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KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.
PROCEEDINGS OF THE MEETING
of Saturday December 27, 1902.
DEC —-
(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 27 December 1902, DL XI).
CA a sar IN TS,
H. W. Bakuvis Roozenoom: “Tin amalgams’’, p. 373.
J. Porrer yan Loon: “Benzidine transformation’. (Communicated by Prof. C. A. Lorry per
Bruyn), p. 377. ;
Kk. F. Wexcxenacu: “On the duration of the compensatory pause after stimulation of the
auricle of the mammalian heart”. (Communicated by Prof. C. A. PeKELMARING), p. 878.
J. Carprssar: “On the geometrical representation of the motion of variable systems”, p. 386.
J. K. A. Warri SALOMONSON: “A new law concerning the relation between stimulus
and effect”, (4th Communieatien). (Communicated by Prof. C. Wixkren), p. 392.
M. W. Brewermcx and A. van DerpeEN: “On a colourless bacterium, whose carbon food
comes from the atmosphere”, p. 398.
- CO : : 5 = -
L. IL. Srerrseva: “The caleulation from the magnetic rotation of the plane of polari-
m
sation, for substances without an absorptionband in the visible spectrum”. (Communicated by
Prof. H. Kamerrinait ONNES), p. 418,
The following papers were read:
Chemistry. — “Tin amalgams”. By Prof. H. W. BaKnurs RooznBoom.
(Communicated in the meeting of November 29, 1902).
As the number of properly studied amalgams is still very small
I directed Dr. van Hereren to conduct an investigation on tin
amalgams in connection with the research on cadmiun amalgams
by Dr. Bur. The more important results are Communicated here.
In the liquid condition tin and mercury are miscible in all pro-
portions. From the different mixtures a solid phase is deposited at
different temperatures. The points at which solidification begins are
indicated in the accompanying figure by two lines AC and CL
25
Proceedings Royal Acad. Amsterdam, Vol. V.
(3745
which meet each other at C (0.3 at. °/, Sn and
angle.
54.5) in a sharp
As the line CB ends in the melting point of tin, the solid phase
Which deposits on cooling must be either tin or mixed crystals in
Which ordinary tin occurs as a component. On analysis, the solid
phase which has separated from the liquid amalgam at 25° was
found to be composed of 94 atom °/, Sn.
On account of the difficulty of obtaining trustworthy results in
Be ro rego tre Hae ADD fo 9 /oo
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LINE BC,
At. °/) Sn. | Temp. | At. 0/, Sn. Temp.
100 231° .6 0 Wi 902.0
89.95 Od .6 40.79 | 79.
76.62 483 .7 5.17 | 65 .2
}
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GOL. 44 15e
49.99 133 .4
Qr OC |
oD soo 107 .4
98.96 | 99 .0
this manner, measurements of the fj, M/S were also made at 25°
of amalgams. of 0.001—100 atom °/, Sn against an amalgam of 16
atom °/,.
These measurements led to the results that the unsaturated amalgams
have a 4. M. F. rising with the amount of tin until at 1.2 atom "/,
saturation sets in. From this concentration up to 99 atom °/, the
potential remains unchanged, consequently two phases of unchange-
able concentration must exist between these limits; one of these is
the liquid one of 1.2 °/,, the other the solid one containing 99
atom °/,.
At 25° the crystals deposited therefore consist of nearly pure tin
which is the case in a still greater degree at higher temperatures.
By a comparison of the values of the /. J/. /. for amalgams of which
the whole mass was liquid at 25° and 50° the heat of amalgamation
could be calculated. The introduction of 1 gram-atom of Sn into
a liquid amalgam with O0.01—1.00 atom °/, Sn, therefore nearly
pure Hg, absorbs about 3000 calories.
The line CB may also be considered as the line of the solutions
saturated with Sn. It takes a very peculiar course. The part from
120° up to the melting point of tin is nearly straight, the centre
part shows a very rapid increase of the solubility with the tempe-
rature, the lower part, however, an exceedingly small increase and
also an exceedingly small solubility. so that the line approaches
very closely the Hg-axis. In the lower part of the figure (p. 374)
this part with its course towards the melting point of He has been
drawn on a larger scale.
5
The extraordinarily great curvature of the central part of the line
would lead to the supposition that the liquid mixtures of Sn + He
in the absence of a solid phase would on further cooling separate
into two layers.
On cooling below —34.5° a change takes place in all amalgams
from 0.3 to 85°/,, accompanied by a decided evolution of heat and
decrease of volume. With increasing concentrations of Sn it first
increases but then decreases in intensity. The maximum lies near
50°/,. This change occurs in the figure on the line CD which
therefore runs to at least 85 "/,.
The change causes a new phase to appear which also belongs to
the second solidifving-line CA. The maximum in the intensity of
the change on CD at about 50°/, would lead us to suppose that
mixed crystals having about this composition are formed. The modi-
fication of tin therein contained must differ from ordinary tin.
Between —934°.5 and -
deposited from the mother-liquor (which moves along the line CA),
38°.5 these mixed crystals continue to be
this is accompanied by expansion. This change in volume diminishes
as the amount of tin present increases and dies out near 75 °/,.
The solidification point of pure mercury and also the final solidifi-
eation point of all amalgams containing up to about 60°/, Sn, lies
at —38°.6 (line AH). As the line (A of the saturated solutions
also ends here it would seem that at the solidifying point of Hg,
the solubility of tin has decreased to 0, so that instead of a eutectic
mixture only the remaining mercury solidifies.
Still, the point A bears quite the characteristic of a eutectic point
as not only the line AF is horizontal, but all mixtures up to 60 °/,
Sn also remain a shorter or longer time at this temperature which
proves that a residual liquid is solidifying completely.
A ereat uncertainty still exists as to the nature of the tin-modifi-
cation which occurs in mixed crystals below —34°.5 chietly because
it has so far not been possible to discover the part played in the
amalgams by the grey modification of tin which may occur below
20° C.
But from the change in volume which takes place in the different
transformations at and below —34°.5 we may argue that the specific
volume of the tin must be smaller than that of the grey modification
and larger than that of liquid and, therefore, also of ordinary tin.
(514
Chemistry. — “Benzidine transformation.” By Dr. J. Porrur van
Loon (Groningen). (Communicated by Prof. C. A. LoBry Dr
BRUYN).
(Communicated in the meeting of November 29, 1902).
It is known that hydrazobenzene when treated with a dilute mineral
acid is converted into benzidine and diphenylene, benzidine being,
however, the main product. 1 endeavoured to ascertain the proportion
in Which the isomers are formed and in how far this depends on the
temperature and the concentration of the acid and L further attempted
fo measure the velocity with which the transformation takes place
under definite circumstances,
_ Benzidine was obtained pure by recrystallisation from water and
distillation in vacuo; the melting point of this substance was 128°
which is in agreement with the statements of Merz and STRASSER.
Gourn= tf. Pract: Cho N; B 60: 186).
For the preparation of hydrazobenzene, azobenzene was used as
the starting point: this was purified by distillation and then reduced
with zine dust in an alcoholic alkaline solution. The hydrazobenzene so
obtained was dissolved by warming in alcohol and the still yellow
liquid decolorised by means of ammonia and zine dust: the filtrate
deposited pure white crystals of hydrazobenzene which could be
separated unaltered from the liquid. A determination of the melting
point gave as result 122°.
For the study of the transformation it was necessary to have a
method for the quantitative determination of benzidine. lt was found
possible to do this gravimetrically by adding potassium sulphate to
a solution containing not too much free acid and so precipitating the
base as sulphate which was then collected on a weighed filter. According
to my experiments, the slight solubility of benzidine sulphate amounts
to 5—6 milligrams per 100 ce. of water at the ordinary temperature
and consequently a correction should be applied. To ascertain in
What proportion the two bases are formed during the transformation
of hydrazobenzene, weighed quantities of this substance were put
into bottles of about 120 ee. capacity and then shaken with a definite
solution of an acid until all had dissolved. The benzidine present
in the solution was then estimated, as directed, and the proportion
calculated from the two data.
At the ordinary temperature, N/10 hydrochloric acid used in this
manner causes 84 per cent of the hydrazobenzene to be converted
into benzidine. Normal hydrochloric, hydrobromic acids convert 90
(3
per cent of the same into benzidine. At a higher temperature ihe
proportion is another, for in four experiments with one-tenth normal
hydrochloric acid, nitric acid, sulphuric acid and hydrobromie acid
the proportions at a 1007 were respectively 66.4, 67.5, 63.1 and
65.8 per cent, therefore, much lower.
To get some data respecting the velocity of reaction a beaker with
50 per cent alcohol which contained hydrochloric acid in tenth-
normal concentration was put into a thermostat and while stirring
violently and passing a current of carbon dioxide over the surface
a few grams of hydrazobenzene were introduced into the liquid in
which that substance is but little soluble.
At 25°, the velocity appeared to be dependent on the concentration
of the acid and it increased more rapidly than the concentration.
The experiments are being continued in the two directions indicated
above.
(Chem. Lab. Univers. Gronimgen).
Physiology. — ‘On the duration of the compensatory pause after
stimulation of the auricle of the mammalian heart.’ By Prof.
Kk. FE. WereKeBacH. (Communicated by Prof. PEKELHARING).
(Communicated in the meeting of 29 November 1902).
When an extrasystole is set up by artificial stimulation of the
ventricle or auricle of the beating frog’s heart, this extra-systole is
followed up by a pause longer than the pause succeeding a spon-
taneous systole. This long interval was studied by Margy, Dastre
and others, and called a compensatory pause, because the longer
quiescence of the heart was regarded as a compensation for the extra
activity of the heart muscle. And it was not without reason that
the word “compensation” was used, because the pause after an extra-
systole is of such length, that the following spontaneous contraction
just commences in the moment when it would have set in if, instead
of an extra, a spontaneous systole had preceded. _ENGELMANN (6)
has given a simple and exhaustive explanation of the pause: the
normal, physiological stimulus to contraction reaching the heart from
the vena cava and causing it to contract finds, after an extra-systole
auricle and ventricle in a refractory phase and so it cannot cause
a contraction. It is only the following stimulus which finds the
heart again in a condition in which it can react on that stimulus;
the contraction (the “post compensatory’’) then commencing, presents
Ne
(379 )
itself precisely in the moment in which it would have commenced
if the heart’s action had been disturbed; so the rhythm of the
physiological stimulation is not disturbed. In fig. I) the case is
represented schematically. An artificial stimulus f reaches 7. When
the second stimulus arrives it finds the ventricle still refractory ; so
one systole is missing, but the following third stimulus, causes just
at the right time again a normal systole. So the pause following
the extra systole is with regard to its duration just Compensatory ;
the time taken up by a spontaneous systole + extra systole and pause
is just equal io that of two normal systoles.
If, however, we stimulate the froe’s heart at the vena cava where
the contraction always sets in, the compensatory pause is entirely
missing and the following spontaneous systole succeeds the extra
systole after a period equal to the normal period of contraction. In
Fig. 1 the second artificial stimulus Y reaches the vena cava; the
following spontaneous contraction sets in after the usual interval 20,
a compensatory pause is missing. Whilst the interval between the
systole preceding the extra systole and the one following the extra-
systole after stimulation of the ventricle (or of the auricle) was
double the normal period = 40, the same interval is here only
12 + 20 — 32.
} Ho Fy r
From this ensues that the stimulus is not rhythmically induced from
1) In these schemes answering to those used formerly by ENGELMANN and by me
the lime is indicated on the three abseissae, and this is done for the duration of the
phase and the stimulation of vena cava (Ve), auricle (A) and ventricle (V). | =
physiological stimulus, ¥= artificial stimulus. The perpendicular lines represent the
contractions of the heart-cavities. The slanting lines connecting the base points of
the systole-mark indicate the direction in which the stimulus is conducted. If
these lines are dotted the conduction does not actually take place. The duration
of the spontaneous period is put at 20 abscis units (= 1 mM.), the interval from
the moment of the physiological stimulus to the ventricular contraction (Ve V's) =5
units.
( 380 3
outside to the vena cava, but that it originates in that place in a
definite period. It is certainly the most natural and the most suitable
explanation of the phenomenon to assume that at the venae cavae
(as is known to be the case in less degree in the other parts of the heart)
continually stimulating matter is formed, till this obtains such a
strength that a contraction is caused. When however, the muscle
fibres contract the stimulating matter seems to have been used up
or at least to have been destroyed, so that every time after a con-
traction the same time is wanted to produce new stimulating matter
to such a strength that again a contraction follows. This destroying
of the stimulating matter (dissociation in tons, chemical changes
or whatever this may be) always takes place when there is a
contraction, whether the systole is caused by the stimulating matter
itself or caused by a stimulus induced from elsewhere. For it
is a well-known fact, that by artificial stimulation of the auricle
or the ventricle, more frequent than the spontaneous rhythm, the
latter can be entirely overpowered.
Another explanation is that at the vena cava there is a continual
stimulation constant in strength, expressing itself periodically in
systoles, because with each systole irritability, contractility and con-
ductive power of the heart muscle are neutralized; so if a systole
has taken place if always again lasts a certain time before the heart
has recovered itself in so far that another contraction is possible.
ENGELMANN Objects to this, that the explosion brought about by the
contraction in the molecular system of the muscle cell will destroy
the stimulating matter in stock together with the other properties of
this muscle cell, (irritability, contractility and conductive power);
moreover did) ENGELMANN show that the period of the formation of
the stimulus can be changed independent of the irritability in the
wall of the vena by chronotropic. nerve influence. So we must
assume that the systole destroys the stimulating matter and that
every time the latter must again develop itself after every systole
to active power. The law of the preservation of the physiological
period of stimulation dominating the duration of the compensatory
pause and all the important data come to light by means of “the
method of the extra-systoles” for the frog’s heart have been traced
by Cusuxy and Marrnnws (1) for the mammalian heart. These in-
vestigators showed that the mammalian heart obeys the same laws
as the frog’s heart, that its activity is dominated by the same fun-
damental properties of the fibres of the heart muscle, that the same
theories hold good for both.
Only in one respect they found a difference: when the auricle is
( 381 5
artificially stimulated, the compensatory pause after the extra-systole
is not as in the frog’s heart truly compensatory but mostly of too
short a duration. Sometimes if was completely compensatory, it was
never entirely missing, it was generally shortened and then at any
rate not equally shortened.
They say on this subject (l.c. page 226): „As long as the interval
i
“A—A. is of considerable length the compensatory pause in the
“auricle is truly compensatory, that is the interval between the last
“spontaneous contraction and the post-compensatory is equal to two
“auricular cycles. When however the stimulus falls earlier in the
“irritable period, no true compensation occurs, the post-compensatory
“contraction being premature,.... when Ad, is short the com-
“pensation (of time W.) before the first natural contraction is always
“imperfect.”
The explanation of this difference is according to them: “either
“ihe contraction wave passes from the auricle to the great veins
“and there sets up a forced contraction which returning to the
“auricle causes the premature systele, or the irritability of the auricle
“oradually increases until if culminates in a contraction which is
“independent of the great veins and initiated in the auricular muscle
“itself. As to which of these two is the correet explanation we are
“unable to give any opinion and feel that it would be useless to
“balance probabilities before the movements of the great veins have
“been exammed.”
Formerly I myself expressed the supposition, that the mammalian
auricle might possess a greater automatic irritability, because in the
phylogenetic development a part of sinus and vena would be taken
up in the auricle.
H. E. Herine (2) has also been able to establish the difference
deseribed for the first time by Cusiyy and Marrirews; he says:
“The earlier the moment of stimulation falls in the irritable period
“of the auricle, the shorter the artificial bigeminus is (interval between
“last spontaneous and post-compensatory systole); the later it falls,
“the more the duration of the artificial bigeminus approaches that of
“two normal cardiac periods.” He continues: “the pause (after the
“extra-systole of the auricle) lasts longer according to the moment
“of stimulation falling earlier in the irritable period.” So here too
he assumes the law of the conservation of the physiological period
of stimulation: “aber die Beziehune ist keine so einfache wie am
Ventrikel”.
We had all overlooked, that Mackrnzin (3) had beeome convinced
already in 1894 after a careful analysis of the venous and liver pulse
( 38201
that also in the human heart a “premature” contraction coming from
the auricle is often succeeded by a too short compensatory pause.
The possibility of distinguishing in this way between auricular and
ventricular extra systoles had not escaped his attention.
When reflecting upon the consequences which extra systoles coming
from the auricle must have on the action of the heart and the cir-
culation of the blood of man, I found the following simple explanation
of the above mentioned phenomenon, an explanation from which
ensues that we have not got anything to do with a difference in
principle between the frog’s heart and the mammalian heart and
that it is founded on an anatomic difference between the two hearts.
ENGELMANN (5) has shown that in muscular tissue of equal com-
position the stimulus to contraction is conducted also at an equal
rate in all directions. So when an artificial stimulus is given to the
auricle, a contraction stimulus and with it a contraction wave will
pass from the stimulated point not only to the lower parts of the
auricle and to the ventricle, but also to the higher parts of the
auricle and to the vena cava, so to the place where normally the
stimulus is formed and the contraction begins. ENGELMANN (6) has
already pointed to the importance which this “antiperistaltie”” move-
ment may have for the action of the heart, Cusuyy and Marrinws
have also seen the possibility of it.
When a stimulus is applied late in the irritable period of the
auricle, so just before the moment when the following physiological
stimulus was to come from the vena cava, the stimulus (and the
contraction) will not be able to reach the vena cava any more
before the physiological stimulus has had its effect there: auricle and
ventricle will obey the extra stimulus, the spontaneous contraction
already begun will not go on, but the rhythm at the venae is not
disturbed.
If the extra-systole sets in a little earlier, the extra contraction
might reach the vena cava just at the moment that the physiological
stimulus had developed to the necessary intensity ; then also auricle
and ventricle obey the extra stimulus, the physiological stimulus is
neutralized or it finds the whole heart refractory, but here too the
rhythm of the formation of the stimulus is not disturbed and the
pause of auricle and ventricle is completely compensatory.
When however the auricle is stimulated still earlier, the extr
contraction will reach the vena cava before the moment, in which the
stimulus to contraction forming there, had attained at sufficient strength
to cause a contraction. The stimulating matter found there at that
moment will be destroyed by the extra contraction : from this moment
new stimulating matter is being formed and after a certain time
equal to the normal period it will have obtained enough intensity to
cause another contraction. So the following spontaneous systole will
not fall in the moment it would have done so if an extra systole
had not been set up, but just so much earlier as the extra contrac-
tion reached the vena cava before the moment in which the following
spontaneous contraction would have occurred.
In the diagrams I] and HIL an attempt has been made at making
these observations clear for a particular case.
In fig. H the auricle is artificially stimulated respectively 18, 15
and 12 units of time after the previous spontaneous contraction ;
auricle and ventricle follow the extra stimulus; in the first two cases
the extra contraction moving to the vena cava intercepted the spon-
taneous contraction coming from the vena cava. In the third case it
arrives in the vena cava just at the same time as the physiological
stimulus becomes active. In all these cases the rhythm remains un-
disturbed and the compensatory pause is complete for the auricle as
well as for the ventricle: the interval between the systole preceding
the extra systole and the one following it is double the period of
the heart, in this case = 40.
In fig. HIL an earlier stimulation of the heart is shown, 10, resp.
8 and 5 units of time after the preceding systole the auricle is
stimulated. The extra systole formed by the first stimulus arrives in
the vena cava 4 units before the following spontaneous contraction.
The stimulating matter present at that moment is destroyed and
a certain time — 20 has to pass before the stimulus has increased
to sufficient strength. So the interval of the spontaneous contractions
is not = 40 but = 16 + 20= 36.
According to the extra auricular contraction falling earlier, this
interval must become shorter, a fact which goes without saving, in
fie: Il resp. — 35 vand = Bd,
From this ensues, that when the stimulation ¢s ejected late in the
irritable period the com pensatoriy pause is complete and farthermore,
the earlier the stimulation ts efiected the shorter the interval between
preceding systole and following spontaneous systole.
Another influence is still at work, which also governs the length
of the pause. The earlier the stimulation is effected in the irritable
period of the auricle, the slower the stimulus is conducted through the
wall of the heart, for the conductive power of the cardiac muscle
returns but gradually after the preceding systole. So the interval A.— Je,
will be longer according to the stimulus being effected earlier and
as this interval also dominates the moment in which the stimulating
material is destroyed by the induced extra contraction it will also
influence the length of the auricular interval. In fig. HL where the
slower conduction when the stimulus is effected earlier is taken into
account this influence is illustrated. And in this way it is to be
explained, that the interval ts longer after an auricular ertra-systole
according to the moment of stimulation falling earlier in the irritable
period of the auricle following quicker upon the preceding systole.
The differences in length of the compensatory pause after stimu-
lation of the auricle are in this way easily explained and it appears
that the rules established for the amphibian heart hold good for the
mammalian heart, in the sense however, as HeRING says, that “die
Beziehung keine so einfache ist”
The peculiar modifications in the course of the extra contiaction
when the auricle is stimulated, derived by Mackenzin from the venous
pulse, by Cusaxy and Marruews from the tracings of the auricular
movements, Will probably find their explanation in the way in which,
as is proved in fig. IL, the contraction waves meet here in the auricular
( 385 )
wall and the differences ; will depend upon the spontaneous or the
extra contraction being the most considerable.
The question must however now be put: why does a complete
compensatory pause always (or almost always, ENGELMANN ®) follow
the extra systole of the auricle in the amphibian heart and why in
the mammalian heart only under certain conditions >
The answer may run as follows: In equally built up parts of the
heart muscle the stimulus is also equally conducted to all sides, but
Where for whatever reason the state of the muscle fibres is not
everywhere the same, the conduction of the stimulus will neither be
the same. This is the reason that the conduction of the stimulus of the
auricle on the ventricle, in general of one division of the heart on
the other, takes place much slower than inside the wall of auricle
or ventricle. When conduction takes place in the direction opposed
to the normal, this distinction will not make itself less felt. And
just as the slower conduction may be the cause that extra-systoles
of the ventricle never recede quickly enough to have a disturbing
effect on the rhythm of the great veins, the differentiation between
veins, sinus and ventricle in the froe’s heart will be the cause, that
here a stimulation of the auricle is not quickly enough conducted
through the transition places to disturb the rhythm at the venae
cavae. Moreover this possibility seems so much the slighter, because
in the frog’s heart muscle fibres with a strong automatic irritability
ascend high up in the vena cava and so cannot be reached so easily
by an extra stimulus. As this differentiation of the cardiac muscle
between vena cava and atrio-ventricular limit is missing for the
mammals, it is no wonder that the disturbing influence on the for-
mation of the stimulus at the vena cava occurs just in the mammalian
heart.
If finally this explanation is the right one, the place where the
auricle of the mammatian hearth is stimulated, will have its effect
on the length of the compensatory pause: perhaps it will be possible
to establish for not too small hearts and where the conduction
of the muscle has already somewhat slackened, that for auricular
stmulation far from the vena cava the compensatory pause is
longer or even complete, whilst the pause becomes shorter according
to the auricular stimulation taking place closer to the vena cava.
For such an experiment the stimulation would always have to be
effected exactly in the same moment of the heart period, every time
equally long after the preceding systole.
( 386 )
LITERATURE:
|. Cusuny and Marrnews, Journal of physiology. Vol. XXI,
9. H. E. Henine, Pflüger's Archiv. Bd. LXXXII.
3. J. Mackenzie, Journal of Pathology and Bacteriology. Vol. IL.
4. K. PE, WerereBacn, Zeitschrift fiir Klin. Medicin. Bd. XXXVI.
5. TH. W. ENGELMANN, Sur la transmission réciproque et irréciproque. Archives Néer-
landaises XXX.
6. Tu. W. ENGELMANN, “Onderzoekingen” Physiol. laborat. Utrecht. IV Series, III
Vol. 1895.
Mathematics. “On the geometrical representation of the motion
of variable systems”. By Prof. J. CARDINAAL.
I. Im two communications ') some theorems have been developed
by me, relating to the motion of variable systems. Also in this sub-
division of the doctrine of motion the method of the geometrical
representation occurring so frequently in Mathematics can be applied.
The following communication has in view to mention some parti-
culars on this subject. The representation in question is treated *)
by R. Srurm. From this treatise L derive the short summary, which
must needs appear here as an introduction to the subject.
2. In the quoted considerations two complexes of rays played
an important part, namely the tetrahedral complex formed by the
directions of the velocities of the points of the moving system and
the ravs of a focal system belonging to it; the latter consists for
the motion of an invariable system of the normals of the trajectories
of the points and for a projectively variable system of rays whose
construction took a great part of the considerations. The purpose
must be to obtain a simultaneous representation of complex and focal
system; it will prove desirable to give the foremost place to the
representation of the focal system.
3. Let thus be given the focal system A situated in the space >,
According to the method of Syivester let us suppose two planes
Sand § with two projective pencils of rays situated in them with
their vertices VY’ and NV situated on the line of intersection §§' w,
!) Proceedings of the Kon. Akad. van Wetensch., section of science, vol. IV,
pages 489 and 58s.
ORT
*) Die Gebilde ersten und zweiten Grades der Liniengeomelrie, 1, p. 257,
( 387 )
v being an homologous ray of both pencils. The rays of A are the
transversals of two homologous rays of (Y§’) and (NS).
Let us now take two sheaves of rays in the space , with the
and: A7
= /
these sheaves and the pointfields s and §’, in such a way that the
vertices _X, , and establish a projective correspondence between
pencil of planes through the axis YA, is homologous to the pencils
CYS’) and (X's). Let / be a ray of A, cutting two homologous ravs
of CNS) and (NS), to which in the homologous plane 4, a ray /,
, and /, intersect
out of NX, and a ray /’, out of X’, correspond; /
each other in a point ZL. This point is homologous to the ray /.
So a projective correspondence is established between the points of
the space =, and the rays of the focal system 4.
As is the case with every representation, also here the knowledge
of its principal curve cannot be dispensed with. It is a conie A?
through the points Y, and WX’,
homologous to the pencils of rays of 4 situated in planes through.
The plane 5, (principal plane) itself is homologous to 2.
To an arbitrary pencil of rays of {a right line corresponds cutting
situated in a plane §,. Its points are
NG, to a hyperboloidic system of focal rays a conic having two
points in common with .X,*, to a linear congruence belonging to La
quadratic surface through WX’.
4. Let a projectively variable moving spacial system be given:
let as before PQRS be the tetrahedron of coincidence of two suc-
cessive positions and let the corresponding focal system A be deter-
mined by PQ and RS as conjugate polars and the conic A? touching
PR and PS in Mand S. According to the indicated method the
focal system can be represented in the space 2; for the tetrahedral
complex of the directions of the velocities, however, we need an-
other representation, which can be taken in such a way that the
same principal curve is retained; we shall succeed in this if we do
not represent the complex itself, but its section with the focal system d.
This gives rise to a congruence (2,2) which we shall first investigate
more closely.
5. Let A be an arbitrary point, @ its focal plane; at the same
time <A is the vertex of a quadratic cone, geometrical locus of the
directions of the velocities through A, but of which only one is the
direction of velocity of A itself. This cone will cut in general « into
two rays belonging to the congruence (2,2); in this way we can
construct the whole congruence. Bv this we have determined the
construction, but not the geometrical character of the congruence ;
this can be done in the following manner;
( 388 )
Let the direction of the velocity « of a point A intersect the
plane of coincidence PRS in L; now the focal plane of A intersects
this plane in the polar p of 4 with respect to the conic A. The
rays of the complex, at the same time rays of the conjugate focal
system, are situated in the focal plane @ of A; from this ensues that
these rays intersect the plane PAS in two coincident points, at the
same time conjugate with respect to A“; so these rays will intersect
A* and now ensues the theorem:
“The rays of the congruence (2,2), which is the section of the
complex with the focal system, have a point in common with the
conic A?; so they are found as rays of A cutting K?.”
So the congruence (2,2) arising from this belongs to those con-
gruences, not possessing a focal surface, but a singular or double
curve'), geometrical locus of the first series of foei of the congruence.
6 The congruence can be constructed as a whole out of points
of the conic A: for these points have the property of being the
points of intersection not only of two but of a whole pencil of rays
of the congruence (2,2), situated in the focal planes belonging to
each of the points. These focal planes envelop a quadratic cone 2,
with the vertex ?; so the congruence must touch the cone. From
this ensues the following construction:
“Let a point A. be taken on A, the focal ray. PA Dendranane
cutting A for the second time in il’. Let the two tangential planes
to P? be brought through PA; each of these planes contains a pencil
of rays of the congruence, the vertex of one pencil being A, of the
other. A’
7. We now proceed by giving some visible properties of the con-
oruence (2,2).
a. The two foci of each ray are the points of intersection with
K*® and the point of contact with 2. The focal surface of points
becomes /??; the focal surface of tangential planes consists of the
tangential planes of A.
Db. All rays of the congruence (2,2) belonging to a congruence of
rays (1,1) of A cut two conjugate polars of 4, and cutting at the
same time A® they form a ruled surface of order four with a simple
come and two double lines.
c. The rays of the congruence (2,2), lying on a hyperboloid of
1) Gongruences of this type are ranged in the “Index du répertoire bibliogra-
phique des sciences mathématiques” under V*? le and placed by R. SruRM in
a separate division; see “Liniengeometrie”, Il, p. 323.
( 389 )
A, pass through the points of intersection of the latter with A, so
they are four in number.
d. Let K? be real and let ? be situated within A?; all focal
rays through P, the focal point of plane PRS, now cut A*: so all
pencils of rays are real. If P lies outside A? two tangents out of
P can be drawn to A?; these tangents are the lines of intersection
of the cone P?? with plane PAS. The planes touching /?? according
to these lines of intersection are focal planes, in which two pencils
of rays have coincided; rays through /, not cutting A®, give rise to
imaginary pencils of ravs of the congruence (2,2). Further ensues
from this:
“If A? is real and all the vertices of the tetrahedron of coinci-
dence likewise are real, the congruence (2,2) is built up of real
and imaginary pencils of rays, where as a transition two are double
ones; if A? is real but the vertices A and S are imaginary, all the
pencils are real.”
e. The cases in which A? is imaginary, or also those in which
all the vertices of the tetrahedron of coincidence are unaginary, do not
give real congruences; so they are not under consideration.
8. We now pass to the representation of the congruence (2,2)
by which the image is obtained of the connection of focal system
and tetrahedral complex.
a. The congruence containing 2 pencils of rays which are
represented in >, by straight lines having a point in common with
X,*, the whole congruence is represented by a ruled surface passing
through N°. To a straight line /, in 2, a hyperboloidic system of
focal rays corresponds, which has four points in common with A?;
so it contains four rays of the congruence and the representing sur-
face S,* of the congruence (2,2) is a ruled surface of order four.
hb. An arbitrary pencil of focal rays of 4 contains two rays of
the congruence; the straight line in 2, corresponding to them cutting
A” has another two points in common with N,*: so \,* is a double
conic: of 5S,*.
¢. To the pencil of rays in > with P as vertex and PRS as
plane a straight line p, in 2, corresponds, cutting V,*. Each ray of
the pencil P/ PFS belonging to two pencils of rays whose vertices are
points of intersection with A, in all points of p, two generators
ot 8,5 concur; from this follows that St is a ruled surface having
as doupie curve a conic with a straight line cutting it; with this the
type of S\* has been established.
26
Proceedings Royal Acad. Amsterdam. Vol. V,
( 390 )
9. A closer acquaintance with the form of S,* is obtained by
tracing the pinchpoints on the double curve; there can be two of
them on p, and two on X,’. Those of p, depend on the position
of P with respect to A?.
a. Let P be outside A’. When a ray through P cuts A? in two
points, we get two pencils of rays of the congruence, to which two
real generators of 5,* correspond, concurring in a point of p,. For
the tangential lines out of P to A? these two generators coincide,
so the point of S,*, from which they are drawn is a pinchpoint; so
for this position there are two real pinchpoints on p, ; from this ensues :
“If P lies outside A’, p, has one part appearing as double line and
another which is isolated; two pinchpoints separate these two parts.”
hb. Let P lie within A’. All focal rays through P cut A’; there
are no tangents to A*, so there are no pinchpoints on p,. So the
double line p, is in its whole length really double line.
Besides the pinchpoints on p, the surface S,* has also pinchpoints
on X,*. To find these we must keep in view that the points on X,*
correspond to the pencils of rays whose vertices lie on YX’ — w,
which are thus situated in planes through w. Let y be a plane through z
and ( its focal point; the pencil of rays (Cy) has two rays cutting
Kk? viz. the two rays connecting C and the points of intersection
B and B of y and K*. These two rays are represented in =,
by a single point B, of X,’. Now CB belongs still to another
pencil of focal rays, viz. to the pencil whose vertex is B and whose
plane is the plane CbP=—?. The latter pencil belongs to the con-
gruence (2,2) and is thus represented by a straight line through B,
lying on S,*. In a similar way it appears that also a second straight
line of S,* passes through 6,, namely the one which is represented
by the pencil of rays (5's') lying in plane CL'P. Now again two
principal cases may occur:
a. « euts the plane PRS in a point 7’ outside A*. The pencil
of rays 7 lying in this plane has rays cutting A’? in two points,
touching A* or having two imaginary points in common with A’’,
In this case these are parts of X,* through which two generators
of S,* pass, which have thus to be regarded as points of a double
curve, and parts which are isolated; the transition is formed by two
pinchpoints, through which two coinciding generators pass; and these
last correspond to the pencils of rays, having their vertices on the
tangents drawn from 7’ to A*.
b. The above mentioned point of intersection 7’ lies within X,’.
All rays through 7’ cut A’; through each point of X,* two generators
pass, so the whole conic X,° is a double curve.
( 391 )
10. Among the particular sections of S,‘ the conics of this surface
come into account. These conics have two points in common with
N°: so (8) to these must correspond in 2 hyperboloidie systems of
focal rays of A. These can be constructed in the following way :
Let again a point A be taken on A, its focal plane « be deter-
mined, moreover the second point of intersection A’ of @ with A* and
the focal plane a’ of A’. If now a pencil of rays be drawn in a’
through A (which rays are not focal rays) and likewise through A’
in a, the pencils (4, a’), (A’,a) consist of conjugate polars of A
between which a projective correspondence is established by means of
the focal rays. In connection with X,* each pair of conjugate polars
causes a hyperboloidie system of focal rays to appear. These two
pencils generate them all, so their number is oo.
11. Finally a few particular cases ask for our attention.
a. The line of intersection w cuts the plane PRS in a point of
the tangent plane PR. The pencil, of focal rays in the plane PR
has as vertex this point of intersection; to this pencil corresponds a
pinchpoint on X,°, but at the same time this pencil of rays has more-
over a ray in common with the pencil of rays in the focal plane of
the point 2; so the obtained pinchpoint is at the same time a point
of p,; from this follows that in the point of intersection of Y,* and
p, two pinchpoints have coincided; so through this point only a single
generator of S,* can be drawn.
6. Application to the motion of an invariable system. In this case
K* is imaginary (the imaginary circle in the plane at infinity); so
the congruence (2,2) consists entirely of imaginary rays. The pencil
of rays P/PRS, however, remains real; so the representation in +
becomes an imaginary ruled surface $,* with real double curve con-
sisting of a straight line and a conic intersecting it. The same obser-
vation can be made for other cases where K* becomes imaginary.
c. Another particular case occurs when the ray AX’ — « is taken
in such a way that it cuts the conic A,’; by doing so the character
of the congruence does not change, but its representation does. If
we now consider a pencil of rays in a plane brought through «, it
is apparent that always one of the two rays of congruence to A’? coin-
cides with w. Of the two rays cutting in >, the double conic N° only
one is situated on $S,*, the other one passes into a ray situated in §, ;
from this follows:
“When the focal ray wv cuts the conic A? the surtace S,* breaks
up into §, and a cubic ruled surface S,* of which p, 1s a doubte
line; so this gives a simpler representation of the congruence ‘2.2)
I6*
( 392 )
Physiology. — “Ll new law concerning the relation between stimulus
and effect” By Dr. J. K. A. WeRTHEIM SALOMONSON, commu-
nicated by Dr. C. WINKLER. (Communication IV).
In three papers, bearing the title “a new law concerning the relation
between stimulus and effect I, Il and Il, I have tried to prove that
by iereasing a stimulus, the effect too will increase in a definite
manner. .
The relation was expressed by the formula
== Ate BAREN PTA ie tye a
In deducing this formula I assumed that the transformation of
chemical substance caused one and only one well-defined effect.
In most cases however from such a transformation several conse-
quences will result, constituting together the total effect : e.g. a mecha-
nical, a thermal, a chemical, an electrical effect may be caused simul-
taneously by some changing of the protoplasma.
The question arises, whether our mathematical expression may be
applied as well to the different parts of an effect as to the total
effect. In order to obtain an answer to this question, we have to con-
sider again the differential equation:
OEZ 1 IRN SS Oy Ses (2)
expressing, that by an infinitesimal increment of stimulus an infini-
tesumal proportional part of the transformable substance was trans-
formed, and at the same time stating the quantity of this transforma-
tion. The quantity —d/ represents the increment of the effect. In
the case of the effect being composed of several different parts,
; 1
the same equality will prevail for any of them, e.g. the — part, and
1
so we shall obtain for a partial effect the equation
UE en k
ADE OR ee Ds: Toa
Nn
in which n > 1.
From this formula we get the expression
Bahl =e BR ne
wherein @ represents another constant than A, and wherein » is a
number larger than 1.
This formula for a partial effect is identical to the formula for a
total effect the only difference being that the exponential constant i
the ease of a partial effect is larger than in that of a total effect.
The muscle may be taken as an example. Every contraction brings
about a mechanical effect, whilst at the same time an electrical response
is given. Finally the production of heat may be taken for the total
effect, at any rate in the case of isotonic or isometric contractions
where the mechanical effect is afterwards converted into heat. Thence
we are justified in presuming that our statement about the formulae
for total and partial effects, may be applied to the thermal effect and
mechanical effect of muscle-contractions.
I have tried to ascertain whether the numbers, given for the thermal-
effects by different authors are in accordance with our law.
In Daninewsky') | found several series of numbers, from which
the following tables were calculated
TAB: EE
DaniLewskKy, 1.c. pag. 184.
Isometrical contraction. Initial
load 40 eram fie. 1.
AS" Di P= 008 OERS
i
R Bw cal.
ie observ.
OOo | Lee ALT
30 | 6.97 1,5
koe) GO. Th td
50 | 14.18 | 46.9
80 | 19.38 | 49.2
100 21.00 19.8
300 99.98 90.5
600 93 22.
|
800 93, ND)
In this table, as in the following /? represents the magnitude of
the stimulus; /2,, observ. the thermal effect as observed by DANILEWSKY.
') B. Danitewsky. Ergebnisse weiterer thermodynamischer Untersuchungen der
Muskeln. = V.e. A. Fick. Myothermische Untersuchungen 1889.
( 39a)
ii, cale. the thermal effect, as calculated with the constants given at
the head of each table.
TABLET
o Ib. Initial load 80 Gr. fig. 2.
A = 24.2 B= 0.0324 C= 20.
i Salted Ey
> fora :
JR | Lw calc. observ.
30 Gey 6
50 15.3 18
100 9 4 Ots
300 94.2 94.8
TABLE IIL
Ib. Initial load 300 Gr.
fig. 3.
A= 7) 8. «B==002875 2 = 16:42
| Ew
R Ew calc. Obd
30 Ds DI
100 17 4 18
400 2087 20
800 20.8 ALAS
The first of the next-following tables, which are much more
important, is also taken from the experiments of DANILEWSKY Lc,
( 395 )
whilst the observations in the 5 and 6 table have been published
by Nawaticuin'): the school of Hemrnnain and that of Fick are
both represented.
The higher importance of the series given hereafter, consists chiefly
in the fact of their having served to determine as well the mechanical
response as the thermal effect with stimuli of increasing magnitude.
In the series of Daninuwsky a double thigh-muscle-preparation of
the frog after the method of Fick was employed, whilst NAWALICHIN
made use of a single gastrocnemius.
The muscle contracted isotonically, whilst simultaneously the thermal
and the mechanical effect of each contraction, were recorded. As it
has been proved with sufficient accuracy in our first papers that
our formula may be applied to isotonic twitches, these may now
serve us as a means of control.
In the following series the magnitude of stimulus is again indicated
in the first column by AR. The second column contains the calculated
height of twitch, the third column the observed height; the fourth
column the calculated and the fifth the observed thermal effect.
The constants A,, B, and C were used for calculating the thermal
effects, the constants Aj, Br and C), for calculating the heights of
the contractions.
TAB TBE:
Danitewsky Le. Load 60 Gr. fig. 4.
An — 40 Bj = 0.05 Cy = 14.4
Ay, = 14.55 By = T02 Cw 14.4
> 7 : En a 4 Ew
R En calc. | observ. Ew cale. | observ.
20 On <98 1.54 Oe
30 .| 21.66 Dirt 3.90 4
50 Br) 33 a eka | hot
400 | 39.45 39.4 11.92 4404
|
300 | 40.00 40 | 14.50 | 14.5
pn ee -
. ee fo Je Wi
1) NawazicHiN, Myothermische Untersuchungen. Pfluger’s Archiv, Bd. 14, p. 297.
NAWALICHIN Le. pag. 297. Load 30 Gr.
Ay ERS B, = 0.0036 Cy
A ae B. = 0.00085 Cz
En
observ.
Ew
Rh 7% calc. | :
observ.
Zw calc.
1,0 SRT ae 2.60 3
450 3.66 3.8 Be) 3.5
500 4.08 4,9, 3.78 /
600 474 49, 4.81 4
SOO 509, 5.4 6275 7
1500 6.48 Tey A ere 10.5
2000 OE 6 13.30 (325
2500 6.25 6.2 14.60 15
2500 6.95 OE 14.60 14
|
TABLE VI.
Ib. Load 90 Gr. fig. 6.
Ag OS b= 00185 C; == 660
A= 7D By = 0.008 Cy, == 660
PD hs gn En EE Lw
R | Zn calc. observ. Ew calc. observ.
700 3.40 3.5 4.70 45
750 5.27 5.3 8.80 9.5
900 | 6.42 | 6.4 14.61 12
1000 6.50 65 | 46.00) |) 46
|
1500 “| 6.50 | 625: he ATEGO ME
| |
Considering that the degree of accuracy with whieh the thermal
effects were measured is not very high, we have some cause for
satisfaction about the results of our caleulations. Though only a first
approximation has been effected throughout all these series, the errors
remain wholly within the limits of the mean errors of observation.
Moreover in some cases it is even possible to apply a correction.
Looking at series VI, we see immediately that the observed numbers
( 398 )
corresponding to the stimulus 900 are rather too small, as well for
the height of twitch as for the heat-production. Calculating from the
observed lifting-height the corresponding magnitude of stimulus, we
find 810 instead of 900. Now taking this number 810, to caleulate
the heat-production, we obtain 12, in perfect accordance with the
observation. The supposition that the number 900 is an error and
that 800 was meant is not very hazardous.
From the communicated series we may draw firstly this conclusion
that the heat-production, considered as total effect, increases virtually
with increased magnitude of stimulus in the manner indicated by the
established formula.
In the three last series B, the increment-constant for the thermal
effect, proved to be always smaller than the B, corresponding to it,
a fact predicted already in our deduction. We found for the number
By en :
n —— in series IN , V and VI the value 2.5, 4.23 and 2.31. Though
w
of course even by this fact our deduction may not be deemed absolutely
proven, it nevertheless affords a valuable support for considering the
deduction proposed by me as a most useful working-hypothesis.
Bacteriology. — “On a colourless bacterium, whose carbon food
comes from the atmosphere.’ By Prof. M. W. Berrerinck
and A. vaN DELDEN.
We give the name of Bacillus oligocarbophilus*) to a colourless
bacterium, whose carbon nutrition in the dark (and likewise in the
light), takes place at the expense of a not vet well-known atmospheric
1) It is probable that W. Herarvs (Ueber das Verhalten der Bacterien in
Brunnenwasser sowie tiber reducirende und oxydirende Eigenschaften der Bacterien.
Zeitschrift f. Hygiene, Bd. I, pag. 226) already in 1886, has had cultures
of B. oligocarbophilus before him. He says the following: .... „Ausser-
ordentlich auffallend war das Ergevniss dieser Versuche in der Hinsicht, dass eine
Vermehrung der Bacterien in einer Flüssigkeit eingetreten war, welche keine
organische Verbindungen sondern nur Salze enthielt. Ein unansehnliches, kaum
sichtbares Piinktchen von Bacterienzoogloeën hatte sich im Verlaufe vom zehn Tagen
so stark vermehrt, dass die ganze Oberfläche der Lösung vor einer dicken Haut
bedeckt war.” Analytical results are not given, and the remark makes the
impression of being accidental and is lost among insignificant observations. —
Winoerapsky’s statement, concerning the accumulation of organic carbon in nitri-
fying solutions, evidently refers likewise to this microbe, but his description suffers
of indistinctness (Annales de l'Institut Pasteur, T.4 pg. 270 et 462, 1891).-— In the
experiments of GopLeswx1 (Bulletin international de |’ Académie d. sc. d. Cracovie,
Dec. 1892 pag. 408 et Juin 1895 pag. 178), the vanished CO? is not, as he thinks,
absorbed by the ferments of nitrification but by the Mg O.Mg CO5.
t Soa)
carbon compound (or compounds), from which the energy, wanted
for the vital processes, is also derived *).
The culture of this bacterium on solid media or in nutrient
solutions, containing soluble organic substances has not yet succeeded,
which may, of course, have been caused by an erroneous choice of
these substances. On the other hand, pure cultures on solid and in
liquid substrata, without soluble carbon compounds, are easy to be made.
1. CRUDE CULTURES OF BACILLUS OLIGOCARBOPHILUS.
Bacillus oligocarbophilus is obtained by the following accumulation
experiment, which, because of the purity of the thereby resulting
vegetation, may be called a “perfect accumulation experiment.”
Into a large ERLENMEYER-flask a thin layer is introduced of a
nutrient liquid of the same composition as used for the water culture
of higher and lower green plants, but with alkaline instead of acid
reaction.
One takes for instance:
Distilled water 100
Kaliumnitrate 0.01 to 01
Dinatriumphosphate _ 0.02
“Mineral solution” 1 drop.
This “mineral solution’ contains in one drop:
8 Merms MgsO, . 7 H,O
0.05 " Mnso, . 4 H,O
0.05 ' FeCl, . 3 H,O
If from this liquid nitrogen, phosphor, kalium or magnesium is
left out, special experiments have proved, that no, or but an insigni-
ficant growth is obtained. As to the necessity of the likewise added
elements sulphur, manganese and iron, there still exists some doubt.
The inoculation is made with a not too small quantity of garden-
soil, the flasks are closed with a cotton plug, or with filter paper,
without impeding the entrance of air by diffusion, and the culture is
left in the dark at 23—25° C. After two or three weeks, the fluid,
which itself remains perfectly clear, is seen to cover with a thin,
white, or feebly rose-coloured, very dry film, difficult to moisten,
and macroscopically resembling a Mycoderma-film, but consisting of
minute bacteria, microscopically often invisible without staining, and
sticking together by a slimy substance. This is Bacillus oligocarboplulus.
1) We also found another, rarer species, belonging to the genus Streptothrix
Coux, with corresponding properties. It will not, however, be further discussed here.
,
( 400 }
The growth of the film continues for months, whereby a considerable
accumulation of organic carbon may be observed, which is not only
visible to the naked eve by the vigorous bacterial growth, but can also
be proved by direct weighing, and by a comparison of the perman-
ganate numbers found before and after the experiment, of which some
instances are given below.
As there is. reason to admit that our bacterium is generally dis-
tributed in garden-soil, and was without doubt always present in the
crude material used for the inoculation, the failing of the film-for-
ination in some of the flasks must necessarily result from the chosen
culture fluid being less favorable to the feebler germs and not allowing
their growth. So we observed that water, distilled in a copper apparatus,
caused many more failures than when distilled in glass; we there-
fore afterwards always used the latter. In other cases monads, which
immediately devoured the bacteria, were cause of the failure; by transfers
and by the use of pure cultures, these voracious organisms could
be rendered harmless or removed. When the distilled water is replaced
by tap-water, the number of flasks remaining without growth after
inoculation with the same quantity of garden-soil is much smaller.
If once a pellicle has formed, transfers into the said culture liquid,
prepared either with distilled or with tap-water, come easily and
without exception to development.
2. SOURCE OF NITROGEN REQUIRED.
In the above mentioned nutrient liquid we have chosen kalium-
nitrate as source of nitrogen. As well, however, kaliumnitrite or
some anorganit ammonium salt may be used. Very good results were
obtained with:
Distilled water 100
Ammonium sulphate (or NI, Cl) 0.01—0.1
Dikaliumphosphate 0.02
“Mineral solution” 1 drop
and with:
Distilled water 100
Kaltumnitrite 0.01—0.1
Dikaltumphosphate 0.02
“Mineral solution” sdi:
As both these liquids answer to the conditions of life of the microbes
of nitrification, the formation of nitrite or nitrate is actually to be
observed when using them, and when inoculating with garden-soil
or with crude cultures. With the easily produced pure cultures
( 401 5
of B. oligecarbophilus, of which more below, a good development of
the film is possible, by which experiment it can at the same
time be proved, that this microbe itself does not nitrify. Hence,
ammonium salts or nitrites, added to excess can, even for a
year or longer, continue unchanged under the luxuriantly growing
pellicle of B. oligocarbophilus, whereas, in the presence of nitrifying
ferments, they completely disappear in a few weeks, being then
found back as nitrates. If the ferments of nitrification alone are
present, there is no question of film-formation and = the nutrient
solutions remain perfectly clear.
Not only the nature of the nitrogen-furnishing substances, but also
their quantity can in these experiments, as already inferred in the
recipes, vary between fairly wide limits, and the same may He said
concerning the conditions for the water culture of higher and lower
green plants. The limits allowable for B. oligocarbophilus, have
not yet been precisely fixed, but they certainly have a broader range
for this organism (circa O.1—10 pro mille) than for the higher
plants (0.5
By many experiments it was established, that in absence of kalium,
5 pro mille).
phosphor, and magnesium, a still slighter growth occurs, than when
no nitrogen compounds are given. Evidently B. oligocarbophilis finds
in the almosphere, in a condition fit for nutrition, a quantity of
nitrogen, which, although insufficient, should not be overlooked.
If the distilled water in the artificial solution is replaced by tap-water,
a somewhat higher rate of organic substance is produced. As in tap-
water a small quantity of nitrogen compounds occur, — here, at
Delft, about 0.4 milligrams of combined nitrogen per litre,
whilst it contains the other necessary elements (phosphor and kalium,
of course, excepted) in an obviously favorable form for the nutrition
of our mikrobe, one can simply use for its culture:
Tap-water 100
Dikaliumphosphate — 0.02.
It should, however, be kept in view, that the productivity in bac-
terial substance, in consequence of the film formation, is not deter-
mined by the volume, but chiefly by the extent of the surface of
the medium, which is in free contact with the air. Hence, in a very
thin layer of tap-water, the nitrogen may soon be consumed, whereas,
with tee same amount of nutrient liquid, but with a smaller surface,
cor seqpuently in a thicker layer, the provision of nitrogen will suffice
for a longer time. Therefore, in order to obtain from a flask of
determined size, the maximum production of B, oligocarbophilus, a
( 402 )
nitrogen compound should be added when a small quantity of tap-
water is used, which addition is not necessary when cultivating in
a greater quantity in a flask of the same size.
3. PURE CULTURE.
Our bacterium does not grow at all or only to a slight extent
on the commonly used bacteriological media, these containing too
much organic food. But it is easy to produce pure cultures on solid
media, when observing the same precautions which I described in
the Meeting of the Academy of 27 June 1892 for the pure culture
of the ferments of nitrification on agar-plates*), and to which I
referred in the Meetings of 30 March 1901 (Proceedings p. 586) and
25 May 1901 (Proceedings p. 5) when discussing the culture condi-
tions of the oligonitrophilous Cyanophyceae.
In all these cases it is necessary as completely as possible to
remove all soluble organic substances from the solid medium, which
is to be effected by a prolonged washing with distilled water. The
agar thus prepared, with the required nutrient salts, for instance in
the proportion :
Distilled water 100
Agar 1.5
K, HPO, 0.01
KNO, (of NH,Cl) 0.01
is boiled and plated, and used for strew-or streakcultures originating
from a film of B. oligocarbophilus. Very soon the common saprophytic
bacteria which never lack in the film, are seen to develop on the
plate and when these by their growth and respiration have consumed
the soluble carbon compounds, which were not yet removed from the
agar by the extraction with water, B. oligocarbophilus itself begins to
erow. This is usually the case after 14 days. Then, however, the
colonies become easily recognisable, our bacterium being the only
species which in the given circumstances can feed on the atmospheric
carbon, and so go on growing, whilst the growth of all other
species soon comes to a stop.
Even the colonies of the nitrifying ferments, which, as I have
demonstrated before (Ll. ¢.), can grow fairly well on this medium, when
instead of nitrate an ammonium salt is used, remain very small,
never exceeding 1 mM. or less. On the other hand, the colonies
of B. oligocarbophilus attain dimensions of 1 cM. and more and
may then easily be transferred in a pure condition into test-tubes
1) Nature, Vol. 46, pag. 264, 1892. e
( 403 )
on the said medium. They grow on the agar as thin, snow-white
or rosy-tinted, very dry, flatly extended layers, which strongly remind
of the pellicle floating on the liquid.
Also on silica plates, prepared in glass dishes, which, after extraction
of the chlorides are soaked with a nutrient solution, B. oligocarbophilus
can produce very fine cultures, appearing after some weeks, as
snowwhite colonies with indented margin, and which by a right
selection of the salts, can finally spread over the whole plate.
Then the remarkable phenomenon is observed, that the silica liquefies
a little in the centre of the colonies and sinks in by evaporation.
The silica plates are made as follows. A commercial solution of
potassium silicate, diluted with a known quantity of water, is titrated
with normal hydrochloric acid. As the solidification is much favoured
by an alkaline reaction, a complete neutralisation at the preparation
of the plate should not occur, and as a plate, with a high percent-
age of silica, contracts strongly after coagulation, and expresses much
water, the dilution must be sufficient for this contraction to be delayed.
Into a small beaker-glass was introduced, in a certain case, 5 cM°
of potassium silicate diluted with 25 ¢M* of water, and into a
second glass the required quantity of hydrochloric acid, amounting
to 10 cM*® of normal acid. The acid is mixed with the diluted
silicate and the mixture poured into a glass dish. The solidification
delays the longer as the mass is more diluted, but it is easy, after
some practice, to make very solid plates. The plate is first freed
from the chlorides by streaming tap-water, then washed out with
boiled water, and afterwards treated with the solution of nutrient
salts. When these have sufficiently diffused into the plate, the glass
dish is gently warmed at the underside, until the adhering water
has evaporated and the plate shows a “dry”, glossy surface. The
surface is flamed in the Bunsen-burner, by which only a partly but
sufficient sterilisation is to be attained.
Not only B. oligocarbophilus, but also the ferments of nitrification
grow on this medium very well. By mixing of the diluted solution
of the silicate with chalk, magnesium carbonate, or ammonium-
magnesium phosphate, snow-white plates may be obtained, which
are particularly fit for the culture as well of all these microbes as
of several lower algae. Even earth-diatoms, of the genus Nitzschia
will grow thereon.
Once more it must be observed, that in the silica plates organic
substances must be absent, even fragments of cork, fallen into the
silicate solution, may disturb the experiment.
The pure cultures, obtained on agar or silica plates, are as well fit
( 404 )
for the further experiments on liquid media as the crude cultures,
of which many experiments, continued for years, have convinced us.
Every thought of symbiotic relations on which the carbon assimilation
by our bacterium might repose is thereby excluded, so that at least
the biological side of this part of our problem is clear.
Concerning the further properties of our bacterium in pure cultures,
we can be brief. In the films, as well as on in the colonies on the
solid media, it consists of minute, thin and short rodlets, probably
always immobile. They are ca. 0.5 u wide and 0.5—4 long. The
length however is very variable and frequently particles are seen
0.5 u wide and 0.7—1 u long. Often, when not using reagents, such
as dyeing substances or acids, no structure at all is to be observed,
neither in the colonies nor in the flowing pellicle, but the bacteria
at once become visible by staining the preparations. The thick cell-
walls form the chief constituent of the colonies; albuminous matter
is only present in a slight quantity in this bacterium,
4. THE NUTRITION WITH ATMOSPHERIC CARBON.
A good appreciation of the carbon accumulation may be had as
well by a direct weighing as by the permanganate method.
For both determinations it is possible, to suck off the fluid, which
is. practically free from bacteria, wholly or partly from beneath the
film, so that the quantity of the culture material, destined for the
filtration or the determination of the permanganate number, is not
foo voluminous.
In our experiments there only resulted a precipitate of caleium-
phosphate or calciumearbonate, when we had used our tap-water,
which is rich in lime, and when kaliumphosphate to excess had
been added. These precipitates can, however, be dissolved beneath
as well as in the film bv dilute acid, and then the acid can be
expelled by further washing. The film is so dry and wetted with
so much difficulty, that all these manipulations may be effected
without much loss of material.
The permanganate number was determined after KeBer’s ') method.
In relation to the quantity of organic matter found by direct
weighing or by the permanganate method and formed from the
atmospheric carbon, the following should be well observed.
As B. oligocarbophilus grows only on the free surface of the
1) TrEMANN-GÄRTNER's Handbuch der Untersuchung der Wasser, 4e Aufl. pag. 205
1895,
( 405 )
medium, and not in the depth, the thickness of the layer of the
nutrient solution and consequently its volume, is, as already observed,
actually indifferent. That is to say, by enlarging the surface of the
solution, a bacterial film of any dimensions is to be obtained, which
circumstance is of importance for appreciating the productivity of a
certain quantity of a nutrient solution, the more so as the thickness
of the bacterial film is usually only one cell-layer. How very thin
the required thickness of this layer can be, growth being. still
possible, may be derived from the fact, that, especially when using
distilled water with nutrient salts, the film can mount at the appa-
rently dry glass-wall from 1 to 1.5 decimeter high, and not seldom
extends on it nearly to the cotton plug. Only in certain vinegar
bacteria I observed the same.
As it seems that our bacterium forms no compounds prejudicial
to its growth, so the only circumstance, which governs its increase
relatively to a given volume of liquid, provided its surface be of a
sufficient extent, is the lack of one or more elements necessary for
the nutrition. Carbon cannot be among the number, our experiments
being made with free entrance of air.
Although it is thus established, that only the number of bacteria,
produced in a certain time per surface-unit, indicates the rate at
which the atmospheric carbon is assimilated, we will yet give the
quantities in relation to the volume of the solution, because then a
comparison can be better made with the numbers found by other
authors for polluted waters.
5. HOW MUCH CARBON IS ASSIMILATED.
First we determined by an experiment, in which, after vigorous
shaking, a culture was divided into two equal portions, how much
one half contained at direct weighing, of bacterial substance, whereas
the other half was titrated with kaliumpermanganate. We used for
this a three months old culture on:
Tap-water 100
Na, HPO, 0.02
KCl 0.02
KNO, 0.02
The film from the part, destined for the weighing, was separated from
the liquid by filtration, washed out on the filter with strongly
diluted hydrochloric acid, and subsequently with distilled water, to
remove the chlorids. Subsequently the filter with the film was
27
Proceedings Royal Acad. Amsterdam. Vol. V.
( 406 )
dried, first at 40°—50° C. and then at 100° C., until the weight
remained constant. So we found that per litre 180 milligrams of
bacterial matter were produced, and that, after deduction of 14
milligrams, used by a litre of our tap-water itself, the corresponding
permanganate number was 94. We can thus, with an accuracy
sufficient for our purpose, accept that the relation between the two
figures is as 2:1, that is to say, that the doubling of the permanganate
number gives the weight of the dry bacterial substance, and, as
this latter number is much more quickly to be found than the
weight, we have contented ourselves with it in most of our further
determinations.
We shall now give some more figures. Like the preceding they
all relate to bacterial films produced in ERLENMRYER-flasks on 100 cM’.
liquid with a free liquid-surface of about 80 cM’.
By weighing we found in one case on:
Tap-water 100
KCl 0.02
KNO, 0.02
K, HPO, 0.04
after 5 months’ culture 235 milligrams per litre. On:
Distilled water 100
KCl 0.02
KNO, 04
K, HPO, 0.02
“Mineral solution” 1 drop
after 5 months 220 milligrams per litre.
Some numbers, found by the permanganate method follow, and
in the first place some relating to tap-water.
The greatest production which we had, was obtained with tap-
water 0.02 K,HPO, and 0.02 KNO,, after a year’s culture and
amounted to 250 mers. of permanganate per litre, nearly corresponding
with 250 * 2— 500 milligrams of dry bacterial substance.
After a shorter time the production is likewise smaller; so we
found in a culture on:
Tap-water 100
Na, HPO, 0.02
KCl 0.02
K NO, 0.02
after 5 months’ culture (January to May) 202 mers. of permanganate,
corresponding with 404 mers. of bacterial matter per litre.
( 407 )
If the tap-water was replaced by distilled water, the production
of dry organic substance was commonly smaller, which cannot, how-
ever, result from the nutrition by substances in the tap-water, oxidisable
by kaliumpermanganate, for the 14 mers. of permanganate, which
our tap-water consumed per litre, we found quantitatively back, at
the end of the cultivation period, in the clear liquid beneath the
pellicle of B. oligocarbophilus, which liquid can easily be sucked off
with a pipette, without any considerable bacterial contamination.
Moreover the experiments with distilled water have likewise exhibited
great divergency in production, and though the cause has not been
established with perfect certainty, we still think it probable, that
these differences result from the greater or smaller density of the
cotton plugs, by which the speed of air entrance is greatly influenced.
We base this supposition on results obtained with flasks, only
differing in the width of the mouths, and to which we shall refer
later. It is furthermore certain that we have not to do here with
the infection of other bacteria, or with monads, for the pure cultures
displayed as considerable divergency as the crude ones. Neither can
the chief cause be attributed to a change in percentage of the air
in gaseous carbon compounds, the differences being observed simul-
taneously in cultures placed side by side in the same locality.
But we now give some further numbers. In an experiment with:
Distilled water 100
K, HPO, 0.02
KNO, 0.1
KCl 0.04
“Mineral solution’ 1 drop
sterilised and inoculated with a pure culture of B. oligocarbophilus,
were found, after 37 days’ cultivation (2 Jan.—19 Febr.) at 23° C.,
66.6 mers. of permanganate, corresponding with circa 133 mers. of
dry bacterial substance per litre.
In another experiment with:
Distilled water : 100
Na, HPO, 0.02
KNO, 0.01
“Mineral solution” 1 drop
likewise sterilised and after a culture of 40 days, at 23°C. the per-
manganate number amounted to 60 mgs., corresponding with 120
mers. of dry bacterial matter per litre.
‘ 408 )
In a third case in:
Distilled water 100
KPO, 0.02
(NH,), SO, 0.02
Na, CO, 0.01
“Mineral solution” 2 drops
after cultivating from 5 May to 1 Dee, 155 mers. of permanganate
per litre were found.
In a culture in:
Distilled water 100
Na, HPO, 0.02
KC] 0.02
KNO, 0.02
“Mineral solution” 1 drop
from 1 June to 1 Dee. we found 165.5 mers. of dry bacterial sub-
stance, corresponding with ca. 83 mers. of permanganate per litre.
As we see, the differences are considerable.
When a little natrium acetate was added to the anorganic solution,
and when using a pure culture for inoculation, we could neither
state an augmenting nor a diminishing of growth.
Thus we obtained in:
Distilled water 100
KC] 0.02
KNO, 0.1
Natriumacetate 0.02
KHBO, 0.02
“Mineral solution” 1 drop
by means of weighing, 220 mgrs. of dry bacterial substance per litre,
corresponding with 110 mers. of permanganate, which figures are
not exceedingly high and might likewise have been producedi n the
same time (4 months) from the air alone, without acetate.
In all these experiments with distilled water, the free surface of
the liquid was also 80 cM’, and the air had to pass through a
dense cotton plug, with which the ERLENMEYER-flasks were closed.
Already before we drew attention to the importance of the way in
which the flasks are closed; be here still mentioned that we made
some special experiments, which proved that a very narrow opening
of the flasks, slackens the growth of B. oligocarbophilus, so that years |
may go by before the film has vigorously developed. We could
not, however, expected anything else, for the considerable volume of
air, required for the growth of the said quantities of bacteria, can
oniy very slowly diffuse inward and outward through the narrow canal.
( 409 )
6. CARBONIC ACID CANNOT SERVE AS FOOD.
Various experiments were made to establish what may be the
volatile atmospheric carbon compound which renders the growth of
B. oligocarbophilus possible. That it cannot be carbonic acid, whether
free or combined, resulted from the following experiments. In closed
culture-flasks with the best nutrient solutions, and arranged in such
a way, that at times a little free carbonic acid mixed with pure air,
could artificially be introduced, it was not possible to get any growth.
This experiment, which seemed of particular interest, has been so
frequently repeated, and so long continued under different conditions,
that we consider it as quite certain, that free carbonic acid cannot
serve for the nutrition of B. oligocarbophilus.
For testing the influence of combined carbonic acid, cultures were
made, firstly in the following solution:
Tap-water 100
Dikaliumphosphate 0.01
Kaliumnitrate 0.01
Natriumbicarbonate 0.1
When cultivating at the free air surely a luxurious growth was
obtained, but it was by no means more vigorous than when the
bicarbonate was left out. |
If in this liquid the nitrate was replaced by an ammonium salt, the
result was quite the same.
Secondly, the bicarbonate was replaced by common natrium car-
bonate, the same quantities of the different salts being used. But in
this case the action proved rather injurious than favorable. It is true
that the film had become considerable after a few months, but it
was directly to be seen that the growth was so much inferior to that
of cultures obtained in the same circumstances but in absence of car-
bonate, that the determination of the permanganate number seemed
superfluous. Here, too, the replacing of nitrate by an ammonium salt
or by a nitrite caused no change.
As a remarkable fact it may be mentioned, that in these experi-
ments, in our large flasks, containing a litre of air, the thin bacterial
film mounted very high up the dry glass-wall, which is likewise often
observed in the solutions made with distilled water, and may repose
on the absence of dissolved lime salts.
If the tap-water was substituted by distilled water, the addition
of natrium carbonate did not cause an increase of bacterial growth
either. We found, for instance, in:
( 410 )
Distilled water 100
HPO, 0.02
(NH), SO, 0.02
Na,CO, 0.1
“Mineral solution’ 1 drop
Pd
after 7 months (5 May—1 Dec.) 155 mers. of permanganate, corre-
sponding with ca. 300 mers. of dry bacterial substance per litre,
which production is less than that, obtained in other cases under
the same circumstances but without carbonate, so that here also,
the action of the carbonate, the long time of cultivation being taken
into consideration, was not favorable. Quantities of carbonate,
smaller than 0.1 °/,, were neither successful.
The results of this examination can be thus summarised, that for
the growth of B. oligocarbophilus an atmospheric carbon compound
is actually consumed, but that this cannot possibly be free carbonic
acid. Furthermore, that also combined carbonic acid cannot serve
for its nutrition.
7. NATURE OF THE ASSIMILATED ATMOSPHERIC CARBON COMPOUND.
If the carbonic acid of the air cannot be the food of B. olgo-
carbophilus, what other atmospheric carbon source might then come
into consideration ?
It is clear, that we should think here of the carbon-containing
component of the air, discovered in 1862 by the botanist Hrrmann
KARSTEN *), and recently discovered anew by French experimenters,
especially by Mr. Henrier’). It is true that the chemical nature of
this substance has been hitherto unknown *), but yet it is certain that
we have here to do with an easily oxidisable compound (or com-
pounds), for a prolonged contact with alkali and air will already
suffice to split off carbonic acid from it. Furthermore, according
to the statement of the French investigator, the substance probably
contains nitrogen.
This latter circumstance gives rise to the question whether this
1) H. Karsten. Zur Kenntniss des Verwesungsprocesses. Poggendorff's Annalen
Bd. 191, pag. 343. 1862. To this place, as also to the not unimportant older literature
on the carbon compound of the air, my attention was drawn by Mr. G. van ITERson.
*) Comptes Rendus T. 135, pag. 89 et 101. 1902.
3) Henriet thinks that the substance must be a monosubstituted formamid with
the formula HCO.NHR, where R represents a still unknown alkylrest. But then it
is not easy to understand, why the production of carbonic acid takes place so
readily. It might then rather be expected that, with an alkali a formiate would
result and no carbonate.
( 444 )
nitrogen, like the carbon, is fit for assimilation by our microbe.
Though this question has already partly been answered in the negative
by the preceding experiments, it should still be remarked here that in
nutrient liquids, without an expressly added nitrogen compound, for
instance in:
Distilled water 100
Kr HBO, 0.02
Mg, S, Mn, Fe traces.
Or still better in:
Tap-water 100
K, HPO, 0.02
without any further addition, a not inconsiderable growth of B. oligo-
carbophilus may occur, so that at least traces of an assimilable nitrogen
compound may be drawn from the air by this bacterium, whereas,
for the possibility of assimilation of the free atmospheric nitrogen
no indications were found.
We now turn to another question, which the assimilation of the
atmospheric carbon gives rise to, namely: How great is the quantity
of the volatile substance wanted for the formation of the bacterial
film produced in our cultures? This question is closely connected
with the following: How much of the compound is moreover consumed
by the respiration of our bacterium, escaping as free carbonic acid?
For answering these questions we have to measure the quantity of
the carbonic acid corresponding with a determined weight of dry
bacterial substance, granted that the carbon percentage of this sub-
stance be known.
Our experiments relating to the measurement of the quantity of
carbonic acid produced, are not yet closed, but as to the first part
of the question, we give the following calculation to fix the volume
of air wanted for the production of the carbon, actually accu-
mulated in the bacterial films. We hereby make two chemical
suppositions which, to be sure, are fairly well in accordance with
truth. First, we admit that the carbon, freed from the unkown
compound, as carbonic acid by a prolonged contact with alkali,
is consumed quantitatively by our bacterium and, secondly, that the
bulk of the bacterial cells consists of a substance possessing nearly
the composition of cellulose *).
1) If accepting that the composition of the bacterial cells corresponds with
that of albuminous substances, then, instead of 44°/) C., 52 to 55°/, C. should be
brought into account, and in this proportion the volume of the air should be
augmented.
( 412 )
Let us now consider the case when, in */, litre-flask with 100 cM’.
of fluid and a free surface of 80 cM’, after a month’s culture a
quantity of 20 mers. of dry bacterial substance is formed, which,
calculated as cellulose, contains 44 °/, C.; we then find in the 20 mers.
of dry matter 8.8 mers. of carbon. According to Hrnrimr the atmos-
pheric carbon compound, present in a certain quantity of air, under
prolonged action of alkali, gives out as much carbonic acid as occurs
already in a free state in the same volume of air, that is per litre
0.3 cM*.—0.6 mers., in which 0.163 mers. of carbon are present.
Thus, for 8.8 mers. are wanted 55 litres of air. Consequently, in the
course of a month these 55 litres of air must have diffused through
the cotton plug inward and outward of our */, litre-flasks, in order
to produce the found quantity of carbon, that is 76 cM*. hourly.
Though this figure should not be considered à priori as impossible, it
still appears to be very high, and the difficulty of accepting it increases,
if still the addition has to be made of a yet unknown, but apparently
considerable amount consumed for the bacterial respiration, which, as
remarked above, seems necessary. We therefore think that it
must be admitted that the quantity of the atmospheric compound (or
compounds) assimilable by 5. oligocarbophilus, is much larger in our
laboratory atmosphere, than in that of the Paris boulevard, analysed
by Henriet, and that we have here to do with an extremely
variable factor. The circumstance, too, that we have not as yet been
able in our greenhouse, where the air, in the common sense of the
word, is surely much purer than in the laboratory, to obtain a vigorous
growth of B. oligocarbophilus pleads for this view. But here we
could not always keep the temperature high enough, so that we
consider our experiments in this direction not yet closed. Besides, we
should observe, that in an empty, isolated room of the laboratory,
the quantities of combined carbon drawn from the air, were as great,
or only little less than in the laboratory itself, where the air was
certainly impurer.
We are accordingly conscious that further experiments, with fresh
atmospheric air are wanted to decide, whether the carbon compound
occurs in the atmosphere in a constant or in a varying percentage.
Only thereby it will be possible to ascertain the distribution of this
compound, by which, at the same time, the signification of B. oligo-
carbophilus us. nature will become clearer.
As to this signification, the question arises whether our microbe
in substrata containing sufficient mineral nutrients (N, P, K, Mg, 5,
Fe, Mn), but being poor in organic substances, is able to build up the
latter in the dark from the volatile carbon compounds occurring in the
( 413 )
atmosphere of the surrounding medium. And furthermore, whether
carbon nutrition takes place exclusively in the floating dry films,
— hence, in the earth, only on the relatively dry surface of the
earth particles, — or that also in the depth of fluids growth and
carbon assimilation be possible. The hitherto gathered experience
about the self-purification of rivers and the biological purification
of water in general, seems to exclude the latter hypothesis, and
our own experiments too, render it not probable. The result of
these experiments consists, in our opinion, in the very discovery of
a microbe, which, in consequence of the film-formation, has the spe-
cifie faculty, to absorb for its nutrition and multiplication, from a
gas, namely the air, traces of volatile carbon compounds, by which
the struggle for existence with the rest of the microbie world can be
successfully sustained. The biological purification of water would,
according to this view, find a counterpart in the biological purific-
ation of the air by Bacillus oligocarbonhilus
a . ? 6 ’ . .
Physics. — “The calculation of — from the magnetic rotation of
mm
the plane of polarisation, for substances without an absorption
band in the visible spectrum.” By Dr. L. H. Stertsema. (Com-
munication No. 82 from the Physical Laboratory at Leiden
by Prof. H. KAMBRLINGH ONNES).
Starting from FrrzerraLD’s ') simple explanation of the magnetic
rotation of the plane of polarisation derived from the ZrrManN effect,
and also from the supposition that the result of the magnetic force
is only shown by the displacement of the dispersion curve of the
medium (n==/(a)) over a distance d, Harro ®) finds for the magnetic
rotation @
27 cdl
| tes) oe
where z represents the thickness of the medium. Har.ro’s investigations
are concerned with the parts of the spectrum in the neighbourhood
of an absorption band and for these we are justified in making the
above supposition, as appears from a formula derived by Vorer
1) Frrzgeratp. Proc. Roy. Soc. 63 p. 31.
2) Harro. Diss. Amsterdam 1902, p. 7.
( 414 )
from a more rigorous theory *). If, however we want to apply it to
points at a greater distance from an absorption band, as is the case
with the magnetic rotation of transparent substances, we must turn
to Vorer’s more general formula *)
en 9? (9 — H, +c, RD)
(#— 9), Eep RO)? + HH
If we may assume that only one term occurs under the summa-
tion in the second member, and also that ¢,/ and 9, are small
compared with 9, a simple reduction shows that the new dispersion
curve may be derived from the original one by moving each point
2
over a distance */, er ——, which depends on & and hence also
9,
on the wave-length. In this case Harro’s relation will hold, if d is
not supposed constant, but proportional to 2’.
Though it is uncertain whether for a given transparent substance
we are entitled to accept the formula for 7 with only one term
under the summation, we may investigate to what results this would
lead. From the elementary theory of the Zeeman effect it follows that
nlt 3
ry rj x
Be ER
m Az
whence for the displacement of the dispersion curve
HIW ‘e¢ Be
t= f= i= = ‘
m Ax m 4a V
This value has been derived for the absorption band. From the
above considerations it follows, however, that we may apply it for
each wave-length, and hence we find
Ane À dn e 2 dn
oS 2z2—H — = 2 H— —__ —_,
rs m AnVd2 m2V da
Whence follows for the rotation constant @
OL AG. ae.
m 2V da’
which formula corresponds with one, given by Vorer®), if we replace
the / occurring there by:
o
ed
—.—V,
m 2
1) Vorer. Wied. Ann. 67 p. 351.
2) Vorer. Wied. Ann. 67 p. 349.
3) Vorer. Wied. Ann. 67 p. 351.
( 415 )
which value may also be derived directly, if we equate the magnetic
1 . 2 '
displacement 5 Ch R after Vorer with that resulting from the elemen-
tary theory. The dispersion of the magnetic rotation expressed by
this formula is the same as that resulting from BreQqverer’s ') relation
and found by him to be confirmed in the case of carbon disulphide
and creosote.
€
U . . .
The relation found for @ enables us to compute — as soon as we
m
5 2 U7 $
know the rotation constant @ and the dispersion a of a substance
a vr
for the same wavelength 2. For we have
€ 2V da
We shall make the calculation for some substances at a value of
4= 589 uu. The rotation constants 7 being usually expressed in
minutes we have
20
OS Daa
360 X 60
and hence we find
e 2X3X10 ar da da
ECE ena a a TS ae al es LOA —,
m 589 360 < 60 wo dn x aS dn
1. Aw (100 KG., 13°.0). I have found *) r= 553.10—°. Perreau a)
finds for the refractive index at (1 atm., 0° U)
A= 644, n—np = 85.10
538 88,10
12
whence = = 0.65 & 10° and 0.58 X 10%, on an average 0.61 10°.
n
Supposing #—l proportional to the density, it follows that for air
(100 kilogram, 13°.0 C.) di/dn = 0.648 Xx 10° and we find:
“ = 2.96 X 553 X 0.648 10‘ = 1.06 X 107.
m
In the same way is found for:
2. Carbon dioxide (1 atm. 6°.5). += 8.62 X 10-5
Bl atm., 0°) =342 ><107
7, | aks Oh See 4
(1 atm, 6°.5) =3.50 M 107
1) BecquereL. C. R. 125 p. 679.
*) SIERTSEMA. Comm. Lab. Leiden. Suppl. N°. 1, p.86; Arch. Néerl. (2) 2 p. 376,
®) Perreau. Ann. de Ch. et de Ph. (7) 7 p. 289,
( 416 )
© — 0.89 X 107.
3. Hydrogen (85.0 Kilogram, 9°.5 C.) p= 456 108
dada atm. 027) == 405
(S5:0°KG 955 Cj = HIL 10%
?
= AO
m
4, Water. From refractive indices of Durer *) and the magnetic
rotation constant O0'.0130 we get
é
= 1,25 07
mn
5. Carbon disulphide. In the same way with 7+ =0'.042 we
find from VAN DER WILLIGEN’s *) refractive indices
e , e
OY aba KOL
me
6. Quartz. r=0.01684 *). By means of VAN DER WILLIGEN’s refrac-
tive indices we find
te a he
= ee Bie 107
Mn
Ca.
It may be remarked that the values of — found here correspond
In
in order of magnitude with those found in other ways.
1) Durer. Bull. Soc. Minér. 8 p. 218.
2) V. op. Wituicen. Arch. Mus. Teyler III. 1. p. 55.
3) Borex, C. R. 128, p. 1095.
(January 24, 1903).
ie
EN
<
KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,
PROCEEDINGS OF THE MEETING
of Saturday January 31, 1903.
| oo
(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
> r € a « 5 r
Afdeeling van Zaterdag 31 Januari 1903, DI. XI).
ORE MN TS.
A. Smits and L. K. Worrr: “The velocity of transformation of Carbon monoxide”
municated by Prof. H. W. Bakuvis RoozeBoom), p. 417.
vee ns “a TE ns : nn AA
J. J. VAN Laar: “The course of the melting-point-line of solid alloys or amalgams”, ‘First
communication). (Communicated by Prof H. W. Bakuuis RoozrBoom), p. 424.
J. J. van Laar: “On the potential-difference, which occurs at the surface of contact of two
different non-miscible liquids, in which a dissolved electrolyte has distributed itself” (Com-
municated by Prof. IL. W, BAkuvis Roozrnoom), p. 431.
J. J. Harro: “The value of some magneto-optic constants”. (Communicated by Prof, P.
p. 438.
Se peo “son: € tn Ronn : :
JE A IE WERTHEIM SALOMONSON : A new Jan concerning the relation between stimulus
and effect”, (V). (Communicated by Prof. C. Wixkren), p. 441.
rr No) PA Cis es : MENE . J
D. J. Korrewee: “Plaitpoints and corresponding plaits in the neighbourhood of the sides of
the g-surface of van DER Waars”, p. 445. (With one plate).
A. H. Sirks: “Some remarkable phenomena, concerning the electric
- (Com-
ZEEMAN),
circuit in electrolytes”,
(Communicated by Prof. H. A. Lorentz), p. 465. ;
The following papers were read:
Chemistry. — “The velocity of transformation of Carbon monoride.”
By Dr. A. Smits and L. K. Worrr. (Communicated by Prof.
H. W. Bakuvis RoozwBoom).
(Communicated in the meeting of December 27, 1902).
Ya vatelet> kh LTA) ‘ *. T T > l 1A ily ” p 1 <_—-(' \
From the researches of Boupovarp!) on the equilibrium 2COSCO,-+C,
where use was made of the accelerating action of the metals Ni, Co,
Fe, it follows that they do not modify the equilibrium but only
1) Ann. de Chimie ef de Physique [7] 24, p. 5 (1901).
28
Proceedings Royal Acad. Amsterdam. Vol. V.
( 418 )
exercise an influence on the velocity and are, therefore, catalyzers.
It was shown by Bovpovarp that, whilst CO, in contact with C is
practically totally converted at 1000° into CO, the amount of CO,
in the gaseous mixture in equilibrium increases at lower temperatures
in accordance with the sign of the heateffect CO,+C=2CO—42000
eal. until at 445° the CO is practically completely converted into
CO, and C.
From this follows that below 445°, CO exists in a metastable
condition,
INVESTIGATION.
a. Preparation of the catalyzer and preliminary experiments.
1. The following research was instituted with the object of
determining velocities of reaction in the metastable region in presence
of a catalyzer. The apparatus employed by us was in the main the
same as that used by van’? Horr in his research on the velocity of
transformation of detonating gas into water. The reaction vessel,
however, was filled with a catalyzer obtained in the following manner.
Pumice stone was broken up into small lumps, drenched with a
solution of Ni(NO,), then dried, ignited and finally reduced in a
current of hydrogen or carbon monoxide.
This reduction, it was observed, takes place in two stages. The
greyish-blaek surface of NiO first turns yellow owing to the formation
of a suboxide (Ni, O7) *) and afterwards on complete reduction again
becomes dark-grev. When operating at a high temperature, reduction
with H, or CO gives apparently, the same material. If, however,
the reduction takes place in a current of CO at 445° a layer of
carbon is deposited on the reduced nickel.
2. The experiments with nickel-pumice obtained by reduction
with either H, or CO at a /agh temperature gave the following
result *).
At 310° (boiling point of diphenylamine) the activity of the catalyzer
did not appear constant. Successive fillmgs continually gave smaller
diminutions of pressure in the same length of time.
1) Miter, Bell (Chemical News 20, 258).
2) Coating the inner wall of the reaction vessel with nickel did not appear to
affect the result, probably because the surface of the glass wall was very small
as compared with the surface of the catalyzer.
( 419 )
We found for instance:
5407
Diminution
Filling. in mM, He.
during 10 minutes,
ee
dst 5,68
2nd 5,00
3rd 3,80
ect.
As we suspected that the retrogression of the activity of the
catalyzer was due to the ever increasing layer of C, which deposits
on the catalyzer during the experiment and fillings, we next used a
nickel-pumice which had been reduced at 445° and was in consequence
already coated with a layer of carbon. Although at first there was
still a perceptible diminution in the activity, the differences in suc-
cessive fillings become gradually smaller and finally, the activity
was constant as seen from the following table:
3dLO°
Diminution
Filling. in mM. He.
during 10 minutes.
1st 1,88
2nd 1,80
3rd 1,78
4th 1,74
oth 1575
6th 1,74
7th 1,74
Being satisfied with this result, we started our investigation with
the catalyzer of constant activity obtained in this way.
b. Measurements concerning the order of the reaction.
For the determination of the order of the reaction the method of
VAN ‘t Horr was first of all applied. It is given in this case by
the equation:
28%
( 420 )
The determination was made at 310°.
In the first experiment the pressure of the CO was 786,8 mm.
He at the commencement; after 50 minutes the pressure amounted
to 739,9 mm. Hg. The diminution of pressure in 30 minutes there-
fore amounted to 46,9 mm. Heg.
de EE f
If we take for = the diminution of pressure per minute then
d
iC
5 becomes 1,56.
3
In the second experiment the pressure of the CO was 535,3 mm.
Hg at the commencement and after 30 minutes the pressure had
come down to 501,7 mm. Hg. Here, the diminution of pressure
in 30 minutes amounted, therefore, to 33,6 mm. Hg or = 1,42
ud
C,=aver. of press. at beginn. and end at the 1st experim.=763,35mim. Hg.
ee a a " 0. ho yay ae = od
If from this we calculate », we find
7 0-60.
from which it is apparent that the reaction is a monomolecular one.
In order to make more certain of this, the order of the reaction
was also determined at two other temperatures according to the
method given by Noyes. In this case » is calculated from the
following formula:
t
log—
t,
n= + —.—
Cy
log—
C;
in which 7, and f, are the times during which the same part of the
original quantity is converted when starting from different concen-
trations c, and «¢,.
At 256° we obtained the following result:
192
300
n=i dd
7 525,1
770,9
The experiment at 340° gave
60
d ME 0,92
Oee tn
loq—
Rye
( 421 }
The observations at the three temperatures 256°, 310° and 340°,
therefore lead to the conclusion that we are really dealing here with
a monomolecular reaction.
e. Determination of the reaction-constant at 256°, 310°, 340°.
These determinations were conducted with the same reaction vessel
and the same catalyzer.
256° (boiling point of amyl benzoate).
Time in minutes. | Pressure | 1 7
EN er in ==: log——— =
|
1 | 2 ‚m.m. He
0 761.0 | aa
5 | 0 Ree 0 00046%
10 ie? 757-6. 0.000384
10 | 756.4 | 0.000987
AD) | | 0.000276
30) Hse 0.000277
40 | 0.3 0.000278
average 0.000279
The following may serve to elucidate this table:
At 256° the catalyzer seemed to still perceptibly absorb the CO,
which caused the diminution of pressure during the first 5 minutes
to be excessive. The values for / are, therefore, not constant when
we start from the pressure corresponding with the time O, but they
gradually diminish which may be seen from the first two figures in
the last column of the table. To eliminate the error caused by absorp-
tion, we have, when calculating 4, started from the pressure corre-
sponding with the time 5 minutes (column 2) and, therefore, have
called this pressure P,. As the CO concentration had diminished very
little in 5 minutes the error thus introduced could be disregarded.
The values obtained for / are found in the last column beneath the
dotted line. The following table relates to the temperature 310°,
| Pressure | D
Time in minutes | in KN == a! log — a
Al | t A aid
| mm. Hg |
| |
0 | 786.8
|
10 | 769.8 | 0.00192
| |
20 | 754.8 0.00184
| |
30 MEC 4 0.00184
40 | 795.6 0.00184
average 0.00186
As was to be expected, the absorption at this high temperature
was scarcely perceptible and in the following table, which shows the
results obtained at 340°, no absorption whatever was noticed.
340° (boiling point of phenantrene)
Pressure 1 P
Time in minutes in k= log aaa
21
m.m. He
0 791.4
10 746.1 | 0.10524
20) 709.9 0.00527
30 668 7 0.00536
50 612.7 0.00521
average 0.00527
In order to make sure that the activity of the catalyzer had not
diminished during these three series, a series of experiments was
finally taken at 310° with the following result.
( 423 )
310°
| Pressure 1 >
: me
Time in minutes | in | k = — lo
/ mm. Hg |
0 805.5
10 188.3 0.00189
20 773.0 0.00183
30 7157 8 0.00182
40 742.8 0.00184
average 0.00184
The activity of the catalyzer had, therefore, undergone no change
during these measurements, so that we were justified in calculating
the temperature-coefficient from the results obtained. The result was
as follows:
ki+10
Temperature. k ab
hu
256° 0.000279
>1,4
310° | 0.00186
ke
340° 0.00527
|
d. Mechanism of the reaction.
What idea are we to form about the mechanism of the reaction
if this takes a monomolecular course?
If we assume the formation of Ni (CO), with an immeasurably
large velocity and the subsequent breaking up of this compound
according to the equation
Ni (CO), = Ni + 2 CO, + 2C
we must also accept the equilibrium
Ni (CO), S Ni + 4 CO
of which the constant is given by the equation:
Ca
je eae
’
Cv: (co)4
This would then necessarily lead to the conclusion, that the velocity
( 424 |
of reaction should be proportional to the 4% power of the CO-con-
centration whereas it appears to be proportional to the 1st power
of the CO-concentration. Rejecting this hypothesis two further sup-
positions remain.
Firstly :
I: CO = C+ 0 (with measurable velocity)
II. CO +0 = CO, (with unmeasurable velocity).
Secondly :
L CO+M=—C+Ni0
IH. CO+ NiO = CO, + Ni.
In the last case it need not be assumed that one of these reactions
takes place with unmeasurable velocity, but only that the second
one proceeds more rapidly than the first.
As regards the nature of the catalyzer we think we may conclude
from the result of several experiments, that if is not the carbon but
the finely divided nickel which possesses the catalytic action.
Amsterdam, Chem. Lab. University. Dec. 1902.
Chemistry. — Professor Bakuuis RoozrBoom presents a communica-
tion from Dr. J. J. van Laar on: “The course of the melting-
point-lines of solid alloys or amalgams.” (First Communication).
(Communicated in the meeting of December 27, 1902).
1. In the researches of vaN HeTEREN *) on Tinamalgams a mel-
tingpoint-line occurs?) of a kind, which has not as vet been studied
over such an extended course (from 0 to nearly 100 atom °/, of mereury).
This is chietly due to the fact, that the temperatures of fusion of the
38.6°. In
consequence the meltingpoint-line of the tin meets that of the mercury
| practically at 100 atom "/, mer-
OT cury‚ so that the meltingpoint-
ft line of the mereury has not even
been observed. We therefore
see for the first time a melting-
two metals are so very different; tin 231°, mercury
mercury | tin point-line in its full course, and
the question arises whether the
course, found by vaN HRTEREN,
may be predicted theoretically.
The answer to this is in the
affirmative. Let us, to start
with, take the most simple view
Fig. 1. as regards the molecular poten-
1) Dissertation 1902. (also Report Meeting 29 Nov. 1902).
2) l. c. pg. 18.
tials u of the tin as solid substance and u, of the tin in the liquid
amalgam, namely that
eS=e— el |
Wesen Te RT log: (zen ee nnn St
In this it has been assumed, firstly that the tin, erystallised from the
amalgam, does not consist of mixed erystals, but of pure tin
a suppo-
sition, which has been proved by experiment to be nearly correct —
and secondly, that the energy-quantity e is no function of «. Later
on we will drop this last simplified supposition, and demonstrate, that
a more accurate calculation of the function u, affects the course of
the meltingpoint-lines quantitatively, but not qualitatively. Then it is
our object to demonstrate at once, that the entire qualitative course,
as represented in the figure, follows from the equations (1) in con-
nection with the course of the logarithmic function of 1—w. By
putting the two potentials equal to each-other, we obtain:
(e, — €) — (ce, —¢e) T = — RT log (1—2),
or calling e, —e—=q (the heat of fusion of the solid tin, when passing
into the amalgam), and the quantity c,—c=y:
q— YT = — RT log (1—2),
from which follows:
T= q
y—Rlog(1—z)
(2)
This is then the most simple form of the meltingpoint-line.
On introducing the temperature of fusion of pure tin 7',, « becomes
O, and we obtain:
a
tf
so that we may also write:
r bs le 7:
acs rr a : Wr pay ye (3)
RE 1—@ log (1—2)
— —— log (1—2) ;
q
RT
if we abbreviate —— to 0.
q
We notice at once, that on the development of the logarithmic
function, the formula, for very small values of w, passes into
Per.
Ri
Ise:
q
v
that is to say into TE lee pS Ea
the ordinary formula of van ’t Horr for extremely dilute solutions.
If, however, the solutions are no longer extremely dilute, we can
no longer be satisfied with one or two terms in the development of
log (A—x), but loy 1—vr) must remain.
I will now show, that the approximative relation
1,
ig iE iecet
1 — Glog (1—2)
4 Al
gives indeed the observed course qualitatively. For BARS find :
U
dT de 0
de (1—@ log (1—z«))?’ i en
Whilst 7” itself, for «— 0, passes into 7,
T= 0, which already agrees with the steadily declining course — it
and for «= 1 into
ryy
a.
appears from —, that this quantity, for «=O, becomes:
C Ai
ar RT’
Sn Se,
fo ( da 0 q
the limiting value of van ’r Horr, whilst for
v—=1 it passes into — oo. It may now
still be asked, whether there will be a point
of inflection or not. In the case, examined
by vaN Herrren, a point of inflection plainly
occurred at about « = 0.8, but it may also
be possible, that the course was like the
one in the following figure, without point
of inflection. Let us therefore determine
dT
Fig. 2. dx?
del re i Zie dh 1 jh 0 |: /) |
0 0 0
de (1H lop =a) (he). © NE NE
en
Evidently i —_=(, when 20= N, that is to say, when
ax”
te log (1—a2) = 20
— log (1—«) iN
: 0
7
As 0———~* will be positive, we see, that the point of inflection can
qd
(427 )
only occur if @ is situated between */, and oo. For 0='/,,a@=0;
for 0=o we find on the other hand « = 0.865. A point of inflection
further than «= 0.865 can only oceur with negative values for 0
(A= till 0=0, when «= 0.865 till a—1). But there is no
point of inflection if 6 << '/,, that is to say, if
MEAT,
q>A4T,.
In our case therefore, where 7, = 505 — when q >> 2000 gram-cals.
This last conclusion will however be modified, when we apply
the necessary correction to the approximate formula (3). But the
fact of the possible occurrence of a point of inflection may already be
completely explained by the simple formula (3), and this by the course
of the function log (4—2).
or in gram-cals.
II. We now proceed to write down a more stringent relation
than (3).
Assuming an equation of condition of the var per Waats’s kind,
the value of gw, (the molecular potential of the component 7,) becomes
as follows:
y= kT (log TI) — RT (log (Vb) 1) + (eo. ie (1) EE
SRT (12 y
aes b, — 7 DIe a Ma OL OE 10 em se |
For 6 has been written:
bn bi ne bo Serkin
whilst for a the quadratic relation
ney a. Sieve
== nN," a, + 2, N, dy, +...
has been taken.
Now, loy (V—+) can be supposed to be independent of w, whilst
the expression
hy okt L, a ) RE 2
VEE ER a pr OG Fs) = ane ae ya eas)
in regard to w will become not of the order, but of v?. Let us, to prove
this, rather start from a more general expression for the total poten-
tial § (in our case we have only to deal with two single components
nm, and 7,), namely
en ny (u) LN, (u) a
2 EMG} 2
a Un He 2 otd, + Ne Mss
n, +n,
ryy ny ny \
+ Ri ny log —_—. + ny log nn
n,n, n,-+n,
+
( 428 )
We then find:
1
w, — moe rie (n,+n,)? (n° Hy, Ae 2 NM, Ny Uy, = na. Mss) ain
2 n
- —(n nu RT lo ——
. ER, 1 Yar Fo Mae) + aT
With n, + n= 1, 2, Sd, n= we obtain:
2, —(e,),-[G-2)"4, DE 2u(1-«)u,,+ Haal 20e), + ou} KT log(d- «),
or after simplification:
A = (). + bn) — AC — 2 tis + Uae) + RT log (1 — 2).
In analogy with (4) we may therefore write:
uw, me —e tT Ha, a? + RT log (l—e).
The terms with 7'log T have not been taken into consideration,
because they disappear on account of the equality of the quantities
k, and Rin the liquid and in the solid phase.
If, for the sake of a closer approximation, we take up some higher
powers of «, we finally get:
(solid tin) p=e—eL ;
(tin in liquid amalg.) we T+ (0? Bye? +10) RT logde)
Equating, we then find as in $ 1: s
y T= — (art + Be +7, 0°) — RT log (lo),
Yo
or
pta BEH)
The heat of fusion of the solid tin in the amalgam is now plainly :
Pen UT et Bef Nr ees (7)
For «= 0, (6) passes into
ZA Je
1 = 3
Y
so we may again write:
aat Be ye
| — eM
|
pete EDE
RT,
1 — — log (1—2)
Jo
a 3
or with — = 4; oi B, Les =e
Yo Jo qo
1-++ (ar?+ Ba’*+y2*) (8
1—G log (le) EAT PAR,
( 429 )
and this is the more accurate formula, which has taken the place of
the simple relation (3).
HI. We will now show, that the above formula quantitatively
yields the values, found by van Hureren for 7’, in a satisfactory manner.
dT 5 :
As t= (|) = T, 0,0 may be determined with great aceuracy from
ny.
the beginning course of the meltingpoint-line. From the values, found
for 7’ (on pg. 16 of the dissertation) for «=O atom "/, of mercury
(pure tin), « = 0,1005, «= 0,1716 and » = 0,2338, the average value,
obtained for — = is = 200. From the determinations of Hvycock and
Av
NEVILLE between «=O and «= 0,1 it also follows, that — En == 200;
: Av
For 0 we may therefore take (7, = 505):
200
6—-— = 0,4.
505 o—
I calculated the values of a, B and y as follows:
ea el tel pet 1 ee 8:
Formula (8) thus becomes:
1+4(0,8250?—1,11e* + 1,33%)
: PAV Aloo ( toon te FE
and so we find the following values for 7.
The agreement is as good as can be expected : the difference between
the calculated value of 7’ and the observed value generally amounts
to fractions of a degree, average 0°,8; as regards to the absolute
temperatures the deviation is only average 0,2 °/,. Only the two last
values are too low (the last 8 °/), but then the influence of a small
inaccuracy in the determination of the coefficients 8 and y makes
itself strongly felt. If we except these two last values, the calculated
meltingpoint-line fully coincides with the observed line in the scale
of the figure in the dissertation. And by means of a slight alter-
ation in the value of 8 and y we might perhaps cause the two last
observations to agree. Let us not forget, that the formula (8)
always remains an approximate one. In the last values of z the
composition of the separated tin must also make its influence felt.
For this is no longer pure tin but contains certainly 1°/,, or perhaps
even 6°/, of mercury.
As regards the value of ¢ (the heat of fusion of tin, when passing into
RT 1010
0
the amalgam) — when « — 0, q = q,, that is to say = —— = ——
8 ) / / . () 0.4
= 2550 gram-cals. At 25° our formula is no longer available, as
El
|
ons O73 |
ea a | de | vs ie fag A) Numer, | Denom. | ES
| | | | | | | |
0,1005 | 0,0101° | 0,001015.0,0001%| 0,1059 | 1,023 | 1,044 | 2194 | 211,6 | 08
0,1716 | 0,0294 | 0,0050% 0,0008% | 01883 | 1,0051 | 1,0758 | 1989 | 198,6 | 0,3
0,2338 | 0,0546 | 0,0127* 0,0029** | 0,2663 | 1,0076 | 1,1065 | 186,7 | 483,72 3,02
0,2969 0,08815 | 0,02617 0,007" 0,3523 | 10099 | 1,1409| 173,8 | 1730 | 08
03856 | 0/1487 0.0573" 0.02911 | 04872 | 40144 | 11949 | 155,4 | 155,9 | 0,9
0,5001 02501 0,1251 (00625? 0,693 10256 12773 | 199,3 | 135,4 — 4,1
0.5973 | 03568 | 02131 01273 | 09095 | 4,0488 | 1,3638 | 115,9 | 4152 0
| | | |
0,6467 | 0,182 0,2705 0,1749 10404 | 41,0682 | 1,4161 | 107,7 | 107,4 | 0,3
0,6754 | 04562 — 0,3081 0,2081 41959 10830 14501 | 404,0 | 4034 | 0,6
0,6813 © 0,4642 0.3162 0,2155 11435 | 1,0866 | 14574 | 1033 | 1024 | 0,9
0,7104 | 0,5047 | 0,3585 '0,2547 19393 | 11047 | 4,4957 | 998 | 99,0 | 0,8
0,7155 | 0,5119 0.3668 0,2620 1,2570 | 1,1083 | 4,5028 | 992 | 98,8 0%
| | | |
0,7477 | 0,5591 | 0,4480 0,31% | 4,3772 | 11935 | 14,5509} 95,9 | 95,4 | 0,5
0,7547 | 0,5696 | 0,4299 03244 1,4053 | 1,1393 | 45621 | 95,1 94,0 | 4,1
0,7963 | 0,634 | 0,5049 0,401 | 41,5912 | 41,1805 | 41,6365) 91,4 90,0 411
0,8189 | 0,6706 | 0.5492 04497 | 4.7087 | 41,2064 1,6835 | 887 | 884 | 03
| | | |
0,8921 | 0,7958 | 0,7100 06333 | 2,926 1,318 1,8906 | 77,5 | 79,7 —22
0,9483 | 0,8993 | 0,8598 0,8087 | 92,9693 | 41,4212 | 2,1849 | 55,3 | 65,2 ips:
| | | | | | | |
according to the above table it only yields trustworthy values for 7
up to about 90°. At 90° r == 0,8, and then, according to (7), we have:
g=Qll + (aa? + Ba? + yet],
or q = q, {A 4- 0.325 wt — 1.11 a + 1.33 wf],
that is to say gq == 1.185 gq, = 9020 gram-eals.,
whilst van HerereN (at 25°) found + 3000 gram cals, by means of
electromotive measurements '). The concordance is absolute.
We, finally, wish to remark, that according to the determinations
of vaN HerrereN and of Hnycock and Nrvintin, regarding the lowering
of the temperature of fusion of tin on adding small quantities of
mercury, g, must be = 2550 cals. We therefore see, that the value,
assigned by Prrson, namely 14.25 118.5 = 1690 gram cals., is much
too small. In a later communication | will show, that the heat of fusion
of mercury, given by Person, is also many times too small.
Dec. 1902.
1) Dissertation pg. 49.
( 481 )
Chemistry. — “On the potential-difference, which occurs at the
surface of contact of two different non-miscible liquids, in
which a dissolved electrolyte has distributed itself.’ By Dr. J.J.
van Laar. (Communicated by Prof. H. W. BaKuuis RoozuBoom.)
(Communicated in the meeting of December 27, 1902.)
|. It has already been demonstrated by Nernst!) in 1892, that
a potential-difference must occur at the surface of contact of two
liquids, which lie together in layers, such as for instance water and
phenol, on account of the unequal distribution of the neutral molecules
and the Ions of a dissolved electrolyte. It is true, that his expression
for the electromotive force relates to the case, that one of the two
phases is a so/id solution, but it will be perceived at once, that the
same formula also applies to our case *).
There is, however, at present no prospect of obtaining direct
measurements of this potential-difference *). But as RiesenrEnp*) has
lately been experimenting on the subject, although in another direc-
tion, it may be as well to give the exact theory of the phenomenon,
which I worked out about a year ago, when engaged in writing a
book on electro-chemistry, which will be published later.
Suppose we have a solution of KCl in the solvents A, and A,
A, A,
Vials rl. a eon
| a C1) K |
| Gi. Ollie, RER
CIK
If now equilibrium has been established between the non-dissociated,
electrically neutral portions of the dissolved KCL in the two phases,
there need not be equilibrium between the Zons in the two solvents.
Indeed, equating the thermodynamic potentials for equivalent quanti-
ties of the non-dissociated portions in the two phases (equilibrium
of partition), we get:
== zal
Uc, — "xc. (1)
But the two dissociation-equilibria give:
=: JE a =f | Pre = aS Oh 2
Crone eg, “ch, Pra Mie et gr (+)
Consequently it will suffice if
- = ~ AE TR ne ELC.
Br + Bey = By, + UG), (5)
1) Zeitschr. fiir Physik. Chemie 9, 137 (1892).
2) Compare Rresenretp, Wied. Ann. (4) 8, 617 (1902).
Sy bids dc
4) Nernst und BurserreLp, Le. p. 600—608; Riesenrerp, 609—615; 616—624;
id. Inaug. Diss., Göttingen 1901; Hrrrorr, Wied. Ann. (4) 9, 243—245 (1902).
( 432 )
and it would be a sheer accident if we also had:
Be = Bg i Bey = Hor
There exists therefore as a rule no equilibrium of partition
between the /ons in the two solvents. For example there may be
in the second solvent relatively too few K-Ions, too many Cl-Ions.
Since a system out of equilibrium tends to pass into a condition of
equilibrium, K-lons from A, will migrate to A,, and remain there
in the boundary-layer, while the corresponding liberated Cl-lons
remain in the boundary-layer of A, (inversely Cl-lons will migrate
from A, to A,, whilst the corresponding liberated K-lons remain in
A,. Both add themselves to the above mentioned similar ions in the
boundary-layer). The consequence is the occurrence of an electrical
doublelayer and therefore of a potential-difference. And it is this
potential-difference, which will restore the originally non-existing
equilibrium between the Tons.
All this may be put into a very simple mathematical form.
Let V, be the electrical potential of A,, V, that of A,, so that
A= V,—V, represents the potential-difference at the boundary (in
the case we are dealing with, 4 is therefore positive), then the
formula for the equilibrium of the K-lons will be:
HP,
aaa
de + Ade=0,
which is at once obvious, when we consider the virtual passage
from the left to the right over the boundary of such a quantity of
K-Ions, that the quantity of electricity transported is de. As the
quantities pg relate to equivalent-quantities, and as these do not cor-
respond with one electric unit, but with ¢ (= 96530) electric units,
IH, must be divided by «.
Ky Ky . . . k Dn,
For the equilibrium of the Cl-lons we find in the same manner:
ea Js
EA Ee — À de —= 0.
&
The sign at 4 is now negative, because on account of the negative
charge the change in the electrical energy is — 4 de.
We therefore obtain from the two relations, after dividing by de:
ih a Ee ee
é é
That these two equations for A are not conflicting, is at once
apparent. For the relation, resulting therefrom
u
LE NT tn
leads at once to (3).
ET
( 438)
If we introduce:
— u + yc A log Cy
in which e is the concentration of the Tons, we may also write:
A LAs ee
cece (u Kk Ki + RT log =|
)
\ 1 ! ! ry eo
A= (Www) + RT log —
€ Cl, Ch b CCh
Il. Now everywhere cx =cq (only in the boundary-layer an
excess of positive or negative Tons is present, owing to the for-
mation of the doublelayer), therefore also
ON ho Clg
as B)
EK, Gen
and so we find’) by addition of the two equations (5):
A Wato) — gt) | Me elo GC)
From this last relation it follows at once, that in d/ute solutions,
where the quantities w are almost independent of the concentration,
the potential-difference A will be also independent of the concentration.
Whether much or little KCl is distributed through the two solvents,
we will always notice about the same potential-difference A.
If we deduet the two equations from each other instead of adding,
: d AE Gan
then we obtain | observing that — = — |:
Cp Us
RT tog Me = — | (uly 0) + Wl (7)
te ee Cle Ch “Fan Aa baa Soar
1
If now we put
! ! ait ry >
U Ur = RT log ee |
(a)
1 f hes p Es Al dd 3
WT ber = RT log Kn |
in which Ag and Ke, are quantities, which depend on the nature
of the two solvents (and which in difute solutions will only be fune-
tions of temperature) — they are the so-called partition-coefficients
of the positive and negative Ions — then (6) and (7) pass into
E Key a |
A = — log — gr SAPS Ae pty ee sad er OG
2e Kk
EK, i
(EE) = kx Ka. OTN NOM iP a oe Ae ACER)
1) The formula (6) was given already, though with a somewhat different notation,
by Luruer [Z. f. Ph. Ch. 19, 537 (1896)]. The first thermodynamic theory of the
equilibrium of partition was given by me in a paper of 1895 (Z. f. Ph. Ch. 18, 264—267),
29
Proceedings Royal Acad. Amsterdam. Vol. V.
(434 )
Nernst’s formula for A, obtained in a different manner, is identical
with our formula (5). (As Nernst's # = V,—V,, our A= -— EK).
F 5 . 5 ‘epl: x ! aa - 4 ee : ! Eel E
or if we replac Wir, by RT log Kp and Wor Wer by
RT log Kor, then (5) passes into
jk KS RT HG
ha log KK — — —— log Ke —,
é oh: é CCL,
and this is Nerrsr’s expression. As has already been observed, the
quantities Kp and Ay; are the so-called ““partition-coefficients” of the
positive and negative Ions. For instance for the positive lons we should
have, when equilibrium of partition occurs:
HT Ur, = 0,
or
an A
u Et K, + RI log ce =a):
1
int 2
so that we obtain = Kx. The same for the negative Ions.
Ky
The relation, given by Nernst *)
C
> > 45 | are
Kx X Ka= X Axe,
in which Ae, is the coefficient of partition of the neutral KCI-
molecules, and C, and C, are the dissociationconstants in the two phases,
follows directly from the thermodynamical meaning of these quantities.
For if we write this relation in the form
RT [log Kx + log Kei] — RT [log C, — log C, + log Kxcr),
it passes, taking into account equation («) and the relations
RT log C, =e
ad Al es ! ee, ! 7 5 il ' = ! .
RP log Kro ro xe, KOE eo Ck?
RT loy C, = u
! !
co, “x; Eat
immediately into the identity
! ! ! ! 2e ' i
wt x) +o, a= Ko,
rae 6 4 Lie
'
tee
Not the formula (5), but the formula (6) or (6a), derived by us from
(5), deserves however the preference, because the concentrations of
the Ions have been eliminated therein, and an expression has been
obtained, in which only the coefficients of partition Ap and Ary occur.
' ! ! !
keh Er Wer) HW xe mE Ke 1:
HI. If the dissolved electrolyte has now distributed itself so, that
1) Z. f. Ph. Ch. 8, 138 (1891).
the total concentration is c, in A, and ec, in A,, we shall have:
CK, =S OC, 5 EK, == A, Cio
in which the quantities c, and c, may be found by chemical analysis,
and «, and a, by determinations of the conductivity. As soon as 4
-
Ke
can be determined by experiment, KR, may be calculated from the
K
equation (6a), and Ax & Ker from (7a), and we can therefore get
to know separately the quantities Ap and A, consequently also
the quantities
UK, — UK, and wo, — uci, -
From (6a) it further follows, that A will be positive (as supposed
in the figure), when
Ko > Kx.
Only when by accident Acj=Kx, A can be 0. In general a
potential difference will always oceur between two non-miscible solvents,
when an electrolyte is partitioned between them. This potential-difference
is given by (6a).
From the equation (7a) it follows, that the relation of the concen-
trations of the Jons in the two solvents in the case of d/ute solutions
will be practically independent of the total concentrations. This
equation may also be deduced directly from (3). For this, being a
result of (1) and (2), that is to say of the equilibrium of partition
and the two equilibria of dissociation, may be written :
wu) (uu) == RT u “Ky + log = |
ea K, are oh EA “Ect, :
and this after substitution passes at once into (7a). For
CK. Fol. We Ek
2 1 log — = 2 log — = — log | — |.
CK, EC | 1 Ch t CK .
The equations (6a) and (7a) moreover lead to an important conclusion.
As the quantities Kp and Aj are, in the case of di/ute solutions,
specific quantities, we must therefore find about the same values for
these quantities in the case of other salts, when employing the same
solvents A, and A,. For NaCl for instance we will have:
Ee 1 ee
RI ig et. & ) NE
C Nas
from which by experimental determination of A' and the quantities
Cya, and Cy, , the two quantities Kva and Kc, may be determined.
The value, found for A, from KCl-solutions in A, and A,, must
then be practically sdentical with the value for K/, determined from
solutions of NaCl in these solvents.
log
29*
( 436 )
The quantities 4 will show an almost complete additive character,
on account of Ag and A/ being independent of the concentration
in the ease of dilute solutions. For instance, in the same solvents
A, and A, we must find:
Axci—4Anact = Okno,—4ONaNo, «
And the same for other combinations.
The above considerations may be readily extended to the case of
non-binary electrolytes such as CaCl,, ZnCl,, ete. In the different
equations the valencies » of the Ions will then also occur, because
the fundamental relation (4) then passes into the more general one:
$+ $+ = =
u, u, U,
AN re
+ =
VE VE
IV. The question in how far and in what manner the value of
A, given in (6) or (64), is still dependent on the concentrations of
the Ions, can only be answered, when we calculate the values of me
A1
ete. with the aid of an equation of condition. If we accept the
equation of van per Waars as also applying to liquid-phases, we
obtain for instance for the molecules Np:
V—b
Th ky T (log T—1) — RT (1 zee 1) vn [ed pol si
1
-{- nel zn, b,— 2 (” aj J- DEE -}- ms) 2 RT log df
ae Re ae A age a
n, stands here for the molecular number of the solvent. For 6
and a@ we write:
bb Fn, bd me
anja de And Ars eS Ny My ln onee
Let us now calculate the value of
Wo Ho) — W Pam Kx)
or, what amounts to the same, of
(nl mk mn Cy):
If we indicate the solvent by the index 1, the non-dissociated KCl,
dissolved therein, by 2, the two Ions by 3 and 4, we obtain for
u Pa a the expression
TIE Ns —k,) if (log Th) == (ede) -T ( (1)5)0)—(74)0) | ale
9
hen ET oy pln (as daa) he N, (43242) zen (253-443) +, (G54-44,1-
( 437 )
Remembering, that », =n
simplified to
4» &,=> djs the last term may be
2
= pe
a rae (ii di) + 2, (daa Bia) tr %; (a,,—4,,)].
For w.—wv', we find a similar expression. In this, however
Ka Cis ae ; Xpression. Ss, however,
the quantities /,, 4, (the heat-capacities of the same Ions, at infinite
volume) and (@s)o. (@4)o> (sor (14), (the energy and entropy-constants
of these Ions) will be exactly the same. a,,,4,,, A and a,, will also
remain unaltered, so that for the difference Wi Wo) — WW)
we may write:
PF bec Dr ETA (nasa) (dpd)
he en evo |—2] ( RE RA ) i
Ne te Ns n',
+ (452-445) TUD + (a;,-4,,) aos
The quantities, relating to the second solvent, are indicated by
accents.
We may now go a step further and accept as a first approximation:
En ! a ! 8 Tey
b=}, D=, a, =a,
If we then also write
V V' n
ee ree eer Oe yt My = 70 (es = ae NERC es
1, u, n,
we finally obtain for A:
Rie ule ear gaan ys LL nd 2
A = ( 31 3 Me 41 „ad, tai a ) { (ago) (} sa =e ( at) )I (65)
€ v Uv v v
HEAD en (leeren
As, in consequence of the equilibrium of partition, tappen, is
—— IC
constant, 4 will have the form
A = as 4- A (l—a)e,
Aert ra Mee kate ac)”
or since, on account of the equilibrium of dissociation, tay =
IG
constant, also the form
A= Ay 4 (ei.
Whether 4 will be positive or negative, depends chiefly on A, If
!
Uzi TT 4, @5,;— Gay
meee
v v
A will be positive. We also see, that A—A, will increase or decrease
with the second power of «ec, that is to say in the case of strongly
dissociated electrolytes, where « is nearly 1, almost with c’.
Dec. 1902,
( 438 )
Physics. — Dr. J. J. Harro: “The value of some magneto-optic
constants.” (Communicated by Prof. P. Zeeman).
In my doctoral thesis, on The magnetic rotation of the plane of
polarisation in the neighbourhood of an absorption-band 5, T have cal-
culated the values which three of the constants, occurring in Vorct’s
theory of magneto-optie phenomena, assume ina particular case. I did
not then know as yet, that Drvpr had already tried — in his Lehrbuch
der Optik (Leipzig, 1900) — to make some estimate as to the order
of magnitude of a constant 7, introduced by him, which is connected
in a simple manner with one of the constants of Vorer’s theory, of
which I have determined the value. Therefore I beg to be allowed
to mention here my results and those of Drupn, and to examine in
how far these results agree.
If X, 9, 3 are the components of the electric polarisation in some
medium, Voigr assumes that every one of these components exists
of a part X, Y, Z, relating to the free ether, and a series of other
parts X,, Dj, 31, indicating the state of the ponderable matter. He
therefore assumes:
EKL SE ete:
A representation of the phenomena of selective absorption, in which
the influence of a magnetic field with components A, B, C is also
taken into account, is gained when the sets of vector-components
A, B, C are subjected to the conditions:
VP A2 § A
Er + ay Bal + by, OE + ¢y (ci —_ B =) = Bj, ONG ues
Ot dt t
The constant Dj, appears to be equal to 7,7/42°, if ty, is the vibratory
period of a free vibration of the absorbing medium; I have derived
the values of the constants aj, cy and ej, for the line D, from the
results of my measurements in a particular case (for a flame which
contained very much sodium); the values I have found are (vide
p. 85 of my thesis):
Urd SAlOrete
0 02. Osea
Sy Wee 10a ae
The constants a, and «, depend on the density of the sodium-
vapour in the flame, the constant c, does not so far as we know.
The data which served for the calculation of these constants are
the following: «a, was calculated from the width of the absorption-
1) Amsterdam, 1902.
( 439%)
band, which is proportional to it; this width was about 1 Angstrém
Unit; c, was caleulated from the magnitude of the Zreman-effect ;
for this magnitude in the field which I used — of 9000 C.G.S.
Units — I took '/,, part of the interval between the two sodium-
lines; e‚ was calculated from the value of the rotation of the plane
of polarisation in the neighbourhood of the absorption-band; on the
magnitude of this rotation as a function of the wavelength, for dif-
ferent intensities of the magnetic field and different widths of the
absorption-bands, I have made measurements of which the results
have been recorded in the tables given in my thesis. From these
tables I shall quote one series here, giving the numbers from which
the above-mentioned value of e, was deduced (vide p. 42 of my
thesis, table 24 1):
d Bas x
| |
15 88 50 11
20 51 55 10
25 31 60 9
30 23 65 8
35 18 70 6
40 14 75 5
AD Thies
Here dis proportional to the difference between the wavelength
of a given kind of light and the wavelength which corresponds with
the middle of the line D,; the coefficient of proportion may be found
from the fact that the difference between the wavelengths of the two
sodiumlines corresponds with a value d= 1380; x represents the
rotation of that particular kind of light in my experiments, expressed
in a unit of which the value is determined by the fact that a rotation
of 180° corresponds with a value y= 105. Thus we read from the
series, given above, that for a value of d corresponding with
35 18
<6 A. U. the rotation of the plane of polarisation is aT 507;
130
from these corresponding numbers the value of e, is deduced in the
way which I explained in my thesis.
Drove, in his Lehrbuch der Optik which 1 mentioned above (p. 353),
in his version of the theory of dispersion gives the equations of
motion of an electron in the form:
dS Ane? ds
nae Sr.
Ot
Here m is the mass, e the charge of the electron, § its displacement
parallel to the axis of X from a position of equilibrium, A the com-
ponent parallel to this axis of the external electric force acting on
the electron; 7 and 9 are positive constants.
In working out the theory it appears that Voier’s constant aj 1s
identical with the expression 7/4a of Drupe. Now the value of 3
was calculated by Drupr himself (p. 490) from the vibratory period
of the sodiumlines; he finds the value of this constant to be 7,6 . 10-27;
from this value and that of Vorier’s constant a, which I mentioned
just now, we find:
r= 16502
here we must bear in mind that this value applies to the particular
sodiumflame to which my measurements relate; 7 must, as well as
dj, depend on the density of the sodiumvapour in the flame.
Drupe tries in his book to fix limits, between which the value of
r must lie. He finds a lower limit by deducing from theory the
proportion between the quantity of light, which the absorbing sodium-
flame itself begins to emit under the influence of incident radiation,
and the quantity of incident light which is absorbed. This proportion
he finds to be 0,126/r. From the fact that reversal of a sodiumline
is possible, he concludes that this proportion must be considerably
smaller than 1, and he therefore fixes the lower limit for the value
of 7 by assuming:
ro >A.
A higher limit is found by Drupr from the consideration of the
phenomena of interference. He deduces theoretically the value of the
coefficient of damping y of the free vibrations of the electron and
finds for this: |
y=0,6.r. 107.
Now this coefficient must be small, as with great phase-differences
interference-phenomena can still be observed. With sodiumlight inter-
ference-phenomena have been observed with a phase-difference cor-
responding with 200000 wavelengths; therefore 200000 y must still be
smaller than 1, therefore in this case:
mz 100;
It is evident that this result is not at all incompatible with the
value of # which I caleulated above. In order to observe interference-
phenomena with such great phase-differences it has been necessary
to use a source of light showing very narrow sodiumlines; with
( 441 )
the width of the sodiumlines to which my measurements relate
(which was about 1 Angstrém-Unit) the greatest phase-difference with
which interference-phenomena can be observed is one corresponding
with 3000 wavelengths; the higher limit is therefore raised to 7000,
so that 7 must in this case lie between 10 and 7000, which it
really does according to the calculations given above.
Some further deductions which can be made from the comparison
of Vorer’s equations with those given by Drupe, have already been given
on pp. 90—95 of my doctoral thesis, with reference to LorENtz’s
paper in the Report of the Congres International de Physique, held
in Paris in 1900, and I will here only refer the reader to that part
of my thesis.
Physiology. — “A new law concerning the relation between stimulus
and effect.’ V. By Dr. J. K. A. WERTHEIM SALOMONSON.
(Communicated by Prof. C. WINKLER.)
From the law connecting excitation and effect,
BAL eee EA Ee EAR ence at 10
we may obtain by differentiating
dE
ees Apt BRO)
or also
LE end
diss BRO MN A eect a) (E
1B
Introducing differences instead of differentials, with this limitation
that the differences should be very small, and taking according to
Frcuner, AZ, the differential sensation-threshold as a constant quan-
tity, we obtain
WR By BORON SA tae | pedis (Ards, Dae
or, by putting the constant e~2°k, =k
AR Rell Wet urine tte tea ate OOS)
the latter formula containing an expression for the absolute differen-
tial threshold-value. We might employ this formula for psychical
impressions of peripheral stimuli, if the peripheral stimulus had caused
excitation of only peripheral neurones with equal stimulation-constants
B, and moreover if all these neurones had been uniformly stimu-
lated. Under a similar limitation we might also admit the validity of
the formula for the relative differential threshold-value deduced from
(4) by dividing both terms by A; we then obtain:
( 443 )
BR
at ie ed nr Oe cans ae ee
R R
As a rule, however, this formula may not be applied in the
ease of psychical processes, because the above-stated conditions have
not been fulfilled. It is impossible to suppose the case of a peripheral
stimulus hitting only one single peripheral neuron, or of one single
group of neurones being exposed uniformly and with equal force to
that stimulus.
Let us see, what happens when a sense-organ in the living human
organism is subjected to a stimulus. For instance we may consider
the action of pressure on the skin.
Suppose the compressing object to be in contact with a limited
surface of the skin at the moment the pressure commences. We
may take it for granted that all end-
organs situated within the limited skin-
fo hoses oOo. | surface in direct contact with the com-
lao 0 4.0%0 ©) pressing object, undergo an equal and
ba AO B 0 uniform pressure, and that in the case
| | of this pressure being increased, its action
will remain uniform. To the neurones con-
nected with the nerve terminations «, ‚aA,
our deduced law (5) may be therefore
applied. As soon as the pressure increases
the skin-surface will undergo a change
of shape and be compressed (see fig. 1).
This implies that nerve-endings 4, 4, situ-
ated outside of the originally compressed
surface, will also enter into an excitatory
state. If this deformation be a slight one,
Fig. 1. only the nearest end-organs 4, will be
compressed. By increased pressure the more distantly situated ones
c, c, d, d ete. will also be stimulated. To all these end-organs,
situated outside of the originally compressed surface, impulses are
given, which are conducted to the central nervous system. From all
the combined impressions finally results the sensation by which our
judgment is decided.
The neurones connected with 6,4 c,¢ d,d ete. will likewise obey
the law of stimulation and effect. The intensity of stimulus however
is different for all these neurones, and also different from that for the
neurones «a, a, a. Therefore, whilst for the neurones aaa, the expression
dR EBR
: R R
( 443 )
might be employed, we must use for the neura 6,4 e‚e d,d etc.
the expression
5 ebr je bry _eBry
9, = K—_, 9, = K—, OC, ue
ry "s us
As the stimuli 7,, 7
stitute for these m,R, m,R, m,F ete.
etc.
"> 7, ete. are proportional to #, we may sub-
The question arises next: how shall we psychically combine these
impressions in order to make use of them for the special purpose
aimed at by our experiment, i.e. to decide whether two stimuli are
different from one another? Summation or addition is out of the
question: this would be in contradiction with the experience that by
fixing our attention on a definite sensation, other sensations are
weakened. It is clear that we will conform our judgment to that part
of the’ sensation that is best fit for our purpose. Starting from this
fact we may continue to treat the question mathematically.
In the first place it ought to be taken into consideration, that by
increment of a stimulus not a small number of new peripheral
neurones are stimulated, but generally a great many. In the case
of a pressure e.g. not only nerve-endings lying sideways of the
compressed surface, but also more profoundly situated end-organs
will be acted upon by increased intensity of stimulus. For every
individual neuron we shall have to put in another coefficient m. If
Fig. 2.
we construct therefore a great many curves @,, 0,, 0, all these curves
will only be different on account of the constant m being changed.
We now suppose the final judgment fixed each time by a part of
a farther situated curve. Thence it may be concluded, that the
( 444 j
enveloping curve will represent the manner in which a judgment
about the final result originates. To obtain the envelope of the
enb
group of curves 9 = K Th if the constant 7 is changed, we put:
embh
RD ea ae) Pe ae AD
2» mR (6)
or
Caleulatine the value of mz corresponding to —- — 0, and substi- .
o Lee
UL
tuting this value into the equation £’— 0, we find the formula for
the enveloping curve. We may state:
ol’ K pp mMBR—1
— = — —, BR) , 2... «= (%#)
Om Rk m
?
By at
Oa KBE NA AN he ee eee
proving that the relative differential thresholdvalue is constant.
3y this process we have deduced from our formula the law of
WEBER.
From our deduction may be inferred that the area, wherein the
law of Weber prevails, is a limited one. ‘The validity of this law
commences within the area of the enveloping curve, and a look on
the figure 2, will make it clear that the first part of the whole
as
From which follows m — an which substituted into “= 0, gives:
sensation-curve is given by the descending part of the curve
BR
é yeh
Kn: The horizontal part then represents the area within
L
the limits of which the law of WeBeEr prevails, whilst in the case of
very great intensities of stimuli the ascending part of the curve
ebmk
= Ke
m
will appear.
There remains still another conclusion to be drawn from our
deduction. This latter was founded on the supposition that the inerement-
constant B was the same for all stimulated neurones. This, however,
is highly improbable: in the most favourable cases we may only
suppose that the A-coefficient of the homogenous neurones will
possess approximatively the same value, from which follows that
we may admit the law of Wesrr at best as an approximation.
Finally it may be mentioned here that apart from the above-
demonstrated correction for obtaining an approximation in the diree-
tion of the law of WeBnr-FrcrNeR, probably still another means of
correction exists in some of our sense-organs; | shall prove this in a
later Communication.
r N 5 ie
A EATERS,
® fi
D. J. Korreweo. On plaitpoints and the corresponding plaits in the neighbourhood of the sides of the Wesurface of VAN DER WAALS.
SIDE OF THE LARGE VOLUMES,
Temperature slightly lower than the
critical temperature of the solvent.
Fig. 1.
SIDE OF THE LARGE VOLUMES.
‘Temperature slightly higher than the
critical temperature of the solvent.
Case 2. Case 6.
Case 3. Case
Case 4.
Case 8. Absent.
—— _
The figures relate to the v, # diagram.
K is the critical point of the solvent.
P the plaitpoint.
R the critical point of contact
KP indicates the direction of the plait-
point curve.
The traced curve represents the
connodal curve.
The dotted curve represents the
spinodal curve.
|
( 445 )
Physics. — “Plaitpoints and corresponding plaits in the neighbour-
hood of the sides of the W-surfuce of VAN DER Waars.” By
Prof. D. J. Korrewee.
(Communicated in the Meeting of December 27, 1902).
First Descrirtive Parr.
1. As in my “Théorie générale des plis” T wish to precede in
this paper the demonstrating part by a short summary of the
obtained results.
As we know a plaitpoint may occur on the side «=O of the
y-surface of VAN DER WAALS, *) which is represented by the equation:
w= - MRT log( v—b,) — i + MRT be log u+(1—«) log (1—z)} (i)
DvD
where:
a,—=a,(1—«)?+2 a, o(1-wx)-+ a, «’? =a, +2(,4,-a,)e+ (a, Ha,-2 ,a,)a?,. . (2)
b,=b,(1-#)? +2 ,b, elle) Hb, #?=b, + 2(,b,-b,)e+(b,+6,-2 ,b,)u?, . . (8)
This occurs only in the case that the temperature 7’ corresponds
with the critical 7; of the principal component; but in that case it
occurs always. This plaitpoint coincides with the critical point of the
principal component for which v= 36, and which in our figures we
shall always represent by the symbol A; the plaitpoint itself will
be represented by LP.
If the temperature varies, the plaitpoint and the corresponding
plait can in general behave in two quite different ways. It will
namely either, as is indicated by the jist four cases on fig. I of the
plate, on which the (v, 2) projections of the sides of the wp-surface are
represented, at increase of temperature leave the v-axis and move
to the inner side, therefore entering the surface, and disappear
from the surface at decrease of temperature, or it will as in the
last four cases of that figure, enter the surface at decrease and leave
it at increase of temperature.
1) Archives Neérlandaises, T. 24 (1891) p. 295—368: La théorie générale des
plis et la surface # de van per Waars dans le cas de symétrie. See there
p. 320—368.
2) We take here the equation of the J-surface as it has been originally derived
by van per Waars, so without the empiric corrections which seem to be required
to make the results agree quantitatively better with the experimental data. So is,
for instance, @z considered to be independent of the temperature, and all the results
and formulae mentioned are founded on this supposition. It would not have been
difficult to take such empiric corrections into account, as has really been done by
VerscHAFFELT and Kersom in their papers, to which we shall presently refer; but
then the results were of course not so easily surveyed. Therefore | have preferred
to leave them out of account, at least for the present.
( 446. )
And this different behaviour of the plaitpoint will necessarily be
accompanied by a different behaviour of the connodal and spinodal
curves. For they must always cut the v-axis at decrease of temper-
ature, the connodal in the points of contact of the double tangent
of the w,v-curve of the principal component, the spinodal in its two
points of inflection; at increase of temperature above the critical
temperature of the principal component, however, they get quite
detached from the y-axis. In connection with this they turn in the
first four cases of fig. 1 their convex sides, in the last four cases
their concave sides towards the side «=O of the w-surface as is
also indicated in the figure, where the connodal curves are traced,
the spinodal curves dotted.
cc At decrease of temperature a figure originates in the /irst
four cases as is schematically given here in Fig. a. At
increase of temperature, on the contrary, in the fast four
cases, the spinodal and connodal curves disappear from the
surface at the same time with the plaitpoint itself.
Besides to this different behaviour it appeared however
desirable, to pay attention to two other circumstances. /irst
to the direction of the tangent in the plaitpoint, whether
if prolonged towards the side of the large volumes, it
inclines to the immer side of the y-surface, as in cases 1, 2, 5 and
6 of fig. 1, or whether it inclines to the outer side, as in the
remaining four cases. For on this it will depend which of the two
kinds of retrograde condensation will eventually appear *). But besides
we have to pay attention to the question whether the plaitpoint,
entering the y-surface, either at decrease or increase of temperature,
will move towards the side of the larger volumes as in cases 1, 3,5
and 7, or whether it will move towards that of the smaller volumes
as in the other cases. In connection with this question we may point
out here that the line KP in fig 1 of the plate may everywhere be
considered as a small chord of the plaitpoint curve of the v,-diagram
and accordingly indicates the initial direction of that curve, which it
has when starting from point A.
The three different alternatives, which we have distinguished in
this way, give rise to the eight cases represented in fig. J, and we
may now raise the question on what it will depend which of these
eight cases will occur at a given principal component with a given
1) See on these two kinds of retrograde condensation inter alia, the paper of VAN DER
Waars: “Statique des fluides (Mélanges): im Tome | of the “Rapports présentés
au congrès international de physique, réuni à Paris en 1900”, page 606—609.
( 447 )
admixture ; of course only in so far as with sufficient approximation the
conditions are satisfied on which the derivation of the equation (1)
of VAN DER WAALS rests.
2. The answer to this question is given in the graphical repre-
sentation of fig. 2. If appears, namely, that the case which will oceur,
by 2
. . ODE ( ) d
is exclusively determined by the quantities — =x and Zot which
a )
1 1
have already played a prominent part in my above mentioned
“Théorie générale des plis.”
In accordance with this a x- and a y-axis are assumed in fig. 2
of the plate and the regions where the points are situated whose x-
and y-values give rise to the appearance of each of these cases, are
distinguished by different numbers and colours.
For instance the white region 1 indicates the x- and y-values for
which the plaitpoint enters the y-surface at rising temperature, moving
from A to the side of the large volumes, while in the well-known
way we can derive from its situation on the connodal curve on the
right above the critical point of contact A (for which the tangent
to the connodal curve runs parallel with the v-axis) that the retrograde
condensation will be eventually of the second kind i.e. with tem-
porary formation of vapour) and also that the temporary vapour
phase will have a larger amount of admixture than the permanent
denser phase.
In the same way the blue field 5 indicates the x- and the y-values
for which the plaitpoint enters the p-surface at decrease of temperature,
moving towards the side of the large volumes; whilst the retrograde
condensation will be of the first kind and the temporary denser phase
will show a smaller proportion of admixture than the permanent
vapour phase.
3. When examining this graphical representation we see at once
that one of the eight regions which were a priori to be expected, region 8,
fails. From this follows that for normal substances the combination
of retrograde condensation of the second kind and of a plaitpoint
which enters the surface at decreasing temperature and moves towards
the side of the small volumes, is not to be expected.
All the other seven regions, however, are represented in the graphical
representation.
4. Further the point x= 1, y= 1, is remarkable, where no less
than six regions meet. This point represents really a very particular
( 448 )
case, namely that in which the molecules of the admixture, both
with regard to volume and to attraction, behave towards the mole-
cules of the principal component exactly as if they were identical
with these latter molecules.
If at the same time a, —a,, 6,=06,, which is of course not
involved in the above suppositions, it is easy to see that at decrease
of temperature below the critical temperature the plait would suddenly
appear all over the whole breadth of the tp-surface.
Now it is true that every deviation from these equalities a, =a,,
h,=6, will prevent such a way of appearance, but it is evident
that then the behaviour of plaitpoint and corresponding plait will
depend on a, and #4,, ie. the first approximation for which the
knowledge of x and y is sufficient and which everywhere else
suffices to make this behaviour known to us up to a certain distance
from the side of the w-surface, fails here.
And also already in the neighbourhood of the combination of the
values *=1,y=1, this first approximation will be restricted, to
the immediate neighbourhood of the point A’ and of the critical
temperature 7), of the principal component. When we are not in
that immediate neighbourhood the influence of a, and 6,, — of the
former of these quantities specially, — will soon be felt. On the
contrary for values of x or y sufficiently differing from unity the
considerations derived from the first approximation will probably be
of foree within pretty wide limits, at least in a qualitative sense.
5. Before proceeding to a discussion of the border curves between
the different regions, we will shortly point out that we cannot
attach an equally great importance to all the parts of the graphical
representation. So all points lying left of the y-axis relate to negative
values of ,a,, Le. to the case that the molecules of principal com-
ponent and admixture should repel each other, which is not likely
fo occur.
In the same way the negative values of y, so of ,/,, of the points
below the z-axis, should be considered as having exclusively mathe-
1
matical signification. If the relation, ,6,— = (0. +4,); should still be
applied also for very unequal values of the ’s, then y would even remain
1
2
mk
always larger than and so the part below the line y =
2,
would lose its physical signification.
6. With regard to the border curves between the different parts,
we have first to deal with the parabolic border curve separating the
de at
( 449 )
regions containing blue (blue, green, purple) from the others. It
, ! Bah.
touches the y-axis in the point x= 0, y= >. Its equation is:
(2y—3x-+ 1)? — 8 (y—x) = 0
or if we transfer the origin to the point y=1, x=1 and therefore
introduce the new variables: x’ = x—1; y’ = y—1, which brings
about a simplification also for the other border curves, we get:
(By Sy =O. ts (Á)
Then we have everywhere inside that parabola, so in the regions
BOA:
Orte 8 —x) 0
and outside it in the regions 1, 2, 3, 4:
(2y 4x) — 8 (y'—z') > 0.
In consequence of this it depends on the situation inside or
outside the parabola, whether on the corresponding w-surface the
plaitpoint will enter the surface at decrease of temperature or at
merease of temperature and whether the spinodal curves turn their
convex or their concave sides to the side «= 0.
Fig. b. For points on the parabolic border curve the plaitpoint
occurring in the point A at the critical temperature of
the principal component, is to be considered as an homo-
geneous double plaitpoint at that moment. The projection
on the v, w-surface appears then as is indicated in fig. 0.
How the transition to this condition takes place may
be made clear by the subjoined fig. c, which represents
the same projection for a temperature slightly below that
of the critical temperature of the principal component
for the case that the x- and y-values indicate a Fig. c.
point, which is still situated in the green region
6, but on the verge of the border curve of the
yellow region 2.
Very near the plaitpoint P we find here already pg
a second plaitpoint ?’, which at further decrease
of temperature soon coincides with 7.
If now the point in the green region approaches
the border curve of the yellow region, the two
points P? coincide nearer and nearer to the critical
temperature of the principal component and to the point A. On
the border curve it takes place in the point A’ itself. Beyond the
limit, in the yellow region, the plait of ? does not develop any
more and P’ takes the place of P.
30
Proceedings Royal Acad. Amsterdam. Vol. Y.
( 450 )
7. As second border we get in the graphical representation the
straight line:
DE DE SA Ee eV
It separates the regions containing red 3, 4 and 7, — for which
2 y’—3 x’<0, and where the tangent in the plaitpoint, continued in
the direction of the large volumes, inclines towards the side c—=0—
from the others, where it inclines to the inner side of the w-surface.
As we saw before, this inclination determines the nature of the
retrograde condensation. Not exclusively, however. For in the first
four cases of figure 2 the result of the same way of inclination 1s
in this regard exactly the opposite of that in the last four cases ;
henee the parabolic border curve acts here also as a separating curve;
so that retrograde condensation of the first kind (i.e. with temporary
formation of the denser phase) occurs in the regions 3, 4, 5 and 6,
in the two first with greater proportion of the admixture in the
temporary phase, in the two last the reverse, and on the contrary
retrograde condensation of the second kind in the regions 1 and 2
(with a larger proportion in the temporary less dense phase) and 7
(with a smaller proportion in that same phage).
8. The third border curve is a eubie curve with the equation:
(2 7'—3 x’)? —4(4y7'—3 x’) (2 y'—3 x) +164 =0. . . (6)
It eonsists of two branches, which possess both on one side the
common asymptote :
DE pee ee OE OE eel 0 OG
and which run at the other side parabolically to infinity.
The right-side branch, whose shape resembles more or less a para-
bola, touches the curve y’ = 0 in the point #’ =0,7/=0(x=l, y=1).
Between the two branches, so in the regions 2, 4 and 6:
(2y — 3x)? —4(4y7' —3x)(2y'— 3x) 4+ 167 <9;
in all the other regions of course > 0.
In the former case the tangent AP to the plaitpoint-curve of the
(v, z)-diagram is directed to the side of the small volumes, in the
second to that of the large volumes.
If we, however, examine, whether e.g. at decrease of temperature
the plaitpoint moves towards the large or towards the small volumes,
the parabolic border curve acts again as separating curve.
It appears then that the plaitpoint moves towards the large volumes
at decrease of temperature in the regions 2, 4, 5 and 7, at increase
of temperature in the others.
( 451 )
9. The following table gives the characteristics for the diffe-
rent regions.
Region
1 (2y'-3x!)?-8(y'-x') 0; 2y'- 3x0; (2y'-3x')?-4(4y'- 8x')(2y'-3x') + 16y'>0
2 x Nt: a) 7303 5 <0
3 zE 0; ” <05 ” >0
4 3 DRAAK secre O's 7 <0
5 ie en Re an, oh i 20
6 7 A a AE rs <0
7 EE) <0; ” <0; ” >0
where :
— b.—b
et En Gete et)
a, b,
A similar tabular survey of the physical properties of the regions
seems superfluous, as these properties may be immediately read from
the illustrations of fig. 1 of the unfolding plate.
10. It seems not devoid of interest to know how the breadths of the
regions change with regard to each other, when continually increasing
ralues of y’ are considered. An inquiry into this shows at once that
the blue region 5, measured along a line parallel to the x-axis, has
2
a limiting value for the breadth of —. All the other regions mentioned,
however, continue to increase indefinitely, and do this proportional
with Wy’ and in such a way that the yellow and the red region get
gradually the same breadth and in the same way the green and the
purple one, but that the breadth of the two first mentioned regions
will amount to 0,732 of that of the two last mentioned.
If we also take the white region (reckoned e.g. from the y-axis)
into consideration then we find its breadth at first approximation to
be proportional with y', so that it exceeds in the long run the other
mentioned; the orange region keeps of course an infinite breadth.
The limiting values of the ratios may therefore be represented
as follows:
white yellow _ green blue purple red orange
eae 007 0 WTS Weg TONE 0)
We may see that if we keep « constant and make y to increase
we always reach the white region, while reversively increase of x
with constant y leads finally to the orange region. Strong attraction
between the molecules of the admixture and those of the principal
30%
( 452 )
component promotes therefore in the long run the relations of case
4, large volume of the molecules of the admixture promotes those
of case 1.
11. We may conclude this descriptive part with mentioning some
formulae which we have obtained in the course of our investigation,
and which will be derived in the second part. We do not, however,
give them as new, as they must essentially agree with similar
equations obtained by Kerrsom’) and VerscHarreLt®), if the simplifying
hypotheses are introduced on which the original equation of the
y-surface, used by us, rests. Nor does the way in which they are
derived, in which the method of the systematic development into
series is followed, differ considerably from that of VERSCHAFFELT.
In these formulae we have restricted the number of notations as
much as possible. They only hold at approximation in the neigh-
bourhood of point A and of the critical temperature 7), of the
principal component.
We shall first give expressions for the radii of curvature Rand
R'conn. Of the projections on the (r, r)-surface of the spinodal and
connodal curves in the plaitpoint; from which appears that the radius
of curvature of the connodal curve in the neighbourhood of the point
K is at first approximation three times as great as that of the spinodal.
3
Rb rie EE
Hees bt [(2y'—3x')?—8(y'—-x)J=BR'y>. - . OD
These radii of curvature are here considered as being positive
when both curves turn their convex sides to the v-axis as in the
cases 1—4 of fig. 1 and negative in the cases 5—7.
We may shortly point out here that the corresponding radii of
curvature on the yw-surface itself, on account of the strong inclination
of the tangential plane in the neighbourhood of the v-axis, are quite
different and much smaller, though the relation 1:3, of course
1) W.H. Keesom. “Contributions to the knowledge of van per Waats’s J-surface.
V. The dependence of the plaitpoint constants on the composition in binary mixtures
with small proportions of one of the components”. Proc. Royal Acad. IV. p. 293—307.
Leiden, Comm. phys. Lab. N°. 75.
2) J. E. Verscuarrett. “Contributions to the knowledge of van per Waats, 4-surface.
VII. The equation of state and the #-surface in the immediate neighbourhood of
the critical state for binary mixtures with a small proportion of one of the com-
ponents”. Proc. Royal Acad. V, p. 32L—350, Leiden, Comm. Phys. Lab. NO, 81.
—— ed
hek Und
( 453 )
continues to exist. They even become zero when the plaitpoint
coincides with the critical point A, so that both curves have then a cusp.
12. The knowledge of the radius of curvature Roy, is of importance
specially because it may be used in connection with the formula:
Fig. d.
1 9 ' € !
CG Pe = = tb (2y —3x je ps é
|
through which we know the small angle which
the tangent of the plaitpoint forms with the v-axis,
to calculate in a very simple way the differences
in density and volume between the phases of the
plaitpoint Z and the critical point of contact R
at first approximation ').
According to fig. d we have, within the indicated
limit of accuracy :
(12)
9D
7 ker — PO—} = Wa = rae) 2 aa 4 24 hade { de we : v e e
Vp UR ar OPE = wh conn. 8 ( 7 3x) L( / 3x) 8(y me )] B a)
1 9
. ss > 2 | LE OO NS 9 VE A2 (oA 2? é
# ,—# ,»=RhQ= 5 Fe donne mie 9x) [(2y 3x) —8(y'-x') Ja 5 (14)
13. We proceed now to give the formulae relating to the plait-
points phase at a temperature 7, which does not differ much from
the critical temperature 7% of the principal component.
They are:
4 TT
eeN Rene EEN
P (Qy'— 8x) B(y'—x’) Ta
3 j ! € IANS, | € ! ¢ ! € ! a} »
—3b,= 5 b, { (2y'—3x')?—4(4y'— 3x’) (2y'—3x')+16y'} Ep: (16)
Pp
Pp—P,
(BA Je, + « (11)
pr :
By means of (15) we may transform (13) and (14), so that they
become :
9b, TE
b] mm 7) en - 2) gm) 4 = . . Kl © . 18
ip oT aah 9 ( oe x) yop ( )
and
9 T'—T;,
tr (2-3) oe . « « (19
oe ify are 16 ( i 3x ) fp Bt ( )
1) A similar method is given by Kerzom at the conclusion of the before-mentioned
paper of VERSCHAFFELT.
( 454 )
to which we add:
Pp rl Pen
Lo ies a 84)" (op) ep = er Bep (20)
Py 4b, Dj
14. We shall conclude with giving some formulae relating to
coexisting phases, where the index one refers to the liquid-, the index
two to the gas phase. Where the index fails, we may arbitrarily
take the value for the one or for the other coexisting phase; either
because it is indifferent at the degree of approximation used, or
because the: formula will equally hold for either state.
v,—=3b,—3b LA “Her —3x')?—8(y'—x')Je « (21)
v,=3b, +3), PA
P—Pk ae r
Ar) — ee (22)
id AA EN EN
Pk 1
DS Cr B) (0, =O 20 ck wt NEE
1 54 ‘ar ce | 7 :
= rde) —36, = — "enb: b, ——— + 3b, ‘| 5 [2y'—3x')?—8(y'— x) +
1 Ì
L = [(2y'—3x')? —24 (y'— x’) (2y'— 3x’) 4+ 16 (8y'—2x')] | Lae (OON
in which formula (23) holds also for non-coexisting phases.
SECOND DEMONSTRATING PART.
Transformation of the Y-sur face and preliminary development
into series.
15. We begin with a transformation of the y-surface by intro-
ducing the following variables:
v—odb, T— Tr ww
== AA EE n,n
ra haat Poy i a eT an
which means that we henceforth measure the volume v’ from the
eritical volume and with that volume as unit, the temperature in
l itl d to the critical Ti we
the same way with regard to the critica temperature Lenn
= 27b MR
and the free energy yw’ with MRT, as unit.
Ou
ae
If we moreover put:
ils @, ! ey i 1 dd, Pear
ee ey in eas. (3
ay b, ‘ ay b ay
we find easily from (1), (2) and (3) for the equation of the new
surface: *):
w! = (LHE!) log 3d, (by! Hv) -
t
Ay
le!
+ (LHE) tw log w 4- (1e) log (1-a)}, (28)
where
TEE 9 9 ! 9 9 ! rl 2 99
Catal Ma ea de yt ae - 5 . E (29)
bir cs ate : Zy! =d!) x? 30
na BEN EAR NEMA CA
further :
Ow MRT). ow! 8 dy’
ee aida oa oa oe ed (31)
Ov 3b Ov a Ov
1
16. For investigations in the neighbourhood of the sides it is
desirable to develop the expression for yw’ so far as possible according
to the powers of w. We write therefore:
W = (LE) v loge + %, an € vu av av ap iat 7 = (32)
where in finite form *)
Xo = — (HL) log b, (243!) — (LF)
; ie 2y' 9x!
x= (lt) nk EE Oe OP
Dy’? ed TN | 9 (2x'—2')
hae a) = Wige e ael mes (Lo!)
1) If we wanted to consider az as function of the temperature, the simplest way
of doing this would be by writing the second term of the second member :
dell Het Het? +...) | : 8a,
- Par —. The formula 7; = a7 MR
x
hold unmodified for the critical temperature of the principal component, provided
we take for «dj the value it has at that critical temperature. With Crausius’ hypothesis
that dr is inversely proportionate to 7, we should get 2, =—1; sal. Also
(29) continues to hold and the modifications in the developments into series and
in the formulae derived from them would be easy to apply.
3) In this form they may be used for investigations concerning the conditions
at the side of the „-surface at temperatures greatly differing from the critical tem-
perature of the principal component, as are made by Kresom: Contributions to the
knowledge of the y-surface of van per Waats. VI. The increase of pressure at
condensation of a substance with small admixtures. Proc. Royal Acad. IV, p. 659—
668; Leiden, Comm. phys. Lab. N°. 79,
9
(33)
(35)
would continue to
(-456 5)
or, after development into series with respect to the powers of v’:
656 be
e= — (AH) log EE — (as )r ne (vi 5 tort
DE Ee re EEN MEE Ch NR
64 160
Rete
Am hi A CO naden zer x42 y't fr Eh
9 9
Fitr et ree te DD
1 9 3 |
Edd ed een arn ma eee eee
for which last expression we write:
== Hotter... Ee
Determination of the plaitpoint and classification of the
different possible CASES.
17. For calculating the coordinates pi and ZIjn of the plaitpoint
we have the following relations: *)
3 = dy”
m ete ee ae =v oren lee ee
ae 07 yp’
ss et vt Wc ORNE N = a,
OTE bene Bs
93 ,! 33 03 9! 03 U
on ~ + 3m? Or Ek + 3m- Eos 4- io = Oi, See
where m represents *) the tangent of the angle formed by the (v’, 2)-
projection of the common tangent of spinodal and connodal curve in
the plaitpoint with the 7’-axis.
If by means of (32), (86) and (387) we introduce in these equations
everywhere the values of the differential quotients at first approxi-
mation, in which, as appears, m, Up and Vass may be treated as
small quantities of the same order, we find:
ge eR) i nt me
1) D. J. Korvewec. Ueber Faltenpunkte. Wiener Sitzungsberichte, Bd. 98,
Abt. IL, (1889), p. 1171.
2) See l. c. p. 1163.
3 grt Barink)
hens IA tn (y—x)e, =0 Prva, A]
m* 27 27 aon BENN i je
ET + — 5 Bn ble AN be (45)
y P —
from which it is easy to deduce :
©
mse A y—3x)e, : (46)
= t 47
er A
1
= = [(2y—3x!)’—4(4y'— 3x!) (23) + 16y'Je,,. … (48)
The formulae (12), (15) and (16) of the first descriptive part of this
paper may be derived from these formulae by means of the reverse
transformation into the original y-surface with the aid of the formulae
(26). Applying equation (31) we may also derive formula (17). In
the course of this we get first at formula (23), which is given at the
end of the descriptive part as serving also for the calculation for
coexisting phases. The last statement might be objected to, because
for those phases not v’ but v’? is a quantity of the same order as
Oy
wand t’; but this objection loses its force when we observe that in —
v
no term occurs with v’? alone.
18. From these formulae (46), (47) and (48) follows now imme-
diately the classification of the plaitpoints according to the eight cases
and all the particularities of the corresponding graphical representation,
as described in $ 2—9. It is only necessary to say a few words
about the construction of the cubic border curve.
(2 y'—3x')* — Jy!) HTO = Oh), (89)
A closer examination of this equation shows, namely, that the
curve possesses a double point, i.e. the point at infinity of the straight
line 2 y’—dx%’=0. A simple parameter representation is therefore
possible and it is really obtained by putting
Af Boe Se oer Te, oa eta Pee
_from which follows:
s'—49(s-+-2y) +1670 vn (OD)
hence:
oes) SEH EN
IC ET
( 458 )
The points of the left-side branch are then given by the values
of s between + co and 2, those of the right-side branch by the
others.
For s=2 we get the two infinite branches belonging to the
asymptote :
ISU Bie OR Ven goo), ages) a" NR
19. Nor do we meet with any difficulties in the calculation of
the breadth-relations of the regions for very large values of y' men-
tioned in $ 10.
For the cubic curve we may put:
Sof 0 yh pial re ee ea
through which its equation passes into:
(—FP+ 8h) YVy7'1+16—4h=0 ... . (55)
from which appears that for very large values of y’ we find
— 22,0 and +2V 2 for k. We get therefore for the leftside
branch of the cubic curve approximately :
2 2
9 a VY oe ee
ra ae Vy (56)
and for that on the right-side:
2 hare
C= ei iar oo wee . e . . . . (57)
while of course the middle branch with asymptote corresponds
with £=0O. For this branch we have:
; Ae 2 58
x = —y'—— . 5
Ba pier (58)
In a similar way we find for the parabolic border curve:
BNE se
! ! : ! ld
hr eer A ° e e » e > (59)
3 9
Taking this into consideration we may equate the breadth of the
2
yellow region at infinity to 5 (3—V3)V2.Vy’, that of the green
2 2
one to ae te that of the blue one to a that of the purple
: 2
P V6.7’ and that of the red one to 9 BV 3V avy
one again to
from whieh the relations of equation (9) easily follow, while
ia. =O ae,
( 459 )
The spinodal curve.
20. The equation of the spinodal curve is found by elimination
of m from (40) and (41). We must, however, take into account,
when writing these two equations, that v’ along the spinodal curve
must be considered to be of the order Vz, so that the terms with
v’? must also be taken into consideration.
We get then:
m 3 é
eae aK ge PA eet Nw tea eget de) a 03 ORD
Usp.
and
a Mn gate ts de ! 0 61
1 (2y —3x) m 1 iG Usp, 5 Y¥—*) Cop. = oo) AST
from which follows for the equation of the spinodal curve:
’2 1 Ns ey Pal ' . 4 ; N
VEN The [(2y'— 3x)? — 8 (y'—#')] wap. + 5 Ds kers (GA)
This is, however, its equation on the w’-surface. In order to
‘know it on the original y-surface, we must transform it with the
aid of (26) into
(wap. — 3b,)? — 8,2 [(2y! — 3x')? — 8 (y' — IT wy, + 120,27 = 0. . (63)
For that of the circle:
(v—3b,)? + (vld)? = R*, (d small)
we may write with the same approximation :
(v—3b,)? — 2Rhe + 2hd —= 0,
from which we may immediately derive the*expression (10) for the
radius of curvature of the (v, 2) projection of the spinodal curve.
The two first connodal relations. Equation of the connodal curve.
21. We shall „now take -P, (z,,v',) and P,@,,’,), for which
v', >v',, as denoting two corresponding connodes.
We put then:
v=o ns ve Ans e= — Sys Le + Sy; « (64)
hence :
1 | 7 : .
vom = vk) N= (7%); e= 5 rt) Sr ; (65)
where therefore (x", v") indicates a point halfway between the two
connodes and § denotes the tangent of the angle which the projection
on the (+, w)-surface of the join of the connodes forms with the
p'-axis.
( 460 )
It is then easy to anticipate, and it is confirmed by the calcula-
tions, that all these quantities 7”, 2" and § with the exception of 1,
are of the same order with each other and with #; on the contrary
not 4 but 2’ is of this same order.
22. Taking this into consideration the first connodal relation :
Oy’, Oe’,
ee
0x,
yields at first approximation :
2
log (2! 489) - 1-3) (v" 4-4) = log (e=) - 4 (273%) (v'-n) . (67)
or also, subtracting on either side log x":
log (: zt =) En ss (2y'—38x') 4 = lg ( i =) ees)
or, as | is a small quantity of the order of 13, we get after deve-
isomeat into series and division by 7:
(Er Btn) eee ee ETD
in which we shortly point out that this formula passes into formula
(46) in the plaitpoint, and further that it leads immediately to for-
mula (24) of the descriptive part.
In the same way the second *) connodal relation:
ET rn EEE ef CA
yields at approximation:
ate Ig ae q Bins 8
en vand Pe, OERS RAE
es Vn aren ern
8
9 3 3 9 9
hg AP Ennn tn
3 q
Rt (2y'— 3x’) Si ate (ye) JE ee, eN
or, after reduction and division by %:
1) We must here have recourse to the terms of the order ¢'? or n°, as all those of
lower order cancel each other. For the sake of clearness we have kept (v" + 1)
and also (v" — 7) together, though it is evident, that we may write e.g. for (v" + 9)?
at once #3 on account of the difference in order of v” and 7.
9 ! 9 3 5 5 PR Ehh pe a ' ' " q r
aen -}- ry 1 — 9 (2y'— 3x’) Ss En 9g (y —%) Lv ==); - a (72)
from which follows in connection with (69):
n° — [(2y'—3x')? — 8 (y'—z’')Ja" +4! =0. . . . (78)
23. This formula yields at onee the radius of curvature of the
(v, w)-projection of the connodal curve. We need only observe that
according to definition :
ON ete Meghna Me Sa GMS ha dk en Be GED
so at first approximation :
etek ee = edt us Rix dias Modern Gare. eu see eels
3b
Substitution of these last relations in (73) now yields immediately the
equation of the connodal curve and in exactly the same way as for
the spinodal curve we find from it the value of the radius of cur-
vature Reon given in formula (11). A further explanation of the way
in which the knowledge of this value leads to the formulae (13) and
and (14) need not be given here, nor need we explain the derivation
of the formulae (18) and (19), (21) and (22).
But the derivation of formula (20) will detain us for a moment;
we require, namely, for it a more accurate expression for p than
that given in formula (23). If we therefore develop (31) as far as
needful for the purpose, we find *):
1
8 3 3 ! 9 | | 3 ! ! 9 ! 1 ! —
Pil zitt reet ve J, (16)
OF:
PP, ! ! | € ! € ! C ! ! '
dt — 6td' 4+ 2 (2y'— 38x) « — 12 (y— x) ve, . (77)
Py,
thence:
LRE las 4e} Dele lr —r y= 22 lose) (ast = ay! Jar 78
Pk a oe vp) ta x) (we, ay? “(Y x) ( P Cr © ol 8)
for, with regard to the last term, the difference of wp, and Tp is
AM . » € T Né € 5!
slight compared to that between 2’, and v'p.
9
1) It might appear as if jg v® ought also to be inserted in the following ex-
pression, but it is easy to see that this term leads to a small quantity of higher
order than those that will occur in the final result.
( 462 )
It is now easy to find:
1 3
Ce fa at (oa U) 7 (2y7'—3x'/) x, (v ao a) ) SEN
either by paying attention to the fact that we eee in Fig. d, § 12
(see the first descriptive part), if applied to the (v’, x)-diagram, with a
sufficient degree of approximation :
pee
1
RQ = PQ.) RPQ= PQ. w=. PQ.tgu == —.PQ.m
2
or by application of the formulae (13) and (14), observing that
v,— Vp= 3b, eae
P rp):
This yields by substitution in (78):
Par Pr . ol 3 sf 9.,!'\3
EE — 6 + (Be le, Je) (80)
Pan
or finally substituting for ¢’ its value from (47):
Pp: ÔR 3 EE) 3 2 ! VNS I as! 2 4,!\2 81
p Pld 7s «a Opt BARS Nee Pen
k
from which we immediately derive formula (20), applying (18).
The third connodal relation.
24. We have now obtained the principal formulae. For the sake
of completeness, however, we shall treat here also the third connodal
relation, the more so as this leads to a new determination of the
formulae (47) and (48), which puts the former to the test.
This third relation reads:
Ole, Oe dees oy’, OW,
Wie igi Gel En oe
Oxi Lh, ne
We first transform w'—a« — —v'— , with the aid of (32). It proves
Our Ov’
to be necessary to keep all terms up to the order # or 1°. So we
find :
dy’ ò 0 05
Boat ot ltd (he! Jor. (88)
Ow Ov’ Ov’ Ov
From this follows:
an v; Wie (1-+-#')(a"+-§y)-(1 + ¢)log 20, Se, + 20") +
9g 63 3
res 13 Si mA wv poe [(2y'—3x') + 2y't \(4+e") (+n) Ed's
5 GOH 20") "HE BY- 2a'-0,(4*H2a"E)-20,101"(84)
sl No)
aid
( 463°)
If we equate this to the corresponding expression for
Ow, òw,
U
1 at -—=— 1 =
5 ; Ou, ' ov’ 1 :
which is obtained by changing 4 into — 4, we get, dividing by 7:
N08 B.A a Ne i
SIPS Ade ape rites 1 +50 | T5 (2y —d3x) a Syt -|-
FOT BEI — x) E qt — 18 (y — x) 0a" +
27
eu oe A Pe LO 0 Ne tt (85)
At first approximation this yields:
En aL (2y'— 8x’) a".
4
This relation is, however, identical with the relation (69) which is
derived from the first connodal relation. So we cannot draw any
further conclusion from equation (85) without bringing it into con-
nection with the first connodal relation; but for this it is required
to introduce a further approximation for the latter.
Second approaimation of the first connodal relation.
25. From the first connodal relation in connection with the equation
Oy
BS 1E H(LHE) log e+-y,+2y,24-.... . . . (86)
the following relation may easily be derived, if we take into account
the terms up to the order ¢? or 7°:
Sn
al" 9
(1+ #') log ir (2y' 3x) Sy nt + Uy xe" — i (By —2x) n° 4
5 |
ms
Hij
oe LS A RC ER nun, nate Whey iS
Within the same order of approximation we have however:
Sn
IED een
Ig a" 25m 28m
0g & a" ar Z's
In the second term of the second member of this equation, however,
we may safely make use of the first approximation furnished by
equation (69). Taking this into account (87) passes after multiplication
with 2" and division by % into:
( 464 )
5)
= (27 —3!) nj" — > (27'—82')a"—3 y' at! + 9(y'— —x')v" a" —
9
rae (By Zult aL 46.6a" + Agia = Oi ae ee.
Further reduction of the third connodal relation.
Derivation of equation (25) of the first descriptive part.
26. By addition of (85) and (88) we find: *)
9 roy 9 27 9
Ev = Een 4___ Q(+! — x’) En —9(y'— Ig!
ee er boo (y'— #') Sy? —9(y'—x!)vtact +
3 9
+ 5 Cr’ —Bulyo'S + 5 (27/3) $16 Gele" = 0... (89)
When we add to this relation (72), which is deduced ae the
second connodal relation, after having multiplied it with v7”, we can
divide by 1? and we get:
9 9 63 peel | A Wad 9 ! ' > ' ' "
5 en a yp! + 50 My) + = [(2y'-3z')? + 16(8y'-2z')Ja"=0 . (90)
.
Making use of (69) we may solve the quantity 7" from this equation :
! 7 1 ' ! ! > 3) ! iy "
y' = 2t +— 7 + 3 - [(2y'-3x')*?-24(2y'-3x') (y'-x') + 16 (By'-2x')J2", (91,
0
or finally with the aid of (73):
18 7 kon
te Bit Ier — B) — 8 (7) +
1 3 3 ! ERN ! ! ? Spe € | "
te a [(2y' — 3x)! — 24 (2y' — 3x’) (y' — x’) + 16 (By — 2a) - (82)
from which equation (25) follows immediately with the aid of (65)
and (26).
In this way we have found the starting-point of the curve in the
(v, .v)-diagram described by the point halfway between the points
which represent coexisting phases. The tangent in that starting point
also is now known.
1) Remarkable is the disappearance of the terms derived from 7 x?, which makes
(lo
D>
alsbek and dere: ae and b. disappear from the result. We have tested the truth
1 1
of this in different ways.
( 465 )
A new determination of the plaitpoint, independent
of the preceding one.
27. It is now easy to obtain such a determination with the aid
of (73) and (91). For in the plaitpoint we have:
"
î "
Wee OE BSS) fy. 8! == oat
From (73) follows immediately (47); from (91):
Tyg
v'p = 2t' + 5 [(2y'— 8x')? —24 (2y’— 3x’) (y’—x') +16 (By'—2x')|wp; « (93)
from which in connection with (47) we find again (48).
Physics. — “Some remarkable phenomena, concerning the electric
. curcuit. in electrolytes’. By Mr. A. H. Sirks. (Communicated
by Prof. H. A. Lorentz).
On etching of metal-alloys by means of the electric current, as
communicated in the proceedings of the meeting of September 27,
1902, I met with a great difficulty. In some cases the hydrogen
developed at the kathode was very troublesome, namely when, instead
of escaping immediately it divided itself in small bubbles through the
liquid and stuck to the object to be etched used as anode. This
obstacle was overcome by surrounding the kathode with fine brass-gauze,
so that the gasbubbles were compelled to escape directly in this case.
The gauze was hung up apart, consequently there was no contact,
Whatever, with one of the electrodes. The etching being finished,
copper proved to have been precipitated on the wires of the gauze,
which deposit was almost conform to the shape of the electrodes.
This was still more visible at a second etching-experiment with the
same copper-alloy: a small cup was placed under the anode, which
partly hung in it. Again on the gauze a copper-deposit was perceptible,
which showed at the lower side a distinctly designed horizontal
margin, nearly as high as the brim of the cup.
It was to be expected, that copper should precipitate on the gauze,
placed between the electrodes, as the whole apparatus can be con-
sidered as two voltameters, connected in series‘). But, why is by this
electrolysis not the whole side of the gauze, facing the anode, cop-
pered, as is the case with the kathode by any ordinary electrolysis ?
To answer this question the experiments were altered somewhat.
1) The anode and the side of the gauze facing it, are the electrodes of one,
the other side of it and the kathode, those of the other voltameter.
31
Proceedings Royal Acad. Amsterdam, Vol. V.
( 466)
Instead of water acidulated with sulphuric-acid a saturated solution
of copper-sulphate was used as electrolyte; the electrodes were
formed in future by two equally large Dutch bronze coins. The back
part of these coins and the battery-wires, to which they were sol-
dered, were varnished, as far as they were immersed in the electro-
lyte, in order to be sure, that, during the electrolysis, the facing-
sides only served as pole-plates. The gauze tube was left away and
a screen of platinum (44¢.m.), hung up isolated, placed just
amidst the electrodes, who were 4 ec. m. from each other. If a copper-
deposit might appear on the platinum, this could be ascribed to
eleetrolytie actions only. Very soon after the circuit was closed
(intensity + 0,3 amp; voltage of the battery = 4 volts) there came on
the piece of platinum facing the anode a sharply bounded copper-
deposit, which, by continuation of the experiment, changed of thick-
ness exclusively and not of size. The experiment was continued for
2 days; still the results remained the same.
Now I resolved to remove the platinum screen between the electrodes,
to do the experiment over again and repeat this several times. The
deposits obtained in all these cases were not exactly of the same
size. The smallest deposit (diam. 18 mM) was obtained by hanging
the sereen between the electrodes (diam. 19 mM.), from which we
can conclude to a small gradual contraction to the middle.
If two electrodes of different shape were used, then, by removing
the platinum screen from the anode to the kathode, the copper-
deposit passed from the shape of one electrode into that of the other.
This was very clearly visible by using a nut as anode and a square
piece of sheet-copper as kathode. The hexagonal copperdeposit gra-
dually took a square shape.
Superticially one would be inclined to suppose, that the only
thing, that has happened is the locally making of sections of the
envelope of the two electrodes by means of the sereen, but consider-
ing, that, if electricity passes from one electrode to the other, the
stream-lines divide through the whole fluid — the current-density is
only larger within the above-mentioned envelope — it will be ob-
vious, that there must have been another cause, which made
some stream-lines prefer to take the way round the screen to the
shorter one through it. Considering, that the resistance of the platinum
can be neglected in regard to that of the longer way through the fluid,
the explanation of the deviation of these stream-lines can only be
found in the polarisation, caused by the screen of platinum.
To prove the supposal, that stream-lines are going out from the elec-
trodes in all directions, the following experiment may serve: The
( 467)
anode was hung in a platinum cup, which must replace the platinum
diaphragm and was therefore partly filled with the electrolyte.
Directly the circuit was closed, the inside of the cup was evenly
coppered, as high as the surface of the liquid, while at the outside
an intense gas-development took place, which was soon impossible
to be observed well, as on account of the polarisation the current-
intensity was considerably decreasing. In some cases from 0,9 amp.
to 0,02 amp. If on the reverse the kathode was hung in the
cup, the development of gas took place at the whole inside. Half
of the outside of the cup facing the anode was partly and unevenly
covered with a copper-deposit.
When making the experiment with a sheet of platinum (5 > 5 em),
dividing the glass in two equal parts, the results were just the
same. Here also the platinum was entirely covered with precipitated
copper. At a distance of the electrodes of about 10 m.m., the copper-
deposit was pretty evenly spread over the platinum. At a smaller
distance of the electrodes (4 m.m.) there came between the electrodes
on the platinum a distinct circular deposit, while the copper precipit-
ated on the remainder of the screen was very faint. A same deposit
perfectly corresponds with the sections of the stream-lines we should
expect.
The same results were obtained, when using two diaphragms
dividing the cup into three parts. At the first experiment two dia-
phragms were used, completely shutting off the fluid and connected
with a copper-wire. The side of the first diaphragm, facing the anode,
counting from the anode to the kathode, was entirely coppered; the
side of the other one, facing the kathode, was covered with gas-bubbles.
At a second experiment only the connecting wire was taken
away. The sides of both diaphragms, facing the positive electrode,
were entirely covered with a copper-deposit. On the other sides gas
was developing. .
At a third experiment two platinum screens (4 4 em.) were
used, thus not shutting off the fluid completely, but connected,
however, with a copper-wire. The same circular copper-deposit
came on the first screen, facing the anode, but, when. breaking the
connection the same side of the second screen was, on the contrary,
entirely covered with copper.
The latter phenomenon can be explained in this manner: The
copper-ions, leaving the anode, yielded their charge to the first screen,
over which it is entirely distributed and which, over the whole side,
facing the kathode, serves in its turn as anode towards the second
screen, which is coppered over the whole surface. If the second
31*
( 468 )
screen was larger than the first, then, the side of the former, facing
the anode, was coppered for a part about as large as the latter.
Then, the experiment was repeated with a screen, dividing the
basin into two equal parts, but having a small hole in the middle.
Just as a part of the stream-lines in some of the former experiments
went round the screen, so here a very great contraction of the stream-
lines towards the hole may be expected. Some of them will deviate
from their straight way preferring the way through the hole, to
the way through the screen. This is confirmed by a circular part of
the screen remaining uncovered.
The following data are the results of a series of experiments, taken
with holes of different size.
Diameter of the hole. Diameter of the uncovered part.
1 mm. 7 mm.
4 14 /
5 I dr "
Ay 25
15 whole screen uncovered.
distance between electrodes 3 em., diameter of electrodes 19 mm.
If the smaller sereen is taken, so that stream-lines can also go
round it as well, then the uncovered part is considerably smaller.
The diameter of it was 3 mm. at a 1 mm. diameter of the hole.
It is worth notice, that, while the electro-motive force remained
the same, the current-intensity increased on increasing the diameter
of the aperture. If for instance at the experiment with the smallest
hole (diam. 1 mm.) the intensity after the beginning of the polari-
sation was 0,1 amp., it amounts under the same circumstances to
0,3 amp., when using the screen with the biggest hole.
It is curious, that at the first experiment a copper-deposit was
seen on the case of brass gauze surrounding the kathode, though
properly it is nothing but a sereen with a great number of small
holes. According to what is said before, it might have been expected,
that all the stream-lines would pass from tise anode through the holes
of the case to the kathode and therefore not form any deposit on
the gauze. In connection with this, some more experiments were
taken with different sorts of brass gauze, but already by using the
next size — stitches of 2 mm? and 0,3 mm. wires — no traces
of copper were precipitated.
If the way through the fluid was made considerably longer,
then, in some cases, the current still seemed to prefer this round-
,-
a
p.
A elk
( 469 )
about way to the undoubtedly shorter one through the sereen.
This was done in the following way: Again the anode was hung
in a platinum cup, over the brim of which hung a bent glass-tube,
filled with the copper-sulphate solution, thus forming the connection
between the electrolyte at the inner- and outer side of the cup.
Even if a capillary tube was used, a deviation was observed in the
copper-deposit, namely: a part of the cup near the lower end of
the tube was not coppered, this, however, only when the tube was
hung over that place on the brim of the cup between the electrodes.
A 3 mm. tube, however, caused a deviation of the deposit, even, if
the tube was hung over the brim of the cup on the prolongation
of the centre-line of the electrodes.
Of course, there must be some relation between the coppering of
the inner surface of the cup in these cases and the circular deposit
on the screen. It must be possible, therefore, to pass gradually from
one deposit into the other. Instead of the cup a cylinder of platinum,
having a diameter of 4 cm., was used, which at the bottom was
melted in a basin with paraffine and projected from the fluid. The
anode was hung in it again. The circuit being closed, the inside of
the cylinder was of course coppered again as far as it was immersed
in the electrolyte (50 mm.). Then a vertical cleft of 1 mm. wide
and 1 mm. high was made in the cylinder on the extension-line of
the centres of electrodes. A part of the inner wall round the cleft
remained again uncovered. When gradually giving the cleft a height
of 20 mm., the uncovered part took the form of an ellipse, till ata
height of 25 mm. a strip of 8 mm. wideness was not covered with
copper, along the whole height, i.e. 50 mm., of the electrolyte.
When still enlarging the cleft, the deposit gradually receded more
from the margins and after unfolding the cylinder into a plane it
finally took the already known circular form again.
To make the explanation, given of the deviation of the stream-lines
on account of the polarisation of the platinum, more acceptible, the
experiments were made with different electromotive forces by inserting
resistance. By means of a resistance box, connected parallel with
the voltameter, the terminal voltage of the latter could be increased.
The current-intensity could be read on a milli-amperemeter, joined
in circuit with the voltameter. As long as the potential difference
was less than the electro-motive force of the polarisation, nothing
was precipitated. After more resistance had been inserted in the
resistance box, a current began to pass through the voltameter, but
without forming a deposit on the sheet of platinum, although the
experiment was carried on some hours. For that reason this current
( 470 )
could not have chosen its way through the sereen and must have
gone therefore round it. If some more resistance was inserted, then
a deposit came gradually on the screen, smaller and more uneven
than in the ordinary ease, but also taking the normal size and
thickness as formerly, when going on inserting more resistance.
Different salts were used as electrolyte, in none however, a deposit
was so easily formed as in cupricsulphate. The phenomenon, when
using this salt, was so clear, that once a deviation in the shape of
the deposit was observed, because the wire which was connected to
the anode, was not sufficiently insulated. In saturated solutions of
zine-, aluminium-, nickel-, cobalt-, ferrous- and ferricsulphate deposits
were formed, one clearer than the other even if in all these cases
the constant current-intensity was secured by inserting resistance.
Chlorides were also used as electrolytes. In chlorides of zine and
cadmium exactly the same circular deposit was formed, but in those
metals, which can form more than one chloride (e.g. iron), a secondary
phenomenon always appeared. When a solution of cupric-chloride
was electrolysed, copper precipitated on the kathode; when, however,
a platinum screen was put between the electrodes, again a circular
deposit of a white substance was formed on the screen, quickly getting
green in the air and being hygroscopic then; probably it might have been
cuprous chloride, afterwards becoming cupric chloride again. When using
a solution of Hg Cl, as electrolyte a white deposit of Hg Cl came on
the platinum. A solution of Au Cl, gave conformable results; a brown
red deposit was formed. Using H, Pt Cl, and a sereen of gold-leaf,
a yellow brown one was formed on the latter. When a solution of
ferric chloride was used no deposit was ever formed. The explanation
may be found perhaps in the solubility of ferrous chloride which
is precipitated on the platinum as copper before.
Though in many of the former cases an explanation could be found
in the polarisation, yet, however, there is one thing, that cannot be
explained, i. e. the curious sharp margins of the deposit. It seems
as if the stream-lines keep their original direction within a certain
tubular surface also in the presence of the platinum screen, while this
screen has a strong influence on the lines outside of it, which change
their direction and go round the screen. Perhaps the explanation
may be found by calculating the course of the circuit, but I am
not able to do it.
In the making of all these experiments I have become indebted
ATL}
to professor ARONSTEIN and professor SCHROEDER VAN DER Kork for
their assistance of various kinds and to these I tender my best thanks.
Also to Professor H. A. Lorentz, professor at the Leyden University,
for his help and information.
Mineralogical Laboratory.
Polyt. School. Delft, Jan. 1903.
(February 25, 1903).
KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,
PROCEEDINGS OF THE MEETING
of Saturday February 28, 1903.
(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige:
Afdeeling van Zaterdag 28 Februari 1903, DL XI).
CONTENTS.
J.P. Kuexen: “Critical. phenomena of partially miscible liquids—ethane and methylalevhol’”
(Communicated by Prof. H. KAMERLINGH Onnes), p. 473.
A. P. N. Fraxcuimonr: “On the so-called compounds of salts of sulphonearboxylic acids with
sulphuric esters”, p. 482.
JAN pe Vries: “On the spheres of Moree belonging to ordinary and tangential peneils or
quadratic surfaces”, p. 484.
J.D. var per Waars Jr.: “The variability with the density of the quantity bof the equation
of state”. (Communicated by Prof. J. D. van per Waars), p. 487.
J. W. Morr presents the dissertation of Dr. J. C. Scnoure: “Die Stelär-Theorie”, p. 497.
H. Kamer tiscu Onnes: “Methods and apparatus used in the cryogenic laboratory. ILI. Bath
of very uniform and constant low temperatures in the cryostat”, p. 502, (with 6 plates).
The following papers were read:
Physics. — “(Hitical phenomena of partially miscible liquids — ethane
and methylalcohol.” By JP. KvexeN. (Communicated by
Prof. H. KAMERLINGH ONNES).
(Communicated in the Meeting of September 27, 1902).
Some years ago Mr. W. G. Rosson and 1 began a systematic
investigation of the phenomena of condensation for mixtures of liquids
Which do not mix in all proportions '). Shortly afterwards Prof. vax
peR WaAALs communicated to this Society an important paper in which
he discussed our results?) and again in the second volume of his
4
treatise on the Continuity *) he devotes some pages to the conside-
1) Zeitschrift für Physik. Chemie 28, p. 342-565, Phil. Mag. (5) 48, p. 180—203e
2) Kon. Ak. van Wet. Amsterdam 25th March 1899.
3) Die Gontinuität etc. If 1900. p. 184—192.
ho
Proceedings Royal Acad, Amsterdam. Vol. V
(474)
ration of the same phenomena. After the publication of Prof. van
DER WAALS’s paper I approached him privately with some objections
to his views to which he replied in the most courteous manner.
Though not completely satisfied it seemed unnecessary at the time
to publish my views until T should be in a position to add to our
knowledge of the phenomena by further experunents.
| have recently resumed the investigation and the results obtained,
though naturally far from complete, seem of sufficient importance to
deserve an immediate publication and to be discussed in connection
with previous experiments.
For various reasons we had fixed our choice on mixtures of lydro-
carbons — first of all ethane — and alcohols. Briefly our results
were as follows:
(Te,
a
é.
For mixtures of ethane with ethyl-, propyl-, isopropyl- and butyl
alcohol there are two temperatures 4A and 5 (Fig. -1) between which
three phases — two liquids and vapour — are possible and the
critical (i.e. plaitpoint) curve accordingly consists of two branches,
CA and C,B, C, and C, representing the critical points of ethane
and alcohol respectively and A/ the three-phase curve. For ethyl-
alcohol A and B are comparatively far apart: for the higher terms
of the series these points gradually approach each other and with
amyvlaleohol no separation into two liquids could be observed; in
this case the critical curve was a continuous curve joining the two
eritieal points CL and (, in the usual manner.
For mixtures of methylalcohol and ethane we found a branch C\A
(475 )
and a three-phase curve ending at 1, as with the higher alcohols,
but not a limit 2 below which the liquids mix in all proportions.
The character of the other branch of the critical curve which
begins at C), the critical point of methvlaleohol, therefore remained
uncertain.
Prof. van per Waats’s remarks concerned firstly the explanation
of the behaviour of the first group of mixtures and secondly of the
different behaviour of methylalcohol and the prediction of the phe-
nomena outside the limits of our researches. ‘The experiments com-
municated in this paper have reference to the latter problem.
First of all Prof. van per Waats shows how the two branches
CA and C,B may be made into one continuous curve by producing
them in the region of the metastable and unstable conditions, a region
which I shall call the “theoretical” region. In our paper we had
pointed out that the phenomena were completely explained by the
formation of a new subsidiary plait with plaitpoint emerging out of
the main plait on the y-surface and the subsequent withdrawal and
disappearance of the main plaitpoint ). Having regard to VAN DER
Waars’s original investigation and to Korrmwna’s treatise *) on the
properties of the y-surface, the simplest interpretation appears to be
to assume that at some temperature higher than 7, a closed plait
begins to develop on the spinodal curve, increasing in extent as the
temperature falls, until one of its plaitpoints — that of the first kind *) —
at A pierces the connodal curve of the main plait, thus giving rise
to the formation of the subsidiary plait and the three-phase triangle.
On further fall of temperature the inner plaitpoint exchanges partners,
so as to form a closed plait with that branch of the main plait: on
which the original plaitpoint lies: at B the connodal curve of the
main plait begins to enclose this closed plait. We may moreover
assume the latter to contract on further cooling and ultimately shrink
to nothing‘). Transferring the above changes to the p-f-diagram
we obtain the figure deduced from ours by Prof. van pir Waars.
1) |. c. p. 358—359.
2) Arch. Néerl. 24 p. 295—368 in particular p. 316 etc.
5) Comp. KoRTEWEG p. 67.
‘) Whether this actually takes place seems at least doubtful. The formation
of the plait on cooling is hardly open to doubt, seeing that at high temperatures
the Q-surface cannot show any abnormalities in the region under consideration ;
but this condition does not hold at low temperatures and the contraction of a
closed plait. on cooling is in contradiction with the rule enunciated by Prof. van
pen Waars regarding the influence of temperature on the extension of plaits.
32%
( 476 )
The possibility of producing the theoretical curves in the p-/-diagram
had escaped our notice *).
In the first place Prof. var ber Waars observes that the completed
figure is in contradiction with the law previously deduced by him?)
that a mixture of non associating substances may have a maximum
or minimum critical temperature, but not both. To this point one
of my objections refers. The law depends entirely on the simple
characteristic equation, but apart from that it only refers to the
critical point of the homogeneous mixtures and it must be looked
upon as a possibility that the curve of the critical points — the
plaitpoints ——- should have both a maximum and a minimum.
Prof. var per Waars replies to this*) that near a maximum or
minimum the two curves in question are so close to each other that
no such difference between them can be admitted. This argument
does not satisfy me. The two curves touch each other at points where
a maximum or minimum rupourpressure exists and the two phases
have the same composition, but points of that kind do not exist in
the case under consideration. [t is true that a maximum or minimum
occurs on the plait when the connodal curve intersects the spinodal
curve, but the character of these points is entirely different from
that of the points referred to. The three-phase pressure for mixtures
of ethane and the alcohol is between the vapourpressures of the
components and there is thus no occasion for assuming the existence
of another maximum or minimum. That being the case, there is
no reason for a close resemblance between the two curves nor any
1) Note added to translation.
The above was wrilten by me in the conviction which I then held that Prof,
VAN DER WAALS’s views of the formation of the new plait — although arrived
at in a different way — still agreed essentially with my own: indeed I do not
even now see, how else the phenomena could be interpreted. From the paper
contributed by him in the October-meeting of this society (critical phenomena of
partially miscible liquids. Kon. Ak. van Wet. Amst. 25th Oct. 1902) it appears
that such was not the case and that I ought to have been more careful in accept-
ing the theoretical curve drawn by him as corresponding to the changes on the
p-surface as understood by myself. Doubt never arose in my mind on this point
at all and I never considered the question. Still I ought to have noticed that the
theoretical curve has no vertical tangent at its extreme points, but ends in cusps,
corresponding to the circumstance that the curvature of the connodal curve is the
same in both plaitpoints of the closed plait. This is the only respect in which I
think my paper requires emendation although some of my arguments would have
been presented in a different manner had I realised how completely lis views
differed from mine,
2) Arch. Néerl. 24 p. 23.
5) Continuität IT p. 188 1. 17.
ate eld
( 477 )
ground why the “homogeneous” eritical eurve should have a loop
as well as the plaitpointcurve.
I am strengthened in this opinion by the fact, that even in the
“symmetrical” case Prof. Korruwee has come across similar peculiarities
in the plait and it follows, that theoretically even those mixtures
Which obey VAN DER Waars’s equation may have a critical curve
with a loop in it.
| do mot mean to maintain that the homogeneous eurve in our
case does not possess a loop or to deny the probability of Prof.
VAN DER Waatrs’s hypothesis according to which the association of
the aleohols plays a part in producing the abnormality. What 1
want to point out is that it has not been proved that with normal
mixtures the abnormality cannot oceur, although it is very probable
that this abnormality and in general the formation of two liquid layers
— While theoretically possible for normal mixtures with special values
of the constants — in reality occurs with associating substances only *).
The critical curve in the p,é-diagram having been completed in the
way deseribed one feels inclined to say with Prof. vax per Waars
that the case is one of a modified eross-plait and not of a true liquid-
plait. According to VAN DER Ler’s experiments *) the liquid-plait for
mixtures of phenol and water has its plaitpoints turned in the direction
of the positive volume-axis and above a certain temperature is entirely
independent of the cross-plait. Prof. van per Waars seems inclined
to look upon those properties as characteristic of the liquid-plait and
to withhold this name from that part of the plait which in our case
is turned towards the w-axis. It will appear presently that this view
cannot very well be sustained so that at any rate this ground for drawing
the distinction in question disappears. Still the peculiarity remains *) that
the critical eurve is a continuous curve, at least when no account is
taken of the objection urged above against joining the curves beyond
B. Even then however it will be observed that on the y-surface two
independent plaits exist completely or partly inside each other and
thus when the y-surface itself is considered the contrast between
our case and one in which a true liquid plait would exist disappears.
Moreover the abnormality is ascribed to the same cause — association —
as the formation of the liquid plait; if both are due to the same
cause, one feels even less inclined to maintain a distinction in the
nomenclature.
1) Continuiliit IL p. 176. 1 doubt the possibility of deducing a relation between
djs on the one side and @, and dy, on the other.
2) Zeitschr. Physik. Chemie, 33, p. 622, 630.
5) Continuität IL p. 188.
( 478 )
The following may be added in further explanation: there is a
well defined contrast between the two plaits as regards the causes
of their existence. The cross-plait depends for its existence on the
shape of the y-curves for the separate homogeneous mixtures, the
liquid-plait on the other hand is due to the manner in which these
curves change with the composition. In the formation of the latter
plait association seems to be the principal factor. But notwithstanding
this distinct contrast there must be a number of cases in which it
will be impossible to say which kind of plait one is dealing with
and to which sort of plait a given plaitpoint belongs. We shall
presently come across a striking instance of this kind where a
cross-plait with its plaitpoint gradually changes into a plait: with its
plaitpoint turned towards the w-axis from which it is impossible to
withhold the name liquid-plate.
Let us now consider the case of methylalcohol and ethane.
Before communicating the new results T will discuss Prof. vax DER
Waars’s views of these mixtures. He assumes that the critical curve
is again a continuous one but with a loop turned upwards this time
instead of downwards as with the higher terms.) There are some
serious objections to this theory.
The critical curve, starting at the critical point of ethane (5,
disappears from the practical part of the surface at a1, as in the
former case, and the part bevond can therefore only represent a
theoretical plaitpoint whieh remains hidden, because at higher tem-
peratures no three phases coexist. Beyond 1 the curve should there-
fore be dotted throughout, and it cannot be interpreted as in part
real. In this case as in the other the shape of the curve was
deduced by keeping in view the homogeneous critical point and a
striking instance is afforded of how this curve does not give us
any clue as to the shape of the real critical curve.
In the second place I think the bending upwards of the critical
curve assumed in this ease is open to doubt. At somewhat high
temperatures there is probably no abnormality on the surface and
no plait except the cross-plait: as the temperature falls a closed
curve develops one of whose plaitpoints pierces the main plait at
A and moves from there towards €,. As in the other mixtures the
three-phase pressure is lower than the vapour pressure of ethane ;
it follows that the subsidiary plaitpoint is turned towards the .r-axis
and represents a maximum pressure on the closed plait. This being
so the simplest) supposition to make is that the other plaitpoint of
1) Comp. his diagram Kon. Ak, v. Wetensch. Amst. March 25th. 1899 p. 5,
( 479 )
this closed plait is one of minimum pressure: starting from this
point the pressure on this plait passes through a maximum and a
minimum successively and reaches its highest value in the real plait-
point. In other words the theoretical part of the bent critical curve
in the p,f-diagram should lie below the practical part, as with the
other alcohols. This supposition seems so much simpler than the
opposite one that I feel prompted to state the following rule: shen
the three-phase pressure is between the vapour pressures of the com-
ponents the theoretical eritical curve bends downwards, when it is
higher than the vapour pressures of the components (as with ether
and water’) ) the curve bends upwards.
In his book on the “Continuity” *) the author discusses the pro-
bable behaviour of the mixtures at higher temperatures. Apart from
a possible plaitpoint on the side of the small volumes on the liquid-
plait, there is no practical plaitpoint left above A. Prof. vax DER
Waars assumes that this condition will continue up to the critical
point of methylaleohol, that the plait will close itself here, gradually
contract and ultimately disappear either at the limiting liquid-volume
or by its plaitpoint meeting with a possible liquid plaitpoint.
This expectation has not been realised by my experiments and
must in itself be looked upon as improbable. The formation of the
liquid-plait is aseribed to the association of methylaleohol. Above a
certain temperature this abnormality has disappeared and in any case
at the critical point it is for most substances very small. Considering
the great difference between the critical temperatures of the two
constituents of the mixture an admixture of ethane to methylalcohoi
cannot but lower the critical point, even if the mutual attraction
of the components were comparatively great. As a matter of fact
methylaleohol seems to have some association left at the critical
point *). Bat this association has the effect of making the mutual
attraction appear even smaller and thus increases the probability of
a lowering of the critical temperature by the addition of ethane. It
follows that the cross-plait has to appear on the y-surface in the
usual manner with fall of temperature, with its plaitpoint turned
towards the ethane side.
In view of the fact that at low temperatures there is a liquid-
1) Kuenen and Rosson |. c. p. 351.
2) Continuität Il, p. 189 verv.
3) Ramsay & Smierps, Zeitschr. Physik. Chemie 15, p. 115. Nobody seems to have
observed as far as | know that the comparatively high value of the eritieal temp-
erature of methylalcohol may be explained by association, as also the deviation
from Koprp’s law for the boiling points of series of organic substances,
( 480: }
plait there are still two possibilities with regard to the development
of this cross-plait: (1) the plaitpoint continues by itself and gradually
begins to form the closing plutpoint of the liquid-plait which may
disappear at the limiting liquid volume or (2) it disappears by meeting
With a second plaitpoint belonging to an independent higuideplait so
that the two plaits then form one large one, with or without a
closing plaitpoint on the liquid side.
The experiments confirm the above view of the effect of an
admixture of ethane on the critical point of methylaleohol and as
far as they go seem to show the first alternative to be the correct
one. It appears that the general behaviour of mixtures of methyl-
alcohol and ethane thus disclosed agrees with that of ether and
water as predicted — without however any grounds being given —
by Korrrwue ®) and laid down in some r-r-diagrams. On the grounds
set forth above L support this expectation as regards ether and water.
Addition of ether to water will lower the critical Lem perature.
„lm,
OR
~e&e
JIJ
300
The results for methylaleohol and ethane are laid down in figure 2.
| can give only a short explanation here. Starting from C, — the
critical point of methylaleohol — the critical curve runs in a per-
feetly normal way at first, owing to the influence of the association
being as yet insufficient. It ascends, passes through a maximum
at 120°, and then falls, evidently tending towards the critical point
2) Arch. Néerl. 24 p. 338— 340.
ae
( 481 )
of ethane; the association however becomes gradually stronger: the
dip in the surface caused by this’) gradually modifies the shape of
the cross-plait: the plaitpoint passes through a minimum pressure
between 25° and 380°, and the eritical curve then begins to rise
rapidly. The end of the eross-plait thus changes without a disconti-
nuity into a liquid-plait; in the mean time the main plait goes on
developing on the approach of the critical point of ethane: as explained
a small subsidiary plait is formed which appears at f on the pract-
ical part of the surface. Probably an exchange of plaitpoints occurs
on the theoretical part, of the same nature as with the higher alco-
hols, the result being that at low temperatures the eross-plait is cut
through by one self-contained liquid-plait. But as far as the phen-
omena are concerned this is entirely immaterial.
As far as the experiments could be carried (i.e. up to 275
atmospheres) the critical curve continued to rise towards the left, so
that there is no indication of the existence of a different plaitpoint.
The rapidity with which the mixing-pressure inereases is truly
remarkable.
If we compare the figures for methylaleohol and for the higher
terms, a certain resemblance will be noticed, especially if we do not
assume the contraction of the closed plait to nothing in the latter
case. The association tends to produce the same modification in
the usual diagram in both cases, but the acting causes appear to be
much more effective with methylalcohol — the stronger association
of the alcohol, possibly a smaller mutual attraction or the influence
suggested by Prof. vax per Waars of the small molecular volume of
the aleohol may contribute to this result. For this substance the
plaitpoint remains outside the eross-plait at low temperatures, with
the others it succeeds in disappearing inside, Whether inside this
plait any changes take place similar to those occurring with methyl-
alcohol on the practical part of the surface we cannot tell. But in
any case T have assured myself that with ethylalcohol a new plait-
point curve does not appear down to — 78 : ethylaleohol and ethane
remain miscible in all proportions. ;
Methylaleohol and ethane mir by pressure. Im this respect they
contrast with mixtures phenol and water for which the liquid plait
above a certain temperature far below the critical region separates
completely from the cross-plait and thus has a plaitpoint on the side
of the positive r-axis. In view of the probable disappearance of the
association at high temperatures it is possible that in the latter case
1) Continuitét ete. I. p. 191.
( 482 j
further experiments will disclose a second plaitpoint on the liquid
side of the plait, as predicted many years ago by vAN DER WAALS
from the value of the volume-constants. L expect to be able to throw
more light on this subject by the continuation of my investigation with
the higher hydrocarbons. Ether and water behave in all probability
in A manner similar to methylalcohol and ethane.
Chemistry. — “Ou the so-called compounds of salts of sulphon-
carboxylic acids with sulphuric esters”? By Prof. A. P. N.
FRANCHIMONT.
(Communicated in the meeting of January 34, 1905).
The first of this kind of compounds was obtained accidentally by
Lacee in 1879 in the laboratory of Grerner in Jena. He wanted to
reduce sodium sulphonacetate with soditun amalgam and water, but
after acidifying with sulphuric acid, evaporating, and extracting with
absolute alcohol, he obtained an acid liquid which gave with barium
carbonate a salt of the empirical composition C, H,, Bad, O,,. This
salt has, therefore, the composition of one molecule of barium
sulphonacetate plus one molecule of ethyl sulphate plus one molecule
of water and may, according to Gmrurmer, be considered as a deriv-
ative of a disulphurie acid in which two hydrogen atoms have been
replaced by ethyl groups and one OH group by the group CH,—COOH.
He obtained the same compound by digesting a mixture of sodium
sulphonacetate, sodium-hydrogen sulphate and alcohol. The acid was
called “ Diaethylessigdischive felsinve”. Acetic acid itself did not yield
wv similar compound.
In 1885, in the same laboratory, STENGEL successfully attempted
to obtain a similar compound with metasulphobenzoie acid; the
analysis gave the composition C,,H,,0,5, Ba + 3'/,H,O. The acid
was called“ Diaethylbenzordischire felsiure”. Analogous compounds
were also obtained with methyl and propyl alcohol. _ Benzoie acid,
however, did not give a similar compound and it is, therefore, attri-
buted to the sulphonic acid) group.
ENGELCKE Obtained similar compounds with isethionie acid but not
with benzenesulphonie acid and _NrermaeK did not obtain it with
methylsulphonie acid.
Greener looked upon these compounds as salts of a derivative of
() ()
/
ck © FOCAL
/ fit 2 u
disulphurie acid S,O,H, such as C, H, — ae > a
0
CO,H OH
( 485 }
In Beusren’s “Handbuch”, however, these compounds are deseribed
as double compounds of salts of sulphoncarboxvlie acid with neutral
sulphuric esters.
Kor a long time, however, [| have felt serious objections to this
theory. T had already repeated the experiments with sulphonacetie
acid and metasulphobenzoie acid but did not obtain pure compounds.
To was also unsuccessful in attempting a synthesis by means of the
salts of sulphoncarboxylie acids and dimethyl- and diaethylsulphate.
The phenomena observed during this research induced me to request
Dr. Artema to try to obtain compounds of the same empirical
composition in a different manner, namely by bringing together
in molecular proportions the barium salts of the acid esters of meta-
sulphobenzoie acid with the barium salts of the alkylsulphuric acids.
If in this proportion they yield a compound this ought then to have
the same empirical composition as the last named compound.
Dr. ATrEMA now observed that on evaporating a solution containing
in molecular proportions the barium salt of the ethyl ester of meta-
sulphobenzoic acid and barium ethylsulphate, the greater portion of
the ethylbarium salt of metasulphobenzoie acid was deposited first
in beautiful crystals; after this a double compound of the two barium
salts made its appearance im the form of large rosettes of tender
needle-shaped crystals whilst) from the motherliquor barium ethvl-
sulphate was obtained. If an excess of barium ethylsulphate is taken
for instance, 5 grams of the same to | gram of the salt of barium
ester the double compound separates immediately and from the
motherliquor barium ethylsulphate is obtained. The double compound
cannot be recrystallised) from water; its aqueous solution presents
the same phenomena as one containing in molecular proportion
the two salts; on evaporation, the salt of barium ester crystallises
first, then the double compound and finally the barium ethylsulphate.
As the double compound cannot be recrystallised from alcohol it
was freed from motherliquor by strong pressure and analysed. The
results of the analyses of three different preparations were concordant
and agreed with the formula:
CO, C, H
u
Aa , Ba + (C, H, SO), Ba + 6 H,O.
Dr. Artema has afterwards repeated STENGEL’S method of preparing
the compounds, but here he also obtained first the ethyl barium salt
of metasulphobenzoie acid and afterwards, although less readily,
( 484 )
the double compound. An analogous result was obtained with the
methyl compound,
We may, therefore, come to the conclusion that there exist no
compounds of salts of sulphoncarboxylic acids with neutral sulphurie
esters; there exist, however, double compounds of salts of the acid
esters of sulphoncarboxylie acids with salts of the acid sulphuric esters.
This result gives rise to a number of questions some of which
Dr. Arrrema intends answering by practical experiments. Both salts
ave alkyl-metallic salts of dibasie acids whose acidic functions (at
all events in the case of metasulphobenzoic acid) have a very
different power, whilst sulphuric acid as oxysulphonie acid is some-
what comparable to isethionie acid which also exhibits the property.
Mathematics. — “On the spheres of Moxan belonging to ordinary
and tangential pencils of quadratic surfaces.” By Prof. JAN
pr VRIES.
1. In Part I of the “Proceedings of the Section of Sciences”
pages 305—310, 1 have developed, making use of FinpiEr’s cyelo-
graphic representation, some properties with respect to the system
of the orthoptical circles of the conics of a linear system. By
extending Firpier’s considerations to a four-dimensional space the
corresponding case of the three-dimensional space might be treated.
In the following essay the indicated extension on quadratic surfaces is
arrived at analytically.
Given P the point of intersection of three mutually perpendicular
tangent planes of the quadratic surface S* represented by the equation
a,, +a, ta, 2+2a,, ey Aa, v2+2 a, yet 2a,, 7+2 a,, yd
4 2a,,2+a,, =0.
These three tangent planes form with every fourth tangent plane
a tetrahedron circumscribed about SS? that may be regarded as polar
tetrahedron with respect to the point-sphere (isotropic cone) /* repre-
sented by
(ee) zie Os Cn la (zz) —
So the invariant @ belonging to S? and 7? is equal to zero’).
Therefore we have:
1) See a.o. Sanmon-Fiepier, Anal. Geom, des Raumes, 3d edition, vol. I, p. 253,
where S? is represented by an ellipsoid,
Gi, A, Ais ove Wa | dir UN, 0 di4
Eend 0 ae yn dan () as,
en EE
Uiz M5, gs Ei O13, Ug I Us,
Gi, yy gy (w? 4 Dn di Gig Cay TT Er Oy, |
| U () (hs hy, | 1. (ths by, |
Us I sy ey 0 daa yy gy
An + = 0
this () pg «Gas () Cag A gy lbs
a, fi Ten in as Ch, 4 uly by, Cs, a 14
If we-vepresent the minor of ain A= = + a,,a,,a,,4,, by
Aj, it ensues from this relation that-the locus of the point 2 is
indicated by the following equation (where the indices of the coor-
dinates are left out)
rt ron nr es Wee ae (Ay eae yA; 2) zin (hee eet
So the locus of the points of intersection of triplets of mutually
perpendicular tangent planes of iS? is a sphere (Moner).
The tangential cone to S’ with vertex / possessing three mutually
perpendicular tangent planes, the tangent planes form according to
a well-known property an infinite number of triplets of mutually
perpendicular planes.
For A,,=0 we find S* to be a paraboloid and the sphere ot
Moncr degenerates into a plane.
The obtained equation can be replaced by
ae) ey ae 1 S (A? 1 A)
U —- ae ee i —— — _ ar Ka nand — ZZE | 4 d EK ml 4 .
Ai, 7 8 A A A? 3 2 ke
/ 44/ 14)
Now however 4,,4,, — A’,, is equal to (a,,4,, — «?,,) 4. *)
The radius of the sphere is indicated by the square root out of
= 1e, = (4,505, — 443)
Consequently the sphere of Moren will be reduced to a point-
sphere when S? is a cone (40) or into an equilateral hyperboloid
if namely the equation
1) This ensues inter alia from
Cit Ome Oya Oy a pas AN As A, A Oye ss, 0
Bie Aer Aas ds | 0 | 0 0 CH Pender dere 0
OR AT UR cc 0 0) 1 0 rl bs Ca. 0
(i) ag EE TI An, sage as Ast EET rds PN A
(See a.o. Batrzer, Determinanten, oth edition, p. 63).
( 486 )
(a,,¢,, — A73) + (¢,,4,,; — @7,,) + (a,,0
is satisfied.
In the latter case the asymptotic cone possesses as is known oe!
triplets of mutually perpendicular tangent planes,
2. When in the equation
Bie (dy He = Er Pein | t Age >) + (Aril Aside 0
we substitute aj, + 2 bij for aj, the new equation represents the
system of the spheres of Moren belonging to the quadratic surfaces
of a pencil.
The equation is a cubic one in 2; so the indicated spheres form
a system with index 3, that is, through each point three spheres pass.
If for brevity’s sake we represent the formula
we -}- a — Py, Lv t 1. U -f- ae
by Cy, the eubie equation is
Cea FAG we Al Oelen S20,
The power of a point with respect to the sphere (4) is then equal to
LCA HLC A HLC AH CE,
ER rens
This expression becomes independent of À for the centre of the
sphere cutting the four spheres (% orthogonally; all the spheres
of the indicated system are intersected at right angles by a fived sphere.
On this orthogonal sphere the point-spheres of the system are of
course situated; so it contains in the first place the vertices of the four
cones, in the second place the centres of the two equilateral hyperbo-
fords”) belonging to the pencil.
From this ensues that the locus of the centres of the spheres is
a skew cubic. This is moreover confirmed by the observation that in
Ek | En A, SA
24 44
the aaumerators and the denominators are cubic forms in 2.
The square of the radius being represented by the quotient of two
forms of order six in 2, the system contains six spheres with given
radius,
3. The quadratic surface indicated by the equation in tangential
coordinates S, 1, §
1) Their parameters are determined by
2 ele A) (a+ ihe A) ae (Gee aes A)*| — ie
( 487 )
pita +22 a, En 220,8 Bij == 0
€ 5 8
has for equation in point coordinates
SS ‚3 RE , ‘ 5 ‘ =
2A, @ +22 Aa ya 2 AL, e+ His == 05
3 3 3
If now ee is the minor of the determinant -+- A
LI As Ais Aye
corresponding to dj, the sphere of Morr of the indicated surface
is represented by
Ce py Pe) Sl ,¢4-a,,y--c,,2) + (Ha He.) = 0.
But we have!) eip=ain£®; so this equation can be replaced bv
REN Bet ap eee rde daalt dare 4 (0, x], as.) == 0,
or by
2 2 3
“ “ a ]
14 24 + 34 mie EN 2
(— ) EE G ) Es (: -—— ) == (Gis ee U):
Wa a Us Ae as
So for a tangential pencil of quadratic surfaces we find
(Apt PI Gey 27) oe = (@,,+6,,4) e+ Bit bin 4) — 0,
3
that is, the corresponding spheres of Monon form a pencil.
To this belong the point-spheres indicated by
a KCP ker en A) (ast daa ANS 0
originating from two equilateral hyperboloids, and the plane determined
by a,,+4,,4=0 belonging to the paraboloid of the tangential
pencil.
Physics. — “The variability with the density of the quantity boy
the equation of state.” By Dr. J. D. van per Waars Jr. Com-
municated by Prof. J. D. van pur Waars.
§ 1. If we suppose the molecules of a gas?) to be perfectly
smooth, elastic spheres, the influence of the fact that their diameter
is not infinitely small, on the form of the equation of state may be
allowed for in first approximation by diminishing the volume |, in
which the gas is contained, with four times the volume of the mole-
eules. If we understand by distance sphere a sphere described) con-
centric with a molecule and with a radius 2 6 (where 6 denotes the
1) See inter alia Barrzer, Lc. p. 65.
2) | say only “gas” not “gas or liquid”, for we must not apply the formula
for a liquid without introducing still other approximated terms than those that will
be discussed here,
( 488 )
radius of the molecule), then we may also say, that we must diminish
with half the combined volumes of the distance spheres, which
quantity is usually denoted by 4, or by 6, if we wish to take into
account the variability of the correction in consequence of variation
in density. Various methods have been followed in order to investigate
this influence; all these methods vielded a conformable result, so that
no reasonable doubt can exist as to the correctness of this statement.
We should be inclined to deduce from this, that the influence may
he correctly allowed for in second approximation by diminishing
I” with half the volume really occupied by the distance spheres, in
Which a segment which two distance spheres have in common, is
counted only once, or what comes to the same, by writing hb, — 2S
instead of b,, 2S representing the sum of all the segments which
are covered by two distance spheres at the same time. The correc-
tion has been introduced in this way by Prof. J.D. vax per WAALS 5);
and Dr. J. J. van Laar?) has made a calculation of a second correc-
tion term, which is based on a similar supposition. 1 will however
confine myself to the discussion of the first correction term, for which
17 15
we find in this way = = The question whether the first correction
term is correctly found in this way has not been answered un-
animously in the affirmative. _ BorrTZMANN *) follows quite a different
» 2
le 4] r
gep.
communication in these Proceedings expressed the wish that his
method for calculating it and finds Phough BoLrzMann in his
publication of this result differing from my father’s would give rise
to a discussion by which this doubtful point might be elucidated,
no discussion has followed by which the question has been settled
conclusively. Now I think I can show that there is no reason for
pee 17h,
introducing the correction in the way which yields the value 30
OL
and at the same time | will give a reasoning, by which the term
3}?
is derived in a shorter way than that followed by BorrzMars,
8 V
The simplest way to show clearly what supposition we must
; ro
make in order to get the correction term 55 738 to start from the
og
1) Versl. Kon. Akad. v. Wetensch. V. p. 150. Oct. 1896.
2) These Proceedings Vol. I, p. 273. Jan. 1899.
3) These Proceedings Vol. 1, p. 398. March 1899; and “Vorlesungen über
Gastheorie” If, p. Lol.
( 489 }
virial equation as my father has done for the external pressure and
for the pressure of the molecular attraction in Chapter IL of his
“De Continuiteit van den Gas- en Vloeistoftoestand” and for the
forces eventuating in collisions of two molecules in these Proceedings
ol Tops too. Oct; 1695.
First, however, T will point out, that the virial equation need not
necessarily be applied for a definite quantity of matter, which is
contained in a definite volume and enclosed within a solid wall, as
is the usual method of applying it. We may as well apply that
equation for a part of a homogeneous phase, separated by an
maginary separating surface from the surrounding substance which
is in the same phase. We shall not always find the same molecules
within such a surface, but we may assume, that at two different
instants f and f, we shall find the same number or at least with
1
very great approximation the same number of molecules within it,
du:
and that the expression = Mit — Will also have the same value af
dt
the instants ¢, and ¢,. We may therefore put:
dede
mt = 0
dt dt
and also the corresponding equations for the y- and for the z-
coordinate.
From this we may deduce ;
dm din iy din 2 7
ams == |t -y—t2 ec ie eee
dt er rel dt
In the ease that we may neelect the volume of the molecules
with regard to the volume in which they are contained, and that
we may assume that the molecular forces act in such a wav that
they yield on average zero for the force exercised on a molecule
Within a homogeneous phase, the righthand member of this equation
has only a value at the border of the volume under consideration:
it may therefore be reduced to a surface-integral.
The lJefthand member of this equation is independent of the circum.
stance whether the space under consideration is enclosed within
an imaginary separating surface or within a solid wall, and in the
latter case it is also quite independent of the properties of this wall.
So the righthand member cannot depend upon these circtunstances
dm ?
either. In the case of a solid wall we may write: 2 = ().. -So'-we
get for the righthand member:
Proceedings Royal Acad. Amsterdam. Vol, V,
( 490 )
fr roo (a, f) do = 3 PVE > teen ee en
Here r represents the radius vector drawn from the origin of the
system of coordinates to a point of the surface, do represents an
element of that surface, cos (7,7) the cosine of the angle which the
radius rector forms with the normal to the surface. 7?’ is the force
per unit of surface which prevents the molecules to leave the space and
compels them to return towards the inside of it. We may distinguish
a
in it the molecular pressure — and the pressure p exercised by the
:
wall.
: , ’ p d's
For the case of an imaginary separating surface, —m— is the
i dt dt
momentum in the direction of the positive v-axis conveyed through
the surface to the inside of it. Momentum conveyed to the outside
has to be taken into account with the negative sign. In this case
also the righthand member may be represented by equation (/)
though here the symbol 7?’ does not any longer represent a force
which really acts on the molecules.
In the case that the volume really occupied by the molecules
is not so small that we may neglect it, also the virial of the
forces eventuating in the mutual collisions of the molecules must be
taken into account. If we denote this virial by / then we may
write equation (4) in the following form:
=ms? = — 1 a Pr cos (n, r) do = — I + 3 PV.
Sms? and J being independent of the properties of the bordering
surface, P cannot depend upon them either. /? appears to be greater
than P’; for a wall this is because the number of collisions is
augmented in consequence of the abbreviation of the mean length
of path which a molecule describes between two successive collisions;
for an imaginary separating surface this is because the conveyance
of momentum through that surface has augmented in consequence
of the fact that in collisions between two molecules whose centers
lie at opposite sides of the separating surface, the momentum is
transplaced instantaneously from the center of one molecule to that
of the other; so the momentum has been transported with infinite
velocity.
But the way in which we have derived the quantity 2? which
may be estimated to represent the pressure prevailing in the gaseous
or in the liquid) phase, warrants in any case that this quantity is
( 491 )
independent of the shape of the vessel and the properties of the
walls in which the phase is enclosed, but on the other hand it
warrants also that we may find the quantity 2? by calculating the
pressure which would be exercised against a plane wall if the
at
molceules did not attract one another, or by adding —— to the pres-
i?
sure exercised by mutually attracting molecules against a plane wall.
The way in which the virial of the forces eventuating in mutual
collisions of the molecules has been introduced bij Prof. vay DER
\Waars is as follows. We assume that in first approximation 7?
represents also the pressure exercised on the distance spheres of the
molecules. This would yield the value 2 /%, for the virial. We
must, however, take only half this value, else all the forces would
have been counted twice. ;
The distance spheres, however, cannot be considered as unmoving
solid walls, but as moving and movable walls and therefore it is
perhaps not quite superfluous to show expressly that they are indeed
subjected to a pressure amounting in first approximation on average
to P.L will give the proof of this proposition in § 2 of this com-
munication.
ar ages ; ; Watney
Phe introduction of the correction term . 5 ir is based on the con-
Fo a)
sideration that the value of the virial given above will be too great
because some of the distance spheres partly coincide. The parts of
the surface of a distance sphere I falling within a distance sphere 11
are protected from collisions with all other molecules but LL. There-
fore the pressure om such parts is assumed to be zero; on the other
parts the pressure on the distance spheres is supposed to be 2. This
comes to the same as the assumption that the average pressure
during a time T (and every pressure which we consider, the pressure
P also, cannot be anything else but an average value during a certain
time tr) exercised on an element do of a distance sphere would
be smaller than /?, because of the fact that the element do is only
during a part of the time 7 exposed to the pressure 7, during ano-
ther part of that time, however, it would have been subjected to no
pressure, because if was protected by the distance sphere of a mole-
cule IL from collisions with other molecules.
IT have two objections to the calculations based on these considerations.
In the first place the assumption is made, that a part of a distance
sphere would never experience any pressure, when it lies within
the distance sphere of another molecule. In fact the reverse is true:
in order that a surface element should experience a pressure, a
33%
(492)
molecule must collide against it and then it lies in the distance
sphere of that molecule; and the considerations in which the pressure
inside the distance spheres is assumed to be zero, outside them to
be P, are certainly not a correct representation of what really happens.
Yet points lying inside distance spheres are in somewhat different
conditions as to the pressure that may be exercised on them, than
points outside distance spheres. It is not clear to me how these
conditions should be taken into account. It is, however, not necessary
to know this in order to caleulate the correction term, as will appear
from my second objection.
In the second place the fact has been overlooked that not only
some paris of distance spheres lie within other distance spheres but
that the same circumstance occurs for parts of the bordering surface.
It is indifferent whether this is an imaginary surface or a solid
wall’), in any case a part of it will lie within the distance spheres
of the molecules, and may therefore with as much (or as little) right
be estimated to be protected from pressure. Now let 1/4 part of the
bordering surface lie within the distance spheres. If we must assume
that this part of the surface experiences a pressure zero, and that the
free surface experiences a certain pressure, that we will call P,,
then the quantity 7, which represents — as appears from the way
in which it has been introduced — the average pressure, would be
A—l
Let us now investigate what part of the total sur-
equal to —— /,.
4
face of the distance spheres lies within other distance spheres, and
let 1/2, represent that fraction, then the average pressure of a distance
A 5 | 7
sphere will amount to /?,. If4, were equal to 4, then the average
R 7)
1
pressure on the bordering surface and on the distance spheres would
be the same, and we should not have to apply any correction to the
term bon :
Lip:
We find the correction ferm 55 5 if we make the following
rp 4)
assumption, but only in that case: every surface element, — no mat-
ter whether it is a part of a solid wall or of an imaginary separating
surface, and whether the surface is plane or curved and no matter
whether it hes within or without the distance spheres of molecules —
1) The virial of the forces excercised by the wall must properly not be integrated
over the wall itself, but over the surface which contains the centers of the mole-
cules colliding against the wall, i.e. over a surface parallel to the wall and lying
at a distance @ from it.
ee a
( 493°)
it will always experience a pressure PP. Only the distance spheres
make an exception to this rule, for parts of them, falling within
other distance spheres experience a pressure zero.
Lean find no reason for this exception and therefore 1 think the
WIED, it
value 39 yr incorrect, The question Whether in fact a correction must
be applied depends on the fact whether 4, is equal to 2 or not. This
may be investigated in the following manner.
Let M/ in the figure represent the center of a molecule and let
the circle described with J/ as center, represent the section of the
distance sphere (1) of that molecule with the paper. Now we are to
calculate the average pressure exercised during a time Ton a surface
element do, the center of which we call the point 7? To this pur-
pose we describe a circle Il with P as center and with a radius
26 and we also consider the tangent plane in 7? which we call ZA.
Two cases may be distinguished:
Ist The space within sphere Il but outside sphere 1 and at the
left of the tangent plane (the section of the space in question with
the paper has been hatched in the figure) may contain the center
of a molecule; if this is the case P lies within the distance sphere
of that molecule.
( 494 j
2nd The space under consideration may not contain the center of
any molecule.
We will call that part of the time + during which the former
T
takes place —; so that part during which the latter takes place
u
‘
ul ik u— 1 Ge.
7. During the time ~——7 the surface element do is quite in
u u
the same circumstances as an element of a plane wall. Therefore if
will experience on average a pressure 7. This pressure Pis a quan-
tity which we may derive from the virial equation; in order to deter-
mine it, it is therefore not required to decide whether the considerations
„ll
in consequence of which we find / equal to —~— P, are correct or
i
2 4 ; 9 T
not. But when the former case takes place, so during the time —,
2
‘
we are certainly justified in assuming that do does not experience
= ec
any pressure. The average pressure on do is therefore re
u
We may find the value of gw in first approximation by determining
the volume 7 of the hatched space, and by assuming that the chance
that a certain definite molecule will lie within that volume is equal
v ‘ : .
to 7: If » denotes the total number of molecules, then the chance
. . v
that the space contains a molecule will be represented by 7 7 On
average the value of */u will be equal to this chance: therefore in
EN
I
first approximation (= 7
We find by a simple calculation for + the value eu r* where
ry = 2¢6= the radius of a distance sphere. Therefore:
i
i May | ’
- LA 4 a ei
u ee = ah
J Seyi
„…)
) he
The internal virial Z will therefore be 3 2?b, (1 — — zl and
equation (1) assumes the following shape:
eel an i a he
Ems = PVP, Ge 8 = )=P(v bd a
§ 2. In order to introduce the internal virial / T started from the
supposition that the distance spheres of the molecules experience a
pressure which is on average equal to P. As I never found a direct
proof of this thesis I will give it here. The pressure / namely may
i. a. be considered to represent the pressure exercised against a solid
wnnoving wall, disregarding the molecular pressure. The distance
spheres, however, are not to be regarded as a solid, ummoving wall.
In consequence of their motion the number of collisions against a
surface element do of a distance sphere is greater than that on an
equal element of the wall; moreover the force in each collision is
proportional to the relative velocity of the molecules, which is greater
than the velocity of each molecule separately.
From these two circumstances we are apt to assume that the average
pressure on the distance spheres would be greater than 7’.
On the other hand the impulse of a molecule colliding with a
velocity sx normally against a solid, unmoving wall is 2ms. If,
however, the molecule collides with the velocity s centrally against
another unmoving molecule with the same mass, then the first molecule
will be stopped and the second will obtain the velocity s; so the
impulse is in this case only ns.
In consequence of this circumstance we should be inclined to expect
the pressure on a distance sphere to be smaller than 7.
The following simple calculation will suffice to show that these
influences cancel each other and that the pressure exercised on the
distance spheres is really equal to /, at least in the case that we
may neglect the volume of the molecules with regard to the volume
in which they are contained.
Let us imagine two molecules | and IL with the same mass. The
same proposition might be proved without difficulty also for mixtures,
so for molecuies with unequal masses, but 1 will confine myself here
io molecules with the same mass. The velocities of the molecules
will be denoted by s ands, and the components of these velocities
by w,v,2 and wu,,v,,2,. The chance that molecules occur whose
velocities have these components will be represented by 4 (az, 7, 1)
and F'(w,,7,,7,) and the relative velocity bv s,. Then we have:
sp? = (uu)? + (ur) + (rw).
If we take the direction of s, as the axis of a system of spherical
coordinates, and if we call the latitude g the longitude yw, then a
surface element of the distance sphere of moleenle 1 will be repre-
sented by 97? sing dys. The number cf collisions per unit of time
of molecules of group IL against such a surface element is:
F (u,v, vw) F (uy, vy, w,) du de dw du, dv, dw, s, 7° sin p cos p dy di.
( 496 )
Not the total relative velocity s, changes its sign in a collision of
this kind, but only the component normal to the tangent plane in
the point in which the molecules touch one another. The impulse
is therefore ms, cos gy.
The total impulse of the collisions of the kind under consideration
will therefore be equal to:
(u,v) F (ur or) dude die du, de, diy s-° 7? sin op cos” g dg dy.
be
The eightfold integral of this expression vietds the total pressure
exercised on the surface of the distance spheres. We have:
a) 9
| | 2 sin gy Cos” Xf dg dw == nr
AR:
…)
if we integrate according to y between the limits O and 2 a and
according to g between the limits O and > =. The limits for g are
not O and a, for the parts of the distance sphere of molecule [ for
which g > > a, cannot come into collision for the given relative
velocity s,, We may write s?-+s,’, for s,? for the terms ss, cos ($,5,)
vield zero on average. Doing this we may integrate the term with
s? according to du,, de, and dir,; so we get:
|” (rayo V1, te) du, do, dre, =n.
«
The term with s,? on the other hand may be integrated according
to du, de and dir; so we get:
B (u. raar) du dv dw =n.
t
This vields for the total pressure on the surface of the distance
spheres :
mr | | ms? fF (7, UW) du de dic Ee | mt EE 1 (Un Vo: ze dit, dr, div,
=e
c
Both integrals in this expression are equal to uus, nes” represent-
ing twice the mean kinetic energy of a molecule. We may there-
fore write this expression as follows:
Dividing this quantity by the total surface of the distance spheres
Aarm, we get for the value of the average pressure:
l
— Nn MS.
Co
( 497. )
This is the same value as we find for the pressure exercised on
a solid, ummoving wall.
In order to ealculate the number of collisions we have here
neglected the extension of the molecule and the mutual attraction of
the molecules. Therefore it is apparent that we cannot have obtained
anything else but a first approximation.
Botanies. — “Die Stelir- Theorie’. Dissertation of Mr. J.C. Scnourn.
(Communication of Prof. J. W. Morr).
According to the idea of van Tinenem, given about the tissues of
root and stem of the vascular plants, they must be divided into three
groups or systems of tissues, namely, epidermis, cortex and central-
cylinder. It is such a natural thing to call the epidermis a separate
tissue that already a long time before vaN PirGrmMm, it was acknow-
ledged and is at present generally accepted.
It is a different thing about the theory that the central part of
stem and root is taken up by aeylinder of tissue, the central-cy Linder
(or ‘‘stele”), which may consist of elements differing greatly, but
Which must nevertheless be regarded as a connected whole, forming a
certain contrast with respect to the cortex. This consideration which
can be called the ‘Stelar-theory” is accepted by some, rejected
by others. It is of the greatest importance for instruction and for
the construction of deseriptions of the inner structure, and it has
undoubtedly for both these reasons such a great practical weight, that
for this reason only it deserves our attention in a high degree.
The scientific foundations for this theory are not in such a good
condition and assuredly its non-acceptance is owing to this. Of course
the important question is, whether this distinction between cortex
and central-evlinder has made its appearance already at an early
period in the phylogeny of plants. With the present state of our
knowledge this can perhaps not be proved with certainty; but to
be able to answer this question in the affirmative two conditions
must be put: st. the central-evlinder must be indicated if not in
‘all, still in the greater part of stems and roots, 294, it must appear
already at an early period in the development of these organs.
As for the root these conditions are amply satisfied, which gives
great support to the theory of vaN ‘TimGHem. But this is not the case
to such an extent for the stem, partly perhaps in connection with
the complications formed already at an early period by the develop-
( 498 )
ment of the leaves, partly in connection with the splitting up of the
central-cylinder in these organs of many plants. Concerning the
latter point vaN TimGHrem himself and of late a number of American
and English investigators: GWYNNE-VAUGHAN, JEFFREY, Boopre, FAULL,
WorspeELL, BRETZAND Farmer & Hir, Miss Farp, TAanstny & LULHAM,
BREBNER have shed much lieht. In all those cases in which stems
show a number of loose strings, regarded by some as parts of a
central-eylinder (schizostely), by others as vascular bundles, a single
central-evlinder, the monostelic structure, is rule in the voungest
internodes of the plant, in hvpo- and epicotvl and in the internodes
following immediately.
But in most cases there is no question about schizostely and so
according to VAN ‘TinGikM we must expect monostely. However it is
a fact, that whilst in every root the most superficial microscopic
investigation easily proves the existence of a central-cylinder, this is
not at all the case for many stems. The inner layer of the cortex
(endodermis), it is true, is often developed as a bundle-sheath
indicating as that of the root does, the boundary of the central-
evlinder, or also it contains starch-grains, so that a distinct starch-
sheath is formed; but in a great many other cases, also in an inves-
tigation made for that purpose, as was done by H. Fiscumr, it has
not been possible to point out a well defined central-evlinder. Fiscuer
found in LOO investigated plants only in 32 cases a distinct endodermis.
It has now been shown by Mr. ScHourr that this objection to the
Stelar-theory does not exist in reality. He collected out of the lite-
rature on this subject numbers of cases, in which a distinct endodermis
had been observed in some shape or other. He himself studied a
great number of stems of different plants and then it was evident
how necessary it is to examine these organs in different and especially
in voung stages of their development, a thing Frsener kad not done. The
result of this method of working was, that of about 400 dicotyledonous
plants only in 7 no distinct endodermis was come across and among
these 7 there were vet 4 which even showed a sharp boundary of
the central-cylinder. Also the greater part of the Monocotyledonous
plants possess an endodermis. It is not to be found in Gymnosperms
but vet here as is the case in most of the above-mentioned exceptions,
a distinct boundary between cortex and central-cylinder is often to
be seen. So this result is very favourable for the Stelar-theory and
is a contribution to its seientifie confirmation.
But in yet another manner has Mr. Senovre endeavoured to test
the Stelar-theorv, a test, which it is true has led to a negative result,
but which enables us to draw weighty conclusions with regard to
( 499 )
the value of the well known Theory of the histogens of Hansrrr.
In working out his theory van /PrrGumMm purposely avoided as
much as possible to make use of the history of development, and as
has been proved justly. Yet it was quite natural to think that there
Was a connection between the structure of the full-grown stem and
root and that of the same organs at avery early period of development,
in embryo or growing point. For THaxstmin had established a doctrine
about the structure of the meristems, very much like var Tinguem’s
theory and had gamed a number of adherents. He thought, especially
on account of the arrangement of the otherwise equivalent cells, to be
able to distinguish three tissues in those meristems, called dermatogen,
periblem and plerome. The last was a column of cells in the middle
part of the stem and root. Of course it was quite natural to think
of an identity of dermatogen and epidermis, periblem and cortex,
plerome and central-eylinder, in such a manner that the latter had
developed out of the former. Tf it were possible to point out such
a correspondence, this would be for the Stelar-theorv as well as for
the Theory of the histogens of great importance, though not of equal
importance for both. If the eentral-eylinder is already found in the
meristem as an independent whole, this points to the faet, that the
differentiation of this tissue is old and then the Stelar-theory has
gained another support. But as 1 said above, it is fully established in
another way and can very well do without this support.
The Haysruiy-theory of the histogens is a different case. Every one
Who studies the literature impartially, will have to own that this
doctrine resis on a very weak foundation, perhaps not with respect to
the dermatogen, but very certainly as far as the plerome is concerned.
It is true, there are some roots and a very few stems in whose thin tops
the cells are arranged in a remarkably regular order, so that a central-
evlinder can be distinguished as plerome. But in many roots and in
nearly all stems there is no question about tracing such an arrange-
ment up to the growing-point. It is really to be wondered at that
this HANsTurN-theory in its generality has found so many genuine
adherents; this is certainly partly owing to the conviction, expressed
by many and silently shared by others, that plerome and central-
cylinder are one and the same.
Yet this had never been accurately examined till it was undertaken
by Mr. Scnourn. But it is clear, that a positive result would be of
the greatest importance for this theory. For there is no sense in
accepting histogens without full-grown tissues corresponding to them.
Moreover might be expected of a positive result the possibility. of
finding an undoubted plerome when following the boundary of
(900.4
the central-cylinder upwards, also in those cases in which up till
now the efforts had not been successful, perhaps on account of the
ereat number of cells.
The investigation of Mr. ScHourr was an accurate comparative
study of connected series of cross and lengthwise sections. It would
lead me too far if L were to speak of this more in particulars. But
in general the investigation was conducted in such a way that an
attempt was made to pursue in the direction of the growing point
the boundary between the series of cells which could be distinguished
as endodermis and central-evlinder in the older parts. The results
were in short as follows.
Of the root of Hyacinthus orientalis and Linum usitatissimum the
series of cells of the endodermis and the outer laver of the central-
cylinder (pericycle) were successfully and uninterruptedly pursued up
fo the growing-point. In these cases a cylinder of tissue could be
distinguished in the top, which could quite naturally be compared to
the plerome of Haxstem and which corresponded exactly to the later
central-eylinder. Also in Helianthus annuus in the main the same
was found, though the plerome did not appear here as a complex
of cells closed at the top. In the stem of Hippurus vulgaris, one of
the few stems in which different investigators have distinguished a
plerome, this was not only successfully found back, but also the series
of cells of endodermis and perievele could be pursued uninterrup-
tedly to the growing-point. However the cells of the plerome proved
fo form not only the central-cylinder but also the endodermis and
two layers of cells of the cortex, so that the required correspon-
dence did not exist here. In the stem of L/odea canadensis an un-
certain result was obtained, as here a starch-sheath and a bundle-
sheath were found, and it was not possible to make out which of
the two must be regarded as endodermis. But in the root of /icaria
ranunculoides and in the stalks of Aesculus Hippocastanum, Lysi-
machia Bphemerum, Heonymus europaeus and Ajuga reptans an im-
portant negative result was obtained. Here it was perfectly evident
that the series of cells of endodermis and = pericycle cannot be
pursued up to the top, but that they very soon stop short and are
replaced by shorter series of cells not exactly im their prolongation
and whieh in their turn soon undergo the same fate. In other words
in all these cases the expectation was not only disappointed that in
this way in difficult cases a plerome was to be found, but it was
also irrefutably established that it does not exist here.
After the above-mentioned explanations it need not be demonstrated
that these results as a whole must be regarded as fatal to the Theory
( 501 )
of the histogens. That in some selected roots there is some corres-
pondenee, makes no difference. That in slender tops built up out of
relatively few, lengthwise series of cells a regular arrangement of cells
may appear as was described above, is the most natural thing in
the world. To give a particular explanation of this is unnecessary,
and in no case are these single indications sufficient to establish
solely on them a theory of histogens as’ that of Hansrmm. And vet
this would have to be done if one wished to adhere to this theory,
for all other facts plead strongly against it. Mippuris, almost the only
plant showing a plerome in the stem, has a structure altogether
opposed to the theory. And the irregularly built tops form without
doubt the overpowering majority.
It seems to me that bv the investigation of Mr. Scnourn the
Histogen theory of HANSTRIN is proved to be erroneous. A conclusion
of somewhat general importance can still be deduced from these
investigations. Many botanists think that to the celldivision in
meristems a certain phylogenetic importance must be given, somewhat
comparable to that of the germinal lavers in zoology. But here is
forgotten that in zoology in the history of development folds and again
folds are spoken of, to a certain extent also histological differentiation
is mentioned, but litthe or nothing of directions of cell-division or of
arrangements of otherwise entirely equivalent cells. If the zoologist
attains at beautiful results by the study of the history of development,
it in nowise ensues from this that the study of the arrangement of
cells in meristems will be able to furnish these. Rather will the
hotaunist have to expect such explanations from the study of the
development of outer forms, and of inner differentiations as a result
of differences in the nature of cells. Experience has taught us ihat
this expectation has a right to exist. But the Histogen-theory has
certainly contributed to nourish the above mentioned wrong opimon.
Now that this has been proved to be incorrect we may expect that the
historie and phylogenetic importance which has often been ascribed
to the divisions and arrangements of nondifferentiated and perfectly
equivalent meristemeells will be reduced to its right and very slight
proportion,
Groningen, Jan. 29, 1905.
( 502 )
Physics. — “Methods and apparatus used in the eryogente labora-
tory. LLL Baths of very muf orm and constant low temperatures
in the cryostat? Communication N°. 83 from the physical
laboratory at Leiden by Prof. TH. KAMERLINGH ONNES,
(Communicated in the meeting of December 27, 1902.)
§ 1. By means of the cryostat deseribed in $ 8, Comm. 14. Dee.
94, and § 3, Comm. 51. Sept. '99 we can obtain a bath of
liquefied gas which is shut off from the atmosphere and boils at
ordinary or diminished pressure. In such a bath the temperature
is sufficiently uniform and constant for many experiments and mea-
surements. If we use almost pure gases and if the evaporated gas
is regularly recondensed by means of a compression apparatus,
which as deseribed in Comms. 14. Dec. °94, 53. Sept. “99 and 54.
Jan. (00, does not contaminate the gas, the bath may be maintained
as long as we wish. The operations in the bath itself as well as the
addition of the liquefied gas can be watched through the observing
glasses. Vacuum glasses are not required so that similar cryostats
may be constructed for measuring apparatus of any dimensions,
Before lone we shall describe a cryostat where the gas apparatus
and the bath are more independent.
I was led to deseribe the form of the cryostat, as it occurs in
Comm. 51, through the communication of the results for the di-electric
constants of liquid gases. (Comm. 52 Oct. 99), for which measurements
only the temperatures of — 90 Cor — 182°C. were required. For
other measurements, however, a measuring apparatus, once immersed
in the eryostat, has been used at the whole range of temperatures
between, — 23° C. (boiling point of methyl chloride at ordinary pres-
sure) and — 210° C. (nitrogen at reduced pressure), given by methyl
chloride nitrous-oxide, ethylene, methane, oxygen and nitrogen as they
were successively admitted into the cryostat.
For a long time improvements have been made in this cryostat
by means of which we can attain a much greater uniformity ane
constancy in the temperature, while retaining the afore-mentioned
advantages. A description of these alterations has now become neces-
sary in order to judge of the accuracy of the temperature readings
in the results from various measurements where we have availed
ourselves of these improvements. These measurements will be treated
in the next communications. Among others I mention here those
bearing upon the isothermals of diatomic gases (Comms. 69 March “OL
=
( 508 )
and 78, March ’02) and the comparison between the platinum resistance
thermometer and the hydrogen thermometer (Comm. 77 Febr. ’02) In
this description, as in Comm. 51. Sept. 99, it seems to me desirable to
illustrate the use of the cryostat by means of a special example. We
will consider the comparison of the hydrogen thermometer with
the resistance thermometer where also a thermo-element had been
immersed in the bath. .
Plate T shows the cryostat and some of the auxiliary apparatus
to scale, the connections are represented schematically. It has been
drawn on a smaller seale than plate L of Comm. 51 Sept. 99, (which
should be consulted together with the one now given) but it will suffice
to give a survey of the whole arrangement and to show some
of the alterations. While the details of the unmodified parts can be
studied on plate 1 of Comm. 51, plate I of the present Communication
shows the details of the parts enclosed by the dot-dash-line of plate I,
as far as they are required for consideration of the new arrangements.
The connection of the apparatus shown in Pl. | with the gas ciren-
lation can be seen in Pl. IV Comm. 51. The comparison of the
platinum thermometer p and the hydrogen thermometer 7% and their
connections to the other pieces of the apparatus are given in Comm. 77
Febr. (02 §3. For the comparison of the thermo-element @ 1 amas
yet obliged to refer to the very rough diagram of 1896 (Pl. 1 of
Comm. 27 Mai and June °96). The communication, however, of some
results for which the temperatures have been determined by means
of a thermo-element will soon call for a description of the recent
considerable improvements in the use of the thermo-elements.
On plates Land If a correction thermometer § which is entirely
independent of the cryostat, will be seen besides the three measuring
apparatus mentioned above. It serves in our case to indicate the
mean temperature of the capillary of the hydrogen thermometer, or
in general, the mean temperature of similar pieces of measuring
apparatus occupying the same part of the cryostat. For this
purpose two spirals of platinum wire are wound round a glass rod,
the one for that part of the rod, where the temperature varies slowly ¢,,
the other for that part where the temperature varies rapidly &. By
means of the leads ¢
~oo?
connected to the places of contact §,,, 6,, and
S,, and emerging through the tube §,,, we can determine the resis-
tance of these spirals.
§ 2. First we shall mention some small changes in the cryostat
of Comm. 5l which have no relation to the question of keeping
the temperature constant and uniform.
( 504 )
The jet of liquefied gas let in at « (plate T) is directed, by means
of the cock 4, and the filter f, against a glass wall from which it
streams along the delivery spout D, into the bath, here a double
beaker B, B, (Pls. I and ID), placed in the beakers 5,, B, Byot
PL. 1 Comm. 51. The cock and filter form part of a cover which as
deseribed in Comm. 51, may be removed together with S, and S, from
the cryostat and may also be replaced by a syphon or a capillary with
a cock outside the cryostat. The spreading of the jet over the
wall may be watched through the windows |,, and the height of
the liquid in the bath through the windows J’,. The filter / serves
principally to prevent opaque dust from the lead (oxide of copper ete.)
from depositing just at the place where the jet touches the glass. In
many cases, however, it happened in spite of the care taken in purifi-
eation, that the liquefied gas itself, while evaporating under reduced
pressure in the cryostat, had deposited a substance, formerly dissolved
in it but solid at the lower temperature, thus rendering the bath
opaque. Therefore, differing from Comm, 51, a glass beaker C, (Pls.
Land U) with numerous openings in the bottom C,, (PL ID and con-
taining some glass wool was suspended by the regenerator spiral 4
(Pl. L Comm. 51). This filter may be lifted from the cryostat together
with the piece S,
With the arrangement as described in Comm. 51 all the gas, formed
after the liquid leaves the cock, goes in the direction indicated by
the arrows on Pl. 1 Comm. 51. With the arrangement as described
here, however, the gas which is formed while the bath is being filled
follows in the main a different direction to that which afterwards
evaporates from the bath. In fact, differing from Comm. 51, a valve
Duo
of the delivery spout D, for gas, but allows liquid to flow through
with a spring D,, has been added, which almost closes the opening
a very narrow opening D,,, along the gutter D,,. The first consi-
derable quantities flowing from the coek, serve to cool all the beakers
and the whole cryostat in the way indicated in Comm. 51 (the arrows
of plate I might be borrowed: from plate I of Comm. 51), unless the
supply becomes so great that the valve D,,, is opened and the gas
also flows out through the opening Zè, im the ring /,, plate IL.
The eas which later evaporates from the beaker DB, finds the valve
D
ned LL
indicated by the arrows on plate II, so that it serves only to screen
closed and escapes only through the opening /?,,, along the way
the immediate neighbourhood of the bath from external heat.
The difference in form between the rings Mè, and FR, on plate I
and those on plate | Comm. 51 is very slight. This follows from the
wish to use the parts that served in the experiments, referred to in
( 505.4
Comm. 51, as much as possible in the arrangement of the measuring
apparatus considered here. Formerly the bath could be excentrically
mounted with reference to the tube // whereas this time a central
mounting was desirable. The existing dimensions of parts of the
apparatus have also had the result that in the experiments described
here the bath must be placed a little too high with regard to the
observing glasses V,, which might easily have been avoided if we
had been perfectly free in our construction.
The glass ring /è,, not occurring in the arrangement of Comm. 51,
serves still better to sereen the bath from external heat. Like the
other beakers and glass cylinders 5, B, B, B, B,,, Bon it is
silvered inside and outside, leaving open, however, vertical strips
nearly corresponding in width with the resistance thermometer p.
The conical rim B, lies loose on the beaker 4,,. When the liquid
boils up, it streams back to 4,, along the wall of the funnel; if,
however, B, is filled to the brim and more liquid is poured in,
this superfluous liquid flows over into the beaker B, which also is
filled before a measurement is made. If an intense cooling of the
neighbourhood of the bath is required, the beakers 5, 4,, 4, must
also be filled. It should be remembered, however, that if this is
done, the evaporation at low pressure, as long as liquid remains
in the outer beakers, requires a powerful vacuumpump.
The bath itself only evaporates slowly. Instead of the double
beakers 2, B, we might take a vacuum glass in order to diminish
the evaporation as has sometimes been done (comp. § 3). But it is
not always easy to obtain vacuum glasses of the required dimensions and
internally finished with the accuracy necessary for the proper working
of the stirring apparatus. Moreover one will not be inclined to
immerse delicate measuring apparatus in the bath before one is suffi-
ciently certain that the vacuum glass will not burst as such of greater
dimensions sometimes do.
§ 3. To make clear the purpose of the arrangements to be described
in the next sections, it seems to me that the following particularisa-
tions will be useful. First of all the temperature gradient in the
bath. Even when the liquid boils regularly we find that in the lower
layers, as a result of the hydrostatic pressure, the temperature exceeds
that of the upper layers. If, as often happens with greatly diminished
pressures when boiling is not produced artificially, only evaporation
at the surface occurs instead of boiling, the temperature in the upper
layers of the bath may fall considerably below that of the lower.
If then the liquid suddenly boils up, which always happens whenever
34
Proceedings Royal Acad. Amsterdam, Vol, V,
( 506 )
we do not stir vigorously, an unexpected change takes place in the
distribution of the temperature in the bath and hence in the tempe-
rature of any measuring apparatus placed in it. In measurements
of the kind considered here, we cannot allow such irregularities and
fluctuations in the temperature of the bath, either as to time or place.
Of the various methods of preventing this sudden ebullition, the
simplest is the generation of small bubbles of gas by means of the
heat of a short resistance (boiling thread). If, however, there are
ignitible gases among those successively introduced into the apparatus
and if consequently an explosive mixture with air might be formed,
this method is not without danger.
To bring about ebullition a current of gas is often led through
the liquid, which, however, has the disadvantage of contaminating
the evaporated gas. To avoid this difficulty I have led through the
bath a current of the gas itself. This means was applied for instance
to avoid the retardation in boiling in the vacuum vessel mentioned
at the end of § 2, and also in order to cause a strong stirring in
the bath by means of the current of gasbubbles. But this means
also presents many difficulties, mostly arising from condensation
phenomena in the delivery tube, or higher temperature of the gas-
bubbles; I therefore, preferred, the arrangement as described in § 4.
If the cryostat is used as it was intended to be in Comm. 51,
the requirements for very accurate measurements would not be
fulfilled, even though a uniform temperature throughout the bath was
attained. There still remains a systematic regular rise of the tempe-
rature, because the gas used is never perfectly pure and the more
permanent part evaporates first. In cases where measuring apparatus
require longer to adopt the temperature of the bath than the time
in which the temperature changes the amount permitted by the
accuracy of the observation, we cannot reach more accurate results
without additional means.
§ 4. We now pass on to the description of the arrangements
which form the subject of this communication. The uniform tempe-
rature in the bath is obtained by stirring. The stirring apparatus
is placed concentrically to the bath, thus leaving room in the most
profitable way for the measuring apparatus. From this space the
stirring apparatus (as in Comm. 27 May and June ’96 PI. III) is
separated by a protecting cylinder §, (comp. the figure to the left of
plate I). The upper ring ¥,, is provided with small valves y,,
covering openings of the same form. If the stirring apparatus moves
in the cylindrical space between §, and B, the valves shut up
( 507 )
during the upward movement and open during the downward
movement. The upward movement is brought about by means of
the thin wires x,, the downward movement by the weight of the
stirring apparatus itself which for this purpose is weighted with the
heavy ring %, by means of the rods y,,. As yet a more rapid
motion of the stirring apparatus than this method affords has not
been required; if wanted a construction with small rods instead of
threads would be necessary. The valves are hinged on bent pins
Yo The complete section of the stirrer to the right of plate II
shows the valves shut, the section of x, at the top shows them
open. When the stirring apparatus is moved up and down and
the bubbles of vapour escape the movements of the valves resemble
those of the fins of fishes.
It is very important that the up and down motion of the ring
should be perfectly perpendicular and that the protecting cylinder
§, and the beaker B,, should have a perfectly vertical position for,
to make the valves work properly, only a narrow space can be left
between the stirrer and the cylindrical walls. The cylinder §, is
enclosed between two rings provided with grooves §, and &, of
which the upper is connected with the ring §, by means of glass tubes.
Through the operation of the spring §,, and the arch §,,, this ring
is pressed against the ring §, on to which the beaker B,, with a
ground upper rim is fastened by means of cords. To this ring §,
the hooks §, are also fastened, against which the upper rim of
the beaker B, is also pressed by means of cords. In this way
a cylindrical space is reserved for the pumping motion of the
stirrer.
In order to admit the measuring apparatus it was advisable to
leave free the whole space offered by tube /’,, which is equal to
that in the bath available for a measuring apparatus. To this end
the threads y,, formed of very thin silk cords enclosed in steel wire
are led through 3 openings M,, in the cover // of the bath and
then over a pulley axis,z, with three grooves to a connecting piece
%;, Which is moved by a single thread passing over the pulleys x,
and y,. The cord must be moved from outside the case and the
case must remain perfectly air-tight. This is obtained by passing the
cord through an india rubber tube 7,,, which at ,, fits hermetically
on to the cover of the cryostat and in which the thread x,, is also
hermetically fixed. A thin steel wire is wound spirally round the
india rubber tube. In this way the walls of the tube offer sufficient
resistance to the atmospheric pressure to prevent them from collapsing
when low pressure exists in the cryostat, while at the same time
( 508 )
they remain elastic enough to permit the movements of the cord.
A regular up and down motion of the stirring apparatus is secured
by the wheel ¥,.
§ 5. A constant temperature is attained by continually adjusting
the pressure, at which the liquid in the bath evaporates, to the
indications of a resistance thermometer p placed concentrically in the
bath. A sensitive thermometer forms an inherent part of the cryostat
under consideration when it is to be used for very constant tempe-
ratures and the dimensions allowing a resistance thermometer to be
introduced, the latter has been chosen as the most trustworthy. Its
inner diameter controls the greatest cross section ot the measuring
apparatus which can be immersed in the bath, and therefore, as
in our case, it must correspond to that of the tube /’,. The con-
struction of this thermometer has been described in detail by B. Mernk
(Comm. 77 Febr. °02) with a view to a comparison between it and
the hydrogen thermometer referred to above. The leads pass through
the openings B, &,, of the ebonite rings R, and A, and then
through the stopper into the tube 7. On the plates I and IL they
are indicated by the same letters as on the plate of Comm. 77.
When the bath has reached the required temperature the galvano-
meter in the Wuwarstore’s bridge, which serves to measure the
resistance of p, is adjusted to zero by introducing suitable resistances.
As soon as the deviations of the galvanometer make it necessary, a
sign is given to the assistant, charged with the regulation of the pressure
in the cryostat, who then raises or diminishes the pressure, whereby
the temperature in the bath rises or falls. The great volume of the
cryostat is here very useful in checking oscillations in pressure. The
arrangements required for the regulation of pressure are shown in plate
I, the separate pieces of apparatus to scale and the connections schema-
tically. (Comp. Comm. 51 Sept. “99, pl. IV). The assistant uses
the oil manometer XN, which is connected to the cryostat by X,
and X, (comp. pl. Il Comm. 51) and the cock X,,, the cock
X,, being open. If we shut the cock X,, the motion of the oil
enables us to very accurately watch the variations of the pressure
in the eryostat by means of the difference between the pressure
in it and of the quantity of gas temporarily shut off in the reservoir
Ns. If through some cause or other the variations of pressure
increase considerably, or if we want to stop the regulation, or to
proceed to another pressure, the oil is prevented from running over
by our opening the cock X,,. The pressure in the cryostat is varied by
more or less opening the fine cocks },, and },, of the regulation
( 509 )
tube}. Two cases are to be distinguished here. With operations
at ordinary pressure it will be sufficient to adjust the cryostat at
a pressure a little higher than that of the atmosphere and to either
connect the cock Y,, with a gasholder Gaz. or to disconnect them,
as the occasion demands. As soon as the pressure passes a certain
limit settled for the cryostat, the gas escapes from the cryostat
through the large safety apparatus. For operations at reduced pres-
sure, the cryostat, after the pressure has been sufficiently lowered
by means of the exhaustpump of the circulation Mvh. 1, is discon-
nected from the latter and connected by means of the cock Y,, to
the exhaustpump Zeh. 2., and is then reduced to a lower pressure.
Obviously we can sometimes avail ourselves for this latter operation
of the same exhaustpump as used with /vh. 1. The evaporation
will proceed more gradually when a connection is made to a reservoir
at reduced pressure Vac., plate. If a reservoir of large volume is
used we can even work without an exhaustpump, which may be
ralnable when it is necessary to avoid vibration for the measure-
ments. Thus with the bath of nitrogen under diminished pressure
the auxiliary compressor of Comm. 54 Jan. ‘OO plate VIT was
connected near Zeh. 1 to the gaslead and the vessel of 5 m* men-
tioned above (comp. Comm. 14 Dec. °94 $ 10) served as vacuum
reservoir, after being exhausted through Y,, and Y,, by means of
a BurcKHARDT vacuumpump, connected to the gaslead at Lirh. 2.
This vacuumpump will be described later.
In a few words we shall indicate the method which we usually
follow in order to get a wellfilled bath at dtminished-pressure.
First the double beaker 2, ZB, or several beakers B,, B,, B,
are filled at ordinary pressure, then we begin to slowly exhaust
through Y,,; all other cocks being shut by means of the pump,
generally used for the circulation /ivh. 1; while boiling is prevented
by rapidly moving the stirring apparatus described in § 4. When
the required pressure is reached the cryostat is to be connected to
the great reservoir Vac. at the same pressure. If this cannot be done
we hardly ever sueceed in admitting through the cock 4, the vet required
quantity of liquid slowly enough to keep the pressure in the cryostat
free from undesirably large fluctuations or even to avoid with the
help of}, momentarily returning of it to nearly its ordinary value.
Therefore, if a change of temperature for some time is allowed, it is in
that case better to shut Y,, before more liquid is added and to connect
the eryostat through },, to the gasholder. As long as the beaker ,,
is not full the gas leaving the cryostat is allowed to pass through
Y,, into the gasholder. If the beaker ,, is full, which is shown by
02
( 510 )
the rise of the level in 6,,, we onee more begin to diminish the
pressure (17, shut, Jj, open) which process generally takes some
time. Then more liquid is admitted as before and if necessary this
process is repeated several times. If the beaker is sufficiently filled
at the desired reduced pressure we begin to regulate the pressure
with the duly exhausted vacuum reservoir as described above.
Plate [IL shows a couple of graphical representations of the varia-
tions of the temperature of the bath. The ordinates show the deflee-
tions on the scale of the galvanometer in centimeters. The abscissae
represent the time in minutes; fig. 1 relates to a measurement in
methane at ordinary pressure; a deflection on the scale of 1 c.m.
corresponds to about 0.009 deg. (the open space in the figure indi-
cates a magnetic disturbance). Fig. 2 refers to oxygen at a diminished
pressure; here a deflection on the scale of 1 ¢.m. corresponds to
0.005 deg. They were borrowed from the measurements of Mink
mentioned above.
The temperature of the measurement is determined by the help
of graphical representations, extending over the whole time of
measurement, from which the portions reproduced on plate [II have
been taken. For this determination the readings of the galvano-
meter are noted down about twice every minute. By means of the
planimeter we derive from the graphical representation obtained, the
mean ordinate, which mean is considered as the temperature of the
bath during the whole measurement.
(March 25, 1903).
H. KAMERLINGH oj/ow temperatures in the cryostat.
PLATE I.
Proceedings Royal
H. KAMERLINGH ONNES. Methods and apparatus used in the Cryogenic Laboratory. III, Baths of very uniform and constant low temperatures in the cryostat.
Proceedings Royal Acad, Amsterdam. Vol. V.
PLATE I.
H. KAMERLING
and const
Proceedings Roy
H. KAMERLINGH ONNES. Methods and apparatus used in the Cryogenic Laboratory. II. Baths of very uniform
and constant low temperatures in the cryostat.
PLATE II.
Proceedings Royal Acad. Amsterdam, Vol. V
aa sa taal i
1 EVA ANITA
iy haut FA AARLAI LBP
H. KAMERLINGH ONNES. Methods and apparatus used in the Cryogenic Laboratory. JIL. Baths of very uniform and
constant low temperatures in the cryostat.
PLATE III,
3 4
a 3
A 2
3 3
® Pie ADU ey |
|
A
He 45 Je 55 rr ED 4e 37 zo u
i i 5
i DN ji A
bane LV
2 \ 2
À VE NSA ay ul \ d
| pv i
i
El 25 w 35 ko 45 so 5 ca Ei 40° a zo 5
Proceedings Royal Acad, Amsterdam. Vol. VY
KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,
PROCEEDINGS OF THE MEETING
of Saturday March 28, 1903.
OG
(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 28 Maart 1903, Dl. XI).
ROTE EN TS.
J. J. vAN LAAR: “The meltingpoint-line of Tin-Amalgams” (Communicated by Prof. H. W.
Baxkuuis RoozeBoom), p. 511.
A. W. Nievwenuuis: “Influence of changed conditions of life on the physical and psychical
development of the population of Central Borneo”, p, 525.
P. H. Scroure: “Relations between diagonals of parallelotopes”, p. 540.
E. Conen and Tu. Strrencers: “On the atomic weight of Antimony (Communicated by Prof,
W. H. Junius), p. 548, (with one plate).
E. Conen and C. A. Lorry pe Bruyn: “The conductive power of hydrazine and of substances
dissolved therein” (Communicated by Prof. C. A. Lopry pr Bruyn), p. 551.
A. H. J. Berzer: “The velocity of transformation of tribroomphenol bromine into tetrabro-
mophenol” (Communicated by Prof. C. A. Lopry pr Bruyn), p. 556.
J. H. Bonnema: “Some new Under-Cambrian Erratic Blocks from the Dutch Diluvium (Com-
municated, by Prof. J. W. Morr), p. 564.
J. J. van Laar: “On the course of the values of 6 for hydrogen, in connection with a recent
formula of Prof. van per Waats.” (Communicated by Prof. J. D. van per Waars), p. 573.
W. H. Jusius: “Peculiarities and changes of Fraunnorer-lines interpreted as consequences
of anomalous dispersion of sunlight in the corona”, p. 589.
P. Tescn: “On the refractive index of rock-glasses” (Communicated by Prof. J. L, C. ScuROoEDER
VAN DER Kork), p. €02, (with one plate).
G. B. Hocenraap: “On an “Eisenrose” of the St. Gotthard”, (Communicated by Prof. J. L, C.
SCHROEDER VAN DER Kork), p. 605.
H. A. Lorentz: “Contributions to the theory of electrons, I. p. 608.
H. KAMERLINGH Onnes: “Methods and apparatus used in the cryogenic Laboratory”. ITI
feontinued) IV, V. p. 628.
H. KAMERLINGH Onnes and H. H. Francis Hynpman: “Isotherms of diatomic gases and their
binary mixtures. V. An accurate volumenometer and mixing apparatus”, p. 636, (with 2 plates)
The following papers were read:
Chemistry. — “The meltingpoimt-lne of Tin-Amalgams.”’ By
Dr. J. J. van LAAR. (Communicated by Prof. H. W. Baxnurs
RoozrBoom). (2Pd Communication).
(Communicated in the meeting of January 31, 1903).
1. In a previous communication (Proc. Dec. 1902) I showed, that
when the molecular potential of tin in a liquid tin-amalgam is ex-
pressed by the formula
Proceedings Royal Acad. Amsterdam. Vol. V.
u, = f(T) + RT log (le) + (a, 2? + Be +...),
a very good agreement is obtained between the calculated values of
the melting-temperatures at various values of «, and the temperatures
observed by vaN HerEREN (compare his Dissertation), at least up till
about 80° C.
In a conference, 1 had since with prof. van per Waats, he called
my attention to an expression for the correctionterm in u,, which
may be taken as a fairly good approximation’). This expression is:
a, x
(1 + ra)? ;
After he had first shown (p. 193), that the correctionterm is
really of the order «* — this I also showed in my previous com-
munication, but in a different manner and had observed, that (in
the case investigated by him) the value of a, does not remain constant,
but decreases when w increases (p. 198), he afterwards arrived at
the said approximate expression (p. 213, 214), in agreement with
an empirical relation of THOMSEN.
Though Prof. van per Waats has briefly given the deduction of
his formula, it may be useful to state once more how this expression
can be arrived at. The matter is of great importance, because the
same quantity u,—(u,),=0 constantly occurs in a great number of
formulae, such as those for the lowering of the freezing-point, elevation
of the boiling-point, alteration in vapour pressures, etc. If therefore
this quantity is once for all accurately known, we may get a better
insight into a great number of problems relating to binary mixtures.
2. As the total thermodynamic potential is represented by
c=—2 (7,/,) T (log T— 1) Se E (2, (e)) Se (n, odo | SE
— | fre V—p r| de RTS (xn logn,);
we obtain for the molecular potential of the component 7, :
05 OV
Wz == -k, T(logT-1) + edo Md] ge frd Vp | +RT+&Tlogn,.
n
n, On, :
With
1) Zeitschrift für Ph. Ch. 8, pg. 188 (1891). Also compare different passages in
the second part of his “Continuität” on p. 43—45; 148; 152.
Recently, Prof. van per Waats has returned to this question in his * Ternary
Systems” (Proc. March to July 1902). He gives there a more general and accurate
expression, wherein occur the critical temperature and pressure of the mixture
(Compare in particular IV, p. 92—96).
~
( 513 )
we find:
foev = ZE nRT log (V—b) + 5
and therefore
=n, RT OCS, &0¥ … BsGg
Vb. on. 4 dn, Von,
2 f par = ar ties te
Deducting from this:
OE en RT a |0V
i Dr. V—b On,
1
we get:
ov gE 7" =n, ay, 2
aa pdV — p rs = RT log (V—b)— en ‚+ 7 a, + n, a,,)-
a
Substituting @=n,?a,+2n,n,a,,+7,? a, for a, and the linear
relation 6=7n,6,+n,6, for 6 in the case of two components, the
expression for u, becomes:
u, = — kT (log T—1) — RT (log (VB) — 1) + [ede — Tne] +
ot Os ue 2 :
See b, — pm Weald: LOM pres tees Miter A a, aL)
in agreement with what I wrote down in my first communication.
If now we write x, = l—e,n, —=w, this then becomes:
p, = — kT (log T—1) — RT (log (V—b) — 1) + [e), — TO] +
RT b En
+o = [(1—a) a, + wal + BT log (1)
For the determination of the complete function of «, which occurs
here outside RV log (1— x), we will now determine the value of
a
UR V (Ae) a, + va,,].
The term with log (V—b) is supposed to be but very little dependent
on # in regard to these two. If in the equation of condition we
put p=0, which is certainly permissible in the case of liquid phases,
r
gi a
z may be replaced by rr and the above expression becomes:
then
(l—a)? a, + 24 (1—a)a,, de a)b, 2((l—2z)a, + va,,)
5 EER r ck
If now we replace V by 6, which will hold for liquids at low
temperatures in approximation, we obtain:
35*
( 514 )
((1-x)* a, + 2 a (1-a) a,, + a? a) b,— 2 (1-2) a, + # a,,)((1-#) 6, Hb.)
ee ’
b?
or:
— a, ((l—e)° b, 4+ 2e (l—a)b.) — 2.4,, a b, + 4, a7 l
b?
which we may also write as
B OO ME
se DGN de
b, b,
We therefore finally and approximately obtain:
u, = — kT (log T—1) — RT (log (V,—64,) — 1) + [(¢,).—T(n,).] —
Bi EF Tog
it pe + RP lg (le)
when we call
a, ba et) ds b, b, — a, be =A.
The corresponding expression for uw, evidently becomes:
i, = — kT (log T—1) — RT (log (V,—d,) — 1) le), Tad —
ds A (1— x)? RT /
—— ———. dD Ve
a ee ae
As (omitting p) it follows from the equation of condition, that
PPV meen op! Bs
V—b= = ;
a a
)
and that, therefore, log (V‚—b,) = log
a
general:
Eo mee oee Mine age (May) e
es e)
u, =e, — CT — (k, + B) Tlog T+ a, ce ze + RT log «
(1 ray’ |
In this equation then
is Len a,
Bm nn
bie Rb,?
c, = (1), — (4, + R) + R log —; C,=(4),),—(4. + 2) + BR log
a, :
whilst
A ea, d A
es Ci an RK at,
and also
2
1 . mn . .
+ log T, we may write in
Tt SES ee ae
OS a
a
7
5
=O} ait b, een
b aa
Tr.
1
5
Remark. The quantity u, = 5, may also be obtained by the opera-
n d
1
»
0g
tion p, —=$— ex De For the term — fpdV4pV, occurring in &, may
x a
. a
be written — (par — RT-D The required function of x
may therefore also be found by calculating (VV —/
a 3 0 a
EE Ee de aah
for which we then find exactly in the same way as above:
a, , a,b,*+a,b,?—2a,,b
re Tee
2
b, bb
woe
The two methods of calculation are, of course, identical. The last
has the advantage, that we see at once that the differentialcoefficient
5 ' ; 24e ‘ aly ee
of the correctionterm of z, 1. €. ze 8 nothing but x sata ase
Dis dd U )
that we have:
Opes NORE ads OG fi Oe (+) 2A
PLO E se eh a ees Ox? Òx?
when &, w, and w'’, represent the quantities ¢, uw, and gu, with omission
of the terms containing log(1—a) and loga. As regards the quantity
ds
u, =~, we must remember, that this is also obtained from the relation
Oz’
ijs
U, = 5 = (1—2) aa :
be’
= )=
3. It is now the question, whether the expression
a?
OR ETE
(1 4-74)
represents the melting-points of the tin-amalgams as well as, or
better than my semi-empirical expression
a, 2 + Be + y, ef.
Let us first observe, that vaN per Waars always found a, negative
in the case of electrolytes and other aqueous solutions (l.c. p. 195).
Now it is evident, that if we may write a,, = Va,a,, the coefficient
(b Va,-b, Va)’
3
b,
a, becomes , and ought therefore to be always found
( 516 )
positive. (Ll found for instance «, positive with tin-amalgams). It
therefore seems, that when one of the components (water for instance) is
an associating substance, or when the other component is electrolytically
dissociated, we must certainly not follow D. Brrrnenor in writing
12 Independent of the fact, that in such cases neither
a, and a,, nor 6, and hb, are constants.
The formule (8) in my previous communication now becomes:
= ey 2
a,a, — da
hs ea?
1+ — 5
ae — ie Jo (14e) ;
7
1— log(1—«)
Jo
RT
or with pee ct, ine
Yo Yo
14 ax
‘1+rex)?
Aid ne) es (SDi)
el (LS
From observations, where the values of « are less than 0,1, the
value of @ was found to be exactly 0,396 *). If we now further
accept for the values of the coefficients @ and 7:
a = 0,0453; r= — 0,74,
which are calculated from other observations with higher values of x, we
obtain (1, = 273,15 + 231,63 = 504,8) the survey on the next page.
We notice, that in this table the agreement is an excellent one; the
average deviation is about 0,9°, whilst in the case of the empirical
formula with ge? and y«* (see previous communication), if the last
value is not counted, it amounted to 0.85°. vaN DER WAALS’s expression
for the correctionterm, therefore, represents at least equally well the
course of the meltingpoint-line over the portion, observed from 212°
to 65°. But what is still more important, is the fact, that whilst my
former empirical formula does not very accurately represent the two
last observations (the difference in the last even amounted to 10°),
VAN DER WAALS’s expression not only satisfactorily represents these,
but also the four observations at still lower temperatures (compare
p. 22 of van Hernren’s Dissertation). In this observations the values
of « and ¢ were determined by analysis of the liquid phase, which
is in equilibrium with the solid phase at a given temperature.
200
1) In the previous communication 0.400 was accepted, but ae = 0,396 is some-
505
what more accurate.
ide
RN re
Denom. Numerat. |p 73045] ia.
2 a av? Lude)? Pre) rat
1—6 log A—2) | 1 -+- (ra desa ieh
0.1005 |0.01019; 4.0420 |0.00045°| 0.8567 1.0005 214.6 244.6.) -O
0.1716 (0.02945; 10745 |0.00433*| 0.7621 1.0018 197:5 {198.6 |—4.4
0.2338 0.0546° 4.14054 |0.00247°| 0.6839 1.0036 185.2 183.7 |44.5
0.2969 |0.0881° 1.1395 |0.003993| 0.6089 1.0066 172.8 {173.0 |—9.2
0.3856 (0.1487 1.4980 (0.00673°| 0.5108 4.0132 155.6 155.2 |+0.4
0.5001 0.2501 1.2745 {0.01433 | 0.3968 1.0286 134.3 |133.4 40.9
0.5973 |0.3568 1.3602 (0.01616 | 0.3114 1.0519 1173 (415.2 |42.4
0.6467 0.4182 1 4119 |0.01894 | 0.2719 1.0697 109.3 |107.4 1.9
0.6754 0.4562 41.4456 {0 02067 | 0.2502 1.0826 105.0 03.4 |44.6
0.6813 0.4642 | 1.4528 0.02103 | 0.2458 1.0856 104.0 |102.4 |+1.6
0.7104 (0.5047 | 1.4997 0 02286 | 0.2250 1.4016 | 99.9 | 99.0 H0.9
Oerlas: 10.5119 1.4978 0.02319 | 0.2214 1.1048 | 99 2 | 98.8 |+0.4
0.7477 0.5591 4.5454 (0.02533 | 0.4995 1.1270 95.0 | 95.4 |—0.4
0.7547 (0.5696 1.5565 (0.02580 | 0.1949 154320 94.4 | 940 |+0.1
0.7963 (0. 6341 1.631 (0.02873 | 0.1687 1.41703 89.3 | 90.0 |—0.7
0.8189 0.6706 | RGO Or 03038) 0). 1552 1.4957 86.8 | 88.4 |—1.6
0.8921 (0.7958 158817 - 0) O8605- 120.4455 1.3491 18.9 | 79.7 |—0.8
0.9483 0.8993 2.173! (0.04074 | 0.C8898 1.4579 65.5 | 65.2 |--9.3
T—973.15| id. |
L ed Denom. aa? |(1-+rz)?) Numerat.
| | | ealeulated! found
0.9879 |0.9759 2.7482 (0.04421 | 0.07231 1.6114 22.9 | 25.0;—2.4
0.9903 0.9807 2.8357 (0.04443 | 0.07140| 1.6223 15.7 | 15.0+0.7
0.9941 0.9882 3.03826 (0.04477 | 0.06991) 1.6403 sti a 0.0\—0.1
0.9964 0.9928 | 3.2282 (0 04497 | 0.0690! 1.6516 — 14.9 —18.8 3.9
The agreement is even unexpectedly great, when we consider, that
the meltingpoint-line runs here almost vertical, and a quite insigni-
ficant change in # causes a difference of several degrees in 7’,
( 518 )
4. Let us examine the formula
xv 2
1 + 0,0453 | ——___—_
ik & =0,74 -)
1—0,596 log (1—za)
more closely. ‘With small values of x it passes into
rr 1 + 0,0453 #° Ti BEE
die ae ee [1—0,396 x + 0,004 #°].
Because the coefficient of «? is accidentally nearly O, the melting-
point-line i this case runs over a fairly large region (from 232° to
120°) as an almost straight line. To ensure this, it is generally necessary,
that 6°? —40-+- a is very small or 0.
id 1
As, for equilibrium between the solid tin and the tin in the amal-
gam, “=U, or
— uhu, =0,
we also De
de
eee en Ark
. 0 A
Now according to a well-known theorem Ui (—yu+u,)=—- 7
The molecular potential u for the solid phase is moreover not depen-
dent on w. Therefore:
( Ou, de
dz dT’
and consequently
7A ee! i) Pm
be
We therefore see, that supposing the solid phase (as in this case)
contains no mercury, = cannot become 0, unless ot == 0, ba
then the liquid phase will be wnstab/e, and we find ourselves on the
spinodal line, so that the liquid amalgam would long ago have broken
up into two phases of different composition.
7
Ou
Now, 5e and therefore also a, May become zero in the case of
U av
two values for «; there are therefore in this case always two hori-
zontal tangents. A limiting case of this is of course a point of
inflection with only one horizontal tangent.
As
Cote)
Re Ae) ES
dz* q Oz dw de \q
this limiting case will evidently oceur when
Ou, d'u,
Se and 72
are O at the same time. Now
Ou, RP GA 4 du, RE LT Ope
Pie de a ey et dy
so that for this point of inflection we shall have the relations
v(1—a) aS RT (a «x)?(1—2re) 7, BN:
(l-Fre)? Za, ° (Lint ien Be,
On dividing, we find :
w (1+ re) = (le) (1—2 72),
or
re—2(14-rne+1=—0.
When 7 is either negative or positive, we find from this :
Lr VIe
1
Wve —
(a)
when «, indicates the value of vz at the point of inflection. 7, may
cree rome. (eran — 0) tot (Of 7 = — 1), when. 7 is negate. TE
however, 71s positwe, «a: runs from */, Gf r= 0) to 0 GE r= o),
/2
r NE . . OZ 5 . . .
The positive sign for W 1 + 7+ 7° would give in both cases impos-
sible values for «,.
We now further obtain :
Pikes ee RT 1 Taede me
PEER gn ke Ty eT
ry.
that is to say, when for —
rm
0
is substituted its value from (8hzs) :
1 arc
a(l—a)— 0 | tra)
(Ll4-ra)? “2a 1—Olog(1-«,)’
Ou
a 5 det 1 :
where the lower sign indicates conditions, where — < 0, and which
Aly
0
are consequently stable. From this then follows:
Bella = ,
( re) (1 — 0 log (1—a;,)) ns OQ + ra)? Haa].
+7x,
2a
Now, from the equation, from which (a) was deduced, we find:
( 520 )
l+r2,—3——_,
+ 97 x, 5
so that also
9
5 av (2 — «,)? (1 — Glog (1 — w)) Ze OLI(1 —e)? + aa? (2 — a,)’],
consequently
== 270(l—e,)?
a Zi m2) [A2 —a)(1—0 log (1—2,)) ay 30ae| . (b)
Ou
If, therefore, @ = or > than this value, then ae becomes 0 on
a“
one or two places on the meltingpoint-line.
Al . . u - . Oo e .
From the expression for — (see above) it follows immediately,
Ow
ti
that when A, and consequently @, should be negative, re can never
d
become 0, still less positive. The occurrence of unstable conditions on
the meltingpoint-line may, therefore, only be expected in the case
of positive a, and only then, as soon as « reaches ov erceeds the
value, given by (Od).
The relations («) and (4), when united, give therefore the con-
dition for stable phases along the entire meltingpoint-line.
In our example 7 = — 0.74, and (a) gives a, = 0.863. The equa-
tion (6) further gives with 06 = 0.396 :
ae 27 >< 0,396 x (0,137)?
“ < 0,863 <(1,137)"}2<1,137(1 0,396 log 0,137) 3 <0,3965<0,863]
that is to say
— 0,180 — 0,180
| 0,0592.
ETET Li a < 0,05
Now, in our case « was 0,0453, so that everywhere we find
ourselves in the stable region (as may in fact be seen from the
shape of the observed meltingpoint-line). If @ had been 0,059,
should have had a point of inflection with horizontal tangent ; and had
a been 0,059, we should have noticed the occurrence of a horizontal
tangent in two places of the meltingpoint-line. This last case is, of
course, not realisable, as the liquid amalgam would break up into
two heterogenous liquid phases of different composition. *)
1) It is perhaps not devoid of importance to observe, that when the solid phase
forms a solid solution of the two components, the presence in the meltingpoint-
line of a point of inflection with a horizontal tangent points as before to unstable
conditions. For in the general relation
a
Ou
Another question is, at what values of « and 7' does — first
U
become 0, or where does the plait commence, independent of the
fact whether we find ourselves on the meltingpoint-line or not, which
had just been investigated.
Ou Oru
We have only to combine the relations — =O and ~— ()
wv wv
2
a ore
dil fess Oa,?
SN —_
da (B
Ihe
a always becomes O in one place only in consequence of #3—, becoming 0,
Av
1e dT
whilst on account of De becoming 0, i always becomes O in {wo places, or
ra Ak ‘
in the limiting case in two coinciding places in a point of inflection with a hori-
zontal tangent. De Visser thinks he has found such a point of inflection with
mixtures of stearic and palmitic acids.}) It is, of course, not impossible, that we
are dealing here accidentally with a case, in which the quantity z possesses the
value indicated by (0). That the line of the end-solidifyingpoints also shows in the
immediate neighbourhood a similar point of inflection, points to the fact, that the
0°6 ik
Jet = 0, 5, Sb are fulfilled on both lines at about the same time,
v i
which renders it more accidental still, because z would then possess the value
required for this also in the solid phase. It should be pointed out, that as arule
conditions
may ye 08
the conditions Pe Die =0 for both phases by no means include x, = #3. For
vu wv 4
y = 05, : .
this requires aa = Hee It is there‘ore a new accident, that both points of
Ly we
inflection appear to coincide. But for this a reason may be given here. From the
equation, from which (a) is found, namely rx? —2(1+7r).a2-+1=0, it follows
that with r=0, «=1/,. De Visser now found both points of inflection to be at
x about 1/, (= 0.525), so that the quantity 7, both in the solid and liquid phase,
is about O (bj = bz). And in that case the values of 2 at both points of inflection
must agree, namely both at x= 1/9.
The case, studied by pe Visser, may therefore be an accidental coincidence of
9 9
2 2
07g
= = (0 and — = 0, both
Oe Òm,? é
the liquid and solid phases must have broken up into two layers, although of
identical composition. The smallest delay in solidification would however imme-
diately have carried the system within the plait, and then both phases would have
broken up into two layers of a somewhat differing composition. It is however
more probable, that both lines nearly show a point of inflection with a horizontal
tangent, and that they approach very near, but not touch each other.
Ee,
the two points of inflection. But then, on account of
1) Rec. Trav. Chim. (2) T. 2, N’. 2 and 4 (1898).
( 522 )
to find the values of x and 7 at the “critical” point. We find as
above
lt-r—V1itr4r
ei een ieee we as. oh
u
a Ned: Ou,
The temperature 7, of this critical point is found from— = 0,
v
that is to say from
a(1l—a,) O Te
Iro)? 2aT,
We consequently find:
2a e(l—e,)
Ee
rj ry
a zl:
IY, as TL == Eel
i 2a #&(2—.2,)*
Rr RL eee STE,
27 0 (1—z2#,)°
Ou
At this, or at lower temperatures, a being then positive, we find
Or 7 '
ourselves therefore in the plait.
In the case of tin and mercury we find for x, the value 0,863
(see above), if r=— 0,74. For 7, we find:
rl. BORE MODE anar
Ee a
The “critical” point is therefore situated at 16° C., that is to say
fully 57° lower than the point of the meltingpoint- ties belonging to
= 0,863 (13,7 atom-percent tin), namely 83°,2 C.
There are of course cases, where that distance is smaller, and
where consequently a trifling supercooling already carries us within
the region of the plait, which then — in the absence of the solid
phase — causes a separation into two layers.
I may observe, that the value z, does not correspond as a rule
with a point of. inflection (with oblique tangent) on the meltingpoint-
line, when the critical point is not situated on the meltingpoint-line.
Ou, Oru ‘eP
For de
=—= 0 do not lead to —~ == 0, when these differen-
DE ” Oa? dx?
tial-coeffients do not become O on the meltingpoint-line.
5. The value of g, the heat of fusions of tin in the liquid amal-
gam, is evidently:
2
ge (: +75).
( 523 )
When the value of « is small, and assuming, that mercury dissolved
in tin is monatomic, we find for q, by calculation 2550 gram-cals.
Person found experimentally 1690 gram-cals. Should this figure be
confirmed, it would prove, that the associationfactor of mercury is
about 1.5.
Now, it follows from the above formula, that at 25°, where w is
about 1, g ought to be
— 2500 to bit 4110 gram-cals.,
whilst van HerEREN, by electromotive measurements, found about
3000 gram-cals. From this it would follow, that the value, used for
q,, is about 1.4 times too large, which would be a confirmation of
the fact, that the mercury in the amalgam is not present as single atoms.
In order to obtain certainty as regards the molecular condition of
the tin in the amalgam, it would be necessary to know the melting-
point-line of the mercury, and to determine the lowering of the
melting-point in addition to the heat of fusion in the presence of
very small quantities of tin. There are indeed indications, that the tin
is also not present as single atoms. Indeed, the quantity 7 = — b, + 4,,
; b,
which was found by us to be — 0,74, gives for = the value 0.26,
)
1
from which it would follow, that the molecular volume of tin (b,)
would be about four times larger than that of mercury (/,). Now,
the atomic volume of Hg is 14,7, that of Sn = 16,1, so if these tro
b,
components were monatomic, — ought to be approximately — 1,
a
whilst in reality that relation is */,; this points to the probability,
that in the case of tin several (may be six) atoms are united to
one molecule.
It certainly would be highly desirable if this question were fully
investigated. For in all our calculations the values of w are only
then valid, when both mercury and tin are assumed to be monatomic.
This is also the case with all similar calculations, relating to other
amalgams.
May I be allowed to point out, that the molecular condition of
mercury may be determined from the lowering of the melting-point
of tin, if this contains a Little dissolved mercury — whilst the molecular
condition of tin may be ascertained from the lowering of the melting-
point of mercury in the presence of a little tin. For in the case of
dilute solutions something is learned only about the condition of the
dissolved subsiance, but never anything as regards that of the solvent.
In the limiting formula
( 524 ) .
2
4 Al rj ETT,
Erna WS ©,
Jo
where 7, and g, relate to tin as solvent for example, everything on
the right hand side will remain unchanged, although tin should not
be monatomic, but say z-atomie. For «, the concentration of the
dissolved mercury, would then become j-times greater, but q, would
also become -times greater, because the heat of fusion relates to
1 mol. = n-atoms. On the other hand, if the mercury were m-atomic,
the value of # alone would change; « would then become m-times
smaller, and we shall, therefore, observe a m-times smaller lowering
of the melting-point than that, calculated on the basis of mono-atomicity.
In this way we might attain to the knowledge of the molecular
condition at the ends of the curve, « being O (for mereury), and 1
(for tin). But in order to form further conclusions with other values
of x, the whole of the meltingpoint-line would have to be accurately
examined, and this may in many cases become an exceedingly com-
plicated matter.
6. There is, however, another way to get to know something
about the molecular condition of the solid tin, and that is the com-
position of the so/id phase, which is in equilibrium with the liquid
one. If we equate the molecular potentials of mercury in the two
phases, we obtain:
a’ (1—z2')’
= ln El
cl ) == oe —c, F. +- RT log BH út ' Ne i
re
—c, T - RT log « - =
C5 Cs ji wd ä (14 ra)? 2
This further gives:
TRT log” a,(l—2)’ _ a, (1—a)’
(e,—e = orn (c,—¢ ES =d are + (1 = re!) Ge (ltre)? ;
or with e‚—e, = 4q',, and with introduction of the meltingpoint 7", of
pure mercury :
7 a!
q', (1- =) = RT log — did,
i i £
0
therefore
cae. z a, (lx)? a’, (1—a’)?
Go| terne Feb
T—T', 5 RT (1 + re) RT (1+ 7'2'y?
Now in the liquid condition
b, Diens ee ape mame Ae ee,
Bnn he 50 RIA RTE ae ae ae T ZE
504,8 50
This quantity is therefore 0,1144 x 0,45.
298,2 °° 13
ke! RN
Putting a, =a, and 7’ =7 as a first approximation, the value of
the correction becomes:
0,012 2 0,99 2
£20,74>< 0,988) \i—0,74% zo) f
and, as at 25° the composition of the liquid phase was found
« = 0,988, and that of the solid phase #'== 0,01 (perhaps 0,06), the
said value becomes:
0,745 X (0,0020—0,9950) = — 0,74.
A change of «' from 0,01 to 0,06 can only cause a slight alteration.
0,745
i igh ©
The value of the chief term log — is:
av
9
BF 23026 = 4,59
0,01 X 2,8026 = 4,59,
so that we obtain (at 25°):
| 2X 298,2 x 234,5
ee 63,7
whereas PeRSON found q' = 2,82 >_< 200,5 = 565 er. cals. We therefore
find a value 15 times too great. And a small error in the correction
term 0,74 cannot upset this result. If, however, the tin in the solid
amalgam is taken as hexatomic, 2’ becomes six times greater and
g, comes down to about 4400 gram-cals. If, moreover, +! is origi-
nally taken not as 0,01, but as 0,06, so that with a hexa-atomicity
x now becomes 0,32, the value g, begins indeed to get more close
to the value, obtained experimentally.
The above, therefore, contains indications enough of the poly-
atomicity of both mercury and tin. To arrive at a decision, however,
accurate experiments will have to be made in the direction indicated,
together with fresh determinations of the two heats of fusion.
log*®
X 8,85 = 8450 eram-cals.,
Ethnology. — “Influence of changed conditions of life on the
physical and psychical development of the population of Central
Borneo.” By Dr. A. W. NreuwenguIs.
(Communicated in the meeting of February 28, 1903).
There is great diversity of opinion among competent authorities
about the influence exerted by external circumstances of life on the
development of a person and on that of the peculiarities of a tribe.
If this difference of opinion already gives evidence of the difficulty,
of determining this influence for the individual, the difficulty is greatly
( 526 )
increased, as soon as we try to find, between two groups of men,
characteristic differences, which are to be ascribed to their different
circumstances of life. Examining the highly cultured nations which
live in very complicated conditions of life, the difficulties become
almost insuperable.
We are not a little hampered in this investigation by the fact that
among civilized nations mutual intercourse and mixture have a
disturbing influence on the eventual effect of special conditions of
existence.
In Europe some data are furnished by the Israelites, which have
preserved themselves as such for centuries in different countries
under the circumstances prevailing there and which have absorbed
few foreign elements. But here, too, the influencing conditions of
life are very complicated, and the Israelites of the different countries
have mixed with each other.
Chiefly because the relations in the societies of tribes, which have
not reached so high a degree of civilization, are simpler and the
conditions of life for all their members do not differ so much as
elsewhere, it is likely that amongst them eventual changes in those
conditions of life will stand out more prominently and that much
becomes clear to the investigator, which was difficult to point out
under more complicate relationships.
It is moreover noteworthy, that among them the influences of
nature, of the surroundings in which they live, have a much greater
effect than in higher civilized societies, which have learned to shield
themselves better against this direct dependence.
We also meet with tribes where the great disturbing factor of
frequent mutual intercourse and mixture is excluded in examining
the modifications which two tribes have suffered by different external
causes. A still simpler case presents itself where two large groups of
the same race have lived for a long time under different external
circumstances and have mixed little, if at all.
Before it has been proved that the people forming these tribes, are
in their original qualities the same as Europeans, we must not directly
apply what has been observed in them, to European society. For
the right understanding of the pre-historic course of the development
of mankind, however, we may refer to the tribes, which have
reached as yet but a lower degree of culture; in my opinion we
are equally justified in drawing certain conclusions as to the corre-
sponding influences on higher cultured nations from many things,
which we have observed in the social matters of the former.
During my second journey through Borneo I had the privilege of
living among two groups of the same tribe, which have existed for
a century and longer under very different circumstances. They were
the Bahaus on the Upper-Mahakam, with whom L lived for two
years, and the Kenjas on the Upper-Kajan, with whom I spent some
months.
The tribe-groups of this name occupy together the upper- and
middle course of all the rivers, whieh fall into the sea on the
North coast, beginning with the river Batang-Redjang, and as far as
the East coast, including the river Mahakam. They are called collec-
tively the Pari-tribes, and they all consider the region containing
the sourees of the river Kajan as their original country. Mutual
quarrels, the result of too dense a population, were the cause, that
for centuries again and again tribes moved away to neighbouring
~
rivers, as e.g. it happened no more than 25 years ago with the tribe
Oema Timé, which settled on the Tawang, a tributary on the left
of the Mahakam.
The Bahau-tribes on the Upper-Mahakam also originate from this
native country, which they call Apo Kajan, but they have lived in
their new home already for more than a hundred years. This was
curiously confirmed on my arrival in Apo Kajan with my Bahau-
escort. Their chieftain Kwing Trang then received for the first time
a full account of the history of his ancestors, which was already
forgotten in his own tribe.
How little intercourse the inhabitants of the Upper-Mahakam have
with those of the Upper-Kajan may be derived from the fact that
among all the younger Bahaus only one man had ever been in Apo
Kajan, and that, when in the company of 60 Bahaus and 20 pseudo-
Malays [ set out on the expedition thither in August 1900 none of us
knew the way. The journey lasted a month, and we had to traverse
uninhabitated land. The way was indicated by sticks put up in
a special way in the river-mouths by some Kenjas who travelled in
boats in front of us, the sticks denoting which rivers we had to take.
We may therefore assume as certain that we have to deal with
tribes of the same origin, to which moreover their language, dress,
morals and customs point, which distinguish them clearly from other
tribes, e.g. from those on the Barito- and Lower-Batang Redjang.
Their descending from Apo Kajan to the Upper-Mahakam, however,
brought the Bahaus in peculiar conditions, which exercised a great
influence on them. On the Upper-Mahakam, namely, the Bahaus
live at a height of from 250 to 200 metres, the Apo Kajan is 600
metres and higher. That this difference as regards the climate is
very considerable especially in Borneo, may be derived from the
56
Proceedings Royal Acad. Amsterdam, Vol. V,
( 528 )
fact that in Java the region of moss vegetation does not begin lower
than at a height of 2500 metres, whereas in Borneo it begins
at a height of a thousand metres. This is caused by the following
circumstances.
The situation of Borneo being under the equator, the middle region
is but slightly affected by the influence of the trade-winds, which
e.g. in Java make the difference between the wet- and the dry-
monsoon so great. Hence it may happen that more rain falls from
Deeember to March than from May to October, but particularly in
the highlands really dry times are unknown, and we may find low
water in the rivers in the rainy period. The regular distribution of
moisture through the whole year is greatly furthered by the circum-
stance that the whole island is covered with one large primitive
forest, which itself retains large quantities of water, and harbours
mouldering rocks which do the same. The annual rainfall amounting
from 3000 to 5000 m.m. at different places, the climate is very
humid all through the year, and the sky is always more or less
overcast, so that a cloudless sky is a great rarity in the higher
regions. Soon after sunset a low hanging curtain of clouds is formed
in the valleys. This does not rise until seven o’clock in the morning
or later and envelops the summits of the mountains till pretty late
in the evening. In consequence of this the maximum temperature at
a height of 250 metres is 30°C. in the shade on the Upper-Mahakam;
at six o'clock in the morning however it was never lower than
20° C. Noteworthy is also that strong winds of long duration do
not occur there, only some blasts of short duration, which are generally
preceded by heavy showers.
The climate of Apo Kajan and of the Mahakam differs but little
in most of its peculiarities, such as humidity, and a cloudy sky, but
the latter is a good deal colder on account of the greater height,
and what is particularly striking is the continually prevailing wind.
This accounts for the fact that though in two months [ never found
a lower temperature than 17° C. at six o'clock a.m. and though it
hailed but once, the climate is yet much rougher. The red cheeks,
specially of the women and children prove this, and also the faet,
that the different kinds of rice require a month longer to ripen in
Apo Kajan than on the Mahakam. Yet the method of growing rice
is the same, and consists in cutting down and drying the wood,
after which it is burned and the rice sowed in holes, which are made
by pushing pointed sticks into the soil, which is covered with ashes.
The geological formation is the same in Apo Kajan as on the
Upper-Mahakam; we find in both a strongly denuded upland, where
( 529 )
everywhere old slate layers come to the surface. Only here and there
younger formations, specially free-stone, cover the older.
If we now take into consideration that only in the last 30 years
either the Bahaus on the Upper-Mahakam or the Kenjas on the
Upper-Kajan have come into such close contact with higher civilized
nations that it induced some of their men to undertake commercial
enterprises for the purchasing of salt and linen, I think that Tam justified
in asserting that the two groups of tribes under consideration belong
to the same race, that they have lived for upwards of a hundred
years in countries with a different climate, that they have had but
little mutual intercourse and have not mixed; that they have not
changed their life as cultivators of the soil and have developed
without external influences.
What effect this difference of climate can have on the popu-
lation, may be derived from the fact, that in my opinion the thin-
ness of the population in Borneo depends in the first place on the
influences of the climate, and much more on the customs of the
people than on the infectious diseases, such as cholera, smallpox, which
are introduced from the coast. As both Upper-Kajan and Upper-
Mahakam are so difficult to reach that infectious diseases but very
seldom extend to them, we have, when trying to determine what
the result of those changed conditions of life is for the Bahaus, only
to deal with those factors which are sometimes comprised under the
name of influences of the climate.
What is understood by influences of the climate in the highlands
of Borneo became clear to me for the first time in the sultanate
of Sambas on the West coast of the island, where I was struck
by the difference in the spread of malaria among the population
of the marshy coast regions and that of the highlands. In order to
—
get a fuller knowledge of this difference, L made an inquiry into
the traces of malaria infection on about 8000 children, both in the
marshy alluvial plain and in the highlands. These children had not
been offered to me on purpose for this investigation, but for an inquiry
into the results of the vaccination among the Malay and Dajak
population.
Among the population of the alluvial plains IT found among 2103
children only 6 with a chronic hard splenic tumor, or 2,8 per 1000.
Among 420 children of the uplands it occurred in 403 children,
or 959.5 per 1000.
The remaining 996 children originated from regions, which in
their formation were the transition between the alluvial plains and
the uplands, Janus, Deuxieme Année 1898,
36%
This inquiry yielded the result, that in the marshy alluvial plains
which consist entirely of vegetable and animal remains, malaria
hardly ever occurs, as opposed to the uplands where nearly all
children suffer from chronic malaria-infection. At the same time |
saw, that soon after birth the hardened and enlarged milt makes its
appearance, for it was long before 1 could find a Dajak child of three
weeks old, whose milt was not to be felt.
It is impossible to give the morbidity and the mortality caused by
the malaria-infection among the population of the uplands in figures.
[ only found the death-rate in Sambas extending over 6 normal vears,
i.e. years without cholera or smallpox, to be for Dajaks 37 per 1000,
for Malays 28 per 1000, which however does not represent the influence
of the malaria, because there are also some Malays who live in the
uplands and among those, who have chiefly settled in the lower plains,
diseases of the digestive organs are much more frequent than among
the hills.
In order to appreciate fully the influence of the malaria-infeetion
on the existence of the inhabitants of the higher regions, we must
dwell for a moment on the phenomenon, which prof. Koc says that
he observed in New-Guinea, namely, that the native, who went
through the malaria-process independently i.e. without any aid except
his constitution, became immune against it. Many are the refutations
adduced against this statement by physicians, who practised in New-
Guinea. They all pointed out how frequently also adult Papoeas
suffered from malaria.
Judging by my experiences among the Dajaks, the truth lies between
the two. I also have been struck by the fact that not so many hard
enlarged milts as symptoms of the malaria-infection are met with
among adult Dajaks as among children under the age of ten, which
certainly points to a less strong influence of this infection. Moreover
there is a great difference between the action of chinine on Dajaks
and on Europeans, who are not immune. Though we must make
allowances for other factors than immunity, vet it is remarkable,
that we obtained much greater results with at most 1 gram sulphas
chinini a day among the Dajaks than with 2 to 3 gr. murias chinini
among European soldiers, seized by malaria in Lombok.
Among the former it was possible to cure not only the acute cases
of malaria, but also cases which had continued from 4 to 6 months
and had not been treated before, by administering 1 gram sulphas
ehinini per day and per dose during 8 days, whereas in the first four
months after the war in Lombok in a mixed garrison of 1500 men
more than 500 Europeans had to be removed, most of them by far
( 501 )
being malaria patients, whom | myself had treated with from 2 to
3 grams per day and per dose, and who had little chance of being
cured in Lombok itself.
Among at the least 2000 Dajak malaria patients, whom 1 treated
specially in Central-Borneo and of whom hardly any died, [ observed
another telling difference between the reaction of their body against
the malaria-infection and that of the Europeans.
Whereas under unfavourable circumstances many of the latter
perished under rabid and strong symptoms, sometimes so quickly, that
chinine was of no avail, such acute cases with strone icterus, uncon-
sciousness and collapse were never found among the Dajaks. | saw,
however, many cases where the disease had reached an advanced
stage after protracted illness.
That this difference was not due to the inferior strength of the
infection in Borneo, was proved by -my European and native
fellow-travellers, most of whom suffered badly from malaria; to them
IT had again to administer from 2 to 3 grams of murias chinini a
day, and one of them I had to give a strong hypodermic injection
of 3,25 gram chinine within 96 hours.
From all this we may assume that the Dajaks become partially
immune if in youth they are subjected to repeated attacks of malaria.
Yet even then whatever weakens the constitution may give rise to
attacks of malaria, so that diseases of the respiratory organs or of
the digestive organs, wounds, diseases of infection and specially
evervthing that is comprised under the name of catching cold, get
complicated with malaria.
As the mountainous regions on the Upper-Mahakam are among
those where malaria is of very frequent occurrence, it is clear, that
the Bahau-population suffer greatly from it and that the individual
experiences its enfeebling influence from early youth till death.
Being used for vears in my practice among them to find that
the great majority of cases were those of malaria, I was greatly
struck by the change after my arrival among the Kenja population
of Apo Kajan. L must add that my reputation as a physician
procured me immediately after my arrival a great number of patients,
though only few had ever seen a European on the coast before.
It first struck me, that so many hvdropie old people called in my
help, which had searcely ever occurred in lower regions, whereas
the malaria-cases retired to the background and during my stay
confined themselves to a few acute cases. found then, that the
change in the siek-rate of the population was chiefly due to the
prevalence of bronchitis with emphysema and heart-disease, bronchitis
( 9320)
being caused by the rough climate and inereased by the smoking
of badly prepared tobacco, which even very young children begin
and which is held to be a remedy against coughing.
Though more acute malaria cases occurred, when the rough, cold
weather set in with violent showers, there was not any question
of a chronic infection of the population, manifesting itself in an
enlarged, hardened milt in the children. This agrees with the well-
known fact, that in a rougher colder climate malaria generally
decreases in violence.
As bronchitis and its consequences do not make their enfeebling
influence felt on the constitution before a more mature age is reached
and are not to be compared in this respeet with strong malaria-
infection, 1 believe to have found the chief factor of the present
difference of the two groups of the same tribe as to their consti-
tution and their character in the difference of the occurrence of malaria
as a consequence of the difference in height of the country of the
Bahaus and that of the Kenjas.
Moreover IT must take into account that syphilis is found ina less
violent degree among the Kenjas than among the Bahaus. Among
some Bahau tribes it was so universal, that 1 thought the fact
that only tertiary forms were found could be explained by assuming
exclusively hereditary transmission. Among the Kenjas, however,
syphilis was also met with only in that form, but the cases were
so isolated that we could not possibly ascribe them to hereditary in-
fluences. The eases observed seemed to have a less injurious influence
on the general condition of the Kenjas than on that of the Bahaus.
That this endemic form = of syphilis is so much less common and
that its symptoms are so much less dangerous among the Kenjas
than among the Bahaus is due to a great extent to their stronger
constitution.
If we now take into consideration, that among all these tribes
every family, even that of the chiefs is dependent for its daily
food and = sustenance on the continual labour of all its members,
Which is not the case in more highly civilized societies, we feel, how
great the influence must be which the more or less frequent oecur-
rence of these diseases must have on the prosperity of the tribe.
A striking example of the better conditions of existence offered by
Apo Kajan which is of equal extent to the Upper-Mahakam, com-
pared with the lower river-basins, is furnished by the fact that for
centuries many tribes have been leaving this country for other parts
of the world and that nevertheless the population there is at present
much denser than in other Dajak regions.
( dda)
Instead of 300 to 800 inhabitants as on the Upper-Mahakam, the
villages count there 1500——2500 inhabitants, though they certainly
do not le farther apart. Moreover the general appearance of the
Kenjas makes a much better impression because of their stronger
build and the less frequent occurrence of deforming diseases among
the scantily dressed figures, which is enhanced by the absence of the
cacheetie persons so numerous elsewhere.
The difference between the Bahaus and the Kenjas is even more
marked in their psychical qualities than in their physical indivi-
duality. The enfeebling moments which on the Mahakam affect
them in a so much larger degree seem to have had a strong
degenerating effect on the psyche of the Bahaus.
This is proved by their history: in the beginning of the 19% cen-
tury they made themselves known not only by head hunting but
also by raids undertaken on a larger scale till far into the river-basin
of the Kapoewas, the Barito and the Mahakam, in which regions no tribe
could resist them; at present smaller forays rarely occur, larger expe-
ditions are quite out of the question and in a fight with other tribes
the wounding or death of one man may put his tribe to flight.
The greatest difficulties which confronted the European stranger
in his intercourse with the Bahaus, arose in his continual struggle
with their timidity, fear and suspicion even after a long intercourse
and in the fact that his movements were continually hampered by
the peculiar religious and other convictions of these tribes. The
strong contrast in these respects between them and the Kenjas is
therefore very striking.
After my arrival in Apo Kajan | was at once struck by the fact,
that the 150 men, who had come under their principal chieftain to
assist me by bringing boats and improving roads, were much freer
and noisier in their behaviour than my Bahau escort, that the chief-
tains gave their commands with much greater energy and that they
were also better obeyed. During my stay in their villages this
impression was greatly strengthened by the want of shyness on the
part of the women and children. Remarkable was the contrast
between the behaviour of the young Kenjas and the Bahaus when
I, as | usually did, distributed small presents, such as beads, finger-
rings, needles and pieces of cloth among them. Among the Bahaus
I could quietly keep in my chair, and though occasionally a little
hand may have been stretched out too quickly towards the coveted
object, yet all the little ones waited patiently for their turn and
never became boisterous. When I distributed things among the Bahaus,
the proceedings were quite different: [ had to begin with taking a
firm footing, for boys and girls pressed in upon me with loud shouts
and extended hands; every one was afraid to be behind hand and
they scuffled among each other, to get nearer. It soon proved that
they are less sensible to the bad smells of their fellow-men than the
Bahaus among whom one can sit for hours with impunity even
in large companies; therefore they also prefer to go a long way
round rather than pass a dead body, and who protest to a disagree-
able smell by violent gestures and spitting.
Remarkable also is the greater perseverance of the Kenjas at
labour, which 1 specially observed when making long expeditions
in rowing-boats on the Mahakam in the great heat to which they
were not used. Though they are more used to walking than to rowing
in their highlands, where the roads are better and the rivers smaller
than in the country of the Bahaus, vet they kept on rowing for days
together much more persistently than the latter, and always arrived
earlier.
These few examples already give evidence of a greater vivacity,
less sensibility and also of a greater power of resistance of the ner-
vous system; moreover their mental capacities are far superior.
When telling the Bahaus about some remarkable features of our
society, [1 got accustomed to meet with an absolute incapacity to
imagine these things, which gave rise to disbelief, and induced them,
but often after a long interval, to try and catch me at an untruth.
Among the Kenjas, however, [ soon concluded from their questions,
that they at least tried to imagine railroads and similar inventions,
and that they really understood other things. A very good criterion
is furnished by the explanation of the motion of the sun, the earth
and the stars with the origin of might and day, and the causes of a
solar- and lunar eclipse. Of course the Kenjas also did not immedi-
ately believe that the earth is round and moves, nor that it is not
a monster that eats sun and moon in case of an eclipse, but they
understood at least my explanation.
Of practical use to us was the greater interest and the more
extensive knowledge of their surroundings shown by the Kenjas.
In the course of our topographical survey of the Mahakam and
When inquiring into the names of the principal mountains and rivers
we met among the Bahaus with such utter ignorance, that we were
for a long time convinced they were unwilling to tell them to us. It
proved however later on, that it was not unwillingness on their part,
but that only few among them knew anything about rivers and moun-
tains outside their immediate neighbourhood, and that e.g. high
mountains, Which, though they stood at some distance on the territory
of another tribe, but commanded the landscape, had no name among
them, and that in order to find out its name, we had to apply to
tribes living nearer the mountain. It was, of course, quite out of the
question to avail ourselves of their help in determining the different
places from such a mountain top.
I was therefore greatly struck, when among the Kénjas I ascended
a mountain, for the purpose of getting a survey of their country
and Boei Djalong, the chief of the country, who accompanied me
pointed out all the mountains as far as the horizon with their names,
also those we could verify in the Mahakam territory; he also
indicated the roads leading to the different adjoining countries as
accurately as a European could have done.
Not only we, but also the Bahaus who accompanied me, were
astonished at the knowledge of the history of times long past, which the
Kenjas displayed. It is a wellknown fact that tribes, who cannot write
and who possess a low degree of civilization, lose quickly the memory
of past events, and the knowledge of the Bahaus about their ances-
tors was therefore very inaccurate. Great was therefore the asto-
nishment of Kwing Trang, when the Kenjas told him the traditions
of his own ancestors during the time of their stay in Apo Kajan.
This greater development of their psyche keeps pace with pheno-
mena, which evidence a stronger personality as regards their sur-
roundings. They are braver, which appears clearly from their
way of conducting warfare. The tribes in Borneo are notorious
on account of their headhunting, a method of taking revenge and of
fighting, which is justly looked upon as being rather cunning and
cowardly than brave, as it consists in the laying of ambushes and the
sudden attack of superior forces on but a few individuals. An open fight
is rare among the Bahaus, and as has been said before, if two tribes
are confronted, the death or wounding of one man suffices to put
his party to flight. Quite different is the warfare among the
Kenjas: hand-to-hand fights are frequent, in which chiefly the
sword is used, and in which many are killed before the battle is
‘decided. Though headhunting occurs also among them, yet it recedes
more into the background, and when it occurs more personal
valour is displayed. A few years ago e.g. a young Kenja chieftain,
when performing a war-dance during a visit on the Mahakam, sud-
denly cut off the head of one of the spectators, and took it with
him in his flight. This was certainly treacherous, but it requires courage
to do such a thing in a large gallery with a great many lookers-on.
It is irritating to see, how the Bahaus submit to be illtreated by
the Malays, who live at their expense by deceit, theft and grave-
(199064)
robbery ete. Only rarily do they take revenge on these unwelcome
guests, who live among them either because they gather the forest
products, or because they had to fly from the coasts on account of
crimes. ‘
The Kenja-tribes are less long-suffering: two gangs of Malays, one
consisting of five members from the Mahakam and one of eight from
Sérawak, who tried to live upon them in a similar way, were all
murdered.
As soon as we come in contact with the Kenjas, this bold perso-
nality impresses us favourably. Among the Bahaus we could not
establish for years the frankness of intercourse between them and
ourselves, which was brought about with the Kenjas in as many
months. Only incidentally and by indirect means could I get to know
among the Bahaus what they thought of a plan and what they
intended to do. When alone with one of them I occasionally suc-
ceeded in getting him to express his thoughts freely, because he
had no reason to be afraid of his fellow tribes-men, but they never
quite relinquished their fear and distrust.
In our intercourse with the Kénjas the last trace of suspicion had
soon vanished, and never shall I forget the impression made by their
political meetings on us Europeans, used to the uncertain, hesitating
and insincere behaviour of the Bahaus, even when discussing affairs
of great importance. In the meeting of the Kenjas all the chiefs
present freely expressed their opinions with peculiar ceremonies on
subjects as e.g. whether it was advisable to adhere to the rajah of
Serawak or to the Dutch-Indian government, and the advantages and
disadvantages were openly discussed.
If on account of these peculiar qualities the behaviour of the Kenjas
is noisier, coarser, braver and less sensitive than that of the Bahaus,
it is interesting to see what influence this has had on their society.
Among the Bahaus on the Mahakam we find a number of perfectly
unconnected tribes, in which every individual considers himself quite
independent of all the others, and perfectly free to look upon his
own interest as of chief importance, which renders the chiefs powerless
to exert any influence over their subjects for more general interests
and enterprises. Everybody entertains the greatest fear for unexpected
sudden attacks from far or near, and while in the day-time the men
always go to their rice-fields strongly armed, in the evening they
dare not even be under their houses without a naked sword. Of
course women and children are still more afraid.
Among the Kénjas, on the contrary, we find a somewhat loosely
constructed, but yet connected whole of all the tribes under the
acknowledged supremacy of the tribe of the Oemo Tow and its chief
Boet Djalong. The country is so safe, that the population goes to the
fields only armed with a light spear as support, and that women
unarmed and unaccompanied dared to come and visit me from neigh-
bouring settlements at many hours’ distance through the primitive
forest or in boats.
In this better regulated society the higher moral qualities of the
Kénjas also stood out to advantage. If among the Bahaus the want of
interest in the public welfare was strongly felt, among the Kenjas
this was different. In the character of the Kenja chiefs a sense of
responsibility and disinterestedness came to the front accompanied
With more moral courage and influence on their subjects. When
questions arose as to wages, the payment of which always consisted
in goods chosen by the party concerned, the Bahau chiefs always
retired for fear of quarrels with their people. Among the Kénjas
the chiefs calculated, how much was due to each of their people,
took it home and distributed it there.
When it had been resolved in the political meetings, that repre-
sentatives of several tribes should go with me to the Mahakam, hundreds
of Kenjas prepared to go. Bad omens for the journey, however, caused
more than 400 to draw back, and though the principal chiefs might
have done so too, they only sent back their followers and went on
themselves, because they felt the great importance of carrying on
the negotiations.
Among the Bahaus no chief would easily have gone to look after
the general interests, and certainly not against bad omens.
Also the conduct of their inferiors during the journey was quite
different. Eighty Kenjas succeeded in deriving the required favourable
omens from the flight of birds, the eries of does and the appearance
of certain snakes, and accompanied us. Though from different villages,
they formed one company, having their victuals in common, and when
the Bahaus and ourselves had not enough they shared their stock
with us, which was then soon exhausted. They had, however, full
confidence in my assurance that L would buy them fresh provisions
on the Mahakam.
The different groups in a Bahau escort never voluntarily share
their rice with each other, and when I and my Malays were in
want of rice on the journey, we could only get some from them
at very high prices. At last a young man had the assurance to ask
me three times that exorbitant price for his rice, though as a physician
[ had saved his life, and had treated all of them without asking
any reward.
( 538 )
In spite of the great advantages, which the Bahaus derived from
our stay, L never met with any direct proofs of gratitude; they only
put somewhat greater confidence in me than in other strangers. When
however | left a Kénja tribe after a six days’ stay, the family of the chief
came personally to thank me for everything | had given to them
either by way of exchange, presents or medicine ; the first expres-
sion of gratitude for many years.
All this proves that the Kenjas of Apo Kajan are far superior to the
Bahaus also as regards those traits of character, which are considered as
higher ones among Europeans.
Another striking example of their stronger personality is furnished
by the way, in which thei religious ideas influence their existence.
From their standpoint as agricultural tribes of fairly low deve-
lopment, with whom the influence of nature on their principal
means of subsistence, agriculture, and on their persons in diseases
and disasters is strongly felt, these peoples contemplate their surroundings
with ereat fear. Their thoughts about these surroundings and the
place they occupy in them, which represent their religious conviction,
are not of a very elevated nature.
They think that their lives are ruled by one chief god, whom they
call Tamei Tingei, our high father, and who punishes already on
earth all crimes with adversity, disaster, disease and death. For the
execution of his will he makes use of a host of evil spirits, who
people all nature around.
All calamities and diseases, therefore, even death on the battlefield or
at a confinement, are to these tribes the manifestations of anger of their
chief god with regard to the sufferer, who has incurred this anger by
the conscious or unconscious violation of human usages or divine laws.
When the attempts, to guard themselves against the manifestations
of the anger of their god by observing these laws and usages scrupulously,
proved fruitless, they tried to reach their aim by extending the prescribed
laws to the minutest details, so that they have definite precepts as to
the course to be followed not only in all emergencies of every day
life, but also in agriculture, the chase and fishery.
All these precepts are called pémali, and they render certain actions
in certain cases lali, pantang or taboe.
If the observation of the pemali is to shield them from the evil
spirits, they enjoy the assistance of a whole multitude of good spirits,
indirectly through the mediation of the priests and priestesses or directly
by warning omens, which are communicated by certain birds, snakes
and does, and also by certain events. These omens are very numerous,
and are strictly followed, especially by the Bahaus.
( 539 )
As hawever these pemali and omens have risen, independent of
the true requirements of the existence of these tribes, they have
constantly a disturbing influence. To give an example: the Bahaus,
when growing rice, do not regulate their work according to dry or
wet weather, or to the condition of their fields, but all the families of
a tribe have to conform to what the chieftain does, and he sees that
the necessary religious rites before the special successive agricul-
tural proceedings are duly performed. When the preliminary rites
for the sowing have commenced, no one is any longer allowed to
burn dead wood on his field; if the chief is weeding, every one must
cease his sowing, ete.
In the same way they begin all important enterprises, such as
travelling, the building of a house, ete. not according to the demands
of the moment, but according to whether a bird flies up to the right
or to the left, and whether a doe is heard or not.
Of course, stronger races do not so meekly submit to the galling
restraints of these pemali and omens, as more timid natures. Thad an
opportunity of observing this as a characteristic difference between
Bahaus and Kenjas. It is true that both have the same religion and
that their pemali and omens are essentially the same, but the pemali
are more developed among the Bahaus and go more into details, than
among the Kenjas. Among the former all the adults in a tribe are obliged
to observe the pemali closely; among the Kenjas the priests are specially
charged with this, so that the mass of the people have more liberty.
Among the Bahaus e.g. nobody eats the flesh of the stag; among
the Kenjas the priests only do not take it.
The Kenjas have not introduced the above-mentioned very injurious
precepts for the growth of rice with the same restrictions. It is true
that also among them the chief causes the necessary ceremonies to be
performed, but still, every one is free afterwards to do in his field,
what will prove necessary, and this is of the greatest importance for
the success of the harvest.
The Bahaus cling much more scrupulously to the existing pemali
and omens than the Kénjas. In spite of my having lived for years
among the Bahaus, I was forced, to observe their precepts as serupu-
lously as they themselves did. Only in case of urgent necessity [dared set
out on a journey or receive a patient during the time prohibited by their
laws, and I was therefore as much shut out from the outer world
as they were. Once they made the inhabitants of their own village
on their return from an eight months’ expedition remain in the forest,
starving, rather than violate the lali of their village by admitting
them or bringing them provisions,
( 540 )
When L arrived with my companions among the Kénjas, the prin-
cipal chief and his family happened to be in the condition of lali,
but in order to be able to receive us he quickly had a new house
built in another. place for the priest family in his house, who were
the principal bearers of the pemali. By this means it was permis-
sible for him to receive us in his house.
Later on we proceeded to another village, where the house of the
principal chieftain was also lali, For our reception he divided his
house, which was very long, into two parts by means of a gate,
so that we strangers could not enter the one part. In the other he
received us.
The Kenjas watch the omens before every enterprise as earnestly
as the Bahaus, but as soon as they are in conflict with the require-
ments of the moment, they dare take their own course to a much
greater extent.
I have already mentioned that the Kenja chiefs ventured to
accompany me to the Mahakam in spite of the bad omens of their
birds.
In case of imminent danger, e.g. if an enemy is thought to be
hidden in the neighbourhood, the Kenjas disregard omens.
So we see among the Bahaus the more serupulous observance of a
more developed system of religious usages keep pace with the deterio-
ration of many of their physical and psychical qualities. In these the
Bahau is inferior to the Kenja, which can originally not have been the
case, but which is owing to the change of abode of the Bahaus more
than a hundred years ago, because through this change they were
exposed to the more injurious influences of their new surroundings,
the principal of which is a greater prevalence of malaria.
Mathematics. — Prof. P. H. Scnourr discusses : “ Pe/ations between
diagonals of parallelotopes” with a view to show by a simple example
how it is possible that investigations of more-dimensional figures lead
to new theorems on figures of our ‘hree-dimensional space. This
example relates, as the title indicates, to those figures which continue
in the spaces with more than three dimensions the well-known series
of line-segment, parallelogram, parallelepipedon .... and can there-
fore be called by the name of parallelotopes. Here diagonal always
denotes a line connecting — across the inner part of the enclosed
space — two opposite vertices. /’rsf our attention may be drawn
fo the fact that the number of diagonals of the parallelotope is doubled
line-segment, parallelogram, parallelepipedon,. ..
wigs L.
every time a new dimension is added, whilst the number of constants
determining the figure, though at first larger than the number of
diagonals, increases less strongly than the latter; this is illustrated by
the following little table, where under each other the corresponding
values of the number of the dimensions, the number dof the dia-
gonals and the number y of the determining constants are indicated,
whilst the meaning of A is explained further on.
na nale om (ele Oe a |” LO |t me
d\|2)4| 8 |16/32|64/ 128 | 256/512}... . 221
gela le ol15|21/28| 36) 45 | 55 |... . Anni)
es 6149) 99° 1919 | 466 | WEEER @ 1)
From this is evident in the second place that when constructing
parallelogram and parallelepipedon all diagonals can be used as
determining lines, but that this is not possible for the parallelotope
P, with five and for the following parallelotopes ?,, P?,... with
still more dimensions; and from this ensues in the third place, what
becomes the principal thing here, that between the 16 diagonals of
P, at least one relation must exist and that this number of relations
for P,, P,.... must increase consecutively to 32—21 or 11, 64—28
or 36,... If in the fourth place we wish to trace those relations
and try to do so under the condition that the length ofall the edges
must figure amongst the determining data, then we find that the
sum of the squares of all the diagonals — always equal to the sum of
the squares of all the edges — is known at the same time, and that
the other relations, between the diagonals only, always present them-
selves in the form of homogeneous equations, the number / of which
is indicated above. This includes that already for the parallelotope
P, we come across a relation between the diagonals. This simple
relation can be expressed as follows: If we divide (lig. 2) the eight
vertices of one of the eight parallelepipeda forming the boundary of
Kd
the four-dimensional figure into two groups (4,, A,, A,, A,) and
(B. B, B. B) of non-adjacent vertices, the sum of the squares of the
diagonals terminating in the four points .f is equal to the sum of
the squares of the four remaining ones, terminating in the points £.
And from this ensues, the common centre of the eight diagonals being
indicated by O, the equation
OA,’ ali OA, Ei OA,” a OA? 5 Ob + OB,? a OB, ai ob,
or in words: If we divide the eight angular points of a parallelepipedon
into two groups of four non-adjacent points, the sum of the squares
of the distances from an arbitrary point © to the points of each of
Fig. 3.
the two quadruples is the same. Tf we now suppose in the fifth place
that this point © lies with the parallelepipedon in the same three-
dimensional space, our space I may say, we finally find the following
theorem belonging to our solid geometry :
“If we connect (Fig. 3) an arbitrary point O of space with the
two quadruples of non-adjacent vertices of a parallelepipedon, we
obtain two quadruples of line-segments for which the sum of the
squares has the same value.”
This simple theorem which up till now TI never came across in
any handbook is of course easily proved; we have but to know the
formula for the median line in a triangle. With the help of this
formula we find that, disregarding quantities not depending on the
place of 0, the sum of O A,* and OA,’ can be replaced by two
times O C°,, the sum of O A,’ and A O,? by two times OC;, and
El >
twice the sum of OC), and OC), by four times OM from which
is evident that for the two sums named in the theorem, disregarding
the same quantities not depending on QO, the same value is found,
namely four times OM, ete,
Ad
( 045
Finally this observation: it is not our purpose to emphasize even
in the slightest degree the above-mentioned theorem, up till now acci-
dentally remained unnoticed. Neither have we in view to point out
that for each parallelotope 7, the diagonals and the sides furnish
equal sums of squares and that all possible relations between dia-
gonals mutually can be represented in the above mentioned form.
Whilst referring for this to a paper, to appear shortly in the “Archives
Teyler”, we repeat here, that this short communication was given to
satisfy the wish to show also to non-professional mathematicians by
means of a simple example how the study of polydimensional geo-
metry may lead ta. to the discovery of new theorems of plane or
solid geometry.
Chemistry. — “On the atomic weight of Antimony.’ By Prof.
Ernst Conrn and Mr. Tu. SrRENGERS. (Communicated by Prof,
Well eJuLmws).
(CGommunicated in the meeting of February 28, 1903.)
I. In connection with a physico-chemical study on the nature
of so-called evplosive antimony conducted by one of us (C.) conjointly
with Dr. W. E. Rixeer, the question of the exact atomic weight of
antimony became a very important one.
Notwithstanding a number of investigators ') have attempted to
determine this atomic weight, it is not as yet known with sufficient
certainty.
CLARKE”) sums up his criticism on the determinations made up
to the present with these words: “..... This result, therefore, should
be adopted until new determinations of a more conclusive nature,
have been made.”
1) Berzeuvs, Poaeenp. Annalen 8, | (1826); Kessrer, ibid. 95, 215 (1855);
SCHNEIDER, ibid. 98, 293 (1856); Rose und Weser, 98, 455 (1856); Dexrer, ibid.
100, 363 (1857); Dumas, Annales de chimie et de physique (3), 55, 175 (1859);
Kesster, Pogg. Ann. 113, 145 (1861); Unger, Archiv der Pharmacie 19%, 194 (1871):
Cooke, Proc. Amer. Acad. 5, 13 (1877); Kesster, Ber. deutsche chem. Gesellschaft,
12, 1044 (1879): Scunemer, Ueber das Atomgewicht des Antimons, Berlin 1880.
Journal f. prakt. Chemie (2) 22, 131 (1880); Cooke, Amer. Journ. Sciences and
Arts, May 1880; B. B. 13, 951 (1880); Premrer, Lies. Ann. 209, 161 (1881);
Popper, ibid. 233, 153 (1886); Boxcartz, B.B. 16, 1942 (1883); G. Cl. Friend
and Kpeéar 1, Sarra, Journal Americ. Chemical Soc. 23, 502 (1901).
2) The constants of nature, Smithonian Miscellaneous Collections Part V,
Washington 1897,
Proceedings Royal Acad. Amsterdam. Vol, Y,
5 )
( 544 )
2. Popprr'), under von PrsBats guidance has tried to make a
determination of the atomic weight by an electrical method.
He connected in the same circuit a silver coulometer and a cell
containing a hydrochloric acid solution of antimony trichloride. A
rod of pure antimony (wrapped in linen) suspended in the liquid
constituted the positive electrode, whilst the negative electrode con-
sisted of a weighed platinum wire.
During the electrolysis the electrolyte was kept in continual motion
by means of a stirrer so as to exclude local changes in the concen-
tration of the liquid.
Under these circumstances explosive antimony is deposited on the
negative electrode *). Popper fused the substance formed in a tube
made of hard glass in an atmosphere of nitrogen; in this way
the antimony trichloride present in the metallic mass was expelled.
As soon as all the chloride had volatilized the antimony regulus was
washed first with solution of tartaric acid, then with water, dried
at 120° and weighed. . Additional experiments had proved that the
glass tube did not suffer any alteration in weight on heating and
melting the metal contained therein.
The silver electrode in the coulometer was wrapped in a piece
of linen. After the electrolysis was completed, the silver which had
deposited in the platinum dishes employed was boiled and washed
with water until this no longer gave a reaction with hydrochloric
acid and it was then dried at 120°.
Porper’s results obtained in the electrolysis of solutions containing
respectively 7 and 22 per cent of SbCl, are given in the subjoined
table. We have, however, recalculated the data as Poppsr still uses
the atomic weight 107.66 for silver whereas more accurate investiga-
tions have shown this to be 107.95.
In a second series of experiments in which a few more improve-
ments had been made as regards the insulation of the silver coulo-
meter, Poreprr found for 7 per cent solutions as equivalent weight
the value 40.33, therefore as atomic weight the value 120.99.
As he could not discover any sources of error in his process and
still believed in the accuracy of the results obtained by Cooke, who,
by purely chemical means, had found the atomic weight of antimony
to be 119.9 he concludes his paper with the words: “Sollte nicht
die Entdeckung des Elements “Germanium” durch Winkrer den
1) Compare 1.
?) Such was the case with solutions containing 22 per cent of Sb Cls. In solu-
tions containing 7 per cent. Popper obtained crystalline non-explosive antimony.
I will fully refer to this particularity later on in my paper with Dr, Ringer. (CGOHEN.)
( 545 )
: ae Weight of the metal Electrolytic | Atomic
Grams of deposited in the same time quivalent reloht
Sb Cl. in 400 (deposited same time — equivalen weight.
Gr ; circuit in the same time.
rams ; ; zi
ED TE EREN of Antimony (Silver
| Antimony | Silver == 107.93)
7 1.4788 3.9655 402% | 190.75
yi 2,0074 5.38649 40.39 Th Temes PV
Zi | he 18903. |) 44 A847 | 10.45 | 121.99
i 4.1885 44.4847 | 1042 121.26
7 5.6869 15.1786 10.43 | 491 .29
7 | 5.6994 | 45.4786 LO. AG 121.38
2 | 1.4856 3.9655 40.43 121,29
22, | 20120 5. 3649 A) 47 AOA AA
29 | 3.8882 | 10.3740 4. AD 191.35
22, | 3.8903 10.3740 AO AT 424.44
22 | SO ENO =" | 14.3868 40.48 | 12 44
22, 4 W752 11
3868 40.52 | 121.56
Wee andeuten, auf welchem die Lösung des vorliegenden Rätsels zu
te) (a! oo
suchen sei?”
3. We have not only repeated the research of Porper but also
extended the same by using hydrochloric acid solutions of SbCI,,
whose concentration varied between 2.3 and 83.3 percents of SbCI, by
weight.
It was necessary to pay particular attention to the purity of the
materials employed. The antimony trichloride was obtained from
Merck; 20 grams were dissolved in solution of pure tartaric acid
and then digested on the waterbath for some hours with excess of
clear sodium sulphide. The liquid remained perfectly clear *).
Some kilos of this antimony chloride were precipitated with sodium
carbonate free from foreign metals, the precipitated Sb, O, was washed,
dried and reduced to metal by fusion with pure potassium cyanide
in a Perror’s furnace. The crucibles used were previously tested to
see whether they would yield any foreign metal to potassium cyanide
but we could not prove the presence of any impurity in the melt.
1) As commercial antimony generally contains lead whose atomie weight exceeds
that of antimony it was absolutely necessary to prevent the possibility of any lead
being present in the materials employed,
ik
vi
ee
( 546 )
The fused metallic antimony was poured into cylinders of asbestos
paper tied round with copper wire: the rods of antimony thus formed
were cleansed with hydrochloric acid and washed.
sy way of control we dissolved a piece weighing 20 grams in
pure strong nitric acid with addition of 75 grams of crystals of
tartaric acid. The clear acid solution so obtained was rendered alkaline
by adding small lumps of sodium hydroxide prepared from metallic
sodium (the lye was free from foreign metals) and digested on the
waterbath with a clear solution of sodium sulphide but gave no
precipitate.
The solutions were prepared by weighing the pure antimony
trichloride roughly and dissolving the same in pure hydrochloric acid
of 1.12 sp. gr. at 15°. The exact composition of the solutions was
determined by electrolysis of the liquid in presence of sodium sul-
phide according to NeuMANN’s directions ').
4. In each experiment two silver coulometers were put into the
circuit; one in front and one behind the series of antimony solutions
which took part in the electrolysis. The coulometers consisted of
200 ce. platinum dishes with rough inner surfaces. We will not
omit to point out that such dishes are particularly suited for coulo-
metric determinations as it is possible to precipitate in them a large
amount of silver with little chance of any traces being detached on
washing the precipitates ©). The amount of silver deposited in our
experiments varied from 25 to 50 grams whilst when using the smooth
dishes usually employed it is difficult to handle a few grams without loss.
As electrolyte we used a LO or 15 per cent neutral solution of
silver nitrate; no difference was noticed with these solutions. The
positive silver plates were cast of silver which we received from
Dr. Horrsema, Comptroller-general at the local Government Mint.
On analysis, we could not trace foreign metals in LOO grams of this
silver. The plates were 6.5 ¢.m. in diameter and 4 min. thick.
They were surrounded by a covering of filter paper (SCHLEICHER and
Seneur). Each silver plate was suspended by a thick platinum wire.
The coulometer dishes after being filled with the silver solution were
covered with a glass plate with a hole in the centre through which
a platinum wire was introduced.
2) Analytical Electrolysis of Metals, Halle 1897, S. 145.
Here, we provisionally took the atomic weight of antimony to be 120; as will be
seen from what follows, the uncertainty of the atomic weight is of no consequence here.
2) Compare Kanre. Wiep. Ann. 67, N.F. 1 (1899); Ricnarps, Coins and Hemrop,
Proc. American Acad. of Arts and Sciences XXXV, 123 (1899), Ricwarps and
Hemrop, Zeitschr. f. physikalische Chemie 41, 302 (1902),
(547)
Great care was bestowed on the insulation of all the apparatus.
The conducting wires were strongly insulated and were, as far as
possible, in contact with air only. Each platinum dish was placed
on a copper plate which stood on a glass plate; the latter was
carried by porcelain insulators which acted as feet.
For a rough orientation a technical ammeter was included in the
circuit; the current was taken from 1 to 3 storage cells.
5. The antimony solutions which were subjected to electrolysis
were contained in spacious beakers (1 litre) (B in fig. 1) in which
constant stirring could take place by means of Wirt’s centrifugal
stirrers. A Herricr hot-air motor kept all the stirrers in motion.
The rods of antimony which served as positive electrodes were sur-
rounded by a piece of linen which was fixed to the rod with platinum
wire, or by glass tubes closed at the lower end containing a large
number of not too small perforations (0, O, 0...) (8 or 4 m.m.).
The object of surrounding the rods was to prevent any loose particles
of antimony from getting into the liquid.
As negative electrodes we used platinum wires (/?) about 10 em.
in length and 0.8—0.4 mm. thick; they were provided at the upper
end with the capillar glass pieces (C), on which a number was
engraved.
Both antimony rods and platinum wires were attached to copper
binding screws which moved along glass standards (GS). In order to
prevent contamination of the liquids by contact with copper, a piece
of platinum wire (1) was placed between the binding screws and
the rods of antimony or platinum suspended thereby.
6. The experiments were now conducted as follows: After the
platinum wires had been weighed they were put in their places;
the silver coulometers were connected up and the current closed.
At the commencement the strength of the current may only amount
to a few hundredths of an ampere; if this is exceeded, evolution of
hydrogen instead of separation of antimony takes place. When the
precipitate on the platinum wires had reached a certain quantity,
when in other words, the surface had become enlarged the strength
of the current was increased and gradually raised to about 0.3 ampere.
At the end of the electrolyses the rods were rinsed with a 12 per
cent solution of tartaric acid’), then washed with water, alcohol and
ether and dried over sulphuric acid in a desiccator.
4) By a special experiment we had convinced ourselves that this did not cause
any perceptible diminution in weight.
( 548 )
To determine the amount of antimony separated by the current
the following method was adopted *).
The rod was placed in a tube of hard Jena glass closed at one
end (length of the tube 30 em, diameter 1 em). This tube had
been previously cleaned, strongly heated in a current of dry air
(dried over H, SO, and P,O) and then weighed. The antimony
rod was now weighed and by way of control the tube and rod
were again weighed together.
The air from the tube was now expelled by means of a continual
stream of carbon dioxide which had been dried over sulphuric acid
and phosphoric anhydride. The tube (explosion-tube) was then closed
with a properly fitting india-rubber cork and put into a metal cooling
vessel made of composition tube in the manner represented in fig. 2.
This tube was connected with the water tap.
If now the explosion tube is shaken for a moment the explosive anti-
mony explodes. The tube is then strongly heated with a triple burner
on the spot containing the rod ; the Sb Cl, evolved condenses on the cold
wall of the tube to a clear white mass. The heating is continued
until the antimony is perfectly fused and this is then allowed to cool
slowly. The tube is then opened, the SbCl, is removed by rinsing
with a mixture of alcohol and ether (3:1) the tube is then rinsed
with ether and dried by heating in a current of dry air as described
above.
The tube with the antimony regulus is now weighed.
A previous experiment had proved that the explosion tube suffers
no alteration in weight by the heating and subsequent treatment.
It was found for instance that an explosion tube weighed 29.6614
gram before the experiment and 29.6610 gram after the experiment
the contents having been removed by means of nitric and tartaric
acids.
By way of illustration one of the experiments is reproduced in
detail whilst the results of the other measurements are united in
a table.
Electrolysis of a 15.6 proc. SbCl, solution.
Silver coulometer N°. 1.
weight of platinum dish + silver 73.1920 grams
" " " 36.7310 fe
weight of silver 36.4610 grams
*) Further particulars about this method will be found in the paper of Coney
and Dr, Ringer.
oP Bet SAO Nee
ERD birtd
AVISIW AAT IMA
PAO ALT IANA Dg
ANS
f
g rH .
| i
| )
\
8
A
4 1
a
i
Bo
‘ ;
4
.
‘7 |
ERNST COHEN and Th. STRENGERS. On the atomic weight of Antimony.”
Proceedings Royal Acad, Amsterdam, Vol. V
( 549 )
Silver coulometer N°. 2.
weight of platinum dish + silver 71.4580 grams
" I" I 34.9902
weight of silver 36.4628 grams
weight of explosiontube + regulus + platinum wire 55.0281 grams
" " 41.0780
weight of regulus + platinum wire 13.9501 grams
weight of platinum wire 0.2696 — »
weight of regulus 13.6805 grams
From this result the equivalent weight of the antimony is calculated
as follows:
107.93
ES 49 6805 — 40.49.
36.4608 °° 19-6805
The results so obtained are collected in the following table. (p. 550).
From this table we see that the atomic weight obtained increases
with the concentration of the Sb Cl, solutions and varies between
120.87 and 121.89 within the concentrations 2.3 and 83.3 per cent.
From this it is quite plain that we cannot arrive at the determination
of the atomic weight of antimony by the electrolysis of solutions of
antimony trichloride and that the values found by Popprr, to which
in the calculation of the atomic weight is attached the same value as
to those of SCHNEIDER, COOKE and BoNnGArtz'), are quite accidental, being
dependent on the concentration of the solutions employed.
It further appears from the above that unknown electrolytic or
chemical changes play a part here which require further investigation
and which may be expected to add to our knowledge of the formation
and composition of the remarkable explosive antimony.
We hope, shortly, to investigate these changes.
1) Compare Osrwarp. Lehrbuch der allgemeinen Chemie I, 53 (1891).
)
z3 a katy Se * es ae >
ee en 8 pes
(5505) = WEET
Er
Grams of | Weight of Weight of the silver in the. nivalis | Atomic
Sb Cl, in 100, the antimony | Coulometer in grams. | weight | weight
grams regulus in | of the of the
solution. | grams. | 04. | No 9. Net | Nea | Antimony. ne e
23 | 16.8747 | 45-2069 45-2019 108 |
| | | 120.87
9.3 | 414.5014 39.C805 39.0816 | 4029 |
—* Hs Sige ae EREA
3.4 18.36 18.7961 Ee 50.3791 50.3860 40.26 190.781)
—|——— AS eed =) Soe
5.0 | 416.9175 | 45.2019 4. 2069 40 38
| | 421.47
5.0 | 14.6298 | 30.0805 39.0816 40,39
En | nd _— rn
3 | | |
5.3 | 48.8627 | 50.3791 50.3860 40,40:
5.3 | 12.6206 | 33.7224 33.7203 40.38 | 124.90
5.3 | 45.0054 | 40.0810 | 40.0794 | 40. |
a KE ke EE
144 | 43129 | 3 9633 | 34.9680 | 40.29 |
14.4 | 48.8881 50.3791 50. 3860 40.46 124A
14.4 | 12.6470 33.7994 33.7208 40.47
a IRE EEE EN
15:6 | 9.5049 | 25.3M6 2 3407 40.48
/
15.6 13.6805 36.4640 36.4698 | 40 49 121.47
„45.6 | 13.6803 | 36 4610 364628 | 40.49
18.8 13.5984 | 36.2088 36.209 40.53
| | 121.59
18.8 | 43.8618 | 36.9531 36.9566 | 40 53
| 3 :
52.2 | 44.6212 | 38.9046 38 9098 40.56
| | | 121.71
522 | “45.0689 | 40-0810 400704 | 40.58”
55.7 | 413.7192 36.4610 36.4628 40.58 8
| 194219
55.7 | 44.7014 39.0805 39.0816 40.59
83.3. | 43.6305 36.2088 36 209% 40.63
83.3 | 14.9494 — | 39.6998 40.61 521,59
83.3 | 13.8998 36.9531 | 36 „9566 40.64
|
'
1) This sent is decidedly loo low, as a trace of antimony got ‘ost during the
washing.
(551)
Chemistry. — “The conductive power of hydrazine and of substances
dissolved therein.” By Prof. Erxst Cone and Prof. C. A. Losry
DE BRUYN. (Communicated by Prof. C. A. Lopry pr Bruyy).
(Communicated in the meeting of February 28, 1903).
The investigation of the conductive power of non-aqueous solutions
has of late years been known to have an increasing significance and
particularly so on account of the important result that the laws and
rules applying to aqueous solutions do not appear to apply in the
case of other solvents. Apart from methyl and ethyl aleohol (the
constitution of which does not differ much from the type water)
sulphurdioxide, ammonia (NH,), formic acid, hydroeyanie acid, pyri-
dine, some nitriles, hydrogen peroxide and others have been studied
as such’). |
The physical properties of free hydrazine ®) N,H, although still
incompletely known, might lead us to suppose that this liquid would
manifest a strong ionising power. In the first place, like water, the
lower alcohols and acids, it possesses an abnormally high boiling
point. This is obvious if this point (about 113° at 760 m.m.) is
compared with of ammonia (— 34°), difference of 147°, and if one
considers that the difference between the boiling pomts of CH, and
C,H, is decidedly less (80°); this fact as well as the high critical
temperature of (at least) 880° point to an association of the NH,
molecules. The solubility of several alkali salts in hydrazine has also
been shown to be very considerable although less than in water.
Another existing observation points to the fact that hydrazine may,
like ammonie take the place of water of crystallisation *). And finally,
the dielectric constant of hydrazine, which Prof. P. Drepr (Giessen)
had the kindness to determine at our request, has turned out to be
rather high, namely, 53 at 22°. It is now a known fact that there
exists a certain although sometimes remote parallelism between the
dissociating power of a liquid on the one hand and the association
of its molecules, the solvent power and the dielectric constant on
the other hand. As according to the experiments of FRANKLIN and
Kraus and of Capy liquefied ammonia is an ionising solvent, this
might also be expected in the case of hydrazine. From the experiments’)
presently to be described it will be seen that such is the case.
1) Compare Joxes, Am. Ch. J. 25. 232. Kantenpere, J. Phys. Chem. 5. 339.
Wapex and Cenrverszwer, Z. phys. Ch. 39. 514, 557 e. by J. Traupe, Chem.
Zt. 26. 1071. (1902).
2) Lopry pe Bruyn, Recueil des Travaux Chimiques des Pays-Bas. 15. 174.
3) Ibid. 179.
3 A: sos ee Wan: Rr at : i476
4) Some preliminary determinations were already m ide in 1896, 1. e. 179,
Let us first observe that the dielectric constant of hydrazine is
only surpassed by those of five other liquids and is decidedly larger
than that of NH,. We have namely:
hydroeyanie acid = 95 acetonitrile 40
hydrogen peroxide 93 nitrobenzene 36.5
water 82 methylaleohol 32.5
formic acid 57 ammonia 22 (at —34°)
nitromethane 56.5 pyridin 20
hydrazine 53
The peculiar properties of hydrazine (its very hygroscopic nature
and liability to oxidation by atmospheric oxygen) demand great
precautions in its preparation. It took place, according to the method
already deseribed *), by treatment of the so-called hydrate with
barium oxide and distillation in an atmosphere of hydrogen.
The heating with barium oxide and subsequent distillation were
thrice repeated and the base was finally collected in six different
fractions in pipette-shaped tubes in the manner previously described.
During the last distillation the base had been only in contact with
purified, dry hydrogen.
Apart from the properties of hydrazine mentioned, the high cost
of the material was a factor which in our experiments had to be
taken into account. A special apparatus (see illustration) was, therefore
constructed which admitted of working with a small quantity of the base
(about 5.5 ee.) and through
Which pure, dry nitrogen *)
could be passed, whilst
through the exit tube for
the gas the weighed portions
of the different salts could
be introduced.
On account of the some-
What limited quantity of
the base at disposal we
could not, as is customary
in the determination of the
conductive power of solu-
tions, start with the largest
concentration and succes-
sively dilute this by adding
the solvent, but the reverse
was to be done.
1) alsem
*) We take the opportunity to call attention to the fact that platinised electrodes
(oane
Weighed quantities of a salt were, therefore, successively dissolved;
on account of the unavoidable errors in weighing it was difficult to
experiment with very dilute solutions of accurately known composition,
but by evaporating a measured quantity of a very dilute aqueous
solution in a pipette which was then rinsed with the hydrazine we
have reached for KCl a concentration of V = + 900.
In view of the above we wish to remark generally that our
results cannot lay claim to very great accuracy, although they quite
suffice even from a quantitative point of view, to prove that free
hydrazine has a strong ionising power comparable with that of water.
We have worked with solutions of H,O, KCl, KBr, and KJ and
made a few experiments with a solution of Na and H,N in N, H,.
In the first experiment the six different fractions of the hydrazine
had not been kept separate; as we had previously found?) that the
meltingpoints of the second and fourth fractions were the same we
thought we might conelude that at least the middle fractions were
similar. It then appeared, however, that the conductive power of
the bases taken from different tubes often showed appreciable
differences.
For this reason a second preparation was made and the hydrazine
of each fraction (each time collected in several tubes) was examined
separately as to its conductive power. From the following figures it
appears that the conductive power gradually decreases and is smallest
for the last fraction.
fraction n°. 2 Wat AS tAO
3 12.8 „
4 12,
5 10.0 ,
6 6:52
We do not know what impurity (in any case very small) is the
cause of this; possibly we are dealing here with a minute quantity
of ammonia which is present in largest amount in the first fractions
The smallest conductive power observed by us in any fraction
prepared previously was 4.10.
Our experiments have been mostly conducted with fraction N°. 6
of the above-mentioned quantity.
dried in the air may occlude such an appreciable amount of oxygen that this
must make its influence felt when working with readily oxidisable liquids. Such
appeared to be the case when filling our apparatus with hydrogen when a spont-
aneous deposit of visible drops of water was formed.
*) Prepared from air and phosphorus.
a Cea De 17.
(BDE
The apparatus was put into a glass vessel containing paraffin oil
which was placed in an Ostwald thermostat; the temperature was 259,
Hydrazine and water (¢ = 25°)
5e fraction. Gono: Ge fraction. G = 4.249.
N. X N x
0 10.0 .40—° 0 6.04.10 —
0.93 9.79 » 41.1 AET Wie
7.94 8.95 » 49.5 45 »
Ay TOS) 58.4 AO)
{dre Neve) 69.5 4.55 »
d5:6 6/04» oO elas gree
82.4 6.09 » 124.7 ees D
101.8 7.85 »
156 10751 >
Daa leen es
Potassiumehloride.
== ee ees
NH,
G (as V Kx a\ 5)
5.369 0,0272 14.7 0D 402.9
) 0,0157 254 4.2» 103.7
» 0,0080 10.7 DF B 109.3
[5.4 0,00045 + 900 143.407 st A07 ZN
Potassiumbromide.
LD x — 6,5.10—°
Nol,
G g V % A
5.350 0,0617 10.3 10.05.103 103.8
» 0,0329 19.3 5.66 » 109.2
) 0,021% 29.9 oth 142,7
» 0,0105 60.7 1.965 » 118.9
1) A could not be determined, so that the degree of dissociation of the salts
is not known. The a’s, however, agree in magnitude with those of the aqueous
solutions of the same salts.
2) This value, obtained in the manner described on p. 553, is as a matter of
fact uncertain. It proves that a very minute quantity of a dissolved substance may
increase the conductive power considerably.
( 500 )
Potassiumiodide.
p25. x= 5,6.10 —°
Na Hi
G g Vv % A
5.600 0,072 12.9 8.19.10 9 105.6
» 0,049 18.8 oe 108.8
» 0,0280 830 3.40 » 112.8
> 0,0129 72 1.64 » 18
G = weight of hydrazine in grams. A = aequivalent conductive power.
g = weight of the salt in grams. V = number of Liters, in which is dis-
; solved one mol. of the substance.
x = specifie conductive power « for the water used = 0,28.10~°
Without committing a grave error the sp. gr. of hydrazine at 25° may be taken
to) te) to) A,
as 1.00.
It is already known that sodium dissolves in hydrazine with
evolution of hydrogen ). Pure hydrazine (9, 1.102) was introduced
into the apparatus and two particles of sodium (weighing about 10
milligrams) were added.
The metal slowly dissolved with evolution of hydrogen and after
solution was complete the specific conductive power appeared to have
increased to 131.10.
It seemed very peculiar that a powerful evolution of gas still went
on after the sodium had dissolved, showing a decomposition of the
hydrazine with formation of ammonia. This decomposition ceased as
soon as the liquid was poured out of the apparatus; apparently it
only takes place by contact with the platinum black present on the
electrodes and is, therefore, quite comparable to the spontaneous
decomposition of an alkaline solution of hydrogen peroxide exposed
to the same influence.
Finally a few experiments were made with a solution of ammonia
in hydrazine. The solubility of that gas at the ordinary temperature
did not seem to be large; about 4.8 per cent of N H, is present in
the saturated solution. After a few bubbles of ammonia had been
absorbed in the hydrazine (with * = 5.2.10~) the conductive power
appeared to be but slightly increased (% = 6.9.10-5); this was also
still the case after the liquid had been saturated with ammonia (about
1) Le. p. 183. Dr. J. W. Drro has found that an atom of hydrogen is replaced
here; the NaH, N, formed is a substance which on being exposed to the air
causes a violent spontaneous explosion,
( 556 )
220 “mer; Of H‚N in 45920: prof ON Av aes a ee
is known that on dissolving ammonia in water the conductive power
is but very slightly increased.
From the foregoing we may draw the conclusion that, with regard
to its ionising power, hydrazine is comparable to water.
As regards mixtures of hydrazine and water it may be observed that
on addition of water the conductive power at first decreases reaching
a minimum with a mixture of 60 mols. of H,O to 100 mols. NH,
(about 25 per cent of H,O and 75 per cent of N,H,) then increasing
again. This minimum, therefore, does not correspond with the com-
position N,H, + H,O, or the so-called hydrate.
Utrecht— Amsterdam, January 1905.
Chemistry. — “The velocity of transformation of tribromophenol-
bromine into tetrabromophenol.” By Mr. A. H. J. Berzer *). (4t
Communication on intramolecular rearrangement, presented by
Prof. C. A. Lospry DE Bruyn).
(Communicated in the meeting of February 28, 1903).
JENEDIKT ?) found in 1879 that tribromophenol brought into contact
with bromine water is capable of exchanging a fourth hydrogen
atom for bromine with formation of a tetrabromo-derivative. The
study of this substance led him to the conclusion that one Br-atom
occupies a peculiar position in the molecule; it is, in fact, the cause
of a certain number of reactions in which that Br-atom is readily
displaced. As moreover the new substance seemed to have lost
the character of a phenol as shown by its insolubility in alkalis,
BENEDIKT gave it the formula C,H, Br,.OBr and the name of tribro-
mophenolbromine. Brenepixr also noticed that, when melted under
sulphuric acid, it passes into the already known isomeric tetrabromo-
phenol, a true phenol which no longer contains a loosely bound
Br-atom.
In his first publication BexepiKT looked upon this transformation
into tetrabromophenol not as an intramolecular displacement of atoms
but as a process taking place between two mol.s of tribomophenol-
bromine; in a later communication however he does so, without
Stating any reasons.
When a few years ago, Jon. Tuimre®) found that BeNEDIKT's
1) Proc. 31 May, 28 June and 25 Oct. 1902.
2) Annalen 199. 127, Monatshefte 1. 361,
5) Ber. 33. 673 (1900),
tribromophenolbromine by means of leadacetate passed into 2.6
dibromoquinone, with substitution of 2 Br by O, he looked upon it
as a dibromoquinone in which one O is replaced by 2 Br | therefore
as a tetrabromoketodihydrobenzene
; he is of opinion that its forma-
tion from tribromophenol can only be explained by assuming that
the latter can react in the tautomeric form of a p-quinoid ketone
as follows:
i Ne AN
a Ve H BEN ve _—>- aN ee
In a paper which appeared a year ago, Kasten’) has come to the
same conclusion as THIELE, as the result of investigations conducted
conjointly with LORVENHART, Rosa SprijnR and Ginpurt. Kasrun has
also established the fact that it is only sulphurie acid which, even at
the ordinary temperature, is capable of causing the transformation
into tetrabromophenol; a dozen other reagents gave a negative result.
In order to explain this specific action of sulphuric acid, Kasrrn
assumes the intermediate formation of an additive product of this
acid with tribromophenolbromine ; this at first would lose HBr, which
would then again react at once with reformation of sulphuric acid
and cause the migration of Br into the benzene nucleus. This inter-
pretation of the transformation requires the appearance of two non-
isolated and therefore hypothetical intermediate products and of three
successive reactions.
Mr. Brerzer has now studied the velocity of transformation of tri-
bromophenolbromine. The circumstance that the first substance readily
parts with an atom of bromine would lead to expect that its
quantitative estimation would be possible in the presence of tetra-
bromophenol. It now appeared that the elimination of free iodine
from hydriodie acid, also observed by Kasrrn, takes place quantita-
tively; tribromophenolbromine may therefore be estimated in the
presence of tetrabromophenol by titration.
At the commencement of the investigation the behaviour of the
solid substance towards sulphuric acid was ascertained. If the crystals
are covered with the ordinary 96 per cent acid it is noticed that
they lose their yellow colour and become opaque and white; of
solution in the acid taking place nothing can be perceived even by
the aid of the microscope. No formation of striae can be observed;
the whole phenomenon seems to be enacted within the solid substance
commencing on the surface where the substance is in contact with
( 558 )
the acid. If the velocity of transformation is measured under these
circumstances it is no matter for surprise first/y that no reaction
constant is found, second/y that the reaction coefficient constantly
diminishes as the inner parts of the crystals get more and more
inaccessible to the acid. As expected beforehand the experiment has
shown that very small crystals or the powdered substance are, on
account of the larger free surface, more rapidly transformed than
the larger crystals. The continuation of the research will show that
the transformation is monomolecular and must, therefore, be taken as
a real displacement of atoms (perhaps of two displacements one of
which takes place with very great velocity). It is a remarkable fact
that there should take place inside the molecule of a solid substance
a displacement of atoms, an internal change of equilibrium leaving
the molecule intact, by mere contact with sulphuric acid, without
there being any question of solution.
Although we could not expect to get reaction-constants for a
heterogenous mixture of a solid substance and sulphuric acid, this
should be duly the case when we worked in a solvent. Here however
a difficulty occurred which at first threatened to put a stop to the
further prosecution of the research. A solvent was wanted which
had no action either on tribromophenolbromine or sulphuric acid.
Acetic acid scarcely dissolved the first substance and chloroform
appeared to dissolve only traces of 96 per cent sulphuric acid. It
was finally decided to choose the latter solvent and to thoroughly
shake the solution with sulphuric acid‘). The experiment proved
that on applying the formula of the first order, constant reaction-
coefficients made their appearance. A first result was thus obtained;
the transformation does not proceed bimolecularly.
Mr. Brizer has now studied the influence of the concentration of
the sulphurie acid and the temperature.
In most of the experiments, 3 grams of the substance were
dissolved in 150 ce. of pure chloroform *), the solution strongly
shaken with the acid and after definite times 25 cc. were titrated.
Use has been made of:
a. H,SO, with about 36°/, SO,, 6. H,SO, with about 1°/, 5O,
c. equal volumes of 6 and d. d. 96 per cent H,SO,.
In the following tables the results obtained are not given in the
form of reaction-constants, but to make the matter more plain, the
1) A uniform emulsion is very soon obtained.
2) The chloroform was agitated a few times with water, dried over calcium-
chloride, shaken with strong sulphuric acid and redistilled; it was preserved in
the dark,
( 559 )
times (T) are mentioned at which the transformation has proceeded
halfway.
A. Influence of the Concentration of Sulphurie Acid
t = 25°. 0,5 ec. sulphurie acid.
acid a | b | c d
Te | 9 min. 49 sec. | 2 hours 57 m. | 13 h. 40.5 m very slowly
= 25°. 1 ec. sulphuric acid.
acid a b
ig too rapid 25 m. 44 s,
% d
2h. 38.5 m. Zh. 45 m.
B. Influence of the Quantity of Sulphurie Acid
= a vac van
1 ec. | 0.6 ce.
ree
too rapid too rapid 5
0.5 ce. | 0.3 cc.
5 m. 49 s, oh. Our:
14 acid Ty
2 ce. pre ) | 1.25 ec. 1 ce. 0.5 ce. | 0.25 ce. 2)
T. | too rapid | too rapid | 25 m. 44 s. | 55 m. 20s
de 2E D7 mA. |
2. ACG
1.5 ec. 1 ce. 0.5 cc.
Ii de he oem. Ei SH So. Am. drh. 40:5, m:
Dh 38m,
C. Influence of the Temperature.
Acid a.
0560. 0.3 ec. | 0.2 ce.
T. at t = 35° eames 6m. 12.58) 4 99| 32m. Bs
» 25° 5 m. 49 .) + 10 (9 hi, Sm: | times ——
» 159 [58 m. 45 s. J times |
Acid b.
1 cc. 0.5 ee.
DA eone — 33. m, 56 s. |
» 5 (B m. Ms.) 49 |2h. 57 m,) times
» 1500 doch 165 m.) times
) Transformation almost completed after 20 minutes.
*) Not yet decomposed to the extent of 15 °/, after 21 hours.
38
Proceedings Royal Acad. Amsterdam. Vol. V
( 560 )
Acid ¢, Acid d.
LNG, A ce.
Ts bh 58 m. 10 s. 1 h- 53:6 m.
» 25° 2 h. 35 m. 7h. 45 m.
» 15 3 h. 27 m. |
From the results obtained it appears in the first place that the
transformation is a monomolecular one and, taking into consideration
the circumstances under which it takes place, must be considered
as an intramolecular rearrangement of atoms.
To this conclusion the following observations may be added.
A. The influence of the concentration of the acid, the other circum-
stances being the same, is very great. The course of the figures leads
to the idea that the active agent, the catalyser is not H,SO, but SO,
Experiments were therefore made to ascertain how chloroform
behaves towards the four acids employed. Whilst from ordinary
96 °/, acid (d) but very minute traces were dissolved, this amount
was perceptibly larger with acid c and still larger with acid 4,
whilst acid « appeared to yield very much SO, to the chloroform *).
The idea that SO, is the catalysing substance is consequently
confirmed. The rapid decrease of the concentration of the acid is
also in agreement with this idea; this velocity is therefore as it
were a measure of the concentration of the SO, still present in a
sulphuric acid of given concentration.
B. It is now also very plain that the quantity of the acid must
have a great influence. As shown by its behaviour to acid a, chloro-
form may dissolve considerable quantities of SO,. On shaking with
sulphuric acid of a lesser concentration, the amount of SO, which
passes into the chloroform will consequently depend on the quantity
of the acid. The equilibrium for the SO, which distributes itself
between the chloroform and the sulphuric acid changes, as is known,
with the relative quantities of the two liquids and with the
temperature.
As a consequence of the view taken here, it must be assumed
that ordinary 96 °/, sulphuric acid still contains a minute quantity,
of free SO,-molecules. This view is admissible *) since it is known
1) The ratio in which different acids yield SO3 to chloroform will be further
determined.
2) KyretscH, in his well-known research on sulphuric acid, has shown that an
acid of 97—98 0/, absorbs SO; much more readily than acids of smaller or
larger concentration. From the results obtained up to the present it does not
appear that, in the transformation of tribromophenolbromine, the 98 °/, acid c
behaves in a particular manner; an extension of the research will elucidate this
question,
that 100 °/, sulphuric acid contains a little SO, and consequently
free H,O.
C. The temperature-coefficient for sulphuric acid a is particularly
large and increases rapidly with the temperature; for acid 5 it is
decidedly smaller and very small for the 96 °/, acid. It will be
readily understood that in the case of the acid « the dissociation of
H,SO, into SO, and H,O and the distribution of SO, between chloro-
form and sulphuric acid are modified in a large degree when a
change of temperature takes place.
The rearrangement of atoms may now be represented by the following
schemes which respectively correspond with Benuprkr’s formula (1)
and Trrmere’s formula (ID):
LEE Gro Br Be br
aC I Som = ng on pals mu Do
Hire Br Ho, Br HBr
Against the acceptance of Turenn’s formule (IL) it may be pointed
out that in the displacement a Br atom must first remove an H
atom; this then proceeds to the O atom with migration of the double
bonds, a rather intricate process practically consisting of three succeeding
displacements. As it has been proved that the reaction is one of
the first order, two of those displacements must take place with
immeasurable velocity. Against BeNepiKT’s formula (I) may be remarked
that, according to experience, the meta-position is hardly ever selected
in the migration of an atom or of groups from the side chain into
the nucleus.
The hypothesis proposed by Kasrrp, which assumes the inter-
mediate formation and decomposition of non-isolated products, is not
at all supported by the observations communicated here.
The investigation as to the transformation of tribromophenolbromine
will be completed and also extended to other analogous compounds.
Geology. — “Some New Under-Cambrian Erratic-blocks from the
Dutch Diluvium?. By J. H. Bonnema. (Communicated by
Biota. VW. Morr).
I. In the Geological-Mineralogic Institute at Groningen is found
a piece of sandstone which a few years ago I found at Odoorn, in
the province of Drente. With muriatic acid applied to it, there is
no effervescence; consequently it does not contain any calcium-
carbonate. The grains of sand are small, but with a magnifying
glass they may be well distinguished. They are peculiarly lustrous.
The colour of this erratic-block is chiefly dark-grey. Im some
38*
places it is brownish. Moreover there are light-grey worm-shaped
parts, varying in length and having a breadth of about 6 millimetres.
This erratic-block is most probably a piece of Under-Cambrian sand-
stone, in which is found one of those problematical things that are
sometimes called worm-passages. As they are not straight and do not
run parallel to each other, they are different from those described as
Scolithus linearis Hall. They show more resemblance with those tubes
that were described by Torrent’) as Scolithus errans of Hardeberga
and Andrarum. According to Horst’), however, there are various
kinds of these worm-passages differing from Scolithus linearis Hall,
whilst they also occur in different layers. This geologist makes men-
tion of them as being found both in many places in the neighbour-
hood of Simrishamn and near Kalmar.
The Odoorn erratic-block bears no resemblance to the Hardeberga
sandstone, in which Scolithus errans TorELL is found. Mosere *) writes
that this sandstone shows a greyish-green colour, and that the worm-
passages are dark-coloured. Nor does it resemble the Andrarum (For-
semölla) sandstone. According to TurrBerG *) the latter is a white,
quartziferous sandstone with yellow worm-passages.
The erratic-bloek also differs from the “Kraksten’, which Horst
mentions, as being found near Kalmar, and which is greenish grey. From
the kinds of sandstone with worm-passages which according to Horst
are met with in the neighbourhood of Simrishamm, differs that which
occurs to the West of Raskarum in being whitish ; and that whieh
is found close by Ljuuglyckorna is different because its worm-pas-
sages possess a dark colour. The sandstone which, according to this
geologist, occurs’ to the North-West of Raskarum, may resemble, in
colour, the Odoorn erratic-block : he says that its colour is sometimes
a dirty-grey one. Unfortunately he does not tell his readers what is
the colour of the worm-passages.
Consequently we cannot with certainty conclude whether this
kind of sandstone still exists as firm rock, or not.
Nor have I been able to find anything whatever concerning the
presence of suchlike erratic-blocks in the German and the Dutch diluvium.
1) Torett, Petrificata Suecana formationis cambricae. Lunds Univ. Arsskrift.
1869: Tom Vip. 12.
2) Horsr. Beskrifning till kartbladet Simrishamn-Sveriges geologiska Undersökning.
1399 Ser Aa. N). 109,p.st3:
Hotsr. Bidrag till kännedomen om lagerföljden inom den kambriska sandstenen.
Sveriges geologiska Undersökning, 1893. Ser. C. NO. 130, p. 6, 13, 14.
3) Mogera. Geologisk vägvisare inom Fogelsingstrakten. 1896. p. 30.
4) TurrBerG. Om Agnostus-arterna i de kambriska aflagringarne vid Andrarum.
Sveriges geologiska Undersökning. 1880. Ser. G. N°. 42, p. 3.
"Ook ee
( 563. )
Il. Some years ago I made an excursion in the surroundings of
Murmerwoude in company with Mr. Borkn, at the time a teacher
at Murmerwoude, now a teacher at a secondary school at Nimeguen.
To the West of this village, situated in the north-eastern part of the
province of Frisia, we found in the sand that lay by the side of a
freshly-dug canal two slab-shaped pieces of sandstone that fit each
other exactly and must have formed one whole. The dimensions of
the bigger piece are about 20, 10 and 4,5 centimetres. The other
piece also possesses the two first-mentioned dimensions, but the third
is 3 centimetres.
These pieces drew my attention as containing many more or less
complete stone-kernels and off-prints of pyramidal Hyolithus-shells.
The pointed ends of all these lie in the same direction, which must
certainly be attributed to the influence of streaming water.
These erratic-blocks consist of hard, grey, very fine-grained sand-
stone. With muriatic acid applied to them there is no effervescence.
Here and there they show small, yellow-brown spots. Some of the
stone-kernels and that which lies close around them show the same
colour.
The stone-kernels are straight and slowly increase in breadth.
The dorsal side is flat or somewhat concave; at the mouth it is more
or less convex. This side is not lengthened towards the front, so that
we have here a specimen of the subgenus Orthotheca. With the
exception of the dorsal side the surface of the stone-kernels is regu-
larly. vaulted. Consequently the transverse section is about circle-
shaped, with only one segment cut off. Towards the pointed end
they become more or less triangular. In one stone-kernel, which is
not exposed to view in its full length, the visible part points to a
length of about 35 millimetres and to a breadth, at the mouth, of
7 millimetres.
It appears from these properties that these stone-kernels originate
from the Hyolithus (Orthotheca)-species, which has been described and
pictured by Hotm’) as Hyolithus (Orthotheca) de Geeri.
Horm tells us already that sandstone with Hyolithus de Geeri is
Under-Cambrian. I have, however, not been able to find in his work,
on what grounds this assertion is founded. Most problably he came
to this conclusion because the nature of the stone points to it. At
the time sandstone with Hyolithus de Geeri was not yet known as
firm rock. Even now I have not been able to find in the books at
my disposal, that sandstone with Hyolithus de Geeri should be known
1) Horm. Sveriges Kambrisk-Siluriska Hyolithidae och Conulariidae. Sveriges
geologiska Undersöknung. Ser. CG. No. 112. p. 54.
( 564. )
as such. As far as I can see this species of Hyolithus, when Holm
described it, had not been discovered in company with a fossil from
which its age might be determined. Mopere’) afterward found many
specimens in a few big blocks of sandstone, which furnished him
the material for the description of the new species of Trilobites called
Holmia Lundgreni. The latter lay in the neighbourhood of lake Tun-
byholm in the eastern part of the province of Schonen; according
to Mosrre suchlike stone with remains of Trilobites occurs as firm
rock not far from this place. As Mopere informs us that sandstone
with Holmia Lundereni is older than that with Holmia Kjerulfi Linrs,
this was probably also the case with the sandstone-layers of which
the Murmerwoude erratic-blocks formerly formed part.
It appears from Mosere’s description of the stone of the erratic-
blocks with Holmia Lundgreni, that this stone in some respects
resembles the material of which the Murmerwoude erratic-blocks
consist. Both are very fine-grained and contain no calcium-carbonate.
There does not seem to be much difference in colour either, at least
as far as some parts of the Swedish erratic-blocks are concerned:
Mosere tells us that the sandstone deseribed by him is chiefly of a
bright light-grey colour, though sometimes showing small brown
spots of ferrihydroxide. My erratic blocks, however, contain no pieces
of phosphorite, which those from the neighbourhood of lake Tunby-
holm do. |
Besides the erractic-blocks spoken of just now, others of sandstone
with Hyolithus de Geeri-remains were also found, as Holm tells us,
in the province of Schonen, near Simrishamn and Köpinge.
The same author makes mention of suchlike stones having been
gathered near Rüdersdorf not far from Berlin, and near Bützow in
Mecklenburg. It follows from the descriptions he gives of these
pieces, that petrographically they bear no resemblance to those found
at Murmerwoude. The latter are least different from the erratic-block
found by Prof. pr Grrr at Rüdersdorf. My pieces, however, contain
no particles of glimmer.
No more have corresponding erratic-blocks of Hyolithus-sandstone
been found in any part of the Netherlands. The first of this kind of
stone were made mention of by vaN CALKER*). They originate from
Steenbergen in the northern part of Drente; they are three stones
1) Mopere. Sveriges älsta kända Trilobiter. Geol. Foren. in Stockholm för-
handlingar 1899. Bd. 21. Haft 4. p. 324.
2) VAN CALKER. Ueber ein Vorkommen von Kantengeschieben und von Hyoli-
thus- und Scolithus-Sandstein in Holland. Zeitschr. d. Deutsch. geol. Gesellschaft.
Jahrg. 1890. p. 581.
ps
( 565 )
resembling each other. From the description van CALKER gives of the
stonekernels occurring in them, Hor already drew the conclusion that
they originate from Hyolithus de Geeri. These erratic-blocks consist,
however, of dark asch-grey sandstone, so that they differ in colour
from the Murmerwoude ones.
Afterward two more pieces of Hyolithus-sandstone were mentioned
by me’). One was found at Kloosterholt (Heiligerlee), the other
at Roden, in the North of the province of Drente. The former is a
small piece of fine-grained sand-stone, yellow-grey on the inside and
brownish on the outside, in which are found some fragments of
stone-kernels of Hyolithus-shells. A few of these fragments are enti-
rely dark-brown, others have a light-grey surface. One of the stone-
kernels shows the transverse section characteristic of Hyolithus de
Geeri. The Roden erratic-block is rather a large slab of sandstone,
containing especially off-prints of pyramidal Hyolithus-shells. This
one is reddish on the inside and light-grey on the outside.
Where the sandstone-layers of which the Murmerwoude erratic-
blocks in former times formed part, were originally found as firm
rock, cannot be said with certainty, as appears from what was
written above. Most probably it was near the western coast of the
southern part of Sweden.
HI. That the knowledge of our sendimentary erratics still leaves
so much to be desired, must certainly be partly attributed to the
fact that so few of them have been gathered up to this time. Non-
geologists, too, by their researches, may deserve well of this branch
of knowledge, as was proved once more by Prof. Dr. J. C. Kaprnyn,
filling a chair at the Groningen University.
This well-known Astronomer, who in summer lives at Vries, in
the northern part of Drente, last summer searched the surroundings
of this village for sedimentary erratic-blocks. To his researches we
owe a piece that is certainly the most interesting of the erratics
described here.
Just outside this village, by the road leading to Donderen, was
found a small, slab-shaped erratic-block three centimetres thick, the
largest dimension of which is 14 centimetres. It consists of sandstone
coloured yellow-grey by ferrihydroxide. At the surface it is brownish.
With muriatie acid there is no effervescence. The grains of sand
1) BONNEMA. De sedimentaire zwerfblokken van Kloosterholt (Heiligerlee). Versl,
v. d. Koninkl. Akad. v. Wetenschappen 1898. p. 450.
VAN CaLKER, Ueber eine Sammlung von Geschieben von Kloosterholt. Zeitschr. d.
Deutsch. geol. Gesellsch. Jahrg. 1898. p. 234.
( 566 )
are for the greater part very small; they are not easily distin-
guished. Among them are bigger transparent ones. The diameter of
these latter grains is at most '/, millimetre; they are mostly arranged
in parallel planes, in consequence of which an indistinct layer-like
construction becomes visible on the vertical sides. On one of the
horizontal sides there are still parts of a few thin layers. In the
stone are a great many small cavities, which were formerly evidently
filled with organic remains.
On both of the horizontal sides we find remains of Tribolites. On
one of them the most important are an off-print of a mid-shell about
8 millimetres long, and a stone-kernel 10 millimetres long, part of the
shell of which, turned into iron-hydroxide, is still present. On the
other horizontal side is found the front part of an off-print of a much
larger mid-shell, which once had a length of about 15 millimetres.
Undoubtedly these remains, which in many respects resemble each
other, have come from the same kind of Tribolites. The two first
mentioned are remains of younger individuals ; the other belonged
to a more or less full-grown specimen.
With the younger individuals the glabella was convex, its length
surpassed its breadth a little, its breadth diminishing towards the front.
On the front side the glabella is somewhat rounded. On the plaster-
cast I made of the off-print of the small mid-shell, it is clearly visible
that the glabella possessed at least 2 side-furrows on either side. The
stone-kernel shows that the neck-ring was broadened in the middle.
The cheeks were vaulted, which is very clear in the stone-kernel
especially. Very characteristic is a deep furrow enclosing the glabella
in front and being continued on either side on the cheeks, where it
broadens and becomes less deep. Before this furrow is a vaulted part,
which does not turn down. The front-edge of this part is on about
the same level with the back-edge, whilst its height is equal to that
of the glabeila. In the off-print of the little mid-shell the glabella is
4°/, millimetres in length, and the part in front of it nearly 3 milli-
metres in breadth. >
It is apparent from the off-print of the mid-shell of the more or
less full-grown animal, which mid-shell is only partly exposed to
view, that the glabella and that part of the mid-shell which is in
front of it, which does not turn down here either, are less vaulted,
and that the furrow separating the two, is less deep. Here are no
side-furrows to be distinguished on the glabella.
With the assistance of the scientific works I dispose of, I found
that these remains are most like those of Arionellus primaevus BRÖGGER,
of which up to this time only mid-shells have been pictured and
2
(phe)
described. The first pictures were given by Kaervrr *, after remains
of the “er¢n skifer” from Tomten (TOmten?) in Norway. He informed
us already that they came from an Arionellus-species. Later on they
were described by BRÖGGER*), who by them was induced to assume the
new species Arionellus Primaevus. Under this head he also ranged the
mid-shell that had been pictured by Kaervrr in fig. 6. Afterward
LaNNARSSON *) pictured and deseribed remains of this Tribolite. He
moreover tells us that the mid-shell pictured by KJerunr as fig. 6
rather seems to belong to a new species called Ellipsocephalus Nordens-
kiöldi, instituted by him in the same essay. His material had been
got from the “egrivacke-skiffern” of Forsemölla near Andrarum. He
dared with certainty to range under the head Arionellus Primaevus
a small mid-shell 5 millimetres long, which had been found in a
sandstone-like variety of the stone mentioned above. This was not
the case with mid-shells from the ordinary stone, which are about
15 millimetres long. He gives as his reasons for not daring to range
these latter among Arionellus Primaevus BRÖGGER: first that they are
much flatter, secondly that the furrows are much shallower, thirdly
that the glabella has no side-furrows, fourthly that the glabella
towards the front considerably diminishes in breadth. Why, notwith-
standing all this, he at first ranged them under this head, though he
had never heard of transition-forms, he explains by saying that
BARRANDE had found exactly the same difference between the old
and the young specimens of the Bohemian species’ Arionellus Cetice-
phalus Barr., of which transition-forms are known.
The very same points of difference occur in the Trilobites-remains
of the erratic-block found at Vries. Here, however, the glabella of
the older specimen does not diminish in breadth more considerably
than that of the younger individuals.
_ As I wished to be as certain as possible in my determination, I
wrote to Prof. Mosrre, director of the Geological Institute at Lund,
to ask whether there was any material for comparison at my disposal
there. Remains of this species of Trilobites seem to be very rare at
Forsemölla, however, so that my request could not be complied with.
I received as a present, however, a mid-shell of the Ellipsoeephalus
Nordenskiöldi, which seem to occur more frequently there, Prof.
1) Kserutr „Sparagmitfjeldet”. Universitetsprogram Kristiania. 1872. p. 81. Vig.
7—9.
2) Bröeerr, Om Paradoxidesskifrene ved Krekling. Nyt Magazin for Naturviden-
skab. 1878. Bd. 24. p. 58.
5) Linnarsson, De undre Paradoxideslagren vid Andrarum. Sveriges geologiska
Undersökning 1882. Ser. C. NO, 54. p. 21. Taf. IV. fig. 3, 4.
( 568 )
Mosere supposing that my Trilobites-remains would prove to belong
to this species, which is not always to be distinguished from Arionellus
Primaevus.
Indeed, I had been thinking of this species, but as Linnarsson declares
that here the vaulted part of the mid-shell before the glabella towards
the outside slopes strongly down, I thought I could not range my
remains under this head. The mid-shell I received from Lund con-
firmed my opinion. | informed Prof. Moprre of this and sent him a
few plaster-casts of the Trilobites-remains occurring in the erratic-
block found at Vries. I was answered that Prof. Mosrra shared my
opinion and considered them as having come from Arionellus Pri-
maevus. At the same time he was so kind as to send me a plaster-
cast of the best of the mid-shells of this species of Trilobites, found in
the collection at Lund. Now I could ascertain that in Arionellus
Primaevus the part of the cephalon in front of the glabella does
not turn down, which is not specially mentioned by Bröcerr and
LINNARSSON.
Also in the mid-shell of which MoBrre sent me a plaster-cast, the
breadth of the glabella diminishes but little towards the front, though
its length is about 14 millimetres.
I think, then, that we now may with certainty conclude, that in
the Vries erratic-bloek we find remains of Arionellus Primaevus
Bröecerr. As this Trilobite occurs only in layers that contain remains
of Holmia (Olenellus) Kjerulfi Linrs, and as these are taken to be
the youngest of the Under-Cambrian ones, the age of the layer of
which this erratic-block in former times formed part, may be easily
determined.
Besides occurring at Tömten in Norway and at Forsemölla near
Andrarum in Schonen, which places I mentioned already, Arionellus
Primaevus is probably found in two more places in firm rock, viz.
at Kiviks Esperöd to the North and at Gislöfs Hammar to the South
of Simrishamn in Schonen. The former place was first made mention
of by Narnorsr *), who told that he had found there an off-print of
an Arionellus? That in Gislöfs Hammar remains of an Arionellus
occur, was first communicated to us by Luynarsson, in his description
of the Arionellus-remains of Forsemölla. According to this writer,
many of the mid-shells found there by von SCHMALENSEE much
resembled the larger shells of Forsemölla, which he dared not with
certainty call Arionellus Primaevus.
1) Narnorst. Om de kambriska och siluriska lagren vid Kiviks Esperöd etc. Geol.
Föreningens 1 Stockholm Förhandlingar. Bd. 3. 1877. p. 264.
As for two kinds occurring in the same place, Horst *) mentions
that the “grivackeskiffer” may also contain a species of Arionellus
(Arionellus Primaevus BRÖGGER °).
From communications made by TerrBere ®) and Hennig *) the
conclusion might be drawn that Arionellus Primaevus Broee occurring
at Kiviks Esperöd and Gislöfs Hammar, had been sufficiently indi-
eated. I think, however, that this should not be done. The list of
fossils which these two authors have drawn up with regard to
the “eravackeskiffer” of the two places mentioned just now and of
Andrarum, must refer, in my opinion, to these places taken collec-
tively and not to each separately. L am confirmed in this opinion
by the fact that remains of Holmia Kjerulfi Linrs (or of a kindred
species) are not mentioned by Moere *) as being found at Kiviks
Esperöd, whereas they are mentioned by them.
The origin of this erratic-block must most probably be looked for
in the eastern part of Schonen or in the Baltic Sea-region bordering
on it. That petrographically it ‘differs from the ordinary “gravackes-
kiffer”, does not clash with this opinion, several writers informing
us that the latter often changes into sandstone. The thin layers on
the lower side indicate that something of the kind has been the
case here.
It is not likely to have come from Norway, for never was a
sedimentary erratic-bloek found in these parts, of which this may
be said.
As was mentioned above, I take this erratic-bloek to be the most
interesting one of the pieces that are described in this paper. |
do this because it is the first piece coming from layers with
Holmia Kjerulfi Linrs that has ever been made mention of. Nowhere
in literature did I find anything about an erratic-block of that age.
IV. Shortly before the summer-holidays of last year | found, when
visiting the loam-pit close by Hemelum, a slab-shaped piece of fine-
grained sandstone three centimetres thick, whilst its largest dimension
is a little more than 20 centimetres. It is layered and contains
calcium-carbonate, so that with muriatie acid it gives effervescence
of dioxide-carbonate.
Owing to the large number of Glauconite-grains it contains, the
1) Horst. Beskrifning till kartbladet Simrishamn, p. 17.
*) TuttBere, Skanes Graptoliter. I. Allmän öfversigt öfver de siluriska bildingarne
i Skane och jemförelse med öfriga kinda samtidiga aflagringar. Sveriges geologiska
Undersökning. 1882. Ser. G No. 50. p. 26.
5) Hennie, Geologischer Führer durch Schonen. 1900. p. 26.
4) Mopere, Sveriges älsta kinda Trilobiter.
( 570 )
stone of which this erratic-block consists is coloured a strong green.
This is the case with some layers especially. Some particles of a
light-coloured kind of glimmer are found in it.
My attention was drawn to this kind of sandstone, because, when
splitting this erratic-block into two parts, I found that it contains
Hyolithus-remains, viz. grey-coloured stone-kernels. The lower part
of one of them is brown.
When visiting the Natural History-Museum at Hamburg last sum-
mer, and admiring its collection of sedimentary erratic-blocks, I asked
Prof. Gorrscne whether he knew of suchlike erratics. Prof. GOTTSCHE
thought he remembered such pieces to have been found in the sur-
roundings of Hamburg. Owing to want of exposing-room, however,
they lay packed up among other pieces, in consequence of which
they could not be shown me. He drew my attention to the fact that
in this kind of erratic-blocks sometimes occur small conical valves
of horn-shelled Brachiopodes. These valves were shown to me in a
brown-coloured erratic-block.
A short time after I found on the beach at Borgholm in Oeland
not only an erratic-block with Hyolithus-rests entirely corresponding
with my Hemelum piece, but also a brown piece of sandstone with
a valve of a small horn-shelled Brachiopode.
I searched my books for anything on the subject of this kind of
erraties or stone, but at first without any result.
As Prof. MoBrrG at Lund in the summer of 1901, when I had
requested him to be so kind as to give me some information con-
cerning Oeland, had noted down on my map of this island that on
its coast, to the North of Färjestaden, occur erratic-blocks with Dis-
cinella Holsti (then unknown to me), and the valves of Brachiopodes
I had found were, like those of Discina, horny and flat-conical, but
much smaller, I supposed that Prof. MoBerG could give me some
information about this stone. For this reason I intended to write to
him concerning this subject, and, was going to do so, when acci-
dentally I discovered in the essay of Hora *) on the Swedish Hyoli-
thidae and Conulariidae, that by Moprre *) a greenish kind of sand-
stone, rich in Glauconites, with Discinella Holsti Mosrre and Hyoli-
thes, occurring as erratic-blocks in Oeland, had been described.
Having studied Mogrre’s essay, ‘I find that the stone of which my
1) Hor. Sveriges Kambrisk-Siluriska Hyolithidae och Conulariidae. Sveriges
Geologiska Undersökning. Ser. CG. No. 112.
2) Moperc. Om en nyupptäckt fauna i block of kambrisk sandsten, insammlade
of dr. N. O. Hotsr. Geologiska Föreningens i Stockholm Férhandlingar 1902.
No. 142. Bd. 14. Haft 2. p. 103.
(OL 9
erratic-blocks with Hyolithus-remains consist, has been described bv
this author as type a. The piece of brown sandstone with the valve
of a small Brachiopode I found at Borgholm, belongs to his type d.
The fossil occurring in it has been determined by me as a vaulted
valve of Discinella Holsti MoBrera. The erratic-bloek that was shown
me by Gorrscur probably belongs to the same type; the organic
remains occurring in it are likely to have come from the same
species of Brachiopodes.
The Hyolithus-remains in the Hemelum erratic-block have been very
imperfectly preserved, which, according to Horm, *) is usually the
case with this stone. A longitudinal section possesses a length of 10
millimetres and at the mouth a breadth of 4 millimetres, so the
dimensions of this shell remind of the one pictured and described
by Mosrre’) under the name of Hyolithus Insularis nov. spec.,
whereas Horm afterward called it Hyolithus Confusus nov, spec.
The relative age of this kind of erratic-blocks does not seem to be
with certainty known yet, as up to this time no corresponding stone
has been met with as firm rock, and the organic remains found in
them have not yet been discovered in company with such as might
contribute to the solution of this question. MoBrere, however, thinks
he may conclude from the general character of the fossils oecur-
ring in them, from their petrographical nature and from the way
in which they are spread, that they come from Under-Cambrian
layers.
Horst *) draws the same conclusion, after tracing the manner in
which they are spread. I think I may infer from his essay, that in
his opinion they come from the youngest Under-Cambrian layers.
In accordance with this is the presence of Discinella-remains, this
genus of Brachiopodes occurring, according to Mosrre, in North-
America, in layers containing Olenellus.
As was said just now, a corresponding kind of stone was not yet
met with as firm rock. Most probably it formerly occurred west-
ward of Oeland; it may be found there even now at the bottom of
the sea, because this kind of erratic-blocks is found in large num-
bers only on the western coast of this island, between Halltorp and
Mörbylânga, and on the little isles and cliffs in the neighbourhood.
Less numerous they are in the other parts of the eastern and western
coasts of the Kalmarsund.
1) Hou loc cit. p. 74.
2) Mopera. Om en nyupptäckt fauna i block of kambrisk sandsten ete. p. 117.
5) Horsr. Bidrag till kännedomen om lagerféljden inom den kambriska sand
stenen, p. 9.
( 3725
MosrerG says that these erratices were found by Dr. Horst on
Bornholm, too. Neither in German nor in Dutch literature have [|
been able to find anything concerning suchlike erratic-blocks. It is
almost doubtless, however, that they are mentioned by Gorrscam *)
as “Cambrische Grauwackeschiefer’”. Only those erratic-blocks which,
according to him, resemble the Swedish “Gravackeskifer”, must be
taken into consideration then. The description of the latter entirely
corresponds with that of type a by Mosrre. The small, round,
horny-lustrous Brachiopodes-valves with a diameter of 2 millimetres,
mentioned by Gorrscue, which may come from Discinella Holsti
Mosere, also cause us to conclude that we have the same kind of
stone here. Gorrscur does not inform us of Hyolithus-remains occurring
in suchlike erratic-blocks. No erraties containing them had perhaps
been found at the time. It follows from what he orally communi-
cated to me, that now they have most probably been found.
The same author says that according to LINNARSSON a kind of
stone entirely corresponding with the one deseribed by him, has
been met with by Hummer near Tereskov (wich HumMet calls Torekov),
on the coast of N. W.-Schonen, as firm rock. Judging from the
description Hummer *) gives of it, it much resembles, petrographically,
type « of the Discinella Holsti-sandstone. Hummer does not say,
however, that fossils are found in it. Perhaps we have here
the same case as with the Glauconitic sandstone from the neigh-
bourhood of Simrishamn, of which Horsr®) writes that a corre-
sponding kind frequently occurs in the “sandstone-region” of the
Kalmarsund. Here, too, the resemblance seems to be petrographic
at best, for Mopere, in his essay, speaks about this sandstone no
more than about that of Torekoy. |
Most probably the thin-layered, greenish stone which resembles
the “Grauwacken-Schiefer” of the Olenellus Kjerulfi-region, and
whieh petrographically keeps the medium between the Olenellus-
stone of Hardeberga in Schonen and the equally old “grén skiffer”
of Bornholm, with stone-kernels of a Brachiopode probably belonging
to Acrothele, and with Hyolithus-remains bearing the greatest resem-
blance to Hyolithus Lenticularis Holm, as SroLLry *) writes, — is
also Discinella Holsti-sandstone.
1) Gorrscue. Die Sedimentiir-Geschiebe der Provinz Schleswig-Holstein. 1883. p. 8.
2) Hummer. Beskrifning till kartbladet ,Bastad”. (No. 60). Sveriees geologiska
Undersökning. 1877. p. 10.
3) Horst. Beskrifning till kartbladet Simrishamn. p. Lo.
4) Srorrey. Die cambrischen und silurischen Geschiebe Schleswig-Holsteins. Archiv
fiir Anthropologie und Geologie Schleswig-Holsteins und der benachbarten Gebiete.
1895. Bel. Hett. asp. 130:
‘ied
7 .
(573)
Finally I must mention that, on the occasion of a later visit to
the loam-pit near Hemelum, I found two more erratic-bloeks, which
must probably also be counted among pieces of Discinella Holsti-
sandstone. Neither contains any fossils. One corresponds petrogra-
phically with what was described; the other is for the greater
part white, but possesses green layers. If I am not mistaken, 1
sometimes saw suchlike stones on the beach of Borgholm.
Physics. — “On the course of the values of b for hydrogen, in
connection with a recent formula of Prof. vaN pur Waars.”
By Dr. J. J. van LAAR. (Communicated by Prof. J. D. vAN DER
WAALS).
1. Making use of the theory of cycle motions, Prof. vaN DER
Waats has given a new deduction of the equation of state of a
simple substance, in which the size of the molecule appeared to be
variable, and to be a function of the volume *).
For a bi-atomic gas the following formula has been found:
b--b, bb, \?
—=—1— ES ee ENE EE ey
v—b bod,
Here }, denotes the smallest value of 6, corresponding to the case
that the two atoms of a molecule touch each other; 4, represents
the greatest value i.e. the value for very great (infinitely great)
volume. The above equation may be easily derived from the so
called “equation of state of the molecule”
vti te et) |b) = FEISS ASS: ways ke aT
yt
when we take »—=o, in which case / assumes the value 4, and
a P
jae De may be neglected with respect to a (b—b,)- So we get:
t
a (6,—6,)’ =A.
If we substitute this value into equation («), paying regard to
we get the equation
1 sf b—b, (ne
—__—— I — 0s) ==,
(ea b (bg—,)? 0, ,
which yields immediately equation (1).
1) These Proceedings of the meetings of February, March and April 1901,
See also “Livre jubilaire dédié à J. Bosscua” of the Arch, Néerl., p. 47, (The
first communication and part of the second discuss principally the specific heat
for very large volume).
The quantity « in the equation of state («) depends on the forces,
which keep fhe atoms together in the molecule. These forces are
supposed to be proportionai to the linear deviation from the position
of equilibrium 7—7,.
The equation of state («) for a tri-atomie gas, e.g. CO, — which
in this case is the combination of two similar equations — will con-
tain besides RT still a factor f, whose value will vary from 1 to 2
according as the different cases occur, which we may distinguish in the
motion of the atoms. For CO, a value of nearly 2 is found for /.
As, however, this quantity f for a certain substance is, strictly speaking,
variable (see the paper in the “Livre déedié à Bosscra”, quoted above)
and as the accurate equation is therefore very complicate, I have
chosen a bi-atomic gas, namely hydrogen, in order to test the new
equation of van DER Waats. In this case f= 1 and the relation
between 4 and v is represented by the simple equation (1). I hope
later to test the equations for oxygen and nitrogen, in order to
examine whether the results found for hydrogen also hold for these
gases.
Il. An accurate knowledge of a is required for the exact calcu-
lation of 5. This is still a great difficulty. Absolute certainty as to
this value cannot be obtained as yet, but still it appears to me that
the value a=30010~-6') has a high degree of probability. Assu-
ming another value for a, I found namely that the values calculated
for 6 decrease much too rapidly, — much more rapidly than agrees
with formula (1); this is principally the case in the beginning, 1. e.
for large values of v. Only the values of 5, calculated for a=30010~6
varied in such a way, that their course was represented by equation
(1) with nearly perfect accuracy. SCHALKWIJK *) also calculated from
his last experiments 10° a = 300 (10° 4, = 910). I therefore thought
myself justified in assuming 300 for 10° a. In the following table
we find the values for 4 at 0° Centigrade, calculated from the equation
(0 + 5) (v—b) = (1 + a) (AB) (Lat).
For (1+a) (1—+) we put 0,9994. All values have been multiplied
by 10°; the same will be the case with all values of 6 which we
give in what follows.
At 0° C. we have:
0,9994
a
p+ ae
1) All values of v, b, etc. have been expressed in the usual practical units.
2) These Proceedings, June 1901, p. 124.
n=
a b b
p pl) p2 - v—b calculated A
oF found. — from (1) |
100 | 40690 | 414.3 9.6* | 9739 | 951 907 | 444
150 | 7353 54 07 5.5 6425 | 998 901 | 427
200-5690 32.38 gor.) ar. | ois" | 396 >} HAT
250 | 4692 | . 22.01 PFGE mt ad oI Sots ny =i
300 | 4030 16 24 18.47 3138 892 | 886 Je
350 3560 12.67 23.65 Dei sist Sho, RE: UM EEn
400 3207 10.28 929.48 9329 SAS si 075 aE
450 2933 8.602 | 34.87 2061 SUL, aes «(Und PS ae
500 2713 7.360 40.8 1S4S 865 | 865 + 0
550 9533 6.416 16.8 1675 858 | 860 =
GOO IBR6° 5.695 apel | 153 855 855 td,
650 9959 |. ~ 5:408 58.8 1410 Gay | Sa bP
700 | 2149 | 4.60 | 64.9 1307 | 843 om | = 9
750 | 2053 | 4.215 74.2 1217 836 | 840 ed
800 1971 3.885 17.2 1139 832 | 835 8
850 1897 3.599 83.4 1071 826 830 4
900 18335 3.362 89 2 1010 823 826 9
950 1774 3.147 95.3 956 818 | 82a 8
1009 17225 9.967 | 101.4 | 908 815 817 i
1100 1637 2.680) 414.9 | ~ 825 812 809 + 3
1200 15575 9465 123 7 757 SO 801 Ee!
1300 1491 93995") 135.0 696 795 793 +2
1400 1432 24051 463 646 786 785 +4
1520 1380 4.904 | 156.3 603 777 777 +0
1600 | 1334 1.781 | 168.4 565 769 770 |
1700: je 429% 1.681 1785 532 762 763 — Á
1800 | 4958 1.583 4189.5 ‚02 756 756 + 0
1900 1225 1.501 | 499.9 476 749 749 0
2000 11945 1.497 | 40.2 152 742 743 = 4
2100 1166% | 1.361 | 290.4 431 736 736 +0
2200 Mal 1.302 | 230.4 “11 730 730 ae 0
2300 1148 {4.250 | 240.0 393 ip a EE an de
2400 10972 1.205 249.0 377 720 149 A4
2500 1078 4.462 | 258.2 362 716 714 hy
2600 1059° 1.423 | 267.4 | 349 714 710 4
2700 1042 1.086 | 276.2 S36 fst 706 705 + 4
2200 102° 1.050 |. 285.7 324 701 700 | +4
1) Up to 1000 atmospheres the values of ¢ have been borrowed from the results
of the “second method” of Amacar (méthode des regards); from GOO atm. to
og
Proceedings Royal Acad. Amsterdam. Vol. Y,
The values of v have been borrowed from the well known expe-
riments of AMAGAT *).
The too large values of 5 in the beginning — here only to about
300 atm.
a = 300 is still slightly too great. But from 300 atm. upwards the
are still present. This indicates probably that the value
agreement is quite satisfactory. Small inaccuracies in the determina-
tion of the value of r have for large volumes a great influence on
the values of 4. To this circumstance also it may be ascribed that
the values of 5 are in the beginning not reliable. So the value
v= 10690 at p= 100 cannot be accurate to a higher degree than
to ten units at the utmost. So it might also have been 10680 or
10670 and 6 or r — (v—+) might have been 10 or 20 units smaller.
The values of 4 “calculated” have been determined with the aid
of equation (1) in the assumption
by 917 ; 0, = 463.
4, may be determined in the following way. If we substitute
into (1)
bb,
— — — WwW,
bg—b,
dl
and pay regard to b—b, = aes (4,—b), then we get for (1):
— .
Pen
Sr nb :
and therefore :
b,—b 12
fe eg)
rb a
For an assumed value of 4, this equation enables us to determine
the corresponding value of . from v and 5 at e.g. 500, 1000, 1600,
2200, 2800 atm. The value of 4, may then be calculated from
b, = b — (1 —a’) wv —b),
which follows immediately from (1). So I found with 6, = 917 at
1000, 1600, 2200, 2800 atm. respectively the values 4,= 455, 463,
462, 466. If we put a—400 instead of a—300, then we find with
6b, = 1000 at p= 2800 atm. in the same way b,— 468. With
1000 atm. the values of v at 600, 700, 800, 900 and 1000 atm. represent the
mean values of the results of the first method (that of the electrical contacts)
and those of the second method. From 1100 atm. upwards the values of v have
been determined by the first method.
1) Mémoires sur l’élasticité et la dilatabilité des fluides jusqu’aux très hautes
pressions, p. 32—33 and 38,
( 577)
a= 500, 6, = 1100 we find at 2800 atm. again 6, = 464. So we
may assume with perfect certainty 4, to differ very little from 463.
With this value of 4, in the first place 4, was again calculated.
From (1) follows: |
(Lb) bb (v—b) poe (4—b,)
OB ay y—b Pee kek:
SO
En ee ee (ee
Ee eat LO ECN
In this way I found at p==500, 600, 700,-800, 900, 1000, 1200,
1400, 1600, 1800, 2000 atm. respectively Gj =— 919: Toe Opa
912, 913, 919, 917, 917, 917 917. From these values I concluded
that b, = 917.
After that the values of 4 (calculated) were determined as follows.
We derive from equation (1):
b—b, (bb)
a a en ae a
If we put bb, = y, then we get for 6,—b, = 454:
y y
el) y ABP
from which follows:
DE ea
RE pe iel
‘ (v—b,) ee
We know the values of 4 already in approximation from / (found).
These values, substituted into the second member of the above
equation, yield the accurate value of y, and so also of 5.
HI. Let us begin with assuming that the values of 4, and 5,
are independent of the temperature, which follows from the supposition
of Prof. var per Waars, that the quantity «‚ which depends on the
forces between the atoms, is proportional to the absolute temperature.
Then we may calculate the critica’ quantities in the following way.
Equation (1) in connection with the following equation :
==> a= a or 0 -— 0 pa em ).
+2(8,+8,) 3 Shai
where
39%
yields after some reductions *):
{a 1—w\'
3 Pan ee
en 5 — (1 —)? 2
2 b
Here is 7 = (=) and u Sar . We may write for the
Jg — 9%
bo |
second member:
2(143 a?)
(1 +2) (2—a-+ 2)?
Therefore we get also:
5 L WW 3(1+.w)(2—a+a’)
Dl HU = — —_ eae ees Pare oe )
Ve 4 1434" ”)
The value of « may be derived from this equation. As 6,=917=1,986,,
1 : een :
u gets the value = 1,02, and we find in approximation for «
the value 0,709.
Therefore
by—b, -
—— — )Y JV,/ 09 = 0.842.
pry
from which we may easily derive:
by ZOZ = 845.
Now we have:
3 vb 2(14 3.7)
Rn Ree
from which we find:
. OE == dot bkr Be + B, — 0,0837.
The critical volume is therefore:
TNB De Deg END Vie 2172.
— 0,9163,
At 0° C. this volume is (comp. the table) already reached at a
pressure of about 700 atm. The values of v at O° range in the
experiments of AmaGat to 1025; the verification of equation (1) of
VAN DER WAALS may therefore be extended over volumes which have
the size of liquid volumes; this fact compensates the want of experi-
ments below the critical temperature.
We may also calculate the quantities 8, and 8, separately. From’)
1) See v. p. Waats, l.c. ILL, p. 652.
1) van DER Waats, Lc. III, p. 651,
| (lx)?
Br Ite Arda?
1+ ——
(lx)?
follows:
S= 030472. ; B, = 0,0365.
We find for £7}: 5)
8 a (L—8,—B,)'\1+2(8,+8,))
Re
AAT by 18,
or
8 a 0.8396 «1,1674 Al 8 a a @
lg DE e000, 805 =.
re acy 2 0,9528 27 by by.
With a = 300, bj, = 845 we find therefore:
ee Tr
AT — (7.9994 —— = 0.108.
273
which gives:
LG — 29°.5 ;
Dewar found 7), = 30° 4.32°*).
The critical pressure is represented by *)
Eel ada ae
=
ie 27 bj? 1—8, ;
or
js) 0,8068 & 1,363 3 i ays: Sa Gf
en Pe = 1,154 X — — = 0,0427 —.
PW A) Pa 0,9528 BO by?
Introducing into this expression the values of @ and bj, we find:
pe = 18,0atm.
Dewar found 15,4 atm.; Onzewski *) 20 atm.
We find for the so called critical coefficient Y: *)
, pv 3 Les
ee ee Cr EE
RT}; 8 (ll)
x 2 ee En 0.961 0.360
A = — K ——— ZZ Oe == UNE
8 x 0.8396 5 x —_
Finally the quantity } may be calculated from *)
or
1") Id. II, p. 583.
2) Proc. Royal Inst. 16 (2), N°. 94 (1901), p. 477.
5) ven. Waars, l.c. II, p. 583.
+) Wied. Ann., 56, p. 133 (1895). See also Verscuarrert, These Proceedings,
Febr., 1899, p. 327.
5) v. p. Waats, l.c. II, p. 584.
6) Id. III, p. 648.
( 580 }
Pd 13 —8, 0,9165 .
VE (5 7) == 4 SS Ax ——_ = 4 1,136 = 4,945.
bat de 0.8068
Just as VY comes again very close to the normal value 0,375, so VY
for hydrogen approaches again close to the theoretical value 4. The
expressions for 7, and py, differ only little from those, found for
these quantities for tri-atomic gases, such as CO,; the expression for
vy, on the other hand deviates strongly from it. This is to be ascribed
to the fact, that 4, has here not the value of nearly four-times 4,, but
amounts to only twice that value. The quantities >, and 3, are there-
fore much smaller than in the case of tri-atomic gases.
VAN DER Waats found for CO, e.g. B, —= 0,138 and 6, = 0,1, the
values we found above amounting to only about one third of these
values. bj is also in this case not 0,86 6, but 0,92 6,, and for vo we
find 2,57 by, instead of 2,03 6;,, or 2,376, instead of 1,75 dy.
It is certainly of the highest importance to know whether the
result for vj agrees with the experiments. At the same time the value
of the critical coéfficient will then agree, for the values of 77 and
pe agree very well. But with the investigation of this question, and
with the verification of }, we will wait till we have investigated
the behaviour of 5 at higher temperature, which will be done in the
next chapter.
IV. In the first place we will repeat the calculations of § 2 at
99°,25 C. We derive the following table (p. 581) from the expe-
riments of AMAGAT') at that temperature.
rh has here been calculated from
0,9994 (1 + 99,25 x 0,0036627)
(bl ==
For the “calculated” values of 4 I determined quite in the same
wav as is indicated above for O°
by SN A b, =S eed)
Again the initial values of 6 “found” (up to about 400 atm.) are
too great. But afterwards the agreement is sufficient, though the
verification was only possible up to 1000 atm, as, alas, no further
experiments were available. We come to the remarkable result, that
the value of 5, has considerably decreased though the limiting value
of 6 has remained unchanged. It seems that at higher temperature
the atoms in the molecule may approach one another closer than at
lower temperature.
1) Le. p. 38 (2nd method).
p | r | v? | 5 el | ; Bd | A
| | | | | found from (1) |
150 9846 | 96.94 | DROS | 8902 | O44 | |
: Qs | 96.§ | ae | &902 QA. 902 | +42
200 7567- | 57.26 | 5.27 | 6640 27 | 897 | +30
250” | 6200 | 38.44 | 7 g0 | 5286 14 | 8 | 499
300 | 5286 | 27.94 Mene | AA8ne PC 001” | - 887 | 4414
350 | 4636 241.49 | 13.99 | 3744 | 802 | ga | 441
A00 | 4447 17.20 Ee 889 — |)! 876 |, At g
450 | 3766 | 14.48 | 91.4% | 9899 | 7) ee ay eel
500 3462 | 11.99 25.0? | 2596 | 866 | 866 | 0
550 | 3214 | 10.33 29.0 985307] Bals IN ‘ger ol er 6
600 | 3006 | 9.036 | 33.99 | 9150 854 Bete ie 6
650 | 284 | 8.015 | 37.0 | 1983 | ss | em | —3
700 | 2680 | 7,182 | 41.8 ABT Se es 273
ue aaneen che. WE: | 4710 [---839 | - 84 Mees
800 | 2436 | 5.934 | 50.6 | 1602 | 834 | 836 ae
850 | 2336 | 5,407 Eken dsc, ERD | 831 Kad
900 one | 5036 | 59.6 |“ 1490 | son | gar | sets
1950 | (2174) | 4.796 | 63.5 1345 IBD gaa | —
1000 | 2093 | 4381 | 68.5 | 1975 | BI ie len
| I
From equation («) follows that for great volumes:
« (bg—b,)? = RT.
Now we find:
OP by—b, = 454 (6,-— 5, )? ==.20,61, x10"
1000 | tl == Oe EP
(bb)? has therefore increased in the ratio 1 :1,368. But 7’ has
increased in the ratio 1 : 1,364, from which would follow that « is
independent of 7.
In order to investigate whether this also applies to still higher
temperatures, I have also performed the calculation for 200°.25.
rh may then be calculated from:
0,9994 (1 +200,25X0,0036627) _1,7324
Di 0 Maree
a
') The value given for ¢ at p=950 atm. appears to be erronious; probably
(Se)
With the aid of the following table we may survey the results.
200° EC.
2 L y
p p r | eb
| found calculated
en |
150 | 19390 | 451.78 | 1.98 | 11399 921 894 +97
200 0420 88.74 | _ 3.38 | 8518 902 ji 889 | HZ
950 | 7680 58.98 5.09 | 6791 8x0 884 | 45
|
300 | 6520 42.51 7.06 5642 878 BO
350 5694 SN) 9.95 1829 872 873 | —1
A00 5075 TS) 4165 4208 867 SGS — 4
450 1503 21.10 14 22 3732 861 863 |. —2
500 | 4210 17.72 16.93 3351 859 858 ze
550 | 3891 15.44 19.82 3040 851 GENE
600 | 3627 | 13.46 | 922.80 2782 845 OE Nae
650 3403 | 41.58 25.91 9563 840 843 ag
700 | 3211 -| 410 31 29 10 2376 835 838 Zee
750 | 3045 | 9272.) AAG We S914 831 833 ee
800 | 9900 | “8.410 | 35.61 2073 827 828 nee
850, | 2772 | 7.684 | 39:20 1949 823 823 Jt
0900 9657 7.060 12.5 1838 819 819 +0
|
Only at 150 and 200 atm. the values for 4 “found” are somewhat
foo high: furtheron the agreement is satisfactory. The experiments
ranged ouly to 900 atm. The values of 4 “calculated” have been
determined from (1) with the aid of:
h, in 6. = 306.
by appears to be slightly smaller than at O° and 100°, but 4, has
again strongly decreased. It is a remarkable fact that the decrease
of 6, between O° and 99° amounts to 77, and that between 99° and
200° to 80; so for each degree the same amount namely 0,8.
As to b,—b,; we have now:
0° by — br A (b,—6,)° =-20,61
200° ren he Fe = BO sae
The ratio of the values of (6,—6,) is 1,77. For 1+ at we find
1,73. Taking for b,— 6, at 200° a value which is only 6 units
( 583 )
smaller, namely 598, the ratio of the values of (b,—b,) would also
have been found equal to 1,738. We may therefore safely assume
that (b,—6)? is found to be accurately proportional to the tempera-
ture within so large an interval of temperature as that between 0°
and 200°, in consequence of which the quantity @ must be quite
independent of the temperature.
It is not astonishing that @ is independent of the temperature:
the contrary would rather seem to be remarkable. Being induced
to make this contrary supposition for the better agreement of the
; Lf dp . e : 4 : :
quantity ( ) for CO, with the experiments, Prof. v. p. WaAats?)
p \dT)y
immediately pointed out its astonishing character.
We shall just draw attention to the following consequence of the
fact, that b,—6, is proportional to V7.
If we put:
b,—b, = VyT,
then equation (1) may be written as follows:
b—bg+ V4 ie SE fad (b—b, + VyT) ae bg—b (b,—b)?
Ln DIT
With small value of 6,—6 and great value of v, we get approxi-
mately :
Vyl by—b
(bj = Vyl
therefore
YT
b,—b En
2v
et tert RT
r being in this case approximately equal to „wesen:
: 4 5
en
2R
or
tS by—y' Pa
i.e. the value of 4 depends only on p and no more on 7 or 7, the
value of 6, being nearly constant. The values of 4, calculated for
the same pressures, have therefore the same difference whether the
temperature be 0° or 200°. For we have:
biel 55 jd (P.—P)-
We found this fact affirmed in the above tables*). For the purpose
DE es UL,» pe 646.
2) L pointed this out already before in a paper in the Archives Teyler („Sur
influence des corrections, etc.” (2) VIL, Bme partie, p. 26—27.) I tested there the
b-values for hydrogen to an empirical formula of KAMeRLINGH ONNeEs.
( 584 )
of a more direet comparison we collect the values of 5 for pressures
differing each time LOO atm. in another table.
L | b | U
p |
0e | 100° 200°
= SE eee eee
| |
100 | 907 | ee pen
| Ad)
20 | 896 | 897 S89
10 10 10
300 R86 887 879
| lf 44—| 11
400 | 875 876 868
10 10 10
HOO S65 | R66 S58
10 10 10
600 855 | 856 848
10 40 10
700 845 S46 838
AD 40 10
800 835 | 836 828
0) q 9
900 826 827 819
{) 9)
1000 817 S18 =
We see that the differences are the same. All the values of 6 at
200° are 8 units less than the corresponding values at O° and at
100”, because the value of 6, at 200° is 7 units less. But the course
is always just the same. And as at a given value of p we always
find decreasing values of v at increasing temperature, so the value
of 6, must of course always decrease.
From the above follows also, that we may determine 4, immediately,
eg. adding 52 units to the values of 4 found at 500 atm., or 32
units to that at 400 atm., ete.
On the preceding reasoning we may base the following short
calculation.
At p,—p, — 100 the initial value of b,—b, amounts to circa 10
a 11; we have therefore:
u ee shia O,10a 3 dee
2R 100 ne
Therefore
bb, VT = 10 VOT REED AE
or
De er eee
So we have at 0° 10°(4,—6,) = 458 (found 454).
At 100° we find 10°(,—,) = V 21><10'S<1,38627—=535 (found 531).
At 200° we find 10°(4,—0,) = V 215<10*<1,7324=603 (found 604).
(“ode
V. A slight correction must of course be applied to the calcula-
tions of § 3 in consequence of the variability of 6,—6, with the tem-
perature. For the assumption that 4, remains constant pleads also
the circumstance, that according to an observation of D. Brrrignor
the experiment yields the value 2,93 a 2,98 for the ratio between
the temperature at which a gas in extreme rarefaction follows the
law of Borrr, and the eritical temperature; for which ratio the sup-
position that 4, is constant over this large temperature interval *) leads
to the value 2,9. If we assume this same supposition, we shall
find 5, to be equal to. circa 920 also for the critical isothermal.
But 6, will be found to be considerably higher than at 0°. We saw
above that the difference amounts to 77 units for 99° difference in
temperature. We shall therefore find 6, at — 242° C. from the equation :
249
b, = 463 + = X 77 = 463 + 188 — 651.
If therefore we put 6, = 920 and 4, = 650, then in the first place
by is no longer equal to 26,, but to:
b, = 1,415 b,.
The variability of 6 is therefore much smaller than at 0°, and in
consequence of this the quantities B, and 8, will also be found to be
much smaller, and the critical quantities will approach still more
closely to the normal values.
) i!
rhe quantity « ——-— is here —_~= 2,41, and the value of
6 Jo ),415
b.—b,\ sf
nj — of equation 4 ceases accordinglv to be 0,709, but becomes
by —b, 2 we
0,852. In consequence of this we find:
brb,
——==/ 0,852 = 0,928,
bg 8;
from which follows:
bir = 0.977 hy = oo)
For +, and for @, + 8, we find (comp. § 3):
vy, = 2,87 be ; B, + B, = 0,0228.
So we find:
Ua, Of brl ==, 80 bo -— 5,9 bere
a volume which is reached at 0° C. at a pressure of + 550 atm.
The values of 8, and 8, taken separately are:
Pi Pa | €
(le) 5
B, — a a 0,0117 ; B. en 0,01 EG
dag OO ne
1) Zie vaN peR Waats, l.c. III, p. 647.
( 586 ) |
Now we return to the experimental verification of vp.
1 Gr. H, at 0° C. and 1 atm. occupying a space of 11127 cM°.,
S19 <K 10-* > 4112) hence she
re is expressed in ccM°. equal to 257%
x
critical density is:
tt = 38,70
According to the theorem of the straight diameter of Marutas we have:
d,+d, 5 1 si
et -— = —— mn — f.
dt. ces
— 0.0348:
which quantity g has been found by Youre and Marmas to differ little
from unity for different non-associating substances.
Dewar?) found the density of the liquid phase at the melting point
of H, (16°,5) to be 0,086, so we find, neglecting the density d, of
the vapour:
0, 086 16,5
Se ee == 0,468,
di. jaye
which yields for dj:
0,086 DRE
di = ——— = 0,0348,
2,466 —_—-
in perfect agreement with the value of d, we have calculated above.
We now proceed to the calculation of the other critical quantities
fg : B
kes Dk X and ¥;
We find for 7:
8 a 9, 9549 1,0456 8.4 a
x ; (ps = 02095
es een — 1,010 x —
oT hi 0.9883 SOF be be
With « == 300, 4, = 899 we find therefore
T;,
0.9994 — — 0.100.
273
sO
C= ede
This value is somewhat too low; the experiment has yielded
e= Be De
We find for the critical pressure:
i 0.9439 1,093 1
akk EN Le == ODSB7
Rr nen E : 044 X =
OT bis 0,9883 27 by be
1) 1. ec. bl. 477. Dewar finds the melting point to be 16° a 17°: the critical
temperature to be 30? à 32° absolute temperature. [The density of the liquid
phase at the boilingpoint (20° à 21°) has been estimated to be + 0,07, but then
the vapour density may no more be neglected. ]
( 587
With the values found for « and 5, we get:
pe = 14,4 atm.
Dewar found + 15 atm.
The critical coefficient VY becomes:
VR ERN EN :
== a x 0.9549 8 XxX 0,989 — 0,371,
so nearly the normal value 0,375.
jn T dp
For Y={— : we find now another value than before. In the
pdT/,.
general expression *)
ft Be ase dPy 7 Ph | db
plat), ne les de
B d db gl N dP,
the factor of — is now no longer zero. For as on -= a(b—b,), we
av av
have:
ao AAP Ib
LT — = =a oll
OT \ db dl
as we found @ to be independent of 7, 4, on the other hand to
db
depend upon 7. We find therefore for the factor of —:
av
We have found above: 6,—b, = V7T, so b, =l a Wyt, and as
6, has been found to be nearly independent of T, we get
„db, pes 1
ri ae = 5 Vy! = == 9 (6,—,).
4 dh
The factor of = becomes therefore :
aU
1
c (0-1, == 3 nee ;
and with
BE Lt ag jet a\fv—b 1) 1
ey Eh) Tie! (hy hy Tr Dn u? tas ay b— 5.
1 1 b—d,
— as according to (1) we have — ll — — =i
= (by ij ETS v cag
we get:
1) v. p. Waats, |. c. III, p. 644,
( 588 )
djb 1 h,—b,
p+- | ie
ye li b, : 2) b—b,
noe : : on dp | ee db
Phis expression for ( -— | becomes therefore, if we put ==:
P d k dv 5
EE)
aa =( PRU ine or: ze 5 ay wars ,
This yields with the panies calculated above (see § 3)
ily COLL Lhd ee et EL 1) Ee ay
"== De 0,0 Wm ==
X 09439 |T i( SG yee ( 2 B49,
= 4 1,035 4 0,0117 >
< 0,747 & 0,45781,
or
FS 4°120 Ss 105064267
T dp
Finally we investigate, whether this value of © a may be
pc
brought into agreement with the few experimental data of Dewar.
Dewar found namely (Le):
Orle a ge Lait
P= 30" 238 (apy = baten:
The two data yield by means of the integral formula
nep log = LE a 1)
P di
for f the value:
5 nep log 15 ae v 7
=— 2 == Net yn a tee were 7 .
Les be FEE alerts
tO
ALE |
according as we take 20° and 32° or 21° and 30°. The lowest
value is 4,51, so still higher than the calculated value 4,27. We
must further note that 20° differs comparatively very much from 7%,
(being */, 7) and that therefore at 20° the factor f will certainly
be found to be greater than near 7), hence 4,51 is probably too
great.
From the above we may in any case conclude, that the large
extrapolation, by “means of which we have calculated the value of
b, at — 242° from the values of 6 at 0°, 100° and 200°, really
0
yields the critical data with a sufficient degree of accuracy at
least in so far as we may judge from the few data, that are available.
Only Mis probably too low.
We have reason to expeet a priori that the new equation, derived
by van DER Waars for the variability of 6 with the volume, does
(OB
not represent the experimental data with perfect accuracy. For the
correction, introduced before for the partial coincidence of the distance
spheres has not been taken into account in the deduction of this
formula. The quantity 6 in r— b for a monatomic gas, ec. e.
mercury vapour, argon etc. would according to the new theory of van
DER WAALS remain invariable; whereas this quantity which according
to the former considerations would for very large volumes be equal
to four times the molecular volume, for smaller volumes would
certainly have a smaller value, and it would approach to about twice
the molecular volume — at least if the shape of the molecules does
not exercise any influence on this calculation.
Physics. — “Peculiarities and changes of Fraunhofer lines interpreted
as consequences of anomalous dispersion of sunlight in the
corona’ by Prof. W. H. Junius.
(Communicated in the meeting of February 28, 1903).
Especially by Jrewerr’s investigations on the coincidence of solar
and metallic lines *) attention has been drawn to several variable
peculiarities of Fraunhofer lines. Here we do not mean the irregu-
larities occurring in the spectrum of spots or of faculae, which relate
to disturbances in comparatively small parts of the sun, but abnor-
malities shown by the average sunlight, as observed when the slit
is illuminated by a long strip of an imperfectly focused solar image.
In that case, according to Doppier’s principle we may, of course,
expect displacements of the lines in consequence of the Sun’s rotation,
of the rotation of the Earth, and of the change in the distance between
Sun and Earth caused by the exeentricity of the Earth’s orbit. But
even when all these influences have been allowed for, some irre-
gularities still remain.
Indeed, Jrwerr has observed that some Fraunhofer lines do, others
do not, exactly coincide with the emission lines in the are spectrum
of elements, and that the displacements are unequal both for lines
of. different elements and for the various lines of one and the same
element. Moreover, the shifting of certain lines on one set of photo-
graphic plates was sometimes found different from that on a set of
DL. E. Jewett, “The coincidence of solar and metallic lines. A study of the
appearance of lines in the spectra of the electric are and the Sun.” Astroph.
Journ. Il p. 89—113, 1896. The same: “Spectroscopic notes. Absolute wave-lengths,
spectroscopic delerminations of motions in the line of sight, and other related
subjects.” Astroph. Journ. XI p. 234—240, 1900,
( 590 )
plates taken at another time. With several lines the intensity too
appeared to be variable.
JEWELL explains these phenomena on certain hypotheses on density,
pressure and temperature of the absorbing and emitting gases in the
different layers of the solar atmosphere, and by variable ascending
and descending velocities of matter.
Harr’s abnormal solar spectrum.
Much greater than the irregularities mentioned are those, found in
an “abnormal” solar spectrum, lately described by G. E. Hare. *)
This highly remarkable spectrum had accidentally been photographed
as long ago as February 1894 in a series of exposures made with
the sole intention of investigating the peculiarities of the grating.
Only a few months later it was discovered that a very extraordinary
phenomenon had been photographed. Hate hesitated to publish this
accidental discovery. Copies of the plate were sent to several spectro-
scopists for examination with the request that an explanation, referring
the phenomenon to: some origin other than solar, might be supplied,
if possible. As no such explanation was forthcoming, the spectra
were very carefully measured and described.
On one and the same plate 12 exposures had been successively
made in the third order spectrum of a plane grating. A solar image
of 51 mm. in diameter was so adjusted that the image of a spot
fell exactly on the slit. The length of the slit (6.5 m.m.) corresponded
to about one eighth of the sun’s diameter.
The first exposures show the normal spectrum without any con-
siderable changes. Then came the disturbance, which culminated in
the eighth spectrum and, in the following four, decreased rapidly.
Hare gives reproductions of four spectra, each of them extending
from 23812 to 24132. N°. 1 has been taken before the disturbance
occurred; N°. 2 is the most abnormal spectrum; N°. 3 is called
by Harr the “intermediate” spectrum, it has been obtained a few
moments after the abnormal one; N°. 4 shows once more the nor-
mal solar spectrum, as it was photographed at another time on
another plate. Nos. 1, 2 and 3 show a dark band throughout the
whole spectrum, corresponding to the sun-spot which had been
focused on the slit.
The most prominent features of the abnormal spectrum awe:
1°. The band due to the spot appears much fainter than in the
spectra, photographed before and after the disturbance.
1) Georce E. Hare. “Solar research at the Yerkes Observatory”. Astroph. Journ.
XVI p. 211—233, 1902.
( 594 )
2°. With several Fraunhofer lines the intensity or the width is
greatly diminished. This is most conspicuous with the
broad, dark calcium bands H and K and with the hydrogen line
Hd, these being almost totally absent in the abnormal spectrum.
3°. Other lines, on the contrary, appear uncommonly
strengthened.
4°. Many lines are more or less displaced.
The same peculiarities are noticed, though generally in a smaller
degree, in the intermediate spectrum, so that the latter, in fact, forms
a link between the abnormal and the normal spectrum.
This marvellously complicated disturbance was not confined to
light coming from a comparatively small part of the solar disk, for
instance from the immediate surroundings of a spot; on the contrary,
it extended almost equally over the whole width of the spectrum and
was therefore nearly the same for all the light which came from a
very great area of the Sun.
The moments of the 12 exposures and the exact date had not been
recorded, but there was sufficient evidence that the whole process
of the disturbance lasted only a very short time.
Harre calls the phenomenon: “a remarkable disturbance of the
reversing layer”. But is it not almost impossible to imagine a rather
thin layer in the solar atmosphere undergoing suddenly and simul-
taneously over a great part of the sun such a thorough change, as
to make its absorbing and radiating power in some parts of the
spectrum for a while nearly unrecognizable ?
It occurred to me, therefore, that the origin of the phenomenon
should be looked for somewhere on the path of the light between
the Sun and the Earth. If on this path there be media, causing
anomalous dispersion, the beam must show an altered composition.
As I formerly indicated 5), the properties of the chromospheric
light may be derived from the supposition, that this light has been
scattered out of the photospheric light by anomalous dispersion.
According to this hypothesis the spectrum of the chromosphere
informs us, which are the kinds of light, that may follow rather
strongly curved paths in the solar atmosphere. So the idea suggested
itself, that the same waves might play a striking part in HaAtp’s
abnormal spectum.
In order to investigate the question as impartially as possible, |
marked (before consulting Hanw’s table or a table of chromosphere
1) Proc. Roy. Acad. Amst. II, p. 575—588; ILI, p. 195—203; IV, p. 162—171;
Physikalische Zeitschrift 4, p. 132 —'36.
40
Proceedings Royal Acad. Amsterdam. Vol. V.
(592)
TABLE I.
Lines whose intensity is less in the abnormal than in the normal spectrum.
Intensity
a
Chromo-
sphere
inter-
normal | mediate | abnormal
Wavelength Remarks,
SPUAU]
(ROWLAND) (HALE) (HALE) [(LoCKYER)
3872.6
in the abnormal spectrum
4012.50 5 4
4033 .29 7 42
4034.64 6 10
o—b- 171; ete.
3-4 |Un, Fe
3—4 |dn, Ve
4063.76 20 RE ee eee
4071.91 15 15 15%
4077 .88 8 10 7e
H 4102.00 40 7 ze
3871.4 | | 4 C |)Not mentioned in Hare's
| | Fe list, but distinctly weakened
3874.09 Be A Dis Yea 2(?)| Fe on the reproduction.
3878. 47 ON ND Vos bs te 3 3 | Fe, Fel 2 = 3878.15 and; = 3878.72;
H, 3889.05 p 15 | = 8 H HALE mentions Ve, Mu.
” 3895.80] 7 Ce 3 | Ze
3899 . 30 5 RN = 2, V2
3903.09 do re — 2—3 le
3905 . 66 12 | LO a 2 Cr, Si
3906 70] 14 | — | 4 2 Ve
3913.63 eat ae eee Mn 6 Ti
TON ne Mie SCE ed, 1i_|_* These intensities are very
3016 54 3 LN ht 3 y {probably estimated too high
J when compared with the
3920.41 40 10% 105 3 Fe |numbersin the second column.
3923.05} 12 12e | 19% 5 <4 tie eee OP ores
K 3933.82 | 10 Ca
3944.16 15 15% 12% 5, Al
3948 91 13 15 — } le
3950.10 3 — 2 "3 fe
3953 .02 17 1D ol AS Fe, ete.
3958 35 5 Ek — i Ti
3961 67 20 DO ci 6 Al
H 3968.63 | (700) 7 7 10 Ca
H, 3970.18 7 8 | — 10 iH
3977 .89 6 RT 2 Fe
3986.90 6 Bree
3998.78 | 4 4 | a ewes,
(593)
lines) on the reproductions of the spectra in the Astrophysical Jour-
nal a number of lines, which struck me as being weakened in the
abnormal spectrum. By means of Grorcr Hiees’ photographie atlas
of the normal solar spectrum the wave-lengths of the selected lines
were easily read; they are to be found in the first column of Table I.
The second, third, and fourth columns show the intensities of
these lines in the normal, the intermediate, and the abnormal spec-
trum as given by Harre (for the normal spectrum from Rowraxp’s
tables, for the other two from estimations by Mr. Abams). Hare
remarks that the intensities of the lines were estimated independently
for the two disturbed spectra’). The fifth column indicates the inten-
sities of corresponding chromosphere lines as found by Lockyer in
TABLE II.
Lines whose intensity is greater in the abnormal than in the normal spectrum,
Intensity.
2
Wave- EET TER eee Chromo- = Remarks.
length normal | mediate | abnormal] sphere =
cen (HALE) (HALE) f(LOCKYER) 3
3921 86 Oe ee Zr, Mn
SHAR — | — 25 P
3930. 45 Seal 18 28 3=4 Fe
BOONE If! ee ede 40 2
GOTE EE Peat, ae eae b> p
3950.50 Paige MEE y
3962.29 3 ee 11 Fe?
3973.77 6 — sy A: Ni, Zr, Ve,Ca
398 |. 92 4 13 30 6 Ti, Fe * In HuMmPHREYS’ table
A 3 | & | 40 ge hee Pmt
3996 . 80 a md 5 p occur.
4013.90 el dr. eta Ti, Fe
4O14 67 En | 9 20 Fe
4923 .38 ae ade Sa 10
4033.77 pA Sarre ileal Oke Gs Mn
4040.79 hare 20 4 Ve
044.09 | 5 | 20 | 45 Fe
1) In selecting the lines that appeared weakened in the abnormal spectrum I
did of course compare the three spectra mutually. That is why in my table some
lines occur, whose intensities, as estimated by Mr. Apams, are not comparatively
low in the abnormal spectrum.
=40
( S59)
the spectrum, secured at Viziadrug during the 1898 eclipse’); the
sixth column shows the absorbing substances.
In a similar way Table IH has been composed; here we find the
lines, which on the reproduction appeared to be strengthened
in the abnormal spectrum.
The result is very striking. Weakened lines correspond
to chromosphere lines, almost without exception;
mostotthe strenzthened lines, on the other hans
are not to be found in the spectrum of the chrome
Bip be re:
Lockyer gives the strength of the chromosphere lines on a scale
such that 10 indicates the strongest and 1 the faintest lines. If we take
into account that in his list the greater part of the lines bear the
numbers 1 and 2, our table shows us, that by merely observing the
abnormal solar spectrum we have been able to pick out strong
chromosphere lines. This cannot be chance. Undoubtedly both phe-
nomena — the weakening of Fraunhofer lines in the abnormal spec-
trum and the origin of the chromosphere spectrum are to be
explained in close relation with each other.
The strengthening of lines in the abnormal spectrum does
not, on the contrary, seem to be so directly connected with the com-
position of the chromosphere spectrum.
If our view be correct that the chromospheric light has been se-
parated by strong ray-curving from the “white” light emitted by
deeper layers, those special radiations must, as a rule, show reduced
intensity in the spectrum of the Sun’s disk *). Fraunhofer lines cor-
1) Lockyer, CurisHotm-Barten and Peprer. “Total Eclipse of the Sun, January
22, 1898. — Observations at Viziadrug,” Phil. Trans., A, vol. 197, p. 151—227, 1901.
2) It might be thought that the rays forming the chromosphere light, need to
be absent only from the spectrum of the edge but not from that of the central
portions of the Sun’s disk. By a simple consideration, following from a look at
Fig. 4 of my paper, read in Febr. 1900 (Proc. Roy. Acad. Amst. II, p. 580) we
see, however, that the chromosphere light visible to us may very well, fora part,
have its origin even in points of the Sun which lie opposite to the Earth’s direc-
tion. The chromosphere light, reaching the Earth, may proceed from any point
of Scuipr’s “critical sphere“. For the greater part it is likely to come from the
back half of the Sun. But then the half, facing us, furnishes the chromospheric
hight which travels to other regions of the universe, and this light, of course, is
wanting in the spectrum of the disk. (There is some reason for supposing that,
on an average, more chromospheric light is sent forth in directions making great
angles with the Sun’s equator, than to the equatorial regions, including the
Earth’s orbit.)
* oor le
ETT B,
er
responding to chromosphere lines will therefore have a more or less
darkened background in the ordinary solar spectrum. The rate of
darkening at various distances from the centre of an absorption line
is, of course, connected with the shape of the dispersion curve near
that line; whereas the average shading depends 1st on the quantity of
matter causing anomalous dispersion and 2°¢ly on the slopes and the
directions of the density gradients in the gases through which the
light is transmitted, viz. on the Sun’s “activity” *).
We distinguish, therefore, a twofold origin of the dark lines in
the solar spectrum: real absorption of those waves, exactly cor-
responding to the periods of the media, and dispersion of the
strongly deviated neighbouring light *).
The dispersion will be especially evident where extraordinary diffe-
rences in the density of the medium occur ; in this way the widening
of most of the Fraunhofer lines in the spectra of spots may be
accounted for.
Dispersed light has not, of course, vanished; the absence of certain
rays in the spectrum of a spot is counterbalanced by the increased
intensity of the same radiations in the light coming from the neigh-
bouring faculae. Thus the distribution of the density in the solar
gases may locally be such, that a limited part of the disk seems to
emit a considerable amount of rays with abnormally high or abnor-
mally low refractive indices. In-the spectrum of such parts not only
will the Fraunhofer lines show narrower and fainter than usually, but
here we may even meet with lines contrasting brightly with their
surroundings. These bright lines will not coincide with the corre-
sponding absorption lines; their average wave-length will in general
be greater or smaller than that of the absorbed light, for, according
to the accidental distribution of the density, we shall find either the
rays with high or those with low refractive indices most prominent
in the beam.
The above considerations suggest an explanation of Hare’s abnormal
spectrum.
In fact, the lines showing especially faint in this spectrum were
exactly those, causing strong anomalous dispersion — witness the
1) The possible influence of the general or regular ray-curving (after Scumpt's
principle) on the feature of the spectral lines has, in the present paper, been left
out of consideration. If we were able to observe or to calculate the radii of the
“critical spheres‘‘ for radiations undergoing anomalous refraction, it would be
possible to estimate that influence; but as yet sufficient data are wanting.
2) Proc. Roy. Acad. Amst. If. p. 580.
a Te we ine
( 596 j
chromosphere spectrum. With MH, A, Hy) and some iron lines it 1s
conspicuous that the abnormal faintness regards mainly the broad
dark shadings of the lines, i.e. those parts, whose darkness in the
normal spectrum we attributed not to absorption, but to dispersion.
Moreover, the dark band due to the spot has nearly disappeared. This
means that waves, which in normal circumstances are wanting in
the spot spectrum on account of their strong dispersion, at the time
of the disturbance had been gathered again into the beam reaching
the instrument.
How all this may happen will become evident as soon as we shall
be able to establish a plausible cause, by which, within an angular
space great enough to include a considerable part of the solar disk,
the strongly dispersed rays might be gathered again.
It is not necessary to introduce a new hypothesis for the purpose.
The same idea about the Sun’s constitution 1) which enabled us to
explain the properties of the chromosphere and the prominences,
furnishes us once more with the required data.
Indeed, if (according to Scumipt’s theory) the Sun is an unlimited
mass of gas, surfaces of discontinuity must exist similar to those,
whose general feature has been determined by Euperx ®) for a sharply
outlined radiating and rotating sun. These surfaces must extend unto
the remotest parts of the gaseous body — a conclusion in excellent
harmony with the visible structure of the corona. For along the
surfaces of discontinuity waves and whirls are formed; the core-lines
of the vortices nearly coincide with the generatrices of these surfaces
of revolution, and in these cores the density is a minimum. This
may account for the streaky appearance, shown more or less dis-
tinctly in all good photographs and drawings of the corona.
This particular appearance may have another cause, though ; for
what follows, however, this is immaterial. We only assume that the
density of the coronal matter varies in such a way, as to correspond
to the striped structure visible at the time ofa total eclipse of the Sun.
A coronal streamer which, at a given moment, runs exactly in the
direction of the Earth may be very roughly compared, then, to a
bundle of glass tubes through which we are looking lengthwise. Such
a structure will gather and conduct rays of various directions, ente-
ring it at one end. This takes place also if the parts with the greater
and those with the smaller optical density do not alternate abruptly,
like glass and air, but gradually.
1) Proc, Roy. Acad. Amst. IV, p. 162.
2) R. Empen, Beiträge zur Sonnentheorie, Ann. d. Phys. [4], 7, p. 176—197.
In Fig. 1 the optical density of the
matter may be represented by the com-
pactness of the streaking. A ray for
Which the medium has a large positive
refractionconstant would for instance
follow the path AA‘, curving round the
denser parts of the structure; aray BB,
for which the medium possesses a large
| negative refractionconstant, would move
in a similar way through the more rare-
fied regions. On the other hand, the light
| CC" for which the constant exactly equals
zero is not influenced by the fluctuations
of the density ; and if for some kind of
light the refractionconstant is very nearly
zero, the ray would have to travel a long
way almost parallel to the structure before
its curving would be perceptible.
Now the corona sometimes shows exceedingly long, pointed strea-
mers. We only have to suppose that the Earth was exactly
inthe direction of sucha streamer at the moment
the abnormal spectrum was photographed; then
all the irregularities observed in this spectrum become clear. Light,
under normal circumstances absent from the solar spectrum through
strong dispersion, has been collected by the coronal streamer ; hence
the weakening of the Fraunhofer lines, especially also of those
in the spectrum of the spot. As the abnormalities were caused by a
peculiar distribution of matter in the vast regions of the corona, lying
between the source of light and the Earth (and not by disturbances
in a relatively thin ‘reversing layer’) they could appear in the
same way over a great part of the Sun’s disk. The rarity of the
phenomenon is the result of the slight chance we have to take a
photograph at the very moment on which an uncommonly long coronal
streamer is projected exactly on the part of Sun’s disk illuminating
the slit; the short duration finally is a consequence of the
difference between the angular velocity of the corona and that of the
Earth in its orbit.
As we have mentioned before, #0 chromosphere lines correspond,
in general, to those lines showing extraordinarily strong in the abnor-
mal spectrum. How are we to account for the strengthening of
these lines?
(598 )
We might be tempted to think of absorption in the corona; for
if it be true that a streamer was turned towards the Earth, the rays
had to go an uncommonly long way through an absorbing medium.
But on closer examination this idea is less probable.
The particles of the extremely rarefied corona gases will hardly
influence each other; their periods will, therefore, be almost absolutely
constant, so as to cause very sharp, narrow absorption lines. Thus it
is difficult to understand, how an absorption line, already present
in the normal solar spectrum, might be strengthened by the absorbing
power of the corona. Further, in studying Harr’s table, we observe
that many lines which are strong in the abnormal spectrum, show
a much smaller intensity in the intermediate spectrum (taken only
a few moments later); whilst the reverse happens as well, viz. that
lines are strong in the intermediate and very weak in the abnormal
spectrum. This hardly fits in with the absorption hypothesis. Some
lines showing this peculiarity are given in table III.
TABLE III.
Lines whose intensity is very different in the intermediate and the abnormal spectrum.
Intensity |
bn | ela eee Pe Remarks.
RowLAND)| (HALE) (HALE) | (LOCKYER |
el Ee GE ee EE SSP ee eee eee
3005.66 2 20 — 2 Cr, ot
3905.81 21 — 20 Si
3921.71 9 14 — Ti,La,Zr, Vii
3921.87 4 -- 20 Zr, Mn
3950.33 = 10 — P
3950.51 De 13 Me
3972.30 2 12 — Ni
3972.61 FS Yin AL ee 42, ?
4005.86 3 25 D ?
4057 .39 4 — any {—2 Cos Fe
4057 . 66 7 40 aa P
In the chromosphere spectrum corresponding lines seem to be
wanting. (At 2 3905.66 and 2 4057.39 the faint chromosphere line
may SNE belong to another element than the abnormally streng-
thened absorption line).
To arrive at a more satisfactory explanation of the strengthening-
phenomenon we suppose that these absorption lines do indeed cause
anomalous dispersion of neighbouring waves, but in a very slight
zi
, ogous
degree. Then, the refractive indices of the neighbouring waves differing
hardly from unity, the direction of those rays will only be percep-
tibly changed after they have travelled a very long way through
the corona and almost parallel to its structure-lines. Whereas the
strongly refracted rays, entering the coronal streamer in various
directions, were obliged to follow the structure-lines, curving about
them, and so in a sense were concentrated on the Earth, it may
happen with the extremely slightly curved rays we are now consi-
dering, that they have been bent for instance only once over the
whole length of the streamer and continue their way in a direction
not meeting the observing station. The divergence of a beam con-
sisting of these rays will have increased, the intensity diminished.
Thus, the resultant spreading of neighbouring light causes the
absorption line to appear somewhat widened and therefore strengthened.
But obviously it must be possible too, that, after a short time, under
the influence of another part of the corona, circumstances turn out
even favourable for that slightly curved light to reach the observer.
In that case the absorption line is weak again. (Similar alternations,
of course, also occur with the more strongly refracted rays, and that
in quicker succession, but this does not alter the fact of their average
intensity appearing increased as long as the structure lines of the
coronal streamer are turned towards the spectroscope. For a detailed
discussion of this case see the Note at the end of this paper).
In both abnormal spectra a number of absorption lines are more
or less dispiaced. Perhaps this is partly due to motion in the line
of sight; but after the foregoing it will not be necessary to explain
in detail, that also anomalous dispersion can account for this pheno-
menon. Dissymmetric form of the dispersion-curve as well as a
peculiar distribution of the density of the coronal matter may une-
qually affect the intensity of the light on both sides of the absorption
line, and thus bring about a seeming displacement of the line.
Certain peculiarities of lines in the normal solar spectrum.
If we have been right in connecting the uncommonly great abnor-
malities in Hare's spectrum with a very particular position of the
Earth with respect to the corona, it is to be expected that similar
irregularities, though to a smaller degree, will ever be found, as the
sunlight always reaches us through the corona.
According to Jewerr’s above mentioned investiga’ ions this supposition
proves to be well founded. Many solar lines have varying intensities
and positions, so that Jewerr deems them unfit for standards for
( 600.)
very accurate determinations of wavelengths. And these are for the
greater part the most prominent lines of the spectrum, especially the
shaded -ones *).
JuWELL emphasizes the fact that all distinetly shaded lines in the
solar spectrum show to a greater or less degree the following typical
feature ®).
Within a broad, shaded, moderately dark background a much
darker central absorption line contrasts rather sharply (Fig. 2).
ed
Tig. 2 Fig.5.
Besides, the absorption curve often shows dippings close to the central
line, as in Fig. 3, sometimes symmetrical, sometimes dissymmetrical.
Jewett affirms that this is not an optical delusion, due to contrast,
but a real phenomenon. He assumes, therefore, that the broad absorp-
tion band is produced in the lower portions of the solar atmosphere
and under a great range of pressure; that in higher levels radiation
prevails again, producing a rather wide emission line ; and that finally
in the highest parts, where the pressure is very much less, the sharp
absorption line is produced. The position of this central absorption -
line with respect to the emission line is usually unsymmetrical, which
is conspicuous in the case of H and A. The central line itself also
varies somewhat in width upon different plates and its maximum of
intensity is not always in the middle of the line. The displacement
of this central line in MZ and A varies in magnitude, but, so far as
has been observed, always toward the red with respect to the emis-
sion line and the corresponding metallic line (in the are).
Jewerr concludes that the absorbing calcium vapour descends all
over the solar surface with a velocity sometimes amounting to about
75 miles per minute.
Upon the same plates showing strong dissymmetry in // and A,
the shaded lines of other elements (Me, A/, My, Si) have been
examined. The strongest iron lines and one aluminium line showed
displacements of the same character as that observed in the case of
1) Astroph. Journ. XI, p. 236, 1900.
2) Jewett, “Certain peculiarities in the appearance of lines in the solar spectrum
and their interpretation”. Astroph. Journ, Ill. p. 99, 1896,
ore aac ill
a Je
zn”
( 601 )
H and kK, but to a much smaller degree and sometimes toward the
violet, sometimes toward the red. Certain shaded lines of My and Si,
on the contrary, showed no evidence of a displacement, nor did the
iron lines without considerable shading, the faint calcium line at
A 3949,056 and many other lines.
If we admit no other explanation of line-shifting and -widening
besides those, based on DorPrer’s principle and on the effect of
pressure and temperature, we arrive at very strange conclusions
relative to the condition of the elements in the solar atmosphere. Not
less surprising is, as noticed by Jrwrrr *), the small amount of the
absorption in the shaded parts of the lines, when we consider the
enormous depth of the solar atmosphere and the high pressure which
must exist in the absorbing layers, for them to produce a broad
absorptionband.
By making various suppositions concerning the condition of the
gases in the solar atmosphere, JrwerL succeeds in finding an inter-
pretation of most of these astonishing facts. But it must be granted
that his explanations include a greater number of arbitrary and mu-
tually independent hypotheses than is the case with our explanations,
founded as they are on selective ray-curving and readily deduced
from that principle for each separate phenomenon, without intro-
ducing new suppositions.
Only the dark central lines of the Fraunhofer lines are to be
ascribed, in our theory, to real absorption. Their shaded background
of varying intensity we consider as an effect of anomalous dispersion
of the not absorbed neighbouring waves. This selective scattering
will be strongest in those places where the density-gradients are
relatively steep, viz. in whirls in the deeper regions of the gaseous
body. But some of the widely dispersed rays may be gathered by
the corona owing to its “tubular structure and be conducted along
its greater or smaller streamers.
This will especially apply to the most strongly refracted waves,
Whose position in the spectrum is very close to the real absorption
lines; thus pseudo emission lines are produced in about the middle
of the pseudo absorption bands. *)
1 Astroph. Journ. ILI, p. 106.
2) A most remarkable fact is that the shading of K, H, the iron-line à 3720.086
and of some other strong shaded lines is sometimes partially kroken up into a
series of faint nebulous lines, symmetrically situated about the central line. In
each case the distance apart of the component lines increased as the distance from
the center increased (Jewett, Astrophysical Journal 8, p. 51—53).
It might have been predicted by our theory that we should meet with this
phenomenon now and then.
( 602 ) Ek 4
Most likely Hare's abnormal spectrum has shown us a case, where
these seeming emissionbands acquired an uncommon extent. We may
therefore expect that a systematical investigation of solar spectra,
photographed at different times, will afford all kinds of intermediate
cases.
It would be desirable, for the moments when the photographs
are taken, to know form and position of the coronal streamers ex-
tending toward the Earth. At all events the actual phase of the sun-
spot period, with which the shape of the corona seems to be con-
nected, should be taken into consideration; and perhaps the simul-
taneous observation of the photospheric reticulation, discovered by
JANSSEN, may procure some evidence concerning the position of coro-
nal streamers, and thus contribute to our knowledge of their influence
on the Fraunhofer spectrum.
Mineralogy. — “On the refractive index of rock-qlasses,” by P. Trscu:
(Communicated by Prof. J. L. C. SCHROEDER VAN DER Kork).
Of the group of the igneous rocks, the origin of which out of
fluid red-hot condition we accept, the voleanie rocks constitute that q
subdivision, which includes the rocks, that as lavas have broken
through the surface of the earth.
The quick cooling at the atmosphere renders it possible that in
these rocks part of the magma congeals amorphously, so that next
to the minerals a rockglass appears, which constitutes either an infe-
rior part or a prevailing one of the rocks. So in general this glass
Let us consider a beam of light of an exactly defined wavelength belonging to
the shaded background of an absorption line. This beam leaves the deeper layers
of the Sun with a certain divergence. As it passes along a “tube” of the corona,
q
|
its divergence will alternately diminish and increase, and on reaching the Earth
it shows in the spectrum an intensity, depending on the divergence (or perhaps
convergence) with which it has left the last traces of the corona. For a beam of
light whose wavelength is only slightly nearer to that of the absorption line, the
medium will have a considerably greater refraction constant, so that the rays of
this beam, on their way through the corona, may make part of a bend more than
the former ones. The beam may therefore arrive with a quite different degree of
divergence and, consequently, of intensity. Thus, proceeding towards the absorption
line from either side, we easily see that we must meet with a periodically changing
intensity. Rays, corresponding to the middle of one of the so formed fringes, will
have made one full bend more or less than the rays, belonging to the middle of
the next fringe.
If this interpretation be correct, the width and the number of fringes visible
must prove to be variable, As far as | know, the observations made on this point
are not numerous. May the proposed views serve to further the investigation of
this interesting phenomenon.
( 603
consists of silica and metal-oxides. We may suppose that the silica,
which is most likely to be the principal part, will also have a pre-
valent influence on the physical characters of such natural glass.
A determination of the specific gravity of the glass is made more
difficult by the presence of many gas-bubbles. If this obstacle did
not exist, the specific weight would be a better expedient for a
quick temporary orientation than the determination of the refractive
index, for which more instruments are necessary. With respect to the
specific gravity it could be stated, that with these rocks where the
value of the index the use of bromoform as liquid of comparison neces-
sitated and whose exponent proved to be greater than that of bromo-
form (1,593), the specific gravity of the glass was still higher than
that of bromoform (2,88). The small air-free, not to be isolated
grains, still sank in this liquid. Now I have tried to find out in how
far the refractive index is dependent on the SiO, percentage. For
that purpose 16 rocks have been examined, forming a series of the
most acid to the most basic magmas, which occur in nature.
The result has been eomprised in the following table:
Name
|
|
|
|
|
Origin sis [tates Index
|
Granite Magurka, Hungary 72,65 1,500
Granite Brocken, Harz Mountains AAG 4,500
Granite | Auvergne 70,62 1,500
Granite ‚_ Korinitsch, Hungary 67,31 1,510
Quartzdiorite | Adamello, Tyrol 66,58 10
Syenite | Plauensche Grund, Dresden 60 26 1,520
Klaeolite-syenite | Ditro, 59,88 1,525
Diorite | Hodritsch, Hungary 59,57 1,525
|
Syenite | Ditro, 57,36 1,530
Augite-syenite | Monzoni, Tyrol 53,79 1,550
Chrysolitenorite Radau Valley, Harz Mountains 53,64 1,550
Diorite | Auvergne 50,86 1,570
Quartzdiorite | Dumkuhlen Valley, Harz 48,89 1,585
Basalt | Dyrafjord, Iceland 4850 1,540
Gabbro Radau Valley, Harz 44,08 1,620
Harzburgite Harzburg, Harz | 42,24 1,630
( 604 )
From this we see that a classification exclusively according to
decreasing SiO, percentage, coincides with an increasing value of
the refractive index.
Apparently the metal oxides present have only little influence on
that value, at least this influence falls within the limits of the
errors of observation.
A chrysolite-norite and an augite syenite with about the same
SiO, percentage have also the same index, whereas the oxides,
especially MgO are sure to be there in quite another relation, for
in the chrysolite-norite the minerals containing Mg come strongly
to the foreground.
As regards the colour of the glass it will be almost wholly
dependent on the iron-percentage.
With the examined glasses the colour changed from light green
to dark brown. Just as with isomorphous mineral series, as e. «. the
enstatite-hypersteneseries, the dark colour most likely points to a
greater iron percentage than the light one.
The typical amorphous glassfracture can be easily distinguished
at the splinters under the microscope.
The fusion of the roek-powder took place in a gasflame in which
compressed oxygen was blown. As an underlayer a cupel of chalk
or bone-ash was used. But care has to be taken that the melted
magma of the cupel remains isolated, because there is a chance that
oxides of alealic earths will be absorbed by the cupel and in
consequence the composition of the magma does not answer any
more to that of the rock. This can be obtained by directing the
point of the flame towards the middle; the upperlayer then fuses
quickly to a little ball, which remains isolated by the underlaying
rock-powder of the eupel. To control the regularity found in the
independence of the refractive index of the Si O, percentage, two
mixtures of the following composition were made:
L IL
SiO, 60 °/, 60°/,
Fe,O, 10 20
A1,O, 10 5
Ja0 10 5
MeO 5 10
K,0,Na,O 5 En
Of both the mixtures the fused glass had the index 1.520; here
we see again the prevalent influence of SiQ,.
At last some slags and melted minerals were investigated,
P. TESCH. On the refractive index of rock-glasses.
Proceedings Royal Acad, Amsterdam. Vol. V,
( 605 )
Composition. Index.
SiO, 45,5 1,600
CaO 19,8
FeO 5,3
SiO, 27,4 1,750
FeO 41,7
Cabr. 0,2
Pb 4a.
ALO 0,8
ZnO 21,8
MnO
In this slag the ZnO plays the part of the MgO. When ZnO is
replaced by MgO, the index remains the same.
Finally the index of the following minerals was determined:
Quartz mit. 100-°/, 1,475
Chrysolite fi 40—45 1,610
Orthoclase i 65 1,485
The last mineral, the pure K.Al.silicate consequently does not fit
into the composed series. After mixing with some grains Fe,O,
(5—10 ,/°’ and fusing anew the index was raised to 1,510.
The method described above can be of practical use for a quick
determination of the SiO, percentage of slags from the refractive
index with an accuracy of + 2 °/,.
A word of thanks for the aid and advice to the Professors Dr. J. L. C.
SCHROEDER VAN DER Kork and 8. J. Vermars Jr. may find a place here.
Mineralogy. — “On an “Kisenrose” of the St. Gotthard”. By
G. B. HoGENRAAD. (Communicated by Prof. J. L. C. SCHROEDER
VAN DER Kork).
Some time ago I tried to get a Hematite-streak with a so-called
“Kisenrose.”’ I did not succeed however, for to my astonishment
the streak was not red but black. Several explanations came to
my mind :
1°. that the mineral was somewhat friable, which was the cause
that the streak could not consist of the very finest particles. But in
rubbing the black colour remained; only the outlines showed a
reddish-brown tint. The same was stated with about 25 other pieces
of the same finding-place. So that the explanation proved to be not
the right one.
( 606 )
2°. that the mineral contained Mn or Ti, since these elements have
a great influence on the colour of the streak. But an analysis only
produced little Ti and no trace of Mn, so that this explanation did
not hold good either.
3°. that the mineral was magnetite. In its favour spoke the very
distinet magnetism, stronger than hematite generally shows.
I then consulted some literature, to see whether anything had been
written before on the streak, the magnetism and the chemical com-
position of “Eisenrose.”
Dana says‘):
St. Gotthard affords beautiful specimens, composed of crystrallised
tables grouped in the forms of rosettes (Eisenrosen), and accompany-
ing crystals of adularia.
Dana calls this occurring Hematite, though he neither speaks of the
chemical composition, nor gives any particulars about streak or
magnetism.
In the “Zeitschrift für Krystallographie und Mineralogie von P.
Grorn”’ I found in Number 13 on p. 301 a report by A. CATHREIN
from Srriver’s account on “Pseudomorphose von Magnetit nach
Eisenglimmer von Ogliastra in Sardinién”’, written in tke Atti della
Reale Accademia Dei Lincei 1886. Volume IL, 2°. Semestre, p. 331.
The report in question follows here :
„Die Hauptmasse der Stufe besteht aus einem grobkörnigen Mine-
ral, dessen unregelmässigen Individuen von mehreren Centimetern
Durchmesser fest mit einander verwachsen erscheinen. Jedes Korn
zerfällt nach einer Richtung äusserst leicht in dünnste Lamellen.
Harte 6, Pulver schwarz, stark magnetisch, schwer schmelzbar, in
Salzsäure leicht löslich. Diese Eigenschaften kommen dem Magnetit
zu. Das Gemenge erscheint ganz frisch, unverändert und ursprüng-
lieher Entstehung. Dass es sich hier nicht um nach {111} blätterig
abgesonderten Magnetit handelt, folgt aus dem Mangel jeder Spur
von Spaltbarkeit nach einer anderen Richtung ausser jener einen.
Die Lamellarstructur als Druekwirkung aufzufassen verbietet die
Richtungsänderung der Lamellen in jedem einzelnen Korn. Nach
des Verfassers Ansicht bleibt nur die Annahme einer Pseudomorphose
von Magnetit nach Eisenglimmer.”
So this appearance as regards streak and magnetism corresponds with
the specimen examined by me. Through the absence of a chemical
analysis it cannot be decided in how far the supposition is right, that
he had to do here with a pseudomorphosis from Magnetite to Eisen-
olimmer.
1) System of Mineralogy p. 216,
( 607 )
In the ‘‘Zeitschrift der Geologischen Gesellschaft” Bd. 22, 1870 I
found on page 719 in an article by G. vom Rarn the following
statement *):
“Pseudomorphische Massen von Magneteisen nach Kisenglanz. Farbe
und Strich schwarz, schimmernd auf dem Bruch, magnetisch. Das
rz ist aber weder dicht, noch körnig (wie es sonst dem Magneteisen
zukommt), sondern schuppig. Man erkennt sogar in einzelnen Drusen
ganz deutlich die hexagonalen Formen des urspriinglichen Eisenglan-
zes; doch auch diese letzteren haben einen schwarzen Strich. Ver-
mutlich is demnach jene ganze colossale Schichtenmasse bei Vallone
urspriinglich Eisenglanz gewesen”.
So to this can be applied what has been remarked on Srriiver’s
article.
Finally D. F. Wiser says *):
Die Eisen-Rosen vom Pomonetto wirken sehr stark auf die Magnet-
Nadel. Das Strich-Pulver is dunkel-röthlichbraun, beinahe schwarz.
Die Wirkung auf die Magnet-Nadel is bei den Schweitzerischen
fisenglanzen gar sehr verschieden, sowie die Nüanzirungen von Kisen-
schwarz bis Stahlerau in ihrer Färbung. Bemerkenswerth scheint es
mir, dass die EHisen-Rosen ohne aufliegende Rutil-Krystalle immer
die schwärzeste Farbe zeigen, und dass dieselbe hingegend immer
heller wird, je mehr Rutil auf den End-Flächen der Kisenglanz-
Tafeln, ich möchte sagen, ausgeschieden worden ist.
Die Mineralien, welche die Eisen-Rosen vom Pomonetto begleiten,
sind: kleine, graulich-weisse Adular-Krystalle, kleine sechsseitige Tafeln
von Tombackbraunen Glimmer und eine schmutzig griinlich-gelbe
Rindenformige Substanz die vielleicht den Chloriten beigezählt wer-
den darf.
Mein Freund, Hr Bergrath Srockar hieselbst, hat die Eisen-Rose
vom Pomonetto analysirt und wird hoffentlich nächstens das Resultat
seiner Untersuchungen veröffentlichen.”
However LE could not find this promised analysis anywhere in
literature, so that I decided to do it myself (1). For a good control
the same analysis was made by Messrs B. H. van DER LANDEN (II)
and G. W. Marrúr (HD. The results of our investigations were as
follows :
1) Geognostisch-mineralogische Fragmente aus Italién, chapter VIIL: Die Insel
Elba, Zeitschr. D. G. G. 1870.
2) Bericht über Mineraliën aus der Schweiz, N. Jahrb. 1854 p. 26.
r
.
Proceedings Royal Acad. Amsterdam. Vol, \
Fe 69,94 69,13 69,50
O 29,97 29,60 30,46
accompanying mineral 1,2
99 91 99 93 SE)
Reckoned for :
Hematite Magnetite
Fe 70 72,41
O 30 27,59.
So that my conclusion is that we have not to do with Magnetite but
with Hematite.
The results of my researches are in consequence the following:
Tst, That I have had to do with Hematite with very obvious
magnetism and a black streak, which in rubbing along the outlines
shows a brown tint (which generally every black streak does) and
not with a pseudomorphosis from Magnetite to Hematite.
2ad- That where in literature of this occurrence of Hematite has
been spoken, no analysis has been added, though the magnetism and
the black streak have been observed more than once.
sed, That it is desirable to convince oneself of the chemical com-
position with every “Eisenrose”, which shows these characteristics.
Physics. — “Contributions to the theory of electrons.” 1. By Prof.
H. A. Lorentz.
Simplification of the fundamental equations by the introduction
of new units.
§ 1. If all quantities are expressed in electromagnetic units, as I
have done in former papers, the relations between the volume-density
o of the charge of an electron, the velocity » of its points, the
1) | here by have to mention that first the figure for the oxygen was determined
by reduction in a hydrogen-current und weighing of the water absorbed by Ca Clo;
that after that the figure for the iron was determined by dissolving the reduced
mineral in dilute H,SO, and making a titra'ion ot this solution (after reduction
in a H,S-current and after removing the H,S by boiling in a CO, atmosphere)
with a KMnO,-solution, of which 1 cM® corresponded with 8,9 m.G. Fe.
The presence of Ti was shown as follows: the mineral was melted together
with KHSO,, the fused mass dissolved in cold water. This solution together with
H,0, gave the well-known orange colour of TiO;. Moreover after adding a
little HNO;, the Ti after having been boiled precipitated as white TO). The
accompanying mineral, which in microscopic examination proved to be adularia,
was removed as much as possible,
( 609 )
dielectric displacement > in the aether, the current {and the magnetic
force § are as follows *):
du} =o,
dod, 0
end uw tors,
onhe Q v)
(=d ov,
do'h= 0,
roth=4Anrl=4r(d dot),
4 ac? rot d = — bh,
where ¢ is the velocity of light in the aether. To these equations we
must add the formula
F=4actd + fy. b]
for the electric force, i.e. the force, reckoned per unit charge, which
the aether exerts on a charged element of volume.
The equations take a somewhat more regular form if we express
o, >, Land f in electrostatic units (preserving the electromagnetic unit
for 6) and a further simplification is obtained, if, instead of the units
for charge and magnetic pole that are usually taken as the basis of
the electrostatic and electromagnetic systems, we choose new ones,
4a times smaller *). Introducing both modifications, we have to
replace’o, >; l- by — ze = ae a
we VA Van’ cVAxr
letter must now represent the force acting on the new unit of charge,
, f by cV4dar.f, because this
and likewise § by V 4a. 6.
This leads to the equations
QS Obs ok Ar EN (1)
s Edin (obi 0 ee es ee
GE bh hd AE ean ee
ei Bn re ne Es (IV)
1 ‘he
rot fh == == — (D+ 00); - 2 . . . (V)
(
1) See my Versuch einer Theorie der electrischen und optischen Erscheinungen
in bewegten Körpern. 1 shall again suppose that all quantities are continuous
functions of the coordinates, so that e.g. the density p will be regarded as passing
gradually to the value 0, which it has outside an electron. With the exception of the
letters, the notations are the same as in the just mentioned treatise. The scalar
product of two vectors a and b will be denoted by (a.b), the vector product by
[a.b]. The axes of coordinates are supposed to remain at rest, relatively to
the aethicr.
2) This change has been warmly advocated by Heavrsipe. The units [ shall
how use are those that have been adopted for the Mathematische Encyclopddie.
41%
( 610 )
eee
pt De EP es (VI)
ul
htss. Di. RDP ARE Oe TE
In connexion with the last formula it may be remarked that d is
the electric force that would act on an immovable charge.
The electric energy per unit-volume is given by
re 1 9 af
We ed pi ee Re rt a at yk,
9
a
the magnetic energy per unit-volume by
ae te
i mS ae De . . . . . . . . . (LX)
and Poyntine’s flux of energy by
TSS Jo . hb] . . . . . . e e (X)
We shall further write for the total electric and 7’ for the
total magnetic energy of a system.
The equations (IV) and (V) suffice for the determination of the
magnetic force b, as soon as the current [ is given in every point.
W, is then known by (IX) and 7’ follows by integration. In this
sense, every motion of electricity may be said to be accompanied
~~ &
by a definite amount of magnetic energy.
Scalar potential and vector-potential.
§ 2. The equations of § 1 apply to every system in which
charged matter moves through the aether, whether the charge be
confined to certain extremely small parts of space (electrons) or
otherwise distributed. Moreover, the motions may be of any kind ;
the electrons may have a pure translatory motion, or a rotation
at the same time, and we may even suppose their form to change
in the course of time. For the validity of the formulae it is however
required that each element of volume whose points move with the
charged matter should preserve its charge, though its form and
dimensions may change. This is expressed by the equation (IT) and
it is on this ground that the electric current |, as defined by (IID,
(the resultant of the displacement-current d and the convection-cur-
rent ee) may always be said to be solenoidally distributed, so that
dio == 02
If now the motion of the charged matter is given, the electro-
magnetic field in the aether, within and without that matter, has
( Git}
to be determined by means of (I)—(VI), a problem that may be
reduced to equations of the form
1 Oy
yc ae
COE:
in which @ is a known, and y an unknown function of w,y, zt.
En Oi Va Un! ay Ae edn See
Let a be any closed surface and 7 the normal to it, drawn out-
wards.
Then, if the equation (1) holds in the whole space JS, enclosed
by o, we shall have for the value of w in a point P of this space,
at the time f,
Ie: vod: Pee Fo any abe
i —}| — |— — | —
he eu r bel er = | r 5 | Ly On ( r )
Here the first integral extends over the space S and the second
over the boundary surface 6; 7 is the distance to P, and the square
brackets serve to indicate the values of the enclosed quantities for
jp
the tme. tn
Cc
Let us now conceive the surface 6 to recede on all sides to infinite
distance and let the circumstances be such that the surface-integral
in (2) has the limit 0. Then, ultimately:
A NE i
p= [> leas . . . . . . . (3)
where the integration must be extended over infinite space.
§ 3. Equations of the form (1) may be deduced from the formulae
DVI) in many different wavs; they may e.g. be established for
each of the components of d and *.') The solution is however ob-
tained in a simpler form’), if one introduces four auxiliary quantities,
a scalar potential p and the three components a, a, a. of a vector-
potential a, These quantities satisfy the equations
Oe
Ag — — ae — 0.
c? Of? Ss
1 074, 1 1 O%a, 1
AN DEN [Ge re ae tte, Une 6 rn
a OF? as ms U, ET . Ly, etc
so that, with the restrictions that are required if (3) is to be true,
we may write
EN A
ofer
|
Am,
1) Lorentz, La théorie ¢lectromagnétique de Maxwett et son application aux
corps mouvants, Arch. néerl. T°, 25, p. 476 1892,
2) See Levi Crvira, Nuovo Cimento, (4), vol. 6, p. 93 , 1897; WrecHERT,
Arch. néerl., (2), T. 5, p. 549, 1900.
if Egat ee 1 ]
Arm I—[om]dS , a,=— |{— [ev] ds, ete.
Ame ifs c Awe, f- ‘
After having found g and «a, we may determine the dielectric
displacement d and the magnetic force bh by means of the relations *)
Ley
betrap ye ee
C
AL Nees aten atd andes ye OE
It is to be remarked that the two potentials are not mutually
independent; they are connected by the equation
| i |
TANN rt ar Nn MEDE Dea
(
Theorems corresponding to the principle of vb ALEMBERT
and that of least action.
§ 4. The physicists who have endeavoured, by means of certain
hypotheses on the mecanism of electromagnetic phenomena, to deduce
the fundamental equations from the principles of dynamics, have
encountered considerable difficulties, and it is best, perhaps, to leave
this course, and to adopt the equations (1)—(VII) — or others,
equivalent to them — as the simplest expression we may find for
the laws of electromagnetism. Nevertheless, even if we prefer this
point of view, it deserves notice that the fundamental equations may
be transformed in such a way that we arrive at theorems of the
same mathematical form as the general principles of dynamics. This
has been done especially by ABRAHAM in his important paper
“Principien der Dynamik des Elektrons’™*). The considerations in
this and the two next paragraphs agree with those of ABRAHAM, though
presented in a form differing from his.
We shall consider a system of electrons moving in the infinitely
extended aether, and we shall fix our attention on the different
states of this system, the aether included, that sueceed each other in
the course of time in any electromagnetic phenomenon. From every
one of these states we shall pass to another, differing infinitely little
from it, and which we shall call the varied state. The variation
or “virtual change” will consist in infinitely small displacements 9 of
1) 1 shall write grad » („gradient of „”) for the vector whose components
0p Op Ap
are <—
2) Drupe's Annalen, 10, p. 105, 1903.
}
( 613 )
the points of the electrons, accompanied by infinitesimal changes in
the dielectric displacement.
We shall write dd for the difference, in a fixed point of the
aether, between the dielectric displacement before and after the
virtual change, the sign of variation d having a similar meaning
when it precedes other symbols representing the value of some
quantity in a definite point. If it is affixed to a letter representing
a quantity belonging to the system as a whole, such as the total
electric energy U, it will simply serve to indicate the difference
between these values in the original or real and the varied states.
The variations to be considered are not wholly arbitrary. We
shall limit our choice by supposing in the first place that each
element of volume of an electron preserves its charge during the
displacements q; this is expressed by the relation
ase ie" (Oa) tN eke ete one ta oa ey MOE)
which may be compared to (IL).
In the second place we shall suppose the variations of ò not to
violate the condition (1). |
In virtue of these restrictions the vector
dd + O4
will present a solenoidal distribution. Indeed, we see from (I) that
div dd = do,
and here we may, according to (7), replace the right-hand member
by — dw (o 4).
Let us now conceive q and Jd» to be chosen for every instant f,
so that they vary continuously with the time. Then, in order com-
pletely to define the succession of varied states, or what we may
call the „varied motion” of the system, we shall suppose the varied
positions of the points of each electron to be reached at the same
insiants at which these points occupy the corresponding original
positions in the real motion; we assume likewise that, in every
pomt of space, the varied dielectric displacement exists at the same
moments as the original one in the succession of real states.
By this the varied motion of electricity is entirely determined ;
indeed, since we know the velocity of matter and the rate at which
> changes, we are able to state what has become of the convection-
current, the displacement-current, and also of the total current [.
The first thing we have to do will be to express d{ in q and Jd,
Of course we may be sure beforehand that the distribution of both
the new ! and the variation dt will be solenoidal. This must neces-
sarily be the case, because we know 1st. that, in the states that
succeed one another in the varied motion, each volume-element of
( 614 )
an electron retains its charge, and 2°¢. that the condition (D) is con-
tinually fulfilled.
§ 5. Let us begin by considering dw. This is the variation in
a fixed point of space. Therefore, if (dv,) is the variation for a
definite point of an electron, we shall have
vx Ov, Ov.
(Sox) = te den 1 Gy ay den,
As to (dv), it is easily shown to have the value
_ dj
(do) = Er
& dq. ; ee
if we understand by fae the rate at which q‚ changes for a definite
dt
Ox
point of an electron. Comparing this to 5, OF os the velocity of
: :
change in a fixed point of ae we get
Oy: r Oja
(de) = de + t= + Wy Oy + Ve ae
These equations, combined with (7), lead us to
dl = 0 (dr + 0 te) = diz + od, + vd =
= J Da: a 0 Qa -- 0 Vr
Oy, Ov, Oy 7
— @ da = — Oy on — ede ya — yr div (a q).
or, if we add to the second member the first member of (IT), multi-
plied by q,, after some further transformation,
Ogu
dq 2
vy = = + 0 bz dE div (0 q) —
0
Ne Di A es
S [a a, Odrie Mere: ae en
i) Vs 0 Dz oe Va i; ke
— 04x aye 0 Ay iy —o4- au + qa div (v ») =
0 0 0
a OL (J De = Q Qa) + Oy lo (Gx Dii 0) | = ae lo (J- On — Oz b,) ]-
Here we may remark that the two last terms taken together repre-
sent the first component of the “rotation” of the vector whose com-
ponents are
0 (qy ve — Jz vy), 0 (Fz te — Gz vz), O (Az by — qy v2);
and that this veetor is precisely the vector-product, multiplied by
0, of q and v. After having calculated dl, and dl. in the same way
as dl;, we may combine the results in the formula
SS ee
eS ae ee PE ee
( 615 5
d | =< (ABE eq ratio [Gath ree ee Ge)
What has already been said about the solenoidal distribution of
di is confirmed by this equation. The two vectors represented on the
right hand side both have this property, the first by what we know
of the vector dd + 04, and the second on account of the mathema-
tical form in which it appears.
§ 6. We may next proceed to determine the variation d7’ of the
magnetic energy. In doing so we shall start from the assumption
that the varied motion of electricity involves a definite magnetic
energy '), to be determined as stated at the end of $ 1.
The formula
leads immediately to
dT =|. dh + by dy + he dh-) S= fo . Sh) dS,
Where the integration covers all space. The same will be the ease
with the other volume-integrals appearing in the following transform-
ations. If an integration is performed, or if the process of inte-
gration by parts is applied, one obtains integrals over the infinite
surface which we may conceive as the boundary of- the field of inte-
eration. These surface-integrals however will be supposed to vanish.
We begin by writing zot « instead of fh, as may be done in virtue
of (5); and we shall next integrate by parts, keeping in mind that,
on account of (V),
:
1
ads
C
The result is
1
dE fee de dh) dS == fos . rot dh) dS = fa sdi sone memes "2
or, if we substitute for dl its value (8),
zefls [ot eal Jas + S(« rot | (ela. ely Jas. (10)
Using (4), we may put for the first term
') This assumption only means to define the value of 7’ we shall assign to the
wholly fictitious varied state.
ah
( 616 )
Lie
edt
1 A
== ale .{dd+09})dS fe {dd+og})dS+ | (gradg.{dd-+-9q})dS. (11)
| cay
Now, it appears from (9) that
1
— f(a. fod + onpas. ; ere |
C
is the change the magnetic energy of the system would undergo, if
we gave to the current the change Jd + 9q. We shall write d’l for
this variation of the current, and d'b, dT for the corresponding
variations of § and 7. As to d’l, it may be defined as the current
that would exist if the changes represented by q and dd were accom-
plished in unit of time.
Ene
fee ten Hodes (a. {dd + eq) dS =
On the other hand, fe-amas is the variation of the electric
energy U and the last integral in (11) is 0, because the vector
Jd Heg is solenoidally distributed. Thus, the first term in (10) becomes
ao T
dt
+ dU + fe . oq) dS.
For the last term in that equation we find, integrating by parts,
1 ee Ghee irr as git Spee 4
ay (rot Wie tolq : v|i)dS == jew A [ q- v| ) AE Fi 0 (4 [v - fy }) dS,
so that finally
dd'T ae; | 1
dente A tfola- fette dS.
Now, the equation (VII) shows that the last term is precisely the
work done, during the displacements 3, by the electric forces exerted
by the aether on the electrons.
Writing d/# for this work, we have
dd'T
da De
an equation closely corresponding to D'ALEMBERT's principle in common
dE = 0 (T—U) — (13)
dynamics.
$ 7. The motion of the electrons themselves may be determined
by ordinary methods; it will be governed by the electric forces
whose work has been denoted by d#, together with forces of any
other kind that may come into play. We shall confine ourselves
to those cases in which these latter forces depend on a potential
energy U; then the total virtual work of all forces acting on the
( 617 )
electrons will be dE— dU. Moreover we shall aseribe to the
electrons a certain kinetic energy 7, which they have by virtue of
their mass in the ordinary sense of the word. Should there be no
==);
One of the forms that may be given to the variational equation
€ . >? rs Vals, 7 . TO T Ay
such “true” mass, we have only to put 77,
of motion for a system of material particles is
dd! T, .
OA -— dT,
dT, being the change of 7), if we pass from the real motion to
some varied motion in which the varied positions are reached at
the same moments as the original positions in the real motion, dA
the virtual work of the forces, and d'7, the increment that would
be acquired by the kinetic energy 7’, if variations, equal to the
virtual changes of the coordinates, were imparted to the corresponding
velocities (the coordinates themselves being kept constant). For our
system of electrons
JA dE dU;
hence, if we use for d# the formula (13),
(mp
Cire TD zee =o:
We shall finally multiply this by dé and integrate from f, to ¢,.
In case both the displacements q and the variations dd vanish at
the limits, we find
ty
| (7 =F 1) = (U -+ U;); di ——
h
This is analogous to the principle of least action.
§ 8. In what precedes there has been question of the variations
of the energies 7 and U, taken for the system of electrons together
with the surrounding aether, which extends to infinite distance.
Similar though somewhat less simple results are obtained, if one
understands by 7’ and Cl’ the magnetic and the electric energies, in
so far only as they belong to the space within an immovable closed
surface 6. In what follows it is to be understood that this surface
may have, relatively to the system of electrons, any position we
like; for simplicity’s sake however we shall suppose that it cuts
none of them, so that, in every point of 5, the density @ = 0. As
to the virtual variations, determined by q and do, they need not
at all be confined to the part of the system within the surface. We
shall denote by # the normal to the surface, drawn towards the
( 618 )
outside, and by à, u. r the angles between this normal and the
positive axes of coordinates.
If now we repeat the above calculations, we have to do with
volume-integrals confined to the space within 6, and every integration
by parts will give rise to a surface-integral.
Thus. to the last member of (9) we shall have to add the term
cos 2, COS U, COSY |
Amr Ayn Mz | do =| la. Sh], do
dh, 0). Jf) - |
and the value of (12) will no longer be d'7’, but
COS wh COS u. COS TY
ee ope vedan le | d od || a.d'b]„ do. (14)
dh dh 09:2
The last integral of (11) becomes
»
of (grad @ . wot J'b}) a5 =< J oe grad g . dh) dS — ‘| [grad gy . dh |, do (15)
e
Here the first term on the right-hand side is 0, since vot grad p=0.
The transformation of the last part of (10) remaining as it was, as
we have supposed g@=0 in all points of the surface, we finally find
for the second member of (13) the additional term
ij i)
| | — [a. dh], + fa. don +efgrad gp. ORNE
Ot
But, on account of (4),
|
[a : Sy |n +- c | grad q 5 dl
a [et (20'D || aie Mente pal otha
— Lo | : fa. dy ” e [grat pd hl
\0d'h
— En — 0 [D db,
We get therefore, instead of (13),
Eh doe Wa. (adh ae ee
dd in —— Sf —e[d. d'b]x; do (LE)
dt Ji: {08 | =
§ 9. The following are some examples of the applications that
may be made of the formulae (13) and (16).
a. Let the virtual changes in the position of the electrons and
in the dielectric displacement be proportional to the rates of change
in the real motion, i.e. let
== EU Od = ed,
( 619 )
e being a constant infinitely small factor. From these assumptions
it follows at once that
ult Ik 05 Zei.
Now the magnetic energy may be considered as a homogeneous
quadratic function of the components of the current; it will therefore
change in ratio of 1 to 1 + 2¢, if the current becomes (1 + <«)'. Thus:
ESS nk
We may also infer from our assumptions that the position of the
electrons and the values of d are, in the varied motion at the time
t, what they are in the real motion at the time ¢+ ¢, so that the
only difference between the two motions is that the one is in advance
of the other by an interval «.
In this way it is seen that
ae dU Of 0 d'l
A eee (WG Ofer ae 1 Ee er tre
Ae i dt ie Ot Ot ;
Substituting these values in the equation (16), we get, after division
by & and multiplication by df, denoting by d the work done by
the electric forces in the real motion, during the time «4,
IES AAH Oee f[d-blede. | REE Glug}
This is the equation of energy. The last term represents the flow
of energy through the surface.
6. Applying (17) to a single electron, whose motion is a translation
with variable velocity along a straight line, one may calculate the
force with which it is acted on by the aether, and which, under
certain simplifying assumptions, is found to be proportional to the
acceleration and directed oppositely to it. The quotient of this force,
divided by the acceleration, may appropriately be called the e/ectro-
magnetic mass of the electron.
c. There will likewise be a force proportional and opposed to
the acceleration, if the latter is perpendicular to the direction of
motion. In this case however, of which the uniform motion of an
electron in a circle furnishes the simplest example, we must recur
to the equation (16), in order to determine the force. The surface 6 may
be supposed to lie at infinite distance and the virtual displacement
must be taken in the direction of the acceleration. The ratio of the
force and the acceleration may again be called the electromaynetic
mass, though, except for small velocities, its value is not equal to
that of the corresponding ratio in the case 5.
In both cases the result agrees with what has been found by
ABRAHAM,
( 620 )
Ponderomotive action on a system of electrons.
§ 10. A virtual change of a very simple kind is an infinitely
small translation of all the electrons, combined with what we may
call an equal translation in the same direction of the whole electric
field. Applying to these variations — which we give as well to the
part of the system outside the surface 5 as to the part enclosed by
it — the equation (16), one may calculate the resulting force exerted
by the aether on the electrons within the surface. This foree may
be shown to consist of two parts, the first of which is the force with
which we should have to do, if the surface 6 were subjected to the
stresses in the aether, whose components have been already determined
by Maxwern, whereas the second part is determined by the rate
of change of a certain integral, relating to the space |S within o.
The latter part will therefore vanish if the state is stationary, and may
be left out of account if, for periodic states, we wish only to know
the mean value of the resulting force, taken for a full period. I
need not here work out the formulae, having formerly deduced the
result in a more direct way. The components of MAXWELL’Ss stress are
, 1 1 |
A ZE > (d, 7 dv, FEE Ò a ) En BY ( Nee ae 7 —— {) ee 2 he etc.
| (18)
X, = dy ie ly ‚etc.
and the just mentioned volume-integral is
S, being the flux of energy in the direction 4, for which we seek
the resulting force.
Thus, the resulting force in the direction of is given by
ce? dt
Aen era! “ie
z= f lee CdS So ee
mf GEN
The vector ol Sd S is called by Apranam the electromagnetic
C t
a
momentum.
$ 11. Similar results would be obtained if we chose for the virtual
variation, instead of a translation, an infinitely small rotation about
an axis passing through the origin of coordinates; the equation (16)
would then serve to determine the resulting couple, arising from
all the forces exerted by the aether on the electrons within the
surface 6, The moment of this couple may however be calculated
in a shorter way, if we start from what we know already about
the forces.
Indeed, in virtue of the formula (19) and the two corresponding
to it, the components of the force acting on an element of volume
dS may be represented as follows :
OX, aig... OX» ee \
XdS = gh gen SAGs aE, dS]
(S245 +52) prs
a rh 48 0 Y, 0 ¥ Y 1 ~ Y
nae dee Ke NGN 0
Ou
u dz c
En ORN ar Lowe
LAS = te dS Gyds
\ Ov dz Ge
and these formulae give a eee for the components of the
couple
iS mp eee kt Z EP fee ;
[a VIS == fe n= 2 Yo) do — aa [es OSE le GEDE
$ 12. Another consequence of the equations (20), analogous to
the well known virial-theorem in ordinary kinetic theory, will perhaps
be thought of some interest. In order to find it, we have only to
add the three equations, multiplied by we, y, 2, and to integrate the
result over the space S, within the surface o. Transforming such
=
“ly = 5 3 ‘ J
terms as | wv dS by means of partial integration, we find
ó wv
| (Xe + Yy + Zz) dS = | Kur + Yoy + Ze) do —
= [G+ % +2 dS — [Eer + Ey + ez) dS. (22)
For stationary states the last term will vanish, so that, if we
substitute in the term preceding it the values (18),
fe + Yy + Ze) dS = fis, ®d Yn y + Zn 2) do + 1 + U.
Particular cases of ponderomotive action.
$ 13. In a large variety of cases, in which the system of electrons
is confined to a space of finite dimensions, the electric and magnetic
intensities in the surrounding field become so feeble at great distances
that the surface-integrals in 19) and (21) approach the limit O, if
the surface 5 moves to infinite en Moreover, the volume-
integrals will vanish if the state is stationary. We then come to
the conclusion that the resulting foree and the resulting couple are
O for the whole system. If the system consists of two parts A and B,
we may express the same thing by saying that the total pondero-
motive action on one of these is equal and opposite to the total
action on the other.
Of course this will be equally true if, for a system whose state
changes periodically, we have only in view the mean ponderomotive
action during a full period.
These theorems are useful whenever the phenomena in one of the
parts, say in A, are not well enough known to permit a direct cal-
culation of the force acting on this part of the system. If the pheno-
mena in B are less complicated, so that we encounter no difficulty
in determining the force or the couple acting on this part, the action
on A will be found at the same time.
We may apply this in the first place to well-known experiments
on electromagnetic rotations.
Let us consider a cylindrical magnet, touched in two points
of its surface by the ends of a conducting wire JV. Let this wire
be the seat of an electromotive force, producing a current that
flows through JV and through part of the magnet. The ponderomotive
forces acting on the wire are known with certainty and may easily
be deduced from the formula (VII); they produce a couple, tending
to turn the wire about the axis of the magnet. Without entering into
any speculations concerning the motion of the electrons in its interior;
we may infer that the magnet will be acted on by an equal couple
in the opposite direction.
Of course this reasoning must be justified by showing that the
surface-integral in (21) is really O, if it is taken for a surface at
infinite distance. This is readily seen to be the case, if we keep in
mind that, at great distances, the magnetic force produced by the
system varies inversely as the third power of the distance, and that
the intensity of the electric field, if it exist at all, will certainly contain
no terms diminishing more slowly than the square of the distance.
.
§ 14. 1 shall choose as a second example some experiments, lately
made by Wuirrnkap') for the purpose of testing a consequence of
Maxwerr’s theory that has been admitted by many physicists and is
unavoidable in the theory of electrons, viz. that a ponderable dielec-
tric, which is the seat of a variable dielectric displacement, and
therefore of a displacement-current, when placed in a magnetic
1) Warregeap, Ueber die magnetische Wirkung elektrischer Verschiebung, Physi-
kalische Zeitschr., 4, p. 229, 1903,
( 623 )
field, will be acted on by a similar force as a body carrying a con-
duetion-current. In WHITEHEAD’s apparatus two cylindric metallic
plates, having the same vertical axis PQ, formed a condenser,
in which a rapidly alternating electric field was maintained; at
the same time alternating currents were passed through the horizontal
windings of a circular coil, surrounding the condenser; the axis of
the coil, which is at the same time the axis of its magnetic field,
coincided with PQ. A sensitive torsion-balance was suspended by a
wire passing along the axis of the instrument; the ends of the beam
carried each a piece of some solid dielectric, so that these two equal
pieces hung, diametrically opposite each other, in the air-space
between the condenser-plates. The two fields, the electric and the
magnetic, had exactly the same period, being produced by the same
alternate current-machine; besides, the arrangements were such that
there was a phase-difference of a quarter period between the two
fields. Thus, at the instants at which the magnetic force had its
maximum values, the rate of change of the electric field and conse-
quently the intensity of the displacement-current was likewise at its
maximum. Under these circumstances a sensible couple acting on the
dielectric was expected, but no deviation of the beam, attributable
to such a couple, could with certainty be observed.
We may remark in the first place that in Wurreneap’s formula
for the expected effect, the specific inductive capacity A appears in
the numerator. If this were right, a couple would act on the aether
between the plates itself. According to the theory of electrons, as here
presented, ponderomotive force acts only on the electrons contained
in ponderable bodies, but in no case on the aether. The theory
therefore regards every ponderomotive action as due to the difference
between the properties of the body acted upon and the aether; it
can lead to a formula containing in the numerator A—1, but never
to one, containing, instead of this factor, the coefficient A’ itself.
In the second place Wourrpurap has overlooked a circumstance by
which the effect he sought for must have been, at least for the greater
part, compensated. The compensation may be shown to be complete
if the properties of the dielectric used differ from those of the aether
to so small extent, that quantities which are in this respect of the
second order of magnitude, i. e. of the order (A—1)*, may be neglected.
If this may be done, the ponderomotive action on a ponderable
dielectric, placed between the condenser-plates, may be considered not
to be altered by the presence in the field of a second or third piece
of the same dielectric. Now, the two bodies suspended at the ends of
WHITEHEAD’s torsion-balance may be taken to have been parts of a
42
Proceedings Royal Acad. Amsterdam. Vol. V.
( 624 )
complete dielectric ring, bounded by a surface of revolution with the
axis PQ. Moreover it will be safe to assume that the action on the
two bodies which it was sought to observe, did not depend on their
relative positions with respect to the wires leading to the condenser-
plates, and remained therefore the same, in whatever position the
torsion-balance was turned. If this was the case, the action on
a body that is the #'h part of the ring (being cut out of it by two
planes passing through the axis) must have been the 2 part of the
couple, acting on the complete ring. Consequently, it will suffice to
show that the effect is 0, if the experiment is made with a complete
dielectric ring.
$ 15. For simplicity’s sake we shall suppose the condenser-plates
to be united by a wire W and their alternating electric charges to
be produced by a periodic electromotive force in this wire. As to the
currents in the coil, they may be regarded as due to electromotive
forces of the same period, acting in the windings themselves; indeed,
the action on the dielectrics can only depend on the magnetic field
and not on the way in which it is produced. For this same reason
it is allowable to ascribe to the windings so small a resistance that
they do not carry any appreciable charges.
Then no other but electromagnetic forces will act on the windings
of the coil and these cannot give rise to any couple about the axis
PQ, because such forces are perpendicular to the elements of the
windings. By the theorem of § 13 the couple acting on the torsion-
balance must therefore have been equal and opposite to the moment
of rotation, acting on the condenser-plates and the wire W. It remains
to show that this last moment has been 0.
I shall denote by I the electromotive forces acting in the connecting
wire JW, by II those existing in the windings of the coil, and I
shall distinguish by the suffixes 1 and 2 the states arising from these
two causes. Let us indicate by 4, the charges of the plates and
the currents in these and the wire W, in so far as they are due to
I, and let A, have the same meaning with respect to II; also, let
F, and F, be the electromagnetic fields excited by the two causes.
In each of these fields there will be an electric force Dd (acting on
charges that are in rest), as well as a magnetic force bh; in virtue of
the first, the field will exert a ponderomotive force on the charges
of the plates and in virtue of the second on the currents, one of
these actions being determined by the first, and the other by the last
term in the general equation (VII). If we denote by the symbol (Pf, A)
the couple acting on the plates and the wire, in so far as it is due
( 625 )
to a field F and a state A of these bodies, the two actions we shall
have to consider may be represented by
| (Fil A.) and. (F,; Ay)
The first of these is readily seen to be 0. Indeed, the magnetic
field, produced by the forces II, though modified by the presence of
the dielectric ring, is symmetrical around the axis PQ. Therefore,
if the periphery of the condenser-plates is nowhere interrupted, the
state A, will consist in circular currents in these plates, without any
electric charge. It is impossible that the field #, should, by its
action on these currents, give rise to a couple, since, whatever be
the nature of this field, each element of the stream-tubes will only
be acted on by a force perpendicular to its length.
In reality the case was somewhat different, each condenser-plate
being cut by a vertical slit. There must have been equal and
opposite charges at the edges of each slit and the field #, must
have acted on these charges, in virtue of the electric force existing
in it. These forces may however be supposed to have annulled
each other, because the distance between the charges on the two
edges was very small.
§ 16. The action (#, A,) is therefore the only one that remains
to be considered. Now, in the state A,, the plates of the condenser
were the seat of charges, whose amount was modified by the
influence of the dielectric ring, and whose alternations were accom-
panied by currents in the wire W and in part of the plates them-
selves. In so far as they are currents of conduction, i. e. in so
far as they consist in a motion of electrons, these currents are evi-
dently unclosed. We may decompose the whole system of them into
infinitely thin stream-tubes, the tubes being all thronged together in
the connecting wire, and widening out in the plates, at whose sur-
faces each stream-tube ends in two elements of surface.
Let S be one of the stream-tubes, G the end of it on the outer,
and A that on the inner plate, e the charge in G, — e that in H,
de 93
(= la
dt (28)
the current in the tube in the direction from H towards G, and let
us consider the action (/’,, A,) only in so far as it depends on this
current ¢ and on the charges e and — ve.
In the first place there will be an electromagnetic force on the
tube S, owing to the current ¢. The couple arising from it depends
on the course of the magnetic lines of force in the field /’,; it is
most easily found by remarking that its work during a complete
J 49%
( 626 )
revolution of S about the axis PQ is numerically equal to the product of
by the number of lines of force that are cut by JS. These lines
C
are precisely those that are intersected by the surface described by
S in its revolution, a surface which may have different forms, accor-
ding to the form of the wire IW, but has at all events for its boun-
daries the circles described by the points G and //. Let MN be the
number of these lines, taken positive if the middle one of them passes
upwards along PQ, and let us take as positive directions for the
rotation and for the couple the direction corresponding to the upward
direction. Then, for a full revolution in the positive direction, the
Ne
work of the couple will be — —4 M, whence we find for the couple
jd
itself
1
——iwW. ee oe
22
. (24)
If this were all, we should indeed come to an effect such as was
expected by Wuirrnnap. We must however keep in mind that there
can never be a variable magnetic field without electric forces. Such
forces, represented in direction and intensity by the vector >, will
exist in the field /’,, the lines of electric force being circles around
the axis PQ.
We must therefore add to (24) the couple arising from the action
of the field on the charges e and — e; its moment may again be
found by considering the work done in a complete revolution in the
positive direction.
The force on the charge e being ed, its work is equal to the
product of e by the line-integral of d along the circle described by
G. Similarly, the work of the force acting on the charge — e in H
is the product of — e by the line-integral of 5 along the circle
described by #H, or, what amounts to the same thing, the product
of + e by the line-integral for this circle, if it is taken in the
negative direction. Now, if we follow the circle G in the positive
and the circle #7 in the negative direction, we shall have gone along
the whole contour of the surface described by the stream-tube $,
in a direction corresponding to the positive direction of the magnetic
force. Hence, by a well known theorem, of which the fundamental
equation (VI) is the expression, the sum of the two line-integrals by
which e must be multiplied, will be
( 627 )
and the couple to be added to (24) will be given by
1 dN
Que dt
Taking into account (23), we find for the total couple
1 IN ‘ N
Mind (ive ,)=- 5D)
2e
dt Once dt
Since this is the rate of change of a periodic quantity, the mean
value will be 0, as above asserted.
The above somewhat complicated reasoning has been used in
order to avoid the difficulties arising in a closer examination of
the phenomena going on in the ponderable dielectrics. The result
may however be verified by making suitable assumptions concerning
these phenomena. It will suffice for our purpose to replace one of
the dielectric bodies by a single pair of electrons A and B, the
first of which is immovable, whereas the second may be displaced
over an infinitely small distance, in a radial direction, by the electric
forces of the field #,. We shall denote by —e and + ¢ the charges
of A and B, by r the distance of A to the axis, by s the infinitely
small distance A B, and we shall write bh. for the vertical component
of the magnetic force in the field /, and D for the value of the
delectric displacement in this field at a distance 7 from the axis.
We shall take the positive directions as follows: for s outwards, for
hb, upwards, and for D along the circular line of electric force in
a direction corresponding to the positive direction of bh, i.e. in the
direction of a positive rotation about the axis.
ds
Now, owing to the velocity 5 of the electron B, there will be,
„according to the formula (VII), a force
6.308
edt
acting on this electron along a circle about the axis, and producing
a moment
2 ds
th ENT MR a er |
This is the couple of which Wurrenrap has sought to prove the
existence. It is however annulled by the moment arising from the
action of the field /, in virtue of its electrie force D. For the
particle A this moment is
—erD
„and for the particle B it is obtained if we replace —e by +,
( 628 )
taking at the same time the value of 7D at the distance r+s from
the axis.
The algebraic sum of the two moments will therefore be
0
e a (7 D)
and for this we may write
Ee Ob: oi
mid 1 SN
since, by the equation (VI)
1 0b:
5e (7 ES rea =?
For the sum of (24’) and (24’’) we may write
é d (s fy-)
MEET :
c dt
whence it is immediately seen that its mean value is O for a full
period.
Physics. — Methods and apparatus used in the eryogemc laboratory.
ITT. Baths of very uniform and constant temperature in the
cryostat (continued). A cryostat of modified form for appa-
ratus of small dimensions. IV. A permanent bath of liquid
nitrogen at ordinary and at reduced pressure. V. Arrange-
ment of a BurckHarpt-WEIss vacuum-pump for use in the
circulations for low temperatures. Communication N°. 83 (con-
tinued) from the Laboratory at Leiden. By Prof. H. KAMERLINGH
Onnes. (Read February 28, 19053).
UI § 6. A cryostat of modified form for apparatus of small
dimensions. If the cross sections of the apparatus that is to be immersed
into the bath are small, vacuum glasses may be profitably used in
the construction of the cryostat. For, vacuum glasses of comparatively
small diameter can then accommodate the stirrer and the temperature
indicator in addition to the measuring apparatus. Plate IV shows a
cryostat of the kind, viz. the one used in the determinations by
HynpmMan and myself on the critical state of oxygen. |
Obviously the arrangement could be much simpler, as it was not
necessary to watch the liquefied gas streaming from the jet or to use
the generated cold vapour for the cooling and as no particles of dust
from the leads had to be feared, a filter was not required. (Comp. Comm.
51, Sept. 99 § 2. Y, p. 12). The principles for obtaining a uniform con-
~ "ta
( 629 )
stant temperature, laid down in the previous communication have all
been applied in this arrangement, a vigorous stirring with the ring
shaped valved-stirrer, the adjustment at the desired temperature to the
indication of a sensitive indicator by regulating the pressure at which
the liquid boils while reading a differential oil-manometer made for
the purpose, and lastly the determination of the temperature of obser-
vation as corresponding with the mean obtained graphically of the
readings of the thermometer (as in § 5).
Plate V shows in detail the differences in the construction between
this form and the former plates I and II (and also Plate I Comm. 51),
the parts unaltered remaining are indicated by the same letters as
before, and the modified parts by letters with accents, while entirely
different parts have new letters.
The height of the vacuumglass 5',, is so chosen that the liquefied
gas cannot be blown out; and the glass itself has been silvered,
leaving open two opposing windows V',. Through these the pheno-
mena in the experimental tube may be watched, and from the position
of an aluminium wire fastened to a cork float the depth of liquefied
gas may be derived. If the insulating power of the vacuumelass is
not perfect, condensation of moisture on its outer wall may be avoided
by placing it into a beaker filled with alcohol, which if necessary
is renewed when cooled. Thus the same principle is followed which
was employed when necessary in the case of the cryostat (Comm. 51)
when the windows had to be kept clear and where hot dry air was
drawn through the outer spaces of the observing glasses (V,, see
Pl. I of this Comm. and for the details pl. I Comm. 51).
The vacuum glass and the auxiliary apparatus are supported by a
copper cover V',,, with its rim tinned to protect it from the action
of the india-rubber ring V',, and which, like the cryostat of § 1, has
been coated with polished nickel-paper. To this cover are fastened the
exit tube of the gas 7, and the safety tube Y,,, the connection
A', with the oil manometer (for details see plate I) and a copper
tube .V’,,, into which the india rubber stopper is placed holding the
apparatus to be immersed in the bath (in our case the piezometer
for the critical phenomena X,, and the correction thermometer 6,,
with its leads 5, (comp. $ 1) while the thermo-element @ may be
considered as forming an inherent part of the cryostat). There is
also a tube through which the capillary a, admitting the liquefied
gas is led and where it is supported by a piece of cork a’, It is
closed by means of an india-rubber tube a’,, drawn over the tube
and a thin cap soldered on to a
Between the cover and the rim of the vacuum glass a wooden
630.)
cylindrical jacket N', is placed resting against the latter by means
of an india-rubber ring N’,. Two cylinders N',, N', of nickel-paper
serve to diminish radiation, especially in the direction of the delivery
tube.
As mentioned the frame which keeps the protecting cylinder in its
place is fastened to ihe cover. For a complete explanation of the
letters and parts of both this and the stirrer reference may be made
to § 4. Further we may note that §, is fastened with silk cords
to &, and this again with silk cords to the cover W’,,, while §', is
supported by the glass tube &, fitting onto the pins §',.
The three threads 4, on which the stirrer hangs are led directly
through the three india-rubber tubes y',,, connected hermetically to tubes
soldered onto the cover and fitting hermetically onto the threads at
x',2, to the brass disc 4’, and rod y',, which is connected by a
small chain y',; passing over a pulley y',, to the motor by means
of a steelwire. The arm of the motor may be adjusted to different
throws, while velocity of rotation can be regulated by means of a
rheostat.
The mounting of the apparatus is very simple. The stopper with
the measuring apparatus is placed into the tube .V’,, of the cover,
to which all the auxiliary apparatus has been connected, then the
vacuum glass is slid into the india-rubber ring which is also connected
to the cover and is fastened there by means of tightening bands. In
order to secure an airtight fit the india-rubber on the metal and on
the glass has been coated beforehand with a solution of indiarubber
in benzine.
With a view to the description given in III the operations for
the adjustments at given temperature require amplification only ina
few points. In the case considered here, the evaporated gas was led
back through the exit tube to the gasholder or to the large exhausted
reservoir of the ethylene circulation in the cryogenic laboratory
(Comm. 14, Dec. ’94) whence the ethylene was further condensed
into the condenser immersed in methyl chloride. As described in
Comm. 14 the circulations of the cryogenic laboratory have been so
arranged that they may be used at any time. Besides the reservoirs
that have to be exhausted, a permanent part of the circulation consists
in branched tubes with cocks as shown on plates I and IV. The
cryostat had only to be connected to the circulation in order to be
easily brought to the required pressure. In the case considered here the
experiments. were not made in the cryogenic laboratory but in an
other room and the length of the lead a’,, was 10 m. Although
the liquid ethylene had to be conducted over such a distance, yet
end
( 631 )
the adjustment of the bath to the required temperature (say at — 120°)
was obtained within one hour after the pumps in the cryogenic
laboratory had been set working.
Instead of a resistance thermometer, to regulate the temperature,
we used the thermoelement ©, the protected junction being placed
at the side of the piezometer (comp. comm. 27 June ’96); it is visible
through the window V', (in plate IV). The electro-motive power of
the thermoelement is compared by means of the zero method with
that of a thermoelectric control element or a Weston-element.
For the same difference of temperature the deflections on the seale
of the sensitive galvanometer were almost as large as in the measure-
ments made with the resistance thermometer (comp. $ 5). An example
of the determination of the temperature is not necessary in addition
to Plate III.
IV. A permanent bath of liguid nitrogen at ordinary or reduced
pressure. In Comm. 14 (Dec. ’94) a short description was given of the
temperature steps obtained by means of circulations of methylchloride,
ethylene and oxygen. In connection with that description I mentioned
my intention of adding more circulations to those already existing
and said that I hoped to replace more and more parts of the existing
circulations by greater and to insert such technical apparatus as
should be found advisable so that the existing apparatus could be
used in the new circulations with pure or costly gases. An example
of this is the circulation of nitrogen added to the existing temperature
cascade, of which a description is now required by the completion
of some of the measurements rendered possible by it. For measure-
ments at temperature between — 195° C. and — 210° C.a nitrogen
is much to be preferred to an oxygen-circulation as the tension at
which the oxygen boils at — 195° is so small that accurate regulation
at constant temperature becomes very difficult. As the preparation of
pure nitrogen in such large quantities as a circulation requires
presents many difficulties, the compressor and the vacuum pump
must be suitable and efficient. These conditions are fulfilled by the
mercury and the auxiliary compressors which are generally used for
the compression of pure gas and which in the originally tempera-
ture cascade served for the oxygen circulation. However when the
BroTHERHOODcompressor (comp. Comm. 14 Dee. "94 and 51 Sept. ’99)
could be used for the oxygen circulation in the cascade they could
be used for the nitrogen circulation.
The nitrogen is prepared from sodium nitrite. Besides being passed
-through ferrous sulphate and sulphuric acid it is led over hot cop-
( 632 )
per and then again through ferrous sulphate and sodium hydroxide,
because otherwise traces of nitric oxide might be left and this blocks
the cocks (this gas is recognised at once by a strong smell of higher
oxides of nitrogen when it mixes with the air). In order to remove
traces of this oxide, I have sometimes added to the gas a quantity of
oXygen as nearly as possible equivalent to the NO contained therein
and have then passed it through sodium hydroxide. The gas is col-
lected and provisionally kept in galvanised iron vessels holding 1 M*.
From these it is driven out later by water heated by a steam jet
and after passing through sodium hydroxide and sulphuric acid it is
forced into a small gasholder floating on oil and holding 500 L.
By means of the auxiliary compressor AC lubricated with glycerine
(see Pl. VI and for details Comm. 54 Sept. *99) and the mercury
compressor HgC (see Pl. VI and for details Comm. 54) the gas is
forced over into a metal cylinder of 18 liters capacity after passing
through the drying tubes D,, D, filled with caustie soda in the form
of sticks.
Plate VI shows the scheme of the entire circulation with the
cryostat Cr, into which the liquid nitrogen is admitted at a and where
it evaporates under ordinary or reduced pressure at the desired tem-
perature. The whole arrangement has been used in the comparison
of the platinum resistance thermometer with the hydrogen thermo-
meter, which has been mentioned in II. The apparatus themselves
are drawn diagrammatically but in their true proportions, while the con-
nections are entirely schematic. A detailed representation of the cryostat
with the auxiliary apparatus appertaining to it for uniform and constant
temperatures will be found on plate I where the same letters have
been used. On the other hand plate VI may be considered as a sup-
plement to plate I. Nothing is wanting for a complete representation
of the circulation except the gasholder and the vacuum vessel of
5 M*. (comp. § 5 for its use) which are too large to be repre-
sented on the same drawing as the parts given. There is an
insignificant difference in the coupling of the leads between plate l
and plate VI, for on plate VI Zeh. 1' indicates the connection of the
compression side of a BurckHarpt—Welss vacuumpump bu Vac.,
described below into which the exhaust Hvh. 2 terminates, to an
exhaustpump (which may also be AC of the circulation). Moreover
next to the lead from Y, to Y,, we have drawn what must be sub-
stituted for it in comparison with the arrangement on plate IV.
RN is the cylinder where the nitrogen has been compressed by
means of AC and HgC through the drying tubes D, and D,, while
Gaz indicates the 500 liter gas holder floating on oil. The nitrogen may
—————— en …_- — dd
( 633 )
be admitted at the required pressure into the condensation spiral CS
from the cylinder RN through a final drying tube D, containing phos-
phoric anhydride, as well as directly from the compressor. The spiral is
placed in a vacuumglass B with a protecting cylinder A. Liquid oxygen
is admitted into B through Oxz./iq from the oxygen circulation of the
eryogenic laboratory, viz. from the condensation spiral which is cooled
in the ethythene boiling flask (Comm. 14, Dec. ’94). The oxygen escapes
through Owv.vap, a wide safety tube S being connected in the ordinary
way, and is compressed into the spiral by a BROTHERHOOD-COMpressor
which is lubricated with glycerine and arranged as deseribed in
Comm. 51. It may be remarked that, with a view to the possibility
of an explosion of a glycerine mist mixed with oxygen, the pressure
in this operation is not raised above 80 atmospheres. (Comp. the
explosion described in the Zeitsch. f. Kohlensäure Industrie 1903).
The nitrogen condenser itself has been drawn in detail on plate
VII. In so far as the parts correspond — either with plate V for
the cover, or with plate I of Comm. 51 for the regulation cock
described there — the same letters have been used, but as some of
the parts differ a little the letters have an additional accent. As in
the case of the small cryostat plate V, the cover is coated internally
with nickel-paper, while the upper turns of CS are protected again
by a ring of paste board and nickel-paper. The condensation spiral
consists in the condenser proper CS, and the regenerator CS,; here
the same principle has been applied which has been followed in the
cryogenic laboratory from the first (Comp. Comm. 14 Dec. *94); the
vapour of the oxygen is forced by the cylinder B, which is closed
at the bottom with the stopper B",, to pass along the regenerator spiral.
As in the ethylene boilingflask (see comm. 14 Dec. ’94) the level
of the liquid oxygen in the glass tube W is indicated by a cork
float dr, with a steel capillary dr, to which a thin reed d, is
fastened; the steel capillary passes through a glass tube b’,,.
Liquid nitrogen flows out through the fine regulatingcoek hh, of
the same kind as that through which the liquid gas is admitted into
the cryostat. For the description of this cock compare Comm. 51
and 54.
It may be added that Gaz’ shows the connection with the auxiliary
apparatus described in Comm. 54 for operations where HgC is used,
which connection make it possible for the gas to stream back to the
gasholder Gaz. |
V. Arrangement of a BorcKkHarDt-Weiss vacuumpomp to be used
with a circulation for low temperature. The well-known excellent
(26347)
vacuumpump patented by BurckHarpt and Weiss has been first used,
I think by Orszewski, for removing the large volumes of gas which
rise from a bath of liquefied gas at a reduced pressure. We shall
now speak of some modifications and auxiliary apparatus by means
of which the perfect purity of a gas is secured in a high vacuum.
A pump arranged in this way may also be introduced into circula-
tions of costly gases. In our laboratory it has been worked very
satisfactorily for many years. A diagrammatic figure of the entire
BurckHArDT-pump has been given on plate VI Bu. Vac., the pump
cylinder with its slide valve box, the beginning of the suction- and
the delivery tubes with the auxiliary apparatus belonging to them
are shown on plate VIL, where fig. 1 gives the side elevation, fig. 2
the top elevation and fig. 3 the section. The well-known working
of the piston and the valve, the successive communication of the
valve ports 5 and 5’, each individually by means of the slide hole
2 with the suction valve port 1 or with the delivery valve port 4
and together by means of the ringshaped opening 3 may be seen
without further comment from the section. The pump displaces
360 M? an hour, hence, when exhausting at a pressure of 2 ¢.m.,
about 10 M*® gas, measured normally can circulate. At Leiden it is
used almost exclusively with an additional vacuumpump exhausting
at the compression side. It exhausts then till 2 m.M.
As a lubricant and for the airtight fittings to be described in the
following pages, only bone-oil is used which after having been tested
at the exhaustpump has proved to have no perceptible vapour pressure.
For the technical work ordinary ring packings are quite sufficient,
I have, however, replaced them by folded packings as described in
Comm. 54 Jan. ’00 for the compressor and the auxiliary compressor.
The leather ring of the packing is supported there as in Plate IV
b,, by the india rubber ring b,, (for an exhausting packing comp.
E,, Pl. VI fig. 3 Comm. 54). The packing cylinders have been made
long enough to contain two folded packings (one for exhausting and
one for compression) and a bronze tightening piece, but as a rule
they only hold the packing for exhaust.
New additions are the vessels 0, and O, see also plate II filled
with oil (or with glycerine for those gases which cannot be used
with oil); they serve to protect the packing cases of the cylinder
and the slide valve box entirely from the atmosphere and also to cool
the piston rod. The covers O,, and Q,, protect the lubricant against
dust or moisture.
For the oil holders S,S, we have chosen the construction explained
in detail in fig 7.~S,, is an ordinary oilpot for visible cylinder lubri-
KAMERLINGH ONNES. Methods and apparatus used in the Cryogenic Laboratory. III. Baths
of very uniform and constant low temperature (continued), A Cryostat of modified form
for apparatus of small dimensions.
Plate IV.
ad
‘Pesedings Royal Acad, Amsterdam, Vol. V.
Plate V.
Mn
5 wr
NT
|
mmm nnen mens
— „à
Plate VIL,
1 KAMERLINGH ONNES. Methods and apparatus used in the Cryogenic Laboratory. IV. Permanent bath of
liquid nitrogen.
Plate VL
SEN
so
|
El
-
L
Lees
Protecdi
toceedings Royal Acad. Amsterdam. Vol. V-
KAMERLINGH ONNES. Methods and apparatus used in the Cryogenic Laboratory. V. Arrangement of a BURCKHARDT-WEISS
H. 4
vacuumpomp for use in the circulations for low temperatures.
Plate VI.
OT
Proceedings Royal Acad. Amsterdam. Vol, V-
(6359)
cation in vacuo. The cover 5S,,, has been tightly screwed on the
hollow rod S,,,, and presses the glass S,,, hermetically on to the
packings. By means of the winged nut /S,,, the point is adjusted
so that the oil drops regularly through the openings JS,,,, into the
space S,,, which communicates with S,,, through S,,, and which
may be watched through the glass windows in S,,,. For our purpose
the oil holder S,, is placed on a stout tube S,, onto which by
means of india rubber rings and tightening bands the glass cylinder
S,, is fixed on a copper bottom, soldered to S,,. The glass cylinder
is filled with oil and covered with a lid $,,. By means of S,,, new
oil can be admitted from the reserve vessel into the lubrication
vessel. In this way the air is sufficiently prevented from entering
the lubrication apparatus.
Lastly, between the exhaust tube z and the compression tube p
a safety valve has been placed, which prevents the pressure on the
compression side from rising above a certain height (usually */, atmos-
phere). Hence it is possible to let the pump work on and to open
and shut the cocks as the work requires. The noise of the safety
valve gives warning that the cocks have not been properly used.
In any case no difficulty is to be feared if the possible output of the
pump might diminish in any way in relation to the intake. Fig. 4
shows a diagram of this connection, some of the parts being drawn
to proportion ; fig. 6 shows a section of the safety valve case itself,
The side tube p, is connected by a joint A with the tube wv,
which opens into the space below the safety valve. The space above
the safety valve communicates with the exhaust tube through the side
tube z,. The broad valve v, is coated at the bottom with an india
rubber sheet which presses against the narrow rim v,. The spring
v, is stretched with the key v, while the plate v, with the nut »,,
and packing is tightly screwed on to the rim 7,,. The packing
cylinder v,,, like the packing just mentioned is kept under oil; a
cover v,, above it protects it from dust.
The connection K between the tubes p, aid v7, could not be brought
about with flanges or with screw joints without causing tension in
the tubes. Therefore it was made in the following manner as shown
by fig. 5. A widened piece #, is soldered on p,, v, fitting into
this piece. The india rubber connection &, is kept in oil; for this
purpose a rim #, was used which was soldered on to p, and a
rim /:, which was soldered on to z,. Over these rims a wide piece
of tubing #, is drawn which is fastened to #, and 4, by means of
india rubber rings /, %, and tightening bands, and forms together
with these an oilreservoir.
125
( 636 )
Besides being connected through the safety valve case and the
above mentioned connection, the compression tube and the exhaust
tube are also connected (comp. again the diagrammatic fig. 4, as an
explanation of figs. 1, 2, 3) by the cocks 7,,7,,7,,7, and may be
connected with an airpump /, an indicator 7 and a vacuummano-
meter m. The use made of this auxiliary apparatus in regular working
or in preparing, mounting, testing, drying and exhausting the pump,
requires no further explanation. As a matter of course, the pump
is not introduced into a circulation unless it has worked for a long
time with the exhaust- and compression sides closed and no change
has been found in the vacuum.
I further remark that the principle of an oilconnection as illustrated
by fig. 5 may be profitably applied when wide tubes have to be
connected, which have neither flanges nor nuts and joints or in cases
where it is not advisable to make these contrivances. The method then
to be followed is illustrated by fig. 8 where K’,, A’, and A’, are
loose pieces slid on the tubes 6, and 6,. which we want to connect
A good fit is obtained by means of the india rubber rings A’,,,
K’,,, K’,, K’,, K’,, under brass tightening bands. K’,, and A,
serve to admit and to run out the oil. In this way one always suc-
eeeds in making within a short time an airtight fit. For the connec-
tion of the pump tubes to the conduit at 7, and f, (comp fig, 1)
this method has been used in a manner which will be clear from
the figure.
Physics. — Communication n°. 84 from the Physical Laboratory at
Leiden “Zsotherms of diatomic gases and their binary mixtures.
V. An accurate volumenometer and nuving apparatus.” (By
H. KAMERLINGH Onnes and H. H. F. HyYNDMAN).
§ 19. A compression tube of larger dimensions. In $ 6 of Comm.
n°. 69 March 'Ol we have explained that the apparatus described in
§§ 3 and 4 hardly gave the accuracy required in the determinations of
density, if the total quantity of compressed gas was smaller than
5 ec. Since, however, at most 600 cc. of gas under normal condi-
tions is available in this apparatus it is not suitable for densities
of more than 120 times the normal.
On Pl. L a compression tube is shown which has about three
liters capacity and hence which is suitable for measurements up to
densities of some 500 times the normal and with at least the same
accuracy as the above. The drawing is, as usual, schematic in
the connections but the individual parts are drawn to scale, it can
be compared with Pl. I of Comm. n°. 69. For those parts which
correspond the same letters are retained, where an alteration has
been made the letters are accented, while new parts are characte-
rised by new letters. A detailed description is hence unnecessary,
but it may be noted that the screw head a, is changed, that a
closed nut screwed on at c,,, has been added by which the pressure
can be suddenly released if necessary, and that a cock c,, has been
introduced, to enable the level glass to be shut off if required.
The compression tube <A’, is designed for use in the first place
with piezometers of the kind described in § 2 but of larger dimen-
sions. The use of this tube A’, is then the same as the original
A, (comp. §§ 3 and 4) and it may be introduced directly in place of
this into the system shown on Pl. I of Comm. n°. 69.
In the second place this compression tube serves to hold glass
tubes with a stem 6,—4#, (cf. Pl. IL fig. 2 Comm. n°. 69) onto which
other apparatus can be screwed in place of the simple nut and
capillary shown there. In Pl. I fig. 2 is shown a three way cock
with two steel capillaries g,’ and g,’’ which is employed as follows.
One of the capillaries g,’ is connected directly with the small
measuring piezometer of the type of f fig. 2 Pl. IT Comm. N°. 69
the other g,’’ with a volumenometer, so that when #,,, is shut and
hes, and A, are open a known quantity of gas can be brought
into the compression cylinder from the volumenometer. On the other
hand when £,,, is open and #,,, shut this gas can be compressed
into the piezometer where the temperature and pressure are measured
as before. The large glass tube with stem and the piezometerreservoir,
form in this way a piezometer of variable volume (constant quantity)
and the difference with the former method consists in the measure-
ment of the normal volume in a volumenometer instead of in the
piezometer itself. The volume of the large glass tube in this
method is not required to any high accuracy and the small w tube
at the bottom may be omitted (g, Comm. n°. 50 PL I fig. 4 June ’99
and 6, Comm. n°. 69 Pl. IJ March ’01). The accuracy is now
really that obtainable with the volumenometer (cf. § 20) in so far
as the determination of the normal volume is concerned. The spaces
Koor Kisos Kiso Of the small three way steel cock must be also
accurately calibrated. Care is taken also that the pins really shut
properly into the sockets which makes the whole absolutely trust-
worthy up to at 100 At.
Although we wish to confine ourselves to the method of variable
volume (constant mass) a second measurement with the volumeno-
( 638 )
meter is required, in the same manner as would be necessary if we
employed the method of constant volume. For, we have already
mentioned in § 1 that this compression apparatus is suitable for this
method. The measurement is made by shutting /,,, under known
pressure and allowing the compressed gas to expand through the
capillaries g,/’ and gy,’ into the volumenometer and reading as before.
This second volumetric measurement, with its necessary corrections,
gives the determination of the normal volume after the measurements
at high pressure and compares with the second normal volume
determination of the original method.
§ 20. An accurate volumenometer. The volumenometer mentioned.
above in § 19 was designed to give isothermal measurements of an
accuracy of ———~ up to 60 Ats pressure. Hence the same accuracy
: 10000 ks
was desired as with the standard piezometers of Comm. n° 50 June ’99,
while at the same time the determination of the deviations from
Boyre’s law at ordinary pressures was kept in view. The most
analogous apparatus is that employed by Lepuc; that of Wrrkowsk1,
who has used a form more closely analogous with ours, does not
appear to have been designed for high accuracy.
The measuring vessel Zj, (Pl. Il fig. 1 and more in detail fig. 2)
where the gas is shut off by mercury entering through /%,, consists
principally of 5 bulbs /), such of 250 ce. and a smaller bulb #4,
of 25 ce. capacity. These are separated by short really cylindrical
portions Zi... Lj, on each of which there is a mark, near to
which the mercury meniscus is brought for the measurements.
At the lower end of the measuring vessel is a contrivance after
the scheme of Comm. n°. 27, for catching any dust or stray gas which
may perchance come from the rubber tube at C/, PI. II fig. 2. At the
upper end the vessel terminates in a capillary tube /;,, which is -
divided almost immediately into two ZZ, and Mt, One of them is
terminated near the apparatus by a cock 7,. The other ends in a
glass or steel capillary terminated also by a cock. On PI. IT fig. 2
e. g. the volumenometer is connected to the mixing apparatus /” by a
capillary tube soldered on to it after it has been mounted in Z, by
the cock 7, At Ei, (Pl. Il fig. 1) e.g. 7, the-steel capillary 9,”
proceeding from the three way cock mentioned in § 19 may be
connected. The small bulb 7, is calibrated by mercury at the same
time as the larger and serves to determine the small volumes above Zi,
To keep the temperature of the gas constant and uniform the
measuring vessel is firmly fixed to the bottom of the copper case Kas,
rachid
( 639 )
through which water at constant temperature flows from the thermo-
stat described in Comm. n°. 70 III May ’01 (see Zo, on Pl. II. fig. 1).
Uniformity of temperature is also assisted by the movement of the
stirrer on to which the thermometer 7% is fixed.
The ring /,, together with the bottom plate is soldered to the case
Ks, and is large enough for the measuring vessel to be put through
it. The closing plate /, is made fast to the measuring vessel and is
so arranged, that it can easily be made watertight and that it can
bear the weight of the whole mass of mercury when the tube is
full without any danger to the glass as long at least as it is not
displaced from its vertical position. The closing plate with flange and
packing is pressed against the ring /,, at the bottom of dy by
the screw s.,. The different parts will be seen by an inspection
of Pi. II fig. 1. &., the ring and packing, made large enough to
be brought over the measuring vessel, /, and “/,, round copper
plates provided with a thread and cut out at /., and , enough
to pass over the tube M,, so that they can be put on from the side
and made fast together by the screws Z,; together they form the
closing plate which is screwed into ,; Hy, and Ly, the halves from
a round vuleanite plate which rest on the ring /,, with bottom Z,
and support the enlargement Zi. Lp, and Zp, the two halves of a
rubber plate which are united by rubber solution and pressed into
the ring ZE, to make the whole watertight.
When the closing plate has been made fast perpendicularly to
the measuring glass and has been screwed against the lower rim of
KE, the two parts of the conical top Z„ are brought together into
place and the measuring glass centered and held fast by the cork Z2
The whole waterbath is then brought into as vertical a position
as possible. N
There are windows in the case #, which enable the tube to be
lighted and read. These are formed by thin pieces of plate glass held
between stout brass frames Zj, and /,, one of which is soldered
to the wall of £, . The screws Lj, enable the plate to be equally pressed
against the rubber packing Zj, and the glass. It is quite necessary to
have the case completely tight, which was here obtained, to prevent
the felt in which MZ, is packed from becoming wet, and hence from
an irregular loss of temperature.
In spite of the verticality of the entire case the glasses require to
be tested with a contact spirit level, in order that the necessary
correction to the cathetometer reading may be made.
To determine the volume of an enclosed quantity of gas the position
of the meniscus is not read with reference to the marks on the glass
43
Proceedings Royal Acad. Amsterdam. Vol. V.
( 640 )
tubes, but on finer lines etched on to small glass plates /,,—4#,,,
provided with connections /,, and screws /,, to fix them to the
cylindricals portions of the measuring vessel. By a proper arrange-
ment of these the meniscus and the lines can be sharply seen over
the whole length of the case.
The measuring vessel is calibrated by temporarily blowing on, at
the lower end, a small glass cock with a fine point (ef. Comm. N°. 70.
IV. May ’OL). The mercury is introduced through this in the care-
fully exhausted apparatus and the menisci are then read in the
manner described above for the measurements and with the same
precautions as to lighting and temperature. The mercury drawn off
at the cock is weighed. As before the readings are made on the glass
plates but in order that the calibration shall not be lost if these have
to be removed, they are also compared with the lines on the eylin-
drical tubes. This would be necessary if the tube had to be removed
cleaned and dried after the method of Comm. N°. 27, but usually
it is sufficient to suck up the various liquids and to dry by repeated
evacuation admission of dry air through 7, and 7, of Pl, II fig. 2.
The measuring vessel can be completely shut off from the mer-
cury reservoir, see Pl. II fig. 2 or the manometer by the clamp C7,.
All these connections are carefully cleaned good thickwalled black
rubber tubes, which are strengthened by wrapping them spirally in
strong tape. The mercury meniscus (ef Comm. N°. 67 Dee. ’00 for
what is here implied) remains quite clean after a series of measure-
ments, if only dry gas is admitted to the volumenometer (this is
only true when the gas has no action on the fat of the cocks and
joints). The small changes in the position of the meniscus to bring
it to the required position are made by manipulating the clamp C/,
and the resevoir. During the measurements this clamp is always closed.
The pressure of the gas in the volumenometer is given by the
height of the mereury in the manometer tube when C7, is quite
open. This is itself connected to a barometer and-a resevoir at con-
stant temperature by airtight connections in the manner of Comm.
N°. 60 June 00 and the same precautions are taken to ensure
accuracy in the temperature determinations of these two mercury
columns. The volumenometer meniscus and etched lines, manometer,
barometer and standardseale (ef Comm. N°. 60) are so placed that
they can be read without altering the telescopes of the cathetometer.
The menisci of the barometer and manometer are read as described
before, that of the volumenometer by the help of a brass plate with
a 2 mm. slit in it, which is brought with a glow lamp to the same
level as a meniscus and gives good definition.
heid
( 641 )
In order that the required accuracy may be obtained it is neces-
sary that the pressure shall not fall below 0,5 Atm.
To determine the theoretical normal volume measurements are
made at two or if possible at three positions with the same quan-
tity of gas. Whenever the third virial coefficient C (ef Comm. N°. 71
June *O1 and N°. 74)*) does not come into account at the pressures
considered and to the accuracy required, the same value of the coef-
ficient B must be found by a combination of any two of the three
measurements. This gives directly the deviations from the law of
Borre and hence the theoretical normal volume.
§ 21. The mixing apparatus. On Pl. IL fig. 2 the volumenometer
described in § 20 is shown connected with other apparatus for the
preparation of accurate mixtures of gases and for the investigation of
their compressibility.
The drawings do not require much explanation. The mixing vessel
F and the reservoir G have about 2 liters capacity. G is provided
with a three way cock and is particularly useful when a number of
mixtures are required with a small proportion of one component
which can be contained therein.
The connecting tubes between 7,, 7,, 7, and from / to 7, are nar-
row so that the uncertainty of their temperature may have no influence
on the accuracy of the measurements, the other tubes are large enough
to allow free connection between the various parts and the pump
and to help rapid exhaustion.
When a mixture of given composition is required, and the mercury
stands above the closed clamps C/,, C/,, Cl, Cl, the whole apparatus
is pumped out through 7, and is filled through 7,, while 7, is shut,
from say the gas apparatus connected to 7,, after being washed out
with this gas.
Then 7, is shut and 7, so turned that the gas is shut up in G
while / is brought into connection with the pump through 7,. The
cocks 7,, 7, and 7, are then opened and /# and # and the connec-
tions pumped out again. By raising Ar and opening C/, widely and
Cl, (to prevent air entering from J/) only partially the mercury
is caused to enter / and to fill first Z,, without enclosing any
gas, then /, up to the required position, when C7, is shut. The
space between 7,, 7,, r, is repeatedly washed out by a small
quantity of gas from G through the cock 7,, from here also gas is
?
ie)
1) Livre jubilaire dédié à J. Bosscua; Archives Néerlandaises, Ser. Il. T. VI.
p. 874—888. 1901.
( 642 )
brought into EZ and the whole pumped to a good vacuum. The
required quantity of gas can then be brought into # through 7, and
y,. The volume temperature and pressure of the gas in /, shut off
by r, and 7, are then accurately measured and when 7, is opened
nearly the whole of this can be brought over into /. The remaining
portion in Zj, and /,, is then measured by expanding to /,, or
E,,, and Cl, is again closed so that # can be again evacuated. The
second gas is then brought directly into the volumenometer from
r, and the volume measured in the same manner.
When this is finished 7, is again opened and the second compo-
nent in # mixed with the first in / where it stands for some
time. The admixture of the total quantity is completed by
drawing the combined gases several times backwards and forwards
between the two vessels. The mixture is then preserved in /’and as
much as may be necessary is driven into /, or through 7, into
other apparatus for measurements on the compressibility.
(April 24, 1903).
H, KAMERLINGH ONNES and H. H. F. HYNDMAN, „Isotherms of diatomic gases and
their binary mixtures. V. An accurate volumenometer and mixing apparatus ”
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Proceedings Royal Acad. Amsterdam. Vol. V.
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H. KAMERLINGH ONNES
Proceedings Royal Acad. Ax
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H KAMERLINGH ONNES and H. H. F. HYNDMAN, „Isotherms of diatomic gases and their binary mixtures, V, An accurate volumenometer and mixing apparatus.” Puate II,
ede)
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Proceedings Royal Acad, Amsterdam. Vol V.
PVA ag ee ee ON
SNe ee Pee
KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,
PROCEEDINGS OF THE MEETING
of Friday April 24, 1903.
EE
(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Vrijdag 24 April 1903, DL. XI).
CONTENTS.
C, A. Losry pr Bruyn and C. L. Juncius: “Dissociation in and crystallisation from a solid
solution”, p. 643,
E. H. Biicunur: “The transformation of diphenyliodonium iodide and chloride and its velocity”.
(Communicated by Prof. C. A. Lopry pr Bruyn), p. 646.
J. J. Branksma: “Nitration of symmetrical dinitroanisol”. (Communicated by Prof. C. A,
Logsry pe Bruyn), p, 650.
J. H. Bonnema: “Two new mid-cambrian erratic-blocks from the Dutch diluvium”. (Com-
municated by Prof. J. W. Morr), p. 652.
J. C. Krurver: “An analytical expression for the greatest common divisor of two integers”,
p. 658.
W. H. Juris: “On maxima and minima of intensity sometimes observed within the shading
of strongly widened spectral lines”, p. 662.
H. A. Lorentz: “On the emission and absorption by metals of rays of heat of great wave-
lengths”. p. 666.
G. VAN Iverson Jr.: “The decomposition of cellulose by aérobic micro-organisms”. (Com-
munieated by Prof. M. W. BEIJERINCK), p. 685, (with one plate).
The following papers were read:
Chemistry. — “Dissociation in and crystallisation from a solid
solution”. By Prof. C. A. Lory pr Bruyn and Mr. C. L. Junatus.
(Communicated in the meeting of March 28, 1903).
It is no longer necessary to be reminded of the analogy between
liquid and solid solutions but it is still a matter of importance to
trace and investigate new instances of the similarity of the two
solutions. For this reason attention may be called to the following
phenomena and observations.
The new phenomena relate to the interesting intramolecular rear-
rangement discovered by CrAmiciAN and Sinper') in which solid or
1) Ber. 34. 2040 (1901).
44
Proceedings Royal Acad. Amsterdam. Vol. V,
( 644. )
dissolved o-nitrobenzaldehyde is converted, under the influence of the
blue rays of sunlight *) into o-nitrosobenzoie acid:
ÁNNO, HOK RO
EN re
23 Sn
and where consequently an oxygen atom of the nitrogroup migrates
to the neighbouring aldehyde group and oxidises the same to carboxyl.
CramiciAN and Singer have investigated this reaction more closely,
principally with solutions in different liquids; as regards the trans-
formation taking place in the solid condition, in which we happen
to be particularly interested, they merely say: „dass die Krystalle
nach und nach ihre lichtgelbe Farbe verlieren, undurchsichtig, griin-
lich und sehliesslieh weiss werden”.
The said changes in colour, the occurrence of the green coloration
and the subsequent turning white render the phenomenon precisely signi-
ficant for the knowledge of the properties of solid solutions. This
will become evident when we think of the general and very interesting
property of the organic nitrosoderivatives to suffer polymerisation and
become colourless when in a solid condition; in solution, however,
they are wnimolecular and coloured (generally blue or green). This
behaviour is quite Comparable to that of nitric peroxide. Ina certain
ntumber of cases the depolymerisation has been traced by cryoscopic
means, as it often takes place very slowly: the lowering of the
freezing point then gradually becomes greater while the colour becomes
more and more intense. In this way it has been ascertained that in
the colourless solid nitroso-compound two molecules have become
united showing that an intense colour must beattributed to the single
molecules. The same happens with NO, (the nitroso-compound of
oxygen) which has an intense colour, whilst its polymerisation product
N,O, is colourless.
After these remarks it is not difficult to see in what manner the
transformation of solid o-nitrobenzaldehyde into solid o-nitrosobenzoic
acid must be conceived. The displacement commences as soon as
the crystal is exposed to sunlight; after about 15 minutes a faint
green tinge is perceptible which gradually deepens ; the nitrosobenzoic
acid, which is formed from and in the solvent, first remains in solid
solution and, to judge from the green colour, in the unimolecular
condition, On continuing the exposure to sunlight the colour becomes
more intense, until finally the saturation point is reached; the outer
') We have ascertained that an elevation of temperature does not cause the
displacement.
( 645 )
layers of the erystal then become dull and a lighter green, the
nitrosobenzoic acid, which erystallises out, is now however white
and consequently bimoleculair'); finally the surface of the crystal
becomes quite white and opaque. The process then apparently comes
fo a standstill because the sunlight cannot any longer penetrate the
interior of the crystal or only in an insufficient degree. In this case
the interior of a sufficiently big crystal still contains a green trans-
parent nucleus.
The titration of five different specimens has given the following
result:
After 2'/, day about 3 °/, of nitrosobenzoie acid.
I 6 /. I I > fl I
I 10 ft I 1 1 I I
I 15 I fl 15 I I
" 34 I fl 24 I I
The surfaces of the last erystals had turned quite white.
Conclusions as to the velocity of transformation cannot of course
be drawn from these figures, as on the one hand the source of light
varied too much in intensity, whilst on the other hand the crystals
were of a different thickness.
It was considered of importance to try and determine the maximum
solubility of o-nitrosobenzoie acid in o-nitrobenzaldehyde. From the
surface of those green crystals, which commenced to deposit the
white acid, the latter was therefore as far as possible removed by
mechanical means. By titration 2.6°/, of nitrosobenzoic acid was
then found; if now we may assume that the concentration of the
acid inside the crystal is not smaller than that at the surface the
saturated solid solution contains about 2.6 mols. of acid per 100 mols.
Another conclusion may still be drawn from the above, namely
that o-nitrosobenzaldehyde is capable of forming mixed crystals with
2.6 mols. of o-nitrosobenzoic acid; whether these two substances
are isomorphous is not known as the system of crystallisation of
nitrosobenzoic acid has not been determined. Very probably they
are not isomorphous as otherwise the power to form mixed crystals
would occur over a larger interval or even for all proportions.
1) It has not been possible to ascertain, by the ordinary means at disposal, not
even by the highest possible enlargement, that the o-nitrosobenzoic acid formed
is crystalline. This cannot be a matter of surprise if we consider that the separa-
tion of the acid proceeds very rapidly and that the diffusion in solid solution is
particularly slow. Still we may speak here of crystallisation as the separated
substance, in contrast to amorphous compounds, exhibits definite physical constants
(fixed melting point, solubility etc.).
44*
( 646 )
By determining the meltingpoint line of the system of the two
substances (the aldehyde melts at 45°, the acid is decomposed at
about 200°) the point up to which they are still capable of forming
mixed crystals may perhaps be determined more accurately. It is
not improbable that in the intramolecular rearrangements of other
solid substances solid solutions may also be formed; if possible this
will be further investigated.
Chemistry. — “The transformation of diphenyliodonium todide and
chloride and its velocity’. By Mr. E. H. Bécuner. (Communicated
by Prof. C. A. LoBrr DE BRUYN).
(Communicated in the meeting of March 28 1903).
It is about 10 years ago that Vicror Meyer and HARTMANN !)
announced the important discovery of a new class of iodine deriva-
tives, the iodonium bases, substances with a trivalent iodine atom,
having about the same basic power as the ordinary alkalis and capable
of forming salts. The simplest representative of this interesting
class of substances is diphenyliodonium-hydroxide: (C,H,), JOH;
the salts, such as the chloride or the nitrate, when dissolved in water,
appeared to possess a conductive power corresponding with that of
the alkali salts ®).
The behaviour of the halogen salts of the base, when heated, is
peculiar; Victor Meyer and HARTMANN noticed that on fusing these
salts at 175° a decomposition sets in, which spontaneously leads to
a complete conversion into halogen-benzene (C,H,), = J—J = 2C,H,J
with strong evolution of heat.
This transformation now deserved a closer study. It may be con-
sidered as a depolymerisation but is distinguished however from
many other similar reactions, not only by the great difference in
character between the decomposing substance and the products of
decomposition but also by the fact that the transformation is not
reversible. At all events, up to the present no process is known
which leads straight from iodobenzene to diphenylodoniumiodide.
In this latter respeet the above mentioned reaction is distinguished
from the transformation with which it has been compared namely
that which tetramethylammonium iodide suffers on heating; the latter
substance is readily prepared from its products of decomposition at
the ordinary temperature.
1) Ber. 27. 502, 1594. (1894).
2) Suruvan Z. ph. Ch. 28, 523. The salts are, therefore, not dissociated hydrolytically.
( 647 )
It was to be expected that the decomposition of the diphenyliodonium-
salt would take place at temperatures considerably below the melting-
point, and this is actually the case.
1. Beforehand, however, it was deemed desirable to study the
behaviour of the iodide towards light as in the study of the velocity
of transformation account had to be taken of a possibly existing
sensitiveness to light *).
I have found that in the case of the iodide the transformation
is caused by exposure to light *); whilst it remains quite intact when
kept in the dark for 2'/, months. It was to be expected that the
source of the light would affect the transformation. The following
results were obtained :
Electric Are-Light: after 1 hour titre: 26.6°/, J, converted about 14.5°/,
" 7] mentele yn 249 , I ded AO
Sunlight: ná I" y 30.0 4 it IJ 3.5 #
" „ 30 " fe EIO i, " pe GON
Auer Light: „170 " oe iar i li IJ FF 6.4 »
Diffuse Daylight: a. „ 10 weeks: 24.7 ‘y " i ee
7 b. / 203 / 1" pes Ln
The decomposition of the iodide is therefore most rapidly effected
by the arc-light.
2. If now the solid iodide was exposed to temperatures consider-
ably below its meltingpoint a more or less slow conversion seemed
to take place. Whereas 1°/, at most was decomposed at 90° after
3 hours, about 36°/, had disappeared at 100° after 13 hours, whilst
after heating at 123° for 31/, hours only 5°/, was left undecomposed.
This shows that the decomposition of the solid substance already
takes place even at temperatures considerably below the meltingpoint.
This also applies to the solid chloride which however is more
stable than the iodide.
Several series of experiments were now made with the solid iodide
1) The quantitative estimation of iodonium haloid and halogen-benzene in the
presence of each other is simply done by titration with AgNO;; the first when
introduced into water yields one of the halogen atoms as ion whilst iodo- or
chlorobenzene does not react with AgNO,.
For diphenyliodonium-iodide was found: according to Garws 62.1 and 62.19/, J,
calculated 62.2°/4; by titration 31.0 and 31.1%, J. The chloride gave on titration
11.158 9 Cl, calculated 11.20/,.
*) V. Meyer states that it turns yellow on exposure to light.
( 648 )
at temperatures of L05—110°; the results obtained will be commu-
nicated on a future occasion.
3. It was obvious that I should try to make a closer study of
the velocity of transformation of the iodide in solution. Its great
insolubility, however, rendered the operation impossible; of the many
solvents which were tried, pyridine proved to be the best; the
solubility of the iodide was however still too small, namely only
about ee
The more soluble diphenyliodonium-chloride was better suited for
the purpose; the solubility in water, although not large, proved sufti-
cient at the temperature at which the operation took place (98—99°).
The results obtained in fifteen velocity determinations were at
first very unsatisfactory and pointed to the existence of many inter-
fering influences. The coefficients obtained on applying the formulae
for unimolecular and bimolecular reactions were anything but constant
and often pointed to a very irregular course. In one experiment
coefficients were obtained which were many times greater than those
got in another apparently quite analogous case. Sometimes the coeffi-
cients diminished equally, sometimes the reaction after proceeding
for a while, suddenly ceased. After many similar negative results it
at last appeared that the conversion of diphenyliodoninm-chloride into
chloro- and iodobenzene is influenced to an extraordinary degree by
the presence of very small quantities of impurities. Very small
quantities of acid retard the reaction to a remarkable extent or bring
it to a standstill: the presence of traces of iodine causes a regular
full in the reaction coefficient; a litthe of the free base (diphenyl-
iodonium-hydroxide) accelerates, on the other hand, the decomposi-
tion in a strong degree. The halogenbenzenes formed during the
reaction appeared hoivever to be inert.
On now using a very pure preparation free from acidity and of
a pure white colour and applying the formula for reactions of the
second order, coefficients were obtained which could be considered
as constants. (see table p. 649).
On adding 6 ce. of ™/,, HCl, the coefficient (which, moreover, was
not constant) fell to about half the value obtained in experiment I
while the presence of 8 ec. of "/,, (C,H,), JOH increased the coefficient
about + or 5 times’).
1) The following experiment also may show how sensitive the transformation is
to very trifling quantities of foreign substances. To a solution of the chloride
(Co = Yo9.2, T— 99.0), which after 3!/, hours had fallen from 30.67 AgNO, to
23.71, was added 39.3 milligr. of a well crystallised chloride which was coloured
Say ri 99° Cat... B
2.909 gr. in 250 em*.
oe ccm. AgNO, | Ky | Ky
Kaa
RENS
18 | 42.95 | 0.0152 | 1.32
20 1.87 | TEN 1.97
99 aa | 443 | 4.31
24 10.87 135 | 1.96
25) 10.50 136 | 190
98 Q 94 | 130 1.97
30) 9.42 | 4199} 4.30
TW. T=99.0 ¢,=%.,
trace of iodine added.
t Keno, |K,
0 715
11/, h 25 1.43
31, 23.00 1.33
Blf. 29.00 1.40
111), 18.37 1.00
gg, |. 45.77 0 88
If, by
0 37.17
1!/5 33.82 0.0973 1.11
All, 27.85 295 | 4.32
9 DT 236 1.49
7 22.95 299 1.16
|
nen
ive PA 6,16. ar
loo; ;
25 om}, n/a, HCl added to 150 em*,
Cone. of the HCI therefore '/,., n.
t AgN( ),
1) PAT MANO,
2 hi. 2150
4 en
22 | 26.61
neutral. with NaOll
26 | 21.32
28 17.87
eneen
means of the van ’r Horr formula’), we ecalculate the
order of the reaction from the communicated experiments and also from
a few which are not yet communicated, we find n= 2.1,1.9 and 2.1.
From this, and also from the fact that in experiment I the K,’s are
constants, it follows that the transformation
somewhat yellow, but gave on analysis the theoretical number for chlorine. By
this addition the titre naturally increased and came to 26.10; 21/, hours later the
solution did not appear to have changed (found 26.08). The somewhat coloured
chloride was found to have a faint acid reaction and to give blue colour with
starch solution a‘ter some time.
i) K, is calculated according to the formula for reactions of the first, Ky according
to that for reactions of the second order.
2) Vorlesungen, I. 193.
—
( 650 )
(Cs He abel Cech GH
is a bimolecular one.
Since the chloride is comparable with a salt such as KCl, it may
be concluded that the transformation does not oceur in the non-
dissociated molecules but between the ions. This idea would agree
with that propounded by Waker and Hamry *) for the transformation
of ammonium isocyanate in aqueous or alcoholic solution into urea,
a reaction which also appeared to be a bimolecular one. WALKER
and Hamry were enabled to support their view by showing that
either ammonium- or isoeyanie acid ions cause a retarding intluence
on the reaction investigated by them as both diminish the dissociation
of ammonium isocyanate. In our case a similar behaviour of chlorine
and iodonium atoms does not present itself. Hydrochloric acid has
certainly a retarding influence but this is too large to be explained
by a diminution of the ionisation. Then again, iodonitum hydroxide
has a strong accelerating power. We must, therefore, think here of
a special catalyzing influence of hydrogen- and hydroxyl ions:
apparently the first acts here as a retarding catalyzer, an influence
of which up to the present but few instances are known. Then, if
the acid is neutralised (compare expmt. IV), the transformation proceeds
in a regular manner whilst the chlorine ion is still present in about
the same concentration.
The most probable view of the mechanism of the transformation
of the iodonium haloids is therefore that the reaction takes place
between two molecules.
A trace of iodine retards the transformation in an increasing degree.
This investigation will be continued later on.
Organic. chem. Laboratory, University of Amsterdam.
Chemistry. — “Nitration of symmetrical diutroanisol.”” By Dr. J. J.
BLANKSMA. (Communicated by Prof. C. A. Losry pr BRUYN).
(Communicated in the meeting of March 28, 1903).
In a previous communication?) it has been stated that pentanitro-
phenol is readily formed by the action of nitric acid on symmetrical
dinitrophenol whilst symmetrical dinitroanisol is attacked with difficulty
by nitric acid. It seemed, however, not impossible that symmetrical
dinitroanisol might still be further nitrated and this indeed appeared
1) J. Ch. Soe. 67. 746 (1895).
2) Proc. Royal Acad. 25 Jan. 1902.
( Got }
to be the case. If symmetrical dinitroanisol is treated for two hours
on the waterbath with a mixture of HNO, (density 1.44) and sulphuric
acid, trinitroanisol is formed m. p. 104°. The nitrogroup introduced
into this substance is mobile and easily replaced by OH, OCH,, NH,
NHCH, ete. If the NO, group is replaced by OH dinitroguaiacol is
formed m.p. 121°. By treatment with alcoholic methylamine, methyl-
amido-dinitroanisol is formed m.p. 168°, which is converted by nitric
acid of 1.52 sp. gr. into oxymethyl-dinitrophenyl-methylnitramine m.p.
118° already obtained by Grimavx and Lerùbvre®) by nitration of
dimethyl-orthoanisidine. This goes to prove that the nitrogroup in
regard to the OCH,-group has been introduced into the ortho place
and that, therefore, the constitution of trinitroanisol is represented by
ott. OOH: (NO eb Bb a.
If trimitroanisol is treated with a solution of Na OCH, in methyl
alcohol the NO, group 2 is replaced by OCH, and the dimethylether
of dinitropyrocatechine is formed, m.p. 101°. Treatment with alcoholic
ammonia yields dinitroanisidine C, H, (OCH,) NH, (NO,), 1. 2. 3. 5,
m.p. 174; with aniline and aethylamine are formed compounds
melting respectively at 155° and 123°.
If trinitroanisol is nitrated with a mixture of nitric acid of 1,52
sp. gr. and sulphuric acid a tetranitroanisol is formed m.p. 154°. On
treatment with 2 mols. of Na OCH,, this substance is converted into
erystals which melt at 165° and assume a purple-brown color when
exposed to light.
Analysis shows that two NO, groups are replaced by OCH,. Lorine
JACKSON *) by treating symmetrical tribromodinitrobenzene with 3 mols.
of NaOCH, has prepared a compound with the same properties as
the above mentioned; he however considered that he had obtained
the dimethylether of dinitroresorcinol. The latter substance melts
however, according to Fruryss®) and Merpora *) at 154°, whilst Merrum
Trrwoer*) and L have found 157°. It is therefore very probable
that Loring Jackson has been dealing with the trimethylether of
dinitrophloroglucinol as, on treating symmetrical tribromodinitrobenzene
with Na OC,H,, all three Br-atoms may be replaced by OC,H, ®.
That the compound obtained from tetranitroanisol and NaOCH, is
really identical with that from symmetrical tribromodinitrobenzene
1) Compt. Rend. 112. 727.
2) Amer. Chem. Journ. 18. 180.
3) Centr. Blatt. 1901. I. 739.
4) Proc. Chem. Soc. 17. 131.
5) Rec. 21. 288.
6) Amer. Chem. Journ. 21. 512,
( 652 )
was shown bv taking the meltingpoint of a mixture of the two
substances; no lowering of the meltingpoint was noticed. It is
therefore proved that from tetranitroanisol and NaOCH, the trimethyl-
ether of dinitrophloroglucinol is obtained and consequently the con-
stitution of the tetranitroanisol is:
C,H OCH, (NO,), 4. 2. 3.
OCH, OCH;
NO 6 NE NO,/ \NOz
|
NO. me JSO, SN / OCH,
If symmetrical tribromodinitrobenzene is treated in aleoholie solution
with six mols. of methylamine, the three bromine atoms are readily
replaced by NHCH, and we obtain fine orange-red needles m.p. 220°
(with decomposition. When this symmetrical C,H(NO,), (NHCH,),
is dissolved in nitric acid of 1.52 sp. gr. and then ited with water
a fine white crystalline powder is obtained which, when dissolved in
elacial acetic acid, deposits small beautiful white needles, which explode
between 200° and 203°, sometimes causing aflame. From the analysis
it appears that this is the symmetrical trinitropheny ltrimethy Hrinitramine.
NO,
NICH, NCH,
Ne No, \NO,
= NO, NO,
cas /smten CHa ANN
2
x NO.
Geology. — “ Two New Mid-Cambrian Erratic- Blocks from the
Dutch Diluvium?. By J. H. Boxxema at Leeuwarden. (Com-
municated by Prof. J. W. Morr).
I. When I had been appointed assistant at the Geologieal-Mineralogie
Institute at Groningen, L was charged with the task of determining
the fossils that are found in the collection of Groningen sedimentary
erratic-blocks. If we succeed in this with a fossil, we can as a rule
more or less accurately, for the erratie-block in which it occurs, fix
the age of the layer of which it formerly formed part; at the same
time it may be found out whether suchlike stone is still known as
firm roek, — and whether the same kinds of erratic-bloeks have
been met with in any other places.
With many pieces I suceeeded, but with a not inconsiderable
number I failed, owing to various causes. To the latter division
belonged i.a. two small pieces of lime-stone, the largest dimensions
( 653
of which are about 4 centimetres. They originally made part of one
erratic-block, which was found when the ramparts near one of the
former Groningen gates (Boteringepoort) were dug off. One of the
pieces still shows a part of the original surface possessing distinct
elacierscratches.
From the pieces preserved it may be concluded that this erratic-
block consisted of green-grey, rather compact, marly lime-stone, in
which with a magnifying glass many little grey grains and here and
there little dark-green lustrous Glauconite-grains may be distinguished.
I observed one single Pyrite-erystal. At the surface it had, to a depth
of about 1 centimetre, become more or less yellow, under the influence
of corrosion.
The part preserved also shows that through this erratie-block van
a layer that was rich in Trilobites-remains. For the greater part the
transverse sections of them are visible. In one piece, however, some
remains are partly or entirely exposed to view. A mid-shell is the
most important of them.
This mid-shell, across which run various flaws, and which conse-
quently is not likely to have entirely retained its original shape, is
lengthwise rather strongly vaulted and has a length of 12 millimetres,
its breadth amounting to about 14 millimetres. It is almost every-
where the same, the lines that connect the beginning and the termi-
nation of the facial suture, running almost parallel to the longitudinal
axis. The front-edge is regularly curved. The occipital-furrow is
shallow, especially on the glabella. The length of the rather broad
glabella is about */, of that of the mid-shell. It is tongue-shaped and
bounded by shallow dorsal furrows. The latter first ran nearly parallel
to each other and then turn to the centre, where they meet. Lateral
furrows are not to be distinguished on the glabella. That part of the
mid-shell which lies in front of the glabella, slants down rather
quickly. The parts on either side slant down more slowly.
As to the sculpture, along the front-edge of the mid-shell, parallel
to it, run fine stripes. The shell moreover shows all over, very near
each other, fine pricked points. The colour of the shell is partly black,
partly yellow-grey (eream-coloured).
In spite of repeated efforts I had never before succeeded in dis-
covering what species of Trilobites this mid-shell came from. This
summer, however, | was more fortunate. On my journey to Oeland
it chanced that near the hospital at Borgholm a pit was being dug
and that, while doing this, people had penetrated as far as the layer
with Paradoxides Oelandicus Sjögren. The stone that had been produced
from the pit, was still present. It consisted of greenish marl-slate,
( 654 )
which had entirely fallen asunder, and of rather large lime-coneretions.
This clashes with LiNNArsson’s ') opinion, that at Borgholm this layer
should consist of marl-slate only, which opinion was afterward made
use of by Rommer *) and Reme.¥ *).
In the said lime-concretions I found, besides some remains of
Paradoxides Oelandicus Sjogren and a couple of nearly complete spe-
cimens of Ellipsocephalus Polytomus Lixnarsson, countless mid-shells
of the latter species of Trilobites.
Here was confirmed the opinion of Linnarsson *) that the absence
of stripes on the front-edge of the mid-shells, and that of the pricked
points, on the scale of the Ellipsocephalus-species occurring at
Borgholm, by which this species was said especially to differ from
the Stora Fré-species, must be attributed to the circumstance that
his Borgholm material came from marl-slate, and that of Stora Fré
from lime-stone. The stripes and the pricked points are remarkably
distinct in the mid-shells I gathered from the lime-concretions at
Borgholm. Consequently there is no reason any more for not ranging
the Ellipsoeephalus-remains of Stora Frö under the head: Ellipsoce-
phalus Polytomus LaxNarssoN, the difference in size only not sufficing
to maintain the contrary.
One of the lime-concretions contained a layer that was peculiarly
rich in mid-shells of Ellipsocephalus Polytomus. While breaking this
concretion to pieces, I was immediately reminded of my Groningen
erratic-block; and now that I have compared the latter with the
pieces I brought from Borgholm, I know that they are exactly alike.
In both the stone is the same, except that the Groningen piece has
a yellow tint, which must be attributed to the influence of corrosion.
The mid-shells of Ellipsocephalus Polytomus, occurring in both, also
resemble each other, in colour as well as in their numerous flaws.
Consequently it may with perfect certainty be declared that the
erratie-block mentioned above has the same age as the layer with
Paradoxides Oelandicus Sjögren (the oldest of the Mid-Cambrian), and
that a corresponding kind of stone is still found at Borgholm in
Oeland. It is probably also met with at Stora Frö in the same
island. I cannot say so for certain, however, as I did not go there
and so do not possess any limestone from that place, which might
be used for comparison.
1) Linnarsson. Om |aunan i lagren med Paradoxides Oelandicus. Geol, Férenin-
gens 1 Stockholm Förhandlingar. Bd. 3. pag. 354.
2) Roemer. Lethaea erratica. pag. 37.
5) Remeceé. Zeitschr. d. deutsch. geol. Gesellschaft. Bd. 33. 1881, pag. 183, 701,
4) Linnarsson. Loc. cit. pag. 364.
This is the first time that mention is made of such an erratic-
block from the Dutch diluvium. Many of the kind, with remains
of Ellipsocephalus Polytomus or of other fossils, occurring in Oeland
in the layer with Paradoxides Oelandicus, have already been found
in the German diluvium. The first of them was mentioned by Damgs’)
and comes from Rixdorf near Berlin. A few years after, RemEns *)
deseribed two such erratic-blocks from the neighbourhood of Ebers-
walde. Later on, Rormer*) made mention of two erratic-bloeks of
the same age. One of them comes from Rostock and bears much
resemblance, according to the description, to the Groningen piece.
This cannot with so much certainty be said of the second block,
which was found at Bromberg and does not seem to be greenish.
In Sleswick-Holstein, too, corresponding erratic-blocks seem to have
been found, as Srornrmu *) writes about „grünliehe Kalkgeschiebe der
Oelandicus-Zone”.
This erratic-bloek also confirms my supposition formerly ®) men-
tioned, that in the Hondsrug occur more sedimentary erratic-blocks
with a West-Baltic character, than was formerly generally supposed.
If. For some time already I have had in my collection several
pieces of an erratic-block consisting of limestone that has been tinted
dark-grey, even almost black, by bitumen. It was found in the loam-
pit near Hemelum. Its calcium-carbonate having for the greater part
crystallized, this limestone approaches antraconite. Some nests of little
pyrite-erystals and a small phosphorite-nodule are found in the stone.
For a long time the only fossil that was exposed to sight was
(with the exception of a few unimportant remains, probably of a
Paradoxides) what I supposed to be the internal cast of the inside of
a piece of Trilobite-shell. Its largest dimension amounts to 9 milli-
metres. This internal cast is almost oval, and strongly vaulted. The
top-part finishes in a bow. On the convex side of this bow it is
steeper than on the concave one. In front, on the least steep part,
is a frame in relief, soon turning round the most elevated point and
then continuing on the steepest part, where it becomes tinier and
tinier. Towards either side springs from this frame a net-work of
1) Dames, Zeitschr. d. deutsch. geol. Gesellschaft. Bd. 31. 1879. pag. 795.
2) Remeré, Zeitschr. d. deutsch. geol. Gesellschaft. Bd. 33, 1881. pag. 181, 700.
3) Roemer, Lethaea erratica, pag. 26.
4) Srottey, Die Cambrischen und Silurischen Geschiebe Schleswig-Holsteins und
der benachbarten Gebiete, 1895. Bd. I, Heft 1, pag. 40.
5) Bonnema. “Cambrian ervatic-blocs at Hemerum in the South-west of Frisia.”
These Proc. 1902, p. 142.
( 656 )
suchlike ones. This net-work is very distinet on the less steep part,
not so distinct on the other, where it is scarcely to be seen with a
magnifying glass. Moreover there are on this internal cast round
elevations.
It being quite impossible for me to find what species of Trilobites
this off-print came from, the exact age of this erratic-block could not
be fixed. The nature of the stone made it likely to be Cambrian,
and that, too, Mid-Cambrian, because of the suppositional Paradoxides-
remains.
When, however, a few weeks ago, my friend dr. GRÖNWALL from
Copenhagen, the author of “Bornholms Paradoxideslag og deres Fauna’
(Danmarks geologiske Undersögelse Il Raekke No. 13.) took a view
of my collection of erratic-blocks, he recognized in the said off-print
that of a right cheek of Conocoryphe Exsulans Linrs.') Herewith
the age of this erratic-bloek was already exactly determined, for the
occurrence of these Trilobites-remains is characteristic of the lower
part of the layers with Paradoxides Tessini Brongn.
This division consists, in Schonen, in Bornholm and (according to
an oral communication of prof. MogerG) to the South of Mörbylinga
in Oeland, of limestone, which after this Trilobite is at present
mostly called Exsulans-limestone, whilst it ceased to be called Coro-
natus-limestone.
GRONWALL’S opinion was brilliantly confirmed, when, on his breaking
the stone further to pieces, remains of the Trilobites Conocory phe
Impressa Linrs,?) Liostracus Aculeatus Ang.*) and Solenopleura Parva
Linrs.*) were exposed to view by him. Moreover a remnant of
Acroteta Socialis v. Seebach was found, which, however, also oceurs
in older and in younger layers, which is not the case with the
Trilobites mentioned just now.
The only remnant that has been well preserved, is a mid-shell of
Conocoryphe Impressa Linrs. It is for the greater part exposed to
view. Only on the sides it is still covered by the stone; so the
facial sutures are invisible. It must have belonged to a young indi-
vidual, its length being only 6 millimetres. It is slightly vaulted, the
glabella a little more than the other part. In front it is bounded by
a flat border along the edge, which border is broadest in the middle.
1) Linnansson. Om. Faunan i Kalken med Conocoryphe exsulans (Coronatus-
Kalken). Sveriges geologiska Undersökning. 1879. Ser. G. No. 35. pag. 15. tafl. II,
fig. 24,20;
2) LinNARsson. loc. cit. pag. 20. tafl. IL fig. 29, 30.
3) _LinNArsson. loc. cit. pag. 11. tafl. 1 fig. 12—15.
4) Linnarsson. loc. cit. pag. 14. tafl. I. fig. 16—19, 20?
( 657 )
The occipital furrow is shallow, especially on the glabella. The neck-
ring broadens towards the centre and bears a little tubercle there.
The breadth of the glabella is at the back equal to its length, which
is half the breadth of the mid-shell. The glabella becomes gradually
narrower towards the front; in front it is rounded. On either side
there are three very indistinct lateral furrows. The dorsal furrows
are little developed. In front of the glabella the cheeks run almost
imperceptibly into each other. On either side an oblong elevation is
visible on the firm cheek, just behind the place where the dorsal
furrow turns down towards the centre. It is scarcely to be observed
that starting from this elevation a line-shaped one runs in the direction of
the corners of the cephalon, as LiNNARSSON tells us. This must certainly
be attributed to the eireumstance, that this mid-shell belonged to a
young individual. The scale possesses no other sculpture than countless
very fine impressed points, placed very close to each other.
From the properties mentioned above one may easily convince
oneself that the mid-shell described comes from Conocory phe impressa
Linrs., and that consequently this erratic-block is a piece of Exsulans-
limestone.
The other Trilobites-remains, all of them pieces of mid-shells, are
too incomplete to be described in such a manner, that the species of
Trilobites which they come from might be recognized from the
description. Moreover, such a description would be more or less
superfluous, as the age of this erratic-bloek has already been suffi-
ciently indicated. So I think I’d_ better leave it and refer to the
authority of Dr. GRÖNwALL with regard to the remains of the other
Trilobites mentioned. As he was so kind as to send me some mid-
shells of these Trilobites for comparison, I could convince myself of
the correctness of his determinations.
As was mentioned above, Exsulans-lime is found as firm rock in
Bornholm, in Schonen, and southward of Morbylanga in Oeland.
Mörbylânga does not seem to have been mentioned yet in literature
in this connection; but Prof. Mosrre told me of it. In Schonen,
Exsulans-lime is without any doubt met with as firm rock near
Andrarum, Gislöf and Kwiks Esperöd. Most probably it is also found
as such, according to Linnarsson, near Fagelsang in the neighbourhood
of Lund.
GRONWALL tells me that my erratic-block does not, petrographically,
correspond with the Bornholm Exsulans-lime, more with that in
South-East Schonen. | cannot decide whether it also resembles that
which is found at Mörbylänga in Oeland.
In the Dutch diluvium an erratic-bloek of this kind was never
before found. They also seem to be very rare in the German diluvium.
As far as I have been able to find out, they are made mention of
by SrouLur *) only.
Mathematics. — “An analytical expression for the greatest common
divisor of two integers.” By Prof. J. C. Krurver.
In this paper we propose to construct certain functions z of two
real variables 2 and y which for positive and integer values of these
variables become equal to the greatest common divisor of . and y.
A very simple solution of this problem is obtained as follows.
Denote by [uw] the integer part of the number w and consider the
arithmetical discontinuous function
1
P (u) S55 [u] =
For any integer 7 we have
1 1
P(u + n) = P(w), P(x + 0) = — —, Pe OS
We will take
]
Pin) =P in —)) == Be
9
and consequently
n= Tn — 0E 2-— 1.
Integer values of w excepted the wellknown relation
1 Si 2 JEAN OL
Pt) EE —
n=l a TN
holds and from it we deduce the identical equation
pil u Pa up
=> Plwt—jJ= 2 Plut+—]= P(e),
p=0 a po a
where « and 3 are relative prime integers. That the identity is
still valid for integer values of 7 may be easily verified.
By the equation
vt pl Mes ot
al) av
a discontinuous function of the variables 7 and y is defined. We
may regard it as a first solution of the proposed problem. For if
1) SrouLey. loc. cit. p. 41.
( 659 )
x and y become integers, say rv—aD, y= D, where « and g are
prime to each other, we have
bf kas ) uy aa it ae ) e eG ‘ ==
zen ee DS Pf ADRS
„0 wv p= at
In a somewhat different form this result is found in a paper by
Stern’). A whole set of functions of the required kind may be
deduced’ in quite the same way. We only have to notice that the
function
N= ¢os 2 HN U
F,(«) = + — = stek)
n=l n
satisfies the fundamental relation
mm | | 3
e ~ y u 5 iy
SF. (ute jas Fl ut | ator, (an),
y=0 3 « vs) a
where again @ and 8 are prime to each other.
Hence if we put
nf] F
P10) 28 = ae (tE) ET GEE
,
=U wv
we get for rc=aD, y= BD
— l 2 „zal 2
F,(0) 2 =D SF, (“) =@IDs XF, (Een, F(0),
mn |) a u) a
that is
z= D.
: : ; + { He : 5
In the functional relation (ID) the term 4, (2) is not easily
Lv
evaluated; hence the series /’,(«#) may be suitably replaced by the
latter of the two series
en sn2wnu
NB vwos2 an U
gay: (u) = 2(—1)-1 ZS ——--
' 9 2:
a (2 bej 4 n)? el
Indeed, if we denote the Bernoullian polynomial of order i
yn+i 1 am jen yin—l B, yn-3
(m1)! Dede. Alet 4. (m—3)!
by jm(u) the series y,, (Ww) is identical with /",, (u) for all values of
uw between zero and unity. Therefore, whatever may be w, the series
Im) may be regarded as a polynomial of the mt degree in
1) “Zur Theorie der Function £(x).” Journal f. Math., 102, p. .
45
Proceedings Royal Acad. Amsterdam. Vol. V.
( 660 )
u—{u| so that, if in the equation (II) we replace F (u) by gar (w),
: ye lt u
(—1)! Be 2k — gl SS Jak (2) REN or 2 (II)
av
p=0
the thus defined function z is algebraically expressed in wv and y.
Jut as well as in the equations (I) and (II) 2 is still discontinuous
for integer values of 1 in equation (IID. By a slight alteration it
is possible to make these discontinuities disappear. Without altering
the value of ¢ for integer values of « and y we may write instead
of (UD)
I yp — [el] 1] 1 Li
(ena as Sees (2) + > gak (0) + gar (4) Pw), (LV)
pay { ik wv 4
and the function 2 has become continuous everywhere. The same
however is not true for the partial derivatives of 2 with respect to
vor y; besides there is as in equations (1) and (II) a lack of symmetry.
By interchanging w and y the value of 2 alters. To some extent
these disadvantages may be eliminated. The process of integration is
apt to level finite discontinuities, moreover symmetry may be intro-
duced by it. And indeed a suitable expression of 2 in the form of
a definite integral can be given.
We consider the function z defined by
1
22k — gk wf gi (ru) ge (yu) da. ay a
0
By,
2k!
Now 2 depends symmetrically on « and y and is continuous
throughout. The function has continuous derivatives; we may different-
iate z a number of £—1 times with respect to # and also 4—1
times with respect to y, either separately or subsequently, before
the derivatives lose their continuity, so that by making / larger
and larger the behaviour of z tends more and more to that of an
analytical function of two real variables.
We now again substitute in (V) «=aD, y= BD and as the
trigonometrical series gz (ev) and yp (yu) are absolutely convergent
(ander the supposition 4 >> 1) we may multiply termwise and
integrate the partial products.
But after integration a nonvanishing amount is furnished only by
those partial products
sim SU
2ahaDu
Cos
‘Qal3Du,
COS
in which we have
( 661 )
henee we find
B. 4 Prk ly=o
Ee Ne Prk
2k! (2.2)? 2 yal gek 2k! 5
and as before
z == D.
Had we integrated the product gn (eu) gu (yi), where m+n is
even, urstead of gn (wt) gm (yu) the result would have been similar,
only symmetry would have been lost.
We may remark that the z in equation (V) is still an algebraical
function. For remembering that
d
— Ok (U) = 94-1 (wu),
du
g, (u) = P (w),
we deduce by repeated partial integration
B. rs y= k—2
in En (lr ale yk lt apy (w) ge (4) +
== || ek
ae (le? veok-l OP (wit) gar (yu) } k -f- (—1)* Py Jar +1 (Y)s
— «
or finally :
Bi. „=k?2
= ai 2 , (—1)? ak yi? gj (€) ge (y) +
wk
seer dk Jh (4) +
Ll (Ly I
Hikari) gon (EL) 4 — you (0) + you (y) P(e}. (VD)
mil d a
„al:
From this equation we infer that the product 22% is a rational
integral function of . and y of degree 4 J + 2, and generally speaking
the equation represents an algebraical surface S of that degree. But
it should be noticed that this surface S in reality is composed of an
infinite number of partial surfaces, having contact more or less close
along a system of plane curves C. And in fact the larger the integer
kk be chosen the closer will be the contact of the partial surfaces.
Equation (VI) contains the equations of all the partial surfaces, but
each of them has a distinct equation the coefficients of which are
made up from the integers
[a], [y] and | | pee a TBS 7 a
Hence we pass from one partial surface to an adjacent one in
all places, where one at least of these integers increases by unity.
45%
WI
Hi
( 662 )
Thus the projections on the .y-plane of the curves € are of two
distinct categories. To the first belong the straight lines w=n, y==n,
regularly dividing the wy-plane in equal squares of side unity. The
second category is formed by straight lines issuing from the vertiees
of these squares and which, if produced, would pass through the
origin. The number of these lines, which have their points of issue
inside the square, bounded by the v-axis, the y-axis and by the lines
vn, y=n is seen to be 22¢(n)'), that is on an average equal to
6
2 wm. Therefore the partial surfaces remote from the origin ultimately
take the form of infinitely narrow strips, the length of which varies
fron. foxy 2:
In order to lower as far as possible the degree of the surface $,
we should take 4=1 and we have from (V) and (VI)
1 ; . \ p=[r] Ly il ts
— 2=ary | Pau) Plyu)du=ad > 9, - J+ —4,(0)+9,(y) P(x) | — — 9, (y)-
12 ; ; | pol ‘4 v Dig: iat \ y LN
0
A comparison with (LV) makes it evident that for integer values
of rv and y the quantity 2 still becomes equal to the greatest common
divisor. The surface S is of the 6% degree, the partial surfaces still
hang together everywhere but in this case they have no contact along
the curves C.
Physics. — “On marina and minima of intensity sometimes obser-
red within the shading of strongly widened spectral lines.” *)
By Prof. W. H. Juus.
While examining a series of photographs of the solar spectrum,
made by Rowrarp in 1888 and 1889, Jewen. discovered one plate
on which the shading of /7 and A was broken up into a system
of faint, nebulous lines, symuinetrically arranged about the central
absorption lines*). The distances apart of the component lines of
the series increased as the distance from the central line increased.
On some other photographs of the solar spectriun, taken by RowraNp
and by himself, he only found feeble indications of these series; but
') » (7) denotes the number of integers less than ” and prime to #.
*) Part of the contents of this communication has already been shortly mentioned
in a foot-note which was added to the English translation of a former paper
(Proc. Roy. Acad. Amst. IV, p. 601) but did not occur in the Dutch original of
the same.
°) L, E. Jewett, Astrophysical Journal, IL p. 108, 1896, and VIL, p. 51—93, 1898,
a
mad Mt in «4 ee ah. RE nan en SE eee ae
ee
eS
( 665 )
in the shading of some of the strongest lines of iron and a few
other elements a similar structure was observed, the component lines
being faint, nebulous, and close together.
The plate which showed the structure of Hand A most plainly,
displayed an additional peculiarity, as on it the general shading of
those lines was unusually weak.
In Hatn’s abnormal spectrum '), which was characterized by the
extreme weakness of the shaded background of many absorption lines,
maxima and minima of intensity were also distinguishable under a
microscope, though they did not appear so clear nor so regularly
arranged as in the case deseribed by Juwerr.
If we suppose the principal cause of the shading of the Fraunhofer
lines not to be the absorption, but rather the anomalous dispersion
of the waves, which in the spectrum are situated on either side the
central absorption line *), we can easily account for the phenomenon,
before mentioned, as well as for the fact, that in very rare cases
only it shows distinetly.
Let us consider a narrow beam of light of an exactly defined
wave-length, belonging to the shaded background of a Fraunhofer
line. This beam has emerged from the deeper layers of the Sun
with a certain divergence; we suppose it to proceed in the approxi-
mate direction of the structure lines of the corona (l.c. p 597). Let
iis wave-length be somewhat greater than that of the absorption
line; for this kind of light, the medium will then possess a positive
refraction constant, and the separate rays of the beam will curve
about the denser parts of the “tubular” structure. If we had supposed
the wave-length to be a little less than that of the absorption line,
the refraction constant would have been negative and the rays
would have curved about the rarer parts of the coronal structure.
In either case the divergence of our monochromatic beam will alter-
nately diminish and increase, and this partieular kind of light will
reach the Earth with an intensity, determined by the degree of
divergence (convergence perhaps) with which the beam left the
ultimate traces of the corona.
With respeet to a beam of other light, the wave-length of which
differs only slightly less from that of the absorption line, the medium
will have a considerably greater refraction constant, so that the rays
of this particular beam may have made a bend, or part of a bend,
more than those, belonging to the former beam, on their way through
1) G. E. Hare, Astrophysical Journal, XVI, p. 232, 1902.
*) W. H. Juus, Proc. Roy. Acad. Amst. IV, p. 589—602,
( 664 )
the corona. This beam may, accordingly, arrive with a quite different,
say a greater, divergence and consequently display a smaller intensity
in the spectrum, than the neighbouring beam, first considered.
Approaching still nearer to the absorption-line we shall come across
waves that reach the Earth in beams whose divergence is smaller
again, showing increased intensity, ete. It is plain that in this way
periodical alternations of light and dark on either side the central
absorption line must arise. The waves, corresponding to the middle
of one of these fringes, will have achieved exactly one whole bend
‘i.e. the distance between two consecutive points of inflexion of the
path) more, or less, than those corresponding to the middle of the
adjacent fringes.
From the familiar type of the dispersion curve it follows directly,
that, in moving away from the absorption line, to equal differences
in refraction constant increasing differences in wavelength will
answer. The distance between the fringes will accordingly increase
from the centre to either side, as has in fact been observed.
Our explanation requires besides, that this system of faint lines
should be visible only when sunlight reaches us exactly along a
coronal streamer of sufficient length. In my last paper (le.) I showed
that, in case this condition is fulfilled, the average shading of the
Fraunhofer lines must be abnormally weak. It is therefore not to be
wondered at, that on the plate, plainly displaying the peculiar structure
of H and A, the shading really was unusually faint. But the
formation of a well defined line-system demands a further condition
to be fulfilled, viz. that the configuration of that part of the (rotating)
corona we are just looking through, offers all but the same aspect
as long as the photographic plate is exposed. This, of course, requiring
very special circumstances, we see why even in cases, in which the
shading of the Fraunhofer lines is weak, the fringes may be missing
all the same.
In a few eases has a like structure been observed with some
strongly widened emission lines of the arc-speetrum. Kayser came
across this phenomenon in a line of the lead-spectrum *) ; ROWLAND
too seems to have observed it once; and after many vain endeavours
JEWELL succeeded in obtaining a photograph of the are spectrum of
calcium, in which at /7 and A the series appeared rather distinetly.
This plate was obtained by using an extremely powerful direct current
and exposing for three or four seconds only. Under these conditions
1) H. Kayser, Handbuch der Spectroscopie, Il, p. 353.
( 665 )
the heated calcium vapour formed a much more extended atmosphere
around the poles than with a weaker current.
Kayser *) asserts, though, that it has hitherto remained unknown,
what are the exact conditions upon which the phenomenon depends.
In connection with the preceding considerations, 1 hold it possible
that in those experiments the metallic vapour has, during the (short)
exposures, formed a kind of flame of tubular structure, which happened to
be in the exact direction of the spectroscope. This view seems reasonable
if we bear in mind the well-known “blowing” which is of frequent
occurrence in a powerful are loaded with much vapour. The radiations,
proceeding from the core of the arc, which caused the wide emission
band, underwent anomalous dispersion in the enveloping vapour and
traversed the flame-shaped streamer, following sinuous paths.
A simple experiment convinced me that the peculiar light-distribution
observed in all strongly widened Fraunhofer lines’), may be strikingly
imitated in the absorption-spectrum of sodium vapour. The only
thing necessary was to force the absorbing vapour into a more or
less tubular structure, such as we presumed it to exist in the corona.
A slightly converging beam of electric light was thrown on to
the slit of a grating-spectroscope. At a distance of rather more than
100 ¢.m. from the sht, and about 1,5 ¢m. below the axis of
the beam was the opening of a specially constructed bunsen-burner,
from which a sodium-flame emerged. This opening was slit-shaped
(30 ¢.m. long, 0,2 ¢.m. wide) and adjusted in a position exactly
parallel with the axis of the incident beam. The pressure of the
gas was somewhat variable, and a good regulator unfortunately not
at hand. In order to supply the long flame with sodium, the con-
sruction of the burner included a kind of narrow gutter on either
side, into which had been poured a solution of a sodium-salt. This
ascended into the flame by strips of asbestos paper. When viewing
this flame lenethwise, it was as if one were looking through a com-
pressed tube, the sides of which consisted of sodium-vapour. The
density of the vapour diminished gradually towards the centre as well
as towards the outside.
The sodium-lines were observed in the spectrum of the third order.
In spite of the great length of the flame the real absorption lines
were narrow; they stood out from a pretty dark softly shaded
background, the width of which amounted to several ÄNGsTRÖM
wuts. The distribution of the light entirely corresponded to JEWELL’s
Ye p. 354.
2) Jewett, Astroph. Journ. Ill, p. 101; Hare, Astroph. Journ. Ill, p. 156—161,
( 666 )
deseription of the strongly shaded Fraunhofer lines. Close to the
central absorption line there was also an unmistakable increase of
luminosity (resembling the supposed emission lines in the solar spec-
trum); but this increase ought, without doubt, to be attributed to
the most strongly curved rays being kept together by the tubular
structure of the flame, and not to direct radiation from the flame.
For, the electric light being intercepted, the emission-lines were
scarcely visible in the dark field. And besides, as soon as the flame
was disturbed by blowing upon it, or when it was partially covered
by a diaphragm, the bright band, as well as the shading, became
unsymmetrical with respect to the absorption line. Neither Doppier’s
principle, nor the influence of pressure on wave-length can here
have played an appreciable part.
I moreover observed fringe-like maxima and minima in the shadings,
but they showed irregular and so unsteady, that T could not think
of measuring their distances. Nor can there be any question
of photographing this peculiarity before means have been devised
to keep a structure of sodium vapour, as deseribed above, steady
for a reasonable time. Such means are however being prepared.
Imperfect as our present experiment must be, it still serves to
bear out the assertion, that numerous peculiarities of the solar speetrum -
may be explained from anomalous dispersion.
Physics. — “On the emission and absorption by metals of rays of
heat of great wave-lengths.’ By H. A. Lorentz.
Gk \ ”
§ 1. Hagen and ReBexs have recently shown by their measure-
ments of the reflecting power of metals *) that the behaviour of these
bodies towards rays of great wave-lengths (larger than 8 u) may be
accounted for, if one applies to the propagation of electric vibrations
the equations that hold for slowly varying currents, and which con-
tain no other physical constant of the metal but its conductivity. It
follows from this result that a theory which can give an adequate idea
of the mechanism of a current of conduction will also suffice for the
explanation of the absorption of the rays that have been used by these
experimenters. A theory of this kind has been developed by Rirckn *)
and Dreper *). According to their views a metal contains an immense
number of free electrons moving to and fro in much the same way
as the molecules of a gas or as the ions in an electrolytic solution,
1) Hagen and Rupens, Berliner Sitzungsberichte, 1903, p. 269; Berichte d. deut-
schen phys. Gesellsch., 1903, p. 145.
2) Riecke, Wied. Ann., Bd. 66, p. 353, 1898.
3) Drupe, Drude’s Ann., Bd. 1, p. 566, 1900,
7
—— =
( 667 )
the velocity of agitation increasing with the temperature. It is to be
assumed that, in this “heat-motion”, every electron travels along a
straight line, until it strikes against a particle of the metal; the path
will therefore be an irregular zigzag-line and, so long as there is
no cause driving the electrons in a definite direction, an element
of surface will be traversed by equal numbers of electrons, travelling
to opposite sides. Things will be different if the metal is exposed
to an electric force. The motion of the electrons will still be an
irregular agitation; yet, motions in a definite direction will predo-
minate, and this will show itself in our observations as an “electric
current.”
Now we may infer from the relation between absorption and
emission that is required by Kirennore’s law, that the mechanism by
Which the emission of a body is produced is the same as that to
Which it owes its absorbing power. It is therefore natural to expect
that, if we confine ourselves to the case of great wave-lengths, we
shall be able to explain the emission of a metal by means of the
heat-motion of its free electrons, without recurring to the hypothesis
of “vibrators” of some kind, producing waves of definite periods.
In the following pages this idea has been worked out. After having
calculated the emissive power we shall find that its ratio to the
absorbing power does not depend on the value of those quantities
by which one metal differs from another. According to the law of
Kirennorr, the result may be considered as representing the ratio
between the emission and the absorption for an arbitrarily chosen
body, or as the emissive power of a perfectly black substance; it
will be found to contain a certain constant quantity, whose physical
meaning will appear from the theory.
§ 2. The ratio of which L have just spoken is intimately connected
With another important physical quantity, viz. the density of the enerey
of radiation in a space enclosed by perfectly black walls, which are
kept at a uniform absolute temperature 7. If the electromagnetic
motions of which the aether in such a space is the seat, are deeom-
posed into rays travelling in all directions, and each of which has
a definite wave-length, the energy per unit volume, in so far as
it belongs to rays with wave-lengihs between 2 and 2 + dà, may
be represented by :
F (a; T) da,
F’ being a function which many physicists have tried to determine.
BOLTZMANN and Wier have shown by thermodynamical reasoning
that the above expression may be written
( 668 )
1
SADE
where f (2 7’) is a function of the product #7. Afterwards Pranck ')
has found for (1) the form
Here ¢ is the velocity of light in aether and / and & are univer-
sal constants.
In the theory of PLaNnck every ponderable body is supposed to
contain a great many electromagnetic vibrators, or, as PLANCK calls
them, “resonators”, each of which has its own period of free vibra-
tion, and which exchange energy with the aether as well as with
the molecules or atoms of ponderable matter. The conditions of
statistical equilibrium between the resonators and the aether may be
thoroughly investigated by means of the equations of the electro-
magnetic field. As to the partition of energy between the vibrations
of the resonators and the molecular motions in the body, PLANcK has
not endeavoured to give an idea of the processes by which it takes
place. He has used other modes of reasoning, of which I shall only
mention one, Which is to be found in his later papers on the subject and
which consists in the determination of that distribution of energy that
is to be considered as the most probable. I shall not here discuss the way
im Which the notion of probability is introduced in PLANck’s theory
and which is not the only one that may be chosen. It will suffice
to mention an assumption that is made about the quantities of energy
that may be gained or lost by the resonators. These quantities are
supposed to be made up of a certain number of ginite portions,
whose amount is fixed for every resonator; according to PLANCK, the
energy that is stored up in a resonator cannot increase or diminish
by gradual changes, but only by whole “units of energy”, as we may
call the portions we have just spoken of. Besides, PLANck has found
it necessary to ascribe to these units a magnitude depending on the
frequency 2 of the free vibrations of the resonator, the magnitude
hn
represented by —.
n
being
o
As to the constant %, it has a very simple physical meaning; — 47
) - | « ORTE)
is the mean kinetic energy of the molecule of a gas at the tempe-
rature 7’.
1) Prange! Drude's Ann., Bd. 1, p. 69, 1900; Bd. 4, p.p. 553 and 564, 1901,
( 669 )
It appears from the above remarks that the hypothesis regarding
the finite “units of energy”, which has led to the introduction of the
constant /, is an essential part of the theory ; also that the question
as to the mechanism by which the heat of a body produces electro-
magnetic vibrations in the aether is still left open. Nevertheless, the
results of PLANcK are most remarkable. His formula represents very
exactly the energy of the radiations for all values of the wave-lengths,
whereas the following considerations are from the outset confined to
long waves. We may at best expect to deduce from them the
form which the function in (1) takes for this extreme case.
§ 3. Since, if we trust to Kircnorr’s law, the ratio between the
emission and the absorption must be regarded as independent of the
dimensions and the position of the body considered, we may simplify
the problem by an appropriate choice of circumstances. 1 shall
therefore consider a plate with parallel plane surfaces and I shall
suppose its thickness A to be so small that the absorption may be
reckoned proportional to it and that the energy emitted by the pos-
terior layers may be supposed to pass through the plate without any
sensible absorption. I shall also confine myself to the absorption’ of
perpendicularly incident rays and to the emission in directions making
infinitely small angles with the normal.
Let o be the conduetivity of the metal, i.e. the constant ratio
between the electric current and the electric force, these latter quan-
tities being expressed in the modified electrostatic units 1 have lately
introduced. *) Then the absorbing power of the plate, the coefficient
by which we must multiply the energy of normal incident rays, in
order to get the absorbed energy, is given by *)
Ee a ae
F
Here we shall substitute for o the value furnished by Drupr’s
theory. Let the metal contain different kinds of free electrons, which
we may distinguish as the 1s, the 2.4, the 3'¢ kind, ete., and let
us suppose that all electrons of one and the same kind have equal
charges, equal velocities of heat-motion, or, as we may say, “molecular”
velocities, and travel over paths of equal mean length between two
successive encounters with particles of the metal.
We shall write e
ae for the charges of the different kinds
of electrons, w,, w,,... for the mean molecular velocities, /,, /,,...
2)
1) Lorentz, Proceedings Acad. of Science, Amsterdam, Vol. 11, p. GOS, 1903,
>] Oo b J ’ | »
*) See § 12 below. In electromagnetic units the formula becomes
A —= Arco.
( 670 )
for the mean lengths of the free paths, .V,, .V,,... for the number
of electrons of the several kinds, contained in unit of volume. We
shall finally suppose, as Drepr has done, that for every kind of
electrons, the mean kinetic energy of one of these particles is equal
to that of a molecule of a gas at the same temperature; we may
represent it bve 7, if 7’ is the absolute temperature, and « a constant.
In these notations Drupr’s value is *)
1
6=- —‘(e;" N, if u, + e,? et. U vete (4)
Aa 1 : ous
so that (3) becomes
1
—(e,? Nil, u, He, N, l,u, +...) Ds
MEN
dae!
It is to be remarked that the formula (4) has been obtained in the
supposition that the electric force remains constant, or at least that
it keeps its direction and magnitude during an interval of time in
whieh an electron has undergone a large number of collisions against
particles of the metal. The results of HaGeN and Rupes are therefore
favorable to the view that even the period of vibration of the rays
is very large in comparison with the time between two succeeding
impacts. Part of the following calculations are based on this assumption,
§ 4. We have now to examine the emission by the plate. It
follows from the fundamental equations of the theory of electrons, that
every change, whether in direction or in magnitude, of the velocity
of an electron produces an electromagnetic disturbance travelling
outwards in the surrounding aether. Hence, it will be at the instants
of the collisions that the electrons become centres of radiation. We
shall caleulate the amount of energy, radiated in this way, in so far
as it is emitted across a definite part @ of the front surface of the
plate; this part of the emission is due to the electrons contained in
a volume m4 of the metal.
Let © be a point within the area w, OP the normal in this point,
drawn towards the side of the aether, and 7? a point on this line,
at a distance 7 frem QO, which is very large in comparison with the
dimensions of w. In this point ? we place an element of surface @’,
perpendicular to OP; our problem will be to calculate the energy
radiated across this element. | choose QO as origin of coordinates and
OP as the axis of 2. The components of the velocity of an electron
will be denoted by vu, u, Uz.
1) Drupe, Le, p. 576. This formula does not change by the introduction of our
new units.
a hs À ee
(GT)
Now, if an electron with charge e, is in O at the time f, and has
du, du, dur
at that instant the accelerations ——, ‚==, it will produce at the
dt dt dt
, y .
point /, at the time ¢ + —, a dielectric displacement, whose com-
(
ponents are *)
e du, e du, :
— —— — ., — Te eS es,
Amer dt
On account of the great length of OP, these expressions may also
be applied to an electron situated, not in QO but in any other point
of the part of the plate corresponding to the area w. The whole
dielectric displacement in 2? in the direction of wv (it is only this
component that will be considered in the next paragraphs) at the
We
time t + — will therefore be
{fs
Dr = — — PNM a onsite de HP
if the sum is extended to all electrons present in the volume wA
at the time ¢.
There will also be a magnetic force of the same numerical value,
and by Poyntine’s theorem a flow of energy across the element w',
in the direction from the plate towards P. The amount of this flow
per unit of time is given by
EE LEENE)
$ 5. It will be necessary for our purpose to decompose the whole
emission into rays of different wave-lengths and to examine the part
of (8) corresponding to the rays that have their wave-lengths within
certain limits. ‘This may be done by means of Fourimr’s series.
Let us consider a very long time, extending from ¢= 0 to f= 9.
During this interval the value of }, at the point 7 will continually
change in a very irregular way ; it may however in every case be
expanded in the series
JE oe 99 …_ matt
Oe ee Ain B en ee des ee (eli
Mm t
whose coefficients are given by
df. … mat
On max | EO OENE EEN: beta. te, (LO)
D. Ù
0
1) The proof of Uus will be found in one of the next parts of my “Contribu-
tions to the theory of electrons.”
Now, if the plate is kept at a constant temperature, the radiation
will also be stationary and d,? may be replaced by its mean value
1 .
Dn == =| De dt
0
during the time 9. Substituting the value (9), we get integrals of
two different kinds, some containing the square of a sine, and others
the product of two sines. The integrals of the second kind will
disappear, and
=
De
Tt ETE 1
sin? i=. 3.
Ya LN
a
so that
=e | z=
%,,|
pee Sawa ee
kli!
As to the frequeney of the terms in (9), it is given by
nr 12)
== 3 En er eN GN: a
5 az
|
it will therefore increase by equal differences if we give to m its
successive values.
By choosing for ® a value sufficiently large, we may make this
ie B
step — as small as we like, so that ultimately, even between two values
vo
of the frequency and # + dn, which are in a physical sense
infinitely near each other, there will be a certain number of values
of (12) and of corresponding terms in the series (LI). The number
0
of these terms will be — dz, hence, if we suppose an, or
eo ip
9
ad
an == ken nbd, ds at oe ER
ut zl
0
to have the same value for each term of this group, the corresponding
part of (11) will be
i, On.
me
Substituting this for »,? in (8), we get for the radiation across
w’, due to the rays with frequencies between 7 and 7 + dn,
co
EDE an RS En oe ee eee: eee (14)
Jt
a
Se ee ll
( 673 )
§ 6. We have now to calculate the coefficient a, by means of
(13). After having substituted in the integral the value (7), we may
still take for its limits O and ®, provided we reckon the time from
5
an instant, preceding by the interval — the moment from which it
c
has been reckoned till now. Thus:
3
il i : dit,
n= — >| ef sin nt. — dt |,
2x Ur / dt
0
or, after integration by parts, since sz nt vanishes at the limits,
1 ut r
tm — —— oe ESM CORI AME Ae en ( 15)
Zrce Or
The sum in these expressions relates to all the electrons in the
part wA of the plate and it is by reason of the immense number
of these particles that a definite value may be assigned to an.
We shall begin by determining «?,, and the amount of the radiation
in the supposition that there are only free electrons of one kind ($ 5).
We shall write ¢= NwA for their number, e for the charge of
each of them, and we shall further simplify the problem by supposing
that the molecular velocity w, the same for all the electrons, is not
altered by the collisions and that all the paths between two successive
impacts have exactly the same length /. Then, the time
l
—
u
will also have a definite length.
§ 7. Let ¢,,¢,,¢,,... be a. series of instants, between 0 and 9, at
intervals + from each other. Then it is clear that, if we fix our
attention on the positions of a single electron at these instants, we
shall have one point on each of the sides of the zigzag-line described
by this particle.
Now we may in the first place determine the integral in (15) for
the lapse of time during which an electron travels over the side of
the zigzag-line on which it is found at the time ¢& As the length
sate ts ee.
rt of this interval is much shorter than the period — of the factor
n
cos nt, we may write for the integral
GOE NIE Ug Wt vab va tee, Wte ALO)
It is clear that we shall obtain the sum in (19), for the g electrons,
if, after having multiplied (16) by e, we perform the two summations,
indicated in the formula
[cos nij = Dil rn EN (17)
k
We have in the first place to take the sum of all the values
of u, for the system of electrons, at a particular instant #7, and
then to add together all the results obtained in this way for the
instants 7,,7%,, ete.
$ 8. If we wish to find Sw, for a given time, we must keep
in mind that the velocities wv of the electrons have at that instant
very different directions. We may represent all these velocities by
vectors drawn from a fixed point C. The ends JD of all these vectors
will lie on a sphere with radius v, and if we let fall from each of
these points a perpendicular DD’ on the diameter of this sphere
that is parallel to OX, the distances of the projections from C will
give the values of w,. The sum of all these values may therefore
be represented by
a qs:
if $ is the positive or negative distance at which the centre of gravity
of the points D’, considered as equal to each other, is situated from
the centre ©.
Of course, on account of the large number of the points, this
distance will be very much smaller than the radius 7, and, if we
repeat the construction of the diagram of velocities for each of the
instants f£,. f,..., the small value that is found for § will be positive
in one case and negative in another. It is to be remarked in this
respect that there is no connexion at all between the values of &,
which we shall find for two succeeding instants in the series ¢,, 4, ...
Indeed, between any two such instants, every electron will have
undergone a collision, and it may safely be assumed that, whatever
be the direction of motion of an electron before the impact, all
directions will be equally probable after the impact ‘).
Now, in order to determine a?,, we have to take the square of
the sum denoted by + in the formula (17). This square consists of
k
terms of two kinds, some having the form
cos? n t FS a = 7 cos* nt 5, | 24S ae ae
eh
1 This is easily shown, as has been done by Maxwett in his first paper on the
kinetic theory of gases, if both the electrons and the particles ot the metal are sup-
posed to be perfectly elastic spheres. z
\
Dn | call
—. ="
and others the form
2 cos nt, cosnt,, [2 = u = 2 q’ cos nt, cos nt > the
2 cos nt, cos n ol ae el, 2 q° cos nt, cosnt,, Ss, 5, (19)
As has already been said, the time 9 contains a very large number
“
of periods ——. A certain value of cos nt, once occurring in the series
VL :
cosnt,, cosnt,, cosnt,,... may therefore be supposed to repeat itself
many times. Also, one and the same value of the product cos nt, cos n ty
may be said to occur for many different values of % and 4.
Such a product will therefore bave to be multiplied by very different
expressions of the form Sz Sp, and, since the different values of § are
mutually independent, the number of cases in which §; and 87 have
opposite signs will be equal to that in which they have the same
sign. It appears in this way that the terms (19) will cancel each
other in the sum. It is only the terms of the form (18) that remain,
and we shall have
Pay ME ee |
5: n'e'T'g
a = [cos? nt. Sl a ee, amet (ADI
mde 97? 7
§ 9. Here we may begin by taking together those terms in which
cosnt, has one and the same value. Let the number of these be
(. Then, we have to repeat Q times the construction of the diagram
of velocities, and it may be asked in how many of these Q cases
§ will lie between given limits § and §+d6, or, what amounts to
the same thing, what is the probability for § falling between these limits.
This question may be reduced to a simpler problem. A series of
planes, perpendicular to O X and at equal distances from one another,
will divide the spherical surface into equal parts. Therefore, instead
of distributing the points D on the surface in an irregular, arbitrarily
chosen manner, we may as well immediately distribute the points
D' at random over the diameter, without giving any preference
to one part of the line over another. The probability in question is
thus found to be *)
; 1 a 2u2 >
er 7, 5
Pie pee den tete
Hence, among the Q terms in the sum, occurring in (20), for
which the factor cos° nt, has equal values, there will be QPdé
terms, which may be said to have the same Sj. Together, they will
contribute to the sum the amount
1) See SS 13—15.
46
Proceedings Royal Acad. Amsterdam. Vol. V.
cos? nt. QPS dE
and the total sum of all the Q terms is got from this by an inte-
gration which we may extend from §=—o to §=-+o. Conse-
quently, the sum of those Q terms will not be altered, if, in each of
them, we replace §*, by
+o
Pa [peas EE
This expression being the same whatever be the particular value
of cos? nt, the sum in (20) at onee becomes
> KEN TT EERE Ee
uv
Again, since the instants f,, ¢,,.... are uniformly distributed at
. , 2%
distances that are very small parts of the period —, the sum will
vi
remain the same, if in every term we write 4 instead of cos? nt.
ae 2 $e:
The number of terms being —, we find for (23)
i 4
a za
De
and for (20)
7, 2
ae Bere
m Sx or? >
We have by (21) and (22)
5e == 5
5 3
l
hence, replacing t by —, we find
u
: n°e? glu n?e? NluA
am — = = == =
24e‘ Dr" 242°C Or?
and for the emission (14), in so far as it is due to the one kind of
electrons that has been considered
nie? NluA
SSS
48m? 6° 7?
This value must still be multiplied by 2 because we may apply
to the second of the components (6) the same reasoning as to the
first component, and the total radiation from the plate may obviously
be considered as the sum of all the values corresponding to the
( 677 )
different kinds of electrons. The final result is therefore *)
2
An? er?
(ec? Nl, u, He, N‚l,u, +...) Aww'dn. . (24)
$ 10. If now we divide (24) by (5), all quantities V,e, uv and /,
by which one metal differs from another, disappear. This is what
might be expected according to KircmnHorr’s law and the result
an T
ww dn
6n?e?r?
may be taken to express the emission by a perfectly black body
under the circumstances we have supposed. It represents the amount
of energy which, in the case of such a body, is transmitted per unit
of time across an element w',‚ in the rays whose frequency lies
between # and „ + dn and whose directions deviate infinitely little
from the normal to the element, being contained within a solid angle
42
= Multiplying by eM „ we are led to the following expression for
r cow
the density of energy of which I have spoken in $ 2:
Zan? T oF
reg dn. ° . e ° . . . . ° (25)
Taking for the group of rays those whose wave-lengths are included
between 2 and 2-++ dà, we get for the corresponding energy per
unit volume
16 xeT
EN EN a
a Cage (a
1) It is easy to free ourselves frora the hypothesis that for all electrons of cone
kind there is a single length of path / and a single molecular velocity u. Indeed,
the motion of an electron along one of the small straight lines 7, which it describes
between the instants O and S, will furnish for the sum in (15) a quantity
€ COS Nt. Uy T,
if w is the velocity for the particular line / we wish to consider, and 7 the time
required for the motion along it.
Now, among all these rectilinear motions between two successive encounters, of
one kind of electrons, we may select those for which « and / have certain definite
values and we may begin by calculating the coefficient @m and the emission, in so
far as they depend on the part of (15) which corresponds to these particular motions;
in doing so, we may use the method shown in §§ 7—%. The total emission
may be regarded as the sum of all the partial values (with different /’s and dif-
ferent w’s) thus obtained, and after all the expression (24) will still hold, provided
we understand by /,, J)... certain mear lengths o° path and by wy, 1»... certain
mean molecular velocities. We need not however enter into these details, because
the conductivity and the coefficient of absorption have not been calculated with
a corresponding degree of accuracy.
46*
ocr v4 : : 2 ane
This is found from (25) by using the relation n = Pe
$ 11. The result of the preceding calculations not only conforms
to the law of Krrennorr; it has also a form agreeing with those of
BorrzMaNN and Wien. Indeed, the expression (26) follows from (1),
if we put
.
ere 16
JAT 5 dl.
Our last task will be to evaiuate the constant @ by applying the
formula (26) to experimental determinations of the radiation of black
bodies, and to compare the result with what has been inferred about
the same constant from other classes of phenomena. Combining the
measurements of LummMEr and Princsuem'), who have gone far into
the infra-red, with the absolute amount of the radiation as determined
by Kuripaum *), I find
erg
gi) ane ;
degree
On the other hand, we get, starting from VAN DER WAALS’ evalua-
tion of the mass of am atonr of hydrogen,
aes:
A comparison of my formula with that of PLANCK is also interesting.
For very large values of the product 27, the denominator in
: ch ‘ ‘ SxkT Tee :
(2) becomes ar and the expression itself dû. This agrees with
Ot ==.
2
Now the mean kinetic energy of a molecule of a gas would be
2)
vo
> kT according to PrarxcK and has been represented in what pre-
cedes by «7. There appears therefore to be a full agreement between
the two theories in the case of long waves, certainly a remarkable
conclusion, as the fundamental assumptions are widely different.
On the absorption by a thin metallie plate.
$ 12. Take the origin of coordinates in the front surface, the
axis of z towards the metal, and let there be free aether on both sides.
Writing € for the electric force, 3 for the current of conduction,
1) Lummer and Prinesnem, Verhandl. d. deutschen phys. Gesellsch., 1900, p. 163.
2) Kurupaum, Wied. Ann., Bd. 65, p. 754, 1898.
(OMD)
DH for the magnetic force and putting the magnetic permeability = 1,
we have for the metal
re
rot D= — J, rot € = — — D, mt Pp
C Y
It is found by these equations that in electromagnetic waves travel-
ling in the direction of the positive z, € and § can have the diree-
tions of OY and O Y, and values equal to the real parts of the
complex quantities
G ee ee arl int —4(1+ i) 2
Ob ae 1
Ay = *ae (27)
a being the amplitude of the electric force, and the constants a and
x being given by
(1 —2) Ce
——— 7 —
2n
1 1
a= nd. x
c Zo
Similarly, waves travelling in the opposite direction may be repre-
sented by
Ve 30 epee es de Gr (25)
gi RE En
For the aether the corresponding formulae are somewhat simpler ;
in the first case
Nn ee rite >
Fr dl Ees Dy = ae 6 Sete ee al
and in the second
int + pe z inti et =
EF, — dE x ’ Jy —=—ae ‘i Set Eee oo Te (50)
Now, if rays fall perpendicularly on the front surface of the plate,
we may unite all the systems of waves arising from the repeated
reflexions into the following parts: 1st. a reflected system in the
aether, 2d, transmitted waves in the aether behind the plate, 3". waves
in the plate, travelling towards the back surface and 4t". rays in the
metal, going in the opposite direction. Representing the incident rays
and the motions mentioned under these four heads by the equations
(29), (80), (29), (27), (28), with the values a,, a,, as, @,, 4; of the
amplitude, we have, in virtue of the conditions at the two surfaces
(continuity of €, and 5)
a, Ja, =a, + 4,
ad, — a, = %(a, — 4,),
”
na +s ape np
desen == ye
el
=S +s —i—f
0 Cc
( 680 )
In these formulae, A is the thickness of the plate, and
Ol eee or ee eee
The solution, in so far as it is necessary to our purpose, is
lm Namen Ard
ays
Get It ee — (Ite
1 ZE
2
<a
4% tA
A, SSS oe 2 de
(x+1)? ets — (x—1)? e—s
In these expressions A and consequently s are now to be supposed
| 3
infinitely small. Replacing es and ets by 1—s and 1-++s, one finds
À | ed A
1 1 ZA
a, =| 4 == ‚(- — | a,
The first of these equations shows that the amplitude of the rays
reflected by the thin plate is infinitely small, so that we may neglect
their energy as a quantity of the second order.
As to the transmitted rays, the amount of energy propagated in
them will be equal to the product of the incident energy by the
square of the modulus of the complex expression
aes}
This square is
Oo
1——A,
C
whence we deduce for the coefficient of absorption
5
eee er
c
On the probability with which one may expect that the centre of
gravity of a large number of points distributed at random
on a limited straight line will lie within given limits.
§ 18. Divide the line into a large number p of equal parts, and
call these, beginning at the end A of the line, the 1st, the 2°¢, the
3d part, ete. Denote by q the number of points and let q be very
much larger than p.
We shall imagine the points to be placed on the line one after
another, in such a way that, whatever be the position of the points
already distributed, a new point may as well fall on one part of
( 681 )
the line as on the other. The result will be a certain distribution
of the whole number, entirely determined by chance. Let us conceive
this operation to be very often repeated, say Q times, and let us
calculate in how many of these Q cases, a desired distribution of
the points over the p parts will occur. Dividing by Q we shall have
the probability of the distribution.
The probability that there will be a,6,... m points on the 1**,
2nd, .... pth part of the line (a+6+...+ m=), is given by
a tL q q! TE
i Os GLb kS met
Ls ee
In the case of a very large value =, this probability becomes
P
extremely small, as soon as one of the numbers a, h,...m is far
q : ae
below —. Neglecting these small probabilities, we shall confine our-
P
selves to those cases, in which each of the numbers a,/,.... i is
very large. Then, by the well known formula of STIRLING,
== WAS
als [2a (<) ‚etc.
é
and, if we put
a es, m ;
===. @,— 6, == ils
g q g
we shall find
log P = — 3 (p—1) log (2279) — g log p —
— [(a'g +3) log dl +...4+(mq4+ })logm']. . . . (32)
It is to be remarked that the numbers a, b, ...7 can only increase
or diminish by whole units. The numbers a’, 6’... m/ can change
|
by steps equal to —; this may be made so small that they may be
q
considered as continuously variable.
$ 14. We shall in the first place determine the values of a’, 5’, . im’
for which the probability P becomes a maximum. We have
1 1
d log P= — (1 Sig Dal + q log aa a+... +(4 x Omi + qlog nt Jan |
with the condition
da’ + ...+ dm =),
which is a consequence of
Cp lad os oN cee ee eens ete. Renee
The maximum will therefore be reached if
so that the uniform distribution will be the most probable.
We shall next consider the probability for a distribution differing
a little from the most probable one. Let us put
1 1 1
a—-—+a , =p , ....mM=—-+4p.. (84)
P P Pp
and let us suppose the numbers «a, 6.... u, to be so small in com-
1 :
parison with —, that in the expansion of the quantities in (32) in
P
ascending powers of a,?....u, we may neglect all powers surpassing
the second. We have for instance
ee ; gered 1 1 1 :
agt log ad) = - PR log p+ q+5 p-qlogp ap 1-5 Pte
1 ‘
where, in the last term, we may omit the term ri, beeause it is
much smaller than g. If we put
1 1
Seat (p—1) log (2 a q) + ae log p = log Pn
and keep in mind that, in virtue of (33),
a s+ feae eb =0 Ceo. NN
the equation (382) becomes ‘
i
log P = log Pn — PG (a? +p? +....+ p’),
1 9 zo 9
P= Pym SPITE te THY,
It is seen from this that ZP, is the maximum of the probability,
with which we shall have to do, if a=f=....=p=0. The
equation shows also that, conformly to what has been said above,
the probability will only be comparable to P,, so long asa, 8... .u
: 1 ms
are far below —. Indeed, if one of these numbers had this last value,
P
P, would be multiplied by
ey id
é 2p’
which, by our assumptions, is extremely small.
§ 15. Let 2u be the length of the line, « the distance along the
; u
line, reckoned from the end A, and let us take — for the value or
Pp
ahh ne dd
TE VE MEP WT TTET ee AET we VT
mc dn dn kene dakini we ee
Knit se
4
( 683 )
; u
this coordinate for all points situated on the first part of the line, 3 —
1
for all points of the second part, and so on. Then, in the distribution
that is characterized by a’, 0',.... i, the coordinate of the centre of
gravity of the g points will be
(eee CT Ss
or, by (34), :
u+fa+ 38+ 5y4+-. .+2p—Yul—.
The positive or negative value of .
§=—[a+368+5y4....4+ pbl et (0
is thus seen to represent the distance between the middle point of
the line and the centre of gravity. We have to calculate the proba-
bility for this distance lying between § and § + ds.
The problem is easily solved by means of a change of variables.
Instead of the quantities a, 8,....u, which serve to define a mode
of distribution, we shall introduce new ones a’, }',....u’, the substi-
tution being linear and orthogonal.
Let us take for the first of the new variables
Ee ay ees. (37)
a = —a-- — See re Ee AN
Vp Vp Pp
and for the second
|
zeef
p-3 pl
a Bp—...+ pe MO
se x x
where the numerators form an arithmetical progression, whereas z
means the positive square root of the sum of the squares of the nume-
rators. These expressions (87) and (38) may really be adopted, because
the peculiar conditions for an orthogonal substitution are satisfied :
in both expressions the sum of the squares of the coefficients is 1,
and we get O if we add together the coefficients of (87) after having
multiplied them by the corresponding coefficients in (38). As to the
coeflicients in the expressions for y',...«, we may choose them as
we like, provided the whole substitution remain orthogonal.
The reason for the above choice of e@ and 8 will be clear; the
condition (35) simplifies to
=O 3 PSA rt EEN
and, in virtue of (35), the value (36) will be equal to
xu
P
in all cases with which we are concerned.
Now, the modes of distribution for which the value of § lies
between & and §+d6§ are those for which #' lies between #' and
ke
a dp, if
/ E
EEE VEE eT
XI
Since «/=0, every mode of distribution may be defined by the
values of 8'...w’, these quantities being, like a, 3,...u, capable of
very small variations.
We can therefore select, among all the modes of distribution, those
for which 8...’ lie between 8' and 8 + d8, y' and y + dy, ete.
The number of these may be represented by
MAB EU et en nl orev: a)
where / is a coefficient whose value need not be specified. It suffices
to know that it is independent of the values chosen for 9...
This is a consequence of the linear form of the relations between
these variables and a, 6,...m.
As the just mentioned modes of distribution, whose number is
given by (42), differ infinitely little from one another, the probability
P may be taken to be the same for each of them. Hence, the proba-
bility for the occurrence of one of these modes, no matter which,
must be
EER ee
From this we may pass to the probability for 9’ lying between
8' and #'-++ d;', whatever be the values of y'...u'; we have only
to integrate with respect to these last variables. Now using the funda-
mental property of an orthogonal substitution
eB ee ep tens ee
and attending to (89), we write for (43)
1 “re m=.
Ri ane
he a Sed:
If we integrate this expression from — oo to + 0, as may be done
for obvious reasons, denoting by / a coefficient that does not depend
on 8, we find for the probability in question
1
Rn ta RP
On account of (40) and (41) this is equal to
Pais
ee ERE
k being a new constant.
zeen ven mn tende gn ee
( 685 )
It remains to introduce the value of x?. According to the defini-
il
tion of this quantity, it is a p(p?—4), instead of which we may take
af p*, because p is a very large number. In this way (44) changes into
(Bae A A EN can rt (45)
We may finally determine the coefficient 4’ by remarking that
(45), integrated from — oo to + oo, must necessarily give 1. This
requires that
1 39
k! EEK ze ’
u 2
so that our result becomes
1 EE
= eS Ceo od S.
u An
Microbiology. — “The decomposition of cellulose by aérobic micro-
organisms.” By G. VAN Irerson Jr. (Communicated by Prof.
M. W. BrIJERINCK).
(Communicated at the meeting March 28, 1903).
When we introduce into the soil or into natural waters substances
consisting of cellulose, such as linen, cotton or paper, it will be
seen, that the greater part comparatively soon disappears, whilst
the cellulose derived from the continually falling dead leaves and
other parts of plants is also soon destroyed under natural conditions
either totally or partly. It is also a known fact that the layer of
humus in the primeval forests has a limited thickness, the decrease
being just compensated by the increase caused by the falling of
the leaves. Investigation shows that the cellulose, although chemi-
cally so stable, is decomposed by micro-organisms. The observations
by MrrscueriicH '), Poporr ®), VAN TieGHEM *), TAPPEINER *), VAN
1) Ueber die Zusammensetzung der Wand der Pflanzenzelle, Monatsber. d. Berl.
Akad., 1850, p. 102.
2) Ueber Sumpfgasgiihrung, Archiv. f. ges. Physiol., 1875, Bd. 10, 5. 118.
3) Sur le bacillus amylobacter et son rôle dans la putréfaction des tissus végétaux,
C. R. t. 88, 1879, p. 88. — Identité du bacillus amylobacter et du vibrion buty-
rique de M. Pasteur, CG. R. t. 89, 1879, p. 5.
4) Ueber Celluloseverdauung, Ber. d. d. ch. G. Bd. 15, 1882, S. 999. — Ueber
Cellulosegihrungen, Ber. d. d. ch. G. Bd. 16, 1883, S, 1734. — Ueber die Sumpf-
gasgihrung im Schlamme der Teiche, Sümpfe u. Kloaken, Ber. d. d. ch. G. Bd,
16, 1883, S. 1740.
( 686 )
Spnvs') and particularly those of Hopper Sryier*) and of OMELIANSKI*)
proved, that cellulose may be broken up by anaérobic bacteria, with
production of methane and carbon dioxide, or hydrogen and carbon
dioxide and simultaneous formation of acetic and butyric acids. In
this communication it will be shown that cellulose may also be
rendered soluble by aërobie bacteria. In the first place it was proved,
that this substance may serve as a source of carbon for denitrifying
bacteria and may, therefore, be made to disappear with great rapidity
in the presence of nitrates. But it could also be shown that cellulose
is fit as a carbonfood for common aérobic bacteria and although the
solution then takes place slowly, there can be no doubt about the
decomposition. The products derived from the cellulose play an
important role in the nutrition of other microbes particularly the
spirillae, so that an elegant accumulation experiment may be based
on the use of cellulose as a source of carbon.
Although the destruction of cellulose by anaërobie or aérobie
bacteria requires a faintly alkaline medium, it may, with sufficient
aëration, also be acted on in a faintly acid surrounding by various
moulds and mycelia of higher fungi. This was first demonstrated in
1886 by pr Bary for the genus Peziza and the same was shown
by later observers for other moulds, whilst the destruction always
appeared to be due to the action of an enzyme. Here we will prove
that the power possessed by moulds to attack cellulose is not confined to
certain species only, as one might imagine from the existing literature,
but that a great number of the species of this group share that property.
Finally, I wish to observe that I will occupy myself exclusively
with the destruction of pure cellulose and not with that of lignified
and corky ecell-walls, where in the first place higher fungi are at
work, as is shown by the researches of R. Harrie *).
1. The decomposition of cellulose by denitrifying bacteria.
Meeser *) states in 1871 that in the presence of cellulose bacteria
1) Bijdrage tot de kennis der cellulosegisting. Dissertation, Leonards, at Leiden,
1890, (this contains a very complete literary review).
2) Ueber die Gährung der Cellulose mit Bildung von Methan u. Kohlensäure,
Zeitschr. f. Phys. Ch. Bd. 10, 1886, S. 401.
3) Sur la fermentation de la cellulose, CG. R. t. 121, 1895, p. 653. — Sur un
ferment de la cellulose, CG. R. t. 125, 1897, p. 970. — Sur la fermentation cellu-
losique, C. R. t. 125, 1897, p. 1131, — Ueber die Gährung der Cellulose, Centrbl.
f. Bakt. Abt. II, Bd. 8, 1902, S. 193.
*) Die Zersetzungserscheinungen des Holzes, Berlin 1878.
5) De la putréfaction produite par les bactéries en présence des nitrates alcalins
C. R. t. 81, 1876, p. 533. Nitritbildung durch Bacterien, Ber. d. d. cb. G. Bd. 8, 1875, 5.
1214,
4
( 687 )
reduce nitrates to nitrites; he has, therefore, proved denitrification, in
the largest sense of the word, as being possible with cellulose, but from
his short notes we do not understand his modus operandi or the nature
of the cellulose used in the experiments. DEn#ratn') positively states in
1897 that he has not been able to observe denitrification with flax
fibres and the attention of OMELIANSKL (l.e.) has also not been attracted
to this process when engaged in the study of the fermentations of
cellulose. This investigator induces the methane or hydrogen fermen-
tation by means of a nitrogenous food composed of ammonium sul-
phate or phosphate and sometimes he also adds asparagine, peptone,
extract of meat or of manure. Strange to say, he has not worked
with nitrates; had he done so, he would have noticed that the nature
of the process is completely modified, for instead of the methane or
hydrogen fermentation denitrification sets in which is characterised
by the production of free nitrogen and carbon dioxide.
In a previous research *) on accumulation experiments with deni-
trifying bacteria, I have shown that these aérobic organisms can
oxidise many different organic substances out of contact with air
with the aid of nitrates or nitrites, according to the formulae:
5C+4K NO, +2H,O —=4K HCO, +2N,+ CO,
3C+4K NO, + H,O = 2K HCO, + K, CO, + 2N,.
Denitrification was noticed with lactates, tartrates, citrates, malates,
acetates, glucose, starch, asparagine, gelatin, broth, methyl and
ethyl alcohol and it was, therefore, thought worth while to try
whether cellulose might also be used as a source of carbon supply
in the denitrificationprocess, which indeed proved to be the case.
Before describing my experiments in detail, I will first make some
remarks as to the nature of the cellulose employed. Asa rule Swedish
filterpaper was taken. Although this paper gives a faint blue colour
with a dilute solution of iodine it was found to be very difficult to
remove the impurity with boiling water; the so-called starch-free
paper from ScHrricHER and Scrürr, which has been purified with
hydrofluoric acid, showed the same reaction. Sometimes linen tissues
and cottonwool were used, from which the first also gives a blue
coloration with dilute solutions of iodine, whilst the latter does not
show this reaction. The little impurities, present in the cellulose
employed, were however, of no moment in my experiments, as
the effect on the cell walls was judged by the changes observed
by a microscopical investigation.
1) Recherches sur Ja réduction des nitrates, Ann. agron. t. 23, 1897.
2) Van Irerson, Accumulation experiments with denitrifying bacteria. Proc. Acad. of
Science, Amsterdam July 1902.
I obtained the best results with a paper pulp prepared by triturating
Swedish filterpaper in water, care being taken that this pulp contained
2°/, of cellulose.
In order to obtain a thorough denitrification with cellulose, a
bottle holding about 200 ce. is filled with the following mixture:
Tapwater ') 100, paper 2, KNO, 0,25, K,HPO, 0,05,
and the mixture is then inoculated with a few ec. of mud (from a diteh).
The bottle is then quite filled up in the manner described in
my former communication (Le), to prevent access of air, and the
cultivation takes place at 35°,
After the lapse of about 8 days the action is perceptible, but only
after 12 days a brisk fermentation sets in. The cellulose is carried
to the top by the generated gasbubbles and a quantity of liquid is
forced out of the bottle by the slimy froth, while the paper-pulp is kept
back by the stopper. In the beginning of the process a strong formation
of nitrite may be observed, but the nitrates and nitrites soon decrease
and after the lapse of about 15 days, these compounds have disappeared.
The liquid is now carefully decanted from the pulp, which may be
done without appreciable loss of paper fibres, as these readily agglo-
merate. The bottle is then refilled with the following liquid:
Tapwater 100, KNO, 0,25, K,HPO, 0,05.
The process now starts much quicker than in the first cultivation,
the nitrate disappears in + or 5 days and by repeating the operation
a few times more, cultures may be obtained of an increasingly active
denitrifying power, with which it is possible to completely reduce in
one or two days 0.5 gram of KNO, dissolved in 200 ec. of water.
This method of working is preferable to adding a fresh quantity of
KNO, to the original culture, as it is then not possible to reduce
on the whole more than about */, °/, of KNO, (calculated in regard
to the quantity of the liquid used, or 25 °/, in regard to the cellulose)
because the process then comes to a standstill by the alkaline potas-
sium carbonate formed from the nitrate.
If now a sterilised liquid is inoculated with the strongly denitrifying
rough culture and the cultivation allowed to take place under the same
circumstances as described above, the action commences much more
rapidiy than in the first preliminary experiment, whilst the same
phenomena occur. Even after repeating the inoculation ten times,
no change in the intensity of the process could be observed.
Not only paper, but raw flax fibres, cottonwool and linen appeared
1) From the Downs at Loosduinen.
u
Eo aes sail
—_— dik se ha il aen dee a
( 689 )
capable of inducing denitrification, the cottonwool, however, being
attacked with great difficulty. No denitrification could be observed
with sawdust or turf, whilst Van Servus (Le. pg. 104) has also been
unable to observe decomposition of wood-cellulose by real anaerobie
bacteria. This extraordinary difficult decomposition of wood-cellulose
out of contact with the air, is, according to this investigator, perhaps
the key to the explanation of the formation of humine substances,
peat, browncoal and coal.
The distribution of the microbes, engaged in the denitrification of
cellulose, in the mud from canals, seems to be a very general one,
as each sample employed contained these germs. Although they
are also very generally distributed in the earth, their number per
cc. appears therein to be less, for, on using earth as infecting material,
the action was delayed. Even in sea water, taken from the port of
den Helder, were always microbes found, which in the presence ot
cellulose could induce denitrification ; in how far these forms are similar
to the terrestrial ones has not yet been ascertained, but I wish to
call particular attention to the fact, that, at least near the shore,
cellulose may disappear by denitrification.
The changes, which cellulose undergoes during this process,
are visible to some extent with the naked eye: the white fibres
soon turn orange and the pulp acquires a viscous consistency.
Microscopically, it appears, that already very soon after inoculation
some of the fibres are inclosed in a bacterial mucus and after
a prolonged culture this is the case with nearly all the fibres.
At first, the whole of the fibre is still very plainly visible within
this mucus, but gradually, on account of the decomposition, it
completely disintegrates into loose fibrillae and at last we only
find a few particles of cellulose left, or the fibre disappears altogether
(fig. 1). This destruction of the cellulose becomes very pronounced,
when instead of paper-pulp strips of filterpaper are used. By
repeatedly adding fresh nitrate we then finally obtain bacteria-mem-
branes, which still have the exact shape of the strips of paper but
in which we only meet isolated fibres disintegrated into fibrillae
or even still more decomposed. As is already stated, the woody
substance is not attacked by denitrifying bacteria, the few annulated,
spiral and pitted vessels, which are contained as impurities in the
filterpaper, are found unaltered in this mucus. Fig. 2 shows the
form of two very strongly dissolved paperfibres (a) and some
non-attacked woody elements (3, y and d), which are still found in
such preparations.
The gases, liberated during the denitrification of cellulose and of
( 690 )
which some litres were collected, consist exclusively of free nitrogen
and carbon dioxide; no trace of hydrogen, methane or nitrous
oxide (N,O) was found.
As regards the micro-organisms which take part in this process,
a microscopical examination of the said bacterial mucus, which consists
of a finely granulated substance, shows the presence of very small
rod-like bacteria (fig. 1) and further there are found in the cultures
infusoria, amoebae, monads, spirillae, other small bacteria and vibrionae;
larger rod-bacteria or spore-forming organisms were not detected.
That the bacteria, involved in the process, are no spore forming
organisms, was also shown by the fact, that no pasteurised material
of whatever origin (mud from a ditch or from the soil) can cause
denitrification in the presence of cellulose.
Many experiments have been made with the object of isolating
the bacteria taking part in the denitrification, but always with a
negative result. By inoculation on meat-gelatin and cultivating at
24°, I several times obtained pure cultures of Bacillus stutzeri: Nev.
and LenM., which bacterium was also found in large numbers in
those cases where other denitrifying bacteria were present, so that
denitrification with cellulose is a new accumulation experiment for this
important species, which, however, does not attack the cellulose itself.
On using meat-agar or one of the following culture liquids:
Tapwater 100, agar 2, sodium lactate 2, KNO, 0,05, K,HPO, 0,05,
Tapwater 100, agar 2, glucose 2, KNO, 0,05, K,HPO: 0058
and cultivating at 35°, other bacteria besides B. stutzeri were found
and these were nearly always denitrifying ones. Very often a mucous
colony of a motionless, non-spore forming demtrifying bacterium
became conspicuous, while in other cases a small, slightly denitrifying
spirillum may be isolated. No permanent denitrification with paper
could, however, be obtained with any of these forms or with any
combination thereof, even the erude mixture as it is formed on the
plates was not capable to do this. The fact, that these bacteria may
cause a temporary faint evolution of gas (which, at first, made me
suspect, that the destruction of cellulose could be accomplished by
ordinary denitrifying bacteria) must be attributed to the presence of
small quantities of impurities in the cellulose. Stil, I think we may
take it for granted, that we are dealing here not with an anaérobic
but with an aérobic bacterium, first of all, because all known denitri-
fying bacteria are aérobie and only behave anaérobically in the presence
of saltpetre, secondly because methylene-blue is not reduced, when
added to a medium in which cellulose is denitrifying, whilst in
( 691 )
cultures of the know anaérobic bacteria this compound is always
decolorised. We therefore come to the conclusion, that the bacterium,
Which causes the denitrification of cellulose, does not grow on the
used nutrient media, or else, growing there, loses immediately its
denitrifving properties.
If now we compare the hydrogen and methane fermentations with
the denitrifying process we find the following points of difference.
Is. In the hydrogen or methane fermentation the liberated gaseous
products are carbon dioxide and hydrogen, or carbon dioxide and
methane.
2d, To those fermentations chalk must be added to neutralise
the formed butyric and acetic acids, whilst in our case the saltpetre
yields potassium carbonate and no volatile acids can be detected.
3d, Those processes take place in a medium wherein sulphates can
be reduced to H,S and therefore methylene-blue is decolorised. In my
experiments such a reduction of sulphates is quite out of the question
as long as traces of nitrates and nitrites are still present.
4. The methane and hydrogen fermentation are caused by
comparatively large, well characterised spore forming organisms, our
denitrification by very small bacteria, forming no spores.
The velocity with which cellulose disappears during the denitri-
fication is about the same as in the methane or hydrogen fermenta-
tion of this substance. In a volume of 500 ¢.c., I succeeded in
completely dissolving 8 grams of cellulose all but a few fibres, by
means of 36 grams of KNO,, in a month’s time. The quantity of
KNO, theoretically required amounts to only 24 grams, but in my
experiments a portion of the nitrate was lost in the expelled liquid
and, therefore, more nitrate was required. By means of the hydrogen
fermentation, OMELIANSKI succeeded in dissolving 41.6 grams of cellulose
contained in a volume of 3 litres in 3*/, months, and about 12 grams
in a volume of 1 litre in 5 months, which velocities agree with the
values found by me for the denitrification.
Notwithstanding the possibility of denitrification of saltpetre under
the influence of cellulose, in the presence of this substance nitrification
of ammonium salts and nitrites can proceed without interruption.
This has already been shown by OmELIANski'), who cultivated the
nitrite ferment on paper. We also observed nitrification of ammonium
salts and nitrites, when a very small quantity of cellulose (about
*) Kleinere Mitteilungen über Nitrifikationsmikroben [, Centrbl. f. Bakt. Abt. II,
Bd. 8, 1902, S. 785.
47
Proceedings Royal Acad. Amsterdam. Vol V.
(692 5
0,05 °/,) was introduced into a thin layer of one of the following
eulture liquids, which were inoculated with earth:
Tapwater 100, NH,Cl 0,05, K,HPO, 0,05,
~~! * » KNO, 0,05, N 0,05,
In my previous communication | have already pointed out, that
nitrification and denitrification may take place together in garden
soil and that the aération decides, which of these processes will be
the predominant one; the same conclusion may, therefore, now be
drawn for cellulose as a nutrient material. A closer examination
however shows, that the two processes cannot occur simulta-
neously in the same particle, but that a localisation must take place,
in this way, that strong aëration is necessary in the particles where
nitrification sets in, whilst the exclusion of air is necessary for the
denitrification process.
As has already been previously observed formation of nitrite
takes place in the first stage of the denitrification process in the
presence of cellulose and as this substance by no means prevents the
oxidation of the nitrite to nitrate, these two processes, occurring simul-
taneously, may cause the steady disappearance of cellulose.
We therefore see, that these same processes may cause the disap-
pearance of cellulose in soil and in waters, which plainly shows their
great importance in the ““self-purification ”, as also in the biological
purification of sewage.
Di. The aerobic decomposition of cellulose hy hacteria.
In order to demonstrate denitrification in the presence of cellulose
in the manner described above, a very small quantity of this sub-
stance (about 0,05°/,) only must be present, for on using more
say, 2°/, the nature of the process is completely changed. This must
be attributed to a strong decomposition of the cellulose by aérobie
bacteria, which then takes place and which produces a large quantity
of soluble organic matter, rendering the nitrification impossible. This
last phenomenon may be best observed when use is made of the
following culture medium :
Tapwater 100, paper 2, NH,CI 0,1, K,HPO, 0,05, chalk 2.
Instead of NH,Cl we may also add KNO, (0,1), KNO, (0,1), peptone
(O,1) or an unlimited quantity of MgNH,PO,. The cultivation takes
place at 28—35° in ERLENMEIER flasks in a layer from 0,5—J cm.
in thickness, thus, under very aérobic conditions, so that on using
KNO, or KNO,, no denitrification can be expected, at least not at
the commencement.
Par Te
( 693 )
If mud from a ditch is used as infecting material a decided growth
is already noticed after 5 or6 days, the cellulose turns to an orange
colour and may even disintegrate to a thin paste after 3 or 4 weeks.
Microseopically, we see, that we obtain besides the cellulose-dissol-
ving bacteria a very rich accumulation of spirillae, which however
do not themselves attack cellulose. I have often repeated these
experiments and always with the same result: the cultures become
extremely rich in spirillae and these consist of many varieties.
As a rule different species were found in a same culture, large
spirillae with several windings in company with small, very mobile
ones, but sometimes it also happened, that it looked under the
microscope, as if we were dealing with pure cultures of special
spirillae. These different results being no doubt connected with the
nature of the germs in the infecting materials employed. Often
however, we meet besides the spirillae, infusoria, monads, amoebae
and small forms of bacteria, sometimes also rod bacteria and spore
forming organisms, but the spirillae are always in the majority.
If such cultures are transported into the same sterile medium,
the chief character remains the same, but the growth takes place
more rapidly and as a rule the mumber of species of spirillae is much
reduced, so that frequently but a single one remains. Here it is perhaps
the proper place to state, that an accumulation of spirillae may also
be obtained in using a nutrient liquid composed as follows:
Tapwater 100, calcium lactate 2, peptone 0,05, K,HPO, 0,05,
which is infected with a small quantity of diteh-mud.
At temperatures from 28—37° exceedingly rich spirillae cultures
are formed in this liquid. It would, however, be too rash thence to
conclude, that lactate is formed as a transient decomposition product
of the cellulose. j
The destruction of the cellulose is not only apparent from the strong
growth of microbes, but also from a microscopical examination of the
fibres. As in the case of the denitrification process, these are here also
found to be enveloped with a bacterial mucus in which is always found
a very small rod-bacterium, and occasionally a large micrococcus, which
itself does not attack cellulose, but much accelerates its dissolution by
the small bacterium. The destruction is no doubt caused by the latter,
for sometimes, we have obtained cultures, which exclusively contained
this species only. |
That the decomposition is here an aërobie one, is shown by the
fact, that it Commences at the surface of the culture and also takes
place equally well when we cultivate in a very thin layer.
47%
( 694 )
Owing to the dissolution of the cellulose the absorption of oxvgen
in the cultures may become so strong, particularly when working
with thick layers of cellulose paste, that anaërobie processes become
possible. If, now, nitrates or nitrites ave still present in the culture
denitrification will set in, but if these compounds are already decom-
posed, or if originally another source of nitrogen had been added,
methane or hydrogen fermentation becomes possible. In the last case
Wwe microscopically observe the very characteristic rods with spores,
accumulating on the fibres. In this anaérobic stadium the spirillae
are for the greater part expelled but the destruction is now much
more intense than when it took place exclusively under aérobiec
conditions so that in a short time the paper pulp gets for the greater
part dissolved and leaves behind a bacterial mucus.
When using as infecting material soil, instead of mud from a
ditch, we observe on the whole the same phenomena, only we
do not find then that variety in species of spirillae noticed with
ditch-water. As a rule a short, thick, granulated spirillum with one
half winding is then conspicuous and 1 have succeeded in preparing
pure cultures of this species, already observed previously *).
An experiment with sea water showed, that this also causes the
aerobic decomposition of cellulose and an accumulation of different
species of spirillae was obtained at the same time. In this case the decom-
position in the anaërobie stadium may also be caused by an anaérobie
spore forming organism, which much resembles the bacteria of the
methane and hydrogen fermentations but still presents a different shape.
| have tried to isolate the bacteria connected with the aérobic
destruction but was not more successful than in the denitrification
experiment. On sowing on broth-gelatin or broth-agar a number of
bacteria species were found: jluorescents, B. coli commune, B. sub-
lis, B. mesentericus and several others unknown to me, but none
of these species or none combination thereof was capable of attacking
cellulose.
Our result that cellulose may be attacked by aërobie bacteria
widely occurring in nature, is confirmed in a particularly convincing
manner by the following experiment :
In a glass box are placed two dises of Swedish filterpaper between
Which has been sprinkled a little quantity of powdered MeNH,PO, ; the
paper is imbibed with a solution of 0.05 gram of K,HPO, in 100 ce. of
tapwater. If now we introduce upon the plate thus prepared a little
') Beterinck. Ueber oligonitrophile Microben. Centrbl. f. Bakt. Abt. IL, 1901
Bd. 7, S. 574,
( 695: )
quantity of water containing in suspension humus, garden soil or, still
better, diteh-mud, and if we cultivate at 24—28", the paper gets covered
after 4 or 5 days with vellowish-brown spots which, microscopically,
are found to consist of bacteria. These spots spread with great rapidity,
and it is highly interesting to observe how in a short time the white
ilterpaper is covered with the rusty culture. This is accompanied by
a decided decomposition of the paper fibre, which is shown in the
first place by the fact that the paper becomes quite soft and pulpy
just on the spots exposed to the action of the brown bacterium, losing
there all coherence and sinking down along the edges of the phos-
phate. The phenomenon becomes still more pronounced, when instead
of filterpaper, linen or cotton is used; after about 10 days, the affee-
ted spots of the originally strong material have lost all power of
resistance and after 15 days large holes will be formed when carc-
fully pouring water on them.
Microscopically, it appears that a powerful destruction of the fibre
is taking place (fig. 3) due to the action of a brown, very mobile,
little rod bacterium (Bacillus ferrugineus fig. 4. The fibre is again
enveloped by a mucus in which is found, in many cases, the
same micrococcus as mentioned above (fig. 5 and 6). Owing to the
combined action of these two bacteria the fibre may disappear com-
pletely and leave behind a mucus containing only microcoeci; we then
obtain an image as shown in fig. 7. In addition to amoebae and
monads other small bacteria are found, but there is no question of
the presence of anaérobics, which occur in the hydrogen or methane
fermentations, the action being a purely aërobie one and taking
place very well in filterpaper both sides of which are exposed to
the air.
On transferring the brown spots to previously sterilised paper dises,
between which MgNH,PO, has been sprinkled and which have been
saturated with a sterile 0,05°/, solution of K,HPO,, the phenomenon
remams constant. On inocculating them into the above deseribed cel-
lulose pulp a culture is obtained resembling that which arises by
the direct action of diteh-mud or earth, but no spirallae are found
this time, for these being microaerophilous cannot grow in the
aërobie culture on the paper dises. On the other hand the cultures
from paper pulp were occasionally capable of producing brown spots
on paper dises, showing that in both cases the destruction of the
cellulose may be caused by the same microbe. I also noticed a few
times that the dises were covered with colorless spots caused by a
larger mucus-secreting rod, and as moreover the paper pulp cultures
often are only little colored, it must be assumed, that the aérobie
( 696 )
decomposition of cellulose may be caused by two microbes at least, but
amone these the brown pigment bacterium is the most conspicuous.
On using sea water as infecting material, similar brown spots were
observed. When these were transferred to paper without addition
of 3°/, NaCl they caused no destruction, which shows that we are
dealing here with a sperifie sea bacterium.
I have made several experiments with various culture materials
in order to isolate this very interesting cellulose-destroying brown
pigment bacterium, which | was particularly anxious to accomplish
after having observed, that the crude bacteria-mixture as grown on
different culture media often again produces spots when spread
over paper, which shows that on these media the said bacterium had
kept alive. But I was again unsuccessful in isolating a species which
either alone or in combination with other bacteria was capable of
causing the brown spots on paper. Though I succeeded in isolating
from these spots a brown and a yellow bacterium, which as a rule,
were present in large numbers, yet, as in the case of the denitrifica-
tion process, no destruction of cellulose could be induced by their pure
cultures. The explanation of this circumstance has not yet been found.
The aérobie destruction of pure cellulose and also the more
difficult destruction of the lignified cell walls, *) on which we cannot
enter in this investigation, must, like the denitrification (which is only
possible with non lignified cellulose and takes place out of contact
with air) play an important part in the disappearance of vegetable
substances in nature. The well known fact that wooden piles, when
partly immersed in water are attacked exactly at the place of contact
between the water and the air, the breaking of ropes, when suspended
in water, exactly at its surface and also the aërobie decay of wood
must be attributed mainly to the action of aërobie destroyers. VAN
Senus (le. 108) who was acquainted with these facts, did not deny
the possibility of a decomposition by aérobic bacteria but thought
it very unlikely “as no phenomenon ever pointed to such a fact.”
That the above-described yellowish-brown pigment bacterium plays
indeed an important part in the disappearance of the cellulose, is
shown by the following experiment.
On October 14, 1902 were buried in the garden of the bacteriolo-
vical laboratory at about 15 ¢.m. below the surface a linen cloth
with a red colored border, and in two other places four sheets of
filterpaper, all in’ a horizontal position. Left in the soil untouched
during the recent winter and on exhuming them March 22, 1903
1 The great stability of wood-cellulose towards microbie life is directly opposed
to the ready decomposition of wood paper under chemical influences,
CORA)
not a trace could be found of the filterpaper, whilst the linen cloth
had become soft and pulpy, had lost all coherence and could only
he removed from the soil in pieces; the red border, however, had
retained its original structure. The originally white tissue had
assumed the same yellowish-brown colour so familiar to me from
the cultures on the paper dises, while on microscopical ivesti-
gation the fibres appeared to be much decomposed and disinte-
erated into fibrillae and besides moulds and amoebae only small bac-
teria were observed. On putting some of the well-cleaned fibres
on the paper dises prepared as described above, [ obtained after three
days the rapidly spreading, yellowish-brown spots of the destructive,
small, rod-shaped pigment bacterium. A cellulose-destroying mould,
Myeoyone puccinioïdes, also could be isolated from the linen, but the fact
that the yellowish-brown pigment bacterium was here predominant,
could not be doubted.
3. The decomposition of cellulose by moulds.
The fact that cellulose may be attacked by certain fungi has been
first stated by pr Bary’) for Peziza sclerotium, and the same was
found by Kissing ©) and by Marswant Warp *) for a kind of Botrytis,
by BrureNs®) for Pseudodematophora, Botrytis vulgaris, Cladosporium
herbarum and Aspergillus glaucus. This last investigator did not notice
any decomposition by JMucor stolonifer, Penicillium glaucum and
Penicillium luteum. KouNstamM *) prepared a cellulose-destroying enzyme
from Merulius lacrymans the common wood fungus. Went") has
shown, that Monilia sitophila, the “ontjom” mould from Java, is capa-
bie of digesting cellulose and Koning’) has found that one of the
1) Ueber einige Sklerotien u. Sklerotienkrankheiten, Bot. Zeit. 1886, S. 377.
*) Zur Biologie der Botrytis cinerea, Diss. Dresden, 1889.
5) A lily disease, Annals of Botany, Vol. IL, 1888/89, p. 346.
4) Troekene u. nasse Fäule des Tabaks. Der ,Dachbrand”, Zeitschr. f. Planzenkr.
3d. HL, 1893, p. SL. — Untersuch. über den Würzelschimmel der Reben, Centr.bl.
f. Bakt., Abt. If, Bd. 3, 1897, S. 584. — Beitrage zur Kenntniss der Obstfäulnis,
Gentrbl. f. Bakt. Abt. If, Bd. 4, 1898, S. 514. — Unters. über die Gewinn. der
Hanffaser durch natürl. Röstmethoden, Gentrbl. f. Bakt. Abt. 11, Bd. 8, 1902, S. 114,
5) Amylolytische, glucosidspaltende, proteolytische u. cellulose lösende Wermente
in holazbewohnenden Pilzen. Beihefte z. Bot. Gentrbl. Bd. 10, Heft 2, 1901, S. 90.
6) The influence of feeding on the secretion of enzymae by Monilia sitophila.
Proce. Jan. 1901. — Ueber den Einflus der Nahrung auf die Enzymbildung durch
Monilia sitophila (Moxr) Sacc Jahrb. f. wiss. Bot. Bd. 36, Heft 4, 5. 643.
7) Genootschap ter Bev. v. Natuur- en Heelkunde Amsterdam, 2 series, dl. IV,
Afd. 5, Zitling 7 Dec. 1901,
( 698 )
most common humus-inhabitants from the forest of Spanderswoude,
Trichoderma koningit, possesses the same property.
We have succeeded in finding an experiment by means of whieh
the cellulose-destroying moulds may be isolated from nature in
a direct and certain manner. Two sterile discs of Swedish filterpaper
are placed in a glass box and moistened with the following liquid:
Tapwater 100, NH,NO, 0,05, KH,PO, 0,05.
As infecting material earth or humus may be used, but the best
results are obtained by simply exposing the opened box for about 12
hours to the open air. If then we cultivate at 24° and take care to keep
the paper moist, colonies of moulds already become visible after 5 or
6 days, but it is only after 14 days or three weeks, that we notice
the enormous richness of these cultures, and then we are surprised
at the great number of mould species, which make their appearance.
Many kinds which we seldom or never notice on malt-gelatin are
found in large numbers on these paper dises. These species certainly
are also capable of growing on malt-gelatin, but their germs, as
they occur in nature, apparently find thereon an unfavorable soil.
Another advantage of the cultivation on paper is that it is particu-
larly favorable to the formation of perithecia and picnidia, which
do not readily develop on rich soils ©).
From these culture experiments it appears that a continuous rain
of spores from cellulose-destroying moulds falls in the garden as well
as in the rooms of the bacteriological laboratory. For instance on
March 11, when the weather was dry whilst the earth was moist, 152
cellulose-destroying moulds were collected on a plate of 275 ¢.m. square,
after this had been exposed for 12 hours to the open air, and among these
moulds about 85 species were recognised. As these germs must con-
tinually drop on the soil, it might be expected that the latter would
be remarkably rich in living moulds and it appeared from experi-
ments. that this is really the ease at the surface of the garden soil,
but in a much less degree than might have been expected, while
lower down in the soil the number of moulds seems to be still less.
Krom this it follows that most of the spores, which fall on the earth
rapidly die oft.
In order to prepare a pure culture of the fungi isolated by the
““paper-experüment”” some material from the raw cultures was trans-
ferred to malt-gelatin, where it appeared that the moulds were
generally much contaminated with bacteria, from which however,
') Compare Morrrarp, Role des bactéries dans la production des périlhèces des
Ascobolus, G. R. t. 136, 1903, p. 899.
( 699 )
they could be freed by another inoculation. These bacteria are sapro-
phytes which do not attack cellulose but grow at the expense of the
products generated by the action of the moulds on cellulose. This
result was not unexpected for, as stated in the preceding paragraph,
the cellulose-destroying bacteria live in a faintly alkaline medium,
whilst in the ease of moulds the reaction is acid, owing to the presence
of KH, PO,. In order to be perfectly certain of the pureness of the
moulds, cultures from the spores were finally made on malt-gelatin.
The following species, which were detected in these cultures, have
been submitted to a closer examination :
1. Sordaria humicola Ovp.
2. Pyronema confluens Tvr.
3. Chaetomium kunzeanum Zoer.
4. Pyrenochaeta humicola Ovp.
5. Chaetomella horrida Ovp.
6. Trichocladium asperum Harz.
Stachybotrys alternans Ovn.
8. Sporotrichuin bombycinum (Corda) Ras.
9, F roseolum Ovp. en Bruner.
10. ie griseolum Ov.
11. Botrytis vulgaris Fr.
12. Mycogone puceinioides (Preuss) Sacc.
13. Stemphylium macrosporoidenm (B. en Br.) Sacc.
14. Cladosporium herbarum (Purs.) Link.
15. Kpicocenm purpurascens. KMRENB.
In the determination of these species, of which Nes. 9) and 4,
are new, we have been kindly assisted by Prof. Dr. C. A. J. A.
OupEMANS, to whom we have to express our thanks.
In order to form an opinion on the destruction of cellulose by the
isolated species, and also to study their fructification, pure cultures
were inoculated on paper discs, which after sterilisation, were drenched
with the above-named solution. Instead of merely placing the spores
on the paper, it was found desirable to push them in it by means of
a platinum wire and then to reduce the spots there to pulp. The culti-
vation is made at 24°, care being taken to keep the paper moist, for
which it was found advantageous not to use water only but the said
liquid, as the nitrogen in particular is rapidly used up. The above-named
moulds all grow over the paper dises, form their fructification-organs
in avery characteristic manner and often produce intensively colored,
brown, black and red pigments, which are absorbed by the paper
1) Nederl, Kruidkundig Archief, Januari, 1905,
( 1008)
fibre. Interesting are the cultures obtained in this way of Chaetomium
kunzeanum, Which sometimes produces a carmine-red pigment and
which forms dark red peritheciae, the asei of which contain eight grey
spores; those of Chaetomella horrida, which forms delicate black hairy
pyenidiae, and particularly those of Pyrenochaeta humicola, which
produces an intense black pigment, stable towards acids and alkalis,
and which communicates a dark colour to the fibres, quite resembling
the humus coloring matters. This latter species however, grew more
readily on an alkaline medium, so that we prefered in this case the
said drenched paper dises, between which Mg NH, PO, had been sprin-
kled. An interesting culture is also that of Sordaria humicola, as
this ascomycete is only then capable of forming perithecia on paper
dises, when these give no longer any reaction on ammonia or nitrates.
Besides the above-named species, a luxurious growth was obtained
of Trichocladium asperum, Mycogone puccinioïdes and Stemphylian
macrosporoïdeum, Which three species exhibit great similarity both
in their morphological and physiological properties. /picoceum pur-
purascens also grew strongly on the paper and formed a purple-
red pigment. This species I met several times in the air and also
(in company with Cladosporium herbarum) on half decayed leaves
of Populus balsimifera.
Cultures of these moulds were not only made on paper dises, but
also on cellulose in ERrLENMEYER flasks, into which was introduced a
thin layer of the following culture liquid:
Tapwater 100, paper-pulp 2, NH, NO, 0,05, KH, PO, 0,05.
In this case a repeated addition of NH, NO, proved very advant-
ageous. On the pulp the cellulose-destroyers grow still better than
on the paper dises and in 3 or 4 days the cellulose is converted
by the mycelium into a coherent mass. Afterwards, the fructification
organs appear, and with Botrytis rulygars even formation of sclerotia
was observed.
The destruction of the cellulose may be regarded as certain when
strong growth on the paper dises and on the paper pulp are being
observed. The impurities contained in the paper may also cause
a slight growth of moulds which do not attack cellulose, but
these soon cease to develop. The decomposition may be seen
very clearly by a microscopic examination of the cultures on -filter-
paper, when these have stood a long time. It will then strike us
how a large number of fibres have suffered a process of dissolution;
sometimes pores are formed perpendicularly to the direction of the
fibre, sometimes the fibres have disintegrated into fibrillae. Fig. 9
ZON
of our illustration shows the image of the destruction by Mycogone
puccinoides, in which the structure of the fibrillae and the said pores
are visible.
The degree of destruction also may be ascertained by direct weighing.
A culture with Mycogone pucemioides was made on a double dise
of filterpaper, two equally heavy filters serving as control. After
a culture, lasting 40 days, the dises, from which the strongly
developed mycelium was not removed, weighed 1.00 gram, whilst
the controlling dises weighed 1.16 gram, showing that about 14°/, of
0
the cellulose had disappeared. A similar experiment with 7richo-
cladtum asperun gave a loss of 9°/,. These great losses only can
be explained by the oxidation of the products derived from the
cellulose under the influence of the respiration process. The oxidation
of cellulose also was studied with filterpaper pulp, namely by
weighing the amount of carbon dioxide, liberated during a culture
of Chaetomium kunzeanum. In this experiment an oxidation of
about 4°/, of the cellulose could be noticed after a 28 days culture,
a quantity large enough to remove all doubt about the destruction
of the cellulose.
No, growth or only a very small one, was observed when culti-
vating the moulds on:
Tapwater 100, agar 2, NH,NO, 0,05, KH,PO, 0,05,
but as soon as cellulose was added a strong development set in,
showing in a surprising manner, that agar is a less nutrient food for
these moulds than cellulose. The cellulose used in these experiments
must be very finely divided and was prepared by treating cottonwool
with concentrated hydrochloric acid, which causes the cotton fibres
to break up into very small fragments. A preparation, which appeared
to be still more suitable was prepared as follows: Paper which has
been converted into soda-cellulose by the action of strong soda-lve,
is readily soluble in sodium xanthogenate to a light yellow liquid:
the “viscose” of Cross and Brvan'), which is purified by precipitation
with alcohol; on adding hydrochloric acid to its aqueous solution
cellulose is precipitated in a very pure condition. I have to thank
Mr. pr JONGH SCHEFFER, for a specimen of this preparation, which
he prepared in the chemical laboratory of the Polytechnie School
at Delft.
I found that, when cultivating on this agarcellulose, the growth
entirely depends on the quantity of the cellulose added: with much
cellulose a strong erowth was observed.
) Cross and Bevan, Cellulose, 1895, p. 25. London, Longman Green and Co,
( 702 )
As in the case of the moulds investigated by the above-named
observers, also the species employed by me showed the presence of
an enzyme, which dissolves cellulose and to which the name of
“cellulase” may be given’). If cultures on cellulose pulp were treated
with chloroform, the liquid, after being freed from chloroform by
evaporation, appeared capable of reducing FRALING’s copper solution.
If the culture had been boiled before being treated with chloroform,
no reduction took place. From these last experiments, which were
conducted similarly to those of BeHRENS (lc), it appears that the
moulds only produce the quantity of reducing matter necessary for
their growth and no more. That the quantity or the nature of the
enzyme secreted by the moulds differs considerably, is shown by the
great difference in destructive power, as may be readily observed
from the growth on the paper dises and from the dissolution of the
cellulose in the paper-pulp cultures. To the powerful destroyers belong:
Trichocladium asperum, Miycogone puceinioïdes, Stemphylium MACTO-
sporoideum, Chaetomella horrida, Botrytis vulgaris, Epicoceum pur-
perascens. To the moderately strong ones: Chactomimm kunzeanum,
Stachybotrys alternans, Cladosporimm herbarium, Pyrenochaeta hume-
cola, Pyronema confluens. To the weak ones: Sordaria humicola,
Sporotrichum bombycinum, Sp. reseolum, Sp. griseolum and Aspergillus
niger. No destruction was noticed with Mucor stolonifer, Mucor
mucedo, Dematiin pulilans and Rizopus oryzed.
Summary of results.
|L. Cellulose may be made to dissolve by the action of denitrifying,
non-sporeforming aërobie bacteria provided there be an (ited supply
of air.
2. Although nitrification cannot take place in the presence of a
somewhat large quantity of soluble organic matter, cellulose does not
feet this process in case of sufficient aëration.
3. The combined action of nitrification and denitrification must play
an important part in the disappearance of cellulose in nature, for
instance in the self purification of waters and of the soil, as also in the
biological purification of sewage.
') This name, already used by Kouystamm (lc.) is preferable to the name cy/ase
which has been used by Brown and Morris (Journal of Chem, Soe. 57, 1890,
p. 408) for the cellulose-dissolving enzyme in germinating seeds and should aceord-
ing to Merscunxikorr (Ann. Inst. Pasteur, 1899, t. 12, p. 737) be given to an
alexin occurring in normal serum.
14, A
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PROCEEDINGS ROYAL ACADEMY AMSTERDAM.
( 708 )
4. Cellulose may also be attacked, when there is a full supply of
air by widely distributed, aérobic, nou-sporeforming bacteria, among
which a brown pigment bacterium (B. ferrugineus) is predominant.
The destruction is particularly strong in symbiosis with a vellow
micrococcus, which itself is inert.
5. Extraordinarily rich spirillae cultures are formed in nutrient
liquids in which cellulose is being attacked by aërobie bacteria after
infection with ditch-mud or garden soil. Probably the distribution of
the spirillae in nature is mainly governed by cellulose.
6. The property of moulds to attack cellulose is a very common
one. The dissolution is due to a specific enzyme to which the name
of “cellulase” may be given.
7. One of the causes of the origin of humus coloring matters is
the formation of pigments from cellulose by bacteria and moulds.
This investigation has been made in the bacteriological laboratory
of the Polytechnic School under the guidance of Prof. BEIJERINCK.
Delft, March 1903.
EXPLANATION OF THE FIGURES.
Fig. 1. Fibre of filterpaper with denitrifying bacteria, disintegrated into fibrillae,
enclosed in mucus. Enlargement 550.
ig. 2. Debris of filterpaper at the end of the denitrification process, most of
the fibres are dissolved. z the last debris of cellulose fibres, B, y and 3 nonaltacked
elements of “woodcellulose”. Knl. 100.
ig. 3. Fibre of filterpaper with aérobic bacteria disintegrated into fibrillae,
enclosed in mucus. Enl. 550.
Fig. 4. Pacterium from the preceding figure more strongly enlarged; arrows
represent motion. Enl. 1500.
Fig. 5. Fibre of filterpaper attacked by an aérobic bacterium with sapropliylic
micrococcus, commencing to disintegrate into fibrillae. Ent. 550.
Vig. 6. Two fibrillae of the preceding fibre more strongly enlarged, with z aérobic
destructive bacteria and 3 saprophytic micrococcus. Eni. 1500.
Wig. 7. End of the destruction in fig. 5 the fibrillae having become invisible;
micrococci only visible. Ent. 550.
Fig. 8. Fibre attacked by aérobic bacteria, disintegrating into fibrillae and enclosed
in a thin mucous layer as medium for a spirillae culture in which 3 species are
recognisable. Enl. 550.
Fig. 9. Destruction of a fibre of fillerpaper by Mycogone puccinioides, besides
the fibrillary structure, cross pores have been formed in the fibrillae owing to the
action of the cellulase. Enl. 550.
(May 27, 1903).
Ss am Sg id gs
ABSORPTION (On the emission and) by metals of rays of heat of great wavelengths. 666.
ABSORPTIONBAND (Observations on the magnetic rotation of the plane of polarisation
in the interior of an). 41.
— (The caleulation “ from the magnetic rotation of the plane of polarisation for
substances without an) in the visible spectrum. 413.
ACCUMULATION experiments with denitrifying bacteria. 148.
ACETALDEHYDE + paraldehyde (Equilibria of phases in the system:) with and without
molecular transformation. 283.
ACID (On the prussie) in the opening buds of Prunus. 31.
actps (On the so-called compounds of sulphonearboxylic) with sulphuric esters. 482.
AEROBIC micro-organisms (The decomposition of cellulose by). 685.
ALBERDA VAN EKENSTEIN (w.) and C. A. Lopry pr Bruyn: “Formaldehyde
(methylene)- derivatives of sugars and glucosides.” 175.
ALLoys (The course of the meltingpoint-line of solid) or amalgams. (I). 424. (II). 511.
AMALGAMS (The course of the meltingpoint-line of solid alloys or). (1). 424. (II). 511.
AMPHIOXUS LANCEOLATUS (On the structure of the light-perzepting cells in the spinal
cord, on the neurofibrillae in the ganglioncells and on the innervation of the
striped muscles in). 350.
Anatomy. J. W. van Wisnr: “A new method for demonstrating cartilaginous mikro-
skeletons.” 47.
ANGLES (On the connection of the planes of position of the) formed by two spaces S,
passing through a point and incident spacial systems. 53.
ANTIMONY (On the atomic weight of). 543.
ARC (The influence of variation of the constant current on the pitch of the singing). 311.
ARONSTEIN (L.) and A. S. vaN Nierop. On the action of sulphur on toluene
and xylene. 288,
Astronomy. E. F. van DE SANDE BAKHUYZEN: “On the yearly periodicity of the rates
of the standardelock of the Observatory at Leyden, Hohwü No. 17.” (1). 68.
(LI). 193.
—- E‚ F. van Dr SANDE BAKHUYZEN: “Preliminary investigation of the rate of the
standardelock of the Observatory at Leyden, Hohwii N°. 17 after it was mounted
in the niche of the great pier.” 267.
— J. Wreper: “On interpolation based on a supposed condition of minimum.” 364.
ATMOSPHERIC PRESSURE (Measurements on the magnetic rotation of the plane of pola-
risation in liquefied gases under). 248.
45
it CO Not ENS:
ATOMIC WEIGHT (On the) of Antimony. 543.
atoms (Intramolecular rearrangement of) in azoxybenzene and its derivatives, 51.
— (The intramolecular rearrangement of) in halogenacetanilides and its velocity,
(1). 178. (II). 359.
AURICLE of the mammalian heart (On the duration of the compensatory pause after
stimulation of the). 378.
AZOXYBENZENE (Intramolecular rearrangement of atoms in) ard its derivatives. 51.
BACTERIA (Accumulation experiments with denitrifying). 148.
Bacteriology. M. W. Bryerinck and A. van DELDEN: “On a colourless bacterium,
whose carbon food comes from the atmosphere.” 398.
BACTERIUM (On a colourless), whose carbon food comes from the atmosphere. 598.
BAKHUIS ROOZEBOOM (H. W.) presents a paper of Prof. ue, Dusots : “Geolo-
gical structure of the Hondsrug in Drenthe and the origin of that ridge.” (LD). 101.
— presents a paper of Dr. W. Rerxpers: /Galvanic cells and the phase rule.” 182,
— A representation in space of the regions in which the solid phases, which oceur,
are the components, when not forming compounds. 279.
— Equilibria of phases in the system : acetaldehyde + paraldehyde with and without
molecular transformation. 283.
— Tinamalgams. 373.
— presents a paper of Dr. A. Smits and L. k. Worrr: “The velocity of trans-
formation of carbon monoxide.” 417.
— presents a paper of Mr. J. J. van Laar: “The course of the melting-point-line
of solid alloys or amalgams.” (L). 424. (ID. 511.
— presenis a paper of Mr. J. J. van Laan‘: ‘On the potential difference, which
occurs at the surface of contact of two different non-miscible liquids, in which
a dissolved electrolyte has distributed itseif” 431.
BAKHUYZEN (E. F. VAN DE SANDE). See SANDE Baknuyzen (B. F. vaN DE).
— (H. G. VAN DE SANDE). See SANDE DBAKHUYZEN (H. G. VAN DE).
BATH of very uniform and constant low temperature in the cryostat. 502. 628.
— (A permanent) of liquid nitrogen at ordinary and at reduced pressure. 631.
BEKMAN (BE. H. M.). On the behaviour of disthene and of sillimanite at high
temperature. 240.
BELZER (A. H. J.). The velocity of transformation of tribroomphenol bromine into
tetrabromophenol. 556.
BEMMELEN (J. M. VAN) presents a paper of Mrs. L. Aronsrern and A. 8, VAN
Nrerop: “On the action of sulphur on toluene and xylene.” 288.
BENZIDINE transformation. 577.
BEYERINCK (M. W.) presents a paper of Mr. G. van Iverson Jr: “Accumulation
experiments with denitrifying bacteria.” 148.
— presents a paper of Mr. G. van Iverson Jr: “The decomposition of cellulose
by aërobie micro-organisms.” 685.
— and A. VAN DELDEN, On a colourless bacterium, whose carbon food comes from
the atmosphere. 398.
CON TEN T Ss. Tit
BLANKSMA (J, J.). The intramolecular rearrangement in halogenacetanilides and its
velocity. (L). 178. (II). 359.
— Nitration of symmetrical dinitroanisol, 650,
BOEKE (J.). On the structure of the light-percepting cells in the spinal cord, on the
neurofibrillae in the ganglioncells and on the innervation of the striped museles
in Amphioxus lanceolatus, 350.
BOILINGPOINT-CURVE (The) of the system: hydrazine + water. 171.
BONNEMA (J, H.). Cambrian erratic-blocks at Hemelum in the South-West of Frisia. 140.
— Some new under-cambrian erratie-bloeks from the Dutch diluvium. 561.'
— Two new mid-cambrian erratic-blocks from the Dutch diluvium. 652.
BORNEO (Influence of changed conditions of life on the physical and psychical develop-
ment of the population of Central-). 525.
Botany. fi. Verscrarrrrr: “On the prussic acid in the opening buds of Prunus”. 31.
— J. ©. Scuoure: “Die Steliir-Theorie”. 497.
BRUIJN (CG. A. LOBRY DE). See Lopry ve Brun (C, A).
BUCHNER (B. H.). The transformation of diphenyliodonium iodide and chloride and
its velocity. 646.
Bubs (On the prussic acid in the opening) of Prunus. 31.
e
CALCULATION — (Ihe) from the magnetic rotation of the plane of polarisation for sub-
stances without an absorptionband in the visible spectrum, 413.
CARBON FOOD (On a colourless bacterium, whose) comes from the atmosphere, 398.
CARBON MONOXIDE (The velocity of transformation of). 417.
CARDINAAL (J.). On the geometrical representation of the motion of variable
systems. 586,
CARTILAGINOUS Mikroskeletons (A new method for demonstrating). 47.
CELIS (On the structure of the light percepting) in the spinal cord, on the neurofi-
brillae in the gangiioncells and on the innervation of the striped muscles in Amphi-
oxus lanceolatus. 350.
CRLLULOSE (The decomposition of) by aérobic micro-organisms. 685,
Chemistry. I]. M. Knipscuren: “Intramolecular rearrangement of atoms in azoxybenzene
and its derivatives”. 51.
— C. A. LoBry pr Bruyn and J. W. Drro: “The boilingpoint-curve of the system :
hydrazine + water”. 171.
— C. A. Lopry pr Bruyn and W. ALBERDA VAN EKENSTEIN: “Formaldehyde
(methylene)-derivatives of sugars and glucosides”. 175.
— J. J. BLANKsMA: “The intramolecular rearrangement in halogenacetanilides and
its velocity”. ([). 178. (IL). 359.
— W. Reivers: “Galvanic cells and the phase rule”. 182.
— H. W. Bakuuis Roozrnoom: “A representation in space of the regions in which
the solid phases which occur, are the components, when not forming compounds”.
279.
iv Gio NTEN Ts,
Chemistry. I. W. Bakuurs Roozesoom: “Equilibria of phases in the system: acetaldehyde
+ paraldehyde with and without molecular transformation”. 283.
— LL. ARONSTEIN and A. S. van Nierop: “On the action of sulphur on toluene and
xylene’. 288.
— H. W. Bakuuis Roozenoom: “Tinamalgams”, 373.
— J. Porrer van Loon: “Benzidine transformation”. 377.
— A, Smits and L. K. Worrr: “The velocity of transformation of carbon monoxide”.
417.
— J. J. van Laar: “The course of the melting-point-line of solid alloys or amal-
gams”’. (I). 424. (ID). 511.
— J. J. van Laar: “On the potential-difference, which occurs at the surface of
contact of two different non-miscible liquids, in which a dissolved electrolyte has
distributed itself”. 431.
— A.P. N. FRANCHIMONT: “On the so-called compounds of salts of sulphoncar-
boxylie acids with sulphuric esters”. 482.
— E. Conen and Tu. Srrencers: “On the atomic weight of antimony”. 543.
— RE. Coen and U. A. Losey DE Bruyn: “The conductive power of hydrazine and
of substances dissolved therein’. 551.
— A. H. J. Berzer: “The velocity of transformation of tribroomphenol bromine into
tetrabromophenol”. 556.
— C. A. Lory DE Bruyn and C. L. Junerus: “Dissociation in and erystallisation
from a solid solution”. 643.
— E.H. Biécuner: “The transformation of diphenyliodonium iodide and chloride
and its velocity”. 646.
— J. J. Buanxsma: “Nitration of symmetrical dinitroanisol”. 650.
cuLORIDE (The transformation of diphenyliodonium iodide and) and its velocity. 646.
COMEN (E) and Tu. StrencErs. On the atomic weight of Antimony. 543.
— and C. A. LoBry DE Bruyn. The conductive power of hydrazine and of substances
dissolved therein. 551.
COMMON DIVISOR (An analytical expression for the greatest) of two integers. 658.
COMPENSATORY PAUSE (On the duration of the) after stimulation of the auricle of the
mammalian heart. 378.
COMPONENTS (A representation in space of the regions in which the solid phases which
occur, are the), when not forming compounds. 279.
COMPOUNDs (On the so-called) of salts of sulphoncarboxylic acids with sulphuric esters. 482,
CONDITION of minimum (On interpolation based on a supposed). 364.
CONDUCTIVE POWER (The) of hydrazine and of substances dissolved therein. 551.
constants (The value of some magneto-optic). 458.
corona (Peculiarities and changes of FrAuNuHorem-lines interpreted as anomalous
dispersion of sunlight in the). 589,
CRITICAL STATE (The equation of state and the g-surface in the immediate neighbour-
hood of the) for binary mixtures with a small proportion of one of the compo-
nents. 321. 336,
© OUN ADS ERIN SP ra Vv
CRYOGENIC Laboratory (Methods and apparatus used in the). ILL, Bath of very uniform
and constant low temperatures in the cryostat, 502. 628. A cryostat of modified
form for apparatus of small dimensions. 628. LV. A permanent bath of liquid nitrogen
at ordinary and at reduced pressure. 631. V. Arrangement of a BurckHaRrpt-WEIss
vacuumpump for use in the circulations for low temperatures. 633.
cryostat (Bath of very uniform and constant low temperatures in the). 502. 628.
— (A) of modified form for apparatus of small dimensions. 628.
CRYSTALLISATION (Dissociation in and) from a solid solution, 643,
CURRENT (The influence of variation of the constant) on the pitch of the singing arc. 311.
DELDEN (A. VAN) and M. W. Beyertncx. On a colourless bacterium, whose
carbon food comes from the atmosphere: 398.
DIAGONALS of parallelotopes (Relations between). 540.
DIFFRACTION of Röntgen-rays. 247.
DILUVIUM (Some new under-cambrian erratic-blocks from the Dutch). 561.
— (Two new mid-cambrian erratic-blocks from the Dutch). 652.
DINITROANISOL (Nitration of symmetrical). 650.
DISPERSION of sunlight (Peculiarities and changes of FrAUNHOFER-lines interpreted as
anomalous) in the corona, 589.
DISSOCIATION in and crystallisation from a solid solution. 643.
DISTHENE (On the behaviour of) and of sillimanite at high temperature. 240.
piro (J. w.) and QC, A. LoBry pe Bruyn. The boilingpoint-curve of the system:
hydrazine + water. 171.
puBOIsS (uUG.). The geological structure of the [londsrug in Drenthe and the
origin of that ridge. (L). 93. (II). 101.
EFFECT (A new law concerning the relation between stimulus and). 392. 441.
EISENROSE (On an) of the St. Gotthard. 605.
ELECTRIC CIRCUIT (Some remarkable phenomena, concerning the) in electrolytes. 465,
ELECTRIC CURRENT (On the advantage of metal-etching by means of the). 219.
ELECTROLYTE (On the potential-differenee, which occurs at the surface of contact of
two different non-miscible liquids, in which a dissolved) has distributed itself. 431.
ELECTROLYTES (Some remarkable phenomena, concerning the electric circuit in), 465,
ELEGTROMAGNETIC PHENOMENA (The fundamental equations for) in ponderable bodies,
deduced from the theory of electrons. 254.
ELECTRO-MECHANIGS (Statistical). (1). 22. (LI). 114.
ELECTRONS (Contributions to the theory of. (I). 608.
— (The fundamental equations for electromagnetic phenomena in ponderable bodies,
deduced from the theory of). 254.
EMISSION (On the) and absorption by metals of rays of heat of great wavelengths. 666.
ENTROPY (Lhe principle of) in physiology. (LL). 57.
EQUATION OF srate (The) and the y-surface in the immediate neighbourhood of the
critical state for binary mixtures with a small proportion of one of the components.
DIEM
— (The variability with the density of the quantity 4 of the). 487.
VI CONTENTS.
EQUATIONs (Reduction of observation) containing more than one measured quantity. 236.
— (The fundamental) for electromagnetic phenomena in ponderable bodies, deduced
from the theory of electrons. 254.
EQUILIBRIA of phases in the system: acetaldehyde + paraldehyde with and without.
molecular transformation. 283.
ERRATIC-BLOCKS (Cambrian) at Hemelum in the South-West of Frisia. 140.
— (Some new under-cambrian) from the Dutch diluvium. 561.
— (Two new mid cambrian) from the Dutch diluvium. 652.
ERRATUM. 217.
rsrers (On the so-called compounds of salts of sulphoncarboxylic acids with sulphuric).482.«
ErHANE and Methylalcohol (Critical phenomena of partially miscible liquids). 473.
Ethnology. A. W. Nieuwenuuis: “Influence of changed conditions of life on the
physical and psychical development of the population of Central-Borneo.” 525,
FORMALDEHYDE (Methylene-) derivatives of sugars and glucosides. 175.
FRANCHIMONT (a. P. N.). On the so-called compounds of salts of sulphoncarboxylic
acids with sulphuric esters. 482.
FRAUNHOFER-LINES (Peculiarities and changes of) interpreted as anomalous dispersion
of sunlight in the corona. 559.
GALVANIC CELLS and the phase rule. 182.
GANGLIONCELLS (On the structure of the light percepting cells in the spinal cord, on
the neurofibrillae in the) and on the innervation of the striped muscles in Am-
phioxus lanceolatus. 350.
Gases (Isotherms of diatemie) and their binary mixtures, V. An accurate volumeno-
meter and mixing apparatus. 636.
— (Measurements on the magnetic rotation of the plane of polarisation in liquetied)
under atmospheric pressure. 245.
Geology. Eve. Dusors: “The geological structure of the Hondsrug in Drenthe and the
origin of that ridge”. (I). 93. (IL). LOL
— J. H. Bonnema: “Cambrian erratic-blocks at Hemelum in the South-West of
Frisia”. 140.
_ J. H. Boxnema: “Some new under-cambrian erratic-blocks from the Dutch dilu-
vium’’. 561.
—_ J. H. Bornema: “Two new mid-cambrian erratic-blocks from the Dutch dilu-
vium”. 652.
GEOMETRICAL representation (On the) of the motion of variable systems. 386.
eiucostpEs (Formaldehyde (methylene)- derivatives of sugars and). 175.
— (Investigations of) in connection with the internal mutation of plants. 295.
HAGA (Hm) and C. H. Winp. Diflraction of Rontgen-rays 247.
HALLO (3. J.). The value of some magneto-optic constants. 458.
HALOGENACEFANILIDES (The intramolecular rearrangement in) and its velocity. (1). 178.
(II). 359.
uzart (On the duration of the compensatory pause after stimulation of the auricle of
the mammalian). 378.
HEMELUM (Cambrian erratic-blocks at) in the South-West of Frisia. 140.
YY = VR
—
CO NSE ENS: VII
HOGENRAAD (G. B). On an /Eisenrose” of the St. Gotthard. 605,
HONDSRUG in Drenthe (The geological structure of the) and the origin of that ridge.
(93. (Snore
HYDRAZINE (The conductive power of) and of substances’ dissolved therein. 551.
— + water (The boilingpoint-curve of the system :). 171.
HYDROGEN (The course of the values of 4 for), in connection with a recent formula
of Prof. van DER Waars. 573.
HYNDMAN (H. H. FR) and H. Kamertinau ONNes, Isotherms of diatomic gases
and their binary mixtures. V. An accurate volumenometer and mixing apparatus. 636.
HYPOTHESIS (An) on the nature of solar prominences. 162.
INDEX (On the refractive) of rock-glasses. 602.
INNERVATION (On the structure of the light-percepting cells in the spinal cord, on
the neurofibrillae in the ganglioncells and on the) of the striped muscles in
Amphioxus lanceolatus. 350.
INTEGERS (An analytical expression for the greatest common divisor of two). 658.
INTENSITY (On maxima and minima of) sometimes observed within the shading of
strongiy widened spectral lines. 662.
INTERPOLATION (On) based on a supposed condition of minimum. 364.
INTRAMOLECULAR rearrangement of atoms in azoxybenzene and its derivatives. 51.
— rearrangement (The) in halogenacetanilides and its velocity. (1). 178. (LI). 359.
ropipE (The transformation of diphenyliodonium) and chloride and its velocity. 646.
ISOTHERMS of diatomic gases and their mixtures. V. An accurate volumenometer and
mixing apparatus. 636.
ITERSON JR. (G. va N). Accumulation experiments with denitrifying bacteria. 148.
— The decomposition of cellulose by aérobic micro-organisms. 685.
JULIUS (W. H.). An hypothesis on the nature of solar prominences. 162.
— presents a paper of Prof. E. Corner and Tu. Srrencers: “On the atomic weight
of antimony”. 543.
— Peculiarities and changes of Pravnuoree-lines interpreted as anomalous disper-
sion of sunlight in the corona. 589.
— On maxima and minima of intensity sometimes observed within the shading
of strongly widened spectral lines. 662.
JUNGIUS (c, L.) and C. A. Lopry pe Bruyn. Dissociation in and crystallisation from
a solid solution. 643.
KAMERLINGH ONNES (H.) presents a paper of W. H. Kersom: “Reduction of
observation equations containing more than one measured quantity”. 236.
— presents a paper of Dr. L. H. Srertsema: “Measurements on the magnetic rotation
of the plane of polarisation in liquefied gases under atmospheric pressure, LL.
Measurements with methylehloride”. 243.
— presents a paper of Dr. J. E. Verscaarreir: “Contributions to the knowledge
of VAN DER WAALS y-surface. VII. The equation of state and the y-surface in
the immediate neighbourhood of the critical state for binary mixtures with a smali
proportion of one of the components”. 321. 336,
Vr CO NAT Nate,
KAMERLINGH ONNES (H) presents a paper of Dr. L. H.Sierrsema: “The
. é . . . . .
valeulation — from the magnetic rotation of the plane of polarisation, for sub-
UL
stances without an absorptionband in the visible spectrum”. 415.
— presents a paper of Prof. J. P. KueneN: “Critical phenomena of partially mis-
cible liquids-Ethane and Methylaleohol”. 473.
— Methods and apparatus used in the Cryogenic Laboratory. LIL. Bath of very
uniform and constant low temperatures in the cryostat. 502. 628. A cryostat of
modified form for apparatus of small dimensions. 628. IV. A permanent bath of
liquid nitrogen at ordinary and at reduced pressure. 63i, V. Arrangement of a
BURCKHARDT-WEISS vacuumpump for use in the circulations for low temperatures. 633.
— and H. H. Fr. HYNDMAN. Isotherms of diatomic gases and their binary mix-
tures. V. An accurate volumenometer and mixing apparatus. 636.
KEESOM (w. H.). Reduction of observation equations containing more than one
measured quantity. 236.
KLUYVER (J. C.). An analytical expression for the greatest common divisor of two
integers. 658.
KNIPSCHEER (H. M.). Intramolecular rearrangement of atoms in azoxybenzene and
its derivatives, 51.
KOLK (J. L.C. SCHROEDER VAN DER). See SCHROEDER VAN DER Kork (J. L. C.).
KORTEWEG (p. J.). Plaitpoints and corresponding plaits in the neighbourhood of
the sides of the -surface of VAN DER Waars. 445.
KUENEN (J. P.). Critical phenomena of partially miscible liquids-Ethane and Methyl-
alcohol. 473.
LAAR (5. J. VAN). The course of the melting-point-line of solid alloys or amal-
gams. (I), 424. (LI). 511.
— On the potential-difference, which occurs at the surface of contact of two different
non-miscible liquids, in which a dissolved electrolyte has distributed itself. 431.
— On the course of the values of 4 for hydrogen, in connection with a recent
formula of Prof. vaN DER Waars. 573.
LANGELAAN (J. w.). The principle of entropy in physiology. (LI). 57.
Law (A new) concerning the relation between stimulus and effect. 392. ALL,
Lire (lufluence of changed conditions of) on the physical and psychical development
of the population of Central-Borneo. 525.
uquips (Critical phenomena in partially miscible). 307.
— (Critical phenomena of partially miscible)-Ethane and Methylaleohol. 475.
— (On the potential-difference, which occurs at the surface of contact of two difle-
rent non-miscible), in which a dissolved electrolyte has distributed itself. 431.
LOBRY DE BRUYN (c. A.) presents a paper of Dr. H. M. Knipscueer: “Intra-
molecular rearrangement of atoms in azoxybenzene and its derivatives.” 51.
— presents a paper of Dr. J. J. Buanxsma: “The intramolecular rearrangement in
halogenacetanilides and its velocity.” (1). 178. (ID. 359.
— presents a paper of Dr. Tu. Weevers: “Investigations of glucosides in connec-
tion with the internal mutation of plants,” 295.
CHAOS NE TAN LS? IX
LOBRY DE BRUYN (Cc. A.) presents a paper of Dr. J. Porter van Loon: “Benzi-
dine transformation.” 377.
— presents a paper of Mr. A. H. J. Berzer: “The velocity of transformation of
tribroomphenol bromine into tetrabromophenol.’’ 556.
— presents a paper of Mr. E. H. Bicuner: “The transformation of diphenylio-
donium iodide and chloride and its velocity”. 646.
— presents a paper of Dr. J. J. BLANKSMA: “Nitration of symmetrical dinitro-
anisol’’. 650,
— and W. ALBERDA VAN EKENSTEIN. Formaldehyde (methylene)- derivatives of
sugars and glucosides, 175.
— and HE, Conen. The conductive power of hydrazine and of substances dissolved
therein. 551,
— and J. W. Divo. The boilingpoint-curve of the system: hydrazine + water. 171,
— and C. L. Junetus, Dissociation in and crystallisation from a solid solu-
tion. 645,
LOON (J. POTTER VAN). See Porrer VAN LOON (J.).
LORENTZ (H. A.). The fundamental equations for electromagnetic phenomena in
ponderable bodies, deduced from the theory of electrons. 254.
— presents a paper of Mr. A. H. Srrks: “Some remarkable phenomena, concerning
the electric circuit in electrolytes”. 465.
— Contributions to the theory of electrons. (I). 608.
— On the emission and absorption by metals of rays of heat of great wave-
lengths. 666.
MAGNETO-OPTIC Constants (The value of some). 438.
MARTIN (K.) presents a paper of Prof. Euc. DuBois: “Geological structure of the
Hondsrug in Drenthe and the origin of that ridge.” (1). 93.
Mathematics. P. H. Scuoure: “On the connection of the planes of position of the
angles formed by two spaces Sx passing through a point and incident spacial
systems.” 53.
— S, L. van Oss: “Five rotations in S, in equilibrium.” 362.
— J. CARDINAAL : “On the geometrical representation of the motion of variable
systems.” 386.
— Jan pe Vries: “On the spheres of Monee belonging to ordinary and tangential
pencils of quadratic surfaces.” 484.
— P. H. Scuoure: ‘‘Relations between diagonals of parallelotopes.” 540.
— J. C. Krurver: “An analytical expression for the greatest common divisor of
two integers.” 658.
MEASUREMENTS on the magnetic rotation of the plane of polarisation in liquefied
gases under atmospheric pressure. IT. Measurements with methylchloride. 243.
MELTING-POINT-LINE (The course of the) of solid alloys or amalgams. (D), 424.
(IL). 511.
METAL-ETCHING (On the advantage of) by means of the electric current. 219.
METALS (On the emission and absorption by) of rays of heat of great wave-lengths. 666,
METHOD (A new) for demonstrating cartilaginous mikroskeletons. 47.
x CONTENTS.
METHODS and apparatus used in the Cryogenic Laboratory. III. Bath of very uniform
and constant low temperatures in the cryostat. 502. 628. A cryostat of modified
form for apparatus of small dimensions. 628. IV. A permanent bath of liquid
nitrogen at ordinary and at reduced pressure. 631. V. Arrangement of a BURCKHARDT-
Weiss vacuumpump for use in the circulations for low temperatures. 633.
METHYLALCOHOL (Critical phenomena of partially miscible liquids-Ethane and). 473.
METHYLCHLORIDE (Measurements with). 243.
METHYLENE-derivatives. See FORMALDEHYDE (methylene)-derivatives.
Microbiology. G. van Iverson Jr.: “Accumulation experiments with denitrifying bac-
teria”. 148.
— G van Iverson Jr.: “The decomposition of cellulose by aérobic micro-orga-
nisms.” 685.
MIKROSKELETONS (A new method for demonstrating cartilaginous). 47.
Mineralogy. E. H. M. Brexman: “On the behaviour of disthene and of sillimanite
at high temperature.” 240.
— P. Trescu: “On the refractive index of rockglasses.” 602.
— G. B. Hocrnraap: “On an /Eisenrose” of the St. Gotthard.” 605,
MIXING APPARATUS (An accurate volumenometer and). 636.
mMIxTuREs (The equation of state and the y-surface in the immediate neighbourhood
of the critical state for binary) with a small proportion of one of the components.
321. 336.
— (Isotherms of diatomic gases and their binary). 636.
MOLECULAR transformation (Some observations on the course of the). 303.
MOLL (J. w.) presents a paper of Mr. J. H. Bonnema: “Cambrian erratic-blocks at
Hemelum in the South-West of Frisia.” 140.
— presents the dissertation of Dr. J. C. Scourge: “Die Stelär-Theorie.” 497.
— presents a paper of Mr. J. H. Bonnema: “Some new under-cambrian erratic-
blocks from the Dutch diluvium”. 561.
— presents a paper of Mr. J. H. Bonnema: “Two new mid-cambrian erratic-blocks
from the Dutch diluvium.” 652.
MONGE (On the spheres of) belonging to ordinary and tangential pencils of qua-
dratic surfaces. 484.
MOTION of variable systems (On the geometrical representation of the). 386.
MUSCLES in Amphioxus lanceolatus (On the structure of the light-percepting cells in
the spinal cord, on the neurofibrillae in the ganglioncells and on the innervation
of the striped) in Amphioxus lanceolatus. 350.
MUTATION of plants (Investigations of glucosides in connection with the internal). 295.
NEUROFIBRILLAE (On the structure of the lightpercepting cells in the spinal cord,
on the) in the ganglioncells and on the innervation of the striped muscles in
Amphioxus lanceolatus. 350.
NIEROP (A. S. VAN) and L. ARONSTEIN. On the action of sulphur on Toluene and
Xylene. 288.
NIEUWENHUIS (A. w.). Influence of changed conditions of life on the physical
and psychical development of the population of Central-Borneo, 525.
CONTENTS XI
NITRATION of symmetrical dinitroanisol. 650.
NITROGEN (A bath of liquid) at ordinary and at reduced pressure. 631.
OBSERVATORY AT LEYDEN (On the yearly periodicity of the rates of the standardeloek
of the), Hohwü n®. 17. (L). 68. (ID. 193.
— (Preliminary investigation of the rate of the standardclock of the) Hohwü no. 17,
after it was mounted in the niche of the great pier. 267.
Oss (Ss. L. VAN). Five rotations in S, in equilibrium. 362.
PARALDEHYDE (Equilibria of phases in the system: acetaldehyde +) with and without
molecular transformation, 283.
PARALLELOTOPES (Relations between diagonals of), 540.
PEKELHARING (c. A.) presents a paper of Prof. kK. F. WenckesBacu: “On the
duration of the compensatory pause after stimulation of the auricle of the mam-
malian heart”, 378.
PENCILS (On the spheres of Monrer belonging to ordinary and tangential) of qua-
dratic surfaces. 484.
PERIODICITY (On the yearly) of the rates of the standardeloek of the Observatory at
Leyden, Hohwü No 17. (I). 68. (II). 193.
PHASE RULE (Galvanic cells and the). 182.
PHASES (A representation in space of the regions in which the solid) which occur,
are the components, when not forming compounds. 279.
— (Equilibria of) in the system: acetaldehyde -+- paraldehyde with and without
molecular transformation. 285.
PHENOMENA (Critical) in partially miseible liquids. 307.
— (Critical) of partially miscible liquids-Ethane and Methylalcohol, 473.
— (Some remarkable), concerning the electric circuit in electrolytes. 465.
Physics. J. D. van DER Waars: “Ternary Systems”. (IV) 1. (V). 121.
— J. D. van per Waats Jr.: “Statistical electromechanics”. (L). 22. (IJ). 114.
— P. ZEEMAN: “Observations on the magnetic rotation of the plane of polarisation
in the interior of an absorption band”. 41.
— W. H. Jurrus: “An hypothesis on the nature of solar prominence”. 162.
— A. H. Srrks: “On the advantage of metal-etching by means of the electric
current’. 219,
— J. D. van per Waats: “On the conditions for the occurrence of a minimum
critical temperature for a ternary system”. 225.
— W. H. Krrsom: “Reduction of observation equations containing more than one
measured quantity”. 236.
— L. H. Srertsema: “Measurements on the magnetic rotation of the plane of pola-
risation in liquefied gases under atmospheric pressure. If. Measurements with
Methylehloride”, 243.
— H. Haca and C. H. Winp: “Diffraction of Röntgen-rays” (2nd communication).
247.
— H. A. Lorentz: “The fundamental equations for electromagnetic phenomena in
ponderable bodies, deduced from the theory of electrons”, 254,
XII C.O,N-2 ENE:
Physics. J. D. van per Waats: “Some observations on the course of the molecular
transformation”. 303.
— J. D. van per Waals: “Critical phenomena in partially miscible liquids”. 307.
— J. K. A. WERTHEIM SALOMONSON: “The influence of variation of the constant
current on the pitch of the singing arc”. 311.
— J. E. VERSCHAFFELT : “Contributions to the knowledge of VAN DER WAALS -sur-
face. VII. The equation of state and the y-surface in the immediate neighbour-
hood of the critical state for binary mixtures with a small proportion of one of
the components.” 321. 336.
4 é - :
— L. H. Srertsema: “The calculation — from the magnetic rotation of the plane
mM
of polarisation, for substances without an absorptionband in the visible spectrum”. ~
413.
— J.J. Harro: “The value of some magneto-optic constants”. 438.
— D.J. Korrewea: “Plaitpoints and corresponding plaits in the neighbourhood of
the sides of the y-surface of VAN DER WAALS”. 445.
— A. H. Srrxs: “Some remarkable phenomena, concerning the electric circuit
in electrolytes”. 465.
— J. P. KveNEN: “Critical phenomena of partially miscible liquids-Ethane and Me-
thylaleohol”. 473.
— J. D. van DER Waars Jr.: “The variability with the density of the quantity 5
of the equation of state”. 487.
— H. KAMERLINGH Onnes: “Methods and apparatus used in the Cryogenic Laboratory:
UI. Baths of very uniform and constant low temperatures in the cryostat. 502. 628.
A eryostat of modified form for apparatus of small dimensions. 628. IV. A permanent
bath of liquid nitrogen at ordinary and at reduced pressure. 631. V. Arrangement
of a BurckHarpt-WeIss vacuumpump for use in the circulations for low tem-
peratures. 633,
— J. J. van Laar: “On the course of the values of 4 for hydrogen, in con-
nection with a recent formula of Prof. vaN per Waats”. 573.
— W. H. Junius: “Peculiarities and changes of FRAUNHOFER-lines interpreted as
consequences of anomalous dispersion of sunlight in the corona.” 589.
— H. A. Lorentz: “Contributions to the theory of electrons.” (I). 608.
— H. KAMERLINGH ONNEs and H. H. Francis HynpMan: “Isotherms of diatomic
gases and their binary mixtures. V. An accurate volumenometer and mixing
apparatus.” 636.
— W. H. Juxrus: “On maxima and minima of intensity sometimes observed within
the shading of strongly widened spectral lines.” 662.
— H. A, Lorentz: “On the emission and absorption by metals of rays of heat of
great wave-lengths.” 666.
Physiology. J. W. LANGELAAN: “The principle of entropy in physiology.” ID. 57.
a
CONTENTS XIII
Physiology. J. Porke: “On the structure of the light-percepting cells in the spinal cord,
on the neurofibrillae in the ganglioncells and on the innervation of the striped
muscles in Amphioxus lanceolatus.” 350.
— K. F. Wenckesacu : “On the duration of the compensatory pause after stimulation
of the auricle of the mammalian heart.” 378.
— J. kK. A. WERTHEIM SALOMONSON: “A new law concerning the relation between
stimulus and effect.” 392, 441.
Physiology of plants. Tu. Weevers: “Investigations of glucosides in connection with
the internal mutation of plants.” 295.
PLACE (r.) presents a paper of Dr, J. W. LANGELAAN : “The principle of entropy
in physiology.” (ID. 57.
— presents a paper of Dr. J. Boeke: “On the structure of the light-percepting cells
in the spinal cord, on the neurofibrillae in the ganglioncells and on the inner-
vation of the striped muscles in Amphioxus lanceolatus.” 850.
PLALTPOINTS and corresponding plaits in the neighbourhood of the sides of the p-surface
of VAN DER WaaLs. 445.
PLANE OF POLARISATION (Observations on the magnetic rotation of the) in the interior
of an absorptionband. 41,
— (Measurements on the magnetic rotation of the) in liquefied gases under atmos-
pheric pressure, 243,
2
: ¢ ; : j :
— (The calculation — from the magnetic rotation of the) for substances without
m
an absorptionband in the visible spectrum. 415.
PLANES OF POSITION (On the connection of the) of the angles formed by two spaces
Sn passing through a point and incident spacial systems. 55.
PLANTS (Investigations of glucosides in connection with the internal mutation of), 295.
PONDERABLE BODIES (The fundamental equations for electromagnetic phenomena in),
deduced from the theory of electrons, 254.
POPULATION of Central-Borneo (Influence of changed conditions of life on the physical
and psychical development of the). 525.
POTENTIAL=DIFFERENCE (On the), which occurs at the surface of contact of two difle-
rent non-miscible liquids, in which a dissolved electrolyte has distributed itself. 431.
POTTER VAN LOON (3). Benzidine transformation, 377.
PRINCIPLE (The) of entropy in physiology. (LI). 57.
PRUNUS (On the prussic acid in the opening buds of). 31.
QuaNTITY (Reduction of observation equations containing more than one measured). 236.
— 4 (The variability with the density of the) of the equation of state. 487.
RAYS OF HEAT (On the emission and absorption by metals of) of great wave-length, 666.
REINDERS (w.). Galvanic cells and the phase rule, 182.
ROCK-GLASSES (On the refractive index of). 602.
RÖNTGEN-RAYS (Diffraction of). 247.
ROOZEBOOM (H, W. BAKHUIS). See BaKuuis RoozeBoom (H. W.).
xIV CONTENTS.
ROTATION (Observations on the magnetic) of the plane of polarisation in the interior
of an absorptionband. 41.
— (Measurements on the magnetic) of the plane of polarisation in liquetied gases
under atmospheric pressure. 245.
— (The caleulation ~ from the magnetic) of the plane of polarisation for substances
without an absorptionband in the visible spectrum. 413.
ROTATIONS (Five) in Sy in equilibrium. 362.
SALOMONSON (J. K. A. WERTHEIM). See WERTHEIM SALOMONSON (J. K. A).
SANDE BAKHUYZEN (BE. F. VAN DE). On the yearly periodicity of the rates
of the standardeloek of the Observatory at Leyden, Hohwü n°. 17. (I). 68. (IL). 193.
— Preliminary investigation of the rate of the standardeloek of the Observatory at
Leyden, Hohwü n°. 17 after it was mounted in the niche of the great pier. 267.
SANDE BAKHUYZEN (H. G. VAN DE) presents a paper of Mr. J. WeEEDER:
“On interpolation based on a supposed condition of minimum”. 364,
scuHourE (J. c). Die Stelär-Theorie, 497.
scuOUTE (P. B). On the connection of the planes of position of the angles formed
by two spaces Sa passing through a point and incident spacial systems. 53.
— presents a paper of Dr. S. L. van Oss: “Five rotations in Sy in equilibrium.” 362.
— Relations between diagonals of parallelotopes. 540,
SCHROEDER VAN DER KOLK (J. L. C.) presents a paper of Mr. A. IL. Sirks:
“On the advantage of metal-etching by means of the electric current.” 219.
— presents a paper of Mr. E. H. M. BEEKMAN: “On the behaviour of disthene and
of sillimanite at high temperature”. 240.
— presents a paper of Mr. P. Tescu: “On the refractive index of rock-glasses”. 602,
— presents a paper of Mr. G. B. HoGenraap: “On an „Eisenrose” of the St.
Gotthard.” 605.
SHADING (On maxima and minima of intensity sometimes observed within the) of
strongly widened spectral lines. 662.
sLERTSEMA (L. H.). Measurements on the magnetic rotation of the plane of pola-
risation in liquefied gases under atmospheric pressure. LI. Measurements with
Methylchloride. 245.
— The calculation — from the magnetic rotation of the plane of polarisation for
it
substances without an absorptionband in the visible spectrum. 415.
SILICEOUS SPICULES (On the shape of some) of sponges. 104.
SILLIMANITE (On the behaviour of disthene and of) at high temperature. 250.
SIRKs (A. H.). On the advantage of metal-etching by means of the electric current. 219.
— Some remarkable phenomena, concerning the electric circuit in electrolytes. 465.
sMITs (a) and L. K. Wourr. The velocity of transformation of carbon monoxide, 417.
SOLAR prominences (An hypothesis on the nature of). 162.
SOLUTION (Dissociation in and crystallisation from a solid). 643.
space (A representation in) of the regions in which the solid phases which occur,
are the components, when not forming compounds. 279.
CONT ENTS. -XV
spaces S, (On the connection of the planes of position of the angles formed by
two) passing through a point aud incident spacial systems. 55.
SPECTRAL LINES (On maxima and minima of intensity sometimes observed within the
shading of strongly widened), 662, |
SPECTRUM (The calculation < from the magnetic rotation of the plane of polarisation
for substances without an absorptionband in the visible). 413.
SPHERES of Monge (On the) belonging to ordinary and tangential pencils of quadratie
surfaces. 484. .
SPONGEs (On the shape of some siliceous spicules of). 104.
STANDARDCLOCK (On the yearly periodicity of the rates of the) of the Observatory at
Leyden, Hohwii no. 17. (L). 68. (ID. 193.
— (Preliminary investigation of the rate of the) of the Observatory at Leyden,
Hohwü no. 17, after it was mounted in the niche of the great pier. 267.
STATISTICAL electro-mechanics. (I), 22. (II). 114.
STELAR-THEORIE (Die). 497.
STIMULUS and Hifect (A new law concerning the relation between). 392. 441.
STRENGERS (TH.) and B. Couen. On the atomic weight of antimony. 543.
STRUCTURE (Lhe geological) of the Hondsrug in Drenthe and the origin of that ridge,
MG) DB (The LOL:
SUGARS and Glucosides (Formaldehyde (methylene)-derivatives of). 175.
SULPHUR (On the action of) on toluene and xylene. 288,
L-surracE (Contributions to the knowledge of van per Waats’). VIT. ‘The equation
of state and the y-surface in the immediate neighbourhood of the critical state
for binary mixtures with a small proportion of one of the components. 321. 836.
— (Plaitpoints and corresponding ptaits in the neighbourhood of the sides of the)
of VAN DER WAALS. 445.
SURFACE OF conract (On the potential-difterence, which occurs at the) of two different
non-miscible liquids, in which a dissolved electrolyte has distributed itself. 431.
SURFACES (On the spheres of Monee belonging to ordinary and tangential pencils of
quadratic). 484.
SYSTEM (On the conditions for the occurrence of a minimum critical temperature for
a ternary). 225,
— Acetaldehyde + Paraldehyde (Equilibria of phases in the) with and without
molecular transformation. 283.
— Hydrazine + Water (The boilingpoint-curve of the). 171.
SYSTEMS (On the connection of the planes of position of the angles formed by two
spaces Su passing through a point and incident spacial), 53.
— (On the geometrical representation of the motion of variable). 386.
— (Ternary). (IV). 1. (V). 121.
TEMPERATURE (Bath of very uniform and constant low) in the cryostat. 502. 628.
— (On the conditions for the occurrence of a minimum critical) for a ternary system, 225.
TEMPERATURES (Arrangement of a BuRcKHARDT-WEIss vacuumpump for use in the
circulations for low). 633.
XVI CON T EV Sets
TERNARY SYSTEM (On the conditions for the occurrence of a minimum critical tem-
perature for a). 225.
TERNARY SYSTEMS, (LV). 1. (V). 121.
rescu (v.). On the refractive index of rock-glasses. 602.
TETRABROMOPHENOL (The velocity of transformation of tibroomphenol bromine into). 556.
TuEORY of electrons (Contributious to the). (1). 608.
— of electrons (The fundamental equations for electromagnetic phenomena in pon-
derable bodies, deduced from the). 254.
TINAMALGAMS, 873.
— (The meltingpoint-line of). 511.
TOLUENE and Xylene (On the action of sulphur on), 288.
TRIBROOMPHENOL bromine (The velocity of transformation of) into tetrabromophenol. 556.
VACUUMPUMP (A BureKHARDT-Werss) for use in the circulations for low temperatures.
633.
VALUES of 4 (The course of the) for hydrogen, in connection with a recent formula of
Prof. van perk Waars. 573.
VARIATION (The influence of) of the constant current on the pitch of the singing are.
311.
vELocity of transformation (The) of carbon monoxide 417.
— of transformation (The) of tribroomphenol bromine into tetrabromophenol. 556.
VERSCHAFFELT (E.). On the prussic acid in the opening buds of Prunus. 31.
VERSCHAFFELT (J. £.). Contributions to the knowledge of VAN DER WAALS’
y-surface. VIL. The equation of state and the \-surface in the immediate neigh-
bourhood of the critical state for binary mixtures with a small proportion of one
the components. 321. 336.
VOLUMENOMETER (An accurate) and mixing apparatus. 636.
VOSMAER (G. C. J.). On the shape of some siliceous spicules of sponges. 104.
VRIES (HUGO DE) presents a paper of Prof. KE. Verscuarrenr: “On the prussic
acid in the opening buds of Prunus.” 31.
VRIES (JAN DE). On the spheres of Monee belonging to ordinary and tangential
pencils or quadratic surfaces. 484.
WAALS (VAN DER) g-surfuce (Contributions to the knowledge of). VII. The
equation of state and the p-surface in the immediate neighbourhood of the critical
state for binary mixtures with a small proportion of one of the components.
321. 336.
— (Plaitpoints and corresponding plaits in the neighbourhood of the sides of the
Y-surface of). 445.
WAALS (3. D. VAN DER). Ternary systems. ([V). 1. (V). 121.
— presents a paper of Dr. J. D, van DER Waats JR: “Statistical electro-mecha-
mies’. {y.ye2, (UL). 114.
— On the conditions for the occurrence of a minimum critical temperature for a
ternary system. 225,
— Some observations on the course of the molecular transformation. 303.
— Critical phenomena in partially miscible liquids. 307.
a
Gr OUNS TREN Tes: XVII
WAALS (J. D. VAN DER) presents a paper of Dr. J. D. van per Waats Jr.:
“The variability with the density of the quantity 4 of the equation of state.” 487.
— presents a paper of Mr. J. J. van Laar: “On the course of the values of 4
for hydrogen, in connection with a recent formula of Prof. VAN DER Waars”’. 573.
WAALS JR. (J. D. VAN DER). Statistical electromechanics. (I). 22. (II). 114.
— The variability with the density of the quantity > of the equation of state. 487.
WATER (The boilingpoint-curve of the system: Hydrazine +). 171.
WEEDER (J.). On interpolation based on a supposed condition of minimum. 364.
WEEVERS (TH.). Investigations of glucosides in connection with the internal muta-
tion of plants. 295.
WENCKEBACH (K. F.). On the duration of the compensatory pause after stimula-
tion of the auricle of the mammalian heart. 378.
WERTHEIM SALOMONSON (J. K. A). The influence of variation of the con-
stant current on the pitch of the singing arc. 311.
— A new law concerning the relation between stimulus and effect. 392. 441.
WIND (c. H.) and H. Haga. Diffraction of Röntgen-rays. 247.
WINKLER (c.) presents a paper of Prof. J. K. A. WERTHEIM SaLomonson: “A new
law concerning the relation between stimulus and eflect”. 392. 441.
WOLFF (L. kK.) and A. Smits. The velocity of transformation of carbon monoxide. 417.
WYHE (J. W. VAN). A new method for demonstrating cartilaginous mikroskeletons. 47.
XYLENE (On the action of sulphur on toluene and). 288.
ZEEMAN (e.). Observations on the magnetic rotation of the plane of polarisation in
the interior of an absorption band, 41.
— presents a paper of Prof. I. K. A. Werranim SALOMONSON: “The influence of
variation of the constant current on the pitch of the singing are”. 311.
— presents a paper of Dr. J. J. Harro: “The value of some magneto-optic con-
stants”. 438.
Zoology. G. C. J, Vosmarr: “On the shape of some siliceous spicules of sponges”. 104,
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