant differences seem soon to stop below 23000. This
may be in connection with the appearance of the second spark
spectrum of potassium.
We have, however, also started an investigation of the lines that
satisfy formulae with fourfold and ninefold RispBEre@ constans. By
this way the proof might be furnished that the observed spectrum
belongs to once ionized potassium; besides, a quantitative comparison
with the red argon spectrum may perhaps be possible.
Physics. — “Further experiments with liquid helium. S. On the
electric resistance of pure metals, ete. XII. Measurements
concerning the electric resistance of indium in the tempera-
ture field of liquid helium’. (Comm. N°. 167a from the
Physical Laboratory at Leiden). By W. Tuyn and Prof. H.
KAMERLINGH ONNES.
(Communicated at the meeting of June 30, 1923).
§ 1. Purpose of the mvestigation. Method of construction of the
resistances. For the further detection of supra-conducting metals it
seems desirable to investigate the behaviour of those elements whieh
take a place near already known supra-conductors in the periodie
system. Indium — above thallium and by the side of tin — seemed °
a suitable metal.
The chemically pure indium (4 grammes) was supplied by E. pr
Hain, G. m. b. H.'). From wire extruded from this to a thickness of
0.1, m.m. we constructed the resistances /n—1922—/, W,=4,704,
£2, In—1922—11, W,=3,708, 2 and n—1922—J//1, W,=3,799,
£2; the resistances were, however, not enclosed in helium gas.
A fourth resistance, /n—1922—A, W,—=4,609, 2 was obtained
by winding another piece of the same wire also bifilarly on a glass
tube; silk thread served here for insulation 7). The values IV’, were
determined on December 22"¢ 1922 in the way as described in
Comm. N°. 160a.
$ 2. Measurements in liquid helium. The four resistances were
placed in the cryostat provided with a stirring apparatus, represented
in Comm. N°. 124c, fig. +. The measurements took place by com-
pensation of the potential at the extremities of a known and an
unknown resistance connected in series, by the aid of a compensation
Ww
W,
from this made us doubt the purity of the indium supplied. On inquiry the firm
told us in a letter dated March 22nd 1923 “that they had sent chemically pure
indium metal, free from impurities”.
2) Old indium wires are difficult to fuse together to obtain the four required
extremities; treatment with HCI removes this difficulty.
1) The high amount ot ( ) of all the resistances constructed
Ftd on Ne
505
apparatus free of thermo-electromotive forces by DirssELHORST’s
method, supplied by O. Worrr; the strength of the current through
the resistances was 4 m.a. For the determination of the tempe-
ratures the vapour pressures of the helinm-bath were measured,
below 400 m.m. Hg. with the cathetometer; the corresponding tem-
peratures were then derived by means of the formula of Comm.
N°. 1476, p. 33%).
The results of the measurements follow in the tables 1, II, 11 and
IV. Near the vanishing-point, where the successive temperature
TABLE I. Indium—1922—I.
Das: = ee | 4 | del en ;
December 8, 1922| 775.4 4.23 K. | 0.1373,
December 20, 1922 | 394.4g 3.60 | 0.1372,
339 .3y 3.48 | 0.1371,
310.1, akan B 0.1370,
308. 83 0.1370,
307.4 0.1367,
306.8, | 0.1367,
305.45 | 0.1364,
| 304.0, | 0.1363,
| 301.5, | 0. 1359,
| | 299.5, 0.132
December 8, 1922) 299.4, 0.120
December 20, 1922 298.13 0.016
295.4, | 3.38 0.0000,
December 8, 1922 12.40 es 0.00000
‘) This formula has been calculated out of measurements performed 1913. If
by the side of these measurements one takes those of 1911 into account, and
interpolates graphically, temperatures are obtained which often considerably deviate
from those calculated with the formula. The vanishing-point temperature of
thallium e.g., graphically derived in this way in Comm. No. 1604, is 2,°32 K;
the formula gives 2,°47 K. Until the vapour pressure curve of helium is more
accurately known, we give the read vapour tensions, and state also. how we have
calculated the temperatures from them.
*) Below the vanishing-point the measured potential differences have been re-
calculated to resistances, as if Oum’s law were valid.
TABLE Il
Indium—1922—II.
Date. Phelium T. w= ey
in m.m. Hg. WS In—1922—II.
| December 20, 1922) 394.3, 3.60 K. 0.03392
339.55 3.48 0.03387
309.84 3.41 0.03387
308.7, 0.03385
307.4, 0.0202
306.8, 0.0067
305.9, 0.00000
304.09 0.00000
TABLE III. Indium —1922--1I1.
W
Dates En E; a (Tali easier
December 8, 1922) 775.4 4.23 K. 0.03390
333.7 3.46 0.03380;
310.5, 3.42 0.03380;
309.0; 0.03377
307.6 0.0207
305.9% 0.0001,
304.7, 0.00000
12. 4p—12.5, 1.87 0.00000
TABLE IV. Indium—1922—A.
pale ae Ë Ar Cae
December 20,1922} 759.7 4.21 K. 0.03420
394.3, 3.60 0.03418
330.55 3.48 0.03415
309.65 3.41 0.03392
308.93 0.0297
307.1, 0.0013,
307.0, 0.0001,
306.2; 0.0000,
304.09 0.00000
507
differences are small, we give only the vapour tensions. Sometimes
the resistance is given here in fewer decimals than elsewhere; the
slightest change in indication of the oil-regulator described in Comm.
N°. 119 is the cause that the galvanometer in the region of the
great decrease of resistance does not settle down.
The tables show (ef. also fig. 1) that the rest-resistance of /na—
1922—T/ above its vanishing-point temperature is much greater
than that of the other wires, that for /»—1922—Z/ the temperature
at which the resistance diminishes most, has been shifted about
0,02 degree with regard to the corresponding one for /n—1922—
II and —I//I/, and that the fall extends over a larger tempera-
ture region. Calculations with the available data by the aid of
0,12
olnd-1922- I.
Alnd-1922I[.
6 Ind_1922-_A.
0.08
0,04
0.00
Fig. 1.
SILSBEE's hypothesis") or by the aid of current-densities render impro-
bable that the said displacement is caused by oxidation of n—1922—/
throughout its length to such a degree that only a small nucleus
of indium remained’); the ratio of the Ws in /n—1922—J/,
1) F. B. SiLsBee. Scient. Pap. Bur. of Stand. No. 307 (1917).
2) In contrast with the other wires /n—1922—TI presents a dull oxide-like
surface. After the construction in July 1922 the resistance was preserved in
benzine; though this was supposed to have been distilled, it seems to have con-
tained impurities, which have attacked the wire.
508
—TII and —//] is incompatible with this’). It is improbable that
the wire is strongly attacked over a small part, because then the
question rises why the resistance of the better part of /n—1922—J]
does not disappear at the vanishing-point temperature of the two
other indium resistances. This leads to the conception that the great
rest-resistance of /n-—1922—/ is uniformly distributed throughout
the whole wire. The equality inter se of this quantity over the
three other wires makes this almost certain for them’). For the
—
fo) Ind_1922_A.
a Ind_1922_ ns
A Ind—1922_I. |
0,02
0,01
Fig. 2.
1) Measurements with Jn—1922—A on the dependence of the magnetic threshold
value of the temperature yield for indium roughly a required field of 1,4 gauss
for a vanishing-point displacement of 0,02 degree. i is always 4 m.a. If in
agreement with SirsBre's hypothesis the inner magnetic field of Jn—1922 —I
is to be 1,4 gauss larger than that of J»—1922—TJ, the radins of In—1922—TI
must have been reduced to about 0,005 m.m. by oxidation, which is incompatible
with the ratios of the W,’s, when it is taken into consideration that the two
resistances do not differ much in length.
The variation of the resistance with different intensities of the current has not
been calculated in the experiments with indium wires. A current density 10-times
greater in a tin-wire gave a vanishing-point displacement of about 0,02 degree ac-
cording to Comm. 133d, table LX. With these values for indium the cross-section
of Im—1922—IT would have to be 10-times that of Jm—1922—J, which also gives
a wrong ratio of the W's.
3) The great value and equality of this rest-resistance for all three wires made
us doubt the purity of the supplied indium.
509
present a uniform distribution of the great rest-resistance of /n—
1922—/ seems strange.
It also appears from the tables (cf. also fig. 2) that there exists
a difference of 0,002 degree in vanishing-point temperature between
In—1922—A on one side, and /n—1922—// and —/// on the
other side. An explanation by the assumption of differences of tem-
perature in the helium bath seems improbable. As far as the influence
of the inner magnetic field is concerned, the windings lie at a
distance of 0,4 for /m—1922—A, at a distance of 2,2 m.m. for
In—1922—J/ and —/[1; in definite parts of cross-section and area
of a winding the inner magnetic field is weakened by that of
adjacent windings, and the more so as they lie more closely together.
On calculation *) this weakening appears.too small to be able to
account for the difference found in vanishing-point temperature
between /n—1922—A and /n—1922—J// and —/II.
§ 3. The supra-conducting metals in the periodic system of the
elements, The question rises whether the vanishing-point temperature
has a periodic character. In the periodic system /n lies above 77,
Sn above Pb; it is remarkable that the said temperature rises both
going from Zn to Sn, and from 77 to Pb. Towards the left, from
Tl to Hg, it also ascends; if this rise continues, the vanishing-point
temperature of Aw would lie higher than of Hg. Since Aw did not
become supra-conducting on cooling to 19,5 K.*), the conclusion might
be drawn that Aw — perhaps with other metals — can never
become so°).
1) Cf. footnote 1, p. 508.
4) Cf. Comm. No. 120b, § 2.
5) In Comm. Suppl. No. 44, p. 35 the possibility is, on the other hand, given
that the vanishing-point temperature of Au has not yet been reached on cooling
toel, 5 K.
Geology. — ‘On the occurrence of diamond as an accessory mineral
in olivine and anorthite bearing bombs, occurring in basaltic
lava, ejected by the voleano Gunung Ruang (Sangir- Archipelago
north of Celebes)” By Dr. W. F. Grsorr. (Communicated
by Prof. Eve. Dusois).
(Communicated at the meeting of June 30, 1923).
Dr. G. L. L. Kemmeruine, chief of the volcanological survey
of the Dutch East Indian Archipelago, having collected some
bombs out of the basaltic lavas from the voleano Gunung Ruang,
composed of a mixture of a dark green to black mineral and glassy
plagioclase, the latter in crystals of a size up to 1 em., kindly
intrusted those to the author for microscopical examination.
Two kinds of rock were collected; the first of these is dense
and black and shows strong magnetic properties; examination with
a magnifying glass reveals the presence of magnetite with a tinge of
blue; under the microscope it proved to be composed of densely
crowded grains of magnetite and between those one can indistinctly
recognize strong pleochroitic hypersthene and green coloured mono-
clinic pyroxene.
The second kind, which contains much less magnetite, is com-
posed of corroded olivine, fringed by a border of strong pleochroitic
hypersthene; it also contains bottle-green monoclinic pyroxene. The
plagioclase in both kinds of rock could be determined as belonging
to members of the group which are very rich in anorthite.
In some of these rocks an accessory mineral occurs in a con-
siderable number of minute grains. They may be seen most clearly
in specimen 285 A in which the olivine can be recognized macro-
scopically; around the bomb a crust of the lava in which it is
imbedded is to be seen; this lava has the composition of a basalt
with bottle-green augite and very basic plagioclase.
The plagioclase is twinned according to the albite- and Carlsbad
laws; one of the thin sections shows a plagioclase with three lamellae ;
the first shows in the conoscope, between crossed nicols, the emerging
of the Z-axis within the field of view, slightly inclined to the surface
of the section; the extinction amounts to 65 degrees. The second
lamel shows in the conoscope the emerging of the Y-axis, also
511
slightly inclined; the extinction is 32 degrees. The extinction of the
third lamel is 85 degrees. These observations unmistakable point to
a plagioclase very rich in anorthite.
The hypersthene is strongly pleochroitic from pale green to brown
pink and has a double refraction rather strong for an orthorombic
pyroxene. The hypersthene often contains freakishly formed grains
of magnetite.
The olivine, as seen under the microscope, is colourless; it has a
high double refraction and is always corroded.
The above mentioned accessory mineral occurs in well-shaped
colourless crystals, which are most like to octahedrons, occasionally
with pyramids on the planes, forming triakisoctahedrons; the size
of these crystals is minute, in most cases they are thinner than the
section is, about */,, mm. The slide was difficult to cut. The crystals
are isotropic, they diminish the colour of polarisation of the host-
crystal, but are dark with the host-erystal between crossed nicols.
They show a large black border in ordinary light, also when they
occur in Olivine, owing to their very high refraction.
In many cases the border is so large that only a cone of light
emerges at or near the centre of the grains; this cone can be followed
by moving the tube up and down. The mineral in question occurs
both within olivine and anorthite; in the latter it is principally
deposited on the planes of zonal structure. Besides the crystals also
some irregular grains occur of the same substance, showing the
same properties.
The hypersthene is, remarkable enough, devoid of this mineral
or contains only some occasional grains.
A fragment of the rock with a flat side was chosen; under ap-
plications of pressure striae could be obtained on topaz and on
corundum. Pressure had to be applied, because in preparing the
slides it became evident that the grains of the mineral were easily
jerked out; consequently many cavities are to be seen in the slides.
To resume: the mineral is isotropic, has an octahedral habitus,
a very high index of refraction and a hardness exceeding that of
corundum, if at least we may assume that the striae on these
minerals are due to the minute grains; about this however little
doubt is possible. From these observations we must conclude that
the mineral is diamond; no further experiment being required, which
would indeed be very difficult owing to the extreme minuteness of
the grains.
Assuming this to be true, it seems to me, that it throws a wonder-
full happy light upon the genesis of this mineral. As everywhere
/
512
else, the mother-rock has a peridotitie nature; but in this case there
can be no question of layers of coal or shales, broken through by
lava, fragments of which possibly could have been taken up in the
lava and could be the source of the carbon in the rock.
The diamond is here a primary mineral and even older than
the olivine.
The question left to be answered is this: why is the hypersthene
free from grains of diamond, the olivine and anorthite containing
them both? notwithstanding the fact that the hypersthene crystal-
lized after the olivine and before the plagioclase.
The solution of this question is presumably, that the rock was
originally wholly composed of olivine, and that in the cavities, formed
by resorption, the anorthite crystallized; the olivine being resorbed
the crystals of diamond were freed and suspended in the mother-
liquor; the hypersthene has, by surface-tension, repelled these grains,
which were collected in the anorthite, in which they occur as above
stated, on the planes of growth or zonal structure. This being true,
the reaction olivine — hypersthene + magnetite cannot have occurred
in the solid phase because in that case there could have been no
reason for the diamond to be driven out.
Mathematics. — “The Complex of the Conics which cut Five
Given Straight Lines.” By Dr. G. ScHaake. (Communicated
by Prof. Henprik De VRIES).
(Communicated at the meeting of June 30, 1923).
§ 1. We can represent the conics 4? cutting five given straight
lines a,, a,, a, @,, a, on the points of space by associating to each
of these conics the pole A of its plane x relative to a given quadratic
surface OV. To any point K there corresponds the conic 4? in the
polar plane x of K passing through the points of intersection
Ae A of adil va with’ x:
For this representation the points of the straight lines a’,,a',,.., a’,
which are associated to a,,a,,..,d, relative to O, are singular.
If we take for instance K on a’,, x passes through a, and A,
becomes accordingly indefinite. To A there corresponds the pencil
of conics k* passing through the points of intersection A,,.., A,
of x with a,,..,a,. These are double conics of the system S, under
consideration of oo* individuals.
There are accordingly five straight lines d'r of singular points of
the second order. To a point of any of these straight lines there
corresponds a pencil of double conics of S,. Each of these straight
lines is the representation of a system of op? conics the planes of
which pass through one of the straight lines ap and which cut the
other four of these lines.
If we choose A on one of the two straight lines #,, and 4,,
cutting the lines @,,@’',,a',,a,, eg. on ¢,,, x passes through the
associated straight line ¢,, intersecting a,,..,a,, and this plane
contains oo’ degenerate conics of S, associated to K consisting
of ¢,, and a straight line through the point of intersection A, of
x and a. iS
There are accordingly ten straight lines Ut ty ts, Of
singular points of the first order. To a point of any of these
lines there corresponds a pencil of degenerate conics and each of
these straight lines is the representation of a system of c* degenerate
conics of which one straight line is fived and the other straight lines
form a. bilinear congruence.
§ 2. If K describes a straight line /, x revolves round the asso-
34
Proceedings Royal Acad. Amsterdam. Vol. X XVI.
514
ciated line land k? has therefore always two points in common
with 1.
To a straight line l of points K there corresponds accordingly a
system S, of oo! conics each of which cuts a line | twice and the
straight lines a,,....a, once.
Also the reverse is apparent.
If K describes a plane 2, x continues to pass through the pole
JE OR ae
A plane a is the image of a system S, of oo* conics the planes
of which pass through a point P and which cuta,,...,a,. Inversely
such a system is represented on a plane.
To the conics of S, passing through a definite point /, the points
of a plane curve kp lying in the polar plane x of Pare associated.
In order to find the order of kp, we try to find the number of
conics of S, through P and through a definite point Q of a,. The
conics through P and Q intersecting a,,a,,a,, form a surface of
the fourth order. For a plane through PQ contains the non-degene-
rate conie of this surface passing through P,Q and the points of
intersection of this plane with a,,a@,,a,, but also the straight line
PQ which is a double line of the surface, because together with
the two transversals of PQ, a,, a, and a,, it forms two degenerate
conics of the surface. As a, intersects this surface in four points,
there pass through a point Q of a, four conics of the system S,
of the conies cutting a,,...,a, and passing through P. It follows
from this that a plane through a’, cuts the curve £p in four points
outside a’. Further &p has a double point on a',, which is associated
to the double conic of S, lying in the plane through P and a, and
passing through P and the points of intersection of this plane and
a,,..,a,. The two tangents to kp at this double point are associated
to the straight lines joining P to the two points in which the
corresponding double conic cuts a,. The curve kp is accordingly of
the sixth order. This curve intersects also the ten straight lines fz,
e.g. the line ¢',, in the point corresponding to the degenerate conic
consisting of ¢,, and the transversal of a, and ¢,, through P.
The system of the conics of S, passing through a point P, is
accordingly represented on a plane curve of the sixth order which
has double points on a',,...,a, and which cuts the ten straight lines
ne aati
As kp has six points in common with an arbitrary plane, sz of
the planes of the conics of S, pass through an arbitrary point.
The system S,' of the conics cutting a given straight line /, is
represented on a surface O, The order of this surface, i.e, the
EE
515
number of points of intersection with an arbitrary straight line m’,
is equal to the number of conics of S,' the planes of which pass
through a straight line m. From the order just found for kp there
follows that through a point P of m there pass six conies of S,
the planes of which contain m. All conics of S, in planes through
m, consequently form a surface which has m as a sextuple straight
line and which is of the eighth order, as a plane through m contains
one more conic of this surface. Consequently among the conics of
S, intersecting /, there are eight the planes of which pass through
m and the surface QO; associated to S,' is accordingly of the eighth
order. Evidently the pencil associated to a point of any of the
straight lines a,',...,a@,) contains a double conic of Sj’ and in 5S,’
there always lies one individual of the pencil of degenerate conics
associated to a point of one of the straight lines ¢,,,...,0;.-
The system S', formed by the conics cutting a straight line | and
a,,.-.4,, is therefore represented on a surface Oj of the eighth
order, of which w,,...,a', are double straight lines and t',,,
single straight lines. The two tangent planes at a point of one of
the straight lines a to QO; are the polar planes of the points where
the double conie of S,' corresponding to this point, intersects the
straight line a associated to a’.
Finally we investigate the surface O, which is the image of the
system 9,’ of the conics of S, touching a plane g. The order of
QO, is again equal to the number of conics of S," the planes of
which pass through an arbitrary straight line m. The surface of
the eighth order of the conics of which the planes pass through
m and which cut a,,...,a,, has in common with p a curve £°
of the eighth order which has a sextuple point in the point of
intersection (m, p) of m with p. As each of the conics of this surface
has in common with &* a pair of points lying on a straight line
through (m,@), the number of individuals touching p is equal to
the number of tangents which can be drawn out of (m, p) to k°,
Le. 8 X 7T—6 * 7=— 14. The system S," contains consequently four-
teen conics the planes of which pass through m and the order of
QO, is accordingly fourteen. Now S," has two double conics in the
pencil corresponding to a point of one of the five straight lines a’
and this system has one individual in common with the pencil of
degenerate conics corresponding to a point of one of the lines {.
This individual is a double conic of S,". For if we take a straight
line m of its plane, it counts twice among the conics of $,” the
planes of which pass through m. The above mentioned pencil of
degenerate conics splits off from the system of the conics of S,
34*
516
cutting m twice, so that there remains a surface of the seventh
order which intersects p along a curve &’ with a fivefold point in
(m, y). Instead of 14 we can now draw 7 X 6—5 « 6 = 12 tang-
ents out of (m,p) to this curve. Hence a straight line m/ through a
point of a straight line ¢ has in this point two coinciding points of
intersection with Op.
The system S", formed by the conics of S, touching a plane g,
is represented on a surface O, of the fourteenth order of which
1
a,,...,@, are quadruple straight lines andt',,...... , t',, double lines.
§ 3. From the investigated representation we can now in the first
place derive the number of conics which cut five straight lines and
which fulfil a threefold condition *).
2x 2—=4 of the 48 points which a curve Ap has in common
with a surface QO, fall in each of the double points of kp and one
in each of the ten points of intersection of kp with the straight
lines £. Accordingly the curve kp cuts a surface Q; in eighteen
points which are not singular for the representation.
There are therefore eighteen conics passing through a given point
and intersecting six given straight lines.
2x48 of the 84 points in which a curve kp intersects a
surface O,, lie in each of the tive double points of kp and two in
each of the ten points of intersection of Ap and the lines ¢’. Here
we have therefore 24 points of intersection that are not singular
for our representation.
There are accordingly 24 conics passing through a given point,
touching a given plane and intersecting five given straight lines.
Of the curve of the order 64, which two surfaces 0, have in
common, each of the straight lines a’ splits off four times and each
of the lines ¢’ once. There remains, accordingly, a curve of the
order 34, &**, which is the representation of the system of the conics
in S, cutting two given straight lines. The conics of this system of
which the planes pass through an arbitrary point, are represented
on the points of intersection of £** with the polar plane of this point.
There are therefore 34 conics which cut seven given straight lines
and of which the planes pass through a given point.
We have found in § 2 that there are eight conics which cut six
given straight lines and of which the planes pass through a likewise
given straight line. Hence the system associated to £** contains eight
1) Cf. ScruBerT: „Kalkül der Abzdhlenden Geometrie’, p. 95.
JAN pe Vries, These Proceedings, Vol. IV, p. 181.
517
double conics the planes of which pass through one of the lines a,
and accordingly 4** has eight double points on each line a’.
Likewise the system corresponding to &** contains pairs of degene-
rate conics of which the image points lie on one of the lines ¢’.
For instance to points of ¢,, there are associated the two conics
consisting of ¢,, and the transversals of ¢,,, a, and the two directrices
outside the lines a ours of the system of conics under consideration.
Hence &** cuts each of the lines ¢’ in two points.
The curve £°* cuts a third surface OQ; in 272 points. Four of
these lie in each of the 40 double points of k**, and 20 belong to
the straight lines ¢ There are consequently 92 points of intersection
that are not singular for the representation.
There are 92 conics intersecting eight given straight lines.
From the number of points of intersection of £** with a surface
O, that are not singular for the representation, there follows:
There are 116 conics intersecting seven given straight lines and
touching a given plane.
A surface QV; and a surface 0, have an intersection of the order
112. From this each of the straight lines a’ splits off eight times
and each of the lines f twice. There remains a curve of the order 52.
There are 52 conics which cut six given straight lines, touch a
gwen plane, and of which the planes pass through a given point.
Let us investigate the intersection of two surfaces O, more closely.
It is of the order 196; each of the straight lines a’ splits off sixteen
times, each line f four times. There remains, accordingly, a curve
of the order 76, 47°.
There are 76 conics which cut jive straight lines, touch two given
planes, and the planes of which pass through a given point.
The curve 4° has as many double points on a’, as there are
conies of which the planes pass through a,, which cut a,,..,.a,,
and which touch the planes g, and ,. In order to find this number
we remark in the first place that the conies through two points
A and B of a, intersecting a, and touching g, and ¢,, form a
surface of the eighth order. For in each plane through a, there lie
four conics satisfying these conditions, and a, is not a component
part of any such a degenerate conic. Hence eight conics intersecting
a, and a, and touching gy, and g, pass through A and B and the
line a, is an eightfold straight line of the surface formed by the
conies through A intersecting a, outside A, cutting a, and a,, and
touching gy, and g,. This surface is of the sixteenth order as appears
from its intersection with a plane through a,.a, is therefore a
1
sixteenfold straight line of the surface consisting of the conics the
518
planes of which pass through a, which eut a,, a, and a,, and
which touch g, and @,, and this surface is of the 24 order. The
number of conics in question is therefore 24, and #7" has 24 double
points on each of the lines a’. As for instance the line ¢,, is not a
component part of any degenerate conic cutting a,,...,a, and
touching ~, and ,, k7* has no point in common with any of the
lines tf’.
If we now determine the numbers of points of intersection of
ki* with surfaces O; and QO, that are not singular for the represen-
tation, we find resp.:
There are 128 conics intersecting six given straight lines and touching
two given planes.
There are 104 conics intersecting five given straight lines and touching
three given planes.
§ 4. The genus of the system of conics through a given point
P intersecting a,,...,a,, is equal to that of the associated curve
kp, which is of the sixth order and has five double points; conse-
quently it is five. According to the first theorem of §3 these conics
form a surface of the eighteenth order, 2**. To a conic of 2** we
associate the two points in which it intersects a plane p which therefore
always belong to the curve #£'° along which @'* is cut by p. To
the (1,2)-correspondence between the conics of @'* and the points
of £'* arising in this way, we apply the formula of Zeurnen:
NN, = 2a,(p,—1) — 2e,(p,—i1). . . . . (1)
In this case a, = 1, a, =2, p, = 5, n, = 0 dnd n, = the number
of conies of 2'* touching @, that is, according to § 3, 24. By sub-
stituting these values in (1) we find that p,, i.e. the genus of £'°,
is equal to 21. Hence the curve £'* has 115 double points. Among
these each of the points of intersection of p with a line ain which
k**® has quadruple points, must be counted six times. Further there
belong to them the ten points of intersection of p with the five
double conies of £2'* of which the planes pass through one of the
lines a, and the ten points where p is cut by the double straight
lines of @'® i.e. the transversals fp of two of the lines a@ which
pass through P and form a conic of @!° together with’ the two
transversals of tp and the three remaining lines a. There remain
accordingly 65 double points.
The surface of the conics through a given point which cut jive
straight lines, has a double curve of the 65" order.
A plane through a, has in common with £'* besides a, a
519
curve of the order 14, £'* the points of which may be associated
| A
univalently to the conies of £2'* passing through them, so that 4%‘
: 13 x 12
has the genus five and accordingly Om = 5=73 double points.
Six of them lie in each of the four points of intersection of y with
one of the lines a,,...,a, and also there belong to them the four
points of intersection outside a, of y with the double conies of
2* the planes of which do not pass through a@,, and the points of
intersection of m with the six transversals through P of two of the
lines a,,...,a,. Besides these there are 39 more double points.
Hence the double curve of @'* cuts the line a, in 26 points. These
are points of a, through which there pass two conics of our system
that have there a common tangent plane through a,
The surface 2'* has a twelvefold point in P, as according to
$ 2 our system contains six conics that cut a straight line through
P outside P. A plane through P intersects 2'* in a curve of the
order eighteen and the genus five as again the points of this curve
may be associated univalently to the conics through them. This
eurve has consequently 131 double points. 66 of them lie in P,
six in each of the points of intersection with the lines a, and also
the points of intersection outside P of the five double conies with
the plane must be counted. There remain accordingly 30 double
points.
The double curve of £2** cuts each line a in 26 points and has
in P a 35-fold point.
To the 35 branches of the double curve through P there corre-
spond as many pairs of comics of $2'° touching each other at this
point. Outside P and a, it must have four more points in common
with the plane (P, a@,). These lie in the points of intersection outside
P of the double conic in the plane (/,a,) and the two straight
lines joining P to the points where the transversals of a,,..., a,
cut the plane. For these two points of intersection are double points
of the curve under consideration.
Analogously we can examine the double curves of the surface
2** consisting of the conies that cut six given straight lines and
the planes of which pass through a given point, and of the surface
8°? formed by the conics that cut five given straight lines, touch
a given plane, and the planes of which pass through a given point.
§ 5. We shall first determine the genus of the curve £** belonging
to the intersection of two surfaces QO; and O/. The cone K** pro-
jecting #°* out of an arbitrary point A, has in common with 0,
520
besides £°* a curve of the order 238, £7°*. This curve bas double
points in each of the double points of £**, because the entire inter-
section of A** and ( has a quadruple point in such a point. Further
K™ cuts each of the lines a’ in 18 more points and here £7** has
double points. But this curve has 32 single points on each of the
lines ¢.
The surface Q/ is cut by k?** in
238 «x 8— 5 x 26 x 4— 10 X 32 = 1064
points that are not singular for the representation. These are points
of intersection of 4** and &7**; a part of them lie in the points
where a generatrix of A** touches the surface QO), hence in the
points of intersection of £** with the polar plane of K relative to
O; that are not singular for the representation. As this polar surface
is of the order seven and passes singly through the lines a’, it cuts
kM in 7X 34—5 & 2 8=158 non-singular points. The remaining
906 points of intersection of k'* and £?** are the points where the
bisecants of 4** through A cut this curve. Hence there pass 453
3433
bisecants of £°* through A, and in a plane there lie = 561
bisecants of this curve.
Accordingly :
The bitangents of the developable surface that is enveloped by the
planes of the conics intersecting seven given straight lines, form a
congruence (561, 453).
As K** has 453 -+ 5 X 8=493 double generatrices, the genus
of the curve 4**, hence also the genus of the system of the conics
cutting the lines a,,...,a,, / and /', is equal to: 16 X 33—493 — 35.
To each conic of the surface 2° corresponding to the curve £*,
we associate again the pair of points in which such a conic cuts
an arbitrary plane g; it belongs to the curve &** along which 2%
intersects the plane p. We apply the formula:
NM, = 2a, (p,—1)— 2a,(p,—1) . .. . (A)
to the correspondence (1,2) arising in this way between the conics
of 2°* and the points of 4’. Here 1, — the number of conics cutting
seven straight lines and touching a plane; according to § 3 it is
116. Further 7, —0, a, =1, a, =2 and p,=35. By the aid of
these values there follows from (1) that the genus of 4°? is equal
to 127.
The number of double points of 4°? is consequently 91 45—127 —
= 3968. As there pass eighteen conics of @°* through a point of
one of the directrices of this surface, whence these directrices are
521
eighteenfold straight lines of 2°, £°? has eighteenfold points in the
points of intersection of p with these directrices and each of these
Sah
oints contains ————_
8 1)
The points of intersection of p with the 70 double straight lines of
Q2°* i.e. the transversals d of four of the directrices, each of which
forms a pair of two degenerate conics of £°* together with the trans-
= 153 out of the number of double points.
versals of d and the three remaining directrices, are double points
of 2°, just as the 112 points of intersection of p with the 7 > 8 = 56
double conies of °° the planes of which pass through one of the
directrices. There remain accordingly 2715 double points.
The surface formed by the conics intersecting seven given straight
lines, has therefore also a double curve of the order 2715.
The intersection of 2°? with a plane p through a,, consists besides
of a, of a curve of the order 74, 47‘. If we associate to a point
of k7* the conie of 2°? passing through it, there arises a (1,1)-corre-
spondence between the conics of 2°* and the points of 47“. The
genus of #7“ is accordingly 35 and the number of double points
73 X 36—35 = 2593. The points of intersection of p and the six
directrices of 2°" outside a, are eighteenfold points of 47‘, and each
of them is therefore contained 153 times in the said number of
double points. Also each intersection of p with one of the thirty
double straight lines of 2° that do not cut a,, and each point of
intersection outside a, of g and one of the 48 double conics of
2** that cut a, only once, is a double point of 47*. There remain
therefore 1597 double points. Hence:
The double curve of £2°* cuts each of the directrices of this sur-
face in 1118 points. These are points through which there pass two
conics of our system that have there a common tangent plane through
the directrix.
Analogously it is possible to examine the double curves of the
surface {2*'* formed by the conics intersecting six given straight
of the touching a given plane, and of the surface 2’** consisting
lines and conics intersecting five given straight lines and touching
two given planes.
Mathematics. — “On the Plane Pencils Containing Three Straight
Lines of a given Algebraical Congruence of Rays”. By Dr.
G. Scnaake. (Communicated by Prof. Henprik pe Vaiks).
(Communicated at the meeting of June 30, 1928).
§ 1. In his „Kalkül der Abzählenden Geometrie’, p. 331, ScHuBERT
finds that the vertices of the plane pencils containing three straight
lines of the congruence which two complexes of rays of the orders
m and m’ have in common, form a surface of the order:
Emm! (mm’—2) (2mm’—.3m—38m’ + 4),
and the planes of these pencils envelop a surface of the same class.
In this paper we shall examine what these results become for an
arbitrary algebraic congruence of rays. With a view to this we
make use of the representation of a special linear complex C on
a linear three-dimensional space Rk, which is described in Sturm:
,, Liniengeometrie’’ 1, on p. 269. First, however, we shall give a
derivation of this representation which differs from the one l.c.
§ 2. If we associate to a straight line / with coordinates p,,...),
the point P in a linear five-dimensional space FA of which the six
above mentioned quantities are the homogeneous coordinates, a
special linear complex C is represented on the intersection of a
variety V with the equation
Pi Pe + Pr Ps + Ps Ps = 9
and one of its four-dimensional tangent spaces A,
This intersection is a quadratic hypercone K that has its vertex
T in the point where R touches the variety V. As the generatrices
of K intersect an arbitrary three-dimensional space in the points of
a quadratic surface, K contains two systems of planes each of which
projects one of the scrolls of the surface in question out of 7. Two
planes of the same system have only the vertex 7’ in common, two
planes of different systems a generatrix of AK. The planes V, of
one system are the representation of the stars of rays of the com-
plex C, which have therefore their vertices on the axis a of C, and
the fields of C the planes of which pass through a, are associated
to the planes V, of the other system. The axis a of C' and the
523
plane pencils of this complex containing a, correspond resp. to the
vertex 7’ of K and the generatrices of this hypercone. A straight
line of K in a plane -V,, represents a plane pencil of C the vertex
of which lies on a, and a plane pencil of C of which the plane
passes through a, is associated to a straight line of a plane V,
Now we assume on KA a point S and in the four-dimensional
space FR, a three-dimensional space A. The representation mentioned
in $ 1 arises, when we associate to each straight line / the projec-
tion ZL of P out of S on R,, if P is the point on K corresponding
to /.)
§ 3. The straight line s of C of which S is the image point on
K, is a singular straight line of the second order for the correspon-
dence (/—L). For all the points of the plane o that the three-
dimensional tangent space Rk of A at S, lying in R,, has in common
with #,, are associated in FR, to this straight line.
In & there lie the two planes WV! and V! of K of which the
intersection is the generatrix 6, of A through S. To these planes
there correspond resp. the star of C, that has its vertex in the point
of intersection A of s and a, and the field of C consisting of the
rays of the plane « that passes through s and a. The star A and
the field « have in common the plane pencil (A, a) to which the
straight line 6, on K is associated.
The planes 4 and PV! cut @ resp. along the straight lines p,
and v, each consisting of points that are singular for the corre-
spondence (/—L). For to each point L of p, there corresponds on
K a straight line of V! through S, hence in C a plane pencil
containing s, with vertex in A. Likewise a plane pencil in « con-
taining s, is associated to each point L of v,. The point of inter-
section B, of p, and v, is the image point L for all rays / of the
plane pencil (A, «). In this way the oo’ straight lines of the star A
correspond to the oo’ points of p,, the oo? rays of the field « to
the oo! points of »v,.
To a plane pencil with vertex on a a straight line on XK in a
plane WV, which accordingly intersects V’,,, is associated ; consequently
to such a plane pencil in FR, corresponds a straight line cutting »,.
Inversely the plane through S and a straight line of AR, cutting v,,
intersects the hypercone K along a straight line in V,, through S,
to which there corresponds the plane pencil of C that is associated
1) The method applied here, has been indicated for the rays of space by
Ferix Krein. Cf. Mathem. Annalen, Bd. 5, p. 257.
524
to the singular point of intersection of the chosen straight line with v,,
and along a straight line cutting V,,, which lies therefore in a plane
V, and corresponds to a plane pencil of C the vertex of which lies
on a. In the same way it is evident that the pencils of C in planes
through a, are represented on the straight lines of A, which cut p,,
and that the plane pencils containing a are associated to the straight
lines through the point of intersection B, of p, and v, (for a plane
through S46, cuts the hypercone K outside SB, along a generatrix).
To a star of C, the vertex of which lies consequently on a, there
corresponds on K a plane V, that cuts V,, along a straight line
and the projection of which on FR, passes accordingly through »,.
Hence a plane through wv, is associated to a star of C in R,. It is
easily seen that also the reverse holds good and that the fields of
C, the planes of which pass through a, are represented on the
planes of A, through p,.
§ 4. A congruence (a, 8) of the order « and the class 8 has in
common with C a seroll @ of the order «a+ 8 that has a as an
a-fold directrix. If further has the rank r, there are r plane
pencils through a containing two straight lines of (2.
The curve y in R, on which 2 is represented, cuts p, in the a
points that are associated to the « generatrices of $2 which pass
through A, and v, in the 8 points that correspond to the > gene-
ratrices of 2 in the plane (a, s). A plane through p,. cuts y outside
p, in the 8 image points of the straight lines which the corresponding
field of C has in common with £2, and it appears in the same way
that a plane through v, intersects the curve y outside v, in « points.
Hence the order of y is a + 8.
To the r plane pencils through a that contain two straight lines
of 2, there correspond in R, as many bisecants of the curve y
through ZB. Besides the lines p, and v, which cut y resp. « and 8
times pass through B,. The number of apparent double points of y
is accordingly :
r+4a(e—1)+ 38 (6—1).
We shall just mention an application that Sturm gives on p. 271
of his book quoted in § 1. The order of the focal surface of the
‘congruence I” is equal to the number of sheaves with vertices on a
containing two straight lines of I, hence also of 2, that are infinitely
near to each other. These are represented on the planes through v,
touching y outside v,. Hence the order of the focal surface of I
is equal to the number of points of intersection outside y of v, with
525
the surface of the tangents of y. The order of the latter surface,
that has y as a double curve (cuspidal curve), is equal to
MaB—r).
We find this by substituting in the formula mn (m—1) —2h for n
the order a+ p of y and for A the above mentioned number of
apparent double points of this curve. As v, cuts the surface under
consideration on the double curve y in 8 points, we find for the
number of points of intersection outside y, i.e. the order of the
focal surface of the congruence I:
28 (a—1) —2r.
The class of the focal surface of Tis equal to the number of
planes through a containing two straight lines of I, hence also of
2, that are infinitely near to each other, or equal to the number
of planes through p, touching y outside p,. As p, cuts the curve y
in « points, we find for the class in question:
2a (B—1) —2r.
§ 5. In order to find the order of the surface formed by the ver-
tices of the plane pencils containing three generatrices of I, we
try to find the number of these plane pencils that have their verti-
ces on a. These belong to C and are represented on the trisecants
of y that cut v, outside this curve.
The order of the surface A of the trisecants of y is found by
substituting in the formula:
(n—2) {h—4 n (n—1)},
given by CaYrEY, for n the order a+ of y and for h the number
of apparent double points of this curve found in § 3. We find in
this case:
(a + B—2) {r+ Halal) + HBB) — 4 (a HB) (a + B—1)}
or, after a simple reduction:
Nt a (ed) (a 2) FED (BAB 2):
In order to find the number of generatrices of A that cut v,, we
remark that these are the common straight lines of A and the special
linear complex that has v, as axis. Now the axis of a special linear
complex C may be considered as a double line of C. This follows
in the first place from the representation of C on a hypercone K
that has been described in $ 2 and through which the axis of C is
transformed into the vertex of , but also from the well known
property that m—2 generatrices of a scroll of the order n cut a
straight line of this seroll. As further v, has 8 points in common
526
B (8—1) (@—2)
6
number of generatrices of A cutting v,, is therefore found by
diminishing the order-number found above, by:
3 8 (8—1) (3 —2).
with y, it is apparently a -fold generatrix of A. The
Hence there are
(a + B—2) r + Ha (a—1) (a—-2)
straight lines of 4A which cut »,.
a(a—1)(a—2)
6
times, for as this line has @ points in common with y it is an
u(a—l)(a—2)
6 Ld
has to be diminished by the number of trisecants of y that cut v,
In the first place the straight line p, must be counted
-fold generatrix of 4. Further the number found above
on y. This is the case in each of the 3 points that y has in common
with v,. We find the number of trisecants of y passing through
such a point, by the aid of the property that through a point of a
twisted curve of the order ” with A apparent double points, there
pass A—n + 2 straight lines that contain two more points of the
curve, if we take into account that in our case for each of the
(8—1) (B—2)
2
passing through them, as v, contains 3—1 more points of y outside *
the point under consideration. Consequently
Bir Aha) + 38(@—1)— « — 8+ 2—4 (BD (GDI
or
said 8 points v, counts times among the trisecants of y
Bir + 4 a@(a—1) (a—2)}
trisecants of y that cut v, on y, must be taken apart.
If we subtract these two numbers of straight lines from the
aforesaid number of straight lines of 4 that cut v,, we find that
4 (a—2) {6r — (a—1) (87 —1)}
trisecants of y intersect v, outside this curve.
According to the beginning of this § we arrive at the following
theorem:
The locus of the vertices of the plane pencils that have three
straight lines in common with a congruence ja, B} of the rank r, ús
a surface of the order:
4 (a—2) {6r — (a—1) (88—a)}.
527
§ 6. In order to show that the result found in $ 5, is in accordance
with the result of SCHUBERT, mentioned in § 1, we have to know
the rank of the congruence I(mm’, mm’) that two complexes C,
and C, of the orders m and m’ have in common. It might suffice
to refer to Scnusert, Kalkiil der Abzühlenden Geometrie, where there
is found on p. 330 a derivation of this number. We shall however
show that the order of [may also be found by the aid of the
representation used in this paper.
The surface 2 consisting of the straight lines of / which cut the
axis a of C, is of the order 2mm’ and has aas an mm’-fold straight
line. It is the intersection of the two congruences >, (m, u) and
=, (m’,m’) consisting of the straight lines out of C, and C, that
cut a.
=, and X, are represented resp. on two surfaces S, and S, in
R,. As C,, hence also S,, contains m generatrices of an arbitrary
plane pencil of C, all points of p, and v, are m-fold points of S,
and all straight lines cutting p, and v, have m more points in
common with S,. S, has accordingly the order 2m and p, and v,
are m-fold straight lines of S,. In the same way S, has the order
2m’ and p, and v, are m’-fold straight lines of this surface. The
intersection of S, and S, consists of the straight lines p, and »,,
each counted mm’ times, and the curve yon which @ is represented.
This curve has the order 2mm’ and has mm’ points in common
with each of the straight lines p, and v,. We first determine the
number of apparent double points of y.
The cone A projecting y out of an arbitrary point L of R,, is
of the order 2mm’ and has in common with S, besides y a curve
oe of the order 4in?m’ — 2mm’ = 2mm’ (2m— 1). The curve oe has
(m—1)-fold points in the 2mm’ points where y cuts the lines p, or
v,, because the entire intersection of A and S, must have there
m-fold points. Further 4 cuts each of the lines p, and v, in mm,
more points, that are m-fold points for gp. As all these points are
m’-fold for S,, e has 4mm’? (Am —1)— 2mm" (m—1) — 2m?m' =
= 2mm” (2m—1) points of intersection with S, outside p, and v,
These belong to y and lie partly in the points where a generatrix
of A touches the surfaces S, on y, hence in the points of intersection
with y outside p, and v, of the first polar surface of L relative to S,.
As this polar surface is of the order 2m—1 and has (m—1)-fold
straight lines in p, and v,, it cuts y outside p, and v, in 2mm’(2m—1)—
2mm’ (m—1) = 2m*m’ points. The remaining 2mm'*(2m—1)—2m?m’ =
= 2mm’ (2inm’ —m—m’) points where @ and y cut each other
outside p, and v,, are points that the bisecants of y through L have
528
in common with this curve. The number of apparent double points
of y is therefore equal to mm/’(2mm’—m—m’).
If we choose L in the point of intersection B, of p, and »,,
el, ,
di deat oe zm) of the chords of y through this point coincide with
each of the lines p, and v,. Through B, there pass accordingly
mm’(m—1)(m’—1) bisecants of y different from p, and v,. According
to § 3 these are the representation of as many plane pencils through
a containing two straight lines of @, hence also of I The rank
of the congruence T that two complexes of the orders m and m’
have in common, is therefore equal to mm’ (m—1) (m’—14).
If we substitute this number for 7 in the expression found in $ 5,
and if we make « and 8 equal to mm’, we find indeed that the
order of the surface formed by the vertices of the plane pencils
containing three straight lines of the intersection of two complexes
of rays of the orders m and m’, is equal to:
+ mm’ (mm! —2) (2mm’—3m—8m’ + 4).
We get another check through the application of our formula to
the congruence consisting of the straight lines passing through one
of n given points. For this congruence «=n and B=r=O0. The
locus of the vertices of the plane pencils which three straight lines
have in common with this congruence, consists of the planes that
may be passed through each triple of the given points. By the said
substitutions in the formula of § 5, we find indeed the number of
these planes, namely:
dn (n—1) (n—2).
To the theorem derived in § 5 there corresponds dually :
The planes of the plane pencils that have three straight lines in
common with a congruence }a,8! of the rank r, envelop a surface
of the class:
4 (8—2) { 6r—(8—1) (3a—8)}.
Physics. — “Transients of Magnetic Field in Supra-conductors’’.
By G. Bruit. National Research Fellow U.S. A. (Commu-
nicated by Prof. H. A. Lorentz).
(Communicated at the meeting of June 30, 1923).
It is known that supra-conductivity is determined not only by
temperature but also by the magnetic field and the current density *).
In view of the considerations of SirsBER and LANGEVIN it is
probable that the only essential factors are the magnetic field and
the temperature °).
This hypothesis will be adhered to below. The problems to be
discussed are the calculations of the manner in which a strong
magnetic field impressed from the outside on a supra-conductor
destroys its supra-conductivity and the way in which the supra-
conductivity is reestablished when the magnetic field is withdrawn.
If the view proposed by BrIDGMAN®) is correct there is an evolution
or an absorption of heat whenever a change in the conductive state
takes place. These phenomena being of unknown magnitude, they
will be disregarded below. If experiments should fail to confirm
the calculations here developed, the source of disagreement may be
then looked for in the neglect of BripGman’s latent heat.
The mathematical difficulty of the problem consists in the existence
of two distinct states determined by the magnetic field. The purpose
of this paper is to point out some special solutions (particular
integrals) of the problem.
We shall employ the electromagnetic system of units. By H
(a vector) and by o we shall denote the magnetic field and the
resistivity. The symbol H, will be used for the threshold value of
the field. The resistivity o may have either of two values o,o,
according as to whether |H\ > H, or |H| << H,. The value o, is
the microresidual resistivity and in a special case may be taken to
be zero. The electric intensity at any point we shall denote by the
1) H. KAMERLINGH ONNEs, Proc. Amst. Acad. Sc. 16, (2) 1914. Leiden Comm.
NO. 133, 139.
3) F. B. SivsBee, Journal Washington Academy 6, 597—602, 1916. Bureau of
Standards Scientific Paper N°. 307 (July 23, 1917).
5) Journal Washington Acad. Vol. 11, p. 455, 1921.
35
Proceedings Royal Acad. Amsterdam. Vol. XXVI.
530
E
vector H. The current density is then —. If ¢ be the time, the
5
fundamental equations of the problem are:
An
div H=0 hin de U
oH
div E=0 curl E = — — Nt (29)
Ot
Hence
sal Ns GSE 3
and in the case of cylindrical symmetry, H being parallel to the
axis, the distance from which is 7
Od 0
Se 0e ON
(= ae r Or B 5e) ef 7 6)
If only small penetrations from the surface are investigated the
approximate form
B, Br ee a eee
may be used. The equations (3), (34), (3!) are analogous to equations
in heat conductions and it is therefore of interest to follow out this
analogy somewhat closer. In the case of cylindrical symmetry and
H parallel to the axis the electric
intensity is by symmetry directed
along a system of coaxial circles
having the axis of symmetry for
their common axis as shown on
H the figure (Fig. 1). Dropping now
the meaning of E and H as
vectors and denoting forthwith
£ by E and H the absolute magni-
tudes of the electric and magnetic
intensities, we have from (1)
and (2)
MES WN 5/2)
ib @)
Fie. 1. aR) re - (6)
531
These equations are analogous to the equations in heat conduction:
001
ia = I
wee ateliers, eet (OE)
1 ò 0
== =enkel: ETA Sr OE ON 51
== F)=— ~ (06) (6!
where @ is the temperature, / the flow of heat, K is the conduct-
ivity for heat, and C is the specific heat. The electrical problem
is the analogue of the heat problem for a substance having unit
ue Le eo
specific heat and a conductivity for heat = BSA Thus a perfect
f ud
supra-conductor corresponds to K=O i. e. to a perfect insulator
for heat. This is another expression for the fact that the shielding
properties of the supra-conductor are perfect.
In view of the difficulty of treating
the cylindrical case accurately we
>
shall specialize the problem by in-
vestigating it within the approximation
(3H) i.e. neglecting the curvature of the
surface within the depth of penetration,
this makes the problem an essentially
unidimensional one.
The shaded region on the right of
d AZ the plane AB (see Fig. 2) is occupied
ZZ) by the metal. The axis OX is perpen-
\
dicular to AB. The changes in the field
are produced from the left side of AB.
H is positive when vertical and up-
Ge ward. £ is positive when into the plane
of the paper. The relations between
E and H are:
he}
=
Fig. 2. rn oe Ge)
OE 0H
See ee
and hence
0? 0H
FE) =e 5 Takes Gran 31E)
We shall consider several problems all of which are similar
35%
532
mathematically to STEFAN’s problem of the propagation of the frost *)
though for one case a slight extension of his mathematical method
will be necessary.
Case 1. The material is supraconducting to start with, the field
inside and outside is homogeneous and equal to H, < H,.. Suddenly
the field outside is increased to a value H, > H..
We begin counting time from the instant of the sudden change.
After the lapse of a time ¢ the non-supraconductive state will have
advanced a certain distance 2, into the metal. A moving plane
separates the regions having the two values of o. The low value go,
is on the right of this bounding plane while the high value o, is
on the left. Corresponding to the two values of 6 here are two values
of 8 on the right and left (8,, 8, respectively). On both sides of the
surface of separation 7H = H,. Also # must be continuous at the
boundary. Letting
x
2
Olm er du
Va
0
we know from the work of Sreran that it is possible to satisfy
all the conditions of the problem by letting H on the left and on
the right of the boundary have respectively the expressions:
H,=4, +B, 0(5|/*). EDE (7
by (El 7%:
#, =A, + Bols ©) <3) a
In fact these satisfy (3!) and by a proper choice of the constants
A,, B,, A,, B, the initial and boundary conditions can also be satisfied.
The equations are
En Ae:
A. = A, + B, o(5 VE), o(Z/%)
2 ; 2 ;
1 KO en el OH,
8, CE RS 8, Gs ex
1) WEBER RieEMANN, Differentialgleichungen der Mathematischen Physik, Vieweg
und Sonn, 1919. Vol. IL, pp. 117—121.
J. Sveran, Wiener Monatshefte fiir Mathematik and Physik, I. Jahrgang, p. 1,
1890.
Sitzungsberichte der Wiener Akademie. Vol. 98, Div. Ila, p. 473, 1890.
533
Xe
It follows from the third of these a — — a where a is constant.
t
4
On account of the constancy of « the fourth equation can also be
satisfied. Eliminating the constants A, B we find for a:
a8,
aor ~ = kane ee (ALL)
increases from 0 to @ as « increases from 0 to oo. We can deduce
from this that whatever the values of ,, H,, H‚ may be (provided
H. is between H, and H,) there is always one and only one value
of « which satisfies (11). An increase in |H,—H.| leads to an
increase in «. An increase in |H,—H,| gives a decrease in a. Since
B, is very large we are concerned with
== 2
1—@ (Eva) Ze
2 Vara
2
lim Vs, e î
ral
whence by (11)
_ #8
Hi Hi pak,
ee nn = Ae EAA (2)
H,--H, aV 8, av B,
2 8 2
TT 5 Le) 5 a de 0 5
NEE = Ovand af gm Va i.e. if the externally applied
hd
La
field is 2.77 H, both sides of (12) are unity and hence al ke
value of « that makes vet O (x) = 1.
This value is about 0.77. Since 8, is roughly 1 for tin the con-
stant « is of the order of magnitude of 1.6 and the law of pene-
tration of the boundary is «,=1.6V¢.
It may be shown that the field is unchanged in the bulk of the
supra-conductor and that only a surface current is induced. From
534
this point of view the problem could be solved without reference
to medium (2) by introducing a boundary condition in the medium
1/0H
(1) which is to express the fact that the flow — (a) is Spent
1 w Jt—To
in supplying the quantity HZ to new regions of the material having
initially H == H, and converted to H = H,. The length of the region
. Ghee pn :
converted per second is aay and thus the boundary condition is:
C
0H HH da. 0
Ge TO a caer rr
The problem can be also solved from this point of view.
This direct solution for the case 8,—=o naturally leads to the
same result which we have obtained by passing to the limit of
B,—o. It may be, however, that other problems may be more
easily solved for the case of 8, =a by this method than by passing
to the limit.
Jase Il. Penetration of supraconductivity into a non-supracon-
ductor.
We next pass to the case of a material in which the supra-con-
duetivity has been destroyed by a magnetic field, we diminish the
field from the outside so as to reestablish supra-conductivity. The
supra-conductivity is reestablished first in the external layer of the
metal and propagates inward as time goes on.
Fixing our attention again on Fig. 2 we suppose that just before
t—0O the magnetic field H has a uniform value H, throughout
2 >0O and « >0. This value H, is greater than the critical fleld
H,. At t=O the value of H at the left of AB is dropped to
A, < He.
After the lapse of a time ¢ the boundary between the two con-
ducting states will have advanced a distance w,. For «< «a, the
metal is microresidually conducting and p= 8,. For z >a, the
metal has its ordinary conductivity and ?=8,. The expression for
H for « H.. At t =0
the field at «=O is suddenly changed to — H, where H, > He.
After the lapse of a time t we may expect to find three regions
in the metal. These will be separated by two critical values of
L, SAY Tes Leg, (Le, Ve). In the intervals (0, 2,), (®c,, Leo) (eq, 0) B has
the values ?,, 8,, 8, respectively.
We shall try to satisfy the conditions of the problem by letting the
magnetic field in these three intervals have the following expressions:
a=H=4, 43, 0(5|/%) VEE
HHA, BO a me Be, CAS Les
NOA
nan=armeli|/®) EE
The equality between H, and H, at x, and the equality between
H, and H, at «x,, leads to the conclusion that
Dn Aes Uc == U, Vie
where «,, «, are constants. Thus the boundary and initial conditions
become:
2
VB, Vg
a He= A, + 8,0(% Ba, 4 no(* 7)
B af B _ «Bs
Ze de 4
VB, VB,
gu ef
Ee end
VB, VB,
H, — Ap By 5 fe = A,
Eliminating the constants A, B two equations in a,, @, are obtained.
These may be written in the form:
sle A H, —H, Ee
„le Brea) @g (* El) Adel 1 (S |
2 2
2 H,
AAE yak (% 7%”) Ba ray a, -)) — a, VB :
B, 2 2
a
Since 8, is very large the comparison of the first two expressions
with each other shows that (¢,*—«,*)3, must remain finite. Thus
writing
B, Ee 7 (Gar OF) Sle is a (UG)
and considering only the case of very large values of 3, we have
He HH:
(16)
«Ba y— 3
“inf ZB ; oe 1% ef) |
o> a
The limit last written is taken under the conditions (16), the
quantities «‚y being kept constant. It is easily found that the Lim
ca
e2—1
in @
in question is
540
Eliminating y and letting
eer VB, H
EN
H.H.
the resultant equation for « becomes
2 He 1 | — -1) 0
eo ie («+ 1) 9@ (18)
H,—H. Va @(a)[1— O(a) ae” .
Solving (16') for y we obtain
2 1 1— 90 (19
Us a el 10 )
2H. il :
If t=O (18) becomes —-—— = — . This formula is
H,—H. V xae“@(a)
readily seen to be in agreement with (12) if in the latter H, = — Ha.
Thickness of Supra-Conductive Layers.
Formulas (14) (19) enable us to make an estimate of the thickness
of supraconductive layers produced by the suppression or reversal
of a strong magnetic field. Thus according to (14) the quantity a is
1
of the order of —. Since 8, is approximately 1, the thickness of the
2
layer reached in 1 sec. measured in centimeters is of the order of
magnitude of the ratio of the conductivities just above and just below
the transition point. This ratio may be 10-® and thus if formula
(14) applies supra-conductive layers the thickness of which is of
molecular dimensions are dealt with.
If the thickness of the slab discussed in (15) is 1 em, the first
4n?t
term of the series 7, \ 0, e BE) ig Zeit (8, being set = 1). Thus
if ¢= 10—* sec. (14) and (15) are nearly in agreement and the effect
of finite dimensions is not sufficient to throw off the conclusion just
drawn because 10-4 sec. is a comparatively easily measurable
interval of time.
The thickness of the supra-conductive layer brought about by the
reversal of the field is according to (19) and (16)
A ARE)
== — log ———
8, a VB, tO
and is thus of the same order of magnitude.
It is also of interest to observe that the amount of heat dissipated
by the eddy currents in the microresidually conducting layer is
541
finite. In fact we have shown that the resistance of the layer per
em.” is finite and further the current sheet in the layer has a finite
{th
strength being 7— of the difference in H on the two sides. Thus for
7
the Case II the amount of energy dissipated per cm. is
1 a Pe:
i HN ST.) (EE)
8x t
The sudden change in temperature which would have to be produced
at the surface in order to supply this amount of heat would be
OE Va [yr (H,—H:) (H.—#H,)
i: CE BA aera!
given by °
and is insignificant.
Other considerations for periodic alternating fields indicate that
heating may be an important factor, the danger being in eddy cur-
rents in the part of the conductor having 6 = o,.
SUMMARY.
Special cases of the propagation of changes in magnetic field in
a supra-conductive metal are discussed. The calculations show that
with the assumptions made (treatment of the conductor as a conti-
nuous medium) the thickness of the supra-conductive layers involved
may be of the order of molecular dimensions during perceptible
intervals of time.
The writer wishes to express his gratitude to Professor Lorentz
for his criticism and advice.
Biochemistry. — “Further Researches on the Antagonism between
Citrate and Calcium Salt in Biochemical Processes, Examined
by the Aid of Substituted Citrates”’. (First Communication).
By Dr. J. R. Karz. (Communicated by Prof. A. F. Honieman).
(Communicated at the meeting of May 26, 1923).
1. Hzxposition of the Problem. ,
In an earlier research’) | have tried to analyse the nature of
the biological citrate action. After addition of citrate a biological
liquid behaves as if it no longer contains any free calcium ions;
addition of citrate acts, therefore, in the same way as addition of
oxalate or fluoride. With this difference, however, that the action:
of the latter salts rests on the formation of a very little soluble
precipitate, and that a gypsum solution remains perfectly clear after
addition of citrate. Complex ions must, therefore, have been formed’);
it is only the question, how they are constituted.
In order to bring light in this still dark question, I compared at
the time the action of the citrates with that of substituted citrates,
in which one or more of the groups which possibly can bind the
Ca to complexes (the alcohol group and the three carboxyl groups)
were made inactive by substitutions (acetylation of the alcohol group;
the carboxyl group esterified or converted to acid amide etc). As
typical representative of a biological citrate action the inhibition of
the rennet coagulation of milk was investigated.
It then appeared that when either the alcohol group or one of
the carboxyl groups is made inactive, the citrate action in a ’/,,
N. solution is reduced to '/,, of its strength; (i.e. is made equally
weak as in a citrate solution of '/,, of the same strength), the
removal of two or more groups reducing the action to less than
If Of the original value. When the aleohol group is made inactive,
the action appears to be equally strong as in other tri-or tetra-basic
acids of allied structure, but without oxy-group (as tri-carballyllic
acid, aconitic acid or iso-allylene tetra-carbonie acid. When one
1) These Proc. Vol. XV, p. 434.
2) SABATANI, Atti della R. Acad. di Torino 36, p. 27—53 and Memorie (2) 52,
p. 213—257 was the first to adduce arguments for this theory.
BromBerG, Diss. Amsterdam.
543
carboxyl group is made inactive, the action appears to be equally
strong as in other bi-basic oxy-acids (as apple acid and tartaric
acid). In the same way it appears that when two or three groups
are made inactive at the same time, the action has become as great
as in the then comparable compounds.
Now the question rises.
1. is it also possible to prove such a diminution of the number
of free Ca-ions in less complicated systems than such biochemical
ones by the addition of citrate?
2. do the substituted citrates show there a similar diminution of
activity as in rennet coagulation ?
The best way to answer these questions — the determination of
the concentration of the free Ca-ions in the original solutions —
is unfortunately barred, because we do not know a method as yet
to determine the concentration of free Ca-ions potentio-metrically.
It is, therefore, necessary to have recourse to indirect methods. The
most natural proceeding is to determine how much calcium is held
in solution by addition of citrate, when a substance that precipitates
the calcium as insoluble compound (e.g. oxalate, fluoride, pyrophos-
phate, soap etc.) is added to a diluted solution of a calcium salt.
The solubility product of this reaction must be chosen so that the
action of the citrate manifests itself so as to be easily measured.
If this solubility product is known, the percentage of free calcium
ions is known at least at this small concentration, while it is known
how much Ca remains in solution. *)
The purest results will be obtained by an analytical determination
by weight of the quantity of the calcium that has been precipitated
or that has remained in the solution, as this can be carried out
without appreciably diluting the calcium solution. 1 shall perform
this experiment later on with citrate and with substituted citrates.
But in order to get a preliminary rough idea, a titration can also
be used, though this has the objection of appreciably diluting the
original solution.
Mr. D. P. Ross van Lennep, who assisted me in my experiments
on the influence of substituted citrates on rennet coagulation, pointed
out to me that the soap-titration of calcium after CLarK (as it is
used in the determination of the hardness of water) might render
us good services here.*) He carried out a number of experiments
1) The question in how far hydrolytic decomposition complicates the matter, will
be treated later.
*) A drawback of this method is that the titration does not take place with
water, but with 56-volume percentage alcohol, which changes the surroundings
544
with citrates and substituted citrates, but our experiments were
left unpublished. I have again occupied myself with this problem,
and performed a number of new determinations as a supplement
and check. The results follow.
2. Experiments.
The examined Ca-solution, which was strongly split up into ions,
was prepared as follows. A saturated solution of CaSO, (puriss.
pro avel.) in distilled water was diluted with the 2,3 fold volume
of distilled water. In a narrow-mouthed glass jar of 250 em*. capa-
city 50 em* of this liquid was pipetted off and mixed with 50 cm‘.
of distilled water or with em? of an aqueous solutions of the sub-
stance under consideration. These 100 cm* were titrated in the
same glass jar by Crark’s method (with a solution of soap in
alcohol of 56 volume percentages.*) In the titration a finely divided
precipitate of calcium moleate is formed in the bottle. The endpoint
has been reached when by the side of this precipitate so much
alkali-oleate remains in the solution that, after shaking, the solution
exhibits a not disappearing soap froth. As endpoint was taken the
condition at which after a from six to eight times repeated vigorous
shaking in the longitudinal axis of the bottle, the soap froth appears
at the rim of liquid and bottle, as a white ring, 1 mm. high and
from 1 to 2 mm. broad, and remains thus for five minutes. This
endpoint can be determined pretty sharply, when the necessary
practice has been obtained; when comparing experiments are
always carried out in the same way, repeated determinations of the
same liquid with a quantity of titration liquid of about 45 cm.*
deviate only some tenths of cm.* from the mean of the determina-
tions. For our determinations this accuracy is amply sufficient.
Without citrate the 100 em.” of calcium sulphate solution require
from 45 to 47 ecm.’ of titration liquid to reach this end-point;
hence the total volume of the liquid at the end of the titration
amounts to 145 or 147 em.” If in consequence of the addition of
citrate the liquid required considerably less titration liquid, I added
so much alcohol of 56 volume percentages (spec. gr. 0,921) from a
burette to the 100 cm.*® that was to be examined, that at the end
of the titration the total volume would again be between 145 and
in which the calcium ions are dissolved If, however, only small differences are
measured, in other words if about an equal amount of alcohol is added, this does
not prevent us from obtaining comparable results.
1) I refer for an accurate description, of CrarkK's method to Jahresberichte f.
Chemie 1850, p. 608; to Lunar and Bert, 6th edition. Vol. II, p. 232.
545
147 em’; and in this liquid the endpoint was determined. This
precaution was omitted, when the total volume was between 140
and 147 em.” at the end of the experiment. This measure purposes
to prevent that in an inguiry into the titratable calcium in salt
solutions of the same molecular concentration, these would have
different molecular concentration at the endpoint of the titration,
and would no longer be comparable for this reason.
1/10 N neutral solutions of the sodium salts were made from
citric acid and its various substitution products (neutral towards
litmus; it was verified that they remained neutral towards litmus
on dilution with the same volume of the above gypsum solution).
As normal solutions were considered those that contained one gramme-
molecule per litre (hence not: One gramme-equivalent in multi-basic
salts). The mixture of gypsum and of (perhaps substituted) citrate
accordingly contained the various salts in the concentration of 1/20 N.
The gypsum solution diluted with the same volume of water
consumed on an average 45.7 cm’. This corresponds with 12.2 parts
of CaO per 100000 parts of water; or with 8.7 parts of Ca per
100000 parts of water. In citrates ete. it was derived from a table
of Luner and Burr *) (calculated from experiments by Fars? and
Knauss), how much Ca was not found back in the titration, calculated
as percentage of the total quantity (8.7).
In the first column is given the consumed quantity of cm* of
titration liquid; in the second column the quantity of calcium that
was not found back as percentage of the total quantity.
Thus I found:
a. Citric acid *) 2.6 cm? OE
b. Te alcohol group made inactive.
Acetyleitric acid 40.9 em° 12/-*/,
Compared with:
Aconitie acid 41.3 cm? A SeHe
Tricarbally lic acid 40.8 em’ 12°),
Isoallylene tetra carbonic acid 39.8 em? 14 °/,
c. One carboxyl group made inactive.
Symmetrical citric acid monoamide 41.1 cm! cla
Compared with:
Apple acid 40.2 cm? 133 °/,
Tartaric acid 40.4 em! 1183 By
1) 6th edition, Vol. II, p. 232.
2) When so few cm$ of titration liquid are sufficient to reach the limiting value,
the limit is much less easy to determine than it is otherwise, and the observations
differ much more from each other.
36
Proceedings Royal Acad. Amsterdam. Vol. X XVI.
546
d. One alcohol group and one carboxyl group made inactive.
Methylene citric acid 43.4 em? Sys
Compared with:
Ambrie acid 43.6 cm? Die
Glutarie acid 43.6 em? Darten
Acetone dicarbonie acid 43.9 cm? Gant /e
e. Two carboxyl groups made inactive.
Citric acid dimethyl ester 43.35 em? 54 °/,
Citro diamide 43.75 em? Srey
f. Three groups made inactive.
Citramide 44.4 cm? Steijn
Di ethylester of citric acid monoamide 44.8 em* A
Various indifferent salts of monovalent acids (sodium chloride,
cyanide, formiate, acetyl-salicylate ete.) consume 44.6 to 44.9 em’
of titration liquid; hence also three per cent less than water.
| refer for the structure formulae of the examined compounds to
my previous publication '), where I have indicated them all.
It appears trom these experiments that substitution in the citrates
very considerably diminishes the action. If one group is made
inactive (it seems to be immaterial whether it is the aleohol group
or one of the carboxyl groups), about 11 or 12°/, of the calcium is
not found back in the titration (instead of 96 °/,). This quantity is,
therefore, bound in complexes in the Ca-ion concentration which
corresponds to the solubility of calcium oleate in an alcohol-water-
mixture of about 17 volume percentages of alcohol (per 100 volume
percentages of liquid mixture). In these solutions the compared
citrates and substituted citrates are present in the same molecular
concentration.
When two active groups are removed at the same time, about
5 or 5'/, °/, of the calcium appears to be bound in complexes, in
three groups only 3 °/,.
To be able to ascertain to what concentrations of the not-sub-
stituted citrate these values correspond, I have carried out some
determinations with citrate of much weaker molecular concentration
(all this expressed in the same units as in the experiments described
before).
thoy No citrate) (O!0050' N) 35.9 em? 24°).
ee Nee citratess(OOO25 PN) 42750 cms aaa a
Leo N citrate (0.00125 N) 44.3 cm* 3.4°/,
no citrate 45.7 cm’ —
1) These Proceedings. Vol. XV, p. 434.
547
Through interpolation it is found that 11 or 12 °/, of not recovered
calcium corresponds to 0.0033 N; 5 or 5'/,"/, to 0.0019 N citrate,
and 3°/, to 0.0010 N citrate; hence that the activity is reduced
resp. to 1/,,, */oe /so Of its value through the substitution in the
unchanged citric acid.
These values show good agreement with the results of the rennet
coagulation experiments, where ‘/,,, '/,,, '/:», was found. In view
of the uncertainty in the determinations with small quantities of
complex formation no better agreement can be desired.
We may still point out that also barium and strontium salts are
deprived of their free ions by addition of citrate. Thus I found in
diluted solutions of barium nitrate, strontium nitrate and calcium
sulphate, which required resp
barium strontium calcium
23.0 cm? 25.4 em° 25.4 em?
of titration liquid, that — when these 100 cm° contained '/,,, resp.
‘/,, N sodium citrate — they consumed only:
eee 21.6 cm?* 6.0 em? 11.2 cm’
HEN 16.85 cm? 1.85 em’ 3.9 cm’
3. Conclusion.
a. The biological citrate action rests on the diminution of the
concentration of the free calcium ions through formation of complex
compounds or ions. This citrate action can also be shown in less
complicated systems than biochemical ones, e.g. in the solubility of cal-
cium oleate in citrate.
6. Substituted citrates show there exactly the same diminution of
activity as has been observed in a biochemical reaction (as the
rennet coagulation). When either the alcohol group, or one of the
carboxyl groups is removed, the activity is reduced to '/,, of its
value; this diminution is much greater when two groups are removed
at the same time.
ce. Citric acid owes its strong activity to the fact that it is a
multi-basie oxy-acid.
Experiments with other multi-basic oxy-acids are in progress. |
refer for the literature to the extensive German publication, which
will shortly appear.
36*
Colloidchemistry. — “Researches on the Nature of the So-Called
Adsorptive Power of Finely- Divided Carbon.” 1. The Binding
of Water by Animal Carbon. By Dr. J. R. Karz. (Communi-
cated by Prof. A. F. HorLEMaN).
(Communicated at the meeting of June 30, 1923).
I. Introduction.
The power of finely divided carbon to bind all kinds of substances
is evidently in connection with the degree of fineness of division ;
for in not finely divided condition the carbon does not show this
property. At present the phenomenon is almost universally considered
as a typical example of real surface adsorption, i.e. as the accumulation
of a substance in the boundary layer simply in consequence of the
surface-forces.
This surface adsorption is generally considered as in sharp contrast
with the formation of a solid solution. In the latter case the bound
substance is not only found in the boundary layer solid-liquid, but
through diffusion it gradually penetrates between the molecules of
the solid substance, so that finally the principal quantity of the
absorbed substance is not found in the boundary layer, but
homogeneously distributed throughout the solid body.
A clear realization of the questions that can be solved by
experiments on the nature of this binding to carbon only dates
from the time of physical chemistry. Bancrorr') and others have
considered the possibility that the substances would have been
absorbed by the carbon in solid solution; but the further development
of this thought failed on account of the form of the binding-isotherm.
If we had to do with a solid solution, — this was the. opinion
some twenty years ago — the laws of Henry and Nernst must be
valid, hence the quantity of absorbed substance must be in direct
ratio to the concentration of the vapour and liquid phase, with
which it is in equilibrium. A curve is, however, obtained which is
almost horizontal at first, and which then turns its convex side
downward. This might be explained by the assumption that the
absorbed substance dissociates in the carbon into many (e.g. four
1) The Phase Rule.
549
or ten) molecules. In most of the substances bound by carbon such
a hypothesis has no sense. Besides it does not become clear why
the carbon works the better as it is more finely divided; this must
then be accounted for as a consequence of the easier diffusion.
In 1907 FreounpiicH showed *) that the binding isotherm can be
represented by the formula:
be
Hi n
SF = 5 G
m
for not too great values of c (m is the quantity of carbon, a the
substance bound by it, e the concentration of this substance in the
solution which is in equilibrium with the carbon, « and n are con-
stants). He showed that we had to do here with real equilibria
which are established within a very short time. The degree in which
a solid substance binds, varies greatly with the absorbed substance,
but is little dependent on the nature of the solid phase. FRrEUNDLICH
demonstrated that these facts become perhaps most easily compre-
hensible when it is assumed that the binding rests on surface
adsorption, on a becoming denser of the surface of the solid phase.
But in 1909 he himself does not exclude the possibility that the
phenomenon rests on the formation of a dissociable chemical bond
or a solid solution; he only calls these explanations “wesentlich
unvorteilhafter” ?).
In course of time, however, in default of new arguments for the
other conceptions, this view has gained so many adherers that it
often makes the impression as if it were an established fact that
the sorption by carbon rests on a real surface-adsorption.
In 1910 I succeeded *) in showing that a deviation from the laws
of Henry and Nernst in solid solutions can have another cause than
the dissociation of the bound substance into molecules, viz. when
the mixing in solid solution is chiefly caused by the attraction
between the molecules of solvent and dissolved substance; whereas
in the ordinary diluted solutions the mixing is brought about parti-
cularly by the diffusion impulse (because mixing is a more probable
state, one that takes place with increase of entropy — also when
the attraction may be neglected). In this case the decrease of free
energy is about equal to the heat effect that takes place in the
') Zeitschr. f. physik. Chemie 57, p. 385 (1907).
2) Kapillarchemie, Iste Aufl. p. 289, Akadem. Verlagsgesellschaft Leipzig 1909.
3) These Proc. Vol. XIII, p. 958: Address at the Meeting of the Bunsen-Gesell-
schaft. Kiel, 1911; Gesetze der Quellung, Kolloidchem. Beihefte Bd 9,
550
binding. If the differential binding heat is great, and if it decreases
on absorption of the substance, then follows from the equality of
the variations of free energy and of binding-heat that the binding
isotherm must bave a course as FrevnpLicd must have found, i.e.
that it begins pretty well horizontally, and then turns its convex
side downwards. This appears to be the case in aqueous solutions
of sulphurie acid and phosphoric acid, and in the swelling albumens
and polysaccharides. In all these cases FRREUNDLICH’s formula appears
to hold as approximating formula for small concentrations, even
particularly well in aqueous solutions of sulphuric acid and phos-
phorie acid, though we have certainly not to do here with real
surface adsorption, but with real mixing.
Hence it is clear that the validity of Freunpiicn’s formula does
not furnish the proof that we have to do with surface adsorption.
Inversely the equality in the variation of free energy and heat-
effect is no proof either that there exists an ideal concentrated
solution. It does not seem improbable to me that this equality also
exists with pure surface adsorption, and possibly with many com-
plicated intermediary phenomena called sorption at present. I found
it confirmed in the absorption of water by cupri ferro cyanide, in
which a strong change of colour from violet black to light brown
is found’). The next step is now in my opinion to test this relation
by a number of typical examples of genuine surface adsorption and
of sorption. For if it appears to be valid everywhere, this is an
important contribution to the knowledge of the sorption phenomena;
and if it holds in some cases and not in others, it may be studied
on what this depends. But apart from this it leads to a better
method of analysis of sorption and adsorption phenomena: the
simultaneous determination of the sorption isotherms and of the
sorption heats. This method gives a much deeper insight than the
prevalent one, which is restricted to the determination of the sorp-
tion isotherm for small concentrations. That FrEUNDLICH's formula
is of such universal validity at these small concentrations, will
probably appear to mean that (in a system in which the variations
of free energy and of heat-effect are equal in approximation) the
differential sorption heat is very great at first, and diminishes
gradually during the absorption; the longer the (almost) asymptotic
horizontal initial part of the isotherm, the longer the differential
sorption heat will preserve a great value. What is important in this
method of investigation of the sorption phenomena is further that
1) Verslag van de gewone vergadering der wis- en natuurk. Afd. Kon. Akad. v.
Wet, Dl, XXXI, Nos. 9—10, p. 542,
551
it can take into account not only the course of the isotherm for
small concentrations, but the whole course. And besides it has the
advantage that it does not bind itself beforehand by a preconceived
opinion on the question which can at present mostly not be decided,
of what nature the sorption phenomonon is (solid solution real sur-
face adsorption, dissociable chemical combination, or two or three
of these possibilities at the same time). The simultaneous determi-
nation of the two curves does, however, supply a collection of facts
important for the decision of this question, which every theory has
to take into account.
2. Experiments.
The purest animal carbon of Merck was used for the investigation
It was placed in air-dry condition in a wide-mouthed glass jar; its
water content was determined at 230° C. after 3 hours’ drying. It
is not impossible that in this way the water percentage is found
slightly too high, the weight of the carbon having possibly been
slightly diminished by oxidation. As in most hygroscopic substances
of this kind it remains somewhat arbitrary what is considered to be
“dry” substance.
For the determination of the sorption heats quantities of from
5 to 12 grammes of carbon were weighed in air-dry condition,
which can easily be done accurately, as the substance is not parti-
cularly hygroscopic in this condition; the carbon cannot be weighed
accurately when quite dry. In crystallisation dishes these samples
of carbon were brought in exsiccators over sulphuric acid-water
mixtures of different strengths; we then waited till equilibrium had
been approximately established. In this way samples of carbon were
obtained in which the water was very uniformly distributed. Where
the water-content of the air-dry carbon was known, the increase
or decrease of weight of the sample of carbon yields its water con-
tent at the known vapour tension.
This carbon was placed in a glass tube, which was closed with
a tight-fitting rubber stopper and placed in a calorimeter vessel
filled with water. The experiments were made in a room in which
the temperature was particularly constant. After temperature equili-
brium had been established, the course of the thermometer was
followed; then the contents of the tube were emptied into the water
of the calorimeter vessel, after which the temperature was again
observed. After from 2—4 minutes the generation ofsheat did not
increase appreciably any longer.
552
Let us call 7 the degree of sorption (gr. of water per 1 gr. of
dry substance), and W the heat of sorption (generation of heat in
cal. when 1 gr. of dry substance absorbs 1 gr. of water). Then I found:
Quantity of heat at
i maximum sorption W
per | gr. of dry carbon
0.— 20.91 0.—
0.049 17.66 3.25
0.090 15.34 ay
0.218 11.79 9.12
0.350 7.90 13.01
0.437 6.05 14.86
0.563 3.12 17.79
0.659 1.59 19.32
0.718 1.09 19.82
0.753 0.29 20.62
sorption-max.
0.93 0.— 20.91
This is the integral heat of sorption. From this I caleulate the
differential heat of sorption for 7 — 0
Gr = 75 cal.
di Jixo
This value is considerably smaller than was found in swelling
substances (250 to 400 eal). At the heat of mixing of sulphuric
acid (with water) it amounted to 550 cal., of phosphorus 100 cal,
of glycerine 20 cal.
The curve of the integral sorption heats is graphed in fig. 1; it
starts as the ordinary curve of the heats of imbibition and of mixing,
as a hyperbola, then follows a flattened, almost rectilinearly rising
part, the end again being a hyperbola. Accordingly it is distinctly
different from the curves described by me formerly for bodies that
can swell up.
I have not yet succeeded in calculating the differential sorption
heat in its full course from these measurements. The curve of the
integral sorption heat has so complicated a shape that a formula
with a great number of parameters is required to give any description
of it. The greater the number of parameters, the more arbitrary is
553
: dW
the calculation of the differential quotient saa But this at least may
ai
cal.
20
10
0.50 1.00
Fig. 1.
Mite, zor.
be said now that the curve begins with a= 75 cal, then decreases
di
pretty rapidly, in a way, which corresponds pretty closely with the
course of this quantity in the heats of mixing (of sulphurie acid or
phosphoric acid with water). At 7—0.10 to 7—= 0.15 it begins to
assume a more or less constant (albeit slowly diminishing) value,
amounting to about 23 cal., which diminishes again greatly past
7 = 0.65, and converges to zero.
It would be very important also to study the volume contraction
at the absorption of water; for, where in expansible and in miscible
substances the relation (+) always appeared of the same order
i=0
of magnitude (between 10 and 30 < 10~-‘), it would be important
to examine what the order of magnitude of this quotient would be
in animal carbon. Unfortunately it is not possible to determine these
volume contractions, as carbon probably acts as an adsorbent on
every pycnometer liquid, at least in anhydrous condition.
The free energy at the sorption can most easily be calculated
from the vapour tension of the water at different degrees of sorption.
These vapour tensions have not been determined directly, but
indirectly by the method of Gay Lussac-vaN BEMMELEN (by bringing
the substance into equilibrium with sulphuric acid-water mixtures
of known strength till constancy of weight is reached). The
absorption and loss of water then appeared to be a phenomenon
of equilibrium, which presents Aysteresis. This result is in striking
554
contrast with FreuNDLICH’s experience that the absorption of dissolved
substances, as iodine, dyestuffs, and organic acids, is an equilibrium,
which is readily established independent of the condition from which
one starts, and within a few minutes; this observation of FREUNDLICH’s
was confirmed for dissolved substances by many investigators.
In order to obviate the influence of hysteresis, the equilibrium
had to be determined from two sides; then the approximative value
of the state of equilibrium was calculated by taking the mean of
the two values found in this way. Accordingly twice thirteen samples
of air-dry carbon, each having a weight of about one gramme,
were weighed off in crystallisation dishes. One half of these dishes
were dried for one or two weeks in a vacuum exsiccator over
sulphuric acid; they then contained no more than 1 or 2 parts of
water to 100 parts by weight of dry carbon. The other half was
placed over water in a vacuum exsiccator for the same length of
time; they then contained about 90 parts of water to 100 parts of
dry carbon. Then thirteen small exsiccators were arranged with
sulphuric acid-water mixtures of known vapour tension; in every
exsiccator there was placed a dry and a moistened carbon. These
acids were refreshed a few times. After 40—90 days, when the
dishes had become almost quite constant of weight long before, it
was assumed that they had reached their onesided equilibrium.
All the experiments took place at a temperature of 16—20° C. in
a room in which the variations of temperature were particularly
small (a room built specially for thermochemistry).
The vapour tension A was expressed as fraction of the maximum
tension of water at the same temperature; the sorbed quantity 7 as
grammes of water per one gramme of dry carbon. The free energy
at the sorption of one gramme of liquid water is found from the
1252
18
Fig. 2 shows the isotherm. The curve begins as a real adsorption-
curve (or as the isotherm of a concentrated solution), but with a
very short horizontal initial portion), at half its height, (A = 0,40
to 0,65) it gets, however, an almost horizontal part; at 2 = 0,65
and 70,57 there begins a new part of the curve (which, however,
issues from the preceding part without any abrupt transition), which
again lias an S-shape. It is remarkable how great the quantity
relation A= log’* h.
1) This has probably been drawn too long; has the weight of the carbon not
been somewhat diminished by drying at 200°C. through oxidation? The horizontal
beginning, if it exists, is probably only little pronounced.
555
of water is which this form of amorphous carbon can absorb; over
a sulphuric acid with a 40,997 the substance absorbed 0,929
parts of water per 1 part of dry substance! Accordingly an absorption
of water of the same order of magnitude as in greatly swelling
i Difference
one)
after moistening| after drying | in equilibrium equilibria
0.010 0.009 0.022 0.016 —
0.083 0.033 0.021 0.027 —
0.176 0.039 0.038 0.039 =
0.278 0.062 0.052 0.057 0.010
0.410 0.172 0.141 0.157 0.031
0.517 0.458 0.266 0.362 0.192
0.596 0.570 0.411 0.491 0.159
0.721 0.649 0.572 0.631 0.077
0.788 0.673 0.631 0.652 0.021
0.853 0.698 0.676 0.687 0.022
0.914 0.730 0.715 0.723 0.015
0.962 0.800 0.814 0.807 —
0.997 = 0.929 0.929 =
1.00
0.50
0.50 1.00
Fig. 2.
556
substances. BacHMANN'), who already determined an isotherm of
carbon and water before me, found in cocoanut carbon a maximum
water absorption of ¢—= 0,25. Bert and ANprgss ®) also found in their
carbon a considerably smaller value than I in mine.
The double-S-shaped curve of the isotherm obtained is practically
the same form as that which van BeuMELEN has observed in gels
of silieie acid and of iron hydroxide. The flat portion there corresponds
to the part of the curve in which the gel, which is first transparent,
becomes opaque.
3. Comparison of Free Energy and Heat Ejfect.
A simple comparison of the curves fig. 1 and fig. 2 shows that
dW :
ie and /og h must have an analogous course as function of 2. Both
di
curves have an almost horizontal, almost rectilinear (slowly descending)
portion between 2—0.10 and == 0.60 to 0.65; both curves have
before and after this the shape as for liquids which mix with water
with strong heat effect. By graphical determination of the differential
dW UE
quotient Dn this can be estimated for some values of 2, for which
dt
logh is known. Thus I find:
|
These are only rough estimations; but they show nevertheless
with sufficient probability that in the large middle portion of the
curve (from 7—0.05 to 70.80) the variation of the free energy
1) Zeitschr. f. anorgan. Chemie 100, p 32 (1917).
) Zeitschr. f. angewandte Chemie 1921. Bd. I.
557
is of the same order of magnitude as the heat effect. But with small
2 the heat effect is much smaller than the variation of the free
energy. This latter is probably in connection with the small value
of the first differential heat of sorption in this substance. Most likely
there is no equality in the middle piece either, but only correspond-
ence in the order of magnitude. The experiments are, however,
not accurate enough to set forth this difference clearly.
4. The Analogy of the Curves with those for Newly-made Silicic
Acid and Zsiemonpy and AnpgErson’s Explication.
As I already observed, the isotherm has the same typical shape
as that found by van BeMMELEN and later by ANDERSON for silicic
acid gel. The ‘turn’, the point where the second S-shaped curve
begins, lies at 70.57 and h—0.65 for carbon. Also BACHMANN
found a curve with a horizontal portion for the cocoanut carbon
examined by him (possibly even with two such pieces). And Bert.
and ANnprEss found a curve of the same shape as mine in the carbon
examined by them.
cal.
20
10
0.50
Fig. 3.
That also the curves of the heats of sorption correspond is shown
by fig. 3, in which I have represented BeLtati and Frnazzi’s results *)
for newly-made silicic acid (temperature 12°—20° C.). Unfortunately
these carefully performed researches have so far escaped the notice
of the writers of the books on colloid chemistry, whence they have
not met with the recognition they deserve. The curve typically
1) M. Becuati and L. Finazzi, Attid. R. Instituto Veneto, Serie VIII, Tomo 4, p. 518.
558
presents the same course as that found by me for carbon; the initial
part as the curve for a heat of mixing, the almost rectilinear middle
portion, the end in a curve with the concavity downward. Unfor-
tunately we have no reason to believe that the silicic acid examined
by Brniati and Finazzi possesses exactly the same constants as that
on which Van BEMMELEN and ANDERSON performed their determina-
tions of the vapour tension, as the properties greatly depend on the
preparation. This is, however, the case in the experiments with car-
bon, described above.
In the absorption of water vapour by carbon we have, therefore,
to do with a system of which the isotherm and the curve of the
heats of sorption are in perfect agreement with the same curves of
those silicic acid gels that present a so-called “turn”.
In silicic acid it is very probable that in the flat piece very fine
capillaries are getting filled with water, for absorption of water
causes the opaque substance to become transparent again. ZsiGMONDY
and ANDERSON *) pointed out that the radius of these fine capillaries
can be calculated from the vapour tension of the water in the flat
piece; they then arrived at values of the order of magnitude 1.3
10-* mm. for the initial part, and 2.6 > 10—-® mm. of the end of
the flat piece. And they showed further that when the same silicic
acid gel is changed into an alcohol or benzene gel, and the radius
of the capillary is calculated from the vapour tension of the alcohol
or the benzene, values are obtained for this radius of the same mag-
nitude as in water. This pleads very strongly in favour of the view
that the flat middle piece is due to the filling of capillaries, which
gradually become slightly wider, hence on micro-porosity.
Patrick’) repeated these experiments with liquid carbonic acid
and liquid sulphur dioxide with silicic acid gel. Then he found,
however, much less concordant values for the size of the capillaries ;
he tried to explain this by the greater thickness of the capillary
layer near the critical point.
BACHMANN®), working in ZsicMonpy’s laboratory, also explained
the flat middle piece in the isotherm of carbon and water by a
system of such fine capillaries. The substance being opaque, it can-
not be ascertained if this property becomes stronger in the middle
piece.
1) Zeitschr. {. physikal. Chemie, 88, p. 191 (1914); Zstamonpy, Lehrbuch der
Kolloidehemie, 4th edition, p. 219—284.
2) Parrick, Diss. Göttingen, 1914.
5) BACHMANN, loc. cit.
559
My experiments lead to the following values for this radius:
ela h, = 0.410 Po = PE Se NG ran
(beginning of the
flat piece)
i, = 0.362 We Oso pa TO Erma:
2, = 0.491 h, = 0.596 he Delo OE mm:
dr OE h, = 0.65 ED SCO Tinie
(end of the
flat piece).
The values found for the radius of the micro-capillaries, are in
such close agreement as regards order of magnitude with the values
of ZsIGMONDY and ANDERSON, and with those of BACHMANN, that it is
astonishing that always this order of magnitude is again met with.
(The second system of capillaries which BAcHMANN thinks that he
can derive from his curves, seems questionable to me).
The agreement in the form of the curves for the heats of sorption
with their typically flattened piece corroborates that the flat part
of the isotherm for carbon and for silicic acid has the same cause.
It is the more striking uuder these circumstances that Beri and
Anpress have found that the same carbon which gives a flat middle
piece in the isotherm with water, has a curve without any flat
middle piece, and with a much longer horizontal initial part (for
small 1) with organic liquids (as benzene or methyl alcohol). If the
correctness of these experiments is confirmed, they furnish the proof
that ZsieMonpy’s explanation, cannot be the true one, at least for
carbon. | am, therefore, occupied with a repetition of these experi-
ments, and also with a determination of the heats of sorption.
Since Zsigmonpy’s explanation is inadequate to account for the
flat piece in the isotherm and for the flattened piece in the heats
of sorption, it is in my opinion natural to see a connection between
the deviating form of the isotherm of water and the fact that water
moistens solid bodies, as carbon, much less easily than organic liquids,
as benzene or methyl alcohol, do. We should then have to do in
water and carbon with surface adsorption at a surface that is not
easily moistened, a phenomenon of which so far only one example
has been studied somewhat more closely’), viz. the adsorption of
watervapour to glass-wool which has been thoroughly dried before-
hand, investigated by Trouron’). The glass-wool had been previously
1) FREUNDLICH, Kapillarchemie, 2nd edition, p. 223. Possibly there is solid
solution present as a complication in the boundary layer also here.
2) FREUNDLICH, loc cit.
560
treated by drying at 162° over phosphorus pentoxide, and then gave
an isotherm with a flat middle piece (possibly even with a faint
retrograde piece), which shows a close analogy with the shape of
the isotherm for water and carbon. When the glass-wool had been
well moistened beforehand, it gave an S-form, as they have been
found in mixtures of sulphuric acid and water, and in swelling
bodies with water as imbibition-liquid; characteristic is there the
beginning with a strongly pronounced horizontal piece for small
2, in which region FRrEUNDIaCH’s adsorption formula is valid. Similar
curves were found by Bert and Anpress for the adsorption of those
liquids that moisten the carbon well.
This conception might also be able to explain why the adsorption
by carbon of water presents such strong hysteresis, whereas that
of organic vapours seems to take place without hysteresis. It is,
however, possible that solid solution in the boundary layers also
plays a part in this’).
The experiments are being continued.
5. Conclusions.
1. In the investigation of the phenomena of sorption it is in-
sufficient to determine the isotherm of binding; it is necessary to
determine at the same time the heat of sorption as funetion of the
quantity of absorbed substance at the same material.
2. The examined animal carbon appeared to have an isotherm
with an almost flat middle piece, analogous to the isotherm of newly-
made silicic acid. The sorption-heat had a course corresponding with
this, a flattened middle piece.
3. By assuming that this course is explained by a system of
micro-capillaries, | calculate the radius of these capillaries from the
isotherm at 1.2 to 2.6 uu (as for silicic acid). That this dimension agrees
so closely with that for silicic acid, is somewhat strange and striking.
4. It is, however, doubtful whether this explanation by | the
assumption of a system of micro capillaries is the true one. It
seems probable to me that the difficult moistening of the carbon by
water accounts for it.
5. Very striking is the strong hysteresis in the isotherm *).
1) In the search for possible explanations for the deviating behaviour of water at
carbon much light was thrown on the subject by conversations with Dr. M. PoLANyI.
1) The complicated results of B. GusrAver (Kolloidchem, Beihefte, 1922) and
HäLLsTRoNo's experiments (Diss. Helsingfors, 1920) will be discussed in a following
paper. Not to lengthen this communication, | confine myself to only mentioning
them here.
Chemistry. — ‘ Volta-Lwminescence”. By Dr. J. Lirscarrz. (Com-
municated by Prof. F. M. JArGeR).
(Communicated at the meeting of June 30, 1923).
§ 1. On the passage of electric currents through Voltaic cells
phenomena of light are often observed at the electrodes. This ‘‘elec-
trolytic’, or rather this “electrode” light can appear both at the
anode and at the cathode, as well on use of continuous current and
of alternate current. The nature of the emitted light has seldom
been investigated, and then only unsatisfactorily. Consequently so
far only little could be said with certainty about the nature of the
process. Some researchers (1, 2, 3) have interpreted some of these
phenomena of light as reaction luminescence phenomena — hence
as belonging to the phenomena of chemi-luminescence. If this should
appear to be true, this would be of importance, because, as is known,
ionic reaction is hardly ever attended with luminescence (4, 5). Besides
the phenomena in question are of importance spectroscopically and
electro-chemically. The light emissions under consideration may
certainly not be considered as of an exclusively thermal character.
For, as earlier experimenters already observed, the phenomenon of
light is as a rule the more intense, as electrode and electrolyte have
a lower temperature. Often the luminescence only occurs at very
small intensity of the current. The spectrum is mostly discontinuous,
or it presents at least a maximum of intensity, as is not pos-
sible with purely thermal radiation. At any rate an incandescence of
the electrode metal can be distinguished with perfect certainty from
the luminescence proper. Hence we are justified in distinguishing
the phenomena in what follows as ‘“Volta-luminescences”; and it
will appear that inter se these are of very different characters, though
on the other hand they resemble each other more or less in the
following respects:
1. There is mostly a considerable increase of the resistance of
the cells, as long as the electrode emits light.
2. Formation of solid or gaseous layers at the luminescent elec-
trode, which sometimes entirely prevent the passage of the current.
3. Often an abnormal course of the electrolysis can be observed.
37
Proceedings Royal Acad. Amsterdam. Vol. XX VI.
562
1. Cathodic Luminescence. (WEHNELT interruptor,
Chromoscope of v. BoLron.)
§ 2. The first data about phenomena of light at the anode, as
they appear in the WenNerr-interruptor, were given by WEHNELT
(6) himself. Vorrer and Warrtner found (7) that much stronger light
effects are obtained when the smaller electrode is made cathode,
hence when the interruptor is inserted reversely. A very pure
spectrum of the electrode metal is then observed, and further some
of the hydrogen lines appear. The phenomena also occur when the cell
is not inserted as an interruptor, hence without induction coil.
Without taking these observations sufficiently into account, v.
Boiron (8) later described an arrangement which was suitable for
spectralanalytic purposes and closely resembled the preceding one.
He called this arrangement ‘Chromoscope”’. As anode served a
thick platinum wire or platinum plate; as cathode he used a pla-
tinum wire, or a rod of the metal that was to be examined spectro-
analytically. The electrolyte (H,SO,, or better HNO, 1:4) contained
in the first case a small quantity of the substance to be examined.
When the current is closed by carefully immersing the cathode,
very clear and pure spectra of the metals are obtained, which are
present as electrode or in the electrolyte, and besides H-lines (espe-
cially H,) and the Na-D-line. v. Bouton used a potential of 110
Volt; then the strength of the current in his electrolyte-chromoscope
amounted to 0,15—0,3 Amp., in his metal chromoscope to 2 Amp.
Morse (9) investigated the light of the WeuNeLr-interruptor more
closely. He used an alternate current of a pretty considerable
strength, and found that cathode and anode give the same spectrum;
the cathodic light was, however, much stronger than the anodic
light. He did not observe H-lines. The spectra obtained sometimes
resembled the arc-speetrum more closely, sometimes the spark spec-
trum, without his being able to give a satisfactory explanation of
this. There are, however, always characteristic differences between
WeureLt- and spark-spectra, resp. WEHNELT- and arc-spectra. We
shall come back to further observations of Morse later on.
For the investigation of the cathode spectra the arrangement of v.
BorroN is the most suitable; this was still somewhat modified for
experiments of longer duration. Fig. 1 represents a simple model of
an electrolyte-chromoscope, with which experiments can be made
without difficulties. A U-tube is placed within a cooling-jacket ;
the legs of this tube are closed by two rubber stoppers, in which
563
the electrodes are fastened. By means of an intermediate piece the
two legs are connected with each other and with the water-jet
suction-pump, which immediately removes the oxyhydrogen gas
formed in the electrolysis. The luminescence is started by the im-
mersion of the cathode, and at the same time the cell is closed
air-tight. In the metal chromoscope the tube drawn in fig. 2 comes
in the place of the U-tube.
In order to photograph the spectra, the light was thrown on the
slit of a HrirGer spectrograph by means of a small condenser with
small focal distance. When Viridin-Inalo plates were used, the expo-
sure had sometimes to be continued from 40 to 150 minutes, be-
cause spraying took place. As electrolyte HNO, 1:4 was generally
used; other electrolytes, however, may equally well be used, e.g.
Fig. 1 Fig. 2
diluted or concentrated H,SO,, KOH ete.; this brings about no
essential difference as to the nature of the phenomena.
She
564
Al spectra.
Spark.
Electrolytechromoscope.
Metalchromoscope.
Arc.
Spark.
Electrolytechromoscope.
Are.
Metalchromoscope.
Mg-spectrum in d.electrolytechromoscope
Mg-arcspectrum.
Strong solution.
Dilute solution.
160—180 V. 68 min.
< 100 V. 136 min.
Spectra obtained with the electrolytechromoscope.
Fig. 3.
565
$ 3. In contrast with what was found by Morss, H-lines (espe-
cially H.) were present in the emitted spectrum; further Pt-lines at
platinum cathodes. Apart from this it was stated that electrolyte and
metal chromoscope, give totally different spectra, — a fact which was
quite overlooked both by v. Botton and by Morse. When the metal
that is to be detected, only occurs in the electrolyte, the spectrum
very closely resembles that of the spark-spectrum of the metal. If
this same metal is, however, immersed as cathode in pure acid, a
spectrum is obtained which agrees closely with the are-spectrum.
As an illustration of these facts, which I could verify repeatedly,
some photographs have been reproduced here (fig. 3).
That we are justified in speaking of a general behaviour here,
follows for the rest, besides from our own observations (with Mg,
Pb, Fe, Wo, Mo, Ta, Al, Cu ete), also from the data of v. Botton
and Morse themselves. If the metal is at the same time in electro-
lyte and electrode, it is to be expected that a superposition of the
two spectra is observed. Since, however, the metal chromoscopes
produce more intense phenomena, it is easy to understand that
Morse observed a strong arc-spectrum that is generally superposed
by a weak spark-spectrum.
If the chromoscopes are to function normally, a definite current
intensity is required in both cases, which though dependent on the
adjustments of the apparatus, always remained within the limits
indicated by v. Botton. With Cu-salt in the electrolyte chromoscope
(fig. 1) e. g. O,4 —0,5 Amp. appeared to be required. A greater
intensity of the current caused incandescence of the wire, and the
disappearance of the luminescence, whilst a- weaker current
caused the total light intensity to become smaller. As appears from
the adjoined photographs, also a selective weakening takes place:
some lines losing much more in intensify than the rest. The same
effect may also be reached by greatly diminishing the concentration
of the metal salt.
In many cases, especially when earth-alkali salts are used, one
has the impression that the whole liquid at the cathode is lumi-
nescent. This effect is, however, not always found; besides the
spectrum was not changed by this. The co-luminescence seems to
be caused by still unknown accessory circumstances.
With regard to the mechanism of the emission process it may be
considered as an established fact that the cathode is surrounded by
a gas envelope. As already Voriur and Warrer observed, this may
be shown simply as follows: when a well-luminescent chromoscope is
566
first cut out, and then immediately inserted again, the luminescence
quickly continues without it being necessary to take the electrode
out of the liquid and immersing it again. If, however, we wait a
short time after the cutting out, a hissing sound is heard after about
2 or 3 sec., and now the chromoscope is not at once luminescent
again when it is inserted. Moreover the experiments of RiksEN-
FELD and Prürzer (11) have described, plead still more in favour
of the existence of a gas layer. There a small of light arc is formed
between cathode and liquid, and I could verify that the same spectral
phenomena are obtained as in the chromoscope. On use of Pt- or
Ir-cathodes, the metal to be detected being present in the liquid,
a spark-spectrum is obtained; when, however, the metal is used as
cathode with pure acid, and are-spectrum.
§ 4. Probably the following idea must be formed about the origin
of these cathodic luminescence phenomena. Between electrode and
electrolyte there is formed a gas envelope containing hydrogen,
water-vapour and some oxygen; within this layer lies almost the
whole fall of potential of the cell. The cations not being able
to traverse this layer, there a current of rapid cathode rays is formed,
which discharge these cations. The discharged metal atoms now
get into the gas layer, and are excited to the emission of a
spark-speetrum by collision with similar flying electrons.
The spraying of the cathode is greatly promoted by the impact
with positive particles. If, as in the metal chromoscope, the current
density and the strength of the current intensity are relatively high,
also uncharged atoms of the electrode metal get into the gas layer
— either because the spraying consists primarily in a scattering of
molecular particles, or because locally a sufficiently high tempera-
ture arises —, and then an light-are is formed and hence an arc-
spectrum is observed.
If the electrolyte at the same time contains a sufficient number
of ions of the electrode- or another metal, a spark spectrum of the
second metal can of course appear by the side of the arc-spectrum
of the first metal. This is, however, not necessary. Depending
upon the nature of the electrode metal, the arc-spectrum is more or
less apparent. Thus Morse showed already that the spectrum of a
platinum cathode is intense in solutions of acids and alkalies, but
very faint in solutions of earth alkalies, while a strong aluminium
(arc-)spectrum appears with an aluminium electrode in almost any
electrolyte. The relations that are valid here must, however, still
be examined; possibly the greater or less tendency to spraying of
567
the electrode material is playing here a prominent part. That melting-
point and evaporation point of the metal are not decisive, has already
been stated by Morse.
(LI) Anodic Luminescence.
§ 5. As might be expected, the phenomena at the anode are much
more numerous and much more complicated than those at the
cathode. Besides gas layers, also layers of solid substance can esta-
blish themselves here between electrolyte and electrode, thus causing
luminescence. The sparks which appear in valve cells at the limiting
tensions (10), have not been examined in what follows.
According to the nature of the emitted light and the cause of the
luminescence at the anode, the following typical cases of lumines-
cence can be distinguished.
1. Line- and band-spectra; to a certain extent these are very
similar to those at the cathode, but they are generally much weaker.
2. Are-spectra, equal to those at the cathode, but which can but
rarely be obtained, and then only on definite conditions.
3. Generally a yellowish luminescence — which in so far as this
can be ascertained, is spectroscopically continuous, — without forma-
tion of a layer of oxide or anything of this kind. The anode metal
(or the carbon used as anode) gets shiny or bright.
4. For so far as this can be ascertained a continuous emission,
with a maximum of intensity in a definite spectrum region; in this
ease the formation of solid layers at the anode always takes place.
First of all we will give some instances and some further parti-
culars of the phenomena in each of these four classes.
§ 6. 1. Already Vorrer and Watrter record that at an interruptor
anode from platinum in sulphuric acid 1:40, they obtained — by
the side of the NaD-line — a faint band spectrum. If this cell
contained sulphuric acid and also metal salts, the lines of these
metals also appeared. The data of these investigators could be fully
confirmed; no more than they, did I, however, succeed in deter-
mining more accurately the band-spectrum lying in the green '). The
intensity of the phenomenon was, indeed, too small for spectroscopic
investigation, though it was always clearly perceptible, also in aqueous
potassium hydroxide 1:10, and on use of other anode metals. Special
phenomena were obtained on use of platinum anodes in sulphuric
acid 1:40, containing at once several metallic salts.
In order to obtain anodic metal lines, greater quantities of metallic
salt must in general be dissolved in the acid. Even then mostly a
1) Very probably these ,bands” belong the oxygen spectrum.
568
few characteristic lines stand out very clearly (e.g. the green TI-
line; the three green Cu-lines). If the acid contains two kinds of
metalions, often only one of these kinds of ions can be detected
spectroscopically. An example of this is furnished by the following
experiment :
A platinum anode was immersed in sulphuric acid 1:40, which
contained a sufficient quantity of sulphate of sodium and sulphate
of copper. First so much current was passed through that the anode
wire became incandescent; then gradually resistance was inserted
until the incandescence stopped and the characteristic yellow lumi-
nescence appeared. Only a very strong Na-D-line was observed then
in the spectroscope. When gradually still more resistance was put
in, the yellow luminescence and the Na-D-line became fainter and
fainter, and the Cu-lines began to appear (in the green). Ata definite
terminal voltage green sparks were also immediately to be observed
by the side of the yellow sparks at the anode.
It is exceedingly difficult to elucidate the nature of these very
faintly luminous phenomena experimentally. It can only be stated
that the luminescence appears to be caused by numerous sparks,
and that there is undoubtedly a gas-envelope present also here, as
already Vorrer and Water pointed out. Very probably a similar
mechanism is to be supposed here as in LecoQq DE BoisBAUDRAN’s ‘‘ful-
gurator’. In this apparatus we have a layer of gas and vapour
between anode and electrolyte, through which the sparks penetrate.
$ 7. 2. A beautiful and very intense anodic arc-spectrum can be
obtained with an iron rod in hot concentrated or diluted sulphuric
acid (sp. gr. 1.80 and H,SO, 1:4); less easily by means of tungsten
anodes in the same medium Then the temperature of the anodes
is pretty high; the colour of the emitted light is a brilliant blue.
The tension in these experiments was 225 Volts. The emission did
not appear until the luminescence described under 3 had been
observed for a shorter or longer time. We shall, therefore, have to
return to the said phenomenon presently.
3. A very peculiar light phenomenon is observed when the current
is closed by immersion of a carbon- or metal-anode in concentrated
or diluted sulphuric acid. The carbon then gets covered by a beautiful
yellow mantle of light, which continues to persist for a long time;
the carbon surface gets smooth, carbon powder and superficial impu-
rites are removed. Metal anodes present an analogous behaviour, as
was by observed by v. Borron (8), to whom we owe a method by
this procedure for polishing and cleansing carbon electrodes. (14).
569
I have been able to corroborate the validity of this experimenter’s
results in every respect — both on use of concentrated and of
diluted sulphuric acid. A digressing behaviour is shown only by typical
valve metals (e.g. Al and Ta). These emit a white or bluish light.
For so far as could be ascertained, the spectrum of the yellow
light is continuous; often the Na-D-line is still to be observed. After
the experiment the electrodes surface is bright and smooth, but
the electrode-diameter is mostly slightly diminished. The white light
from valve metals is continuous, but on the boundary electrode-electro-
lyte-air sparks often appear then, which certainly emit line-spectra.
The terminal voltage during the yellow luminescence (in Cu, Fe,
Mo, Wo, Ni, C) is about 100 Volts, the intensity of the current
some tenths of an Amp., i.e. on use of wire-electrodes of a diameter
of some mm., which were immersed 1— 2 cm. deep. The temperature
of concentrated sulphuric acid then rises very rapidly to the boiling-
point, that of diluted sulphurie acid (smaller intensity of current)
somewhat more slowly. When once the boiling-point temperature has
been reached, the colour suddenly changes from goldish to brilliant
blue; at the same time the current is reduced to less than 0,1 Amp.,
the terminal voltage rising to the total value available (225 Volts).
Then the well known are-spectrum of iron or tungsten is seen in
the spectroscope. This experiment is very suitable for demonstration.
Analogous phenomena can most probably also be obtained in other
metals, though less easily.
§ 8. The appearance of an anodie are of light particularly at hot
anodes, is, indeed comprehensible; the yellow luminescence is, how-
ever, less easy to understand. A purely thermal emission of the
metal cannot be supposed. Nor can there be any question of a
reaction luminescence, since the light always possesses the same
colour, no matter what anode material is used. Von Borron
suggested that the anode gets covered with ‘‘a yellow incandescent”
oxygen mantle. In fact oxygen can be brought to an emission of a
yellow continuous light by an electric current at higher pressure
(13). At lower pressure a maximum of intensity in the green or
yellow green occurs in this continuous spectrum. It may, therefore,
be assumed as very probable that our electrodes are surrounded
by a mantle of oxygen generated electrolytically, in which the gas
is brought electrically to light emission under pretty high pressure.
At higher temperatures the pressure in this oxygen layer must
diminish, perhaps the layer must become quite unstable, and finally
conditions are reached which give rise to a metal are of light.
570
§ 9.4. Anodic light emission has often been observed during electro-
lyses, when an insoluble or sparingly’ soluble reaction product is
formed at the anode. This product can then form either a solid
layer firmly attached to the anode, or a layer that gets more or less
easily detached.
The former can often be observed in valve cells. Already below
the limiting tension a dullish white light may be seen at the valve
anode (10), which becomes pretty intense under definite cireumstan-
ces, (e.g. with Al-anodes in borax solution, Ta in diluted alkali or
carbonate solution). With this emission of light should also be
classed the emission of light of magnesium anodes in diluted
alkali (15).
In all these cases the potential rises to the maximum value avail-
able, the passage of the current is almost entirely prevented. The
luminescence begins very soon after the closure of the current, often
with periodie oscillations of the intensity during the first minutes,
and then continues to persist till the current is broken. The light
emission is, however, generally soon prevented, when electrode or
electrolyte are heated by the weak current that continues to pass.
In prolonged experiments it is, therefore, necessary to ensure good
cooling.
The light, which is almost always a dullish white, sometimes more
greenish or bluish, appeared to be continuous on spectroscopic in-
vestigation.
It is also noteworthy that with magnesium anodes the maximum
of light intensity is reached in potassium hydroxide 1:100; a very
strong luminescence is also obtained by using an ammoniac solution
of di-sodium phosphate instead of the hydroxide. In this medium also
zine anodes produce an exceedingly beautiful light emission, a borax
solution being the most suitable electrolyte with aluminium. But
also with aluminium and with tantalum diluted alkali hydroxide
solution ete. can be used.
In these processes the electrolyte is covered by an adhering layer
of the oxide or of another insoluble anode product, as this was
already shown by other experimenters. The generality of such
phenomena is brought out by the fact that always new observations
of the kind described are being communicated (cf. e.g. 1a).
But also when no direct valve actions are to be observed, such
phenomena of light are nearly always found when at the anode a
sparingly soluble product is found. To these belong, among others, the
following phenomena of luminescence which have partly already
been known for some time:
571
Electrolyte Phenomenon
KJ aq, saturated a bright luminescence at anodes of Cd, Hg, Pb.
„nm " ” n » Pb, Al, Ta; Mg gives a
H,SO4 conc. j
short flash; at Cd anodes there is seen a ring of light, which
moves up and down.
KOH aq, strong Fe (a bright luminescence, but which cannot very easily be
examined on account of strong foaming), Ni (very slight
intensity of the current).
Na,HPO, NH,aq Cu gives a circle of sparks.
Exceedingly intense is the luminescence at an Hg-anode in saturated
Kl-solution at sufficient density of the current. The bright anode-
surface is covered with a thin layer of mercury iodide immediately
after the closure of the current, and then begins to emit a golden
light. After a short time the intensity of this light reaches a maximum,
and then diminishes again. By renewal of the mercury surface,
either by stirring or by allowing the mercury to overflow from a
funnel-shaped anode vessel, etc. the luminescence can be restored
with full intensity.
In agreement with former experimenters (2) the spectrum of the
emitted light was found to be continuous, with a maximum of the
intensity in a definite spectral region. WiLkinsoN (2) has _ pointed
out that the colour of this light also agrees with that of the light
emitted by the anode product in question, when it is bombarded
by cathode rays.
§ 10. [t is exactly these kinds of luminescence that are very often
considered as reaction luminescence (chemi-luminescence). Formation
or decomposition of the anode products were thought to be accompanied
by a luminescence which could reach a considerable intensity with
sufficient reaction velocity’). Bancrorr (1) and his pupils, also
Wixkinson (2) have endeavoured to give support to this view. In
the course of our own observations on comparison with those of
other investigators it appears, however, that this conception is untenable.
In the first place it can be established that all the phenomena
described in this chapter, are related. And this not only because
they appear to be of the same nature spectroscopically, but also
because their occurrence always appears to be bound to the formation
of sparingly soluble or unsoluble anode products.
1) On this conception compare (5).
572
Premising this, it may be inferred from a pretty great number of
reasons that a conception of these luminescence phenomena as reaction
luminescence phenomena must be considered as erroneous.
In the first place with this view of the matter it cannot be ex-
plained why only formation of unsoluble products gives rise to
luminescence. It can, indeed, be predicted that the probability of
anodic luminescence and its intensity will be the greater as the
anode-product dissolves with the greater difficulty. For it appears
in particular that on formation of readily soluble anode-products,
luminescence never seems be observed.
Nor can the considerable increase of intensity of the luminescence
at low temperature (hence at smaller reaction velocity) be accounted
for on the ground of the said conception. For with valve anodes
the luminescence is by no means most pronounced on particularly
strong anode-reaction, but only when the excluding layer is as stable
and homogeneous as possible, and is attacked as little as possible
by the electrolyte. Thus magnesium emits the brightest light in
diluted KOH, aluminium in borax solution, which would certainly be
unaccountable in the case of real “chemi-luminescence”’. A mag-
nesium anode is particularly strongly attacked by diluted sulphuric
acid, though all the same, there is no luminescence at all to be
observed.
Moreover it remains inexplicable how anodes which are rapidly
covered by an insoluble layer, yet continue to emit light. It might
much sooner be expected in this case that the light would cease
after the formation of a covering layer. But this is by no means
observed in the majority of the cases.
Finally the increase of light intensity after the closure of the
current, as is particularly clearly observed with mercury anodes in
KlI-solution, is unaccountable in a reaction luminescence. For, how
a certain quantity of reaction products would be able to increase a
direct chemi-luminescence, is not clear. Nor can periodic and rhythmic
light emissions (Cd in Kl-solution, Mg immediately after the closure
of the current) be accounted for in this way.
§ 11. The only conception which can be brought to harmonize
with all the experimental facts, is in contrast with the conception
diseussed just now, in my opinion the following: at once after the
closure of the current a layer of reaction products is formed at the
anode, which hampers the passage of the ions to the anode, or
renders it impossible. Then the electric discharge of these ions takes
place (at sufficiently high potential) under the influence of split off
573
anionic electrons, which fly through the anode layer with strong
acceleration. By this the matter in this layer is brought to lumines-
cence in the same way, hence with emission of the same spectrum,
as this would happen by means of cathode rays. If the Jayer becomes
too thick, higher potentials will be required to bring about a passage
of the current, and finally current could only pass in certain
cases when the layer is traversed by sparks (limiting tension with
anodes). When on the other hand the layer is attacked by the
electrolyte in some way or other, if is very well possible that also
the light emission at the anode can vary locally, and in particular
the periodic oscillations of the intensity along the anode become
possible. Increase of temperature will always hamper the lumines-
cence, either because the solubility of the anode product is in
general increased by it, or because the layer is rendered less stable
by it in mechanic respect. If the anode layer has little mechanical
stability in itself (e.g. mercury iodide), a certain minimum current
density will be required to form a coherent layer with sufficient
velocity, and to allow this to continue to exist, in spite of continued
decomposition.
By this conception also the analogy between the anodic and
cathodie luminescences is clearly brought out.
Summarizing we may say that also in these anodie luminescence
phenomena, as this was earlier shown for ordinary chemi-lumines-
cence (5), not the anode-reaction in itself takes place with light
emission.
It must rather be admitted that first reaction products are formed
which are brought to emission, in this case by means of the electric
energy of a source of current outside the system examined '). Hence
there is no question of an ion reaction, which takes place with light
emission, and of a departure from the general rule that it is just
these reactions, which proceed practically with infinite velocity, that
are never accompanied by a light-emission.
The above considerations show further that Vorra-luminescence
occurs very frequently, but also that it can be of a very different
character. On further investigation of these phenomena it will be
necessary to distinguish these kinds of Vorra-luminescence scrupu-
lously. The present investigation may be considered as a first attempt
at reconnoitring the ground in this respect.
1) In cases of common chemi-luminescence the reaction itself furnishes the
energy necessary to excite to light emission some of the kinds of molecules present
in the system. (see 5).
574
LITERATURE.
1) Wirper D. Bancrorr and his pupils in Journ. of Physic. Chemistry 18;
213, 281, 762 (1914). 19; 310 (1915).
2) WILKINSON, ibid. 18; 695 (1909).
3) KATALINIC, Zeitschr. f. Physik., 14; 14, (1923).
4) J. Lirscuirz, Helv. Chim. Acta, 1; 472, (1917).
5) J. Lirscnirz u. O. E. KALBERER, Zeitschr. f. physik. Chem. 102; 393, (1922).
6) WEHNELT. Wied. Ann. 68; 233, (1899).
7) VoLLER u. WALTER, ibid. 539, (1899).
8) W. v. Bouron, Zeitschr. f. Electrochem. 9; 913, (1903).
9) H. N. Morse, Astrophys. Journ. 19; 162, (1904), 21; 223, (1905).
10). A. GÜüNrBER SCHULZE, numerous communications in the Annalen d. Physik.
11) RiEsENFELD u. PriirzpR, Ber. 46; 3140, (1913).
12) Lecoq DE BorsBAUuDRAN, Spectres lumineux, (Paris 1874), compare also the
data given by URBAIN, Introduction à l'étude de la Spectrochimie (Paris 1911).
13) Zie H. Kayser, Handbuch der Spectroscopie.
14) D. R. P. v. Stemens & HALsKE.
15) BaBorovsky, Zeitschr. f. Electrochem. 11; 474, (1905).
Groningen. Anorganic and Physico-Chemical Laboratory
of the State University.
Physiology. — ,,/s Caesiwm Radio-active?” By Prof. H. ZwAARDF-
MAKER, W. E. Ringer and B. Smits.
(Communicated at the meeting of June 30, 1923).
Up to the present potassium and rubidium are the only elements
in tbe series Li, Na, K, Rb, Cs, which have been proved to be
radio-active. It has often been suspected that caesium also possesses
a slight radio-activity, but thus far this is not certainly known.
E. RurarrrorD') simply remarks that caesium is barely radio-active
and St. Mryger and KE. von ScuwinDLER’) suggest that radio-activity
may possibly exist, but the penetrating power of the rays emitted
is so low that it does not reach beyond the limits of the substance.
We know for certain that commercial preparations of caesium exert
no photographie action, even in exposures for months. Neither could
one of us*) detect in carefully purified caesium preparations any
ionization of the air of a flat ionization-chamber.
It is a fact, however, that biologically caesium exerts in many
cases an influence similar to that of potassium and rubidium. This
influence was already known to Sipnny Ringer‘) and has, moreover,
been purposely studied by one of us.*) After an unsuccessful effort
in winter we succeeded in the summer of 1917 in keeping hearts
of coldblooded animals beating on a dosis of caesium-chloride that
only slightly differed from the usual potassium-dose. It appeared that
potassium-, rubidium- and caesium-chloride could be used promis-
cuously, but that a much larger quantity of caesium had to be
applied for a toxic effect. With regard to uranium, thorium, radium,
and radium-emanation it behaved antagonistically, which was after-
wards also confirmed by Miss L. Kaiser °).
Here, then, a contrast manifested itself. Physically well-purified
caesium-compounds are to be considered as non-radio-active, whereas
1) E.°RurHERFORD in Marx's Hdb. der Radiol. Bd. II S. 531, 1913.
2) Sr. Meyer und E. v. ScHwiNDLER, Radioaktivität, 1916 S. 428.
8) W. E. Rineer, Arch. néerl. de Physiol. t. 7 p. 484, 1922.
4) 5. RINGER, Journal of Physiol. Vol. 4 p. 370, 1883,
5) H. ZWAARDEMAKER en C. DE Linp VAN WIJNGAARDEN, K. Akad. v. Wetensch.
27 Oct. 1917, Proc. vol 20 p. 773.
6) L. Kaiser. Arch. néerl. de Physiol. t. 3 p. 587, 1919.
576
biologically a well-proportioned dosis of caesium behaves like ‘the
radio-active elements potassium and rubidium.
To elucidate this we undertook an experiment with preparations
of various origin. They were carefully purified and examined phy-
sically and biologically before and after the purification.
By a physical inquiry we tried to determine the ionization-power
of the perfectly dry caesium-salt in a flat, air-tight ionization chamber.
The salt had been spread evenly on a copper dish of 30 em.
diameter.
The dish was isolated with amber and charged to constant poten-
tial of 500 volts by a battery of small accumulators. 34 ¢.m. above
the salt layer was a copper disc also of 30 em. diameter, which
was connected with a pair of quadrants of a sensitive electrometer.
The “needle” of this electrometer was maintained at 40 volts.
A uranium-unit of Me Coy of 50 square m.m. showed with this
arrangement a deflection of 100 scale-divisions in about 2 minutes;
a layer of dried potassium-chlorid in 5 minutes about 50 scale-
divisions *).
Our caesium-chloride preparations yielded widely differing results,
of which a survey is best obtained by a comparison with the ioni-
zation power of potassium ceteris paribus.
Activity Impure Pure
CsCl of E. DE HAËN 1/6 of the act. ifpotassium | 1/37 of the act. of potassium
CsCl of MERCK WAKO ay 5 inactive
CsCl of KAHLBAUM WEI 6 aie ; 1/80 of the act. of potassium
CsCl of Pourenc fr. VEN B 5 Wind, 5 5 5 5
The biological examination was carried out with an isolated frog’s
heart (ventricle + right auricle suspended to a Symes cannula with
an overflow, so that the pressure could never exceed 5 cm. of water.
Three Mariotte-flasks with a cock-system provided a means of per-
}) We see, then, that in this flat ionization chamber the ionization power of
potassium (beta-radiator) is 7000 times weaker than that of uranium (alpha-radia-
tor). This ratio will be quite different in a high ionization-chamber. RUTHERFORD
(p. 528) estimates the ionization power in the ordinary ionization-chamber at !/1000
of the beta-radioactivity of uranium. The beta-radioactivity of uranium in its turn
rests on uranium X, with which the uranium of the ordinary preparations is in
equilibrium.
577
fusing the heart alternately with Ringer-solutions of various com-
position. First we determined the minimum dosis of potassium-
chloride that the individual heart required, after which it was per-
fused with a RiNGer-solution, without potassium until it came to a
standstill. After ten minutes, in which interval we ascertained that
no latent automaticity existed, we proceeded to caesium perfusion.
We determined in succession the minimum-, the optimum- and the
maximum-doses. The dosage was gradually increased with the great-
est care. By means of an air-injector, such as was used by Lockr
and RosENHeIM, the same ‘/, or 1 Liter of circulating fluid was sent
round. The fluid that went through the heart was thus loaded witb
as much oxygen as is soluble in a weak salt-solution.
The dosis of potassium-chloride and of caesium-chloride that proved
just sufficient to make the heart beat regularly, was considered as
the minimum dosis; as optimum dosis we took the one which yielded
the greatest frequency and maintained it. It was difficult to find the
maximum-dosis, because an increase in the caesium dosage brings
on an inconvenient negative inotropism.
We then considered as highest practicable dosis the one which
produced lytic symptoms of cessation of contractility. Strictly the
maximum dosis lies somewhat higher. Meanwhile the caesium has
penetrated deep into the heart-cells, for it takes hours before a heart
can be deprived of the profusion of caesium and before its action
can be arrested by a RinNeer-solution that contains neither potassium
nor caesium.
A survey of our results can again be best obtained by an inter-
comparison of caesium and potassium.
Minimum-dosis of the impure preparations.
CsCl of DE Hain 8.7 >_< KCI-dosis
CsCl of MERCK 5.3 & KCl-dosis
CsCl of KAHLBAUM 4.9 > KCI dosis
CsCl of Pourenc fr, 4.1 > KCl-dosis
The minimum-, optimum-, and highest practicable doses are, for
the impure preparations in milligrammes of caesium-chloride per Liter
on an average in the ratios of:
4194; 1538. 1998:
min. opt. highest pract.
38
Proceedings Royal Acad. Amsterdam. Vol. XX VI.
578
Of the purified doses the quanta must be much larger:
Minimum-doses of the purified preparatigns.
CsCl of DE HAËN 9.5 & KCI-dosis
CsCl of MERCK 19.4 KCl-dosis
CsCl of KAHLBAUM 7.2 < KCI-dosis
CsCl of PouLenc fr. 12.3 & KCl-dosis
The minimum-, optimum-, and highest practicable doses are for
the purified preparations of caesium in milligrammes of caesium-
chloride per Liter, on an average in the ratios of:
1678 : 2760 : 4134.
min. opt. highest pract.
When comparing impure and pure caesium we obtained the
following mean results:
Impure CsCl Pure CsCl
in minimo 5.5 & min. KCl 10.7 X min. KCl
in optimo Lisle ea (TT ee
highest pract. OE Len _ 20D ar 5
So we see that in minimo the quantity of pure caesium must
be from 2 to 3 times larger than that of impure caesium.
On the 16 of May 1923 it appeared that of the preparation,
purified to such a degree that no radiation whatever could be
demonstrated for a given heart, in minimo 39, in optimo 47 and
as highest practicable dosis 58 grs. had to be added per Liter of
circulating fluid. It is obvious that in such cases the quantities of
NaCl had to be largely diminished in order to prevent hyper-isotonia.
‘One of us has set up for the radio-active substitutes of potassium
a working-hypothesis, viz. that in general isolated organs require
so much of a radio-active element in their physiological circulating
liquid as is necessary to generate per second the emission of a
number of ions that is equal for all substitutes. This hypothesis can
be expressed in a logarithmic graph.
In such a graph rubidium and caesium cannot be taken up directly,
since we do not know how many ions these substances emit per
579
second, so that no place can be assigned to them on the axis of
the abscissae. When, however, the minimum-, and the maximum-
IT
ES OAD ERGE
El |
|
Fig. 1.
dosages are known, a place may be found for them on the axis
of the ordinates, and when assuming the law to hold good also for
these substances, their hypothetical place on the axis of the abscissae °
may be determined by erecting a perpendicular. We have plotted
the graph accordingly and thus given a value for rubidium as well
as for caesium. We know then the presumable number of ions that
will be emitted under the given premisses per gram and per second.
For our pure preparation of caesium it appears to be 55 per gram
and per second. With such a small number of ions we can expect
a photographic effect only after 9 years. It is easy to understand,
therefore, that up to the present endeavours to produce any effect
of caesium upon a sensitive plate, have not been successful.
The 55 ions per gram and per second that, according to the
hypothesis of the corpuscular equivalence, should belong to pure
caesium, cannot really belong to the caesium as such, but must be
due to the impurity of the commercial preparation, which had been
removed from the caesium in the following way :
Addition of copper sulphate; perfusion of sulphureted hydrogen
for */, hour; after 24 hours removal of the precipitate of copper
38*
580
sulphide by filtration; removal of the residue of sulphureted hydrogen
by boiling the filtrate.
A second precipitate is generated by adding to the filtrate some
drops of ferro-chloride solution and afterwards an excess of ammonia;
this precipitate of iron bydroxyd is filtered off again after some
hours; this process is repeated three times.
Lastly a third precipitate is generated by adding barium chloride
at boiling heat; next day the precipitate is filtered off; this process
is repeated under an excess of sulphuric acid, so that all the barium
is precipitated; now the filtrate contains a small amount of caesium
sulphate over and above all the original caesium chloride.
This procedure serves to remove a heavy radio-active element,
which is left behind in the precipitate.
Originally the caesium-salts we used contained some of this
impurity. If the dosis is high enough then there will be enough of
the impurity to produce a biological action such as we may expect
of a radio-active substance.
This biological action has the nature of a beta-radiator as is
obvious from the antagonism of our caesium to uranium. Miss L. Kaiser
has recorded some instances of Cs-U-equilibria.
We annex a recent instance.
RUE
a WAN NY
PP.»
et 45°00 Cale
kloppen = beat Fig. 2.
A frog’s heart beats initially on a Ringer solution, which contains
per Liter instead of potassium 10 mgr. of uranyl nitrate. By adding
to this solution a quantity of 1500 mgrms of Caesium-chloride a
radio-physiological equilibrium is engendered between the alpha-
radiator uranium and the beta-radiator caesium. A standstill corres-
ponds with this equilibrium in which there is not even latent auto-
maticity. However, directly when we increase the quantity of caesium,
a caesium beat is developed. Another equilibrium will then again
be called forth by increasing the quantity of uranium, which now
is on a higher level, because more has been taken of the two
581
components. Finally a larger amount of uranium restores the heart’s
beat.
Considering that besides radio-active, also non-radio-active para-
doxes occur, (Noyons, Busqurr) no conclusive value can be ascertained
in the easily generated, transient standstills when passing from a
uranium liquid to a caesium liquid and vice versa. It is different
with the equilibria, which can only be interpreted radio-physiolo-
gically. This is most evident with the higher equilibria in which
each of the components, co-exist in the mixture in quantities that
undeubtedly surpass the threshold-concentration.
Our inquiry, then, is to the following effect:
1°. the impurity that imparts to the commercial preparation of
caesium a feeble radiating power, is presumably a heavy radio-
active element.
2°. the biological action of the impurity has the nature of a beta-
radiator.
Hydrodynamics. — “On the resistance experienced by a fluid in
turbulent motion’. By J. M. Burgers. (Communicated by
Prof. P. KurenFEst).
(Communicated at the meeting of May 26, 1923).
§ 1. Introductory remarks.
The problem which is discussed in the following lines is to search
for a method to calculate the resistance experienced by a fluid in
turbulent motion. A definite solution has not been arrived at; a
first attempt only is given.
As is generally known, in most cases the motion of a fluid through
a straight cylindrical tube or channel is not in parallel lines with
a constant velocity along each line. On the contrary it is usually
very irregular: the velocity of a particle changes its value and its
direction continually, and particles situated very near to each other
have very different velocities, whereas there seems to be no definite
law governing these deviations. This type of motion is called sinuous
or turbulent, as distinguished from the streamline or laminar motion,
which occurs at low velocities only. In studying turbulent flow the
conception of the mean motion or principal motion has been introduced
by various authors. This mean motion is obtained if in every point
of the space occupied by the fluid the mean value of the true
velocity with respect to time is determined, and then the steady
motion is imagined the velocities of which are equal to these mean
values. The true motion may be described as the resultant of the
mean motion and of a fluctuating relative motion. The mean velocity
of the latter is zero *).
A turbulent flow usually experiences a high resistance, which is
approximately proportional to the second power of the velocity of
the mean motion. If the law of resistance is written:
een ev
loss of pressure per unit of length J=C ES
1) In connection with the distinction between mean motion and relative motion
the reader is referred to: H. A. Lorentz, Turbulente Flüssigkeitsbewegung und
Strömung durch Réhren, Abhandl. über theoretische Physik I (1907), p. 58—60.
583
in which formula V represents the mean velocity (i.e. the volume
of fluid which in unit of time flows through a section of the tube,
divided by the area of that section), d the diameter of the tube,
and o the density of the fluid, then C is called the coefficient of
the resistance, and appears to be a function of the characteristic
Vdo
u
viscosity of the fluid). The value of C for different cases is given
in textbooks; as an example may be mentioned:
a. for rough walled tubes C is approximately independent of R;
however, it is a function of the roughness;
6. for very smooth tubes of circular diameter:
C= 0,1582 R-*),
The greater part of the theoretical investigations on the turbulent
motion treat the problem: how does it originate? *) An explanation
of the increase of resistance which accompanies the appearance of
the turbulent state of flow has been given by Rernorps and Lorentz *).
More than once it has been remarked that this problem is one of
statistical nature“). The resistance experienced by the fluid and
indicated by our measuring apparatus is a mean value. It is possible
that such a mean value may be calculated sufficiently approximate
without an exact knowledge of the fluctuating and never exactly
number introduced by Rrynonps: R = (u is the coefficient of
returning relative motions.
In the following lines a preliminary attempt is made to determine
the value of the resistance and to explain the quadratic law. In the
first part (paragraphs 2 and 3) two equations given by RxyNno.ps
and Lorentz are discussed and put into such a form that immediately
appears what quantities are wanted in order to calculate the resistance.
In the second part (paragraphs 4 and 5) a simple idealized “model”
of the turbulent flow is constructed which allows these quantities
to be determined.
Instead of the flow through a tube or channel a more simple
1) Comp. fi. R. von Mises, Elemente der technischen Hydromechanik I (1914)
p. 57 and H. Brasius, Mitt. über Forschungsarbeiten, herausgeg. vom V. D. I.,
Heft 131 (1913).
3) Cf. F. Norruer, ZS. für angew. Math. u. Mechanik 1, p. 125, 1921.
3) O. Reynorps, Scientific Papers IL, p. 575—577;
H. A. Lorentz, le. p. 66—71.
4) Among others by TH. von KARMAN at a lecture at the “Versammlung der
Mathematiker und Physiker” in Jena 1921; comp. a remark in the ZS. fiir angew.
Math. u. Mechanik 1, p. 250, 1921,
584
type has been chosen: the motion of a fluid between two parallel
walls, one of which has a translational motion in its own plane with
the velocity V with respect to the other, while the distance between
the two walls has the constant value / (comp. fig. 1). To ensure
this motion forces of magnitude S per unit of area must be applied
to the walls in opposite directions. The tangential force between
any two adjacent layers of the fluid has the same value S. The
law of resistance will be written:
SCG ahh ese | ee
The coefficient C is a function of Reynrorps’ number:
vl
sae (2)
u
For small values of R the motion is laminar, and the value of
C is easily seen to be:
CSS RETE PA Ne
3 (8)
If the value of R is high, the motion becomes turbulent, and C
decreases much slower. There do not exist any direct measure-
ments for this case of motion; however, the arrangement of the
experiments made by Couerre comes very near to it’). According
to this author we may expect a formula of the following type:
CRS Cn ee ener we (Lt
Investigations by von KÁRMÁN on the law of decrease of the
mean motion in the neighbourhood of a smooth wall*) point to:
C= 10.008 RN nan on | u dy .
The relative motions, however, are not independent of the mean
motion. In order that the relative motions may always retain the
same energy, it is necessary that the following equation is fulfilled:
l I
5 —dU —
— fayom T= f ayuP ERE eee oh (©)
dy
0 0
586
The equations (8) and (9) are substantially the same as the
formulae (36) and (46) from Lorentz’ paper l.c. above, only simpli-
fied according to the conditions of the problem before us.
LU
Now firstly oe will be eliminated from eq. (9) by the aid of (8):
y
l
l
=~ Sf dyer =f dier Gay +0 FF. 1 sake
0 0
Secondly by integrating (8):
=S dou. oo =
This equation allows the elimination of S from (10):
l
[over ve foes]
ulo
r= Ar MD
7
— { dy 9 uv
0
In order to simplify the equations we may introduce undimen-
sioned variables by means of the formulae:
V
oan lays u Varo = Ve! Ee cr AR (LS)
If now in the following equations the accents are omitted again,
we obtain:
1 ph 1
| dy (uv)? — (fa =) | dy ©?
0 0 1 0 1
= tiga aes (14)
— | dy wo fare
0 0
and by the same substitutions, from (11):
S niel
hm KE mende de ee (15)
The equations take a very simple form if the following abbre-
viations are used:
587
1
— [ain =o
0
1
[ aycoor 1 + not Mitr 0) A)
0
1
fe
0
It will be easily recognized that the three quantities o, tr and x
are all of them essentially positive.
The equations (14) and (15) now reduce to:
(17)
and:
EO En 18
ev: SR a)
Formula (17) will be denoted as the principal equation.
§ 3. Discussion of the principal equation.
Equation (17) shows first of all that an increase of the velocity
V of the mean motion cannot be accompanied by a proportional
change of the relative motion: in this case o, rand * would remain
constants, whereas A increases, which would violate equation (17).
If the value of A is given, (17) gives a condition to be fulfilled
by the relative motion. If a certain type of relative motion, fulfilling
this condition, accompanies the mean motion, the latter will experience
a resistance determined by the value of C, calculated from (18).
Now the problem arises: can we find admissible values of the
quantities + and x, without an exact knowledge of the true relative
motion? If r and x are known, (17) gives 6 (i.e. in some measure
the relative intensity of the relative motions), and (18) gives the
resistance coefficient. If we look at the application of statistical
methods in the dynamical theory of gases, we should expect that
for high values of A (which mean a fully developed state of tur-
bulence), it may be possible to calculate + and x in the following
manner: firstly we determine all kinds of relative motions which
fulfil eqq. (6) and (7); secondly we admit that all these motions may
be present independently of each other, their weights being governed
588
by some law of probability, or by a maximum- or minimum-con-
dition. Then the mean values are calculated for this assembly.
Prof. von Karman from Aix-la-Chapelle pointed out to me that before
trying to find a condition governing the weight of the different types
of motions, it would be advisable at first to search for the maximum
value of S, or of o. In this way a higher limit for the resistance
of turbulent flow would be found.
That a maximum value exists may be shown thus:
From (17) it is deduced that 5 may become great (i.e. especially :
if
great as compared to Rp? only if x< R and if t becomes small.
The value of + is determined by the distribution of the values of
uv over the interval O ea
op): D 630 D
A simplification further arises from the fact that the second and
third equations (16) which determine t and x are homogeneous as
regards to the intensity of the vortices. In using these equations it
is allowed to multiply 6 with an arbitrary factor. The true value
of a is found from the principal equation (17). It would be possible
to calculate the true value of b afterwards, but this is of no use.
The problem put in paragraph 3: to make o as great as possible,
obliges us to search for a function 6(D,&) which gives a value of
— uv as nearly constant as possible. Two rather simple types of
functions will be discussed.
I. We will begin with an investigation of what can be reached
if all vortices have the same thickness D. In that case in order to
595
obtain a constant value of — uv, it is necessary to make b independent
of §, in other words to distribute the vortices uniformly over the
breadth of the current. However, it is obvious that the vortices cannot
pass through the walls of the channel; hence we must take:
=constans, if0< §<1— D
b=0 ,if§<0o0r§ >1—D
Consequently the quantity —wuv will have a constant value in the
region defined by: Daqy<1—VD only; in the two remaining
strips it decreases to zero.
With the omission of a constant factor, the following expressions
for — uv are found:
a) if y< D:
y|D
y
je
— wo =far (TG) f dre
0 0
D y 6 y 6 y 7 y 8 y |
EE) EN 754 0( <4 || 315 ES ES
zoo '**(3) ~ 42°(5) +845) -9(5) +70(5)
b) if Do y<1—D:
y 1
x — D
— uu ik so) =D {a LDS
y—D 0
c) if y >1— D: in the expression given under a) y has to
be replaced by 1 — y.
(32)
(33)
By means of these formulae we find:
1
ig oe: vane 9)
— | Mn eed
0
1
7 = hie D 2
| dy (uv)? nn) (1 — 1,172 D).
0
ONS BRD rr ten (BA)
All vortices being of the same dimensions, equation (30) gives
immediately :
hence:
294
HI D? (35)
Inserting these values into equation (17):
1 294
j= — = (36)
"0,828 DR 0,828 D'R
39*
596
(if the terms of the highest order only are written down). This
formula gives a maximum value for o if the thickness D of the
vortices is determined by:
peel (37)
Smeren e «
which gives:
0,027
SER sene sc ee)
The coefficient C of the resistance formula (1) now becomes,
according to (18):
S 0,027
1
Pere es VE + terms of the order Ek (39)
mea Sy, l :
C' diminishes proportionally to vat hence we do not obtain the
quadratic law of resistance, but the resistance appears to be propor-
tional to the 14-power of the velocity. This does not conform to
the result of paragraph 3. In the latter paragraph, however, it was
assumed that the most intensive vorticity was concentrated in the
neighbourhood of the walls only, whereas in the model considered
above it is distributed uniformly over the whole breadth. If all
vortices have the same dimensions, it is not possible to distribute
them otherwise, without disturbing the field of uv-values. Hence we
must try to obtain a better result by using vortices of different
dimensions.
Il. If we take vortices of different dimensions, say with thick-
nesses ranging from D—1 to a lower limit D, (to be determined
later on), the thickness of the boundary layers in the most favourable
case will be of the same order of magnitude as D,. The same
applies to the quantity r. If now the contribution of the vortices of
thickness D to the integral [5 dy becomes asymptotically propor-
1D
tional to “~ for small values of D, the value of this integral will
IPP
1
become of the order of: magnitude of D.’ In this case we shall be
0
in the circumstances considered in the deduction of equations (19)
and (20). Paying attention to equation (31), it is necessary that
2 1
B= fas shall be proportional to D for small values of D.
Now it appears that a distribution of vortices fulfilling these
597:
conditions can be found, if all vortices are put against the walls.
If this be done, it is of course unnecessary to use the variable &
introduced in the beginning of this paragraph, as the positions of
all vortices are fixed. Only a determination of the function B(D)
is wanted. The following form of this function gives the right
distribution of wv-values:
1. the class of vortices whose thicknesses lie between the limits
dD
D’
these vortices are divided into two equal groups, each of them
situated along one of the walls;
2. besides the vortices mentioned under 1), there is a number of
vortices of thickness ) — 1, which have the total intensity */, (in
D and D+dD have a total intensity proportional to Bd D= 2
game unit as used above).
With this determination of B(D), the value of — uv appears to
HEBE << t=):
il 1
EN aD ayy aD (ly ae
v 154
1 1
“dy dy 1 (40)
=| — p(y) + | —p (1) + PY) =
y al ai 4
y 14
1
7 20)
The first term represents the contribution of the vortices lying
along the wall y= 0; of these vortices only those are of importance
for which D>y. The second term represents the contribution of
the vortices situated at the other side; here only those for which
D> 1—y are of importance. The third term represents the contri-
bution of the group of vortices whose thickness D is equal to 1 *).
1) If we should take the quantity B proportional to D—”, with n <1, the
integral [@ay would take a smaller value, but now the first term of equation
(40) which gives the contribution of the vortices situated against the wall y = 0,
would become:
: 1 1
{ee LEN esate 5 24+” (l—n)* (for D
pio \p) =! fans i)* (for y >D,)
y y
If y becomes small, this expression approaches to zero. Only if „=l it ap-
proaches to a value independent of y, which is necessary in order that a constant
value of — uv at all points outside of the boundary layer may be obtained.
598
In the boundary layer defined by O Ao
8
ERE 1 2 3 4
Fig. 2.
The method for measuring the magnetisation, it sources of errors
1) In the paper these deviations have been mentioned as probably due to
inaccuracy in the topography.
615
and its corrections form the subject of the following paragraphs;
we will consider more especially the topographic calibration of the
electromagnet. It was carried out partially by means of the investiga-
tion of gadolinium sulphate in liquid hydrogen and so it furnished
new material for the knowledge of the susceptibility of this sub-
stance, confirming old results. This new material will be communi-
cated at the same time.
§ 2. Apparatus and method. The magnetisation was calculated
from the force exerted by an inhomogeneous magnetic field on a
small quantity of the material. For the measurement of the force
the same apparatus was used as in the investigation of gadolinium
sulphate in 1914, except a small alteration in connecting the tube
containing the substance under consideration. At that time no de-
scription was given, so now some details may be mentioned. The
apparatus was constructed by Mr. G. J. Fim, chief of the Technical
Department of the Cryogenic Laboratory, mainly on the same prin-
ciples as the apparatus of KAMERLINGH Onnes and Perrier *) for the
investigation of paramagnetic substances. The substance to be
investigated is placed at the bottom part of a long rod, the “carrier”.
This carrier is suspended to one or two floats swimming on mercury.
The force exerted by the magnetic field on the substance is com-
pensated by a known force and the compensation is checked by
means of a telescope and a scale attached to the carrier (Sc. fig. 3).
Some modifications were required with a view to the special cir-
cumstances. The apparatus is introduced at the top of the helium
eryostat (C) and is supported by the rim FR. It is counterbalanced
by weights acting on the connecting tube between cryostat and
liquefactor. The weight of the apparatus has been minimised. Par-
tially for this purpose the ringshaped trough of the apparatus of
KAMERLINGH Onnes and Perrier has been replaced by a small glass
reservoir (G) with only one float (Dr). The comparatively large
forces occurring in the experiments (up to about 200 gr.) induced
to prefer magnetic compensation instead of electrodynamic compen-
sation by two coils, though the accuracy was diminished thereby.
The compensating force comes from the attraction exerted by a
current of suitable intensity passing through a coil D at the top of
the apparatus on a weak iron rod S at the top of the carrier; by
putting rings (#z) under the coil D its height can be taken such
as to exert upward or downward forces, as appears convenient. The
distance of the weak iron rod to the interferrum of the electro-
1) These Proceedings 16, p. 689 and 786. Leiden Comm. N°. 139a.
616
magnet has been chosen such that the action of the latter on the
former may be neglected.
Fig. 3.
617
The tube (hb, ef. the diagram of this detail in fig. 3) containing
the magnetic substance, has been made and placed to obtain a
symmetrical distribution of glass with respect to a horizontal plane
passing through the centres of the poles of the electromagnet. In
this way the attraction exerted by the magnet on the glass has
been minimised and may be neglected. The dimensions have been
0H")
chosen such that the sample is at the place of maximum aor if
z
the tube has been placed symmetrically in the field. The lower part
(b,) of the tube has been evacuated, in the upper part (b,)-a small
quantity of helium gas has been introduced in order to improve
the temperature equilibrium of the powder and the surroundings
and of the particles of the powder mutually. The substance is
enclosed between two glass disks, one of which has been melted
on the tube, the other is free but is kept in its place by a small
plug of cotton wool. Two flattened spiral springs, V,, V, prevent
a lateral displacement of the carrier. The lower one has been
attached to the earrier and not, as in previous work, to the tube,
so that the tubes may be replaced without changing the position
of the carrier.
The end faces of the large size Weiss magnet have a diameter
of 4 em and are 26,5 mm apart. The semi-angle of the coneshaped
boundary faces is 60°.
The compensating force as function of the intensity of the current
in the coil D has often been determined as carefully as possible by
suspending weights to the tube. Notwithstanding all precautions
unexplained differences subsisted between the different calibrations.
The extreme ones differ about 2 °/,. In calculating a series of
observations use was made of the mean of the calibrations “before”
and ‘after’.
The specific magnetisation, 6, is calculated from the force measured
by means of the relation
0H
VN he | ee i RS PS)
: Òz
where F represents-the force (in grammes) exerted on the mass m.
The z-coördinate is measured along a vertical from the middle of
the interferrum; H is the magnetic force at the point indicated by
z; g = 981.3.
1) If the susceptibility does not depend on the field strength, the maximum of
0H?
dz
is preferable. |Note added in the translation].
618
In every set, i.e. every measurement of the force corresponding
to a definite value of the magnetic field and a definite temperature,
the intensity of the current in the coil D necessary to bring the
carrier into a chosen zero position was read the magnetic field being
“of” and “on”. These readings were taken for both directions of the
currents in the coil and in the magnet.
$ 3. Corrections, auxiliary measurements and sources of errors.
a. Forces on the carrier without sample. These forces appeared to
be not quite negligible and they increased with decreasing tempera-
ture. Investigation of the different parts of the apparatus showed
that those forces were caused especially by a small serew at the
bottom of the carrier (near V,). The comparatively large increase
of these forces when the temperature falls from 20° to 14° K. is
very striking, e.g. 70 amp. passing through the electromagnet the
attraction amounts to
0,259 gr. at atmospheric temp.
0,326 ,, 20° K.
0,350 „ 14
This is not what would be expected if the brass of the screw
mentioned contained iron as an impurity. Further, such a compara-
tively very large increase in the liquid hydrogen region would
give reason of suspecting much larger forces in the range of
helium temperatures. However, they are then not large as appears
from there being no systematic difference between the observations
in whieh the mentioned parts of the carrier were certainly below
and those in which they were certainly at some distance above the
liquid helium level *). Particular circumstances prevented determining
those forces (whose comparatively large increase in the hydrogen
region appeared firstly afterwards) at helium temperatures and in the
light of the foregoing remark it seemed not absolutely necessary.
In the following observations the correction for the forces on the
carrier without sample bas been applied for the hydrogen tempe-
ratures only.
b. Correction for demagnetisation. This correction may attain
considerable values at the temperatures of liquid helium. In the
case of a sphere of a homogeneous substance of density d in a
homogeneous field the demagnetising field is —4.2od. In our expe-
riments the cirumstances did not correspond exactly to these con-
ditions. The sample is a powder in the shape of a small cylinder
1) Cf. the following communication § 3 note.
619
and is placed in an inhomogeneous field. Dr. Brum) has made a
careful investigation in the case of a powder. According to him a
first approximation for the demagnetisation is obtained if the formula
mentioned is applied, taking for d not the density of the powder
itself, but of the substance. If necessary this correction has been
applied in that manner,
OE
c. Topographical corrections. ap 8 in first approximation propor-
z
tional to the field strength in the middle of the interferrum: H..
The factor of proportionality was calculated from a ballistic topo-
graphical calibration of the magnet’). At currents of 10 and 20
amp. no appreciable difference in the topography was stated and
oH
for z = 2.45 cm. ( being there a maximum) was found:
Òz
0H
7 = 0.815: HS, oe ORS ORE eere (2,43)
If however for gadolinium sulphate *) the force #' is calculated
as a function of H,, no proportionality of F to H,* is found, as
might be expected on account of previous measurements *) (apart
from small corrections if Lanervin’s formula is followed) but devia-
tions occur up to 20°/,. This appears from table I and fig. 4. To
the observed value of #, given in the third column now first a
correction for the demagnetisation is applied: F is multiplied by
1+ 4ard,y; according to the remark 6 (see above), d, is taken
equal to 3°), for x, the specifie susceptibility, the value following
from the un-corrected measurements has been taken. At 20°.42 K.
this correction is 1.2 °/,, at 13°.98 K. 1.8°/,. In the column headed /
the corrections for the deviations according to Lanexvin’s formula
have been given. With those two corrections an apparent Curie-
constant C’ = x7 has been calculated.
The values found for C’ appear to be strongly dependent on the
field strength (cf. fig. 5). This may not be due to errors in the
1) These Proceedings 25, p. 293; Leiden Comm. Suppl. N°. 46.
*) The calibration really refers to a pole distance of 26 mm., not to 26.5 mm.,
the distance occurring in the experiments described.
The parameters of this field do not belong to those for which Forrer has
given so much and such important data (J. Forrer, thesis Zürich, 1919).
5) The gadolinium sulphate, Gd,(SO,); . 8H,O, originated from the supply previously
kindly sent by Prof. URBAIN. Two tubes have been filled with it, Gdl and Gall,
containing resp. 0.4735 en 0.4414 gr. of gadolinium sulphate.
4) H. KAMERLINGH ONNEs and E. Oosreruuis, these Proceedings 15, p. 322
§ 6, Leiden Comm. NO. 1295, § 6.
5) P. Groru, Chem. Krystallographie Il (1908), p. 460.
620
calibration of the magnetic field. This calibration may be estimated
to be accurate to a few thousands. The deviations must be cansed
by the circumstance that at large and at small values of H, the
proportionality mentioned may not be expected to hold *).
TABLE I.
Gadolinium sulphate II (7 = 0,4414 gr.)
T = 20°.42 K.
Nr I E BORE 1 nore. eld 102 C Ee
4 | 5amp.( 0.81gr. 3295 |0.0\ 2.100 | 1.018 | 2.064 | 1-79,
Br ls | 0.80
6 | 10 3.10 | 6605 |0.1| 2.015 | 0.997 | 2.021 | —0.45
3 | 15 6.98 | 9875 |0.2| 2.031 | 1.000 | 2.031 | 0.0
7 | 20 12.00 | 12040 | 0.4| 2.038 | 1.005 | 2.028 | —0.1
2 | 30 20.66 | 17320 | 0.8| 1.962 | 0.963 | 2.037 | +0.3
8 | 30 lees
9 | 45 25.99 | 20235 |1.2| 1.820 | 0.897 | 2.029 | —0.1
1 | 60 28.17 | 21600 | 1.4] 1.729 | 0.856 | 2.021 | —0.45
10 | 60 ne
T = 13°.98 K
15 | 4 0.74 | 2627 |o.1| 2.093 | 1.026 | 2.040 | +0.5
16 | 5 1.13 | 3295 |0.1| 2.032 | 1.018 | 1.996 | —1.7
14 | 10 4.52 | 6605 |0.2| 2.025 | 0.997 | 2.031 | 0.0
13 | 20 17.41 | 12040 | 1.0) 2.046 | 1.005 | 2.036 | +0.3
17 | 20 cs
18 | 30 29.32 | 17320 |1.9| 1.942 | 0.963 | 2.017 | —0.7
12 | 45 37.36 | 20235 | 2.6| 1.826 | 0.897 | 2.036 | +0.3
11 | 60 40.33 | 21600 |3.0| 1.739 | 0.856 | 2.033 | +0.1
19 | 60 ee
20 | 70 41.71 | 22230 |3.2| 1.701 | 0.835 | 2.037 | +0.3
1) In fig. 2 the points for the higher field strengths show the same kind of
deviation from the LANGEVIN curve at 4°,25 K. as at i°,9 K. In my opinion this
fact is caused by the absence of proportionality mentioned in the text.
621
Fig. 4.
We have put:
Hs 0.819. Hf,
0H en ei eae tee 8 "25 (eb)
a = r.0,199 EIK
0 SPORT ea OVS | A Te (PPR ee)
Bnd efor OSamp sg == sip == dt
The quantities g, s and 7 are called the topographical corrections.
The apparent Curie-constant C" is connected to the true Curie-
constant C by the formula: C'—qC and does not depend on the
temperature. Fig. 5 shows that within the limits of accuracy of the
experiments at both hydrogen temperatures’) the same values for
C' are found. Only at 5 amp. (H, = 3295) where the forces are
small and the measurements less accurate there exists a larger
deviation.
The values for C' have been smoothed graphically and then the
i
topographical correction q has been determined from le 0
15 amp.
In the column 10°C the value of 10?C’ correeted with q lias been
1) The circles refer to 20°,42 K., the squares to 13°,98 K.
622
given and in the last column the difference (in percents) of 10°C
with the mean value 2,030.
2,0)
|
62 H 5 10 15 20 25
Fig. 5.
r was determined from experiments on the attraction of two
small ellipsoids ') of Swedish Carbon iron placed as well as
possible at the same spot as the substances in the actual experiments.
Use was made of the measurements of SreinHaus und Gumracu *)
on the relation between field strength and magnetisation when satu-
ration is nearly reached, the so called law of approach
s was calculated from formula (5). The values found for 7 and s
have also been smoothed graphically *).
In these determinations the distribution of magnetism on the pole
faces of the magnet has been supposed to be perfectly rigid *).
1) Masses 30.0 and 32.0 mg., major axis 6.2 mm., minor axis 1.1 m.m.
4) Ber. d. Physik Ges. 17 (1915) p. 271.
3) This causes the product of the given 7 and s to be not exactly equal to q.
4) Cf. P. Wess, J. de Phys. May 1910 and P. Weiss and H. KAMERLINGH
Onnes, Leiden Comm. NO. 114, p 16.
Strictly speaking: for a magnet current of 15 amp. the distribution of magnetism
on the pole faces of the magnet has been supposed to be perfectly rigid and as
regards the other current intensities it has only been supposed to be the same
for gadolinium sulphate at hydrogen temperatures and for the S.C. iron ellipsoids.
In fact, the magnetic moments are of the same order in both cases (though the
volumes on which they are distributed are different); in the case of gadolinium
sulphate at heliwm temperatures they are much larger, yet the same values of r
and s have been applied (cf. next communication) {Note modified in the translation].
623
So the values given in table II have been found.
d. Corrections for diamagnetism of the liquid bath and of the
anion could be left out of consideration.
e. As regards the accuracy and the sources of error may firstly
be pointed out that the Aeliwmtemperatures are rather uncertain,
especially the lower ones. There was no room for a special stirrer
and so the liquid could be stirred only so much as was possible
by moving the floating system up and down. Therefore probably
the temperature was not always evenly distributed and not pertectly
well defined. This is especially important at temperatures below the
maximum of density; then the cooling at the surface by evaporation
does not give rise to downward convectional currents. However the
lower temperatures are not only somewhat indefinite, but the values
accepted are not very accurate. They have been determined graphi-
cally by means of the total existing material for helium vapour
pressures'), but this leaves at the temperatures between 1° and 3° K.
uncertainties of the order of 0,1 of a degree.
TABLE II.
Pole distance 26.5 mm.; s = 2.45 cm.
I r Ss
|
3 amp. 0.973 F062
4 0.983 1.044
5 0.990 1.030
10 0.999 1.003
15 1.000 1.000
20 0.995 1.002
30 0.960 1.010,
45 0.893 1.021
60 0.837 1.030
70 0.808 1.035
f- Much care was bestowed on the adjusting of the sample to
the proper place in the magnetic field, or more accurately, of the
adjusting of the magnet to the sample, the eryostat not being movable.
1) H. KAMeRLINGH Onnes and Sopnus Weger, these Proceedings 18, p. 498;
Leiden Comm N°. 147b; H. KAMERLINGH ONNES, Leiden Comm. N°. 159 p. 35.
624
Once the magnet was adjusted in its place, it was marked by means
of two plummets suspended to the cryostat and marking two pointers
on the yoke of the magnet, for the magnet had temporarily to be
removed to afford opportunity of bringing the Dewar vessels V ge
and Vg (fig.3) into place. The large magnet is very heavy and there
was no device for moving the magnet sligthly in horizontal direction,
so the horizontal adjustment was accompanied by great difficulties
and possibilities for inaccuracy.
During the operations with liquid helium and liquid hydrogen the
cryostat, forming one whole with the liquefactor, moved slightly in
an irregular way as a consequence of the changing temperature
circumstances in the different parts. By means of pulling rods the
initial position with respect to the magnet was restored.
As far as the adjustment in vertical direction is concerned, it
must be pointed out that the distance (at atmospheric temperature)
from the centre of the mass to the centre of the field is considered
as “place” of the sample in the magnetic field. This place determines
the values of the constants in formulae (2)—(5). In the measure-
ments in liquid hydrogen and in liquid helium this place has changed
really by the shortening of the carrier in consequence of its cooling.
The influence on — will be very small as is maximum, but for
Oz dz
the same reason the influence on H has to be taken into consider-
ation. In itself there is reason for a correction. In the (rather
unfavorable) case that the carrier up to 20 cm above the sample
has the temperature of the boiling point of liquid hydrogen and the
other part is at atmospheric temperature, a shortening of 0,3 mm
would follow from the data of Ca. LiNDEMANN.*) H would be 0,006
H, smaller than corresponds to formula (2) i.e. about 0,7 °/,. Yet
no correction has been applied, because it would have required a
accùrate determination of the place of the substance during the
measurements as the sinking of the liquid level changed the tempe-
rature distribution along the carrier and thus the place of the sample.
Moreover in the measurements in liquid hydrogen and in liquid
helium (and the experiments only refer to these temperatures) the
correction is nearly equal when the liquid level is on the same
height, as the expansion coefticient at these !ow temperatures rapidly
decreases to zero.
g. Finally it must be mentioned that no trace has been observed
of the powder particles getting directed or remaining directed by
the magnetic forces.
1 Physik. Zs. 13, (1912), p. 737.
625
§ 4. The Curie constant of gadolinium sulphate. In § 3e it has
been mentioned already that for Gd Il 2,030 < 10-2 has been found.
For the Curie constant of Gd I we find:
PDO IE n= 05 GOM 1053 (SOLO 2
T = 14°.68 A 2663). | 5, CAD
mean : 2,149
The measurements on Gd I have been considered as less accurate
than those on Gd Il, because (ef. § 3f on the difficulties of the
adjustment) the tube appeared afterwards for unknown reasons to be
not exactly in the middle between the pole faces, but 1,6 mm out
of the center. A previous determination of the Curie-constant of
Gd I quite independent of the present research had given 2,113 « 10-2.
So it is not very probable that the large difference between the
Curie constants of Gd land Gd Il is due to inaccurate adjustment
of the tube only. Besides it must be remarked that different observers
have found values differmg more still than the values mentioned:
from the results of Mlle Ferris *), KamertinGH Onnes and Perrier ’),
and KaAMBERLINGH Onnes and Oosrernuis *) the Curie-constant of gado-
linium sulphate is found to be *).
Mile Frymis 2,167. 102
K. O. and P. 2,086
K. O. and O. 2,016.
These differences are not yet explained.
Finally, I wish to express my sincere thanks to Professor KamEr-
LINGH Onnzs for his kind interest in my work.
1) Paris C. R. 153 (1911), p. 668.
*) These Proceedings 14, p. 115; Leiden Comm. N’. 122a.
3) F 5 15, p. 322; Leiden Comm. NO. 129b.
4) A correction has been applied for the diamagnetism of the crystal water and
of the anion. The first correction had been applied already by Mlle Frytis.
41
Proceedings Royal Acad. Amsterdam. Vol. XX VI.
Physics. — “Further experiments with liquid helium. T. Magnetic
researches. XXII. On the magnetisation of gadolinium sulphate
at temperatures obtainable with liquid helium.” By H. R.
Wo rtser and H. KaMmeERLINGH Onnes. (Communication N°. 167c
from the Physical Laboratory at Leiden).
(Communicated at the meeting of September 29, 1923).
§ 1. /ntroduction. Previous’) preliminary researches and a detailed
discussion’) of the results then obtained have shown the importance
of a closer investigation of the magnetisation of gadolinium sulphate
at very low temperatures: this substance is one of the compara-
tively few, that follow Curir’s law down to the region of tempera-
tures obtainable with liquid hydrogen. Now in the light of LANGBVIN's
theory the Curt law holds only approximately, viz. as long as the
susceptibility may be considered to be independent of the field strength:
LANGEVIN gives for the ratio of the specifie magnetisation, o, to the
specifie saturation magnetisation, 6,,,
1
OIS WHR —= = 5 5 6 5 6 0 a (lg)
a
pensive (15
RET
(Om, being the saturation magnetisation of one gram molecule, R
the gas constant per grm. mol., 7 the magnetic field applied and
T the absolute temperature).
For small values of a
1 OO: Ome 1
WO —— S= wies Ten ZE
Te TATIE ERE SEN
(2)
If 7 is small and thus a large, x is no longer independent of H,
but the curve 6:6, = f(a) deviates from the straight line 5:60,
1 F
ae becomes concave towards the a-axis and approaches asymp-
totically to o: 0, = 1 (ef. fig.) The detailed discussion of the preli-
minary experiments has already made very problable the existence
)) H. KAMERLINGH Onnus, these Proceedings 17, p. 283; Leiden Comm. N°. 140d.
3) H. KAMERLINGH ONNes, Rapport Solvay 1921, p. 131; Leiden Comm. Suppl.
NO. dda. 1.
627
of deviations of this type. Yet it is not to be expected a priori that
LANGEVIN's theory would be followed in this case, for this theory
has been deduced for a gas with perfect rotational freedom of the
molecules and starts from the assumption of the equipartition of
energy in al degrees of freedom. Now the case of powdered gado-
linium sulphate at low temperatures does not correspond to either
of these assumptions. It is true that Lanenvin’s theory has been
extended by Weiss‘) to powdered crystals, but Weiss confines him-
self to small values of the parameter «; on the other hand Exren-
FEST’) has developed a theory in which the relatition (2) is obtained
for crystal powders on the assumption of the existence of quanta
but then the saturation magnetisation is only half the value corres-
ponding to perfect parallelism of all elementary magnets and in the
preliminary experiments a higher value seemed to be reached.
Contirmation and extension of the preliminary results was thus
very desirable; the same method has been followed as in the
previous work: the specific magnetisation, 6, is calculated from the
force F' (in grammes) exerted on the mass 7 by an inhomogeneous
: : OH
magnetic field with aid of the formula HG MO A detailed
study of the apparatus, the corrections and the sources of error, a
comprehensive account of which has been given in the preceding
communication *), has made it possible to attain a much greater
accuracy than in the previous work, at least as far as the magnetic
measurements are concerned. The determination of the temperature
from the vapour pressure of the bath is still a weak point, especially
since the vapour pressure law is as yet not sufficiently well
known‘). The research relates to the same tubes, Gd/ and Gd//,
that have served for the research in liquid hydrogen and that have
been mentioned in the preceding communication (§ 3c).
§ 2. Observations. The direct results of the observations may be
given first: tables I and II (/ being the number of ampères in the
magnet coils; H, the field strength, in gauss, in the centre; # the
force in grammes, on the total mass of substance).
With GdJ/ between the points N°. 15 and N°. 28 points have
been left out in which the observations have been taken at increas-
1) P. Weiss, Paris C. R. 156 (1913) p. 1674. According to O. Stern (Zs. f.
Phys. 1 (1920) p. 147) Weiss’ deduction is not sound.
2) P. EHRENFEST, these Proceedings 23, p. 989; Leiden Comm. Suppl. N°. 44b,
8) H. R. Worrser, these Proceedings p. 613; Leiden Comm. No. 167).
Woes Gere
41*
628
TABLE I.
Gadolinium sulphate I
Date Vapour pressure di Nr. I Ay jn
_
30 17320 90.14
20 12940 55.26
10 6605 15.76
March 1th, 1923 761 mm.!) | 4°.20 K.
” ” . 5 3295 3.89
” ” ” 3295 4 . ol
9875 33.83
30 | 17320 89.94
60 | 21600 | 114.76
70 | 22230 | 117.81
10 | 45 | 20235 | 109.54
112 | 30.) 17320 90.96
360 mm 30.53 „| 12 | 70 | 22230 | 136.93
4 E d 13 | 45 | 20235 | 123.42
14 | 30 | 17320 | 103.78
5 8 15 | 20 | 12940 65.61
© 0 A aas wD
a
” ” 3 16 10 6605 19.04
” ” en 17 5 3295 4.76
D - Dn 18 5 3295 4.75
19 15 9875 40.26
20 30 17320 102.54
21 60 21600 129.12
[22 10 22230 130.68
3 100 mm. Donia 5 {23.4 +710: ||. 22230) | 1522
8 î 24 | 45 | 20235 | 148.13
5 . 8 25 | 30 | 17320 | 121.71
" ¥ 3 26 | 20 | 12940 19.75
8 8 8 27 | 10 6605 24 36
5 ‘ j [28 5 3295 6.12]
} 163 mm. 49.20 „| 29 | 30 | 17320 91.11
5 9.5 mm. | 1°.66 „| 30 | 70 | 22230 | 173.70
2 4 mm. 19.48 „| (31 | 60 | 21600 | 173.41]
EET AEN DN Arc Uh ere aE
1) The difference between international and local m.m. mercury (these Proceed-
ings 21 p. 658 note 2; Leiden Comm. No. 152d p. 47, note 4) ) is here of no importance.
TABLE II.
Gadolinium sulphate II
Date Vapour pressure Li Nr / A Je
April 13,1923 761 mm. 49.20 K. 1 60 21600 108.27
” ” 7 2 30 17320 85.67
” ” 7 3 15 9875 32.44
” ” 4 5 3295 3.74
” ” 5 5 5 3295 3.77
” ” "4 6 10 6605 15.10
” 5 : 1 20 12940 53.00
” ” 5 8 30 17320 85.80
” ” 5 9 45 20235 102.76
” » 5 10 60 21600 108.04
2 300 mm. SCO) es al 30 17320 98.48
630
ing pressure in order to test whether temperature corresponded to
pressure, the only stirring possible being made by the moving up
and down of the carrier‘). The magnetisations observed pointed to
much lower temperatures than corresponded to the actual pressures
and thus to a large temperature lag. Therefore these points have
been left out of consideration.
§ 3. Discussion. For Gd II 0,02024*) has been accepted as Curie-
constant and with this value o, and 6,,. have been calculated
according to formula (2). Half the real molecular weight has been
used in calculating 6 from 6,, as the atoms of Gd are assumed
to have rotational freedom. This is usually done for salts containing
Map
more than one metal atom in the molecule ®); moreover, if the
whole molecular weight had been taken, 6,,,, would have become V 2
larger, 6. V2 smaller and thus 6:6. again 2 larger and one would
have found values larger than 1, as for 6:6, the value 0.84 has
been attained (Cf. table IV).
We find:
Ome — 434,2 ~ 10? (38.65 Weiss-magnetons).
Os MGL
For the Curie constant of Gd / we found *)
C = 0,02149
Ono == 447,4. 10° (39.82 Wauiss-magnetons)
Os == iI SE
From the tables I and Il 6:6, and « have been calculated for
Gdl and Gd ll, with its own particular Curie constant for each
substance. The results have been collected in tables II] and IV. The
values placed in square brackets are a priori less reliable, mostly
because during or immediately after the measurement the gadolinium
sulphate appeared to be not sufficiently below the liquid helium
level °). The differences between the observed values of 5:60, and
1) le. § 3e.
2) Cf. the preceding communication § 4, where on account of a later somewhat
modified calculation 0,02030 has been given. The difference is of no importance.
3) P. Weiss, Arch. d. Se. phys. et nat. (4) 31 (1911)
B. Caprera, J. de Chim. Phys. 6 (1918) p. 442, especially p. 462.
4) Cf. the preceding communication § 4, where the difference between both
results has been discussed.
5) At the points marked with an asterisk the helium level was certainly below
the spring Vs (ef. the preceding communication § 3a). Though a general tendency
“ to higher values of :c, (cf. the diagram) must be acknowledged to exist, there
is no systematie difference between the points with and without asterisk.
631
TABLE III. Gadolinium sulphate I.
4°.20 K. 3°.53 K. 297713) KK. 19,665 K. 1°.48 K,
ERS 5 IG 310 SS) Ss O0
Nr.| a. a sle INK 4 TS JP Nr. a. de ol? Nr a. ae JP ING es = op
oS a = | = ke say Pe
| A | Deca | |S |
4 | 0.2888) 01036 |+ 7.6] 17*| 0.3384 0.1268 +-11.7 | [28*| 0.4267) 0.1630 |+13.8]
5 | 0.2882) 0.1068 |+ 10.5) 18*/0 3384] 0.1266 11.6
3 | 0.6174) 0.2075 |+ 3.2) 16*| 0.7246) 0.2508 |+ 6.9} 27*| 0.9162) 0.3208 + 9.8
6 | 0.9408) 0.2977 |+ 0.4] 19*| 1.106 | 0.3544 |+ 3.6
2 | 1.239 | 0.3732 |— 0.8] 15*| 1.458 | 0.4430 |4 3.2] 26 | 1.857 | 05384 |H 5.0
1 | 1.675 | 0.4710 |— 1.0) 14*| 1.976 | 0.5425 |+ 1.7] 25 | 2.528 | 0.6362 |H 3.0
7 | 1.675 | 0.4700 |— 1.2} 20°) 1.977 | C.5360 |+ 0.5
11 | 1.673 | 0.4753 0.0)
29*| 1.673 | 0.4763 |+ 0.2
10 | 1970 | 0.5269 |— 1.0] 13 | 2.328 | 0.5936 |+ 0.7] 24 |2.975 | 0.7124 |+ 61 [31*| 5.917 | 0.8339 |+ 0.3]
8 | 2.140 | 0.5516 |— 1.7] 21*| 2529 | 0.6209 |+ 06
9 | 2223 | 0.5702 — 0.6] 12 | 2.624 | 0.6627 |H 5.0}[23 | 3.371 | 0.7369 |+ 4.2]] 30*|5.475 | 0.8406 |+ 2.8
(22*| 2.631 | 0.6324 + 0.3]
632
TABLE IV. Gadolinium sulphate II
4°.20 K. 3°.40 K. 2°.30 K. 1°.48 K. 1°.41, K. 1°31 K. ee
Sjo dl 4/Sfo EBUS So ile
I |Nr.| a. Bree ew Nr.| a. Ei Nr} a Oee: Nr.| a Ta. Nr.| a. als Nr.| a. (ales
ve} ee 8 GE ee 8 Sele wt
3 34*| 0.5260) 0.1854/-++- 7.1 €
4 33 | 0.6952! 0.2403 + 6.5
5 | 4 | 0.3238) 0.1102|4 2.7 32 | 0.8587] 0.3005)+- 9.1
„ | 5 | 0.3238] 0.1111)+ 35 ;
10 | 6 | 06315] 0.2199/+- 6.7
15 | 3 | 09433) 0.3157|-+ 5.9
20 | 7 | 1.243 |0.3956|-+ 4.7
30 | 2 | 1.682 | 0.4951/-+ 3.6]11 | 2.063 | 0.5691/+ 3.7 12 | 3.009 | 0.6928)+ 2.9 [13 4.634 | 0.7716/— 1.7 |31 | 4.839 | 0.7878)}— 0.7
„ | 8 | 1.682 | 0.4959|+ 3.8 15*| 4 634 | 0.7721|— 1.6
, |28"| 1.684 | 0.4941|+ 3.3
45 | 9 | 1.995 | 0.5464/+ 1.8 30 | 5.777 |0.8119)— 18
60 | 1 |2.150 |0.5756/4- 2.3 14*| 5.973 | 0.8096)— 2.9 36* | 6.738 | 0.8385|— 1.6
» 10 | 2.150 | 0.5744/4- 2.1
70 29 | 6.467 |0.8365|— 1.1 |35*| 6 982 | 0.8439/— 1.5
633
the values calculated according to Lanervin’s formula, expressed in
percents of the observed value, are given in the columns headed
O— C :
NOU
0
je |
‘ POOT
OR AN
i zel egal |
oo
Fo se AAV ©
> fon - le
: ee ae ©
SH NWrBe
‘ ro) LONT TT |
OLAVS
an ee Te)
634
It cannot be denied that while on the one hand, one gets the
strong impression that LANGRVIN's formula is followed (cf. the figure,
in which the LANGEVIN curve and the observed points have been
drawn), on the other hand the deviations are larger than was anti-
cipated. However they may be explained from the sources of error.
Besides all that has been said in the preceding communication as
to the accuracy, it must be pointed out that the larger deviations
occur especially at the lower field strength values, where the topo-
graphical corrections are rather uncertain and also the measurements
of the field strength less reliable. Further, the magnetic moment
acting at the very low temperatures is so large that the assumption
of a rigid distribution of the magnetism on the pole faces (and on
this assumption the field measurements and the determination of
the topographical corrections are more or less based) certainly holds
no longer.
Moreover it must be observed, that errors in 6,, and in H, exert
on the abscissae an influence opposite in direction to that on the
ordinates and thus appear greater in the diagram. Taking all
these circumstances into account, especially also the uncertainty of
the demagnetisation, it may be concluded, that powdered gadolinium
sulphate follows LANGEVIN’s formula down to about 19.3 K; thus it
seems possible to use the magnetic susceptibility of gadolinium sul-
phate in thermometry.
§ 4. Results. The specific magnetisation of powdered hydrated
gadolinium sulphate has been investigated for the temperatures of
liquid hydrogen and liquid helium. It appears that though the fun-
damental assumptions to LanGrvin’s theory do not apply, yet LANGEVIN's
formula is followed. For the parameter a of LANGEVvIN's theory the
value 7 has nearly been reached. The highest magnetisations obtained
are about 84°/, of the magnetisation corresponding to perfect paral-
lelism of all elementary magnets. This result is independent of the
uncertainties in the temperature and the value of the demagnetising
field. So it appears that Prof. Eurerrest’s theory is here not
applicable without further extension, since this theory (which is based
on quanta assumptions and holds, contrary, to LANGEVIN's theory,
directly for crystal powders) gives for the saturation magnetisation
only 50°/, of the value mentioned.
Physiology. — ‘The string galvanometer in wireless telegraphy’’.
By W. F. EiNrHoven. (Communicated by Prof. W. EiNrHoven).
(Communicated at the meeting of March 24, 1923).
The string galvanometer, as is well known, consists of a conduct-
ing fibre stretched like a string in a strong magnetic field. A cur-
rent passing (through the fibre induces a displacement of it in a
plane perpendicular Sto the lines of magnetic force. The deflection
can be observed with a microscope and the magnified image can
be photographed.
Many attempts have been made to use this instrument for the
reception of wireless signals, but only ordinary models, with a
relatively long, not very much stretched string have been tried, and
these show great sensitiveness towards disturbing direct currents.
The wireless signals were received in such a way that the high
frequency oscillations were rectified by meaus of some device, and
the rectified current impulses were passed through the string; this
was affected in the same way as when conveying a true direct
current.
But, used in this way, the string galvanometer has only brought
disappointment in wireless telegrapby, for it reacts to every current
of some duration with the same sensitiveness, and even the smallest
atmospherics are sufficient to give trouble. Some large Companies,
who have tried to use the string galvanometer at their transatlantic
stations, have abandoned work with it.
The application here to be described of the instrument is based
on a quite different method *). The incoming high frequency oscil-
lations are not rectified but are sent through the string immediately.
The string is short and stretched so much, that its own period
corresponds to the period of the ether waves used in wireless sig-
nalling. Choosing the lenght of the string conveniently and adjusting
its tension, we can bring it in tune with practically all continuous
waves available in radio-telegraphy. If for instance these have a
length of 1 kilometer corresponding to 300.000 periods per sec., the
string is adjusted so that the proper frequency of its vibrations is
also 300.000 per sec.
1) Patented.
636
The length of the string, being about 10 millim. for waves of
(for instance) 10 kilom., is only 1 millim. for waves of 1 kilom.
We have also experimented with shorter strings showing a still
higher frequency of their proper vibrations. Heretofore as far as we
know it has not been possible to induce these frequencies in any
mechanism.
The string, for which we take a fine quartz fibre, is rendered able
to conduct by cathode bombardment, and stretched between two
microscopes; one of these serves to concentrate the light, the other
to project the image, whilst both microscopes, in order to obtain a
sharp definition of the string, must be very near to one another.
The objectives, having a numerical aperture of 0,95, are no more
than 0,2 millim. away from the string. Since the front lens of such
an objective has a diameter larger than the length of the string, a
special device is necessary fo fix the string; this is done in such a
manner that the rays of light are not intercepted, and the full angle
of aperture of the objectives is made use of efficiently.
Fig. 1.
Diagram of the string s between both of the microscopes M, and Mg.
B, and By, fine metal strips to which the string is soldered. The
direction of the rays of light is indicated by the dotted lines and
arrows.
The difficulty was overcome by soldering both ends of the string
to fine metal strips placed in the optical plane perpendicular to the
string, and rigidly attached to the apparatus in order to tighten and
slacken the string.
It is important to have the string vibrating as freely as possible.
Therefore it has not only to be fine but also strongly stretched like
a string of a piano or a violin. Its minute mass per unity of length
causes it to suffer a strong damping effect from the air, and this
must be avoided. Therefore the space around it is evacuated, and
in order to make the vacuum efficient it has to be made high: We
637
attained vacua of 1 u Hg and even higher and were able to show,
that under such conditions the air damping has practically no more
influence on the movement of the string. The vibrations do not die
away more slowly when the vacuum is made higher than 1 u, since
the internal friction of the string itself, i.e. the fact that the material
of the string has no perfect elasticity is another cause of damping.
It is not to be expected, that the vibrations of a coated quartz
fibre stretched like a string would die away as slowly as those of
a pure quartz rod which has been fixed at only one end. Experi-
ments of Haper and KeRrSCHBAUM *) have shown that it took more
than 12 minutes, before the amplitude of a quartz rod vibrating in
vacuo was diminished to one half of the original size. LANGMUIR ’)
succeeded in lowering the pressure in an incandescent bulb lamp so
much that the time of halving the amplitude was lengthened to nearly
two hours.
But if we cannot make the vibrations of our string die away
equally slowly, nevertheless for the purpose aimed at the result is
satisfactory. We could for instance show, that a string performing
40.000 vibrations per sec, without the intentional application of a
damping factor needed a time r — 0,65 sec. to diminish its ampli-
ered
tude in the proportion of Li, wherefrom it may be inferred, that
the logarithmie decrement of the movement amounted to4 < 102,
conf. fig. 2.
Fig. 2.
A string the vibrations of which are dying away freely.
A=7,5 km, 7>—0,65sec., ò — 4 XK 10—5.
This decrement is of the greatest value for our purpose, for the
smaller it is so much the better is the selectivity of the instrument.
If the string has been put in tune with a definite wave, it will
react to atmospheric disturbances and to currents of different wave
lengths coming in from other stations so much the less, the smaller
the decrement is. Generally speaking we may say that the efficiency
of a receiving apparatus is determined by the amount of its decrement.
For purposes of comparison it may be recalled, that the smallest
1) Zeitschr. f. Elektrochemie. Bd. 20, 1914, p. 296.
*) Journal of the American Chem. Soc. 35, 107 (1913) cited from Hager u.
KeRsCHBAUM.
638
available decrement of an electric circuit is about 0,01 and that in
most cases this value is higher. The decrements of all the receiving
apparatus known to us, which mechanically register the signals are
larger than that of the string galvanometer.
However it is only possible to profit fully by a small decrement,
A
B
D
Fig. 3
Field magnet of: 5
current : |
|
A 0,5 Amp. 0,27 ‘seciaa |) 99:25 > KIO KC MDENE di LEEG)
or also
Sis
BSB in a
dem
where dij, is again supposed to be small in comparison with den.
This is always the case with a good string, a moderate field and
an attainable vacuum. Under the conditions of the figures 2 and 3
we have d4,=4 10 9%, whilst de, with a magnetizing current of
4 amp. attains a value which is 75-times larger viz. 3 X 10-% and
therefore B = 0,01338 B.
What value is to be computed for B when ase is made of formula
(4)? The result depends on the dimensions, especially on the diameter
of the string inserted in the galvanometer.
If we take a fine string’) with a diameter of 0,2 u, a vibration
amplitude of the same dimension will already be visible and suitable
to be recorded. We have then U —= 2 >< 10~-° centim. The mass of
a string of the above mentioned diameter and of 1 centim. length
may be taken as M=210~° grams. Suppose, moreover, NV=20.000,
and de, = 0,001, then we find, for the number of watts wanted,
that B= 3,2 X 10 1. From this we infer, that the sensitiveness of
the galvanometer is to be evaluated to an amount of the same order
of magnitude as that of the telephone.
The use of such fine strings is attended with certain practical
difficulties, so that we prefer to work with strings 5 to 6 times
thicker and therefore considerably less sensitive. Moreover the sen-
sitiveness decreases, when the wave-length is shorter and the speed
of transmission higher, as may be seen from formula (5).
1) Conf. W. E:ntuoven, Ueber die Beobachtung und Abbildung dünner Faden.
Pruiicrr’s Archiv. f. d. ges. Physiol. Bd. 191, S. 60.
645
However, in view of the comparison between string and telephone
it may be pointed out, that the maximum sensitivity of the latter
named instrument is by no means available in radio practice, for
there is a great difference between the intensity of a signal just
barely audible and one which is readable.
It will be noticed that we only have compared the power sen-
sitiveness of the galvanometer and of the telephone as such, and
that the application of these instruments in combination with the
oscillating audion and with low and high frequency amplifiers has
been left out of consideration. For the sensitiveness of reception by
telephone in combination with the oscillating audion we may refer
to the paper of Austin *). He mentions that for a just audiblesignal
the absolute sensitiveness of the oscillating audion is 1,2 ~ 10-15
watts, that is to say a power, which is about 2,5 times greater
than that needed by the telephone as such.
For the practical use of the string galvanometer in radio-telegraphy
it is superfluous to try to obtain the greatest possible sensitiveness
of the instrument. It is not the sensitiveness which determines its
usefulness, since weak signals may be strengthened by means of
amplifying vacuumtubes without limit. The efficiency of a receiver
is much more determined by its selectivity i.e. its freedom from
disturbances.
If we wish to compare the reception by the galvanometer to that
by the telephone from the point of view of their selectivities, we
must discuss once more the properties of the human ear. As is well
known we are able to distinguish by means of hearing many sounds
produced simultaneously. If we pay special attention to one of the
numerous musical instruments of a complete orchestra, we are able
to follow its performance separately. So also the Marconist can
distinguish the tone of a signal, although many other sounds or
noises of, for instance, extraneous stations or atmospheric disturb-
ances reach him at the same time. This secures for reception by
telephone an important advantage over every form of reception
which has the object of recording the signal graphically. In the
graphical image of a concert of sounds it is extremely difficult to
follow the tone which we wish to analyse and often it will be
even quite impossible to do so.
But against this disadvantage of the galvanometer there is the
Ij Louis W. Austin. The measurement of radio-telegraphic signals with the
oscillating audion. Proceedings of the Institute of Radio engineers, 1917, Vol. 5,
p. 239.
646
advantage of a much smaller decrement, and we may ask how
far in practice advantage and disadvantage are counterbalanced.
The answer depends on the possibility of deriving the full profit
from the small decrement of the receiver. Let us for instance try
to receive in Leyden the signals of the present high frequency al-
ternator at Bandoeng. It does not keep its wave of 7,5 kilom.
absolutely constant, but according to our measurements the wave
varies by amounts of 1 to 2 per thousand. If, by diminishing the
field intensity, we decrease the string decrement so much as would
be desirable when receiving a constant wave, a signal would only
be received now and then, that is to say only at those moments,
when the varying wave of the transmitter coincides exactly with
the wave to which the string is put in tune. To different wave-
lengths the string does not respond, so that the dots and dashes
transmitted are not received regularly and the telegram becomes
unreadable. We are obliged to increase the string decrement and
so to enable the reception of a greater range of variation of the
wave-length of the transmitter.
On experimenting we obtained the impression that the reception
by telephone of the high frequeney alternator of Bandoeng is
disturbed by extraneous noises about as much as the reception by
the galvanometer. In both cases practically as many signals become
unreadable by atmospherics. But we have not yet had the opportunity
to carry out exact measurements on this point and it may be noticed,
that the difference in skill of the various Marconists, who are
carrying on the comparative experiments must also be allowed for.
If the wave transmitted oscillates still more than is mentioned
above, the Marconist will obtain the better result, but if it is being
kept steady, such as actually is the case with many modern trans-
mitters, then the advantage will pass to the side of the galvanometer.
The dots and dashes on the strip of paper will then be like those
of fig. 4 and of the upper part of fig. 6.
The slower the rate of transmission so much the smaller the string
decrement may be made; the freedom from disturbances becomes
improved proportionately and thus the possibility of receiving with
the galvanometer increases. On the other hand the Marconist is not
able to take advantage of a more constant transmission wave; it is
impossible for the human ear’) to perceive the minute variations
in pitch, to which a string vibrating with a small decrement is
capable of responding noticeably.
1) Practically also when the Marconist is applying beat reception.
647
But it is not only with a slow transmission that the string is
superior. If, in relation \to the disturbances, the signals are strong
enough to make a record of them with a moderate or even a large
string decrement, then high speeds of transmission will become
possible and soon the Marconist will no more be able to read the
signals, while the galvanometer is recording easily a few hundreds
of words per minute.
Dr. pr Groor of Bandoeng, to whom we are much indebted, has
suggested a valuable idea. For his enthusiastic collaboration in the
difficult experiments carried on at Bandoeng with the galvanometer
some time ago, we thank him heartily here.
Dr. pr Groot has suggested the application of two galvanometers
simultaneously when an are generator be used for transmission ; one
string may be put in tane with the active wave, the other with the
wave of rest. An atmospheric appearing at a given moment may
be easily recognized as such, if it influences the registration of only
one of the two waves. Thus the possibility of making the signal
readable throughout the atmospheric disturbances will become greater.
In fig. 6 a record is reproduced which has been made at Leyden
according to the suggestion of Dr. pr Groot. The string of one
MT ee as
dare en en ee an, € ol 2
Record of the are generator FL, Paris with 2 galvanometers
in parallel. The signalling wave is registered by one, the non
signalling wave by the other galvanometer.
galvanometer is seen vibrating every time the other is standing still
and vice versa. How great the practical value of this method will
be has yet to be determined, but the first impressions which we
have obtained from the result of a few experiments are favourable.
The idea of using 2 galvanometers simultaneously may find another
application when signals are to be received, the wave-length of
which is not very constant. Hither string may be put in tune with
a different wave; one with a wave which is a little longer, the
Other with a wave, which is a little shorter than the mean length
around which the transmission wave is fluctuating. So the admissible
range of fluctuation is increased, while the decrement of the vibrations
of either string may remain small.
However, rather than applying this, after all, somewhat defective
648
means, it is better to try to improve the transmitter. As a matter of
fact present technique is actually capable of producing transmitters
which keep their wave practically constant.
The advantages of the reception by galvanometer in distinetion
from the reception by telephone are worth mentioning. On trans-
mitting slowly it will be possible to receive signals with the galvano-
meter, which are not readable by telephone. Every improvement in
this direction of the receiving apparatus, which always remains
relatively simple, saves, as Austin!) observes rightly, large sums
needed both for the erection of high power sending stations and for
their working expenses. And that, as matters stand at present, im-
provements are still wanted, is obvious from the many difficulties
experienced even with the best installations. To quote an example it
may be noticed, that during the whole of July 1921 the communi-
cation between two of the Trans-Atlantie stations, which are con-
sidered among the most reliable, was so poor that only 23 per cent
of the words sent were successfully received *).
The high speed reception with the galvanometer makes it possible
to take full advantage of the installation at those hours of the day
and the night, which are the most favourable for the transmitting
of the signals, and to transmit many more words than could be
received by telephone. Moreover the secrecy of the telegrams can
be better secured since the numerous telephone-receivers will not
be able to read the quick signals.
In time of war the interference by a second station will be hin-
dered, when the signalling wave and the non signalling wave of
an are transmitter are received simultaneously with two galvano-
meters.
Finally we may mention another advantage which bears upon
the general use of wireless telegraphy in the world. It is Dr. DE
Groot, who has placed it on the fore-ground. During night and day
numerous signals are sent from many hundreds of transmitters. The
installations interfere with one another, if they use waves the lengths
of which do not greatly differ. The difference in wave-lengths which
are applicable for transmitting signals is limited; only these waves
are useful, which range neither below nor above a certain length;
in other words: the spectrum of the useful waves is comparatively
small. Everyone using a part of it takes it away from another man.
1) Conf. L. W. Austin, Long distance radio communication. Journal of the
Franklin Institute, Vol. 193, Apr. 1922, p. 437 (458).
2) Conf. L. W. Austin l.c. p. 443.
649
The smaller the part of the spectrum he uses, the larger the part
which remains for others.
Owing to the small decrement of the galvanometer a wireless
installation may be restricted to using a smaller part of the spectrum
than heretofore, with the result that it will be possible to increase
the number of simultaneously working installations. This increase
is badly needed, so we may expect on good grounds, that the gal-
vanometer will be capable of rendering a service to radio commu-
nication in general. ;
We do not finish this paper without rendering our tanks to the
many persons who have been ready to help us with our work.
Especially: we wish to express our gratitude for the interest and the
support, which we have received from Mr. Th. B. Preyre wo was
at that time our Colonial Minister.
Anthropology. — “The Menarche in Dutch Women and its preci-
puated appearance in the youngest generation”. By Prof. L. Bork.
(Communicated at the meeting of September 29, 1923).
With the aid of several physicians | have collected a number of
data with regard to the menarche in Dutch women, about which
nothing was known so far. In collecting these data the greatest
accuracy has been observed and in this communication we have
only made use of the cases, in which not only the year, but also
the month of the first menstruation has been noted. Besides this the
colour of hair and eyes of the various subjects had been stated, as
I also wished to ascertain through this examination, whether the
degree of pigmentation is of influence in the commencement of
sexual maturity in the young girl.
Although it is not easy to obtain accurate data, | have succeeded
in collecting 1800 reports of non-Jewish women as well as 165 of
Jewesses.
On working out this material, several unexpected and surprising
results came to light, which I will relate in succession, leaving the
data obtained from the Jewesses until the end.
The first question which could be answered with the aid of these
reports concerned the age at which the menarche appears in Duteh
TABLE I.
Age Number | Percentage Age | Number | Percentage
| |
8 years 2 16 years 121 6.7
Ore 2 Wie 54 sn
LON 31 | |l | LS | 25 1.4
mee 131 TST ACER 3
pee 302, yl ada | 20 , 2
Swe 4640 Ie Meostaon all hon: 2
aaa 408 22.6 ie meaek «4
is. 251 13.9 3, 2
651
women in general. It is well known that this age shows great indi-
vidual variations, and this is also seen in the Table I, in which
the actual numbers, as well as the relative percentage, have been
stated according to the age.
In fig. I curve A shows, in percentages, its appearance at each
separate age.
26%
Fig. 1.
From this table and graph it appears that the beginning of the
function of the sexual glands varies between the tenth and eighteenth
year; it is true that in 4 cases the menses already appeared before
the 10% year (8 years 2 mths; 8y 12m; 9y 4m; and 9v 12m),
but these cases do not join regularly on to the variability-curve and
may be regarded as abnormal precocity.
The varability-curve of the menarche begins as an unbroken line
at the age of 10 years and 4 months, mounting continually after
this. This mounting during the 10° and 114 year is to be seen in
Table Il, in which the number of cases per month during these
years has been noted. I have inserted this table, as it shows that
the earliest age at which the menarche, as a physiological pheno-
652
menon, begins, is actually the middle of the 10" year, so that when
a girl has passed the age of ten-and-a-half years one cannot look
upon the beginning of the menstrual process any more as a sign
of pathological precocity, at most as a rapid development of the
sexual glands.
TABLE Il.
Age Number | Age | Number
10 years 1 month 0 11 years 1 month 3
re ge 2emonths 0 oy 2 ORI TS 5
a By es 5 0 yi ee ; 6
na net ij 1 ary 7 ii
OE eh OE) 5 2 alae ba 6
i gy ad 7 3 | pee 5 6
oe Kopke ë 2 | meme 5 9
Pe OG x 2 ENEN boy Wer 11
minor LE: 3 ION, 14
ME 7 | Beak oe 19
ye mill 6 A LM 24
my ag nd 6 | en le iN 21
I
The beginning of the variation-curve in the middle of the tenth
year is a sign that sexual maturity in our country can begin at a
comparatively early age and the further course of this line confirms
this fact, for it mounts rapidly to reach its top in the 13 year.
Sexual maturity made its appearence before the 12 year in
°), of the girls, before the 13 year in 26°/,, and in more than
half before the 14% year. The average age of the menarche, taking
the months into consideration as well, appears to be 13 years, 9
months and 15 days. If one compares this average with others
mentioned in the literature, drawn from the population of Western
Europe, then it appears that in our population of the present day
the menarche, on an average, begins early.
This commencement, however, is dependent on so many external
conditions, that if any conclusions are drawn from a comparison of
these averages, this should be done with the greatest care.
As one of the internal influences determining the age of the
menarche, the racial factor is usually mentioned. Several authors
653
deny this influence entirely, others attach great importance to it,
which shows how difficult it is to determine whether the race is
really of any influence on the menarche, as it also is influenced
by other, external, factors, (social surroundings, temperature, soil, etc.).
I do not know of any investigation in which the influence of
the race on the commencement of sexual maturity has been actually
proved, and this induced me, while collecting the data, to inquire
into the degree of pigmentation.
The material was sorted and divided into the women with light
and those with dark eyes; these will in future be called “blondes”
and “brunettes”; of the former my material contained 1130, of the
latter 670.
The appearence of the menarche was worked out statistically for
each of these groups separately, the result is seen in Table III and
the graphs plotted out from this table have been sketched in fig. 2.
in which curve A refers to the Jewesses, curve B to the “blondes”,
curve C to the “brunettes”.
654
The result of this investigation into the relation between menarche
and degree of pigmentation was surprising, as it was in contra-
diction with what one might expect. It is a well known pheno-
menon that the menarche appears at an earlier age in the dark-
coloured races than in the fair ones. Most writers ascribe this to
climatic influences, especially to the high temperatures in which
the dark-skinned races live.
TABLE III.
| ae ae a> Ga ike
Age | Blondes | Brunettes
| : |
8 years 1 | |
9 „ I 1
10 , 22 1.8 Oo | 9 1.3 %
UL 5 | 104 Oel gel 27 4 5
on 220 | 19.5 | Boa Taio
NS 294 26 NLO 25 E20
14 2440 21 5a ROGEN 2 AGE
15, | 136 | pat el eal (17.2
16, 65 5 veel 56 85 ,
ies 26 EM 28 130,
ieee 12 Toes 13 2 eis
19g. | 1 | 2
207, le RIKZ Abeta
Pal a 1 1
23, 1 1
I myself, however, conjectured that the racial factor would be of
importance here and that an earlier appearance of the menarche
would be a biological characteristic of the more pigmented races.
It appears, however, from the data given in Table III that for
the Dutch population the contrary holds good; it is just the fair
types which, in comparison to the dark ones, are characterized by
an earlier maturity.
The difference is even considerable, for while 56.4 °/, of the girls
of the fair type have come to maturity before their 14th year, this
is only the case in 42.8°/, of the dark type. As one can, however,
655
see from the graph and from Table III, the beginning of the varia-
bility-curve lies for both types in the 10% year; in the “brunettes”
this begins at 10 years 5 months, in the “blondes” at 10 years 4
months; so for both groups what one can designate as the thres-
hold-age of sexual maturity, is the same. After this beginning the
curve for the fair type mounts more rapidly than for the “brunettes”;
the end of the normal variability, however, is the same for both
types, and lies in the 18* year.
The exact difference between both groups appears from the
following average figures, which have again been calculated inclu-
ding the months:
Average age of menarche in “blondes”: 13 years, 5 months, 17
days; in “brunettes”: 14 years, 4 months, 5 days. So this makes
a difference of full 10 months between both types.
A difference of this sort, and in a contrary direction to what |
had expected, is very remarkable. As we have to do here with two
groups of people living in the same circumstances, which excludes
external factors which might influence the menarche, this difference
must be entirely regarded as the result of an internal factor, and it
is only the racial factor which can be taken into consideration here.
The light-eyed component of our population belongs, in general, to
the race which peoples the North of Europe, the ‘Homo nordicus’’,
while the brown-eyed, which constitutes about a third part of the
Dutch people, as is proved by a former investigation of mine, belongs
to the race inhabiting the centre of Europe, the “Homo alpinus”.
It appears, therefore, that a lesser development of the pigment
is accompanied by an acceleration of the sexual development. The
relation between both phenomena is, however, not so simple; which
can be seen from the fact that the average age of the menarche in the
more strongly pigmented Jewesses, is earlier than in the “blondes”.
The activation of the sexual sphere of the developing individual is
dependent on very many factors; and, in considering the difference
which has come to light, we must not forget the possibility that the
racial factor which is here at work, could be of a psychological
instead of a physiological nature. The blonde as well asthe brunette
girl has reached the threshold-age of maturity on arriving at the
age of 10-and-a-half years. (Later on it will appear that this also
holds good for the Jewish girl). The time which passes for each
individual between this age and the activation of the sexual functions,
is determined by a number of external and internal factors, and
among the latter we leave room for the special psyche of each race.
Thus far on the average age of the menarche in the Dutch
656
population in general; I will now proceed to another result of my
investigation, which was as surprising as it was unexpected.
It had attracted my notice, while working out my material, that
the older people mentioned therein were often characterized by a
late appearance of the menarche. This observation gave rise to the
question whether the menarche could have undergone some change
during the last decades, in such a manner that sexual maturity in
the youngest generation begins, on an average, at an earlier age
than in the former generations. | have tried to find an answer to
this question in two ways. In the first place | collected from my
material data referring to persons born before 1880, and calculated
from these the average age of the menarche. Secondly | tried to obtain
data relating to the menarche in mother and daughters. Especially
this last is difficult, considering the fact that only a very few of
the women can actually mention the year of the menarche, much less
the month. Yet I have succeeded in collecting a number of such data.
Both ways led to the same result, viz. that the menarche in what
we may call the youngest generation, as regards sexual maturity,
arrives at a considerably earlier period than formerly. | will return
to the cause and significance of this phenomenon after communicating
the pure facts.
Let us begin with the menarche in women born before 1880.
In my material concerning them there were 98 data of the menar-
che according to year and month, and furthermore I possessed 104
cases in which only the age was mentioned. These 232 cases have
been systematically arranged in Table IV, and curve B in fig. I
gives the direction in percentages for each age.
If one compares Table IV with Table 1, the following will be
seen: the beginning of the variability-curve lies, for women of the
TABLE IV.
Age Number | Percentage | Age | Number | Percentage
| | | [
10 years 2 0.8 | 17 years 27 V1
1 Wala 12 5.— | He, 19 8.1
1D 5 21 9.— | IO 10 4.3
13 27 NIE | AY 5 2.2
l4, 37 15.9 21 4 155
15> 5 35 15.1 22
165 31 13.3 | 23 2 0.8
657
older generations, also in the 10" year. This fact confirms the opinion
already mentioned above, that the middle of the 10% year is the
physiological threshold-age of sexual maturity in woman.
Opposite to this very constant starting-point of the variability-
curve stands the most changeable ending-point. This falls in the
older generations in the 21s year, in contrast to the 18 in the
younger generation. The top of the curve, which in the latter indi-
viduals lies in the 13 year, has been shifted to a higher age in
the older generations and lies in the 14% and 15" year.
From this it already appears that formerly the phase of sexual
latency, after crossing the threshold-age, lasted considerably longer
in a great many girls than nowadays. This also follows from the
fact that, as shown in Table I, more than 50°/, of the youngest
generation menstruates before the end of the 13" year, while of
those born before 1880 this was only the case in 26 °/,.
During the last 40 years, therefore, the period of the menarche
has gradually become earlier, and how much earlier can be learned
from both the following averages. The average menarche of the
persons worked out in Table | (fig. 1, curve A) of whom the greater
quantity was born between 1897 and 1906, is 13 years, 9 months,
15 days; while the mean age of the first menstruation in the per-
sons born before 1880 (fig. I, curve B) is 15 years, 3 months, and
20 days. From this it follows that in the last decades the menarche
arrives a year and a half earlier than formerly.
I must point out, in passing, that the last mentioned average
more resembles those found in literature regarding the West-Kuro-
pean population, which depend on investigations of an older date.
A second manner in which the earlier appearance of the menar-
che has been proved, is the comparison of the age of the menarche
in mothers and daughters. I arranged these data in two groups; in
the first I collected the data in which the age of the menarche was
accurately known, even up to the month, for both mothers and
daughters. To this group belong 45 mothers and 71 daughters. The
second group contains the data in which only the year could be
mentioned; here there are 56 mothers and 82 daughters.
It seems to me of interest to discuss the data of the first group
more extensively, as one or two remarks must still be made about
them; they may be seen in Table V, in which the data have been
arranged according to the menarche-age of the mother.
From this table follows, in the first place, that of 71 daughters
the menstruation of 52 begins at a younger age than in the
mother, though, as remarked already, also in the older generation
43
Proceedings Royal Acad. Amsterdam. Vol. XXVI.
658
it was not a rare thing for the menses to begin at the early age of
11. The average age of the menarche of the mothers was 14 years,
9 months, and 25 days; and of the daughters 13 years, 7 months,
and 1 day, which means that in one generation the menarche has
precipitated with fourteen-and-a-half months. That the difference
found here is not so great as what we find on comparing the
menarche of women born before 1880 with those born about the
beginning of this century (one-and-a-half years), can perhaps be
explained by the fact that among the former there were persons of
a much older age, and the process of precipitation of the menarche
is presumably already longer at work.
The appearance of the menarche in the youngest generation, 14'/,
months earlier than formerly, as found in Table V, almost coincides
with the results of the second group of mothers (56) and daughters
(82), of which only the year of the menarche could be mentioned.
Here the mothers were, on an average, 15 years, 1 month, and
3 days old, and the daughters 13 years, 10 months, and 15 days;
that is again a difference of 14'/, months.
These results undeniably prove the considerable precipitation of the
function of the sexual glands during the last decades; for although
the figures of this earlier appearance of the menstration may vary
a little, one can fix the average at about 14 months.
This is a fact of great importance, highly interesting as physiolo-
gical phenomenon, and of not less great significance from a social
and paedagogie point of view. For the appearance of the menarche
14 months earlier, means to say a shortening of childhood with
this period, an earlier activation of the sexual sphere in the present
generation, compared to the former. Much of what the attentive
observer and listener sees and hears in modern social life is explained
by this earlier awakening of the consciousness of womanhood. This
is, however, not the place to enter into this question further.
Extensive speculations as to the cause of this phenomenon will
not be given here; I will restrict myself to a few general remarks.
In the individual process of development of woman the first men-
struation is an event of more than ordinary significance; with the
commencement of sexual maturity far-reaching changes take place in
the general physiology of her development. And if this process makes
its appearance considerably earlier this must be looked upon as the
expression of a hastened process in her development. Now in the
first place the question arises: have we to do here with asymptom
of an accelerated development in general, or is it an independent
phenomenon? Without special investigations this question cannot be
659
answered. One would have to examine whether other signs of
development are accelerated in the phase before the menarche, e.g.
the growth, changing of teeth and such like. The developmental
phenomena after the menarche cannot be counted of course, for
TABLE V.
Mother Daughter | Mother Daughter | Mother Daughter
|
9.12 10.3 | 13.7 13.4 DE EN PN
10.5 | 12.8 } | 12.6
11.6 Oa 12.7 15.9 TT
11.8 11.6 | 13.7 13.1 | 12.8
11.9 cate | 12.3 eiste 11.10
1.11 | 13.8 aten Gee 13.11
15.2 iso) tito ee 12.11
11.10 14.12 12.12 || 16.6 16.1
11.10 11.10 TT | 17.1 13.6
12.7 14.10 | 13.11 13.10 | 12.8
12.9 10.6 | 14.1 10.8 | 17.4 14.9
12.7 Tet AL 16.3
13.1 12.8 15.9 | 16.6
13.1 B 4) lean etiam 13.8
13.2 (25-8) Agee 13.11 | 13.3 (12.12) !)
149 || 143 12.6 | 13.9
16.11 14.4 11 vallend 14.2
13.3 11.12 14.5 11.6 i 13.5
Uien 15.2 | 18.10 16.6
13.4 13.2 15.2 13:3) |\yeulee 15.3
13.1 | 15.3 14.4 | | 14.14
|
13.12 152 © oad 17.8
13.5 DS IN see 14.10 | 17.9
13.6 une | 19.8 15.4
|
1) Grandchild.
660
then the development also undergoes the influence of the ovarial
function. That this latter should have a retarding influence, on the
growth of the girl is doubtful, considering the fact that the full-
grown daughters of the youngest generation generally surpass their
mothers in height.
A second question concerns the cause of the phenomenon; is this
early appearance of the menarche a reaction on external stimuli, or
is it a primary change in the developing process? That we should
have to do with a primary biological phenomenon, with the effect
of an internal cause, is doubtful. | cannot imagine that an internal
factor could, as it were suddenly, so hasten a developmental pheno-
menon as appears to be the case in the menarche. If this was an
individual phenomenon, an exception, this could be possible, but it
is a general thing, which makes it necessary to accept some external
influences as cause. I will not enter into speculations as to what
these are, but will close this part of my communication with a last
remark.
The question can be raised whether, in this considerable precipi-
tation of the menarche, one has to do with a phenomenon which
falls beyond the limits of normal physiology. I cannot ascribe such
a significance to it, and may venture the following idea. I have on
purpose often drawn the attention to the fact that in all the groups
which I examined (brunettes, blondes, jewesses, older and younger
generations), the variability curve of the menarche begins at 10}
years; that is the threshold-age of sexual maturity. In every girl
who has passed this age the sexual sphere can be awakened, though
in the one it remains latent longer than in the other. The duration
of this period of latency is determined by hereditary factors and
by external circumstances. While the part determined by the former
is an unvariable one, that dependent on external circumstances is
on the contrary very variable. It depends on and changes with the
external conditions of life, with the mode of living, nature of food,
temperature etc. Whether it is advantageous for the individual or
not that the sexual sphere is awakened early under the influence
of those circumstances, is a question difficult to answer; but its
activation after having once crossed the threshold of maturity, falls
within the limits of the physiological norm.
The time of activation of the sexual functions is, as just remarked,
dependent on hereditary and external factors. The material I have
collected enables me to furnish a proof for both influences.
The significance of the heriditary factor has already been shown
by comparing the average age of the menarche in blondes (Homo
661
nordieus) and in brunettes (Homo alpinus). A still more convincing
proof can be drawn from Table V, for this table shows that if the
menarche appears at an early age in the mother, this is, on an
average, also the case in the daughter. I have on purpose arranged
the data in this table according to the age of the mother.
A simple calculation shows us the following: the average age of
the menarche of those daughters, whose mothers began to menstruate
in the 11, 12% and 13 year, is 12 years and 10 months; of the
mothers whose first menses appeared in the 14%, 15" and 16 year,
the daughters were, on an average, 13 years 7 months old, and
finally this mean age was 14 years and 11 months in those daughters
whose mothers first menstruated in their 17%, 18th, or 19' year.
These ages prove that a retarded menarche in the mother is inherited
by the daughter.
Among the external factors which are of influence on the menar-
che, the temperature, as has been remarked already, is regarded as
being of great significance. This opinion was, up till now, only
grounded on the fact that the menarche arrives at an earlier age
in the population of a warmer zone than in that of a colder climate.
Now I can prove from my investigation that this external influence
can be demonstrated even in the population of our country. I put
the question whether the menarche appears with equal frequency
in the different months of the year; and it became clear that this
is not the case. The frequeney-curve of the menarche, arranged
according to the months of the year, has a most typical direction,
as may be seen from Table VI. In this table the frequency for
each month is expressed in percentages of the whole.
TABLE VI.
January. . . . 8.2 % | May . . . . 10.8 %|September. . 6.9 %
EEDE UE en 10— sew October .. (6.200
Manchigvs oie te lul ‘5 O5 MENO vem berge Sn
ADL SSN August en 0 1029) Ser eiDecemberas: 8:6...
This table shows that a first menstruation appears more frequently
during the warmer months (May, June, July, and Aug.) than during
the rest of the year; for the total frequency during these 4 months
is 41.3°/, to 29.5°/, during the first and 29.7 °/, during the last
4 months of the year.
The monthly course, however, is somewhat more complicated.
Besides the greater frequency during the summer months there is
662
another rise in December and January. I should feel inclined to
explain this monthly difference in the following way: Beginning
with February | should like to regard the rapid and regular rise
up to May as a reaction on the general climatological factor, the
influence of awakening nature, and not so much as an influence of
temperature, which seems to me in these months not capable of
doubling the frequency in May, compared to what it was in February.
[ would thew be inclined to see an influence of the temperature in
the fact that during the actual summer months the frequency remains
almost equal to what it was in May. The rise of frequency in
December and January can perhaps be looked upon as the result
of the artificial higher temperatures to which the organism is subjected.
As has been mentioned in the beginning of this communication,
| have also been able to collect the data of 165 Jewesses, referring
to the age of the menarche. Naturally these almost entirely relate
to inhabitants of large towns. The following Table VII gives a
survey of the frequency, according to the age of the individual, in
absolute figures and in relative percentages, which are made clear
by curve A in fig. 2.
TABLE VII.
Age Number Percentage Age Number | Percentage
| |
9 year 1 | 14 year | 30 18.1
10555 3 | 1.8 15 17 10.3
ie | 20 fom Me apes ge Medea
ae 43 EIN 2 1.2
WS ps 39 23.6 | Sm 1
The following remark must be made with regard to this Table.
In the 3 cases arranged under the 10 year, the first menses
appeared in the second half of this age (10 years, 7 months; 10
years, 9 months; and 10 years, 11 months). The variation curve of
the menarche begins, therefore, in the Jewish girls at the same age
as in the non-Jewish. It is true there was one case in which the
menarche already began at the age of 9 years, but this case (9 years
1 month), is separated by an interval of a year and a half from
the following, and must therefore be regarded as asign of abnormal
precocity. For the Jewish race also, therefore, the middle of the
10 year counts as the threshold of sexual maturity. | would again
663
emphasize the fact that we have been able to demonstrate this age
in different groups. In this manner a criterion has been given to
determine in each separate case whether one has to do with a real
premature development, or with a normal, though perhaps rapid
one. A menarche after the age of ten and a half years is a normal
event. As far as the threshold-age of maturity is concerned there
is no difference between the Jewish and the non-Jewish girls. And
yet there is a difference, viz. the greater frequency of the menarche
immediately after the threshold bas been crossed, so that before
the age of 12 the sexual function has begun in 40°/, of the Jewish
girls compared to 30°/, in the non-Jewish blondes, and 18 °/, in
the brunettes.
It is very curious that after this rapid rise in the variability
curve, through which the top is already reached at the age of 12,
the variation line descends very slowly. Next to a group with
accelerated sexual development comes a second with a retarded one.
The result is, of course, that the average age of the menarche in
Jewish girls is not much earlier than in non-Jewish individuals ;
for among the blondes I found a mean age of 13 years, 5 months,
and 17 days, while for the Jewish girls the average was 13 years,
3 months, and 24 days.
The averred precocity of the Jewish girls compared with the rest
of the population, seems, therefore, not to exist, for the slight differ-
ence which can be discerned by the above methods, is sufficiently
explained by the fact, that the data of the Jewesses, with the ex-
ception of a few, refer to inhabitants of towns. I can, therefore,
on the ground of my investigation, agree with FisnBerG’s conclusion
that precocity is not a characteristic of the Jewish race. *)
1) M. FisHpera. “Die Rassenmerkmale der Juden.’ München 1913.
KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.
PROCEEDINGS
VOLUME XXVI
Nes, 9 and 10.
President: Prof. F. A. F. C. WENT.
Secretary: Prof. L. BOLK.
(Translated from: “Verslag van de gewone vergaderingen der Wis- en
Natuurkundige Afdeeling," Vol. XXXII).
CONTENTS.
B. SJOLLEMA and Miss J. E. VAN DER ZANDE: “Researches on the Metabolism of Milch-cows
suffering from Acetonemia”. (Communicated by Prof. C. EYKMAN), p. 666.
O. POSTHUMUS: “Etapteris Bertrandi Scott, a new Etapteris from the Upper Carboniferous (Lower
Coal-Measures) from England, and its bearing to stelar-morphological questions”. (Communi-
cated by Prof. J. W. MOLL). (With one plate), p. 669.
O. DE VRIES: “The coagulation of Hevea latex”. (Communicated by Prof. P. VAN ROMBURGH), p. 675.
M. W. WOERDEMAN: “On the Determination of Polarity in the Epidermal Ciliated cell. (After expe-
riments on Amphibian Larvae)’. (Communicated by Prof. L. BOLK), p. 702.
M. W. WOERDEMAN: “A Contribution to the Histophysiology of the Ciliated Epithelium”. (Commu-
nicated by Prof. G. VAN RIJNBERK), p. 707.
S. W. VISSER: “A non-tangent infralateral arc”. (Communicated by Prof. E. VAN EVERDINGEN Jr.),
p. 712. :
F. A. H. SCHREINEMAKERS: “In-, mono- and divariant equilibria’. XXIV, p. 717.
J. W. VAN WIJHE: “Thymus, spiracular sense organ and fenestra vestibuli (ovalis) in a 63 m.m.
long embryo of Heptanchus cinereus”, p. 727.
Miss L. KAISER: “Contributions to an experimental phonetic investigation of the Dutch language.
I. The short 0”. (Communicated by Prof. G. VAN RIJNBERK), p. 745.
TH. WEEVERS: “Ringing Experiments with variegated branches”. (Communicated by Prof. J. W.
MOLL), p. 755.
J. VAN DER HOEVE and H. J. FLIERINGA: “Determination of the Power of the Accommodation-
Muscle”, p. 763.
J. G. DUSSER DE BARENNE and J. B. ZWAARDEMAKER: “On the Influence of the vagi on the frequency
of the action currents of the Diaphragm during its respiratory Movements’. (Communicated
by Prof. H. ZWAARDEMAKER), p. 771.
V. VAN STRAELEN: “Description de Raniniens nouveaux des terrains tertiaires de Borneo”. (Présenté
par M. le Prof. G. A. F. MOLENGRAAFF), p. 777.
F. KOLMEL: “Ueber die zu einem Punkte und einer Geraden gehorigen Polarkurven inbezug auf
eine gegebene algebraische Kurve”. (Mitgeteilt von Prof. JAN DE VRIES), p. 783.
L. E. J. BROUWER: “Ueber den natiirlichen Dimensionsbegriff”, p. 795.
R. WEITZENBOCK: “Ueber Invarianten von Bilinearformen”. (Mitgeteilt von Prof. L. E.J. BROUWER),
p. 801.
A. MICHELS: “The Influence of Rotation on the Sensitiveness and the Accuracy of a Pressure
Balance”. (Communicated by Prof. P. ZEEMAN), p. 805.
JOHN I. HUNTER: “The Forebrain of Apteryx Australis”. (Communicated by Prof. L. BOLK), p. 807.
Mistress E. WINKLER-JUNIUS and J. A. LATUMETEN: “The histopathology of Lyssain respect to the
propagation of the lyssavirus”. (Communicated by Prof. C. WINKLER). (With one plate), p. 825.
G. BREIT and H. KAMERLINGH ONNES: “Magnetic Researches. XXVI. Measurements of Magnetic
Permeabilities to Chromium Chloride and Gadolinium Sulphate at the Boiling Point of
Liquid Hydrogen in Alternating Fields of Frequency 369,000 per second”, p. 840.
J. A. SCHOUTEN: “On a non-symmetrical affine field theory”. (Communicated by Prof. H. A.
LORENTZ), p. 850.
Proceedings Royal Acad. Amsterdam. Vol. XXVI.
Biochemistry. — ‘Researches on the Metabolism of Milch-cows
sujeriny from Acetonemia”. By Prof. B. Sjourema and Miss
J. E. vaN DER ZANDE. (Communicated by Prof. C. Eykman).
(Communicated at the meeting of September 29, 1923).
It does not unfrequently happen that in milch-cows acetonemia
reveals itself a few days after parturition. Then the animals become
extremely emaciated within a few days; the milk-yield decreases
considerably ; they give off a smell of acetone and their appetite is
largely diminished. As a rule they recover after a short time, and
very soon when put oat to grass. The examination of the urine,
the blood and the milk of more than twenty milch-cows suffering
from typical acetonemia showed us that the urine of these animals
often contained from 10 to 13 grms of acetone-bodies per liter. In
many cases the blood contained 0.6—1 grm of these substances per
liter, while the content in the milk was about half the amount in
the blood. These results point to an abnormal fat-metabolism, for
the acetone-bodies result mainly from abnormal metabolism of the
fats '), the alkali-reserve of the blood was in serious cases lowered
to */, or */, of the normal value. The determination of the glucose-
content of the blood shows that hyperglycemia was absent. Sugar
was never found in the urine. So the sugar-metabolism was in no
way abnormal. The acidosis, brought about by the acetone-bodies,
caused a rise of the calcium- and the ammonia-content of the urine.
The disturbed fat-metabolism, was not attended with lipemia. The
total content of lipoids and of fat in the blood was not or little
higher than normal. This rise was chiefly due to hypercholesterol-
emia. Instead of about 0,1 °/, we found namely about 0,2 °/, of
cholesterol in the blood-plasma. The lipoid-phosphorie acid did not
seem to have increased.
Basing ourselves on the formula that expresses the border-value
1) GeetmMuypDen’s hypothesis (Erg. d. Physiol. 1923), that acetone-bodies are normal
intermediate products from the conversion of fat into sugar, may be considered
highly debatable.
667
for the relation between ketogenic and antiketogenic substances *)
(SCHAFFER, HuBBARD and WricHt) we are in a position to calculate
from the obtained data (from which is also deducted that the animals
consumed about 375 grams of protein) that a cow must metabolize
about 1 k.g. of fat before this border-value is reached. With an
ordinary diet normal cows oxidize only little fat. The above relation
is then far above the border value. If the animals, as was often the
case in our experiments, secrete about 120 grms of acetone-bodies
a day. more than a kilogram of fat must be metabolized. So while
the animals then ingest little fat with their food, about one kilogram
of body-fat is burnt daily. It is evident, therefore, that in the case
of acetonemia one of the organs concerned in the fat-metabolism
must be seriously interfered with in its function.
The simplest way to account for this is to consider the liver as
the etiological factor, as in experiments with Ecx’s fistula and with
the reversed Kck’s fistula acetone-bodies are formed in the liver. *)
This view is supported by different observations on the diminished
activity of the liver during pregnancy (N.B. acetonemia in cows
manifests itself a few days after parturition) and on the abundance
of fat in the liver of cows shortly before parturition.
That the disturbance regards only the function, is proved by
the speedy recovery when the animals are sent to grass.
It may also be conceived that abnormally large mobilization of
fat is the primary anomaly which is controlled from another organ
than the liver.
That milch-cows do not easily secrete such large quantities of
acetonebodies as were found with acetonemia, was evident e.g. from
our experiments with cows: that we allowed to fast after some
injections of phloridzin (which engendered glucosuria). Indeed, some
acetone occurred in the urine but only little.
Neither were the quantities of acetone-bodies considerable in the
urine of cows that, on account of indigestion or for some other
reason (foot- and mouth-disease) ingest little or no food.
In a diabetic cow we found the same. Although the urine contained
for a considerable time from 3 to 4°/, of glucose, the amount of
acetone-bodies was normal or scarcely higher.
1) Recent researches have shown that the border value for the healthy organism
may also be taken for the organism with disturbed metabolism.
3) Of course these experiments do not prove that in no other parts of the
organism acetone-bodies may be formed. There is this against them that their
conclusiveness is greatly diminished owing lo the radical measures taken, and
consequently to highly abnormal circumstances.
44*
668
From the wide ratio between the intake of carbohydrate and
that of fat in normal cows it is clear that in milch-cows secretion
of acetone takes place only with a very abnormal metabolism.
Our researches go to show that in milch-cows suffering from
acetonemia waste of body fat takes place on a large scale, often about
1 kilogram daily. Lipemia, glucosuria and hyperglycemia do not
occur. The total quantity of acetone-bodies amounts to about 120
grms. per day. The cholesterol-content of the blood is 50 to 100°/,
higher than normal sometimes even more. The alkali-reserve has
decreased. It is probable that the disturbed fat-metabolism is caused
by intoxication of the liver.
From the Chemical Laboratory of the Veterinary
University at Utrecht.
Palaeo-botany. — ‘“‘Htapteris Bertrandi Scott, a new Etapteris
from the Upper Carboniferous (Lower Coal-Measures) from
England, and its bearing to stelar-morphological questions.”
By O. Posrnumus. (Communicated by Prof. J. W. Mot...)
(Communicated at the meeting of October 27, 1923).
Remains of this plant have been found in a coal-ball from Shore,
Lancashire; only the petiole is known, of which a series of trans-
verse sections has been cut by J. Lomax. Of this series 3 sections
are present in the Palaeo-botanical collection of the Mineralogical-
Geological Institute of the Groningen University (N°. 140—142);
besides [| have seen 6 other sections in the collection of Dr. Scorr
in the British Museum (Natural History) in London (N°. 2835— 2840).
The species has been mentioned by Dr. Scorr in his catalogue of
the collection as Etapteris Bertrandi, and is distinguished, as he
remarks, from the other species of the genus by the well developed
sinus in the xylem of the vascular bundle of the petiole.
The sections in the Groningen collection, though less in number,
show some features which are not present in the British Musenm
specimens, and enable us to form an opinion of the relation of the
species to its nearest allies.
The following description is chiefly derived from the sections
present in the Groningen collection.
The order of the-sections is 140—141—142; | cannot give with
certainty the exact place in the series of the British Museum sections,
but of the series the end is in Groningen. They are all transverse
sections of the petiole, which is about 2'/, mm. thick. *)
The epidermis is wanting; it could not be made out whether
assimilating tissue with intercellular spaces had existed under the
epidermis, but it is unlikely from analogy with allied species. Under
these missing layers we find sclerotic tissue: thick-walled cells with
a narrow lumen without intercellular spaces. In its innermost part
the thickness of the cell-walls decreases and the lumen is wider.
The inner cortex consists of thin-walled parenchymatous tissue
without intercellular spaces; it is only preserved at the extremities
1) The other dimensions are shown in the microphotographs which are enlarged
45 times.
670
of the vascular bundle near the pinna-bar; it contains scattered
cells, slightly larger than the others and with a black content. In
the space caused by the destruction of the inner cortex, the pigment
derived from these cells, is also scattered.
The tissue surrounding the vascular bundle has been partially
preserved with it. It is thin-walled without intercellular spaces ; its
elements, though often very indistinct, possess a narrow lumen;
they are more clearly shown in some places near the pinna-bar;
there the peripheral elements seem to be smaller in size than the
inner ones; this tissue may be considered as phloem. It is separated
from the inner cortex by a continuous double layer of tangentially
elongated cells, the endodermis.
The arrangement of the xylem-tissne of the vasecular-bundle in
the petiole is characteristic. Its structure is in agreement with the
symmetry of the petiole and its appendices. The pinnae are placed
in alternating pairs, their position to the petiole is similar to that
of a leaf to an erect branch: their upper side is turned towards
the petiole.
A pair of pinnae is symmetrical to a plane going through the
axis of the petiole and passing between the pinnae.
The vascular bundle is symmetrical to the same plane. The
structure at one end of the vascular bundle will be found at a
higher or lower level to be on the opposite side. This is caused by
the alternation of the pairs of pinnae. It is evident by comparing
analogous structures at one end with those at the other side, that
the pairs of pinnae had not quite alternated, but approached the
subopposite position, often also present in the fronds of existing
Ferns.
In section 142 the pinna-bundles are clearly shown, passing the
cortex and lying halfway between the periphery and the vascular
bundle. They are surrounded by an endodermis. The xylem-tissue
ig nearly round, with the narrower elements (protoxylem) lying at
the inner side. The outer row of trachieds seems not to be fully
differentiated yet. When followed in their downward course, the
two pinna-bundles fuse, thus forming the pinna-bar, a tangentially
elongated reniform bundle, with two protoxylems at its inner side.
This bundle is seen at different levels in section 141, 140 and 142.
At a somewhat lower level it becomes more flattened, approaches
the petiolar bundle and its endodermis fuses with that of the petiolar
bundle. The xylem of the latter shows in transverse section the
H-form, so characteristic in this genus. From a middle band, the
apolar, which is slightly thickened in its middle part and consists
671
of relatively large elements, two arms, the antennae, are given off
at each side; they are slightly recurved and prominent at the outer
side at their insertion into the apolar. Thus a more or less well
developed sinus is formed. The endodermis but slightly incurves
on both sides of the vascular bundle.
When followed in its downward course, the pina-bar fuses with
the petiolar bundle; the ends of the xylem of the pinna-bar fuse
with the two prominences on both sides of the sinus (N°. 140).
Thus an elliptical mass of parenchymatous, or at any rate thin-
walled tissue, is enclosed. At a lower level, as seen in section 141,
the pinna-bar has wholly fused with the petiolar bundle; the enclosed
parenchyma has diminished in size, especially im breadth. The
peripheral loop, the downwards prolongation of the pinnabar has
diminished in thickness and is but a few elements thick in its
middle part.
At a still lower level its continuity is interrupted; now on the
surface of the rather flat xylem a deep sinus is seen, which is
bordered on both sides by prominent ridges of tracheides. These
become more rounded at a lower level, and the original condition
is reached again.
The continuity of the peripheral loop which is formed by the
fusion of the pinna-bar with the petiolar bundle occurs in 2 of the
sections of the Groningen collection. It is not shown in the London
specimens. But in these the well developed sinus is clearly shown;
in this feature they differ much from the other species of the genus.
It is on these grounds that Scott distinguishes in his Catalogue this
form from the other species; it is shown here that the deeper sinus
is not an independent character but caused by the fusion of the
pinna-bar, when still continous, with the petiolar bundle; a feature
which is aberrant from that usual in the genus.
If one tries to make a stereometrical model of this structure, the
result is shown in fig. 4. In the other species of Etapteris e.g.
E. Scotti Bertrand, the pinnae-bundles are also placed in pairs and
fuse on their downward course in the cortex. But at a slightly
lower level before their fusion with the petiolar bundle, the pinna-
bar is split up, and the two bundles resulting from this division
fuse independently with the vascular bundle of the petiole. An
amount of parenchyma is thus never enclosed by the fusion of the
petiolar bundle with the vascular tissue coming from the pinnae.
That this difference with the features in E. Bertrand: is but a relative
one is shown by comparing the model of the structure of E. Scotti
(fig. 5) with that of the former species. Here we see the pinna-bar
672
fusing with the petiolar bundle. At a somewhat lower level the
continuity of the peripheral loop formed by this fusion is disturbed.
The interruption thus formed is limited on both sides by the down-
ward continuation of the halfs of this peripheral loop. The xylem
of the next pinna-bar fuses with the two ridges at its extremities.
In E. Scotti we see the pinna-bar approaching the petiolar bundle
too. But just before its fusion with the latter it is split up in its
middle part; thus two separate bundles are formed, which fuse
with the petiolar bundle. We see here the same fusion with the
petiolar bundle and the same interruption in the pinna-bar; but in
E. Bertrandi the highest point of the interruption is below the
fusion of the pinna-bar with the petiolar bundle and in E. Seotti
it lies above this point.
The interruption, the height of which is different in these two
species, is always limited below by the next pinna-bar. It lies above
the insertion of the pinna-bar. The relative length of the interruption
to the distance between two pairs of pinnae determines the condition
of the transverse section. In BE. Scotti the distance between two
successive pairs of pinnae is but small, often the bundles of two
pairs of pinnae are shown on the same side in one and the same
transverse section.
Thus the structure of Etapteris Bertrandi Scott enables us to
explain the features in other more complicated species of Etapteris.
On the other hand it has many points in common with simpler
forms, e.g. Diplolabis Römeri (Solms) Bertrand. In this plant an
interruption above the insertion of the pinna-bar is present too.
If the petiolar bundle is followed here in its downward course,
which Gordon’s') researches enable us to do, it can be shown, that
the lowest pinna-bar encloses at its inner side an amount of paren-
chyma by the fusion of the pinna-bar with the two sides of the
interruption. At a lower level the two protoxylems which are situated
on both sides of the parenchyma fuse. The parenchymatous tissue
diminishes in size and ends blind below.
But throughout its course to its lowest point it is in contact with
the protoxylem; it seems as if the lowest part of the parenchymatous
tissue follows the course of the protoxylem when penetrating into
the tracheides of the metaxylem.
It is remarkable that in these plants the protoxylems are always
associated with parenchyma except in the lowest part; this paren-
chyma, or at any rate thin-walled tissue, is situated at the adaxial
1, W. T. Gorpon, 1911.
673
side of the protoxylem. If we assume that the protoxylem was
originally wholly immersed in the metaxylem, but that afterwards
the development of tracheidal elements has been arrested at the
inner side, except in the very lowest part, we can explain the
existence of the interruption above the insertion of the pinna-bar.
For when the pinna-bar approaches the petiolar bundle and fuses
with it, the parenchymatous tissne at its adaxial side is enclosed.
The parenchyma associated with the protoxylems of the next pinna-
bar approaches in its downwards course the peripheral loop formed
by the pinna-bar next above, and as the development of the procambial
cells into tracheids has been arrested, a break is formed in the loop.
Through this interruption the parenchyma at the inner side of the
pinna-bar is connected with that enclosed by the fusion of the
pinna-bar next above with the petiolar bundle. The parenchyma
which is enclosed and that which lies in the sinus is formed by the
fusion of the strands of parenchyma lying adaxially to the proto-
xylems of successive pinna-traces. These interruptions in the peri-
pheral loop show some resemblance to the leaf-gaps in the stele of
many Ferns. Here, too, parenchyma situated adaxially to the proto-
xylems of the leaf-trace penetrates into the xylem of the stem, either
connecting the softer tissue in the interior of the stele with that
without, or hollowing the xylem of the stem by the fusion of these
parenchymatous formations of successive internodes. In the first case
a little strand of parenchyma, ending below blindly, can be found
some distance below the insertion of the leaf-trace; in the other
case this funnel in the xylem is absent. The parenchyma enclosed
inside the peripheral loop may be compared with the pith, formed
after the second method, but the connection of the successive paren-
chyma-strands of successive pinna-traces is not caused by reduction
in tissue which was present before (in phylogenetical sense). This
structure, caused by the peculiar symmetry of the bundle, is present
on both sides.
This species agrees in the form of the antennae with E. Scotti
Bertr.,') but differs from it by the simpler structure of the pinnae-
bundles, its smaller dimensions, and the more scattered position of
the idioblasts in the inner cortex. It differs from E. shorensis Bertr. ’)
by having another form of the apolar. In this species the continuity
of the pinnabar is maintained for a rather long distance, but the
presence of a peripheral loop has not yet been noted. A continuous
1) P. Bertranp, 1909, p. 140—147, 209, pl. XVI, fig. 111, 112.
3) P. BeRrRAND, 1911, p. 30—38, pl. II, fig. 23—31, 34, 35.
674
peripheral loop however has been found once in EK. Tubicaulis
Göppert sp.*) from Lower Carboniferous strata of Silezia, but in
many other respects it is very different from the species under
discussion. Perhaps E. Bertrandi may turn out to be really a portion,
e.g. the highest portion of the petiole, never before observed, of
some species already known, e.g. E. Scotti or E. shorensis. By its
aberrant structure however it seemed to me desirable to describe
this form.
LITERATURE.
P. Berrranp, 1909. P. Berrranp. Etude sur la fronde des Zygopteridées. These,
Lille, avec atlas, 1909.
P. BERTRAND, 1911. P. BERTRAND. Nouvelles remarques sur la fronde des Zygo-
pteridées. Bulletin de la societé d'histoire naturelle d’Autun.
t. 25, 1911, p. 18—25, 2 pl.
W. T. Gorpon, 1911. W. T. Gorpon. On the Structure and Affinities of Diplolabis
Römeri (Solms). Transactions of the Royal Society of
Edinburgh, vol. 47, 1911, p. 711—736; 4 pl.
EXPLANATION OF THE PLATE.
Fig. 1—3. Etapteris Bertrandi Scott. Transverse section of the petiole; N°. 140,
141, 142 respectively.
Fig. 4. Etapteris Bertrandi Scott. Model of the xyleem tissue of the petiolar
bundle (the sides of the sinus are too sharply accentuated).
Fig. 5. Etapteris Scotti Bertrand. Model of the xylem-tissue of the petiolar bundle.
1) P. BeRTRAND, p. 206.
Groningen. Botanical Laboratory.
O. POSTHUMUS: “Etapteris Bertrandi Scott, a new Etapteris from the Upper
Carboniferous (Lower Coal-Measures) from England, and its bearing to
‘ stelar-morphological questions’’.
Fig. 4. Fig. 3.
Fig. 5.
Proceedings Royal Acad. Amsterdam. Vol. XXVI.
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‘
Chemistry : ,, The coagulation of Hevea later’. By Dr. O. pu Vrins.
(Communicated by Prof. P. van RoMBURGH).
(Communicated at the meeting of January 27, 1923).
I. Influence of the miving-proportion of later, water and acid,
irregular series.
It was known from previous investigations, that the coagulation
of Hevea latex with acids shows irregularities. The observations
of several investigators, which we intend to discuss shortly in one
of the following paragraphs (§ 9), had only been made occasionally,
and did not give a sufficient insight into the phenomena; therefore
it seemed desirable to us to obtain a total view of the proportions,
by a systematical investigation into the complete range of mixing
of latex—water—acid.
Sule lhe Later:
Hevea latex is a milky liquid, which, under the microscope,
appears to consist of oval globules, } to 2u in size, and showing
a vivid Brownian movement; particles of less simple form occur
now and then. The fact, that one has not to deal with globular
particles, shows that latex is not a system liquid: liquid, an emul-
sion in the sense of Wo. Ostwatp’s classification. On the other
hand, one should not speak of liquid: solid (suspension); the pro-
perties of the coagulum obtained under various circumstances, make
it probable that the rubber-particles in latex have a buttery consist-
ency, ie. between liquid and solid. If we have to look upon this
as a more or less liquid nucleus, enclosed in a more solid super-
ficial skin, as some investigators assume, is a matter we do not
intend to discuss here. If we apply FreuNpDLIcH’s classification of the .
colloids to latex, then undoubtedly it is a lyophilic colloid, as shown
by the hydrous voluminous gel, obtained on coagulation, and by
the behaviour of the latex with regard to dehydrating and salting-out
substances; on the other hand, the hydrating power of the rubber-
globules is decidedly only limited, and the latex, as regards its
behaviour towards mono- bi- and trivalent anions, is strongly remini-
scent of lyophabie colloids. So in this classification as well, latex
676
occupies an intermediate place. Moreover, the rather complicated
properties of the latex may be understood, if we bear in mind,
that it is a vegetable juice, in which besides the rubber-carbo-
hydrates, also proteins, resins and other colloids play a part, and
in which each in its turn may come to the front.
The composition of Hevea latex is not constant. The quantity of
rubber and the quantity of secondary constituents depend on several
factors, which cause changes in the physiological condition of the
tree; moreover the tapping-system has a great influence. Besides we
have to bear in mind, that after tapping the acidety of latex prin-
cipally by bacteriological transformations, increases, even to such
an extent, that after twelve hours “spontaneous” coagulation sets in.
If, however, circumstances are carefully chosen, it is an easy
matter, to get a regular daily supply of latex of a certain compo-
sition. For that purpose one has to be restricted to a certain group
of trees, from which, according to a certain tapping-system, latex
is gathered daily, which moreover is always treated in the same
way. The only remaining changeable factor, the meteorological
circumstances, are then immaterial, if one keeps separate the latex
of those days, on which in the morning the trunks were still wet,
after nocturnal rains, or on whieh the latex gets drenched by an
early shower.
We could, by taking these precautions very carefully, obtain
quite sufficiently constant results, in the coagulation-experiments to
be described here, with series of observations covering several weeks.
If, however, later on, one reverts to such observations with latex
of a different group of trees, or a different tapping-system, the quanti-
tative data do not correspond exactly any more, though the general
course of the phenomena remains the same. In § 8 we intend to
give a few examples of the differences caused thereby, and also
of the influence of the gradually increasing acidity of the latex.
The results to be discussed here, have therefore to be interpreted
in such a way, that the principal features of the view are generally
available, but that the limits of the different ranges may be moved
more or less, according to the composition of the latex with which
one operates.
Against this drawback, that one operates with a non-constant,
and not arbitrarily reproducible material, we find, as a great ad-
vantage, the fact, that Hevea latex is mixable with water in any
proportion. So one may easily prepare all percentages of rubber
from the original percentage (30—40 °/,) down to the lowest one,
and one may, without great difficulty, traverse and search systematic-
san Minn ann
ae ee eee ee eee eee nn
677
ally in all directions the whole range of the mixing-proportions,
by serial determinations with decreasing quantities of more or less
diluted latex, and increasing quantities of acid, either diluted or not.
The „irregular series’ being only found with the lower percentages
of rubber, it was possible to determine completely the range where
these occur. In most cases, described in literature, the ,,irregular
series” have only be examined with one single or with a few con-
centrations, the higher or lower concentrations of the colloid not
being accessible. The latex, used for most of the observations to be
described here, originated from a group of trees, fifteen years old,
in the experiment garden at the opposite side of the Tjiliwoeng at
Buitenzorg. The trees were tapped daily, with two cuts over '/, of
the circumference of the trunk, and the latex was used for exami-
nation between 10 a. m. and noon. The percentage of rubber (on
coagulation) varied from 31,0 to 32,8, and on the average amounted
to 31,8°/,; the acidity was 0,02—0.04 N. (cf. § 8), the acids pre-
sent are principally carbonic acid, lactic acid and a little butyric
acid *).
In 1922 complementary observations were made with Jatex from
a few groups of trees in the Botanical garden.
§ 2. The phenomena of coagulation.
With the proportions, as they are chosen in the practice of the
preparation of rubber, the coagulation of Hevea latex proceeds
slowly. After a quarter of an hour the liquid has become thick,
with the consistency of porridge; gradually it begins to cohere, and
after one hour a coherent lump is formed, but still with milky
serum; only after a few hours the separation into a solid coagulum
and a clear serum, is complete. In other cases one causes the coa-
gulation to proceed more rapidly, by adding more acid, so that,
after one hour, one obtains a coagulum sustable for working
purposes. Or one saves acid, so that only after a few hours
the first phenomena occur, and the coagulum can only be worked
up next morning. Sometimes the latex is used undiluted, but mostly
one dilutes with water to a rubber percentage of 20 or 15°/,, on
account of which the coagulum becomes softer, and may be worked
up more easily. The more the latex is diluted, the softer the coa-
gulum becomes, and the stronger the contraction after the coagula-
1) For the composition of Hevea latex in general we may refer to „Estate
Rubber, its preparation, properties and testing’ by Dr. O. pe Vries (Ruyarok
& Co., 1920), chapter 1 and 2.
678
tion will be, so that more serum is set free. Only with very
strongly diluted latices a flocky coagulum is separated, which does
not form a coherent lump, or only gradually coheres after one or
more days. If we use less acid, the coagulation sets in slowly; but
with decreasing quantity of acid the spontaneous coagulation, caused
by bacteria which decompose the sugars and the proteins under
formation of acid, begins to play a more and more important part.
Ordinary, non-sterilised latex always coagulates, even without any
addition of acid, during the first night after tapping; the coagulum
is then spongy by the formation of gases, and the surface exposed
to the air is covered with a yellow, evil smelling layer of porridge-
like separated rubber, mixed with decomposition products of proteins.
So in the range of very little acid there are no mixtures, which
remain liquid in the long run; the observation “liquid” may be
made after a quarter of an hour or after two hours, but after 24
hours one will find the mixture coagulated. The liquid mixtures
with more acid, so in what one might call the second liquid range,
remain liquid for an unlimited space of time. Sometimes, after being
left fo themselves for several days, a separation of very thin little
flocks, lying on an almost clear or whitish serum, sets in, but in
any case one can control and confirm the observation “liquid” after
24 hours. This liquid range passes into the ranges of coagulation by
a strip of transition, being broad especially towards the side of the
higher acid concentrations, and distinctly showing different stages.
The first beginning of coagulation phenomena is the appearance of
a thin skin at the surface of the liquid, caused by evaporation in
the air, which, on stirring with a glass rod, attaches itself to it as
a streak or rolls itself up.
On approaching the range of coagulation a little more, this streak
becomes thicker and more cloddy. Advancing further, we get to
clotting or curdling of a greater part of the latex; a pap and finally
a coherent coagulum is formed. If it is left longer to itself, the
coagulation in this range of transition proceeds further; what after
two hours was a pap, may after 24 hours have become a coagulum
and a mixture which after two hours only showed a thick streak,
has changed the next morning into a pap, or even may be coagu-
lated. What is liquid in the middle of the second range, remains
liquid even after days, but “liquid” on the limit of “streaky”, may
have changed into streaky after 24 hours. “Coagulated” of course
remains such after one or several days, only the coagulum gradually
contracts itself a little and becomes harder.
It may be clear, that with these gradual transitions, we shall
679
never be able to fix any sharp limits for the different ranges. The
ordinary discrimination, by gently shaking or stirring, can only be
a rough one. We examined if sharper criteria might be found by
means of the microscope, but it appeared, that the formation of little
lumps of a few or a great many small rubber-globules also took
place quite gradually, without sharp transitions, and that neither the
decrease nor the stopping of Brownian movement opened the way
for any sharp limitation.
So most of our serial experiments were confined to judging at
sight, by means of a stirring rod, only completed occasionally by
microscopic oberservations. A short time, about 15 minutes, after
the addition of the acid the first observation was made, which
in certain ranges is already sufficient. The principal observation
followed two hours after the mixture was made, and was
controlled the next morning, viz. if then a stage was reached so
much further advanced as might be expected from the condition,
such as it was two hours after the addition of the acid. In order
to be able to sufficiently overlook the whole, we have, in the
following paragraphs, interpreted the observations in a somewhat
simplified way; therefore, with the classifications ‘streaks’, “curdled”’,
“porridge”, and ‘coagulation’ we have to associate the meaning of
conditions of separation gradually passing into each other, as described
above.
As a rule we worked with 50 ce. of liquid for each determina-
tion, the liquid being left open to the air in a small cylindric glass
till the next morning, for the last control-observation. With very
small quantities of acid the mixture of latex and water was meas-
ured with a measuring-cylinder and the acid was added by means
of a burette. It was not necessary to measure the diluted latex
more exactly than within 4 or 1 ¢.c., but the acid had to be
measured exactly within one drop, especially with the very diluted
latices, where the range of coagulation is narrow and sharply
limited. With mixtures with larger quantities of acid, the latex,
either diluted or not, was always mixed with the diluted or un-
diluted acid in such quantities that the total volume was 50 c.c.;
while the liquid, which occupied over half of the total volume,
was poured out first, and the other one added to it.
Especially in the range of a large quantity of acid, or if one
uses strong acid, it is necessary to stir vigorously from the beginning,
so as to prevent local coagulation, which would cause enclosure of
acid, not being set free any more by further stirring. By making
one same final mixture, starting from latices of different dilutions
680
and differently strong acids, one may however control the observa-
tions in a satisfactory way.
On account of the increasing acidity of the latex itself it is not
advisable to use it more than about two hours before the observa-
tions; we only did determinations between 10 a.m. and noon, but
during that time one can easily prepare a few series, in total about
thirty to fifty mixtures, so that in a rather short time by many
hundreds of observations one can search the whole range of mixing
in all directions.
Operating in small, open cylindrical glasses, causes a certain
evaporation and results in the formation of a small superficial skin
of coagulated rubber, which on stirring attaches itself to the
stirring-rod.
Apparently this causes an undesired complication; but for distin-
guishing different liquid mixtures this formation of skin appeared
on the other hand an advantage, because it enables us to recognize
the liquids inclined to coagulate. By repeating a few series in small
Erlenmeyer-flasks, closed with a cork, we have ascertained that
really these skins are formed by evaporation at the surface.
§ 3. Hydrochloric acid.
The easiest way to summarise the phenomena at different dilutions
and different quantities of acid, is to draw these in the wellknown
triangle-figure. As angular points (components) we choose water,
concentrated hydrochloric acid (9.14 N) and undilated latex, ie. a
liquid with 31.8°/, coagulable rubber, about 35°/, totally solid
substances and about 65°/, water, and with an acidity of about
0.03 N. A _ recalculation of the results, so as to express these as
quantity of acid, resp. rubber compared to the whole liquid (water
of dilution plus serum) can never be correct by the phenomena of
adsorption and, as regards rubber, there is not much sense in it,
as coagulable rubber is a substance containing so many secondary
substances in small quantities.
In the annexed figure 1 the lines show how the different mixtures
are formed by mingling latex and hydrochloric acid, of different
dilutions. The mixtures, in which after two hours a well coherent
coagulum was formed, are marked with a little cross. As we see
this range almost oecupies the whole triangle; only in a narrow
strip along the latex-water side, we find mixtures, which are
represented by an encircled point (pap or curdling) or by a little
cirele (liquid), and there we can, though indistinctly on account of
681
the scale-size used, recognize irregular series liquid: coagulation :
liquid: coagulation. This narrow strip, the range of small quantities
L
Fig. 1.
of acid, is, with hydrochloric acid, the only interesting item; the
remainder of the triangle shows nothing particular, the less water
the mixture contains, the harder the coagulum, while in mixtures
with little water and much hydrochloric acid the serum assumes
a violet tint.
The narrow strip along the latex-water side is represented on a
larger scale in fig. 2, where the acid is drawn perpendicularly, as
ordinate, and expressed in normality (grammolecules HCI per Liter
final mixture).
For quite small concentrations of acid, at any dilution, we first
come into the liquid strip, where coagulation has not yet started
after two hours. After 24 hours this part shows spontaneous
coagulation. At higher acid-concentration (from about 0.007 N) we
find after two hours more or less strong curdling or formation of
pap, and after 24 hours coagulation. The limit at which after two
hours complete coagulation with a clear serum has taken place, is,
45
Proceedings Royal Acad. Amsterdam. Vol. XX VI.
682
found with mixtures beyond 50°/, latex, to be fairly constant at
0.012 N. We should bear in mind, that this means the acidity of
SS joen
Fig. 2.
the hydrochloric acid added, which has to be increased with the
original acidity of the latex, recalculated on the final mixture. For
mixtures, containing less than 50°/, latex, this bottom-limit of
coagulation is regularly lower. Because of reasons mentioned above,
the observations could not be made so sharply that the relation
between rubber-concenuation and limit of acidity appeared quite
clearly, but especially with the lower concentrations the small
irregularities may be considered to be due to observation errors,
and we may assume that the lowering of this limit is inversely
proportional to the latex concentration.
With mixtures containing over 80°/, latex to which more acid is
added we always get a strong coagulum, and so from the beginning
we are in the range of coagulation, which fairly occupies the whole
triangle of Fig. 1. At 75°/, latex we get the first indications that
another phenomenon is about to appear, because the coagulum at
first is hard, with more acid (about 0.05 N) soft or even like pap,
and only with a still larger quantity of acid hard again. A distinetly
liquid range only appears with mixtures with 65°/, latex and less.
The strip of coagulation between both liquid ranges, the lower
range of coagulation, regularly decreases in latitude at lower latex-
concentrations, but still remains distinctly perceptible even at the
lowest coneentrations (1°, latex). Im those very diluted liquids the
683
rubber does not separate itself as a coherent coagulum, but in the
form of white flocks. The separation goes much quicker than with
higher concentrations and with the liquids with 1 and 24°/, latex,
reminds one of a titration of warm nitrate of silver with hydro-
chlorie acid.
At those low concentrations the range of coagulation is so narrow,
that, in an acidified but still unchanged liquid, one can see, with
a single drop of diluted acid, the white flocks separating themselves,
and that one sees the original milky liquid remain unchanged on
addition of a few drops more. With mixtures with 5°/, latex one
may get at first, with a small quantity of acid, a flocky separation,
cohering fairly quickly as a coagulum; on addition of a little more
acid a very soft coagulum may be formed at once. Mixtures with
24°), and 1°, latex cause flocky separations, which may remain
unchanged for a long time, and with which the coherence as a
coagulum is the more difficult, according as the mixture contains
less latex.
At higher concentrations, just above 5°/,, sometimes the liquid
separates itself in a remarkable quick way into a coagulum and a
clear serum, but the instantaneous coagulation is not found there
any more. At still higher concentrations the separation of the coa-
gulum goes slower.
The lower range of coagulation, described here, is limited by a
transition to spontaneous coagulation, as discussed above; at the
upper part we find a narrow range of transition, where the mixture
after two hours is like pap or curdling (after 24 hours mostly
coagulated). Only towards the higher latex-concentrations this strip
gradually becomes a little broader, and at about 65°/, latex bends
itself in an upper direction, limiting the top of the liquid range,
and converging into the broad strip, which separates the liquid
range from the upper range of coagulation. Thus the liquid range
is perfectly limited, both at the upper- and at the lower side, at
least till the lowest concentration, which was examined (1°/, latex,
so 0.3'/, rubber in the mixture). Whether, at still smaller concen-
trations, the lower strip of coagulation is continued, or if both the
liquid. ranges meet there, has not been examined vet. The limits of
the various ranges are found at the following normalities of the
added acid in the final mixture: (See Table following page).
These figures are illustrated by fig. 2.
We shall now give a short description of the course of the pheno-
mena at a few typical concentrations. To the latex-water-mixture
10°/, hydrochloric acid (0.914 N) was added from a burette; the
45*
684
TABLE I.
Latex Lower | Upper limit Upper timit| Lower limit
in the | limit of Canes liquid | SAC MADE
mixture. | coagulation coagulation. range | coagulation.
| |
.
65 % | 0.012 | 0.04 0.08 | 0.10
50 0% | 0.011 0.029 OO eee Sent
40 0 | 0.009 0.019 0.11 0.14
30 0% OXOOn NeR ST O2 | 0.15
20 0% 0.005 | 0.009 | 0.12 0.155
10 % 0.0035 0.0055 | 0.11 0.16
5 fp, /4\,0,0018,,. 18 O.00aT | Oste 0.155
21/5 Ofo 0.0009 | 00018 | 011 ke ORG
1% 0.0008 | 0.0011 | 0.14? 0.16
quantities were chosen in such a way that the final mixture was
always 50 ec, so that the latex-concentration, at larger quantities
of hydrochloric acid, decreased a little, and that the serial deter-
minations in fig. 2 are found on slanting lines.
With a mixture with 70°/, latex the result of the examination
two hours after the addition of acid was (ef. fig. 2):
After being left to itself for three hours, the coagulation of course
had proceeded further; now 2'/, had become a pap, 2°/, a thick
liquid with a good many skins, 3—4'/, remained liquid, 5°/, was
softly coagulated. The mixtures in the strips of transition show a
further advanced coagulation, but the true liquid mixtures remain
liquid, even after 24 hours. When it is left in open small cylindric
glasses, a skin is formed at the surface, evidently by evaporation,
for in closed Erlenmeijer-flasks it was not formed. So the limits of
the ranges are somewhat displaced, according to the moment of
observation being delayed, but the phenomenon coagulated — liquid —
coagulated remains. It strikes us, that the transition at the lower
side of the liquid range is very acute; at the upper side however
much more gradual. The little skins formed on stirring, are partly
due to evaporation at the surface, or to latex, drying upon the side
of the glass; yet these skins point to a higher inclination for coa-
gulation, as such mixtures after 3 or 24 hours are coagulated further
than the purely liquid ones.
685
cc. 1000 HCI per
50 cc mixture.
0.1
0.3
0.4
0.5
0.6
0.7
0.8 and 0.9
1
he
21/,
3e, 385, 4, Al,
41,
DESCRIPTION.
liquid.
liquid.
thick pap; beginning of strip of transition.
thick liquid, a few little lumps.
the same.
a somewhat thick pap, coagulating on stirring; begin-
ning of the range of coagulation.
strong coagulum, serum whity.
coagulated, serum fairly clear, (acid added 0.018 N).
the same, serum fairly clear.
the same, serum white. Upper-limit first range of coa-
gulation.
liquid, a few small lumps on stirring. Therefore sharp
transition.
liquid with some skin.
liquid; lower limit liquid range.
liquid; no skin.
liquid on stirring some skin or streak. Upper-limit
liquid range.
the same, a piece of skin (therefore irregularity).
the same, more skin.
the same, a fair quantity of skin.
like pap (at an other time only a fair quantity of streaks).
very soft pap, almost coagulated.
coagulated, but serum quite white, therefore far from
complete. Lower-limit second range of coagulation.
coagulated, fairly stiff, serum white.
the same, serum white.
the same, serum white. The percentage of latex in this
mixture is 58.8 0/0.
An other example with 30°, latex: (See following page).
p 0 g pag
Of course the coagulum is
only contain 30°/, latex, i.e. about 10°/, rubber.
always soft, because the mixtures
Quite typical are the sharp transitions at the first range of coa-
686
ce 10% HCl per
50 cc mixture.
DESCRIPTION.
liquid.
liquid.
liquid, somewhat thickish, small lump of coagulum.
coagulated, rather stiff, serum rather clear, lower limit
first range of coagulation.
coagulated, serum clear.
coagulated, serum perfectly clear like water.
| well-formed, but soft, jellied coagulum, serum nearly
clear. Upper limit first range of coagulation.
quite liquid, only somewhat streaky, lower limit liquid
range. Sharp transition.
quite liquid.
quite liquid, somewhat streaky, like 1. (later determin-
ation liquid without streak).
liquid.
liquid, somewhat streaky, upper limit liquid range.
liquid, rather streaky.
| for the greater part liquid, a good deal of streaky soft
coagulum.
soft coagulum, serum white. Lower limit second range
of coagulation.
soft coagulum, serum white.
well-formed but soft coagulum, serum quite white.
the same the same.
the same serum almost clear.
gulation of very dilute latices; e.g. at 1°/, latex (0.3°/, rubber in
the mixture), see fig. 2, lower, enlarged part.
The microscopic image of the liquid in the second liquid range,
is, e.g. for a mixture with 2°/, latex, as follows.
At a small acid-concentration almost all the rubber-globulus are
still free from each other, and have a Brownian movement; only
very few small lumps are seen, consisting of some little globules
touching each other. Starting from an acid-concentration of about
0.02 N to increase somewhat, but by far the greater part of the
particles are still free and in vivid Brownian movement. Only at
cc 1% HCI DESCRIPTION
0.25 liquid, containing a few small flocks.
0.4 liquid, with a few small flocks.
0.45 after about '/, hour rising flocks are separative, so that
after | hour the serum is almost clear.
0. | coagulates almost momentarily in flocks, rising to the
| surface in a layer, serum almost clear.
0.55 flocks are separated slowly. serum remains white.
0.6 liquid. |
1.0 liquid.
about 0.11 N, ie. at the upper-limit of the liquid range (see fig. 2),
the number of small lumps increases and the Brownian movement
decreases, and at 0.13 N hardly any particles move, and only very
few show Brownian movement. At 0.14 N the decreaming begins,
which, at 0.15 N, leads into the range of coagulation. From 0.10
to 0.15 N therefore, there is a gradual transition from “free parti-
cles with Brownian movement” into lumps, particles yet free but
not moving, and decreaming. Whether perhaps the few little lumps,
which are found in the second liquid range, were formed by a local
excess of acid during addition, was not examined.
If we keep a liquid from the middle part of the second liquid
range, e.g. 2°/, latex with 0.06 N. hydrochloric acid, in a high
cylindric glass, no decreaming takes place within the first’ few
weeks, but the Brownian movement gradually decreases. After two
months most of the particles have joined into small lumps, a few
consisting of two or three, but most of them consisting of a great
number of globules, so that, after that time, only a fairly small
number of free particles remain in Brownian movement; yet only
part of the rubber is decreamed, and superficially the liquid is still
equally white.
We regret we were unable to examine, whether in the second liquid
range the negative charge, which the rubber-globules show in the
original latex, had given place to a positive one, as required by
the theory of „change of charge” '). Some experiments concerning
1) Cf. F. Powis, Z. Phys. Chem. 89 (1915), 105.
H. R. Kruvyr, these Proceedings 17 (1914), 615, and 19 (1917), 1021.
688 .
the coagulation with different salts, will be described in a following
communication.
We shall discuss in § 8 a few examples of the influence of the
original acidity of the latex on the position of the limits of the
ranges.
$ 4. - Mitric acid.
We likewise made serial determinations with nitric acid and
sulphuric acid, but less detailed, so that the limits of the different
ranges were only roughly determined. For these experiments latex
was used from a different group of trees, containing 28°/, rubber.
Fig. 3 gives the determinations tor nitric acid. The general type is
0.14 Nn
70.10
0.06
Fig. 3.
exactly the same as with hydrochloric acid, buth the liquid and the
pappy ranges are smaller. Fig. 3 only goes as far as mixtures with
70*/, latex; the top of the pappy range, being with hydrochloric
acid at 75 °/, latex and about 0.07 N, is found here at a little less
than 60°/, latex and about 0.04N. The top of the totally liquid
range is comparatively still more displaced towards the right, so
that, between both these tops, a very wide ,,pappy’” range is found,
in which we separated, by a dotted line, that part where, after
two hours a thick or fairly thick pap is formed, from the part
still showing fairly liquid mixtures with streaks or a beginning
curdling. With nitrie acid the upper-limits lie at about half the
normality of that with hydrochlorie acid.
In $ 7 we intend to compare more closely the figures for the
four acids, and also diseuss more detailed the data for mixtures
with 5 and 2°/, latex.
$ 5. Sulphuric acid.
The data, which we gathered for coagulation with sulphuric
689
acid, have been put together in fig. 4. The large range of coagu-
lation at acid-concentrations above 0.1 N (normal = 49 Gr. H, SO,
per Liter) has again been quite left out, and also the mixtures
with over 70 */, latex, where coagulation constantly takes place
as soon as more than 0.01 N acid is added. On account of the
smaller number of observations, the course of the limits in fig. 4
seems to be somewhat irregular, yet the data are sufficient to
mm = = = == = Ol N
conclude, that the pappy and the liquid range, compared with
hydrochloric acid and nitric acid, have shrunk still more. Figures
of comparison are again found in $ 7.
We may still mention, that, starting from a mixture with 70°/,
latex, we get a distinct indication regarding the existence of the
„irregular series’, though all the mixtures coagulate; the mixture
with 0.04 N. acid gives a perceptibly softer coagulum than that
with 0.025 or 0.05 N. acid.
§ 6. Acetic acid.
For acetic acid — the general and usual means of coagulation
at rubber plantations — the course of the phenomena generally
speaking appears to be the same as in the previous cases, but the
proportions of the various ranges are quite different ones. Whilst
with the three previous acids the whole range of the irregular series
lies in a narrow strip along the latex-water side, which in a re-
presentation like fig. Ll is hardly discernible, the irregular series
with acetic acid are extended to far higher acid concentrations, and
a triangle-figure like fig. 5 opens the best general aspect. Here
likewise the range of coagulation occupies by far the greater part,
viz. almost */, of the triangle; but in the neighbourhood of the
690
angularpoint for water we find that over '/, of the triangle is
oceupied by the liquid and pappy range, while naturally in this
case also, close along the latex-water-side a first liquid range is
found, not showing any coagulation on addition of a very small
quantity of acid, but, after keeping, showing spontaneous coagula-
tion by the action of bacteria.
The proper liquid range in fig. 5 is again limited by a dotted
line; the pappy range is divided by a somewhat thicker dotted line
into two parts, a fairly liquid and a more pappy one. Formation
of a coherent coagulum takes place in the narrow strip parallel to
the latex — water — side and towards the side of the angulair-point
Latex; the total range towards the side of the angulair-point acetie acid
gives a perfect coagulation, but in the shape of flocks or as a pap,
and not as a coherent lump. Both these ranges of coagulation are
roughly separated in fig. 5 by a dotted line. Therefore in this
respect too, there is an important ‘difference between acetic acid
and the three other acids, with which the whole range of coagula-
tion gives a coherent coagulum.
691
We traced the coagulation with acetic acid once more by a
considerable number of determinations, viz. in the latex of both
the above-mentioned groups of trees; in fig. 5 we have represented
the results, obtained with the 28°, latex of the second group
(see § 4). The normality of acetic acid added is given in table 2
for the limits of the various ranges.
TABLE 2.
Quantity of latex in the mixture in %.
100 80 60 | 50 40
30 | 20 10
Limit lower | | |
liquid range. e008 0.003 (0.003 |0.003 (0.003 10.003 |0 0015
Beginning | | | | | |
lower creamy | | | | |
range. |(0.008 (0.008 (0.008 |0.009 |0.009 (0.009 (0.003 | — —
| | | | | | | | |
| |
|
Lower limit
range of coa- | | | | | |
gulation. 0.017 (0.024 0.031 (0.030 (0.028 | — (0.016 (0.006 |0.0015/0.0012
Upper limit | | | | |
first range of | | |
coagulation. | — | — | — (0.52 |0.35 |o.21 |0.13 |0.08 |0.05 |0.026
Lower limit |
second liquid | | |
range. = a | = 0.8
0.24 (0.16 0.10
On comparing these figures and fig. 5 with the results described
in $$ 3—5, we distinctly see the great difference in the distance
between the limits. A comparative review is given in § 7.
In judging the above figures one has to bear in mind, that the
phenomena, in the sense in which we consider them here, are not
exactly the same as in plantation practice. So here we take as
lower limit of the range of coagulation those mixtures, where a
coherent coagulum is formed after two hours, whilst with regard
to the coagulation at the plantations it is moreover required, that
the serum is clear or almost clear, and the coagulum sufficiently
stiff to be mangled. With undiluted latex the lower limit of the
range of coagulation, as it is described here (0.017 N or about 1
Gram acetic acid per Liter latex), will be lower than the amount
used in practice, if we wish to mangle a few hours after the coa-
gulation. With 50°/, latex (i.e. 1:1 diluted) the dose (0.030 N = 1.8
Gr. acetic acid per Liter) is higher, because with diluted latex one
692
mangles the next day, when with a much smaller quantity of acetic
acid, a coagulum fit for use has formed itself.
To this we add the results of a less complete series of observa-
tions, made in November 1922 with latex from the Botanical garden
at Buitenzorg, where a few groups of trees were tapped with a
cut over '/, of the circumference.
This latex contained 37°/, rubber, and had an acidity of about
0.025 N. We see that the general type is the same, that the lower
limits fairly well coincide, but that, with regard to other limits,
rather important differences appear, that may be attributed partly
to the difference in composition and acidity of the latex, partly
however, to the difference of appreciation between the observers.
This example illustrates, together with the cases to be discussed in
§ 8, the restriction we made already in § 1, regarding the quanti-
tative value of the results.
TABLE 3.
Quantity of latex in the mixture in 0/0.
| 80 60 | 40 | 20 10 | 5 | 2 1
| - 7 ! ] ] ]
Beginning lower creamy or | |
pappy range. 0.009 (0.010 0.009 (0.006 (0.002) — | — —
| | |
Lower limit first range of |
coagulation. |0.018 (0.022 (0.017 |0.009 0-0053/0..0026/0.0020 0.0016
Upper limit first range of | | |
coagulation. — | — (9.40 |0.20 |0.083 0.04 |0.033 |0.023
Lower limit second liquid | | | | |
range. | SEY 1. | — 0.5 (0.17 (0.066 lo.059 |0.040
| | |
|
§ 7. Comparison of the four acids.
We now intend to compare amongst each other the results, ob-
tained with the four acids. Whilst, roughly speaking the general
course is exactly the same, we may notify interesting differences
and conformities.
Considering first of all the top and the upper limit of the liquid
range, we can use for that purpose the data mentioned in § 3—6,
although they refer to two different latices, and the principal obser-
vations covered a period of over half a year, because these limits,
can only be roughly determined. So we get:
693
TABLE 4.
TE:
HCI | HNO, H»SO4 C,H,0;
Top liquid range, with mixtu-
res with latex 00/9 350/0 250/0 250/0
Top pappy range, with mix- | |
tures with latex 71% | 5170/9 650/0 570/0
Upper limit liquid range for | |
20 Oo latex, at acidity 0.12 N 0.06 N 0.03 N 3—4 N
|
Upper limit pappy range (lower |
limit second range of coagula- | |
tion) for 20°, latex, at acidity | 0.155 N 0.10 N 0.06 N 71-8 N
|
The limit, at which irregular series do not appear ary more —
the top of the pappy range — is found for nitric acid, sulphuric
acid and acetic acid at almost the same percentage of latex, but for
hydrochlorie acid it is somewhat higher. With all this we have to
bear in mind that with nitric acid in a mixture with 60°/,, with
sulphuric acid in one with 70 °/,, a distinct interruption in the series
can still be observed, owing to the coagulum, at a level of the
above-mentioned top, being softer than at higher or lower concen-
trations of acid. A striking difference in the position of this top
cannot therefore be stated with the four acids.
On the other hand there is an undeniable difference with regard
to the top of the really liquid range, which, with hydrochloric acid
extends to much higher latex-concentrations, than with the three
remaining acids.
In the upper limit of the liquid range, te. the beginning of the
upper curdling range, and likewise in the upper limit of this range,
i.e. the lower limit of the second range of coagulation, the difference
is very striking too. With acetic acid these limits are by far the
highest; then follows hydrochloric acid, about halfway lower nitric
acid, and half way lower again sulphuric acid. If we assume, that
in the second liquid range the colloid rubber particles have changed
their charge from negative into positive, the stronger coagulating
action of the bivalent sulphate-ion would be fully explained; mono-
valent ions then would show a decided difference in the series
nitrate-, chlorine-, acetate-ion.
A comparison of the action of the four acids in the first range
of coagulation seemed of particular interest to us, viz. with small
latex-concentrations, where, with a small increase of the acid-
694
concentration we so sharply get with the three inorganic acids the
phenomenon liquid-rapid coagulation-liquid, described in §3. There-
fore, for the same mixture of latex, we once more determined these
limits for all four acids separately, in order to get absolutely com-
parable figures (which figures therefore do not fully correspond with
those in $$ 3—6, as we explained in § 1 and intend to discuss
more in detail still in § 8).
The figures were for the acid-concentration in normality :
TABLE 5.
| HCI | HNO, | H,SO, | C‚H,O»
|
5 °/) latex, lower end: | 0.0011 | 0.001 1 | 0.0011 | 0.0015
5 % latex, upper limit 0.00265 | 0.00265 0/0029) | |, aes
2% latex, lower limit 0.0007 0.0007 0.0007 | 0.0010
| |
2 9 latex, upper limit 0.0013 0.C013 0.0014 =
The lower limit of the range of coagulation is exactly the same
with the three strong inorganic acids, and here it is quite clearly
demonstrated, that, at least in this range of strongly diluted latices,
the phenomenon is ruled by the positive Hions; the action of
acetic acid is somewhat weaker.
With hydrochloric acid and nitric acid the upper limit again is
exactly the same; also the strips of transition (which are very
narrow with these strongly diluted latices) show exactly the same
phenomena if the same quantity of acid is added; so the action of
hydrochloric acid and nitric acid in the lower range of coagulation
is exactly the same, whilst the limit of the upper range of coagu-
lation, as we have seen just now, is considerably lower with nitric
acid. With sulphurie acid the upper limit of the first range of coa-
gulation is a little higher; the difference is not important, but for
all that, with this exclusively comparative experiment, it could be
stated clearly, also because corresponding differences were noticed
in the strip of transition lying above the range of coagulation. With
acetic acid the upper limit is much higher (at about 0.05 and 0.026 N,
see table 2) and has not been determined again in this experiment.
A determination of the hydrogen-ions concentration in these various
liquids, which would be necessary for a correct interpretation of
the phenomena, could not as yet take place; we only wish to draw
the attention to the fact, that the subsequency of the four acids at
695
the upper limit of the first range of coagulation (hydrochloric acid
and nitrie acid — sulphuric acid — acetic acid) is not the same as at the
lower limit of the second range of coagulation (sulphuric acid — nitric
acid — hydrochloric acid — acetic acid).
§ 8. Injluence of the acidity of the latex itself.
As already stated in $ 1 latex is feebly acid, and on being left
to itself gradually inereases in acidity. The acidity of the latex,
which is used for the researches, is of course not without influence
on the figures obtained, though the relation need not be purely
additive, as the acidity in latex is caused by carbonie acid and
organic acids amongst which, after the action of bacteria, lactic acid,
acetic acid and butyric acid.
First of all we made a few observations in ordinary latex and
in the same latex after neutralisation with hydroxide of potassium,
Le. again for the limits, to be fixed sharply, of the first range of
coagulation in mixtures with little latex. A mixture with 5°/, latex
(percentage of rubber 1.43°/, needed) for the neutralisation (phenol-
phthalein as indicator) 16.6 ce. *‚, N hydroxide of potassium per
Liter, and therefore was 0.00166 normal; for the original latex we
calculate from these data an acidity of 0.033 N. A mixture with
2°/, latex (percentage of rubber 0.54°/,) required 6.6 ce. hydroxide
of potassium and therefore was 0.00066 normal (i.e. also 0.033 N
calculated for original latex).
The limits of the first range of coagulation appeared to be with
hydrochloric acid:
TABLE 6.
een TR | Addition hydrochtoric acid =
| | in normality
| Own ss
| acidity |
| | Lower limit Upper limit
|
5 0/o latex, original | 0.00166 0.0015 | 0.0032
id. , neutralized | 0.0030 0.0048
2 0/ latex, original | 0.0066 | 0.0013 0.0020
id. _, neutralized | = | 0.00195 0.0027
We see, that the neutralization has increased the necessary addition
of acid with about the amount of the own acidity of the latex. In
judging tbe figures we should bear in mind that the neutralized
696
latex contains by the neutralization a small quantity of potassinm
salts, that may somewhat displace the limit of the ranges.
A second experiment related to the increase of the own acidity
of the latex, when left to itself. The latex used for this purpose
titrated, when left to itself undiluted, at 10 o’clock 0.026, at noon
0.030 and at 1.45 p.m. 0.032 N. From the observations resulted :
44} cc. 70°/, latex, diluted at 10 o’clock with 54 ee. 10°/, HCl,
(i.e. mixture 0.1 normal, belonging in the upper pappy range of
transition, see Fig. 2): after one hour still liquid, but containing a
fair-sized lump of streaks, and after three hours a thick pap, fairly
well coagulated, with quite white serum;
the same mixture, but prepared only at 12.30 p.m. from the
undiluted latex, was already coagulated, after being left to itself for
one hour, though the coagulum was still very soft. So the influence
of the higher own acidity of this latex was quite noticeable.
43 cc. 40°/, latex, prepared at 10 o'clock with 7 ce. 10°/, HCI
(i.e. about 0.13 N, again in the middle of the upper pappy range
of transition, see Fig. 2) caused after one hour a small lump of
little skins, and was still liquid after three hours with a fairly
strong skin;
the same mixture, prepared at 12.30 was still liquid after one
hour with a small lump of skins, which was somewhat larger than
in the above-mentioned mixture after one bour. So in this case the
difference was noticeable, though not important.
It appears from these experiments, as might be expected, that,
TABLE 7.
May Oct 8th |Oct.9thand| Oct. 14th May
1920 | 1920 12th 1920 1920 1922
=
Own acidity undiluted | 0.026— | i 0.041— | 0.033 0.022
latex 0.030 | 0.044 |
Upper limit 5 0/0 latex 0.0027 | 0.0025 | 0.00265 | 0.0032 | 0.0044
Lower limit _ ib. 0.0018 0.0012 0.0011 0.0015 | 0.0020
Upper limit 2%, 0/0 latex gloort le) he: 2
Lower limit ib. C0009) RMA a =
Upper limit 2 0/0 latex — | 0.0014 | 0.0013 0.0020 0.0026
Lower limit ib. — | 0.0007 | 0.0007 0.0013 | 0.0014
Upper limit 1 0/, latex 0.0011 — — — 0.0020
Lower limit ib. 0.0008 — | — — | 0.0014
697
by operating with the latex later, the quantity of acid that has to
be added in order to reach a certain stage, is found to be a little
smaller.
We will still give a few examples, how much the percentages
of acid found may vary when latex from different origin is used,
viz. for hydrochloric acid and for the limits of the first range of
coagulation with mixtures with 5 and 2°/, latex.
If we calculate the differences in own acidity of the diluted latices,
we see that the differences in acidity for the limits differ fairly
strongly from them, though a general relation can be clearly noticed.
In fact a strictly quantitative correspondence could not be expected
as the latices differed not only in acidity but also in percentage of
rubber and in secundary substances.
§ 9. /nvestigations of others.
As mentioned in the introduction, we find in literature a good
many investigations, pointing to the existence of irregular series
with Hevea latex.
J. Parkin, one of the first investigators who was engaged with
acid-coagulation of Hevea latex *), used for his experiments ten
times dilnted latex and stated therewith the transition liquid — coagu-
lated — liquid. Parkin, whose experiments were limited to small addi-
tions of acid, did not notice the second range of coagulation. As
an explanation Parkin assumed, that the protein, present in latex,
is insoluble in a nentral liquid, but dissolves in alkali or acids.
ParKIN was of opinion that- Hevea latex is alkaline; - therefore
addition of acid would first cause neutralization, with precipitation
of the protein and, as a result, of the rubber as well, whilst, at a
higher acidity the protein would dissolve again. Parkin further stated
that with acetic acid the range of coagulation is wider than with
other acids, and thought this a decided advantage for practice,
because by addition of too much acid the coagulation would not
fail. so soon.
Because in the practice of plantations one never causes the per-
centage of rubber of the latex to sink below 15 or 12°/, (i.e. in
our terminology, one never uses mixtures with less than 50 to 40 °/,
latex), where with acetie acid no irregular series occur, there was
for a long time no further interest for these phenomena. W. Crossrer *)
again gave a few figures for upper and lower limit of the
1) Circulars Royal Botanic Gardens Peradeniya Vol. | (1899), 149.
*) India Rubber Journal 41 (1911), 1206.
46
Proceedings Royal Acad. Amsterdam. Vol. XXVI.
698
first range of coagulation with a mixture with 7°/, rubber (i.e.
about 25°/, latex) which had been preserved with formaline. We
found the lower limit at 0.014 N. acetic acid, the upper limit at
0.29 N, whilst the own acidity of the diluted latex was 0.015 N.
These figures correspond fairly well with ours (tables 2 and 3).
CrossLeY’s lower-limit is somewhat lower and his upper-limit some-
what higher, whereby the unknown action of formaline, may have
been of influence. Moreover CrossLuy determined the lower limit of
the first range of coagulation for dilutions of the above-mentioned
latex witb 7°/, rubber, and found that, as far as a hundredfold
dilution, the total acidity (acetie acid added plus calculated own
acidity) decreased with great exactness proportional to the percentage
of latex. For dialysed latex with a percentage of 12°/, totally solid
substance (i.e. a mixture with about 40°, latex) CrossLEY *) found
the following figures for the lower- and upper-limit of the first
range of coagulation:
TABLE 8.
Lower limit Upper limit
Acetic acid 0.02N 0.18N
Trichloracetic acid 0.005 0.026
Formic acid 0.008 0.022
Hydrochloric acid 0.004 | 0.016
Sulfuric acid 0.005 | 0.018
The dialysed latex had an acidity of only 0.001 N; all the limits
(except the upper-limit with sulphuric acid) are lower than those
we found for normal latex, so that the dialysable serum substances
in natural latex would have an anti-coagulating action.
As a criticism of these investigations B. J. Eaton’) published a
few series of observations with hydrochloric acid, nitric acid, sulphuric
acid and acetic acid, which however are very incomplete and did
not throw much light on the phenomena; Eaton found mixtures
which remained liquid, but this he attributes to a retardation of
the coagulation on account of high dilution, or to an inclusion of
the acid in the little lumps on partial coagulation. Eaton denies the
India Rubber Journal 42 (1911), 1345.
Bull. of the Dept. of Agric., Fed. Malay States No. 17 (1912), p. 10.
699
existence of a maximum-limit for the first range of coagulation, as
fixed by Crosser; from the above it is perfectly clear that this
criticism is absolutely without ground, and that the maximum-limit,
described by Parkin and Crossiny does really exist; but only with
mixtures with a percentage of latex below a certain limit.
G. S. Wuirusy’) was the first one wbó emphatically pointed out
the existence of the second range of coagulation above the second
liquid range and described a few complete series liquid coagulated —
liquid — coagulated. Wuirsy for these phenomena assumed the explana-
tion that small quantities of acid have an activating influence on an
enzym, which is found in latex, coagulase, which, at a small acidity,
would cause the coagulation, but at a higher acidity would become
inactive; the second range of coagulation then would be a direct
precipitation of protein by larger quantities of acid.
We shall now compare the observations of the last two investi-
gators with our own.
1. Hydrochloric acid. In Fig. 6 the limits have been taken from
Fig. 2, and therein have been drawn the observations made by
Eaton and Wuitsy.
Starting from undiluted latex Eaton found with 10°/, acid (line 1
in fig. 6) a continual series of coagulations, but with 1 °/, acid
So 80 70 60 50. 40 30 20 IOS
Fig. 6.
(line 2) he got into the liquid range. Two series with 1:2 diluted
1) Zeitschr. Koll. Chem. 12 (1913), 156, India Rubber Journal (London) 45
1913), 945; further Agric. Bull. of the Dept. of Agr. F.M.S. (Kuala Lumpur) 6
(1918), 381.
46*
700
latex (our 33'/,°/,) showed him the transition from coagulated to
pappy, but did not show distinetly, that he had got again into the
second liquid range (lines 3 and 4). Eaton did not observe the upper
range of coagulation.
Wuitsy made a complete series at about 30°/, latex; his limits
do not fully coincide with ours, which for the reasons already men-
tioned (own acidity latex etc.) is not astonishing, and also may be
caused by wrong reproduction, as Wuirsy does not mention the
exact titre of his hydrochloric acid. So except small differences the
observations of both investigators fit satisfactorily in the frame of
our recapitulating-figure (see fig. 6 and 2).
2. Nitric acid. Eatox made two series of observations, starting
from undilated latex, and always found coagulation at increasing
acidity, corresponding with Fig. 3. Moreover a series with 1°/, acid
with 1:2 diluted latex, with which he passed from the range of
coagulation into a pappy range (“incomplete coagulation”), which
again be attributes to the above mentioned causes (inclusion of acid
in the lumps).
Wuirsy also described for nitric acid a complete series, viz. for
a latex with 12°/, rubber (corresponding with a mixture with 40°/,
latex); he found at 0.016 N coagulation, at 0.021 a pap, at 0.032
and 0.052 liquid mixtures, at 0.063 a pap again, at 0.105 and 0.21
coagulation. These observations tally with ours (see Fig. 3), except
both the liquid mixtures (WuirBy only says “coagulation failed to
occur”, which possibly may correspond with our mixtures with a
little eurdling).
3. Sulphuric acid. Eaton made a series with undiluted latex, which
(as might be expected) showed coagulation at all acidities ; moreover
one with latex diluted 1:3 where after the range of coagulation
came a few mixtures with incomplete coagulation, and a series with
latex diluted 1:10, where coagulated —incompletely coagulated —liquid
was stated. The fact of remaining liquid is attributed again by EATON
to a retardation of the coagulation with strongly diluted latex, but
he does not explain in which way he accounts for the coagulated
mixtures with less acid found in this series.
Wuirpy only gives a short indication about a series liquid — coagu-
lated —incompletely coagulated (pap) — coagulated, without mentioning
the percentages of acid and the percentage of rubber. Probably this
has been the same diluted latex with 10°/, rubber (30°/, latex) as
ip. his experiments with hydrochloric acid, and therefore WarrBr
probably remained at a concentration, up to which the liquid range
does not reach. (cf. Fig. 4).
701
4. Acetic acid. Eaton again mentions a few series with undiluted
and diluted latices, in which for the diluted latices the pappy, skinny
or liquid range was reached at acidities, corresponding fairly well
with those found by us. For this acid WarrBr does not give an)
quantitative data, but only says that the first range of coagu-
lation is much wider than with the previous acids, and that, after
that, liquid mixtures are reached. With 30°/, latex we did not find
any liquid mixtures (top at 25°/, latex), but probably Wuhirsy’s
mixture had come, by the addition of diluted acetic acid, to a lower
percentage of rubber. Wairsy did not find an upper limit of the
liguid range, as could not be the case (see Fig. 5) on dilution of
30 °/, latex with acetic acid of less than 50 °/,.
As we see, the data of both these investigations fit in a satis-
factory way in the frame of our recapitulating-figures and their
observations, partly seeming confused, are explained by the system
of ranges, as they have become known to us at present.
SUMMARY.
Mixtures of Hevea Latex and water show, on addition of acids,
the phenomenon of the irregular series. For bydrochloric acid, nitric
acid, sulphuric acid and acetic acid the limits of the ranges (first
and second liquid range, first and second range of coagulation, strips
of transition) were completely fixed for all mixing-proportions of
latex, water and acid (see fig. 1—5), and a comparison was made
between the position of the limits for these four acids.
Buitenzorg, December 1922.
Histology. — “On the Determination of Polarity in the Epidermal
Ciliated cell. (After experiments on Amphibian Larvae)’. By
Dr. M. W. Woerpeman. (Communicated by Prof. L. Bork).
(Communicated at the meeting of September 29, 1923).
It is a well-known fact that in the early stages of their life the
larvae of amphibians have an epidermis, provided with ciliated cells.
This cannot be observed distinctly in all species, for they differ largely
as to the number of ciliated cells. Nor are these cells evenly distributed
over the epidermis of one and the same larva; there are spots where
they are scattered thickly, while they occur more sparsely in other
spots. 5
The ciliary movement causes a slow rotation of the larvae while
the latter are still inclosed in their jelly-like envelope. When this
envelope is removed, the exposed larvae will be seen to keep up
their rotatory motion owing to the ciliary movement, just as the
larvae that have already left their envelope. At the same time a
rather violent current may be observed in the water encircling the
larva. It is self-evident that this current is strongest where most
ciliated cells are collected. Strong currents are, therefore, distinguishable
along certain parts of the larval body, weaker streams along other
parts, which e.g. have been minutely examined by AssHnton') for
Rana temporaria and Triton cristatus and have been represented: in
plates for larvae of various age-periods.
It appears that in these animals the first action of cilia is noticeable
in larvae where the neural folds are still open, shortly before their
closure. There is a strong current in the water round about the
larva from head to tail along the neural walls. My own researches
were made on Rana esculenta and Triton alpestris larvae. I found
that in these amphibians the ciliary movement begins when the
neural walls are in part united. The direction of the fluid-streams
along the larval body | found to agree in the main with AssHETON’s
schemata, although there were also some differences. This,
however, is not to the purpose. The direction of the ciliary move-
ment in normal larvae of Rana esculenta and Triton alpestris was,
1) R. Assneton. Quarterly Journ. of micr. Science. New Series. Vol. 38. 1896,
p. 465.
703
therefore, closely examined and represented in diagrams. It was
further established that the fluid-streams flow invariably in the same
direction. A reversed direction of the ciliary movement seems to
have rarely been observed in metazoa. (ERHARD)').
This implies such a structure of the ciliated cells that a ciliary
movement is only possible in one direction, the cells present a
certain asymmetry in their structure; besides their polarity (by
which base and ciliated free surface are distinguished) there is an
“accessory polarity’ (vide Roux’) for these ideas). The question has
been considered whether this accessory polarity could be reversed
artificially, in other words, whether the ciliated cell could by some
artificial method be made to move in the opposite direction. This
question is connected with another, viz. in how far the ciliary
movement depends on the position of the ciliated cells relative to
the axis of the body.
Experiments performed by v. Bricker’) and those made this very
year by Merton‘) bear on this question. They did not succeed in
bringing about a reversion of the polarity. Now it has been evidenced
by numerous experiments that in the embryonic development there
is a period in which the ectoderm, from which the larval epidermis
is derived, is still indifferent. SPEMANN ‘) e.g. found that at the beginning
of the gastrulation ectoderm, destined to build up the medullary plate (so-
called presumptive medullary plate), could be replaced by presumptive
epidermis. Larvae developed with normal medullary plate and normal
epidermis. The fate of the ectoderm-cells in that stage of develop-
ment bas not been, or has not yet been determined. The ectoderm
is still in a high degree liable to change (,,umbildungsfahig’’).
Whether in that phase it is still completely indifferent cannot be
decided without a detailed inquiry. It occurred to me that an inquiry
into the polarity of the cell might afford some indication, as the polarity
of the cell may already be determined before its organogenetic function.
SPEMANN’s experiments regard the organ-determination. Now, how about
the polarity of the cell? When is it determined? The experiments
in which I tried to solve these questions;:I performed on larvae of
Rana esculenta and of Triton alpestris in the Zoological Institute of
the Freiburg University (Director Geheimrat Prof. Dr. H. SPEMANN).
1) ERHARD in ABDERHALDEN’s Handbuch der biologischen Arbeitsmethoden.
2) W. Roux. Terminologie der Entwicklungsmechanik der Tiere und Pflanzen.
Leipzig. Engelmann. 1912.
8) E. Tu. v. Brücke. Pfliiger’s Archiv. f. d. ges. Physiol. Bnd. 166. 1917.
4) H. Merton. Pfltiger’s Archiv. f. d. ges. Physiol. Bnd. 198. 1923.
5) H. Spemann. Sitzungsber. d. Gesellsch. naturf. Freunde. Berlin. 1916. NO. 9.
704
I started. by ascertaining whether there were developmental stages
in which the polarity of the ciliated cell is reversible, that is stages
in whieh the ciliated cells can be forced to move in a direction
other than the normal.
After cireumeision with fine glass-needles patches of ectoderm
were detached from their sublayer and after a rotation of 180°—90°
brought again to coalescence. After the wounds thus made. were
healed, which occurred in a marvellously short time, the direction
of the ciliary movement was determined by examining the larvae
in water in which granules of carmine had been suspended. A
disadvantage of this procedure appeared to be that the borders of
the wound are soon altogether invisible, so that the extent of the
reversed regions cannot be traced out. For this reason I used the
method adopted by W. Voer *), who interchanged ectoderm patches
of larvae stained vitally and those of nonstained larvae. After it
had first been ascertained that vital staining with Nile-blue sulphate
did not affect the ciliary action, | stained one of two larvae of the
same age-period, and the other | did not. Of these two larvae frag-
ments of ectoderm of a very well-defined shape and of the same
size were excised and interchanged. In the transplantates the colour
remains very well localized, it does not diffuse and enables us to
recognize the contour of the implantate for many days still. More-
over, the shape of the implantate is indicative of its original position,
consequently of the direction of the currents produced by the ciliary
movement under normal circumstances. I shall not give an account
of the various experiments, but | will deseribe briefly the final result
of all of them.
It became evident that when a ciliated cell has once begun to
vibrate it cannot be made to move in another direction. Patches of
ectoderm being implanted in the wrong direction persisted to move
in their original direction for days, nay, even till the ciliated cells
had disappeared from the epidermis. Even before the ciliary move-
ment has begun, its direction has already been established. When
ectoderm fragments are reversed 180° before the ciliary movement
begins, the ciliated cells will afterwards reveal a vibration opposite
to that under normal circumstances. The youngest stages of develop-
ment, however, are excepted in this respect, as it appeared that
in blastulae and in incipient gastrula-stages the blastula-roof resp.
ectoderm-patches can be reversed, without affecting the direction of
the movement, when afterwards the larvae begin their ciliary action.
1) W. Voer. Verhandl. deutsch. zoolog. Gesellsch. Bnd. 27. Sept. 1922. p. 49.
705
It is evident, then, that-in the young stages, just referred to, the
polarity of the cell has not vet been determined. lt also appeared
from the experiments that the determination takes place during the
gastrulation. If the blastopore is still lke a straight or slightly
crescent-shaped slit, the future ectodermal ciliated cell is still indifferent.
But as soon as the blastopore has become horseshoe-shaped and still
later circular, reversion of ectoderm without reversion of the future
direction of the ciliary movement is not possible.
It follows, then, that the period of determination of the polarity
of the epidermal ciliated cell falls in an early stage of gastrulation.
Now we had to ask if the determination of the polarity of the
cell coincided with the organ-determination.
To ascertain this we interchanged patches of presumptive epidermis
and presumptive medullary plate in very young larvae, and we
watched tlie subsequently developing ciliary movement while giving
due attention to the original position (vital staining). Stated briefly
the results were to the following effect: When after the operation
larvae appeared with a normally developed medullary plate (part
of which was consequently generated by presumptive epidermis) and
with a normally developed epidermis (part of which was consequently
formed by presumptive medullary plate), the larvae exbibited normal
direction of ciliary movement i.e. the ciliated cells have not developed
as they would have done originally, but have adapted themselves
to their new environment. If the organ-determination has not yet
been effected, the direction of the ciliary movement can still be
influenced by the environment. But if abnormal larvae developed with
a deficient medullary plate or with pieces of the medullary plate
in their epidermis, then the direction of the movement appeared to
have developed on the implantates according to the origin of the
implantates and appeared not to have been influenced by the new
environment.
Our experiments, therefore, seem to imply that the determination
of the polarity of the cells and of the organogenetic function either
occur synchronously or at all events with a very brief interval of
time.
It should be borne in mind, however, that the organ-determina-
tion in the ectoderm does not occur everywhere at the same time.
SPEMANN's and Mrs. Mancoip-ProscHHop’s ') experiments have shown
that this determination starts from what they have termed an „or-
ganisation centre’, which is located in the dorsal lip of the blastopore.
') H. Spemann. Arch. f. Entw. mech. der Organismen. Bnd. 48. 1921.
706
Furthermore, experiments by ©. Manaorp') tend to show that after
the conclusion of the gastrulation, i.e. when the region of the medul-
lary plate has already been determined, ectoderm of the ventral
half of the larva can still form mesoderm or entoderm. From this
we see that this ectoderm has not yet been determined.
My experiments to find an answer to the question if there is
any relation between the determination of the polarity of the cell
and of its organogenetic function, were carried out in the region of
the future medullary plate. A more extensive investigation is required
for the purpose of ascertaining whether the phenomenon that the
determination of the polarity of the cell almost coincides with that
of the organogenetic function of the cells holds generally or only
for the region of the medullary plate.
In a subsequent communication I intend to discuss the histo-
physiological data regarding the ciliary movement obtained in the
experiments reported in this paper.
1) O. Mancotp. Verhandl. deutsch. zoolog. Gesellsch. Bnd. 27. Sept. 1922. p. 51.
Histology. — “A Contribution to the Histophysiology of the Ciliated
Epithelium”. By Dr. M. W. Woxrpeman. (Communicated by
Prof. G. van RIJNBERK).
(Communicated at the meeting of September 29, 1923).
The sudden reversion of the direction of the ciliary movement
which we know to be a property of a number of protozoa, is of
very rare occurrence in metazoa (literature Ernarp'). As far as I
know it has hitherto not been found in ciliated cells of amphibians.
v. Brücke ®) hit upon the idea of detaching small patches of the
oral mucous membrane in frogs and allowing them to coalesce again
after having turned them 180°. These experiments were hampered
by all sorts of difficulties, such as inflammation, necrosis of the
patches, suppuration ete. Macroscopically it could be observed in
two animals that the epithelium of the patch was not destroyed, so
that v. Brücke was able to study the direction of their ciliary
movement for 40 days. The cells continued acting in the original
direction.
In three other animals the epithelium of the patch was most likely
(v. Brücke did not examine it microscopically) displaced by epithe-
lium that arose from the borders of the wound. This regenerated
epithelium exhibited a normal direction of the ciliary movement.
Experiments made by Merton’) in the past year substantiate v.
Brücku's data, so that it seems quite certain that in adult frogs it
is not possible to reverse the direction of the ciliary movement, i.e.
to alter the polarity of the ciliated cell.
Indeed, the negative results of ScnHöne's*) and of WkiGEL’s *)
experiments with other epithelia had already made us suspect this;
but, then, it was exactly in ciliated epithelium that the direction
1) Eruarp in Abderhalden’s Handb. d. biol. Arbeitsmethoden.
4) E. Tu v. Brücke. Pfliiger’s Arch. f. d. ges. Phys. Bnd. 166. 1917.
3) H. Menron. Pfliiger’s Arch. f. d. ges. Phys. Bnd. 198. 1923.
*) Scudne. Die heteroplastische und homoioplastische Transplantation. Berlin 1912.
5) Wereer. Arch. f. Entw. mechan. der Organismen. Bnd. 36. 1913.
708
of the ciliary movement of the environment could readily be ima-
gined to influence the movement of the cells of the turned implant-
ate, considering our view of the conduction of the stimulus in the
ciliated epithelium.
Classic experiments have in this tield been carried out by VeRWORN *).
They tended to show that every ciliated cell, nay, every separate
cilium has a movement of itsown. However, for the regular action of
the entire epithelium, in which not a single ciliated cell begins to
move before its predecessor (‘‘metachronic” ciliary movement after
Verworn), an interconnection of all those cells is indispensable. If
one of the anterior vibrating elements (ciliated plates on the ribs of
Beroé. Inquiry by Verworn) is checked in its movement, all the
rest will stop vibrating. If an incision is made, the part distad of
the incision will not vibrate any longer with the same rhythm as
the part proximad of it. The first element posterior to the incision
now marks the rhythm, which is taken over by the succeeding vibra-
ting elements.
We cannot but assume that a conduction of the stimulus must
take place in the ciliated epithelium (in the free border of the cell),
and that all the ciliated: cells are interconnected (literature ERHARD).
If this is the case, we might imagine the direction of the ciliary
movement to reverse in the rotated patches of ciliated epithelium
that have coalesced with the environment, since the conduction of
the stimulus in these patches will now be just the reverse of the
normal conduction.
But the fact that the healing of the patches of the oral mucous
membrane was rather tardy and was attended with inflammation of
the borders of the wound, justifies our doubt as to the existence of
any normal organic connection between implantate and surroundings.
With a different object in view I have been working on larvae
of Rana esculenta and of Triton alpestris, in the Zoological Institute
of the Freiburg University (Director Prof. Dr. H. Spemann). Ectoderm
patches were detached and after a rotation of 90° or 180° they
were allowed to coalesce again. As the larval epidermis contains
ciliated cells and exhibits a very regular ciliary movement (vide
AssHETON °)), I was now in a position to study the effect of these
rotations on the ciliary movement.
Beforehand it should be stated that the rotated patches of ectoderm
in young amphibian larvae coalesce in, a wonderfully short time
1) M. Verworn. Pfliiger’s Arch. f. d. ges. Phys. Bnd. 48. 1890.
2) R. AssHeron. Quarterly Journ. of microse. Science. New Series. Vol. 38. 1896.
709
without reaction, so that a few hours after the operation no traces
are distinguishable of the borders of the wound, even under the
microscope. Now in order to verify the extent of the rotated region
we had recourse to a special technique, which enabled us to recognize
the contour of the rotated patch for many days together (Trans-
plantation and vital staining after W. Voer *)).
The commencement of the ciliary movement in amphibian larvae
nearly coincides with the closure of the neural canal. When au
ectoderm region is rotated in a stage, in which the ciliary move-
ment has just commenced or has been proceeding for some time,
the ciliary movement will keep up its original direction. This lasts
for days until the ciliary cells disappear from the epidermis. An
influence on the rotated region by its environment cannot be
made out.
If the experiment is made after the conclusion of the gastrulation,
that is hours before the commencement of the ciliary movement,
the result is the same. So before the movement commences its direc-
tion has already been determined.
Only in blastulae and the youngest gastrula stages can the future
ciliary movement be influenced successfully.
From these experiments it may, therefore, be concluded that after
the conclusion of the gastrulation the polarity of the ciliated cell
has been determined. The following experiments were now made
with stages immediately succeeding the conelusion of the gastrulation,
I have extended the experiments to various spots that might be
considered as a source of the ciliary movement. They were turned
long before the movement began. Nevertheless the process of the
ciliary movement in the non-rotated regions progressed quite normally.
In another set of experiments vibrating patches of ectoderm were
implanted into young stages that did not yet possess ciliary move-
ment. Now it might be supposed that on the appearance of the
movement, its direction would be dictated by that of the implantate.
In every experiment this influence failed to appear.
Furthermore, non-vibrating patches of ectoderm (of very young
stages) were implanted into older larvae with vibrating epidermis.
Now also it might be supposed that, when the ciliary movement
of the implantate commences, its direction would be determined by
the epidermis of the host.
it appeared, however, that the ciliary movement of the implant-
ate commenced simultaneously with the movement of the larva
1) W. Voer. Verhandl. deutsch. zool. Gesellsch. Bnd. 27. Sept. 1922. p. 49,
710
from which the implantate had been derived and that the direction
of the movement was determined by the origin of the implantate,
not by the new surroundings (a true case of ‘“Selbstdifferenzierung’’
after Roux).
Now it may justly be assumed that in the younger stages that
1 operated upon, the implantates are readily taken up into organic
connection with their surroundings. In experimental embryology
numerous cases are known in which such an implantate behaves
in every respect like the region it has displaced. Nay, the fact that
the implantate is competent to incite remote cells to display their
organogenetic function, points indeed to conduction of a stimulus
from the implantate to its environment, which also implies that the
implantate has an organic relation with its environment.
In order to account for the beautiful metachronism in the ciliary
movement it is generally supposed that there is a conduction of
stimuli from one ciliated cell to the other. Recent experiments by
WintrEBERT') have proved, moreover, that this conduction exists
and takes place in young stages without the help of the nervous
system, i.e. in the epithelium alone.
The experiments on blastulae and young gastrulae go to show
that the turned patches vibrate co-ordinately with their environment.
This implies that not only the direction of the movement of every
cell is opposite to that in which the cell would originally have
moved, but also that the regulation of the ciliary movement is
reversed and agrees with the sequence of vibrations in the environ-
ment of the rotated patch.
This co-ordinate movement simultaneous with the environment
proves: 1° that the patch is apparently stimulated by the environ-
ment (so that the conduction of stimuli has not been interrupted) ;
2° that the polarity of the cell is reversed; 3° that the direction of
the stimulus-conduction is reversed. If in an older larva a patch of
epidermis is turned, then the cilia on this patch persist in moving
co-ordinately, but not in co-ordination with the environment. There
is not a single reason why the patch should not receive stimuli
from its environment now. Various experimental embryological data
point to the fact that also in these stages such a relation arises
again after the wounds have been healed. If this is the case, the
results of the experiments with older stages would imply 1° that
then the polarity of the cell is not reversed; 2° that the conduction
of the stimuli still takes place in the original direction.
1) P. WiNTREBERT. Comptes rendus de l'Acad. des Sciences. Paris T. 172. 1921,
p. 934.
711
We are, therefore, impressed with the idea that the direction of
the conduction and the polarity of the ciliated cells are determined
simultaneously, and that conduction of the stimulus is possible
only in a special direction. We are justified in assuming that this
phenomenon depends on the nature of the connection between the
ciliated cells. However, microscopical researches have not yet
produced positive evidence of this nature.
Meteorology. — “A non-tangent infralateral arc’. By Dr. 8. W.
Visser. (Communicated by Prof. E. van Everpinern Jr.).
(Communicated at the meeting of October 27, 1923).
On 24" June 1923 | saw at the Astronomical Observatory at Lembang
a beautiful halo, which I will deseribe in the following pages.
Already early in the morning a mock-sun was visible on the right
of the sun. Direct measurements of its distance were impossible, as
the sun itself was hidden by thick clouds. About twelve o'clock a very
bright lower tangent arc appeared, which after a few minutes became
so intensely luminous as to be visible from time to time through
the lower clouds. Soon this are spread and developed into a com-
plete circumscribed halo within which a weak ordinary ring became
also visible. [ succeeded between 12" 17m and 12 49m in taking
some 26 measurements of both rings by means of the cloud theo-
dolite, mounted at the Observatory expressly for observations of
halo’s. To these measurements | will refer afterwards. In the mean
time I kept a keen lookout for other halo’s. Not before 12b 49m
my effort was rewarded by the apparition of a spot of light on
the left below the sun, near the place where the mayor ring (46°)
was to be expected. This spot soon grew more intense and developed
into a short, oblique are. Colours (red and green) were visible. On
the other side of the sun nothing could be observed, because there
the Cu-cloud around the Tangkoehan Prahoe shielded the Cirrus
layer from our vision. | now concentrated my full attention on
this are and obtained 12 measurements until 1" 4m. Sometimes
clouds prevented the observation. Moreover between 12 16m and
1% 2m fourteen control-observations of the sun were made. At 154m
the lower cloud had so much increased, that the measurements had
to be finished. At half past seven in the evening the Ci-St proved
to be still present, there was a bright lunar halo, but without any
particularities.
The same halo’s were seen by M.M. Vofrrr and Risen Rapp
713
during their railway journey between Tjimahi and Bandoeng. However
they saw the small are not on the left (west) of the sun, but on
the right (east). Though on the left hand side the sky presented an
equally smooth Cirrus-veil as on the right, nothing was to be seen
there. According to Rijken Rapp the are was intensely coloured and
bent like a portion of the greater ring. | have not been able to note
any curvature at Lembang.
Before discussing my measurements | give here a short review
of the theory of the infralateral arc.
Bravais explains the are by the refraction of light in ice-crystals
with a horizontal principal axis, the light entering at a vertical basal
plane (the hexagonal terminal plane of the crystal) and leaving at
a sideplane of the prism. The refracting angle is 90° then. For a
definite position of the principal axis (defined f.i. by its azimuth)
we get a circular arc perpendicular to this axis and at a distance
from the sun, depending on the sun’s height. In a simple way we
may imagine this circle by drawing the case of the circumzenithal
arc and rotating the drawing then over 90°, so that the axis which
at first was vertical, now gets a horizontal position. To each azimuth
of the axis such a circle belongs. The envelope of all these minor
circles is the infralateral arc. One among these circles is tangent to
the greater ring. For the rest, this are does no more then the
cireumzenithal are fulfil the conditions for minimum deviation of
the refracted rays of light.
PeErnter (Meteorologische Optik, 1st Edition) sticks to these conditions.
He considers the arc as a “Lowitz are of the greater ring” and
deduces the form and position of the lateral arcs to the smaller and
greater rings in an exactly analogous way. Without going into the
details of the calculations, we may state, that the are according to
PERNTER in consequence of the conditions for minimum deviation
which he imposes, generally will be less distant from the ring
than Bravals’s arc.
Bresson (Sur la Théorie des Halos, Paris 1909, p. 51, p. 70) has
shown, that PeERNTER’s theory is not very satisfactory. EXNER (PERNTER-
Exner, Meteor. Optik, 2°¢ Edition 1922 p. 405) concurs in this
opinion and develops a new theory. During the normal fall of an
ice-prism the principal axis and one of the bigger diagonals of the
hexagon are placed horizontally. An infralateral are may than be
formed by light, entering the basal plane and emerging from one
of the oblique prism-planes. The plane perpendicular to the refracting
edge is inclined to the horizon at an angle of 30°. For one definite
47
Proceedings Royal Acad. Amsterdam. Vol. XXVI. 8
714
height of the sun (27°45') the lateral are is tangent to the ring.
For all other suns-heights the are deviates towards the outer side.
If we allow rotations about the principal axis, minimum deviations -
are possible up to a suns-height of 80°50'. According te Exner
(fi. pag. 402) measurements are lacking. However there exists one
by Besson (le. pag. 71). 238" April 1908 with a suns-height of 53°
he saw an infralateral are on the left below the sun at a height
of 19°, whereas from Bravais’s theory a height of 18°57' would
follow.
This case bears some resemblance to that of Lembang. “Three
minutes afterwards’ Besson writes “the ring of 22° and the circum-
scribed halo appeared, complete but scarcely visible’. In both
observations the same forms of halo’s appear. *)
For the measurements at Lembang as a rule’ the red of the are
was vised at. Once green was measured. Two times the left- and
righthand ends of the red were determined.
The readings and some distances and angles calculated from these
lave been entered in the following table.
| TK TN T Th are aen B ij
Nr. | M.J.T. | © az. lo hi Azw |hw] Ay | Aw | hb | Ab] Ap | hw—b|Aw_—p| Aw—b
| |
| | | | NK Eed
1 | 12u 50m (N17.2W|58.2|N 60. 1W/22.8j46° 44’ di
Be es » | 58.3 |22.4/46 17 VF due jah
„58° 19/[20.6/45.7/48.0|-+1.9el40.9 | 10.19
0
|
|
| (so 10 20.5/45.5/48.4}41.4 |+0.9 | 7.8
Dt „| 56.4 [20.9146 24 er
2
312 51 | 17.6 | , | 60.3 (22.4147
4 | |, | 58.9 |22.546 17
5/12 52 | 18.0 58.1 60.4 |22.9]46 23
6
| |
112 54 | 18.8 |57.9] 58.2 |21.5/46 10/54 57|20.5/45.3/48.8|—1.0 40.9 | 6.2
EI Ae) 19.3 [57.8] 56.4 |20.3/46 1 |
| | 754 10 20.5/45. 2449. 1 +0.5 |+1.0 | 5.1
9/12 56 19.7 |57.7) 60.3 |21.8/46 19 |\
10 (12 57 | 20.1 |57.6] 60.2 |20.3/47 22/55 13}19.4/46.2/50.5)+0.4 41.2 | 4.8
1 {12 58 | 20.5 [57.5] 59.6 21.1146 10) 54 39/20.4/45.3/49.6/+0.7 +0.9 | 5.1
12] 1 4 | 23.0 |57.1) 59.5 (20.045 46|51 17 20.3/45.2/50.3}—0.3 |; 0.6 | 1.0
The observations 5 and 9 refer to the lefthand end, 6 and 8 to
1) See also: E. van EveRDINGEN. Halo's in April, Hemel en Dampkring 21,
1923, p. 216, 217.
715
the righthand end, 10 to the green. The time is Middle-Java time. The
suns-height and azimuth were calculated and with these the readings
of the theodolite were reduced. Az, and h stand for the observed
azimuth and height of the arc; Ay is the distance of the observed
points from the sun calculated from the 4 foregoing columns; Ay is
the angle between the suns vertical and the radiusvector from the
sun to the arc, deduced from the observations.
The column under A, shows, that the points measured deviate
sensibly from the ring, for the red of the ring is formed at a
distance of 45°6’ from the sun. The mean deviation is 1.1°. Gradually
the distance decreases, but for Nr. 12 it is still 0.6° larger than that
of the ring. This deviation is so big and so systematic, that it is
impossible to think of observational errors. Indeed there is question
here of a non tangent are. The position of the tangent-point of the
are was calculated according to Bravais’s theory. The results have
been entered under hp, Ay and Ar. The calculation was carried
through for the 10% observation for green (n = 1.3115) for the rest
for red (n==1.307). In taking the differences between observation
and calculation the first four points, which in consequence of the
initial weakness of the are happened to be less accurate than the
others, were combined to a mean value. The observations 5 and 6,
8 and 9, which refer to the ends of the arc, were substituted by
their mean values.
Almost all the observed points are too high (column hs, gives
the difference observation and calculation), but they approach the
height calculated from theory. The angle A, which according to
theory should increase for a sinking sun, in reality rapidly decreases.
In consequence the difference between observation and calculation
decreases from 10° tot 1°. Finally, the distance from the sun remains
almost constantly 0.9° too big, hardly showing any tendency to
decrease.
During the whole time of observation the arc remains outside of
Bravais’s arc; the position with respect to the sun approaches more
and more that of the theoretical tangent point.
This are deviates from that of Bravais and hence still more from
that of Pernter. No more is it in harmony with Exner’s theory. For in
this case we have to assume a normal plane inclined at an angle
of 30°. In our case the rays of the sun are in their turn inclined
to this plane at an angle of at least 57.1°—30°=27.1°. The
smallest distance from the are to the sun is then 57.6°, which is
quite out of question for the observed arc.
47*
716
As was explained above, crystals showing various orientations of
the principal axis in the horizontal plane contribute to the formation
of the infralateral are.
That is why I calculated what position in space the axis ought
to present in order to give rise to the phenomenon as it was observed.
| supposed, that the refraction took place in the normal plane —
for in this case the deviation is a minimum and the intensity of
light a maximum.
We consider the spherical triangle ZSN, formed by the zenith
Z, the sun S and the vanishing point of the crystal-axis N. We know
ZS, the complement of the suns-height, 7S, the supplement of the
angle A we already determined, and are SN. The latter is the angle
of incidence ¢ of the rays of light and is to be deduced from the
observed A. Are ZN and /Z may then be calculated, ZN gives
the height of the vanishing point, /Z is the difference in azimuth
with the sun. From this follows the azimuth of the axis, as the sun’s
azimuth is known.
The results are as follows:
Nr | ff ZN Z az.ax.
1—4 | 746° PI RG2 EAN 5529 NNI 2 7 OW,
Bel 14.2 \oaz0) | v5.2, |, . Thee
aut 19:5 | 2-1
12 | 72.2 | 98.9 | 481 | 721
Hence in the mean the crystal-axis is inclined at an angle of 3°.3
to the horizon and its azimuth is N 71.8 W.
The position of the axis appears to be stationary. The differences
with the mean value are as a rule below 1°. The conclusion is the
more remarkable for the azimuth, as the difference in azimuth with
the sun decreases more than 7° during the observations.
In trying to find an explanation of such a position by taking
into account the influence of gravitation, wind *) and atmospheric
1) M. Princuor. Bijdrage tot de theorie der halo-verschijnselen. Verhandelingen
Kon. Akademie van Wetenschappen le Sectie, DI. 13, N°. 1, p. 21, 1919.
ANY
electricity on the position of the ice-crystals, | met among others with
the difficulty, that the complete development of the circumscribed
halo seemed at varianee with the explanation proposed. Therefore
I hope to come back to this point afterwards. For each explanation
however the observations on the ring and its envelope may be wanted.
They follow therefore as the concluding part of my remarks.
BRB = lower tangent arc; O.H = circumscribed halo; K = ring
of 22°; |= left; r=right. The remaining symbols have the same
meaning as in the other tables.
The mean of the 6 observations on the red of the ring is 21° 54’,
only 2’ more than that found from the measurements on the top.
The calculated Ay is meant for white light, the observed A, for
red. Leaving apart the 4 very discordant differences for the first 4
observations, the mean difference observation minus calculation is —0.3°,
that means exactly the difference in distance for red and white.
Hence these observations of the circumscribed halo are in harmony
with the calculation for red. In the 15 measurements on the ordinary
ring however, on the contrary a very distinct difference of +0.3°
remains.
A. Measurements of the upper and lower top (red).
height of the top A
M. J. T. Oh as
lower upper lower upper
12u 18m 59.7° 37.5° — 22:20 —
21 59.6 == 81.3° = 21e
22 59.6 — 81.7 — 22.1
24 59.5 38.0 — 21.5 zy
31 59.4 = 81.1 — 27
32 59.3 37.7 21.6 —
35 59.2 37.1 = 22.1 —
36 59.1 — 80.9 | = 21.8
48 58.4 36.3 = 22.1 | —
mean 21.9 21.8
Mean of all measurements 21°52’, for red according to
PERNTER 21°34’
718
B. Measurements of the ring and the circumscribed halo.
nr. | Time | ©h © az hw aZw JAN Aw JAN WV VAN
1 (12u 17m | 59.7 | N2.8°W) 38.1° |No°.oW/BRBr {22°37} 5°49’ | 21.90 | +0.7°
2A ST 50.7 | 28 38.1 16 | , 1/22 48| 955 |220 | +08
3 | 19 |507 | 35 |303 A{T |, +22 32| 3158 |228 | 03
al 20. |597 | 42 |393 | i72 | , 1/2159] 2142 | 23.0 | —10
5| 26 |595 | 7.0 |585 | 550 |O.H 1|24 11 | 108 34 | 24.4 | —0.2
6) 27 |595 | 74 |585 | 506 | K 1/21 53 | 10620) — =
| | |
7| 29 [594 | 83 |594 | 560 [OH 1/24 11 | 110 40 |244 | —02
8 29 |504 | 83 |594 | 523 | K 1|2158|100 1 | — =
9 31 |59.0 | 118 | 59.0 | 60.0 |O.H 1/24 15 110 47 245 Piz
10) 38 |590 |122 | 59.0 —67 OH r|2435 lun 5 | 245 | +041
u 41 \589 \135 |589 | 568 | K 12158 |10845 | — =
12} 43 |588 | 143 | 588 —288 | K r|2154|10822 | — =
13 | 43 |588 | 143 |588 |—330 |O.H r|2358 |110 23 | 245 | —05
14 | 46 | 585 (156 | 43.7 |—164 (OH r [24 34 | 69 11 | 250 | —04
15 47 |585 | 160 | 51.6 |—208 | K ©2152) 8715 | — =
i6| 47 |585 | 160 |509 |-25.7 |oHr|243| 90 0 | 25.1 | —06
17/49 |s83 lios |4i1 | 448 | K rar 46| 7232) — =
Weltevreden, July 1923.
Chemistry. — “Jn-. mono- and divariant equilibria’. XXIV. By
Prof. F. A. H. SCHREINKMAKERS.
(Communicated at the meeting of October 27, 1923).
Components and composants.
In our considerations we have represented the composition, the
thermodynamical potential ete. of the different phases with the aid
of the quantities of the components; we may, however, also represent
them in another way.
For example we take a quaternary system with the components
X YZ and U. The composition of an arbitrary phase may be
represented by:
F=eX%+yY¥4+2Z44+ (1 —w*—y—z)U ... (i)
wherein wX, y Y ete. represent « quantities of X, y quantities of
Y, ete. In a system of coördinates with the axes w y z the com-
ponent U is situated, therefore, in the origin of the coordinates; we
call U the fundamental-component.
We now take in the quaternary system under consideration, four
arbitrary phases M N P and Q; we may represent the composition
of the phase F’ by: :
F=mM+nN+pP+(l—m—n—p)Q... (2)
As definite values of m n and p belong to each composition of
F, we may, therefore, also consider the composition of F’as a function
of m n and p.
We call the phases M, N, P and Q, in which we express the
composition of a phase F, the composants of the system; we shall
call Q the fundamental composant.
When we represent the composition of a phase F’ by (4), con-
sequently expressed in its components, then its thermodynamical
potential, its free energy etc. a function of w y and z; when we
represent the composition by (2), consequently expressed in composants,
then we may represent its thermodynamical potential, its free energy
etc. also as functions of m n and p. Of course there exist relations
between those two way of representations; we shall deduce them
further.
We now consider the equilibrium between a variable (fi. liquid)
720
phase £ and a constant (fi. solid) phase F. The composition of L
may be w, y, z and 1—a—y—z expressed in the components, the
composition of #: a, 6, ¢ and 1—a—b—c.
When we deduce in some way the condition of equilibrium for
this system F+ L, then we find:
eo =u 5 e-ID
wherein ¢ represents the Rl potential of L and ¢,
that of F.
We now express the composition of 1 and F in the composants
M, N, P and Q. Let be the composition of ZL: m, n, p and
1—m—n—p; that of F: «, B,y and 1—a—8—y. In a similar way
as we may deduce (3) we then find:
= 6... NEE
ag ag ns! ;
6 —(m—a) A-One =e. @
Let us take two variable phases L and L, (fi. two liquids or
vapour + liquid or mixed crystals + liquid etc). We express the
composition of those phases with the aid of the components viz.
eye and x, yv, 2,, with the aid of the composants viz. mp and
m, n, p,. In the first case we find as conditions for equilibrium:
0g 05 0g 0S, 0c, 0,
5 as MPT: a ee agi egy nie dz, (s
a as, ag as, ag as, fa
de da, dy Oy, dz dz,
When expressed in the composants, we find:
Sc—m 05 — ee RE m 06, n Be Pp ER |
Om On Op “Om, * dn, * Op, |
ag Os, as ag, as 9b, | en
Om ~ Om, Òn On, dp Op,
Generally we may say that the equations for equilibrium have a
same form, independent on the fact whether they are expressed in
components or in composants.
We now shall consider more in detail the relations between
components and composants. For this we take again the composants
M N P and Q. We represent, expressed in components, the com-
position :
of M by Te ey Aa Se
OE nat €
a BY » 1—a,— 8%:
ann Aai Bie
721
In order to express the composition of a phase
FeeX+y¥4+27Z24+(l—e#—y—2z)0... (9)
in the four composants, we put:
F=mM+nN+ pP+(1—m—n—-p)Q... (8)
so that Q is the fundamental composant. As (7) and (8) represent
the same phase F, it follows:
m(a, — a) + n(a, — a,) + p(a, — a,) =a — a, |
m (8, — B) +n(8,— 8) +p, —B) =y— 2B (an
Ans Ve). teh st.) TP (Ys, ta) Ee He
so that mn and p are defined.
In order to define, however, mn and p from (9) the determinant,
formed by the coefficients of m m and p may not be zero. Conse-
quently in general we have the following:
in a system of n components we may choose n arbitrary phases
like composants, notwithstanding their determinant is not zero.
For a ternary system this means: we may choose three arbitrary
phases as composants notwithstanding those are not situated on a
straight line. In a quaternary system we may take 4 arbitrary phases
as composants notwithstanding those are not situated in a flat plane.
When we represent the composition of a phase F as in (8) with
the aid of composants, then we may consider the thermodynamical
potential ¢ of this phase also as a function of m n and p. Hence
it follows:
OG nO Ge ROE aay 0 > dz
Òm Ox. dm : dy dm | dz dm ;
(10)
and still 2 similar relations, which we obtain by substituting in (10)
m by n and p. With the aid of (9) we now find:
dE ag ws ag
dm = (a, ee) dz =F (8, f ) dy Ein mt OE
06 ò 0g ijs
— == (a a) = in (8, B) a (Y, see) dz 0 9 (1 1)
av z
On dy
ag g as ag
dp Ca) + Ge), + mt EP
From those equations it follows also, with the aid of (9)
ds 0c
Lure +n Ia zi Pon (ee) an te Wier) dy + (z—y,) ret
(12)
722
Above we have seen that for an equilibrium F+ ZL as well
equation (3) as (4) is valid; we are able also to prove this by
converting equation (3) into (4) with the aid of the above relations.
We write (3) in the form:
0s 0g ds ds A05 0g
= a
Ow Dy dz : Ox Oy dz
With the aid of (12) we may write:
Er A0 05 ò5
s—m Te n a Pp op
Se
0s 4 0s
= 5, En OA 5 mk AF 3, - (18)
The composition of the phase in components is represented by
a, band c; « § and y represent the composition of this same phase
in composants. [In accordance with (9) the following relations are
valid :
a (a,—a,) + B(a,—a,) + y (a,—e,) = a—a,
«a (8,—8,) + B(B,—B,) + ¥ (8,—8,) = 6-2,
et) + Bada) cts a Tee
When we add those three equations to one another, atter having
multiplied the first one with a the second one with = and the
vu Y
third one with an then we find, with the aid of (1)
z
ac 0S 0g
oe are — (a “) 5, + (b 5 ay Sn Pas
With the aid of this (13) now passes into:
0c 0s 0c US 0g
TEE à EN òn ain
which is in accordance with (4).
We may also write the four equations (5) in the form (6). For
the first one of the equations (5) we may viz. write:
ds 0¢ 0g
Ceed dn tt |
ae a Pe . (14)
=t,—(2, CU z A B) dy, =(E; Ye) dz, |
With the aid of (12) (14) passes into the first one of the equations (6).
The three equations (11) excepted, which are valid for the phase
without index, we have still also three similar equations, which we
obtain from (11) by giving to all variables and to ¢ also, the index 1.
723
We call those three equations 11e. As, however, in accordance with (5)
dE a, ae oF 0k,
— = — etc. it follows from (11) and (11%) also — = — etc.
or Oz, dm Om,
For a ternary system with the composants /, F, and F, we
have, when we choose F, as fundamental component:
F=mF,+nF,+(l1—-m—n)F, ... . (15)
When we represent the compositions of the components by « and
P with the corresponding index, then the equations (9) pass into:
m (a,—a,) + n (a,—a,) = «—a,
m (8, Es B) 1? (8,—8,) = y—P,
We now shall deduce those equations also in another way, by
which at the same time the meaning of m and ” in the graphical
representation becomes clear.
We take a system of coordinates with the axes OX and OY
(Fig. |) in which we represent the composition of the phases,
(16)
|
|
{
'
“a
Fig. 1.
expressed in the components. We imagine the three composants
F, F, and F, and the arbitrary phase F to be represented by the
points F, F, F, and F. Consequently in the figure is Fv = «,,
F.u= 68, ete. Now we take FF, as new X-axis and FF, as new
Y-axis; then the new coordinates of the point F are Fg and Fr;
we put Pg=2’ and Fry’. When we call the angles, which the
new axes FF, and F,F, are making with the original X-axis p,
and p, then it follows from the figure:
724
(17)
&£=a, + 4 cos p, Hy cosy,
vB, + a! sing, + y'sing,
When we represent the length of FF, and FF, by /, and /,,
then we may write for (17)
LET dE nes + TICE)
lf 7 |
' r . - 4 i (18)
y—B, a a a B,) a. Se |
Now we shall express the composition of the phase #' in that of
the three composants: F, F, and F,. We find:
quantity of #,: quantity of (7, + F\)= Fs: FF,
or: quantity of #,: quantity of (7, + F, + F,) = Fs: F,s
When we put the total quantity of #— F, + F, + F, equal to
zero, and when we bear in mind that:
INP ES a Ye
/
then follows: quantity of mi
l,
In a similar way we find: quantity of F, =a
Consequently there are wanted for forming the unit of quantity of the
phase Ff’: = quant. of J, and 5 quant. of F, and consequently also
1 2
i—> — ie quantities of F,. We may write, therefore;
EE LD)
l, l, l, l,
ae y' A
When we put 7 =m and 7 =n then (18) and (19) pass into
(15) en (16).
Hence it appears a.o. that m and n do not represent the coordinates
xv and y’ of the phase F, but they are functions of them; when
m and » are known, then also x’ andy’ are known and reversally.
For this reason we may call m and n yet also coordinates.
The coordinates of the composant
F, are « =0 y'=0 consequently m=0 and n=0
EES, sre ial iia =O 7 n= ME
ET AO ‘i isd nd
725
Of course this is also in accordance with (15); when herein we
put fi. m=1 and n=O then phase /’ represents the composant /’.
When we express the composition of a phase in its components,
consequently in w and y, then ev and y are positive and x+y <1.
When, however, we express its composition in composants, then m
and n may also be negative and also 7 + >1. The latter is the
case f.i. for a phase, represented by the point P. In (15) m and n
are then positive and 1—m—wn is negative.
When we have a quaternary system then similar relations exist
between the coordinates viz.
sl ye= nil
zi nil
Till now we have assumed that each of the m composants of a
system of 7 components contains also those » components. It is
apparent, however, that we may choose the composants also in such
a way that one or more or even all composants contain less than 7
components. Of course the ”» composants together must contain the
n components. We may consider the representation with the aid of
components as a special case of the representation with the aid of
composants; each of the composants then contains a single component
only. We shall, however, continue by calling this a representation
with the aid of components. When, however, there is at least one
composant, which contains more than one component, then we shall
speak of a representation witb the aid of composants.
As it is known, the deduced functions of the thermodynamical
potential become infinitely large when the quantities of one or more
-
0
of the components approach to zero. In a quaternary system f.i. =
U
becomes infinitely large when w or 1—a—y—z approaches to zero;
05 0c
— when y or 1—x—y—z and — when z or 1—x—y—z< approaches
oy Oz
to zero.
Using composants this is otherwise, however. It follows viz.
S= and— become infinitely large, only then when
dm on dp : ;
dt AS oc
one or more of the functions —, — and— are infinitely large and
du’ OY dz
this may take place, as we have seen above, only when one or more
of the conditions:
i—i) yi zi) l—2—y—z=0.. (20)
from (11) that
is satisfied. In general or — become, therefore, infinitely
os ee
dm’ On Op
726
large when we give such values to 7, and jp, that one or more
of the conditions (20) are satistied. It is apparent that this may be
casually only for m=0 or n=O or p=O or 1—m—n—p=0.
At the same time the following is apparent. When we give to
m, n and p such values that fi. wv becomes = 0, then in (41)
C : : 0¢ is
— becomes infinitely large, so that — , — and — become infinitely
Ox Om On Op
large at the same time. When, however, we have chosen the com-
Ys
òf og
posants in sach a way that @¢,=a, then only 5 and a become
n p
ee es
infinitely large, while 5 remains finite.
m
When a liquid has the composition :
L=e«eX+yY4 2244+.
wherein A. } ete. represent components, then the stability requires
that for all values of dz, dy ete.
0S 0g (2)
— de + —dy +t... Su te EN
Ow Oy *
When we imagine L to be divided into
L=xL, + (i—x) L,
wherein :
L, = (a# + de) X + (y+ dy) YH...
L, = (a + da,) X + (y + dy) Y 4
then must
bie Sie (lS) 5,
from which (21) is following. When we now express the composition
of Z in composants viz. :
L=mMitnN+pP4+....
then it follows in the same way that
(= dm + are Le sae ) >
Om dn
must be true for all values of dm, dn ete.
(To be continued)
Leiden. Inorg. Chem. Lab.
Anatomy. — “Thymus, spiracular sense organ and fenestra vestibult
(ovalis) in a 63 m.m. long embryo of Heptanchus cinereus’.
By Prof. J. W. van Wine.
(Communicated at the meeting of September 29, 1923).
Many years ago | received this embryo from the Zoological Station
at Naples. It was fixed in sublimate and preserved in alcohol. Just
as another specimen it was treated with methylene blue, in order
to make a skelet preparation of it.
This having proved quite successful with the one embryo, I decided
to preserve the other, so as to make a series of cross sections later,
in order also to be able to examine the remaining organs. I intended
to wait with this until | had more of this rare material in different
stages. | however received only one more embryo, 255 m.m. long,
which was simply treated with alcohol and was much too large
for making a series of sections. Here one would have to restrict
oneself to only a few parts. For this specimen | am again indebted
to the direction of the Station at Naples.
When in the autumn of 1922 I had finished with the development
of the skeleton of Acanthias vulgaris’) | decided not to wait any
longer, and a series of cross sections of the 63 mm. long embryo
was made. The preservation proved to be excellent, notwithstanding
the previous long treatment of HCI alcohol necessary for the elimination
of the methylene blue from the remaining tissues, in order to restrict
the colour to the cartilage. The staining of the sections with ammonia-
carmine was also successful; but the light blue tint of the cartilage
could not be intensified by the after-treatment with methylene blue
or victoria blue. The reason for this remained unknown to me.
In the 255 m.m. long embryo, which had been in alcohol for
many years, the cartilage suffered itself to be stained deep blue.
1) Van Wine, J. W. Frühe Entwicklungsstadien des Kopf- und Rumpfskeletts
von Acanthias vulgaris. Bijdragen tot de Dierkunde, publ. by the Kon. Zool.
Genootsch. Natura Artis Magistra at Amsterdam. Afl. 22, Feestnymmer voor Max
Weeen, 1922,
728
1. Thymus.
The development of the thymus in the Selachians was first
described by Dorn (1884). The facts then found by him were
principally confirmed by later investigators. Hammar, who had given
many years to the study of the structure, development and funetion
of this organ in nearly all the principal groups of vertebrates,
described the development in the Selachians in 1912, and gave a
detailed account of the results of his predecessors.
He found, that in all vertebrates from fish up to man, the
thymus continues to grow till the time of puberty. Then an involu-
tion period begins, wherein it as a rule atrophies, without totally
disappearing.
The thymus, in all vertebrates, begins to form as a local pro-
liferation of the epithelium of the gill clefts.
Jn man it appears principally, if not exclusively, on the third
gill cleft, but in the Selachians, which generally have six gill clefts,
a beginning of the thymus is described on each gill cleft. These
however speedily disappear on the first and last, sometimes even on
the last two gill. clefts.
Not all investigators are of opinion that the thickening of epithe-
lium cells of the first gill cleft (spiracle) may be considered as a
thymus, and it is possible that here an interchange may have taken
place with the place of origin of the spiracular sense organ.
Soon after its appearance, one can distinguish in the thymus two
different kinds of cells, viz. a network of flat epithelial cells, which
encloses groups of round cells in its meshes.
These round cells multiply themselves so quickly, that the net-
work can no longer be discerned unless in very thin sections.
The whole organ, which formerly was pear-shaped and after-
wards has the shape of a grape bunch, appears to be wholly
constituted of round cells, which form a solid mass without lumen.
These cells hardly have any protoplasm, and therefore give the
appearance as if one only has to do with an accumulation of nuclei.
There are two opinions concerning the derivation of these round
cells, which strongly resemble the lymphocytes of the blood. Many
hold them for epithelium cells, which have rounded themselves off;
others again take them to be true lymphocytes, which have
penetrated the organ from the bloodvessels and the neighbouring
mesenchym. The latter opinion is emphatically upheld by Hammar for
all classes of vertebrates.
The question as to which of the two opinions is correct, cannot
729
be settled by the study of the 63 m.m. long embryo of Heptanchus,
but a further question can be explained thereby, viz. whether the
thymus has to be considered as a gland which has lost its original
excretory duct and thus only has internal secretion left. It would
then find itself in a similar condition as the anterior lobe of the
hypophysis and the thyroid gland, which, however, in the embryo
of vertebrates, always have an excretory duct which is only lost
during the further course of development.
The thymus does not sever itself from the epithelium of the
branchial gut in Crelostomes and most of the bony fishes. This is
however the case with the remaining vertebrates. But a true ex-
cretory duct, as a rule, does not appear. This would be expected
in sharks, but Frrrscar (1910) says: “Kin Lumen und einen Aus-
führungsgang habe ich bei Spinax ebensowenig auffinden können
wie Doran bei seinen Haifischen.”
In a very early stage of rays (Torpedo), they however noticed
something which resembled an excretory duct.
In some of the sharks examined up to now, the body of the
thymus separates itself directly, without a pedicle, from the epithelium
of the branchial gut; while in others it still remains connected
for some time by a stalk to the epithelium.
This stalk lacks the characteristics of an excretory duct, because
it not only has no lumen, but also shows the same structure as the
body of the thymus and consists almost exclusively of the rounded
cells, which resemble lymphocytes.
In our embryo of Heptanchus we on the contrary find an ex-
eretory duct im optima forma for each of the thymus divisions
(thymomeres) which are found on both sides of the body, one for
each side from the second to the seventh branchial cleft. There are
8 gill clefts, but in the first (spiracle) and last the thymus is
absent.
It is the largest in the second and third cleft and has the form
of a bunch of grapes. The bunch is smaller in the 4 cleft, in the
5% still smaller, and in the 6' the thymus no longer has the bunch
form, but is composed of a single acinus, into which the excretory
duct opens.
In the 7 cleft every acinus is found missing from the short
excretory duct.
In the figure of the section we see the large thymus of the 2d
branchial cleft. lt runs over the top of the 1st epibranchial and
then continues as the fairly long excretory duct. This has an obvious
lumen, which with ifs one end opens at the top of the branchial
48
Proceedings Royal Acad. Amsterdam. Vol. XXVI
730
cleft, with the other reaches to the body of the thymus without
entering it.
Fig. 1. Cross section
through _2nd branchial
cleft of a 63 m.m. long
embryo of Heptanchus
cinereus. In this and in
the following figs. the
cartilage (stained blue in
section) is striated hori-
zontally.
The wall of the duct is 2 cells thick, and is constituted of a
double layer of fairly flat epithelium cells, amongst which not a
single round cell is to be found.
The excretory duct of each of the remaining thymomeres shows
a similar structure, viz. a double layered epithelial wall, encircling
a lumen, which opens into its respective gill cleft.
These ducts from the 2°¢ caudally, gradually shorten; the last
(6) forming a rather unimportant, yet distinct attachment to the
7) branchial cleft.
The excretory ducts are not permanent. They later on lose their
epithelial structure and lumen. This e.g. happened in the 225 m.m.
long embryo. Here, in the place of the excretory duct of the first
(anterior) thymomere, one finds a long pedicle, which appears as
an outgrowth of the thymus. The pedicle runs over the top of the
_1stepibranchial and reaches the wall of the branchial cleft.
It shows itself as a chord, which appears entirely to consist of
lymphocyt-like round cells. No traces are left of the original epithe-
lial structure and lumen. I however do not wish to deny the
presence of a reticulum. It would also be possible to make it
clear in the pedicle by appropriate methods.
For completeness the so called epithelial bodies and the supra-
pericardial organ should also be mentioned. In the 63 m.m.
embryo an epithelial body is found, immediately above the opening
of the 1st and 2"d thymomere. Each little body is a round isolated
cellmass, which resembles an acinus of the thymus in form and
731
size, but is more compact; owing to the fact that it has finer lymph-
spaces than the thymus. No trace of such a body was to be found
at the 3rd, 4th, 5th and 6th thymomere.
The suprapericardial body was discovered by van BEMMELEN !)
(1885) at the end of the branchial gut. Later it was found in all
classes of vertebrates. It is generally taken as the last indication of
an abortive branchial pouch, and mostly appears on only one side
of the body.
In 1906 Bravs found it in the 67 m.m. long embryo of Heptan-
chus, which very likely originates from the same mother-animal as
mine, and | can corroborate his statement. [t is only well developed
in the left half of the body, and shows itself as a little bladder,
the lumen of which is encircled by a single layer of fairly columnar
epithelinm cells. It is to be seen on 35 sections, and is situated as
Braus stated, behind the last visceral arch, in the angle which this
makes with the ceratobranchial. Just as Braus, 1 found it near its
posterior margin connected with the epithelium at the base of the
branchial gut by a short pedicle.
On the right side the organ is rudimentary.
| found it represented by a flattened little group of epithelial
cells without a lumen, and totally severed from the gut epithelium.
This is visible in the sections passing through the posterior half of
the vesicle on the left. Braus does not mention this little group.
His specimen was probably somewhat further developed than mine,
1) Owing to the presence of a suprapericardial body in the embryos of Heptanchus
(van BEMMELEN in vain sought for it in the adult animal) one cannot assume that,
in higher animals, this little body is the remains of a branchial cleft, which is
present in the Notidanides as such. The morphological significance of this organ
is a problem. One may of course believe that it is the remains of a branchial cleft,
which still lies further caudally than the last (8th) of Heptanchus. Braus e.g.
takes it to be the rest of a 10th branchial pouch.
He professes to find the remains of a (9th) branchial pouch in a slight
protrusion of the intestinal wall behind the last branchial arch, in the angle
between the last (7rb) ceratobranchial, and a caudalwards directed protuberance
on its ventral side.
Although this protuberance chondrifies continuous with the 7th ceratobranchial,
he considers it to be the remains of an 8th branchial arch.
1 cannot agree with these conceptions. In my specimen the rather long protuber-
ance is still quite prochondral, and just like the prochondral cardiobranchial end,
lies in the beginning of the oesophagus. In the protuberance | can only discern
a processus muscularis of the 7‘) ceratobranchial, morphologically insignificant.
An intestinal protrusion which could also be considered as a 9th branchial pouch,
is not present, and [| must consider it as an artificial product in the specimen
of Braus.
48*
732
and this little group more atrophied. He thought he saw an indica-
tion of an antimere of the left vesicle on the right side of the body,
in the shape of a more caudally situated diverticulum of the
branchial gut.
Let us however return to the thymus. The genus Heptanchus is
indeed rightly regarded as the most primitive of the living Sela-
chians. The number of visceral pouches (i.e. 8) surpasses that of
all other fishes and higher animals. Only the anterior 5 are still
formed in mammals.
Concerning the 63 m.m. long embryo of Heptanchus, we may
now assume, that also its thymus appears in a more primitive form
than in the development of higher animals.
The original function of the thymus could then not have been
internal secretion only, but it must also have removed products
through its excretory duets.
Originally each thymomere was a true gland, according to the
old notion, with an excretory duct even as was the case with the’
thyroid and the anterior lobe of the hypopbysis.
The presence of excretory ducts is also of importance for the
conception of the morphological significance of the gland. Since the
researches of Donun, it is generally accepted that the thymus is a
branchiomere organ, a division of which occurred on each branchial
cleft.
Now Amphioxus has on each of its many branchial clefts a
glandular body, which opens with its excretory duct into the top
of the cleft. This branchionephros functions as an excretory organ,
and for many years I have presumed, that it would prove homo-
logous to the thymus of higher animals.
This presumption was strengthened, when in 1909 GoopricH found
that the branchionephros does not develop from the coelomic epi-
thelium, as one would rather be inclined to assume for an excretory
organ in chordates.
But he does not siate that it develops from the branchial epithe-
lium. His drawings however give this impression. Might this
impression prove .to be correct by later investigations, then the
branchionephros develops from the same tissue as the thymus of
higher animals. Cells resembling lymphocytes are never found in it.
Lymphocytes do not occur in the blood of Amphioxus, the blood of
which only consists of plasma, without any red or white blood
corpuscles, just as the blood in its earliest stage in craniates. *)
1) A few investigators profess to have found cells in the blood of Amphioxus.
| have never observed any in my numerous sections of larvae and adult animals.
738
The presumed homology of the thymus and branchionephros has
also been supported from the side of the craniates, now that, in
the development of such a primitive form as Heptanchus, the presence
in the thymus of excretory ducts, which in Amphioxus analogously
open into the branchial clefts, has been shown.
If the branchionephros develops from the branchial epithelium,
the chief difficulty to homologize it with the thymus, 1 think then
lies in the period of development of this gland. One should expect
the thymus to become perceptable in a very early period of its
development, but this only happens very late.
The reason for this is because the original function no longer comes
to development. It is taken over by the pronephros and the meso-
nephros. The other function of the thymus i.e. its internal secretion,
caused by the lymphocytlike cells, must phylogenetically have origin-
ated much later.
2. Spiracular sense organ.
In no vertebrates does a division of the thymus come to develop-
ment in the first branchial cleft (spiracle). It appears not even to
be formed there at all. On the other hand, we find on the wall
of the spiracle in the embryos or larvae of the more primitive
fishes: Selachians, Ganoids and Dipnoi a sense organ, which is not
met with on any of the remaining branchial clefts. These adult fishes
also possess one.
We find it even in those forms (Dipnoi and Holostei) in which
the spiracle, which is developed in the manner of an intestinal
pouch, no longer breaks through outwardly.
It was discovered by Ramsay Wricnt in 1885, who found it as
a protrusion of the medial wall of the spiracular visceral pouch of
the Holostei (Lepidosteus and Amia). This protrusion (diverticulum)
is directed upwards and surrounded by the cartilaginous auditory
capsule; in other words, it lies in a canal of the lateral cartila-
ginous wall of the otic region of the skull, but otherwise has no
relation to the auditory organ.
A similar canal in the cranial cartilage, into which adiverticulum
of the spiracular wall penetrates, was discovered by BripGE in
Polyodon. The same was also observed by Wricut in the sturgeon.
The presence of a sense organ in these Chondrostei is, however,
not mentioned.
Wricat found, that in the Holostei this sense organ is innervated
by a branch of the ram. oticus of the facial nerve, which in the
734
Ganoids (Chondrostei and Holostei) is likewise overgrown by the
cartilaginous auditory capsule, and of which (ram. oticus) it was
known that it sends out branches in this region to the sense organs,
belonging to the lateral line system.
These sense organs, called neuromasts (Nervenhügel) by Wricat,
lie either free on the surface, or protected in little sacs, grooves
or canals; all are of ectodermal derivation. Now it was noteworthy
that the sense organ of the spiracular pouch also resembled the
structure of a neuromast, although Wricur evidently thought it to
be of entodermal origin. It seemed as if one here had the unexpected
example of a sense organ of the Chordates, which did not originate
from the ectoderm, although it was still supplied by a nerve,
belonging to the lateral line system of the epidermal sense organs.
The study of the Dipnoi dispelled the singularity of this pheno-
menon. In this group Pinkus (1895) discovered in Protopterus
annectens a little bladder with a sense organ on its wall, and
imbedded in the cartilage of the otic region. The sense organ —
evidently a neuromast according to the fig. — is supplied by a
caudalwards running branch of the facial nerve, the branch
belonging to the lateral line system.
Pinkus still describes two more caudalwards running branches
from the lateral line system of the n. facialis. The one forms the
well known anastomosis with the ramus lateralis vagi (and glosso-
pharyngei) the other he calls ram. oticus. He, however, draws the
origin (Le. fig. 3) of these branches so close to each other that,
according to my opinion, one has to consider them as the strongly
developed homologue of the ram. oticus of the Ganoids.
Of this organ Pinkus says (l.c. p. 307) “Das Organ ist zweifellos
ein Derivat des Seitenkanales. Ueber seine Bedeutung vermag ich
übrigens nichts auszusagen, da vergleichend anatomische und ent-
wieklungsgeschichtliche Thatsachen mir bisher fehlen”’.
For the knowledge of the development we are indebted to AGar,
(1906) who examined the first stages of the spiraculum in Lepi-
dosiren and Protopterus.
He showed that this sense organ is of ectodermal origin. This
seat of origin reaches the top of the solid gut protuberance, which
represents the spiracle, and then severs itself from the ectoderm.
The organ then naturally gives the impression of having been derived
from the entoderm.
Acar like Pinkus, was not aware of the work of Ramsay WeIiGHr,
otherwise he would undoubtedly have mentioned, that the presence
of a spiracular sense organ in Holostei was already known. He also
would not have neglected to point out, that, in the Holostei, we
have no reason to believe in the entodermal origin of the sense
organ, now that in the Dipnoi ‘') its formation from the ectoderm
is manifest.
As opposed to Pinkus, AGAR says “This organ has no relation to
the lateral line system of sense organs’. To my opinion, however,
it undoubtedly belongs to this system, because it possesses a neuro-
mast, is supplied by a branch from the lateral line system of the
facial nerve, and moreover is clearly of ectodermal origin in the
Dipnoi.
The majority of epidermal sense organs, sinks under the epidermis
during the ontogenetic period, and finds protection by the subeuta-
neous connective tissue. Only one organ having its seat of origin
in the immediate vicinity of the spiracle, sinks therein, acquiring a
considerable development.
In my opinion this not only happens when the spiracle no longer
breaks through outwardly, retaining its opening into the gut, as in
the Holostei, but also, when it moreover loses its connection with
the gut, as in the Dipnoi.
Let us now proceed to the Selachians. In these WricuT examined
the spiracle of a 60 m.m. long embryo of Mustelus. Here he found
two diverticula, situated above each other, on the medial wall. The
dorsal diverticulum reached till under the canalis semicircularis late-
ralis of the auditory organ, and was already discovered in a number
of adult Selachians, by Jon. Mürrer (1841).
The ventral diverticulum did not reach the cranial cartilage, and
at one place contained columnar epithelium, which he took for
sense organ epithelium, and which according to him, was supplied
by the ram. praetrematicus of the facial nerve. This innervation
would lead us to expect, that we have here to deal with a different
sense organ to that in the Holostei. PHeLps Auris, however, in 1901,
examined a 122 m.m. long embryo of Mustelus, and was able to
trace the nerve from the organ till near the ram. oticus, the same
branch which also supplies the sense organ in the Holostei.
Independent of Weient's work, that of van BEMMELEN appeared
in the same year (1885). The latter, besides in Mustelus, found both
the diverticula in a great number of Selachians, in embryos as well
1) Grew (1913) mentions the ectodermal origin of the sense organ (“Hyoman-
dibular organ”) in Ceratodus, and its innervation by a branch from the lateral line
system (“ram. hypoticus”) of the facial nerve. Whether the sense organ in Ceratodus
is afterwards also surrounded by the cranial cartilage, | do not find mentioned.
736
as in the adult fishes. He found both (the dorsal and the ventral)
simultaneously in the same animal, in the forms which now-a-days,
after Tare Rean, are called Galeoidei. In rays on the contrary, only
the ventral diverticulum of the examined fishes: Raja, Torpedo, Trygon
and Myliobatis was found to be present. The dorsal one was absent
in concurrence with the results of Jon. Mürrer, who found it in
rays only in the family of the Rhinobatidae.
Vice versa the ventral diverticulum was found missing, while only
the dorsal one was present in Acanthias and Heptanchus; each of
which is a representative resp. of the groups Squaloidei and
Notidanoidei.
On the ventral diverticulum a follicle, resembling an oval bladder,
develops in all forms which possess it. It nearly touches the auditary
labyrinth, is lined on the inside with columnar epithelium, and is
connected to the wall of the spiracle by a pedicle, which may, or
may not have a lumen. In an adult Torpedo the bladder was found
to be very large.
As regards the morphological significance of the follicle, van Bem-
MELEN thought of the probability of a homologue with the supra-
pericardial body, which primarily is also a single little bladder. He
says (l.c. p. 178) “[später] tritt aber der grosse Unterschied ein:
die Suprapericardialkörper entwickeln sich zu drüsenartigen Gebilden *)
die Spritzlochbläschen treiben nur eine oder zwei acinöse Ausstül-
pungen oder bleiben wohl ganz einfach.”
VAN BrMMELEN further thought of the probability of considering
the follicle, even as the suprapericardial body, as the remains of an
original gill cleft.
My opinion is that this conception cannot be adhered to any
longer, and that the follicle is a spiracular sense organ bladder.
Van BEMMELEN did not consider this possibility, because he had
evidently not observed a supplying nerve.
No mention is made of the appearance of a follicle from the
dorsal protrusion of the spiracle in the Galeodei. We may thus
accept that it is absent there.
Acanthias and Heptanebus only show the ‘dorsal protrusion. Is
the spiracular sense organ now also found missing in them or not?
Van BrMMELEN speaks of a “dorsale Ausstülpung’’, but also calls
it an ““Anhang” of the spiracle. He says: (l.c. p. 176). “Bei erwach-
senen Exemplaren von Acanthias endlich konnte ich den Anhang
') Their structure in the Selachians, then has much in common with that of the
thyroid gland, from which they, however, totally differ morphologically.
737
als ein sackformiges, ungefähr 3 m.m. langes Gebilde aus dem
Bindegewebe frei präpariren, seine Wände zeigten sich ausserordent-
lich dicht und inwendig glatt, das Epithelium hoch und driisig.
’Ebenso zeigte sich der dorsale Anhang von Heptanchus, aber relativ
noch kirzer’. As it will presently be seen, he undoubtedly dissected
out the sense organ bladder.
Horrmann (1899) inter alia also investigated the development
of the divertienlum of the spiracle in Acanthias. He found it to
make its appearance first in 28 m.m. long embryos and innervated
by a branch from the lateral line system of the facial nerve.
He considers this branch, which also supplies epidermal sense
organs, most likely homologous to the ram. otieus of the Ganoids.
The diverticulum is soon directed forwards with its blind end, and
unites itself there with the nerve. | can confirm this from my
material of Acanthias.
Horrmann discovered the innervation, well knowing of the work
of Wrientr, from which he quotes in detail. He, however, missed
the conclusion that a sense organ had to be present. He was too
much under the impression of having bere to do with the vestigial
part of a branchial pouch, whieh had disappeared.
Besides the two embryos of Heptanchus, my own investigation
also includes a series of sections (15: thick) through embryos of
Acanthias varying in length from 238 to 98 w.m.
In the 23 m.m. long embryo, the anterior wall of the spiracle
forms a rostrally directed diverticulum, next to the auditory organ,
from which it is separated by the jugular vein (the nervus facialis
running under the vein). The diverticulum is to be seen on 7 sec-
tions anterior to the external opening of the spiracle, and has the
shape of a cone flattened on one side, the axis of which runs
parallel to the longitudinal axis, passing through the notochord. The
three anterior ones of the seven sections pass through the top of
the cone, which is distinguished by its columnar epithelium, so that
the lumen appears for the first time on the third section. One also
sees the termination of the branch of the ram. oticus connected
here to the group of the columnar cells. HorrMann already pointed
out, that one could stipulate, through this connection the situation
of the organ before it is more clearly defined.
A eross section through the anterior margin of the external opening
of the spiracle on the skin at the same time passed through the
internal opening towards the intestine in an embryo of 394 m.m.
of which | in 1922 described the skull. The diverticulum is to be
seen on 21 sections rostralwards. Just as in the embryo of 23 m.m.
738
it runs forwards along the auditory capsule and is separated from
it by the jugular vein and the facial nerve’).
If we trace the diverticulum from the base rostrally, we see
it after 8 sections already changed into a flat and narrow duet
with a lateral and medial wall. The duet is prolonged over 4
sections, and then with nearly no change of lumen, passes over
into the top part of the diverticulum, which is perceptable on 9
sections. The medial wall of this part has over its whole length
a neuromast, whose posterior end is clearly defined. Near the rostral
end (the blind top) of the diverticulum the branch of the ram.
oticus unites with the neuromast.
We may now, proceeding from the anterior margin of the spiracle,
distinguish three parts, seen resp. on 8, 4 and 9 sections which we
shall call vestibulum of the spiracle, excretory duct and corpus of
the sense organ bladder.
Excretory duct and corpus are partners, but the vestibulum is
nothing more than an ordinary diverticulum of the anterior wall
of a visceral pouch, and disappears later, in consequence of the
enlargement of the external opening of the spiracle.
The vestibulum is still present in an embryo 69 m.m. long, but
in embryos of 78 m.m. or more, it has disappeared. We then only
see son a section, passing posterior to the anterior margin of the
spiracle, the opening, which meanwhile has become very minute, of
the excretory duct. Then the condition of the sense organ bladder
principally corresponds to that of the organ which occurs in the
adult animal. It then forms an appendix of the spiracle. The descrip-
tion by vaN BEMMELEN of the Galeoidei and rays also applies to the
sense organ of Acanthias.
Probably these bladders are homologous in all the Selachians and
of ectodermal origin. They have in some forms sunk somewhat
deeper into the spiracle, than in others. We shall still examine the
little bladder sowewhat closer in a series of cross sections of the
Acanthias embryo 98 m.m. long.
The very minute opening in the anterior wall of the spiracle is
only to be seen in one section. From here the organ passes rostral-
wards over 50 sections. It runs along the auditory organ from
') During the translation of this paper I prepared a series of sagittal sections,
stained with haematoxylin and eosin, of a 22 m.m. long embryo of Torpedo
marmorata. I found the deep neuromast at the inner wall of the spiracle innervated
by a branch of the ram. oticus, crossing the outer side of the vena jugularis, just
as in Acanthias.
739
which, — as previously — it is seperated by the jugular vein and
the facial nerve.
The corpus of the bladder, with its long neuromast, is visible on
the anterior 21 sections. The excretory duct falls in the following
29 sections. The neuromast thus nearly constitutes half the length
of the organ, and is much larger than in the lateral line system
organs of the skin. Round the corpus one sees the mesenchym in
more compact formation, the first stage of a connective tissue cap-
sule. The excretory duct, immediately posterior to the corpus, shows
a different construction than further caudalwards.
Fig. 2a. Cross section through the otic Fig. 2b shows the spiracular organ
region of the skull and the anterior wall under high power. Its contents, mucus
of the spiracle, from a 98 m.m. long (stained blue in section) are seen as thin
embryo of Acanthias vulgaris. striations.
On the first 5 sections behind the corpus, the medial wall of the
duet is thickened, as the result -of the proliferation of the outer
layer of epithelium cells. Here the oval lumen is wider than in
other places. The longitudinal axis of the oval is more or less twice
as long as in the corpus. On the following 24 sections this lumen
continually decreases, the wall consisting of two layers of cells.
Those of ‘the inner layer are very flat, those of the outer layer
may be called cubic.
It is of importance that the corpus of the sense organ bladder
and the proximal part (5 sections) of the duct, should be filled with
mucus, which in this stage (and later) allows itself to be stained
blue, just as-in the ampullary and canal organs of the lateral line
system. In the distal part of the duct (24 sections) the mucus is
present in lesser quantity.
740
From this we may see, that the spiracular sense organ shows
itself to belong to the lateral line system of epidermal sense organs,
which is generally also understood by the term mucus-organs. The
direct proof has not yet been given, but may perhaps be found in
stages earlier than those which | have studied.
The ram. oticus, in all the studied embryos, arises with a ganglion
like thickening from the buceal ganglion of the facial nerve,
In the 394 m.m. long embryo, it runs along the cartilage of the
ear capsule — but not yet surrounded by the cartilage — dorsally
and caudalwards. It sends off a few thin branches to the organs in
the lateral line canal of the regio otica, and a thick branch, which
goes to the spiracular sense organ across the jugular vein.
In the 98 m.m. long embryo, a part of the ram. oticus is over-
grown by the cartilage of the ear capsule. This is also the case with
the Ganoids. Contrary to the Selachians the sense organ itself is
-surrounded by cartilage in both Ganoids and Dipnoi.
We shall now pass on to the 63 m.m. long embryo of Heptanchus.
The small external opening of the spiracle is here situated far back-
wards. The fissure like opening in the gut reaches still farther
rostralwards. If we accept that the beginning — the base — of
the vestibulum falls on the section which passes through the anterior
margin of this fissure, then the top of the vestibulum lies still 28
sections further forwards. In this top the sense organ bladder
opens without an excretory duct. It can be traced in 12 sections
rostralwards, along the auditory organ, from which it is separ-
Fig. 3a. Cross section through the otic Fig. 3b shows the spiracular organ
region of the skull of a 63 m.m. long under higher magnification.
embryo of Heptanchus cinereus.
741
ated by. the jugular vein. The neuromast on the medial wall just
projects with its posterior margin from the vestibulum.
I was not successful in finding the supplying nerve. Perhaps it
is Owing to the intensely stained connective tissue capsule. which
is more developed than in the largest of the examined embryos of
Acantbias. In the 225 m.m. long embryo the organ was so badly
preserved, that nothing of importance can be mentioned °).
3. Fenestra vestibuli.
In the 63 m.m. long embryo of Heptanchus, the attachment of
the hyomandibular to the anditory capsule is brought about by a
thin layer of connective tissue, wherein | can find no cavity of
Fig. 4. Lateral surface of the model
of a disk from the cartilage of the
regio olica of an embryo of Heptanchus
cinereus. The disk is placed in such
a position that a part of the anterior
surface with the canalis semicircularis
lateralis, is just visible, and the fenestra
veslibuli is not covered by the upper
part of the hyomandibular.
') Before the translation of this paper, the work of Viravi (Anat. Anzeig. 1911
and 1912) had escaped my notice, and [ am indebted to Dr. BENJAMINS of Utrecht
for having called my attention to it. As he remarks, this paratympanic organ in
birds must be the homologue of the spiracular sense organ. An interesting referate
of the works of Vrraur on this organ by Rurrinr “Sull organo nervoso para-
limpanico di G. Vrrarr od organo del volo degli uccelli” is to be found in
“Archivio Italiano di Otologia Rinologia e Laringologia” publ. by GRADENIGO.
Vol. 31, 1920.
742
articulation. It is prolonged over 49 sections, 15 u thick. Imme-
diately ventral to the anterior portion of this place of attachment
One sees in the sections 5, 6 and 7 (in antero-posterior sequence) a
connection through a small opening in the wall of the auditory
capsule, between the mesenchym which in this stage fills the peri-
lymphatic space, and the mesenchym outside the capsule. The posterior
margin of the opening is not clearly defined, so that it remains
dubious whether the hole is present in the next three sections or not.
On the contrary the margins of the opening in the 255 m.m. long
embryo, are clearly defined. The attachment of the hyomandibular
to the capsule takes place here on about 59 sections 30 u thick (in all
the other embryos the sections are 15 u thick).
The opening reaches from the 8 to the 25" section (counted
antero-posteriorally). It is closed by a deeply red stained connective
tissue, which also helps to connect the hyomandibular to the skull,
and which is rather conspicuously surrounded by the blue colour of
the cranial cartilage. The opening lies in the under part of the
fossa for the hyomandibular, which partly covers it.
From the wax model of Mr. P. J. pr Vries, made according to
the method of Born, one can see that the opening is not truly oval,
but rather kidney-shaped, because the under margin forms a re-
entering concavity. The mesenchym which formerly filled the peri-
lymphatie spaces, has to a large extent disappeared and been replaced
by a liquid, which is prevented from flowing out, by the connective
tissue closing the opening.
The opening, owing to its position, has to be considered as the
homologue of the fenestra vestibuli, which in Amphibians and Am-
niotes is closed by the stapes, and which according to general
opinion would be absent in fishes.
Owing to the great length of the embryo, it must have been
more or less fully developed, and it is improbable that the fenestra
would not persist after birth.
I, however, had no opportunity of examining adult material.
Irrespective of the autostylie Dipnoi and Holocephali, fishes are as
a rule hyostylic. Their powerful hyomandibular functions in the
first instance as a suspensorium. This fact evidently has to do with
the absence of a fenestra vestibuli. Only two primitive forms viz.
Heptanchus and Hexanchus are amphistylic. Their hyomandibular,
owing to the firm attachment of the palatoquadrate to the skull, can
only feebly function as a suspensorium. It is therefore conceivable,
that the hyomandibular, at least in Heptanchus, may still have the
function of transferring vibrations to the auditory organ.
743
The presence of the fenestra in the embryo is in any case a
support to the old theory, which in later years has frequently been
attacked, the theory namely: that the stapes in higher animals is
homologous to the hyomandibular in fishes.
INDEX LETTERS.
Csl. Canalis semicircularis lateralis.
Csp. Cart. spiracularis. Each of the two spiracular cartilages (fig. 2a) is sectioned
twice.
Ek. ‘Top of the epibranchial of the first branchial arch.
Ep. Epithelial body.
Fv. Fenestra vestibuli (ovalis).
Hm. Hyomandibular.
K,. Second branchial cleft.
Pq. Palatoquadrate.
Ro. Regio otica of the skull.
So. Spiracular sense organ.
Th. Thymus.
Vj. Vena jugularis.
LITERATURE.
YAaar, W. E. The Spiracular Gill Cleft in Lepidosiren and Protopterus. Anat.
Anzeiger, Bd. 28, 1906.
“ALuis Jr. E. PHetps. The Lateral Sensory Canals, the Eye Muscles and the
Peripheral Distribution of certain of the Cranial Nerves of Mustelus laevis. Quart.
Journ. of mier. Science, Vol. 45, 1901.
y BEMMELEN, J. F. yan, Ueber vermuthliche rudimentäre Kiemenspalten bei Elas-
mobranchiern. Mitth. a. d. zoologischen Station zu Neapel, Bd. 6, 1885.
‘Braus, H. Ueber den embryonalen Kiemenapparat von Heptanchus. Anatomischer
Anzeiger, Bd. 29, 1906.
vBriper, F. W. On the Osteology of Polyodon folium. Phil. Trans. Roy. Soc.
Vol. 169, 1879.
‘Dourn, A. Die Entwicklung und Differenziruug der Kiemenbogen der Selachier.
Mitth. a. d zoologischen Station zu Neapel, Bd. 5, 1884.
vFrirscHe, EF. Die Entwickelung der Thymus bei Selachiern. Jenaische Zeitschr.
f. Naturwiss. Bd. 46, 1910.
“Goopricn, E. S. On the Structure of the Exeretory Organs of Amphioxus. Quart.
Journ. of micr. Se. Vol. 54, 1909.
vGreit, A. Entwickelungsgeschichte des Kopfes und des Blutgefässystemes von
Ceratodus forsteri. Denkschr. d. Medicinisch Naturwiss. Ges. zu Jena, Bd. 4,
1913.
vHamvar, J. AuG. Zur Kenntnis der Elasmobranchier-Thymus. Zool. Jahrbücher,
Abt. f. Anat. und Ontog. Bd. 32, 1912.
744
“HorrMannN, C. K. Beiträge zur Entwicklungsgeschichte der Selachii. Morph. Jahr-
buch, Bd. 27, 1899.
“Mürrer, Jon. Vergleichende Anatomie der Myxinoiden. Dritte Fortsetzung. Abh.
der Kön. Akad. d. Wissensch. zu’ Berlin, 1841.
. Pinkus, F. Die Hirnnerven des Protopterus annectens. Morph. Arbeiten, herausgeg.
von Schwalbe. Bd. 4, 1895.
Wericut, R. Ramsay. On the hyomandibular Clefts and Pseudobranchs of Lepidos-
\ teus and Amia. Journ. of Anat. and Phys. Vol. 19, 1885.
Physiology. — ‘Contributions to an experimental phonetic investigation
of the Dutch language. 1. The shorto’’.*). By Miss L. Katsxr.
(Communicated by Prof. G. van RuNBeRK).
(Communicated at the meeting of September 29, 1923).
When listening carefully to the pronunciation of the “0” in closed
syllables in Dutch, we perceive that — apart from the influence
which all sounds undergo from preceding and following vowels or
consonants — two completely different ways of pronunciation can
be distinguished *).
One of these two pronunciations is heard in words like: kok, tot,
hol; the other in words like pop, bot, vol, hond. At the suggestion
of my former master Dr. Promp, | have tried to go further into
this question.
| first tried to determine experimentally this difference, suggested
by linguistic feeling and observed by simple hearing.
Experimental phonetic analysis of the speech movements.
Several methods used in experimental phonetics were consecutively
applied in order to determine the essential movements and positions
of the vocal organs during the pronouncing of @ and © *). In doing
so | chiefly made use of one trial person, while the results were
afterwards tested to those obtained with other speakers.
1. Observation and measuring of the mouth opening while pronounc-
ing different sounds proved that in this respect a, ©, 00, 0, oe form
a series in which the mouthopening gradually decreases, the height
1) From investigations made at the Physiol. Lab. of the Amsterdam university
and at the Phonet. Lab. of the Czech university at Prague.
*) | am aware of the fact that so called educated speech varies considerably
in different parts of this country. As far as 1 know facts mentioned here hold
good for the pronunciation of Amsterdam and surroundings and probably not or
only partially e.g. for that of the Hague and surroundings in which the o-sound
°
seems to predominate.
5) The o of kok is represented by o, that of pop by o.
49
Proceedings Royal Acad. Amsterdam. Vol. XXVI.
diminishing regularly,
746
while the width also decreases but not so
regularly. The latter, namely, shows a sudden decrease between
O and oo. In this series the height of the mouth opening was 16
Fig. 1.
1) Vox. Heft 3/6, 1922.
*) Onderz. Physiol. Lab.
p. 98.
mM., 12 mM., 8mM., 6mM., 4 mM. respect-
ively, the width 36 mM., 31 mM., 16 mM.,
14 mM., 7 mM. respectively (see fig. 1).
Closely connected with this are curves of
the lipmovements made with the apparatus
of von Wicznwski"). This apparatus has
been so construed as to have the curves
indicate the natural size of the vertical lip-
opening. Fig. 2 illustrates this. Fig. 3 shows
a curve obtained with the same apparatus
by pronouncing alternatively dol and del.
The difference is clear; the dimensions are
about the same as those mentioned above.
Consequently, if we exclusively consider
the shape of the mouth opening, we can
imagine that © is an oo that became more
or less like an a while © is an oo that bas
acquired some of the qualities of the oe.
2. By means of ZWAARDEMAKER’S apparatus?)
for registering speech movements, the pouting
of the upper lip, the movements of the lower
jaw relative to the upper jaw, and the con-
traction of the muscles that form the bottom
of the mouth, were recorded. Fig. 4 shows
that also as regards jaw opening a, 9, 00, 0,
and oe form a descending series, while the
pouting of the lips increases, (with this trial
person there is less pouting of the lips for
© and oe than for oo in connection with
the downward movement of the upper lip,
during which the latter is sowewhat flattened).
The curve of the mouth bottom is not
dealt with bere because of its complexity.
What interests us most in this curve is that
it shows considerable and characteristic dif-
te Utrecht. Ve reeks | 1899—1901 p. 76. Leerb. II
Fig. 3.
747
ferences between the two o-sounds. These results
harmonize quite well with those obtained by
EYkMAN ') who, working with the same instrument,
found an average jaw opening of 7,25 mM for a
in “bat”, 5,50 mM for o of “pot”, 4,75 mM for
oo of “boot”, 4,50 mM for o of “bot” and 2,25
for oe of “boet”.
Fig. 5 also shows curves of lip, jaw, and mouth
bottom, but these curves are obtained in another
way, viz. by means of a “mouth-funnel” that per-
mits of registering the above mentioned movements
at the same time. This instrument, constructed
by me for another purpose, will be dealt with
elsewhere. As it has no fixed support, it misses
the exactness which characterizes ZWAaARDEMAKER’S
apparatus. Still it is very useful to give a provi-
sional impression of something relative. It can be
noticed in fig. 5 that in pronouncing “derscht”
there is less pouting of the lips and a larger jaw
opening than for dorst’, while the curve of the
mouth bottom is almost the same for both words.
From the mouth-funnel curve it appears that the
air current for @ is stronger than for o, as is
easily comprehensible. From the above, therefore,
it becomes evident again that the two sounds differ
considerably.
1) Onderz. Physiol. Lab. te Utrecht Ve reeks II 1899—1901
p. 202
748
3. With the majority of speakers the hard palate is either hardly
touched or not touched at
o, or o. Consequently the
artificial palate cannot be of
much use here. Yet I had
the words ‘“‘pop” and “bob”
pronounced by two trial per-
sons with whom a rather
large part of the palate was
touched. The results can be
found in fig. 6. The difference
between the two sounds is
clear with both persons: the
surface touched for o being
smaller than for e, while it
is a wellknown fact that for
athe palate is not tonchedatall.
4. Finally the movement
of the larynx was registered.
It can be easily felt that the
larynx assumes a somewhat
different position in the two
cases, viz. it is advanced
more for o . However, | did
not always succeed in record-
ing this difference. I tried to
do so with ZWaaRDEMAKER’S
method ').Theeurvesobtained,
however, were too unlike in
appearance but that definite
conclusions could be drawn.
Still it appeared from these
curves that the larynx was
retracted for o (as for a and
00), while it was advanced
for o as for oe, though by
no means to such a degree.
Fig. 7 shows part of acurve
in which the difference be-
tween 9 and © can be seen.
all by the tongue in pronouncing oo,
1) Leerboek der Physiologie Il, p. 86.
LoL
Lip /
Lie EEK a, Cone ol — ed
Kwak |
Pred o Diem
hoi ahd An hk kes
ih my
dls dol
oO Re
750
That the speech movements made to produce 9and o asdistinguished
by the ear differ considerably, has been sufficiently proved in the above.
Fig. 6. Rpt.
Fig. 6.
Experimental phonetic analysis of the sounds.
Also the characters of the sounds themselves proved to show a
difference which could be easily recorded. In the first place the
sounds can be easily registered on the kymographion. It need hardly
be said. that the tambour used for this purpose has to answer
special requirements. This part of the inquiry was made under the
guidance of Prof. Cuumsky. The tambour had the same shape as
the recorder of a phonograph, the membrane was made of mica.
An aluminium “mouthfunnel” after RousseLor was connected with
this tambour by means of a wide rubber tube. Fig. 8 shows curves
of the two sounds as registered in this manner. As a matter of
fact the vibrations of a membrane like this are not large, owing
to its stiffness; it is however partly due to this fact that we get
curves which are thoroughly characteristic of the sounds recorded.
So in our case there is a clear difference between the curve of
o and that of o.
The sounds can also be registered by means of a phonograph.
A few monosyllabic words in which either of the two sounds
occur according to the meaning (e.g. bod and bot) as well as the
751
sounds pronounced separately were recorded by means of an
Edison phonograph (old type)
The difference between the sounds as recorded by the phonograph
can be made much more illustrative and easily measurable by
bes ae, sug eat
| OO 00E
.
| Kk ru dn: IV
—
Fig. 7.
transforming the indentations of the wax cylinder into a curve on
smoked paper. This is done by the apparatus constructed for this
purpose by Liorer. A sapphire follows the groove of the phonographic
cylinder; the movements made by the sapphire in doing so are
transferred to a writing-lever, recording them ona rotating cylinder.
As there is no such apparatus in Holland, as far as I know, also
this part of the investigation was made at Prague under the guidance
of Prof. Catumsky. The words ,,bod” and ,,bot” were again recorded
phonographically, making use of the apparatus of Liorrr. By means
752
of the same instrument these curves were subsequently magnified
300 times and registered on a smoked cylinder. Fig. 9 shows part
Fig. 8.
of these curves. The upper and lower curves represent the o-sound
in ‘bot’, pronounced in a low voice in the former and loud in the
latter. The curve in the middle gives © cound in „bod” The differ-
ence between the two sounds is clearly revealed in this way and
can be easily put into figures. The curve of o is much the same
as that which characterizes the aa-sound.
After a considerable and constant difference bas thus been
ascertained, it may be desirable to get an idea of the circumstances
in which 9 and o occur in Dutch.
Fig. 9.
753
Linguistic remarks.
Every Dutch word of one syllable, containing o and also syllables
with o, not occurring by themselves but with which influence from
other syllables can be safely excluded (e.g. lom(mer)) were considered.
Combinations of sounds that can be pronounced quite well, but are
not found in the Dutch language, have been omitted.
As regards the influence by the several consonants, a few facts
could be ascertained.
The most constant influence is that of following nasals. In this
combination, namely, the o-sound occurs invariably. This can be
easily comprehended, as the narrow mouth-opening and weak current
of air passing through the mouth, promote the air current through
the nose which follows.
Another influence is that of the lip-sounds; these promote the
producing of the o-sound especially when preceding it. Also this
becomes clear if we consider the narrowness of the mouth-opening.
Guttural sounds like h, g, k, ete. are as a rule followed — and as
far as they can be final, also preceded — by o. This also holds
good, though in a less degree, for z, s, 1, r, n and j; n of course
only when preceding. D and t have no clearly manifested influence.
The r occupies a position of its own; its influence varies according
to the way in which it is pronounced, which is different even with
one and the same speaker at different times, its place of articulation
varying between point of the tongue gums and root of the tongue-
uvula. Taking this into consideration we can say that the advanced
r promotes the ©, the retracted vr the o-sound, both whether preced-
ing or following the vowel.
From this itappears that the adjoining consonants either promote
the o or the ©. It should be borne in mind, however, that the only
absolute influence is that of nasals as following sounds. The other
influences only work to a limited degree. The fact that the influence
of several sounds appears to be inconstant proves that there is
at least one factor more playing a part. This becomes evident
from the fact that several words, have either © or © according to
their meaning, eg:
bot (noun = flounder, & bod (noun of bieden = to bid)
bone; adjective = blunt)
dol (adjective = mad) & dol (noun, part of a rowing-
boat = thowl)
dorst (noun = thurst) & derscht (from the verb dorschen
= to thresh)
754
motje (dialect of moet-je=must you) & motje (noun, dimunitive of mot
= moth)
port (from the verb porren=to stir) & port (noun from porto, oporto)
tobbe (noun = tub) & tobben (verb = to worry)
It seems to me that the above may induce us to think of etymo-
logical influences. Words that have o in Dutch, usually occur in
German with u, while those with 9 either have o, a, or au in
German. | do not venture to judge about the value of this pheno-
menon. Other cognate languages as well may give indications. It may
be wortwhile to make an etymological inquiry in this connection.
If etymological influences are ascertained indeed, we can imagine
that they be inconsistent to a certain extent with the other influen-
ces described above. The word “pols”, for instance, may be men-
tioned in this connection, because the pronunciation is wavering. It
appears to me that this word is pronounced “pols” by more careful
speakers, while the majority say “pels”. Judging by its etymology
the former pronunciation would be the right one; the latter may
be easier because of the | that follows.
Summary.
There are in Dutch two short o-sounds that can be clearly
distinguished both acoustically and phonetically (perhaps also ety-
mologically).
Botany. — ‘‘Ringing Experiments with variegated branches.”
. By Prof. Ta. Weevers. (Communicated by Prof. J. W.
Mout.)
(Communicated at the meeting of September 29, 1923).
For a long time already the transport of carbohydrates and
proteins in plants has been considered as a question that seemed
fairly set at rest. Of late years, however, the problem has again
been brought into prominence.
The well-known ringing experiments, notably the extensive ob-
servations made in this field by J. HansteiN*) had settled the belief
that the organic matter was transported along the elements of the
phloem. It was left undecided whether the elements of the cribral
system (sieve-tubes and companion cells) or those of the paren-
chymatous phloemsystem (cambiform cells) play the principal part.
CZAPEK's*) experiments favoured the first view, however, owing to
the diametrically opposite conclusions of DELEANO*) a decision
was impossible at the time.
The primary and the secondary phloem was generally considered
as the passage for the conduction of the organic products, which,
being formed in the leaves, have to be conveyed to the growing
points and the reserve-organs.
In accordance with Tu. Hartie’s‘) conception it was, however,
generally received that in the early spring, when the woody plants
start new shoots, the organic matter finds its way from the reserve-
stores to the shooting parts through the xylem. This hypothesis was
based partly upon the results of Hartie’s experiments with ringed
plants and partly upon A. Fiscner’s*) observations regarding the
occurrence of carbohydrates in the wood vessels. Researchers refrained
from approaching the question as to how this happens in shooting
herbaceous plants.
Now the above theory has latterly been impugned from various
quarters.
1) J. HANSTEIN, Jahrb. f. wiss. Botanik, 1860.
2) CZAPEK, Jahrb. f. wiss. Botanik, 1897.
8) N. DeLwAro, Jahrb. f. wiss. Botanik, 1911.
4) To. Harrie, Bot. Ztg., 1858.
5) A. FiscHer, Jahrb. f. wiss. Botanik, 1890.
756
On the one side Oris Curtis') made single and double ringing
experiments and arrived at the conclusion that the transport of
carbohydrates and proteins to the shooting parts may occur through
the secondary phloem just as well as the transport in the opposite
direction does, when the surplus of assimilates is removed from the
place of formation. In my judgment, however, his view has not
been sufficiently reintoreed by indispensable quantitative examination.
On the other side it is Akins?) and Dixon’) in England, and
Luise Briren Hirscurenp*) in Germany who deny almost any signi-
ficance to the phloem for the matter-transport. Their arguments
consist in the main of indirect evidence. ATKINS argues that the
bleeding saps are more or less rich in carbohydrates not only in
spring but also in other seasons. Luise Biren Hireurrup and after-
wards Dixon base their most cogent arguments upon their belief
that an adequate transport of matter along the phloem can hardly
be presumed. This difficulty had already been obviated by Hueco pe
Vries’), who made a quicker transport than the law of diffusion
admits conceivable by assuming protoplasm-streams in the phloem-
elements. Dixon, however, considers the impossibility of a transport
of adequate capacity along the phloem as conclusive evidence for
denying any significance to the phloem in this respect. Birch: HirscHFELD
is less positive in her assertion.
That, beside an ascending stream in the wood, there may also
be a coinciding transport along it towards the bottom of the stem,
may be concluded from various investigations ia. the above-named
by L. Biren Hirscurenp. Then the rate of transport can be much
quicker than in the phloem and the capacity of the condueting
channels can likewise be greater, as it is a fact that the phloem-
production of cambium is invariably smaller than that of the xylem,
while the generated phloem is obliterated much sooner.
This conception of Dixon’s, however, does not square with the
result of the ringing experiments of HansreiN, which result points
indubitably to the stream of assimilates being stopped when the
ringing wound is made deep enough to reach the cambium. Dixon
therefore assumes the transport to pass through the youngest parts
of the secondary xylem, which parts being located close to the
cambium, are by him believed to be injured and thus rendered
inactive by the ringing.
1) Ons F. Curtis, American Journal of Botany, 1920.
2) W. R. G. Arkins, Some recent researches in Plant Physiology, 1916.
3) H. H. Drxon, Pres. Address. Bot. Society, 1922.
4) L. Brreu HirscureLp, Jahrb. f. wiss. Botanik, 1920.
5) Hueco pr Vrixs, Bot. Ztg., 1885.
757
To my knowledge this hypothesis has not yet been substantiated
by experiments, so that it seems expedient to reconsider the question
along what way the carbohydrates and the proteins are transported
in plants.
The question can be approached from different sides; in this
paper I will confine myself to a discussion of some experiments
with ringed branches of variegated plants.
Similar experiments have been made repeatedly with green
branches, but then the trouble is that after the buds have opened
out, the younger parts above the ring begin to assimilate.
Stripping off the leaves or moving the plant to a dark space in-
volves other difficulties; with variegated shoots it is much easier to
state any supply of organic matter.
In consideration of Dixon’s hypothesis due precautions should be
used in the ringing and the protection of the injured part. A coating of
melted butter of cocoa | deem more effectual than one of paraffin. It was
applied to the wound at a temperature of 32°—33° C. and can
hardly injure the exposed surface, as it does not penetrate into the
intact cells.') Moreover, it soon congeals and then affords sufficient
protection against outside influences. The parts were then screened
from immediate effect of the sun’s rays in order to prevent melting.
We performed our experiments with variegated branches of
Aesculus hippocastanum L. and Acer Negundo L. The former were
derived from a stout specimen, whose green top provided the trunk
with abundant food and from this trunk numerous yellow shoots
had developed. In about 20 years these shoots attained a length of
1 M. and a thickness of 7—8 mm. in diameter. The specimen of
Acer Negundo was provided at the top with green-white variegated
leaves and developed from the main stem and side branches perfectly
white shoots. In neither specimen did the yellow-white leaves contain
any chlorophyl®). An iodine test pointed to the absence of starch.
In the spring experiments the branches were ringed (1—2 cm.)
just before the buds began to open out and at a distance of 1—2dm.
below the end-bud.
Three series of experiments were always made at a time.
1st series: green shoots ringed all round.
2nd series variegated (yellow-white) shoots ringed all round.
3rd series variegated (yellow-white) shoots partially ringed, viz. so
as to leave as trip of bark as a connecting link, 2—4 mm. in breadth.
1) R. H. Scurmprt, Flora Bd. 74, 1891.
*) Guard-cells of the stomata excepted.
758
After rather more than a week a contrast was noticeable between
the green and the partially ringed variegated shoots on the one side
and the completely ringed variegated shoots on the other. The first
two (1st and 3"! series) continued growing normally. The third
(2nd series) lagged behind and died off after 2 or 3 weeks, the
leaves having previously shrivelled and dried up.
Fig. 1
That ringing in itself did not injure the plant appeared distinetly
from the results of the first and the third series. (See the photos):
from left to right we see first 4 completely ringed yellow branches,
some brown and dead, others small but still living; the next
following are two completely ringed green ones and lastly to the
right two partially ringed. The last four have developed normally.
It is clear that with the completely ringed green shoot the supply
of water is normal; why then does the completely ringed yellow
branch die off under symptoms that point to a deficiency of water?
The reason is obvious. In consequence of too little osmotic pres-
sure the absorptive power of the tissues is too low as compared
with that of the other parts.
The researches by Dixon and Atkins’) on the determination of
the osmotic pressure by lowering the freezing point of the expressed
1) Notes Botanical School. Trinity College Dublin, 1912.
759
sap, clearly show how the osmotic value of the leaf-cells increases
with the possibility of assimilation.
Now 1 endeavoured to determine the suction force by Ursprune’s *)
method but the subject appeared to be difficult to experiment on.
A quantitative determination gave in the green leaves of Aesculus
an amount of reducing sugars of 3°/,*), in the variegated (yellow)
leaves 1°/,, in the ringed variegated (yellow) branches only traces.
In general also the amount of extractable salts is trifling; in green
and variegated leaves 0,9°/, of the fresh weight’). SprecHEr finds
in yellow varieties lower osmotic values for the cell sap than in
the green specimens *).
True, the variegated leaves of the ringed branehes of Aesculus
contain from 18 to 20°/, protein and 5°/, dextrin (calculated at
dryweight) but the influence of these amounts on the osmotic pres-
sure is nothing to speak of. Yet this does not explain all, for in
the variegated completely ringed shoots wood and hark above the
ringing appeared to contain still a fair amount of starch (6 °/, of
the dryweight, against 9°/, in the partially ringed branch), while
the leaves were already shrivelling.
Why this starch is not converted into sugar and why, when
transported to the leaves, it does not raise the osmotic pressure has
not yet been explained.
However this may be, the partially ringed variegated branches do
not die off. It appears, then, that there the supply is not cut off
and that consequently the young parts are provided with the nutri-
ment that in the green finged branches is produced by assimilation.
According to HANSTEIN the organic products are conveyed along
the bridge of bark, but if this is the case, we must relinquish Hartie’s
hypothesis that the transport is effected along the xylem while the
branches are budding.
Oris Curtis (le) does so and was led by his ringing experiments
to regard the phloem exclusively as the path, along which the saps
') UrsprunG, Ber. d. d. bot. Ges., 1918.
*) Strictly speaking 2°/, and 1°/, reducing sugars derived from glucosids
(calculated at dry-weight).
8) The starch determinations were performed by putting the pulverized material
immersed in water for 3 hours into an autoclave at 4 atm., and by subsequently
boiling the aequeous extract with diluted hydrochloric acid during 60 minutes.
Plasmolytic experiments are objectionable on account of the osmotic pressure
in the various cells being unequal. Still, a 10%, saccharose solution plasmolyzes
the variegated Aesculus-leaves, not however the green ones.
4) A. SPRECHER. Rey. Gen. Bot. 1921.
760
are transported. From Dixon’s point of view, however, it might be
objected that in Curtis’s experiments the peripheral woodlayers were
injured and thereby the transport along the peripheral xyleem had
been suspended indirectly.
This objection can hardly be raised against the above experiments,
in which a coating of butter of cocoa was spread on the injured
part.
Fig. 2.
Moreover, another series of ringing experiments was carried out.
In these experiments the ringing was performed as much as
possible aseptically by previously washing the branch bark with
96 °/, alcohol and then peeling it off aseptically down to the cam-
bium. Subsequently the decorticated surface was covered with steri-
lized absorbent cotton wool saturated with water; finally the whole
was wrapped up with wax taffeta.
These experiments were carried out mid-June in the same way
as the others described above, and yielded after four weeks an
unequivocal result in connection with the midsummer growth which
was very abundant, especially in Aesculus.
With the normal yellow variegated shoots the formation of mid-
summer growth occurred at the top of the branch and the yellow
young leaves contrasted sharply with the others, which had been
damaged by the high wind and browned by the sun. (See photo).
761
It appears then, that here also the yellow leaves suffer under a
deficiency of suction force, and under circumstances brought about
by stronger evaporation are sooner destroyed than the green ones,
although the latter evaporate comparatively more intensely.
With partially ringed variegated shoots the midsummer growth
occurred also at the top. With completely ringed specimens, however,
it appeared below the surface of the wound from lateral or dormant
buds. (See photo). This occurred as well when the surface of the
wound was covered with butter of cocoa, as when it was dressed
with a water-bandage.
The cheek to the food-supply is apparently as great with Aesculus
as with Acer Negundo, in spite of the greatest precaution used in
cutting the ring. It follows, then, that the experiments do not yield
any evidence whatever, to lend support to Dixon’s theory. They
rather go against it.
Stall conclusive evidence to disprove Dixon’s theory cannot be
brought forward by this procedure, since in spite of all due precau-
tion the peripheral wood may be prevented by the ringing from
performing its function, as far as the transport of the organic
products is concerned.
With regard to other inquiries, whose results tell strongly against
Dixon’s theory, we first of all have to think of Hansrein’s experi-
ments (I.¢.) on the roet-growth of ringed branches in water culture.
Hanstein finds that detached branches placed in water send out
roots chiefly at the basal extremity of the stem, which VöcnrinG
ascribes to the polarity of the parts. Leafless branches when ringed
develop a large number of roots just above the wound; whether
and to what number they will grow at the bottom of the branch,
depends on the distance between that extremity and the ringing.
Hanstein ascribed this to the check to the transport of nutriment
consequent on the removal of the phloem, and established, indeed, in
such circumstances a distinct difference in the root-growth, between
dicotyledonous plants with an anomalous stem-structure and those
with a normal stem-structure, in which the stem derived its thick-
ness form a ring of collateral vascular bundles. With the former
the transport of carbohydrates and proteins is believed to be only
partially checked. This is ascribed to the fact that the vascular
bundles are contained within the xylem (as with Piperaceae and
Nyctaginacea) or (as in the case of Apocynacea and some Solanacea)
to the fact that there are originally bicollateral vascular bundles or
rather medullary phloem strands and consequently phloem remains
also within the secondary xylem. Owing to this HaNnsTrin stated
50
Proceedings Royal Acad. Amsterdam Vol X XVI. =
762
in this case only a very slight influence of the ringing upon the
root-growth.
This evidently does not fit in with Dixon’s view; if the transport
is effected along the peripheral parts of the xylem, ringing must in
these plants have the same effect. It struck me, therefore, that it
would be worth while to. repeat some of HansTEin’s experiments.
The Solanacea Cestrum aurantiacum proved to be an unsuitable
subject since detached branches sent out roots very sparingly in
water culture, but Nerium Oleander yielded quite satisfactory results:
all the twelve cuttings presented an aspect, quite in harmony with
HaANsTEIN's description. The root-growth may be somewhat more
abundant above the wound, but the behaviour is quite different
from e.g. that with Salix and Cornus spec. In these the roots
appear almost exclusively above the wound, unless the stem-piece
below it be very long, and the once formed roots are even destroyed
when the bark above them is stripped off.
Provisionally all this tells very strongly against the validity of
Dixon’s conception of a transport of the carbohydrates and the
proteins along the peripheral xylem.
If the above-discussed experiments with variegated shoots could
also be made with variegated Oleanders, the medullary phloem of
these plants would probably cause a quite different result from
that yielded by Aesculus and Acer. But unfortunately variegated
Oleanders | had not at my disposal, so that now | made a trial
with ringed, normal shoots, which, while still attached to the plant,
were wrapped up in black paper. The result was rather conclusive.
Although some leaves had fallen off, the shoots themselves were
still alive ten weeks after the ringing and had increased in length.
We see, therefore, that not only in the formation of the roots of
branches in water-culture but also in the budding and the growth
of Oleander Aesculus and Acer Negundo in spring, the results of our
experiments with ringed branches imply a transport along the phloem.
In a subsequent publication | intend to diseuss the question
whether the capacity of these paths is sufficient.
For the present the above observations on Aesculus and Acer Negundo,
where the detached branches did not bleed, are not applicable to the
cases in which this bleeding is so copious, and as with Betula alba
the highly sacchariferous sap is exuding directly after the ringing’).
1) The cases described by Mo.iscH, (Bot. Ztg. 1902) as wound-reaction with
local bleeding pressure, are of quite a different nature; then the bleeding pressure
manifests itself only after days or weeks.
Physiology. — “Determination of the Power of the Accommodation-
Muscle’. By Prof. J. van per Horve and H. J. Friprinea.
(Communicated at the meeting of September 29, 1923).
The action of the accommodation muscle, the M. Ciliaris, makes
itself apparent to us by the increase of refraction of the lens, the
so-called accomodation of the eye.
There are still many obscure points in the subject of accommo-
dation; for instance, it is still entirely unknown to us what relation
exists between the contraction of the accommodation-muscle and
the increase in refraction of the lens
A few ophthalmo-physiologists are of opinion that contraction of
the accommodation-muscle increases the tension in the ligament of
the lens, the Zonula Zinii, while most of them assume, with Huermnoirz,
that contraction of the ciliary muscle causes a relaxation of the
Zonula Zinii, so that opportunity is given to the lens to curve
according to its elasticity. When, through increase of age, the elasticity
disappears, contraction of the ciliary muscle does not assert itself
by increase of refraetion of the lens.
Even if one assumed the last theory, one meets with many unsolved
questions, eg.:
a. Is the strongest possible contraction of the accommodation
muscle necessary to obtain the greatest possible accommodation ?
Donpers and Lanpor? assumed this and find still followers in these
days, amongst others CraARKE and Duane.
Fucus, Hess and others, on the contrary, are of opinion that the
accommodation muscle can contract far more strongly than is necessary
to obtain a maximal accommodation.
Fucus expresses this in the following way: the accommodation-
muscle can first contract so far that the lens can follow its elasticity
completely, resulting in a maximal accommodation; the eye is then
focussed on a point, which is determined by a physical property,
viz. the elasticity of the lens. Fucas therefore calls this point the
“physical near point”. Now he muscles can contract considerably
more, so that the Zonula hangs entirely relaxed and the lens could
if only its elasticity were unlimited, increase its refraction considerably,
allowing the eye to foeus on a point, lying still closer by, and
50*
764
determined by a physiological property, viz. the power of con-
traction of its accommodation-muscle: the physiologic near point.
Hess says that it is almost generally assumed that every increase
in lens-fraction of one dioptrie exacts an equal increase of the
contraction of the ciliary muscle.
Although this simple relation is not self-evident, considering the
complicatedness of the accommodation-process, we will accept it for
a moment, in order to try and prove it, taking as unit of contraction
of the ciliary musele, the contraction necessary to bring the accom-
modation from 0 to | dioptrie, which unit we can call ,,myodioptrie”’.
If Hess’ unproved supposition is correct, one will need a contraction
of 10 myodioptries in order to be able to accommodate 10 dioptries.
We can now also express the total power of the acecommodation-
muscle in myodioptries, for in an emmetropie person this will be
the reciprocal value of the distance of the physiological near point,
or otherwise expressed, it will be equal to the number of dioptries
one could accommodate if the lens had an unlimited elasticity.
So we stand here before the following two questions:
6. Is the myodioptrie for one person a fixed unit? Thatis to say:
is a contraction of the accommodation-muscle of one myodioptrie
necessary for every accommodation-increase of one dioptrie?
c. How great is the power of the accommodation muscle expressed
in myodioptries ?
Other questions which rise before us are the following:
d. Is it possible to detect the very slightest paresis of the
accommodation muscle?
e. Is it possible to make curves of the paralysing influence certain
substances exert on the accommodation muscle?
Up to now we were accustomed to determine the action of the
accommodation-muscle by finding the nearest point.
Let us now suppose a person (fig. 1) who can accommodate 10
dioptries, and who possesses a power of the ciliary muscle amounting
to 24 myodioptries, then the accommodationmuscle can be more
than half paralysed, while the nearest point need not have changed
its place. In this way we only notice the possible presence of a
paralysis of the accommodation muscle, when it is far advanced.
In consequence we know little about the paralysing action of
certain substances which only slightly affect the accommodation
musele, even about those substances which we use daily, such as
cocaine. We find the most divergent communications in the literature
about the paralytic action of cocaine on accommodation.
Some writers assert that it does not act at all on the accommo-
765
dationmusele, others say that it acts very strongly, and a third
group states that it does work, but only slightly.
Abscis vom hebphysiclogiedh maasbe pam
%
4
40
18
16
14
42
Vig. 1.
Abscis van het physiologisch naaste punt = Abscis of the physiologic near point.
Latent ciliairspiercontractie-gebied = Area of latent ciliary muscle contraction.
Convergentielijn van Donders - Donders’ convergencelire.
Abscis van het physisch naaste punt = Abscis of the physical near point.
Manifest ciliairspiercontractiegebied of = Area of manifest ciliary muscle con-
accommodatiegebied traction.
Dr. Frrerinca and | have tried to solve the foregoing questions
by a minute study of the relative accommodation.
By relative accommodation we understand the accommodation at
a certain given degree of convergence. A certain connection, probably
congenital, exists between accommodation and convergence; if a
normal emmetropic person wishes to fix his eyes on an object, he
must converge as many metreangles as he accommodates dioptries.
If, in Fig. 1, we plot out the myodioptries and dioptries on the
ordinate, and the metreangles on the abscis, then we can draw a
line through all the points for which accommodation and conver-
gency are alike; if, in our scheme, we take the linear measure for
766
metre angle and dioptrie the same, then this line divides the right
angle between ordinate and abscis exactly in two equal parts. This
line, which unites all the points denoting an equal number of
metreangles for convergence as dioptries for accommodation, is
called: ‘““Donpers’ Convergence-line’’.
If the relation between accommodation and convergence was
absolute and unfringible, then a normal person would only be able
to see the points of the convergence-line sharp and single at the
same time, and no other points; every person with an abnormal
refraction or a heterophoria would not be able to see one single
point sharp and single at the same time.
Luckily the connection between accommodation and convergence
is more or less a loose one, so that at every convergence the
acommodation can, to a certain degree, be made stronger or slighter
than coincides with the degree of convergence.
If one converges 6 metreangles, then an accommodation of 6
dioptries coincides with this, an accommodation, which one can raise f.i.
to 8 dioptries, or decrease to 3 dioptries. This interval between 3 and
8 dioptries is called the relative accommodation for a convergence
of 6 metreangles; the interval from 6 to 8 dioptries is called the
positive, from 6 to 3 dioptries the negative relative amplitude of
accommodation.
The relative amplitude of accommodation differs a great deal in
each individual case and can be increased to a certain degree by
long practice. It is not necessary that the negative and positive part
of the relative accommodation are alike.
One can determine the relative accommodation for all points in
the area of manifest contraction of the ciliary muscle and connect
the relative near and far points to get the lines of the relative near
and for points.
According to Hess the relative accommodation is the same at
every convergence, so that for every normal person the lines of the
relative near and relative far points run parallel to Donprrs’ Con-
vergence-line. (See fig. 1: pq and R.S.)
Huss is of opinion that one can continue these lines in the area
of latent ciliary muscle contraction, but could not prove this, as no
measuring could be done in the ‘latent’ area.
The next question therefore is:
f. How do the lines of the relative near and far points run in
the area of latent ciliary muscle contraction ?
Our reasoning is as follows: if the supposed individual of fig. 1
converges 6 metreangles, the unparalysed ciliary muscle can contract
767
through the stimulus of this convergence, and with the utmost
exertion, 8 myodioptries, and can therefore accommodate at M; if
however, the muscle is paralysed in the slightest degree, it will
contract less strongly through this same stimulus, e.g. only 74
myodioptries, and will therefore accommodate at H.
By determining the relative accommodatiou, we can therefore
detect the slightest paralysis of the muscle in an individual of whom
the accommodation-figure is known (question d).
To see if the myodioptrie is a constant value, we paralyse the
muscle to a certain degree, for instance so that on converging 6
metreangles, accommodation is only possible as far as Q; the muscle
then has an action of 7 instead of 8 myodioptries; if all myodiop-
tries are of equal value, then the muscle only possesses 7/8 of its
power and is for 1/8th paralysed. We control this by measuring
the relative accommodation and determining the degree of paralysis
for the same paralysis and other convergencies too.
If one constantly finds the same degree of paralysis, so that on
converging 4 metreangles an accommodation only takes place up
to gy = 95} myodioptries, instead of 6; and on converging 3 metre-
angles, there is only an accommodation to U = 3% myodioptries
instead of 4; then the paralysis appears to be constantly 1/8. One
can control this with as many degrees of paralysis and convergen-
cies as one wishes, so that question 6, whether the myodioptrie is
a constant value in one particular person, can be definitely solved.
To determine the course of the lines of the relative near and far
points in the latent area, one paralyses the accommodationmuscle
to a certain degree, say the half, so that one finds by convergence of
two metreangles (in fig. 1) a greatest accommodation of 2 D., instead
of 4 D.; 3 D. instead of 6 D., on converging 4 m.a.; and 5 D.,
instead of 10 D., with a convergence of 8 m.d.; if, now, on
converging 12 metreangles a greatest accommodation of 7 D. is
reached (to Y in fig. 1), then one may say that the half-paralysed
muscle contracts 7 myodioptries with this stimulus; the normal
muscle would therefore have reacted with 2 » 7 = 14 myodioptries,
so that the relative near point with a convergence of 12 metreangles
would lie at W., on the ordinate of 12 and the abscis of 14.
If, with a convergence of 14 metreangles, one finds a greatest
accommodation of 8 D., (to X in fig. 1), then the healthy muscle
would be able to contract 16 myodioptries, in answer to this stimulus,
thus fixing the point Z on the abseis of 16 and the ordinate of 14.
If with a convergence of 18 metreangles one finds an accommoda-
tion of 10 dioptries, then point j on the abscis of 20 myodioptries is
768
determined. In this manner one can determine in the latent area
as many points of the line of relative near points as one wishes,
with different convergencies and different degrees of paralysis, and
so plot out the entire line.
The course of the line of relative far points in the area of latent
ciliary muscle contraction, is determined in the same manner, so
that question f. is solved.
We determine the strength of the accommodation muscle in the
following manner :
When the area of relative accommodation has been completely
ascertained, the muscle is paralysed. Supposing that in the individual
of fig. 1, the accommodation muscle is paralysed for '/,"> part;
the absolute near point is now determined; if this still lies at a
distance of 10 em, then one can say that */, of the muscle-power
produces a contraction of at least 10 myodioptries, the total muscle
power is therefore at least 4/3 > 10 = 13 1/3 myodioptries.
If the paralysis is 1/3 while the accommodation remains 10 D.,
then firstly one may consider question a. as answered; for a partially
paralysed muscle can evidently give the greatest possible accom-
modation, so the strongest possible contraction is not necessary, and
secondly 2/3 of the muscle-power produces a contraction of at least
10 myodioptries, the muscle-power is therefore at least 3/2> 10=15
myodioptries.
If again with a paralysis of } an accommodation of 10 D. is
reached then the power is at least 20 myodioptries. But if, on para-
lysing the muscle for one third of its power, only 8 D. accom-
modation is reached, then the power is 3. 8 = 24 myodioptries.
Control is obtained by further paralysis; if, after paralysing three
quarters of the power, 6 D. accommodation is reached, then the
total power is 4 X 6 = 24 myodioptries; if there is still an accom-
modation of 4 D., after the muscle has been paralysed to */,, then
the power is 6 X 4= 24 myodioptries, etc., so that the result obtained
can be controlled by as many observations as one wishes.
If all the values obtained coincide sufficiently, then one has not
only determined the muscular power, but has also proved that the
myodioptrie has a constant value and that the method must be
correct, otherwise the values could not constantly be found to coincide.
A curve of the paralysing action of q substance can be obtained
by first determining the total power of the muscle in a certain
individual, then dropping the paralysing substance in the eye, and
determining the power again, at regular intervals, the results being
plotted out in a scheme.
769
To this purpose we note (fig. 2) the time in minutes on the abscis,
the muscle-power in myodioptries on the ordinate.
A B Obscu won Dek Jysiologirch naaste umd E
ONNEN Honk As 26.925 So 35 40 45 50.66 60 bk Yo, ZE
Fig. 2.
Abscis van het physiologischenaaste punt = Abscis of the physiologic near point.
Abscis van het physisch naaste punt — Abscis of the physical near point.
Supposing the power, at the beginning of the examination, to be
24 myodioptries, when after 5 minutes there is no sign of paralysis,
then one notes point B on the abscis of 24 and the ordinate of 5;
if, after 10 minutes, the muscle is paralysed for '/,® part, then
the power is still 21 myodioptries, and one has found a point R
on the abscis of 24 and the ordinate of 10. Continuing in this
manner, and continually determining the degree of paralysis of the
muscle, one can find and plot out the entire paralysis-curve A. B.
C. D. E. This examination gives an excellent control of the correctness
of the method; for as soon as the curve surpasses the abscis of the
physical near point, we can also directly find the degree of paralysis
by determining the absolute near point. The part C.D. of the curve
can therefore be ascertained in two entirely different ways.
If these two give entirely the same result, or if they agree
770
sufficiently (taking into consideration the possible errors of the method)
then we may look upon this as a proof of the correctness of the
method.
We have determined the “accommodation-figures” for a couple
of persons, aged respectively 31 ‘and 24 years, and have examined
the paralysing action of cocaine and homatropine on the ciliary
muscle.
One sees from our curves that the result is such that we feel
justified in concluding that the method is good. In one patient we
found a power of the ciliary muscle amounting to about 24 myo-
dioptries; in the other 20 myodioptries.
It appeared that total contraction of the ciliary muscle is not
necessary to obtain the greatest possible accommodation; that the
myodioptrie has a constant value for each of these two persons,
that tbe lines of the relative near and far points in the area of
latent ciliary musele contraction, run parallel to each other and to
the convergence line of Dorpers, and that it is possible in persons
whose “accommodation-figures’” are known, to detect even the
slightest decrease in power of the ciliary muscle.
Cocaine has on the accommodation-muscle a cumulative paralysing
action, which shows considerable individual difference; it is there-
fore not at all surprising that one comes across such different reports
of its action in the literature; as the possibility of detecting this
action was dependent on:
the number of times cocaine is dropped in the eyes; the age of
the observer; individual peculiarities; the duration of the observations
and from the intervals between the observations.
One can draw still more conclusions from the results obtained,
with regard to the influence of heterophoria, condition of refraction,
ete. on the “accommodation-figures”, and of the influence, which
feebleness of the ciliarymuscle has on the power to do our work
at short distance.
My only object at present, however, was to draw attention to
the fact that the method of examining the relative accommodation
enables us to widen our insight into the accommodation, and makes
it possible to examine the influence of different substances on the
accommodation muscle.
It is a pity that the method itself is so diffieult to master, that
it will never become a method for clinical examination in the hands
of many, but will have to be limited to the laboratory work of a few.
Physiology. — “On the Influence of the vagi on the frequency of
the action currents of the Diaphragm during its respiratory
Movements.” ') By Dr. J. G. Dusser pr BARENNE and Dr. J. B.
ZWAARDEMAKER. (Communicated by Prof. H. ZWAARDEMAKER.)
(Communicated at the meeting of September 29, 1923).
In a previous paper one of us*) was able to show that the
frequency of the action currents of the striped muscles, as they occur
in the cerebrate rigidity of the cat and in the voluntary contraction
in man, undergoes a distinct diminution after elimination of the
proprioceptive impulses, originating in the muscles during their con-
traction. The elimination of these proprioceptive impulses was pro-
duced by section of the posterior roots in the animal and by local
intramuscular injection of novocain in the human individual.
We then investigated if this experimental fact could also be
established in other innervations and first of all in the diaphragm.
We will not dwell here on this investigation which gave us similar
results for this muscle as in the researches mentioned above. But
in the course of these investigations on the frequency of the action
currents of the diaphragm, we got results which gave rise to the
supposition that perhaps the vagi might have an influence on the
action currents of this muscle during its respiratory contractions.
We, therefore, had to investigate this problem separately and
propose to deal in this paper with the obtained results. The question
to be answered, was therefore the following: Which is the frequency
of the action currents of the diaphragm during its respiratory con-
tractions before and after elimination of both vagi.
At first we made use of the cat: later on, when we had already
obtained a definite answer to our question, we did another set of
experiments on the rabbit and could show that also in this animal
1) A preliminary communication of this paper was made at the Xlth Inter-
national Physiological-Congress at Edinburgh, 25th July 1923.
3) J. G. Dusser pe BARENNE, Untersuchungen über die Aktionströme der quer-
gestreiften Muskulatur bei der Enthirnungsstarre der Katze und der Willkürinner-
vation des Menschen. Skandin. Arch. f. Physiol., 1923, Vol. XLIII, (Festschrift für
R. Tigerstept), S. 107.
772
he vagi have the same influence on the action currents of the dia-
phragm, as found in the cat, this influence in the rabbit being even
much more distinct than in the cat.
Anaesthesia of the animal by subcutaneous injection of urethane (ca. | gr. pro
KG. of body-weight). By means of artificial heating we tried to keep the body
temperature of the animal as constant as possible. Incision of the abdominal wall
in the linea alba, of about 3 em, beginning directly caudally of the ensiform
cartilage. This processus was kept in upright position by fixing it with a forceps
to a support, which was isolated electrically from the table on which the animal
was lying. Then we isolated as carefully as possible one of the anterior slips
of the diaphragm and put a small piece of celluloid under it, so as to insulate
this part of the muscle as well as we could from the other parts of the diaphragm
and its surroundings. In this slip were hooked two very small hooks at a distance
from each other of about 1—1,5 cm, which served as electrodes, through which
the action currents of the muscle were lead off to the string galvanometer (large
pattern of EpELMANN). In our earlier experiments these hooks were of copper and
therefore polarisable electrodes, in our later experiments we made use of similar
shaped silver hooks, galvanoplastically coated with a layer of silver chloride; these
electrodes were non-polarisable. As was to be expected we could not find that the
use of these different electrodes gave rise to any appreciable difference in our
curves, because it cannot be expected that the polarization of the copper hooks
has a distinct influence on the weak, frequent and alternating action currents of
the muscle. The hooks were connected with very thin copper wires to the thicker
wires leading to the galvanometer, so that the movements of the muscle could be
followed quite freely by the electrodes and connecting wires. By closing the opening
in the abdominal wall with a pad of dry cottonwool loss of heat of the muscle
and other disturbing influences were prevented.
The respiratory movements of the diaphragm were reproduced on a kymograph
with blackened paper and underneath these tracings we marked electromagnetically
during which part of the pneumogram the action currents were registered. The
table with the animal was carefully insulated by putting it on large blocks of
paraffine.
After these preliminaries we first took the action currents of the diaphragm
during normal inspiration, i.e. before the elimination of the vagi. Then both these
nerves were carefully prepared at the neck and eliminated without excitation,
either through local anaesthesia with ether vapour or through local application
on the nerves of a 1%, solution of novocain. When the elimination of the vagi
established itself by a change of the respiratory movements of the animal, we
again registered the action currents of the insulated anterior slip of the diaphragm.
We might draw attention to the fact that by a special devise it was possible to
take our electrophysiological records in every desired phase of the respiratory
contraction of the muscle.
In all our experiments in which the elimination of both vagi is
followed by a distinct change of the mechanical type of respiration,
we could establish the fact that the elimination of the nervous
impulses gives rise to a distinct augmentation of the frequency of the
773
action currents of the diaphragm during its inspiratory contractions.
Only in those few cases, already known to RoseNrHaL, in which
the respiratory movements remain nearly unaltered, could we find
but a small augmentation. But even in these experiments an aug-
mentation of the frequency was to be seen, though slight. Until now
we have not yet met with an experimental result, pointing in an
opposite direction, i.e. a diminution of the frequency of the action
currents of the diaphragm after elimination of the vagi.
First of all we will give some curves as evidence of our statement.
fig. la
fig. 1b
Cat. Experiment of the 27th Febr. 1923. Fig. la action
currents of the diaphragm before, fig. 1b after elimina-
tion of the vagi. Time ().1 sec. On the original photo-
graphs in la 56, in 1b 65 action currents could be
counted during the marked 05”. So the frequency was
112 before, and 180 per sec. afler the elimination of the
vagi. (The date in these figures is wrong.)
fig. 2b
Cat. Experiment of the 19th Dec. 1922. As
foregoing figure. Frequency in 2a 98 per sec.,
in 2b 120 per sec.
774
Figures la and 15 show, although unfortunately not quite so distinet
as the original photographs, that the frequency of the action currents
before and after elimination of the vagi is 112 resp. 130 per second.
In fig. 2a and 26 these numbers are 98 and 120 respective.
The results of our 8 experiments on the cat in the order in
which they were performed, are given below in the table. In ex-
periment IV only a slight augmentation of the frequency was found;
in this animal the change of the pneumogram of the diaphragm
after the anaesthesia of the vagi was not very distinct.
TABLE
of the frequency of the action currents of the diaphragm in the cat.
| Before After
Number
of ex eriment
= 0/, augmentation.
| the elimination of the nervi vagi.
|
]
|
I. 98 120 22.45
IL 118 130 | 10.17
Il. 102 | 17 | 14.7
a | ‘| no distinct change in
F 95 | 101 |; the pneumogram of the
| | diaphragm
V. 118 130 10.17
VI. 112 | 130 | 16.07
VIL. 113 | 132 | 16.81
VII. 119 | 133 11.76
On the rabbit 6 experiments were made: in all of which an
augmentation of the frequency of the action currents after elimina-
tion of the vagi was also found, for the most part still more
evident than in the cat. In one of the rabbits this augmentation was
even 40 °/,.
We will now try to answer the question, how one has to look
at this experimental fact.
As is already long known the effect of double vagotomia, either
by cutting or by local anaesthesia of the nerves, is that the respira-
tory movements become less frequent and are increased in amplitude.
We will for the present confine ourselves to this last point. The
muscles which perform inspiration and in the first place the most
important, the diaphragm, contract more vigorously, after the elimin-
775
ation of the vagi. One might consider the most plausible explana-
tion of our experimental fact to be the following, viz.: that this
stronger contraction of the muscle might show itself in an augment-
ation of the frequency of its action currents. This explanation how-
ever is not consistent. First of all we know the fact already ascert-
ained by Piper, that the frequency of the action currents in
voluntary contraction of human muscles remains unaltered under
various strengths of contraction, a fact which one of us (D. pr B.)
lately confirmed. But it might be argued, that this fact, though it
may be true with regard to voluntary contraction of the human
muscle, might not apply to the diaphragm of the rabbit. We, there-
fore, tried to get direct experimental evidence on this point by in-
ducing a deepening of the inspiratory movements with other methods,
fi by letting the animal breath an atmosphere rich in CO, or by
closing the trachea during a few seconds. It was found that the
deepening of the inspiration which follows these procedures is „oi
accompanied by an augmentation of the frequency of the action
currents of the diaphragm. We could establish this in many experi-
ments; only in one of them we found that after breathing a CO,-
atmosphere there was also an augmentation of the frequency of the
action currents. In this experiment we had already performed a
local ether anaesthesia of both vagi; it might be possible that the
nerves were still functionally slightly damaged ; anyhow in all our
other experiments, in which the increase of inspiration through CO,-
breathing preceded the vagotomia, we never found an augmentation
by CO,
Only one objection must still be taken into account.
One of the other results of the elimination of the vagi is an
acceleration of the heart. In our experiments, in which the anterior
slip of the diaphragm was not detached from the ensiform cartilage
for the sake of leaving the muscle in as normal a condition as
possible, we generally also found in our curves of the action currents
traces of the electrocardiograms of the animal, especially in the cat,
where the insulation of the anterior slip of the diaphragm is much
more difficult than in the rabbit. These electrocardiograms present
themselves under these circumstances as simple, diphasic action
currents, which look very much like the action currents of the
diaphragm itself and often cannot be distinguished from them. So,
when one counts all the peaks during 0.5 a second, as we always
did, a few of these electrocardiograms are always included. The
objection might now be made that after the vagotomia through the
acceleration of the heart, the number of electrocardiograms is aug-
776
mented, and that this increase in the number of the electrocardiograms
might be responsible for the augmentation of the action currents
of the diaphragm.
A simple calculation however overthrows this objection. Let us
assume that the frequency of the heart in the cat (the same reasoning
with somewhat other numbers holds true also for the rabbit) is
about 180 per minute'), then there will be present in the curve
180
60
2 electrocardiograms. Supposing that after the elimination of the
vagi the heart accelerates from 180 to fi. 240 or even 360 beats
per minute, an acceleration of 100°/,, which will only be seldom,
if ever, present, then we can expect to find in our curves over
360
60 = 3 electrocardiograms, i.e. an apparent
over a length of 0.5 a second, mostly 0.5 = 1.5 and at most
0.5 a second 0.5
augmentation of mostly 1 or at utmost 1.5 per 0.5 second. So this
would give an apparent augmentation of the frequency of the action
currents of the diaphragm of 2 or 3 per second. From this reasoning
it is clear that even with these numbers, which we took as un-
favourably as possible, this factor, which undoubtedly exists, cannot
explain the augmentation present in our experiments. :
We tbink it therefore permissible to conclude that for the greatest
part, the augmentation of the frequency of the action currents of
the diaphragm after elimination of both vagi is due to the elemination
of the centripetal impulses, which normally travel along the vagi to
the central nervous system and obviously exert an inhibitory influence
“on the respiratory movements, at least in the cat and the rabbit.
Since the researches of Herinc and Breuer it is wellknown that
centripetal vagal impulses have an important influence on the respirat-
ory movements, especially on the inspiration. The fact shown by
our experiments gives clear and, as far as we know, until now
unknown evidence of this influence.
September 1923. Physiological Laboratory of the
University of Utrecht.
1) This assumed number is on the high side; for a smaller number our reasoning
becomes yet more conclusive.
Géologie. — ‘Description de Raniniens nouveaux des terrains
tertiaires de Borneo’, par V. vaN STRAELEN.
(Présenté par M. le Prof. G. A. F. Movenanaarr à la séance du 24 novembre 1923).
Les Raniniens décrits ci-dessus ont été recueillis par M. J. A. Lonr’),
au cours d'une exploration effectuée dans la vallée de la rivière
Toehoep, affluent de rive gauche du fleuve Barito, au S.E. de l’île
Borneo. Ils font actuellement partie des collections du Musée géolo-
gique de la “Technische Hoogeschool” a Delft. M. le Professeur G. A. F.
MoreneraarrF, directeur de ce Musée, a bien voulu attirer mon
atiention sur ces matériaux et me les confier pour étude.
Famille: Raninidae Dana 1852.
1. — Genre: Ranina Lamarck 1818.
Sous Genre: Hela Minster 1840.
Ranina (Hela) Molengraaffi nov. sp.
(Fig. la et 6).
Af
oe
pee
Fig la. Fig. 10.
Ranina (Hela) Molengraaffi nov. sp. — Grandeur naturelle.
la. Face dorsale. — 15. Face latérale droite. — R. Rostre.
Cette espèce est connue par les restes d’un seul individu, se
présentant par la face tergale. Le céphalothorax dont la longueur
dépasse la largeur d’environ '/,, s’élargit de l'arrière vers l'avant.
Sa largeur mesurée au niveau de l’insertion des deux dents marginales
et celle mesurée au bord postérieur, sont dans le rapport de 3 a2.
Le céphalothorax est bombé, la courbure s’accentuant dans la région
médiane, au point de constituer une créte surbaissée. La région
frontale s'incurve vers le haut, de sorte qu'elle semble précédée par
1) J. A. Lor, Mededeelingen over de Geologie der Doesoen-landen. Verhande-
lingen van het Geologisch en Mijnbouwkundig Genootschap voor Nederland en
Koloniën, Vergaderingen, N°. 45, 1914, pp. 174 —175.
51
Proceedings Royal Acad. Amsterdam. Vol. XXVI.
778
une faible dépression. Une autre dépression plus forte que la précé-
dente, existe dans la région médiane du céphalothorax, au tiers
postérieur. La région cardiaque est indiquée par une paire de sillons
en are de cercle, à concavité ouverte vers les bords latéraux.
Le bord frontal sensiblement rectiligne est occupé par un rostre
triangulaire, large et long, bordé par des échancrures oculaires limi-
tées chacune latéralement par un lobe triangulaire a base très large.
Au dela de ces lobes, se trouvent deux petites épines et enfin une
forte dent effilée et incurvée extérieurement, constituant le ‘prolon-
gement des bords latéraux. Ceux-ci sont un peu incurvés et a angle
droit avec le bord postérieur. Ce dernier est à peu près rectiligne
et bordé par un étroit sillon.
Le test paraissant lisse, est garni de fines granulations, légerement
acuminées, disposées sans ordre apparent.
La face sternale n’est pas connue.
L’attribution au genre Ranma pourrait être contestée, en se basant
sur la petite taille, la simplicité du bord frontal et surtout le carac-
tére de l’ornementation, fine au point que le test parait lisse. A
première vue, A. Molengraaffi se rapprocherait plutôt du genre
Notopus Du Haan, par la forme et l’ornementation du céphalothorax.
Cependant, il lui manque entre autres caractères de Notopus, la
crête épineuse située en arrière du bord frontal et unissant les deux
dents latérales. Les autres genres de Raniniens a test lisse, dont ils
constituent le groupe le plus nombreux, sont:
Raninoides H. Muunr-Epwarps Holocene,
Lyreidus De Haan, Oligocène-Holocène,
Notopoides Sp. Bare, Mioeène et Holocène,
Cosmonotus ApaMs et Waits, Holocène,
Notosceles Bourne, Holocene,
Raninella A. Minne Epwarps, Cénomanien-Sénonien,
Raninellopsis J. Boenm, Miocene,
Notopocorystes Mac’ Coy, Cénomanien,
Eucorystes Brit, Albien-Cénomanien,
Palaeocorystes Brrr, Albien-Cénomanien,
Hemioon Breur, Cénomanien,
et n'entrent pas en ligne de compte, a cause de la forme générale du
céphalothorax et des caractéres du bord frontal. Par le contour de
son céphalothorax, Notopus est très voisin de Ranina.
179
M. R. Fasrani') a distingué deux sous-genres dans Ranina, établis
sur le caractère de l’ornementation. Le sous-genre Lophoranina
réunit toutes les especes dont le test est orné de côtes transversales
épineuses et flexueuses, le sous-genre Hteroranina groupe les formes
dont le test est soit a peu priès lisse, soit orné de petits granules
ou de petits tubercules acuminés, disposés en rangées et quelquefois
sans ordre apparent. C'est pour des espêces appartenant a ce dernier
groupe que G. zu Ménsrer*) avait créé le genre Hela, dont le type
Hela speciosa Minster provient du Chattien de Bünde. Je considére
Hela comme synonyme de Eteroranina sur lequel il a la priorité.
Les Ranina déerites jusqu'à ce jour et qui se rapprochent le plus
de celle trouvée a Bornéo, sont:
Ranina Ombonii Fasiani, de |’Yprésien des Colli Berici (Vicentin),
R. notopoides Birtner, du Lutétien du Monte Masua (Véronais), °
Rk. budapestinensis Loxvrentury, du Bartonien du Kis-Svabhegy
Hongrie),
R. Bouilleana A. Mune-Epwarps, du Tongien de Biarritz (Aquitaine)
et de Monteechio-Maggiore (Venétie),
R. granulosa A. Mirne-Epwarps, de l'Oligocêne des environs de
Dax (Aquitaine),
R. (Hela) oblonga Münster, du Chattien de Bünde (Hesse).
R. Molengraafft se distingue:
de A. Ombonii par son céphalothorax moins long et plus large,
beaucoup plus convexe, son bord frontal coïncidant à peu près avec
la plus grande largeur de l'animal, enfin une ornementation beaucoup
plus fine;
de R. notopoides par son bord frontal et son bord postérieur plus
large, la présence d'une seule paire d’épines latérales, un rostre
plus long et deux épines situées entre les lobes et l'épine latérale;
de A. budapestinensis par une forme beaucoup plus massive, le
bord postérieur plus large, le rostre plus développé, les échancrures
orbitaires plus profondes et les lobes correspondants plus développés,
enfin des épines et des dents plus fortes;
de R. oblonga par son bord frontal plus étendu par rapport au
bord postérieur et moins profondément découpé et une ornementation
plus fine;
de &. granulosa par son bord frontal beaucoup moins découpé
et le bord postérieur plus large.
1) R. FABIANI, Sulle specie di Ranina finora note ed in particolare sulla
Ranina Aldrovandii. Atti dell’ Academia scientifica Veneto-Trentino-lstriana,
ser. 8a, t. 3, 1910, p. 85.
2) G. zu Monster, Beitrdge zur Petrefactenkunde, Heft 3, 1840, p. 24.
51*
780
Parmi toutes les espèces citées, c'est avec B. budapestinensis que
R. Molengraafft a le plus d’affinités.
Type. Musée géologique de la “Technische Hoogeschool” a Delft,
échantillon n° 6 du lot K.A. 6491.
Gisement. Septaria argileux, légérement calcarifère, coloré par
de l’oxyde de fer, d'âge miocène d'après la carte de M. G. L. L.
KEMMERLING. *)
Localité. Vallée de la rivière Toehoep, entre l'embouchure de son
affluent Bangkelan et Kampong Brawai (Borneo).
Je dédie cette espèce a M. G. A. F. Morenaraarr, Professeur a
la “Technische Hoogeschool” de Delft.
2. — Genre: Raninella A. Mine Epwarps 1862.
Raninella Toehoepae nov. sp.
(Fig. 2a et b et c).
ETE
Fig. 2a. Fig. 20.
Raninella Toehoepae nov. sp.
Qa. Face dorsale, grandeur naturelle. — 2b. Face latérale droite,
grandeur naturelle. — 2c. Plastron sternal, X 2. A, B, C.
Sternites. D. Episternum. — &. Rostre.
Le céphalothorax est fortement bombé, s'élargissant considérablement
vers l’avant, la plus grande largeur se trouvant a peu près a
hauteur des sillons cardiaques et correspondant au double de la largeur
du bord postérieur. Le bord frontal est faiblement convexe, porte
un rostre droit à son origine et se terminant en une pointe triangu-
laire. De part et d'autre du rostre, le bord frontal présente des
1) G. L. L. KeMmMerLing, Geologisch-Topografische Schetskaart van het Stroom-
gebied der Barito (Borneo). Tijdschrift van het Koninklijk Nederlandsch Aardrijks:
kundig Genootschap, 2de ser, Deel 32 (1915), kaart NO. 6.
781
échanerures limitées par deux faibles épines, au dela desquelles se
trouve une forte dent. Une dent marginale plus robuste encore, est
insérée un peu au dessus de linflexion du bord latéral. Le bord
postérieur est a peu près rectiligne, les bords latéraux sont convexes
dans la région antérieure, mais rectilignes dans la région postérieure.
Le bord postérieur et les bords latéraux postérieurs présentent un
sillon marginal limitant une faible carène latérale.
La région cardiaque est marqnée par deux sillons cardiaques,
ayant a peu pres la forme d’arcs de cercle a concavité ouverte
vers les bords latéranx, surmontés chacun d'une paire de petits
sillons parallèles.
Le plastron sternal est trés large tout au moins dans ses parties
antérieures. Le premier sternite placé entre la premiere paire de
thoracopodes, est fort large et présente les deux entailles latérales et
circulaires habituelles. [| se termine en avant par un épisternum
arrondi. Le deuxième sternite est un peu moins large que le
précédent, se rétrécissant vers l'arrière et pourvu d’un profond sillon
médian. Le troisième sternite est étroit.
Le pléon se recourbe sous la face sternale. Sa largeur à l'origine
est égale a celle du bord postérieur du céphalothorax. Ce qui reste
des thoracopodes est trop fragmentaire pour permetire une descrip-
tion. L’ornementation du test est constituée par des granules extré-
mement fins.
Le genre Raninella est un genre essentiellement crétacé. On en
connait actuellement les espèces suivantes:
__Raninella Trigeri A. Mine-Epwarps, du Cénomanien du Mans (Sarthe),
R. elongata A. Mune-Epwarps, du Cénomanien du Mans (Sarthe),
R. Schloenbachi Scurtirer, du Sénonien (Emsien) de Wöltingerode
(Saxe) '),
R. baltica SrerrBrre, du Danien de Faxe et d’ Annetorp (Danemarck).
R. Toehoepae se distingue nettement des trois premieres espèces
citées, par la forme plus ovalaire de son bord frontal. Elle se rap-
proche de R. baltica dont le céphalothorax est également ovalaire,.
mais elle s'en distingue: 1° par son bord postérieur plus étroit, 2°
son élargissement antérieur proportionellement plus considérable et
reporté d’avantage vers l’arriére de l'animal.
1) R. SCHLOENBACHI est une espéce imparfaitement connue, basée sur un individu
chez lequel la région frontale est en partie détruite et dont on ne connait que le
moule interne des régions postérieures. Je la maintiens provisoirement dans le
genre Raninella.
782
Jusqu’a présent le genre Raninella n'a été rencontré que dans le
Crétacé moyen et supérieur. U présente parmi les Raninidae un
certain nombre de caractéres que je considére comme primitifs:
grande dimension du deuxiéme sternite et rétrécissement relativement
faible des sternites postérieurs et du pléon. Il rappelle ainsi les
genres Palaeocorystes Bri. et Notopocorystes M’Coy du Gault du
Kent, que je rattache aux Raninidae *).
Type. Musée géologique de la “Technische Hoogeschool” a Delft,
échantillon K.A. 6504.
Cotypes. K.A. 6491, 6497, 6504, 6505, 6517, 6522.
Gisement. Septaria argileux, légerement calcarifères, colorés par
oxyde de fer, d’age miocene d'après la carte de M. G. L. L.
KEMMERLING°).
Localités. Vallée de la rivière Toehoep, entre l'embouchure de
son affluent Bangkelan et Kampong Brawai (Borneo).
Le nom spécifique est tiré de celui de la rivière Toehoep, affluent
de gauche du Haut-Barito.
Les stratigraphes qui ont étudié les couches dans lesquelles la
rivière Toehoep a creusé sa vallée, ne semblent pas d'accord sur
leur âge. M. G. L. L. Kemmertine*) les rapporte au Miocene, M.
J. A. Lour*) hésite entre un âge anté — et post — éogène. Les deux
Crustacés décapodes qui viennent d'être déerits ne permettent pas
de trancher ce differend.
Qiil soit cependant permis d’attirer l'attention sur le fait que
Ranina Molengraaffi, forme lisse a bord frontal peu découpé et
s'élargissant peu vers l’avant, a un cachet archaique la rapprochant
de ses congénères dont l'âge éogène et même crétacé n'est pas dou-
teux. Quant a Raninella Toehoepae, elle appartient a un genre méso-
et supracrétacé et présente d’ailleurs également des caracteres pri-
mitifs accentués.
1) V. vAN STRAELEN, Note sur la position systematique de quelques Crustacés
décapodes de Vepoque crétacée. Bulletins de l'Académie royale de Belgique, Classe
des sciences, 1923, pp. 116—125, 6 fig.
2) G. L. L. KemmerLinG, Geologisch-Topografische schetskaart etc., loc. cit.
3) G. L. L. KeMMERLING, Topografische en Geologische Beschrijving van het
Stroomgebied van de Barito, in hoofdzaak wat de Doesoenlanden betreft. Tijd-
schrift van het Koninklijk Nederlandsch Aardrijkskundig Genootschap, 2de ser.,
Deel 32, 1915, pp. 575—641 et pp. 717—774.
4) J. A. Loup, loe. cit.
Mathematik. — “Ueber die zu einem Punkte und einer Geraden
gehörigen Polarkurven inbezug auf eine gegebene algebraische
Kurve” Von F. Körmer in Baden-Baden.
(Mitgeteilt von Prof. JAN pE Vries in der Sitzung vom 24 November 1923).
1. Die Aufgabe. Wird eine algebraische Kurve n-ter Ordnung durch
eine Gerade in den n Punkten &,, R,,.. R, geschnitten, so ist nach
Jonquizres ') der harmonische Mittelpunkt r-ter Ordnung A zu diesen
n Punkten und einem Zentrum O detiniert durch die Gleichung
OG) EE EG) DE
SG) DE EG)
1
wo GE) Binomialkoeffizienten und > =! die Summe der Produkte
k 1 OR; k
der reziproken Abschnitte OR; zu je & bedeutet, 11, 2,...7.
Beschreibt die schneidende Gerade ein Strahlbiischel mit dem
Zentrum Q, wahrend O eine Gerade p durchliuft, so beschreibt der
harmonische Mittelpunkt r-ter Ordnung eine algebraische Kurve, die
ich die zu dem Zentrum Q und der Geraden p gehörige Polarkurve
r-ter Stufe inbezug auf die gegebene Grundkurve n-ter Ordnung nenne.
Allgemein lassen sich die Polarkurven auch auffassen als Erzeugnis
des Strahlbiischels Q und des ihm projektiven Büschels der gewöhn-
lichen Polaren der Punkte der Geraden p.
2. Die vorliegende Mitteilung behandelt zunächst den Fall:
Die feste Grundkurve ser em Kegelschnitt.
Hier kommt nur die Polarkurve erster Stufe in Betracht, da die
zweiter Stufe identisch mit der gegebenen Kurve ist.
1) Vgl. Jonquizres. Mémoire sur la théorie des polaires etc. Journal de Liouville.
1857 oder
Cremona. Geometrische Theorie der ebenen Kurven. Deutsche Ausgabe von
Curtze, Greifswald 1865.
784
I. Geometrisches. Es sei f der gegebene Kegelschnitt, P der Pol von
p inbezug auf f, q die Polare von Q und y die Polare des Schnitt-
punktes Y von p und q.
Um auf einem Strahle « von Q den gesuchten vierten harmonischen
Punkt zu finden, schneiden wir @ mit p (der Schnittpunkt sei %)
und konstruieren zu die Polare a inbezug auf /, die durch P
geht. Der Sehnittpunkt A von « x a ist dann der gesuchte vierte
harmonische Punkt. Daraus ergibt sich sofort: Jedem Strahl « des
Strahlbüschels Q ist die konjugierte Polare a inbezug auf f durch
den Punkt P zugeordnet, daher sind diese beiden Büschel projektiv
und der gesuchte Ort des vierten harmonischen Punktes ist ein Kegel-
schnitt. Diesen nenne ich den Polarkegelschnitt des Punktes Q und
der Geraden p inbezug auf den gegebenen Kegelschnitt f und bezeichne
ihn mit D.
Aus dem obigen folgt, dass Q und p mit P bezw. q vertauschbar sind.
3. Die ® geht jedenfalls durch die Schnittpunkte C, D von p mit f,
ferner dureh die Sehnittpunkte U, V von gq mit /, durch die Punkte
Q und P und berührt die Geraden Y Q und YP in Q bezw. P.
X Y Z ist das gemeinsame Polardreieck für f und ®. Es ist auch
leicht zu entscheiden, welcher Art der Kegelschnitt @® ist. Soll
namlich ® einen unendlich fernen Punkt Be haben, so miissen die
2 entsprechenden Strahlen 3 und 5 der projektiven Büschel Q und P
parallel sein, somit liegt der vierte harmonische Punkt in der Mitte
der Schnittpunkte von 8 mit f.
Verbindet man diese Mitte mit M, so erhält man einen Strahl,
der zu 2 konjugierte Polare ist. Konstruiert man also zu allen
Strablen 8 von Q die konjugierten Polaren durch J/, so erhält man
wieder ein zu dem Büschel Q projektives Büschel M und das
Erzeugnis dieser zwei projektiven Büschel ist wieder ein C, =2,, der
alle Sehnen in f, die durch Q gehen, halbiert. Schneidet man 2, mit p,
so geben die Verbindungsgeraden dieser Schnittpunkte mit Q die
Richtungen der Asymptoten von ® an. Je nachdem also 4, die
Gerade p in 2 Punkten schneidet, oder beriihrt oder gar nicht trift,
ist D eine Hyperbel, oder Parabel oder Ellipse. 2, geht durch
M,Q, U, V. Es gibt noch einen zweiten solchen entscheidenden
Kegelschnitt 2,, der durch M, P, C und D geht und analog wie 4,
konstruiert wird. Dessen Schnitt mit g gibt dann die Entscheidung.
2, und 4, bleiben dieselben, wenn Q bezw. P erhalten bleibt,
während p bezw. q sich ändert. Für alle möglichen Lagen von p
bilden die 2, ein Netz von C, durch die Punkte Q, V, U; ent-
sprechendes gilt für A,
Auch der vierte Schnittpunt O von 4, mit @ ist leicht anzugeben :
785
Man verbinde MM mit P und schneide MP mit 4,, der Schnittpunkt
ist der gesuchte Punkt O. Denn PM und p sind konjugierte Rich-
tungen inbezug auf f. Zieht man also QO//p so sind QO und PO
(= MO) entsprechende Strahlen in den projektiven Büscheln Q und
P bezw. Q und M; somit ist der Schnittpunkt von PM und QO
sowohl ein Punkt von 2, als von @. Zieht man ferner QM und
PG//q, so ist der Schnittpunkt dieser 2 Geraden sowohl ein Punkt
von ® als von /,. Entsprechendes gilt für 4,.
Endlich kann man noch den Mittelpunkt M, von ® bestimmen.
Die Verbindungsgerade von Y mit der Mitte von QP geht durch
M,; ebenso die Verbindungsgerade der Mitten der Sehmen CD und
QO und die Verbindungsgerade der Mitten von UV und PC. Auf
den Durchmessern QM, und PM, lassen sich auch die Endpunkte
E bezw. H bestimmen, die Tangenten in AH und ZE sind dann
parallel bezw. zu den Tangenten YQ und YP, so dass YSTR ein
dem @® umschriebenes Parallelogramm ist.
4. Von besonderen Fallen je nach der Lage von Q und p seien
kurz folgende erwähnt;
a. Ist p die unendlich ferne Gerade, so wird P=M, =d,
b. Wenn p den f berübrt, so berührt # den f in P und osku-
liert 4, in diesem Punkte.
c. Wenn p durch M geht, hat ” mindestens einen (reellen)
unendlich fernen Punkt.
d. Wenn p==g, so ist auch P=Q und ® degeneriert in das
von Q an f gehende Tangentenpaar. (Vgl. Analytisches.)
e. Wenn p durch Q geht. so liegt P auf q und ® zerfällt in p
bzw. g. (Gewöhnliche Polare.)
Il. Analytisches.
Bezeichnungen.
5. Es seien:
flesys2) =a,, 2 + 2a,, ey +a, y? + 24,, m2 4 2a,, yz+a,, 2? = 0 (1)
die Gleichung des festen Kegelschnittes 7, ebenso
g(a,y,.z)=b,, 2 + 2b, ay + 6,,y7-+ 2 6,, ez + 26,, y24+6,,27 = 0 (2)
die Gleichung eines zweiten Kegelschnittes g; F (u, v, w) und
G (u, v, w) die adjungierten Formen zu /, bezw. g;
A und B die Determinanten von f, bezw. g: Ai, Bip die Unter-
determinanten von A und B,
Or SA (5)
1,k=1,2 ik—1,3
786
die beiden simultanen Invarianten von f und g,
OF _( 9G
iS sa be) = 25 ain =H (u,v,w)= A, w+ 2H,, uv +
Oaix Ob ik
+ Hv +2H,,w +2 A,, w+ Hw
die simultane Contravariante zu f und g, ferner x,, y,, 2, die
(4)
Koordinaten von Q, «,, Yor z, die von P, u, v,, w‚ die L. K. von
q und u, v,, w, die L.K. von p, sodass
0?
Ue = fe) % = Ss Yo) Me = Ss (2); u, =f; (25), De =f, (7) =f, (2)
und umgekehrt:
NE =S Le (GRIENE
Dabei ist
cl ’ 0 949 0 : U, Us
ie LE ry Gj Me) Pee de
Oy dz
r 0 ae U, > Of}
Gs AW) =e
te L=X9, YFU 220 UE Y=Vo, ——20
Pt OF (u, v, w) Laer OF (u, v, w)
du du U==Ug, V=Up, W=Wy
woraus die übrigen Bezeichnungen sich von selbst ergeben.
Dann ist auch
DS VER SN), Sa AS OD)
und
ze sin B,,a 13 t= Bosc. a EO zin H,,b 13 = TTT Ons = 30
A,,6 11 ze A,,6 13 ir A,,b 13 oF Ha af Ha 13 si H ‚a nn 3H
6. Für einen Punkt R der Polarkurve erster Stufe zu O und p
gilt dann
- (6)
2 1 1
a en 7
OR TOR * OR, (7)
wo O der Schnittpunkt eines Strahles des Büschels Qsmit sh nn
die Schnittpunkte mit f sind. Sind &,%,8 die Koordinaten von O,
so folgt aus Obigem:
2 ZE ia
(a—§) + 4, («,—8&) a (re 8) +4,(¢,—§ | (8)
ae ae
(y—m) + 4, We) ij (y—n) + 4, We)
787
wobei 4,, 4, die Wurzeln der Gleichung
F Eder) FAA) HAY) y +A (2) 2} 4 2?.f (29.2) =9 (9)
sind, und für En,{ die Gleichung besteht:
vEt ontw E=0.
Durch Elimination von 4,§,7,¢ erhält man als Gleichung für die
Polarkurve erster Stufe:
2f(e, of) 2). (u, Bot Va He + w, zo) ay
eg ed 2 (10)
if). e Hf) 4 + Allo). 2h. tao ror + wy =O P(z,y,2)
Unter Anwendung der oben angegebenen Beziehungen zwischen
den uv, und 24,72, kann man der Gleichung noch verschiedene
andere Formen geben, von denen wir gelegentlich am passenden
Ort Gebrauch machen werden. Erwähnt sei nur folgende Form:
PD (x,y, 2) =if (z) a + fy (y)-¥ t if (2) +2}. Wh (a,) «, +f, (y.) Vo +f, (z,) NZ
—{f,(a)e+4i)-9¥ th lz)-2) A(@)e + Gedy SAC Mi}
aus der die Vertauschbarkeit von Q und P besonders evident ist.
7. Zunächst ersieht man, dass die #-Kurve durch den Schnitt
von f mit p geht, und dass sie, wenn Q auf p liegt, in p und q
zerfällt; auch die Vertauschbarkeit von Q und p mit P und q
ergiebt sich mit Riicksicht auf die in (5) gegebenen Beziehungen.
Ist
(iz a2) A WZ Ue ED
das Strahlbüschel Q, so ist das Strahlbüschel der Polaren zu den
Schnittpunkten mit p gegeben durch
th (x) u zy ar es (y) ; = Ug ity sr Wy 2) + he (z) 7 TEA
we aa ao EL (12)
-+ 2. hh (x) © (v, Yo =P We Zo) ijn (4) =U Yo in (2) - Us z,} =0
Durch Elimination von + erhält man wieder ®(z, y,z)—=0O. Aus
der Gleichung für “ lassen sich die Gleichungen für die Kurven
2, und 4, in (2) ableiten. Diese sind nämlich spezielle ®-Kurven,
wenn p, baw. q zur unendlich fernen Geraden wird. Nehmen wir
Cartesische Koordinaten, sodass z= 0 die Gleichung der unendlich
fernen Geraden ist, so haben wir:
À, (2,y,2)=2 f(w,y,2). Mein Hes (z).@, + Te (Y) «Yo za (2). Zoi. 2 == (13)
hey) =2f (@ysz)-2,— woe + voy + Wy 2). 2 =0.
788
Für den Sehnittpunkt O von 4, mit ® haben wir:
Sv hu Caines oC) 9 Op rey cay) eg
und
LIEN re Oad — Wn 2 (Oy ay Orde
letzteres ist die durch Q gehende Parallele zu p. Für die Schnitt-
punkte der beiden Kurven À, und 4, findet man:
a) ze U
b) z,(u,2 + v,y + w, 2) —2,.(u,e + voy Hw, 2) = 0,
d.h. b) geht durch den Mittelpunkt M und den Sehnittpunkt Y von
p und q.
8. Die ®-Kurve lässt sich auch auf folgende andere Arten erzeugen :
Die Gleichung
f@yoze) a? Uw 4 oy Hea, 2)? = On) | sec GX
stellt ein Büschel von C, dar, die f in den Punkten C und D
berühren. Das Büschel der Polaren des Punktes Q in Bezug auf
dieses C,-Biischel ist dann gegeben durch
jk (x,) oat! +7, (44) “Y tty Fi (2,) 2 1
Ue pen peewee ty eye (144)
+ 2A% (uyx+vi,y+tw,z) (1,7, +, y, + w, z,) = 0. :
Durch Elimination von À* ergiebt sich wieder ®; ebenso aus
dem Biischel
fayz+ ur (ue t+ouy+tu,y?=0. . . . (15)
und dem zugehörigen Polarenbüschel fiir P in Bezng auf dieses
Biischel.
Wenn man endlich die beiden Biischel in den Gleichungen (14)
und (15) in Beziehung setzt durch die Relation:
Qau(u,cz, +», y, +, 2,)=1,. ee | ~| (10)
so erhält man durch Elimination von 2,u wiederum @ (x,y, 2)=— 0,
neben einer zweiten, ebenso gebauten Gleichung.
9. Eine wichtige metrische Beziehung für die Punkte der ®-Kurve
ergiebt sich durch folgende Überlegung:
Es seien x, y,2 die rechtwinkligen Koordinaten eines Punktes A,
dann ist die Polare desselben in Bezug auf f= 0:
Fre). Adf We. Y HF, (2). 7 =,
789
wenn X, Y, Z die laufenden Koordinaten sind. Somit ist der Abstand
d, des Punktes A von seiner Polaren:
ah ee A GE)
VAE) + AW) VREE FAW)
Der Abstand des Punktes A von p ist
d
1
ue toy te, 2
i= we
Vu? + Vv
Der Abstand des Panktes Q von der obigen Polaren des Punktes
A ist
5 _ Ji (4). %, ra (y)-Yo + fe (2). Ze
yaar SO
Ve) + f°)
und der Abstand des Punktes Q von p ist
u, vy ite Ve + w, Ze
n=
Vut + v,?
8 Gh WW, : :
Setzt man nun es und bringt nach Weghebung gemeinsamer
Gh We
Faktoren alles auf eine Seite, so erhält man wieder die Gleichung
Due) =O. ‘
Somit ist ® =O der geometrische Ort des Punktes x,y, 2, für den
das Verhdltnis der Abstiünde von seiner Polaren und von einer ge-
gebenen Geraden p gleich ist dem Verhältnis der Abstinde eines
gegebenen Punktes Q von denselben zwei Geraden, absolut genommen.
10. Das dualistische Gegenbild der @&-Kurve erhält man auf
folgende Art: Die Strahlen des Büschels Q schneiden auf p eine
Punktreihe aus, ebenso die des projektiven Büschels der konjugierten
Polaren durch P auf g. Die Verbindungsgeraden der entsprechenden
Punkte dieser zwei projektiven Punktreihen erzeugen einen Kegel-
schnitt Ws; die gemeinsamen Tangenten von f und ¥ sind die
Tangenten von fin C, D, U, V; P hat mit f und @& dasselbe
Polardreieck gemeinsam.
11. Biischel von Grundkurven und zugehörigen Polarkurven.
Die 4 Punkte C, D,U,V bestimmen ein Büschel von C, : kg-—f=0.
Nimmt man für die ®-Kurve eines jeden C, jeweils die in ein
Geradenpaar zerfallenden C, des Büschels als p- und g-Gerade an,
so gehören zu jedem C, des Büschels 3 ®-Kurven, und nmgekehrt.
790
Da diese ebenfalls durch C, D, U, V gehen, so muss @ (a, y, z)
von der Form uw g—/ sein und es muss sich u aus & und dem zu
den zerfallenden Kurven gehörigen Parameter 2 der Gleichung :
C(4) = Bat —304H3Hi—A=0. . … . (17)
bestimmen lassen. Die Beziehung zwischen 4, A, u erhält man auf
folgende Weise. Es ist
@ (kg —f) = 2 (kg —f)- (uy % + re Yo + We 2) —
—(u,2 4+ vy twe). (ur + vy + w, 2) = 0
oder = 2 (kg —f). (uy #, + vv + % %) —
— tlkg, — fi). 2e + hg, — fe) He + (kos — fe) + 2:3 -
woe + oy + w, 2) = 0.
Zur Berechnung von u. TN Yo + w, 2, haben wir:
2, =k. G, (u,) —k. Ho (u) — EU)
=2h*.(B,, u + Bu, +B), wi) —2k-(A,, u, + Hoeve + Hy, es)
+ 2 (Ay, uM, + Ara % + Ais Wo)
und zwei entsprechende Gleichungen für y, und z,.
Zur Elimination von w,,v,,w, und w,,v,,w, vergleicht man. das
Produkt (u,v + v,y + 2,2) . (ux + VY + we) mit 4g —f.
Dadurch findet man:
(wer + LY + Woz) (u, Td Ug HW 2) = 18
=4.(Bk —36k + 3Hk — A). (Ag —f) Co
und
ue + 44, + Wz, = 6 HA —2A—120k2 + 12 Hk + 2Bk'À— 6K (19)
und endlich daraus dann:
A(—k+a)—3 6 .(k+2)4+6 Hi?
"= BECKI) BHD) — OOK oe
oder
en (Bk'u— A) — 3 (Ok? + Hu) + 6 Hk
(BEERS Hu) 66a
(20a)
neben C' (2) = 0.
Setzt man-hierin k = 4, so erhält man u == 2. D.h. nur dann ist
®(b)=f, wenn f und folglich auch ® eine zerfallende C, des
Büschels sind. Geometrisch erhellt dies, wenn man beachtet, dass
die Pole P und Q sich auf den Seiten des dem Biischel gemein-
791
samen Polardreiecks XYZ bewegen. Die Schnittpunkte der Tangenten
in U und V z. B. an f und ® bestimmen auf der Seite XZ des
Polardreiecks zwei coincidente projektive Punktreihen, deren Dop-
pelpunkte eben die Schnittpunkte der zerfallenden Kurven des
Biischels sind. Setzt man den für 2 in (20a) gegebenen Wert in
die Gleichung C(2)=3 ein, so hat man eine Relation zwischen
k und 2.
12. Netz und Biischel von Polarkurven bei fester
Grundkurve f.
Halt man f und p fest, so bildet die Gesamtheit der ®-Kurven
ein Netz mit den Stiitzpunkten P, C, D. Jede solehe C, ist aber nur
Polarkurve für einen Punkt auf ihr, nämlich den Pol für die ge-
meinsame zweite Sehne von f und #. Macht man die Tangenten
von f in C und D bezw. zur X- und Y-Achse und die Berührungs-
sehne CD zur Z-Achse, so wird
F(a ¥, 2) =zy + 27 =O
und
P(x, y, z) = 22, cy —y, Dye =.
Die Gleichung einer C, durch P, C, D hat dann die Form
ary + Ppueze+yyz = O; daraus folgt für den Pol a,:y,:2,=
a: —2B: —2y. Beschreibt nun der Pol eine Gerade
Q (@,, Yor 2) = ue, + vy, + wz, — 0,
WO 2, Y,,2, die laufenden Koordinaten sind, so kann man das
Büschel der zugehörigen @-Kurven in der Form schreiben :
a(ucz —vyz)+2,.(2vey + weze)—9.
Für den vierten Grundpunkt dieses Büschels hat man also:
nt a OEE See ay (418)
und
2) SLO ie ae ios fae el a REN HOP ALI)
woraus folgt
uetoytwe=—d0.
(21) ist die lineare Polare des Schnittpunktes von p mit der
Geraden Q(x, y, z) = 0. Somit liegt der vierte Schnittpunkt auf der
Geraden Q(a, y, 2) =0 und eben dieser Polaren.
13. Beschreibt der Pol Q einen Kegelschnitt:
Q (F514 2) Zeh B + 2e,, wy + 64,4? + 20, #2 He, yz + ¢,,27=0, (22)
792
während /, P und p festbleiben, so erhält man für die Enveloppe
des Büschels der ®-Kurven die Gleichung:
E(&, 7, S)=4 (Opts n° mee 4 Cs. S76 - 3 4 Cn SH Ceca +
Lue wae “a 23
SASS = On Gea si
wo die Cy, die Unterdeterminanten zu den cy sind. Die £ ist also
eine rationale Kurve vierter Ordnung mit den 3 Doppelpunkten *)
in den Punkten P, C, D.
Die Q und Z berühren sich in den 4 Punkten, die gegeben sind
durch die Gleichungen :
CNE ea POT NOROEZ LE
Durch #=2Enz, —SSy, — ns, =O ist jedem Punkte 2,, y,, z,
auf Q ein Punkt &,5,5 auf ZE zugeordnet und umgekehrt. Der
Ubergang von 2,,y,,2, auf QQ geschieht, indem man, wie oben
angegeben, zu £ übergeht und den Berührungspunkt von ® und £
bestimmt. Der Übergang von einem Punkte Ss, 7,5 auf ZE geschieht,
indem man diesen als Pol betrachtet und durch das entsprechende
Verfahren die Enveloppe der zugehörigen ®-Kurven bestimmt, wenn
&,,6 auf E wandert. Diese ist dann eben wieder die Q-Kurve und
die doppeltgezählten Seiten des Dreiecks PCD (abgesehen von dem
auftretenden Faktor 4 der Determinante der ci).
Zu einer anderen Darstellung dieser Berührungstransformation, die
deren Bedeutung erst kennzeichnet, gelangt man durch folgende
Überlegung: Es sei £(&, 1,8) =0 gegeben, dann ist die Gleichung
der Tangente in einem Punkte §, 4,6:
E, (&).« + E,(y) y + £, (6). 2 — 9.
Soll nun eine C, transformiert werden, die Z in diesem Punkte
berührt und durch die Punkte C, D, P geht, so ist diese C, von
der Form:
a
Ney Nee US, yz == 0,
14) Die Schnittpunkte der Tangenten in dem Doppelpunkt « = y = 0 liegen auf
der Co:
Ly (a; ya) == (1, «= ce yi c,, 2) -- Ahr vy) —— 0!
Diese berührt die Tangenten von f in C und J) in deren Schnittpunkten mit
der gewohnlichen Polaren des Punktes «= 0. y =O in Bezug auf Q.
daher muss sein:
En En Bn ieee
QEnc ae) ea
(23 — SSR Lr
nn al IS = I 5S
|
m=)
Indem man für ZE, ZE, LE, die Werte einsetzt, erhält man als
Abbildungskurve :
2.(—20C,,54 sie C,,5 ate Ci, ti Cc). xy
ty: G 2 C,, § q ata C,, Ss zi Oi 1 5) „tz,
== 2 CS n ar Ci, 5 C ote C,, | 5).yz = 0,
(26)
———
oder abgekürzt:
2 U, ay — U, wz — U, yz =0.
Durch Vergleich mit der früheren Form der ”-Kurve ergiebt
sich die Beziehung :
Rij
Bv VINO Ds ak eere Relan ene mln (PAL)
woraus durch Auflösung nach &, 4, ¢ folgt:
ERAN en on: We. AVAN VAE enen eee ret (rd)
wobei
V4 =2 Q, (x,); Ve =2 Q, (4), Ig = Q, (z,)-
Somit vermittelt unsere @-Kurve eine birationale quadratische
Transformation. Daraus erhellt jetzt auch, dass Z rational sein muss.
Die Gleichung @ (x,, y,,2.,§, 1,6) =O und die Gleichungen (27)
und (27a) zwischen den w,, y,,2, und den &, 9, ¢ sind also äquivalent.
14. Es soll hier noch gezeigt werden, dass diese Abbildung eine
spezielle Berührungstransformation repräsentiert, ohne auf das zuletzt
Auseindergesetzte Bezug zu nehmen. Es seien zwei Z-Kurven gegeben
EW=S4 C,, ay? — 4C,, w yz—4C,, ey? ed Cte +
k 28
KOEN Cn he rk Cn
INSIDE IDE — 2. Dyas = 0. (28a)
Soll dann einem Punkte §, 7,¢, der beiden Z-Kurven gemeinsam
ist, derselbe Punkt x,y,z, entsprechen, so muss sein:
52
Proceedings Royal Acad. Amsterdam. Vol. XX VI.
—2C,,54+0,,6¢ an are Dl BON IE DENS:
—2C,,§4+C,,$6+C,,.no =e.(—2D,, En + Des a DS) ie (29)
—20,,57+C,,664+C,,45=e-(—D,, 5% tp ce ek Dns)
Nun ist:
(1)
2 EEn) GE EAO 814-6, £5 + CaM] gy
2 He) (67,6) — Ey (S) . s = Se : (cae ID 5 t Di S Gel Dans)
und entsprechende Gleichungen bestehen für die Ableitungen nach
n und 6.
Wegen #0) (&, nf) = BO(En,£)=0, ergiebt sich also: BE) =
a). py) — py; EN — BY! Dies sind aber gerade die Bedingungen
für die Berührung von £! und ZE® im Punkte §, 4, =. Ebenso
ergiebt sich, wenn man statt der &, 1, < die 2,, y,, 2, einfiihrt, dass die
den A) un £2) entsprechenden Kurven Q® und Q® sich in dem
Punkte x,y, 2, berühren.
Jede C,, die f in C und PD berührt, geht in sich über, indem die
entsprechende Z-Kurve in diese und die zwei Tangenten an f in
den Punkten C und PD zerfällt. Wenn die -Kurve Q im Punkte
for Yor 2, berührt, so geht auch die #-Kurve durch diesen Punkt
und beriihrt die Q-Kurve daselbst.
Mathematics. — ,, Veber den natürlichen Dimensionsbegrijj.” ') By
Prof. L. EK. J. Brouwer.
(Communicated at the meeting of November 24, 1923).
Auf Grund der Invarianz der Dimensionenzahl*) lässt sich die
Dimensionenzahl einer Mannigfaltigkeit *) definieren als die Anzahl
der Parameter, durch welche sich die Mannigfaltigkeit in der
Umgebung eines beliebigen ihrer Punkte eineindeutig und stetig
darstellen lässt. Diese ,arithmetische” Definition trägt aber nach
Poincaré *) unserer intuitiven Raumanschauung ungenügend Rechnung.
Poincaré erhebt deshalb die Forderung einer rekurrenten Definition
von etwa folgender Form *):
„Ein Kontinuum heisse n-dimensional, wenn man es durch ein
oder mehrere (n—1)-dimensionale Kontinua in getrennte Stücke
zerlegen kann.”
Obgleich der „-dimensionale Jorpansche Satz") auf die Möglich-
keit einer derartigen Definition deutet, so lässt sich diese in der
zitierten Form dennoch nicht aufrecht erhalten.
Zunächst bemerken wir, dass das Wort „Kontuvuum’”’ hier sicher
nicht etwa im Sinne von ,,Mannigfaltigkeit” aufgefasst werden dart ;
in diesem Falle würde nämlich die Definition erst brauchbar werden,
nachdem eine von der Parameterdarstellung unabhängige Charakteri-
sierung der Mannigfaltigkeiten unter den abstrakten Mengen gelungen
sein würde. Weil dies aber bis jetzt nicht der Fall ist, so müsste
der PorincarÉschen Definition irgendeine allgemeinere abstrakte Cha-
rakterisierung des Kontinuums vorausgeschickt werden, z. B. diese:
„Eine Normalmenge (im Frécnerschen Sinne) + heisse ein Kontinuum,
wenn es fiir je zwei ihrer Blemente m, und m, eime zusammenhän-
1) Die vorliegende Mitteilung bildet bis auf den Inhalt von Fussnote !%) und die
in Fussnote !!) angegebene Berichtigung einen Wiederabdruck meiner in 1913 im
Journal fiir die reine und angewandte Mathematik (Bd. 142, S. 146—152) unter
demselben Titel erschienenen Abhandlung.
2?) Vgl. meinen Beweis in Math. Annalen 70, S. 161—165 und die daran an-
kniipfenden Entwicklungen von Lepesgue in U. R. de l'Acad. des sciences, Paris,
27 mars 1911.
8) Für die Definition des Begriffes ,Mannigfaltigkeit” vgl. Math. Annalen 71, S. 97.
4) Revue de métaphysique et de morale, 1912, S. 486, 487.
5) a. a. O., S. 488.
6) Vgl. den teilweise von LeBesavr, teilweise von mir erbrachten Beweis in C. R.
de l'Acad. des sciences, Paris, 27 mars 1911, und Math. Annalen 71, 5. 305—319.
94”
796
gende, abgeschlossene’) Menge gibt, welche Teilmenge von n ist und
m, und m, enthdlt.*). Für solche allgemeinere Kontinua, welche
keine Mannigfaltigkeiten sind, wiirde aber unsere Definition zu
Schwierigkeiten fiihren; z. B. würde man einem Kegel des Cartesischen
Raumes, der sich ja durch einen Punkt zerlegen lässt, nur eine
Dimension zusprechen dürfen.
Auch die Worte „ein oder mehrere’ könnten nicht unverändert
beibehalten werden, weil mehrere m-dimensionale Mannigfaltigkeiten
zusammen eine (m + p)-dimensionale Mannigfaltigkeit bilden können.
Alle diese Mängel lassen sich nun beseitigen, indem wir zunächst
die Porncarésche rekurrente Definition wie folgt abandern:
Es sei x irgendeine Normalmenge’), 2,,e und o' drei Teilmengen
von zr, welche innerhalb a abgeschlossen **) sind und keine gemein-
samen Punkte besitzen. Alsdann heissen @ und o' in a durch x,
getrennt, wenn zr, in a eine o enthaltende, aber ' nicht enthaltende
Gebietsmenge g bestimmt. **) Der Ausdruck : „zr besitzt den allgemeinen
Dimenstonsgrad n’, in welchem n eine beliebige natürliche Zahl
bezeichnet, soll nun besagen, dass für jede Wahl von g und o' eine
trennende Menge x, existiert, welche den allgemeinen Dimensions-
grad n—1 besitzt, dass aber nicht für jede Wahl von @ und g'eine
trennende Menge a, existiert, welche einen geringeren allgemeinen
Dimensionsgrad als n—l besitzt. Weiter soll der Ausdruck: „zr be-
sitzt den allgemeinen Dimensionsgrad Null bew. einen unendlichen
7) Unter einer abgeschlossenen Menge verstehen wir hier eine ihre Grenzelemente
enthaltende Menge, in welcher jede unendliche Folge von Elementen mindestens
ein Grenzelement aufweist.
8) Diese Definition ist der von Scuoenruies für die Kontinua des »-dimensionalen
Raumes gegebenen nachgebildet (vgl. Bericht über die Lehre von den Punktmannig-
faltigkeiten, Bd. IL, S. 117).
9 Inwieweit die Definition des Textes auch für Mengen allgemeinerer Art einen
naturgemässen Sinn behält, soll hier unerörtert bleiben.
10) Dieser Ausdruck besagt, dass 7,, ¢ und ¢’ alle ihre in z gelegenen Grenz-
punkte enthalten.
1!) Diesen der Gebietsmenge g auferlegten Bedingungen können natürlich mehrere
Gebietsmengen von zr genügen. Im in *) zitierten Original hat sich an dieser Stelle
eine andere, mit dem übrigen Inhalte des Aufsatzes in keinem Zusammenhang
stehende Trennungsdefinition eingeschlichen. Dass die obige (übliche) Definition die
in der vorliegenden Abhandlung in Wirklichkeit gebrauchte ist, geht aus dem Zu-
sammenhang hervor, insbesondere aus Fussnote!ë) und dem zugehörigen Passus des
Textes. Die daselbst eingeführte, von zg in 7j bestimmte, an die Kante 2, Ey
grenzende Gebietsmenge kann nämlich keinen anderen Sinn haben, als den des
Durchschnittes einer schon vorhandenen von 7» in 7, bestimmten, an &) E, gren-
zenden, an Ey Ey... En41 jedoch nicht grenzenden Gebietsmenge mit 7,. Auf die
Berichtigung, welche hier anzubringen war, bin ich von Herrn P. Urysoun in
Moskau aufmerksam gemacht worden.
797
allgemeinen Dimensionsgrad’”’ bedeuten, dass a kein Kontinuum als
Teil enthält, bzw. dass zu 2 weder die Null noch irgendeine natürliche
Zahl als ihr allgemeiner Dimensionsgrad gefunden werden kann. ’’)
Dieser Definition lasst sich leicht eine von der Rekurrenz unab-
hängige Form geben. Dazu denken wir uns die Menge z von zwei
Personen A und B der ,, Dimensionsoperation”’ unterzogen, worunter
wir folgendes verstehen: A wahlt in a zwei innerhalb a abge-
schlossene Teilmengen @ und o' beliebig aus, worauf B g und @' in
a trennt durch eine innerhalb a abgeschlossene Menge z,. Sodann
wahlt A in a, zwei innerhalb 7, abgeschlossene Teilmengen g, und
o', beliebig aus, worauf Be, und g', in zt, trennt durch eine inner-
halb 2, abgeschlossene Menge zr, Dieser Prozess wird unbeschränkt
wiederholt, bis eventuell eine Menge 2, auftritt, welche kein Kon-
tinuum mebr als Teil enthält. Wenn einerseits B unabhängig von
den Wahlen der oe, und g', dafür sorgen kann, dass eine Menge
x, auftritt, deren A< 10° the sample of chromium chloride
was balanced by a combination of wires the effect of which was
soon afterwards compared with the effect of one of the standard
wires (2N). The ratio of the effects of the combination of wires
to the effect of 2N as measured by A was The correction
(0
Gini
factor due to the inhomogeneity of the field as measured on 2N
was —. Finally the correction for the length (the sample of chromium
ow
6
4
or)
chloride was larger than 2N) was = (This was determined from
the results on iron wires cited above). The resultant correction is
GH) Gah altske!
Gs) 267 21-5
Again at the frequency 3.69. 10° the wire 2 N has aq = 9.01
and hence 1 — (gq) — 0.841. Thus the volume susceptibility of the
== disi
then
0.841
wire is x = — Tae — 0.0669. Now the radii of the wire and of
oT
the sample were 0.705 mm. and 3.5 mm. respectively. Hence the
ze. GO Oos
volume susceptibility of the sample is x = 1.11 x 35
> 0.06692 = 0.00305. The weight of chromium chloride was 3.192
0 geh 3.192
grams and its length 9.7 cm; the density is — = 0.85
xX 9.7 X (0.35)'
848
and the specifie susceptibility y= 0.0036. The value obtained in
direct fields, according to unpublished results of Dr. H. R. WorrJer
is 0.0048 *).
$5. Results for Gadolinium Sulphate at the boiling point ot hydrogen.
At the same frequency of 3.69 X 10° the gadolinium sulphate
was balanced against a different combination of wires which when
compared with 2 N had an effect smaller than 2 N in the ratio
1.48
Ton: The length of the sample was 8.74 cm. and the corresponding
correction The weight of the sample is 2.897 grams. The
22.7
specific susceptibility is hence y= 0.00051. The value obtained at
the same temperature for the same sample in a steady field was
0.0010 *). Measurements on manganic and nickel sulphate have
been also made and gave results of the same order of magnitude
as those for steady fields.
§ 6. Conclusions and Discussion.
A. The order of magnitude of the susceptibility is unchanged if
the frequency is increased to 3.69 X 10°.
B. The results seem to indicate that the susceptibility is smaller
than for direct fields. The values obtained in alternating fields for
CrCl, and Gd sulphate are 0.75 *) and 0.51 ‘) respectively of what
') This value is obtained by the method of weighing a rod of the material in
an inhomogeneous magnetic field (KAMERLINGH ONNEs and Perrier, these Proc. 16,
p- 689, Leiden Comm. N°. 139a). However, the susceptibility seems to depend on
the field strength, decreasing with increasing magnetic force. The value given
relates to a field ranging from 4500 gauss at the top of the rod to 220 gauss at
the bottom. The limit for very weak magnetic fields may be about 20°/, higher
(as found by extrapolating the susceptibility-magnetic force curves), so the ratio
0.75, given in § 6B for the susceptibilities in alternating and direct fields, may be
too large.
3) KAMERLINGH Onnes and Oosteruuis, these Proc. 15, p. 322, Leiden Comm. N°. 129d,
§ 6. However, it has to be pointed out, that it was not sure the sample was
really at the temperature of the bath, as it appeared afterwards, that in the
experiments of KAMERLINGH ONNES and OosreRHUIS it took some 4 hours before
the susceptibility had taken a definite value, probably owing to lag in the tempe-
rature equilibrium. Even in order to avoid this difficulty and to ensure a better
temperature equilibrium of the powder and the bath, the tubes for the magnetic
investigations were later on not evacuated but filled with a small quantity of non
condensing gases (hydrogen or helium). The value 0.00051 obtained with the
present tube is probably too low.
8) See note § 4.
4) See note § 5.
849
they are in direct fields. However, it would be preposterous to con-
clude that the susceptibility is actually decreased by the amount
found. Further work will be necessary for that. The choice of the
place of the suspended tube was rather unfortunate. It was situated
rather close to one of the slits in the tinfoil. Even though capacity
effects appear to be absent this is dangerous because the magnetic
field in the neighborhood of the slit is not homogeneous. It is pos-
sible that the divergence between the values for alternating and direct
fields is due to insufficient caution in the manipulation of the sus-
pended tube and a slight displacement of it during the experiment.
This would hardly explain, however, the similarity ') of the results
for the two substances investigated.
The writers wish to express their sincere thanks to Dr. H. R.
Worrser for help in comparing the results with those in steady
fields and for making unpublished results of his measurements
available.
1) Especially, if the value 0.75 is too high and 0.51 too low (see notes §§ 4 and 5,
this similarity is perhaps not only qualitative, but also more or less quantitative.
Mathematics. — “On a non-symmetrical affine field theory.” By
Prof. J. A. ScHoUTEN. (Communicated by Prof. H. A. Lorentz.)
(Communicated at the meeting of October 27, 1923). —
1. Introduction. In his last publications) Einstein has given a
theory of gravitation which only depends on a symmetrical linear
pseudo-parallel displacement (“affine Uebertragung’’) and a principle
of variation. From the equations, that result in this case, we see
that the electromagnetic field only depends on the curl of the electric
current vector, so that the difficulty arises that the electromagnetic
field cannot exist in a place with vanishing current density.
In the following pages will be shown that this difficulty disappears
when the more general supposition is made that the original dis-
placement is not necessarily symmetrical.
The equations which define such a displacement are
5 Ov’ :
Var = = Pl Th
eh ‘
dw) ;
Vu wì = ee T'iuw, ’
/ Onl /
in which the parameters I), (with an accent to distinguish them
from the I, of a symmetrical displacement) are not symmetrical
in À, u.
Einstein’) has defended the use of symmetrical parameters with
the remark that in the non symmetrical case not only
Ow
zt a ar Wy,
wv
but also
Ow?
one —T ph Wy
as
can be regarded as the covariant differential quotient (Erweiterung)
1) Berliner Sitzungsberichte 1923 p. 32—38, 76—77, 137 —140.
2) Lic. p: 33:
851
of a covariant vector, and thus the unambiguous character of this
quotient would vanish. But when the second expression is used the
transvection v’ 2, of two vectors v’ and 2; is no more an invariant
with a pseudo-parallel displacement, so that the differential quotient
of the first formula occupies a well defined preferred position.
We will not consider the most general case, but the semi-sym-
metrical case in which the alternating part of the parameters has
the form
ls
CB Ne a rn) == 10S; A, rs Sy A) ) ' A TE Omer
in which |S; is a general covariant vector’). It will be shown that
already with this simplified supposition the above mentioned difficulty
can be made to disappear.
About the special form of the world function Dd, nothing will be
supposed, so that the resulting expressions are quite general.
2. Deduction of the field equations. The Ty, of asemi-symmetrical
displacement can always be divided into a symmetrical and an
antisymmetrical part:
P]
(1) Pe = Aap + Sy Any + A= Apr”).
Be R';;, the curvature quantity belonging to I), :
Oat
=
TRR
ned ‘y "vy ne Ly "x
(2) Jil) = Ye — Re Du =F Typ Yor
Rous the curvature quantity formed in the same way with the
parameters 4;,, ',, the quantity obtained from Psi by eon-
tracting, w= pv:
OM 0
a 'a '% ‘a ox
Sete jee Du — Dye Dita Day Dix
id a
(3) WN
and R%, the quantity obtained in the same way from R%,)", then
we can easily deduce the relation
1) That the differences Tr, always are the components of a quantity of
the third rank may be supposed as known. Cf. the author's paper in Math.
Zeitschrift 13 (1922), p. 56—81, Nachtrag 15 (1922) p. 168.
2) In this paper the symbol Dr, W‚‚j means Ig (v, ww).
852
; dS, Ei 0S, 0S; y
4 Ri Ze Ee ; == = +! a memes DV” S, —! 7 S) —
(4) A / (a ser) ij JAC Die 1, ) /,(r—1)8) S,
ARV SEAN (aD) Vu San) SoS
in which Y* is the covariant differential operator belonging to 4;,.
We suppose that the determinant R’ = Lt, does not vanish. Hence
there exists an inverse quantity 7”:
(5) Rr = pe es ar a RRD Aj.
OR), .
When Tas and Cy are the antisymmetrical and the symmetrical
part of Bs
(6) a RR yee)
and when the word function = HW —R (sealar density) is a
still unknown function of G,,; and F,,, we then have the variation
equation :
(7) df Dar =[vdh',, dr =0"),
in which
(8a) Dt en VER (9"” oF We) V—R'
wp 09 ui ÒP
8b EE Pee GR SE
( ) 9 ÒG',, J òF'
When we substitute into (7) the value of (4), we get for n= 4
a ate =/0S), 0S —(0S) ly =
(9) 0 = fs ve) dR, ‘Ld Noa — rss S‚)
e ; Oa” Ox? Ou!
’
an equation that, ,, being independent of S,, is equivalent with
the two equations
(10) wad Ae = Peet ya eo a Prose yy — 9
yA yA
(11) dS {V, f ="), (0.0 Pre)" 8.97 |=,
Sa B
1) In this paper v,, w,, means }/)(v,w, +V, W,).
)
*) We use the variation symbol d in place of 3 to prevent confusion with the
symbol 5 of the covariant differentiation.
853
in which P, is a vector depending on B, and r'” in the following
way:
(12) B=), River = —— he
Since 4), is symmetrical in Au, we get from (10):
* J) (u pr Me ayAy u aA
dh mee ay Al Pag — A Yap AY ppd +
de
a= rg) Sag == 0
pa
+ ve ale
and from (11):
ont A
=
CN Ee Poe ye Sag" 0:
For Vif “—Puf “ we introduce the notation i”. It is easily
shown that
yn on 1 òf VER
= a 0 we f
From (J) follows by contracting, «=u:
(13) i =Vaf —Puf
dp. ) dp.
(14) ae Paget eS ag
When this value is substituted into (/), we get
un u
) Di a2 i yp : Py
(ieee Pig) — — Ab AG et See Sag.
In the supposition that also the determinant | g*”| does not vanish
this equation can be simplified by the introduction of the tensor
en TR
ìu —
(16) Cf ae aa
C9
as fundamental tensor and the vector
(17) , V—R Dld
y= —_——1
Vg
Then, because of
“oe 0 VSR
(18) P. cre He 9 Vin 4 = log ’
the equation (15) passes into:
Vv.
(u A)
(19) “Veo: "Ig da, Vg ts A Se
Transvection of this equation with gj, gives:
(20) — ga, Vag?! = "lie +5 Sa,
so that we get the resulting equation :
(21) ve a Ens A ere AS Ge Se
and
(111) eh Gn eee) /, A oe) i if 5e ee 9) S q” 4
in which 7' is the differential operator belonging to Ne
From (21) we deduce:
3 Au ” an vi. ey 2 y
(22) Ain = | ej | “We Ju t a [As ty, + he A, vy, — hs A) S,— ahs A, Sj.
so that, with regard to (1):
v
zl y y v y
(23) Piz hs gin’ A ANS
i
Substituting (22) into (3), we obtain:
(24) By Ka NE Wa TSAS en
= Sie Vi Sj + mie Su Si,
in which Kj, is the contracted curvature quantity K5,5 belonging
to the fundamental tensor g;,. By substituting (24) into (4) we obtain
the field equations: ;
Ean = Kn + Ei (Ve 2) En Vi Ly) =F Bi U 1, — (Vi. S) = Vi Sn)
a Calin: ey Ce.
ae ee in) eae re a
From (/V) follows for the bivector B of the electromagnetic
field :
855
Ou 07, 0S. 0S
an = y= en —— "J.
(25) wd [ua] = le (== sr) he =)
We now return to the equation (Il) obtained from the variation
principle. With regard to (13), (14) and (17) this equation leads to
(26) iv =O.
Since 2” has the character of a current vector, it is not allowed
to consider variations of the alternating part of ie, when we wish
to keep the current vector in the equations. In regions where only
an electromagnetic field exists and no current, the variation principle
remains valid without any restriction.
The expressions (JV) and (25) only differ from those of EinsreiN
by the terms in S;, hence an electromagnetic field is also possible
in places with vanishing current vector ’ There the vector 5S;
behaves as a potential vector.
We can further make the following important remarks:
1. In the field equations (JV) S, does not contribute to the sym-
metrical part of R'.
2. When there is no current the displacement is by (///) con-
formal, the fundamental tensor being diminished with 2 dx S, 9’
when the pseudoparallel displacement is dev.
3. When there is no current and no potential (23) passes into
the ordinary equation of the gravitational field, in the same way
as KINSTEIN’s equation.
3. The potentialvector S). It is remarkable that here the potential
vector 9, occurs as unambiguously determinated, not as a vector to
which an arbitrary gradient vector may be added. This difficulty
disappears when we make the supposition that the parameters which
define the displacement are not the same for covariant and for
contravariant vectors') and thus no longer adopt the invariance of
transvection. It is namely possible to alter covariant parameters
independently of the transformation of the original variables by
changing the measure’) of the covariant vectors. This change of
measure
1) For these displacements ef. the above mentioned paper in Math. Zeitschrift 13.
2) This change of measure has nothing to do with an introduction of a ds.
856
(27) tT Ww) = w)
in which r is an arbitrary function, leaves the parameters of the
contravariant displacement unaltered, while the covariant parameters,
which we will also further denote with 7, will be transformed
in the following way :
ry’ (> ò lg T d
(28) if a r Nan CL A) 5
U
Such a change of measure cannot be applied in the same easy
way to contravariant vectors, the new components T—! da” being in
general no more exact differentials. In this case we would be obliged
to consider space-time as a system of non-exact differentials, and it
would no more be possible to represent a point by four finite co-
ordinates. This case has doubtlessly but little attraction so long as
there are other possibilities.
When we wish to ‘loose
the vector S, in the above mentioned
sense, we have only to consider the I, as the parameters of the
covariant displacement and to define the I,, the parameters of the
contravariant displacement, in the following way :
) y Au v ME 7 ei:
(29) Duit A= tant ENNE,
We then have obtained that I, is independent of S, and that,
when covariant measure is changed, S) is transformed in the
following way:
dlg rt
(30) Su = Su oi Sn 5
En
It is very remarkable that by (23) T', has just a form that
leads to the desired transformation of the potential vector. If f.i.
'
r;, contained a term with §, A,, it would not be possible to
obtain an equation of the form (30).
Representing the covariant differential operator determined by
rr, and De by v, (III) is changed into:
NT) | (a) Ve
UL’) Vaid == /, Aa CNS = | te 9
Vann == le Gent — Ie Gai tu + Jode Jin — 2 Su Gru -
The tensor g), is a quantity variable with transformation of co-
variant measure, for its components do not change, while the
857
components of a genuine quantity of second order obtain the
factor t—®. When the current vanishes, this quantity has the same
character as the variable fundamental tensor of Wry1’s theory, and
— 2 S, behaves as the vector which Weyr calls gz.
4. On the law of conservation of energy and momentum. The law
of conservation of energy and momentum in gravitation theory is
a consequence of the identity of Brancur. The form of this identity
is known for non-symmetrical displacements and for displacements
with non-invariant transvection *). Hence it must be possible to
deduce, starting with this identity, an equation that can be considered
as an analogon of the equation that expresses the law of energy
and momentum. This possibility exists already before any supposition
is made relating to the special form of Hamilton’s function.
(Noorpnorr, Groningen 1923), p. 357.
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GON TE NES:
ACCESSORY MINERAL (On the occurrence of diamond as an) in olivine and
anorthite bearing bombs, occurring in basaltic lava, ejected by the
volcano Gunung Ruang (Sangir — Archipelago north of Celebes). 510.
ACCOMMODATION MUSCLE (Determination of the power of the). 763.
ACETONEMIA (Researches on the metabolism of milch-cows suffering from). 666.
ADDITION of water (Researches cn the) to ethylene and propylene. (Preli-
minary communication). 321.
ADSORPTIVE POWER (Researches on the nature of the so-called) of finely-
divided carbon. J. The binding of water by animal carbon. 548.
ALCOHOL (The light oxidation of). III. The photocatalytic influence of some
series of ketones on the light oxidation of ethyl alcohol. 443.
AMPHIBIAN LARVAE (On the determination of polarity in the epidermal
ciliated cell. After experiments on). 702.
Anatomy. C. vAN GELDEREN: “On the development of the shoulder-girdle
and episternum in reptiles’. 15.
— Kyozo Kupo: “Contributions to the knowledge of the brain of bony
fishes”. 65.
— C. U. Artins Kapprrs: “The ontogenetic development of the corpus
striatum in birds and a comparison with mammals and man’. 135.
— O. H. Disxstra: “The development of the shoulder-blade in man”. 297.
— J. W. vaN Wine: “Thymus, spiracular sense organ and fenestra vesti-
buli (ovalis) in a 63 m.m. long embryo of Heptanchus cinereus”. 727.
— J. Il. Hunter: “The forebrain of Apteryx australis”. 807.
ANTAGONISM (Further researches on the) between citrate and calcium salt
in biochemical processes, examined by the aid of substituted citrates.
(First comm.). 542.
Anthropology. L. Bork: “The menarche in Dutch women and its precipi-
tated appearance in the youngest generation”. 650.
APOGAMY (Cytological investigations on) in some elementary species of
Erophila verna. 349.
). 807.
ARC, INFRALATERAL (A non-tangent). 712.
ARGON (A relation between ‘the spectra of ionized potassium and). (Second
APTERYX AUSTRALIS (The forebrain of
comm.). 498.
ARIENS Kappers (C. U.) v. KAppers (C. U. ARIËNS).
Proceeding Royal Acad. Amsterdam. Vol. XXVI.
II CON TEN TS
Astronomy. E. HERTZSPRUNG: “On the magnitude equation of OsTHoFF’s
estimates of star-colours”. 12.
ATOMIC STRUCTURE (Nitrogen fixation by means of the cyanide-process and). 480.
BACKER (H. J.). The second dissociation constant of sulphoacetic and
z-sulphopropionic acids. 83.
— and J. H. pe Boer. n. x-Sulfobutyric acid and its optically active
components. 79.
BACTERIA (The splitting of lipoids by). I. 436.
BACTERIES VIVANTES (Culture du bactériophage sans intervention de). 486.
Bacteriology. P. C. Fru: “On the bacteriophage and the self-purification
of water”. 116.
— G. M. Kraay and L. K. Wo er: “The splitting of lipoids by bacteria”.
I. 436.
— F. D'HERELLE: “Culture du bactériophage sans intervention de bacté-
ries vivantes’. 486.
BACTERIOPHAGE (On the) and the self-purification of water. 116.
BACTERIOPHAGE (Culture du) sans intervention de bactéries vivantes. 486.
BALANCE-PRESSURE (The influence of rotation on the sensitiveness and the
accuracy of a). 805.
BANNIER (J. P.). Cytological investigations on apogamy in some elementary
species of Erophila verna. 349.
BARENNE (J. G. DuSSER DE) and J. B. ZWAARDEMAKER. On the influence
of the vagi on the frequency of the action currents of the diaphragm
during its respiratory movements. 771.
BEAUFORT (L. F. DE) and H. A. BROUWER. On tertiary marine deposits with
fossil fishes from South Celebes. 159.
BELINFANTE (M. J.). A generalisation of MERTENS’ theorem. 203.
— On a generalisation of TAUBER’s theorem concerning power series. 216.
— On power series of the form: xfo — xf1+x?2 — ... 456.
Bertus’ method (Hydrogenation of paraffin by the). 226.
BiEezENO (C. B). An application of the theory of integral equations on
the determination of the elastic curve of a beam, elastically supported
on its whole length. 237.
BiLINEARFORMEN (Ueber Invarianten von). 801.
Biochemistry. J. R. Karz: “Further researches on the antagonism between
citrate and calcium salt in biochemical processes, examined by the
aid of substituted citrates”. I. 542.
— B. SjoLLeMa and Miss J. E. VAN DER ZANDE: “Researches on the
metabolism of milch-cows suffering from acetonemia”. 666.
Birps (The ontogenetic development of the corpus striatum in) and a com-
parison with mammals and man. 135.
COUN sD EGN (ESS Ill
Birb’s HEAD (,,Vogelkop”) (Geological data derived from the region of the)
of New-Guinea. 274.
Boer (J. H. pe) and H. J. BACKER. n. x-Sulfobutyric acid and its optically
active components. 79.
BöESEKEN (J.). The valency of boron. 97.
Bork (L.). The menarche in Dutch women and its precipitated appearance
in the youngest generation. 650.
Bomes (On the occurrence of diamond as an accessory mineral in olivine
and anorthite bearing), occurring in basaltic lava, ejected by the volcano
Gunung Ruang (Sangir-Archipelago north of Celebes). 510.
Bony FISHES (Contributions to the knowledge of the brain of). 65.
BORIC ACID COMPOUNDS (Provisional communication on) of some organic
substances containing mere than one hydroxyl-group. Boron as a
pentavalent element. 32.
Borneo (Description de crustacés décapodes nouveaux des terrains tertiaires
de). 489.
— Description de Raniniens nouveaux des terrains tertiaires de). 777.
BORON as a pentavalent element. 32.
— (The valency of). 97.
BoscHMaA (H.). Experimental budding in Fungia fungites. 88.
Botany. J. M. JANSE: “On stimulation in auxotonic movements”. 171.
— J. P. BANNIER: “Cytological investigations on apogamy in some
elementary species of Erophila verna’. 349.
— F. W. T. Huncer: “On the nature and origin of the cocos-pearl.” 357.
— TH. VALETON: “The genus Coptosapelta KorTH. (Rubiaceae)’’. 361.
— D. TOLLENAAR: “Dark growth-responses”’. 378.
— D. S. FERNANDES: “A method of simultaneously studying the absorp-
tion of Os and the discharge of CO» in respiration’. 408.
— Tu. Weevers: “Ringing experiments with variegated branches”. 755.
BRAIN (Contributions to the knowledge of the) of bony fishes. 65.
BRANCHES (Ringing experiments with variegated). 756.
Breit (G.). Transients of magnetic fleld in supra-conductors. 529.
— and H. KAMERLINGH ONNES. Magnetic researches. XX VI. Measurements
of magnetic permeabilities of chromium chloride and gadolinium sulph-
ate at the boiling point of liquid hydrogen in alternating fields of
frequency 369,000 per second. 840.
BRINKMAN (R.) and A. v. SzeNT-GyOrGyI. Researches on the chemical
causes of normal and pathological haemolysis. 470.
BROUWER (H. A). Fractures and faults near the surface of moving geantic-
lines. III. The horizontal movement of the Central-Atlantic ridge. 167.
— and L. F. pr BEAUFORT. On tertiary marine deposits with fossil fishes
from South Celebes. 159.
Iv GEOENDT ESN Saas:
BROUWER (L. E. J.). Ueber den natürlichen Dimensionsbegriff. 795.
BupDING (Experimental) in Fungia fungites. 88.
BuRGERS (J. M.). On the resistance experienced by a fluid in turbulent
motion. 582.
CAEsIUM (ls) radio-active ? 575.
CARBON (Researches on the nature of the so-called adsorptive power of
finely-divided). I. The binding of water by animal carbon. 548.
CARBONIFEROUS (Etapteris Bertrandi Scott, a new etapteris from the upper)
(lower coalmeasures) from England, and its bearing to stelar-morpho-
logical questions. 669.
CARDIO-REGULATIVE NERVES (The presence of) in Petromyzon fluviatilis. 438.
CENTRAL-ATLANTIC RIDGE (The horizontal movement of the). 167.
CHEMICAL CAUSES (Researches on the) of normal and pathological haemo-
lysis. 470.
Chemistry. P. H. HERMANS: “Provisional communication on boric acid
compounds of some organic substances containing more than one
hydroxyl-group. Boron as a pentavalent element”. 32.
— H.R. Kruyt and W. A. N. Eaaink: “The electro-viscous effect in
rubbersol”. 43.
— H. J. Backer and J. H. pe Boer: “*n. x-Sulfobutyric acid and its
optically active components”. 79.
— H. J. Backer: “The second dissociation constant of sulphoacetic and
x-sulphopropionic acids”. 83.
— J. BOESEKEN: “The valency of boron”. 97.
— H. I. WATERMAN and J. N. J. Perouin: “Hydrogenation of paraffin
by the BEerGius’ method”. 226.
— A. Smits: “The phenomenon of electrical supertension’’. III. 259.
— A. Smits: “The influence of intensive drying on internal conversion”.
I. 266.
— A. Smits: “The system sulphur trioxide”. I. 270.
— F. A. H. SCHREINEMAKERS: “In-, mono- and divariant equilibria’.
XXIII. 283.
— J. P. Wisaut and J. J. DiEKMANN: “Researches on the additon of
water to ethylene and propylene.” 321.
— A. Smits: “The electromotive behaviour of magnesium.” IJ. 395.
— J. P. Wisaut and Miss E. DINGEMANSE: “The synthesis of some
pyridylpyrroles”. 426.
— W. D. Couen: “The light oxidation of alcohol. III. The photo-catalytic
inrluence of some series of ketones on the light oxidation of ethyl
alcohol”. 443.
— L. HAMBURGER: “Nitrogen fixation by means of the cyanide-process
and atomic structure’. 480.
COUN ETL IEENIETSS Vv
Chemistry. J. Lirscuitz: ‘Volta-luminescence’’. 561.
— O. pe Vries: “The coagulation of Hevea latex”. 675.
— F. A. H. SCHREINEMAKERS: “In-, mono- and divariant equilibria”.
XXIV. 719.
CHROMIUM CHLORIDE (Measurements of magnetic permeabilities of) and
gadolinium sulphate at the boiling point of liquid hydrogen in alternating
fields of frequency 369.000 per second. 840.
CILIATED CELL (On the determination of polarity in the epidermal). (After
experiments on amphibian larvae). 702.
CILIATED EPITHELIUM (A contribution to the histophysiology of the). 707.
CITRATE (Further researches on the antagonism between) and calcium salt
in biochemical processes, examined by the aid of substituted citrates.
(First comm.). 542.
COAGULATION (The) of Hevea latex. 675.
Cocos-PEARL (On the nature and origin of the). 357.
COnEN (W. D.). The light oxidation of alcohol. III. The photo-catalytic
influence of some series of ketones on the light oxidation of ethyl
alcohol. 443.
Colloidchemistry. J. R. Katz: “Researches on the nature of the so-called
adsorptive power of finely-divided carbon. I. The binding of water by
animal carbon’. 548.
COMPONENTS (n. «-Sulfobutyric acid and its optically active). 79.
CONGRUENCE (1.0) (A) of twisted cubics. 126.
CONGRUENCE OF RAYS (On the plane pencils containing three straight lines
of a given algebraical’’). 522.
Conics (The complex of the) which cut five given straight lines. 513.
CONSTANT (On Eurer's). 316.
Continuity (On the points of) of functions. 187.
COPTOSAPELTA KorTH (Rubiaceae) (The genus). 361.
CORPUS STRIATUM (The ontogenetic development of the) in birds and a
comparison with mammals and man. 135.
CRUSTACES DECAPODES NOUVEAUX (Description de) des terrains tertiaires de
Borneo. 489.
CURRENTS (On the influence of the vagi on the frequency of the action)
of the diaphragm during its respiratory movements. 771.
Curve (The critical) of oxygen-nitrogen mixtures, the critical phenomena
and some isotherms of two mixtures with 50%, and 75°/) by
volume of oxygen in the neighbourhood of the critical point. 49.
— (An application of the theory of integral equations on the determina-
tion of the elastic) of a beam, elastically supported on its whole length.
237, 247.
VI CO WaT EON IS
CYANIDE-PROCESS (Nitrogen fixation by means of the) and atomic-structure.
480.
CYTOLOGICAL INVESTIGATIONS On apogamy in some elementary species of
Erophila verna. 349.
DARKGROWTH-RESPONSES. 378.
DeEcapopeEs (Description de crustacés) nouveaux des terrains tertiaires de
Borneo. 489.
Deposits (On tertiary marine) with fossil fishes from South Celebes. 159.
DiAMOND (On the occurrence of) as an accessory mineral in olivine and
anorthite bearing bombs, occurring in basaltic lava, ejected by the
volcano Gunung Ruang (Sangir-Archipelago north of Celebes). 510.
DiAPHRAGM (On the influence of the vagi on the frequency of the action
currents of the) during its respiratory movements. 771.
DIEKMANN (J. J.) and J. P. Wipaut. Researches on the addition of water
to ethylene and propylene. (Preliminary communication). 321.
Dik (H. W. J.) and P. ZEEMAN. A relation between the spectra of ionized
potassium and argon. (Second comm.). 498.
DIMENSIONSBEGRIFF (Ueber den natiirlichen). 795.
DINGEMANSE (ELISABETH) and J. P. Wisaut. The synthesis of some
pyridylpyrroles. 426.
DIRICHLET’s series (A theorem concerning power-series in an infinite number
of variables, with an application to). 278.
DISPERSION LINES (The relation between the widening and the mutual influ-
ence of) in the spectrum of the sun’s limb. 329.
DisSOCIATION CONSTANT (The second) of sulphoacetic and x-sulphopropionic
acids. 83.
DoorMantop (On the rocks of) in Central New Guinea. 191.
DROSTE (J.). An application of the theory of integral equations on the
determination of the elastic curve of a beam, elastically supported on
its whole length. 247.
DryinG (The influence of intensive) on internal conversion. I. 266.
DUSSER DE BARENNE (J. G.) v. BARENNE (J. G. DUSSER DE).
DukKsTRA (O. H). The development of the shoulder-blade in man. 297.
EGGiNK (W. A. N.) and H. R. Kruyt. The electro-viscous effect in
rubbersol. 43.
EINTHOVEN (W. F.). The string galvanometer in wireless telegraphy. 635.
ELASTIC CURVE (An application of the theory of integral equations on the
determination of the) of a beam, elastically supported on its whole
length. 237. 247.
ELECTRIC RESISTANCE (On the) of pure metals, etc. XII. Measurements
concerning the electric resistance of indium in the temperature field
of liquid helium. 504.
CON T EIN Tis VII
ELECTROMOTIVE BEHAVIOUR (The) of magnesium. II. 395.
ELECTRO-VISCOUS EFFECT (The) in rubbersol. 43.
EMBRYO (Thymus, spiracular sense organ and fenestra vestibuli (ovalis) in
a 63 m.m. long) of Heptanchus cinereus. 727.
EPISTERNUM (On the development of the shoulder-girdle and) in reptiles. 15.
EouiriBRIA (In-, mono- and divariant). XXIII. 283, XXIV. 719.
EROPHILA VERNA (Cytological investigations on apogamy in some element-
ary species of). 349.
ETAPTERIS BERTRANDI SCOTT, a new etapteris from the upper carboniferous
(lower coal-measures) from England, and its bearing to stelar-morpho-
logical questions. 669.
ETHYL ALCOHOL (The photo-catalytic influence of some series of ketones
on the light oxidation of). 443.
ETHYLENE (Researches on the addition of water to) and propylene. 321.
EuLer’s constant (On). 316.
Fautts (Fractures and) near the surface of moving geanticlines. III. The
horizontal movement of the Central-Atlantic ridge. 167.
Fauna (On the) of the phosphatic deposits in Twente (Lower oligocene). 235.
FERNANDES (D. S.). A method of simultaneously studying the absorption
of Oy and the discharge of CO, in respiratiton. 408.
FIELD THEORY (On a non-symmetrical affine). 850.
FisHes (On tertiary marine deposits with fossil) from South Celebes. 159.
FLIERINGA (H. J.) and J. vAN DER Hoeve. Determination of the power
of the accommodation-muscle. 763.
Fru (P. C.). On the bacteriophage and the self-purification of water. 116.
Fruip (On the resistance experienced by a) in turbulent motion. 582.
Foetus (A partial) removed from a child. 493.
FOREBRAIN (The) of Apteryx Australis. 807.
FRACTURES and faults near the surface of moving geanticlines. III. The
horizontal movement of the Central-Atlantic ridge. 167.
Functions (On the points of continuity of). 187.
FUNGIA FUNGITES (Experimental budding in). 88.
GADOLINIUM SULPHATE (On the determination of the magnetisation at very
low temperatures and on the susceptibility of) in the region of tempe
ratures obtainable with liquid hydrogen. 613.
— (On the magnetisation of) at temperatures obtainable with liquid
helium. 626.
— (Measurements of magnetic permeabilities of chromium chloride and)
at the boiling point of liquid hydrogen in alternating fields of frequency
369.000 per second. 840.
GALVANOMETER (The string) in wireless telegraphy. 635.
VIII GOON TEN as
GASTEROSTEUS PUNGITIUS L. (Secondary sex-characters and testis of the
ten-spined stickleback). 309.
GEANTICLINES (Fractures and faults near the surface of moving). III. The
horizontal movement of the Central-Atlantic ridge. 167.
GELDEREN (CHR. VAN). On the development of the shoulder-girdle and
episternum in reptiles. 15.
GEOLOGICAL DATA derived from the region of the “Bird’s head” of New-
Guinea. 274.
Geology. H. A. Brouwer and L. F. pe BEAUFORT: “On tertiary marine
deposits with fossil fishes from South Celebes”. 159.
— H. A. Brouwer: “Fractures and faults near the surface of moving
geanticlines. III. The horizontal movement of the Central-Atlantic
ridge”. 167.
— L. Rutren: “Geological data derived from the region of the “Bird's
head” of New-Guinea”. 274.
— V. VAN STRAELEN: “Description de crustacés décapodes nouveaux des
terrains tertiaires de Borneo”. 489.
— W. F. Grsorr: “On the occurrence of diamond as an accessory mineral
in olivine and anorthite bearing bombs, occurring in basaltic lava,
ejected by the volcano Gunung Ruang (Sangir-Archipelago north of
Celebes)”’. 510.
— V. VAN STRAELEN: “Description de raniniens nouveaux des terrains
tertiaires de Borneo”. 777.
Giso ur (W. F.). On the rocks of Doormantop in Central New-Guinea. 191.
— On the occurrence of diamond as an accessory mineral in olivine and
anorthite bearing bombs, occurring in basaltic lava, ejected by the
volcano Gunung Ruang (Sangir-Archipelago north of Celebes). 510.
GROWTH-RESPONSES (Dark). 378.
GUNUNG Ruana (Sangir-Archipelago north of Celebes). (On the occurrence
of diamond as an accessory mineral in olivine and anorthite bearing
bombs, occurring in basaltic lava, ejected bij the volcano). 510.
HarMoLysis (Researches on the chemical causes of normal and pathological).
470.
HAMBURGER (H. J.). A new form of correlation between organs. 420.
HAMBURGER (L.). Nitrogen fixation by means of the cyanide-process
and atomic structure. 480.
HazEeLHOrFF (F. F.) and Miss HELEEN WiERSMA. On subjective rhythmi-
sation. 462.
HerLrum (Further experiments with liquid). S. On the electric resistance of
pure metals, etc. XII, Measurements concerning the electric resistance
of indium in the temperature field of liquid helium). 504.
COUN TVEON EDs: IX
HewviuMm (Further experiments with liquid). T. Magnetic researches. XXIII.
On the magnetisation of gadolinium sulphate at temperatures obtainable
with liquid helium. 626.
HEPTANCHUS CINEREUS (Thymus, spiracular sense organ and fenestra vestibuli
(ovalis) in a 63 m.m. long embryo of). 727.
HERELLE (F. d.’). Culture du bactériophage sans intervention de bactéries
vivantes. 486.
HERMANS (P. H.). Provisional communication on boric acid compounds
of some organic substances containing more than one hydroxyl-group.
Boron as a pentavalent element. 32.
HERTZSPRUNG (E.). On the magnitude equation of OsTHOFF’s estimates
of star-coulours. 12.
HEVEA LATEX (The coagulation of). 675.
Histology. M. W. WoERDEMAN: “On the determination of polarity in the
epidermal ciliated cell (after experiments on amphibian larvae)”. 702.
— M. W. WOERDEMAN: “A contribution to the histophysiology of the
ciliated epithelium’. 707.
— E. WINKLER-JUNIUS and J. A. LATUMETEN: “The histopathology of
Lyssa in respect to the propagation of the lyssavirus’’. 825.
Horve (J. VAN DER) and H. J. Fiierinca. Determination of the power
of the accommodation-muscle. 763.
HuNGER (F. W. T.). On the nature and origin of the cocos-pearl. 357.
HUNTER (JOHN I.). The forebrain of apteryx Australis. 807.
Hydrodynamics. J. M. BurGers: “On the resistance experienced by a
fluid in turbulent motion”. 582.
HYDROGEN (On the determination of the magnetisation at very low tempe-
ratures and on the susceptibility of gadolinium sulphate in the region
of temperatures obtainable with liquid). 613.
HYDROGENATION of paraffin by the Bercius’ method. 226.
HyproxyL-Group (Provisional communication on boric acid compounds of
some organic substances containing more than one). Boron as a penta-
valent element. 32.
HYPERBOLOID (A representation of the line elements of a plane on the
tangents of a). 129.
INpiuM (Measurements concerning the electric resistance of) in the temperature
field of liquid helium. 504.
INFRALATERAL ARC (A non-tangent). 712.
INSECTES (Sur quelques nouveaux) des lignites oligocènes (Aquitanien) de
Rott. Siebengebirge (Rhénanie). 605.
INTEGRAL EQUATIONS (An application of the theory of) on the determination
of the elastic curve of a beam, elastically supported on its whole
length. 237. 247.
X CEOENSTSESNEIES
INTENSIVE DRYING (The influence of) on internal conversion. I. 266.
INVARIANTEN (Ueber) von Bilinearformen. 801.
ISOTHERMS of di-atomic substances and their binary mixtures. XX. The
critical curve of oxygen-nitrogen mixtures, the critical phenomena and
some isotherms of two mixtures with 50°, and 75% by volume of
oxygen in the neighbourhood of the critical point. 49.
JANSE (J. M.). On stimulation in auxotonic movements. 171.
Jurius (W. H.) and M. MINNAERT. The relation between the widening
and the mutual influence of dispersion lines in the spectrum of the
sun's limb. 329.
Kaiser (Miss L.). Contributions to an experimental phonetic investigation
of the Dutch language. I. The short o. 745.
KAMERLINGH ONNES (H.) v. ONNES (H. KAMERLINGH).
Karrers (C. U. ARIENS). The ontogenetic development of the corpus
striatum in birds and a comparison with mammals and man. 135.
Katz (J. R.). Further researches on the antagonism between citrate and
calcium salt in biochemical processes examined by the aid of substituted
citrates. (First comm.) 542.
— Researches on the nature of the so-called adsorptive power of finely
divided carbon. I. The binding of water by animal carbon. 548.
Keesom (W. H.) and J. pe SMepT. On the diffraction of Röntgen-ravs in
liquids. II. 112.
Ketones (The photo-catalytic influence of some series of) on the light
oxidation of ethyl alcohol. 443.
KLOOSTERMAN (H. D.). A theorem concerning power-series in an infinite
number of variables, with an application to DiriCHLET's series. 278.
KLUYVER (J. C.). On Eurer’s constant. 316.
K6LMEL (F.). Ueber die zu einem Punkte und einer Geraden gehörigen
Polarkurven inbezug auf eine gegebene algebraische Kurve. 783.
KOMITANTENSYSTEM (Ueber das) zweier und dreier ternärer quadratischer
Formen. 2.
Kraay (G. M.) and L. K. Worrr. The splitting of lipoids by bacteria. I. 436.
Kruyt (H. R.) and W. A. N. Eacink. The electro-viscous effect in rubber-
sol. 43.
Kubo (Kyozo). Contributions to the knowledge of the brain of bony fishes. 65.
KuUENEN (J. P.), T. VERSCHOYLE and A. TH. vAN URK. Isotherms of di-atomic
substances and their binary mixtures. XX. The critical curve of oxygen-
nitrogen mixtures, the critical phenomena and some isotherms of two
mixtures with 50°/, and 75 °/) by volume of oxygen in the neighbourhood
of the critical point. 49.
Kurve (Ueber die zu einem Punkte und einer Geraden gehörigen Polarkurven
inbezug auf eine gegebene algebraische). 783.
C'ON'T SE NAT S XI
LANGUAGE (Contributions to an experimental phonetic investigation of the
Dutch). I. The short o. 745.
LATUMETEN (J. A.) and E. WiINKLEr-JuNius. The histopathology of Lyssa
in respect to the propagation of the lyssavirus. 825.
Lava (On the occurrence of diamond as an accessory mineral in olivine
and anorthite bearing bombs, occurring in basaltic), ejected by the
voleano Gunung Ruang (Sangir-Archipelago north of Celebes). 510.
LirscuHiTz (J.). Volta-luminescence. 561.
LIGHT OXIDATION (The) of alcohol. III. The photocatalytic influence of some
series of ketones on the light oxidation of ethyl alcohol. 443.
LIMITING SETS (Inner). 189.
LINE ELEMENTs (A representation of the) of a plane on the tangents of a
hyperboloid. 129.
Lirorps (The splitting of) by bacteria. I. 436.
Liouips (On the diffraction of Röntgen-rays in). II. 112.
Lyssa (The histopathology of) in respect to the propagation of the lyssavirus.
825.
MAGNEsIUM (The electromotive behaviour of). Il. 395.
MAGNETIC FIELD (Transients of) in supra-conductors. 529.
MAGNETIC RESEARCHES. XXII. On the determination of the magnetisation at
very low temperatures and on the susceptibility of gadolinium sulphate
in the region of temperatures obtainable with liquid hydrogen. 613.
— XXIII. On the magnetisation of gadolinium sulphate at temperatures
obtainable with liquid helium. 626.
— XXVI. Measurements of magnetic permeabilities of chromium chloride
and gadolinium sulphate at the boiling point of liquid hydrogen in
alternating fields of frequency 369.000 per second. 840.
MAGNITUDE EQUATION (On the) of OsTHOFF’s estimates of star-colours. 12.
MAMMALs (The ontogenetic development of the corpus striatum in birds
and a comparison with) and man. 135.
— (New findings of pliocene and pleistocene) in Noord Brabant, and
their geological significance. 199.
Mathematics. B. L. vAN DER WAERDEN: “Ueber das Komitantensystem
zweier und dreier ternärer quadratischer Formen”. 2.
— JAN DE VRIES: “A null system (1, 2, 3)”. 124.
— JAN DE Vries: “A congruence (1,0) of twisted cubics’’. 126.
— JAN DE Vries: “A representation of the line elements of a plane on
the tangents of a hyperboloid.” 129.
— J. Wo Fr: “On the points of continuity of functions’. 187.
— J. Worrr: “Inner limiting sets.” 189.
— M. J. BELINFANTE: “A generalisation of MERTENS’ theorem’. 203.
XII CONTENTS
Mathematies. M. J. BELINFANTE: “On a generalisation of TAUBER’s theorem
concerning power series’. 216.
— C. B. Biezeno: “An application of the theory of integral equations on
the determination of the elastic curve of a beam, elastically supported
on its whole length.” 237.
— J. Droste. “Idem”. 247.
— H. D. KLOOSTERMAN: “A theorem concerning power-series in an infinite
number of variables, with an application to DiRICHLET's series”. 278.
— J. C. Kiuyver: “On Eurer's constant.” 316.
— JAN bE Vries: “Representation of a tetrahedral complex on the points
of space.” 390.
— M. J. BELINFANTE: “On power series of the form: xPo — xpi + xp — .,
456.
— G. SCHAAKE: “The complex of the conics which cut five given straight
lines”. 513.
— G. SCHAAKE: “On the plane pencils containing three straight lines of
a given algebraical congruence of rays.” 522.
— F. KörMer: “Ueber die zu einem Punkte und einer Geraden gehörigen
Polarkurven inbezug auf eine gegebene algebraische Kurve.” 783.
— L. E. J. Brouwer: “Ueber den natürlichen Dimensionsbegriff.” 795.
— R. Weirzenséck: “Ueber Invarianten von Bilinearformen.” 801.
— J. A. SCHOUTEN: “On a non-symmetrical affine field theory.” 850.
MENARCHE (The) in Dutch women and its precipitated appearance in the
youngest generation. 650.
MERTENS’ theorem (A generalisation of). 203.
Merars (On the electric resistance of pure), etc. XII. Measurements con-
cerning the electric resistance of indium in the temperature field of
liquid heliuim. 504.
Meteorology. S. W. Visser: “A non-tangent infralateral arc.” 712.
MEUNIER (FERNAND). Sur quelques nouveaux insectes des lignites
oligocénes (Aquitanien) de Rott. Siebengebirge (Rhénanie). 605.
MicueE ts (A.). The influence of rotation on the sensitiveness and the
accuracy of a pressure balance. 805.
MircH-cows (Researches on the metabolism of) suffering from acetonemia. 666.
MINERAL ACCESSORY v. Accessory mineral,
MiNNAERT (M.) and W. H. Jurrus. The relation between the widening
and the mutual influence of dispersion lines in the spectrum of the
sun’s limb. 329.
MiocENE (Otoliths of teleostei from the oligocene and the) of the Peel
district and of Winterswijk. 231.
CONTENTS XIII
Mixtures (isotherms of di-atomic substances and their binary). XX. The
critical curve of oxygen-nitrogen mixtures, the critical phenomena and
some isotherms of two mixtures with 50°/, and 75% by volume of
oxygen in the neighbourhood of the critical point. 49.
Movements (On stimulation in auxotonic). 171.
Nerves (The presence of cardio-regulative) in Petromyzon fluviatilis. 438.
Neurology. C. WINKLER: “A partial foetus removed from a child.” 493.
NITROGEN FIXATION by means of the cyanide-process and atomic structure.
480.
Nurr system (A) (1, 2, 3). 124.
OLIGOCENE (Otoliths of teleostei from the) and the miocene of the Peel-
district and of Winterswijk. 231.
OLIGOCÈENEs (Sur quelques nouveaux insectes des lignites) de Rott. Sieben-
gebirge (Rhénanie). 605.
ONNES (H. KAMERLINGH) and W. Tuyn. Further experiments with
liquid helium. S. On the electric resistance of pure metals, etc. XII.
Measurements concerning the electric resistance of indium in the
temperature field of liquid helium. 504.
— and H. R. Wottjer. Further experiments with liquid helium. T.
Magnetic researches. XXIII. On the magnetisation of gadolinium sulphate
at temperatures obtainable with liquid helium. 626.
— and G. Breit. Magnetic researches. XXVI. Measurements of magnetic
permeabilities of chromium chloride and gadolinium sulphate at the
boiling point of liquid hydrogen in alternating fields of frequency
369.000 per second. 840.
Oorprtr (G. J. vAN). Secondary sex-characters and testis of the ten-spined
stickleback (Gasterosteus pungitius L.). 309.
ORGANS (A new form of correlation between). 420.
OsTHOFF’s estimates of star-colours (On the magnitude equation of). 12.
Oro.itHs of teleostei from the oligocene and the miocene of the Peel-district
and of Winterswijk. 231.
OXYGEN-NITROGEN (The critical curve of) mixtures, the critical phenomena
and some isotherms of two mixtures with 50°/) and 75"/, by volume
of oxygen in the neighbourhood of the critical point. 49.
Palaeo-botany. O. PostHumus: “Etapteris Bertrandi Scott, a new etapteris
from the upper carboniferous (lower coal-measures) from England, and
its bearing to stelar-morphological questions.” 669.
Palaeontology. |. SWEMLE and L. RuTTEN: “New findings of pliocene and
pleistocene mammals in Noord Brabant, and their geological signific-
ance.” 199.
XIV CONTENTS
Palaeontology. O. PostHumus: “Contributions to our knowledge of the
palaeontology of the Netherlands. I. Otoliths of teleostei from the
oligocene and the miocene of the Peel-district and of Winterswijk.” 231.
— O. PostHumus: “Contributions to our knowledge of the palaeontology
of the Netherlands. II. On the fauna of the phosphatic deposits in
Twente. (lower oligocene).” 235.
— F. Meunier: “Sur quelques nouveaux insectes des lignites oligocénes
(Aquitanien) de Rott. Siebengebirge (Rhénanie).” 605.
PARAFFIN (Hydrogenation of) by the BErRGius’ method. 226.
PERMEABILITIES (Measurements of magnetic) of chromium chloride and
gadolinium sulphate at the boiling point of liquid hydrogen in alter-
nating fields of frequency 369.000 per second. 840.
PERQUIN (J. N. J.) and H. I. Waterman. Hydrogenation of paraffin by
the BERGIUS’ method. 226.
Petrography. W. F. Grisorr: “On the rocks of Doormantop in central
New Guinea.” 191.
PETROMYZON FLUVIATILIS (The presence of cardio-regulative nerves in). 438.
PHOSPHATIC DEPOSITS (On the fauna of the) in Twente (Lower oligocene). 235.
PHOTO-CATALYTIC INFLUENCE (The) of some series of ketones on the light
oxidation of ethyl alcohol. 443.
Physics. J. P. KUENEN, T. VERSCHOYLE and A. TH. vaN Urk: “Isotherms
of di-atomic substances and their binary mixtures. XX. The critical
curve of oxygen-nitrogen mixtures, the critical phenomena and some
isotherms of two mixtures with 50°/, and 75°/) by volume of oxygen
in the neigbourhood of the critical point.’ 49.
— W.H. Keesom and J. pe SMEDT: “On the diffraction of Röntgen-rays
in liquids II.” 112.
— W. H. Juurus and M. MINNAERT: “The relation between the widening
and the mutual influence of dispersion lines in the spectrum of the
sun’s limb.” 329.
— H. W. J. Dik and P. ZEEMAN: “A relation between the spectra of
ionized potassium and argon.” II. 498.
— W. Tuyn and H. KAMERLINGH ONNEs: “Further experiments with
liquid helium. S. On the electric resistance of pure metals, etc. XII.
Measurements concerning the electric resistance of indium in the
temperature field of liquid helium.” 504.
— G. Breit: “Transients of magnetic field in supra-conductors.” 529.
— H. R. Wo tier: “Magnetic researches. XXII. On the determination of
the magnetisation at very low temperatures and on the susceptibility of
gadolinium sulphate in the region of temperatures obtainable with
liquid hydrogen.” 613.
CONTENTS XV
Physies. H. R. Worrser and H. KAMERLINGH ONNES: “Further experiments
with liquid helium. T. Magnetic résearches. XXIII. On the magnetisation
of gadolinium sulphate at temperatures obtainable with liquid helium.”
626.
— A. Mrcners: “The influence of rotation on the sensitiveness and the
accuracy of a pressure balance.” 805.
— G. Breit and H. KAMERLINGH ONNEs: “Magnetic researches. XXVI.
Measurements of magnetic permeabilities of chromium chloride and
gadolinium sulphate at the boiling point of liquid hydrogen in alternating
fields of frequency 369.000 per second”. 840.
Physiology. H. J. HAMBURGER: “A new form of correlation between organs.”
420.
J. B. ZWAARDEMAKER: “The presence of cardio-regulative nerves in
petromyzon fluviatilis.” 438.
— R. BRINKMAN and A. v. SZENT GyorGy!: “Researches on the chemical
causes of normal and pathological haemolysis.” 470.
— H. ZWAARDEMAKER, W. E. RINGER and E. Smits: “Is caesium radio
active?” 575.
— W. F. EiNTHOVEN: “The string galvanometer in wireless telegraphy.”’
635.
— Miss L. Kaiser: “Contributions to an experimental phonetic investiga-
tion of the Dutch language. I. The short o.” 745.
— J. vAN DER HOEVE and H. J. Frieringa: “Determination of the power
of the accommodation-muscle.” 763.
— J. G. DussER DE BARENNE and J. B. ZWAARDEMAKER: “On the influence
of the vagi on the frequency of the action currents of the diaphragm
during its respiratory movements. 771.
PLANE PENCILS (On the) containing three straight lines of a given algebraical
congruence of rays. 522.
PLIOCENE and pleistocene mammals (New findings of) in Noord Brabant,
and their geological significance. 199.
POINTS OF CONTINUITY (On the) of functions. 187.
POINTS OF SPACE (Representation of a tetrahedral complex on the). 390.
Potarity (On the determination of) in the epidermal ciliated cell. (After
experiments on amphibian larvae). 702.
POLARKURVEN (Ueber die zu einem Punkte und einer Geraden gehörigen)
inbezug auf eine gegebene algebraische Kurve. 783.
PostHuUMUSs (O.). Contributions to our knowledge of the palaeontology of
the Netherlands. I. Otoliths of teleostei from the oligocene and the
miocene of the Peel-district and of Winterswijk. 231.
— Contributions to our knowledge of the palaeontology of the Netherlands.
IL. On the fauna of the phosphatic deposits in Twente. (Lower oligo-
cene). 235.
XVI CON T EN TS
PosTHumus (O.). Etapteris Bertrandi Scott, a new etapteris from the upper
carboniferous (lower coal-meastires) from England, and its bearing to
stelar-morphological questions. 669.
PorassiuM (A relation between the spectra of ionized) and argon. (Second
comm.). 498.
POWER SERIES (On a generalisation of TAUuBER’s theorem concerning). 216.
— (A theorem concerning) in an infinite number of variables, with an
application to DirICHLET’s series. 278.
— (On) of the form: xPo — xpi + xp2—... 456.
PROPYLENE (Researches on the addition of water to ethylene and). 321.
Psychology. F. F. HazeLHorF and Miss H. Wiersma: “On subjective
rhythmisation.” 462.
PYRIDYLPYRROLES (The synthesis of some). 426.
RADIO-ACTIVE (Is caesium)? 575.
RANINIENS NOUVEAUX (Description de) des terrains tertiaires de Borneo. 777.
Rays (On the plane pencils containing three straight lines of a given alge-
braical congruence of). 522.
ReprtiLes (On the development of the shoulder-girdle and episternum in). 15.
RESEARCHES (MAGNETIC) v. MAGNETIC RESEARCHES.
RESISTANCE (On the electric) of pure metals, etc. XII. Measurements concern-
ing the electric resistance of indium in the temperature field of liquid
helium. 504.
— (On the) experienced by a fluid in turbulent motion. 582.
RESPIRATION (A method of simultaneously studying the adsorption of Oz and
the discharge of C O; in). 408.
RHYTHMISATION (On subjective). 462.
RINGER (W. E.), E. Smits and H. ZWAARDEMAKER. Is caesium radio-active ?
575.
RINGING EXPERIMENTS with variegated branches. 756.
Rocks (On the) of Doormantop in Central New Guinea. 191.
RONTGEN-RAYS (On the diffraction of) in liquids. II. 112.
RorarioN (The influence of) on the sensitiveness and the accuracy of a
pressure balance. 805.
Rorr (Sur quelques nouveaux insectes des lignites oligocènes (Aquitanien)
de), Siebengebirge (Rhénanie). 605.
RuBBERSOL (The electro-viscous effect in). 43.
RurreN (L.). Geological data derived from the region of the “Bird's head”
of New-Guinea. 274.
— and I. SweMmre. New findings of pliocene and pleistocene mammals in
Noord Brabant, and their geological significance. 199.
SCHAAKE (G.). The complex of the conics which cut five given straight
lines. 513.
CONTENTS XVII
SCHAAKE (G.). On the plane pencils containing three straight lines of a
given algebraical congruence of rays. 522.
SCHOUTEN (J. A.). On a non-symmetrical affine field theory. 850.
SCHREINEMAKERS (F. A. H.). In-, mono- and divariant equilibria. XXIII.
283. XXIV. 719.
SEX-CHARACTERS (Secondary) and testis of the ten-spined stickleback. (Gaster-
osteus pungitius L.). 309.
SHOULDER-BLADE (The development of the) in man. 297.
SHOULDER-GIRDLE (On the development of the) and episternum in reptiles. 15.
SJOLLEMA (B.) and Miss J. E. vAN DER ZANDE. Researches on the
metabolism of milchcows suffering from acetonemia. 666.
SMEDT (J. DE) and W. H. Kegsom. On the diffraction of Röntgen-rays in
liquids. II. 112.
Smits (A). The phenomenon of electrical supertension. III. 259.
— The influence of intensive drying on internal conversion. I. 266.
— The system sulphur trioxide. I. 270.
— The electromotive behaviour of magnesium. II. 395.
Smits (E.), H. ZWAARDEMAKER and W. E. RinGer. Is caesium radio-active ?
575.
Sourn CereBEs (On tertiary marine deposits with fossil fishes from). 159.
SPECTRA (A relation between the) of ionized potassium and argon. (Second
comm.). 498.
SPECTRUM (The relation between the widening and the mutual influence of
dispersion lines in the) of the sun’s limb. 329.
STAR-COLOURS (On the magnitude equation of OsTHOFF’s estimates of). 12,
STELAR-MORPHOLOGICAL QUESTIONS (Etapteris Bertrandi Scott, a new etapteris
from the upper carboniferous (lower coalmeasures) from England, and
its bearing to). 669.
STICKLEBACK (Secondary sex-characters and testis of the ten-spined). (Gas-
terosteus pungitius L.). 309.
STIMULATION (On) in auxotonic movements. 171.
STRAELEN (V. VAN). Description de crustacés décapodes nouveaux des
terrains tertiaires de Borneo. 489.
— Description de Raniniens nouveaux des terrains tertiares de Borneo. 777.
STRING GALVANOMETER (The) in wireless telegraphy. 635.
SULFOBUTYRIC ACID (n.x-) and its optically active components. 79.
SULPHOACETIC ACIDS (The second dissociation constant of) and z-sulphopro-
pionic acids. 83.
SULPHUR TRIOXIDE (The system). I. 270.
Sun’s tims (The relation between the widening and the mutual influence
of dispersion lines in the spectrum of the). 329.
XVIII CONTE jNaTus
SUPERTENSION (The phenomenon of electrical). III. 259.
SUPRA-CONDUCTORS (Transients of magnetic field in). 529.
SWEMLE (I.) and L. RurreN. New findings of pliocene and pleistocene
mammals in Noord Brabant, and their geological significance. 199.
SYNTHESIS (The) of some pyridylpyrroles. 426.
SZENT-GYöRGYI (A. v.) and R. BRINKMAN. Researches on the chemical
causes of normal and pathological haemolysis. 470.
TANGENTS (A representation of the line elements of a plane on the) of a
hyperboloid. 129.
TAUBER’s theorem (On a generalisation of) corcerning power series. 216.
TELEGRAPHY, WIRELESS (The string galvanometer in). 635.
TELEOSTE! (Otoliths of) from the oligocene and the miocene of the Peel-
district and of Winterswijk. 231.
TERRAINS TERTIAIRES (Description de crustacés décapodes nouveaux des) de
Borneo. 489.
— (Description de Raniniens nouveaux des) de Borneo. 777.
TERTIARY marine deposits (On) with fossil fishes from South Celebes. 159.
Testis (Secondary sex-characters and) of the ten-spined stickleback (Gaster-
osteus pungitius L.). 309.
TETRAHEDRAL COMPLEX (Representation of a) on the points of space. 390.
THEOREM (A generalisation of MERTENS’). 203.
— Ona generalisation of TAuBER’s) concerning power series. 216.
THyMus, spiracular sense organ and fenestra vestibuli (ovalis) in a 63 m.m.
long embryo of Heptanchus cinereus. 727.
TOLLENAAR (D.). Dark growth-responses. 378.
TURBULENT MOTION (On the resistance experienced by a fluid in). 582.
Tuyn (W.) and H. KAMERLINGH ONNES. Further experiments with liquid
helium. S. On the electric resistance of pure metals, etc. XII. Measure-
ments concerning the electric resistance of indium in the temperature
field of liquid helium. 504.
TwIsTED CUBICS (A congruence (1,0) of). 126.
Urk (A. Tu. van), J. P. KUENEN and T. VERSCHOYLE. Isotherms of di-atomic
substances and their binary mixtures. XX. The critical curve of oxygen-
nitrogen mixtures, the critical phenomena and some isotherms of two
mixtures with 50°/) and 75/, by volume of oxygen in the neighbour-
hood of the critical point. 49.
Vaar (On the influence of the) on the frenquency of the action currents of
the diaphragm during its respiratory movements. 771.
VALETON (TH.). The genus Coptosapelta Kortu. (Rubiaceae). 361.
CROONSE Ey Ne DS: XIX.
VERSCHOYLE (T.), A. TH. vAN Urk and J. P. KUENEN. Isotherms of
di-atomic substances and their binary mixtures. XX. The critical curve
of oxygen-nitrogen mixtures, the critical phenomena and some isotherms
of two mixtures with 50°/, and 75°/, by volume of oxygen in the
neighbourhood of the critical point. 49.
Visser (S. W.). A non-tangent infralateral arc. 712.
VOGELKOP v. BIRD’s HEAD.
VOLTA-LUMINESCENCE. 561.
VRIES (JAN DE). A null system (1, 2, 3). 124.
— A congruence (1,0) of twisted cubics. 126.
— A representation of the line elements of a plane on the tangents of
a hyperboloid. 129.
— Representation of a tetrahedral complex on the points of space. 390.
Vries (O. pe). The coagulation of Hevea latex. 675.
WAERDEN (B. L. VAN DER). Ueber das Komitantensystem zweier und
dreier ternärer quadratischer Formen. 2.
WATER (On the bacteriophage and the self-purification of). 116.
— (Researches on the addition of) to ethylene and propylene. 321.
— (The binding of) by animal carbon. 548.
WATERMAN (H. I.) and J. N. J. Perouin. Hydrogenation of paraffin by
the Bergius’ method. 226.
WEEVERS (Ta). Ringing experiments with variegated branches. 756.
W EITZENBOCK (R.). Ueber Invarianten von Bilinearformen. 801.
WisBautT (J. P.) and J. J. DiEKMANN. Researches on the addition of water
to ethylene and propylene. (Preliminary communication). 321.
— and Miss ELisaBETH DINGEMANSE. The synthesis of some pyridyl-
pyrroles. 426.
WieRSMA (Miss HELEEN) and F. F. HAZELHOFF. On subjective rhythm-
isation. 462.
WINKLER (C.). A partial foetus removed from a child. 493.
WINKLER-JUNIUS (E.) and J. A. LATUMETEN. The histopathology of Lyssa
in respect to the propagation of the lyssavirus. 825.
W OERDEMAN (M. W.). On the determination of polarity in the epidermal
ciliated cell. (After experiments on amphibian larvae). 702.
— A contribution to the histophysiology of the ciliated epithelium. 707.
Worrr (J.). On the points of continuity of functions. 187.
— Inner limiting sets. 189.
Worrr (L. K.) and G. M. Kraay. The splitting of lipoids by bacteria. I. 436.
W oLTJer (H. R.). Magnetic researches. XXII. On the determination of the
magnetisation at very low temperatures and on the susceptibility of
gadolinium sulphate in the region of temperatures obtainable with
liquid hydrogen. 613.
XX CCOyNST ENED a
Worriser (H. R.) and H. KAMERLINGH ONNes. Further experiments with
liquid helium. T. Magnetic researches. XXIII. On the magnetisation of
gadolinium sulphate at temperatures obtainable with liquid helium. 626.
Women, Dutcu (The menarche in) and its precipitated appearance in the
youngest generation. 650.
Wine (J. W. van). Thymus, spiracular sense organ and fenestra vestibuli
(ovalis) in a 63 m.m. long embryo of Heptanchus cinereus. 727.
ZANDE (Miss J. E. VAN DER) and B. SsorLEMA. Researches on the
metabolism of milch-cows suffering from acetonemia. 666.
ZEEMAN (P.) and H. W. J. Dik. A relation between the spectra of ionized
potassium and argon. (Second comm.). 498.
Zoology. H. BoscuMa: “Experimental budding in Fungia fungites.” 88.
— G. J. vaN Oorpr: “Secondary sex-characters and testis of the ten-spined
Stickleback (Gasterosteus pungitius L.).”’ 309.
ZWAARDEMAKER (H.), W. E. RINGER and E. Smits. Is caesium radio-active ?
575.
ZWAARDEMAKER (J. B.). The presence of cardio-regulative nerves in
Petromyzon fluviatilis. 438.
— and J. G. Dusser DE BARENNE. On the influence of the vagi on the
frequency of the action currents of the diaphragm during its respiratory
movements. 771.
KONINKLIJKE AKADEMIE
VAN WETENSCHAPPEN
-- TE AMSTERDAM -:-
PROCEEDINGS OF THE
SECTION OF SCIENCES
VOLUME XXVI
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