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Koninklijke Akademie van Wetenschappen
te Amsterdam.

PROCEEDINGS

OF THE

pepe Oven Och: SC RMR Ns CSR 00

A

VOTE er NAE "MV

reerd

AMSTERDAM,
JOHANNES MÜLLER.
June 1903,

EA NOM A UUR A ID,
POAT PEATE et

(Translatedfrom: Verslagen van de Gewone Vergaderingen der Wis- en Natuurku!

Afdeeling van 31 Mei 1902 tot 24 April 1903. Dl XD,

ail

LIERALS

Koninklijke Akademie van Wetenschappen
te Amsterdam.

PROCEEDINGS

OF THE

BREE LON Or SCEEN- CES.

a

OT: Wray aah

(ist PART)

pO ee

AMSTERDAM,
JOHANNES MULLER.
December 1902.

us i) uth i

aN

(Translated from: Verslagen van de Gewone Vergaderingen der Wis- en }

Afdeeling van 31 me 1go2 tot 29 November 1902. Dl. XI).

‘ vor BAS). mevr.

stULLT¥

i

wy Le ee ieee A

Proceedings of the Meeting of May 31

Sor,

» >» June 28 yo atte PEL aig oe

-

Y
Yv

September 27 rde eee, Mo hte

» » October 25 » By Gh RER ne © Cet

» » November 29 » VE bis, ER Og CSS et ler

NOR AOR ae,
AT AG

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING

of Saturday May 31, 1902,

Ce

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 31 Mei 1902, DI. XI).

Ce I SS A DPS.

J. D. vAN DER Waats: ,,Ternary systems,” IV, p. 1

J. D. van per Waats Jr.: „Statistical electro-mechanics,’ (Communicated by Prof. J. D,
VAN DER WAALS). p. 22.

E. VERSCHAFFELT: „On the prussie acid in the opening buds of Prunus,’ (Communicated by
Prof. Huco DE Vries). p. 31.

P. ZEEMAN: „Observations on the magnetic rotation of the plane of polarisation in the interior
of an absorption band.” p. 41. (with one plate )

J. W. van Wine: ,,A new method for demonstrating cartilaginous mikroskeletons,” p 47.

H. M. Kniescuerr:.,Intramolecular rearrangement of atoms in azoxybenzene and its derivatives”,
(Communicated by Prof. C. A. Lopry pr Bruyn). p. 51.

P. U. Scuovre: „On the connection of the planes of position of the angles formed by two
spaces Sn passing through a point and incident spacial systems,” p. 53.

J. W. LANGELAAN: „fhe principle of entropy in physiology”, IL. (Communicated by Prof.
T. Prace). p. 57. (with one plate).

E. F. van pr SaNpe BAKHUYZEN: „On the yearly periodicity of the rates of the standard-
clock of the observatory at Leyden, Hohwii Nr. 17,” (First Ee p. 68.

The following papers were read:

Physics. — “Ternary systems.“ IV. By Prof. J. D. van DER WAALS.
(Continued from Vol. IV pag. 694).

B. If we put 7’ —constant in equation I of our previous com-
munication, we find the relation between dp, dv, and dy, at constant
temperature in the following form: .

025 075
0. ap = “oe oa + (y,—y em Oy, 7

:
+ je EL er ee dee (on Re Sak car ELI

da, +

Proceedings Royal Acad. Amsterdam. Vol. V.

(2)
For a binary system this relation is simplified to:

06
v., dp = («#,—2,) aa dx,
al

We know from the properties of a binary system, that we have
then a curve p=—/(x,) and a curve p= f(r,), and that the branch
representing liquid phases is always found higher than the one repre-
senting vapour phases. Both curves start at the point representing the
vapour-tension of the first component, and finish at the corresponding
point for the second component. This however is only true if the
temperature is lower than 7, of that component. If 7 > (7;,,), then
the two curves are joined fluently so that they form a single one.

For a ternary system we have to deal with two surfaces p = f (#,,/,)
and p= f (w,,y,) instead of the curves p= f (w‚) and p — f(«,). We
will use as a rule the index 1 for a liquid phasis, the index 2 for
a vapour phasis. These surfaces cover the rectangular triangle OXY,
and above the angles of this triangle they have points: in common.
The common ordinates represent the maximum tensions of the three
components. This hoids good, if the temperature is lower than 7,
of each of the components. In some cases these sheets may have still
another point in common, just as is the case with the two branches
for a binary mixture if a maximum pressure occurs. But for the
present we will disregard the existence of such a maximum pressure.
If T< 7. of one of the components then the two sheets of the
p-surface do not cover any longer the whole rectangular triangle, but
they have joined fluently to one surface.

In the above equation II the properties of these two sheets of the
p-surface are expressed in the form of a differential equation ; — we
will now proceed to deduce the principal properties from this equation.
Even for the pressure-curves of a binary mixture the number of these
properties is already considerable. For a ternary system they will of
course be still much more numerous, and even properties occur which
have no analogon for a binary system. But many of the properties
of the pressure-curves of a binary mixture may directly be extended
to the corresponding ones for the pressure surfaces of a ternary
mixture. Such properties need hardly be treated here, as we sup-
pose the properties of a binary mixture to be known. Accordingly
I will limit myself in the main to treating those properties that are
proper to ternary systems but not to binary systems. The study of
the ternary systems however has induced me, to give a more detailed
discussion of some equations, given in Cont. II for a binary mixture,
from a more general point of view. And in some cases this detailed

(3)

diseussion has enabled me to give a more precise and accurate form
to some of the equations and to some of the quantities occurring in
them. In these cases I shall discuss some properties more extensively,
concerning which I had else confined myself to refer to Cont. IL.
From a theoretical point of view the relation between p, , and y,
at given temperature is not more important than that between »,, 7,
and y, or between v,, 7, and y,. But even for a simple substance
the experimental investigation concerning the maximum pressure has
first been executed, and only in these later years it has been followed
by an investigation concerning the densities. In the same way we
may expect, that also for a ternary system the experiment will occupy
itself in the first place with the determination of the pressure, and
that the investigation as to the densities of the phases coexisting with
other phases, will follow later. The surface representing for all tem-
peratures the pressure as function of the composition of a binary
mixture has been called by me “surface of saturation”. We might
call for a ternary system the surface whose properties we are about
to investigate “surface of saturation for a given temperature”. Wherever
it is not ambiguous I shall speak simply of “surface of saturation”
In the following considerations we will take triangle OXY in a
horizontal plane; the direction in which the pressure is laid off is
then vertical. We represent the maximum pressures of the three com-
ponents by p,, p, and p, where we choose the indices in such a way that

Ie OER NES
If 7 > T, for one of the components, then the surface of satu-
ration does not reach the corresponding angle and the corresponding
maximum pressure does not exist any longer.

a. Curves of equal pressure.

For curves of equal pressure, we have dy ==0, and equation 11
is reduced to:

05 05
(eme) Oa, TF (Ya) Oa Òy, at
0*5 en |
a (v,— Blan ‘Oy, + (y¥,— En dy, —— Ue

The projection of these curves is of course the same as the
projection of the connodal curve of the &-surface construed for this
pressure. We have discussed this projection in our first communi-
cation p. 461. If p is chosen such that p, <p <p. the two
branches of this projection cut the two sides of the triangle adjacent

i a

Cay)

to the right angle. If p, <p <p, then they cut the hypothenuse
and the other side corresponding with the third component. If
p=p, then the two branches cut one another in the angle of the
second component. We might find the equation of these curves if

0% 07s 07g
and

02,7 Ow, Oy, Oy,”

were known. And though this is not completely possible in all cases,

we could express zr, and y, in wv, and y,, and if

yet in some cases we may find the equation approximately. A
digression in order to discuss these quantities cannot be left out here;
else we shall always be confronted with the same unanswered
questions in all subsequent problems.

The value of § is given p. 449, vol. IV, in the following form:

$= MRT \(1—a—y) log 1 —a—y) + a log a + y log y} + pv =) pdv.

We omit the linear function of rv and y, as it has no influence
on the phenomena of equilibrium. So the value of & consists of a
pure function of « and y, and of another part which fulfils the well
known condition :

(dr = vdp.

This second part is known if the equation of state is known. In
fig. 1, p. 450 1 have represented graphically this second part such
as we may conclude its course to be if we only assume the principle
of continuity. In what follows we will extend the principle of con-
tinuity so far, that we assume the equation of state to vary fluently
if « and y vary fluently. We now imagine the second part of § to
be construed for all mixtures, i. e. for all values of x and y, and
for all values of p. If we now put p == constant, then we have an
auxiliary quantity, which varies with « and y, and the knowledge
of whose properties is the condition for the solving of all questions
relating to the equilibrium, either of a binary, or of a ternary mixture,
or of any system of still more components. As we have already stated
the knowledge of this quantity depends on the knowledge of the
equation of state. From this appears, how absurd the opinion is, that
knowledge of the equation of state would not be required for the
knowledge of these systems. Yet we find this opinion often expressed.
For the knowledge of the equilibrium of a simple substance it would
be required, but for much more complicated systems it would be
totally superfluous! I have introduced this auxiliary quantity already
before (see i. a. Cont. II, p. 147); I shall represent by u the quotient,
obtained by dividing it by MRT. Now we have:

| (9)
$= MRT (lay) log 1—a—y) + w log a + y log y + yi.

From this follows
a“ lu
log ‘El
lay dee }»,T,y

1
Ke = MRT
da:
8 y du
= MRT } log —— a d
“ l—a—y dy Jp, Ter
1— Pu
nnie ets ag a,
xv(1—w—y) dec? ps Ty
of dp
dedy ),,
43
i = MRT | eel ")
dy’ pl Ht y(1—a— dy? P, 1

: du
For brevity’s sake I shall represent (9 by ws. With analogous
de)
p Ty
signification the symbols wy, we, ws, and uw’, will be used.
We deduce from the conditions of coexistence (see p. 551, 553
and 554 Vol. IV) the. following relations.

: a dEN. v dt © u
From | — | =| — | follows : Ji = Gina thane We) (ld)
Cr da}. le, —y, l1—w,—y,

d i 1 vl u!
From 3 = 2 follows Pid Ages SA Piet se (2)
dy), dy), l—a,—y, 1—x,—y,

1G i 1S 1
And from F =e pe cat pec En aen y a follows:
da Sdu. lav i

Ween
Al As
8 art
wee,
=
8
=

log (1-2,- Y‚) a Ut, We, ms Wy} ne t log (1-#,-¥,) + Uyt; Wes Ys yn} (3).

From these equations (1), (2) and (3) again follows, that we can
express the relation between the composition of the coexisting phases
only then, if we know what variation in the equation of state is
caused by the substitution of one of the components by another. So
we find e. g. for the determination of the limiting value of the
ratio of 2, and w, in the case that xz, and y, are infinitely small the
equation :

2

if ®, Agel) !
0g Swale? Us, Se U za |
a,
If we exclude the knowledge of the equation of state, we can in
nowise account for the considerable differences which this ratio shows

(6)

in different cases, and we have to consider it as a primary datum
without any relation to other properties of the solvent or of the
solved substance. Neither can we account for the value of this ratio,
if we think that the application of the law of Boyur is sufficient for the
theory of mixtures; for this law is the same for all substances and
cannot therefore account for the different values which this ratio has
in different cases. Therefore it appears convincibly that a closer
investigation of the quantities pw, wy, >, wr, and uw", is required.
I pass now to this investigation.

We start from the following equation, which may be considered
as the definition of the quantity under consideration:

*p
MRT u =| rdp

So in the first place this quantity depends on p, but as the equa-
tion of state for a mixture depends on the composition, it also depends
on x and y. We deduce from this equation:

du a, © P/ dv
. MRT — MRT u DE dp
de )pTy da pTr,
0

‘ dv Op Ov
If we write | — see , we find also:
da v Op Jax
MRT a da ee SG |
1 u PN te G ; G) dp = ==

d
UR Ts = (GE)

In Cont. II, p. 9 and p. 19 I have started from this last
equation, and making use of the form of the equation of state given
there, I have obtained the result, that for low temperatures «',, may
be neglected and gw’, may be put approximately proportional to

ahs es

dx
would be the critical temperature of a liquid mixture, if this mixture
might be considered as a simple substance; or, what comes to the
same, 7, represents that temperature for which the theoretical iso-
thermal of that mixture which we think always homogeneous,
presents only one horizontal tangent, and for which therefore maxi-
mum- and minimum-pressure have coincided.

, if by the symbol 7% we represent the temperature which

It is true that this quantity 7, is no experimental quantity, and

(4)

that we therefore might superficially think, that the introduction of
Tr is of no use; but in the first place in very many cases the
critical temperatures, found experimentally, do not differ much from
this quantity and in the second place even the simple assumption,
that this quantity varies fluently with the composition, will yield
many conclusions, confirmed by the experiments. As an instance |
mention the connection of the fact, that if a mixture has a minimum
critical temperature, a maximum-pressure is found on the connodal
curve. A closer investigation of the signification of the quantity wu
itself will however enable us to give a still more exact form to all
further conclusions which have been deduced in this way, and to
all further deductions which are important for the theory of mix-
tures. For the present I shall occupy myself only with the case
that one of the coexisting phases is a rarefied gas-phasis. In this
case wr, and «w',, may be neglected. For in the equation:

MRT u =| vdp

MRT
P
rare, and this holds for every mixture whatever its composition may
be. Therefore we get by integration :

the value of v may be represented by if the phases are very

MRT u = MRT Ip + gp (T)

In order to remain in accordance with the form of p. 450, |
will determine g(7’) such, that we may write:

f= log, zi pent

This signifies in fig. 1 that the vapour branches coincide, whatever
the value of x, y and 1—«—y may be.

In all such cases the equations (1) and (2) may be simplified as
follows :

Dey, Peg ey

1 U u!
and vds = eee en
leg, leg,

If the pressure increases mw’, and w', begin to differ from zero, and
properly speaking these quantities always differ from zero. This is to
be aseribed to the deviation from the law of Borre which occurs
in a different degree for different mixtures. But just as we do not
commit considerable errors if we neglect the deviation from the law

(8)
of Borre for rare vapours, but obtain utterly absurd results, if we
neglect this deviation for liquids, in the same way we may neglect
the difference in the degree of this deviation according to the different
composition, if we are treating of a rare vapour phasis, but if we
should disregard this difference in the case of a liquid phasis it would
lead to absurdities.

Let us now imagine for the different mixtures the pressure to be so
far increased, that the double point in fig. 1, p. 450 is reached
Experimentally this can of course not be performed without disturbing.
the homogeinity, and without condensation of a part of the vapour
phasis, which is compressed. But though what we imagine cannot
be realised, yet we may put the question, what would happen with
the quantity under consideration, if we according to the principle of
continuity, should imagine the homogeneity to continue to exist. Then
we find the value of w for the liquid phasis in that double point, and
we may write the equation :

'
)

}
Mrt NDE EEn

The pressure pin this equation is that one, which we have before
alled coincidence-pressure. As has already been observed this state
cannot be realised. Such a liquid, coexisting with such a vapour
would be a state of equilibrium; but an unstable one, or one that
is metastable. It is however possible by increasing the pressure still
more to get in this way a homogeneous liquid which differs only
slightly from the one under consideration and which in fact can be
realised as a homogeneous phasis. It appears from fig. (1) that u for
this more compressed liquid is somewhat greater than the value
written down in the last equation. But again that surplus of the
amount of uw may be neglected. For we have always:

MRT du = vdp.

But if we calculate the surplus of uw, v represents the liquid-volume.

vdp
MRT
is a quantity without significance, if » is a volume ofa liquid. From
this follows that the quantity which we have represented by w',, may
be found approximately in differentiating the above equation (4) and
therefore may be represented by :

1 dp!
Battie p' de,

And unless the increase of the pressure should be excessive

In the same way we have:

(9)

!
sig los PD
le te and,

p dy,
‘ ry > ! € a! ’ AN ‘ 7
so the dependence of w'‚, and «', on the coordinates x, and y, is
reduced to the dependence of the coincidence-pressure on x, and y,.
The coincidence-pressures would be the maximum-pressures of the
different mixtures, if they behaved like simple substances. The fol-
lowing relation exists for the coincidence pressures, at least approximately:

Consequently we find:

VA Cs dlog per
+- EES

eN Ne ee
re ie da, da,
' UE aT, d log per
and Un SO ee
4 ff dy, dy,
; Vee dilog: Ter d lod per
or Fe ese Ae et TEES ee tome IM)
oa Ml du, da,
OGL ox d log Por
ce spe cee OR Aa
grey: dy, dy,

It is clear from the deduction that these formulae may only be

considered as an approximation for the case, that the vapour-pressure is
low, and therefore 7’ much lower than 7. Putting f == 7 we may
put the factor of the first term at a value of about 12 or 14, and the
; ad bon Le
factor of the second term is unity. If therefore the values of ———

wel,

d log Tey _ d log per d log per

and — — have moderate ratios to those of —— ‘ Ss
dy, da, dy,

we find for u a course not differing much from proportionality to

dT

dx,
in which I had obtained it before (Cont. I, p. 148 ete.) But in the way
we have now followed we are enabled to add a correction term. Of course
these equations (5) and (6) are only approximations, and that, for several
reasons. But we must distinguish between the character of these appro-

So we obtain a result in a way, totally differing from that

ximations. In the first place we have assumed that «’,, and w',, vanish
for a vapour phasis, and so that u for different mixtures at the same
pressure has the same value. If the density of the vapour phases is
so small, that they do not perceptibly deviate from the laws of Borin
and Gay-Lussac everyone will agree that this approximation may be
admitted. In the second place we have ascribed to uw for the liquid

Gai)

state the value which it has in the double-point, though the pressure
exceeds that of the double-point. This approximation comes to the
same as to say that we neglect the volume of the liquid compared
with that of the vapour; and also this approximation is of no signi-
fication if the gases are very rare. But the chief reason, for which
we have to consider these equations (4) and (5) only as approximations
is that we make use of the following relation for the pressure of the
double-point :

if we suppose in this equation f for all substances and so also for
all mixtures to be the same and independent of the temperature.
Therefore if we set:

1 dp’

pda,’

!
We =

we assume a relation, which is incontestable in all those cases, in
which the vapour-phasis may be considered as a perfect gas. But if
we do more and if we assume a peculiar property of the equation
of state, as that one assumed in the formula for the pressure p' of
the double-point, the decision of the question, whether the equations
(5) and (6) are contestable or not depends upon the question whether
the relation used is accurate. Therefore in applying the equations (5)
and (6) it is not our aim to obtain numerically perfectly reliable
results, but only to get an idea of the course of the coexistence pressure
for different mixtures which is in the main reliable, and which makes
us understand the phenomena.

According to these considerations, knowledge of the pressure of
the double-points is required for the determination of the shape of
the surface of saturation. If we introduce this pressure also into the
graphical representation, we add a third surface to the two surfaces,
liquid sheet and vapour sheet. The third sheet is found between the
first and the second one, and the only points which it has in common
with them are those above the angles of the rightangled triangle. In
the case, that points of maximum pressure occur, in which points
the liquid sheet and the vapour sheet touch each other, this third
sheet also will touch both of them. If we cut these three sheets by
a plane p=, we get three sections and the projections of these
sections are the curves, which we have already mentioned in (a)
p. 3 as curves of equal pressure; to these however is added the
curve of equal coincidence pressure. After this expatiation on the
signification of the quantities occurring in formula II, p. 3, we

Bi

Cie

will return to the question if we can determine the shape of these
projections. In these calculations we confine ourselves to the case of
small vapour pressure.

We may put (see p. 7):

d hi u /

8 == zt Ti
l—x, -y, lr,
Ys U. DM
and = eg Me Hi
Ud eee h 1—w#,- U,

Adding these equations we get:

1 ve “ye A
en _ eb Ce
—w,—Y, 1—«#,—y,
1 Lta(e"™—1)+y,(e"% —1)
or = = —
1—a,—y, ee 41
Hence also :
x. Meas
ae gS vay AD Mead)
Yo é My a

and eT

Hs pe, TAD
Oe, (I—e,)(e” 7 Anke —1)
ade, (1) tye" * 1)
that AID"

In thesame way:

and
Ji 1e, (e” : Ln be (e” BE
If we substitute in equation II these values of #,—, and of y,—y,,
DES 075 % if
and the values of ——, and — found on page 5 and if we
Oz,?’ Oz dy, Oy,”

divide by MRT then we find the following differential equations,
where we denote for brevity’s sake by MN the nominator of the
fractions ne the values oh Ld, and y,—y,

NES dean a seo aa y 1_]) 7 Gd ea aun, | aa, ae
LV p= ened

ze (l—y, ye” a gee eae Bd EEn DEE ae rae | de, sE
dh Wa zb

Ed 9002) ne en | dr +
ie aaa {i

Baye En

se end cae

(12)
ae. " :
If we put: uw", de, + we dy, = du, and «ny, de, + w'y dy, = Oy yee
then we may write this equation in the following form:

0 d log (1 +2, (e 5 cn 1—]) 4. U, (e” ej vds, — yd’,

Hr Wits
or C= log dt, (e i kart) = Yy (e =); = (ay, Ux —Y Wy,

Applying equation (3) of p. 5 it would have been possible to
obtain this integral for the projection of the curves of equal pres-
sure in a simpler way. In this equation, where the index 2 indicates
ei a rare vapour phasis, we equate «,, and w'‚, to zero and u, to

lo 1; so we get:
a Ar as 5
log Aar) Pl Hr Wy = log (1—w,—y,) log A + 1

MRT
from which follows:

A a ao ru — - Bay, — 2s x Yi y, —1
MR en th
In connection with the value I have given before
) 1—z

I Sel | po te
HO pin sap eee ee at Me

This equation may be written in the following form:

log a log} pla ‚(e im sl) tye OM — 1) Yan U Ur IY Wy, == (7)

Already long ago I have given a corresponding equation for a
binary system. It may also be found Cont. H, p. 146, though in
a somewhat modified form. I have shown for the case of a binary
mixture, that such an equation in some cases may represent a straight
line, but that it in other cases represents a curve, which at certain
values of 7, presents a maximum value for p. The intermediate
forms may also occur of course. The course of the function u being
at least approximately determined by that of the functions 7, and pe,
knowledge of the dependence of these functions on a and y would
be required for an adequate discussion of equation (7). This would
be possible according to my equation of state putting

8 a Leia

1 Se and Per = SS .
A 27 b 27 b?

Liter nig a lees
But as the quantities En and De depend rather intricately on 2 and 4
) ge

this would lead to an elaborate discussion, and I have not yet sue

ceeded in drawing simple conclusions from it in a concise manner
and to formulate them sharply. In the formula

the discussion of the term 7’. and of its first and second derivative
function according to vw and y would already require extensive cal-
culations, and the discussion of log Per and its derivatives would still
augment the difficulties considerably. And though it is true, as we
have observed above, that generally the influence of log p. is not

: RT dT
great, yet some cases occur, namely those, in which Fag and En
are small, in which this influence is decisive. Therefore for the
present I will not enter into an accurate discussion, and only inves-
tigate some peculiar cases.

So as first case we may suppose that the three components have
been chosen in such a way, that the course of p will be represented
by a straight line for each of the three pairs, which may be formed
from the components of the ternary system. This may be the case if
the difference of the critical temperatures of the components of these
pairs is considerable and the critical pressures either differ but slightly
or have such values that the expression :

AT cy dper

| Tdx Der dat

may be considered to be constant for each of the three pairs. Then
we may expect that for the ternary system u and w,, will be
everywhere constant or nearly constant, from which follows that
du’ and dw',, may be neglected compared with ws, and w,,. If we
in fact neglect the values of du and du, the differential equation
of the curves of equal pressure assumes the following form:

0 = dlog {1 +a, (ei) fy, eh = 1}.

And we get for the equation of the projection of these curves:

C=1+a,e""—1)+y,("%—)).
And we find for the value of p from equation (7)

Po

1 Wy pea
La, (SI) + y, CPI

The supposition namely that du’, and du’, are zero comes to the

p=MRTe

CED

same as to take two different constants for pw’, and w',. But then
we have also:
Urn = Uo + GC, = Yrs»
where mu, denotes the value of u, for the first component.
From this we deduce that the liquid sheet of the saturation surface
is a plane, and so that:
P= Pi (le, Sy.) TF Pst, Pe, es
We deduce this form for p by making use of the relations for
each of the components:
D= MRT eo
Pp, = MRT evt
Pp: = MRT evo #1

Wa : : : : . Pp
The value e * which is constant in this case, is equal to > and
1
» By . z Ps
the value of e “ is equal to >.
Pa
The lines of equal pressure for liquids are therefore all parallel
to each other. If p= p, the projection of such a line is:

he
lr — rs j=
Pam Pa
ae ae : PaP:
It cuts therefore the Y-axis at the point y= —. It appears
Paws

that in this case we have the interesting circumstance, that the
addition of a substance with a given maximum tension to a binary
mixture whose vapour pressure is equal to that maximum tension,
does not bring about any variation of that pressure, however great
or small the added quantity may be.

The other line of equal pressure, the section of the vapour sheet,
lying at the same height of p, and representing phases coexisting
with those of the first line, may be deduced from:

P= Pa (f—7 + Ps + Psi

if we express in this equation wv, and y, in 2, and y,; and this may
be easily done if w' and w’, vanish, and wi, and w'‚ may be con-
sidered as constants. We write then:

ye } SS ue
1 2 esa
— e 1

BSS ee ip 1

ha Yo =e

1—#,—y, aN Lela

and

(5%)

These equations would also hold, if w, and u’, still depended
on w, and y,, but then it would not be possible to express 7, and
y, in w, and y,. Performing the substitutions mentioned we get:

ik l—a,—y, @,
- RAE ae Sea ey av os, Nog EON
P va Paths

As it is however not only our aim to obtain the results, but as
we also wish to interpret the equations given before, we return to
equation IL in order to determine the line of equal pressure for the
vapour phases.

If we continue to use the index 2 for the vapour phasis, and the
index 1 for the liquid phasis, but if we now apply equation II to
the vapour phases, it assumes the following form:

2 2

5 5
Vie dp == | (vw, — 2) jas an Kiel, Òz,dy, | ie

5 5
(v,—2,) Apes Se isd al Das | dy, d
y

B: 0v,0Y 4 J2

As we may neglect wo, and uw’, for the vapour phases, we may
also neglect the second derivatives of u; and we may put:

02 N 12 d? 1
SURT ETR pees :
Om? wv, (l—a,—y,) 0x,0y, 1—e,—y,
0? Td
and SURT LE
Oy,” nlt

dv dv dv
We have v,, = 7, —-v, — («,—2,) — (y¥,—y,)| —— | ;and| —
de, p dy, d de, p

dl) are zero for the vapour which we assume to follow the
dy, Jp

law of Boyle, and so to occupy the same volume, if the pressure and
the number of molecules are constant. If we neglect moreover the
volume v, of the liquid compared with v, the volume of the vapour,
then we get after division by MRT:

dp 1—1 Y,—Y,
ea = Wer) ——— Ys ties ee kel da, +
P 4 «(1—a#2,—y,) 1 Ts Us |
Ld l—wz |
af | ene ae ede) dy,
Loy, : ve)
For a binary system this yields the well known equation:
‘dp Ld,

P ave «,(1—«,)

da

(AD)
If further we substitute for «,—7, and YY, the values:
mee SDI)
(le, sy) dee ned

u!

(1 ailes —1)—w#,(¢ "“ —1)

} Sib — wv,

and YY = Y. -

2 ==
(lr) + a,¢ a dye Bn

then we get by integration:

GC

: : 3 nn —p! 5 3
or in connection with the value of e * Sande ‘ ” given before:

ie

/ ——

D )
nl a el Van

The constant Cis of course the pressure for the case that x, and y,
are equal to zero, so it is equal to p,, and we find again equation
(9). If we now give to p the same value as for the liquid sheet,
we find the second branch of the curve of equal pressure. So we
ind Tor p=
PaP Pi

va

Ps PaP:

Le,

a line which yields y,=1 for 7, =O and:

Ps PoP.
UP Tt Bry,
Ps Pe ar
for the point of intersection with the axis for the third component.
This value is of course the value of 4, for the pressure p, of the
vapour phasis of the binary system consisting of the first and the
third component. The projections of these vapour lines of equal
pressure are again parallel.
: ;
Phe line:

il 1 ( 1 ij ) ( it if )
heee
P Pi Ps Py Ps Pr

is displaced parallel to itself, when the value of p varies. The vapour
sheet consists therefore of parallel lines and may be considered as a
cylindrical surface. The section with the ?OX plane is a hyperbola,
and also that with the POY plane.

If we cut the sheet of the coincidence pressures also at the same

CL)

height, we get a third line, which lies between the two former ones, and
which we have already mentioned in our first Communication as the
projection of the line of the double-points. The equation of this line
may be found from the equations of p. 8 and 9 namely from:

1 dp'

Sha ea

p de

i dp! :
and en |

p dy

: Pp Bau: ‘
In this case we have p’,, = log — and u’, = log; integrating we
Pi Pr
find for the equation of this curve:

log p' = ¢ + « log Pa + y log Ps :
Pi Py
If 2 and y = O, this third sheet coincides with the two others, and
p'=p.; from this the value of C may be calculated. We may also
write this equation in the following form:

p =p, (l—z—y) pps?

or logp = (lL—a—y) log p, + w log p, + ylogps-
This equation also represents a right line, which is displaced parallel
to itself, if p' varies.

So we find very simple lines for the three curves, which we get
in this case for a binary system, namely a right line, a hyperbola,
and between them an exponential curve.

We shall now discuss the case which differs most from that which we
have treated, namely that, in which each of the pairs that may be
formed from the components of the ternary system, presents a maxi-
mum pressure. The critical temperatures of the components do not
differ much in this case, and for each pair a composition may be
found, for which the function u’ vanishes. Then we may expect,
that for the ternary system a value for x, and for y, may be found
for which the values of w’,, and u’, are equal to zero. If the function
uw’ depended only on 7%, then we might simply express this in
properties of 7, and we might say: for each of the pairs a mini-
mum critical temperature occurs, so we may also expect a minimum
value for 7, for the ternary system. As u still contains the term
log per, the same set of values of x, and y, which yields the mini-
mum value of 7, will not make u’, and u’, vanish. This agrees
indeed with the considerations for a binary mixture, given in Cont. II.

For values of v, and y, differing only slightly from those, for which

2

Proceedings Royal Acad, Amsterdam, Vol, V,

(18 )

u, and uw’, vanish, the first derivatives of u may be considered to
be small in this case but the second derivatives on the other hand
will be decisive for the course.

In order to determine for this case also the projection of the curves
of constant pressure we will make use of equation (7):

P horde y!
log mla DID ttn neil Td
“mm

If we call the values of #; and y,, for which u’, and u’, vanish,
en and ym and the corresponding pressure pj, then we have:

Pu
log BET inl hence also:

Pp ( vy A y ' '
loy DE =logil de (e ™—1)+y,(6 PID He y, Lln Yp Um:
in

It appears already from this form of p„ that this pressure of this
system may be considered as a coincidence pressure, and as this
system can be realised, it may be considered as an ordinary maxi-
mum tension. If we now consider w/,, and gu’, to be small, so that

'
JA )

"Tbe ;
we may put ¢ “—1=—w’, and ¢ “—1=yp’,, and
' ! ' 1 '
log tl Ar 4, Ur, 5 u mj er ae u n°
then we find for mixtures, whose composition does not differ much

from en and Yy :

Pp

log Pm — Ux — En
m
If we write:
Ene ee] 9 . , " j "
Urn = En + 4 (em) u Bei 2 (a io ie) (4, — Ym) UW xmym 1 (y, —Yn)* Le zond
’

we may write the last equation:

P 4 € \ " 2 '
log ——— 4 {(a, Ei) ed + 2 (wv, —2£») (7, — Ym) {t mjm En (y, —Yn)* fl ‘yom .
Pm

If we only inquire into the mathematical consequences of this last
equation, without trying to answer the question, if the suppositions
as to the values, which we have ascribed to Wom, (rym ANT U jn, MAY
be found in nature, we may only say, that if wom and gyn vanish,
the curves of equal pressure in the immediate neighbourhood of
this singular point will be conic sections. In order that p, may be
really a maximum pressure, the first member must be negative for
all real values of z,n and y,—ym and this requires, that gom and
yn are both negative and that (& omm)" SW em "ym. Then the curves
of equal pressure are ellipses whose centre is the singular point.
For a binary mixture the quantity mw’, has always appeared to be
negative in accordance with this theory, when the components were

(19 )

substances, which do not exercise any chemical action upon one
another, for which therefore the molecules in the mixture may be
considered to be simply mixed, without suffering any internal modi-
fication. For such binary mixtures minimum critical temperatures have

fy
a minimum value of 7, corresponds to a negative value of We —
Bit never with certainty maximum critical temperatures. If u’ and
Wm Could be positive, and u em By (U! L'zmyn)y then we should also
get ellipses for the curves of equal pressure, but then we should
have p>pm, and the ternary system would present a minimum pressure,
which would also lead to minimum pressures for the pairs of which
the system consists. If maximum critical temperature for a binary
system should really occur in nature, and if we then formed a ternary
system, of which one pair of components Posen a actu and
another pair a minimum value of Ds then Won and p" ym might have
opposite signs, and the point for which Wem and u’ ym Vanish would be a

Ter
actually been found, — and the chief term of u being — /( — 1)

a PR stationary point as to the pressure, and
\ ba the curves of equal pressure would
intersect in that point.

In figure 12 the course of the curves
of equal pressure has been represented
schematically for the case of maxi-
mum pressure for the three pairs of
components and for maximum pressure
for a point of the system. The suc-

cession of the values of the pressure
b EE * is then:
Fig. 12.
ag OY <P GPS Pas < Pm
only the order of succession of Py, and
ps and of p,, and p,, may be reversed.

The figure does not require any further
explanation.

As intermediate case for the course
of the curves of equal pressure, we
assume a system, in which for two of
the pairs the pressure increases or decrea-
ses regularly, but the third pair has a

Rist os Pi Pp, maximum pressure. So in fig. 13 the
vindek Pek pressures follow each other in this
Fig. 13, Way: PD, <P; << pi, LPs One of the

( 20 )

eurves of equal pressure, namely that one for which p = p,,, touches
the (X-axis.

In the following chapter we will give some indications concerning
the course of the curves of constant pressure for the vapour phases
in this case, and in the general case. Let us return to that purpose
to equation II of p. 3 of this communication.

Db. Displacement of the curves of equal pressure with
variation of the pressure.

We have already observed that the projection of the connodal curve
of a Gsurface, construed for a certain value of p coincides with the
projection of the curves, for which the pressure is equal to p, and
that therefore all laws, which hold for the connodal curve, also apply
to the curves of equal pressure.

If in the equation:

a O76. 7 05 |
Vo, UP = (z,—2,) On, + (¥,—Y;,) Ow,0y, | du, +
a le, Dir Sarde re) se | dy,
we choose the values of dv, and dy, such, that
de, ae dy, dl
ee eae

where ZL represents the length of a line, connecting the point P,,
whose coordinates are v, and y, with the point P,, representing the
phasis coexisting with P, and whose coordinates are x, and y,.. Be
further d/ the length of a line, whose projections are dv, and dy,
then the point w, + dz,,y,-+ dy, lies between the points P, and P,.
It lies therefore in what we may call the heterogeneous region. The
above equation may then be written :

dp | 076 de, 2 075 Ox, dy, 076 dy, *}
v., — = Li 2 — = ler .
gh | Bel | ag a dl \( dl ) NE eel = |

The second member of this equation is positive for the points of

the connodal curve, as the ¢-surface lies above the tangent plane for
all phases which may be realised. If the point P, represents a
Wes hs dp 5

liquid phasis, then #,, is positive, and therefore 5 also positive.
When the pressure increases the liquid branch is displaced in such
a way, that it moves towards the side of what was before the
heterogeneous region. This rule for a ternary system is equivalent

( 21 )

to the rule of Konowanow for a binary system, if this latter rule is
duly extended. If on the other hand /, lies on the liquid sheet,
dp

then v,, and therefore also a is negative. This signifies that the
(

vapour branch of the eurves of equal pressure moves on towards
the heterogeneous region if the pressure decreases, and on the other
hand towards the region which at constant pressure belonged to the
homogeneous region, if the temperature imereases. If the pressure
is varied the two branches move, in such a way, that one of the
branches retreats for the other. If there is not yet question of eri-
tical phenomena, a point for which v,, =O does not yet exist, and
the given rule holds without exceptions. For the case that no
maximum pressure exists, the two branches of the projection of the
curves of equal pressure consist of two curves, originating both
in the same side of the rightangled triangle, and ending again in
the same side. Every point on one of the branches has a conju-
gated point on the other branch. We will eall the lines joining such
a pair of conjugated points (coexisting phases) chords. The first of
these chords have the direction of one of the sides of the rightangled
triangle and the last the direction of the other side. If these two sides
are the sides containing the right angle, then the chord turns over an
angle of 90°. It oecurs however only as an exception that the chord
is directed towards the origin in other points than the extremities.
Afterwards we will return to this question.

If a maximum pressure exists, the branches of the curves of equal
pressure form closed curves near the phasis, whose pressure is maxi-
mum. The liquid branch contracts if the pressure increases, and
according to the rule, deduced above, it moves towards the branch of
the vapour phases. This branch therefore must also form a closed
curve round the point of maximum pressure and that a smaller one.
For the limiting case, the curve for the liquid phases is an ellipse
the curve for the vapour phases is also closed, but has other dimen-
sions, and its axes have other directions and another ratio, in the
limiting case, however, it must coincide with the ellipse of the liquid
phases. At any rate therefore, the position of the liquid branches being
given for increasing pressure we may immediately conclude to the
relative position of the vapour branches.

(To be continued.)

(4

Physics... — “Statistical Hlectro-mechanics.“. By Dr. J. D. vaN DER
Waars Jr. (Communicated by Prof. vaN DER WAALS).

Prof. Gipss has newly published a treatise entitled “Elementary
principles in statistical mechanics”, in which he communicates some
considerations, belonging to a science, which he calls “Statistical
mechanics,” and of which he states that “on account of the
elegance and simplicity of its principles” it is eminently worthy
that the laws to which it is subjected, are studied. The laws relate
to the behaviour of a great number of systems, whose motions are
mutually independent. These systems quite agree with one another
as to their nature, and only differ in so far, that the integration
constants of the differential equations of motion have different values,
or, what comes to the same, that the values of the generalized coör-
dinates and of the generalized velocities at an arbitrary moment
(e.g. at the moment ¢= 0) differ for different systems. The laws,
which hold for such ensembles of systems have a very general
character, as GiBBs shows; yet in their application they are confined
to systems, consisting exclusively of ordinary matter. Now the
question arises whether such like considerations might be applied
to electro-magnetic systems, and whether in doing so we might
extend our very limited knowledge of the phenomena of radiation in
connection with the laws of thermodynamics.

We cannot deny however that we must not expect foo much from
these considerations. The greater part of the theses deduced by GrBBs
are exclusively or principally applicable to ensembles of systems which
he calls canonical and which have such an important phace in his
considerations, because they represent the simplest law possible of the
distribution ot the systems over the different “phases” *). Mathematical
simplicity, however, is not a trustworthy criterion, when we want
to investigate, what is actually to be found in nature. For our
mathematical representation e.g. the simplest motion, a vibrating
string can perform, is an harmonic motion, yet we should be utterly
mistaken if we should assume, that every vibrating string would
execute such a motion. Perhaps we run the risk of making similar
mistakes if we assume, that all systems in nature will follow the
laws which we have deduced on the supposition of a canonical
distribution of the systems of an ensemble.

It is true that Gress shows in his chapters XI—XIII that the cano-

1) Two systems are considered to be in the same phase when they are to be

found in the samé element of extension in phase.

nical distribution is the most probable one, provided the only condi-
tion, to whieh the ensemble is subjected, be that the mean value of
the energy of the systems is a preseribed quantity; but the main
difficulty happens to be to answer the question whether this is indeed
the only condition. Systems e.g., consisting of spherical, mutually
equal molecules, will not be distributed canonically, for they are still
subjected to another condition, namely the distance of two centres of
molecules can never be less than the diameter. To assume the cano-
nical distribution comes therefore to the same as to neglect the volume
of the molecules, but it is not easy to decide whether nothing else
is neglected. In fact choosing the distribution of the systems of an
ensemble is equivalent to choosing the cases, which we are to consider
as “eases of equal probability” in a more direct application of the
‘alculus of probabilities. Both are subject to the chance, that the proba-
bility a posteriori will prove to be another than we had assumed a priori.

Yet such like considerations can be useful, in the known region
of thermodynamics, because they bring its laws very simply and
elegantly together under one point of view ; in the yet wnknown region,
because they may perhaps suggest formulae, for which comparison
with the experiments may decide, whether they are in accordance
with the phenomena of nature or not.

Law of conservation of density-in-phase.

In an investigation, whether the considerations of GiBBs are also
applicable for electro-magnetic systems, we have in the first place to
examine, whether the “law of conservation of density-in-phase” holds
also for them. In the beginning we will confine ourselves to systems
devoid of material, electrical or magnetical masses.

Now we imagine an ensemble of systems. The different systems
are congruent spaces, enclosed by perfectly reflecting walls. We divide
each system into m equal eubie elements of space de dy dz. These
elements are so small that the eleetrie and magnetic forces in them
may be considered to be constant.. The state of each system will be
perfectly defined, if in each element of space the components
?, g and h of the electric displacement, and the components a, Band y
of the magnetic induction are given. So the state is determined by
means of 67 data; according to the assumption, that electric energy
is potential, magnetic energy kinetic, the 3 7 components of the electric
displacement would represent coordinates, the 8 7 components of mag-
netic conduction generalized momenta, or at least they wouid be
proportional to them.

( 24 )

We mark the elements of space with successive numbers and
represent the components of the vectors in the rt element by fr, g,,
h,, a, Br and y,. Let us select from an ensemble those systems whose
data lie between the limits f, and f,-+df,, f, and f£, 4 df, …
Jn and fy, + df, and in the same way for the other components:
the number of these systems may be represented by:

Ddf, «+f, dg, ---- dgn dh,....dhy da,.... da, dp, ....dBy dye dye
or DFDE ree ee

Here the brackets indicate, that also the other components, the
parentheses that the same quantities also for the other elements of
space are to be taken. We will call {(d7,)] [(de‚)| an element of

a a: D
extension-in-phase, 1 the density-in-phase, == the coefficient of

probability-in-phase (.V representing the total number of systems in
the ensemble) and 4, defined by the equation P= e%, the index of
probability -in-phase.

Let us consider the same ensemble after a short lapse of time dt,
then the number of systems being ina certain phase, will have varied.
We may conceive the variation of that number to be composed of
12 n parts, as the systems may enter or leave a certain phase by
passing one of 127 different limits, [(/)), [(/ + df)|, [(e,)] and
(a, + da,)|.

The systems passing the limit 7, contribute:
« c vil

df p N
D on VION EE On dg, zee do Oh, es dr (OON SN
3

to the total number with which the quantity D |(/7,)| |(da,)| increases.
The systems passing the limit 7, + df, contribute a decrease
amounting to:

} ee -t- 5 | D | df, | at Of weiss OR lNdat:) | So ND
Adding these quantities we get an increase with:
pay pul a (AF) [(de,)] (4)
Ta Gers je axe a ates, ate ng ek
Now we have:
Op pe re
Of lic? de | Òf, dt Òf, dt -

bead.
The second term of the second member is zero, for a depends only
at

on the rotation of the magnetic induction, and is independent of the
value of f,.

it ed

In the same way we find the increase in consequence of the

systems passing the other limits, — taking into account that all
eye . . da, rr . .
quantities of the form — „are zero. — Faking the sum of all these
a, at

1
partial increases and dividing by |(d¢/,)| [(da@,)| we find:

OD OAD GFN er OD dae .
Cy alae ale ene a ay
OD (OD df, “(0D das] 4D F
a ae ice ll ET PRG,

0D
Here ee represents the fluction of the density for a phasis whose

limits are constant, = for a phasis whose limits partake of the motion
Ll
of the systems of the ensemble.

So the density proves to be constant for a phasis, partaking of
the motion of the systems, and as, of course, the systems can never
pass the limits of an extension-in-phase, when these limits move with
the systems, the total number of systems within every extension-in-
phase, i.e. D{(df,)] [(de,)] remains constant, and so also [(d¢7,)] {(de,)].

This proof of the laws of conservation of density-in-phase and of
extension-in-phase quite agrees with that one given by GiBBs. Im
our case, however, we have still to pay attention to one circumstance.

is OD fe
In calculating ra A) \[(da,)|, we have assumed, that this number

is the sum of the numbers of systems passing the different limits.
This comes to the same as to say that no system will pass more
than one of the limits during the time dé, or at least, that the number
of the systems that pass more than one limit is so small, that it may
be neglected. In the proof of GriBBs we may assume, that this is

dy
really the case, provided we take df so small, that ms dt is small
compared with dy (where g represents one of the generalized coor-
dinates, and (/q one of the dimensions of an element of extension-in-
Y phase). For our case however this proof is
incomplete. Be 7 and s two adjacent elements
of space, then [f,] and [fs], [@,] and [a;) are
no independent quantities, but they must be
A approximately equal, as [7] and [a] vary only

fluently from point to point.

In order to investigate the consequences of
O x this circumstance we imagine an ensemble of

( 26 )

systems with only two coordinates « and y, which are subjected
to the condition that and y must be equal and continue to be so. All
systems will then be found on the line OA and will move in the direction
of this line, so all systems leaving the element of space drawn in
the figure, or entering into it, will pass the two limits dv and dy at the
same moment. If the condition is not that r and / must be rigorously
equal, but only that thei difference must be very small, then all
systems will be huddled up very near the line OA and a great part
of those that pass the limit dv will also pass the limit dy. It is evident,
that this circumstance is caused by the fact, that within the element
dx dy the density is not homogeneous. If we choose therefore the
the dimensions dr and dy so small, that the whole element lies with-
in a region, where the density may be considered as constant, then we
may again assume that the number of systems, passing both limits
may be neglected, compared with the number of systems passing only
one of the two limits. —

If we choose therefore [(df‚)| and [(de‚)| small compared with the

ROE A i DE Og ae
mean vaiue O ae : ale (Gia)

ratio to de®, and Jt again small compared with the quantities |(//,)|
and |(da,)|, so e.g. having a finite ratio to dr”, it appears that in
fact the number of systems passing more than one of the limits may
be neglected. So the proof of the law of conservation of density-in-

‚so e.g. having a finite

phase is complete.
The quasi-canonical distribution.

If we wish to distribute the systems of an ensemble over the
different phases in such a way, that the distribution does not vary
with the time, so that the state of the ensemble is stationary, it is
evident that we have to choose for P a function of the coordinates,
which is constant in time. GaBBs chooses for this purpose the function

/

e where & represents the energy of a system, and wp and @ are
constant quantities for a given ensemble. He calls this distribution
the canonical distribution. This simple law cannot be applied to
systems consisting of ether. If we assumed it, the quantities |‚f] and
[el would vary abruptly from element to element instead of varying
fluently, and moreover the distribution would depend on the dimensions
of the elements of space, which we have arbitrarily chosen. We
must therefore assume another distribution which secures a fluent
variation of the electric and magnetic displacements.

To this purpose we will assume a distribution closely resembling
those, discussed by Gusss in his chapter IV as “other distributions
having the same properties as the canonical.” These distributions
have the characteristic property, that the index of probability # is a
linear function of one or more functions /’,, /’, etc. of the coordinates:
the functions /,, PF, ete. are subjected to the condition that their
average value, taken over all systems of the ensemble must be a
prescribed quantity. We might form different distributions, all satisfying
the conditions. Now we seek the average value of # for all these
different distributions; this average value of 9 will be a minimum
for that ensemble where % is a linear function of #,, /, ete. This
is proved by Gaas in his chapter XI. I shall call such a distribution
a quasi-canonical distribution. The canonical distribution is nothing
else but such a quasi-canonical distribution where there is only one
function /’, and that represents the energy. As the canonical distri-
bution is of little application, e.g. not for systems of molecules with
finite diameter, it would perhaps have been preferable to give a
broader meaning to the word canonical and to use it in the sense,
in which I use quasi-canonical. As GiBBs has however used the word

canonical exclusively for ensembles for which a= I will use
the expression quasi-canonical for ensembles for which
y= wp — al’, — bF, — ete.
In the ether we cannot have canonical ensembles, and so we will
discuss only quasi-canonical ensembles. We put:

== eee (-)
0 k J, J, (°)

where, dr representing an element of space:
del Ca =) toert) + (i - 2) | de tf)
if (5 8 Le) i (= a =) 4 (- =) | de (10)
RT Vy? Oy Ow Oz Oy Ow \
2 = (+ uo i x) dt (11a)
Q. hk kern ars dv Ie BT oke EN
o =((= a: 5 be x) rates Edd (11h)
Gn hen ate Eren Je ME

oP" be + de. id NAD)

k, J, and d, are constants, and d, and d, are infinitely small. The

if

term — -—-——— has been added, that we should have only to

( 28 )

deal with systems, consisting of free ether. Systems, containing electric

masses are not absolutely excluded, but still their number is very

small and may be neglected compared with that of the systems which
0a 05 STO

are devoid of these masses. As + ie En 5 is always zero, systems

Ox
for which this expression has another value can never occur; yet
we may admit them in such a small number, that they have no
influence on the results. Finally we cannot take into consideration
systems consisting of infinite space, for a finite quantity of energy
would spread in it and we could not have a stationary distribution
in the ensemble. Therefore it is necessary to enclose the electro-
magnetic energy within absolutely refleeting walls. But then it is
necessary to add a term to 4, which expresses, that the walls reflect
absolutely, i. e. the quantities [7] are always zero at the walls. The
WwW
term’ — g expresses this; 4 represents a small line in a direction
2 .
normal to the surface; we make this line decrease indefinitely ; do
represents an element of area.

If this distribution is to be for ether systems, what the canonical
distribution is for material systems, then in the first place 1j must be
a constant in time. For the other terms this is immediately evident,

OTK

so we have only to show it for the term ——

U

The relation, we have to prove may be written :

dp dy
Le pe ae Ng tog cre EE AE ee 13
dt a dt ( )

We will make use of the relations

da — es Og oh (14)
di == Jt ded . . » A >
zgeen EE BR Pee
dt An \dz Oy
and of the following relations, that may be deduced from them :

ry af OF, OF

— — V7 { — — ot Ste ae NN

dt? a dy? EE cy,

da Oene tpt
2 Hr ee : - ee ee ers 17
de (S+5et5) ie

and also of the corresponding relations for the other components.

Now we have
( d
ey Bes pL | FA ae
dt dz dt\ Oz Oy

( 29 )
Integrating partially we get :

— = a number of surface integrals
df, df Ee Hi 07h 074 dy 0’ 0 a 07h
Ni dt gent Oy? dede ry a dt\ dz? ‘5 Ow? Od a ail
4 dh(O?h _ Oh df dy | , ‘9
dt\ Oy? zt dw? Owdz Òyde \ SVT ed

df. HR
In the coefficient of a in the cubic-integral we have:
Lt

Oh dg ag 0 (0g oh ML Hs
Oadz Oxdy Ow Oy ey TE Se (20)

ee df Og 1
at least if we put, 5 ERA dn =, so if we neglect the systems in
& y z

oe ‚df
which electric masses occur. So we get for the coefficient of dE the
(

LN d
expression — ~— and for the cubic integral :

V? ot

1 ; df df 1 03 Oy d Op Oy dy
Baer A ec) ys egg En Baie eee
V2 dt dt? iz Kore: Vi? § dz Oy dt de Oy e dt

df
As at the absolutely reflecting walls [7] and therefore also | =|

continue to be zero, the surface integrals disappear; so equation (13)
is proved.

The quantities g and xy which are introduced in order that the
variation of the electric displacement and the magnetic induction may
take place fluently, are defined as the sum of the squares of the
components of the rotations of those vectors, if we disregard the
coefficient mae — introduced in order that equation (18) may be satisfied.

LO weve
This seems to me the simplest definition for p and x. It might,
òf 0g Oh
however, appear that we are not yet sure that —, — am g
: On Oy dz
convenient values. In order to show that this is not the case, we
will prove the following relations

òf 2 òf 2 òf 2
fe eek see ey d Hink 4 21
4 Hf 6) Ge) : 5) ‘ i
} 0a \? da\? da?
rd el B EE eet (SD
Per Tor zl) +65) JE , oe

where again the brackets indicate that we have to take also the cor-

( 30 )

responding terms in which the other components occur, In order to
show this we expand the squares of equation (9) and consider sepa-
rately the terms:

S a Og Oh 49 oh of 49 of Oy ) j aa
| =-f PEPPEN: IE ee
Og Oh Og Oh Oy Oh
dz Oy dz dy | Oz dy
partially according to z, the second according to y. The surface inte- .

For 2 we write and integrate the first term

erals vanish again and we get:

3 ml 07h : O74 ‘ 077 027 j Og 077 :
S= + |t Hop: Has + tans Tamy Hal

Sr a LN
| =|} J Ove (= 1e Oz v9 Oy de Ku =) ole Ow Si dy | dr. (24)

OF
sa— {| f55 dt. ° . ° 5 en 9 s 5 ; . ; k k (25)

By integrating once more partially, where onee more the surface
integrals vanish, we get:

EDE

so equation (21) is proved. Equation (22) is proved in the same way.

Three constants occur in the exponent 4 namely w, @ and 4. wis
a constant which must be chosen such, that integration of P over
all systems of the ensemble yields 1. The two constants @ and 4
determine therefore the state of the systems. This is connected with
the fact, that the nature of the radiation inside a closed surface, as
Lorentz*) has shown, depends besides on the temperature, also on
the charge of the electrons by which the radiation is emitted. The fact
that inside all bodies radiation of the same nature is formed, proves
that in all bodies the electrons have the same charge. The constant
quantity #4 must depend on that charge; it will therefore have the
same value for spaces enclosed within all bodies as they are found in
nature at least if the temperature is the same and its value would
for a certain temperature only be different, if we imagined walls
with electrons whose charge was different from those actually occurring.

1) Lorentz. Proceedings. Vol. II, p. 436,

( 31 )

Botany. — “On the prussic acid in the opening buds of Prunus.”

By Prof. B. Verscnarrent, (Communicated by Prof, Hugo

DE VRIES).

During last winter and the spring of 1902 I made a series of
determinations to ascertain the amount of hydroevanie acid which
can be prepared from different organs in species of Prunus. They
were untertaken with the view of investigating the changes that
occur during the budding, regarding the prussic acid-compounds.
In these analyses the titration-method of Lrepig was always used in
the following manner. The parts of the plants to be examined — mostly
D_— 15 vers. freshly gathered material, — were heated in 200—300 em?
of water to 60° C., so as to kill the protoplasm without destroying
the emulsin. Though it will directly be shown that this treatment
answers the purpose, the heating to 60° was repeated after some
hours or the next day, to be certain that no cells were still living.
Between both treatments and also during 24 hours after the second
heating, the organs remained, immersed in water, in a well corked
flask, that the emulsin might have time to splitcompletely the HCN-
glucosides. After that, the distillation was performed, the prussic
acid being collected in a little flask containing some drops of KOH-
solution, and the titration was made after the method deseribed in
the treatises, with */,, normal nitrate of silver. The distillate was
always collected in a flask of 100 em.” capacity; by taking with a
pipette a known volume, I was able to repeat the titration two or
three times in the same experiment. The quantities of plant-material
and water being as above, it appeared without exception that the
whole of the prussic acid had been condensed together with the first
100 em.” of water.

The necessity of allowing the objects to macerate for some time
after the killing is clearly shown by the following preliminary
experiment.

From 25 leaves, one year old, of Prunus Laurocerasus (Bot. G.
Amsterdam) gathered 9. 12. Ol. the halves of the blades were cut
on each side of the middle-nerve. The halves a weighed 11,85 ers,
the halves 5 11,35 ers. The first portion was immediately submitted
to distillation after having been immersed in the proper quantity of
water, and gave 0,0160 grs. HCN. The portion 4 was heated to 60°
C., and remained under water till the next day ; this time the amount
of HCN was 0,0254 gr. As soon however as both portions are
treated as 6, the concordance of the results is very satisfactory :

( 32 )

12,12. 01: 2b Lea 7030225 yar) 0. C0226. eT: HCN
43: 4912.01. 2b lea O05 1S wrs a Os0501 ten AEN:
10,1: 902) 25 AS va 0;0288 er. 1D: 0 0242 ror. HON,

Le

In the same manner. it could be ascertained that it was quite
sufficient, after killing at 60°, to macerate during one day only, to
obtain a complete splitting of the glucoside; also that the heating in
200—300 em.” at 60°, at two different times or even once, had
left no living portions in the plant-organs.

The species studied were Prunus Laurocerasus L. and Prunus
Padus L. It was chiefly my intention to follow the changes undergone
by the prussic acid-compounds during the opening of the leaf-buds.
As of both above named species the second is the earliest, and also
yielded shoots a long time before the cherry-laurel, when cut bran-
ches were placed in the hot house, it was with P. Padus that the
most complete experiments were made, those with P. Laurocerasus
rather serving to control the former.

In the very first place, I asked myself the question whether the

amount of HCN in resting buds — whatever might be the form of
combination — did exhibit changes, when the buds began to grow.

To know this, the estimation of the percentage in buds and young
shoots issued therefrom is insufficient; one must compare the absolute
quantity of prussic acid contained in a given number of buds with
the amount in a same number of shoots. As the dimensions of both
the buds and the shoots vary considerably, a satisfactory medium-
value could only be obtained by the analysis of a great number of
these objects, a precaution already made necessary on account of the
buds being small.

The amount of HCN contained in resting buds of P. Padus will
appear with sufficient exactness by the following three estimations:

10. 2. 02. 195 buds (Bot. G. Amsterdam); weight: 4,80 er.-HCN:
0,0067 er, i.e. 0,14 °/,; in 100 buds: 0,0034 gr.

11. 2. 02. 280 buds (B. G. Amsterdam); weight: 6,35 gr.-HCN:
0,0094 er, i.e. 0,15 °/,; in 100 buds: 0,0034 er.

20. 3. 02. 100 buds (B. G. Amsterdam; the buds are about to
open, many show a green top); weight: 2,75 gr.-HCN: 0,0040 er.,
ie: 0,15 °/): an 100 buds: 00040 ser.

In the first two analyses, the buds, as always was the case with
the parts examined, in order to avoid losses of hydroeyanie acid,
were immersed in water without being cut into fragments, and killed
by heat. However, as it might be feared that the bud-scales should
hinder the diffusion of glucoside and enzyme, the buds were, in the

Kd

( 33 )

third experiment, cut in halves, to see whether they should yield
more HCN. As no marked difference was to be noticed, there surely
was no prussic acid that in the first two instances had remained
unestimated.

It was presently the turn of the opening buds to be studied. On
the 2% of February cut branches of P. Padus, dipping in water, were
placed on a well lighted spot in the hot house, the temperature being
circa 20° C. After some weeks, a great number of buds had opened,
and yielded shoots, which, though short, were nevertheless well fur-
nished with leaves.

5. 3. 02. 75 shoots taken; weight: 5,20 er.-HCN: 0.0079 er, i. e.
0,15 °/,; in 100 shoots: 0,0105 er.

>

Cut branches placed in hot house 26. 2. 02.

14. 3. 02. 60 shoots; weight: 8,70 gr-HCN: 0,0108 er.; i.e.
0,12 °/,; in 100 shoots: 0,0180 gr.

When one considers the weight of the shoots examined, it will be
seen that in the second experiment they were more fully developed
than in the first. It is clear that, as the shoots go on growing, a
steadily increasing absolute amount of HCN-compounds gathers therein,
so much so that even at a very early stage they contain three
to four times the quantity found in the resting buds. As, on the
other hand, the percentage of prussic acid depends on a number of
circumstances, chiefly on the proportion of water in the shoots, a
factor which itself is so very lable to modification, the changes under-
gone by this relative amount of HCN are much less interesting. It
will however be noticed that, notwithstanding the fact that the weight
of the young shoots exceeds many times that of the buds, the per-
centage of prussic acid is but feebly or not diminished.

I should wish to recall here that Adm. and Lm. Tuma *), estimating
the HCN in young leaf-buds of P. Padus, while these were opening
in April, found no higher proportion than 0,05 °/,. This undoubtedly
is due to the fact that the authors, distilling off after having added
some sulfuric acid, did not obtain a complete splitting up of the
elucosides.

It will now be asked, whether the prussie acid which appears in
the growing shoots is formed in the same, or perhaps transferred
to them from the branches. As the green unfolding leaves will very
probably begin to assimilate, it seems credible enough that the hydro-
eyanic acid should be made by a process of “photosynthesis”. Whether

1) Zeitschr. Allgem. Oesterr. Apoth. Ver. 1892, p. 330.

Proceedings Royal Acad, Amsterdam. Vol. V,

( 34 )

this is the case or not will easily be ascertained by analysing shoots
developed in the dark.

Branches of P. Padus, placed in the hot house 10. 2. 02., covered
by a blackened box. After some weeks, numerous etiolated shoots
had been developed.

5. 8. 02. 50 short shoots taken; weight: 5,40 er.-HCN: 0,0061
er, i.e. 0,11 °/,; in 100 shoots: 0,0122 gr.

Branches put in the dark 24. 2. 02.

17. 3. 02. 30 well grown, etiolated shoots, for the most part } —
1 dM. in length; weight: 7,90 gr.-HCN: 0,0054 gr; i.e. 0,07 °/,;
in 100 shoots: 0.0180. gr.

There can be no doubt, from the results given above, that shoots
erown in the dark also contain a much larger quantity of HCON-com-
pounds than the resting buds, and that these substances cannot have
been built up by an assimilatory process, under the action of sunlight.

Results of quite the same kind were obtained in studying prunus
Laurocerasus.

Resting buds.-28. 12. Ol. 115 buds, mostly axillar (from the growers
of medicinal plants GROENEVELD and Linprour, at Noordwijk); weight:
1,65 er.-HCN: 0,0040 gr; i.e. 0,24 °/,; in 100 buds: 0,0035

Shoots developed in the light (also mostly from axillar buds).-24. 4.

or.
02. 50 shoots, still short, eut from the shrubs growing in the Botan.
G. Amsterdam; the pale green leaves are not quite unfolded; weight:
9,30 gr-HCN: 0,0278 er, i.e. 0,30 °/,; in 100 shoots: 0,0556 gr.

27. 4. 02. 50 shoots, younger than the former, or newly opened
buds; weight: 4,90 er-HCN: 0,0138 gr.; 1. e. 0,28°/,; in 100
shoots: 0,0276 er. *)

Etiolated shoots. — Branches of P. Laurocerasus (B. G. Amsterdam)
placed in the hot house, under blackened cylinders 23. 4. 02.

10. 5. 02. 5 shoots taken; weight: 2,25 gr.-HCN: 0,0047 er. ;
i. e. 0,21°/,; in 100 shoots: 0,0940 gr.

Branches in the dark 25. 4. 02. 4. 5. 02. 10 very short shoots; weight:
1.65 er-HCN: 0,0087 gr. i. e. 0,22°/,; in 100 shoots 0,0370 gr.

Branches in the dark 27. 4. 02. 12. 5. 02. 11 shoots; weight:
4.70 egr.-HCN : 0,0083 gr.; i. e. 0,18°/, ; in 100 shoots : 0,0755 gr. *)

1) A. J. van pe Ven. (Cyaanwaterstofzuur bij de Prunaceae. Dissertation
Amsterdam. 1898; also Archives Néerlandaises, 2e Série, tome II, 1899 (reports
(p. 34 resp. p. 391) for young shoots 0,19-0,23"/.

2) Van DE Ven (1. c. p. 37 resp. p. 393) applying the test of Gresnorr—TRevs,
was not able to detect prussic acid in etiolated shoots of P. Law ocerasus, This
affords a new proof that microchemical reactions, as soon as the substarces are
not very abundant, necessarily require analytical confirmation. Mostly so when the
test yields negative results.

( 35 )

Referring to what has been said with relation to P. Padus. the
above given results require no further discussion. That in both
species the percentage of HCN appears to be smaller in the etiolated
shoots than in the green ones, has no very great importance. Etio-
lated shoots indeed are known to contain much more water. the
evaporation being less active under the opaque bell-jar.

After it has thus been shown that buds opening in the dark also
increase, as they grow, their amount of HCN, there still remain two
ways of accounting for this augmentation. Perhaps the prussic acid —
in whatever form it may be present — is made in the growing shoots
out of other substances ; it could however be drawn from other parts
of the plants; that is to say the branches in P. Padus, possibly also
the leaves in the evergreen P. Laurocerasus. I regret not to have
succeeded in establishing with certainty which of the two explanations
is the right one. All I can say for the present is that the HCN
gathering in the shoots is not derived from the internodes, which
bear the buds examined. However, the possibility of the acid being
supplied by more distant parts cannot at the present time be said to
be excluded completely.

In this part of the. research, I again chiefly made use of P. Padus,
as this species, bearing no leaves in winter, was especially favourable.
The point to be ascertained was whether the increase of HCN in the
opening buds should be accompanied by changes in the adjacent
internodes.

In the first place the amount of HCN was determined in the inter-
nodes below resting buds. As the length and thickness of these organs
are exceedingly variable, it once more was necessary to analyse a
not too small portion of plant-material.

10. 2. 02. 100 internodes (Bot. G. Amsterdam) ; weight : 11,75 er.-
HCN : 0,0108 gr, i. e. 0,09°/, ; in 100 internodes: 0,0108 er.

7. 3. 02. 250 internodes (B. G.); weight : 18,95.-HCN : 0,0246 er. ;
i. e. 0,13°/,; in 100 internodes : 0,0098 gr.

With these amounts will be compared those observed in the inter-
nodes below etiolated shoots.

Branches (B. G. Amsterdam) placed in hot house 24. 2. 02., and
covered by opaque bell-jars.

17. 3. 02. 30 internodes are taken from below long etiolated
shoots; weight: 3,85 gr-HCN 0,0057 gr; i. e. 0,15°/,; in 100
internodes : 0,0190 er.

Already this first experiment does not prove in favour of the view,
that the HCN-compounds should be drawn from the adjacent inter-

3*

( 36 )

nodes. That this really is not the case will clearly be shown by the
further analyses, in which were examined, on the one hand resting
buds, on the other etiolated shoots, both with the corresponding
internodes.

Resting buds —18. 2. 02. 80 buds Z. Padus (Bot. G.), and inter-
nodes bearing them; weight: 8,80 gr.-HCN : 0,0121 er. ; 1. e. 0,14°/, ;
me tO00250,0151 er.

18. 2. 02. 125 buds and internodes; weight: 9,90 gr.-HCN :
0,0159 gr. ; i. e. 0,16°/,; in 100: 0,0127 er.

21. 3. 02. 100 buds and internodes (the buds beginning to open
at the top for the greater part); weight: 8,35 gr.-HCN : 0,0092 er. ;
ie. 0,11°/, ; in 100: 0,0092 gr.

29. 3. 02. 127 buds and internodes (eut on other shrubs as the
foregoing ; buds about to open); weight: 13,30 gr.-HCN : 0,0125 er. ;
Loe, O09")? sin L00 + 0,0008 “er.

Young shoots. — Branches placed in the dark 24. 2. 02.

17. 3. 02. 30 shoots and internodes; weight: 11,75 gr. HCN:
00144. er ie. 0,09°/, ; mi! 100: 00370 er.

Branches in the dark 24. 2. 02.; 25. 3. 02. 25 shoots and inter-
nodes; weight: 5,05 gr.-HCN: 0,0051 gr; ie. 0,10°/,; in 100:
0,0204 er.

The considerable increase in the quantity of prussic acid: two to
three times the original amount, shows clearly that it has not been
augmented in the shoots at the cost of the internodes immediately
belonging to the buds. I can even go farther, and suggest that
neither it can have been supplied by the more distant internodes,
one year old. In the analyses of shoots with the adjacent internodes,
as well as in the experiment with internodes only, the material was
taken from twigs developed the summer before, which in the experi-
ment had yielded shoots at different heights. Therefore, if the more
basal internodes had furnished the HCN-material for the shoots nearer
the top, then the estimations would have shown it, since in that case
so great an increase as was noticed would have been impossible.
If consequently during the growth of the young shoots prussic acid
might be drawn from the branches, it could be only from the older parts.

I should have liked very much to establish with certainty whether
the shoots form themselves the hydrocyanie acid they contain. For
that purpose I several times analysed branches of P. Padus as well
as of P. Laurocerasus, so as to determine the amount of HCN pre-
sent in the entire branches, before and after the opening of the buds.
These estimations however did not yield satisfactory results, because,
when the branches used were small, the buds in the dark only gave

( 37 )

short shoots, containing too small a quantity of HCN, and the diffe-
rence between the two portions compared lay within the range of
individual variation. If on the other side one will use larger branches,
it is exceedingly difficult to choose two portions which can be compared;
the limits of error of the experiment presently widen, and consequently
the desired end is not reached. The experiments on branches longitudi-
rally cut in two, which were undertaken with P. Laurocerasus, one
moiety being immediately analysed, the other one, bearing the buds,
being put in the dark till it had given off etiolated shoots, failed for
the same reason. In consequence this question must remain unan-
swered for the present; perhaps experiments to be made next spring
with rooted cuttings will meet with more success.

1 will now endeavour to show that the cherry-laurel behaves in
so far quite like P. Padus, that the parts situated immediately below
the growing shoots retain their percentage of HCN nearly completely
unchanged. Here the experiment becomes in a certain degree com-
plicated, but also on the other hand is made more interesting, by the
presence of the leaves. Therefore L must begin to tell something
respecting the amount of HCN in these organs.

They have been analysed several times for pharmaceutical purposes.
I only will recall here that FrücxKiGer *) gave as the average of esti-
mations, protacted during ten years, on cherry-laurels growing
on the banks of the lake of Thune, 0,12°/, of the weight of
fresh leaves. Folia Laurocerasi, bought in December and January
from GROENEVELD and Linpnout, yielded O,14—0,16°/,, while the
shrubs grown in the Botanical Garden at Amsterdam were found to
contain in their leaves an amount ranging from 0,12 till 0,21°/,,

0°?

according to the individual analysed. Those were at least the quantities
found in the course of the season December—May. The last named
high figure is regularly yielded by the leaves of a certain shrub,
that consequently could if wished be made the starting point of a
selection to obtain a race containing much prussic acid.

It also may be of importance to acquire an idea of the absolute
quantity of hydroeyanie acid contained in one leaf. Of course, owing
to the variable dimensions of these organs, this quantity also varies

considerably. L found 0,0015 — 0,0036 gr. HON, the maximum-value
in large leaves supplied by GROENEVELD and Laxpnoer, with a per-

centage of 0,15°/,. ,
Before studying the modifications in the amount of HCN in the

1) Pharmakognosie des Pflanzerreichs. de Aufl. 1891 p. 766.

leaves, brought about by the opening of the buds, also in the dark,
one should know the changes caused by the occlusion of the light,
independently of the formation of shoots. I properly ought to have
done the same with the twigs of P. Padus, but nobody will, I trust,
expect that these organs, with their peridermal coating, should show
energetical processes of assimilatory kind.

The experiments with P. Laurocerasus took place not only with
cut leaves, but also with branches bearing leaves. To examine
Whether cut leaves should change in the dark their amount of HCN,
the halves of the freshly plucked organs were cut off along the middle-
nerve and killed immediately. The other halves, with the middle-nerves
still adhering to them, were brought in the hot house, and placed,
under blackened bell-jars, in a glass, the petioli dipping in water. At
the end of the experiment, the middle nerves were cut off, and the
remaining halves of the blades analysed.

It appears that by staying even a fairly large number of days in
the dark, the leaves undergo no modification whatever as regards
the amount of HCN, at least not in winter *).

25 leaves (Noordwyk). 13. 12. O1.

Halves @ analysed immediately: HCN: 0,0155.

Halves 4, after staying in the dark till 29.12. 01., HCN: 0,0142 er.

25 leaves (Noordwyk).

Halves a: 13. 12. 01., 0,0357 er. HCN.
Halves 6:95 od 03 10 035 Leer. IEN:

It follows that even after about one month no change whatever is
to be noticed. Recently F. F. BrACKMAN and G. L. C. MarrHarr ®)
have shown that the leaves of the cherry-laurel remain fresh and
living in the dark even after fifty days. On the other side, the results
given above quite agree with those obtained by A. J. vaN DE VEN ®),
using microchemical methods.

=

However, after a longer stay in the dark, or even, in certain cases,
at a temperature of 20° C., after a shorter stay, pathological changes
become noticeable in the leaves. Yellow spots, originating along the
middle-nerve and the more important side-nerves, cover by and by the
surface of the leaf till it becomes uniformly yellow. However, these
organs don’t die at once; they remain fresh many days, but the
analysis shows that they lose rapidly their hvdroevanic acid.

1) J. Corarp: (Journal de Pharmacie de Liège, 2e année, 1895 p. 1) states that
leaves of cherry-laurel, when the entire shrubs remained in the dark from May
till August, yielded a percentage of HCN, somewhat inferior to the percentage in
plants exposed to the light.

2) Annals of Botany, XV. 1901, p. 553.

8) Dissertation Amsterdam. 1898, p. 35. Archives Neerlandaises, 1. c. p. 392,

. En

( 39 )

25 leaves (Noordwyk).
Halves @: 20. 12/01. 0,0165 er: HCN.
Halves 6: 7. 1. 02, (beginning to show yellowstreaks
along the nerves): 0,0142 gr. HCN.
20 leaves (Bot. G. Amsterdam).

ere ate. Oa teh ow Te ORG oor: HEN:

b: 9. 5. 02. (yellow patches) 0,0113 or, HCN.
25 leaves (Noordwyk).
OPOLE ver 0268 ore HON,
b: 20. 1. 02. (yellow) 0,0089 gr. HCN.

25 leaves (Bot. G. Amsterdam),
mh keer cs). OO28S. Se CN:
G: 20. 4 O2 (yellow) 00,0067 gr. HCN.

Just the same processes can be observed, when cut branches bearing
leaves are placed under opaque cylinders. The leaves can remain
fresh and green many weeks, and keep their amount of HCN unal-
tered. The halves « of the blades were analysed immediately ; the
halves 6 remained, adhering to the middle-nerve, on the branches
till the end of the experiment.

25 leaves, from branches placed in the dark 5. 12. Ol.

me ao OL. OCO2 ZOET iG:
6: 22. 12. O1. 0,0283 gr. HCN.

25 leaves, from the same branches (5. 12. O1 in the dark).

31. 12. O1.; halves cut off; the other ones remain on the branches.

a: 00,0243 er. HCN.

b: 16. 1. 02.; remaining halves yellow ; it appears that in this
stage they fall off, or sit but loosely on the branches : 0,0196 gr. HON.

3ranches placed in the dark 17. 12. 01.;

1. 1. 02.; 10 yellow leaves, about to be dropped; weight:
17,65 er.-HCN: 0,0094 gr; i. e. 0,05 °/,.

From the same branches I took the same day 25 fresh green
leaves, and cut off the halves; weight: 13,15 er.-HCN: 0,0229 er,
epee OT */

Halves 4; 14. 1. 02 for the greatest part yellow, and falling off
— HCN: 0,0155 er.

This experiment therefore is also of importance, because it shows
how the diminution in the amount of HCN goes clearly together with
the discoloration and dropping of the leaves, and does not directly
depend upon the length of the stay in the dark. In fact, when I
placed separated branches in the hot house, but exposed them to the
light, there always were a certain number of leaves that became

( 40 )

vellow ; and in those the amount of HCN could also be shown to
have diminished considerably.

Branches in hot house 26. 12. Ol. Leaves yellow and falling off
22. 1. 02. ; weight: 20,10 gr-HCN: 0,0089 er.; i. e. 0,04°/,.

Moreover, the same is the case with certain leaves directly taken
from the shrubs grown in the Botan. G.

27. 4. 02.; 15 yellowish leaves are picked; weight: 24,95 er
HCN: 0,0158 gr. ; i. e. 0,06°/, ; in one leave: 0,0011 er.

The figures for fresh leaves, mentioned formerly, show that but a
small part of the HCN normally present had been retained here.

As the hvdroeyanie acid was also observed to disappear from the
cut leaves, when they became yellow, it seems very probable that
this substance — or its Compounds — are not transferred from the
leaves to the branches, but must have undergone a chemical trans-
formation.

The budding however, at least in the first periods that I examined,
has no influence whatever on the quantity of prussic acid in the
leaves and twigs. For instance, 30. 4. 02 were gathered, on the
cherry-laurels of the Bot. G. Amsterdam, 10 leaves, one year old,
each being inserted below a well grown young shoot; weight:
11,60 gr.-HCN: 0,0251 er.; 1. e. 0,22°/,; in one leaf: 0;0025 er:
These figures are of quite the same order as were yielded in December
by the same shrub. 30. 4. 02 also were cut, below opening buds,
twigs one year old; I chose intentionally twigs which though they
bore numerous, and fairiy big shoots, had no more leaves, these being
cut or having fallen off at an earlier period, before the budding ;
weight: 8,25 er-HCN: 0,0086 ger, i. e. 0,10 °/. I have found
however, in twigs one year old, taken from the different shrubs in
the Bot. G., during winter, a percentage of HCN ranging from 0,06
till O11 °/,. It is clear that there was no diminution after the opening
of the buds.

Neither was this the case after the budding in the dark. Branches
having been placed in the hot house, under darkened boxes, 29. 4. 02,
leaves were cut 4. 5. 02, below etiolated shoots. The percentage: 0,14°/,,
was the same as leaves from the same shrub had yielded before.

Finally, it could be shown in P. Padus that, though the young
branches issued from the winter buds are already considerably deve-
loped, and bear numerous leaves of fair size, the amount of HCN-
compounds in the internodes below is still the same as before the
budding.

This was observed 25. 4. 02, when 130 internodes of P. Padus,
from the year before, were taken below long shoots, well furnished

a

CAL )

with leaves; weight: 10,90 gr-HCN: 0,0140 gr; i. e. 0,13 °/ ;
in 100 internodes: 0,0108 er.

Resuming, [ am brought to the conclusion that in both species of
Prunus examined (P. Padus and P. Laurocerasus), when the buds
open, there appears in the shoots growing from them a steadily
increasing absolute quantity of HCN-compounds, whereas the percentage
changes little in the period examined. In this same period at least,
and at any rate for a great part, these substances appear independently
of the light. Neither is this prussic acid drawn from the internodes
directly bearing the buds, and developed the year before. Whether
it is supplied by more distant organs, or is formed in the growing
twigs out of other substances, this remains to be shown.

It is also still a point of research in what form the prussic acid
is contained in the growing paris. That it is necessary to macerate

‚the killed organs before the total amount of hydrocyanie acid can be

distilled off, speaks in favour of the presence of a compound that
can be split up by an enzyme. Moreover, as the liquid distilled from
etiolated as well as from green shoots of P. Padus and Laurocerasus,
has an intense smell of benzaldehyde, it is very probable that these
organs also contain glucosides of the amyedalin-ty pe.

Physics. — “Observations on the magnetic rotation of the plane of pola-
risation in the interior of an absorption band”. By Prof. P. Zeeman.

1. The difficulties of a complete theory of emission are partly
avoided in a treatment beginning with the absorption, and this may
have been the reason why Vorer') has followed this procedure,
though it must be granted that in his method an explanation of
the mechanism of the phenomenon as in LorENtTzZ’s theory cannot be
given ®). In Vorer’s theory the separation of a spectral line by the
action of a magnetic field is found as the separation of an absorp-
tion line.

Some particulars in this separation were anticipated by this theory *)
and confirmed by experiment *).

1) Voiet. Wied. Ann. 67, p. 345, 1899.

2) For a comparison of the advantages of the theories of Lonenrz and of Vota,
see Lorentz. Rapports, congrés, Paris T. [IL p. 16, 33, 1900. en Phys. Zeitschr. 1
p.:39, 1899. cf. also Puanck. Sitz.ber. Ak. Berlin, p. 470, 1902,

5) Vorer. Drude’s Ann. 1, p. 376, 1900.

4) Zeeman. Versl. Akad. Amsterdam. Dec. 1899, Archiv. Néerl. (2), 5, p. 237.

(42)

The long since known phenomenon of the rotation of the plane of
polarisation and the magnetic separation of the spectral lines were
closely connected *).

One result however of Voier’s*) theory relating to the rotation
of the plane of polarisation in the interior of an absorption band
seemed to be in contradiction with the results of CorBINO *) or at
least were not confirmed by the experiments of Scumauss*) The
theory of Vorer requires a negative °) rotation of the plane of polarisation
in the interior of an absorption band, CorBrxo however only succeeded
in observing a very small positive rotation.

It would be very remarkable however, if there existed a disagreement
between theory and observation in this special field so closely con-
nected with other well understood phenomena.

I have been experimenting already some time on this subject. In
executing these experiments I have been aided in an excellent manner
by Mr. Harro.

I have succeeded in observing a negative rotation in the interior
of an absorption band, the results of my observations being in perfect
qualitative agreement with Vorer’s theory.

2. The method used in the following observations on the rotation
in sodium vapour is principally the same as that which has been
used by Vorer®) in his demonstration of the double refraction of
sodium vapour placed in a magnetic field. Already Hvussen’) used it
in a determination of the naturel rotation of the plane of polarisation
in quartz, and also Corpino in his first experiments on sodium.

By means of a system of quartz prisms (as has been used by
FresneL in his experiment on the division of a plane-polarised ray
into two circularly polarised rays) a number of horizontal interference
fringes are formed in a spectrum. The light traverses the prism in
the direction of the axis and the edges are horizontal and perpendi-
cular to the slit of the spectroscope. The prism system (length 50 mm.)
was placed in my experiments as near as possible before the slit of
spectral apparatus and a small Nicol, used as analysator, behind the
slit. The polarising Nicol was placed, of course, before the eleetro-

1) cf. also Larnwor. Aether and Matter, p. 203.

2) Vorer. Ann. der Physik. (4), 6, p. 784, 1901.

5) Corpino. Atti R. Ace. dei Lincei. Vol. 10 p. 137, 1901, Nuovo cimento
Febbraio 1902.

') Scumauss. Ann. d. Phys. 2 p. 280, 1900.

5) The magnetic rotation in the vicinity of the band is positive in sodium vapour,

6) Vorer. Wied. Ann. 67, p. 360, 1899.

1) Husser. Wied Ann. Bd. 43, p. 498, 1891,

( (fo)

magnet (of the RuamKorrr type). The spectroscope was a Row1anp’s
erating, for which I am indebted to the kindness of the Directors of
the Dutch Society of Sciences at Harlem; it has a radius of 6.5 M.,
10.000 lines to the inch and a divided surface of nearly 14 em.

The grating was mounted for parallel light in the manner indicated
by Rurer and Pascuen'). The source of light was in most eases the
electric are, in some the sun.

Using this arrangement of the experiment we can deduce immediately
from the deformation of the interference fringes in the neighbourhood
of the absorption bands, when the sodium vapour is under the action
of the magnetic field, the value of the rotation of the plane of
polarisation for different wave lengths. Fig. 1 of the Plate gives an
idea of the aspect of the fringes in absence of the field in the
neighbourhood of the sodium lines, rather much sodium being present
in the flame between the poles. The observations were made in the
second order.

3. In the experiments first to be described, the distance between the
perforated poles was about 4 m.m. and the intensity of the field about
15.000 ¢. g. 8. units. In this field was placed a gas flame fed with oxygen
and a small quantity of. sodium introduced in it by means of a glass
rod. After removal of the polarisator and of the FRrSNer prism the
two doublets, in which the sodiumlines are separated, in the inverse
magnetic spectral effect were observed. Between the components of
the doublet were seen the very narrow reversed sodiumlines due to
the are light itself.

The polarisator and the prism were now introduced in their proper
places. The field of view was then crossed by the above mentioned
(2) dark, nearly horizontal interference fringes.

IT now wished to ascertain the deformation of the fringes by
increasing continuously the quantity of sodium vapour, the field
remaining constant. This method must be preferred for obvious
reasons to the other which might: have been followed also, viz: the
examination of a flame with constant percentage of sodium under
varying magnetic intensities.

The following observations refer to D, :

If the quantity of sodium in the magnetic field was only extremely
small, the interference fringe exhibited at the place of the reversed
sodium line a protuberance — let us say downward — the lines
of the doublet being somewhat stronger just above the interference
fringe. In fig. 1 this behaviour is represented schematically.

C

( 9

Big. 1. Fie.

bo

Fig. 3.
Increasing now the quantity of sodium (always remaining very

small however, absolutely) the interference fringes moved upward
along the components of the doublet, whereas the part of the fringe
between the components seemed no longer connected to the exterior
fringes and accepted the shape figured schematically in fig. 2.

Increasing still further the density of the vapour the interior part
of the fringe slid downward with increasing velocity and then
resembled an arrow with point directed upward, the parts more
removed from the medium line fading away and disappearing (cf, the
schematic fig. 3). At last the arrow entirely disappeared by the
increase of the density of the vapour. It then became impossible to
distinguish the fringes or any trace of structure in the field between
the components. Rather much light was transmitted. The entire
width of the components of the doublet was now about of the same
order as the distance of their central lines. ;

A further increase of the quantity of sodium obscured the central
part more and more (see further (8)).

The exterior fringes moved continuously upward while the density
was being increased.

In a field of about 20000 units the downward displacement could
be followed over a distance of more than the double of the distance
between two. fringes, corresponding to a negative rotation of above
2 x 180°, say 400°. The distance between the poles was 4 mM.

Some more accurate data will be given on another occasion.

In the case of D, the phenomena were in the main of the same
character.

For D, it was however characteristic that the stage of the nearly
or entirely vanishing of the interior fringes was reached with smaller
field, whereas also the shape of the interior fringe differed from the
one observed in the case of D,. Hence there exists also in this case a
difference between J), and D,, a difference already known to exist
in the phenomena of reversal, of the separation by a magnetic field
and of the rotation of the plane of polarisation in the vicinity of
the absorption band.

4. It appeared possible to keep stationary each of the stages des-
eribed in (8) during a considerable time. Excellent photographs could be
secured with plates which were sensitised for yellow light with erythro-
sine silver. Instead of the gasflame fed with oxygen it was easier,
in the ease of greater distances between the poles, to use a Bunsen
burner wherein common salt was introduced.

5. If the density of the vapour was maintained as constant as
possible and if it and the fieldintensity corresponded to the eireum-
stances represented in fig. 3 (3) then an merease of the field gave
a motion of the arrow (fig. 3) (3) upwards, corresponding to a decrease
of the negative rotation and reciprocally. It was possible to observe
by eye observation very clearly this decrease when the field was
changed e.g. from 18000 to 25000. If the circumstances were more
in accordance with fig. 2 (3) then the same change of field produced
a change only just perceptible of the negative rotation but in the
same sense as mentioned in the case of fig. 3.

An enlarged reproduction of one of the photographs is shown
in fig. 2 of the plate. The distance between the poles in this experi-
ment was 6,3 mM., the field intensity about 14000 °). The negative
rotation in the case of D, is somewhat less than 90°. In the case
of D,- yet only some traces of the interior fringes can be seen (3).
The negative rotation is ‘about 180°. In the photograph are seen
also the reversed very narrow J,-line and the broader D-line,
which are due to the are itselfand have nothing to do with our subject.

6. The observations (3, 4, 5) agree qualitatively in an excellent
manner with the conclusions from Vorer’s theory. According to it,
the negative rotation must be of the same order of magnitude as the
positive one. This last was known from Macatuso’s and CorBrxo’s
experiments to be very great. The enormous value and the sign of
the negative rotation given in (38) may thus be regarded as a beautiful
confirmation of the theory.

As much is this the case with the direction (5) of the change of
the negative rotation with increasing field. In order to see this we
| cht
9
( = fieldintensity, c and 9 parameters of the absorptionband), for

must know the value of the quantity occurring in the theory ? =

which the comparison must take place. It was possible to assign a
value to P by comparison of the phenomenon with Vorert's figure 1 *).

1) The intensities of the field were measured by means of a bismuth spiral in
the centre of the field. Probably the values given are somewhat too high. Measure-
ments of the magnetic change of the spectral lines give lower values,

2) Annalen der Physik, 6 p. 789, 1901.

( 46 )

This figure gives ny, (y, angle of rotation, 7 a mean value of the

index of refraction) as function of a certain variable 4, whereas our
phenomenon is a representation of %, as a function of 2. Reducing
the abseis of the mentioned fig. 1 to */,, or */,, we obtain diagrams
resembling in the main features fig. 2 of the Plate. To the
greater observed negative rotation (3) correspond values of , which
can be estimated at 5 or 8. The smallest easily observed rotations in
the used strong field are probably in the vicinity of the critical value
Pe tid.

7. The slope of the exterior interference fringes is greater towards
the side of the greater wavelengths than towards the violet, at least
so far as the rotation due to one band does not influence visibly the
rotation due to the other. At the same distances, if not very small,
of each of the two YD lines the rotation at the side of the violet is
greatest. The interior fringes also show a slight asymmetry, so e. g.
the point of the arrow in fig. 3 (8) ought to be asymmetrical. The
part at the side of the violet is predominating.

It is clear that these phenomena depend upon an asymmetry of
the dispersion curve.

8. With very dense sodium vapour, hence under circumstances
which are beyond the last stage of (5), 1 observed phenomena very
probably identical with those observed by CorBiNo. In my first expe-
riments with those dense vapours I thought it absolutely necessary
for securing sufficient intensity to widen the slit beyond the width
used in the already given- experiments. I now see however that
this is unnecessary.

Using these very dense vapours one sees in the absorption banda
horizontal part of an interference fringe, which seems to have under-
gone a very small displacement wpwards by the action of the field.
These horizontal parts are more ill-defined and broader and the
whole phenomenon in the bands is darker than under the circum-
stances described in (3), (4), (5).

Figs. 3 and 4 of the Plate will give a clearer, impression of the
change in the phenomenon than a long description.

Fig. 3 was obtained with a field of 4500 units and much sodium.
I have made some measurements, according to a method not to be
given here, concerning the displacement of the central (in horizontal
and vertical direction) part of the interference fringe, and | have
found a displacement, which would correspond to a positive rotation
of about 8° with both D-lines. Fig. 4 was taken with a field of 10700
and much sodium. The exterior interference fringes are very clear
and much deformed; the rotation in the parts adjacent to the absorp-

P. ZEEMAN. Magnetic Rotation in the Interior of an Absorption Band

re emd EE mete = See

Ds D,

Proceedings Royal Acad. Amsterdam. Vol. V.

GL

tion band surpass 180°. The interior interference fringes are very
indistinet. Their appearance would suggest that in the case of D, in
Fig. 4 the stage has been scarcely surpassed, reached for D, in fig. 2.

This however cannot be the case because there was too much
sodium in the flame. A comparison with fig. 2 will show that the
lines are much broader in fig. 4. Measurements taken on other
negatives gave me for fields of 11000, displacements of about ‘/,, of
the distance between two fringes, corresponding to a positive rotation
of 11°. Hence the displacements in these eases are precisely of the
same order of magnitude as in CorBiNo’s experiments. The paleness of
the boarders of the band is easily accounted for by the remark that there
the intensity one of the circularly polarised rays largely exceeds the other.

I do not believe that these facts are in contradiction with theory.
It is true that it requires for very high values of P a value zero for
Wy), If we must take as the locus of the fringe the mean vertical
height, then really the rotation would be positive. It seems possible
that with those broad fringes the case is different. It is also possible
that the circumstances, assumed in the theory are not wholly realised
in the experiments with dense vapours. 1 am making some new expe-
riments about this subject and therefore shall not discuss further the
different possibilities.

EIA NATEON, OF THE PLATE.
The Plate gives about sixfold enlargements of the photographs.
Wig. 1. Interference fringes and absorption liaes in absence of the field and
rather much sodium. (2)

Fig. 2. Same lines. Field intensity about 14000, little sodium. (3) (5)
Fig. 3. Same lines. Field intensity about 4500, much sodium. (8)
Fig. 4. Same lines. Field intensity about 10700, much sodium. (8)

Anatomy. — “A new Method for demonstrating cartilaginous
Mikroskeletons.! By Prof. J. W. van Wise.

It is a well-known quality of cartilage that it firmly retains certain
anilinstains. Taking advantage of this quality, I have for some years
endeavoured to find a stain, which will remain permanent in the cartilage,
after it will have been entirely extracted out of the other tissues.
If the object is made transparent in canada balsam, the cartilaginous
skeleton will then be seen as if it were prepared. I was more or
less successful with most of the so-called basal anilin-pigments, best
of all however with methylene-blue, and so I was induced to use this
latter stain exclusively,

( 48 )

The coloring of the cartilage was attempted with full-grown objects,
as well as with embryos, but as the coloring-method is chiefly useful
when applied to small objects, with which the ordinary preparation-
method proves deficient, it will chiefly be applied to embryos.

Whenever we wanted to examine the cartilaginous skeleton of an
embryo, we were, up to the present time, obliged to make series of
sections and to construct an enlarged model after these sections, all
of which took up a good deal of time. As arule it would have taken
much too long to model a whole skeleton ; therefore in most cases
only a part was constructed, for instance the head-skeleton or
the pelvis.

Working on this plan a single object requires many months of
labor, and besides at the end you have not the object itself, but an
imitation.

Following the coloring-method, on the contrary, a great number
of entire skeletons are obtained in a short time with little trouble,
not clumsy imitations, but the objects themselves with all parts in
their natural connection and the contours of the whole embryo and
of different organs besides, for notwithstanding the transparency of
the organs the outlines of many are still clearly recognizable. Although
the cartilage is colored intensely blue, it remains transparent: so
for instance the spinal column glimmers through the shoulder-blade.

The method is as follows:

The embryo is fixed in the usual way in 5°/, sublimate-solution,
or 10°/, formol, or in ZeENKER’S liquid and is preserved in alcohol.
No doubt it may be fixed in many other ways; I even obtained
useful results with old preparations of alcohol from the collection.
I mostly fix the embryos in 5°/, sublimate-solution, to which is added
‘/,, Volumen formol, shortly before using.

The object may now be brought immediately from the alcohol
into the pigment-solution, but it has seemed advisable to me to extract
previously for a day or two with alcohol, which contains some
(*/,°/,) hydro-chlorie acid. The acid aleohol must be renewed if it
has turned vellow the next day, which often happens when iodine has
been used in extracting the sublimate. The iodine is fatal for the
coloring, as it forms with methylene-blue an almost insoluble preci-
pitate and with neutral alcohol the iodine cannot be quite removed.
This is proved when seemingly white objects, preserved for a year
and more in aleohol which has remained colorless, being brought
into acid alcohol, cause this liquid to turn yellow the next day. The
yellow color disappears after the addition of a few drops of sublimate-
solution,

( 49s)

From the acid alcohol the object is placed for a day at least, rather
for a week, into an alcoholic solution of methylene-blue, to which
1°/, hydro-chloric acid has been added. It is sufficient when 1/, gram
of methylene-blue is dissolved in 100 ce. alcohol of about 70°/,. If
more coloring-matter is taken, a sediment remains on the bottom of
the bottle. After the addition of the hydro-chlorie acid, blue erystal-
line needles separate themselves from the liquid. For this reason it is
desirable that this addition should be made not at the moment of
using, but some time before.

The object when taken from the pigment, should not show
any sediment. If it does, it has not been extracted long enough
with acid aleohol. Although it is not lost yet, it may cost months
hefore the sediment is removed. The intensely blue-colored object
is treated in the usual manner in the above mentioned acid alcohol,
which is renewed several times on the first day and once daily
afterwards. The renewal is continued until the aleohol shows no
blue tinge the next day. The time required for this is, of course,
dependent on the size of the embryo. This time can be shortened
by taking alternately alcohol of about 70°/, and a stronger one and
hanging the object one day in the stronger alcohol, whereas the
next day it is allowed to settle on the bottom of the bottle; this
is not necessary however. In about a week the stain has been removed
from all the tissues, except from the fundamental substance of
the cartilage. It is not necessary anxiously to observe the day
when the alcohol shows no more coloring; objects kept for a year
and longer in the colorless acid alcohol, showed the cartilage still
distinctly blue. {

The object is now dehydrated in absolute alcohol, in the usual
way, and rendered transparent in xylol. To avoid wrinkles, it
is not put immediately from the alcohol into xylol, but first in
a mixture of two parts of absolute alcohol with one part of xylol,
then in a mixture of one part of absolute alcohol with two parts of
xylol and only after that in xylol only. Larger-sized embryos are
cut in halves or in different pieces with the razor. After that the
objects are put first in a thin, afterwards in a thick solution of
canada-balsam in xylol and finally in a solution, which in ordinary
temperature is solid, but liquid at 60°. In this solution they remain
in the thermostat at 60° during a couple of hours and are then
enclosed in glass-cells under a covering-glass.

The glass-cells in trade are usually too low, higher ones can easily
be obtained by fixing stripes of window-pane with canada-balsam
on an object-glass.

+

Proceedings Royal Acad. Amsterdam. Vol. V,

( 90 )

My experience has not been long enough to enable me to assure
that the objects will not fade in the long run, I ean only say, that
even my oldest preparations, which have been enclosed in canada-
balsam for a couple of years, have not faded visibly. I have taken
care however to dissolve in xylol the solid, neutral canada-balsam
of GRÜBLER’'s myself because the commercial solution often contains
turpentine.

The staining method here described has been suecessful with the
cartilaginous skeleton of representatives of all classes of vertebrate
animals, as for instance with Amphioxus, with embryos of sharks
and rays, of salmons and roaches, of frogs and lizards, of birds, of
mice, rabbits and man.

With regard to man, it is of importance that the coloring can
still be suecessful with embryos in a far proceeded state of dissociation
and which otherwise one would be inclined to throw away.

Magnified slightly, the preparations are particularly suitable for
demonstration. I here demonstrate the skeleton of a human embryo
of about five weeks old and draw your attention to the rudiment of
the shoulder-blade. It is still exclusively adjacent to the neck, on a
level with the 5%, 6 and 7 cervical vertebrae, with the point
still above the first rib. Eleven ribs show the blue color of the
cartilage, the undermost, the twelfth, not yet.

In this second embryo, which is somewhat older, the shoulder-
blade has left the 5 cervical vertebra and lies on a level with
the 6 and 7 cervical- and the 1st and 2d thoracic vertebrae; it
reaches with its point as far as the third rib. Not only all the
twelve ribs are visible on the twelve thoracic vertebrae, the rudiment
of a rib on the last cervical vertebra is seen besides, which rudiment
fuses with this vertebra later on, as is well-known.

In this third embryo, which I received in perfect condition and
which after fixation was 25 mm. long in its natural curve, it may
be seen that the shoulder-blade has again gone down a little. At
the neck it does not reach higher than the level of the last cervical
vertebra and reaches with the point as far as the 4 rib. Further
the rudiment of the pelvis may here be noticed, on the level of the
fourth lumbar and the first sacrum-vertebrae and on the head the
cartilage of the occiput, the ear case, the cartilage of Meerrr and the
rudiment of the incus.

Other preparations show the paired rudiment of the rabbit’s and
the chicken’s sternum.

Also for macroscopic museum-preparations this is a suitable method;
I could show you, for instance, the cartilaginous skeleton of shark-

(51)

embryos more than 2 dm. long, preserved in xylol. These preparations
were exceedingly beautiful at first and the non-cartilaginous tissues
transparent, as clear as crystal; later on however they lost the
transparency for the greater part and became opalescent. The cause
of this change is unknown to me. Such macroscopic preparations
ought therefore also to be enclosed in canada-balsam or dammar-resin.

Chemistry. — “J/ntramolecular rearrangement of atoms in azory-
benzene and its derivatives.” By Dr. H. M. Kyrescuner. (Com-
municated by Prof. LoBry pr Bruyn.)

Watiach and Beru *) noticed a long time ago that azoxybenzene
is converted into its isomer p-azoxybenzene by gently heating it with
sulphuric acid, or by means of fuming sulphuric acid at the ordinary
temperature. BAMBERGER found that in this process there is also formed
half a percent of o-oxyazobenzene a substance discovered by him
some time ago when acting on nitrosobenzene with aqueous caustic
soda at 100°. The reaction noticed by Warract and Berrr must be
represented as follows :

N—N
REN

Sulphuric acid was up to the present the only reagent capable of

C,H C,H, > C,H, N—=NC, H, OH (1.2 and 1.4).

causing the said intramolecular rearrangement of atoms. W ACKER ®),
however, when stating in his paper on «-azoxynaphtalene that this
substance turns red by exposure to direct sunlight, also remarks that
azoxybenzene is likewise sensitive to sunlight, but he only mentions
that it turns deep yellow without having investigated the nature of
the change.

Various derivatives of azoxybenzene also appeared to be liable to
the same intramolecular rearrangement of atoms, but again sulphurie
acid is mentioned as the only reagent capable of causing the change.
The result of those investigations showed that some of the substitution
products, namely the meta-derivatives, are almost quantitatively con-
verted into the isomeric phenols, while the ortho- and para-derivatives
are only affected to a small extent or not at all.

1) Ber. 13. 525 (1880).
2) Ber. 38, 3192 (1900).
5) Ber. 33. 1939 (1900).
4) Ann. 31%. 313 (1901). N
4*

(52)

Scuuurz searcely obtained any dichloro-oxyazobenzene when treating
p-p-dichloro-azoxybenzene with fuming sulphuric acid, but p-p-dichloro-
azobenzene was formed ; m-i-dichloro-azoxybenzene however yielded
m-m-dichloro-oxyazobenzene in large quantity.

Krier and PrrscuKe ®) succeeded in almost entirely converting
m-in-dinitro-azoxybenzene into m-im-dinitro-oxyazobenzene by heating
the same with sulphuric acid at 140°. By heating 0-0-azoxytoluene
with sulphuric acid at 100°—120° they could only obtain 0-0-az0-
toluene accompanied by acids such as o-tolylazobenzoie acid.

Limpricut') converted azoxytoluidine into oxvazotoluidine in an
analogous manner, whilst ErBs and Scuwarz *) succeeded in converting
p-p-diamino-0-0-azoxytoluene into p-p-diamino-o-o-oxyazotoluene by
heating it with sulphuric acid at 100°—105°.

My object now was to ascertain whether the above described intra-
molecular rearrangement might be realised by other means than
by the use of sulphuric acid. It was ascertained that the intramole-
cular rearrangement of atoms in azoxybenzene is also possible by
raising the temperature to at least 200° and by the influence of direct
sunlight. In the first case a mixture is formed of p- with much
o-oxyazobenzene ; in the second case only 0-oxyazobenzene is obtained.
None of these changes is reversible. Also those derivatives of azoxy-
benzene which undergo intramolecular rearrangement by the action
of H,SO, are converted by the said agencies, but the action is slower
and the amount is smaller than that obtained from azoxybenzene. The
investigation of these derivatives has not yet been quite concluded.

Acetic anhydride is without effect on azoxybenzene at the boiling
temperature ; on heating however at 200° the change already takes
place in a notable degree, much better than by merely heating the
substance itself, while an acetate is either not formed at all, or only
in very small quantity. P-oxyazobenzene is not formed at 200° but
only the o-isomer. Solutions of azoxybenzene derivatives in acetic
anhydride do not however suffer any intramolecular change at 200°,

Addition of Zn Cl, or P,O, to acetic anhydride does not enable it
to cause the change at the boiling point; heating with the so-called
BECKMANN’S mixture is also without avail. By heating a solution of
azoxybenzene in this mixture at 150° and 180° it appears that azoxy-
benzene which, when prepared in the ordinary way is a yellow
substance, is perfectly white when in a pure condition. The ordinary
5) Ber. 17, 464 (1884).

6) Ber. 18, 2552 (1885).
1) Ber. 18, 1405 (1885).
2) Journ. f. pr. chem. 1%1. 567 (1901).

(93)

product therefore contains a yellow impurity, which cannot be
removed by recrystallisation.

The intramolecular change was attempted in vain by means of
the following reagents :

Acetyl chloride, butyryl chloride, benzoyl chloride, phosphorus
pentachloride, phosphorus oxychloride, phosphoric acid, aluminium
chloride, aqueous caustic soda, copper oxide, zine oxide and zine
carbonate. Of these reagents the following deserve to be specially
mentioned on account of their action on azoxybenzene :

Acetyl chloride : formation of p-p-dichloro-azobenzene and p-chloro-
acetanilide ; benzoyl chloride: formation of azobenzene ; phosphorus
pentachloride : formation of azobenzene with evolution of chlorine ;
aluminium chloride: formation of p-chloro-azobenzene.

Mathematics. — #On the connection of the planes of position of
the angles formed by two spaces S, passing through a point
and incident spacial systems.” By Prof. P. H. Scnourr.

1. If in a space Sy, with 27 dimensions two spaces S, are given
arbitrarily, these have in general only a single point OV in common
and they form in this point with each other angles differing in general
respectively. These angles are situated in » definite planes through
Y and the line at infinite distance of such a plane of position has
a point in common with the two given spaces S,(, S,@ as well as
with the spaces 5/0, S:’@ drawn perpendicular to the just named
spaces through any arbitrary point, say OV, not at infinite distance.
In this way the two planes of position of two planes ¢,, e, taken
arbitrarily in S, are determined by the common transversals of four
lines: situated in a three-dimensional space, viz. of the lines g,, g,
of «,, «, in the space S, at infinite distance in S, and the lines
Jy’, Js, normally conjugate in this 133. 10! Oy ze

2. Let us consider the particular case when the » angles formed
by SD, S,@ are alike; as an introduction we take in JS, again two
planes ¢,, ¢, forming with each other in their point of intersection O
two equal angles. It is known that in that case the four above
mentioned lines g,, 4, 41’, J’ ave generators of an hyperboloid ; so they
admit of not only two but of an infinite number of common trans-
versals, to which answer likewise an infinite number of planes of
position. If the system of those transversals ¢ is indicated by (4), the

( 54 )

system of the lines g intersecting all the lines (4) by (9), there exists
between the two incident systems of lines (y), (d at infinite distance
this reciprocal connection that the plane passing through an arbitrarily
chosen point QO at finite distance and an arbitrary line of one of the
two systems is a plane of position for the pair of the planes connect-
ing the point OV with two arbitrary lines of the other system. From
the manner in which the quadratic scroll (/) is formed out of g,,
Yo J.» Jy Namely ensues that the surface //° of order two, bearer
of the two systems (y), (4, agrees with itself in the polar system
at infinity in S, of which the imaginary sphere 22 common
to all hyperspheres is at the same time the locus of the points lying
in their polar planes and the envelope of the planes passing through
their poles; for to each line ¢ intersecting y,, g,, 9,’, g’, regarded as
locus of points agrees in that correspondence a line ¢’ lying with
Yi > Jo's Yrs Jo M a plane regarded as axis of a pencil of planes, ete.

If we make the lines y, g’ of (g) normally conjugate to each other
to correspond to each other, then between the lines of (9) a quadratic
involution is formed; the double rays g;,g; of this involution must
lie on Ay, being normally conjugate to themselves. Likewise does
45; contain the double rays ¢,, t of the involution formed in quite
the same way between the lines f, {normally conjugate to each
other. So H and 42 intersect each other in the sides of a skew
quadrilateral whose pairs of opposite sides are the double rays
(gi, g,) and (ty, t) of the pairs of rays (g, g’) and (¢,t’) of (g) and (#)
normally conjugate to each other.

If (g,g’) are two normally conjugate rays g and (f, t’) likewise
two normally conjugate rays ¢ and if we take the planes Og, Og’
and Ot, Ot’ as coordinate planes O.X,X,, OX,X, and OX,X,, OX,X,,
then the surface M/ must be characterised with respect to this rectan-
gular system of coordinates by the equation er, = wr, between the
infinite coordinates. For the quadratic surface vr, + priv, = 0,
brought through the lines at infinite distance of the four mentioned
coordinate planes, corresponds to itself in the polar system with the
sphere wv? + 2,? + .,? +.7,—=0 at infinite distance as surface of
incidence only when the absolute value of p is equal to unity. For
the normally conjugate Jine of «, = 2x,, Av, + pr,=0 is Ar, +2,=0,
pe, =de, and this new line lies only for p?—=1 with the original
one on «, 2, + Pt, ‚== 0. So by reversing if need be the sign of
one of the coordinates we can always bring the equation of HZ into
the form Sn een wae

3. Before passing on to the general case we shall consider the

( 55 )

case, when in S, two three-dimensional spaces SD, 8,2) are given
arbitrarily. The line g, at infinite distance of the plane of position
of one of the angles formed by those spaces in their point of inter-
section © is then a common transversal of the planes at infinite
distance el, «2 of S,%,.S,@) and the planes &), &(2) normally con-
jugate to these. As the common transversals y, of the three planes
el), eV), €( form a “variety” W,? of order three of three dimensions
and this curved space is intersected in three points by &(), the spaces
5,0, 5, make in O three angles with each other. This variety V,
is not only (compare i. a. the first part of my “Mehrdimensionale
Geometrie”, vol. XX XV of the Sammlung Scuusert’, N°. 102, 103) the
locus of a twofold infinite series of transversals g,, but at the same
time the locus of a simple infinite series of planes ¢, , each of which
determines with ed, ed, el on the lines y, quadruples of points
with a definite anharmonic ratio, i. e. V,* is the bearer of two

nm?

incident systems which we represent according to the nature and
the multiplicity of the elements by (y,,), and (¢,),. Beside the general
case, where &!?) has in common with J’,? three points not situated
on a right line, the particularity may arise that e€@®) has a line in
common with one of the planes ¢, of (e‚), or coincides with one of
those planes; to this answer the particularities that two of three generally
different angles of position or all three of them become equal to each
other. In the last case of the three equal angles of position, to which
we restrict ourselves here, there is between the two systems of incidence
this connection, that the plane passing through an arbitrarily chosen
point © at finite distance and an arbitrary line g, of (g,,), 1s a
plane of position for the pair of spaces connecting © with each of
two arbitrarily chosen planes ¢, of (¢,),. If namely we make on
each of the lines yg, of (y,), those points to correspond to each
other which are conjugate to each other in the involution determined
by the pairs of points of intersection of that line with the planes
ai), ef) and es, e@, then between the planes «, of (&,), is
formed a quadratic involution, from which ensues that the plane ¢,
normally conjugate to the plane ¢, of the variety J’,* lies likewise
im Vas etc:

The two double planes ¢;, ¢; of the involution (¢,, €,,) form part of
the imaginary hypersphere £,° with four dimensions at infinite
distance common to all hyperspheres £,? with five dimensions of
S,- So the section J," of J’,* and 4,° consists of these two planes
and a J,‘ which must now necessarily be the locus of the trans-
versals g, of (g,), lying entirely on /,*. Whilst as is known the

lines g, vesting on any arbitrary right line of ¢, form a surface

( 56 )

of order two, the locus of the lines y, resting on the conic of section
ofse. Sand Bis a. VA

4. If finally in Ss, two spaces S, are taken arbitrarily, these
form with each other, as was mentioned above, in their point
of intersection QO in general » angles differing from each other
and the line at infinite distance of the plane of position of each of
those angles in the space at infinite distance Soi of 92, intersects

: ; ; iy ee ; 1 13
again four spaces ni the spaces at infinite distance Ss! ) 2 S ,
oe a

(1 (2) a (2

of the two given spaces S° ) S and the spaces S° ef S ) normally
n n i Nm ee

conjugate to these. If now the special case presents itself that each

E 1) (2 ld 4(2

right line cutting three of the four spaces oe or) de Ss = es :
n— I— — —

also cuts the fourth, the 7 angles of position are mutually alike and the

locus of the v-fold infinite system (y,), of the lines q,, at infinite distance
. . wpm . . „1 ” . . .
of the planes of position is a variety 7" of order 7 with n dimensions,
n
appearing likewise as the locus ofa simple infinite number of spaces S,—1,
Le. in the form of (S,—1),, namely of the spaces Sj, determining with

(1) (2) 2, = ) e xy (2) 2 5 :
5 S Fey and now also w Si oe Ge 5 E85 OEFA
Pe ee ya MR and n als ith & a jon the lines g, (Joo )n

mutually projective series of points. In that case a plane connecting
an arbitrary point at finite distance with a line g, of (yy)a is
always a plane of position of each two of the spaces 5S, connecting
O with spaces S,—1 of (Si),

Bing dE : ° > . : . r2n :
As is immediately evident, in this special case the section | of

rn : ~y2 ; 2 5 > = :
J” with the hypersphere S , with 27—2 dimensions common to all
be |

2 Y .
hyperspheres 5 of Sa, breaks up into the two double spaces
==

aC (J oy : 2 ; = ¥ eat Ach EA
S ) E Se of the involution of the spaces S,—1, S’n—1 Of (S,—1)

n— nd

é 3 -An—l) Er ik
normally conjugate to each other and into a | ‚ „locus of the lines
. i

2
Ja Of (J,)m lying entirely on B, .

(57)

Physiology. — #The principle of entropy in physiology.” By Dr.
J. W. LANGELAAN. 3'¢ part. (Communicated by Prof. T. Pracr).

All investigations made with the intention of testing the law of Fecunnr
at the experiment, have proved, that this law is only satisfied within
a small interval and within that interval only by approximation.

In order to find out the causes of these deviations, I have tried
to deduce the law of Frcuner (considered as a physiological law)
from a general physical principle. It has appeared from this deduction
that this formula rests on very special premises, and that the cireum-
stances assumed in these premises, are never realized in nature.

In a series of experiments I have tried to fulfil as accurately as
possible the conditions required by this law according to its dedue-
tion. To this purpose the spinal cord of a frog *) was cut between
the cranium and first vertebra; then the whole frog, with exception
of the hind leg which was used for the experiment, was wrapped
up in wads and fastened to a glass rod. The leg hung down in a
wide vessel which could contain about 600 ccm. of fluid. In the sole
of the foot a hook was put and a horsehair was attached to this hook,
which passed outside through a very small opening in the bottom of
the vessel. This horsehair was fixed to the arm of a length-recorder.

The small opening through which the hair passed was filled up
with vaseline; this prevented almost perfectly the fluid to drip out,
while the friction experienced by the horsehair was very slight. By
suspending a weight to the length-recorder the leg was charged with
15 grams. Then the vessel was filled with 350 eem. of water, and
the lee immersed till the knee. To the stand bearing the glass and
the frog, a clamp was fixed bearing a burette. This burette contained
a solution of oxalic acid in distilled water. By opening the tap this
solution flowed into the water in which the leg hung. A bent stirrer
always kept in slow motion (but which did not touch the leg), caused
the acid to be thoroughly mixed with the fluid. Then so much acid
was slowly added to the liquid till the leg began to contract. The
vertical motion of the leg, three times magnified, was registered on a
slowly rotating cylindre by the length-recorder. In order to prevent
too large excursions, the length-recorder struck against a piece of cork,
so that the contraction in the beginning took place isotonically, at
the end isometrically.

After the leg had returned to rest, we waited about 5 minutes and

1) Small male specimens of Rana esculenta proved to be the most suitable for
the experiment,

( 58 )

then again so much acid was added, till a new group of reflex-con-
tractions appeared. In these experiments the acid in the burette con-
tained 40 grams of oxalic acid per liter solution. As a measure of the
stimulus in physical units the concentration of the solution, in which
the leg was immersed, was chosen. The concentration is defined as
the proportion between the quantities of oxalic acid and water, while
as the unity of weight the molecular weight was chosen (126 for
oxalic acid, 18 for water).

The result of the experiments was given in a table in the following
way. The first column gives the concentration of the solution in the
vessel, just at the moment the leg begins to show a group of
reflex-contractions. The second column contains the increment, which
the concentration in the vessel must undergo to produce again a set
of reflex-contractions. The third column gives the relation between
this quantity and the absolute value of the concentration at the moment
that the reflex-contractions appear. This column contains therefore
the quotient of WEBER.

Let us now consider in how far this experiment satisfies the con-
ditions put by the formula. The researches of EckHARD, KOSCHEWNIKOFF,
C. Meyer and SHERRINGTON have proved, that the same spinal segments
which innervate the skin of the hind leg, supply also the muscles
of the leg with nerves. If we have cut the spinal cord at the upper
end and have therefore annulled the influence of the higher centra,
we have in the hind leg a segmental primary reflex-apparatus. The
receptive organs of this reflex-apparatus lay in the skin, while the
muscle forms the transformer. Adopting the simple law of distribution,
I record only the mechanical effect. In this respect the experiment
fulfils the required conditions.

The interpretation of the mechanical effect is very difficult as
the new state of equilibrium is not reached at once, but only after
oscillating round this new state. It is therefore hard to say what
part of the total effect must be considered as the quantity A / of
the formula. Fig. I is the reproduction of a typical tracing. After the
reflex-apparatus is in perfect rest, the tap of the burette is opened at
the moment indicated in the curve by a couple of vertical small lines
on the base line and oxalic acid is slowly added under continuous
stirring. At the moment that the first contraction appears, the tap of
the burette is closed and no more acid is added. At this moment the
increase of concentration amounted to 3.210 the initial concen-
tration being 15.910—5. The curve represents the mechanical effect,
following upon this increase of the concentration of the acid in the
vessel. This effect consists of a group of great contractions, followed

by some smaller ones of decreasing size. If we should be at first
inclined to consider this group of large contractions as the mechanical
effect corresponding to the quantity A / of the formula, this concep-
tion offers many difficulties when the mechanical effect assumes a form
as is represented by the curve which is reproduced by fig. IL. In con-
sequence of a small increase of concentration we do not see a definite
effect appear, not even partly defined, but the reflex-apparatus comes
in rythmical contraction. Where in the first case the resistances in
the chemical system are such that the oscillations rapidly die away,
and the new state is reached after a few oscillations, these resistances
in the second case are so small, that once the equilibrium disturbed,
the system remains oscillating round its new state of equilibrium.
This oscillation documents itself as a rythmical mechanical effect. If
the rate of decay of these oscillations is very small, these rythmiecal

TABLE I. (Fig. V). TABLE IL (Fig. VI.)

IN oe (AE OO) Non (250 19 NEON)

| | Ò Cone.

: : | | & Conc.
Cone. pM Gomer al =e 5 Cone, A Conc. | ——
| Cone. | | Cone.
0.0><10-° | : 0.0<10-° | ii
(UES Beg Oia 2650 10 |
10.1 | 26 6 |
2.8 b G28 ese 0.158
12,9 | | SRO
3.4 | 0.209 P29 0.086 ?
16.3 | oa)
4.0 i) *O-4,96 3m 0.085
20.3 31.7
| 4.1 0.167 | 2.3 0.058
M.A | | A) 0 |
| 4,3 0.150 2.0 0.047
98.7 / | 12.0
| 4.9 | 0.447 1.6 0 037
530 Ì 43 b
| 4.8 0.123 2.7 0.059
38.4 | 16.3 |
10.7 0.218 Pio sD 0.069
49.1 49.8 |
| 20.8 | 0.298 Parr’ 0.098
69.9 55.2 |
OET 0.155 ‚10.8 | 0.164
80.6 | 66.0
| | 19.3 0.226
85.3 | |
Section of the medulla 10 A.M. | Oren

beginning of the experiment 11.15 A.M.
Temp. 13.5 C, Section of the medulla 10.35 A.M.
beginning of the experiment 12.40 P.M
Temp. 13 C.

nenten ee ees

( 60 )

contractions can last for several hours and often with great regularity *).
Under these circumstances, however, A K is no more a determined
quantity and the experiment cannot fulfil the condition of the formula,
that A / be a constant quantity in the successive determinations. If
we only use those experiments, in which the resistances are pretty
considerable, and the new state of equilibrium is reached after a few
oscillations, 4 / fulfils the condition, that it represents a small quantity
in successive determinations. The experiment does not allow another
more definite conception of this quantity.

By the addition of acid from the burette to the liquid in which
the leg is immerged, the level of the liquid rises, and the stimulated
surface increases. So the experiment does not fulfil the condition of
the formula in this respect either.

TABLE III. TABLE IVS (Fig VII.)
No 21 (7.42. OS) No. 14. (isa. 01.)
| eps A Cone.
Cone. | AConc. | 5 Pela Cone. | A Cone. —____—_.
| Cone | Conc.
2 C3105 ‘ 00 107 >i
9.610" 15-90
Seo 1529
427 0.327 ED 0.168
5.3 19.4
1.4 0.203 4.5 | 0.499
6.7 Del 9°
24 0.236 ee | "0.935
88 30.9
DO 0.299 8.0 0.207
12.4 38.9
Ole 0.339 4.3 0.098
18.7 43.9
10.5 0.359 Bie) 0.082
99 9 47.0
12.4 0.297 19.9 0.997
41.6 66.9
8.7 0.173 27.6 0.292
50 | 94.5
| 96.0 yy art | 46.8 |, Ota
16.3 | | 7 ebi |
| 155 | OEL De
TEER TA EE 126.6

Section of the medulla 10.15 A.M.
beginning of the experiment 12.56 P.M. .
Temp. 15 C. Section of the medulla 10 P.M. 20.9. _
beginning of the exper. 12.4 P.M. 21.9
Temp. 16.5:°C,

') It seems to me that the heart is in this condition, and it would be worth
while to repeat many experiments from the physiology of the heart on this ryth-
mically acting reflex-apparatus.

» =

7

( 61 )

Similar experiments as described by me, were performed by
Winker and VAN WayEnsurG some years before. The method followed
by them, which slightly deviated from mine, enabled them to extend
the experiment only over a small interval of variation of concentration.
They concluded for this small interval, that the reflex-apparatus of
the frog follows the law of Frenxer *). In the experiments communi-
cated by them slight deviations from this law proved to occur and
it was with the purpose of learning something about these deviations.
that I repeated these experiments extended over a greater interval.
Table I, H, Ill and IV represent four of these experiments. If we
take A as the value of the stimulus in physical measure (i.e. the
concentration of the solution of the acid in which the leg is immerged)
and if we take A R as the value of the increment of this stimulus
which is required to call forth a change in the system, the quotient

ES Bve, ; ee
a is not constant, but in general a function of R.
L

OUDE PLO 90 | Gr MO tO? aD

Fig. V (table I, exper. 4).

Gh 70 80: TA ZE CAD OVS OCS 70
Fig. VI (table II, exper. 35).

OP Oa tn See en ed go Wo wo Zo Jo

Fig. VII (table IV, exper. 14).

1) Van Wayensere, Dissertation 1897. pag. 117,

( 62 )

Fig. V, VI, and VII are the graphical representation of Table I,
II and IV. In this graphical representation I have considered the
amount of water as constant (10° unities of weight) and put as
abscissae the number of solved unities of weight of the acid. The
relative increases of the concentration, in percents, have been chosen
as ordinates. The points, representing successive determinations, are
connected by a curve. The graphical representation of the result of
the experiment by a continuous curve is only an approximation,
remaining in, the same course of thoughts as that, which has led us
to represent the phenomenon analytically by a continuous function.

If the law of Frcuner was satisfied, the line representing graphically

>

as function of R, would be a straight one. But

the quotient

instead the experiment furnishes a curved line. In order to elucidate
the form of this curve further, fig. V is given, which is the graphical
representation of an experiment, where the first descending branch
is determined by as large a number of observations as is possible.
Fig. VI shows a reduction in the extent of the first descending
branch and this enables us to determine the ascending branch by
a greater number of observations. In the experiment represented
by fig. VIL this reduction of the first descending branch is so con-
siderable, that it no more appears in the experiment; this makes it
possible to determine the top of the ascending branch and the de-
scending branch following on it. The whole course of the second
descending branch cannot be given, as always a discontinuity occurs
at a point which seems to be near a second minimum. After this
discontinuity a new period sets in, and as far as it is possible to
follow this new period, it appears to be considerably greater, whereas

R

shows in this

the oscillation which the value of the quotient

period, seems to be relatively smaller. For a skin-muscle reflex-
ee es: : ee
apparatus the quotient ET must therefore be considered as a periodie

function of . If we inquire what is the signification of this disconti-
nuity, it seems that only those variables, which are the representation
of the independently variable components of the chemical system, can
be able to show discontinuities. This brings about a change in the
nature of the system and this must be attended by a discontinuous
variation of the quantity A, which occurs in formula I of the second
communication. The experiment communicated by Massarr *) seems

1) Bull. Acad. royale de Belgique 3me Série, T. 16, 1888, pag. 590.

( 63 )

480 S 40 50 60

jo

go

Fig. VIII (table V, exper. 25).

TABLE V. (Fig. VIIL)

go

No. 25. (41. 412.

OL.)

Cone, A Cone. ———_——_
| Cone.
OEOsAOr 5
co Pee (Umma

8.8
Al OE

En)
2.7 0.187

14.9
ORG 0.156

16.8
2.4 0.129

19.2
2.0 0.093
DAL SDs
4 0 0.160

D2
4.0 0.136

99.9
44 0.123

Soe
45 0.120

37.8
43 0.423

42.1
3.8 0.079

45.9
3.0 0.061

48.9
Dass 0.050

51 4
oO 0.289

72.4
LAGS 0.141

84.2
so | 0.097

93.3
5.0 0.051

98.3

Section of the medulla 8.30 A.M.

beginning of the experiment 12.5 P.M.

Temp. 13 C.

/00

( 64 )

to show the same phenomenon. Another phenomenon, which sometimes
occurred in my experiments, was the dividing ofa period into several
parts. Fig. VIII (table V) is the graphical representation of such an
experiment.

As far as my experiments go, this small discontinuity can appear at
every moment in a given period, followed by the outset of a new period.

If we compare these results obtained by the primary reflex-apparatus
with those of experimental psychology, they appear to concord in
many points. As appears from the critical summary of Foucauut *)
also there a variable quantity showing a minimum is found for the

oo page
quotient =e most cases. The shape of the curve representing the

be fer
quotient R 38 function of 7, makes us suppose, that the experimental
L

psychology has seen only part of a large period. By the dividing of a
)

Eet Ak
period into several parts, the quotient pp Seems to show multiple
L

minima and this occurs also in some experiments of the experimental
psychology. Hence there is agreement in these respects between the
results of the psychological and the physiological experiment.

With regard to the mechanical effect I have pointed out, that this
is greatly dependent on the rate of decay of the oscillations of the
system. The rapidity of this decay is determined by the passive
resistances in the chemical system. If these passive resistances are

slight, a small increase of ? will be sufficient to call forth a change
2

AR
in the system. Therefore the value of the quotient ER which is a

measure of the value of these passive resistances, will determine the
rapidity of the decay of these oscillations.

In correspondence with this the experiment shows that the height.
and the number of the elevations in every successive determination

Cc

increases with decrease of the value of the quotient Rr: Fie. “ie

(table ID) observation 2, 3, 4, 5 shows this clearly. At the 5 obser-
vation the resistances are so slight, that the system continues to oscillate
for several seconds. Observation 8 and 10 show this same phenomenon
at a higher value of PR, in the same series of observations. If we
compare, however, observation 8 with observation 5, in which two

AR
observations the value of the quotient ri almost the same, and
vu

1) M. Fovcaurr. La psychophysique, 1901,

( 65>)

also observation 10 with observations 3 and 4, it appears, that in’
the second place the rate of decay is dependent on the absolute value
of FR. Supported by these and more similar observations we may
say that the rapidity of the decay of the oscillations increases with
ie NE AR
increasing value of # and with increasing value of the quotient -
L
In this we have to keep in view, that the first observation always
occupies a special place; for this observation AP is always very

large, and though the method followed does not enable us to deter-
J?

R |
mine the quotient RE for this observation, this quotient is probably
? :

also very great. Notwithstanding this we always see that the rate of
decay is very slight and from this we should have to conclude, that
the influence of the absolute value of 2 on the rapidity of this decay
is preponderant in the beginning.

The same experiments which I have described for the frog whose
spinal cord is cut through, can also be performed with perfectly
intact frogs. For this it is necessary to wrap up the whole animal
carefully in wads with exception of the hind leg which is used
for the experiment. If we take care to avoid tactile and auditory
stimuli, the frog remains quiet during the experiment also under these
circumstances *). In this case the result of the experiment is the same
as that of the preceding one.

Fig. IX (table VI) is the graphical representation of an experiment,

0 40 #0 60 JO foo 120 140 160 FO 200 120 10 260 so
Fig. IX (Table VI, exper. 46).

If the first period is small, it is possible to see also here a part of
a second period appear (Fig. X, table VIL). This second period seems
also greater than the first, while the oscillation, which the value of

J

. \ . . . .
the quotient R shows in this period, seems relatively to be smaller.
JA]

1) In these experiments the solution of acid in the burette contained 80 grams of
oxalic acid per liter solution.
D

y
.

Proceedings Royal Acad, Amsterdam. Vol. \

‘IadX9 [JA oraen X Sur

“(Og

No.2462) 2 (18%. T5202)
A Cone
Cone. A Cone.
Cone
0.010~° É
26-9107"
26.9 |
| 34.6 0.562
61.5
eel | 60.282
85.6 |
bl 0.273
Bf
55.9 0.322
1730
Se 6.231
225.9
2.9 0.187
978.4

Medulla intact. Beginning of the experi-
ment 11.46 A.M Temp. 13.5 C.

TABLE VII. (Fig. X.)

No 50. (26. 4. 02)

Conc. A Cone. aes
| Conc.
OLORAOT? 5
29.3><10~°
99 3
4A 9 0.605
74.9,
SM} 0.234
96.8
39.0 0.546
135.8
A 0 206
174-0
24.4 0.125
195.4
530 0.213
48.4
71.6 0.294
320.0
55.4 0.148
375.4
38.5 0.C93
413.9

Medulla intact. Beginning of the experi-
ment 3.0 P.M. Temp. 11.5 C.

AN

Es evecare A Roemer

J. W. LANGELAAN. The principle of entropy in Physiology. (II.)

|
|

Lt

Fig. ll. (Exp, N°. 24.) Tuningfork 2 vibrations per second

==

V. (Exp. N' 50.) Cuningfork 2 vibrations per second

u 10 R 2 10
ay 059 aM 0.098
I R
I ill Exp, N Puningfork vibrat id

(67)

The number of my experiments in which a second period appears,

. i rm . d « ‘
is, however, not great. Therefore we may say also in this case, that
)

R
the quotient Ri probably to be considered as a periodical function
v

AR
of A. The value of the quotient ard however, is in these experi-
tv

ments considerably greater than in the preceding experiments, while
in concordance with this the rapidity of the decay of the oscillations
of the system is also greater.

Figure IV (table VII) which is the reproduction of four observations
from the same series, shows this clearly ; the new state of equilibrium
is reached after a few oscillations. If we compare observation 3, 5
and 6, the system proves to be a periodical one, at the third obser-
vation; at observation 5 and 6 the rapidity of the decay de-

AR
creases with decreasing value of the quotient Rp At the tenth obser-
AR

%

vation, where the quotient shows a very low value, the rapidity of

the decay is very small notwithstanding the high value of 2. If we summa-
rize these differences briefly, we conclude that in consequence of the high
section of the spinal cord, the passive resistances in the chemical
system of the skin-muscle reflex-apparatus considerably decrease. On
account of clinieal observation chiefly regarding the plantar-reflex,
it seems to me, that we have to deal here with a very general pheno-
menon occurring always where there is a wasting of systems. In this
case the rapidity of the decay of the oscillations of the system is
very small in consequence of the decrease of the passive resistances in
the chemical system. If is obvious that a good motor function can
only exist, when the rapidity of the decay is so great, that the system
is almost aperiodic. The motor disturbances, which occur in multiple
sclérosis, in locomotor ataxy and many other diseases of the nervous
system seems to be partly due to the decreasing resistances in the
chemical system of the reflex are.

If the system is perfectly aperiodic, then the quantity AZ is a
perfectly determined quantity. This condition must also be fulfilled
by the systems, to which the experimental psychology extends its
experiments; if this condition is not satisfied, then the effect is a
not determined quantity as in the physiological experiment.

5%

( 68 )

Astronomy. — #On the yearly periodicity of the rates of the
Standard-cloch of the observatory at Leiden, Honwt Nr 17.4
First part. By Dr. EB. F. van DE SANDE BAKHUYZEN.

I. Zntroduction.

1. When the observatory at Leiden was founded in 1861, it was
fitted with a clock made by Mr. A. Honwié of Amsterdam, and by
him designated as Nr 17. Accurate investigations of Kaiser *) soon
showed the great regularity of its rate, in which point it was superior
to all clocks about which an investigation had so far been published.
Since that time it has continually been used as the standard-clock
of the observatory and at the present moment its rate is still
eminently satisfactory.

The clock was originally mounted in the transit-room of the
observatory on a brick pier which rests on the foundations of the
meridian-circle. The stability of the mounting thus left nothing to be
desired. On the other hand the temperature at this place was rather
variable, showing very clearly a daily period; moreover entirely irre-
cular changes of temperature were often caused by the opening and
closing of the shutters. b

From 1861 the clock has been going regularly until 1874, with-
out being touched during this time except for the purpose of winding
once a week. On the 17 of June of the latter year however it
stopped spontaneously, after having shown for about a month a
particular irregularity.

As the intention existed already to make considerable changes as
well in the transit-room as in the meridian-circle, it was thought
best to defer a thorough cleaning and overhauling of the clock till
the time of these alterations. Accordingly the clock was then only
provisorily cleaned, and was set going again after a few days.

The intended alterations were made in the second half of 1876
and the beginning of 1877, and in June of that year everything
was again in working order, and also the clock Honwi 17 was
mounted again.

Though Prof. H. G. van pr SANDE BAKHUYZEN did consider the
possibility of removing it to a better position, out of the transit-room,

1) F. Kaiser, Onderzoekingen omtrent den gang van het hoofduurwerk der
sterrenwacht te Leiden, de pendule Honwi N°. 17. Versl. en Meded. K. Akad.
Amsterdam D. X VII, 1865.

F. Kaiser, Untersuchungen über den Gang der Hauptuhr der Sternwarte in
Leiden, Honwii NY’. 17. Astr. Nachr. NO. 1502.

(69)

this gave rise to too many difficulties at the time, and it was only
tried to diminish the variations of temperature by making a second
wooden case round the clock. *)

In the meantime the ehronographie method had been generally
adopted at the observatory for the meridian observations. Now it
had been shown repeatedly that the introduction of an electrical
contact in a clock diminishes the regularity of its rate, and on
the other hand we had found that the comparison of two clocks
could be effected with extreme accuracy by means of signals given by
hand *). Accordingly the clock Honwié was not connected with the
chronograph, but the clock by KNosiich was used for this purpose.

On the 26th of November 1877 the clock was stopped for a short
time in order more completely to adjust its beats; since that date
however it has been going uninterruptedly until August 1898. At
that time the clock was again dismounted at the occasion offered
by alterations in the transit-room, and cleaned and overhauled by
Mr. Honwi,

In December 1898 the clock was remounted, and this time the former
plan of removing it from the transit-room was carried out, and it
was fixed to the pier of the 10 inch refractor. In order better to
secure a constant temperature, Prof. H. G. van pr SANDE BAKHUYZEN
resolved to have a niche cut out from this pier in the large hall
of the observatory, and to place the clock in this niche.

The clock Honwié N° 17 has now been in its new place for over
three years. It is still enclosed in two wooden cases, and the niche
itself is closed by a glass door. We may remark already at this
place that by this arrangement the aim of excluding rapid variations
of temperature has been attained in a very perfect manner.

2. In 1887 Mr. WirrerpiNK investigated for a special purpose the
rate of the clock Honwü 17 during the period 1886 January to
1887 July. It then appeared that after reduction for temperature
and barometer the mean rates for the summer- and the winter-
half-vears were in very satisfactory agreement, while on the other

1) At the same time a small mirror was attached to the pendulum-bob, to permit
more: accurate determinations of the amplitude of oscillation. See: H. G. van pe
Sanne Baxuuyzen, Verslag van den staat der sterrenwacht te Leiden 1876—1877,
page 12.

2) From series of signals given by the two observers Witrerpink and FE. F,
VAN DE SANDE Baxkuvuyzen immediately after each other, on a great number of
days, the Mean Error of the result of a series of about 24 signals, (including the
variation of the constant error during an interval of about a month) is found to
be © 08.0077,

(70)

hand a very marked systematic difference existed between the means
for the half-years January
Mr. WiLrTERDINK found

June and July—December.

Obs.—Comp.

1886 January—June + 0°.045
July—December — 0.08

1887 January—June + 0.035.

Consequently, when in 1890 I undertook the definitive discussion of
the time-determinations and clock-rates for the period 1877— 1882, it
appeared desirable to me to investigate whether a similar phenomenon
would again show itself. I then found that the years 1878—1882
(before May 1878 the rate was not yet sufficiently regular) were in
this respect entirely similar to 1886—87, and, investigating the pheno-
menon more closely, | moreover found that the rates, after correction for
temperature, still showed a yearly periodicity which accordingly
had its maxima in the months of equal temperatures April and October
and the amplitude of which was about O0°.10.

1 then continued my investigation (the results of which were briefly
published in the # Verslag van den staat der sterrenwacht te Leiden
1889—1890,” pages 14—15) in the same direction and included on
the one side the years 1882

90, using provisional results of the
time-determinations, and on the other side the years 1862—1864,
using the results of Kaisers investigation in Astr. Vachr. 1502. For
these two periods I also found the same unexplained inequality.

After 1890 this investigation was abandoned for the time being,
and it was only taken up again last year. In the mean time the
clock had been removed to its new position, and it now appeared that,
notwithstanding the fact that the changes of temperature had become
much more gradual, still the yearly periodicity of the rate showed
itself in the same way as before, and its deviation from the yearly
periodicity of the temperature was certainly not less evident’).

It became thus evident that there was no question of accidental
circumstances, which could be altered by cleaning the clock, nor of
such conditions as depend on the special nature of the changes of
temperature to which the clock is subjected, but that the cause of
the phenomenon must lie deeper.

It therefore appeared desirable to subject the way in which it
showed itself in the three periods (viz: before and after the cleaning

1) See also „Verslag van den staat der sterrenwacht te Leiden 1898—1900 pages
12—13.

C iy)

of 1877, and after the cleaning and removal of 1898) to a new
investigation which had to embrace the whole of these periods. The
results of this investigation are given in the present paper.

I have confined myself to such results as could be derived from
the mean daily rates during periods of about a month. Thus it was
not necessary that the time-determinations on which the investigation
is based were discussed with the utmost accuracy. In this way I inves-
tigated successively the three periods, 1877—1898, 1862—1874
and 1899—1902. The results for these three periods will be com-
munieated in this order. Then the observed amplitudes of the period
1877—1898 will be investigated, so far as their yearly periodicity
is concerned, and finally the several results will be compared with
each other.

As a consequence of the restriction of the investigation to the
monthly means, the question is considered from one point of view
only. In the mean time however Mr. Wreper has definitively discussed
all the time-determinations from 1882—1898, and has undertaken
investigations about the rates of the clock during shorter periods.
It is to be expected that, when these investigations will be completed,
the comparison of his results with mine will also throw more light
on the phenomenon which is here treated.

Very recently, while my investigation was already nearly com-
pleted, I had occasion more closely to study the computations which
Kaiser made about the clock Honwi 17 during the last years of his
life, and which are preserved in manuscript at the observatory. |
then found that as early as 1870 his attention had been drawn to
this particular yearly inequality as to a remarkable phenome-
non. Among the papers I found a summary of monthly means
of rates, corrected for barometer and temperature, from which mean
results had been formed by combining the corresponding months of
the years 1862—1870. These means show clearly a periodicity having
its maxima in May and October, and a total amplitude of 0°.09.
Further I found means for the half-years February—July and August—
January for each of the years 1863 to 1870. The differences between
the two half-years vary between + 0.°026 and + 0.8048 and Kaiser
adds the remark that the only difference between the two half-years is

that in one of them the temperature is, in the mean, rising, while
in the other it is falling.

I. The period 1877—1898.

3 The eloek-rates which were taken as the basis of the inves-
tigation were, for the period 1877—March 1882, derived from the

(72 )

definitive discussion of the time-determinations during that period. For
the following years they were taken from the provisional results which
had been computed immediately after the observations, Mr. Wrrprr’s
results being not yet completed last year. L only applied small corrections
in a few cases for the personal differences between the observers,
which have become better known since the provisional computations
were made. I always used time-determinations as near as possible to
the beginning of each month.

The mean temperatures and barometerreadings required for the inves-
tigation were derived in the following way.

The temperature was read on two thermometers suspended in
the clock-case, one at the level of the upper part of the pendulum rod
the other at the level of the pendulum bob. These thermometers were read
five times a day viz. at 8 a.m., noon, 4 p.m., 8 p.m. and midnight.
The scales were Reaumur’s and were divided into full degrees.

We will first investigate the relation between the results given by
the two thermometers. The readings of the years 1878, 1879, 1884
and 1885 were discussed for this purpose. In the following table the
monthly means of the differences between the two thermometers are
given for each of these four years, after application of the index-
corrections. The differences are taken in the sense upper thermometer-
lower thermometer. The last column gives the means of the four years.

| _ 4878 1879 1884 | 4885 Mean

January ...., + 0.46 | +042 | +0419 | +0416 F+ 0.16
February...) + 0.18 + 0 16 + 0 19 + 0 21 + 0.18

Meirelins fects: + 0.20 | + 0.214 + 0.22 + 0.20 [+ 0.21

Atrios mare [40.33 | +095 |+0.9% | +. 0:97 FH 0.97

EE 0.28 | + 0.99 0.27 024 0.27

Fay er | Ie +027 | 4-024 | 4- 0.27

Tuer tara te, }+ 0.299 | +0. |H0% | 40.99 | + 0.98
| | | |

July.... ...| + 0.26 [40.4 | +025 [4028 | + 0.

August. ...| + 0.22 | + 0.22 | + 0.27 + 0.25 | + 0.24
September ..| + 0.21 | + 0.20 | + 0.92 | +092 |+ 0.91

October..... +048 | + 0.149 | +0.20 | +0419 | + 0.49
November...| + 0.16 | + 0.18 [ce 0:20 OS | or Oa
December...) + 0.48 | +048 | + 0:48 | +0417 | + 0.16

There appears to be a constant difference of about + 0°.2 between

EEE

( 73 )

the two temperatures. There also seems to be a small yearly
inequality. We will return later on to these small differences between
the separate months, and investigate the influence which they can
have had on the rate of the clock, ¢f they are real.

For the rest of the investigation the readings of the upper thermo-

meter were used exclusively. I first formed daily means‘) — the
day being reckoned from midnight to midnight — and then means

for the periods of about one month. The index-correction, which may
be taken constant and equal to — 0°.6 for the whole period, was
not applied.

Until May 1886 the heights of the barometer were read and
reduced in exactly the same way as the temperatures. The readings
were made on a mercurial barometer which was suspended in the
transit-room from the same pier which also carried the clock. After
that time a barograph of Richard was used, which was placed on
the top of this same pier. Its corrections were determined by
comparison with the mercurial barometer ®). The daily means were
then derived by integration by means of a planimeter of AMSLER.

During the period in question three different cistern barometers
were used; in consequence of cleaning and refilling we must however
distinguish 7 periods. The corrections for these 7 periods were
determined by intercomparisons, by comparisons with simultaneous
readings of the barometer of the Meteorological Institute at Utrecht,
and finally by comparisons with a #Cistern-syphon” barometer by
Furss, which in 1890 was provided for the observatory, to be used
as a Standard barometer. Since however before 1890 no correction
had been applied and the neglected corrections amounted to approxi-
mately + 0.3 mm. during the whole period, the readings after 1890
were reduced to: Normal barometer — 0.3 mm.

The barometer-readings were not reduced to 0°. This reduction
was omitted on purpose, though the errors introduced thereby are
by no means negligible (at 7608" the effect of 1° Raum. is 0.15 ™").
The influence of these errors on the rate of the clock is however
nearly completely compensated by the fact that also the influence
of the temperature on the rate, which is thus found, differs from the
true one. It is here supposed that the temperatures of the barometer
has always been equal to that of the pendulum, which condition is

1) The mean was taken of the readings at 12, 205, 40, 12, giving half weight
to the extreme values.
2) A constant correction was taken for each weekly barograph sheet derived

from one or two readings of the mercurial barometer daily.

(74)
nearly fulfilled in the present case"). The only thing that is thus

neglected is the difference between the influence of the same tempe-
rature on high and on low barometer-readings, which is extremely small.

4. The observed rates were first reduced to 760™" and + 10° R.
by means of previously determined values of the coefficients 6 and c
in the formula:

Daily Rate = a + 6 (h—760) + e (t—10°)
b= + 08.0140
— — 0 .0268

The value of 6 was derived from a rigorous discussion of the
period 1877—1882, in which only rates observed under high and

‘©

low barometric pressure during the same month were compared. This
value must be very near to the truth. In all investigations, not only
about Honwii 17, but also about other clocks with similar, or
even with different forms of pendulum, barometer-coefficients have
always been found of nearly the same amount, and it is not prob-
able that its value would vary with the time for one and the same
clock.

The value 6 == + 0°.0140 has therefore been considered definitive,
and I have not attempted to improve it.

The following table gives, for each month from 1877 December
io 1898 July, the mean observed daily rate, the mean height of the
barometer and the mean temperature, and, in the column headed
„Redd. D. R. 1.’, the daily rates reduced to 760™" and + 10° R by
the formula given above. The meaning of the two last columns
can only be explained later.

1) See also the particulars given in connection with the investigation of the
period 1862—1874,

aes

1877 Dec.
1878 Jan.
Febr.
March
April
May
June
July
Aug.
Sept.
Oct.
Nov.
Dec.
1879 Jan.
Febr.
March
April
May
June
July
Aug.
Sept.
Oct.
Nov.
Dee.
1880 Jan.
Febr.
March
April
May!
June

July

Obsd
D. R.

4+ 0.144
0.941
0.191
0.165
0.448

0,106

0,529
0.205
0.321
0.214
0.245
0.078

0,070

„0

Redd
Drivel

5
— 0.016

ey
— 0
+ 0

0

()

0.
De
0.
0.
0.

0.

—

0.

„016
„020
„034
„118
152
206
479
184

149

088
„042
„092
191]
145]
„102

AM

.158

183
.149

„167

8
+ 0.112
097
144
106
149
146
161
163
145

458

( 76 )

DE “| zeae cau ep LR Redd
Be ED SE | D. R. U

i
|

Ss | S S
1880 Aug. | + 0.111 763.3 | + 15.4 | + 0.208 | + 0.236

Sept. | 0.080 | 62.0 13.8 0.152 214
Oct. 0.171 60.0 | 94 | 0.147 | 2AG
Nov. | 034 | 64.2 | 5.7 | 0.183 | 269
ieee ot 0.279 | 58.7 5.9 | 0.189 249
ARA an: ee | 0.471 | 58.7 | 0.4 | [0.233] Dh
Febr. | . 0.938! 58.2 | -34 | - 0474) 201
| |
March 0.375 | 59.2 5A 0.255 | 265 J
April 02364 | Ber 6.8 | 0.258 | 259 |
May | 0.306 | 65.5 10.4 | 0.230 | 999 | — 13
June 0.226 | 62.6 12.3 0.250 | 288: |R |
July 0480 | 63.7 | 45.0 | 0.264 | 952 | + 45 |
|
Aug. | 0.073 | 58.0 13.4 | OA | 209 | — 26
Sept. | 0.128 | 62.2 | 12.0 0.452 | 208 | — U
Get. U 0 217 | 61.8 | 7.4 0.40% | 931) +9
Wor. | 4.7 0.975). 68.0 Wenge}: "0.458 45 | 449:
Dec. | 0.322 62.7 | 4.6 | 0,440 5 vee
4882 Jan. 0.479 | 710 | Li DRE 0.170 | 295 + 5
Febr. | 0.499 | 71.0 | 3.5 | 04 | 93 | — 4
March | 0.352 64.5 | 70 0.208 | 219 + 5
April | 0.189 | 57.7 | 8.4. | 0.474 | AM | — 40
May 0250 | 646 | 41.3 | 0.29 | DG» |e
June 0.135 | 60.7 UE) 0.192 | 479 | — 2%
July | 0.413 | 60.9 13.9 0.205 | 199 | — 2
Aug. | 0.086 | 59.7 13.6 0.187 | 0s Sn
Sept. | 0405, 4508 te 4200 0.102 | A3 | + AU
PE A A ELC DAD IR EN = ot 118 | — 43
Nov. 0.443 | 54A | 6A | 0.001 | 185
Dec. | 0.456 | 54.0 | 4.3 0.087 | 164 | — 20
1883 Jan. 0.309 | 60.9 | 3.5 0.122 181 | 0
Febr. | 0.361 | \66.4 | 5.2 0.142 | 175° |. = 3
March | 0.349 | 59.8 | 3.3 0.472 | 202 | + 27

ee Bar Temp. Lend I
fi Ss Ss
1883 April OL CEN 764 oh fe). 7 + 0.223
May 0.203 | 62.4 11.0 0.196
June 0.134 62 6 13.0 0.178
July 0.053 | 592 13 9 0.169
Aug. 0.107 3.8 foes 0.159
Sept. 0 020 59.5 12.7 0 099
Oct. 0.050 600: / 9.8. 0.045
Nov. 0.078 59.0 | his 0.020
Dee. 0.4 | 642 | 4.9 0.058
1884 Jan. 0.82 |-63.4° /' 5.9 0.058
Febr. 0.242 62.1 5.0 0.078
March 0.921 61.0 6.6 0,116
April 0.182 57.3 pha 0.153
May 0.205 64.0 44:2 0.181
June 0.150 | 65.9 A2 0.151
July 0.052 62.7 15-6 0.164
Aug. 0.087 64.3 Vr 0.179
Sept. 0,078 63.6 13.8 0.150
Oct. 0.104 62.4 10.1 0.073
Nov. 0.323 65.9 DA 0.125
Dec. 0.272 50.0 44 0.136
1885 Jan. 0.405 58.8 1.4 [0.190]
Febr. 0.262 57.2 5.6 0.183
March 0.599 65.6 4.8 0.210
April 0.201 56.5 8.7 0.215
May 0.148 58.1 9.2 0.154
June 0.151 63.6 13.2 0.187
July 0.191 67,7 14.5 0.204
Aug. 0.117 61.9 12.9 0.168
Sept. 0.097 60.3 4457 0.138
Oct. 0.031 54.2 8.8 0.080
Nov, 0.305 60.5 48 0.159

|

Redd

p.R.m | OC

+ 0,95 | -- 58

163 | — 2
UGA: eel 1
174 | ++ 16
Lol — 4
139 | — 43
107 | — Al
132 | — 13
105 | — 37
142 fi 28
129 | — 9

I

212

dk dd dt F+

208

994 | +. 34

153 | wa,
194 Fi u
25 | +15
Nen.
211 | 8
180 | A3

239 | + 1

Reda

| DR Dr ne ae DR pan | 0

1885 Dée | 4 04a | 76547] 48 | 0407 | dom |e
1886 Jan. | 0.313 BE 26 <1 2.3 0.225 257 | + 21
Febr. | 0.505 | 63.4 15 0.229 Ws | 15
March 0.451 | 63.6 | 5.0 0.267 269 | + 6
April 0.353 | 61.7 | a EO ED 256 | +10
May 0.250 6123 | 441.4 0.269 | 268 a 18
June 0 207 61.6 12.2 0.244 | 9251 — 2

July 0193 | 61.4 14.4 0.221 9 | — 44
Aug. 0.123 | 63.0 14 4 0.199 | 241 | — 19
Sept. | 0.196 | 64.4 | 444 | 0478 25 | — 12
Oct. | * 0.447 | 59.4 | 9.9 0.197 997 | — 30
Nov. 0.197 | 59.0 | PRS: 0.439 919 —

Dec. 0.936 | 52.4 | 3.7 [0 178] | 215 | — 57
1887 Jan. 0.492 | 63.3 1.4 [0.215] 7] 4 = ae
Febr. 0.595 70.4 | 2.9 0.259 287 +1
March 0.437 62.4 | 3.8 0.241 957 — 21
April 0.304 | 62.2 | 6.6 0.272 or | + 4
May 0.957 | 61.3 | 9.7 0.230 939 1: =e
June 0.296 69.0 | 15.1 0.253 269 =>

July 0.200 | 64.4 | © 45.0 0.272 300 | + 14
Aug. 0.195 | 62.4 | 14.0 0.268 310 + 22
Sept. oat | 61.7 | 123 0.219 | 273 | — 16
Oet. 0.307 | 61.4 | 8.0 0.233 | 994 | + 5
Nov. 0.304 56.4 | Dio 0.233 | 204 + 4

Dec. 0.384 | 55.9 | 3.5 0.268 | 392 | + 32
1888 Jan. 0,588 4° 67.601. 22,8 [0.271] | 305 | 415
Febr. 0.530 | 59.3 | 4.3 [0.307] 299 1 7
March | 0.395 | 50.9 3.3 0.273 ogg | = 4
April 0.391 | 59.2 | 6.6 0.31 300 | + 30
May 0.384 | 64.9 10.2 0.320 329 | + 39
June 0.188 | 60.0 13.4 0.279 205 | + 5

Tuly 0.115 | 57.8 13.0 0.226 254 | — 36

D. R. | Bar. | Temp. |
1888 Aug. +0.188 | 763.6 | +434
Sept. 0.257 66 2 AE)
Oct. 0.304 62.6 8.2
Nov 0.333 59.4 5.9
Dec 0.415 63.0 4.7
1889 Jan. 0.544 66.5 2.6
Febr 0.420 57.3 oud
March 0.437 60.6 44
April 0.970 | 56.0 7.6
May 0.204 59.7 13.0
June | 0.216 64.4 15.0
July 0,15 60.5 14.0
Aug. 0.133 59 13.6
Sept. 0.232 65.1 12.2
Oct. 0.181 Die 7 8.8
Nov. 0,408 66.9 6.4
Dee 0.518 66.1 Aa
1890 Jan. 0.420 60.9 4,3
Febr. 0.589 67.4 2.6
March 0.324 dl 6.1
April 0.282 Das Pez
May 0.226 58.4 11.4
June 0.282 63.6 12.4
July 0.199 60.0 13.7
Aug. 0.480 61.3 43.5
Sept. 0.264 66.8 134
Oct. 0.285 63.4 9.6
Nov. 0.245 of fee «ie ey |
Dec. 0.677 63.3 — 0.8
1891 Jan. | 0.741 64.8 | — 0.2
Febr. | 0.620 13.2 |+ 3.3
March 0.320 56 8 AT

Obsd

DRI RE a’

+024 | +03 | —97
0,291 975 | — 415
0.220 281 — 9
0.231 292 | + 2
0.231 285 — 5
0.255 TOT ie tan
[0.273] 206 | + 6
0.279 25 | + 5
0.262 om | — 19
0.289 Ae 8
0.292 308 | 18
0.252 980 | — 10
0.239 1 | — 9
0.247 301 | + 44
0.210 gr Ad
0.215 276 | — 14
0.242 26 | + 6
0.254 296 | + 6
0.287 315 | + 25
0.260 276 | — 14
0.270 279 | — 10
0.285 204 | + 5
0.295 311 | + 23
0.299 327 | + 40
0.256 998 | + 13
0.251 305 | + 22
0.225 286 | + 5
0.198 259 | — 19
[0.340]
[0.368]
0.256 984 | +15
0.223 239 | — 98

(80 )

| DR | BOE: | Temp. | DR | phil Dirge
1801 Apri’ | + 0°300 | 760.8 |+.5.8 | +0°036 | o's | — 90
| |
May | 0.483 | 57.0 96 | 02 994 | — 40
June. | 0.184 | 63.4 13.4 0.223 | 939 | — oh
July | O58 | 62.2 14.3 | 0.949 | 970 [Pt 7
Aug. | 0.411 58.0 | 13.3 | 0.227 © | 269 | + 7
Sept. | 0.125 | 63.7 (Bok ls oi *Obatee a! 18 .| — 44
Oi rel 0.436 | 57.4 10.9 | 0.198 259 | — 3
Nov. | 0.556 61.3 | 50 | 0220 | 281 of 19
Dee. 042% | 622 | 1.2 | [0.238] 262 0
102 Jam’. 1 0.382 | 573 | 2.6 | [0.921] | 237 | — 9%
Febr. | 0.326 | 56.6 | 3.6 | 0.202 | 230 — 32 |
March 0:466 | 63.0 | 3.3 | [0.244 | 955 | 29 |
April | 0.375: | 61.3 | fs. 0.285 | 994 | + 32 |
May — | 0.296 | 62.4 9.9 0.261 66 + 4
June 0.220 62.8 “Oa 0.253 | 254 — 8 |
July | 0.172 | 63.6 437 0.221 | Pe Re |
Aug. 20 0.153 | 62.6 14.6 0.239 | 59 | — 3
Sept. | 0.469 | 62.7 13.0 0.12 | 250 bee 12
Oek 214 0.448 | 55.3 | 9.2 0.192 2 ek!
Nov. | 0.263 | 62.3 | zE 0.169 234 | — 28
Dee sr OBS vl IDE he ard [0.206] 959, | a
1893 Jan. ONES el) 684th. 056 [0.272]
Febr. 0.313 | 56.2 4.3 0.214 58 | — 4
March | ~~ 0.391 64.7 1 Gel 0.224 247 — 15
April 0.498 | 67.4 9.2 0.307 314 | + 52
May 0.275 64.2 447 0.265 261 — 1
June 0.250 Gaal Sn, 0.292 290 + 28
July 0.453 | 60.7 14.9 0.274 270 Alt a
Aug. 0.168 | 64.9 15.5 0.248 265 | + 3
Sept. 0.184 | 59.5 12.6 0.260 300 | + 38
Oct. 0.213 | 60.4 10.6 0.227 981 | + 19
Nov. 0.333 | 60.9 5.7 | 0,204 276 | +44

‘Sate

( 81 )

ak Bar. Temp. |
1893 Dec. |H 0.300 | 762.2 | + 5.0
1894 Jan. 0.459 61.3 2.5
Febr. 0.431 62.1 4.2
March 0.348 61.7 6.2
April 0,265 60.5 9.9
May 0.293 | 60.2 10.5
June 0.252 62.6 42.0
July 0.139 60.9 4550
Aug. 0.136 61.2 13.8
Sept. 0.246 64.7 41.9
Oct. 0.221 60.9 9,3
Nov. 0.297 63.4 #5
Dec 0.310 60.0 4.7
1895 Jan. 0.520 54.3 da
Febr. 0.562 61 3 0.0
March 0.247 56.2 4.6
April 0.250 60.8 8.6
May 0.296 64.0 fed
June 0,273 64.6 13.6
July 0.141 60.2 14.6
Aug 0.133 61.4 14.6
Sept. 0.238 67.4 14.2
Oct. 0 190 58.4 9.7
Nov 0.291 61 6.9
Dec 0.273 55.9 4.2
1896 Jan. 0.458 68.9 3.3
Febr. 0.481 72.4 4,9,
March 0.279 58.5 5.9
April 0.359 64.3 7.6
May 0.356 66 2 10.0
June 0.171 62.7 14.2
July 0.166 64.4 14.9

Proceedings Royal Acad. Amsterdam. Vol. V.

Redd —
D.R. 1

+ 0,904

[0.2393

Reda
DD; Reaoll

+ 0.999

Ek dt +

( 82,5

Reda

D. R. | EN OA DARM | D. R. II | wage

1896 Aug, | 40.456 | 7627 | 14.0 | +0.996°| + 0.995 | +42
Oo epee) 500080 | 57.8 | 13.2 | 0.206 | 994 | 4 44
Oct. | 0.148 | 57.2 9.5 | 0.473 | 98 HU
Nov 0289 | 62.1 57 |, =n0,445 230 | + 5

Dec. | 0.948 | 58.8 3 0.081 180 | — 93

1897 Jan. | 0.300 | 58.4 24 041 206 A4 04
Febr. | 0:12 1 63.3 4d 0.419 188 | — 44
March | 0.161 | 5.2 6.4 0.130 184 — 17
April 0.99% | 60.7 BA Lal MAD tes 203 | + 2
May 0.491 61.4 | 10.9 | 0.195 | 212 | + 11
June 0.170 | 63.8 13.8 | 0.218 | 212 44
July 0.129 65.6 14.8 | 0.206 | 492 — 9
Aug. | 0.034 | „0.1 14.7 | 0.172 158 — 43
Sept. | oat | 644 12.0 | 0.470 | 178 | 8
Oet. 0.329 | 67.5 | 9.2 0.908 234 | + 33
Nav: a 0588 (4 166-6 3-64 0.491 | U | + 46
Dec. 0.340 | 62.3 4A 0.148 220 | +49

1898 Jan. 0.367 | 70.0 5:5. |< 0.406 167 | — 34
Febre 0.216 | 58.4 | 49 0.106 172 | — 29
March | 0.248 | 58.6 5.0 0.133 198 |= 8
April | 0.90% | 60.5 | 88 0.182 46 | +15

May 0.185 | 58.3 10.4 0.211 235 | + 34
June 0.474 | 63.5 | 13.4 | 0.207 206 | + 5
July 0481 | 648 | 13.4 | 0.905 202° | ed

| |

The table shows clearly that during the first months following the
starting of the clock the rate has been varying rather considerably,
as probably will be the case with all clocks. It will be seen at the same
time that oniy after about 10 years the greatest regularity was
attained. In the last years however the rate again began to get slightly
less regular, which is shown especially in the mean rates during
short periods, and when the clock was taken to pieces in 1898 it
appeared that this ought not to have been deferred so long. It was

ke

(oa)

found that the pivots were more or less affected, and on the suspen-
sion-spring there was a small stain of rust, which had fortunately
not eaten into the metal.

Further rather large deviations are shown by the reduced rates,
whenever the temperature was below O°. This is clearly shown
by the monthly means for 1890 December and 1891 January, during
which months the temperature was almost constantly below zero.
It might be thought that this points to the existence of a term depend-
ing on the square of the deviation of the temperature from its mean
value. Such a term might be explained by an influence of the
temperature on the elasticity of the suspension-spring. ')

It appeared however, as will more amply be shown below, that
the monthly means show little evidence of the influence of a qua-
dratie term, so long as the temperature remains above zero. It
would seem that the temperature-coefficient changes more or less
abruptly near O°, its value for lower temperatures being much larger.

I have therefore excluded all periods during which the tempera-
ture was below O° (or rather below — 0.°6 R.) Four months, viz:
1879 Dec, 90 Dec, 91 Jan. and 93 Jan. must consequently be exclud-
ed entirely. In 16 other months the temperature was below zero on
104 days. For these months new means were formed, excluding
those days. ® The following table gives the altered reduced mean
daily rates, together with the corresponding mean temperatures.

Redd:

Redd |
Temp. DRI

Temp. | Heed

5 s
1880 January .| + 2.4 | + 0.133 1891 December} + 5.4 + 0,208

|

1881 January.) + 2.3 | „199 1892 January ., + 3.4 „195
1885 January.) + 2.5 161 » March. | +39 | „239
1886 Decéthher | + 4.2 161 » December; + 4.6 190
1887 January. +--1.5 | „205 1894 January .| + 3.2 „216
1888 January .| + 2.9 | 263 » February | -+ 4.9 „232

» February! — 2.7 „264 1895 January.) + 2.3 „174
1889 February | -+ 3.4 | 268 » February) +422 | 146

1) Investigations by Dr. P. J. Karser about the clock Honwi 27, belonging to
the Bureau of Verification of the Nautical instruments belonging to the Dutch navy,
have shown that the nature of the suspension-spring has a considerable influence
on the value of the temperature-coefficient.

2) Since there were not always time-determinations exactly at the beginning
and the end of each cold period, some more days had to he excluded.

6:

(OF }

These means have further been used instead of the original values.

5. The reduced daily rates 1, as given in the tables above, formed
the basis of the further investigation. The first 5 months have been
excluded from the beginning.

To begin with, it is possible without much computation, simply
by combining the reduced rates into groups, to show that they must
still contain a term of yearly period which cannot be explained by
a direct influence of the temperature.

This is done as follows. The monthly means of the rates and of
the temperatures were arranged in groups of one year each, the year
beginning with May and ending with the following April. Then the
means were taken of the rates for each year, and the differences between
the monthly means and their yearly mean were formed. Thus I derived
for each year a series of 12 differences: monthly means of rate —
yearly mean, and also a series of 12 corresponding temperatures. In
each of these series the mean was then taken of the first and the
last value, of the second and the last but one, and so on. Finally also
similar results were derived substituting for the temperatures the
differences between the actual temperature of the month and that of
the preceding month (4 Temp).

Then the same process was repeated with the only difference that
the vearly groups commenced with February and ended with January.

The aim of this process will become clear when the results are
considered. For brevity’s sake I confine myself here to the five years
1884 to 1888. The differences: monthly means of rate — yearly mean
are given separately for each year, and also for the mean of the five
years. For the temperatures and the 4 Temp. only the means are given.
The differences of the rates are expressed in thousandth parts of a
second as unit.

It is evident at first sight that in the first arrangement all the series of
rates show a very marked progression, while the temperatures are
nearly the same. In the second arrangement the reverse is true. On the
other hand the variation of the rate is roughly parallel to that of
the 4 Temp. Hence the rates contain a term which does not depend
on the actual temperature, but of which the maxima coincide with those
of the yearly change of temperature, or, in other words, the yearly
periodicity in the rate cf the clock does not coimeide with that of
the temperature, and from the values just quoted we easily derive
that the first lags about half a month behind the latter.

6. Before a closer investigation of the phenomenon is possible, it

( 85 )

Temp.

A Temp.
84 — 88

| |
84—88

=
1884 | 1885 | 1886 | 1887 | 1888

|

ST a en ee EN es Ie
MEt Arrien a pot] oe09 (SEAB k1607| 44 |) AS) tgs f+ 8.9 P+ 30
Juner Mareby 0444 | +22 | +38 | | +32 | WEE 6! 27 | +95 [4+ 8.5] 4 2.0
July, February..... Mat | 8 be +30 | HU ;)/—5] +16 [+88] 413
|
lea?

August, January ...| HM | + 8 8/+8);+A6] +1 [4+ 8.27 —138
September, December) —26 | —22 | —40 | —14 | —296] —26 J+ 85] — 1.5
October, November..| —60 | —70 | —77 | —24) —24] —5l J+ 7.4] — 3.5

February, January | —18 Laon, 9 pe Oa NOM ay aimer Ove

March, December. . | -41 | +97 | + 6 | +4 —2] +5 [+ 4.5] — 0.2
April, November... | +2/+10|)--9|+2 | +20} +5 [+66] — 0.2
May,» October. …:…. 406040 | —20 | H6 | 17 |+96] — 0.4
Tone, September )..) ikl ial 43 | As af — 5 | 49.8] 4 0.6
DU eA TE USE his 431 | +9j|+ 2; HI, —30 +7 |414.2] + 0.6

must first be ascertained whether the adopted temperature-coefficient
represents the observations for the whole period.*)

For this purpose each year was treated separately. The years
beginning with February were used, since in that case the temperature-
coefficient is found nearly independent of the changes in the rate
which are proportional to the time.

Gradual variations with the time are namely clearly marked,
and over long periods they are not even proportional to the time.
This is seen from the following summary of the yearly means in
which I have taken the years beginning with May in order to be
able to include 1878.

1878 + 0 ; 122 1885 + 0. 111 1888 + 0. 252 1895 + 0 9 AS
1879 „120 1884 159 1889 „254 1894 „208
1880) „189 1885 „189 1890 „247 1895 „220
1881 „186 1886 „210 1891 ‚218 1896 „176
1882 ee by) 1887 „251 1892 „222 1897 „169

1) In the investigation of this section and also in that of 8.7, it was in-
advertently omitted to apply corrections amounting to 0%.005 to six rates of the
years "88 and °89. The influence of this omission is negligible. For the four
months, in which the rates were rejected on account of the low temperatures,
interpolated values were used.

( 86 )

Two methods have been applied to derive the temperature-coeffi-
cients. In the first method I used the deviations of the monthly means
from the yearly means, while in the second the deviations of these
same monthly means from approximate values of the term a, i.e. the
non-periodic part of the rate, were used. These values were derived
from a curve which represents as nearly as possible the yearly means
for years beginning with May, with August, with November and with
February ').

These two methods gave the following series of corrections, headed
I and II respectively, which must be applied to the value — 0.50268
of the temperature-coefficient. They are expressed in units of one
tenthousandth part of a second.

I II I II

Be dG ee a a (889 A: at AD
Co ee NE Speers ae 1) 1800, A a oF
Ts uae ey Sipe Bad LEDE oe ee
ABD - 1. 70, “2 68 1892 + B + 98
re ae ae Ba 1893 + 52 1+ 46
Ien Mags mc 1894 14+ 6 + 64
885 VE Dea 1895 + 9 +96
188615 32 ee 1896 +1402 + 96
agen, Erg Pe is Sy aoe NE DE
te MF

The two methods thus give practically the same results. Although
this agreement is of course not a measure of the real accuracy of
the corrections found, it is nevertheless evident that the temperature-
coefficient has not been constant during the whole period, but that
the adopted value requires a positive correction as well in the first
as in the last years, the latter being the most marked.

If the whole period is divided into three parts, we get the following
mean results, according to the second computation (those of the first
method are nearly the same) :

18791884 A c=—= + 38
1885-1892 de
1893-1897 S78

}) In first approximation it was assumed that e.g. the mean for the year from
"78 May to ’79 April gave the value of a for ’78 Nov. 1. Afterwards these
values were in some cases slightly altered.

( 87 )

Throughout the preceding investigation it was assumed that the
influence of the temperature is proportional to its first power. It is
important to investigate the results which will be found, if we repre-
sent the influence of the temperature by the formula:

e, (t{—t,) + ¢, (¢—t,)’.

For this purpose I used the deviations of the monthly means
from the values of a derived from the curve. These deviations were
represented by the formula

Aa + Ae, (t—t,) He, (tt).

I did not investigate the separate vears, but I derived mean results
for the three periods mentioned above; f, is then in each case the
mean temperature of the period, and differs but little from —+ 8.7
(= + 8.1 Réaumur).

In this way I found the following values of Ac, and c,, both
expressed in tenthousandth parts of a second:

Ae C5
19792=1964° 1-30 439
Ke EE
1893—1897 19 —7.9

The values of Ac, nearly agree with those previously found
for Ac. Those of c, are small and of different sign, and their reality
is doubtful. The rates for temperatures below zero would require
positive and much larger values of c,. In order to represent e. g. the
two results for the months 1890 Dee. and 1891 Jan. it would be
necessary to assume c, = +15.

I think therefore to have acted correctly by exeluding the rates
corresponding to temperatures below 0°. For the other temperatures
we may certainly provisionally adopt a linear formula for the influence
of the temperature.

As to the coefficient c of this formula, I do not think that it could be
represented as a function of the time which would have any real
meaning. Probably, however, it will be better to assume if constant
during shorter periods only, e. g. thus:

Ac C
1819-801121; AAT
1881—83 -+ 52 — 216
1884 +31 — 237

1885—91 ste
189093.) Sir oad
(Bode IT EB, aay

Finally [I will show how these coefficients would be altered (see

( 88 )

before) if the barometer-readings had been reduced to one tempe-
rature, in other words, what are the values of the true temperature-
coefficients. For 760 m.m. the reduction for 1° Réaumur amounts to
0,152 m.m., of which the effect on the rate is 0'.0021. Consequently
the 4e temperature-coefficient is found by applying a correction of
+ 00021 to the apparent value.

7. We shall now apply to the reduced mean rates the reductions
due tothe corrections found for the temperature-coefficient. The adopted
corrections are of this coefficient:

1878 May—1884 April 6¢=>-+ 39
1884 May—1893 April 0
1893 May—1898 July +75

Though probably the values mentioned at the end of § 6 are
preferable, it did not seem necessary to repeat the computations with
these altered values.

After this the deviations of the corrected monthly means from the
values of a) derived from the curve were formed and these
means were arranged in yearly groups, each year beginning with
May. ®) For brevity’s sake L do not give the results for the separate
years, but only the means for four groups of years, viz: 1879—1882,
1883—1886, 1887 —1891 and 1892—1896. If the deviations of the
monthly means from the yearly means are used, the mean results

for those four groups are not appreciably altered. All values are
given in units of one thousandth part of a second.

It will be seen that the results of the first and the second groups
agree very well inter se, and also those of the third and the fourth
groups, I have therefore finally formed the means for the periods
1879—1886 and 1887—1896. The principal difference between these
two periods seems to be that the low minimum in October which
is shown in the first, has disappeared in the last. In the years,
1892—1896, however, the whole periodicity begins to be less marked,
and in 1897 it is no longer shown by the monthly means. The
monthly means of 1878 (i. e. ’78 May—’79 April) are in good
agreement with the results for the period 1879—1886.

1) Since this curve is relative to the temperature + 10°, while the mean yearly
temperature is + 8°.7 its first and last part had to be slightly altered, to account
for the altered values of the temperature-coefficient.

2) The curve for a can only be drawn from 78 Noy. to “98 Jan., therefore

the present investigation can only include the period "79 May—’97 April.

( 89 )

ie 1879 | 1887

79—82 | 88—86 | 87—91 | 92—96 B

| 1886 | 1896
May... .)s. 4-37 | +38) + 22 | + 40}, +38] + 31
JUNE. |. Ks. +414; +24) +23; +27] +19) +2
July.... .| 4-12) +22) +13) — 4] +17} + 5
August.... — 3| + 7] — 4] — 16] + 2! — 10
September.) — 38} — 32} — 27} — 9] — 35] — 18
October...) — 64 | — 85 | — 29 | — 23] — 74 | — 26
November. — 22 | — 54 | — 26| — 21] — 38| — U
December. — 22 | — | —13| —16}] — 24| — 14
January..| +12} — 5| — 7| — 6] + 4] — 6
February.| — 1; +19; +41) — 9] + 9; + 1
March....| + 40} +34} +1411} — 8] +37; + 1
April sa +39; +46) +30; +24) +2) +97

During the period 1887—1896 the periodicity can be very satis-

factorily represented by a simple sinusoide. We find:

T— May 5

3650

where the amplitude has been expressed in tenthousandth parts of a
second *).

For the first period such a representation is impossible, and even
when a term containing the double angle is introduced, the repre-
sentation is not entirely sufficient. In that case we find:

T— Apr. 24 T— Apr. 23
Ar = + 455 cos 22 —_——— — 95 cos 42% ——______.
360 365

An entirely satisfactory representation can only be obtained by an
empirical curve.

This curve, together with the points which indicate the observations
to be represented, is here reproduced in fig. 1. The sinusoide of the
second period is given in fig. 2”).

Moreover the following table gives for the first period the differences

Ar = + 254 cos 22

1) From the period 1887—1891 alone we find
= T— May 1
Ar = + 274 cos An ————_...
5365

2) These figures will be published together with the second part of this paper.

( 90 )

Obs.—Comp I and Obs.—Comp. II, where Computation I means
the representation by the formula, while Comp. II refers to the curve.
For the second period the differences Obs.—Comp. are also given.
Everything is expressed in thousandths of a second.

79 — 86 | 9796 | 79 — 86 | 37-96
—_—— -
0.-C.1)0.-C11} 97% 0; = 6.41 10.0.) 27 ae
Mary Saken | ep | ae a) eal | November |) 4149) Se eo eas
Jone heer EAD Zn D iden December. + 3) — 5| + 6
a teen act ae UPS are tg January: i= eS Aa
August.....; + 11 | +9, — 6 February ..| — 14} —M | — 3
September... | + 2| + 3) — 2 Marel, ...-: + 4 | + 4; — 15
| }
October. t i) Oy ON ares ON) Aprile Sven de 6 | a | SE

Finally attention must be drawn to the fact that a term with the
argument 427° might be explained by the direct influence of the
temperature, if a quadratic term is assumed therein. In fact the
yearly variation of temperature can be approximately represented by :
T—May 1

Ein — + 5.°S sin An — 365
565

whieh would introduce into the rate a term:

T—May1
365

Ar = — 15e, cos 4a

which agrees nearly with the second term in the above formula
for the period 1879—1886, if we take c, = + 6. The probability of
this explanation is however lessened by the fact that a similar term
does not exist after 1886.

8
used to free the monthly means from all periodic terms and then

>

The results which have so far been derived have finally been
to represent them by a simple curve.
For this purpose

Ist the reduced rates I were reduced to the mean temperature
+827

2nd the corrections, which become necessary if the temperature-
coefficients given at the end of § 6 are adopted, were applied.

RS 4D

ged corrections were applied for the supplementary periodic term
in the following way, viz. for 1878 to 1886 according to the curve
for 1887 to 1896 by the formula, while for 1897 and 1898 the
correction was adopted = 0.

The reduced rates found in this manner are contained in the
general table of the rates given above, under the heading „Redd
De i Ls. |

The drawing of a curve was to a large extent arbitrary. I have tried
to make it as simple as possible. It is reproduced in Fig. 3 5). The
residuals O.—C. (Obs. — Curve) are given in the last column of
the general table.

For the years 1879

1896 the mean error of a monthly mean
derived from these residuals is
Mees aot 0,028
If the supplementary term had not been applied it would have been
M.E. = + 08.0364

The difference is considerable.

1) The curves derived from the yearly means, which were previously used, agree
with this one in the principal points, but were more complicate.

(June, 25 1902). ‘

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING

of Saturday June 28, 1902.

———__- 5 Co

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 28 Juni 1902, DI. XI).

ER ORE: bs MTS:

Eve. Dusors: “The geological structure of the Hondsrug in Drenthe and the origin of that
ridge”, (Ist. Part Communicated by Prof. K. Marri), p. 93, (2nd. Part Communicated by
Prof. H. W. Baxuvis RoozrBoom), p. 101.

G. C. J. Vosmarr: “On the shape of some siliccous spicules of sponges”, p. 104.

J. D. van DER WAALS Jr.: ,,Statistical electro-mechanics,” II. (Communicated by Prof. J. D.
VAN DER WAALS). p. 114.

J. D. VAN DER WAALS: ,,Ternary systems,’ V, p. 121.

J. H. Boxnema: “Cambrian erratic-bloeks at Hemelum in the South-West of Frisia”. (Com-
municated by Prof. J. W. Morr), p. 140.

G. van Iverson Jr: “Accumulation experiments with denitrifying bacteria’. (Communicated
by Prof. M. W. Brrerinck), p. 148, (with one plate).

W. H. Jurivs: “An hypothesis on the nature of solar prominences”, p. 162.

C. A. Losry pe Bruyn and J. W. Diro: “The boilingpoint-curve of the system: hydrazine
+ water”, p. 171.

C. A. Lospry pe BRUYN and W. ALBERDA VAN EKENSTEIN: “Formaldehyde(methylene)derivatives
of sugars and glucosides”, p. 175.

J. J. Branxsma: “The intramolecular rearrangement in halogenacetanilides and its velocity”.
(Communicated by Prof. C. A. Lopry pr Bruyn), p. 178.

W. Reivers: “Galvanic cells and the phase rule”. (Communicated by Prof. H. W. Baxuuis
RoozreBoom). p. 182.

E. F. van DE SANDE BAKHUYZEN: „On the yearly periodicity of the rates of the standard-
clock of the observatory at Leyden, Hohwü Nr. 17,” (2nd Pari). p. 193, (with one plate).

Erratum, p. 217.

The following papers were read:

Geology. — “The Geological Structure of the Hondsrug in Drenthe
and the Origin of that Ridge.’ By Prof. Eve. Depors. (Com-
municated by Prof. K. Martin.)

(Communicated in the meeting of May 31, 1902).

North-west of Eksloo, on the Hondsrug in Drenthe, remarkable
sections of the soil are now to be seen in about fifty pits, due last
winter on behalf of the projected Noord-Ooster Lokaal-Spoorweg.

—

‘

Proceedings Royal Acad. Amsterdam. Vol. V.

eC»)

The greatest part of these pits are found on the Noorder Veld of
Eksloo, at a distance of about 1'/, K.M. from this village and at a
mutual distance of 50 M., a few at 100 M. mutual distance, in the
directions from north-east to south-west and north-west to south-east;
some, nearer to the village, on the Hooge Veld. Seven others are on
the Buiner Veld, at about 1'/, K.M. farther N.N.W. from the principal
group, succeeding each other at intervals of 100 M. in the direction
from south-east to north-west. The pits are square, the edges measuring
about 3 M., and though many are not quite as deep now as they
have been, owing to their being partly filled again by blown-in sand,
the vertical sides of the greater number are still uncovered to a depth
of 3 or even 3'/, M.

Excepted two of them, situated most to the north-eastern border of the
Hondsrug, we observe in all a similar section. In the upper part
a relatively thin bed of sand, being near the surface of a dark
greyish or nearly black colour, owing to much humus contained
in it, but for the rest of a light yellowish or brownish grey,
this bed showing hardly any traces of stratification and containing
irregularly scattered stones of very different size, among which
granites and coloured quartzites are predominant '). The sand is
intimately mixed in some places with a noticeable quantity of brown
clay. It is the well-known bouwlder-sand of the Hondsrug. Under it,
to the bottom of the pits, rather coarse, loose, white quartz-sand,
which is clearly stratified and in which are to be seen, locally,
irregular small banks and strings of well rounded, water-worn pebbles,
principally of white vein-quartz and next to it of light-grey quart-
zites and Lydian Stone, the largest of which pebbles have for the
greater part only a dimension of 15, some however of 25 mM.
The grains of this sand seen through the magnifying-glass prove to
be also well rounded and almost all clear as glass. This description
of the underground is completely applicable to the 4 Preglacial or
Rhine- Diluvium’.

Whilst near the bottom of the pits the stratification of this plei-
stocene alluvium of the Rhine is often nearly undisturbed and pretty
well horizontal or sloping in undetermined directions, it is upwards
always fantastically folded and wrinkled, contorted, a feature
becoming very prominent on account of thin or sometimes thicker veins
of sand of a yellow or brown colour, evidently derived from the

1) In most cases we find only smaller stones, the bigger ones having already
been dug up, which appears from the unevenness of the surface, caused by the
irregular reposition of the swards. There where this is not the case, large stones
and boulders are still to be found.

( 95 )

upper bed, alternating with the white head mass. In short, the
consequences of the pressure and the moving of the land-ice with
its bottom-moraine material over the loose underground are beauti-
fully illustrated here.

Of the most part of the pits on the Noorder Veld of Eksloo, viz,
of those numbered from VII to XLV, I have measured the thickness
of the boulder-sand bed. These dimensions are given (in Meters) in
the following small table. Some pits could not be measured on account
of the indistinetness of the lower limit of the bed. From those on
the Hooge Veld the thickness of the boulder-sand is not more than

NW,

XLV XLIV XLI
DSA. 0.94.0". 0.432008
XLI XLI XL XXXIX XXXVII
08-400 0.84.0") 0620.9 Ort 0.4
XXXII XXXIV XXXV XXXVI __ XXX VII
Ones ALO 076-008 Av Glee
XXXII XXXI XXX XXIX XXVIII -
| NE 0.6—0.7 0.6—0.7 LI, 0.20.5
XXIII XXIV XXV XXVI XXVII
0.70.8. 06-008. 0.40.9 en +0.3
XXII XXI XX XIX XVII XVII
0.7 0.3—0.5 +04 +0.3 +0.25 08
10: cl
XII XII XIV XV XVI
0.6—0.7 0.3 (30:5) >. 8320 0.3
XI x IX VII VII
0.3 0.5—0.6 0.7—0.9 0.3 0.3

SE.

( 96 )

about 0,25 M. On the Buiner Veld (XLVIII to LIV) it varies from
0.2 to 0.8 M., attaining in a single case, locally, 1.5 M. Ata distance
of 200 M. north-west of XLIII there is on the Noorder Veld, near
the Tippen, a pit numbered XLVI, with 0.4 M. of boulder-sand,
and, 100 M. N.N.W. of the latter, another pit, numbered XLVII,
showing a very irregular thickness of this upper bed, it locally giving
way in the stratified white Rhine-sand. Moreover the latter contains,
unto a depth of 2 M., boulders of granite and other rocks of Scan-
dinavian origin.

From this table, that refers to an area long 400 M. in the same
direction as the Hondsrug extends (from north-west to south-east) and
broad 250 M., at right angle on it, and from the other given data,
it appears that the thickness of the boulder-sand bed is very slight,
attaining seldom 1 M., further that it varies greatly at small distances
(often in the selfsame pit). The fact that the difference in height of
the position of these pits is much larger than those differences in
thickness, proves that the upper or boulder-sand bed follows the
undulations of the preglacial nucleus of the Hondsrug and is rather
regularly laid down upon it. |

Some details may still be mentioned. In pit XII the brownish
boulder-sand, having an average thickness of 0.6 to 0.7 M., penetrates
wedgelike in the white sand unto 1.25 M. beneath the surface, whilst
the strata of that underground are rent asunder unto about 2 M. lower
than this wedge. This brings to the mind straining forces having
worked laterally to the Hondsrug, such as would have arisen from
an uplifting of the sand masses now constituting the nucleus of that
ridge. In pit XXXIV two boulders from 0,2 to 0.3 M. in dimension
are sunk totally below the general inferior limit of the boulder-sand
bed in the pit. In pit XXXIX and XLI the sand, of a darker brown
colour, is partly containing enough clay, that it becomes plastic, and
also by alluviating it is proven that no small quantity of clay is
present there.

But besides such particularities there are to be observed phenomena
of greater importance. This is the case with N°. XLVII, showing
fluvio-glacial mixing of the bottom-moraine with the sand of the under-
ground, and with the two pits N°. XLI and XVII. In pit XLI there
is in the south-western side a boulder of quartzite, almost square, about
measuring 0.35 M. in every dimension. It is fixed at the bottom of the boul-
der-sand bed, having there a thickness of 0.7 M., and depressing, pocket-
like, the strata, there rather undisturbed, of the white quartz-sand, unto
0:4 M. below its inferior extremity. Its basis is a plane ascending
in the direction from north-west to south-east; but this basis belongs

( 97 )

properly to a sheet of the boulder, about 4 c.M. thick, extorted accor-
ding to a lamination plane parallel with that sloping basis, and the
large upper piece has been pushed on, sliding upward 1'/, ¢.M. in the
direction from north-west to south-east. The boulder with its extorted
sheet are immovably fastened in the upper boulder-sand bed, which
here contains rather much clay and is tolerably hard. In the opposite
side there is a somewhat larger boulder of granite, polished and
scratched. The contortions in the white sand of the underground are
particularly fine in this pit. Apparently no boulders were extracted
here, as is shown also by the appearance of the surface.

Pit XVII, which (with XLVID) is nearest to the eastern border of
the Hondsrug, at a distance of about 150 M. from the first house
along the Beekslanden, shows, as already has been said, a section
different from those in the other pits. Above, again the common
yellowish grey boulder-sand, 0.8 M. thick, in its lower half without
boulders, under this, however, + 1 M. of reddish brown, hard
boulder-clay, containing much sinall stone fragments and some boulders.

This hard, red boulder-clay is well known in the underground of
some of the Velds of Eksloo, where, locally, it occurs, at small
distances from the eastern border of the Hondsrug, as far at least
as Weerdinghe. .

Quite identical reddish brown boulder-clay, under 0.7 to 0.9 M.
of block-sand, is visible in a clay digging at the west of the Honds-
rug, along the Langhiets Kamp near Odoorn. Going from there in
the direction of Valthe it soon disappears from the underground,
so that the boulder-sand bed is resting immediately upon the loose
Rhine-sand. In a sand digging 2'/, M. deep, at a distance of about
1 K.M. N.N.E. from Valthe, the boulder-sand is 0.4 M thick.
The white sand below it contains well rounded pebbles of white
quartz and also of lydite. Halfway Odoorn and the side-branch of
the Oranje Kanaal the boulder clay begins at a hunderd Meter west-
ward from the road to Emmen. There, as well as nearer to the
road, where the boulder-sand rests immediately on Rhine-sand, this
boulder-sand is 0.7 M. thick; but already before the side-canal the
boulder-clay reaches the road which remains on it as far as Emmen.
Following the high road from Odoorn in north-western direction to
Ees we find the boulder-clay in a clay digging, a little farther than
the churchyard, under 1 M. boulder-sand. In a well sunk still somewhat
farther off, in a meadow to the right of the road, about 3 M. of this
boulder-clay was met with, which contained, next to other rock species,
especially flint nodules; under the clay again coarse white loose
sand with small well rounded pebbles of white quartz. Ata distance

( 98 )

of 4 K.M. from Odoorn, where the way from Eksloo to Brammers-
hoop crosses the high road, boulder-clay is seen again, under 0.7 M.
of boulder-sand; here it is partially of a yellowish brown spotted
with greenish grey colour, a difference in connection with the not
flowing off of the water in the soil. In sinking a well, this clay
proved to have a thickness of 2'/, M. Farther north it is found
at least as far as Ees.

At 2, K.M. south-west of Odoorn, in the Peat-moss of Odoorn,
that is in the midst of the Peat-moss of Schoonoord according to
Lorik, the boulder-clay is wanting under the + 1 M. thick bed of
boulder-sand, which came to light after the opening of the peat-moss
for digging fuel. In its place a bed of light bluish grey clay, 0.3
to 0.4 M. thick, is found. This was observed at a pit dug on purpose
and is the case with the whole Peat-moss of Odoorn, as has been
observed when digging ditches. This plastic clay, containing no
palpable sand, is entirely different from the boulder-clay. It is
hardly to be doubted that we have to regard it as lake-clay, the
same as the wellknown preglacial Pot-clay from the underground
of Drenthe, Groninghen and Friesland, which gave rise to peat-mosses
in such cases where it was shaped in the form of basins.

Thus the considered part of the Hondsrug, about the half of the Honds-
rug in Drenthe and almost a third of the whole of that ridge which
is extended from north-west to south-east, between Groninghen and
Emmen, and is elevated only on an average 5 M. above the
„surrounding region, is constituted by preglacial Rhine-sand, super-
ficially covered, in the same manner as the adjoining ground, by a
bed of boulder-sand not 1 M. thick.

That the boulder-sand cannot owe its origin to washing out of
the boulder-clay may be admitted for the following reasons:

1st The hard boulder-clay offers great resistence to eroding agencies.
This appears amongst others from its forming steep and more or
less projecting parts at the coast of the Roode Klif, the Mirdummer
Klif and the Voorst, and even isles, at Urk and Wieringhen.

2°¢ Though undoubtedly the quantity of boulders in the boulder-
sand has from the beginning been very variable, it is however a
fact, that in the neighbourhood of the villages most boulders have
already been dug out and that they were formerly very numerous
almost everywhere. At some places one stone was lying next to the
other in the sand. An average condition is to be met with at some
parts of the Noorder Veld of Eksloo. Now to the north of pit XLV
on a surface of 1500 M*. and to a depth of 0.5 M. there had been
freshly dug out 40 M*. of stones, from the size of a child’s fist up to

( 99)

1 M. in length. Estimating the air spaces between the stones heaped
up at '/,, we find about */,, of the volume of the boulder-sand bed
to have consisted in stones. Between pit XV and XVI a similar
1
24

estimate, from a surface of 484 M’., leads to for that proportion.
What an enormous thickness of boulder-clay, which in this region
is particularly poor in stones, must have been washed out to leave
all these stones!

ged The boulder-sand contains very little flint, the boulder-clay very
much, everywhere. Flint is the kind of rock most frequently occurring
in the clay (Odoorn, Zwinderen, Nieuw-Amsterdam, Mirdummer-Klit,
Nicolaasga, Steenwijkerwold, Wieringhen etc.)

4th Even the deepest and evidently not washed out parts of the
boulder-sand, which rest immediately on the Rhine-sand, are as a rule
poor in clay.

5th Boulder-clay and boulder-sand are found jointly or the latter
alone without this being expressed in the form of the surface.

That the Hondsrug cannot be a terminal moraine, as has been
supposed by some geologists, follows sufficiently from the description
of its structure as given above.

It neither can owe its’ origin to an upward folding or pressing
of the underground, perpendicular to the direction of the motion of
the pleistocene land-ice; for how then to account ‘for the deposition
of boulder-clay parallel to the Hondsrug ridge?

The distribution of the boulder-clay in our north-eastern provinces
is so, that there can hardly be any doubt that from the beginning
it has been very unequal and the boulder-clay has been laid down
parallel with the actual Hondsrug ridge.

Can it perhaps by its weight have pressed upward the Rhine-sand,
when the soil was still totally drenched with melting-water? This
apparently has not been possible. The specific weight of a well
compressed sample of that Rhine-sand from the Hondsrug, quite
drenched with water, is 2.05. If now that of the boulder-clay had
even attained the high value of 2.5, it would require a bed of
boulder-clay of a thickness of 20 M. to cause an uplifting of 5 M.,
as is the average height of the Hondsrug above the surrounding

'/, of that

region. In reality the thickness is most probably only *
supposed value.

Other causes must have been in action to bring about this elevation
of the Hondsrug, but causes which nevertheless were not inconsistent
with the deposition of the boulder-clay parallel to that ridge.
These causes may be found in what CHAMBERLIN, RUSSELL, SALISBURY,
VON Drrycarskr and already Nansen have taught us regarding the

( 100 )

structure and motion of the inland-iee in Greenland. According to
the earlier ideas the bottom-moraine was pushed forward under
the ice, from the centrum of dispersion of the latter; to day we
know that stones, sand and mud are transported included strata-like
in the inferior parts of the ice mass, by the gradually melting of which
the bottom-moraine is formed. Further it is known, that the motion
of the inferior strata of an inland-ice mass becomes the slighter
the more these are laden with stones and mud. Evidently this load
was less above the strip of land which actually constitutes the eastern,
most elevated portion of the Hondsrug than at the west of this portion,
where the ice in its downmost parts must have been thickly laden
with clay. Above this strip we may suppose to have existed a
relatively more rapid motion of the inland-ice in comparison with
above the extensive western clay banks, the result of which difference
would have been a lower level of the ice in the first and a higher
in the latter parts. Thus, actually, in Greenland a considerable diminish-
ing of the motion and a swelling of the ice is seen there where in
its undermost strata it is strongly laden with debris of rock, and
lowering of the surface where this motion is not hindered, on account ot
the lowest ice-strata being relatively pure. Thence considerable pressure
on the underground where those clay banks are now to be found
in the Hondsrug and a minimum of pressure near the eastern border;
there then the loose Rhine-sand, drenched with water was as a whole
mass uplifted.

The situation of the elevated ridge of preglacial sand side by side
with the long and broad western strip of boulder-clay makes us also
suppose that the direction in which the ice moved was not, as is still
generally admitted, from north-east to south-west or from north to south,
but the same as the extension of the Hondsrug, from north-west to
south-east. Now with this supposition perfectly agrees the at first
sight paradoxical direction of motion as derived from the shifted
boulder of quartzite.

But how then can we account for the fact that the boulder-clay
was laid down principally in a long and broad strip along the western
part, whilst the boulder-sand above it is uniformly thick with that
in the eastern part on the Hondsrug where clay is generally absent
under it? This question too is not difficult to solve with our
actual knowledge of the phenomena of the motion of an inland-ice
mass. The material of the boulder-sand bed may have been trans-
ported as a continuous bed by higher ice-strata, at the same time as
disjuncted strips and patches of clay were included in the lower
ice-strata, or the sand with its boulders may have been transported

Pot te ee

s
me Me

pr, TR Te

En .

( 102)

at a somewhat later time. Small variations in the direction or in
the velocity of the motion of the ice can easily have divided the
boulderclay in strips and patches.

Thus all the observed geologieal phenomena can be viewed in the
light of known actual phenomena, which appears to be impossible if
we start from the opinions embraced up till now on the nature of
the Hondsrug.

Now that it is known that the direction of ice streams which ended
in North-Germany has often been considerably modified by the
form of the basin of the Baltic and also by the meeting with other
ice streams, it is less surprising, that, notwithstanding the predominating
or exclusive occurrence of Swedish, at least Scandinavian rock
species in the bottom-moraine of our north-eastern provinces, these
can nevertheless have arrived there in north-west—south-eastern
direction. Suchlike factors, as supposed to have modified the di-
rection of the North-German ice streams, may have been the cause
of the deviations of an ice stream, which, coming from Sweden, first
took a south-western direction over Denmark, till it arrived in the
North-Sea. We do not know how far the ice which came down
from southern Scotland and northern England did progress south-
eastward in the North-Sea; it might be possible, at least, that as a
very powerful stream it has met there with the ice stream coming
from Sweden and has pushed this back south-eastward in the direction
of Friesland, Groninghen and Drenthe.

Very likely as a result of this motion of the ice over our north-
astern provinces the Hondsrug and some parallel less extended
elevations have then arisen, in such a way as indicated above.
Farther west of the Hondsrug, however, probably a real folding,
under the pushing ice, of strata impermeable for water, should they
consist in Potclay or in the boulder-clay itself, raised, perpendicular
to that direction, a number of north-east—south-western ridges, leaving
between them valleys now occupied by rivulets. Indeed an elevation
by folding is more readily to be admitted for compact soils than for
the loose sand which constitutes the nucleus of the Hondsrug.

Geology. — “The Geological Structure of the Hondsrug in Drenthe
and the Origin of that Ridge.” Second communication. By
Prof. Eve. Dusots. (Communicated by Prof. BaKavis RoozeBoom).

Further researches in that part of the Hondsrug, considered in my
former communication, led to the following results.
At a short distance north-east of pit LI, the boulder-sand bed of

( 102)

which, up to a depth of 1.5 M., shows an irregular mixing with
brown clay, there is on the highest part of the Buiner Veld (and the
Hondsrug in those parts), under 0.5 to 0.8 M. of boulder-sand, a
yellowish red boulder-elay bed of 1 M. thickness. It is situated at
about 1 K.M. south of Buinen and measures about two hundred
Meters in every direction.

The clay found in pit XVII extends, as shewn by borings, only
some 50 Meters in different directions.

Another patch of boulder-clay is found south of the Zuider Esch
of Eksloo on the southern Hooge Veld, in an oak-underwood, under
about 0.5 M. of boulder-sand. This patch too is of small dimension.
The same is the case with another on the Zuider Veld of Eksloo.

Farther, in the neighbourhood of Valthe, a clay bed is found on
the Kwabben Veld, under + 0.5 M. of boulder-sand, 1.5 M. thick,
at least, of about 300 M. dimension in every direction and extending
still somewhat farther south-east on the Nieuwe Esch; a smaller one
exists south-east of the Kampen Veen.

The four latter clay patches are situated, with the two first men-
tioned, pretty well in one direction, from north-west to south-east,
but they are separated by large intervals in which the boulder-sand
rests immediately on preglacial stratified white Rhine-sand. The
mutual distances of these clay patches are resp. 2, 3, 1, 2,1.5 K.M.
With the only exception of the small clay patch on the Noorder
Veld, all these, though situated very near to the eastern border of
the Hondsrug, are on the highest parts of that ridge.

The stratified white Rhine-sand is, amongst other localities, to be
seen in a sand digging on the Kleine Esch of Eksloo (under + 0.4 M.
of boulder-sand) in a sand digging at the northern border of that Esch
(under 0.38 M. of boulder-sand) and on the Zuider Veld, near to the
southern border of the Achter Esch; further at the Valther Schans
(under 0.3 or 0.4 M. of boulder-sand), in a sand digging east of the
Kampen Veen (under a bed of boulder-sand of the same thickness)
and further, along the great Bourtangher Peat-moss, from Valthe to
Weerdinghe.

The western boulder-clay, on the contrary, forms a long and
broad strip, which from Ees to Emmen seems not to be interrupted
and is 1 to 1'/, K.M. wide. It has probably in its whole length a
thickness of 2 or 3 M. and is covered by 0.7 to 1 M. of boulder-sand.

The origin of the Hondsrug according to the hypothesis indicated
in the former communication can thus only be applied to that
western strip of boulder-clay. Other facts now observed have brought to
my mind, besides the already mentioned factors, others which may have

( 103 )

been of still greater importance in the formation of the Hondsrug.

Beyond the Hondsrug also, even as far west as Hoogeveen, the
underground consists of preglacial “Rhine-Diluvium”. In the Peat-
moss of Ees it is covered by at most 1 M. of boulder-sand. In the
Elders Veld between Schoonoord and Schoonloo the preglacial Rhine-
sand is of a yellowish grey colour, on account of its intimate mixing
with parts of the upper bed. The occurrence of small water-worn
pebbles of white quartz and lydite, repeatedly stated to a depth of
2 M., serves to show, that here too we have chiefly before us old
Rhine-alluvia, which only later on were mixed with the bottom-
moraine. At Schoonloo, in a sand digging, a kind of “Mixed Dilu-
vium” (Gemengd diluvium) is to be observed; water-worn pebbles
of white quartz and lydite are seen in the sand side by side with
Scandinavian granites. On the Elders Veld boulder-clay is only found
in single small patches, such as the one at 1.5 K.M. south-west of
Schoonloo.

In the midst of the Peat-moss of Ees, at a distance of 4 K.M.
exactly south from Westdorp, a round hillock rises above the perfectly
level environs, not unlike a small volcanic island above the sea. With
a basis of about 30 M. of diameter and a height of circa 5 M. it resembles
a very large tumulus; it is the renowned Brammershoop.

The constitution of this hillock, however, is inconsistent with the idea,
which presents itself at first sight, that we have before us a
work of mans making. It is indeed composed of white quartz-
sand with well rounded small pebbles of white quartz and lydite,
the same preglacial Rhine-sand, which also constitutes the underground
of the surrounding region with a mantle of glacial boulder-sand only
0.2 to 0.5 M. thick.

Still less than in the case of the Hondsrug it will do here, to
attribute the origin of the elevation to pressure of the pushing ice;
for how could the motion have been directed from all sides towards
that single point! As it appears to me, the only way to explain how
only there the soil was pressed upward, in the form of an isle, is
to suppose that a minimum of pressure of the ice, has existed there,
most probably in consequence of a former Gletschermühle (moulin) in
the period of the melting of the ice.

Not’ improbably then we have, partially or perhaps chiefly, to impute
the elevation of the preglacial Rhine-sand in the Hondsrug to a
similar minimum of ice-pressure, at the place of a large river-bed,
formerly occupied by melting water, and carved in the surface of
the ice in the direction from north-west to south-east, or may-be to
a large and long crack in the same direction.

( 4104 )

Zoology. — “On the Shape of some Siliceous Spicules of Sponges” ;
by Dr. G. C. J. Vosmarr.

The perplexing amount of variety exhibited by sponge spicules
has since long made it desirable 1°t to designate certain spicules by
special terms, and 2rd to divide the spicules into groups. The first
attempt to such a classification was made by BOWERBANK in 1858 ;
later, in 1864, modified by the same author. BowerBANK divided
(1864 p. 13) the spicula into “essential skeleton spicula” and “auxiliary
spicula”. It is obvious that this primary classification is not based
on morphological characters. Since KOLLIKER (1864) has pointed out
the morphological value of the axial canal or, more correctly, the
axial thread (“Centralfaden”), Oscar Scumipt has rightly based his
classification of siliceous spicula on the presence of one or more of
such axial threads, which after all represent the axes of the spicula.
Scumipt distinguishes (1870 p. 2—6) four types of spicules:

1. „Die einaxigen Kieselkörper.”

2. Die Kieselkörper, deren Grundform die dreikantige reguläre
Pyramide.”

3. Die dreiaxigen Kieselkörper.”

4. Die Kieselkörper mit unendlich vielen Axen.”

Neither Gray (1873, p. 203— 217), nor Carrer (1875, p. 11—15)
understood the fundamental value of Scumipt’s classification. My
attempts to draw attention to it (1881 a and 1884 p. 146—168)
have had but little influence. Thus, in 1887, Riprey & Dernpy divide
the spicula of the Monaxonids in the first place into Megasclera and
Microsclera, a classification which practically agrees with those of
BoweRBANK and CARTER. The example was followed by Sorras in
spite of his being well aware of the fact that the distinction is far
from “absolute”. This author quite correctly remarks (1888, p. LIID): the
microscleres and megascleres pass into each other by easy gradations,
so that it is not possible to say where one ends and the other begins,
indeed there would be a certain convenience in accepting a third
division of intermediate or middle-sized spicules, which we might call
mesoscleres.” Finally, in 1889, Scuunze & LENDENFELD accept SCHMIDT’S
primary division into “polyaxone, tetraxone, triaxone, and monaxone
Nadeln.”

I do not intend to discuss here the triaxons and tetraxons; for
the present I only wish to draw attention to some monaxons and
some spicules hitherto generally considered as polyaxons.

In the group of the monaxons, i.e. spicula with one single axis,
two fundamental divisions may be distinguished, according to the

fact whether the ideal axis lies in a plane or not. In the former
case the line may of course be straight, curved, bent, flexuous ete. :
in the latter case the line is a screw helix’). The spicula belonging
to the former case I propose to call pedinarons*), the others
spirazxons ®). To the group of the pedinaxons belong e. &. oxea, styles,
however, to the spiraxons, that I wish more especially to draw
attention.

Again we can distinguish here two cases: a. the screw line is
formed on the surface of a circular cylindre or 8. on that of an
elliptical cylinder. The former group I wish to call a-spiraxons; the
pitch is here generally large. The latter I call #-spirarons; the pitch
is here small.

Let us first examine the «-spiraxons. To this group belong the
spicula known as sigmaspires, toxaspires, spirules; further those which
are usually called spirasters and which are by the majority of spon-
giologists erroneously considered as modified asters. This mistake is
due, I believe, to Oscar Scumipt. „Eine blosse Modification dieser
Kugelsterne,” he says, 1870, p. 5, sind die Spiralsterne oder Wal-
zensterne. Sie werden zwar in manchen Spongien nur allein, d. h.
nicht untermischt mit den Kugelsternen angetroffen (Spirastrella
cunctatriv Sdt. Chondrilla phyllodes N.), haufiger aber, wie wir unten
in die Specialbeschreibung (z. B. von Sphinctrella horrida N. und
Stelletta hystrix N.) hervorheben werden, liegen alle Uebergange von
den normal centralen Sternen zu den gezogenen Spiralsternen vor.”
Unfortunately did Scumipr not keep his promise; for in the description
of Sphinctrella horrida we find nothing more about it, and Stelletta
hystrix is forgotten altogether. Scumipr failed, therefore, to give any
proof whatever for his statement that /Spiralsterne” are modified
“Kugelsterne’. ScHmipt’s suggestion has nevertheless generally been
accepted, myself not excluded.

SOLLAS (1888, p. LXI) distinguished two chief series of spicula
(microsclera): “the radiate or astral, and the curvilinear or spiral.”
The former are called “asters,” the latter “spires.” With some
astonishment we further read that the asters are divided into two

tylostyles, some of the “amphidisci’, some of the #toxa”. It is

1) These terms are to be taken cum grano salis. No biological formation will
ever be absolutely mathematical; thus it may be that the axis of a flexuous or
undulating spiculum is not exactly lying in a plane, without, however, being in
any way comparable to a screw helix.

2) redivoc, plane, even.

3) gmeita (lat. spira), everything which is twisted.

( 106 )

subsections: “the true asters or euasters, and the streptaster or those
in which the actines do not proceed from a centre but from a larger
or shorter axis, which is usually spiral’. Evidently one should
expect that those #streptasters” were arranged under the “spires.”
As a matter of fact neither Sorras, nor any other author has
given very striking arguments to consider the spiraster as a modi-
fication of the euaster. We know examples of very young stages of
spirasters; they always possess the twisted character. But no instance
is known of spirasters originating from or forming transitions to true
asters. It is true that such supposed transitions are mentioned by
some authors; but probably we have here to do with a mistake due
to optical delusion. For instance, Schat described (1862, p. 45) a
Tethya bistellata, possessing in addition to ordinary asters, double
ones (/“Doppelsterne’’). But LENDENFELD described (1897, p. 55—58)
a Spirastrella histellata (which he considers identical with Tethya
histellata O.S.), in which he found that the supposed asters are true
Ispirasters”. Judging from what I saw in a type specimen of SCHMIDT's
sponge, | have no doubt that Lexpexrerp is right. Quite correctly
LENDENFELD believes that Scumipr has been misled by an optical
delusion, “da diejenigen Spiraster deren Axen im Preparat aufrecht
stehen und daher verkürzt gesehen werden, häufig wie Euaster
aussehen … s.24- I fail to find a single proof that spirasters are modi-
fied euasters, either in previous papers, or in my preparations. On
the contrary, everything speaks in favour of the view that #spiras-
ters” are a sort of e-spiraxons. The fact that in some cases it is
difficult to get certainty about the twisted shape, is no proof against
my suggestion in general. For in the great majority of cases the
twisted nature is certain, as can be demonstrated by allowing the
spieulum to roll in the preparation when observed through the
microscope.

Let us proceed now to examine the different sorts of e-spiraxons.

1. Sigmaspira.

Sorras (1888, p. LXID) gives the following definition of the sigmaspira :
„a slender rod, twisted about a single revolution of a spiral”; he
adds that it appears in the form of the letter C or S, according to
the direction in which it is viewed. Te definition of the #toxaspire”
runs as follows: “a spiral rod in which the twist a little exceeds a
single revolution. The pitch of the spiral is usually great and the
spicule consequently appears bowshaped when viewed laterally”....
It seems to me not quite exact when Sorzas pretends that the bowshaped
appearance is in the first place due to the number of revolutions.

Bhs

( 107 )

Considering the facts that these spicula are generally very small,
and that consequently a microscope of very high power is wanted to
understand the true shape, it is evidently not easy to determine the
number of entire revolutions or parts of it; the same may be said
of the pitch of the ,spiral’ — or rather of the screw helix.

In order to obtain certainty about this I constructed wax models,
the axis of which were screw helices of various length and various
pitch, of course all drawn on the same circular cylinder. The dia-

‘meter of the models I made in accordance to the relative size observed

in the spicula. Such a set of models ought to be carefully studied
im projection. This can be done by looking at them with one eye,
or, which is far better, by studying the shadows of the models in
various positions. These projections are then compared to the camera-
drawings or microscopical projections of the spicula themselves. This
method most clearly shows fs“ that the bow-shape can be obtained
with models of less than one revolution; 2"¢ that the C- or S-shape
can be obtained with models of more than 1'/, revolution. This
depends both on the length and the pitch of the screw helix, as is
shown by the following table *):

of icone anes |
Fiend PAN 10°
2/5 Ung = C [S] (A)| C [Sl A |
3/4 C [Ss] — Cs (A) | Ge Sota
|

5/e C (S) [A] | [Oe Ae 1S CAS 5 0 aN
1 [C] (S) [A] | Cone Sy LAS) Cert ae Gt Sane |
cae SRG ACI EN "Sr io, |LOG SIS Meer |
11/, © A} © SA] GA
11/s ==. (8) A Ce SAL On EEN
11/, ne Ie VAG), (S) AS | CS
B | — SIA — SB] A] — — A} — BA
15/, | eh de
2 En er ake a Sah Fee

1) CG, S or A means: C-shape, S-shape or bow-shape distinct; ( ) means
indistinct; [ | means very indistinct. A dash — means that the shape cannot be
obtained with the wax model.

( 108 )

This result leads us to a dilemma. Either the definitions of sigma-
spira and toxaspira will have to be modified, or we have to drop the
distinction between the two forms of spicula. I believe that it follows
from the above table that the latter way out of the difficulty is
preferable. We may maintain the name sigmaspira for smooth, 1. e.
not spined a-spiraxons of no more than 1°/, revolution.

LENDENFELD (1890 p. 425) has another conception of the sigmaspira :
“ein einfach spiralig gewundener oder bogenförmiger Stab.” Hence
he seems to accept two different kinds, instead of considering them
as belonging to one sort, the shape of which simply differs according
to the direction in which it is viewed. Since he says that his “spiral”
has “mehr wie eine Windung”, he seems to accept no more than
one revolution for the sigmaspire. This is not in accordance with my
observations, as laid down in the above table.

2. Spirula.

Although Carrer did not give a special definition of the spirula,
it is clear enough what he understands by this name. In his paper
on the “spinispirula” (1879 @ p. 356) he calls the spiculum which
he formerly (1875 p. 382) described as “sinuous subspiral’, simply
“the smooth form of the spirula” and he refers to an illustration of
the spicule as it occurs in Cliona abyssorum (1874, PL XIV, p. 33).
Obviously the term spirula used by Carrer is an abbreviation of
4spinispirula’, not as terminus technicus. Riprey & Drnpy (1887 pp.
XXI and 264) introduce the term spirulae as synonym with spinispirulae
of CARTER, adding that “these are more or less elongated, spiral or
subspiral forms, which may be either smooth or provided with more
or less numerous spines.” SoLLAS creates (1888 p. LXAII) the term
polyspire for spirula, stating that it is 4a spire of two or more revo-
lutions”, adding, however, that he is inclined to adopt the term spirula.
In the list given by ScnutzE & LENDENFELD (1889 p. 28) we find a
Ispirul” described as “spiral gewundene Nadel mit mehr als einer
Windune”. Consequently we learn that the term spirula by some
authors is used both for smooth and for spined forms, whereas others
leave the question open. LENDENFELD (1890 p. 426) proposes the
name for smooth spicula only: “eine sehlanke und glatte, spiralig
gewundene Nadel mit mehr wie einer Windung”. I herein agree with
LENDENFELD and I understand by spirula: a smooth e-spiraxon of at
least 1°/, revolution.

3. Spinispira.

As long as the a-spiraxons are smooth it will as a rule not create
any difficulty to distinguish sigmaspirae and spirulae. But there are

( 109 )

a quantity of spined a-spiraxons. Evidently such spined a-spiraxons
will exhibit the twisted nature the less distinctly the more the
spines are developed. It is, therefore, not practical in this case to
make distinctions, based on the number of revolutions. Especially not
because there exists a great diversity with many transitions. I prefer,
therefore, to propose for spined @-spiraxons the general term spini-
spirae, to which I bring the spicula called by previous authors spira-
sters, metasters, plesiasters, and also (partly) spinispirules, sanidasters ete.

Sorras (1888 p. LXIIT) has given the following definition of the
spiraster: “a spire of one or more turns, produced on the outer side
into several spines.” Scnurze & LENDENFELD (1889 p. 28) say that it
is a leicht gewundener gestreekter Aster mit dickem, dornenbesetztem
Schaft”, a definition which LENDENFELD (1890 p. 426) modified into:
„ein kurzer und meist dicker, leicht spiralig gewundener Stab mit
starken, meist dieken und kurzen, kegelförmigen Dornen”. Sorras
distinguished #metasters” and #plesiasters” from his spirasters, but
he acknowledges himself that: “the three forms present a perfect
eradational series, so that it is frequently difficult when they all occur
associated in the same sponge, to distinguish in every case one variety
from the other’. Now it happens very frequently indeed that they
all oeeur associated in the same sponge and that all gradations are
met with. One only needs to read Sorras’ own descriptions and to
compare them with his illustrations, e.g, of the many “species” of
Thenea, Poecillastra, Sphinctrella i.a. in order to become convinced
that it is practically impossible to distinguish spirasters, metasters and
plesiasters. ScHurze & LeNDENrELD, therefore, did not adopt the latter
two terms.

I am of opinion that the name spinispira can be likewise applied
to the spicula which Sorras calls amphiaster; at any rate to such
amphiasters as are said to occur in Stryphnus niger Sou.) A great
confusion exists, with regard to the word amphiaster. The name
is first used by Ripuuy & Denny (1887 pp. XXI and 264), who
say that the amphiaster is composed of „a cylindrical shaft bearing
a single toothed whorl at each end; occurring for example, in
Awoniderma mirabile...’? The authors give an illustration by fig. 9 on
their Pl. XXI, and a further explication saying: “amphiastra = biro-
tulates (Bowerbank); amphidisks (auctorum).” But SoLnas says (1888
p. LXIV) of Ais amphiaster “the actines form a whorl at each extremity
of the axis, which is straight”; herewith a woodcut on p. LXI.

bi]

1) In his preliminary account on the Challenger-Tetractinellids (1886 p. 193)
Soutas calls this spiculum “amphiastrella”,
5
Proceedings Royal Acad. Amsterdam, Vol, V,

( 110 )

Scnurze & LENDENFELD (1889 p. 8) have about the same conception
of the spiculum: “gestreckter Aster; ein Schaft, von dessen beiden Enden
Strahlen abgehen.” Comparing now the three quoted illustrations, it
becomes evident that there are important differences between them.
Notwithstanding Scnvrze & LENDENFELD illustrate a spicule with a
long “Schaft” and long pointed “Strahlen”, we find in the definition
of LenpenreLpD (1890, p. 419) that the amphiaster is: „ein in die
Lange gezogener Stern, die aus einem Aurzen, geraden Schaft besteht,
von dessen Enden mehrere /urze Strahlen abgehen”. Indeed: tot
capita tot sensus. If, therefore, I bring certain amphiasters to the
spinispirae, only such are meant as Sous describes e. g. in Séryphnus
niger.

Carter (1879 a, p. 354—357) has introduced the term “spinispirula”
for spiniferous spirally twisted spicules.” Such spicula are, according
to CARTER exceedingly polymorph. They may be “long and thin” or
“short and thick”. The spines may be “long and thin... or long
and thick... or obtuse... The spines may be arranged on the spicule

in a spiral line, corresponding with that of the shaft... or they may ~

be scattered over the shaft less regularly... Lastly, the shaft may
consist of many or be reduced to one spiral bend only...”

Instead of chosing one of the various terms mentioned above, I
prefer the new term spinispira, which is then simply: a spined
a-spiraxon. If in future it happens become to a desideratum to have
more than one name for such spicula, one might distinguish two
groups of spinispirae, viz. forms with long spines and such in which
the spines are small, in comparison to the total length of the spiculum.
In the former group the ratio between the length of the spines and
the total length is usually no more than 1:38; very seldom as much
as 1:7; the number of revolutions is generally not more than 17/,.
In the latter group this ratio is usually at least 1:10; the number
of revolutions as a rule more than two.

4. Microspira.

In some sponges very minute spicula occur, especially in the super-
ficial (dermal) layers and lining the canals, which are either distinct
a-spiraxons, or modifications by reduction. For obvious reasons it can
only be made out with a microscope of very high power and in favourable
situation in the preparation, whether they are smooth or minutely
spined. In such small spicula it is not always possible to distinguish
with certainty whether they -are minute spinispirae, sigmaspirae or
spirulae. Moreover they show generally manifold transitions in one
and the same sponge specimen. This is e.g. the case in Placospongia

€ 110)

carmata. And still, we want to designate them with a name; I
propose to use for this the term microspira.

5. Sterrospira.

In the remarkable genus Placospongia the stony cortex and axis
are almost entirely composed of spicula, which very strikingly resemble
the sterrasters of Geodidae. Keller (1891la, p. 298) was the first
to demonstrate that these spicula are of quite a different nature ;
whereas the sterrasters develop from true asters, the cortical spicula
of Placospongia take their origin from “Spirastern”. This observa-
tion is confirmed by Lrenpenrecp (1894d, p. 115). Hanrrsen (1895,
p. 214216) found the same for the corresponding spicula of Physca-
phora (= Plancospongia) decorticans; as they possess in this species
an elongated, somewhat crescent-shaped appearance Hanirscu called
them ,selenasters”. In 1897 LENDENFELD, not acquainted with the
paper of Hanirscu, proposed the name #pseudosterrasters” for the
cortical and axial spicula of Plancospongia graeffei (= Physcaphora
decorticans Han.). Uf one wishes to apply the rules of priority in this case,
the spicula under consideration have to be called selenasters. I am,
however, of opinion that these rules, excellent as they are for specific
nomenclature, need not to be applied in other cases and I propose,
therefore, the name sterrospira, which at the same time reminds us
of the sterrasters (of the Geodidae) and the spiraxons. *)

In the group of the fB-spirarvons the ideal axis of the spiculum is
a line drawn on an elliptical eylinder. The simplest type of such
a spiculum is

1. Sigma.

This term is introduced bij Ripiny & Denny (1887, pp. LXIII
and 264) for spicula called by BoweRrBANK “bihamate’”’, “contort
bihamate” and “reversed bihamate”. The authors say that the sigma
consists of a “slender, cylindrical shaft, which is curved over so as
to form a more or less sharp hook at each end. The two terminal

-hooks may curve both in the same direction, when the spicule is

said to be simple... or they may curve in different directions, when
it is said to be contort... There is, however, no real distinction

between the two, and, as a matter of fact, the spicules are nearly
always contort to some extent”. Sorras (1888, pp. LXII) modified
the definition into “a slender rod-like spicule curved in the form of
the letter C. This spicule is not spiral though it probably arises

1) For details I refer to a paper on Placospongia from Dr. Vernnovt and
myself, to appear within a short time (Siboga-Expeditie. Monogr. VI. Porifera).

8*

( 112 )

from a sigmaspire by increase in size and loss of the spiral twist”.
SCHULZE & LENDENFELD (1889, p. 28) stick to the contorted nature:
“oewundene, eine halbe Spiralwinding bildende Nadel”. Finally the
definition is again somewhat modified by LenprenreLD (1890, pp. 426) :
“einfach spiralig gekriimmter oder bogenförmiger Stab.”

The spicula belonging to this type, appear, like the sigmaspirae in
the shape of the letter C or S, or as a bow. Here too these various
appearances depend on the direction in which the spiculum is viewed.
According to my conception only such forms belong to this group,
which are contorted, not such in which rea//y the “hooks curve both

in the same direction”. The latter are curved pedinaxons, the former’

are spiraxons. The axis, as a rule, has less than one, but more than
half a revolution, which is easily proved by wax models.
As a derivation or modification of the sigma we have

2. Chela .

BowERBANK has already shown (1858, p. 304— 805 ; reprinted 1864
p. 47—48) that the chelae develop from sigmata. This observation is
confirmed and enlarged by Ripiry & Denpy (1887, p. XX), Levinsen
(1886 and 1894), H. W. Witson (1894), PeKELHARING & Vosmagr (1898,
a p. 36—88). We remarked (1. e. p. 37): “not only can we confirm
this but we can give a new strong argument in favour of it. This
lies in the fact that the anisochelae of Esperella syrine are twisted.”
I can add now that this twisted nature is found in isochelae as well
as in anisochelae. Consequently we may regard both as (#-spiraxons.

8. Diancistra.

According to Riprry & Derpy (1886, p. XIX) the spicula, which
BowrrBANK called “trenchant contort bihamate”, and for which they
propose the name diancistra are “usually... more or less contort,
the two hooks lying in two different planes’. My own observations
confirm this statement and I bring the diancistra, therefore, likewise
to the $-spiraxons.

Resuming we may divide the monaxons into the following primary
groups:

I. Pedinarons. Monaxons the axis of which lies in a plane;
(oxea, styles, tylostyles, etc).
IL. Spiravons. Monaxons the axis of which is a screw helix.
A. a-Spiravons. The axis is a line drawn on a circular cylin-
der; the pitch is generally great, to this group
belong :

1. Sigmaspura. ;

bo

Spirula ;
Spinispira ;
4. Microspira;

Ge

5. Sterrospira ;

B-Spuravons.

1. Sigma;
det Chela

3. Dianceistra;

References.
BOWERBANK in: Philos. Trans. R. Soe. Londen, CXLVIII.
Scumipt in: Spongién Adriat. Meeres.

BowrErBaNk in: Monogr. Brit. Spong. I.

Körtaker in: Icones histiol. I.

Scumipt in: Grundz. Spong. Atl. Geb.

Gray in: Ann. & Mag. (4, XII.

CARTER in: Ann. & Mag. (4) XVI.

CARTER in: Ann. & Mag. (5) III.

Vosmaer in: Tijdschr. Ned. Dierk. Ver. V.

Vosmaer in: Bronn’s Klassen u. Ordn.-Porifera.

LeviNseN in: Dympha-Togtets Zool. Udbytte.

SoLLAS in: Scient. Proc. R. Dublin Soe. ;

Riptey & Denny in: Challenger Rep. Zool. XX.

Sorras in: Challenger Rep. Zool. XXY.

Senurze & LENDENFELD in: Abh. K. Pr. Akad.Wiss. Berlin 1889.
LENDENFELD in: Abh. Senekenb. Naturf. Ges. XVI.

1891(@) Kerner in: Zeitschr. Wiss. Zool. LIL.

1894(d) LenprenreLp in: Biol. Centralbl. XIV,

1858
1862
1864
1864
1870
1873
1875
1879(«)
1881 (a)
1884
1886
1886
1887
1888
1889
1890

( 143 )

smooth a-spiraxon of no more than 1'/,
revolution.

smooth a@-spiraxon of at least 1°/, revolution.
spined «-spiraxon.

very minute, smooth or spined «-spiraxon:
it unites the characters of 1 and 3 dimi-
nutively, and frequently forms transitions
and reductions.

the young stages are spinispirae, from which
develop by secondary soldering together of
the spines the adult forms.

The axis is a line, drawn on an elliptic
cylinder; the pitch is always small; always
less than one revolution. Hereto belong:

smooth #-spiraxon.

the young stages are sigmata; in course of
development very complicated siliceous pro-
cesses grow out; we distinguish two sorts,
viz. isochelae and anisochelae.

the young stages are (probably) sigmata
from which develop the adult ones by
outgrowth of siliceous processes.

(144 )

1894 Lxrvinsen in: Vidensk. Medd. Naturh. Foren. [1893].

1894 | Witson in: Journ. Morph. IX.

1895 Hanrrscu in: Trans. Liverpool Biol. Soc. IX.

1897 LENDENFELD in: Nova Acta Acad. Leop. Carol. LXIX.

1898(a) Vosmaur & PEKELHARING in: Verh. Kon. Akad. Wetensch.
Amsterdam. VI.

Physics. “Statistical electro-mechanics.” IT. By Dr. J. D. vaN DER
Waars Jr. (Communicated by Prof. Van per Waars.)

The distribution of the energy over the different periods in quast-
e … Ld … / d
canonical ensembles.

In equation (8) of my previous communication *) a distribution of
the energy over the different periods is included. If therefore this
equation really represents the condition of a space filled with “black
radiation”, then a complete spectral formula for black radiation may
be derived from it with the aid of the law of Wren on the shifting
of the wave-length with the temperature.

Instead of discussing the rather intricate equation (8) I have taken
a simpler equation which I expected to yield the same distribution
of the energy over the different periods. This simpler equation,
however, proves to include a distribution which does not at all agree
with the distribution of the energy which is found in black radiation.
Now it is possible that the distribution, determined by the simpler
equation does not agree with that, determined by equation (8). But
it is also possible and for the present this seems more likely to me,
that equation (8) does not represent the condition of a space filled
with black radiation, or in other words that the nature of black
radiation is not correctly determined by the suppositions that ¢, p and 4
have a most probable value, and that for the rest the distribution is
as irregular as possible. If this second explanation is the true one,
the systems are still subjected to other conditions, besides those con-
cerning the most probable values of €, p and x, or, what comes to
the same, the distribution of the systems of an ensemble in which
the conditions for the values of ¢, p‚ and xy are satisfied, are more-
over still partially ordered.

The simplification I have applied to equation (8) is the following.

u)
In the first place I have omitted ie this will no doubt have very
2

1) These Proceedings IV, p. 27.

SO

( 115 )

little influence on the distribution of the energy. Then I have con-
fined myself to treating one dimension only, and this has induced

Ken +- Gm

me to omit the terms If, however, we admit electric and

1
magnetic masses into the space, statical forces may occur. When
analysed with the aid of Fourtmr’s integrals these statical forces
actually yield a distribution of the energy over the different wave-
lengths. Yet they do not contribute to the propagation of radiation,
the distribution of which we wish to investigate. It is for this reason
that I have preferred a distribution in time to one in space.

So we consider the component / in a certain point during the time
between the moments ¢=0O and t=t,. This time we think divided
into 2 equal parts T and the values of / during those parts we call
respectively “/,, fas fa. er fn Then the index of probability gets
the following value:

1
ww 1 d je
En in Pe pL ae Mee aia fet,
en aan af dt Ka)

If we wish to make the agreement of this equation with equation
(8) as great as possible, we have to give to / in this equation 4a |”?
times the value it has in equation (8); this follows from the equations
(10) and (15).

Now we will proceed to the investigation of the distribution of
the energy over the different periods, included in equation (8a). To
that purpose we represent / as a function of ¢ during the space of
time between ¢=o0 and ¢=4,, by means of the integrals of Fourier.
As we will begin with treating f as a discontinuous function, determ-
ined by the » values /,, f,...fn, we will represent the integral as
a sum, which only becomes an integral if we make 7 assume the
limiting value ©. Therefore in the expression

I (t) =f Fw) {sin (ug) sin (gt) + cos (ug) cos (gt) du dy, « + (26)

in which the limits for w are O and ¢, and those for gare Oand o ,

t
we will replace u by — v or by tw and du by + where v represents
n
the series of the integers between O and 7.
So we get
vn

Hi (6) =e = fo {sin (aq) sin (qt) + cos (eg) cos (qt)} dq.

If we wish to separate in this equation the energy for a deter-

(446)

mined period we must give g a determined value p and then take
the square of the amplitude for ou vibration. So we find:

2

=| Dm (| 2
Ay ="? | & fo sin (rop) En T° | = f, cos (rop)
t—0 =

In what follows we may omit the limits as all summations are
to be executed between O and 7”; and we may omit the constant

factor T°

quantities A, for different values of p: So we get:

A, = J fy fw {sin (cep) sin (te'p) + cos (tvp) cos (te'p) }
Afi ff LOS (U OPT Ene eee ae

For this quantity A, we seek the mean value for all systems of
the ensemble. To this purpose we have to multiply the value of

equation (27) with the probability that the quantities 7,....j, have
a determined, arbitrarily chosen value and consequently we have to
integrate according to df, df, between the limits — o and + oe
| df Joti—fo
To that purpose we will represent — by eS and we get:
di T
Prijs (fe)
a krt ae 4 an
Ay ==" he Sof v cos (v—v') tp df, ..+.dfn - (28)
D
=.

If we bring the factor e outside the integral sign as well the
exponent of e as the other factor under the integral sign are homo-
geneous quadratic functions. By the introduction of other variables
we may transform both functions to terms of 7 squares and in the
same time it is possible to choose the variables in such a way, that
all coefficients which occur in the exponent are unity. So we may
bring the integral into the following form:

lp jens APN) 8 »
fi EE (8, PUB, Pa? +B; Ps Bn Gn") A dy,... dp, (29)

where A represents the determinant of Jacot. The linear substitution
required to get this form may be thought to be executed in two
operations: 1s* a substitution which yields
Ai HA

for the exponent and:

a1, Yas = As om == s+ e+ Cnn An “= 2 ds ta he Sas Ph oe 2 An—1 jn Zn Yn
for the other factor; 2°¢ an orthogonal substitution in consequence
of which both functions assume the form they have in equation (29).

The determinant of Jacosi for the total substitution is the product
of the determinants for the partial distributions. The determinant

as it is only our aim to determine the relative values of

ee EE

(E279)

for the orthogonal substitution has the value unity; so only the
determinant for the first partial substitution remains. This substitu-
tion has been chosen without taking into account the form of the
second factor. The coefficients which determine this substitution
depend therefore only on the coefficients of the exponent; as p does
not occur in these coefficients, the determinant also cannot be a
function of p, and so we may omit it in what follows.
The integral (29) can easily be integrated and yields:
C8
So we have only to calculate the sum of the coefficients 8. These
coefficients may be found by the solution of the following equation
of which they represent the 2 roots:

a,,—B Bis Gis F Ae he,
da: @,,—-B 43 ostinato,

: aah | bet es Dl
Ue ee das «dn 0 (50)
Gnd Ono An3 » + + Gn—B

The sum of the coefficients 8 is the sum of the roots of this
equation, ie. the coefficient of 8". Only the product of the elements
of the diagonal of the determinant yields terms containing 8* 1; and
as is obvious, the coefficient of 2! will be

Gy, + 5, 1 33 H+ + + Gan

In order to determine this sum we have to find an arbitrary
substitution for which the exponent assumes the form 2° and then
we must substitute the new variables x into the second factor. A
substitution fulfilling this condition may easily be found. The exponent
namely may be written as follows:

if
EEA + 2 Foi = = (efo)
T 2 2
where : dd and —2ep=>— —
‘ kr kr

So we find for @ and 8:

ee ” Eee 4 capes pene 31)
feet, at a Ge Fi of RS

Now we dn as new variables:
afs — Phti=R-
This substitution does not yield the accurate coefficients for f,* and

tel
wh

tf. for, in order to get » quantities %, we have to take as one of

the new variables x, = ea fn —Bf,; so we introduce moreover a
term 2a8/,/f, which does not occur in the exponent. As however
the exponent consists of an infinite number of infinitely small terms,

( 118 j

these three terms which have not the proper coefficients will be of
little importance.

These new variables are now to be introduced into equation (27).
Yet it is not necessary to execute the substitution completely, for, as
we have only to determine the sum of the coefficients of the squares
ye", we may leave the coefficients of the products x, %, out of account.
In the first place we have to express the old variables f in the new
variables z We have:

%, = 4), — BS,
i as, Bf.
4; = aje— BY,

From this follows:
vre) BDE a [uk 0 0 0... 0
Ou see 8 eee 0 Mae a een ee
i ) VO) AB 20 2.5). OTS x: Og. "OZ

RS 40e en ue es | 0 0 0 ty a
or fy (BY) = Of 2B Ff, BE yy BI

In the same way we find for /;,

Po (AR) = yo OA + opr 2B + ype ap...
he fn OU nk Kn at aa

In determining the products /./f, we shall always suppose that
r’>vr, and so we shall integrate 7 between the limits O and +’;

- between the limits O and x. In this way we get only one half
of the quantity we have to determine. In order to find the amount
contributed by the product ff cos(v'—r)tp to the coefficient of x.
we have to distinguish three different cases:

dist. O<r<v. Then the coefficient has the following form:

| avdv? B2n+2r—v—v" cos (v' — v) Tp

2nd. p< ld p'. Then:
ante-po'—2r—2 nr -v- v eos (v'—v) Tp

au rens Then:
a2ntoyo'—2r—2 rvd’ cos (v'—v) T p.

We have to seek the sum of these quantities, when 7 gets suc-
cessively the value of all integers 1st. between 0 and v, 2°¢. between
vr and #' and 34. between 7 and v. v has all values between 0
and #', and v those between O and 7. We may write these sums in
the form of integrals, if we put:

EDU re == u Er =d Et

al tand spie B:

mans den ee

( 119 )

The integration according to w may directly be executed. It yields

for the three cases:

Pe) en
IF dw = 5
a
if 2l —
b

If we substitute in this equation for each case the proper limits
and if we then-add the results for the three cases, then we get:

tu

. / el!
2] 2 + ah bh { que! bh gn’ fu 4} +
b

0 0
+ ant} ast buut — qu’ bw} | cos p (1! —u) du dul.

In the exponent of a we have neglected the term 27 as it is small
compared with the other terms. If we arrange the terms in another
way and again suppress the constant factors we may write the

integral in the following form :

hw

ffe) 5 cos p (u —u) du dul +
0) .

0

tw
UF a) 1 u a —u.
+ {fee (*) (5) COS plu — u) du dies Ata», (55
00

Integrating partially we find:

uy

(Ya \u 1 Ha \t ; uy p ity u

| — cos plu —u)du—=— Jeo plu —u) | —— SUN plu —u) du=
. l a / iy? oat ase h
0 l 9 i‘ l

) )
nd

Db

1 : fa \u la p a 2 u lu p a \% f
ee — cos plu — U) | — sn plu —%)|) — | cos plu — u)du
lo jr a x ob lo de b

From which follows:

j a ae ; ;
u L —{ — COS Pu } —p sin p
a aise sh nd ast clean?
| — [COS plu — u)du— LES d a
b ot »
rte 8
)

0

In the same way we have:

as B. rd ! $ '
2 =| 008 — psinp
vaN b b oo pu psimpu
— eos plu —u)du= See 2 ;
b in = os
— D
b /

0

(4909

If we introduce these values into expression (33), it assumes the
following form:

t
1 : al a a\") a
dt it (a4 — bh) Ll — — Sal — =p l—cos pul —
a : b b b p
Meee 0 |
b
a hes =e bt a rv j In!
— Iah = — bt 5 psinpu | du

Integrating this equation we get:

1

—| —bh)l - t, — (ar—bh) | 7 p — (ah + 64) 7? -L
fp’
)

+ (ai + bh) P ; (sin pt, + cos pt,) + (ai—bh) pl 7 (sin pt, —cos vt) |
)

The fact that the terms with si pt, and cos pt, occur, shows that
the distribution depends on f,. We might have expected this, specially
as we have chosen @ /,,—/, as one of new variables for the substitution
and therefore introduced the condition that 7, and Jn have about the
same value. If however we take a considerable value for ¢, then

a . . . .
the term ioe pat = t, will have decisive influence. If we now con-

sider a region of the spectrum of some, though it be an extremely
small extension and not a rigorously simple wave, then we have to
admit slight variations in the value of p. The terms si pt, and
cos pt, will then have alternately the positive and the negative sign
and yield zero on an average.

If 7, has a sufficiently great value then the course of the function

an : 1
is principally determined by the factor ——. This expression does

a
j=
Neu
not present a well defined maximum value, but it has its greatest
value for p= o (i.e. for infinite wave-lengths), it decreases gradually

with increasing p and is zero for p= (i.e. for infinitely small
wave-lengths).

So this equation does not at all represent the distribution of black
radiation. I only communicate these calculations in order to show
that equations analogous to (8) or (Sa) determine in fact a distribution
of the energy over the different periods and to indicate a method
for analysing such like equations.

( 194 }

Physics. — “Ternary systems.” V. By Prof. J. D. van per WAALs.
(Continued from pag. 21).

If the temperature is so low that there is no question of eritical
phenomena, and if therefore both liquid sheet and vapour sheet cover
the whole triangle, »,, is for all points either positive or negative,
and the given rules for the displacement of the curves of equal
pressure will therefore be followed by all points of these curves. If
on the other hand the temperature is chosen so high, that the surface
of saturation does not cover any longer the whole triangle, and if
therefore the liquid sheet and the vapour sheet pass into each other
above a certain locus in the triangle, v,, vanishes for the phases
represented by this locus.

We may form an idea of the shape of the surface of saturation
with the aid of fig. 11 (Cont. II, p. 185). Let us imagine that this
figure represents a section by the vertical plane which contains the
X-axis of the triangle and let us take a similar section by the
vertical plane which contains the Y-axis. The value of 7’ is then
chosen such that 77> (7), and also 7’ > (7), In the figure men-
tioned P is the point, where a vertical tangent may be drawn, so
this point represents a phasis which is in critical point-of-contact
circumstance, and for which »,,=0. The point C represents the
plaitpoint. If we now imagine different planes which contain the
axis erected in the point 0 normal to the plane of the triangle, these
planes will cut the surface of saturation, and the sections will be
analogous figures, which however change their shape fluently from
that which they have in the POX-plane to that which they have
in the POY-plane. If the pressure is lower than the lowest pressure
of the points Z, the two branches of the curves of equal pressure
are perfectly separated lines which, if the pressure is increased, will
be displaced according to the rules given above. If however the
pressure has risen till the pressure of a point P has been reached,
then the two branches are still separated, but on the vapour branch
occurs a point for which »,,=— 0. Such a point is not displaced
when the pressure increases. The locus of these points forms the
limit of the mixtures which may be splitted up into two phases at
the given temperature. From a geometrical point of view it is the
envelope of the projections of the horizontal sections of the surface
of saturation, or the envelope of the projections of the curves of equal
pressure. If the pressure has been increased till it has attained the
value of the lowest of the pressures of the point C, then the two
branches of the curves of equal pressure pass continuously into one

(1345)

another. But if we continue to call those phases represented by the
lower sheet, vapour phases, and those phases represented by the
higher sheet, liquid phases, then the vapour phases do not reach
the point, where the connection of the two branches has taken
place (the plaitpoint), but only the point where the value of »,,
is zero, i.e. the point, where two successive curves of equal
pressure intersect. For all points lying on one of the sides of that
point of intersection, — e.g. on the side where the plaitpoint occurs, — v‚,
is positive.

These points will be displaced towards the conjugated point, when
the pressure is increased; all points on the other side of the point
of intersection will move away from the points, representing coexisting
phases. If we, therefore, continue to use the expressions “liquid
phasis” and “vapour phasis” with the same meaning as we have
done till now, we must say that for points between the plaitpoint
and the point for which v,,= 0 two liquid phases coexist. If for
the two pairs of the ternary system we had a course of the pressure
as is represented in Cont. Il, p. 135, fig. 12, the above rules would
continue to hold; but in this case we find a series of vapour phases
coexisting with vapour phases between the plaitpoint and the point,
for which v,,=0. For these points we have then retrograde con-
densation of the second kind. We may expect that it will be easier
to observe this phenomenon for a ternary system, than for a binary
one. In order that retrogade condensation may be easily observed a
rather great distance between the two sheets of the surface of satur-
ation is required; and the distance between the sheets will be
more considerable in the middle than at the ends, where we have
to deal with a binary mixture, because the requirements for sta-
bility and coexistence for a ternary mixture are stricter than those
for a binary mixture (See Vol. IV, p. 577). But then we have to
avoid the case that a real maximum pressure occurs, for in that case
we have also in the middle of the figure a point in which the two
sheets touch each other.

c. Curves of slope and nodal envelopes.

If for a binary mixture we have construed the curves p= ACs
and p= f(w,), we have at the same time answered the question,
what phases may coexist with each other. Every line parallel to the
X-axis joins a pair of coexisting phases. If on the other hand we
have construed the two sheets of the surface of saturation for a ternary
system, this is not sufficient in order to answer the question which

(123)

phasis coexists with a given phasis. It is true that we know that
the pressure must be the same, and that therefore the second phasis
will be found on the other sheet at the same height as the first
phasis, but as the section of the second sheet by a plane ata height
equal to p is a curve and not a point, the question is not yet per-
feetly determined. Therefore, besides the series of curves of equal pres-
sure, which are already given as the points which have the same
height, still another series of curves must be traced on the surface
of saturation which pass from lower to higher pressure and whose
properties enable us to answer the question, which phasis of one
of the sheets corresponds with a given phasis of the other sheet.
We will again begin with treating the simplest case, in which
maximum-pressures are excluded, as well for the pairs of components
of which the ternary system consists, as for the ternary system itself,
so the case for which the lowest pressure is equal to p, and the
highest to p,. The question is then, what systems of curves, starting
at the point where the pressure has the lowest value and ending in
the point where the pressure has the highest value, may be traced
on one of the sheets or on both sheets of the surface of saturation
which enable us to find, what phases coexist with each other. Such
a system of curves will be found in the course of a person who
would climb the inclined sheet, e.g. the liquid sheet, always moving
in such a direction that he has the phasis, coexisting with the point,
where he is at the moment, just in front of him. If we now project
the tangent to the way which he has followed ona horizontal plane,
the point in which this projection cuts the vapour sheet will indicate
the coexisting phasis. The projection of such curves on the plane of
triangle OXY has therefore the property that the tangent passes
through the conjugate point, and is therefore the chord, joining the
points 1 and 2; from this follows again that these projections are the
envelopes of these chords. If therefore in the plane of the triangle
we have drawn the two branches of the curves of equal pressure,
and if we have joined a pair of nodes by a chord, an element of
the curve in question will be represented by an infinitely small part
of this chord. Let the point from which we start represent a liquid
phasis and be its coordinates x, and y,. The projections of the element
of the way followed are then the quantities dr, and dy,. At the end
of the elementary way the second phasis is also changed, of course,
and the consequence of this will be that we have to follow a curve.
But the direction of the infinitely small way will always be the same
as that of the chord joining the nodes; and the differential equation
will therefore be given by:

(124)
de, | IN dy,
tdi a U

For these eurves on the surface of saturation I have chosen the
name of “curves of slope”. This series of curves begins and ends
with the following curves: 1st the curve p= f (y,) for the pair (1, 3),
and 2°¢ the eurve consisting of ap = f (r,) part for the pair (1, 2) and
of a corresponding part for the pair (2, 3). If we draw these curves on the
vapour sheet, we must imagine that we descend instead of ascending.
For the projection of these curves on the plane of the triangle I
have chosen the name of “nodal envelope’. The outmost curves
of this series are: 1s* one of the sides of the triangle, adjacent to
the right angle, namely that one corresponding to the third component,
and 2°¢ a line consisting of the other side adjacent to the right
angle and the hypothenuse of the triangle.

For the solution of the differential equation of these curves it is
required that we may express 7, and y, in, and y,. This is
possible (p. 7) when the second phasis is a rare gas phasis, if we
namely assume the functions gw, and w,, to be known. For that

case the equation we have to integrate may be written:
du, dy, E
ees ;
Ties ps es De
Bles ik fe hl} y, (1—y,) (e e —1)—u,(e ce —1)}
or É ;
dit, dy,
F Pa, 1) ae pe m2 meus Chee En Wa, En 8
miley) “*- tye Te 7). 4 id-«,-y)e ™-)-«,¢ =e ) j
or zi (en en Oh of et (en —é' tij scene
ay U, Ed
py! le i SS wu! ] 7 Ein | p
mi (en D |: Ly d(1 ar 1) zi (em ea dy, is d( LY.) i
| ik 1—w#,—y, Mn La;
The last equation may also be written as follows:
u, v, al U, |
(e° 4% —1) d log ————_ = (¢ “—1) d log ————_ . i
1—2z,—y, 1—z,—y, . 5
:

; : = pw Pr
For the case that the liquid sheet is a plane, e° *—l ande’ *—l

el Paes a
are constant, and equal to — and — and so the equation of
Pi Pi
the nodal envelope will be given by:
Pa Di Ran PL

( Ly ) (et ae ( Y, ) Pi
LE 1—a,—y,

( 125 )

Ph Pi Pi
or ©, ee O/B (l—a#,—y,) :
an equation in which all exponents are positive as appears from the
values of p,, p, and ps.

For C=O this equation is satisfied by 7,—=0 and therefore the nodal
envelope coincides with the Y-axis, For C=o either y, or 1—7,—y,
is zero, and for this value of C the nodal envelope coincides with
the X-axis and the hypothenuse. For the special case, for which
P, = 2p, and p,=3p, the equation assumes the following shape:

n= C Ni Gr 4):

This is the equation of a conic section which touches the X-axis
and the hypothenuse in the points in which they cut the Y-axis.
Whatever the values of p,, p, and p, may be, the curve will touch
the X-axis and the hypothenuse in the points mentioned, if only the
condition p, <p, <p, be satisfied, and the same would hold true
if on the other hand p, >> p, > p, be fulfilled. The nodal envelope
for which C=O will of course be an exception to this rule.

In the adjoined figure 18 the

Ps general course of the nodal envelope

is represented in the above de-
scribed circumstances. Though the
calculated formula only holds for
ws, and w', == constant the shape
of the curve will agree in main
features with the one, drawn here,
always if neither on the sides,
nor anywhere in the middle of

p the surface of saturation a maxi-
FP. 1-X 2
: mum pressure occurs.
Fig. 13. Only the details are different.

For the locus of the points where the tangent of the nodal envelope
is parallel to the J’-axis for instance, we find in the case that
ue, and w',, are constant a right line passing through the intersection of
x, Yi .
the X-axis and the hypothenuse. For sate for such points and
1
so dx, == 0. But then also z,—7x, = 0.

As follows from the equations (p. 11).

vn _ Ale)" YI
pal 1+ 4, (ei —=1) Hf (=H)

Proceedings Royal Acad. Amsterdam. Vol. V.

( 126 )
and
das di dike (1—y,) (e” *—1) Soin (ei ft
4 ib a, iu —1) +Y, (es —1l)
we have: EED
eh —1
i pared We
Ne et

This equation represents a right line, if the factor of #, is constant,
and it yields «,—1 if y,=0. If the surface of saturation is a

: “¢ fy Ps ey Ps 8 :
plane, ie. if e * =— and e “4 =—, then the equation of this
Pr Pr
right line is:
——
1—2#,=y, eT :
Ps =P:

This right line coincides with the liquid branch of the projection
of the curve of the pressure p,. (See our previous Communication,
p. 14).

If wt, and w’,, are not constant, ie. if the factor of y, is variable,
then the locus of the points for which zr, = 0 is of course not
straight, but it will be a curve, which, however, if the condition
wy, > u's, continues to be satisfied, will start from the same angle
of the triangle. In this case the line for which «,—v,—=0O does no
longer coincide with the line for which the pressure is equal to p,.
If we put in equation (7) of p. 12.

eN Eik

u ’

e' Ei if,

lr, = U.

then we find:
P
MRT
If we denote the value of u for r=1 and y=0 by u, then
we have:

log — Urn, = (1 —a,) Ws, sae Uy, —1.

p |
ee Urn + Aa) Un IH Bj Hor

3
The second member of this equation represents the distance between
the point of intersection of the tangential plane to the g-surface and
the vertical axis of the second component, and between the ordinate
Ho If the whole surface lies below the tangential plane, as is
probable, then the second member is positive and p > p,, and the
difference between p and p, increases, if the point of intersection

NES

de

lies at a greater distance from the second component, and if the
deviation of the surface u from a plane surface is more considerable.

The succession of the values of the pressures p,, p, and p, involves
that the condition y, — y,=90, which would lead to:

ld
Ses ae |

Ry) =e, a
e A]

cannot be fulfilled, for in that case the factor of w, would be less
than unity, and the equation:

yen
| = 2, ie
Page) ame
with constant value of w',, and w',, would then in fact represent a
line through the summit of the triangle; but a line outside the
triangle. But we will return to this condition presently.

These nodal envelopes have an analogous significance as that of
the lines of force in the magnetic field. In the same way as
the tangents of the lines of force determine the direction of the force,
but not its intensity, so the tangents of the envelopes determine the
direction in which the second phasis is to be found; but they do not
indicate the distance between the points 1 and 2. This distance,
however, is perfectly determined if also both branches of the curves
of equal pressure and triangle OXY are drawn. Then we find the
second phasis which coexists with a given liquid phasis, by drawing
in the point representing the liquid phasis the tangent to the nodal
envelope of that point; the point of intersection of this tangent and
the vapour branch for the pressure of the liquid phasis represents
the second phasis. If we do this for all points of the same nodal
envelope then we get a new locus, which we may call conjugated
curve of the nodal envelope. In order to give the equation of this
conjugated curve we must be able to express v, and y, as functions
of x, and y, and we must substitute these functions in the equation
of the envelope. In general, however, we are not able to do this,
not even in the case that the second phasis is a rare gas phasis.
Only in the case that u’, and w’,, may be considered as constants it can
easily be executed. If we write the equation of the envelope as follows :

wey pe 3
( a, y Ji oa o( Y, y' ls Jp
ee CE or Fe et

which only may be admitted for constant value of u’, and w',, , and
if we take into account that:

gi

el 5 — Bx,
ii. re

12,4, a 1—z,—y,

Enig?
‘

1,
and eet ONE
a yy tie

then the substitution into the equation of the envelope yields the
following formula:

pre de NG cet
ee Pe de 7.

( a, id N oi 1) ( v5 Vs 4 1)
Ol En C : 7
L,Y, Lea

From this follows that the conjugated curve of a nodal envelope
of liquid phases, is, in the chosen circumstances again a nodal enve-
lope, with another value of the constant, namely:

PSP Pr PL

C'=C (2) a Gales
Pr Ps

li <p , ),, the factor of Cis greater than unity and the con-
Pe Wa À

jugated curve is therefore to be found nearer the hypothenuse. Only
in the case that p,=p, we have C’ = C; but then the system is

only apparently a ternary one, and the envelope degenerates into a
straight line with the equation:
elis

It appears therefore that the conjugated curve in this case always
coincides with the envelope.

We might also have considered the nodal envelope for vapour
phases. Then we consider the projection of the way which we should
follow, if we descend on the vapour sheet from the point where
the pressure has the highest value towards the point, where it
has the lowest value, always moving in such a direction that we
have the liquid phasis just in front. We find the equation of this
curve if we express the values of wv, and of y, as functions of «, and
y, and if we substitute those functions into:

de, Pes df dy,

pire De dir
This is only possible if wx, and uw’, are constant as we have
already mentioned several times. With the aid of the equations:

Lv 1 dT nd pe

ZE ——@ 71
PS 1 — &,—Y,
and 41 = Ys a é
a yy ae

a

(aS)

we find a differential equation, which differs from the one treated
p. 124 in so far that x,, y,, dv, and dy, are substituted for
B, Yo dx, and dy,, and that —w',, and —w',, are substituted for
wr ande. In the integral found there the same substitutions must
of course be performed. So we find:

a wy Pas 1 mae fede ab
EEEN Ree nine 221
1—wz,—y, dan
P1 PM ;
——l ——_—]
or vs ( P3 ae C Ys ( v2 )
ln lier

This equation may also be written in the following form:
Ka heh He DaTEbE babe
a PL Gs 7. [AV td nn
For C,=0, we have also «,=0, and the Y-axis is therefore the first
of the envelopes, just as was the case for the liquid phases. For C,—= a
we have y,—O and 1—7,—y,—0. The last of the envelopes is
therefore also here the N-axis and the hypothenuse. Though the
equation of the two series of envelopes is different, the course is in
many respects analogous. These envelopes also touch the hypothenuse
in their beginning and touch the X-axis in their final point. They
have a tangent parallel to the Y-axis, and the locus of the points
where this is the case, is found from the equation:

rt, = 0
1e En
or 1e, = y, ——-——
le ©"
Pais rots
or le, = y, fay os tas
Pear it

This locus coincides with the vapour branch of the curve of press-
ure p,. This nodal envelope has a conjugated curve, which is again
a nodal envelope with greater value of the constant, just as is the
case for the liquid phases.

Before we proceed to the discussion of the nodal envelopes in more
complicated cases, namely in those in which a maximum pressure
occurs either on the sides of the triangle or for a point inside the
triangle, we will make some general observations about peculiar points
of these curves, which, however, only apply to the case that the
second phasis is a rare gas phasis.

. aH, a M

From the equation : = ann
Nore aan By at Tae

Ya Yi a4 U

( 130 )

we deduce that the nodal envelopes have tangents which pass through
the angles of the triangle, if either w‚,, or wy, or wy, Ur are
equal to zero. The tangent contains the angle representing the third
component, if w.,—O; that representing the second component if
u, =O; and that for the first component if wy, = tr

The conditions that a tangent of the envelope is parallel to one
of the sides of the triangle may be deduced from the values of 7,— 7,
and y,—y,- So from «,—7r,=0 follows the condition that the
tangent is parallel to the side of the first and the third components.
This condition has the following form:

1

U. op
Ys PAB helene, |

= , P
== a, ef |

ll
Now ahs = tana, where a represents the angle enclosed between
— WV
1
the radius vector drawn from the second component, and the A-
axis. As « must be less than 45°, we get for the condition for the |
existence of points where the tangent is parallel to the Y-axis: |
We
el
tan A=
A
ef nh re |

and u, < u, if both are positive.
The condition that the tangent is parallel to the N-axis may be
derived from y,—y,-—= 9 and has the following form:

/
“ ure | eee
cs e 1

Dy

oo, — tan 8, where 3 represents the angle, enclosed between
a a

the radius vector drawn from the third component, and the Y-axis,
we may write this condition as follows:

As

et tes Og a
tan B=—,
2

e 01 nn

and w'‚, >> wy, if both are positive.
The condition that the tangent is parallel to the hypothenuse may
be derived from:

Orte eae

Lt ‘

2 1

(CAREN)

From this we deduce:

Therefore a tangent of the nodal envelope parallel to the hypo-
thenuse can only occur in the case that w, and w',, have different
sign.

All these relations apply only to the case that w',, and w',, may
be equated to zero; and the given rules will require corrections when
the temperature is increased and approaches one of the critical
temperatures. If 7 has reached a value higher than (7%), for instance,
and consequently the surface of saturation does not cover the whole
triangle any more, the envelopes can no longer pass through the
angle of the third component. Even without knowledge of the equation
of the envelopes we can understand in the following way what
peculiarity will then come into the shape of those curves. The
surface of saturation has in the vertical plane containing the }’-axis,
and also in that containing the hypothenuse still the shape of fig. 11,
Cont. IL. The first curve of slope lies in the first mentioned ver-
tical plane and consists of that part of the p curve of the figure
mentioned which extends to the maximum, i.e. to the point C. All
other points of this pressure-curve, as well those between C and P
as those forming the lower branch, represent coexisting phases and
belong to the conjugated curve of this curve of slope. The last of these
curves of slope lies above the X-axis and above the hypothenuse, but
above the hypothenuse it also extends only to the projection of the
point of maximum pressure. Every intermediate nodal envelope has
initially the shape of fig. 13, has also still a vertical tangent, but ends in a
point (the projection of a plaitpoint) before it has reached the locus
which represents the limit of the points above which the surface of
saturation extends. Above such a limiting point of the nodal envelope
the curve of slope of which it is the projection has reached its highest
point. Before the limiting point however the course has been modified.

In order to discuss this modification we will derive the second
2,

5 : : yy
derivative function, namely rary From:
5

da eo

mee IS follows

dea, Ed,

Ps gy — Crdi) dede)
ey ’

de,” BA (z,—2,)°

( 132 )

| dy,
(dy,—dy,) — — (dx,—dz,)
dix,

d*y, 1
or UT =

du,’ ‘ (t,—2,)

d
dy, ae a dir,

d*y, dix,
or : ; db —

dx, (z,—,)

Oy ae dy,

When we write it in this form we see that - == © for: that
ar =

1
phasis for which dv, and dy, are zero, so for that phasis which
coexists with the critical point of contact. If we write:

dy, dy,

ap ie” de AE,

9

de," de, (#,—«,)
‚dy, aoe
then the value of >, assumes for the plaitpoint, where «, = «,
av
1
dy, dy, Bian
and 7 =e = a shape which is indefinite. As, however, the points
aL av
3 1

1 and 2 are situated on opposite sides of the plaitpoint, and the
point 2 must always lie on the tangent of 1, and the curve contain-
ing the points 1, the nodal envelope will present a point of inflection
in the plaitpoint, i.e. in the point where it ends. The further con-
tinuation to the locus of the critical points of contact belongs to the
conjugated curve, and this must reverse its course either abruptly or
fluently, where it meets the locus mentioned.

Let us now pass to the discussion of the course of the nodal
envelope in the case that a maximum pressure exists on one of the
sides of the triangle. We shall suppose it to occur on the X-axis,
so that the succession of the pressures is given by:

Pr Pi S Pi SPs

If for a certain value of 7, a maximum pressure occurs on the
X-axis, then zr, = 0, and y, =0; from which follows that for
the point representing the phasis with maximum pressure we have:

en 0:

The locus, represented by u, = 0, (see our previous communication
p. 9) cuts therefore one of the sides of the triangle adjacent to the
right angle, namely that one which joins the angles representing the
first and the second component. Inside this triangle therefore also a
continuous series of points occurs for which this condition is satisfied.
The shape of this locus cannot be determined without the knowledge
of the equation of state. [t might be derived from the equation on

C4133.)

p. 9, if 7, and pe were known as functions of v and y. If we

a : a
assume, that 7 is proportional to — and »„ is proportional to —

; 5
as follows from the form of the equation of state I have adopted,
then we see that w',,—=0 in the case under consideration represents
a feebly bent curve, which starting from the _Y-axis intersects either
the Y-axis or the hypothenuse. Which of these lines will be cut
depends on the values of (7), and of (7), and on the size of the
molecules of the components 1 and 2. As intermediate case the curve
WU, = 0 might pass through the angle of the third component. In
fig. 14 I have represented it by
curve DI’, so I have assumed it to
cut the hypothenuse. The area of the
triangle may be divided into two
parts according to the value of u’, .
On the left of DF this quantity
is positive; on the right of DF
it is negative. As the quantity uv’,
does not change its sign in the case
under consideration (the pressure
not presenting a maximum on the
lines AC and BC), the value of
(Ux, —1

Fig. 14 OE is positive on the left of
Vr

DF, and negative on the right. The points in which the tangents
to the nodal envelopes are vertical, can therefore only be found on
the right of DF; tangents parallel to the hypothenuse on the other
hand can occur on the left of DH. On the line DF itself the tangents
have a direction, passing through the point C. The curve D/ repre-
sents the locus of the points whose tangent is vertical, and the curve
DH that of the points whose tangent is parallel to the hypothenuse.
We may easily form an idea of the course of the nodal envelopes
themselves in main features if we consider them as slight modific-
ations of the shape they should have if the curve DF were a straight
line, directed towards the summit C. In that case namely the course
of the envelopes in the left part is the same as that of fig. 13, —
with the modification which follows from the fact that one of the
sides, adjacent to the right angle is smaller than the other, and
in the right part it is symmetrical with fig. 18 with regard to the
Y-axis, — with the modification which follows from the fact that an
obtuse angle occurs instead of the right angle. In the left part AD + DC
is one of the outmost envelopes; in the right part BD 4 DC.

( 134 )

If also one of the other sides of the triangle presents a maximum
pressure, e.g. the Y-axis, then we have to deal with still another
locus: wy, =O. The circumstance whether the two curves gr, = 0
and w',, =O intersect or not decides whether for a ternary system
a maximum pressure exists or not. The given rules concerning the
peculiar points of the envelopes enable us in this and other cases
to conclude to the course. But I will no longer dwell upon this
subject. I consider the preceding discussion as sufficient to draw
attention to the significance of these curves for the knowledge of a
ternary system.

d. The addition of a third component to a gwen binary system.

If we have a binary system consisting of 1—r, molecules of the
first kind and «, molecules of the second kind, and we add to it a
third component so that the final composition is given by 1—vr—y,
v and y, then we have:

a“ v

ley ne EN

From this relation we derive:
d
—=1—-y;

Lv

0
from which we conclude, that the points representing the ternary

system lie on a straight line, which counects the summit of the
rightangled triangle with that point on the opposite side that represents
the composition of the binary system.

: 075 075 th ME

Taking into account the values of Epa? a and of aa given on

1 as & OY, Ji
p. 5 and substituting the value —., dy, for dz,, we find from
formula IL of p.

Vs. dp ‚ (1—y) 1 " <Any |
2 —e + Flag ela HH
MRT dy, — ) Ee IE —y,) 1—wz,—y, mn a

1—wz
re (y =) TEN oe i en DU my, %
c la stank! Wy (1—#,—y,)

This equation may be simplified to:

v dp " " ! !
MRT dy = («,—a,){ mn — Voll x Gm b= Y‚) U (1 en, "nh —& lh zal .
4 Gy 1

In order to get the corresponding equation for the vapour phases,
we must interchange the indices 1 and 2; it has the following form:
Vn dp

MRT dy, = (Bj) Wl rijn old ro} + (WV: Nett pa |

( 135 )

If the gas phases are very rarified the latter equation may be sim-

plified to:

1 dp a Pee hi

p OP y,(1—y,)
which form is identical with that which applies if a second component
is added to a simple substance, and from which accordingly the
quantity «’, has disappeared. This identity of the form of the equation
does, however, not justify the conclusion that also the shape of the
curve p= Ff (yz) will be identical. The same form of the equation
applies also to a binary system, and yet it includes the great variety
of curves which the pressure as a function of the composition of the
vapour can present. All those differences in shape are to be ascribed
to the different ways in which y, and y, depend upon each other.
In the same way every plane section of the vapour sheet for a
ternary system by a plane, normal to the plane of the triangle and
passing through the summit, will be represented by this equation,
though these sections may present an infinite variety of forms, which
again may differ from those of a binary system. Yet we may make
use of this equation and deduce some general properties from it.

So e.g. will be zero if on the chosen section a point 7, 7,
dy, ;
occurs for which
YY =O.

If the succession of the values of the pressures is p, << p,< p,
this can never occur. In this discussion, however, we will think the
succession to be changed according to the circumstances in order
that we are not obliged to draw the section every time through
another angle of the triangle. If the succession is p, << p, <p: &
locus oeeurs indeed, for which y, = y, and this locus coincides with
that for which the pressure of the vapour phases which oceur on the
chosen section is maximum or minimum. We might have expected
a priori that in general a maximum or minimum would be found
on the section which passes through the angle for the component
whose pressure lies between those of the other components, and
which cuts the opposite side in a point with the same pressure.
This maximum or minimum will, however, not have the same
significance as that of a binary system. For in the case of a binary
system the composition of the vapour is the same as that of the liquid
phasis; for a ternary system only y, and y, are equal, but 2, and x,
differ. In such a point the pressure of the liquid phasis is not
equal to that of the vapour phasis as is the case with the
maximum pressure of a binary system, — but the pressure of

( 136 )

the liquid is higher than that ot the vapour. The two sheets
do not touch one another in such points.” It is true that the
pressure for a point conjugated to such a point is the same, but

dp. the ; ì dp
_— is different from zero, as appears from the equation for ——.

dy, dy,
If we substitute in this equation y, = y,, we find:
EP ED Rn
CE ze («,—2,) egy eye
p dy,
r ’ : . . du
The factor «,—v,, which also may be written depends on the
dy,

curvature of the g-surface, and in all cases in which the surface is
only slightly bent it will have only a small value; but only in very
special cases it will be rigorously zero. In general therefore we
may assume, that this locus of the maximum liquid pressures does
not deviate much from the locus for which y,—y, =0. If the pro-
jections of the curves of equal pressure are drawn, the points of
maximum pressure and the sections discussed by us are of course
immediately to be determined, by tracing the tangents, passing through
the angles of the triangle.

Lee RUSS el ; :
The value of — 5 assumes exactly the same shape it has for ¢
MRT dy,
ah Ae 9 dus,
binary system if either (r‚—t,) or TI are zero. The value of 7,—a,
ay,

vanishes in the first place if the quantity we have denoted by «, is
zero, and in the second place if it is equal to unity. But in these
cases we are really dealing with binary systems; in the first case
with the pair 1,3 and in the second with the pair 2,3. In the first
case we have:

Deep 1 ae
MRT dy, = (Y¥s—43) eee Tey |
and in the second case, if
1—2x,—y, = 1—2,—y,, or &,—a, =— (YY):
Deed 1 2 8 F
MRT dy, == CASA Een ze Un — 2 Won =f U ay '

The quantity uw’, — 2u’, + u',, has for the pair 2,3 the same
signification as u’, for the pair 1,3, as is easily understood.

Vie sl
MRT dy,
peculiar points, where «,—x, =O either inside the triangle or on

The quantity assumes also this simple shape in the very

one of its sides, and also in the points where vanishes.

ay

( 187 )

But in general the quantity (wr) Wijde Ur, ) Will cause a
modification in the course of the value of the pressure which is
very slight. The value of the pressure depending principally on the term
Ya

ny) ; : : d
We will consider more closely this last quantity, which represents

d vod dp
the limiting value of — — for y,=0 or y,=1, for a binary
p dy, ; ‘
mixture and which for a ternary system is to be augmented with
t
VG ES
(7,—2,), 1 2
ay,
5 . ’ . . Yay.
We have found before the following value for >:
Yi.

gat Ag) LI) ale “1
I Ch Yi) = de ne ae ye En

From this value we deduce, if we set y, —=0 and x, =

9

0

Var Ui (e an —1)—a,(e"™ ty) eh 1

— — = ae
Lt staa Br

ny) La (ef * —1)

where w‚, and w,, have the values they have in the point whose

coordinates are #, ==, and y,—0. This value, which for 2, == 0
d 3 . 2 3 p Ae pe
is equal to e “"—1, has for «, —1 the final value e #* “" —1,

and varies fluently with increasing «,; and now the way in which
1 dp
—-— varies depends upon the relation between u’, and w,. This
p dy,
value may have reversed its sign, either from negative to positive
or from positive to negative. The quantity u, — tt, represents the
variation of g for the motion along the hypothenuse towards the
summit of the triangle in the same way as wu’, represents the varia-
tion for the motion along the N-axis towards the summit. If there-
fore 7, for the summit is lower than (7%), then w',, is positive,
and if 7, for the summit is higher than (7), then wy — us, is
negative.

It is not superfluous to point out in how high a degree the value

i ,dp oe fess
geen depends on the value of u’, , if it represents the initial
p dy, |
direction of a curve of equal pressure for a binary system. According
: : , : pe : .
to our former observations this value is equal to e “—1. If we
1 dp yy, ae
also draw the vapour curve, then — =>, and soit is equal to:

Pp dy, Ys

( 188 )

u'
e [> 1 ji :
ze —1—e '”“. If we draw moreover the curve of the double

ol th
dp fey Ses
points then we have —-—wy,. For the case that u',,=0 we always

pdy
find zero as well for the value of ee as for Rae: En
p dy, p djs pay
If w,, is positive, the three lines ascend, and they descend if wy, is
negative. If the value of «,, is very small, there is only a small
difference in the slope of the three curves. But if wy, has not so
very small a value, then there is a very great difference in the slope
of the three curves, and the liquid branch ascends exceedingly fast.

F dTer , dlog per

As Eat a T dy, dy,

ag.

sae

we shall have a great value u, if - has a considerable negative

value, so if the 7%, of the second component is much lower, e.g. if

we press a permanent gas into a liquid. As in general 7%, does
: d log per An :
not depend linearly on 4, and ae has a value differing from
ay,
zero, we shall not find the accurate value for w, putting:

.

' J ry ryy
Ba T i( Ter), — (Fer) af

but only a more or less approximated value. If we choose for the second
component a substance whose 75, is much lower than fand for the first
component a substance, whose 7%, is much higher than 7’, we do not take
an impossible value for w,,, if we give it the value 14 or 15 for

ordinary temperature. In that case é A may in rough approxima-
tion be represented by 10°. If we might apply the results we have
obtained, also in the case of water, though its behaviour is specially
at low temperatures very abnormal, then we might form an idea of
the degree of approximation by means of the absorption coefficients
of gases solved in water.

According to our results we find for small values of y,, if we
neglect the vapour pressure of the first component compared with
the total pressure:

PE Pa (YI).
Here p, represents the vapour pressure of the first component.
Further we have, denoting the absorption coefficient by @, and ‘the
molecular weight and the density of that component by m, and d,:

( 139. )

m, 90,0013
— & p.

ao) 28,8

GAN

. . DM 2 . n e
If we neglect unity toe ”, we may derive from these two equations :

uw, d, 28,8 1
e n — @ Een, 8
m, 0,0018 ap,
4.6
If swe. put in. this” equation, Jd, — 1, m,=18 and es ae
7

Atmospheres, and a = 0,02 as is the case for .V,, then we find for
uy, a value between 16 and 17. This result shows that the equation

Uy = (Lr) — (Ter) Ng}

ag
273
does indeed hold as an approximation.

If we had chosen as second component a substance of small
volatility and whose 7, is much higher than (7), then we might
form an idea of the value of wt’, by making use of the approximation:

' jn 7 a al
ne hoe): a= CP wats

EN
but then we should find a very great negative value for u’, and
‘ y DM : : : 3
for S ==e Ya value which differs only slightly from zero.

Yi
When we add a third component to a binary system whose com-

position is determined by w,, then we have found for the value of

Wd, ees :
—-—, if y, is infinitely small:
p dy,
1 dp en " "
p dy, —1+(#,—#,)o tue a a, — Lo x i

ie sa A
le, dere

The two branches of the pressure-curve of this section do not start
in the same point and so they differ already from the beginning from
those of a binary system. Only if (w‚—), = 0 they start at the same
point. But as the factor of v,—v, depends on the curvature of the
u surface the influence of this term may be neglected specially when
wy is great or when the curvature is considerable. So we find for

1 dp : ;
the value of x, for which — —- vanishes approximately :

p dy,
/
gdh et
xy —- away
dio etl

Only when ,,<w,, this yields a possible value for 2, at least
if as well u, as wz, are positive.
by 1

( 140 )

Geology. — “Cambrian Erratic-blocks at Hemelum in the South-west
of Frisia.’ By J. H. Bonnema. (Communicated by Prof.
J. W. Morr).

To the East of Molkwerum, a railway-station between Leeuwarden
and Stavoren, stretches a region that from a geological point of view
is very remarkable; as was especially shown by the interesting
researches of Dr. VAN CAPPELLE. *)

The road first leads in a North-eastern direction to the village of
Koudum, which is situated on elevated ground. As far as here the
surface showed alluvial clay only; now we see for the first time
diluvial formations. The outer part of this elevation consists of
boulder-clay, whereas in two sand-pits it may be easily observed
that preglacial layers form the inner part.

A little farther on, when the alluvial grounds are reached again,
one comes to the Galama-dams. They are found on the Morra,
according to the above-named author a bottommoraine-lake.

About a mile farther upward we again find diluvial soil, and on
continuing our journey in the direction of Rijs we see, just before
leaving Hemelumer-Oldephaert and Noordwolde, and entering the
domain belonging to Gaasterland, in a meadow to the right of the
road a large pit 8 metres deep. From this pit for some years
boulder-clay has been dug in behalf of the brick-works of the Comp.
IGaasterland”’, at a short distance, on the other side of the road.

As far as I know, these are the only brick-works in the Northern
part of the Netherlands, where bricks are made of boulder-clay.

The boulder-clay, which forms a bottom-moraine here and which
must be found very deep in the earth, is coloured blue-grey. Only
quite near the humus-layer it has become red-brown, under the influence

1) Van Carpeue, Les Escarpements du ,Gaasterland” sur la côte meridionale de
la Frise. Extrait du Bulletin de la Société Belge de géologie, de paléontologie et
d'hydrologie 1889.

Van Cappette, Bijdrage tot de kennis van Frieslands bodem. II. Eenige mede-
deelingen betreffende de Gaasterlandsche kliffen. Tijdschrift v. h. Koninkl. Nederl.
Aardrijksk. Genootschap. 1890.

Van Cappette, Bijdrage tot de kennis van Frieslands bodem. IV. Eenige mede-
deelingen over de diluviale heuvels in de gemeente Hemelumer-Oldephaert en Noord-
wolde. Tijdschr. v. h. Kon. Nederl. Aardrijksk. Genootschap. 1892.

Van Carperre, Bijdrage tot de kennis van Frieslands bodem. V. Karteering van
't diluvium van Gaasterland en Hemelumer-Oldephaert en Noordwolde. Tijdschr. v.
h. Kon. Nederl. Aardrijksk. Genootschap. 1895.

Van Cappetie, Diluvialstudien im Südwesten von Friesland. Verhandelingen der
Koninkl. Akad. v. Wetensch. te Amsterdam. 1895.

( 141 )

of the weather. It contains comparatively few erratie-bloeks. They
often show very fine glacier-scratches and are mostly of average size.

During the time when this opportunity of gathering erratic-blocks
has presented itself, I have several times visited, from Leeuwarden,
this loam-pit. The result of these visits is that I brought home rather
a large number of erratic-blocks (probably between 300 and 400).

The sedimentary ones are still here at present; after studying them
I intend to present them to the Geological Institute at Groningen.
The others, whose number is small compared with that of the sedi-
mentary stones, have already been given to this Institute.

Though my collection is still small, it is large enough to confirm
my opinion that our knowledge of our sedimentary erratic-blocks
leaves much to be desired. I formed this opinion already after
examining the erratic-blocks of Kloosterholt. *)

In gathering erratic-blocks in the Gron. Hondsrug I had gradually
come to the conclusion that our sedimentary ones almost exclusively
originated from Silurian layers, and that the latter must have shown
much resemblance to those of the Russian Baltic-sea provinces, perhaps
are still to be found there. ‘On getting acquainted with the erratic-
blocks in the boulder-clay of Kloosterholt, however, I could not but
see very soon that at any rate this rule does not hold good in all
cases. In this place I often found pieces of older and younger forma-
tions, while corresponding stones occur as firm rocks in Sweden and
Denmark. The very same phenomena, as I hope I shall indicate, are
seen in the erratic-blocks of Hemelum. Besides Silurian formations,
others, both older and younger, are numerously represented. At the
same time all of them show almost exclusively a West-baltie character.

We should then see the remarkable phenomenon that at Groningen,
which is situated between Kloosterholt and Rijs, erratic-blocks greatly
differ from those of the two places mentioned.

Gradually, however, I am beginning to doubt whether my opinion
about the character of the erratie-bloeks in the Groningen Hondsrug
should be the right one. In the years when I used to gather there,
digging was atmost entirely confined to the upper layers, so the
chances are, that deeper parts contain other kinds of erratic-blocks.

A few facts seem to indicate this. First of all : while a deep cave
was being dug under the brewery called Barbarossa, at Helpman,
big blocks of Saltholmlime with Terebratula lens Nilss made their

1) Van Carker, Ueber eine Sammlung von Geschieben von Kloosterholt. Zeitschr.
d. Deutsch. Geol. Gesellsch. Jahrgang 1898 p. 234.
Bonnema, De sedimentaire zwerfblokken van Kloosterholt. Versl. v. d. Koninkl.
Akad. van Wetensch. te Amsterdam 1898 pag. 448.
LO
Proceedings Royal Acad. Amsterdam. Vol. V.

( 142 )

appearance. Some pieces of this material are still to be seen in the
Geological Institute at Groningen.

Secondly : van Canker’), — when the ramparts near one of the
gates (Boteringepoort), which ramparts had certainly been made of
the boulder-clay from the very deep ditches in that neighbourhood,
were dug off, — found some erratic-blocks consisting of kinds of
stone such as I never found afterward, and which do not occur in
the Russian Baltic-Sea provinces, La. slate with graptolites, Faxe-lime
and sandy glauconite lime-stone with Terebratula lens Nilss.

Deeper cuts made into the Hondsrug may afterwards give us an
opportunity of learning whether my original opinion was entirely right,
or is the true one only as far as the outer layers are concerned.

I should now like to tell something about the chief Cambrian pieces
that are found in my collection. L am going to treat only of those
stones whose age may be more or less precisely determined.

I. Lower-Cambrian Stones.

1. Seolithus-sandstone. Eleven stones consisting of this material
are found in my collection. Nine of them are typical grey, quartz-
iferous Scolithus-sandstone, showing a peculiar, fatty lustre on the
side where they were broken off. No layers are visible as long as
the stone is not changed by the influence of the weather. Only if
this takes place, the layers become more or less visible. In one stone
they are rather distinct and turn upward (perhaps downward) near
the “scolithus.” Two other stones, one of which is blue-grey, whilst
the other moreover contains red parts, are clearly divided into layers
and contain much finer tubes than are found in the typical stone.
In the regions from which our erratie-bloeks come, Scolithus-sand-
stone was first seen as firm rock in the isle of Runö near Oscars-
hamm, where according to Torerr *) it was discovered by Dr. Horm-
strom. Afterwards it was also met with as such by Natnorst *), in
the isle of Furön, not far from Runö.

I was wrong when, in treating of the Kloosterholt erratic-blocks,
I told that Scolithus-sandstone as firm rock is found in Sweden, in
the neighbourhood of Lund and Kalmar. The same mistake was

1) Van Carker, Beiträge zur Kenntniss des Groninger Diluviums. Zeitsch. d.
deutsch geol. Gesellsch. Jahrg. 1884 pag. 718 and 727.

2) Tore, Petrificata Suecana formationis cambricae. Lunds Univ. Arsskrift.
Tom. VI 1869 pag. 12.

5) Narrorsr, Geol. Föreningens i Stockholm Förhandlingar 1879. Bd IV, pag. 293.

( 143 )

made by SCHROEDER VAN DER Kork *) and by Srrusrorr ®). The latter
and | probably came to make it unter the influence of what was
told by Rormer*) with regard to the origin of this kind of erratic-
blocks. With SCHROEDER vy. bp. Kork this is certainly the case, as
appears from the note at the bottom of the page.

As to their being found at Hardeberga in the neighbourhood of
Lund, Rormer seems to have forgotten the fact that Toren. *), though
he at first communicated that the Hardeberga sandstone contained
worm-shaped bodies probably belonging to Seolithuslinearis Hail,
afterwards makes mention of a new kind, viz. Scolithuserrans Tore *),
The latter are distinguished for being mostly curbed and running
through the stone in various directions.

Rormer’s information that Tori describes Scolithuslinearis from
an erratie-bloek found near Lund, and that according to Ninsson
Scolithus-sandstone occurs near Calmar (as firm rock), must be attri-
buted to an error. If my imperfect acquaintance with the Swedish
language does not deceive me, Torri. *) writes that the place where
the pictured stone (an erratic-block) was found, cannot be indicated
for sure, but that Ninsson thinks he remembers that it was found
near Calmar.

In the Northern part of the Netherlands erratic-bloeks of Scolithus-
sandstone are rather common. In Frisia were found, besides the
stone treated of above, one in the Roode klif (Red Cliff) ”), one in
the Mirnsercliff*) and one at Warns (see number 3). Among the
erratic-blocks of the Gron. Hondsrug *®) only one piece was found up
to this time, whereas I formerly deseribed already two pieces from
Kloosterholt '°) and afterwards gathered more of them there. In the

1) SCHROEDER VAN DER Kork, Bijdrage tot de kennis der verspreiding onzer kris-
tallijne zwervelingen. Dissertatie pag. 50.

*) Srevustorr, Sedimentiirgeschiebe von Neubrandenburg. Archiv des Vereins der
Freunde der Naturgeschichte in Mecklenburg. Jahrg. 45 pag. 162.

5) Roemer, Lethaea erratica pag. 23.

4) Torero, Bidrag till Sparagmitetagens geognosi och paleontologi. Lunds Univ.
Arsskrift. Tom. IV. pag. 3d.

5) Tore, Petrif. Suec. format. cambric. pag. 12.

6) Tore, Bid:ag till Sparagmitetagens geogn. och paleontol. pag. 29.

1) Van Carpeuw, Bijdrage tot de kennis van Frieslands bodem. IL pag. 12.

5) Van Carperre, Les Escarpements du „Gaasterland”, pag. 236.

) Van Carker, Ueber das Vorkommen cambrischer und untersilurischer Geschiebe
bei Groningen. Zeitschr. d, deutsch. geol. Gesellsch. Bd XLIIL pag. 793.

10) Van Carker, Ueber eine Sammlung von Geschieben von Kloosterholt, pag. 235.
Boynema, De sedim. zwerfblokken van Kloosterholt, pag. 449.

10%

( 144 )

province of Drente vaN CaLkeR') mentions Buinen, Steenbergen and
Zeegse as places where he came across these stones, whereas I
myself found some at Odoorn.

2. Grey sandstone with interlaced coloured layers.

A small piece of quartziferous sandstone, 7 centimetres long, 1s
almost entirely grey-coloured. Two systems of coloured layers, varying
from red to violet, interlacing under angles of about 30 degrees, are
also found. The layers of each system separately run parallel to
each other. Surfaces of deposit do not occur and the size of the
grains of sand is everywhere the same, so that it is impossible to
examine which layer-system runs parallel to them.

This sandstone was made mention of for the first time by Nar-
HORST *), who found erratic-blocks consisting of it in Jungfrun in the
Kalmarsund. With Dames ®) he found the same kind of stone in
Oeland, a few years after. Later on the latter writer *) could tell
about this kind of erratic-block occurring in diluvial layers in the
neighbourhood of Berlin.

As one of the pieces found there contains Scolithus-tubes, he could
also draw the conclusion that their age is the same as that of the
above mentioned Scolithus-sandstone. This conclusion is confirmed
by means of a piece of Scolithus-sandstone that I found at Warns a
short time ago. Through the grey piece of sandstone run on one
side a few violet-coloured layers, which are intersecting the Scolithus-
tubes under an angle of 60 degrees, while the latter always stand
perpendicularly on the surfaces of deposit, which are not seen here.

That this stone also occurs in the Dutch dilnvium, was already
shown by van CALKER®); he proves that it is found in the erratic-
bloeks of the Gron. Hondsrug.

IT, Mid-Cambrian Stones.

3. Limesandstone with Paradoxides-remains.
In my collection I have also a piece of grey, fine-grained sand-
stone with a large quantity of caleium-carbonate as binding-material.

1) Van Canker, Ueber ein Vorkommen von Kantengeschieben und von Hyolithus-
und Scolithus-Sandstein in Holland. Zeitschr. d. deutsch. geol. Gese'lsch. Jahrg.
1890 pag. 583.

2) Narnorst, Geol. Föreningens i Stockholm Förhandlingar 1879. Bd IV pag. 293.

3) Dames, Geol. Reisenotizen aus Schweden. Zeitschrift der deutsch. geol. Gesell-
schaft. Jahrg. 1881 pag. 417.

4) Dames, Zeitschr. d. deutsch. geol. Gesellsch. Jahrg. 1890. Bd XLIIL pag. 777.

5) Van Carker, Zeitschr. der deutsch. geoì. Gesellsch. Jahrg. 1891. Bd XLIII
pag. 793,

( 145 j

Through the stone run intersecting passages of the same mineral.
Here and there are small grains of glauconite and pyrites-crystals.
Besides many Paradoxides-fragments arranged in layers, my stone
contains remains of horn-shelled Brachiopoda. The former are eream-
coloured and do not allow of being further defined. Among the latter
are easily found valves of Acrotele granulata Linn.

About this stone I have up to this time nowhere found any infor-
mation. It is probably of the same age with the layers of Paradox-
ides Tessini Brongn., or it is a little older than these are.

4. Gravel-stone with Paradoxides Tessini Brongn.

a. It is a piece of fine-grained, hard sand-stone, yellow-grey inside
and light grey nearer the surface, whilst the surface itself is brown
in some places. With a magnifying-glass some grains of glauconite
and a few mica-scales may be distinguished in it.

With muriatie acid applied to it, there is no effervescence; conse-
quently it does not contain caleium-carbonate. There are no layers.

The chief remnant occurring in this erratic-block is a mid-shell, a
little more than 1 centimetre long, of a Paradoxides, which mid-shell
is visible for the greater part. The eream-coloured shell is still almost
entirely present. That this remnant originates from Paradoxides Tessini
Brongn., could be easily determined by means of the description and
the pictures which Linnarsson ') gave us of this kind. Prof. Mosrre,
to whom I had the honour of showing this erratic-block, when visit-
ing Lund, thought my determination right.

The glabella increases in breadth towards the front; quite near
the front it is broadest. The front-edge is rounded off. On each side
the glabella has two side-furrows, which in the middle run into those
of the other side, which is also the case with Paradoxides Oelandicus.
Of smaller furrows, which according to LINNARSSON are sometimes
found in the latter, nothing is to be seen here. The edge before the
glabella is very narrow in the middle and broadens towards the ends.
This is characteristic of Paradoxides Tessini, whilst with Paradoxides
Oelandieus the breadth of the edge before the glabella is rather con-
siderable, and remains about the same towards the sides.

We also find here a piece of a thorax-ring of a kind of Paradoxides,
in which it may be seen that the pleurae first run straightway towards
the outside and then turn to the back, forming an almost right angle.
This also oceurs with Paradoxides Tessini, whereas with Paradoxides
Oelandicus this turning to the back takes place gradually.

1) Linnarsson, Om Faunan 1 Kalken med Conocoryphe exsulans (,Coronatus
kalken"). Sveriges geologiska undersökning. Series CG, N° 35 pag. 6. Scene | fig 1—4,

( 146 )

Finally are found in this erratic-bloek a few small valves of horn-
shelled Brachiopoda, among which is one of Lingula or Lingulella.

6. Besides the piece treated of just now I found a piece of sand-
stone with Paradoxides-remains, which shows no effervescence when
hydrochloric acid is applied to it, and which consequently is gravel-stone.

It is a flat piece, consisting of two parts of a different nature. One
of them is formed by sandstone and does not present many layers.
This sandstone greatly resembles the material of which consists the
erratic-block treated of under «, but is a little bluish. Some small
mica-scales and glauconite-grains are also present here. The other part
shows many more layers and has a dark bluish-grey colour. Some-
times the layers are as thin as paper, so that the material becomes
slate-like.

Just as in the other piece of stone, the Paradoxides-remains are
cream-coloured here. They are, however, too fragmentary to enable
us to draw the conclusion that they originate from Paradoxides Tessini.
As up to this time, however, only sandstone with this kind of Para-
doxides has been found in diluvial grounds, and the petrographical
nature of one part of them bears a great resemblance to that of the
previous piece, I think I may suppose this much, and I venture to
range this erratic-block under this head.

I think that both pieces originate from a layer-complex of gravel-
stone with Paradoxides Tessini-remains, which complex consisted both
of slate-like blue-grey parts and of thicker light-coloured layers. The
last-mentioned erratic-block may originate from the former, whereas
the one treated of under « would be a piece of a thicker layer.

If my supposition is not false, it may be easily explained from the
difference in firmness and the difference in fitness for being trans-
ported issuing from this, why in literature nothing is found about
erratie-bloeks that should bear resemblance to the last-mentioned
piece, whilst two or three Communications have been received about
the finding of erratic-blocks that most probably are more like the
piece treated of in the first place.

The first communication we got from Rorer.') It deals with a
piece of gravel-stone that was found in a sand-pit of Nieder-Kunzendorf
near Freiberg in Silesia. It seems to have been more exposed to
the influence of the weather than the erratie-bloek found by me, the
writer mentioned speaking of a ferrugious outer crust, while round
my piece such a crust begins to form itself.

Probably I must also range among this kind a piece of sandstone

1) Roemer, Zeitschr. der deutsch. geol. Gesellschaft. Bd 9. Jahrg. 1857 pag. 511,

( 147 j

with Paradoxides Tessini-remains that was found in the collection of
Groningen erratic-bloeks, given to the geological Institute at Lund by
Mr. pe Sirrer, L. L. D., then burgomaster of Groningen. It was
deseribed by LUNDGREN *). I am sorry that we do not learn whether
it is gravel-stone or lime-sandstone. L wrote to Prof. Moere, director
of the Institute mentioned above, in order to ask after this, but he
could not give me any information concerning the piece just then.
I think, however, that it is gravel-stone, LUNDGREN telling us that
the colour is perahvit”, while according to Rormer*) lime-sandstone
with Paradoxides Tessini is dark grey.

While in the previous ease it has not yet been with certainty
determined which kind of sandstone one has to deal with, RrmerÉ”)
has announced another gravel-stone with Paradoxides-remains having
been found. This erratie-block differs from the piece I described under
a in the fossils being coloured brown by manganite-superoxide.
However, I think this of little importance, as it may be just as well
a consequence of infiltration that occurred in diluvial grounds or
even before that time.

Gravel-stone with Paradoxides Tessini has up to this time not been
met with as firm rock. Probably it occurs as such, or did so in
former times, in the neighbourhood of Oeland; for on the Western
coast of this isle is found, in several places, lime-sandstone with the
same kind of trilobites.

ITD, Upper-Cambrian Stones.

5. Alum-slate with Agnostus pisiformis L. var. socialis Tullb.

One time I was so fortunate as to find a piece of black slate, in
Which are scattered the grey head- and tailshields, preserved in relief,
of a kind of Agnostus. They have a length and a breadth of 3
millimetres at most.

The head-shields are moderately vaulted. The dorsal furrows
meet in front, and a tongue-shaped glabella is bounded by them.
At the front-part of the glabella is on each side a lateral furrow.
The two lateral furrows run into each other and in this way cut
off a small part in front. At the foot of the glabella two smali
lobes are separated from the rest by means of two lateral furrows
slanting backward. The central, largest part of the glabella shows

1) Lunpcren, Geologiska Föreningens i Siockholm Förhandlingar. 1874. If N° 2
ATA
pag. 44,
2) Roemer, Lethaea erratica, pag. 29.
3) Remeré, Zeitschr. der deutsch. geol. Gesellschaft. Bd 35. Jahrg. 1883 pag. S71,

( 148 )
in the midst a wedge-shaped elevation. The cheeks are in front
separated by a furrow running from the front of the glabella to
the edge-furrow.

The tail-shields are much more vaulted. This is especially the
case with the rhachis, which broadens towards the back and stretches
nearly as far as the edge. Consequently, the lateral parts of the
pygidium, which are already narrow, become even more so towards
the back part. They are not separated by a furrow, as it is the case
with those of the head-shields. The pygidia have at the back-edge
on either side a little cog pointing backward. The rhachis of the
pygidia is clearly divided into three parts. The back-part is the
largest by far and is particularly swollen. The lateral farrows of
one side do not meet those of the other, as they are separated by a
wedge-shaped elevation passing on from the second part to the first
and ending towards the back in a blunt point slanting upward.

From the properties mentioned it may be easily seen why this
kind of Agnostus was described by TULLBERG*) as Agnostus pisifor-
mis L. var. socialis. Pictures of it have been given by BRÖGGER ®)
and PoMmPrckr *).

Up to this time this erratic-block is the only piece of alum-slate
with Agnostus pisiformis L. var. socialis that was found in our
diluvial grounds. In Germany they also seem to be very rare. Only
GorrscHe *) mentions such a piece from Scnvrav. This one also
contains, however, remains of Olenus truneatus Briinn. As firm rock
such alum-slate with this variety of trilobites occurs in Sweden
(Oeland and Bornholm included), in different places, as I learned
from Prof. Mopere, to whom I showed a piece of the erratic-block.

Microbiology. — “Accumulation experiments with denitrifying
bacteria’. By G. VAN Irerson Jr. (Communicated by Prof.
M. W. Beijerinck).

The great signification of the denitrifying bacteria for the circulation
of nitrogen in organic life and the important biochemisms to which
they give rise, made the study of these organisms very attractive.

1) Tuttperc, Om Agnostus-arterna 1 de Kambriska aflagringarne vid Andrarum.
Sveriges geologiska Undersökning. Ser. CG. N° 42 pag. 25.

2) Bréecer, Die Silurischen Etagen 2 und 3 im Kristianiagebiet und auf Eker.
Pag. 56. Taf. 1. fig. 10abe.

3) Pompeckt, Die Trilobiten-Fauna der Ost-und Westpreussischen Diluvialgeschiebe.
Beiträge zur Naturkunde Preussens herausgegeben von der Physikalisch-Oekono-
mischen Gesellschaft zu Königsberg. Pag. 15, Taf. IV, fig. 24a b.

4) Gorrscue, Die Sedimentär-Geschiebe der Provinz Schleswig-Holstein, pag. 11,

( 149 )

In the first place it was necessary to subject their distribution in
nature and their isolation to an investigation, beeause the literature
thereon offers but very deficient data. The best way to attain this
object seemed to try whether the method of “accumulation” gave
in this case, as in so many others, any definite result, and that for the
following reasons.

The character of this way of experimenting is the cause, that many
biological properties of the species there by accumulated may be
predicted ;

it renders it possible, in a simple way, directly and with certainty
to isolate from nature a determined species; this is of special
interest imasmuch the cultures of most bacteria, by being kept in
the laboratoria, change their character to such a degree as to become
irrecognisable, so, that the descriptions, found in bacteriological literature,
according as they are made after newly isolated or long kept material,
may be wholly different ;

it teaches us to recognise the sought- for species in the different
varieties occurring in the material used for infection, as these varieties
are bound to corresponding culture conditions;

the identification and synonymy of the bacteria, which are always
extremely difficult, even in case we possess good descriptions, made
of freshly isolated cultures, are much facilitated by good “accumu-
lation experiments”;

these may, moreover, be controlled by anyone, and render the
investigator independent from material isolated by others.

For the arrangement of my experiments I have followed the
example given by Dr. H. H. Gran’) of Bergen in his researches in
the Bacteriological Laboratory at Delft on denitrifying sea bacteria.

By exclusively using nitrate as source of nitrogen in the culture
liquid, which was contained in a cotton-plugged flask, so that the air
could freely enter, he succeeded to restrict considerably the number
of developing species of bacteria, when taking fresh sea-water for
infection, bringing the denitrifying species to vigorous growth. He
furthermore selected, as source of carbon the caleiumsalts of organic
acids, by which the prejudicial alkaline reaction, which appears in
bouillon in consequence of the decomposition of the alkalinitrate,
was avoided. Mostly calciummalate was used, which is a very
good bacterial food, and has moreover the advantage of solving only
to 0,8°/, at 25° C., so that it can be added to an excess, whence,
as the salt is oxidised, a new quantity is solved.

1) Studien über Meereshacteriën 1, Bergens Museums Aarbog 1901 N°, 10,

(130 5

After 2 or 3 successive inoculations in the same liquid a constant
bacterial mixture was obtained.

I tried to apply these principles to the isolation of denitrifying
land-bacteria, and so-doing [| succeeded indeed, when using calcium-
tartrate as source of carbon, to accumulate Bacillus vulpinus, hereafter
to be discussed.

It proved however to be a fundamental improvement wholly or
partly to exclude the access of air as thereby the growth of the
denitrifying bacteria is not in the least impeded, whilst a number of
other aerobie bacteria are very much hindered in their development.

Of the numerous methods of culture under exclusion of air I have
followed the simplest, namely the “bottle method”, long since
in use in the Bacteriological Laboratory at Delft for the examination
of the sulphate reduction by microbes and the lactie-acid fermen-
tation. For my experiments this method proved perfectly adapted,
as the quantity of air which finds access, can thereby easily be
regulated. An ordinary, narrow-mouthed stoppered bottle, with an
exactly fitting stop, is quite or partly filled with the culture liquid,
and after sterilising or not, according to circumstances, the bottle is

placed in the thermostat for culture.
1. Historical.

The reduction of nitrates by bacteria constantly begins with the
formation of nitrite. This may be further converted in five different
ways, VIZ. :

1st. It may be reduced to ammonia.

24, Tt may be converted into unknown, nonvolatile nitrogen
compounds.

Zed, Tf in the liquid acid is formed simultaneously, it may give
rise to the development of nitrogen-oxygen compounds.

Ab Tt may be decomposed in alkaline solution under formation
of nitrogen-oxygen compounds.

5th, The nitrite may, in alkaline solutions, give rise to the devel-
opment of nitrogen without the production of nitrogen-oxygen com-
pounds. This is denitrijication proper, of which here is only question.

Already in 1814 Davy’) states that during putrefaction of aninal
matter nitrogen as such is freed. “Here it is again seen,” says in 1860
G. J. Munprr?), from whom I borrow this particular, “if one wishes

1) Elemente der Agriculturchemie, Berlin 1814, ea:
2) De Scheikunde der Bouwbare Aarde, 1860, dl. 3, blz. 58.

Js

( 154 }

truly to give the euique suum in this part of science, one often must
retrograde half a century.”

Not before 1856 the problem was again taken into research. In
that year Reiser’) pointed out, that at the putrefaction of dung and
flesh free nitrogen is produced. Later investigators have not been able
to observe free nitrogen under these circumstances, in asmuch as
no nitrate or nitrite are present, but the putrefaction of albuminous
matter as such has still remained an open question from this point
of view.

It was Prrouzr ®), who in 1857, for the first time, with certainty
stated the disappearance of nitrate during the putrefaction of animal
matter.

BoussinGAuLtT *) observed in 1858 the disappearance of salt-peter in
the soil. He aseribed it “a une cause purement accidentelle, a une
action réductrice, exercée par de la matiere végétale morte”.

From the year 1873 date very interesting observations of SCHLOESING *)
on nitrification. By studying the influence of oxygen on this process,
he was led to the examination of denitrification. He found that nitri-
fication in the soil was still very active, when it was held in a current
of gas, which contained but 1,5 °/, oxygen. If he worked in a current
of pure nitrogen, there not only occurred no nitrification, but even
the nitrate, originally in the soil, disappeared entirely. He furthermore
proved that at this decomposition nitrogen is formed.

Experiments of Pasrrur and the well known investigation of
SCHLOESING and Münz on nitrification, induced Gayon and Durerir *)
to ascribe denitrification to the action of micro-organisms. In 1882 they
communicated their first results and these put the bacterial nature of
the process out of all doubt. Their elaborate and excellent researches
on this subject were published in 1886 °).

Our compatriots Girtay and ABERSON ‘) isolated, for the first time, in
1892 a denitrifying ferment, and the prescription given by them for the
artificial culture liquid has been followed by various later investigators.

The attention of bacteriologists was again fixed on these ferments

1) Expériences sur la putréfaction et sur la formation des fumiers. G. R. 1856,
T. 42, p. 53,

2) Remarques de M. Perovze. G. R. 1857, T. 44, p. 119.

3) Nouvelles observations sur le développement des helianthiws soumis iV action
du salpètre donné comme engrais C.R. 1858, T. 47, p. 807.

4) Etude sur la nitrification dans les sols, C.R. 1873, T. 77, p. 203.

5) Sur la fermentation des nitrates, G.R. 1882, T. 95, p. 644.

6) Recherches sur la réduction des nitrates par les infiniments petits. Naney. 1886.

7) Recherches sur un mode de dénitrification et sur le schizomyeéte qui la
produit. Arch. Neerl. T. 25, 1892, p. 341,

( 159 )

by interesting agricultural experiments of P. Wacyer ') in 1895, which
seemed to point out a danger produced by these bacteria for agriculture.

His experiments gave direct cause to the research of Burri and
STUTZER®), who, in the same year, elaborately described two denitri-
fying bacteria.

From that time this group has been laboriously studied and at
present a number of twenty denitrifying species have been described *).

To these I for my own part might add some ten species more,
but of these I will only discuss those, for which I can point out an
accumulation experiment, which gives a constant result.

2. General considerations.

The hitherto isolated denitrifying bacteria are all aerobic. In
liquids containing nitrate or nitrite, they can, however, grow vigor-
ously with a very slight or without access of air, so that in this case
they behave like anaerobie bacteria. They then transfer the oxygen
of the nitrate or the nitrite to the organic compounds present in the
culture liquid. Thence nitrogen is freed and the metals of the salts
pass into carbonates or bi-carbonates, which process may be represented
by the formulae:

5C..+4KNO, + 2 H,0 = 4 KHCO, + 2 N, + CO,
3C..+4KNO, + H,O = 2 KHCO, + K‚CO, + 2N,

The correctness of this representation has been proved by the
observations of Gayon and Dvprtir, Gintay and ABERSON, PFEIFFER
and LEMMERMANN, AMmPora and ULprant, and also by my own researches.

We see from this, that in a liquid, simultaneously with the nitrate,
the rate of organic substances decreases, and accordingly also the
permaganate number. From a practical point of view this must
necessarily be of signification for the explanation of the processes on
which is based the biological purification of sewage and water *).

My experiments have furthermore convinced me that denitrification
is inseparably connected with the growth, for which traces of free
oxygen are always necessary.

1) Die geringe Ausnützung des Stallmiststickstoffs und thre Ursachen, Landw.
Presse, -1895:"$:..92:

2) Ueber demitrifizierende Bakterien. Centrbl. f. Bakt. Abt. II, Bd. 1, 1895, S. 257.

5) OQ. LEMMERMANN. Kritische Studiën über Denitrifikationsvorgiinge. Jena. 1900.
C. Horuicu. Vergleichende Untersuchungen über die Denitrifikationsbakt. ete.
Centrbl. f. Bakt., Abt. Il, Bd. 7, 1902, S. 245.

4) Dr. Jenny Weyerman. Biologische stelsels tot reiniging van rioolvocht, enz,
Vragen des Tijds. Febr. 1901, Sep., blz. 38.

( 153 )

In 1897 WersseNBerG ') pronounced the hypothesis, that, at the redue-
tion of nitrate to free nitrogen, nitrite constantly appears as inter-
phase. I ean perfectly well share this view, and that for the following
reasons:

1st. All denitrifying species which I have studied in the course of
this research could, in as much as they produced free nitrogen from
nitrate, do the same from nitrite.

2nd. Like Burrt and Srurzer (l.c.) I have been able to isolate a
species, which does convert nitrite into free nitrogen, but leaves
nitrate intact, so that from a mixture of nitrite with a little nitrate,
all the nitrite is removed by this bacterium, whilst the nitrate remains
unchanged.

Here I must however observe, that at the conversion of nitrate into
free nitrogen, not always nitrite can be detected in the culture. ‘This
fact has already been stated by SewerIN ®) and KÜNNEMANN *). It is
however by no means in contradiction with WersseNBerG’s hypothesis,
for if the course of the second process: decomposition of nitrite, is
quicker, or as quick as the first : reduction of nitrate, the nitrite-phase
is no more to be demonstrated.

Ktnnemann observed this fact in a variety of B. stutzeri’, which
observation I have been able to confirm ; however, in my opinion, the
cultural conditions played in this experiment a much more important
part than the character of the variety. In bouillon with 0,1 °/, KNO,,
I could often point out no nitrite, whilst here a strong development
of gas took place. On the other hand, I obtained with 4 and 5 °/,
KNO, only a slight gas development, but a strong reaction of nitrite.

For the investigation of a colony on its denitrifying power, sterile
test-tubes were filled with 10 a 15 Cem. of bouillon, as well with
0,1°/, KNO, as with 0,1 °/, KNO, and then inoculated. Denitrifying
bacteria grow therein sufficiently, after 24 hours to produce a distinet
turbidity, whilst, at the surface they form a scum-layer. Sometimes
the scum is wanting, but is produced at shaking the test-tube.

Besides were used solutions of calcium-salts of organic acids, decocts

/, cane-sugar, and decocts of potatoes, likewise
with 0,1 °/, KNO, or KNO,

In this case a control experiment was made to decide, whether

of pease-leaves with 2 °/

without addition of nitrate or nitrite, these solutions might cause

1) Studien über Denitrification. Arch. f. Hygiene. 1897, Bd. 30, 5. 274.

2) Zur Frage über die Zersetzung von Salpetersauren Salzen durch Bakterien.
Centrbl. f. Bakt. Abt. II, 1897, Bd. 3, S. 504.

3) Ueber denitrifizierende Mikro-organismen. Landw. Versuchs-Stat. 1898, Bd.
50, S. 65.

( 154 )

development of gas, which proved never to be the case with denitri-
fying bacteria.

In order to obtain perfectly convincing results, to the said culture
liquids 10°/, gelatin often was added and, when in the boiled solu-
tion, at about 380° C., some of the culture had been suspended, it
was poured into a test-tube and solidified. The developing gas then
remains as bubbles, nearly at the place of its origin, in the gelatin.
This method (#tube-culture”) produces a sharp reaction on denitri-
fication, especially when controlled by a parallel experiment, using
the same culture gelatin, without nitrate or nitrite.

This principle may also be used for a rough computation of the
number of denitrifying germs in any material. So it was proved
that circa 2000 of these organisms occur in 1 gr. of garden soil,
and circa 100 in 1 gr. of canal water.

In these experiments the potassium-salts may be replaeed by natrium-
or magnesium-salts; calcium-nitrate, on the other hand, prevents even
in dilute solution the growth of many bacteria.

Before passing to the deseription of the different accumulation
experiments, I have to make a general remark about their arrangement.

Which species finally becomes most common in the used culture
liquid depends on many circumstances, difficult to control, in parti-
cular on the mutual numerical proportion of the individuals and the
nature of the different species in the material originally used for the
infection, and likewise on the condition of the microbes themselves
in consequence of previous circumstances.

This explains why, when using different materials of infection for
the accumulation of one and the same species, it is sometimes necessary
to modify the cultural conditions in accordance with the nature of that
material.

I insist on this circumstance in particular to explain the different
accumulation experiments deseribed under B. stutzert, on the one hand
from water by using tartrate, on the other hand from soil by using
malate.

3. Accumulation of Bacterium stutzeri, LEHMANN and NEUMANN !).

This interesting bacterium was isolated in 1895 from straw by
Burri and Srvrzer (le), whilst in 1892 Breau’) had already shown
the presence of denitrifying bacteria thereon.

1) LEHMANN i. Neuman. Bakteriologie. München 1896, S. 237.
*) De la présence dans la paille d'un ferment aérobie, réducteur des nitrates.
C.R. 1892, T. 114, p. 681.

In 1898 Kiinnemann (Le) isolated the same species from soil and
a variety from horse-dung and straw.

By accumulation experiments, logically carried out, L have succeeded
in obtaining this bacillus from soil, canalwater, sewage-water and
horse-dung.

The following experiment always led practically to a pure culture
from canalwater :

A bottle of about 200 Cem. is partly filled with fresh canalwater
with addition of 2°/, calcium-tartrate, 2°/, KNO, and 0,05°/, K,HPO, 9,
computed after the whole capacity. Then the bottle is filled up to
the neck with canalwater and the stop is loosely put in, so that
a little water is pressed from the bottle. In this way it is filled
without a single bubble of air and, after shaking, put in a thermostat
of 25° of 28°. The calcium-tartrate solves at this temperature for
only 1°/,, so that this salt remains for a great part at the bottom.

Commonly already after one day a feeble production of gas is to be
observed, issuing from the non-solved calcium-tartrate at this bottom.
The process gets into full course after three or four, sometimes only
after five days. So much gas thereby is produced that a coarse,
slimy scum originates at the surface and a great quantity of the
liquid is pressed out of the bottle. The gas containing only
nitrogen and carbondioxyd, the culture remains anaerobic. The liquid
grows turbid by the growth of the bacteria and the fine, cristalline
calcium-tartrate changes into coarsely granular calcium-carbonate.
After a week, in consequence of the scum formation, the bottle is
nearly half void, and after about 12 days the reaction is at an end,
in as much, corresponding with the chosen quantity of tartrate, all
nitrate has disappeared.

If a vigorously growing culture is sown on broth gelatin, a mixture
is obtained of colonies of various different species, from which
B. stutzeri ean easily be isolated, if we are once acquainted with it.

From such a bottle some drops are inoculated into a bottle of
about 50 eem. capacity’), which, after sterilisation, is filled for */,
with the following sterile culture liquid: ;

Tap-water, 2 °/, calcium-tartrate, 2°/, KNO, and 0,05 °/, K,HPO,.

After inoculation the bottle is quite filled up with the same liquid
in the above described way, and after the lapse of two or three
days, the same phenomena appear as in the first bottle.

If now, once more, of this transport a plate culture on broth
gelatin is made, the great diminution in the number of species is

1) The capacity of the bottle is not indifferent,

( 156 )

surprising. All liquefying colonies, and most flnorescents have disap-
peared, whereas, among two common and some less frequently
occurring species, B. stutzeri developes in great numbers and is easily
recognised by the characteristic properties of its colonies.

By repeating the said transport this bacterium may still be more
multiplied, so that, after three or four successive inoculations, practic-
ally a pure culture of this species is obtained.

From soil of the garden of the Bacteriological Laboratory I regularly
obtained the same bacterium, in the course of the winter of 1901—2
by applying the “bottle method” with this liquid:

Tap-water, 2 °/, calcium-malate, 1 °/, KNO, and 0,05 °/, K,HPO,,.

In the spring, however, though there were constantly some colonies
of the species, the number of its germs proved so small that they
were replaced by other denitrifying bacteria, particularly B. denitro-
fluorescens, of which more presently.

A detailed description of B. stutzeri is given by Burri and Sturzer
(l.c.), as well as KÜNNEMANN (l.c). It will therefore be sufficient
here to give the chief characteristics by which this species is directly
recognised.

The bacterium is a short, thick rodlet with a peculiar vibrio-like
motion.

The colonies on gelatin are extremely characteristic (see Plate). After
three or four days they have a diameter of about 0.5 mm. and after a
week they attain 1 to 1.5 mm. When magnified they then resemble
a rosette, or have an irregularly folded or crispate, greyish surface.
The peculiar structure appears only distinctly, when the glass-dish
which contains the plate culture, is reversed and the colony is seen
through the bottom with about a 30-fold magnification. The most
frequent shapes are represented in figures 1—4.

But it may happen that the crispate character becomes still more
conspicuous and then the image is as in fig. 5.

Commonly it seems as if regularly arranged smaller colonies are
situated in the larger ones, which may often be observed till in
the outer border, and points to a peculiar periodicity of the mucus
secretion in the interior of the colony.

In the colonies moreover a fine deposit is observed, and sometimes
very distinct crystals, which may also be found in the gelatin around.

All these characteristics are particularly marked when the cultures
have been recently isolated, but they may in the course of time get
lost or become indistinct. Another property however remains always
quite distinct, i.e. the adhering to the gelatin. Young colonies can only
be removed in one piece, and of the older always part remains behind.

( 157 )

Very characteristic also is the growth of this bacterium on a
sterilised slice of potato, where the curled and folded structure of the
colonies is quite distinet, in consequence of the large dimensions they
attain. The colour changes thereby into flesh-red. Old cultures grow
soft in consequence of a dissolving process the slimy substance.

The compounds which can provide the carbon and nitrogen
nutrition of this species were determined by means of the auxano-
graphic method ®, this giving in a simple way a measure for the
difference in assimilability of the nutritive substances.

With KNO, as source of nitrogen, a feeble growth was observed
with glucose and maltose. Kalium-succinate, malate, malonate, citrate
and caleium-tartrate, gave rise to a vigorous growth. No growth
was obtained with cane sugur, milk sugar, mannite, galactose and
oxalic acid. |

The auxanograms prove that tartrate belongs to the best assimil-
able substances, which explains why its use in the accumulation
experiment with canal water produces such good results.

With kalium-citrate as source of carbon, NH, Cl, KNO, KNO,,
asparagin, kalium-asparaginate and pepton, could serve as source of
nitrogen.

B. stutzeri: produces no invertin, does not split indican and ureum
but it secretes diastase, although in very slight quantity. This latter
fact explains the possibility of denitrifying by this species in solutions
containing, besides the salts, only amylum and KNO,. In broth no
indol and no sulphureted hydrogen are produced.

B. stutzeri produces much alkali; even the presence of glucose
does not prevent the production of it in a plate of broth gelatin.

Very remarkable is the behaviour of B. stutzert towards free oxygen.

If the arrangement of the moving individuals under the influence
of the oxygen of the air*) is examined in the glassroom, we find an
accumulation in a line at rather great distance from the meniscus.
On the other hand, growth is only observed *) in the meniscus itself.
Hence, in this respect the bacterium behaves quite in accordance with
the aerobic spirilla.

B. stutzeri is a very active denitrifying species; to broth could be
added up to 4°/, KNO,, and up to 1°/, KNO,, without thereby preven-
ting the development of gas. If in the before described way a “tube

1) Beyerincx. L'auxanographie ou la méthode de I’hydrodiffusion dans la géla-
tine appliquée aux recherches microbiologiques. Arch. Neerl. 1889, T. 23 p. 367.
2) ENGELMANN, Zur Biologie der Schizomyceten. Botanische Zeitung 1882, Bd. 40, S. 320.
3) Beijerinck, Ueber Atmungsfiguren beweglicher Bakteriën. Centr.bl. f. Bakt.
1893, Bd. 14, S. 827.
11

Proceedings Royal Acad. Amsterdam. Vol. V.

( 158 )

culture” in broth gelatin is made, with 0,1°/, KNO,, after two or
three days the gas bubbles will appear over the whole length of the
tube, and herein this species differs from B. vulpinus, where the gas
bubbles originate at some distance from the meniscus only.

I will finally make mention of an instructive experiment I performed
with B. stutzeri. Some garden soil was mixed with tapwater with
0,05 °/, K,HPO,, and a thin layer of this mixture in an ERLENMEYER-
flask exposed to a temperature of 25°C. Under these circumstances
the production of nitrate becomes very marked after two weeks.
If now the whole content of the ERLENMEYER flask is poured into a
stoppered bottle, which thereby is quite filled, whilst B. stutzeri, is
used for infection, soon a development of gas sets in and the nitrate
disappears completely. Hence it follows that according as the air
enters our culture liquid well or not, nitrification or denitrification
may occur. This is quite in accordance with older experiences
described by ScHiorsine (le) in regard to the soil in general.

4. Accumulation of Bacillus denitrofluorescens n. sp.

SEWERIN (I. ¢.) found in 1897 that B. pyocyaneus belongs to the
denitrifying ferments. But the group of fluorescents proper was long
fruitlessly examined as to their denitrifying power, first by LEHMANN
and NeUMANN and afterwards by Weissenpere (I. ¢.). In 1898 KinneMann
isolated for the first time a denitrifying bacterium, which liquefied
gelatin and fluoresced.

Though in my experiments [ often obtained fine cultures of a
similar species, I did not succeed in finding a satisfactory accumulation
experiment for it. On the other hand I found such an experiment
for a non-liquefying fluorescent Bacillus, which I named B. denitro-
Huorescens.

The culture liquid for the accumulation of this species is:

Tap-water, 2 °/, calcium-citrate, 1°/, KNO, and 0,05 °/, K,HPO,.

In a bottle of 50 Cem. capacity, 1 to 2 gr. fresh garden soil is
put; it is then quite filled up with the culture liquid, in the way
described under B. stutzeri. The culture is made at 25° C.

When sowing on broth gelatin the 2"¢ or 3"¢ transport, successively
kept in the same culture medium, [always obtained cultures containing
almost exclusively colonies of that species.

In horse-dung, canal water and sewage water, I also observed this
bacterium, but it is with more certainty to be isolated from soil.

In exterior appearance of the colony this species differs in no
respect from one of the most common fluorescents, characterised by

( 159 )

lacking, on the culture gelatin, the smoothly spreading border. In
young broth gelatin cultures, the pigment fluoresces blue, and after
some time a white precipitate forms in the gelatin.

Examined auxanographically, KNO, as source of nitrogen proved
to cause a feeble growth with mannite, a vigorous one with kalium-
malate, citrate, malonate, succinate and tartrate, as well as with
elucose and levulose. On the other hand no growth is seen with
cane-sugar maltose, milk-sugar, and raffinose.

In broth, with 2°/, glucose, this bacterium, like all fluorescents,
produces acid. Broth with 2°/, cane-sugar, becomes however strongly
alkaline, which is observed also in all other fluorescent secreting no
invertin.

This bacterium neither produces diastase, nor can it hydrolise indican
or ureum. In broth it forms no sulphureted hydrogen and no indol.

In its behaviour towards free oxygen it likewise corresponds with
the fluorescents, i.e. with the cover-glass culture in the humid room,
both motion and growth cause accumulation in the meniscus.

This makes the bacterium strongly contrast with B. stutzert and
B. vulpinus, whose motion figures show the spirillum type.

As to the energy of its denitrifying power B. demtrofluorescens
corresponds with B. stutzers. At the “tube experiment” with broth
gelatin with O,1°/, KNO,, the bubbles form over the whole length
of the tube, quite in the same way as with B. stutzeri.

5. Accumulation of Bacillus vulpinus ne sp.

Already in my introductory observations I remarked, that an
accumulation experiment with full access of air, when using tartrate
and nitrate, produced this species, but the accumulation obtained in
this way was still very imperfect. By cultivating under partly
exclusion of air, I succeeded in improving the experiment very much. |
obtained this result by enclosing in the culture bottle with the liquid a
determined volume of air, and reinoculativg from bottle to bottle under
the same conditions three or more times. It is true that thereby not
all other species are totally removed, but this is no obstacle to the
recognition of B. vulpinis, whose colonies are extremely charac-
teristic, possessing a quite unique brown-red pigment.

The experiment is as follows:

Into a bottle of 50 Cem. 1 to 2 grams of fresh garden soil is put,
and further it is filled up with the following culture liquid, whilst
leaving on air bubble of 2 Cem: Tap-water, 2 °/, Calcium-tartrate,
Ont NOS, and 0:05 pO KAP O:.

11%

( 160 )

Here likewise the culture is effected at 25°.

With observation of the said proportion and operating as described
under B. stutzeri, the different varieties of B. vulpinus can also be
obtained from canal water.

The denitrification sets in very slowly and the development of gas
gets not by far the intensity perceived in the preceding species.
Here, too, by the complete disappearance of all liquefying bacteria
already at the first transport, the isolation of the wished for species
is much facilitated. Although at sowing the crude cultures on broth
gelatin some B. vulpinus colonies may already be perceived, they
multiply so much in the transports, that plates therewith prepared,
appear, so to say, quite covered with the large, flatly spread, trans-
parent, fox-coloured colonies of this species.

If for the accumulation other organic salts than tartrate are used,
or a higher rate of nitrate than 0.2°/,, not a single colony of B.
vulpinus is detected, though it was certainly present in the infection
material as it is universally, distributed in the soil.

By their growth the colonies strongly remind of the flatly spread
variety of B. fluorescens non liquefaciens, but of fluorescence nothing
is seen. In shape and motility the bacterium corresponds with
B. stutzeri.

An interesting property of B. vulpinus is, that the brown pigment
only develops under the influence of light. If simultaneously two
cultures of this species are made on broth gelatin, and one, wrapped
in black paper, is put in the dark, and the other in the light, for
the rest in equal conditions, a great difference is perceptible. This
becomes more obvious still, when making reinoculations or transports
of either culture, likewise keeping these respectively in the dark and
the light. So-doing a perfectly colourless culture can be obtained,
but if this is again inoculated in the light, the brown colour returns.
The pigment formation only takes place at growth, so that colonies,
full-grown in the dark do not colour when exposed to light.

B. vulpinus belongs to the group of real chromophores *), i.e. the
pigment is bound to the bacterial body, and the behaviour towards
light is, in my opinion, another indication that in this group the
pigment „has a biological function.

The auxanographic examination proved, that with nitrate for nitrogen
nutrition, a feeble growth is obtained with kalium-malonate, a
vigorous one with levulose, glucose, maltose, kalium-citrate, succinate

') See Beuertvcx, La biologie d'une bactérie pigmentaire. Arch. Néerl. 1892,
T. 25, p. 227.

( 161 )

acetate and tartrate, whereas cane-sugar, milk-sugar, mannite and
raffinose produce no growth at all. Ammonium-chloride may also
serve as source of nitrogen, when using tartrate for carbon nutrition.

Pepton, asparagin, and kalium-asparaginate may simultaneously
serve as C and N nutriment.

The bacterium secretes neither invertin nor diastase and does not
split indican or ureum. In broth it produces no sulphureted hydrogen
but a little indol.

In the “tube experiment” in broth gelatin with 0,1 °/, KNO,,
bubbles of nitrogen are exclusively seen to form at a little distance
from the meniscus, and moreover, the culture of this species not
succeeding in a bottle wholly filled with a culture liquid containing
nitrate, we must needs conclude, that /. vulpmus wants considerable
quantities of oxygen for the denitrification.

As regards the other species, which form gas bubbles also in the
depth of the tube, I have come to the conviction that they too,
want traces of free oxygen to this end.

Notwithstanding this different behaviour towards free oxygen, the
motion figure, like that of B. stutzeri, shows the spirillum type.

By modifying the nutrient liquids and temperatures [ have succeeded,
as observed above, in accumulating various other denitrifying bacteria,
beside those deseribed. Thus I obtained, at 37° C. with calcium-citrate
and 0,2°/, KNO,, under exclusion of air, and using garden soil for
material of infection, the spirillum-like . mdigoferus Voors), which
denitrifies only feebly, but is interesting by its indigo-like pigment.
When using sewage water, I obtained a strongly denitrifying, liquefying,
blue pigment bacterium, not yet deseribed.

Of all these experiments however, the result is not constant enough
to be inserted here.

6. Summary and conclusions.

1st. The fundamental principle of my accumulation experiments
was partly or completely to prevent the access of air. By this means
I have succeeded, by cultivating in solutions of organic salts and
nitrate, only by repeated transports in the same liquid, in bringing
many denitrifying bacteria to a more or less perfectly pure culture.

1) Crarssen. Ueber einen indigoblauen Farbstof erzeugenden Bacillus aus Wasser.
Centrbl. f. Bakt. 1890, Bd. 7, S. 13.

Voces. Ueber einige im Wasser vorkommende Pigmentbacteriën, Centrbl. f. Bakt,

1898, Bd. 14, S. 301.

( 162. }

Of these experiments three always gave constant results, and pro-
duced respectively ZB. stutzert NEUMANN and LEHMANN, B. denitro-
fluorescens n. sp. and B. vulpinus n. sp.

2nd 2B. stutzeri deserves attention on account of the unique structure
of its colonies, as seen in Fig. 1—5 on our Plate.

3rd B. denitrojluorescens is the first example of a denitrifying, non
liquefying fluorescent.

4 B vulpinus is a chromophorous pigment bacterium, whose
pigment only forms at growth in the light.

5th B. stutzeri and B. vulpinus behave towards free oxygen like
aerobic spirilla, B. denitrojluorescens behaves like an ordinary aerobic
bacterium.

Gh. Like in soil and dung, in which it had also been found by
other experimentators, | have established the general distribution of
denitrifying bacteria in canal and sewage water.

7h. The denitrifying bacteria can, even with the slightest quantities
of various organic substances, cause the disappearance of determined
quantities of nitrate under development of free nitrogen.

Sth. In one and the same culture medium, where nitrification is
produced during aeration, denitrification may be caused by exclusion
of air, this holds good also in regard to the soil.

At the end of this paper I want to express my sincere thanks to
Professor Dr. M. W. BrijerincK for his kind, invaluable guidance
and efficacious assistance, afforded me in these researches.

Delft, July 1902.

Physics. “An Hypothesis on the Nature of Solar Prominences.”
By Prof. W. H. Joxivs.

The introduction of the principle of anomalous dispersion into
solar physics makes it possible to form an idea of the Sun’s consti-
tution from which necessarily follow ia. a great many peculiarities
of prominences, which, until now, it has been impossible to deduct
in a satisfactory manner from other physical laws. This I will
show in the following pages.

In my paper on “Solar Phenomena, etc.” read Febr. 24, 1900.
I put forth the following hypothesis with respect to that part of the
solar atmosphere, situated outside what is called the photosphere *):

1) W. H. Junius, Solar Phenomena, considered in connection with Anomalous
Dispersion of Light, Proc. Roy. Acad. Amsterdam, Il, p. 585.

G. VAN ITERSON Jr. ,,Accumulation experiments with denitrifying bacteria.”

Fig.

.

‚s Royal Acad. Amsterdam. Vol. V.

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Proceedin

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(163 )

“The various elements, whose presence in that atmosphere has
been inferred from spectral observations, are much more largely
diffused in it than has generally been assumed from the shape of
the light phenomena; they may be present everywhere, up to great
distances outside the photosphere, and yet be visible in few places
only ; their proper radiation contributes relatively little to their
visibility (with perhaps a few exceptions); the distances, at which
the characteristic light of those substances is thought to be seen
beyond the Sun’s limb, are mainly determined by their local differ-
ences of density and their power to call forth anomalous dispersion.”

How we were to imagine the condition of the matter inside the pho-
tosphere, was not considered there. Our hypothesis on the origin
of the light of the chromosphere was kept free from any special
conceptions as to the nature of the photosphere. Only where the
principle of anomalous dispersion was made use of also to explain
spectral phenomena observed in sunspots '), we had to fall back upon
A. Scumipt’s theory *), according to which the Sun is an unlimited
gasball, so that the apparent surface of the photosphere should not be
considered to be the real boundary of a body, but to correspond to
a “eritical sphere”, defined by the property that its radius equals
the radius of curvature of horizontal rays, passing through a point
of its surface.

At present, however, in working out the problem of the nature
of the chromosphere and the prominences, we likewise will take as a
starting point the first of the three Theses, in which Scumipr sums
up the main points of his theory. Accordingly, we suppose the Sun
to be an unlimited mass of gas, in which the density and luminosity
(not considering local irregularities) gradually diminish from the
centre outward. But our conception of the properties and composition
of this gaseous body can in a certain respect be much simpler than
would be the case, if we accepted the whole of Scumipt’s theory.

Indeed, Scumipt explains both the edge of the Sun’s disk by the
laws of regular refraction (or ray-curving) in a stratified medium,
and the prominences by refraction in “Schlieren” *); but in order to
account for the fact that the light from the prominences as well as
that from the chromosphere, instead of being white, shows a bright
line spectrum of varying appearance, he supposes the strongly radiat-

ele: ps O80.

2) A. Scummt, Die Strahlenbrechung auf der Sonne, Ein geometrischer Beitrag
zur Sonnenphysik. Stuttgart 1891.

3) A. Scampt, Erklärung der Sonnenprotuberanzen als Wirkungen der Re raction
in einer hochverdiinnten Atmosphire der Sonne, Sirus XXIII S. 97—109, Mai 1895,

( 164 )

ing mass of gases in its outer parts to be composed so as to emit
almost exclusively hydrogen-, calcium-, heliumlight, whilst the radiations
of sodium, magnesium, titanium, iron are supposed to originate in deeper
layers, a.s.o.'). We, on the contrary, by the introduction of anomalous
dispersion are permitted to suggest, that throughout the
gaseous body, as well inside as outside the critical sphere,
the various elements are altogether intrinsically mixed
(granting that in the mixture the quantity of materials with greater
specific gravity must grow with the depth). For wherever there
are local differences of density in the mixture, caused by currents,
whirls ete., the conditions for irregular ray-curving are present, and
it is evident that specially those elements of the mixture, which
possess an exceptionnally high dispersing power for certain waves
of the transmitted light, will be able to reveal their presence even
at great distances from the disk, while other substances, though
also present at the same places, remain invisible there. Thus a
purely optical explanation may be given of the fact, that the different
gases of the sun are seen separated, even though we suppose them
to be thoroughly mixed.

And surely this last supposition is the simpler by far; it even neces-
sarily follows from the fundamental idea, that the Sun may be considered
as a rotating, heat-radiating mass of gas, for in such a body the
constituent parts must continually mix.

A few months ago the main character of the motion that must go
on in a sun, supposed to be gaseous, has been discussed by R. EMDEN *).
He applies to the Sun the same mathematical deductions, which had
been devised by von HerMmHoLtz for investigating the kind of motion
which in our terrestrial atmosphere must result from the united
influence of heating by the Sun and of the daily rotation *). Though
EmMpEN supposes the gaseous’ Sun to be limited by a well-defined
surface, and so far accepts the prevailing views on the constitution
of this celestial body, still his mathematical formulae are absolutely
independent of the existence of a boundary surface, and so are fully
applicable to a sun, such as we are considering here.

Radiation causes the outer layers to cool down soonest; they
sink inwards and are replaced by ascending hotter gases, so that,

1) As appears from a paper in the Physik. Zeitschr. 3. S. 259—261: entitled
,Ueber die Doppellinien im Spectrum der Chromophäre” Scummr adheres to this
conception, even after having taken into consideration the possibility of explaining
the light of the chromosphere by anomalous dispersion.

2) R. Eupen, Beiträge zur Sonnentheorie. Ann. d. Phys. [4] 7, p. 176—197.

3) H. von Hermnorrtz, Gesammelte Abhandlungen I, p. 146, III p. 287—355.

if the Sun did not rotate, we could only expect radial convection
currents. But the rotation of the sun completely changes this form
of motion; the angular velocity of descending masses increases, of
ascending masses diminishes; there will be found side by side gas-
layers of different densities, and rotating at different speeds.

It has been shown by von HermHorrz, that during a certain time
such gaslayers can flow side by side, sharply separated by a so-called
surface of discontinuity (i.e. by a surface, on passing which the
values of the velocity and the density change with a leap); but
gradually the friction causes this surface to undulate; the waves
advance with the more swiftly moving layer, they grow steeper,
overhang and break, forming whirls; and thus, by the mingling of
the adjacent parts of the two layers a new layer is formed between
them, the properties of which will be intermediate between the cor-
responding properties of the original layers.

From the conditions of the problem we may deduce the position
of the surfaces of discontinuity. This has been performed by von
HerrmHoLtz with regard to the air-currents in our atmosphere, and
by Emprn for the rotating layers of the Sun. He arrives at the con-
clusion, that in the Sun the surfaces of discontinuity must in the
main have the shape, figured in the accompanying sketch and reminding
us of hyperboloids of revolution *).

N
a“ 7 ED .
7 N
\
/ \
H \
Aequ ator
‘ |
/
\ /
4
SS a“
Fig. 1.

1) EmpeN draws the intersections of the surfaces with the plane of the paper
only inside the circle, representing the sun’s boundary. | have dotted this circle,
with a view to indicate, that the border is only a seeming one; accordingly |
prolonged the intersections outward.

(466)

\

In every annular layer, bounded by two consecutive surfaces of
discontinuity, the moment of rotation of unit mass (@ = w7?) as
well as the so-called potential temperature @ are constant; but in a
following layer, farther from the Sun’s axis, 2 hasa greater and 4 a
smaller value. Within every laver there exists a velocity potential,
but at the separating surfaces the linear velocity changes discontinuously,
the difference between the velocities on each side of one and the
same separating surface increasing as that surface approaches the axis.

The waves, that are formed in the separating surfaces, will proceed
in the direction of the rotation, and when, after growing steeper and
steeper, they break, the resulting vortices will have their core-lines
perpendicular to the direction of motion of the waves, i.e. coinciding
with the generatrices of the surfaces of discontinuity. So, the curves
in our figure also give an idea of the position of the vortex-cores.

From the theory follows, as we already mentioned, that at each
definite surface of discontinuity the leap of the velocity is greater
at a short than at a long distance from the Sun’s axis; therefore,
the transition from a wave into a whirl must, as a rule, begin in
those parts of that wave, which are nearer to the axis, and appear
afterwards in the outer parts.

Further it is clear that, because every whirling leads to mingling
of the adjacent parts of two layers and to the formation of two new
surfaces of discontinuity, there will never exist a complete surface,
such as indicated by our sketch. Everywhere we shall meet with
pieces of surfaces of discontinuity; only their main character and the
average direction of the vortex-cores will correspond to the sketch.
And in spite of the continual mixing of layers, which leads to
equalization of differing rotational velocities, the motion still remains
nearly stationary; for within each layer, temporarily enclosed between
two surfaces of discontinuity, the convection currents carry cooled
matter inwards and hot matter outwards, by which process the
differences in rotational velocity are renewed.

Forced as we are to admit, that such an uninterrupted mixing
process is going on in the Sun, the advantage of explaining the
chromosphere and the prominences by anomalous dispersion of white
light, must appear to us very obvious. All other explanations, that
I know of, must start from the hardly tenable supposition, that the
different gases of the chromosphere are separately present in large
quantities.

Emprn has succeeded in deducing many properties of sun-spots
from the supposition, that the spots show us the places, where huge
whirls attain the Sun’s surface. It seems to me that EMDEN’s views

on sun-spots would become even much more acceptable, if the notion
of a real surface of the Sun were given up and if the consequences
of normal and anomalous refraction (better ray-curving) in those
whirls were allowed for. But to this subject I desire to come back
on another occasion.

For the present we will confine our attention to those parts of
the whirls, optically projecting beyond the edge of the Sun’s disk,
and we propose the hypothesis, that the whole chromosphere
with all its prominences is nothing but this system
of waves and whirls, made visible within shorter or
longer distances from the Sun’s edge by anomalous
dispersion of light, coming from deeper layers.

(Perhaps the structure of the corona, with its polar streamers,
arches, ete, might tell us something about the course of the surfaces
of discontinuity at very great distances outside the critical sphere ;
this point too, however, I will only hint at here).

So we ascribe the chromosphere to the smaller vortices, to the
continual rolling up of the surfaces of discontinuity ; in the prominences
we see the whirling, in which the rarer, very large waves of the
solar ocean dissipate.

The particular structure of the chromosphere, suggesting the com-
parison with a grass-field in vertical section, follows immediately from
this hypothesis. Prominences likewise nearly always show a tissue of
stripes, bands and filaments '). These, according to our view, indicate
the position of the whirl-cores. In the whole region, where whirling
is going on, the density will, of course, vary in a very irregular way ;
we therefore may expect to find in the spectrum of that region as
well the light on the red as that on the violet side of the absorption
lines, i. e. the chromospheric and flash lines must be double lines ®).

Along the core of a vortex
9 the density is a minimum. If,
now, a vortex intersect the ap-

= parent limb of the sun obliquely,
a as in Fig. 2, where pg represents
| | the core-line, the light coming
Fig. 2. from a point @ must differ from

the light, coming from 5. Indeed, following in a the Sun’s radius

1) J. Fry S. J., Protuberanzen, beobachtet in den Jahren 1888, 1889 und 1890
am Haynald—Observatorium, p. 5. (Kalocsa, 1902).

2) W. H. Junius. On the Origin of Double Lines in the Spectrum of the Chromo-
sphere, Due to Anomalous Dispersion of the Light from the Pho'osphere. Proc.
Roy. Acad. Amst. Vol. III, p. 193.

( 168 )

outward, we at first get into layers of increasing density, whereas,
ascending from 6, we meet with layers of decreasing density. Conse-
quently, in the spectrum of @ the #violet-facing” components of the
double lines must be prominent and in the spectrum of 4 the red-
facing ones. If the slit be placed tangentially, through the points a
and 5, the two cases will be seen at a short distance on the same
spectral lines. And when during a total eclipse of the Sun the
chromosheric are itself functions as a slit (the prismatic camera being
used), the same phenomenon may be met with on numerous places
of the crescents. Many instances thereof are visible on the plates,
obtained in Sumatra by the Dutch expedition for observing the total
eclipse of May 18 1901.

With large prominences the phenomenon sometimes appears very
intensely. In the important work by FFfxv1, mentioned before, we
read for instance on p. 121, in the description of a carefully
observed prominence, the following passage:

.ylm unteren Teile zeigte die Protuberanz am Anfange ihrer
Entwickelung eine grosse Störung in der /7, Linie. Bei engem (tan-
gentiell gestelltem) Spalte reichten zwei Spitzkegel über denselben hinaus,
der eine, grössere erstreckte sich gegen rot, der andere kleine gegen
blau und stand etwas siidlicher. Die Grosse des ersteren betrug 9” im
Gesichtsfelde ; auf Grund einer neuen Bestimmung der thatsächlichen
Dispersion des Spektroskops ergibt sich daraus fiir diese Stelle der
Protuberanz eine Bewegung von uns mit der Geschwindigkeit von
240,4 Klm. in der Secunde. Die Verschiebung gegen blau betrug nach
dem Augenmaasse etwa die Hälfte der ersteren gegen rot.

Die entgegengesetzten Bewegungen neben einander und die Kegel-
formige Form des veränderten Lichtes würden unschwer die Deutung
auf eine Wirbelbewegung am Grunde der Protuberanz gestatten. Aus
der Ungleichheit der Kegel würde ein Vorschreiten des Wirbels won
uns mit der Geschwindigkeit von 180 Klm. sich ergeben. Die Beobach-
tung steht auch nicht allein da; eine ähnliche Erscheinung wurde
von Youre am 3. Aug. 1872 (The Sun, p. 210) eine andere von
THOLLON in Nizza (C. R. XC p. 87, XCI p. 487) beobachtet ; ahnliches
wurde auch von mir bei anderen Gelegenheiten beobachtet.”

Thus, interpreting the light on both sides of the hydrogen-line
after Dorerer’s principle, FÉnNyr arrives at the very astonishing con-
clusion, that the whirling mass of hydrogen moves at a speed of
180 kilometers per second. Moreover, there is a much greater diffi-
culty, not even mentioned by Fényi, viz. that the coherent outbuds
of the line impose upon him the necessity of supposing that velocity
to be very different for the various parts of the whirl, adjacent

( 169 )

pieces of the prominence not even taking any part in the enormous
motion along the line of sight.

The above-given explanation of the phenomenon by anomalous
dispersion solves all these mysteries.

It occurs very seldom that prominences show a rapid sideward
motion, i.e. a motion in the meridian of the Sun. FÉNyr mentions as
an exceptional case a sideward velocity of 25 kilometers per sec’).
As, on the other hand, velocities of 250 kilometers and more in
the direction of the parallel (calculated after DorPrer) are by no
means a great exception, we meet with contradictions — as is admitted
also by FExy1 — from which it appears impossible to escape, unless
we doubt the reality of the velocities.

It is surprising and satisfactory to see how nearly all the pecu-
liarities in the behaviour of prominences, as deseribed by Young,
FÉNyr and many others, appear quite intelligible as soon as we look
at these phenomena from our point of view.

Let us choose only a few more examples out of the vast material.

FéNyr says (le. p. 115): „/Schon seit Jahren habe ich bemerkt,
dass helle hervortretende Punkte in der Chromosphäre, welche eine
kleine Verschiebung gegen blau.zeigen, der Ort sind, wo alsogleich
der Aufstieg einer Flamme oder einer kleinen Protuberanz erfolgt”

Now the process of whirl-formation in a surface of discontinuity
proceeds, as a rule, from the inner parts of the Sun outwards. In
the axis of a whirl the density is a minimum. Consequently, at the
moment the whirling reaches the apparent edge af the Sun, a mini-
mum of density will be found just projecting beyond the edge.
Here we have a place, where the density increases from the photo-
sphere outward and where, therefore, the violet-facing component of
the chromospheric double-line temporarily prevails: it seems as if a
shifting towards the violet occurs. Shortly afterwards the more
distant parts set a whirling and the prominence appears.

In the description of a great prominence, observed by FENyr on
the 18th of Aug. 1890, we read ia. the following particulars *):

„Ein ganz besonderes Interesse verleihen dieser an und für sich

schon grossartigen Erscheinung die Eigenbewegungen in der Gesichts-
linie, die an derselben beobachtet wurden. Eine ungefähr zwischen
40" und 50” Höhe liegende Schicht, (deren Lage in der beigegebenen
Figur genau bezeichnet ist), zeigte eine heftige Bewegung gegen die
Erde zu. Das rote Licht des Hydrogeniums ergoss sich daselbst in
verworrenen Formen über den Spaltrand gegen blau hinaus ohne

1) FéNy:, l. c. p. 114.
2) Fenvi, |. c. p. 129.

( 170 )

indessen den Spalt ganz zu verlassen. Die Bewegung war durchaus
local, die Umgebung zeigte keine Spur einer Bewegung. Die Geschwin-
digkeit derselben war keine ungewöhnlich grosse; ich erhielt aus 4
mit dem Fadenmikrometer gemachten Messungen zwischen 11 h. 45 m.
und 12 h. 15 m. verschiedene, zwischen 94 und 201 klm. schwan-
kende Werthe. Was aber die Erscheinung zu einer besonders merk-
würdigen gestaltet ist der Umstand dass, während diese in der Höhe
vor sich gehende ganz locale Bewegung nicht einer Ausströmung
zugeschrieben werden kann, dieselbe trotzdem doch eine halbe Stunde
lang beobachtet wurde! Nehmen wir als Mittelwerth der Geschwin-
digkeit 150 klm. per Secunde an, so hätte dieser bewegte Teil
der Protuberanz während der zwischenzeit von 30 Minuten gegen
270.000 klm. durchlaufen, also wohl auch den scheinbaren Ort
ändern müssen.”

Of course this contradiction immediately vanishes if we only
suppose, that in the part of the prominence, showing the persistent
shift of the hydrogen light towards the blue, the density of the solar
matter was increasing in the direction from the photosphere outwards.
This supposition is quite in harmony, too, with the fact, that the
picture of this prominence shows very important whirling below the
part in question and no disturbance worth mentioning above it.

Observers have often been puzzled at the rapid disappearing of
enormous prominences and at the perfect calm in the whole region,
including the Sun’s surface, a short time after such a violent “erup-
tion” had taken place. It was hardly conceivable that the ejected
incandescent gases could loose their huge quantities of heat so rapidly,
nor that the eruption had no further visible consequences.

In our theory a large prominence is nothing but the visible token,
that whirling is going on almost simultaneously over vast regions.
The very important varieties of density in the whirling mass may,
however, be annulled by displacements of much matter over relatively
small distances, which process, of course, may go on without violent
movements and yet be accomplished in a short time. So there is no
reason whatever to expect, that a great prominence will leave the
medium in a highly disturbed condition.

Whosoever wishes to consider prominences as eruptions, must
grant, that it is one of the most difficult problems to account both
for the tremendous values of the ascending velocities sometimes observed
and for the most capricious way, in which the speed often suddenly
changes without any conceivable cause. The 20% of Sept. 1893
FÉNyr witnessed a prominence ascending 500000 kilometers in a
quarter of an hour, that is at an average velocity of more than

— See ne Te =d

C171

990 kilom. per sec. In another case, also observed by Fúxvr (July
15% 1889), in the course of 10 minutes the ascending velocity
passed through the values 72, 6, 65, 24, 154 kilometers per second;
and with the prominence of Oct. 6, 1890, in 30 minutes’ time
iheoneh the valués 33,8;..79,8, 67,6,-72,7, 127,7 275,5, 249.3. 121.
57,3 kilom. per sec.

Considering the problem from the new point of view we see the
difficulties disappear in consequence of the observation, that, properly
speaking, we have not to do with velocities at all. We
may speak of the velocity with which matter moves or with which
a disturbance is transmitted by a medium; but neither of these cases
is met with here. Wherever the whirling sets in, it results from local
conditions and cannot be considered as directly transmitted from places,
where whirling was going on a little earlier. Though it is true that,
as a rule, the breaking of a wave begins in those parts of a surface
of discontinuity, that are nearer to the Sun’s axis, and from there
proceeds outwards, yet this does not involve that we should have a
right to call this process a transmission of matter or of motion in
the direction of the vortex-cores. And where there is no transmission,
there is no velocity.

When at the sea-shore a wide wave approaches and breaks, now
here, then farther and farther, nobody will speak of the velocity”
with which the foam or the whirling is moving alone the coast.
Every body knows, that the foam, the visible token of the whirling,
is successively formed at different places. Such about is the case
with the prominences, the visible spots in the breakers of the solar ocean.

Chemistry. — Professor Losey pr Bruyn communicates a paper
by himself and Mr. J. W. Drro. “The botlingpoint-curve of
the system: hydrazine + water”.

In a previous report’) Mr. Drro has communicated the results of
determinations of the densities of mixtures of hydrazine and water;
the figures showed that a maximum density corresponds exactly (or
nearly so) with the composition N, H,-H,O. At the end of that note
it was stated that we would endeavour to determine the boiling-
point-curve of the system: hydrazine + water.

We have lately been engaged with that determination; the result
is given in the following table and annexed curve,

1) Proc. of April 19, 1902, p. 838.

Amount of mixture | Number mols. of N,H, on 100 mols.

Temp. |
and barometer. liquid, | vapour.
102.2 | 9.4 0.18
300 erm. 755.5 | 104.6 | 14.2
” 105.9 | 1.6
pn 107.45 19 5 2.7
” 109.15 3.9
” 111.0 6.2
” 114.95 | 34.0 13.8
Z 117.95 | 4A .7 25.0
85 g1 768 .0 118.6 12.9 30.3
” 41320 | 45.2 24.9
” 119.8 | 50.3 | 4.7
38 gr. 770.8 120.2 51.8 44.6
” 120.35 53t3 | 48.75
„ | 120.45 | 54.8 | 52 8
” | 420.5 56.0 53.5
[120°5 58.5 | 58.5]
daken 120.45 62.5 |
" 120.95 65.8 72
” 119.9 68.3 15.5
; | 419.5 Ho Si Pie
“ 119.25 73.6 83.7
50 gr. ” t | 418.8 76

It should be observed beforehand that the figures obtained, parti-
cularly those relating to the mixtures.rich in hydrazine, cannot pos-
sess that accuracy attainable with other mixtures. In the first place
free hydrazine is a costly substance; working with a large quantity
such as is required for the accurate determination of a boilingpoint
curve, therefore, leads to not inconsiderable expenses. Moreover, free
hydrazine and its mixtures with little water (also the hydrate N, H,.
H,O) are very hygroscopic and also easily oxidisable by the oxygen
of the air. During the volumetric determination of the amount of

(173)

120

119 ed

118 IN IN

117 \ ‘

116 \ =

115 . oN

414 B ax

113

412

111

110

109

108

107

106

105

104

103

102

101 if

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

hydrazine in the liquid and condensed vapour, it was impossible to
avoid contact with the atmosphere. The operation was carried out
in such a manner that each time after distilling off a certain quan-
tity (LO—20 cc. in the case of the greater concentrations), two por-
tions (3—4 drops) of the condensed vapour and residue were simul-
taneously collected in tared weighing bottles containing about 5 ec.
of water. On account of the many weighings a certain time neces-
sarily elapsed between the taking of the samples and the titration
and, considering that the bottles also contained a little vapour of
hydrazine mixed with air, this must have excercised some influence.

A vapour
B liquid

This explains why the agreement between the various duplicate
determinations often left much to be desired; in one case a discre-
pancy occurred amounting to 2 mols. per 100. Finally, another
source of error is found in the fact that on account of the many
weighings and titrations, the determinations had to be done on dif-
ferent days, so that the distillations were conducted under different
barometric conditions.

Notwithstanding this, the results allow of the construction of a curve,
the regular course of which is a guarantee that the figures observed

12
Proceedings Royal Acad. Amsterdam, Vol. V.

(174 )

express the entire phenomenon with a certain amount of accuracy.
As already stated, more correct results can only be obtained by
repeating the experiments with larger quantities of hydrazine *).

Our experiments have led to the interesting result that hydrazine-
hydrate does not at all represent a chemical compound N,H,.H,O with
a constant boilingpoint of about 120°, as hitherto believed. This
however is not surprising, particularly after Kxrerscn’s experiments
on the system sulphurtrioxide + water’). The tendeney of SO,
and H,O to enter into combination is greater than that of N, H,
and H,O. As the boilingpoint curve of the system sulphurtrioxide
+ water shows a maximum not belonging to the compound H, SO,
but to a mixture of 98,5°/, of H, SO, and 1,5°/, of H,O, it is not
at all surprising that in the system hydrazine + water the maximum
does not correspond with the composition N,H,. H,O. It is seen
from these figures that a liquid boiling at 119°.8 and having the
composition 50 mols. N,H, + 50 mols. of H,O yields a vapour
containing about 42 mols. of N, H, and 58 mols. of water, while
a vapour of about the composition N, H,.H,O is given off at 120°.4
by a liquid containing about 54 mols. of N,H, and 46 mols. of water.

From the course of the curve it appears that a maximum boiling-
point of about 120°.5 corresponds with a liquid with about 58 mols.
of N,H,. The experiment has shown that a mixture of about 58.5
mols. of N,H, and 41.5 mols. of H,O has a constant boilingpoint
of 120°.1 at 760 mm. In the table 120°.5 therefore corresponds
with 771 m.m.

The course of the first half of the curve plainly shows the pheno-
menon observed by Curtius namely, that on boiling dilute solutions
of hydrazine the distillate consists at first almost exclusively of water,
although the boilingpoint has very sensibly increased. It may be
assumed that the same thing happens in the reverse case of much
hydrazine and little water; for reasons stated we have not been able
to ascertain this.

One of us (Dito) is already engaged with the determination of the
viscosity of the system: hydrazine + water; while with the co-operation
of Professor Ernst Conen experiments have already been started,
several months ago, on the electrolytic conductivity of the same
system and of solutions of salts in hydrazine *).

1) Ber. 34. 4088 (1901).
2) Curtivs states that concentrated solutions of hydrazine attack glass when
boiling at ordinary pressure. We did not notice any such action of even highly

concentrated solutions on our glass fractional distilling apparatus and condensing tube.
3) Recueil 15, 179,

a EED

Chemistry. — Professor Lory pe BrurN presents, also in the name
of Mr. W. ALBERDA VAN EKENSTEIN a communication on
4 Formaldehyd (methylene) derivatives of sugars and glucosides.”

In a previous communication’) we have already stated that an
aqueous solution of formaldehyde when evaporated with some of the
sugars reacts on the same. This was shown by the great changes
in the rotation. We then also remarked that attempts to isolate the
crystalline compounds from the syrupy mass had not proved successful.
These, moreover, are readily dissociated by evaporation in the pre-
sence of much water, the pure sugars being left behind. ’)

About the same time *) TorreNs had prepared a crystallised methy-
leneglucose by mixing a solution of glucose in formaldehyde with
hydrochloric and acetic acids and setting the liquid aside for some
months. He obtained a monoformal-derivative which still powerfully
reduced Fruiine’s liquid. Other sugars gave a negative result.

On continuing our researches it appeared that substances, of an
apparently different nature and more stable than those occurring in
the said syrups, are formed when the dry sugars are melted with
polymerised formaldehyde (trioxymethylene). The rotatory power
then appears strongly modified and the reducing power decreased :
this, however, reaches its normal figure on boiling with dilute acid.
From this follows that during the reaction of the sugar with the
formaldehyde, the aldehyde groups disappear.

We now succeeded in isolating in the case of several sugars
(and glucosides) crystallised compounds or such having a constant
boiling point, by introducing the fused mass into sulphuric acid of
various concentrations or phosphoric acid and then agitating the
liquid with an organic solvent such as chloroform, which dissolves
the diformal compounds. In some cases there are formed, simulta-
neously, monoformal derivatives which are readily soluble in alcohol
and water, but sparingly soluble in chloroform and so behave in this
respect quite the reverse from the diformal derivatives.

Both the di- and the mono-methylenesugars no longer react with
Frniine’s solution and behave indifferently toward phenylhydrazine ;
the carbonyl groups have therefore disappeared during the action
of the formaldehyde. After boiling with dilute acids, the reducing
power returns. These substances must therefore in the first place

ty Prog, 1900, 9.

2) Rurr and Outenporrr, Ber. 32. 3236 (1899), have regenerated some sugars
from different hydrazines by evaporation with solution of formaldehyde.

5) Ber 32. 2585 (1900); his experiments had commenced some years previously.

12*

( 176 )

be regarded as glucosides, derived from methylenglyeol CH, (OH), »,
which is unknown in the free state. Two of the alcoholic hydroxyl
groups of the sugar-molecule have also taken part in the formation
of the diformal-derivatives. A hydroxyl group is no longer present
in formalmethylenexyloside and -arabinoside, for acetic anhydride
and benzoyl chloride do not act on these substances. As, according
to the analysis, two mols. of water have been eliminated, the following
constitutional formulae, for instance, may be drawn up for the said
pentose derivatives.

O
HCD ERGs
eo CH, HC SH,
/ HC—0/ hele“
Oo. ait CH
ee) or |
en HC—ON
OE MOE: OE HED
renee \ HC—0/
H,C—O oF
CH,

Diformalxylose (C, H,, O,) erystallises very neatly from benzene
or light petroleum; melting point 56°—57°,[a@|p(2°/, solution in
methylalcohol) — + 25°,7; may be readily ~ sublimed.

Diformalarabinose is a somewhat oily, colorless liquid which may
be distilled in vacuum without decomposition. Boiling point 155°
at about 32 m.m. pressure; [alp (2°/, solution in methylaleohol)
= — 16°.

With glucose a syrupy diformalderivative may be separated from a
solid mono-compound by taking advantage of the said difference
in solubility. Neither of these substances have any reducing
power or react with phenylhydrazine. They are probably mixtures;
the white substance, although crystalline, does not possess a definite
melting point (140—150°) and on analysis gives no satisfactory figures,
but it could not up to the present be resolved by recrystallisation
into components. The diformal-derivative, left in contact with solvents
for many months, remained syrupy.

Both compounds still contain one or more free hydroxyl groups ;

10

1) The methyleneglucose obtained by Torens (1.c.) has still a strong reducing
action; it appears to us that it should not be regarded as a glucoside (which
Tottens does); apparently two alcoholic groups of the glucose have taken part
in its formation,

the products of the reaction with acetic anhydride and benzoyl chloride
could not as yet be obtained in a crystalline form.

They are not liable to fermentation but do not prevent the fermen-
tation of any free glucose, although they retard the same.

The simultaneous formation of various isomeric mono- and diformal-
olucosides may, as will be easily seen, explain the unsatisfactory result.

Galactose yielded products comparable with those obtained from
glucose. The indistinctly crystalline methylenegalactoside (monoformal
derivative) seems, however, to be a pure substance as the melting
point (203) remained unaltered; [alp (in 2°/, aqueous solution) =
+ 124°.8. It is still being investigated.

Fructose yields a well-erystallised formalmethylenefructoside ; when
preparing the same a 50°/, sulphurie acid should be used. Melting
point 92°; [a@]p (2°/, aqueous solution) = — 34°.9.

d-Sorbose yields a derivative melting at 54° and [el p (2°/, aqueous

solution) = — 25°. Rhammose yields a product melting at 76° and
[a|p [0.4°/, aqueous solution) = — 18°; mannose also yields a crys-

talline derivative.

The (mono)methyleneglucosides also derive a certain importance
from the analogy which they show, as regards their properties, with
ordinary canesugar. In the same way as the latter has been formed
from glucose and fructose, they are also formed, with the loss of
two carbonyl groups, from two aldehydes from which one mol. of
water has been eliminated. The reducing power is lost; towards
phenylhydrazine they have become indifferent. On boiling with dilute
acids, however, the components are regenerated.

It cannot be a matter of astonishment that the methylglucosides
are quite as capable as the hexites, the oxy-acids and the sugars to
give condensation products with formaldehyde. They are formed in
abundance by simply melting the powdered glucosides with dry
trioxymethylene.

In a properly crystallised state were obtained the formalderivatives
of methylmannoside [m.p. 127°, [alp = + 10.5], of g-methyl-d-gluco-
side m. p. 186°, inactive] and of «- and g-methyl-d-galactoside.

The derivatives of a-methyl-d-glucoside and of amyl- and aethyl-d-
glucoside are viscious liquids.

It is worthy of notice that saccharose melted with trioxymethylene
is decomposed with the formation of a mixture of formalderivatives
of glucose and fructose, from which the latter was separated in a
crystalline condition.

(178 }

Chemistry. — “The intramolecular rearrangement in halogen-aceta-
milides and its velocity”. By Dr. J. J. Buanksma. (Communicated
by Prof. LoBry pe BRUYN).

In a former paper *) attention was called to the fact that the ready
bromination, nitration, sulphonation ete. of phenol and aniline deri-
vatives may be explained by assuming that the halogen atom or the
groups NO, or SO, H first enter the side-chain and then pass into
the nucleus by intramolecular migration. Although a great many
compounds are now already known containing groups linked to N
or O which, under the influence of certain agencies, shift towards
the nucleus, it was in these cases up to the present not proved with
absolute certainty that we are really dealing here with a rearrangement
of atoms or groups in a molecule and not with a reaction in which
several molecules take part, which according to some authors is not
improbable *). In order to investigate this it became necessary to
know the velocity of reaction. If the reaction took place mono-
molecularly, we should be really dealing with an intramolecular
displacement; a bimolecular reaction would point to a double decom-
position between two molecules.

As a suitable example for this research, Prof. Losry pr Bruyn
pointed out to me the conversion of acetylehloroanilide into para-
chloroacetanilide under the influence of hydrochlorie acid, first
discovered by Brnpmr *)

EEN ns,
CH, CO NC JH — CH, CO NC fol.
RD 4

It is known that the chlorine in acetylehloroanilide may be determ-
ined by adding potassiumiodide to its acetie acid solution and titra-
ting the liberated iodine; p-chloroacetanilide does not react with K I:

C, H, NCICOCH, +2 HI=C, H‚ NH CO CH, 4 HC +1,

The acetylehloroanilide was prepared according to the directions of
Carraway and Orron ®) by shaking acetanilide with a solution of
bleaching powder containing potassium bicarbonate. Within half a
minute to a minute it will be noticed that the acetanilide has nearly
entirely dissolved; after a few minutes the acetylchloroanilide sepa-
rates in a crystalline state. CHarrawar and Orton state that this

1) Proce. 25 Jan. and 29 March 1902.

2) Armstrone, Journ. Chem. Soc. 77. 1053.
3) Ber. 19. 2273. Srossen, Ber. 28. 3265.
4) Journ. Chem. Soc. 79. 278.

(179)

compound is unstable and is spontaneously converted into p-chloro-
acetanilide. A closer investigation showed me that the cause of this
must be attributed to the action of sunlight. After 14 days exposure
to the light (May 14-28), the atmosphere being cloudy, this substance
was entirely converted into p-chloroacetanilide while on a brieht
day in June the conversion was complete in a day. In the same
manner it was shown that the analogous bromo-compound C, H, N
Br CO CH, had been entirely converted after 3—4 hours exposure
to direct sunlight on an afternoon in June and in 70 hours by exposure
to imeandescent gaslight; in diffuse daylight the conversion was
complete after a few days, while both the cblorine and the bromine
compound, could be preserved unaltered in the dark.

We therefore see that Br and Cl linked to N, shift to the nucleus
under the influence of light. On consulting the literature it was
found that Bamprrenr’) had already shown that phenylnitramine is
converted by sunlight into o- and p-nitraniline, while he had also
found that nitrosophenylhydroxylamine is very rapidly decomposed
by direct sunlight and sometimes even explodes. The reaction takes
here a more complicated course, the first stage of the reaction is
probably the migration of the NO group to the nucleus.

Reeently KNiPscHrer *) has shown that azoxybenzene is converted
by direct sunlight into 0-oxyazobenzene.

We therefore see that under the influence of sunlight Br, Cl, NO,,
NO and O attached to N migrate from the side-chain to the nucleus
and change place with an atom of hydrogen *),

In the previous communication (Le.) attention was called to the
analogy of the CH,-group with NH, and OH. Now however, we
notice a difference. Whereas sunlight promotes the entering of atoms
or groups into the nucleus of the NI,-derivatives, it causes the for-
mation of Brand Cl compounds in the side-chain of the CH,-derivatives,
for instance in the bromination or chlorination of toluene *). |

We may briefly refer to the experiments of Srprk *) and Errara ®)
who have proved that on chlorinating parabromotoluene p-bromo-

1) Berichte 27, 364, 1554, 34, 66.

2) Proc. 31 May 1902.

3) No experiments showing the effect of light have, as yet, been made with
phenol derivatives containing atoms or groups attached to the oxygen, It is probable
that sunlight will in this case also excercise an influence on the migration of atoms
or groups of the side-chain to the nucleus. This should be borne in mind when
preparing these compounds.

4) Scuramm, Ber. 18, 608.

5) Monatsch. f. Chem. 11, 431.

6) Gazz. Chim. Ital. 17, 202,

(180 )
benzylbromide is formed in addition to p-bromobenzylehloride; in
this case the bromine leaves the nucleus and is introduced into the
side-chain *). ‘This question merits further investigation.

After several preliminary experiments which showed that the
interchange of Cl and H is much promoted by the eatalytieal action
of acids, I determined the velocity of reaction in the following manner.
3—4 grams of the acetylchloroanilide were dissolved in 100 grams
of glacial acetic acid (100°/,), 10 ce. of hydrochloric acid containing
2,9127 grams of HCI were added and finally the liquid was diluted
with water to 500 ce. This solution was put into a black bottle
and kept in a thermostat at 25°. As soon as the temperature had
reached 25° 50 cc. were removed with a pipette and delivered into
100 ce. of water to stop the reaction. Excess of solution of potassium-
iodide was added and the liberated iodine titrated with sodium
thiosulphate (0,150 N). The following results were obtained.

é in hours. ec, Na BO: k.

0 49.3

4/5 42 0.160
1 35.6 0.162
ye 30.25 0.163
2 240 0.162
ha 21.8 0.1638
3 18.5 0.160
4 13.8 0.160
6 Vso 0.160
8 4.8 0.162

1 A
By applying the formula for the monomolecular reaction aa Sr:

values are found for / which may be regarded as constants.

This proves that the reaction is really monomolecular and that we
are dealing with an actual intramolecular rearrangement of atoms.

If instead of 10 ec, 20 ce. of hydrochloric acid were added the
value for 4 was found to be 0.610; (the average result of eight obser-
vations); by using double the quantity of acid the velocity has there-
fore increased nearly four times. If instead of hydrochloric acid
sulphuric acid of the same concentration was used, the conversion
was very slow and a good constant was not obtained (32.8 ce. of
Na, 5,0, at first, 29 cc. after 24 hours).

In glacial acetic acid (99—100 °/,) the reaction takes place much

1) Cf. Hanzscu, Ber. 30, 2334. Trör and Ecker, Ber. 26, 1104.

( 181 )

more rapidly so that addition of very little hydrochloric acid suffices
for the complete conversion.

The substance was again dissolved in glacial acetic acid and 3 ce.
of a solution of dry hydrogenchloride in glacial acetic acid were
added. The quantity of HCl thus introduced into 500 ec. of the
solution amounted to only 0.0135 gram or not quite '/,,, part of the
quantity present in the experiment with aqueous acetic acid.

The progressive change of the reaction was as follows:

t in hours ee Nao 5,0,

0 ale
oy 29.7
1 28

En 24

2 22.6
Di 19.8
3 WED
ot. 14.2
4 12.4
4'/, 10.5

: 5 1 A
On calculating A according to the formula == ae ee it will

be seen that it keeps on increasing; this shows that the amount of
the catalyser increases. On repeating the experiment it was found
that, after the reaction, more hydrochloric acid existed (weighed as
Ag Cl) than corresponded with the quantity added.

A graphic representation of the above figures plainly shows that
we are dealing here with a reaction the velocity of which has been
accelerated by an increase of the catalyser *). In the experiment with
20 per cent acetic acid the small increase of the relatively large
amount of HCl is not perceptible.

Even when we do not add hydrochloric acid but set the acetic
acid solution aside in the dark we meet with the same type of
progressive change of the reaction. 10 ¢.c. of a solution in glacial
acetic acid were titrated from day to day and took:

13,12, 9, 6,7 72,6 TD ands Ll 6.¢, Nas POE

which figures again reveal the character of a reaction accelerated
by a catalyser. It moreover shows that it is not the glacial acetie
acid which starts and continues the reaction, but that the conversion
is due to the catalyser formed from the product itself; in the first

1) Osrwatp, Lehrb. d. allgem. Chem. Bd. Il, T. Il, 266.

( 182 )

case it ought to be possible to calculate a constant by means of the
formula employed for monomolecular reactions.

We are, therefore, dealing here with a case quite analogous to
that of the spontaneous decomposition of alkyl sulphurie acid and
nitrocellulose mentioned by Osrwarp; it is known that this may be
prevented by adding a little K, CO, or Ca CO,,

The reaction in the presence of alcohol takes place in a similar
manner ; on warming on the waterbath it may according to CHATTAWAY
and Orton become so violent that the aleohol begins to boil. This
may be prevented by adding a trace of Na,CO, which fact has been
noticed by ARMsTRONG (L. ¢.).

We therefore, see:

1. That the conversion of acetylechloroacetanilide into p-chloro-
acetanilide proceeds like a monomolecular reaction and that it repre-
sents a true intramolecular rearrangement of atoms. It may therefore
be compared to the case of the transformation of the bromo-amides
under the influence of alkalis studied by van Dam and ABERSON ’).

2. That Br, Cl, NO,, NO, and O attached to N change place, under
the influence of sunlight, with an H-atom present in the nucleus.

3. That the conversion of acetylchloroacetanilide in aleoholie or
acetic acid solution is caused by the formation of a catalyser which
causes the reaction to proceed at an increasing rate (particularly in
sunlight); this may ‚be prevented by adding a trace of sodium carbonate
or acetate as this removes the catalyser.

The investigation will be continued in various directions.

Chemistry. — “Galvanic cells and the phase rule.’ By Dr. W.
Rempers of Breda. (Communicated by Prof. H. W. BaKnuis
RoozrBoomM).

9

Nernst 7) and, more recently, Bancrorr*) have tried to establish a
relation between galvanic cells, consisting of a combination of two
metals surrounded by electrolytes in communication with each other,
and the phase rule. Neither of them, however has paid sufficient
attention to the fact that: When the phase A is in equilibrium with
B and also with C, then B must be also in equilibrium with C.
They regard the liquid electrolyte, in contact with the metals, as
one homogeneous phase, whilst in reality two phases exist which are
1) Recueil 19. 318 (1900).

2) Theor. Chem. le Aufl. p. 560, 3e Aufl. p. 660.
5) J. of phys. Ch. Il 427 (1898),

( 183 )

not in equilibrium with each other; in facet various means are
employed to prevent them from forming a homogeneous mixture.

The following contains a new effort to study the galvanic cell
from the point of view of phase rule.

Those cells have been considered, which consist of a combination
of 2 metallic electrodes, each surrounded by an electrolyte, containing
the cation of the metal and connected with each other either directly
or by means of an electrolyte.

Equilibrium may exist between both the electrodes and the sur-
rounding electrolyte and when that equilibrium is reached, there
exists at the plane of separation a certain potential difference, which
is the measure of the energy required to transfer an equivalent of
the metal from the one phase into the other.

Bancrorr is therefore in error in regarding the E.F. as an in-
dependent variable, as a further condition of equilibrium. He says:
“In addition to the ordinary conditions of equilibrium there is also
the electromotive force.”

The variables would then be the 7 components, temperature, pressure
and the potential difference and from this it would follow that for
an invariant system » + 3 phases were required.

This is not the case, for a is completely defined when 7» phases
are present in a system of 7 components at a given temperature and
pressure (for instance by the formula of Nernst when „==? or 3).

There exists, however, no equilibrium between the two electrolytes
in the cell. They will tend to form a homogeneous mixture in
which ease the composition is changed and the equilibrium with the
electrode disturbed.

Therefore, there can be no question of a real equilibrium in the
whole of the cell so long as both electrodes cannot be in equilibrium
with the same electrolyte and the EMF becomes zero. An apparent
equilibrium may, however, be got by preventing as much as possible
the diffusion of the two electrolytes.

Considering the cell as a combination of two systems consisting
of metal and electrolyte, the equilibrium of the separate systems should
be diseussed before alluding to that existing in the cell.

The equilibrium between the metallic electrode and the surrounding
electrolyte and the potential difference at their plane of separation.
A. The electrode consists of a single metal and the surrounding
electrolyte also contains cations of that metal alone.
When the electrolyte is a fused salt of the metal, we have a system
of 2 components in 2 phases which at a given temperature and press-

( 184 )

ure is completely defined. If the electrolyte is a solution of a salt of
the metal, there will be 3 components and, therefore, the concentration
must also be given. The potential difference is determined by the for-

’ RGP

mula of Nernst: ar =—l— in which P=the solution tension of
nh P

the metal, p= the osmotic pressure of the cation and n= the

valeney of the metal.

B. The electrolyte consists of two different metallic salts M,Z and
M,Z and in the electrode both metals of these salts may be present.

Assuming that the electrolyte forms one homogeneous phase, the
following distinction may be made in the equilibria of the electrode
and electrolyte.

I. At the given temperature there is no reaction between the two metals;
they form therefore neither a compound nor a liquid or solid
solution.

Starting from the electrolyte, containing only the salt M,Z (fused
or in solution), there is a series of electrolytes with an increasing
amount of J/,Z, which ean only be in equilibrium with J/,, and
another series, starting from J/,7 with increasing quantities of JZ, Z,
which are only in equilibrium with J/,.

Where these two series meet, we have an electrolyte, which is
in equilibrium with both JM, and J/,. When there is no solvent
and we are consequently dealing with a fused salt mixture, there
is only one electrolyte which satisfies this equilibrium. We then
have 38 phases: electrolyte, JM, and J/, and 3 components M,, M,
and the acid group Z. The equilibrium at a given ¢ and p is, there-
fore, completely defined.

If, however, a solvent, and consequentiy a fourth component is
also present, then, according to the quantity of this solvent, there will
be a series of electrolytes which satisfy the conditions of equilibrium.

To follow the change in the potential difference, we may imagine,
that a part of the ions J/, in the electrolyte containing J/,Z, has
been replaced by J/,, but in such a way, that the total concentra-
tion of the ions J/, + J/, remains constant. The potential difference
between Ms and the electrolyte will increase, because in the equation

x, = — ‘| —, p, becomes smaller and consequently 2, becomes greater.

The same ae to z,, the potential difference between the metal
AM, and an electrolyte containing only JZ, cations, when part of these
ions is replaced by ions J/,.

( 185 )

Bw In fig. 1 AD and BD are the lines fiving
7 a graphic representation of the change of a as
5 function of the ratio of the ions J/, and

B WM, at a constant total concentration of the
cations. A point on AD, therefore, gives
the concentration of the M, and M, ions in
an electrolyte, which is in equilibrium with

A
M, and the potential difference at the plane
A JZ, of separation between this electrolyte and the
electrode. BD does the same for M. Both
~ °My-ions. lines are logarithmic curves. AD, therefore,

asymptotically approaches the ordinate M/,B, until it is intersected in
D by the line LD.

In D the electrolyte is in equilibrium with the two metals J/, and
M,. To the left of it, M, is precipitated by M,, to its right, M, by
M,. The condition of equilibrium in D is a, = a,

1 Py 1 Pr

therefore log — = — log —
n 1 P 1 n 2 Ps
ny Pi Ny Pr
or oe Noe aes
Pa Ps

and, for metals of the same valency P: Piz = p, : py.
In words: in this equilibrium the ratio of the concentrations of the
cations is equal to the ratio of the solution tensions of the metals.

Owing to the great difference in the solution tensions, p, must
in most cases be very small and consequently the possibility of the
second metal existing in contact with the mixed electrolyte, is limited
to very minute concentrations of the first metallic salt; whereas the
first metal may be in equilibrium with almost all the electrolytes,
whatever the proportions of the two salts may be. The point D
is, therefore, situated nearest to the less noble metal and almost
coincides with B.

DanNEEL *) has investigated an instance of this equilibrium, namely
2HI + 2 Ag=@2 AgI+H,. The solution, which is in equilibrium
with both Ag and H, under 1 atm. pressure, is saturated with Agl
(c = 0,567X10—-8) and 0,043 normal in HI.

Il. The two metals form a homogeneous liquid or solid solution.

This is the case with the liquid amalgams and other fused metals,
with Zn—Ag ®), Sb—Sn ’*) and other alloys.

1) Z. f. Phys. Ch. 33, 415.

2) Heycock en Nevittr. J. Chem. Soc. 1897, 415.

5) Heycock en Nevitte. J. Chem. Soc. 330, 387; van Burerr, Z. f. phys. Ch,
8, 357 en Reinpers Z. f. anorg. Ch. 25, 113.

( 186 )

Starting with the one pure metal and a solution, containing only
the first metallic salt, it is found that on addition of the second
metallic salt a small portion of the second metal will be separated
and dissolved in the first one until the metallic phase is again in
equilibrium with the electrolyte.

This equilibrium requires that a, ==, or for dilute solutions:

YB ae ag de RTG MD

ue je

ny, Pr ns Pa:

ny Pp No P.
or also Vie — El
Pi Pr

in which P?, and P, are the partial solution tensions of the two
metals in the homogeneous metal phase. P, and P, are not constant
here, but vary with the composition of the electrode.

This formula was obtained by Nernst’) and verified by Oae ®)
by means of the example Hg + AgNO, 2 HeNO, + Ag.

The electrode now contains both metals, as may also happen in
the case of non-homogeneous mixtures (D in fig. 1). The difference,
however, is that there the metals form 2 phases and here only one.
If the electrolyte is a mixture of fused salts or a solution in which
the total concentration of the two cations is constant, then, at a
constant temperature and pressure, the system will still be monovariant

ny Ng nj Ng
and the relation WP :WP, or Vp, :Vp, may still be variable. Once
ny Ne

however, the relation Vp,:V/p,, that is the composition of the electro-

n Neo
lyte, having been given, WP, VP, or the composition of the metal
phase, is also determined and consequently also a.

At each temperature a series of two such coexisting phases are
possible. The potential difference continuously changes with their
composition.

In order to trace the general course of this a-line it must first be
ascertained how P, and P, depend on the composition of the electrode.

If, in the metal phase, there are « atoms of J/, and 1—v atoms
of JV, and « is small, the lowering of the solution tension may be
taken as proportional to the number of dissolved molecules of the
second metal, which is analogous to the lowering of the vapour
pressure in liquid mixtures. If we call the solution tension of the
pure metal M, P,, then P, = P;(1—2).

For small concentrations P, is proportional to the concentration

1) Z. fiir phys. Ch. 22, 539.
*) Z. fiir phys. Ch. 27, 285.

(1877)

of the second metal, as has already been proved by the investigations
of Meyer *), Richard and Lewis’) and Oee *). Therefore P, = Kv.
The factor AK is unknown. For «—1 it becomes however = P7;.
For small values of « however this is not necessarily the case, for
it is to be expected that its value will be influenced by the nature
of the first metal. 7
The condition of equilibrium then becomes:

uy Pil —2) A Ku
atk Ps

Ng Ke Use
Vp V Ka
or aye BN Ee C8
ny ‘Gi ny
Vo, VPid—a)
: K «
and for n,n, Ps en

VNU: VEEN)

In words: The ratio of the ions in the electrolyte is to that of
the atoms in the metal as A: Py.

When the ratio A: Py is very great, p,:p, will also be great, even
when w has but a small value, that is to say that the electrolyte will
contain almost exclusively cations of the baser metal even when
the concentration of that metal in the electrode is small.

In calculating the potential difference, the concentration of these

Br Kye
ions (p,) may, therefore, be taken as constant. oar i
a logarithmic function of « and, for small values of v, will increase
aen. dar REY
rapidly with it. (Er )

Av Nn, &

is then

The graphic representation of this function is a curve rising rapidly
from the potential of the nobler metal at a small distance from the
a-axis. As wv increases, K approaches to the value P, becoming
equal to P; when 2=1. The curve, therefore, bends sharply and
after a small further rise reaches to the value of the potential of J/, in
a solution of pure M,Z.

The ratio of the ions in the coexisting electrolyte Ee increases

| " PitPs
from O to nearly 1 for quite small values of wv. The curve, which
represents a as a function of this ratio, runs, therefore, at a slight
incline towards the ordinate representing these baser metal, finally
approaching it almost asymptotically.

My ay apis. Cl. 7, 417.

Ps we) 4 „ 28, |.

Oh Ge

( 188 )

The same results are obtained by considering the equation

RT, Pr (1—2)

ise Teoria

a. When the two metals form homogeneous mixtures in all pro-
portions, the curves will therefore possess the

4

Fig. 2,
general form shown in figure 2.

ie B The points on these curves, which are
situated on the same horizontal line, are co-
existing phases. The ordinate of the points
gives the potential difference at the plane of
separation.

Although it is not impossible, a maximum

or minimum will rarely occur, unless the

>

* solution tensions of the two components

Ps 1 ay i erv 1 4

Ee differ very little.
PitPs 4. If the metals are not homogeneously

miscible in every proportion, and the series of mixtures is therefore
discontinuous, the two metallic phases, which are in equilibrium with
each other (the end points of the break), will also be in equilibrium
with the same electrolyte. The potential in this electrolyte must be
the same for both metallic phases, for if such were not the case, a
current might be generated and the equilibrium would be disturbed.

According to whether the potential difference in this non-variant
equilibrium is greater than those of the pure metals in solutions of
their salts or intermediate between them, the figures 3 or 4 are

obtained.

Fig. 3. Fig. 4.

—> v or ES (OT =
PFP: PP.
C and PD are the two metallie phases in equilibrium with each
other. Mis the coexisting electrolyte.
The case of fig. 3 becomes identical with that of fig. 1 if Cand D

( 189 )

coincide to the right and the left with the a-axis, that is when the
metals do not mix.

An example of the case of fig. 4 is found in my investigation *)
of the equilibrium between fused lead, zinc and their chiorides. At
elo we yu 100 9), nok ed Ob ns 1) == IA OF Zn, 3-5/5 :0F PD
H= 99,9 °/, of ZnCl,, 0,1 °/, of PbCl, and if 74 is taken as 0 then
Korp — 0,277. Volt and. wp = 0,288. Volt.

A second example is found in the cadmium amalgams, investigated
by Janerr*) and Bun’). Further researches are those of Mrynr and
RrcHarps and Lewis on the dilute amalgams, those of LiyprcK *) and
those of HerscHkowitscH®), who met with the case represented by fig. 4
in his investigation of Cd—Sn, Cd—Pb, Zn—Sn, Zn—Bi, Cu—Ag.

In all these cases the concentration of the nobler metal in the
electrolyte is very small; to a large extent the curve ALB almost
coincides with J/, 2.

I. The two metals form a compound.

If the compound is present in a pure condition there will only
be 2 phases and at least 3 components. Even without solvent the
system is still monovariant at constant temperature and pressure. As
in case I, if one of the pure metals forms the electrode, a series of
solutions exists with varying proportions of the salts MZ and
M,Z, which may be in equilibrium with this compound. The
limit of this series is reached when the solutions are also in -equili-
brium with a second metallic phase (one of the pure components, a
liquid? or solid solution or a second compound).

In order to make use of Nernsv’s formuia to calculate the potential
difference, it is necessary to assume that the electrode forms ions of
the same composition as the compound, for instance of AuAl,, Zn, Ag,
etc. and to substitute the concentration of these ions in the formula.
The solution pressure is then a definite constant for this compound,
as it is for every pure metal:

PO se

1,2

therefore ier Merc ES fede

1) Z. f. anorg. Ch. 25 126.
2) Wied. Ann. 65 106.
5) Inang. Dissert., Amsterdam 1901.
4) Wied. Ann. 35 311.
5) Z. f. phys. Ch. 27 123.
13

Proceedings Royal Acad. Amsterdam. Vol. V.

( 190 )

If the formula of the compound is Me J/,’ , then owing to disso-
ciation, ions M, and J, will occur along with ions Mt /," and
between these an equilibrium will exist expressed by the equation:

Pi pt = KP

When the total concentration of the ions remains constant, /—p,
may be substituted for p, and the equation becomes
pPi* (k—p,)? = Kp

12°

The maximum value of p,, is reached when the first differential
quotient with respect to p, = 0, that is, when

ap, (k—p,)’ — b p,* (k—p,)’ = 0
or atk =p:) = bp,
ee Pi? P,.—: b.

P,. therefore reaches a maximum and a a minimum where the
ratio of the ions J/, and MZ, in the electrolyte

Fig 5.

is equal to that of the metals in the compound.

a. If the compound can be in equilibrium
with an electrolyte in which the ratio of the
cathions is the same as that of the metals in
the compound and if in addition to the com-
pound only the metals in a pure condition

are capable of existence, then the a-curve
will have the form indicated in fig. 5.

The points on the line AG give the compositions of electrolytes in
equilibrium with pure J/, and the corresponding potential differences.
With the electrolyte G both JM, and the compound are in equilibrium.
So long as both metal phases are present, the potential difference remains
constant. Should JM, have entirely disappeared, so that the electrode
consists of the pure compound (composition = /), the electrolyte may
vary from G to K while the potential difference first falls to Hand
then again rises to A. In A there is again a non-variant equilibrium
between the compound, pure J/, and the electrolyte A’ and so long
as these phases exist the potential difference remains constant. But
when the compound has disappeared, it falls to B, while the
electrolyte changes from A to pure J/,Z.

From an electrolyte having a composition situated between G and A”
the compound .W,M, is precipitated by J/, and also by M,.

( 194 )

Owing to the small rise of the line AG, the first case is sure to
occur but rarely, as the line GHK then stands a chance of not being
again intersected by AG and this case will pass into that of D (see below).

H may be situated higher or lower than A.

Fig. 6. If, in addition to the compound, two solid
solutions are possible (J/, in which a little
M, and MM, in which a little J/, is dissolved),
the a-curve takes the course indicated in fig. 6,
which differs from fig. 5 in this, that in presence
of the electrolytes A to G pure M, is replaced
by an electrode of varying composition, repre-
sented by the line AC, and in presence of the

electrolytes B to A metallic phases 6 to occur. |

The line BF may either rise or fall ’).

An example of this case is probably the system Hg, Ag, NO,, examined
by Oge (Le.) for dilute solutions of Ag in He.

b. If the compound cannot exist in presence of an electrolyte in
which the ratio of the cations is the same
as that of the atoms in the compound and if
we consider the case in which in addition to
the compound two solid solutions are possible,
we get fig. 7.

Metallic phases from A to C are in equili-
brium with electrolytes from A to G. From
C to D the electrode consists of a mixture
of the two phases C (a solution of M, in M)

and D (the compound). The potential difference
is constant.

As therefore, the compound is not in equilibrium with an electrolyte
having the same ionic ratio, it will, in contact with such an electrolyte,
dissolve with separation of J/,, and tend towards the equilibrium
G, D, C. If, before attaining this, D has totally dissolved, a metallic
phase on the line AC and an electrolyte on the line AG will remain.

From D to MZ the pure compound is in equilibrium with an elec-
trolyte of varying composition, situated on the line GA. The potential
difference rises. The metallic phase /” and the compound / are in
equilibrium with the electrolyte A. As long as these three are present,
the potential difference is constant. If, however, the electrode reaches
a composition to the right of /’, the compound will have disappeared

1) In fig. 6 to read K instead of F and F instead of P.

and there will be equilibrium of the metallic phases /” to B with
the electrolytes A to B. a rises or falls (as in fig. 3).

It may be expected here as in II, that the line AGAA will toa
large extent run close to the a-axis of J/, and that in consequence
the concentration in M‚-ions in G and K will be very small.

When no solid mixtures of the two metals are possible AC and
BF coincide with the z-axis. # then lies above JB.

If there is more than one compound, the sudden change of potential
DE is repeated for such compound. Hrrscukowrrscn (Le.) has noticed
these sudden rises with Zn,Cu, Zn,Ag, Zn Sb,, Cu,5n, Ag,Sn and
has regarded them as evidence of the existence of these compounds.

We should, however, be careful when drawing such conclusions
as to the composition of alloys from measurements of potential dif-
ference, for an alloy, obtained by melting together the two components
and rapidly cooling the mass, is a badly defined substance and often
contains more than two phases which are not at all in equilibrium.
When they are brought into contact with an electrolyte consisting of
a salt of the less noble metal, the unstable compounds in the alloy
may be converted into the more stable ones and this reaction, which
is caused by a short circuited element (unstable compound, electrolyte,
stable compound), continues until only the two phases, which are
really in equilibrium, remain. During this period the ZMF observed is
not necessarily constant.

The constant cells.

As already stated, there is no equilibrium between the two elec-
trolytes of a cell; they tend to form a homogeneous mixture by
diffusion. The potential difference between two electrolytes is, howe-
ver, generally very small and when the diffusion is small, it will
change very little. As, moreover, the ZM F of a cell consists of
the sum of the potential differences between the two electrolytes and
between electrolytes and the electrodes, an apparent equilibrium and
consequently a constant 4 M/F may be secured by making the dif-
fusion as small as possible.

To attain this it is necessary that there should be equilibrium
between the electrodes and their electrolytes. But, in a constant
cell, that equilibrium must not be modified when the current is allowed
to flow and an interchange between the phases takes place in con-
sequence. At constant ¢ and p the system must be invariant.

If the electrode consists of a single metal, the concentration of the
ions of the metal in the electrolyte must be kept constant. In case

1
nen te dS OO

( 193 )

the electrolyte consists of a solution of the metallic salt, the presence
of this salt in a third phase of constant composition, such as a solid
hydrate, is required. These conditions are satisfied in the original
form of the Clark cell, which contains on one side Zn and a saturated
solution of ZnSO,, 7H,O and on the other side mercury and a
saturated solution of He, SO,.

If the electrode consists of two metals forming only one phase
liquid solution, solid solution or compound), the current will neces-
sarily cause a change in the equilibrium, because the ratio of the
metals in the electrolyte is generally different from that in the elec-
trode. The equilibrium will only then become invariant when a
second metallic phase appears.

If there is no solvent, and the electrolyte therefore consists of a
mixture of the two fused metallic salts, its composition is completely
defined by the presence of 3 phases of the 3 components (M,, M,
and the common acid radicle). If, however, there is also a fourth
component in the form of a solvent, a fourth phase must be present
to make the equilibrium invariant such as’ the crystals of one of the
two salts. The choice between the two salts is not an arbitrary one,
but is regulated by the required relation of the concentration of the
cations and the solubility of the two salts.

From this it follows, that on passing the current, only that metal,
the salt of which is present in a second constant phase, can dissolve
or deposit on the electrode (which consists of a mixture of the two
metal phases). The ratio of the quantities of the two metallic phases
must be regulated accordingly.

An example, from among the commonly used normal elements
is the Weston cell in which the Cd-electrode consists of a mixture
of a liquid phase (Hg with 5°/, Cd) and a solid one (Hg with 14 °/,
Cd)') while the surrounding electrolyte consists of a solution of

©

Ap 5
Cd SO, and traces of Hg, SO,, saturated with Cd SO, a H,O.

The Clark cell in which a zine amalgam with 10—15°/, of zine
is used, is clearly a similar combination.

1) Byl, lee.

( 194 )

Astronomy. — “On the yearly periodicity of the rates of the
Standardclock of the observatory at Leyden, Honwü No. 17.”
Second part. By Dr. E. F. van DE SANDE BAKHUYZEN.

I. The period 1862—1874.

9. As was mentioned, several investigations about the rate of the
clock Houwt 17 during this period have been made by Kaiser.
They have been partly published. These published investigations are
relative to the period 1862 May—1864 August *).

Afterwards, in the autumn of 1870, Kaiser undertook a new
investigation founded on the period 1862—1870*). In 1872 this
investigation was continued and extended over the last year and a
half *). Kaiser was engaged in this investigation, the results of which
were intended for the 3% Volume of the Annals of the observatory,
till the last months of his life. It was unfinished, however, at his death.

The results which Karser had obtained did not wholly satisfy him.
Several singular irregularities had shown themselves; moreover he
was aware of the fact that the barometer-readings, one of the foun-
dations of the investigation, might still be affected by rather consider-
able systematic errors, even after they had been corrected as well
as possible. These barometer-readings had been derived by him from
observations repeated three times every day on an old defective mer-
cury barometer oi Burtr hanging in his study (during a year and a
half on an Aneroid-barometer). The correction of this barometer
was derived from simultaneous readings of the barometer in the
transit-room. It appeared to be variable with the height of the
barometer and increased considerably in the course of the years ;
moreover the temperature of the barometer was quite uncertain.

For these reasons H. G. VAN DE SANDE BAKHUYZEN, when in 1873 he
planned the continuation of the investigation of the clock, deemed it
necessary, first of all to procure better data about the atmospheric
pressure to which the clock had been exposed *). He intended to derive
these by the help of the regular barometer-readings made at the
meteorological Institute at Utrecht.

In the first place the constant differences between the barometer-
readings at Utrecht and those at Leyden (the barometer in the transit-
room) had to be derived. From extensive calculations, which have

1) F. Kaiser |. c.

2) Vide: Verslag van den staat der sterrenwacht te Leiden. 1870—71 pp. 15 and 16.
3) Vide: Verslag van den staat der sterrenwacht te Leiden. 1871—72 pp. 14 and 15.
4) Vide: Verslag van den staat der sterrenwacht te Leiden 1872—73 p. 4.

195 )

been continued afterwards, it finally appeared that, when the neces-
sary corrections ') and the reduction for difference in altitude had
been applied, the mean barometer-readings at both places are in
perfect agreement *). |

After the completion of this preparatory work H. G. vaN Dr SANDE
BAKHUYZEN has been prevented by want of time from further inves-
tigations of the rates of the clock Honwé 17.

10. When last year the investigation of the clock in the period
1862—74, was resumed by me, I have soon given up the attempt to
derive trustworthy corrections for the barometer of Burrr and I too
have used the readings at Utrecht. It appeared that in this way we
can get a precision sufficient for our purpose, at least for the mean
monthly barometer-readings.

I had at my disposal readings of the barometer at Utrecht for
205, 2% and 10". From these I derived mean barometerreadings
reduced to 0° for the whole of our period *). In addition to these,
however, we have readings of the barometer at Leyden for the last
months. For, to begin with July 1873, the barometer in the transit-
room has been regularly read five times a day. From these I could
derive, in the same way as I had done for the time after 1877 mean
barometerreadings, which afterwards I reduced to 0°. The comparison
of the monthly means obtained in the two ways stands as follows

L. — U. L. — U.
1873 July + 0.3 Mm. 1873 Dee. + 0.8 Mm.
Aug. 0.0 1874 Jan. — 0.2
Sept. — 0.2 Febr. + 0.2
Oct. — 0.2 March + 0.3
Nov. — 01 April + 01

The differences thus appear to be very small. They would have
turned out still smaller perhaps, if we had not neglected the hundredth
parts of the millimeters in all the computations. The mean value
amounts only to + 0,05 Mm.

1) About the errors of the barometer at Utrecht see: J. D. van per Praars,
„Over den barometer van het K. Nederl. Meteor. Inst.” (Meteor. Jaarboek voor 1888).
At Leyden the barometer-readings were reduced to those of the standard-barometer
of Furss.

2) See also: Annalen der Sternwarte in Leiden. Vol. VI pp. GXIV—CXVI.

3) Ly taking the means of the readings at 10°, 205, 2%, 10° and giving half
weight to both the extreme values I obtained the daily means from midnight to
midnight.

( 196 )

1. For the derivation of the temperature of the clock 1 had the
following data at my disposal.

From 1862 to 1866 May a thermometer hanging at the pier of
the clock was read at 8h 30m in the morning.

Beginning from that time two thermometers suspended in the clock
ease were regularly read, but from 1866 June to 1873 June these
readings were only made at 8" 30" in the morning. Since 1873 July
both thermometers were read five times a day.

From July 1873 it was possible therefore to take daily means of
the temperature according to the upper thermometer in the clock
case in the same way as was done for the time after 1877.

For former periods I had to find corrections in order to reduce to
daily means of the latter thermometer.

For the purpose of finding these corrections I compared:

1st. For the years 1871, 1872 and 1873 the readings at 8" 30m in
the morning of the upper thermometer in the clock case with those of
the thermometer at the clockpier ;

Ind, for the years 1873-—75 the readings at 8" in the morning
of the upper thermometer in the clock case with their daily means.

From the two comparisons [ found the following monthly means
of the differences 4, — clock case — pier and 4, = daily means —
readings at 8", everything being expressed in degrees RÉAUMUR.
The index-corrections have been taken into account.

LS Bs, A, Ap
Jan. + 0.21 + 0.22 July + 0.01 + 0.36
Febr. ili wis) Aug. ake) Al
March ‚14 ‚44 Sept. 16 46
April 5 ‚48 Oct. „20 ‚26
May 06 38 Nov. 16 29
June ‚03 47 Dec. 16 O4

For all the months I adopted for A, the general mean — 0,15.
For A, I adopted
October—February + 0.20
March—September -+ 0.45

With the aid of these values and of the index-errors determined
at regular intervals the necessary reductions were applied.

Lastly I compared the temperatures according to the upper and
lower thermometer, as has been done for the subsequent period,

nn

the difference in the two eases being that, for the period now under
discussion, the clock was only enclosed in a single case. 1 will set
down only the results which I found for the means of the 5 daily

readings in the years 1873—76.

u.—l. u.—l.
Jan. + 0.32 July + 0.44
Febr. + 0.34 Aug. + 0.40
March + 0.38 | Sept. + 0.5
April + 0.42 Oet.” 20:30
May + O44 Nov. + 0.31
June + 0.44 Dee. + 0.31

These differences are corrected for index-errors.

12. With a few exceptions I used for the time before 1872 the
same time-determinations from which Kaiser had formed his monthly
means of the rates. Some corrections however could be applied.
The clock had been set going in June 1861 but I left out the first
year and placed the beginning of my investigation at 1862 May, as
Kaiser had done. It ends April 1874, a short time before the oceur-
rence of the perturbation.

The observed rates were first reduced to 760 Mm. at 0° and to
+ 10° R. For the coefficient 6 I again took + 0:.0140 (Kaiser in
his last investigation found ++ 0.0134) and for ¢ I adopted the value
— 0.0174 which is the mean result of Karser’s last investigation,
allowance being made for the fact that I now reduced the barometer-
readings to O°.

In the following table all the columns have the same meaning as
the corresponding ones in the table for the period 1877—1898.

10805 „al

SR | ae | mer | Re | DR, joe

1862 May — 0.392 | 759.5 | 449.7 | — 0.98 | —0.999 | + 155 ae
June 0.390 | 58.2 13.0 0.313 pee) Mere gts
July 0.408 | 60.3 13.8 0.346 5508) = 36
Aug. 0424 | 60.6 14.5 0.354 3H) 97
Sept. | 0.308 | 62.9 13.0 0.317 290 | + 4
Oct. 0346 | 59.4 10.6 0.398 294 | + 90
Nov. 0.245 | 60.0 6.2 0.31 280 | + 34
Dec. 0.192 | 61.6 5.0 0.301 ost | + 33
1863 Jan. 0301 | 56.9 4.8 0.348 344 | — 30
Febr. 0.14 | 69.4 5.2 0.352 365 | — 54
March 046 | 584 6.4 0.287 314 0
April 0.937 | 610 8.8 0.972 306 | + 8
May 0213 | 61.7 10.8 0.223 254 | 4-60
June 0.388 | 59.9 13 6 0.394 344 | — 30
Tuly 0.947 | 64.3 149 0.234 238 | + 76
Aug. 0.415 | 60.4 15.4 0.327 314 0
Sept 0.404 | 58.9 11.8 0.348 S91. | ay
Oct. 0.442 | 58.8 10.3 0.420 386 | — 72
Nov. 0.237 | 63.9 6.4 0.355 394° | 340
Dec — 0.277 | 634 6.0 0.390 370 | — 56
1864 Jan. 4+ 0.032 | 68.8 0.8 0.951 ar | + 67
Feb: — 0465 | 598 22 | 0.298 Bel ota
March | 0 305 54.0 | od 0.306 333 — 18
April o1n | 639 | 69 | 0.930 964 | + 54
May 0208 | 61.4 1041 0.296 257 | 4 50
June 0.342 | 60.2 12.7 0.298 tse a
July 0.375 | 62.0 19.9. “0885 330 | 2 18
hie 0307 03.8 150 AD EN 323 | 4/9
Sept 0.401 |. 61.2 12.5 0.374 SUT U
Oet. | 0.369 | 59.0 Bur Des 344 0
Nov. | 0.308 | 588 LG Miles ine eo 314 | 4 35
Mee 0 AEB bese ape [0.3697 370 =| 2245

| |

1865

1866

1867

Jan. Bozen 750-0) (ee aid) | SD | ean | = See
Febr. 0.210 | 59.5 se Bites
March 0.264 | 57.9 2.7 | 0.362 S800 EA
April 0.978 | 65.2 rn Geaae 409 | — 31
May 0.390 | 61.4 12.3 0.365 SA | wee ch
June 0.352 | 65.3 12 6 0.381 AOL | — AA
July 0.464 | 61.2 15.4 0.387 to a ae ats
Aug. 0.487 | 59.0 14.0 0.403 390 | + M
Sept. 0.389 | 68.2 MA 0.433 HOG nele df
Oct. 0.485 | 53.3 9.5 0.400 166 | + 46
Nov. 0.376 | 60.1 6.5 0.438 407 | + 44
Dec. 0.937 | 68.6 4A 0.460 ade} dT
Jan. 0.366 | 58.7 5.4 0.433 490 ae
Febr. 0.473 | 544 4.7 0.487 500 | — 69
March 0.425 | 543 4.8 0.435 462 | — 97
April 0.394 | 609 ou 0.425 459 | — U
May 0.347 | 61.7 9.2 0.385 46 | + 25
June 0 479 60.2 14.9 0.397 AAT + 26
July 0.477 | 599 144 0.405 409 | + 35
Aug. 0.536 | 56.6 13.3 0.431 M8 | + 97
Sept. 0.599 | 56.7 12.5 0.509 482 | — 36
Oct. 0 392 | 64.9 9.1 0.477 ENE er
Nov. 0.424 | 58.6 7.4 0.451 120 | +. 6
Dec. 0.351 | 60.6 5.2 0.443 493 | + 93
Jan. 0.376 | 52.9 2.2 0.448 409 | + 36
Febr. 0.285 64,4 5.5 0.425 438 | + 7
March 0.407 | 56.2 3.8 0.462 489 | — 45
April 0.457 | 559 re: 0.438 a ea
May 0.396 | 59.8 10.4 0.386 47 | + 25
June 0.43 | 63.4 13.0 0.409 49 | + 11
July 0.497 | 59.4 13.3 | 0.427 431 | + 7
Aug. 0.505 | 62.2 14.4 0.459 446 | — 10

( 199 )

| oe | Bar. | Temp. | DRI | ven | ee

1867 Sept. | — 0-484 7637 | 143.2 | — 0.480 | — 0.453 | — 19
Belk aN, beh 0 Aes | ae 8:9 | 0.466 439 0
Nov. 0.312 | 65.9 6.4 0.458 4078 2
Dec. 0.266 | 62.2 3 1 0.417 397 ae)
1868 Jan. 0.288 | 58.9 94 0.440 406 | + 19
Febr. 0.298 64.6 4.9 0.451 A64 EN |
March 0.302 60.6 9:84 0.383 AAO 4144
April 0.344 | 60.4 7.4 0.395 429 | — 40
May 0.359 | 62.6 12 5 0.351 382 | +. 35
June 0.396 65.6 14.0 0.404 A2 = 5g
July 0.493 | 62.4 16.5 0.414 4A8 =e
Aug. 0.592 | 60.0 16.4 | 0.486 VEN
Sept 0.540 [59.3 | 43.2 | 0 444 AAT 2/15

Oct. 0.381 | 603 8.4 | 0.413 oo |=
Nov. 0.263 | 61.7 5.6 | 0.364 348 AE

Dec 0.421 52.4 59 0.386 366 | + 36
1869 Jan. 0.237 | 63.7 2.9 | 0.413 ie de
Febr. 0.269 | 60.9 5.7 | 0.357 370. dees
March 0.318 | 56.4 3.7 | 0 378 Mis | 9
April 0.336 | 62.4 8.8 | 0.391 495 | — A

May 0.383 | 57.2 9.9 0.346 311. 44
June 0.358 63.0 44.0 0.383 403 — 14

July 0.445 | 64.2 14.4 0 397 MA | — 14
Aug. 0.420 | 64.2 13.6 0.446 | 403 | — 18
Sept. 0.456 | 58.0 12.8 0.379 | 352 | + 31

Oct. 0.409 | 61.3 9.2 0.44 Di | == 2
Nov. 0.340 | 58.6 6.0 0.390 | 359 | + 20

Dec 0.349 | 56.5 | 2.9 0.494 | VY Ae Se
1870 Jan. 0.202 | 62.7 3.4 0.360 356 | + 19
Febr. 0.132 60.0 0.9 [0.290] | 344 + 29
March 0.280 | 61.6 | 3.9 0.408 | ABS W268
April 0.296 | 65.4 | 7.7 0.337 | 371 0

Ks

| | at. fat = a
| DR Ae hemp. BEND ap
ay era ee te ee
1870 May — 0.299 9.9 | — 0.349 | — 0-380 |
June 0.352 12: 0.363 383
July 0.457 14. 0.387 391
Aug. 0.536 14. 0.438 425
Sept. 0.341 11 0.379 352
Oct. 0 475 8 0.420 386
Nas 0.388 5. 0.407 376
nen 0.217 A [0.353] 366
4874 Jan. 0.167 0. 0.324 320
Febr. 0.414 2. 0.293 306
March 0.198 6.C 0.306 333
April 0.348 fie 0.363 397
May 0.250 9, O34 342
June 0.391 14. 0.348 368
July 0.458 14. 0.370 374
Aug. 0.427 15 0.381 368
Sept. 0.475 do 0.416 389
Oct. 0.357 yt 0.423 389
Nov. 0.309 3. 0.432 401
Dee 0.178 Zi 0.378 358
1872 Jan. 0.285 ER 0.320 316
Febr. 0.273 4; 0.366 379
March 0.294 5. 0.329 356
April 0.317 8. 0.330 304
May 0.344 9. 0.344 375
June 0.385 13,’ 0.337 357
July 0.400 15. 0.314 318
Aug. 0.430 14, 0.356 343
Sept. 0.464 13. 0.376 349
Oct. 0.430 8. 0.392 358
Nov. 0.417 6. 0. 405 374
Dec. 0.377 5. 0.354 334

( 202 )

Dn Bar, @ Temp lpt gn eG

1873 Jan. OEL oh TAD oe RLS Oos — 0.359 | + 1
Febr. 0.208 | 63.6 2.3. | 0.392 | 405 — 45
March | 0.29 | 575 | 48 | 0.304 331 | +. 29
April 0 263 | 59.8 Zep 0.304 sa be

May | 0.310 | 604 | 8.7 0.334 heee
June | 0.337 | 60.9 12.7 0 303 828 Ihr
Bd vo ss ELD 14.8 0.338 342 | 148
Mel 0.429 | 60.7 14.6 0.359 | 346 | + 14
Sept. | 0.406 60 5 (455 0.387 | 360 | 0
Ont) 0849641", 5820 9.7 0.403 560 ed
Nov. 05352))|-.59:2 5.9 0 412 381 | — A

Dee. 0.193 69.2 90 0 409 „80 —— ae
A874 Jan. 0.253 | 63.0 4.3 0 394 390 | — 30
Febr. | 0.480 63.8 aime} | 0.344 357 + 3
March | 0.168 | 658 5.5 0.327 304 | + 6
April | 0.275 59.0 8.5 | 0.287 321 | + 39

Before | undertook the further investigation of the reduced rates I *)
I tried to find out the relation of the rates below O° to those
above that temperature. It appeared that a systematic deviation of
the former is far less evident than it was in the period 1877—98. In
fact such a deviation shows itself clearly only in the two months
1870 February and December. Finally I excluded the days with tem-
peratures below O° only for these months and for 1864 December *).

The modified reduced rates I, together with the corresponding tem-

peratures, are as follows:

Temp. zede 1 Besl
1864 December + 2.4 == 02390
1870 February + 1.9 REE
December + 3.6 — (0 .386

') In comparing my values of the reduced rates I for the two first years with
those occurring in Katser’s papers, allowance must be made for the fact that my
values apply for a pressure of 760 Mm. at 0°, whereas those of Kaiser may be
assumed to apply for a barometer-height of 760 Mm. at +10’.

2) During 8 other months the deviations were small and variable in sign.

( 208 )

13. In the first place I have investigated in how far the non-pe-
riodie part of the rate, the constant @, has varied during the period
under consideration.

For this purpose I have combined the monthly means to yearly
means. They are as follows, the years beginning with May.

1862 — 03.316 1868 — 05.400
1865 309 1869 384
1864 „350 1870 368
1865 A21 1871 367
1866 436 1872 000
1867 428 1875 98

It is seen that the negative rate has somewhat increased in the
beginning and somewhat decreased afterwards and that it remained
nearly constant during the last four years.

With these values and the corresponding ones for years beginning
with August, November and February, I drew, in the same way as
was done for the period formerly considered, a curve representing
in a first approximation the change of @ with the time.

14. In the second place the influence of the temperature was
investigated. I tried to find out:

ist. In how far, if we assume a linear influence of the temper-
ature, the adopted temperature-coefficient applies for the whole of
the period ;

Ind whether there is any term varying as the square of the
temperature.

For the first investigation the several years were kept separate.
They were assumed to begin with February.

I used 1st. the deviations of the monthly means from their yearly
mean, 2"¢. the deviations of these same monthly means from the
values of a taken from the curve. In the third and fourth place
the computations were repeated using, not the monthly means them-
selves, but the mean value for the first month combined with the last,
that for the second combined with the last but one, ete. By this device
the influence of the “supplementary term” must be nearly completely
eliminated at the outset.

In this way I found for the correction of the adopted coefficient
—-0:.0174, the following four series of values; they are expressed
in tenthousandth parts of a second.

I Il I IV
BBE Ar En AAG TTG
REDE oe ete) ci 2 WON, V0 ig Dare ae 0
165. ETM Sate a ry aL nae
PEGG) Se Epes kp oe Sater
AS aha os Bern ean a ER
[eG si Ae Berens ag" hE Tagua flee eae
TAO ERE AE
ISnO her ALE OR vB ES
IS pdre OG) ht Oe VE
SRD or DO. NB Es TD De ED
187: NEI MEDE Me

The results of the four computations are nearly accordant. The
value of the temperature coefficient appears to have varied far less
than it did subsequently. A small fluctuation however, of the same
nature as that which existed afterwards, appears to have occurred.
It might be allowable to assume, in accordance with the second com-
putation, which in my opinion is to be preferred:

1863—66 Ac= aL 9) C = —.03:0165
iSo7— 71 Zy) EOS
187273 ope — 0.0148

From all the years together we should find

L3G3a— 13 Press = C= = 00175

The investigation about the existence of a quadratic term I only
executed for the mean of the 11 years.

For this purpose I used the deviations according to the second and
fourth computation.

If 4c, and c, represent the correction of the coefficient of #—t, and
the coefficient of (—t,)*, ¢, being the mean temperature (= + 8°.6 R.),
we have, expressing both in tenthousandth parts of the second as unit,

A C, Cy
2nd Comp. + 0.5 — 0.92
4th on — 6.2 — 0.43

At least for the mean of the 11 years, therefore, a quadratic term
must be quite insensible.

15. It seemed unnecessary to apply corrections to the reduced
rates I on account of the temperature coefficient, before proceeding to
the investigation of the supplementary term. For the mean value of

( 205 )

this coefficient all but
adopted and its fluctuations are certainly inconsiderable.
I made use of the deviations of the monthly means from the values
of a taken from the curve and I made the years begin with May.
For the sake of brevity I will only give the mean results for 4
groups, each of three years. In the last column the general means
are set down.

agrees absolutely with the value originally

62—64 | 65—67 | 68—70 | T1—73 1862 —1873
MAY f.5i +76) HM | +46; +99 + 48
PORE were: + 4) +29; + 9} + 30 + 18
duke ee +12; +20) — 9} +19 + 10
August .... — 20} — 3] — 58] — 5 — 22
September, — 26 | — 45 | —14| — 32 — 29
October...| — 52] — 47 | —40 | — 45 — 38
November.| — 10 | — 18] — 4[ — 55 — 22
December. | — 30} — 8] —17 | — 20 — 19
January...) — 9 | +1414} +14] + 1 + 5
February | — 2| — 22} +54/ — 8 + 5
March....| +18 {| + 6) +138); + 39 + 19
Apel, +46) +143] +13 | + 52 + 31

In each of the 4 partial results the supplementary inequality is quite
evident. Its amplitude is of the same order of magnitude as in the
period 1877—98. There appears to be no reason for assuming any
change in this amplitude during the 12 years 1862—74. I theretore
tried to represent the general means by a formula and it appeared
that a pretty satisfactory representation may be obtained by a
simple sine:

T— Apr. 23

Ag = + 08.0341 cos 2 x -
565
The sinusoïd corresponding to this formula, together with the
points given by the observation is represented in Fig. 4.
The differences between the observation and the curve, in thou-
sandth parts of the second, are as follows :
14

Proceedings Royal Acad, Amsterdam. Vol. V.

( 206 )

May + 17 Sept. — 2 Jan. + 9 -
June — 2 Oct. — 4 Febr. — 8
July + 6 Nov. + 9 March — 8
Aug. — 9 Dec. + 1 April — 3

The fact that the supplementary term can be represented by a
simple sinusoid and that a half-yearly inequality is not shown, agrees
with the result found a moment ago, that no term varying as the
square of the temperature is indicated *). Properly speaking the two
results are equivalent.

16. Finally I have again tried to clear the monthly means of the
rates, as well as possible, of all periodic terms. In doing this I have
applied no further corrections for the influence of the temperature
because the variation of its coefficient — the results of the years
1871 and 1873 are just those differing most considerably — did not
seem as yet sufficiently demonstrated.

No other reductions were applied, therefore, but those for the
supplementary term according to the formula found above.

The rates corrected in this way (= term a) have been inserted, in
the table already given, in the column Red. D. R. IL.

These values of the term a have been represented as well as
possible by a simple curve reproduced in Fig. 5.

In this figure the results of the observation are also shown, not
for every month separately, but for the mean of any three consecu-
tive months ®).

I have tried to draw this curve about as simply as that for the
period 1878—98. The outstanding differences O—C (C = curve)
are contained in the last column of the table.

These differences lead to the following mean amounts, which we
might consider as the mean errors of a monthly mean :

1862—1867 M. B. =>+ 05.0309
1868—1874 ‚0273

1) The remark made at the end of § 7, p. 23 (90) does not make sufficient
allowance for the fact that, as long as no physical explanation has been given for
the ‘supplementary term’, a variability of this term might be deemed no more
probable than the variability in the course of time of a term varying as the square
of the temperature.

2) On page 24 (91) I forgot to remark that the same was done in Fig. 3, which
represents the period 1878—1898,

( 207 )

whereas, if we had neglected the consideration of the supplementary
term, we should have found :

1862—1867 M. E. = + 05,0382
1868—1874 0377

which values are considerably greater.
IV. The period 1899—1902.

17. Since the time, 1898 December, that the clock Honwi 17

has been mounted in the niche of the pier of the 10-inch-refractor,
its rates are kept under constant control by computations which are
made, immediately after the time-determinations, by Mr. Hamersma,
computer at the observatory. He computes moreover mean values
of the rate at the end of every month, which are at once inserted
in graphical representations. The following investigation was founded
on these results only slightly modified.
‘The modification is the consequence of a small correction of the
barometer-readings caused by the fact that the temperature of the
clock is no longer the same as that of the barometer in the transit-
room. The barometer-readings were reduced therefore to what they
would have been at the former temperature *). As my investigation,
which includes no more than three years, must be considered as a
preliminary one, it seemed useless to replace the original mean rea-
dings by the mean values according to the barograph-diagrams. More-
over the constant correction of the barometer used was neglected.

As before the temperatures were determined from the readings of
the upper one of the two thermometers suspended in the clock ease.
The former thermometers had been replaced however by two other
ones having centigrade scales.

Besides the temperature in the niche below the eloekease has
been determined for the period of a year by means of a thermo-
graph of Ricnarp. It appeared that, even there, no trace of a daily
period in the temperature is noticeable.

In general the changes in the temperature have now become much
slower and much more regular. At the same time the temperature
in winter time does not nearly sink to so low a point as formerly ;
this is shown even in the monthly means. In the years now under con-
sideration the temperature in the clock case never sunk below + 2° C.
_ As was done for the other periods, | have computed the differences

1) The reduction amounted to 0.4 Mm, in maximo.

i?

( 208 )

between the upper and lower thermometer for this period after the clock
had been mounted in the niche. The monthly means of these differences,
resulting from the five hours of observation and from the three years
1899—1901, are as follows:

January —+ 0.02 July > 0.21
February + 0.01 August + 0.17
March + 0.01 September + 0.06
April + 0.02 October + 0.02
May + 0.05 November + 0.01
June + 0.15 December + 0.02

The differences are now expressed in degrees Celsius. The index-
errars of these thermometers are insensible.

18. The observed daily rates were originally reduced to 760 Mm.
and + 10°C. by means of the coefficients :

b= + 05.0140

In the following table, however, the Red. D. R. I. have been
computed, not with this value of the temperature coefficient, which
had originally been derived from only the first months, but with the
value

C= 00220

which accords better with the observations. The meaning of the
two last columns of the table will be explained hereafter.

The four months immediately following the mounting and the
regulation of the clock, during which the rate proved to be still some-
what variable, have been left out of consideration and have not
been inserted in the table.

| Obst | NE | foe: ‘| Redd Reda | Reda
AE: | DRI | DRT DR

| _ 0157 | —0'169

1899 May 0146 | 7632 | 4044.8 | — 040 en 2) eee
June 0.132 | 65.7 15.0 0.402 | 4-647 ee

July 0.192 | 65.4 18.4 0,090 | +45 A2 AE
Aug Je beau dee Dek A87 0.490 EE VET An
Sept. 0.353 | 59.4 16.0 0508 is ae

Oe Bar. | Temp.

1899 Oct. — 0.160 | 767.0 | 4+ 11.7
Nov. 0.156 67.4 146

Dec. 0.048 61.7 Rod

1900 Jan. 0.097 59.6 Soy
Febr. 0.158 52.8 5.4
March 0.058 61.4 GES
April 0.065 62.2 8.4

May 0.453 62.2 |

June 0.247 61.7 16.4

July 0.258 63.8 18.3
Aug. 0.328 62.8 18.2
Sept. 0.252 67.4. 16.5

Oct. 0.278 Ging 136

Nov. 0.255 | 58.4 10.2

Dec. — 0.129 61.2 8.8

1901 Jan. + 0.052 63.2 5.2
Febr. + 0.023 61.4 Sid
March — 0.098 ae 6.7
April 0.105 On 9.6

May 0.104 65.1 12.6
June 0.216 64.3 16.0

July 0.266 64.5 49:3
Aug. 0.286 645 19.2
Sept. 0.315 61.7 16.2

Oct. 0.266 61.7 13.5

Nov. 0.120 64.0 9.7

Dec. 0.185 56.5 7.3
1902 Jan. 0.070 62.8 ai,
Febr. 0,034 59.6 4.6
March 0.107 ay ae Dats
April 0.085 61.6 10.0

( 209 )

Redd
Dik

Redd
De. Ro

Ss
— 0.157

oe

-+-

+ +

1
13
13

Redd
D Rol

—0.169
eat
eG
+ 10
ze ad

Es:
wo @

|
—_—
ot

+ +

+ +

( 210°)

19. The reduced daily rates I of this table show at once and
with evidence the. presence of the supplementary term; for the rest
the rate of the clock in the present period appears to be a very
regular one. If, first of all, we combine the monthly means into 3
yearly means, from May to April, we find:

1899 — 0.5158
1900 . 156
1901 „157

There is no trace of a progressive change in the rate and for the
further investigation of the influenee of the temperature we may
simply use the deviations from the general mean = — 0.*157

If in the first place we assume that the influence of the temperature
is a linear one, we find

1st from the monthly means,

2nd from the means for two months sorahined in such a way that
the supplementary term is nearly completely eliminated, respectively :

¢ = — 0.50224
and — — 0. 0220
which values are practically identical with that used for the deter-
mination of the reduced daily rates I.

In the second place let us assume the existence of a term varying
as the square of the temperature. In this assumption we find,
proceeding in the same way as before, for the total influence of the
temperature: *)

— 0.°0253 (t—10°) + 000074 (t—10°)?
and — 0. 0247 (10°) + 0. 00069 (#—10°)?
respectively. We thus find for this period a quadratic term of appre-
ciable value. The difference between the two formulae is small;
I will definitively adopt the former.

20. It thus becomes necessary to use a quadratic formula in order
to clear the rates completely from the direct influence of the tem-
perature, as is required for the determination of the supplementary
inequality. We may, however, as well take the influence of the tem-
perature to be proportional to its first power and then consider the
remaining periodic part of the rate as “supplementary inequality”.

I have followed both ways. In the following table I have inserted,
first, the values found for the supplementary term in the first way,
giving the results of the three years separately, as well as in the
mean. These mean values are pretty well represented by the following
simple sine-formula:

1) The mean temperature of the 3 years was + 11°.6 C.

( 241 )

T—May 3
(OSS LO ens Dg ee
The last column of the table contains the differences between the
observation and the computation. Everything has been expressed in
thousandth parts of the second.

| 1899 1900 | 1901 | Mean 0.—C.

| ae
Mass + 52 + 26 + 55 + 44 — 2
ME kee + 65 + 30 ++ 19 + 38 + 3
MN sen ren + 58 + 17 + 12 + 29 + 14
August. + 22 — 40 — U — 14 — 5
September ..| — 45 — 54 — 42 — Al — 16
October..... — 48 — 54 — 41 — 48 — 4
November...| — 52 — 59 — 14 — 42 + 4
December... — 25 — 8 — Al — 25 + 10
January ....| — 44 dS — 7 — 5 + 10
February ...| — 20 + 36 — 17 0 — 9
VE Sic) serena — 2 + 15 + 32 + 15 — 16
ADRI Teas sh + 31 + 58 + 62 -+- 50 + 6

The mean monthly results of the observations, together with the
sinusoid by which they are represented, have been reproduced in
fig. 6.

In the second place we give, in the column O of the following
table, the values of the supplementary inequality which we find in
the mean, if we assume 00220 (t—10°) for the influence of the ,
temperature. These values are represented by a curve reproduced in
fig. 7. The column O.—C. of the table contains the deviations from
this curve.

Ch O.—C. 0. 0.—C.
May - 28 —12 Nov. — 55 6
June + 32 — 6 Des. — 21 + 2
July + 43 + 18 Jan. + 8 +7
Aug. -+ 1 0 Febr. + 22 +5
Sept. — 51 —11 ; March +20 —8
Oct. —63 + 2 April + 41 +5

As might have been expected, the curve shows clearly a half-
yearly inequality.

21. Finally IT have reduced the monthly means of the rates both,
by the linear temperatureformula with the curve of fig. 7, and by
the quadratic formula with the sinusoid of fig. 6. The rates, thus
reduced, have been inserted in the columns Red. D. R. II and Red.
D. R. III of the general table.

These columns do not contain the reduced rates themselves, but
their mean values, together with the deviations from the latter.

These deviations lead to a mean error of a monthly mean

Mo ae O20 21a
if we adopt the linear formula (Red. D. R. ID), and
ME 200218.

if we adopt the quadratic formula (Red. D. R. III).

The two methods of reduction thus lead to nearly the same degree
of agreement and a decision about the preference to be given to one
of the two Gannot, therefore, be derived from the monthly rates.

If no reduction for the supplementary inequality had been applied,
we should have found in the two cases :

ME = == 00422
+ (0 .0398.

The increase of the M. H. is still considerably greater than it is
for the other periods. The quadratic formula now leads to slightly
better results than the linear one; the difference is small, however.

|

Il

V. Amplitude of the oscillations of the pendulum in the
period 1878—1888.

22. As has been mentioned before, H. G. vAN DE SANDE BAKHUYZEN
caused a small mirror to be attached to the pendulum in 1877 5),
for the purpose of determining accurately the amplitude of the oscil-
lation by the aid ot the reflected image of a metallic wire placed
before a flame of petroleum. The image was projected on a divided
scale by means of a lens. 1 Mm. in the scale nearly corresponds to
0.'5 in the total amplitude; the reading could be made accurate to
tenths of the millimeter. In this way a determination of the amplitude
was made, generally 4 times a day, from 1878 April to 1899.

The determinations of the years 1878, 79 and 80 were elaborately
studied by H. G. vaN Dr SANDE BAKHUYZEN. The influence of the
temperature, of the atmospheric pressure and also that of the position
of the driving weight were thoroughly investigated. Having the inten-

1) See: Verslag van den staat der sterrenwacht te Leiden 1876—77 pag. 12,

(135

tion of prosecuting this investigation he did not yet publish his
results.

23. It seemed possible that the investigation of these amplitude-
observations might contribute to the discovery of an explanation
of the supplementary term found in the rates. I intended therefore
to inquire whether the corrected amplitudes too would still show a
yearly inequality.

As H. G. VAN DE SANDE BAKHUYZEN gave leave to take advantage
of his results for the present paper, his corrected amplitudes could
be compared at once with each other for the period 1878—80.
Furthermore I tried to execute a somewhat provisional investigation
for the eight following years. For these years the monthly means
of the amplitude found in a first approximation ') were corrected for
the influence of the atmospheric-pressure, as found by H. G. van
DE SANDE BAKHUYZEN. A correction for the temperature was not
so easily applied, because it appeared that its influence has conside-
rably increased in the course of the years. Finally I proceeded simply
in this way, that I derived the value of the amplitude for + 8° R.
for every spring and every. autumn by interpolations between monthly
means corrected for the barometer-reading.

The results have been brought together in the following table:

= | Spring. ree | Autumn. | A.—S.
(STS |. 377 38.22 39.71 + 1.49
1879 38.68 38.76 37.66 — 1.10
1880 98,8% 40.06 39 50 — 0.56
1881 4A 27 40.48 40.47 — 0.01
1882 39.70 39.18 39.19 + 0.01
1885 38.66 35.42 35.67 + 0.25
1884 32,19 30.70 29.22 — 1.48
1885 29,20 30.55 28,35 — 2.20
1886 31.90 82:30 32.33 + 0.05
1887 32,71 „1.86 31.68 — 0,18
1888 31.01

1) As many observations are wanting the corresponding values had to be assumed.

( 244 )

These results are expressed in millimeters of the scale and they
represent the total amplitude on that scale diminished by 320 Mm.

The 2ed and the 4% column contain the results obtained for the
spring and the autumn; the 3rd contains the means of two consecutive
results for the spring; the 5 the differences autumn — spring
obtained by substracting the numbers of the 3"4 column from those
in the 4%, The differences prove to be very small; their mean
amounts only to — 0,38 Mm. or, if we exclude 1878 on account of
a possible displacement of the lens, — 0.58 Mm., 7.e. —0’2 or
—0./3 respectively, whereas the effect of 1° R. is 0.’6 in the beginning
and about 1’ afterwards. Besides, the sign of the mean difference is
the reverse of what we should have found, when the amplitude of
the pendulum lags behind the temperature. Thus already this superficial
investigation seems to show, that there is no term in the amplitude
analogous to the supplementary term in the rates.

VI. Comparison of the results.

24. If we consider the results obtained in the preceding pages in their
mutual relation, we are struck in the first place by the fact that the

clock Honwt 17, which at present has been going for more than,

forty years, far from showing the defects of old age, has increased on
the contrary in regularity of rate in the course of the years. We
have seen that both in the period 1862—1874 and in that of 1878—
1898 the greatest regularity was only reached after some years. It
may be pointed out now that this regularity has also increased from
period to period.

For we found for the mean deviation of the monthly means from
a simple curve (1st and 2"d period) or from a constant value (3"4
period) the numbers:

1862—1874 + 0:.0291
1879—1896 "0237
1899— 1902 ‚0215

The diminution of the mean deviation is considerable and where-
as in the 34 period the amelioration in the clock’s position may have
contributed towards this diminution, the difference between the first and
the second is very striking. We have to consider in this connection
that, for the two former periods, a whole year at the beginning has
been left out of consideration, whereas for the third the 5t® month
has already been taken into account.

The only point in which the second period is at a disadvantage

(5 )

as compared to the first is that the influence of the temperature has
been more variable.

This however is mainly the case only for the last years, when, evi-
dently, the cleaning of the clock had been already too long deferred.

If we reduce the temperature-coefficient found for the third period
to what it becomes for 1° R. instead of for 1° C., if further we reduce the
mean coefficient of the first period to the value which would have
been found, had not the barometer-reading been reduced to 0°, and
if, lastly, we add the value found for the middle part of the second
period '), leaving the quadratic terms out of consideration throughout,
we find:

1862—1874 c = — 0:.0196
1885—1891 — 0.0269
1899—1902 — 0.0275

Between the 2nd and the 34 period the pendulum has not been
taken to pieces and only a small stain of rust has been removed
from the suspension-spring.

25. Let us now consider the results obtained for the supplemen-
tary inequality. Setting aside a half-yearly inequality, sometimes
shown, which is connected with the precise form of the influence
of the temperature, we find in all the periods a supplementary yearly
inequality in the rates which can be nearly represented by a simple
sinusoid having its maxima about May 1 and November I, the semi-
amplitude of which amounts to:

1862—1874 + 0:.0341

1878—1886 0455
1887—1896 ‚0254
1899—1902 0465

In the latter part of the period 1878—1898 the amplitude of the
supplementary inequality seems to have appreciably diminished so
that in the years 1897—1898 it is hardly sensible. For the rest
the amplitude of the inequality appears to have had nearly the same
amount under any circumstances.

The question now arises:

What explanation can be offered of this inequality ? If we consider
only the monthly rates, we may mathematically represent it as a
lagging behind of about half a month of the influence of the tem-
perature. This cannot be the true physical explanation, however,

1) See also the va'ues of ¢ for the 2nd period on p. 20 (87).

( 2146 3

because it appears from the rates during short periods, that abrupt
changes in the temperature are reflected almost immediately. Not-
withstanding this, I deemed it possible, at first, that the true expla-
nation might be found in such a cause, by assuming that part of the
effect of the temperature on the rate — perhaps by the intervention
of the elasticity of the suspension-spring, — is only felt after along
time. In this case however, we ought to find another and smaller
temperature-coefficient from swift changes in temperature than from
the comparison of summer- and winterrates. In reality, however, it
seems, that the coefficients obtained in the two ways agree in the
main, at least as far as can be judged now, before the completion
of a more elaborate investigation by Mr. WeepeRr.

Besides a change in the elasticity of the suspension-spring, lagging
behind the yearly change of temperature, has become improbable since
we found no trace of it in the amplitudes of the oscillations.

Another possible explanation might be found in the hypothesis that
the temperature of the different parts of the pendulum is permanently
unequal and that the distribution of temperature varies systematically
with the season, in such a way that it is not identical in the spring
and the autumn. The influence of a small inequality of the tempera-
ture is considerable. For if the temperature of the pendulum-rod changes
only by so much as 0°.1 R., whereas that of the mercury remains
constant, the daily rate changes by 05.065.

The differences between the readings of the upper and lower
thermometer in the clock-case must throw light on this distribution
of the temperature. The information however must be defective
1st. on account of the small accuracy of the thermometers, 2nd because
we do not know the relation existing between the temperature of the
steel and the mercury of the pendulum and that of the surrounding air.
If we consult the mean values of these differences of tem-
perature for the three periods, we see that in the two former the
difference: Upper temperature—Lower temperature has been really
found + 0°41 R. greater in April and May than in October and
November. This would produce a difference in the rate agreeing in
sign with that which is really found. In the Srd period, however,
spring and autumn agree nearly perfectly.

It seems to me still very uncertain, therefore, whether the cause
of the phenomenon in question may be found in this distribution of
the temperature. The fact that, whereas the clock was in very diffe-
rent circumstances, the inequality of the rate was very nearly constant
and also the fact that it seems to have diminished in the second period,
seem, even a priori, contrary to such a hypothesis.

+0:

+0050 x +0050
4o Lo
30 30
20 x 20
cae x 35 40
a,
2000 = = era 2000
a
zo a 1G J ai ca 0
20
20
o
3 jo
Ao
40
—O050
5 td

Fig. 4.

+0.050

pF. VAN DE SANDE BAKHUYZEN : „On the yearly periodicity of the rates of the standardclock of the observatory at Leyden. Hohwii Nr. 17”,

+eose LED EE : ne
AD x ze poke
Je el a= a ze
” x Aass 10
oer - = esse e000 -
poo eae Gr war hy ce 2 7 F 5 rn
ae A zo zo
fe fe Jo Je
é / 4e eoke
=e0so
Fig. 2. i
Fig. 4.
x
Fig. 1.
Be +0100
i = EK. EE RS 190
aro +2050 - tn
‘70 ko 5 ke
aa Se x 260 30 x
as 74 : ze x, ; ase zo
we En xe . d x kw zo fans
+0. ees do, ELN da AA] FL irr ES se 65 De gj a os Site Er PA eis
x 7 mo om J JANS DIT
5 ee 410 / zo
be — — = zee Jo
ve IE he
(Se had « 0850
4 rie
: ‘ io Fig. 6.
fx eso
i : Je
verte
Fig. 3.
~2,180 x aib
290
joo
die
gro
330
tho
350 0050
360 he
“ ne 30
190 zo
je zo
66 69 ze pie ne
ch ae bs Asa so
x hao zo
k x Aso 30
x 4ho ho
450 se
ra Abe -2060
x Ae
-0.480 Fig. 7.
Fig. 5.

Proceedings Royal Acad, Amsterdam. Vol. V.

CMA

And so as yet I feel unable to give a sufficient explanation of the
inequality which has been found.

EXPLANATION OF THE FIGURES.

Fig. 1. Supplementary inequality 1878— 1886.
2. ‘ 5 1887 — 1896.
» 9 Non-periodic part of the daily rate for + 8°.7 R. 1878—1898.
» 4. Supplementary inequality 1862—1874,
» 9. Non-periodic part of the daily rate for + 10° R. 1862—1874.
„ 6, Supplementary inequality 1899—1902.
„ 7. The same inequality if the influence of the temperature is assumed to
be linear.
In the Vig. 1,2,4,6,7 the letters D., J. etc. stand for: December 1, January 1, etc.
In the Fig. 3 and 5 the numbers: 78, 62 etc. stand for: 1878 June 15, 1862
June 15 etc.
In Fig. 5 for 79 read 69.

ERRATUM:

p. 47. Behind the title of the communication of Prof. J. W. van
WisHr is omitted :

(Communicated in the meeting of April 19, 1902).

(August 8, 1902).

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING

of Saturday September 27, 1902.

DC kt

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

Afdeeling van Zaterdag 27 September 1902, Dl. XI).

COT EEE AT LS:

A. H. Sirks: “On the advantage of metal-etching by means of the eleetrie current”. (Com-
municated by Prof. J. L. C. SCHROEDER VAN DER Kork), p. 219, (with one plate).
J. D. van per Waars: “On the conditions for the occurrence of a minimum critical temperature

for a ternary system”, p. 225.

W. H. Kersom: “Reduction of observation equations contaiaing more than one measured
quantity”. (Communieated by Prof. IT. KAMERLINGH Onyes), p. 236.

E. H. M. Beekman: “On the behaviour of disthene and of sillimanite at high temperature”.
(Communicated by Prof. J. L. C. SCHROEDER VAN DER Kok), p. 240, (with one plate).

L. II, Siertsema: “Measurements on the magnetic rotation of the plane of polarisation in
liquefi:d gases under atmospheric pressure. IT. Measurements with methylehloride”. (Communi-
euted by Vrof. H. Kameruixcu ONNES), p, 243. (with one plate).

H. Haca and C. WH. Wip: “Diffraction of Röntgen-Rays”, (2nd Communication), p. 247,
(with one plate).

H. A. Lorentz: “The fundamental equations for electromagnetic phenomena in ponderable
bodies, deduced from the theory of electrons”, p. 254.

E. F. van pr SANDE Bakuuyzen: “Preliminary investigation of the rate of the standard-
clock of the observatory at Leyden, Hohwü Nr. 17 after it was mounted in the niche of the
great pier”, p. 267.

The following papers were read:

Physics. — “On the advantage of metal-etching by means of the
electric current’. By Mr. A. H. Siks. (Communicated by
Prof. J. L. C. SCHROEDER VAN DER Kork).

(Communicated in the meeting of June 28, 1902).

Side by side with the tension- and bending-tests to which metals
and their alloys are submitted, with the object to find out, whether
the material answers to the requirements, Prof. BEHRENS gives, as a
new method: a miscroscopic examination, which is deservedly made

15
Proceedings Royal Acad. Amsterdam. Vol. V.

use of on a large scale. In a special work on the subject: “Das
mikroskopische Gefiige der Metalle und Legierungen,” this method
and the practical use made of it, is treated exhaustively. The main
substance of it is this:

A piece of the material, which is to be submitted to microscopie
examination is filed, till it is perfectly smooth, different numbers of
carborundum-powder being used for the grinding, after which it is
polished with tin-oxide or chrome-oxide, if a perfectly smooth slide
is required; then, by means of the annealing colours, the ground plane
will show a design, sharp-outlined. Since most metals and alloys
have crystal-formations at their fractures, the annealing colours will
produce a very strongly marked outline between the crystals and
the ground-mass, because it is a known fact, that two substances,
submitted to the same temperature, but of different formation (the
erystals- and the surrounding mother-water) will not take the same
tempering-colours. Next by making scratches on the surface, with
needles of known hardness (analogous with the known hardness-scale
of Mons) the hardness of the material may be fixed.

A similar design, not so minutely detailed however, may be called
forth by the corroding influence of acids, bases or salt-solutions,
which the crystals and the encompassing matter are not equally
proof against. For this purpose the rubbing and polishing need not
be done so carefully.

This method however has also its difficulties, which may often be
very troublesome. As is always the case, when an acid operates
upon a metal, also in this etching-process gas will be developed.
The. microscopically small gas-bubbles which are formed on the
slide will locally prevent the corroding process of the acid and be
the cause of little holes and dots that have nothing to do with the
design and may easily lead to faulty conclusions. The very long
time the grinding and polishing sometimes takes (I state here the
grinding of different species of iron and babbits) will keep many
from applying this method.

No satisfactory results, in some cases, being obtained oy this method,
although the material showed distinct crystals at its fracture. Prof.
SCHROEDER VAN DER KOLK was struck by the idea, whether it would not be
possible to etch metal-planes in another way than by corroding
through acids. It is a known fact that a metal in a galvanic cell
will corrode at its negative pole. I need only state the equally known
fact, that the zine of a bichromate cell, after the electric current is
set working, shows a magnificent structure. To forestall the objec-
tion, that the chromic-acid of the cell has been predominating here

wy AS,

( 221 )

in the etching-process, I will just remark that a slight experiment,
Le, by putting the zine into the fluid, without letting the cell give
a current, was sufficient to prove that the eteh-desien obtained in
the first case, stood out in much stronger relief than had been the
case, when exclusively applying acids.

As in any electrolytical process anions are formed which together
with the metal of the electrode may produce dissoluble salts,
it was important to find out what disturbing influence this would
have, and combine with it an examination into the practicability
of this etching method and see whether it could replace the
one of Prof. BerreNs, in case the results might be unsatisfactory.
The corroding influence of acids having to be avoided as much as
possible, preference has been given to use the electric current of a
battery instead of producing it within the apparatus itself, as happens
in any cell. The apparatus was constructed as simply as possible
and is exactly the same as that used for ordinary electrolytical
experiments.

The object that was to be etehed was used as anode (the place
where the electric current enters), whereas a piece of copper-plate
serves as cathode. The electric current was furnished by an accu-
mulator-battery, having a terminal voltage of 4 volts. In etching alloys
of copper, it proved recommendable, every time to connect two appa-
ratuses in series or in some other way to diminish the potential
difference, on account of the highly fleeey deposit on the cathode. As
electrolyte, water was used to which for every 100 em? + 6 drops
of diluted sulphuric-acid had been added, in the first place better to
conduct the electric current; in the second place, as much as possible,
to prevent the formation of base metal-deposits *). Of course a controll-
ing experiment was taken by hanging a second piece of the alloy, per-
fectly alike, in a fluid of which the percentage of acid was the same,
in order to be able to eliminate etching by the acid. I have prefer-
red to begin experimenting with copper-tin- and copper-zinc-alloys on
account of the sometimes beautiful results obtained by the rubbing
and polishing method.

In most cases I melted myself the alloys to be sure of the absence
of foreign substances, which may cause very great changes in structure.

The metal-slides were hung to a piece of copper-wire, but precau-
tions were taken that there was no contact between the wire and
the electrolyte, to be sure that the metal-plate, which had to be etched,
did its work as electrode. For half an hour the electrolysis went

1) In alloys containing lead (babbits, type-metal, ete.) the sulphuric-acid on
account of the indissolubleness of the sulphate of lead was replaced by nitric-acid.

15*

( 222: )

on so as to produce a sharply outlined design on the brass- and
bronze-slides.

That to no other cause any difference might be attributed, all slides
were finished off in exactly the same way as had been done for the
acid-etchings of Prof Brnrens; the etching standing out much stronger,
this soon proved to be entirely superfluous and so the slides were
filed only with a smooth-file. The first experiment was taken with a small
piece of cast-brass, which proved to be composed of 58.5 °/, of copper,
40.5 °/, of zine, also traces of lead and of tin being found. For half
an hour it was submitted to electrolysis, the density of the current
being + 2 amp. p. dM’. The result of this experiment is reproduced in
fig. 1. The indented structure is very distinctly visible, there being
in the slide besides a marked difference in colour between the crystal-
formation and the encompassing ground-mass. Bright yellow, the crystals
stand out from the enclosing mother-water.

When a second experiment was taken the same alloy was submitted to
electrolysis for 12 hours. Under the anode a glass-cup filled with
glycerine and with oxide of magnesium was placed to catch up the
erystals that might be hollowed out by electrolysis and which will be
caused to sink by their weight, for as was to be expected (a thing which
was proved by the experiment) the crystals having a higher percentage
of copper than the mother-water (in which zine prevails) will be better
proof against electrochemical influence and so in the end get isolated
and detached. The residue left in the glass-cup was washed out with
aleohol it being found that without this precaution the crystals, that
had got detached, easily corroded, leaving nothing behind but a green
powder; they were then dried in ether; the residue proved to contain
1.78 mG. metal-crystals. Although these crystals had not got loose
entirely intact, they were distinctly angular in form and showed facets.
Being submitted to electrolysis (I wish to thank Mr. Vermass for
his assistance in this) these crystals were found to contain 1.19 mG.
of copper, equal to a copper-percentage of 66.8°/,. Traces of lead were
found on the anode and proved to be PbO, but the quantity was
too small to permit weighing.

The second design is of a piece of plate-brass, of which the ground
slide is in my possession. Etching and colouring after perfect grinding
and polishing, had yielded no result. The result of half an hour’s
electrolysis with a current of the same density as with the first expe-
riment, and the same fluid as electrolyte, is shown in the adjoined photo-
gram. Also the effect of the mechanic treatment can be distinctly noticed.
Everywhere in the slide twin-erystals are to be found, which as
Prof. Brurens explains in his work, are apt to be formed in conse-

‘A ‘JOA ‘Wiepiajsury ‘peoy [edo ssurpasd01g

ik) 2 1OJ AZUOA te) Feil >
A To ee ML! ‘SSEIA-JSEN) 'T "SLA

*SSUAQ-0]®8] °G Sl]

‚uerrno orgoeje 944 Jo suvout Aq Suryogo-yezou JO oSeJULAPB AUF UO“ 'SHUIS 'H 'V

( 223 )

quence of the mechanic treatment to which the material has been
submitted. This slide was the first which was no longer ground
with carborundum-powder, but only filed.

The ordinary bronze for coining (see fig. 3) equally shows a struc-
ture in which the mechanic operation is visible, both in its crystal-
formation and in the position and direction of the crystals, where
the more or less flattened parts meet.

From a piece of cast-bronze of a connecting rod a thinnest possible
sheet was filed and polished; after heating, stuck on a slide-glass
and submitted to etching by electrolysis. A beautifully executed,
right-angled lace-work remained, very typical for bronze structures.
The encompassing matter of high tin-percentage had been etched
away; the crystals, rich in copper, had remained. From a piece of
heavily wrought phosphor-bronze, which had remained unaffected by
colouring, I have obtained a slide with such a strong relief, that
I have not succeeded in taking a photography of it. Also here even
the bare eye could see the right-angled structure. The arrangement
of the erystals was like that of tiles on a roof.

On account of the great practical use made of white-metal in the tech-
nical branches, I have experimented also with that. After half an hour
also here, intact cubes of alloy of tin and antimony outlined themselves;
also. here it was possible to go on etching very deep and without
much difficulty to detach the cubes, entirely intact from the alloy.
The little time left to me for the moment, necessitates my putting
off the analysis of those cubes till later.

Whereas at the beginning only copper-tin and copper-zine alloys
were etched, now also iron has been experimented with. The fact,
that it is fine-grained, that the etched facets easily oxidize, that base-
metal-deposits *) are apt to be formed, all that naturally causes
difficulties. The use made of salt-solutions, as electrolyte, to diminish
the internal resistance, has yielded no result worth mentioning
I have submitted to etching a piece of an iron-bar rolled square.
After a few hours the fibrous structure was distinctly visible
with the bare eye, both lengthways along the fibres and crosswise,
vertically on them. With some difficulty I succeeded in isolating
iron-slivers, which, if only collected in sufficient quantity, might be
analysed quantitatively. A socle of a gaspipe sawed through, showed
cubes in the profile: all the crystals having grouped themselves
in the rolling-direction. A piece of a steel angle-iron having
been submitted to the bending-test, yielded no other result as

1) For on account of the corroding influence of acids on iron and steel a very
small quantily of sulphuric-acid can be experimented with.

eee

yet, but the one that also here, just as with the piece of bar-iron,
the direction of the fibres could be seen with the bare eye, as well
as a very distinet difference between the drawn and the compressed fibre.

As to the structure and formation of the carbide crystals nothing
could be fixed at this first experiment, I do not doubt however,
but also here the results will be satisfactory.

Worth mentioning still is the etching of a cylinder-shaped piece of
cast-steel, which was submitted to electrolysis for 36 hours. Although
outwardly no etched design could be seen, a porous coat of + */, inch
of some iron-carbide appeared to be have been formed, which, coming
in contact with the air, was apt to oxidize, could be cut with a knife,
and in the incision glittered like metal. When analysed the iron-per-
centage proved to be 91'/, °/,.

The great results, obtained also here, are a stimulus to me, to
investigate this matter later more thoroughly.

Those experiments suggested to Prof. ScHROEDER VAN DER KOLK the
idea, whether crystals of minerals treated in this way, would show
a design. Considering the results, obtained with copper-alloys, a piece
of a copper-ore was used for the first experiment. After an hour,
also this material showed a distinct etch-design, which is probably
connected with a crystal formation. Not to be led away from my
subject, L will only just mention the phenomenon.

Before concluding, I will resume the advantages, gained by the
way indiceted.

Lely, Results having been obtained, where the ordinary grinding-
polishing- and eteh-methods had failed.

Quy The obtained preparations show a far more detailed design,
which stands out in much stronger relief than the ordinary etch-slide.

sly) Tt is not necessary to finish off the slides half so carefully,
as the tempering-method requires.

gele From different alloys erystals or fragmentary crystals have
been detached which permit of analysis and show remarkable
differences with the average percentage of the alloys.

The good results are a sufficient recommendation for practical
purposes, time may still be saved by connecting many apparatuses

( 295 )

in series, so as to be able to etch different slides at the same time.

To my opinion it will be possible with careful treatment (regulating
the power of the current and using different acids) in this way, from
all cast-metals and alloys, to detach the crystals, thus making it
possible to find out the quality and formation of the materials.

After I had concluded these preliminary experiments, it came to
my knowledge that the electric current had already been used as an
etching medium in the work called “Contribution a Vétude des
Alliages” edited by the Société d’ Encouragement de l'Industrie Nationale,
Mr. Crarey describes a method, successfully made use of by him
and which according to the added photograms, shows great resemblance
with our method. He namely used an ordinary Danrent-cell to
furnish the electric current and in it replaced zine by the alloy,
that has to be etched, made a short circuit of the cell and obtained
an etched design after having submitted the previously polished plane
for half an hour to electrolysis.

To my opinion however there are great objections here. For to
obtain a somewhat powerful current it is necessary to reduce the
inward resistance to a minimum, either by using larger electrodes or
by considerably increasing the acid-percentage of the electrolyte.
Especially with the etching of iron and steel the high percentage of
acid will be an unsurmountable obstacle. A second objection is the
impossibility, on account of that acid, to go on etching deep enough
to detach crystals, for the angles and ribs which will be laid open
by the etching-process will very soon dissolve again.

Before I conclude, I will here openly thank Prof. SCHROEDER VAN
DER Kork for his readiness in furnishing me all [ wanted, to render
this investigation possible.

The Hague, June 1902.

Physics. — “On the conditions for the occurrence of a minimum
critical temperature for a ternary system.” By Prof. J. D.
VAN DER WAALS.

Already in my “Molecular theory” [ have derived the condition
on which a binary system presents a minimum critical temperature
(Cont. II, p. 20). Starting from the form of the equation of state I
have assumed there, we namely find:

Biya =

( 296 9

where 7, represents the temperature, for which the maximum and
the minimum of the isothermal coincide. Discussing the conditions
of coexistence we have pointed out that the critical phenomena for
a binary system, though they are different from those which oceur
for a simple substance, yet in the case that the value of 7’. defined
by the above equation is a minimum, differ so slightly from those
for a simple substance that this equation has a sufficient degree of
approximation for the determination of the critical phenomena as we
may realize them experimentally. Also for a ternary system the
critical phenomena will differ from those for a simple substance,
and we may expect that the difference will even be more consider-
able than in the case of a binary system. Yet also for a ternary
system this difference will not be so great, that the conditions for
the existence of a minimum value of << will differ sensibly from
ery

the conditions for the existence of the minimum critical temperature
as it may be realized experimentally.

In order to find this condition for a binary system I have investig-

F Ay
ated in what circumstances Er taken as a function of wv, Can assume
x

a minimum value, and so I have discussed the equation:

Analogous to this we should have to discuss the following equa-
tions in order to find this condition for a ternary system:

Cry

d

and _"*—(),

At present however I will foliow another way, which leads us
more easily to our aim and which yields the results in such a
manner that they may he better surveyed.

If we write for a binary system:

a, (lay + 2a,,«(1—e) + a, 2? ey
b, (le)? + 26,, «(1—a) Hb, e?
then the solution of the equation:
(a,—A 6,) (1— 2)? + 2 (a,,—28,,) « (Le) + (a,—2 b,) a? = 0

A . ‘ F Ay d ,
vields that value of , for which -— assumes the given value 2. So
IX

we find:

ee ae is er (a AD) (4,4 b)
eee a, —Ab, (a,—A b,)? |

If:
(a,,—4 b,,)? — (a,—4 b,) (a,—2 b,) i 0,

v . . “ye
the quantity is complex. This cannot be the case if the value
th
nae 3 ° a, a, . fe ° .
of 2 lies between — and —. It can only occur if 2 is chosen either
), )
a, a,
smaller than — and — or greater than both these values.
) )
1 2

If 2 is chosen such that
Kie) (Hg SADE erheen OE A er ze AS
then this equation will yield the minimum value of 2. If we put in
this equation either:
qe

N a,
eS ont =
b, b,

then the first member will be negative. If we put:

then the sien of the first member will be the same as that of

Cc

. . . . “ye a .
(a, 26,)(a,—ab,). The second member is positive, if a is smaller

ia

a a, Hi
than — and also smaller than i Consequently a value of 4 must

a My

; : 3 In : ay Skee
exist for which (1) =O and for which therefore 5, assumes a mini-

)

&
: 4 a a vds AGE
mum value. This value lies between — and —; or if “<=
bs b, b, b,
Ge. a,
between — and —.
bi, b,

a a a
15 . 2 .
In the case that — is both greater than — and than —, the first
ia b, b,
2
member of equation (1) changes its sign in the same way, and the
value of 2 for which the first member vanishes, lies also between

O19 eine So ot yy ‘ : at
and — or if bn, between ; and . So for a minimum

) D b, dy 2 ia

( 228)

a a
Sorat 12 . ‘ . 12
value of à we have an > and for a maximum value dn
)
12 12

If 2 has the value of 2, also the following two equations hold:

0 A,,—And,,
lt a,—Anb,
and
ae se Qig—Am)
Ld a, Amb,
v xe
As must be positive because » must lie between O and 1,
eu

the sign of @,,—4,b,, is opposite to that of a,—Anb, and a,—Anb,. This
agrees with what we have deduced concerning the relative value of
1a
bi

We should have obtained the same results, if we had written the

Am and

relation @, = 2), in the following form:

—Ab,.}?
ne RAe AD a) ME
| (a,—Ab,)

a,—Ab,
In the ease that a,—db, is positive namely this equation cannot
be satisfied if the coefficient of «7 is positive; so if
(a,—Ab,) (a,—4b,) — (a,,—46,,)? > 9.
If the coefficient of 2? is zero, then this equation can only be
satisfied if we put:
(a,—4b,) (1—z) at (Oe) oa 0;

„On the other hand in the ease that ¢,—2, is negative this equation
cannot be satisfied if the coefficient of 2? is negative. This however
also yields:

(a, —Ab,) (a,—4b,) — (a,,—4b,,)° > 0.
If therefore we have the equation:
(a,—Ab,) (a, —ab,) — (a,,—Ab,,)* > 9
then the value of 2 must be either less than the minimum value of
Ay

At .
—~ or more than the maximum value.

dor

We must however distinguish between a minimum’ value of 4

EH
which occurs at positive value of iL and a minimum value of 2

tI bi

v&

. The former, which really

corresponding to a negative value of
ih

: : Qi, . a a
exists, requires that — is both smaller than — and than ~. The

ie 4 b,

(229 )

latter cannot of course be realized. Solving the equation
(a, —Ab,) (a, —Ab,) — (a,,—Ab,,)? = 0
we find:
pn boch) HM Nb
2(b, b, ay 2) 1
This equation can be satisfied by a mal value of À if

bb. (are de th, one ONE te Mt
ia Bee tds % 12 0.
4b, a ie b, 1 b, Ore b, Big >
a

a
: . ° : ye e sl as
This equation is certainly satisfied if — is both smaller than —

12 Ji

a : bo ;
and than —, but it may also be satisfied in other cases. Let us
b,
a, at a, .
assume that — > and ee pe If we then have:
BIE bb

12 12 2

My, ty a Ee bb, (a, GoNs
Wig b, b, Ds Ab,” b, b,

a minimum value of 2 occurs indeed, but in this ease it corresponds,

} ; ; 2
according to our previous observations, to a negative value of jae
5 SUH

We arrive at the same result starting from the equation of Cont. II p. 20.
For a ternary system we have, putting Ss
xy
(a, —ab, )(1—a«—y)? + (a, —2b,)x? + (a, —1b,)y? + 2(a,,—Ab,,)a(1-a-y) +
+ 2(a,,—4b,,)e(1 — «—y)+2(a,,—4b,,)ay = 0.
We may represent this by the sum of three squares:

(a,b) Gra )+(4,.—46, ,)a+ (do Mra

(a,—4b,)
—Ab »— Ab, .)(a,3;—40,5)) |?
v aren aa)" +y [ett Oreste he)
a, Jb a, —db,
ue a +
(a,,—4,,)*
(a,—Ab,) k —
a,—db,
| | Zeh ae
as) | “Va
—db
SN Sa ae ‘ Ser
: . a,—db, ( al ) (4,.— Ab)’
_ & ). —_—s———- _ SS
= ; a, — db,

In the case that a,—ab,>0 and (a,—ab,) (a,—Ad,) ) > (aa aD.)
this equation cannot be satisfied if the coefficient of y* is positive.
If this coefficient decreases to zero, then the equation is satisfied by
only one set of values for ez and y, namely by those values for

( 230 )

which both the other squares are equal to zero. If the coefficient
of y? is negative, then a locus exists (a conic section) which indicates
: - : Urn : : J
all mixtures for which 2=—” has the same value. If this locus is
xy

reduced to one point, as is the ease if the coefficient of y* vanishes,
then 2 is for that point a minimum, respectively a maximum. The
-minimum value of 2 satisfies therefore the equation:

5 25/, - ; ;

(a, —4b, (a, —4b,)—(4,,—4D, ,) $ (a, 4b, )(a, —b,)—_(a,, —4b,,)"|—

4 | (a Es

— f(a, —Ab,)(a,,—Ab,,)—(4,,—4,.)(4,,; —49, 5); = 9,

or | a, —Ab, , a,,—A),,,

4) a, —Ab, , a,,—Ab,, ing OAT en

dis —Âbiss %3—A4b,,, a, —Ab,

a,,—Ab,, |

a,,—4b,, ’

For the determination of rz and y we have moreover the equation :

(a, —ab,)(1—a—y) + (a,,—Ab,,)u + (a,,—6,,)y — 9
and the equation, which follows from the other square when it is
equated to zero.
Another way in which we might have reduced the equation
zy—Abx, = 0 to the sum of three squares, would have yielded the
following two equations for the determination of rv and y.

(a,,—Ab,,)(1—#—y)+(a, —Àb, )e+(a,,—2b,,)y = 9
and (a,,—Ab,,)(1—«—y)+(a,,—Ab,,)¢+(a, —Ab, )y = 0.
Eliminating 1—vr—y, « and y from these three equations in which
they. occur linearly, we find again equation (2).
In order to calculate « and y we may derive the following rela-
tions from these three equations.

lay = y
41, —4b,, : a,,;—Ab,,| |a,;—20,; , a,-—Ab, | |e —Àb, , a,,—4b,,|
| bee, é |
a, —ab, , obs zg Raabe s alb es a » a, = 2b, |:
or

1—w«-y D y
a, —Ab, , a,,—Ab,, © [Gan Abas » a,,—Ab,, eae VEE
a,,—A4b,,, a, —Ab, | la, —2b, , a,,—ab,,| la, abe » @,,—Ab,,
and

1—a—y es a y
Ass dbs ‚ a, —Aab, | [4s —ab, , aa Abal lage edn —4b,|

> |
ladi 5 as = bi; | B se ae ee

In order that 2 have a minimum value for positive values of w, y
and 1—w—y the following relations must hold:

eg!

ere Tet

( 281 )

a,—ab, > 0

a,—Âb, > Q
a,—Ab, Pee 0

(a,-—Âb,) (a, —Âb,) — (a,,—Ab,,)? > 0
(a, —Ab,) (a, —Ab,) — (a,,—Ab,,)? > 0
(a,—Ab,) (a, —Ab,) — (a,,—Ab,,)? > 0
(4,,—40,,) (4,;—40,;) war's (a, —4b,) (a,,—40,;) De, 0
(a,,—4b,,) (4,3 —40,;) — (a, —Ab,) (a,,—40,,) > 0
(@,,—A40, 5) (4,3 —40,;) — (a, —Ab,) (a,,—Ab,,) > 9,
and 2, must satisfy equation (2).

The first set of three inequalities indicates, that this value of 2
must be lower than that of the components. The second set indicates
that it must be lower than the minimum value of 4 for each of the
pairs of components of which the ternary system consists. The third
set must be fulfilled in order that 2, y and 1—a—y be positive.

2 ys a
Sn

2 1

a,

b,

a,
Tine

Let us assume Sand suppose that the values of
)

23 . 1
a, a i Gs,
— and — are higher than that of —
b, b, , 03

without deciding anything

1 . ann a a
about the relation between the values of the quantities 7 », and 5
)
1 2 3
According to our assumption the expression

(a,,—4 bi en A Bis) AT (a, —À b,) (a,,—A be)

a a et yt Je
is negative for A= and also for 4=—* and it is positive for
12 13
Cos > a, 5 e a >
IE aa and for 2 = Re: This is perhaps best illustrated by a graphical

)
23 1

a, 3
and

, ‚a
Here the points 12 and 13 represent the values of —* and
13 13

the parabolic curve passing through these points the value of

(aA b,,) (4,3—4 4,,)-
In the same way the points 23 and 1 represent the value of

a a d ’ :
i and of and the parabolie curve passing through these points
23 1

the value of

( 239 )

(a,—A b,) (a,,—4 b,,)-

These parabolae intersect between the points 13 and 23 and on

the right side of the point of intersection the first mentioned parabola
lies higher than the second mentioned; the expression under conside-
ration is there therefore positive.

The graphical representation of the expression

(a,,—4 Da) ian) Ni b) (a,,;—A Oa)

has the following shape:

pO Sain
from which we see in the same way that these parabolae intersect
between the points 13 and 23 and that this expression is positive for
higher values of A.
The third expression :
(a,,—A b,,) (a,;—A4 bs) — (a,—A bo) (a,, —2 0,,)

: ong . asta as a;
is positive for 2 equal to —,—,— and and, when equated to
ae ee ae b,
zero, it will in general not yield a real root; at least not between

12 and 3.
The graphical representation of this third expression has the

following form:

where the parabola passing through the points 13 and 23 lies every-
where higher than the other one. The first mentioned parabola would,
if there should exist roots, descend below the second one between the
points 13 and 23, and so the two roots would lie between those points.
But in this case also the third expression is positive above a certain

5 U: . .
value of 4 below ae Or both parabolae might also intersect on the

)
23

En.

left side of 12 and on the right side of 1. Also in this case this expression
is positive and even within broader limits.

In the case that a value of 2 for which the left hand member of
equation (2) vanishes, is higher than the value discussed for these
three expressions, a minimum value of 2 will exist, which represents
a really occurring minimum critical temperature. Let us write equation
(2) in the following form:

{(4,—4,) (a, Ab) — (an Ab) (a, —20,) (aA) — (a,,—26,,)3} —
—{(a,,—A b,,) (a,;—4 b,,) — (a,—2 b,) (a,, —4 Oasis

The first member is negative if we choose for the value of 2 either
the minimum value of 4 for the pair 1 and 2, or for the pair 1 and
3. We will denote these minimum values by (Ax), and (2,), 5-

On the other hand the first member is positive if we choose for 2a
value for which the expression, the square of which must be taken,
vanishes, — this holds however only in the case that the value or
this last root is lower than that of the quantities (4), and (amn),,. In
this case the equation (2) has a root which satisfies all the requirements
for a minimum value of 4 at positive values of 1—w—y, wv and y.

As an instance we choose the following numeric values:

ON Lea gS A GA Puna? eme PAN OS
Ee tk
b, b, bs Dis 4 beg 03
a=48, 0,=448, a,=3.872, a,,=4.2, ABT , a,,—3.4924
From this we find:
(Ain), = 2.933
(Gy = 9.969 2.
Gai =o bores
A value for 2< 2.933.... makes therefore the three following

expressions positive :
(a,—A b,) (a,—a b,) — (a,,—4 b,.)°
(a,—2 b,) (a,—A b,) — (4,,—4 Db)
and (a,—A b,) (a,—A b,) — (a,,—2 ba)
For the value of à for which the quantity:
(a,,—2 b,.) (a,,—4 6,,) — (a,—A b,) (4,,;—A bs)
is positive we find: A >> 2.884....
For the value for which the expression
(a,,—Ab,,) (a,,—46,,) — (a,—A46,) (a,,—A4,,)

is positive we find: 2 >> 2.855 and the last of the given expressions

. wie 4 5 7 - d,. al
is positive within the limits “~<“a<—.
bs b,

( 234 )

The value of 2 for which the equation (2) vanishes, lies therefore
between 2.884 ... and 2.933, and the shape of this equation
shows that it must le nearer to 2.933 than to 2.884. We find in
fact, Ant 29252.

With the aid of this value of 2, we may calculate the values of
AGES ane ee Hot Ue equations of p. 230. But if the degree
1—x—y Uy
of approximation with which 2, is determined is not high, the
coordinates of the point to which À, relates, are only known inac-
curately.

These coordinates however may be caleulated directly by means
of the following equations :

a,(1-w—y) FG tty a toll) Ha, ef, _5(1-w-y) Ha +a, Ui

ba U ub at+b,y vb (1-a-y) +3, ab, ef bisll-e-y) dbs Hbey

We obtain these equations when we determine the centre of the
ellipse |
Ary = A Dery

and when we eliminate the quantity 4 from the equations /’, = 0
and j’, = 0. So we find:

_ (a, — U, Ja it sij) de (a,,—«, ) y 2 (4,,— Pigs

bb) (le) + Ek dy + Uit, HP
Ak (a, —d,3) (1—«—y) + (4,,— “3 yy + (ais a y

TIE (1—«—y) En pre a y+ B b) y

Introducing the condition, that the centre lies on the ellipse itself

we get the given equations.

bb, ee b. +0,
In the case that 6,, = ——, b,,= Bs. and b,, =———

equations may be satisfied approximately, then the locus of the centres
is greatly simplified and may be written as follows:

(a,—a,,)(l—«—y) + (a, 2a, )u+(a 1s— 4 My ER

ich

bk
(a,—a,,)1 — &—Y) Ha, dp) (413 — 45) ¥
oi b,- 6,

It is therefore a straight line, at least in approximation. With the
given numeric values we find:

0, 6(1—a mil 280 +0, 2076 — 1,1(.1—x—y) +0,70762+0,528y

0,2 0,6

:
,
|
j
:
j
.

rrr. Tew ee VEE Lee

i]
en
—~
et
—

or
0,7 (l—w—y) - 1,5476 @ + 0,2948 me
With this simplification the determination of the coordinates comes
therefore to the same as the determination of the point of intersection
of a conic section, e.g.

a, (ley) Fat +O, .4,f1— ty) Jar day

b,(1i—a—y) + b,,u+b,5y RET ball —e—y) 4 De dban
with a given straight line.
In this case we find:

ee 1
EN 4 Et
y 1
and ste: =

In fact the given numeric values for «,, and a, were chosen such
that we might find simple values for the coordinates.

Because of the asymmetry round the mixture with minimum
critical temperature we might of course have expected that the centre
of the ellipses which vary with the temperature, would change its place.

For the theory of binary systems it was necessary to introduce
the quantity «,,, whose value we are not vet able to deduce from
the properties of the components. From the calculation of (2), by
means of the equation

(a,—Ab,) (a, —db,) om, (cs ibe =)

follows, that for substances with a minimum critical temperature

this quantity cannot be equal to Va, but that it must be less. If

it were equal to Ya, the equation would yield a value 2= 0.

ct TN
Moreover it would follow from a,4, = a,,° that = : zi would be
) ,
1 2

9
2

greater than an as 6,6, in any case will be probably less than d,,°.
ia

For the application of our theory on a ternary system therefore,
also knowledge of the quantities «,,, @,, and a,,, is required, which
however must be assumed to be known from the knowledge of
binary systems.

The theory of the ternary systems therefore does not require any
new data, above those of the theory of binary systems.

16

Proceedings Royal Acad. Amsterdam. Vol. V.

( 236 )

Physics. — W. H. Kensom. “Reduction of observation equations
containing more than one measured quantity.” (Supplement
N°. 4 to the Communications of the Physical Laboratory at
Leiden by Prof. H. KAMERLINGH ONNES).

(Communicated in the meeting of May 31, 1902).

§ 1. The most widely read text books on the theory of probabi-
lities and the method of least squares treat of the reduction of observation-
equations each of them containing one variable.

In physical measurements, however, we obtain equations between
different quantities each of which must be considered as liable to
an accidental error. This, for instance, occurs when we have measured
the pressure of a gas or a liquid at different volumes and temperatures,
and we want to deduce from the observations the equation which
represents the most probable relation between these quantities inves-
tigated. As in the literature on this subject I have not found a general
solution for such a case, it may be useful to give it here. *)

1) Literature on this subject:

Cras. H. Kummer. Reduction of observation equations which contain more than
one observed quantity. The Analyst. July, 1879 (Vol. VI, N°. 4).

[ have not been able to find this volume of the periodical in Holland.

Merriman. The Determination, by the Method of Least Squares, of the relation
between two variables, connected by the equation Y= AX-+ B, both variables
being liable to errors of observation. U. S. Coast and Geodetic Survey, Report
1890, p. 687. A Textbook on the Method of Least Squares, § 107.

Here an elegant solution of the problem is given for the case in which a
linear relation exists between the two measured quantities.

Jures Anprape. Sur la Méthode des moindres carrés. C. R. t. 122, p. 1400, 1896.

The author gives a solution for the case when:

yg CR yc tera Seeman lh Vie
in which ¢; and N; represent measured quantities, and a, b, c.... are to be
determined.

Ravensuear. The use of the Method of Least Squares in Physics. Nature,
March 21, 1901, p. 489.

The author, apparently not acquainted with the literature mentioned above, points
out that in treating equations between several measured quantities, we must make
allowance for the fact that each of these quantities has an error of observation,
and he gives a graphic solution for the case in which a linear relation exists
between two quantities, some supposition regarding the accuracy of the measure-
ments of each of those quantities being assumed.

K. Pearson. On Lines and Planes of Closest Fit to Systems of Points in Space.
Phil. mag. (6) Vol. 2, p. 559, Nov. 1901.

The author gives an elaborate essay on the lines and planes (if necessary m a
higher-dimensional space) which are such that the sum of the squares of the
perpendicular distances between a number of points not situated in a straight line
or a plane, and those lines or planes becomes as small as possible.

_—

§ 2. Suppose, we have measured some series of the quantities
L,M,N...., between which the following relation exists:

NP Ze ye Dn
where X, Y, Z.... are unknown quantities which we want to calculate.

We assume that the number of equations between the observed
quantities is larger than the number of unknown quantities, so that
we want to calculate the most probable values of X, Y,Z.... by
means of the method of least squares.

Let L,, M,, N,.... be a set of values belonging together, as yielded
by the observations,
l,,m,,n,.... the errors made in these observations,
DU > Mn, > M2n,.... the mean errors in those measurements ZL,
M,, N,...., which we assume to be known
before hand,
A,, Y,,4,-~-- & set of approximate values for X, Y,Z....
DE the corrections to be calculated, which must

be applied to those approximate values.
Each measurement gives then according to (1) an equation:
¢ oD

Bt Mm Nn). SPH Xe Krey Bee... = 4, (2)

where:
(37),
OL di, = Lr MS

x=X,,Y=Y...

my = aaa:

= ED ee
diel Me Eset a) TEAR

0

N
|

Fo=F(L
Yet zw, y,2.... must be chosen so that ')

Ee m,? n,?
1 dj | 1 . . . ©
= ( — dt rig ge ) Is a minimum. . . (3)

Ml Mm? Mn,

If now the coefficients Y, ,Z...., are known, what errors, /,, mn, 7

en
correspond to the observed quantities ,, .1/,,.V,...? It is evident
that various sets of quantities L, J/, V.... tay have given rise to
the same sets of quantities ce M,, N,...., and that those values of
L, M,N and hence of /,,m,,n, are the most probable for which

ba a n,? eel

GE | Gear ee INE

eS Wii ta Ny,

1 Koti auscu, Lehrbuch der praktischen Physik, p. 16 considers the equations:

Ub =f (AS BC nat Sraa)
“where r,s...., and often « are instrumental readings” and yet he determines
(see p. 11) A, B, C so that the sum of the squares of errors in u is as small as possible.

16%

while we have the relation:

Ll + Mm, + Non, +... = 9, = constant.
We then obtain /,, m,, n,...., from
—_+K LD, =0
h
m
K.M, =0
Mm,
Ny
EN SD
A
where :
pa Ny

Lm +M mm + Nm, ae
With this (3) becomes
7

Ss
Rand
Lm +M md Nm, Bat

If we define the weight of the observation equation by:

isa minimum . (4)

Sots iar = : = > oa
Lm, le de Mm, + ANG My een
then (4) is reduced to
+ 9, 4,° is a minimum,
and the equations for the determination of x, y, z....: become:
Zig, An, —0
= 9; ys 7, = 9
= 9; Z, ien: 0
or:
[og XX Je + [gp XV ly + [op XZ ]e...- + [op XP] = 0]
(pV¥X}e+l9Y¥V¥wity¥Ze...-+ fo ¥FI=% . (6)
[ZN Jo + [9ZV + [ZZ Je. HEE] = 0

where, according to the usual notation :
GAN = 9, Xt 9, XP +. Pa
ANT Ho, AE +9 XY gan VY;
if n stands for the number of observations.
We hence arrive at this very simple result, that from the equations
oe ay ee ee
Ar le ee

reduced to the linear form, the normal equations are deduced in the
same way as when the quantities /,, #,.... are directly derived

( 239 )

from the observations, if we accord the weight determined by equation
(5) to each of those observation equations *).

This treatment of the equations with several observed quantities
agrees with the solution for two measured quantities given by ANDRADE.
For the case that a linear relation exists between two measured quan-
tities this one is simpler than MeRrRIMAN’s solution.

§ 3. In the following way it is easily shown that the mean error
in the result is also found according to the usual rules, as applied
to equations with one measured quantity. From the normal equations
(6) we find

Ro te! le ea Parse a, Fn

Here zv is expressed as a function of the measured quantities
OE ER © nal! APU feral

The mean error in « is obtained from:

1) For the equations, which Scraukwijk used (Comm. Nr, 70, Continued, Pro-
ceedings June 1901; Thesis for the Doctorate, p. 115) viz.

PV,,—1.07323 = Bg,,(d—0.93177) +- Cs,,(d?— 0.868),
1
where P and Vas have been measured, BS, and C's, are to be calculated

according to the method of least squares, we find from (5) the weizht of each
observation equation:

Oe 1

aero NA AE DE TAR TLE 2
{la fs 1 y loo ("py i dE eb log | Bs, ,d oO Sy d ) U,
if Ey, and Ld, respectively represent the mean relative error in the pressure- and

density measurement, and py the mean relative error for a measurement to which

‘ : 5 1 3
the weight 1 is assigned. If we put bi, = Ba, = Ko (= —~—), then if:

10000
5 1
d= 6.2394: g—=-—,
: 2.23
== 55.988: = :
0) === aay . TE

The terms with d will have little influence in the value for g, as long as d does
not become very large, as appears a priori from the fact that the coefficients
BS, and CS, are small. (Comp. Semarkwik’s Thesis for the Doctorate p. 115,
where he gives: BS, 0.0006671, Cs, 0.00000099%), In this case errors of
observation in d will have little influence on the second member, and this second
member may be considered as precisely known. As the values of PV, differ com-
paratively little for the different densities at which the observations are made, an
equal weight has been assigned to each observation equation. This is the more
justified if we consider that he was able to measure the higher pressures with
greater precision than the lower, as in the former in adding the measured lengths
of each column of mercury the accidental errors partly neutralise each other,

( 240 )

My — a? D,?m)3 —+ aM °m, J al,’ 1 eee GeO ea Hae De Tete Se Ns

. . . . Ld hd e e . . .

ae Ton bj act
or ME zes een

This form is the same as that obtained in equations with one
measured quantify"), so that here also the weight of the result is
found from the coefficients, which occur in the solution for ., U, Een
if the quantities |yX./,| ete. in the normal equations are left unde-
termined.

Mineralogy. — “On the behaviour of disthene and of sillimanite at
high temperature.” By E. H. M. Berkman. (Communicated by
Prof. SCHROEDER VAN DER Kork).

In nature occur three varieties of aluminium-silicate (Al, Si O,)
Le. disthene, andalusite and sillimanite. Sillimanite and andalusite
are orthorombic; disthene however triclinic. So the two first show
parallel, the last oblique extinction.

According to the experiments made by VurNapsky*), disthene is
said to turn into sillimanite, at about 1350 degrees; the same tem-
perature is said to turn also andalusite into sillimanite. As a proof
that they had actually become sillimanite, he urged that, whereas
before being heated, their hardness and specific gravity differed,
they now showed the same. Moreover the extinction of disthene
had become parallel.

The results to which he came are these:

RE eenen
| S.G. before S.G.

Name. | heating. (after heating.
Frets : 3.045 :
Sillimanite | 3 986 id.

| pe

5. Se BEAD
Disthene 3 AB | 3 90

|
Andalusite DES 3.165

Directed by Prof. SCHROEDER van DER Kork, I experimented, as
stated by VRRNADSKY, and came to the following results, as to their
specifie gravity:

1) See for instance Merriman, Method of least Squares, p. p. 83 and 84.
*) See Bulletin de la Société Min. de France (1889 et 1890),

( 241 j

S.G. before S.G
Name. : :
En heating {after heating.
En ; 5152 hay
Sillimanite Sonne EEE
|
CY Vl — 2 OA
Disthene 3 a ane
; 345 3.14
Andalusite dee ep

To determine the specifie gravity, I made, as much as possible,
use of the floating method. The fluids I used were methyl-iodide
(spec. gr. 351) and acetylenetetrabromide (spec. grav. 2.84). The
instrument I used to fix these spee. grav. was the “Westphal-balance’’,
except when the fluids were too light, in which case I made use of
a xylolareometer.

Consequently the results, as shown above, are pretty much the
same, as those of VERNADSKY.

The extinction of disthene, after the heating, had become parallel
also, however before the melting temperature of copper (1100 degr.
C.) had been reached.

What is a strong argument against the change of disthene into
sillimanite is its index, which I fixed in a way, indicated by Prof.
SCHROEDER VAN DER Kork, i.e. by using fluids of which the refractive
index is known). They were: methyl-iodide (#2 = 1.74); monobro-
mine-naphtaline (2 == 1.66); monochlorine-naphtaline (2 = 1.64);
mono-iodine-benzol (n = 1.62) and mixtures of them. The index of
those fluids, I have fixed by using a Pulfrich with changeable
refracting angle.

Thus I could fix the index of very small pieces and moreover
acquire a precision up to the second decimal.

I have fixed the index only in the direction of the c-axis. The,
double refraction not being great, this was sufficient. That index is
the greatest, since in sillimanite, the ellipse of intersection, with the
indicatrix, has its long axis in the direction of the c-axis.

Before the heating process, the index of sillimanite was 1.68.
Heating did not in the least affect it.

Andalusite remains equally unaffected by it, it has an index of 1.64.

1) See „Tabellen zur Mikroskopischen Bestimmung der mineralien nach ihrem
Brechungsindex” by Dr, J. L, C, SCHROEDER VAN DER Kork.

( 249 j

The highest temperature to which IT have submitted my materials,
was acquired by blowing into an open Bunsen flame with an artificial
blowpipe-apparatus. ) The very small splinters of the mineral can
be thus brought to a very high temperature probably to 2000° Jh
A platinum wire of '/, mM. at once melted in it.

As investigation material for disthene, I used the blue variety
(find-place Gängerhausen). Before the heating, the index was 1.73
and after it (I experimented in the way just described), it sank to 1.62;
so far below that of sillimanite.

If disthene had actually turned into sillimanite, it should have
kept its index (1.68); sillimanite submitted to the same temperature,
not changing its index in the least. So this shows that heating does
not turn disthene into sillimanite. i

To try whether 1300’ would bring the index to 1.68, I pro-
ceeded thus:

I took several earthen mugs, put in each a piece of disthene together
with other metals of which the melting temperatures are known,
heated the metals to a temperature that would keep them for a moment
in melting condition and thus obtaining constant temperatures, I could
fix the indices of disthene, which proved to be gradually lower. Lower
than 1.62, it could not be reduced, in spite of continued heating.
On the subjoined diagram, the different temperatures and indices are
stated. On one of the axes are the indices, on the other the degrees
from hundred to hundred. The line starting from 1.68, running
parallel with the axis of the temperatures, represents the direction
of the index of sillimanite. That line remained constant. The broken
line marks the direction of the index of disthene. They cut each other,
as will be seen, at about 1250? C.

The deviation in silver is probably caused, either by the not absolutely
accurate melting temperature or by a slight inaccuracy in the index.

The reason of it is probably that we have a mixture of materials
of which one more and more prevails; what pleads for this, is the
erowing intransparency of disthene, a fact noticed also by VurNapsky.

At a degree of 1.62 disthene grows entirely opaque, consequently,
it has got entirely amalgamated with the other material.

Of course this argument is open to discussion, but up to now, I
have not been able to find a better one. This phenomenon, may
be of some practical usefulness in making maxim-pyrometers, since
it proves that a constant index may be obtained by heating to a certain
temperature.

1) To be had at Atrmann’s in Berlin,

ot

4g

bY

"A JOA “urepaogsuy ‘peoy [eAoy ssutps0001g

‘soinjetadwia} JO SIXV

Pl fey 9/

EIND

£/ 7/ €/

Y/ 1 o/ / 8 i 9 c 4 € ay /

emngezoduer ys qe oyrwewrjis Jo pue ouougsip Jo Anoraeyoq oy} UO“ “ZK NVWMGad NH a

Axis of indices,

( 243 )

Physics. — “Measurements on the magnetic rotation of the plane
of polarisation in liquefied gases under atmospheric pressure.

Il. Measurements with methylehloride? by Dr. L. H. Siertsema.

0

(Communication n°. 80 from the Physical Laboratory at Leiden,

by Prof. H. KaAMERLINGH ONNES).

(Communicated in the meeting of June 28, 1902).

0

I. In a previous communication n°. 577) an apparatus for the
measurement of the magnetic rotation in liquefied gases under atmos-
pherie pressure was described and a few results with methyl chloride
were given. Further measurements with this apparatus have not
fulfilled my expectations, so that it appeared to be necessary to make
considerable modifications.

In the first place it was difficult to insulate the apparatus properly
from heat. It had been packed in cotton-wool, yet if was not easy
to obtain a perfectly quiet liquid, entirely free from rising bubbles.
The pressure of as many as six glass-plates between the nicols was
also very disturbing, owing to thei depolarising influence. This was
more noticeable after filling the apparatus when tensions appeared
to arise in the plates, in contact with the eold liquid, which often
rendered adjustment quite impossible.

To remedy this defect the nicols were immersed in the cold
liquid in the tube marked / of the plate in the previous commu-
nieation. The nicols were lying loose in this tube and were connected
by a brass wire, running along the outside of the tube. One of
the nicols could revolve in its holder and could be adjusted at a
given angle before the apparatus was closed. The rotation for different
wave-lengths could then be found by measuring the intensity of the
current required to bring the dark band in the speetrum to that
wave-length. The apparatus being arranged in this manner some
measurements could be made with it, but always after some time
the nicols appeared to have lost their transparency, either because
the layer of canada-balsam was dissolved or became laminated.
Nieols with a layer of linseed oil instead of canada-balsam lasted
longer, and the layer seems not to dissolve so easily, but in the
long run these too lose their transparency, perhaps in consequence
of irregular deformation of the calespar by the sudden and intense
cold of the liquid gas.

2. Then a new apparatus was constructed, in which also the

1) Proceedings Royal Acad. of Sciences. May 1900,

(944)

first mentioned difficulty was overcome, and with which some
satisfactory measurements of the magnetic rotation dispersion in
liquid methyl chloride have been made.

In this apparatus, shown in fig. 1, the experimental tube D and
the nicols C are enclosed in a brass jacket A with double walls,
filled with liquid methyl chloride, insulated from the heat of the coil
by a layer of wool. The space within the jacket is closed on either
side by the ebonite caps .V of the previous apparatus, with the
india-rubber rings O as packing-washers and 6 tightening rods. In
these caps the glass plates B are fixed with the serew-rings P, and
thin india-rubber leaf as packing. The other nuts and rings connected
with them have remained unchanged.

The circulation of liquid methylehloride through the jacket is
obtained from the cryogenic laboratory, where a connection with
the methyl chloride reservoir with its Compression pump can be
made 5. The liquid is supplied through a high pressure cock /,
(see fig. 2) while the escaping vapour streams back to the cryogenic
laboratory through the tubes AA. A float / enables us to know
at any time whether the jacket is filled.

The experimental tube D consists of a glass tube of 35 ¢.m. having
an opening G in the middle and closed by two glass plates 1 m.m.
thick, fastened to it by means of fish glue. The nicols C, rotating in
elastic brass rings, are mounted on either side. It is true that now
there is glass between the nicols, and the unfavourable influence of
this makes itself felt, however to a much smaller extent, so that
adjustments can be now made.

The apparatus is filled through a steel capillary MH, passing through
an india rubber stopper in an aperture in the jacket and entering
the testing tube.

The methyl chloride required to fill it is obtained by distilling the
commercial article, which has been once distilled already, onee more,
the vapour passing through a drying tube into a spiral immersed in
a reservoir of liquid methyl chloride under atmospheric pressure,
supplied by the same tubes which were used for the liquid in the
jacket deseribed.

Liquid methyl chloride flows from this spiral through the steel
capillary HZ connected with it, into the experimental tube under
atmospheric pressure and hence having the same temperature as the
jacket and the space within. The tube // to which a piece of india
rubber tubing is connected, serves to remove the vapour formed

1) Comp, Communication N°, 14, These Proceedings, Dec. 1894,

( 245 j

inside the jacket. This arrangement proved very satisfactory, the
liquid in the testing tube is perfectly quiet and free from bubbles
of vapour.

At first the space round the nicols formed one continuous space
with that round the testing tube, and so the nicols were also sur-
rounded with an atmosphere of methyl chloride vapour. In conse-
quence of this, vapour still condensed on the nicols and accurate
adjustments could not be made. In order to avoid this the spaces
round the nicols have been separated from that round the testing
tube by the brass rings £, fastened on the testing tube by means of
sealing wax and closed by means of india rubber rings on the jacket.
As at the low temperature a considerable decrease of pressure is to
be expected in the imperfectly closed nicol spaces, the caps V have
been pierced by copper tubes MZ, connected to U-tubes with narrow
openings and filled with pieces of sodium hydroxide.

Before closing the apparatus, the nicols have been adjusted at a
given angle by fastening to one of them a long bent copper-wire,
the end of which could be moved over a divided scale. This adjust-
ment is not accurate and no use has been made of this angle in the
ealeulation of the results, the rotations having been compared with
those in water.

The rotation at different wave-lengths is again obtained by varying
the strength of the current, by doing which, the dark band can be
caused to move over the whole spectrum.

The optical and magnetical part is almost the same as that de-
seribed in the previous communication, except that for the measure-
ment of the current we have again used a pb’ ARsonvAL-galvanometer
with shunt (comp. Comm. Suppl. 1 p. 25, Arch. Néerl, (2) 2 p. 305).
3y comparing it with a Weston-millivolimeter it is found that the
sensibility of the galvanometer is constant within the limits we had
to fix for the accuracy.

Fig. 2 gives a general survey of the apparatus used. C represents
an are lamp, ZB Arons-LumMMER’s mereury electric lamp, A a colli-
mator, ) a water reservoir, P? a prism and Q a telescope on a
circle from MryersrriN. Further G represents the coil with the
methyl chloride apparatus, 47 the cock, by which the supply of liquid
methyl chloride for the jacket is regulated.

The arrangements for regulating the current and measurement,
with resistances and switches, are similar to those for the experi-
ment on the magnetic rotation in gases *).

') Comm. Leiden Suppl. 1 p. 25; Arch. Néerl. (2) 2 p. 315.

( 246 )

3. For the measurements with methyl chloride of which the results
are given below, the nicols were adjusted at an angle of 11 degrees
from the crossed position.

The dark band moved from one end of the spectrum to the other
as the strength of the current varied from 20 to 60 amp. The
observations were made with the electric are light and the calibration
of the spectrum was obtained during the measurements by the
brightest mereury lines, while the dispersion curve of the prism had
been determined by means of sunlight. At each strength of the
current three adjustments of the dark band were made and the
means have been taken of the three pairs of readings of the galvano-
meter and the cirele. Table 2 gives the galvanometer defections a
so obtained, together with the wave-lengths 2 of the position of the
dark band in the spectrum.

Then on a subsequent day the testing tube was filled with water
and the other parts of the apparatus remounted entirely unchanged.
The dark band reappeared at strengths of the current deviating little
from those found before, from which we could derive immediately
that the rotation constants of liquid methyl chloride differed little
from those of water. Thus the numbers of table 1 have been found,
where « and 2 have the same meaning as they had before, and 7
stands for the rotation constants in water. The latter have been
derived from my measurements of communication n°. 73 '), and from
them ar has been caleulated, which quantity must be constant for
all values of 7, as it is equal to the rotation angle divided by the
magnetic potential difference at the ends of the testing tube, and by
the reduction factor of the galvanometer with its shunt.

TABLE 1.

|

en iS r | ar
!
|

el

|
935 | 588 ‘0.01307 | 3.071
KOOI =o jeia | 3 062
908.51 Dok 4487 3.100

mean 3,078

The mean value of ar, being 3.078, now served to derive the
rotation constants @ of the methyl chloride from the a found. These
2 . pe 1: EE m7

values of @ have been plotted in a curve, from which ep = 001572

1) Arch. Néerl. (2) 6 p. 825 (1901).

zl FSR

|

wy

Lalita

Proceedin

H, SIERTSEMA. „Measurements on the magnetic rotation of the plane of polarisation in liquefied gases Ki gy a.
de under atmospheric pressure. II. Measurements with methyl chloride.

| Proceedings Royal Acad, Amsterdam. Vol, V.
|

is derived and the values e/ep have been caleulated finally, which
values determine the dispersion of the magnetic gases. These different
numbers are combined in table 2, while fig. 8 shows graphically
the values of o/ep.

TABLE 2,

4 | 4 | Q | elen} 4 A e | o/ep
112 490 |0.02748 | 2.003 | 214.5] 575 |0.01455 | 4.061
116 131 2653 | 1.835 | 216 579 | 4425 | 1.039
194 AAG 482 | 1 810 919.5 583 1402 1.092
130.5 | 458 9358 | 1.719 [589] | [1372]} 4 000
165 5LO 1865 | 1.360 EN 599 tara be 0 971
166 59, 185% 1301 2390 G04 | TOU |e Oe Gas
476.5 | 597 1744 | 1.971 | 237 60% 1299 | 0.947
184.5 | “536 1668 | 4.216 | 49.5 | 616 1234 | 0.899
189.5 | 543 | ac lass | 950 | car | 42931 | 0.898
196.5 | 554 1566 | 4.142 | 273 | 643 1127 | 0.822
196 555 1570 | 1.445 | 283 659 1089 | 0.794%

In this calculation the rotation in the glass plates has been neglected.
A simple calculation shows us that this is permissible ; for it should
be remembered that this is done both for the measurements with
methyl chloride and with water.

As the result of this research I find that the magnetic rotation
constant for liquid methyl chloride under atmospheric pressure for
sodium light is 001872, and that the rotation dispersion is normal,
deviating little from that with gases and with water.

The research will be continued with other gases.

Physics. — “Diffraction of Röntgen-Rays”” By Prof. H.- Haga

and Dr. CG. H. Winxp; second communication.

In the March meeting 1899 we stated as the result of our expe-
riments that Réntgen-rays show diffraction; with these experiments
the rays passing through a narrow slit first fell on a second wedge-
shaped slit, then on a photographic plate. The image proved not

( 248 )-

to be what was to be expected with rectilinear propagation but
presented broadenings from which an estimation could be derived
concerning the value of the wave-length which proved to be of the
order of 0,1 u u.

In September of last year in one of the meetings of the “Deutsche
Naturforscher Versammlung” at Hamburg Dr.W arrer') protested against
those experiments; he had arranged his experiments in entirely the
same way as we had; moreover he had taken still greater precautions
to get a steady mounting of the slits and the photographic plate and
he had used stronger Röntgen-rays. WaLrer obtained images quite
similar to the second slit and attributed our broadenings to inac-
curacies of the photografic plate brought about by long development.

These negative results gave rise to a renewed investigation on our
side, now that we had greater means at our service than three years
ago. We have succeeded in obtaining more clearly than before
phenomena of diffraction, so that according to us one can no more
doubt the character of Réntgen-rays to be that of disturbances in
the ether.

The method of investigation has not changed in principle, but
making use of the experience obtained by Dr. Warrrr and ourselves
we have been able to make improvements still in some respects.

On the upper surface width 5.5 em. of an iron beam of I-shaped
profile, long 2m. and high 12.5 em. three pieces of angle-iron were
screwed down, one at the end, the two others 75 em. and 150 cm.
distant from it, the edge perpendicular on the length of the beam and
the side of 3.5 em. erect; in the figure the two first pieces of angle-

iron are visible; against the vertical sides brass plates — 12 em.
high, 10 em. wide and 4 mm. thick — were screwed. In the

middle of plate I was the first slit, in the middle of plate II the
wedge-shaped diffraction slit while against the third plate in a
black envelope the photographic plate was clamped’). During the
experiments the second and the third of these brass plates were enclosed
in an oblong leaden case, which had to prevent the secondary
Öntgen-rays or rays diffused by the air, from affecting the photo-
graphie plate and causing a fog.

The iron beam was fastened by means of plaster of Paris on
two free-stone plates borne by free-stone columns ; the columns were
placed on a firm pillar; on this same pillar, likewise on a free-stone
plate borne by a stone column, was the Réntgen-tube in a large leaden

1) B. Warrer, Physik. Zeitschrift 3. p. 137, 1902.

*) Scuteussner’s “Röntgenplatten” were used.

H. HAGA and C. H. WIND. „Diffraction of Röntgen-Rays.”
(Second Communication).

r
.

Proceedings Royal Acad. Amsterdam. Vol. \

ven

=
se PA:

:

i.

CURL UE OL
COR

riA Aa
rite

( 249 )

case (thickness of the side 2 mm.); only the back of this case was
left open for the connecting wires of the induction coil, whilst in the
front a small aperture was made opposite the first slit to let the
Röntgen-rays pass. The first slit was formed by two platina plates,
thick 2 mm. and high 2 cM; a leaden sereen left but the middle of
it free over a height of 4 mm.; the width of this slit was 15 u.
The diffraction slit was formed by two platina plates thick */, mm.,
high 4 em., tapering at the upper end from a width of 25 u to
nearly zero at the other. Greatest care was given to the grinding of
the platina plates. For these slits, just as in our former experiments,
the sides were everywhere equally thick and not ground wedge-shaped
at the edge of the slit as is the case with slits for light-experiments.

To produce the Röntgen-rays an induction coil of Siemens and
Harskr was used with a sparklength of 60 em, a primary with 4
coils and a Weanevr-interruptor. The current was furnished by a
battery of accumulators of 110 Volt. The newest Röntgen-tubes of
Mitimr (Hamburg), were exclusively used; the anticathode being
kept cool by water.

More care than formerly was taken to bring the passages of the
two slits accurately into the same line. Peculiar difficulties are incident
to this, which is a result of the extraordinarily great depth of the
slits together with a width so slight that common light, on account
of the arising phenomena of diffraction, cannot be used to fix accurately
the direction of the passage. For this last reason we had to have
recourse to Röntgen-rays to do so. And here again the slight width
of the slits caused the pencils of rays passing through them to be so
very faint, that in the ease of the jist slit, wide 15 u, they could
be observed on a fluorescent sereen at the place where it was
necessary, namely near the second slit only with an eye accustomed
to complete darkness. The pencil of rays, allowed to pass through the
most interesting part of the second slit viz. that part, where the width
was about 5 u, could be observed not even by this way, but only by
the impression it made on a sensitive plate after a lengthy exposure
(4 hours). In order to deduce from this impression a mark for the
direction of the passage of the second slit, a small strip of brass was
fastened near and slightly above the first slit; (see figure); in this strip,
held by an arm fixed to plate IL, some vertical rows of small holes
had been drilled side by side, differing in number and size. A Röntgen-
tube was placed behind plate IL in 4 and a photographie plate between
the brass strip and plate I; a small leaden sereen left of the second
slit but the part to be observed free. On the photographie impression
one or two of the rows of the holes became visible and from this

( 250 )

could be deduced without difficulty, which part of the strip was
situated in the direction of the passage of the second slit. It was
now easy to place plate IT with its piece of angle-iron in such

a way — the holes in the iron were somewhat larger than the
diameter of the screws — that, seen from the centre of the second

slit, the part of the strip, just now determined, appeared exactly
above the first slit. Plate I being able to revolve round an axis
through the first slit, the latter could be directed in such a way that
the rays from a Röntgen-tube placed near « fell on the second slit ;
by means of a fluorescent screen we could make sure that this had
been obtained. During the course of the diffraction experiments itself
the exact position of the tube was several times controlled and if
necessary corrected.

The width of the second and first slits were arrived at from
photographs when the photographie plate was placed immediately
behind plate I and the Röntgen-tube at « or the photographie plate
at « against plate I and the Röntgen-tube at 4; the photograph of the
second slit was taken both before (namely April 10%, plate N°. 1)
as after (namely Aug. 23°¢, plate N°. 2) the experiments.

As has been mentioned before the self-regulating tubes with water-
cooling were exclusively used; how well these tubes work and how
excellent they are for the usual medical purposes, for the uncommon
demands of this investigation only a few of them could be of ser-
vice. For we wanted tubes which were “soft” and remained so for
hours at a stretch, whilst the effect was so great that the cooling-
water kept on boiling; most of the tubes became harder after a ten
hours’use; when the discharges took place to the sides of the leaden
case another tube had to be taken.

Three very good photographs were obtained, to be distinguished
as A, B and C.

A, obtained on May 7 and 8 after an exposure of 9 hours and
a half, principally by a very excellent tube furnishing very strong
rays and of great softness; developed during three quarters of an
hour in 200 eem. of glycine *) 1 to 5.

B, obtained on July Sth, 9%, 10%, 12; time of exposure 31 hours;
two tubes were used, one of which was soft for four hours
and after that became hard and the second continually hard ;
developed in one quarter of an hour with glycine 1 to 5.

1) Voget’s Taschenbuch, 1901, pg. 128.

( 254)

C, Aug. 14th) 15th, 16th, 17th, 18. time of exposure 40 hours;
two tubes used, one of which worked 10 hours and was pretty
hard, the other a very good tube which remained soft for the
remainder of the time; developed in 10 minutes with glycine
1 406:

There is scarcely any fog on the plates.

In order to enquire how wide that part of the diffraction slit was,
through which the rays have. passed that have worked upon the
photographic plate at a definite point, small round holes were drilled
just as in our preceding investigation in one of the sides of the second
slit and close to it at the extreme ends and in the centre. On
account of this on the plates N°. 1 and N°. 2 serving for the
measurement of the second slit, circular images had appeared and
elongated ones on the plates A, B and C. (From these. pinhole-
photographs of the active part of the anticathode, limited by the
width of the first slit, is proved that this active part was only
2mm. high). The distances between the centres of these images
were divided by the dividing-machine into the same number of
equal parts, so that the corresponding division-marks point to corre-
sponding places of slit and image.

For the measurement of N°. 1 and N° 2 object-elass D and
measuring-eye-piece 2 were used where one division of the micrometer
corresponds to 3,6 u.

For the measurement of the image of the slit on A, B and (the
mieroplanar I*, 2 was used as object-glass and as eye-piece the com-
pensation eye-piece 6; one division of the eve-piece-mierometer corre-
sponds to 55 gu, the magnifying power was 27 with a distance of the
image of 25 cm.

In the following table are mentioned for the successive division-
marks indicated by their number in the first column:

in column 2: the mean of the values derived from N°. 1 and
N°. 2 of the width of the second slit in micra:

in column 3: the double width of the second slit augmented by
the width of the first slit (15 4), thus the theoretic width of the image,
without diffraction ; the distanee between the photographie plate
and the first slit being double the distance between the first and
second slit;

in column 4, 5 and 6: the width of the images respectively on
A, B and Cas measured in divisions of the eye-piece-micrometer

(div == 55);
in column 7: the mean width of the images in miera (rounded off).

EZ
Proceedings Royal Acad, Amsterdam. Vol. V.

( 252 )
es Width | Theor. width Measured width.
Aine . of the i of image _
mark. | second slit. ee diffraction A | B. C. Moa

1 27 pm 69 p et) | 1.0 | 1.0 DD u
2 22,5 GO 0583140485 1400 50

3 19,5 54 0.75 170,75 0/8 A)
4 18 yl 0.6 OW Oey 40
5 17 49 0:55 WIT 7 3D
6 16 47 0.45 | 0.65 | 0.65 30
7 14 43 0.4-| 0.6 | 0.65 30

|

8 | 12 | 39 0351055 | 0.6 95
Ds) 0,5 4 | 0.3. | 0.4 | 0.6 25
10 S 31 12023 Oss O25 20
11 6 27 |} 0.4 | 0.4 | 0.55
411/, 10.6 | 0.45 | 0.6
12 4 | 93 4 0.45 | 0.7

121/, lat Allo Sr dele

13 3.5 22 | +1,

When considering these figures we must keep in view that the
image on account of the width of the first slit is not sharply
outlined but is hazy; this causes the measurement to remain uncertain
and so somewhat deviating figures are found by different observers or
by the same observer at various times; all measurements, however
taken, proved, as can be noticed from the figures mentioned in the
table, that for the wzde part of the slit the figures of the third column
are larger than the corresponding ones of the last column. The
figures of this third column indicate the theoretic width of the image
for the case that the plates have been affected to the outer edge of
the rays to which they were exposed and that no diffraction, vibra-
tion, displacement or photographie irradiation has played a part; the
latter three causes might bring about a broadening, yet this would
necessarily have been greatest on the places of greatest influence thus
at the wide part of the slit. Now that no broadening whatever is found
there, the brush-shaped broadenings, whose width is 2 or 8 times
greater than the theoretic, found on all the three plates at the narrow
part of the slit, can certainly not be attributed to those three causes.

in Pa |

These broadenings, however, are exactly ofa character as is to he expected
in the case of diffraction; and therefore as long as another explanation
is wanting, we can but consider our three plates as so many proofs
of diffraction of the Röntgen-rays.

Of the most important parts of N°. 1, 4, B and C we have made
enlarged copies on glass by means of the microplanar, on which, if not so
clearly as under the microscope, the broadening of the image of the slit
is yet verydistinct; the difficulty of reproducing these enlargements well
has made us refrain from publishing them; we are quite willing to
send these copies to those who are interested in them.

As to the question to estimate the wave-lengths of these rays,
various ways are open; but in no case can one attain at anything
but a very rough estimation, as on one hand the real nature of the
kind of radiation dealt with is unknown, so that it is uncertain
with which kind of diffraction-image our images must be compared,
and on the other hand it is very difficult to find out what is accur-
ately the physical meaning of the limits of the image, on which is
pointed when measuring. |

If however we are forced to limit ourselves to a very rough esti-
mation it is rather indifferent, as far as the result goes, which
of the ways already indicated*) we take; the simplest method
deserves recommendation, namely the one we followed in our first
communication about this subject, based upon our estimating the
tabular width v of the slit equal to 1.3 at the place where the
broadening begins to make its appearance in the image. With a radiation
of simple periodical disturbances this tabular width is connected with the
wavelength and the linear width, and with the known distances
a and 6 by means of the relation :

2 (a+b) 8° 2 (a+d)
UZ Oe - - 8
ab 2 tie? ab
As in the experiments « and 6 both amounted to 75 em. we
obtain after substitution of the value of +,
A ONE Ee
From the above table ensues for s: the width of the slit where

En deed

‘
for the plates A, B and C. From this would ensue for the

the broadening begins to appear, respectively about 7

1) H. Hac and C. H. Wino. These reports 7 page 200, 1899. CG. H. Winn
Wied. Ann. 68, page 896 and 69, page 327, 1809; Physik. Zeitschrift 2. p. 189,
265 and 292, 1901. A. Sommerrenp, Physik. Zeitschrift 1, pg. 105, 1900 and 2,
pg. 58, 1900; Zeitschrift. f. Math. und Physik. 46, pg. 11, 1901,

ta
~
sk

( 254 )

wave-lengths if Röntgen-rays are simple periodical disturbances :

for plate A, B: en
A= 016 0,05 Os 12E is

Now that this supposition does certainly not hold, we shall have
to consider these values as estimations of wave-lengths, which in
the three different experiments have been more or less prominent
in the curve of energy *) of the Röntgen-rays.

Mention ought to be made here, that, although not too much im-
portance must be attached to the three values of 4 as far as the
absolute figures go, the difference they show is probably real and
connected with the difference in hardness of the tubes. As was
mentioned above the tubes used for plate were distinguished
by a considerable hardness from the others, which were relatively
very soft.

Worth noticing is also the fact, that the values of À found here
are of the same order as those deduced from our former experiments.

Finally we wish to state emphatically that we continue to regard
as the chief result of our investigations the proof they furnish that
the Röntgen-rays ought to be considered as a phenomenon of radiation
in the ether.

Physical Laboratory University Groningen.

Physics. — H. A. Lorentz. “The fundamental equations for electro-
magnetic phenomena in ponderable bodies, deduced from the

theory of electrons.”

$ 1. In framing a theory that seeks to explain all electromagnetic
phenomena, in so far as they do not take place in free aether, by
means of small charged particles, electrons, we have to start from
two kinds of equations, one relating to the changes of state in the
aether, the other determining the forces exerted by this medium on
the electrons. To these formulae we have to add properly chosen
assumptions concerning the electrons existing in dielectrics, conductors
and magnetizable substances, and the forees with which the ponder-
able particles act on the electrons in these several cases.

In former applications of the theory I have restricted myself to

1) GC. H. Wino. Il. ec,

>:

the problem of the propagation of light in transparent substances,
moving with a constant velocity. I shall now treat a more general
case. I shall transform the original equations into a set of formulae,
whieh, instead of quantities belonging to the individual electrons,
contain only such as relate to the state of visible parts of the body
and are therefore accessible to our observations. These formulae will
hold for bodies of very different kinds, moving in any way we like.

The greater part of the results have already been established by
Poincaré in the second edition of his Hlectricité et Optique. The mode
of treatment is however rather different.

$ 2. With some exceptions, I shall use in the fundamental equa-
tions the same notation and the same units as on former occasions.
The aether will again be supposed to remain at rest and to penetrate
the charged particles; the equations of the electromagnetic field are
therefore to be applied to the interior of the electrons, as well as to
the spaces between them, We shall consider a distribution of the
charges with a finite volume-density, whose value is a continuous
function of the coordinates. If we speak of “electrons”, we think
of the charges as confined to certain small spaces, wholly separated
from one another; however, in writing down our first equations, we
may as well imagine a charge distributed over space in any arbitrary way.
We shall conceive the charges as being carried by “matter”, though
we might, if we chose, leave the latter out of consideration. We
should then speak of the forces acting, not on charged matter, but
on the charges themselves.
Let us call
g the density of the charge,
» the velocity of the charged matter,
d the dielectric displacement, *)
8 the current,
bh the magnetic force,
V the velocity of light.
Then we shall have
TORO ET Ue hast AED a cg bns ade nj

d
ss +. Div (o v) zb 5 5 ; ° ° - ‘ ° ° . (11)

1) The dielectric displacement, the current and the magnetic force are here
represented in small type, because we wish to keep in reserve large type for
corresponding quantities which we shall have to introduce later on.

ft ee ee ee

Burl. Ate eae ek So ig ee

Sod eV? Rope eer oe eS Bee
de ea eS ee ee

and the electric force f, i.e. the force acting on the charged matter
per unit charge, will be given by
f=] far? 8 le hv os. Toe

§ 3. If it were possible, by means of our observations, to pene-
trate into the molecular structure of a ponderable body, containing
an immense number of charged particles, we should: perceive within
and between these an electromagnetic field, changing very rapidiy
and in most cases very irregularly from one point to another. This
is the field to which the equations (D—{(V) must be applied, but it
is not the field our observations reveal to us. Indeed, all observed
phenomena depend on the mean state of things in spaces containing
a very large number of particles; the proper mathematical expressions
for such phenomena will therefore not contain the quantities themselves
appearing in the formulae (I)—(V) but only their mean values. Of
course, the dimensions of the space for which these values are to
be taken, though very large as compared with the mutual distance
of neighbouring particles, must at the same time be very much smaller
than the distance over which one must travel in the body in order
to observe a-perceptible change in its state. We may express this by
saying that the dimensions must be physically infinitely small.

Let ? be any point in the body and @ a physically infinitely small
closed surface of which it is the centre. Then we shall define the
mean value at the point 2? of a scalar or vectorial quantity A by
the equation

xe jr
zn PK EE PE
A= il Z (2)

in which the integration has to be extended to all elements dr of
the space 5, enclosed by 6. It is to be understood that, if we wish
to calculate the mean value for different points P?, P’, the corre-
sponding spaces S, S' are taken equal, of the same form and
in. the same position relatively to P, P'. The result A will depend
on the coordinates of the point considered; however, the above
mentioned rapid changes will have disappeaed from it; it is only
the slow changes from point to point, corresponding to the perceptible
changes in the state of the body, that will have been preserved in
the mean value.

oe

( 257 )
It is easily seen that
(A ak O_O
Oe Ov’ pek Ot Ot

Hence, if we take the mean values of every term in the equations

(D—{(V) and (4), as we shall soon do, we may replace d and b by

d and 6, Divy by Div 3 ete.

§ 4. Before proceeding further, it is necessary to enter into some
details concerning the charged particles we must suppose to exist in
ponderable bodies.

Each of these particles calls forth in the surrounding aether a field,
determined by the amount, the distribution and the motion of its
charges, and it may be shown that, if x, y, 2 are the coordinates
relatively to an origin © taken somewhere within the particle, and
if the integrations are extended to the space occupied by it, the field,
at distances that are large as compared with the dimensions of the
particle, is determined by the values of the expressions

fear. etl ere ct ee Ee Cae are ees (3)
fox fever fener, NDE eN

.

ford, ford forser we Serr. ee eto
a =

fervar |

a

Now, we might conceive particles of such a nature that for each
of them all these quantities had to be taken into consideration. For

Ovcy dt, forende, cte., Ronse (5)

the sake of clearness, it will however be preferable to distinguish
between different kinds of particles, the action of each of these kinds
depending only on some of the integrals (3)—(6).

a. If the charge of a particle has the same algebraic sign in all
its points, the actions corresponding to the integrals (8) and (5) will
far surpass those that are due to (4) and (6); we may then leave
out of consideration these latter integrals. Such particles, whose field
is determined by their charge and their motion as a whole, may be
called conduction-electrons. We shall imagine them to be crowded
together at the surface of a charged conductor and to constitute by
their motion the currents that may be generated in metallic wires.

( 258 ) oe

4. In the second place, we shall consider particles having in one
part of their volume or surface a positive and in another part an
equal negative charge. In this case, for which a pair of equal and
opposite electrons would be the most simple example, the surrounding
field is due to (4) and (5). We shall say that a particle of this kind is
electrically polarized and, denoting by r the veetor drawn from the
origin towards the element of volume dr, we shall call the vector

fertr=y Et ei eee RN

the electric moment of the partiele. In virtue of the supposition

fesr=o,

this vector is independent of the position of the origin of coordinates.

From (7) we may infer immediately

| ox PE Pax , etc. : fe dr pe . ete.

In all dielectrics, and perhaps in conductors as well, we must ad-
mit the existence of particles that may be electrically polarized. We
shall refer to their charges by the name of polarization-electrons. d

c. Finally, let there be a class of particles whose field is solely |

due to the expressions (6), the integrals (3), (4), (5) being all 0. If

we suppose the values of :
'
fexar, fessvar, feszde, etc.
= a .
not to vary in the course of time, we can express all the integrals
(6) by means of the vector :
-
ee fe F
= ae fe ie) a nk RA ieee
— e a
ay ; :
Le. of the vector whose components are [
4
log:

Me = 5 Oo (y vz — 284) dr, ete.,

Indeed, we shall have

Je WX as. |
bs e

The field produced by a particle satisfying the above conditions

»

0 Tr ea | er 2dr + m, ete. (9)

may be shown to be identical to the field due to a small magnet
Whose moment is yw. For this reason, we shall speak of a magnetized
particle and we shall call m its magnetic moment.

a
Ea;
TN va

According to the view here adopted, this moment is caused by
rotating or eireulating motions of the charges within the particle,
similar to Amprrn’s molecular electric currents. Tf, for the product
ed of a charge e and its velocity, we introduce the name of “quantity
of motion of the charge”, the integral in (8) may be said to repre-
sent the moment about the origin O of the quantities of motion of
all the charges present.

A very simple example is furnished by a spherical shell, rotating
round a diameter, and enclosing av immovable, concentric sphere,
the shell and the sphere having equal and opposite charges, uniformly
distributed.

Whatever be the motion of the charges whieh call forth the mo-
ment m, we may properly apply to them the denomination of mag-
netization-electrons.

§ 5. In the determination of the mean values of the quantities
in (1), (ID) and (1), the following considerations and theorems will
be found of use.

a. Consider a space containing an immense number of points Q,
whose mutual distances are of the same order of magnitude as those
between the particles of a ponderable body. Let NVN be the number
of these points per unity of volume. If the density of the distribution

gradually changes from point to point — in a similar way as may
be the case with the observed density of a body — the value of

N belonging to a point Pis understood to be derived from the
number of points Q lying within a physically infinitely small space
of which P is the centre.

Draw equal and parallel vectors Q/? =r from all the points Q,
and consider a physically infinitely small plane do whose normal,
drawn towards one of its sides, is 7. The question is to find the
number of the vectors QF that are intersected by the plane, a
number which we shall call positive if the ends of the vectors, and
negative if their starting points lie on the side of ds indicated by 7.

If N has the same value throughout the whole space, and if the
points Q are wregularly distributed, like the molecules of a liquid or a
gas, the number in question will be the same for all equal and
parallel planes, whence it is easily found to be

LN BiB od a OO a ed es (10)

The problem is somewhat less simple if the points Q have a
regular geometric arrangement, such as those one considers in the
theory of the structure of crystals. If, in this case, the length of
the vectors QQ is smaller than the mutual distance d of neigh-

( 260 5

bouring points, it may come to pass that there are a certain number
of intersections with one plane ds and none at all with another
plane of the same direction. We shall meet this difficulty by irregu-
larly undulating the element of surface, in such a way that the
distances of its points from a plane do are of the same order of mag-
nitude as the distance d, and that the direction of the normal is very
near that of the normal # to this plane; so that the extent of the
element and the normal to it may still be denoted by do and n. It
is clear that, if MN is a constant, the number of intersections of the
vectors Q FR with such an undulated element may again be said to
depend only on its direction and magnitude, and that it may still
be represented by the formula (10).

The same formula will hold in case the value of WV should slowly
change from point to point, provided we take for V the value belong-
ing to the centre of gravity of the element.

hb. Let us apply the above result to the elements do of a closed

surface 6. Let n, be the number of ends #, and n, the number of

starting points Q lying within o.
Supposing the normal # to be drawn in the outward direction,
we may write for the difference of these numbers

| ING BG. 5 vide ene SEN

an expression, which of course can only be different from O, if MN
changes from point to point.

c. Leaving the system of points, we pass to a set of innu-
merable equal particles, distributed over the space considered. Let ¢
be a scalar quantity, whose values in the points A,, A,,. . . A, of
one of the particles are q,, qs, - + + Ye, the position of these points
and the values of g being the same in all particles, and these values
being such that

Gy = V2 =} st eae En Vk —= 0) . . . . . . (12)

We proceed to determine the sum +g of the values g, belonging
to all the points A that lie within the above mentioned closed sur-
face 5. Of course, the particles lying completely within the surface
will contribute nothing to this sum. Yet, it may be different from
0, because a certain number of particles are cut in two by the sur-
face, so that only a part of the values g,, q,, -- - ge belonging
to each of these are to be taken into account.

Assume in each particle an origin O (having the same position
in each) and regard this as composed of & points O,, O,, . . . Ok.
Attach to these the values — q,,—4q., ...—gk. Then, in virtue

of (12), we may, without changing the sum Yq, include in it not
only the points A, but likewise the points O. Now, if the vectors
0, A,,
Yq due to the points O, and A, will be

.
— | N q; tin do,
a

as may easily be inferred from (11). There are similar expressions

OF Ae 2.3, On Ay are denoted byt, fs, Vy, the: part of

for the parts of the sum corresponding to QO, and A,, O, and A,,
etc. Hence, if we introduce for a single partiele the vector

Weert sata leg tamed Gete (13)
and if we put
ema EC LN

the final result will be

= ay do . . . . . ° . e (15)

In this formula, the vector 9 is to be considered as a function of
the coordinates because the number N may gradually change from
one point to another (this $, @) and the vector q may vary in a
similar way. If now the surface o is taken physically infinitely
small, though of so large dimensions that it may be divided into
elements, each of which is large in comparison with molecular dimen-
sions, the expression (15) may, by a known theorem, be replaced by

SNe ayo the REENER eh) Set ot EO)
S being the space within the surface .

d. It has been assumed till now that the quantity q occurs only
in a limited number of points within each particle. By indefinitely
increasing this number /, we obtain the case of a quantity g con-
tinuously distributed. We shall then write gdr instead of ¢, and
replace the sums by integrals. The condition (12) becomes

.

faar=0

which we shall suppose to be fulfilled for each separate particle,
the vector q is now to be defined by the equation

.

gf AAE DEE on (17)

and the sum +g, whose value we have calculated, becomes | q dt,
a

taken for the space enclosed bij 6. If we still understand by © the
vector given by (14), the value of the integral for a physically infinitely
small space will be

( 262 )

— Days). 5.
Now, according to the definition of mean values (§ 3), division of
this by 5 will give the mean of g; hence

GA INA et gl > eee ee eee

This result may even be extended to a state of the body, in which

the distribution of the values of g is not the same in neighbouring

particles. In this case we may again apply to each particle the

formula (17), but 9 can no longer be calculated by (14). We have
now to define this vector by

pes Se Ts = 5 es = beaten 2 (19)

the sum being taken for all the particles that lie wholly in the space
5,
We may express this in words by saying that 9 is the sum of all

without attending to those that are cut in two by the surface.
the vectors q, reckoned per umit of volume.

e. The case still remains that a quantity qg, given for every point,
has such values that the integral (4) sl gdt, taken for a single par-

ticle, is not O. If this quantity were constant throughout the space
occupied by a partiele, it would be unnecessary to take into account
those which are cut in two by the surface @ and we should have

g == IN):
ml A = . ° 2
The most general case may be reduced in the following way to

this case and to those that have already been disposed of before. If

q is distributed in some arbitrary manner, we begin by calculating

for a single particle the mean value q,=— (q), s being the volume
5

of the particle, and we put in every point g — g, — ‚. We shall then have

I=h ts:

The problem is therefore reduced to the determination of two
mean values, one of which may be found by what has just been
said, and the other by applying the formula (18).

§ 6. The mean value of each of the quantities gandgv in the
equations (I), (ID) and (1) may be decomposed into three parts, be-
longing to the eonduction-electrons, the polarization-electrons and the
magnetization-electrons. In determining them, we shall suppose the
ponderable matter to have a visible motion with velocity w, and we
shall write » for the velocity the charged matter may have in
addition to this. We have therefore to replace v by w + », and to

determine separately 9 Wando v.

a. Conduction-electrons. The mean value of 9, in so far as it depends
on these, may be called the (measurable) density of electric charge;
we shall denote it by @,.

The mean value © of ow may be represented by

¢ — 0, Ww.

This is the convection-current, and the vector

= pe:
taken for the conduction-electrons, may fitly be called the conduction-
current.
bh. Polarization-electrons. Let the body contain innumerable particles
electrically polarized, each having an electric moment ». The vector
defined by the equation

1
Dh Nt a! lew acre a ett) oP (0
JN ge (20)

where the sign + is to be understood in the same sense as in the
formula (19), is the electric moment for unit volume or the electric
polarization of the body. Replacing q by 9 in the formulae of $ 5, d,
and taking into account (7); we find for the part of @ that is due to
the polarization-eleetrons,
One Div W.

We may next remark that the visible velocity w is practically the

same in all points of a particle. Since, for the space occupied by it,

fe desi
we have likewise

fe Ww, dt = fe W, be => ko Wd ==.0,
a

so that the values of gw, @W,, @ w. may be found by means of
(18). The result is

EW = — Div (W, ), etc. ntt hd RER)

We have finally to determine gv. Now, the quantities ev,, ory,
ov. are of the kind considered at the end of $ 5, ¢. However, there
are cases, especially if the velocities ¥,, ¥,, Do and the dimensions of
the particles are sufficiently small, in which the parts of or, Ov, ov.
corresponding to g, of $ 5, e, may be neglected. Confining ourselves
to such cases, we shall determine g> without taking into consideration
the particles intersected by the surface o.

For a single particle we may write

( 264 )

/
fe Ml te ok
4 dt

and for a physically infinitely small space, partaking of the visible

motion
/ “ad =
ODIE = = Pa
hi dt

On account of (20) this is equal to

/
(SW).

dt
so that

fe 1 éi 1
y= — dt—=- 5D
oO „Je oat 5 En Dj

In performing the differentiation we must attend to the change of Pin
a point that moves with the velocity Ww. If relates to a fixed point
of space, we have
= a oy
— == fy aire ny

and, since

ds '
a Lie Ie,

dt

5 i oy op ,
ov = P + W‚ Ste Wy, Te +- We aa = Y Div w.
ae

~

Combining this with ie we get for the mean value of the cur-
rent corresponding to the motion of the polarization-electrons

PH Rot [P. rw].
c. Maynetization-clectrons. If the body contains magnetized particles
(§ 4, c), we have nothing to add to 9 and gw. There will however be
a new part of ov. We can calculate it by applying (18), because the
quantities (5) vanish for every particle.
Let us first replace, in the formulae of § 5d, q by ev,. We
then find
qn 10; dy = — Wz, qz = + m,,
and, if we denote by M the magnetic moment for unit volume or
the magnetization, a vector that is to be defined in a similar way as p;
DE Dn Me, =d 9
Finally, by (18),

My.

os OM, ON,

with similar expressions for ov, and ove.

(A

The mean value of the current, in so far as it is due to the
magnetization-electrons, is therefore
Rot NM.
It may be called the current equivalent to the magnetization.
$ 7. It remains to take together the different parts of the second
member of (1). Putting

Oy geen et NE é (22)
EN, (23)
and di ROED iW - (24)

we have

SBL FHC H NH Rot M.

Now, we might understand by the current in the ponderable body
the whole of this vector. Conformly to general usage we shall however
exclude from it the last term. We therefore define the current as
the vector

re ee Gh El Mt see ees (25)
so that
SIRE DEL a soar Ree (20)

We may call 9 the dielectric displacement in the ponderable body,
and & the displacement-current. As to the total current ©, the for-
mula (25) shows that it is composed of the displacement-current, the
conduction-current 3, the convection-current € and the fourth vector X,
for which Porcaré has proposed the name of Rdntyen-current, because
its electromagnetic effects have been observed in a well-known expe-
riment of RONTGEN.

§ 8. We shall now write down the equations that arise from
(DV) and (1) if every term is replaced by its mean value. In order
to obtain these formulae in a usual form, we shall put

OPN Eh ta A A ES te (27)
Dn MB En OS EARN
Baya Ne EE Te en LL EN

these quantities being the magnetic induction, the magnetic force in the
ponderable body and the electric force in the body.
Beginning with the equation (I), and writing @ instead of 9, for
the (measured) density of electric charge, we find
Dvd = 0 — Div J,
whence
DO yr EES 5X a Ree, Se AE Se (I')

N

(966 )

We may further deduce from (1), taking into account (1) and AD,
Div & == 0,

and consequently Div 8 = 0.

Now the expression MotM we have found for the current that
is equivalent to the magnetization, shows immediately that the distri-
bution of this current, taken by itself, is solenoidal. We conclude
from this that

DE ne En

From AL) we may deduce, if we mtroduce the value (26),

RotB=AarS Aa Rot M,
or, taking into account the relation
= H+4aM

which results from (27) and (28),

Rot DURE eeN eS NN
Finally we find, by (IV)
Rot @ == = Seiad Keer ei
and by (V)
Din B Dir or Se er oe

We have thus been led back to the equations of the electromagnetic
field in a form that has long been known. In this form we may use

them without even thinking of the individual electrons. As soon however

as we seek to penetrate into the mecanism producing the phenomena,
we must keep in mind the definitions that have been given of the
different quantities appearing in the equations and the manner in
which they are connected with the distribution and the motion of
the elementary electric charges. The formulae (27) and (28) e. g. show
the precise meaning that is to be attached in the theory of electrons
to the terms “magnetic force” and “magnetic induction”:

The equations (I')—(V') may be applied to all bodies indifferently.
If is otherwise with the formulae expressing the relation between
S (or ®)-and &, and that between B (or DM) and H 5: the form of
these depends entirely on the particular properties of the bodies con-
sidered. I shall not here diseuss these more special formulae ; in order
to deduce them from the theory of electrons it is necessary to con-
sider the forces acting on the electrons in a conductor, the “molecular
motion” of these particles and the cireumstances which determine the
electric and magnetic moments of a single molecule or atom.

") See Vorer, Electronenhypothese und Theorie des Magnetismus. Nachr. d. Ges.
d. Wiss. zu Göttingen, 1901, Heft. 3.

‘

25

Astronomy. — Preliminary investigation of the rate of the standard
clock of the observatory al Leyden Honwt N°. 17 after it
was mounted im the niche of the great pier.’ By Dr. E. F.

VAN DE SANDE BAKHUYZEN.

1. In a preceding paper on the clock Honwé 17 I communicated
the investigations I had made on an inequality of a yearly period
noted in its rate which does not depend on the actual temperature.

Besides the periods 1861—1874 and 1877—1898 I discussed also
the period 1899—1902 when the clock had been mounted in the
hall of the observatory in a niche cut out for this purpose from the
great pier. From the mean daily rates during periods of about a
month each, I derived formulae for the rate in two different ways,
and this research clearly brought to light that during this period the
rate of the clock had become considerably more regular than before
and now satisfies high demands.

Since that time the same formulae have been compared with the
daily rates observed during much shorter periods and an investigation
has been undertaken about the barometer coefficient, for which purpose
the monthly rates were less appropriate.

The latter calculations have so clearly shown the excellence of the
‘clock also with regard to its rate during periods of a few days, that
it seemed to be of interest briefly to give here the results to which
they led.

2. The results we obtained from the previous investigations may
be resumed thus. |

Under all the conditions in which the clock Honwt 17 has been
placed, its rate, after correction for the influence of the temperature,
has always shown a residual yearly inequality. As the former influence
had been derived from the yearly variation of the temperature, the
residual inequality must necessarily show a difference of phase of
three months with respect to the temperature.

If the influence of the temperature had been derived and accoun-
ted for in the form = c, (#—t,) + c, (t—t,)", whether we had found
for c, a small negligible value, as in the period 1862—1874 or an
obviously real quantity as in the period 1899—1902,, the residual
inequality could with sufficient accuracy be expressed by a simple
sinusoid. If on the contrary only a linear influence of the temperature
had been accounted for, while an investigation of ¢, showed it to
have an appreciable value, the residual inequality showed a half-
yearly term besides. This could be expected; for as long as only the

Re)

Proceedings Royal Acad. Amsterdam, Vol. \

i re NL LS <7) re ce Erin ?
TEESE Es A AMOR AC
= aie: 5 ete bt jj
4 \ : i 8, * » Ne nih cee eth 4 oe er
A a ie, alien La pe
ES ed dak

‘SN

vearly variation of the temperature is concerned, a quadratic influence —
of the latter and a half-yearly inequality are completely gein 8
3. For the rate of the clock during the period 1899—1902 I~

EE
derived in the first place the formula: he 4 je
D. R. = — 0.169 + 0*.0140 (4 — 760). ee
— 05.0253 (¢ — 10°) + 000074 (£ — 10°). aa
| on
T — May 3 wan
4+ 05.0465 cos 22 oe EERE
505 oe

,

secondly the formula:
D. BR. = — 05.157 + 05.0140 (h — 760). E
— 050220 (£ — 10°) + Suppl.inequal os. ER
The supplementary inequality in the second formula was an

sented by a curve. Yet it can as well be represented by a yearly — a 4
and a half-vearly term. We then find: Ln

IS aes 5 L 05,0471 5 T— Apr. 29
MUD DE. ANNE as 08 450 ————_<_$—_———_—
tp} neq Ul zin ry COS ed 365
Dn arts a
Wet RG cde Mey meee oe ID} ae

365
From the term depending on the square of the temperature found —
by the first method of calculation and from the yearly variation of —
the temperature in the clock-case, which is approximately represented by
T— Moy 4,
365
we derive for the half-yearly term ; Ooms

2 T — May 4
— 05.0158 COS Ax aS Soho
365

= + 11°.6 + 6°.54 sin 2a

which is in sufficient agreement.

The two formulae must however give different results, as soon as
the accidental variations of the temperature become of importance,
and therefore it was of interest to compare the rates during short —
periods with either.

4. Hence two comparisons were made for the three years 1899
May 3—1902 May 3. ?)

T— June 9
365 ;

*) In this and the following calculations the supplementary inequality for for--
mula If was read from the curve.

1) For the next term we find: + 00.55 sin 4=

F te he
te Se eal) 2 ae

(269° )

Within that period L could dispose of 182 time-determinations
at average intervals of 6 days, giving 181 values for the daily rate.
We can assume as mean error of the result of a time-determination,
largely accounting for systematic errors such as variations of the
personal errors of the observers, + 0.04.

I do not give here in full the results of the comparison of these
181 observed rates with the two formulae and only lay down the
mean values found in both cases for a difference: observation—com-
putation.

1 found:

Formula | M. Diff. == = 03.0333
i il + 0 .0344

Hence this mean difference is nearly the same for the two for-
mulae; indeed, if the three years are kept apart, it is found to be a
little greater for formula I in two of the three years.

We may therefore say that the two are in equally good agreement
with „the observations and for the investigation of the barometer
coefficient it was sufficient to use either.

I chose formula If (linear influence of the temperature) and I
proceeded in the following way. The rates reduced with that for-
mula to 760 m.m. and 10° and freed from the supplementary ine-
quality were divided into five groups according to the barometric
pressure and for each group the mean of those reduced rates was
calculated. The results are laid down in the following table, where
the first column gives the number of rates from which each mean
has been derived.

Number. | Barom. Reduced. D. R. 0.—C.
17 132.8 — 0:.174 — 0s .002
3H | 757.6 | 162 ay
GS 762.6 | 154 ee OH
4h 767.4 145 send

| 7 ,
21 | 112.2 | 141 — 02

From these results [ derived as correction for the barometer
coefficient: .
Ab = + 0:.0017
joe

( 270 )

while I found for the daily rate for 760 mm. — 05.160. With these
values we obtain a very good agreement with the observations as
appears from the differences obs.—comp. contained in the last
column of the foregoing table. Hence it appears that the value for
the barometer coefficient 6 == + 05.0157 is determined with great
precision *).

For the constant term of the formula we find from all the rates
—O8.161, while, if we put 6= + 0°.0157 also in formula I, the

constant term here becomes — O0%.173.
5. With the formulae thus modified :
Don. ==" 04.73. 4200157 (4760).
— 08,0253 (t—10°) + 0500074 (£—10°)*.
+ Supplementary mequality. . . . . … (Ia).
D. R. = — 08.161 + 08.0157 (h—760).

— 08.0220 (t 10°) + Supplem. inequal. và EEN

we have again compared all the observed rates and this time the
comparison has been extended to 1902 Sept. 20 i.e. till almost five
months after the period from which the formulae were derived.
Besides the observations have been compared with a third calculation.
This we obtained by applying the formula Ila so that we did
not use the actual mean temperature but that of five days earlier.
It is obvious that in doing so also the value of the supplementary
inequality must be altered. An assumed lagging behind of the
influence of the temperature of five days is equal, so far as the
general variation of the temperature (as found above) is concerned,
to 0.27 X the yearly supplementary term. Hence the latter had to
be diminished by this part of its amount. The formula thus modified
I call 115.

The results of these three comparisons are given in full in the
following table. The first column gives the dates of the time determi-
nations, the next column gives the mean temperature for the period
between the date of one line above and of that on the same line,
while the third, fourth and fifth columns give the differences between
the observed rates for those periods and the computations Ia, Ila
and 114 respectively. These differences are expressed in thousandth
parts of seconds.

1) According to the investigations of Mr. Weeper a value little different from
this follows for the period 1882—1898,

Obs. | Obs. [ Obs. | . Obs. | Obs. | Obs.
Temp. | — — — | Temp. | — — —
la a | Ith Pte PS tae, NAI
1899 1899
May 3 Nov. 42 |+12.6 | — 12 | — 14 | — 28
Se RA Ove | Sh AO 5 90 PAM O Pe SP BAER
» 17 12.0 | + 33 | + 2 |H 9 Dre IS 10.8 | — 42 | — 51 | — 63
» 30 Teen 0;—42);— 4 Dec. 7 10,4 | — A= 22 | — 49
June 3 13.9 | — 17 | — 32 | — 40 y. 13 6.8 | + 83 | + 83 | +140
PR Heche feels Ay ALE SSE Su ne, AG (21 BEERS 76) fpf AOS, hak 70
Peed pate, @ hoe OF EOD eB TT a AO 80 le 4tG | 46 oe 59
» 99 | 15.4 | + 36 | + 22 | + 12 nr MOE 2.3 | — 4%] + 21 | + 31
Rrk. oor eet ier abe hha’ CSL |A bo hgh | 88
July 7| 46.5 | 4.7 et ThA 900

ze
=
=x
|
5
|
bo
dee)
|
A]
oa)

Jan.» 8 5.3 | — 32 | — 26 | — 62

Cl
I
=S
Co
ze
Ee
ad
oS
ot
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EN
=
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a
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aa

(=P)
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z
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co
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ler)
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er)
to

=
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gen ZON nde Nea ad
ob

» AR 4.3 |.— 98 | — 2

wie
i)

=

~

76 | + 74 March 2 69) — 4 OS 28

44. » 9) Ove thon | ee 7 + 23

=|
_—

Ek dt +
++++4+4+4+4
——

12 » 9 6.8 | — 30 | — 20 | — 40

z
LO
we
me
~l
I
—
—

++ +
+++

» 13 Auge ae

+
--
hides
| 44 IE > dB 6.6) BS Ad | — 4
-|-
+
+

a
~
—
~~
—_
—

Oct. D 14.4 | — 35-|.— 32 | —- 24 » 12, | Lia EN AN ret
» 9 13A IH 3 |H 714 15 oS) TORO OE OO Ra AO
» 16} 411.9}/— 9|— 5;+ 8 » | 9.9} + 37) + 34) + 95

5 BEE. AO: Or =S ONE AE | EH D/W | MOA EE HG LOG Lr 4

; ‘| .4)—1|—77|- 3

1900

May

»

10

| Temp. |

419.4

44. |

<I

Je)

6

Obs.

la

Se)
—

Obs. _

Ila

~ Obs.

Il

1900

Oet 29h}
|

» 99

) 7
» 16
y 23
» OT
Dec. 7
» 10 |
» 15
) 19
paws
1901
Jane soe
» G

y= ie
» 4 Fi
» 93

114
» Y()

March 5

» | 3
vy
ict a
A pr. |
) 4
> 7
» 17

~1

—

=

apes

lw

|

os

A eae aoe
Hdd tt +

Ila

+
—
Ke

|

+ + +

1 Obs: OR OLE

(Temp. | —
|

Id

1901

Apr. 20

» 93,

» 99
May. 3

» 8

» Ml

) 14 |

» 90
June 2

) 7

) 18 |

D) 25
July 3

) 10

» 15

» 20

» 1

| Temp. |

(2)
Obe. | Obs. | Obs. Obs. | Obs. | Obs.
= == == Temp. | as ri Bley oe
la Ila 114 | la lie | La

ae

++ 4+

~

—

| 1901
No Vite df

D) 15 9.9
par | 9.6
» 96 9.0

Dec. 6| 8.4
» 16 | 18
pt A, De
1902

Jan 5 6.6
» 11 8.6

Pee Si A10
Febr. 4 6.4
» 7 49
ieee te 4.6
» | ) 4. 9
» 2() 3.9
Dade eR)
March 4 D40
) 10 7.0
» 14 Ti
» 19 IR
Apr. 3 | 8.3
» 8 S 9
) 12 8.0
ert IES 053
15 it Ban
nd Ae 12.4

ed
=
>
a
we
~
~—

|

+ +

sE

+ ++ +

+++4++

( 274 3

Obs. | Obs, | Obs “Si Sawa Ober | Obs, TOU
Temp. | — —_ — | Temp. — — —
ET EEN Ps TAM (OE PETN KE
1902 | 1902
May 2% [440,4 | — 10 | — 18 | — 9] | July 34 [447.4 | — 52 | — 63 | — 55
| | |
>» | 49.7 | A26 | 4-42 | — 431) Aug. 5 | 16.8 | — 54 | — 68) — 64
Tune 44.45.9487 | E32) 446 MD oe 41) 46-9 | — 0 Lob
SRT de bl Ba AB 4g IN » 5-1 A60 SSA STO em
RENEE Ash A3 99 Sak Ps 904° 46.59) A DEN ND
peu 26a) 16.84) | Ont 28 » 9 | 16.8 | — 49 | — 55 | — 66
July 5 | 18.4} 4+ 44/448] Off Sept. 3| 47.1 | — 16 | — 19 | — 36
» 421 17.9 = 80 | Sd ber AB SPR Dee Ae CE
> 45 | 17.4) — H | — 38 | ON TE? De A | To) 06 eee
pee et HT | 96) |) 2432 Phe TD on OAN eo Ie
| |

From these differences we derive the following mean errors of a

rate computed by means of the three formulae:

| ; : :

| Form. fa. Form. Ila, Form. IIb.

|
1899 May—1900 April...... 08.0343 TE 0s.0345 + 0s 0424
4900 May—1901 April... . OAD | O87 AAT
1901 May—1902 Sept...... 21 266 274
1899 May—1902 April...... + 0.0314 + 0.0327 TF 0.0385
1899 May—1902 Sept...... | T 0.0344 zE 0.0832 F 0.0382

First let us compare the mean errors of the three formulae inter
se and with the corresponding values formerly obtained for the for-
mulae I and IT with the uncorrected barometer coefficient.

Then it appears in the first place from the values for the period
1899 May—1902 April that the correction of the barometer coeffi-
cient has markedly improved the agreement with the observations. *)
Secondly it would appear that the quadratic formula now represents
the observations a little better than the linear formula, and thirdly
we find that the supposition of a lagging behind of the influence of
the temperature markedly impairs the agreement.

') Each of the three years separately also leads to the same result.

( 275 )

A consideration of the differences obs. [Ie and obs. shows
however, that the latter conclusion does not equally hold good for
all parts of the year and that the agreement with formula Hd is
especially bad in the winter months. In order to investigate this more
closely, I divided the observations into groups of two months and
calculated for each group the mean value of the differences, first for
each year separately, then after combining the corresponding groups
of the different years. The latter values follow here.

Form. Ha. | Form. Ib.
Jamaar y,sKebPUarg: na aie cues eae 2E 0s.0402 | =F Qs. 0549
RPE AEN se aa ale OEREN ed 208 214
DEAN UNE Ber et Alant oe vei ken 285 284
TIN AATIETSG. lor sn tie BBL mend 423 368
September, October........ oden 215 | 932,
November, December ......%....... 309 | 559

They lead to the singukw result that during the four winter months
formula Il / agrees much less with the observations than lr, whereas
in the middle of the summer the agreement with 115 seems to
be better, and in the other months both formulae may be said to
agree equally well. In this respect the different years practically
lead to the same conclusion and hence we cannot say that this has
been brought on by entirely accidental causes. However this may be,
we are not entitled yet to assume a lagging behind of the influence
of the temperature.

Let us now consider separately the resuits for formula Ta, which
seems to represent the observations with the greatest precision (those
for Ila do not essentially differ from them). It will be seen immediately
that during the last seventeen months the rate has been considerably
more regular than during the first two years *); a smaller M.E. has
been reached although the 5 last of these 17 months were not
included for the derivation of the formula. Thus the feature observed
before, i.e. the gradual improvement of the regularity of the rate after
the mounting of the clock, shows itself once more. The mean result
for the whole period (M.E. — + 08.0811) may already be regarded
as very satisfactory, and the great regularity represented by a mean
difference of + 08.0251 between a daily rate from a 6 days interval
and a relatively simple formula gives us a high sense of the supe-

1) Already at the beginning we had left out the first 4 months after the remounting.

( 276°)

rc

riority of Honwt 17 in its present state. That this regularity markedly
surpasses the one reached formerly is shown also by the results of an
investigation of the vears 1886—87, which are among those of the
ereatest regularity in the period 1877—1898. This investigation was
made in a similar manner as the present one, the mean interval
between the time determinations used was 5 days and the mean
error found was = 0+.0365.

6. We may also investigate the rates of a clock in such a manner
‘that only the irregularities of a very short period are considered.
A simple process for attaining this is to caleulate the mean value of
the difference between two consecutive reduced daily rates.

Applying this method to Honwt 17 during the period under
consideration *) I found:

Mean difference 1899 May—1902 Sept. + 08.0315.
; 7 1901 May 1902 Sept. + 0%.0253.

From these mean values considered in connection with the mean
errors of the rates in 6-daily and in monthly intervals formerly found
we can draw some, albeit rough, conclusions about the amount of
the perturbations of longer and shorter periods.

The values found, as well those for the whole period as those
derived for the last year only, are given in the following table. The
columns A contain the values found directly, the columns / those
diminished by the amount that can be ascribed to the errors of
observation, assuming + 004 as the total mean error of a time-
determination. M.E. @ of a 6-daily rate stands for the total mean
difference from the formula Iv, found above, M. B. « represents the
error derived from the mean differences between two consecutive
rates. The mean errors of the monthly rates differ a little from
those of my previous paper as they now also refer to formula Ia.

‘mmm

1899 —1902. 1901—1902,

M. Diff. of two 6 d.r. | + 050313 | = 050267 | = 080253 | = 0.0193

M. E. z of 6 d. r. | 189 | | 137
| |
M. E. # of 6 d. r. | 314 | 207 251 | 233

M. E. of monthl. r. | 209 208 164 163

1) The rates were reduced by means of formula Ila, but a reduction according
to Ia would practically have led to the same result.

Ard À

Although these calculations are inaccurate owing also to the fact that
the intervals between the time determinations often differ rather much
from 6 days, yet it is evident that the M. E. 3 are much larger
than the M. E. @ and hence that considerable perturbations of long
period exist, as, indeed, a glance at the table of the obs.—comp.
also shows. It would be possible to account tolerably well for the
values found for the three different mean errors by assuming, quite
arbitrarily of course, that there are two kinds of perturbations, one
constant during 6 days and another consiant during a month. We
should then have to assign for the whole period an average value
to both of + 05.02 and for 1901—1902 alone one of + 05.015.

There are not many clocks about which investigations have been
published, which allow us directly to compare the regularity of
their rates with that of Honwt 17 and most of these embrace but a
short period.

An investigation extended over 4 years about the standard-clock of
the observatory at Leipzig Drenckrr 12 has been published by Dr.
R. SCHUMANN '). He uses 224 time determinations at mean intervals
of 6'/, days and derives for the rate a formula containing a linear
influence of the temperature and of the barometric pressure and besides
a term varying with the time elapsed since a zero-epoch. As mean
value of the difference obs.—comp. he finds + 0%.059 and there is
no evidence of a residual yearly inequality. I calculated also the
mean value of a difference between two consecutive rates and
found 450.055:

In the latter respect we possess also data about the four normal
clocks of the Geodetic Institute at Potsdam. An investigation by
Mr. WaracH ®), about the rates during last year gave the following
mean differences between consecutive rates after correction for the
barometric pressure, while the temperature was kept very nearly
constant:

STRASSER 95 = O8.054
RiEFLER 20 + 0.062
DerNCKER 27 + 0.047
DeNCKER 28 + O .049.

These values are considerably larger than that for Honwé 17, but

respecting the Potsdam clocks we must keep in view that DENCKER

1) R. Scuumann. Ueber den Gang der Pendeluhr F. Dencxer XII. (Ber. Sächs.
Gesellsch. d. Wiss. 1888).

*) Jahresbericht des Direktors des Königlichen Geodätischen Instituts für die Zeit
von April 190L bis April 1902, pg. 35.

( 278
27 and 28 had lately been cleaned, while Strasser 95 during the
period of observation had twice been replaced and meanwhile had
been exposed to great differences of temperature. For DeNcKer 12
at =Leipzig also some perturbations from outside shortly before and
during the period under consideration are noted.

7. For a clock which is used for astronomical fundamental deter-
minations the regularity of the rate during the 24 hours of the day
is of the very highest importance, but it is obvious that only long
continued observations reduced with the greatest possible care can
give us any information on this subject.

As yet I can only state that we may confidently expect Honwt
17 not to be inferior in this respect to other clocks kept at constant
temperature, seeing that, while the amplitude of the yearly variation
of temperature has diminished comparatively little in its present
place, the daily variation has almost entirely disappeared.

This will be seen from the following values of the difference
between the temperature at 4 o'clock in the afternoon and the mean
of the temperatures of the preceding and the following 8 hours in
the morning. These differences taken for about 240 days have been
combined in 6 two-monthly groups, and their means follow here:

Temp. 4h—Temp. 20h

damuary, PELI LI ee oes cee oe: + 0?.09
MENGEN; Api er ten ot EE mains + 0.15
Baty. JUNG oy rae iit eet tot eee + 0.12
A RY AMD ECs zn ar Ms ic OEE ay + 0.20
September, Outabereee aoe. ee a Chee
Rotan bet, Deerns hae wee + 0.08

The mean difference is greatest in summer, but even then very
small, while no difference ever reaches to 07.5.

(October 22, 1902).

a

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.
PROCEEDINGS OF THE MEETING

of Saturday October 25, 1902.

eCG —-

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 25 October 1902, Dl. XI).

ee Ties, Bar 52

H. W. Bakruis RoozrBoom: “A representation in space of the regions in which the solid
phases, which occur, are the components, when not furming compounds’, p. 279, (with one
plate).

H. W. Bakuvuis RoozrBoom: “Equilibria of phases in the system acetaldehyde + paraldehyde
with and without molecular transformation”, p. 283.

L. ARONSTEIN and A. S. van Nierop: “On tie action of sulphur on tolucne and xylene”.
(Communicated by Prof. J. M. van BEMMELEN) p. 288.

Tu. Weevers: “Investigations of gluco-ides in connection with the internal mutation of
plants”. (Communicated by Prof. C. A. Lospry pr Brryy), p. 295.

J. D. van DER Waars: “Some obs ‘rvations on the course of the molecular transformation’, p. 303.

J. D. var per Waars: “Critical phenomena in partially miscible liquids”, p. 307.

J.K. A. WERTHEIM Saromonson: “The influence of variation of the constant current on the
pitch of the singing arc” (Communicated by Prof. P. ZEEMAN), p. 311.

J. E. Verscuarrecr: “Contributions to the knowledge of van per Waars' ¥-surface. VIL. 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 components”, p. 321, (with one plate).
Continuation p. 336.

J. Boerke: “On the structure of the light-percepting cells in the spinal cord, on the neuro-
fibrillae in the ganglioncells and on the innervation of the striped muscles in Amphioxus lan-
ceolatus”. (Communicated by Prof. T. Prace), p. 350, (with one plate).

The following papers were read:

Chemistry. — #A representation in space of the regions in which
the solid phases, which occur, are the components, when not
forming compounds.” By Prof. H. W. Baknvis RoozeBoom.

(Communicated in the meeting of September 27, 1902).

In the course of my researches, I have often made use of special
kinds of graphical representations to indicate the limits of the exis-
tence of single phases or complexes of phases. It was only after
the year 1896, when it could be taken for granted that the general

19
Proceedings Royal Acad. Amsterdam. Vol. V.

( 280 )

character of the equilibria between liquid and vapour in binary sys-
tems had become fully understood, that efforts could be made to con-
struct a complete graphical representation of the conditions of equili-
brium in which solid phases occur.

The simplest possible case is found when only the two components
of the binary system occur as solid phases. For such a case, I have
since 1896 arrived at the representation in space of which photographs
are given in the accompanying figures. For the case that chemical
compounds or mixed crystals occur as solid phases other figures have
been constructed which, however, may be deduced in a simple manner
from the present ones.

In this figure the length represents the temperature, the breadth
the concentrations « of the mixtures which can exist as vapour
or liquid, the component A being placed at the left and the
component B at the right. The height represents the pressure. The
figure does not represent any particular case, but is so constructed
that the different details come out plainly and the dimensions are not
too great.

We start from the equilibria between liquid and vapour, which
researches on the critical constants of mixtures have proved to be
capable of representation by a surface of two sheets, the upper part of
which represents the liquids and the lower part the vapours. The
coexisting conditions of these two must have equal values of p and ¢
and are therefore, situated on a horizontal line which is parallel to
the r-axis. The said surfaces meet at the left side in the vapour-
pressure line O4 C of the liquid A, at the right side in the vapour-
pressure line Op D of the liquid B and in front in the critical curve CD.

The points in the space between the two surfaces indicate complexes
of liquid and vapour. In the representation, this space is massive,
like all other spaces which represent complexes of two phases.

The surface of two sheets for liquid + vapour is so constructed that
A is the substance with the greatest vapour pressure. It has further
been assumed that the liquids are miscible in all proportions and that
no maxima or minima occur in the equilibrium pressure.

Descending continuously, the surface would reach the absolute zero
if A or B or both did not solidify first.

The pure liquids A and B solidify in O4 and Og; from there the
vapour-pressure lines O47 and OgK of the solid substances run in
the left and right vertical side-plane.

Considering now the liquid-mixtures with an increasing amount of
B, solid A can only be deposited at temperatures lower than O4.
At each temperature there is a definite liquid and a definite vapour

( 281 )

which coexist with the solid phase A at a definite pressure which
is larger than the vapour-pressure of solid A alone, but the same
for each of them, The three coexisting phases are represented by the
lines O4G, Oul, Oul? respectively standing for solid, gas and liquid.
They are situated together on a cylindrical surface, because for equal
t, also p is equal. The part O42 is also a limitation of the surface
of two sheets.

In the same manner we have for the equilibrium of solid B with
liquid and vapour the three lines OgpH, Opb, OpF, for solid. liquid
and gas respectively, again situated on a cylindrical surface, while
the part HOpF thereof forms below a second limitation of the
surface of two sheets. This cylindrical surface first rises from Op but
afterwards falls again.

The surface of two sheets terminates, as far as the liquid-surface is con-
cerned, finally in //, the gas-surface in J’. This liquid and this vapour
may exist in contact with solid A (point G) and also with solid B
(point H). As the points G, F, WM, H belong to the same values of
p and ¢, they are situated on a horizontal line and represent the
only possible complex of four phases.

To the gas-line O4f' a second gas-surface joins, representing
the vapours capable of coexisting with solid A, when the quantity
of B in the vapour increases; also to Ogi’ the gas-surface for
the vapours in equilibrium with solid B with increasing amounts of
A. From the melting points of the pure substances down to the tem-
perature of the quadruple-point G / MH these two gas-surfaces
are not in contact with each other, but each of them singly is in
contact with the gas-surface of the surface of two sheets.

Below that temperature they intersect each other immediately,
forming the line /’Z which represents the vapours capable of coexisting
with solid A —+ solid B. To this belong the lines GM for solid A
and HN for solid B which are again situated on a cylindrical surface.

All complexes of the solid phase A and of the coexisting vapours
are situated within the space formed by the gas-surface J/O0,FZ,
the surface of the solid phase /O4GJ/ and the two cylindrical
surfaces GO4F and MGFL. All complexes of the solid phase B
and the vapours which can exist in contact with it, are situated
in the space bounded by the gas-surface KOpFL, the surface
of the solid phase AOgHN and the cylindrical surfaces HOpF
and N AFL.

Both spaces extend to the absolute zero if no new phases are
formed.

The three surfaces representing the equilibria of gas with liquid, with

19*

( 282°)

solid A and with solid 5 meet each other in the point /. In the same way,
two other liquid-surfaces must join in the point Zat which the liquid
surface coming from higher temperatures ends, namely those which
indicate the p,f,# values of the liquids which can coexist with solid
A or solid B. The lower limits of these surfaces are the lines O4H
and Op which represent the equilibrium of solid and vapour. Set-
ting out from these lines the vapour disappears when the pressure is
increased. On account of the small changes which the composition
of the liquid undergoes with an increase of pressure, the liquid-
surfaces O4HEPU and OgEPV will rise almost vertically. They ter-
minate to the left and the right in the melting point lines O4 V and
OpV of the solid substances A and B, whilst they intersect each
other in the line ZP which indicates the liquids which at different
p‚t values can coexist with solid A and 5. To this line belong
the p,¢ lines GQ and HR for the solid phases, which again form a
cylindrical surface with EP.

In this way we arrive for the complexes of solid A + liquid at
the space included between the liquid-surface, the surface of the
solid A, O4 UQG and the cylindrical surfaces GO, HE and GEPQ.
A similar space includes, at the right, the complexes for solid
B + liquid.

Finally, the region of the complexes of solid A + solid B is situated
behind the cylindrical surface GHRQ and above the cylindrical sur-
face NHGM.

The spaces last described terminate in the figures at the back at
an arbitrary temperature and above at an arbitrary pressure. One
must suppose that, in reality they continue their course.

The remaining space outside the massive parts constitutes the
regions of homogeneous liquids and vapours which pass into each
other beyond the critical curve. The other six massive parts repre-
sent complexes of two phases, the states of matter forming the complex
being represented by two side surfaces.

They further are connected with each other by four cylindrical
surfaces on which three lines are always situated representing
the systems of three coexisting phases and these cylindrical surfaces
intersect each other in one straight line on which is situated the only
possible complex of four phases.

If for any system of two substances the figure described were
studied completely, it would enable us for each mixture at each
temperature and each pressure to read off, of what phases it has been
built up and as far as liquid and vapour are concerned it would
also show their separate composition.

H. W. BAKHUIS omponents when not forming compounds,

Fig. 2e

Proceedings Royal

H. W. BAKHUIS ROOZEBOOM. .A representation in space of the regions in which the solid phases, which occur, are the components when not forming compounds

cedings Royal Acad. Amsterdam, Vol. Y.

( 283 )

For the complexes of fwo phases, the relative proportions may also
be read off in the figure; for those of (ree or four phases it would
be necessary to also know the relation of the volumes.

The figure also makes it possible to ascertain what changes a
mixture will undergo, when the temperature, pressure!) or concentration
are changed.

Chemistry. — “Lquiibria of phases in the system acetaldehyde +
paraldehyde with and without molecular transformation”. By
Prof. H. W. Baxkauis RoozrBoom.

(Communicated in the meeting of September 27, 1902).

The character of the equilibria of phases is exclusively determined
by the number of independently variable constituents — components —
of which the system is built up.

Sometimes this is equal to the number of the different kinds of
molecules. It may also be smaller, if there are among the molecules
those which may pass into each other as in the case of associating,
ionizing or isomeric substances. If these molecular changes proceed
more rapidly than the equilibria of the phases, they exercise no
influence on them.

Although water, for example, is a mixture of at least two kinds
of molecules, its freezing point is quite as sharply defined as that
of a single substance.

If however, the velocity of the molecular change is small, the
system on being treated rapidly will behave like one with more
components than it shows if treated more slowly. The effect of
this on the phenomena of solidification has already been mentioned
by Bancrorr in 1898 and by myself in 1899. So far, however,
no suitable example has been found which would enable us to consider

1) It demonstrates, for instance, in a simple manner that on compressing vapour
mixtures with a sufficient amount of A, the component B first deposits in the
solid state in increasing quantity, but then again completely disappears at a certain
pressure to make room for a liquid phase,

This phenomenon has recently been observed by Kuenen (Phil. Mag. July 1902)
with solid CO, mixed with CjHg.

It must always show itself with the component which in the liquid-mixtures is
the least volatile: in this case B. When however, the liquid-surface has a maximum
pressure as in the instance cited by Kurnen, the phenomenon will be noticed with
both components. If the surface has a minimum pressure it can only occur with
one of the two.

( 284 )

Fig. 1
| _M
250) INE el
Leh
OE
aa
240) Pe

Temperature.

0 100

Mo L 9/9.
Acetaldehyde.

the whole of the equilibria of
phases from that point of view.

Such a system has now been
investigated in my laboratory by
Dr. HoLLMANN of Dorpat. It is the
systemacetaldehyde--paraldehyde,
which has the further advantage
of not undergoing molecular trans-
formation except in the presence
of a catalyzer and so behaves
like a system with two components,
whilst it undergoes transformation
rapidly enough on addition of a
trace of sulphuric acid to appear
as a system with only one com-
ponent. It becomes possible, thus,
for the first time to obtain a general
insight into the position which
equilibria with apparently one
component occupy among the sys-
tems with two components.

The chief results of the research
are the following.

First of all the solidification
phenomena of mixtures of acetal-
dehyde and
investigated.

paraldehyde were
As is well known,
paraldehyde in a pure state melts

Paraldehyde, at 12°.55 (point B). This melting

point is lowered by addition of acetaldehyde along to the curve BLDC,
which continues until the liquid consists almost entirely of acetaldehyde.

With the aid of the apparatus of Prof. KAMRERLINGH Ones *) the
melting point of acetaldehyde was determined at — 118°.45 (A).
The melting point line of acetaldehyde does not extend further than
— 119°.9 (C) where it meets that of the paraldehyde. C'is therefore

a eutectic point,

Melting point.

Be ANA SS

EENS
De a ED
Gases
Ae Sees

1) LADENBURG gave — 120°.

0/

/, Paraldehyde.
100
88.1
67.6
1.4
0

as

( 285 )

The boiling points of the mixtures were next determined at a
pressure of 1 atmosphere and the composition of the vapour of these
boiling mixtures was also determined by means of a special apparatus.
The former form the line “HG, the latter the line #/G of which
the following points are the most important:

F 20.7 boiling point of acetaldehyde
I 41.7 vapour 2.5 °/, paraldehyde
ER ek 7 liquid — 33.5. 4 1

G 123 .7 boiling point of paraldehyde.

On account of the great difference in volatility of the two components
the liquid- and vapour lines are situated far from each other. The
vapour of a boiling mixture is much richer in acetaldehyde than
the liquid, for which reason the two are readily separated by
fractionation.

In the third place the critical temperatures of the components and
of a few mixtures were determined. (Only that of acetaldehyde had
been previously found by Prof. van per Waats to be 184°).

Result :

Critical temp. */, Paraldehyde.
te TSS" 0
Brel Me 11.0
Q 241° 22.0
IN A70 50.0
M 286° 100.0

These are the relations when there is no transformation of acetal-
dehyde into paraldehyde, or the reverse.

If, however, a trace of a catalyzer is added, acids in particular, the
two molecules can be converted into each other, till the condition of
equilibrium corresponding to p and ¢ has been reached *).

It appeared that by these means the boiling point of all mixtures
came in a very short time to 41°.7 and as this point according to
the line HG is situated at 53.5 °/, of paraldehyde, it represents
the relation of equilibrium in the liquid condition at that temperature
and 1 atm. pressure. As the corresponding vapour according to
point J of the vapour line FJG only contains 2.5 °/, of paraldehyde
a rational explanation has thus been found of the long-known fact

1) A little meta-aldehyde is also formed but the quantity remaining in solutior
is so very trifling that its influence on the system considered may be utterly ne-
elected. It must still be ascertained what place meta-aldehyde occupies in regard
to the two forms at high temperatures.

( 286 )

that on distilling paraldehyde with a little sulphuric acid, nearly pure
acetaldehyde is collected.

At temperatures below 41°.7, the equilibrium appeared to be dis-
placed along the line HL, which at 6°.8 and 88.1 °/, of paralde-
hyde meets the melting point line of paraldehyde.

The consequence is that, from whatever mixture we may start,
paraldehyde will always erystallise out on adding a trace of sulphuric
acid and cooling to 6°.8 and as the transformation of acetaldehyde
into paraldehyde proceeds very rapidly even at this temperature, the
whole mixture becomes at last a solid mass of paraldehyde. This
even proved to be the case when pure acetaldehyde was taken as
starting point. On the other hand paraldehyde in the presence
of a trace of a catalyzer does not melt at 12°.5 but at 6°.5 owing
to partial conversion into acetaldehyde.

We have no knowledge of the equilibrium in the vapour at these
low temperatures but something can be said regarding higher tem-
peratures.

The lines FL HG and F/G have regard to 1 atm. pressure. Simi-
lar lines might however, be determined for a higher pressure and
in that manner the displacement of the points A and / with the
pressure would be determined. Finally, we should thus arrive at
the critical line ZM and here the compositions of the vapour and
liquid, which indicate the relation of equilibrium, must become the
same. It appeared from a series of determinations that the point P
at 224° and 11°/) of paraldehyde is this very point.

At these high temperatures, the equilibrium is also reached after
some time without a catalyzer.

It appears from the position of P that the line which gives the com-
position of the liquid when equilibrium is attained slopes in the begin-
ning very rapidly, with rising temperature, towards the acetaldehyde
side of the figure (portion “7H A)*) but afterwards much less rapidly.

The line of equilibrium of the vapour certainly does retrograde,
for at 41° the vapour still contains 2.5°/, of paraldehyde, at 100°
less, and at 221° again 11°/,. In this case the influence of the pres-
sure prevails obviously. As paraldehyde is a triple polymer, the
influence of the pressure is very marked.

If we make a representation in space of the whole figure, like the
one mentioned in the previous Communication, it will be noticed that
the equilibria where the possibility of the mutual transformation of
acetaldehyde and paraldehyde is admitted, are lines on the surface

1) The point K has been determined by TurBaBa at 50°.5 and 39.40/,.

( 287 )

which represents the case that the two components are not subject
to transformation.

For this another new representation may be given which consi-
ders the matter from a more general point of view.

Taking p, ¢ and & as coordinates, a surface may be constructed
which shall represent the equilibrium between the two kinds of
molecules in a homogeneous phase, vapour or liquid.

Ac. Conc. Par. Ae. Cone. Pa.

Fig. 2. Fig. 3.

The general form of such a surface of equilibrium for the system
acet-paraldehyde may be readily deduced from analogy with other
known equilibria in the gaseous condition, if one considers that
paraldehyde requires heat to pass into acetaldehyde and may be
reobtained from the same by compression.

The general course of the equilibrium line at a constant pressure
is indicated in fig. 2, that at constant temperature in fig. 3. If we
now imagine that on the different points of the ¢, v-line in a hori-
zontal plane, p,-lines are erected in vertical planes, we obtain a
Pp, t, & surface of a very peculiar shape which gives the equilibrium
relation between acetaldehyde and paraldehyde for every temperature
and pressure.

The course may be theoretically calculated for the vapour if the
pressure is not too large. With greater pressures and for the liquid
state this becomes a difficult matter but the general course remains
fairly certain. We might therefore, imagine this equilibrium surface
first of all at temperatures higher than those of the critical curve
LM. Here, the surface would for some time extend itself undisturbed
both vertically and horizontally. At lower temperatures, the surface,
on account of its form, must necessarily meet first of all the
surface for liquid-vapour; according to the investigation this takes
place in the point P. From here to lower temperatures, the

( 288 )

equilibrium surface which was at first continuous will become dis-
continuous and break up into an equilibrium surface for the vapour
state and another for the liquid state.

The lines of intersection of these two surfaces with the surface of
two sheets are the lines PJ and PA HE in fig. 1. To these must,
of course, also be added lines of intersection with the other gas-
and liquid surfaces, which have been mentioned in the previous
communication. f

In this manner, it appears that special equilibria, which occur
when transformation between the two components is possible, may
be always considered to originate from the intersection of the general
space figure for the equilibria of phases with the surface of equilibrium
for the molecular equilibria in each phase.

Chemistry. — “On the action of sulphur on toluene and xylene.”
By L. ARONSTEIN and A. S. van Nierop. (Communicated by
Prof. J. M. vAN BEMMELEN).

(Communicated in the meeting of September 27, 1902.)

The researches on the molecular weight of sulphur according to
the boiling point method of L. ARONsTEIN and S. H. Mernuizen *)
showed that this molecular weight was found to agree with the
formula S, and this in liquids the boiling point of which varied
from 45° to 214°. But when toluene and xylene were used as solvents
for sulphur the determination of the molecular weight had given
values which corresponded with those calculated from formulae ranging
between S, and S,. It was then suspected that this difference might
be due to chemical causes. In the following lines we will communicate
the results of our efforts to trace those causes.

Action of sulphur on toluene. It had already been noticed that on
boiling a solution of sulphur in xylene hydrogen sulphide was given
off which was shown by means of lead acetate. A similar evolution
of hydrogen sulphide was not noticed on boiling sulphur with toluene.
As the chemical action of sulphur on toluene at the usually observed
boiling point could probably not amount to much, a preliminary
experiment was made by heating a solution of sulphur in toluene in
sealed tubes at 250°—300° so as to accelerate the action until on

1) Proc. Kon. Akad. Wetensch. 1898. First section VI, 3.

( 289 )

cooling the tubes no crystallisation of sulphur took place. In the
case of a mixture of 2 grams of sulphur and 10 grams of toluene, this
lasted 10 days; in the interval the tubes were repeatedly opened to
allow the accumulated hydrogen sulphide to escape. The product
obtained was freed from undecomposed toluene by distillation; a
preliminary investigation of the residual mass showed with certainty
the presence of stilbene, thionessal and probably also of tolallyl
sulphide. As moreover the contents of the tube had a strong odour
of mercaptane it was supposed that the action had taken place in
one of the following ways. Firstly, benzyl sulphydrate might have
been formed by a direct addition of sulphur according to the equation :
C, H, CH, +S —C, H, CH, SH
and this on losing hydrogen sulphide according to the equation:

2 C, H‚ CH, SH — (C, H‚ CH,),$-+H,8

might have yielded benzyl sulphide, which according to Forst ') may
yield as final products stilbene, totally] sulphide and thionessal.

Secondly, the sulphur, according to the equation:

Ge CH, Fis C,H, CSH Hes
might have yielded thiobenzaldehyde or rather (C, H‚ CS H)x, which?)
according to the equation :
2C,H. CSH=>C.H,,+28
might have formed stilbene, which then might have formed thionessal
according to the equation :
20.) He SS =O Hs os HS:

In order to test the accuracy of these theories 4 grams of sulphur
were boiled in a reflux apparatus with 150 ce. of toluene for 120
hours, care being taken that any hydrogen sulphide which might
have been formed and the non-condensed benzylsulphydrate were carried
off by means of a current of carbon dioxide and passed through an
aleoholie solution of lead acetate. Although perceptible quantities of
lead sulphide were precipitated during that time not a trace of the
well-known yellow lead mereaptide was found. Both the toluene
solution and the crystalline mass obtained therefrom were carefully
tested for the presence of benzyl sulphydrate and also of thiobenzal-
dehyde but notwithsfanding the delicate tests for these substances
their presence could not be demonstrated. But from the toluene
solution we succeeded in isolating stilbene melting at 124° and from
this was prepared the characteristic dibromide (m. p. 285—236°) by
1) Liepie’s Annalen, Band 178. P. 370.

*) Baumann & Krerrt. Ber. D. Chem. Ges. Band 24, P. 3307.

( 290 )

means of an ethereal solution of bromine. The result justified the
belief that the formation of stilbene had taken place in a more simple
manner than was formerly supposed, and according to the equation :
2C,H, CH, +2S=C,H, CH:CHC, H‚ + 2H,S

The thionessal found in the preliminary experiments might then
have originated from the action of sulphur on the stilbene which
according to Baumann and Krerr readily takes place at 250°. Fresh
experiments in which toluene was heated with sulphur for hundreds
of hours in sealed tubes at 200° yielded as sole crystallisable product
a large quantity of stilbene which was obtained in a perfectly pure
condition and of which the bromine addition product with the
correct melting point was prepared. In connection with the results of
the action of sulphur on xylene to be mentioned presently, we took
into consideration the possibility that as a first product not stilbene
but dibenzyl might have been formed according to the equation:

2C, H, CH, + S= C, H, CH, CH, C,H, 4 H,S

and efforts were made to isolate this if possible. As, however,
according to the researches of Rapiszewsk1'), sulphur converts dibenzyl
very readily into stilbene and as we had found by special experi-
ments that this already takes place at 200° when a solution of
dibenzyl in benzene is heated with sulphur and as we had also
proved that this action does not take place at a temperature of
140—145° we have heated sulphur with toluene in a sealed tube
for eight days at 140°. As sole product we obtained stilbene besides
hydrogen sulphide from which fact we are justified in concluding
that by the action on the toluene two atoms of hydrogen are directly
withdrawn and the two remaining groups are condensed to stilbene.

Action of sulphur on p-xylene. When a solution of sulphur in
p-xylene is boiled there is a much more perceptible evolution of
hydrogen sulphide than on boiling a solution of sulphur in toluene.
If, as in the previous experiment with toluene, the gas evolved was
removed by means of a current of carbon dioxide and passed through
an aleoholie solution of lead acetate 16 milligrams of lead sulphide
(equal to 2.1 milligrams of sulphur) were obtained after boiling for
an hour and a half. Here again there was no sign of any lead
mercaptide; neither did the xylene solution ‘contain a mercaptane
as was plainly shown by the fact that no reaction was obtained
with mercuric oxide. We next proceeded to heat one gram of sulphur
with 30 ce of p-xylene in sealed tubes for 120 to 160 hours at
200 to 210° similarly to what was done in the experiment with

1) Ber. D. Chem. Ges. Band 8. P. 758.

( 291 )

toluene. On opening the tubes much hydrogen sulphide escaped and
from the liquid obtained the xylene was distilled off. The residue
became quite solid and apparently consisted of sulphur and a ery-
stallised hydrocarbon. To remove the greater part of the sulphur,
the hydrocarbon was dissolved in ether which was then distilled off.
By recrystallising the residue from alcohol a mass was soon obtained
which melted at 81—82°. Two determinations of the molecular
weight by the freezing point method with benzene gave, respectively
the values 200 and 205. No change took place on heating with
hydrogen iodide in sealed tubes and no addition product was obtained
on adding an ethereal solution of bromine. The product in fact
appeared to be identical with p.p. dimethyldibenzyl p—CH, ©, H,CH,.
CH, C, H, CH, — p. which Moritz and Wotrrenstuin ') had obtained
by the oxidation of p-xylene with potassiumpersulphate.

The result which was not analogous to that obtained with toluene
caused us to repeat the experiment which now yielded a crystallised
product which unlike the first substance was found to consist of a
mixture of hydrocarbons. In order to completely eliminate the sulphur
the mixture was boiled with solution of sodium sulphite, then dissolved
in ether and after distilling off the same, the residue was treated
with cold alcohol. The alcoholic solution again contained p.p. dimethyl-
dibenzyl (m. p. 81— 82°) as was proved by repeated recrystallisations.
The portion insoluble in cold alcohol was solved in boiling alcohol
and by repeated recrystallisation a product was obtained which melted
at 176—177°, yielded, on adding an ethereal solution of bromine, a
bromine product melting at 208° and proved to be identical *) with
p-p. dimethylstilbene p — CH, C, H, CH CH C, H, CH, — p.

In order to find out the cause of the difference in these results a
further investigation took place. As far as we were aware, the only
difference between the two experiments was that this time the tubes
had been repeatedly opened thus causing the removal of the greater
part of the hydrogen sulphide. The temperature during the experiment
was in both eases the same and constant between 200 and 210° ;
the heating was also continued for about the same length of time.
It was now possibie that originally in both cases p.p. dimethyl-
stilbene had been formed. Whilst in the first experiment this sub-
stance might have been almost completely reduced to p.p. dimethyl-
dibenzyl by the action of the hydrogen sulphide, this reaction could
only have occurred in a limited degree in the second experiment.

1) Ber. D. Chem. Ges. Band 32. P. 2531.
2) Gotpscumipt & Hepp. Ber, D, Chem. Ges, Band 5. P. 1504,

(9907)

For this investigation a solution of p.p, dimethylstilbene in benzene
was saturated with hydrogen sulphide, introduced into tubes the air
of which was totally displaced by hydrogen sulphide and after sealing
the tubes, the contents were heated for 40 hours at 200°. From these
tubes there indeed was obtained, besides unaltered p.p. dimethyl
stilbene, a product which proved to be identical with p.p. dimethyl-
dibenzyl. This showed that under the given circumstances the expected
reaction might have taken place.

On the other hand, dimethyldibenzyl was heated with a solution ot
sulphur in benzene for 40 hours at 200° and, although it was not
yielded in a quantity sufficient to admit of a thorough purification, p.p.
dimethylstilbene was obtained; at all events a hydrocarbon melting
between 140° and 150° which absorbed bromine and yielded a product
melting between 185° and 192°, whereas the melting point of p.p.
dimethylstilbene dibromide is situated at 208°. From these experi-
ments it is, therefore, probable that the formation of stilbene is here
the primary and that of dibenzyl the secondary reaction, but we here
got no certainty about this.

On repeating the experiments on the action of sulphur on p-xylene
in sealed tubes some of which were opened from time to time unequal
proportions of stilbene and dibenzyl were still obtained, but the result
of the first experiment (nearly exclusive formation of dibenzyl) was
never again obtained.

It should be mentioned here that p.p. dimethylstilbene was often
obtained in two different forms. Generally, it was a coarse crystalline
powder, but occasionally it consisted of very thin leaflets with a silky
lustre and showing a violet-coloured fluorescence. The original form of
both was retained after reerystallisation from alcohol. Once we succeeded
after a good deal of trouble to convert the coarse granular form by
grafting, into the silky condition. The melting point of both forms
was identical. On treating them with an ethereal solution of bromine
they both gave the same bromine addition product. To see whether
this was a case of stereo-isomery, solubility determinations were made
of both modifications in absolute alcohol at 25°. In both instances
the same solubility value. was found, namely 0.21 part per 100 parts
of alcohol 5. Notwithstanding the difference in appearance which was
also retained in these solubility experiments, a stereo-isomery has
thereby been rendered very improbable.

1) Exps (Journal f. Pract. Chemie. Neue Folge Band 39. P. 299 and Band 47.
P. 46) gives the solubility of p.p. dimethylstilbene in alcohol at the ordinary
temperature as 0.76 per 100.

( 293 )

Action of sulphur on m.-aylene. Sulphur boiled with m-xylene not
only gave a much smaller evolution of hydrogen sulphide than in the
case of p-xylene but the amount was even less than that obtained on
boiling sulphur with toluene. m-Xylene which had been boiled for ¢
considerable time with sulphur was quite as free from mercaptane
as the similarly treated toluene and p-xylene.

We now proceeded to heat sulphur and m-xylene in sealed tubes
at 200°. After the heating had lasted for 70 hours, the sulphur had
totally disappeared and the tubes could be opened. Streams of hydrogen
sulphide escaped. From the liquid obtained the xylene was distilled
off and the liquid non-crystallisable residue was freed from sulphur
by boiling with solution of sodium sulphide. As it was not impro-
bable that both m.m. dimethylbenzyl and dimethylstilbene might have
been formed (to judge from the behaviour of p-xylene) and as the
first named substance is, according to Vorrraru ') and Moritz and
WOLrPrENSTEIN *), a liquid and the unknown m.m. dimethylstilbene
probably a erystallisable substance it was tried (although in vain) to
effect a separation of these two substances by heating in a current
of steam, by fractional distillation at ordinary pressure and also by
solvents. The suspected presence of a stilbene in that liquid was,
however, soon proved when bromine was added to its ethereal solu-
tion and the whole placed in a freezing mixture. A bromine-addition
product now crystallised in abundance. The addition of bromine was
continued until a small excess was present. The crystallised
product after being recrystallised twice from xylene had a constant
melting point of 167—168°. A bromine determination according to
Carrus gave 44.02 °/, of bromine, the calculated quantity for dimethyl-
stilbene dibromide being 43.50 °/,.

The dibromide was used to prepare the hydrocarbon itself. For this
purpose it was dissolved in xylene and boiled with molecular silver
or sodium wire for 6 hours in a reflex apparatus. From the xylene
solution obtained the xylene was removed by distillation ; the residual
liquid crystallised on cooling and the crystalline mass could be readily
purified by reerystallisation from alcohol. The substance is very diffi-
cult to burn; the combustion only succeeded by intimately mixing
it with lead chromate and potassium bichromate. The elementary
analysis gave the following result :

69410 Ae HE A OLEN
©. 92.80. 17E 70

Oneca en ete ate rd ze
Calculated for C,, H,, .

1) Zeitschr. f. Chemie 1866. P. 489.
2) Ber. D. Chem. Ges. Band 32. P. 2532,

( 294 )

The melting point was constant at 55—56°.

That the obtained hydrocarbon was really m.m. dimethylstilbene
was proved by adding bromine to its ethereal solution which imme-
diately yielded erystals of the dibromide with the previously found
constant melting point of 167—168°.

The ethereal liquid from which the dimethylstilbene bromide was
precipitated, contained, of course, free bromine from which it was
freed by treatment with aqueous potash. After distilling off the ether,
the liquid was submitted to fractional distillation when hydrogen
bromide was evolved owing to the presence of brominated products.
The hydrogen bromide present in the distillate was removed by
treatment with aqueous potash and the liquid distilled once more.
When it appeared that this distillate, passing over between 298° and
302° was not yet free from bromine it was dissolved in toluene and
boiled for three hours with sodium wire which completely removed
the bromine. The liquid then showed a constant boiling point ot 298°.
On analysis was found:

CA 30 SBE
Caleulated! for Catan 20 LG OUA ELST:

Two determinations of the molecular weight by means of the lowe-
ring of the freezing point in benzene gave 201 and 199; calculated
210°. All data agree with those of VorrrarH and those of Morirz
and Wotrrenstein for m.m. dimethyldibenzyl. Only the boiling point
was found to be two degrees higher.

From this it, therefore, appears that m-xylene on treatment with
sulphur yields stilbene as well as dibenzyl as discomposition products.

To ascertain whether stilbene was here also the first product,
m.m. dimethyldibenzyl was submitted to the action of sulphur by
boiling it with this in a reflex apparatus. The product of the reaction
dissolved in ether and treated with bromine did not yield a trace
of the characteristic m.m. dimethylstilbene dibromide. This sub-
stance could not even be recognised by means of the microscope.

From this we think we may come to the conclusion that during
the action of sulphur on m-xylene the first product is most proba-
bly stilbene and that dibenzyl is a secondary product formed by the
reducing action of hydrogen sulphide.

The results of this research are, as we believe, a confirmation of
the opinion expressed by ARONsTEIN and Merinuizen in their treatise
on the molecular weight of sulphur. A trifling action of the sulphur
on toluene and xylene must cause a derivation of the molecular
weight in the direction previously found. One mol. of sulphur causes
the formation of 8 mols. of hydrogen sulphide and 4 mols of stilbene.

( 295 3)

Although hydrogen sulphide is volatile and most of it escapes during
the boiling, the increase of the number of molecules formed during
that action (however small this may be) is large enough to account
for the observed difference. The fact that the deviation has been
found larger in the case of toluene than with m-xylene as solvent
is also in agreement with the observed fact that more hydrogen
sulphide is evolved in the first than in the second case.

Our research on the action of sulphur on p-xylene was not conducted
merely with the idea of confirming the researches of ARONSTRIN and
MEIHUIZEN (we were not quite sure whether the mm-xylene then used
had been completely free from p-xylene) but also to throw more
light on the mechanism of the process and particularly on the ques-
tion of the primary formation of stilbene and the secondary forma-
tion of dibenzyl.

Chemical Laboratory of the Polytechnical School.

Derrr, September 1902.

Physiology of Plants. — “J/nvestigations of Glucosides in connection
with the Internal Mutation of plants,’ by mr. Tu. Weevers.
(Communicated by Prof. C. A. LoBry pr Bruyn).

(Communicated in the Meeting of 27 September 1902.)

The purpose I had in view in this investigation was to trace for
some plants, whether the amount of glucosides remains unchanged
during the development or not; and to investigate in the latter case
by what conditions these changes are determined.

At the same time the manner in which those changes took place
formed another subject for study: whether glucosides were trans-
ported as such, or whether a decomposition could be stated, and in
the latter case what were the components in which this took place.

Salix species and Aesculus hippocastanum lL. were especially used
for the investigations; Gaultheria procumbens L. and Fagus sylvatica
were also submitted to a prefatory study.

The glucosides to be mentioned here are salicine for the Salix
species, gaultherine for Gaultheria and Fagus, aesculine and more-
over some glucosides not yet chemically determined for Aesculus
hippocastanum.

As for salicine the quantitative valuations were made as follows.
The salicine was entirely extracted by boiling water from the parts
to he examined: and the extract treated with basie lead acetate. The

| 20

Proceedings Royal Acad. Amsterdam. Vol, V.

( 296 )

surplus was removed by dinatriumphosphate and the liquid then
obtained reduced to a definite volume. In this two estimations of
sugar were made, one before, the other after allowing emulsine
to work in upon it for 48 hours. Prefatory experiments with pure
salieine had proved that in this way it was completely decomposed:
the increase of the reduction after inversion was to be attributed
only to the glucose formed of salicine. *).

From this increase of the glucose the quality of the salicine could
then be calculated.

This same method was followed in order to state the salicine in
various parts of the plant; then however, after inversion the liquid
was extracted with ether, so that saligenine might enter into it. This
substance is easily recognised by the physic qualities of its crystals
and by the substitute of bromine obtainable with brominewater and
moreover by its salt of copper. The efforts to point out salicine in the
tissue itself were unsuccessful; the method formerly used by THrORIN ©),
namely that of adding concentrated sulphuric acid, proved impracti-
cable, as it during the produced erroneous results.

For the above mentioned Salix species salicine is found in the
bark of the branches, but not in the wood; young buds are rich in
it, likewise the assimilating leaves. It appears in young ovaries
but disappears during the process of ripening.

Although an inverting enzyme was not to be extracted, it proved
necessary to kill the parts immediately in boiling water, otherwise
considerable alterations in the quantity of salicine presented them-
selves. Thus e.g. after slow drying 25 pCt. disappeared out of
the bark.

The following series of determinations for the purpose of invest-
igating the quantity of salicine during the budding period, was made
with one specimen to exclude individual differences.

The total quantity in various successive stages was calculated by taking
a branch with a definite number of sidebuds as object. The weight of
the different parts of this branch together with the procentie values
of the quantity of salicme in corresponding parts of the same object
in the successive stages gave the total quantity of salicine of this
branch in those stages *).

1) Before inversion a solution of salicine does not reduce even with boiling ; neither
does saligenine formed by means of inversion at the same time as glucose.

2) See Theorin Ofversigt af Konel Vetenskaps. Akademiens Förhandlingen 1884.
No. 5. Concentrated H, SO, gives with salicine a coloring of red.

3) In corresponding parts of one object was an equal quantity.

( 297 )

Under observation were only branches without genitals; those
with catkins gave a different result *).

Branches of 1'/,—4 mM. diameter (wood and bark together).

March 24th 3.2 pCt. *)
April 47th 2 1
May, 21% 04 ,
Branch of 4—8 mM. diameter (only bark; hence the quantity is higher).
March 24th 4.1 pCt.
Apri 17 2807
May ALS A Sp
For Salix Helix L. the figures for the bark of branches were
March 24% 4.4 pCt.
April 27 2.7

The quantity of glucose is a little variable ; however, it does not
rise above 0.5 pCt.; the quantity of fecula diminishes when budding
from 9.5 pCt. to 6 pCt.

In the young buds of Salix purpurea there is before the budding
4.4 pCt. and of Salix Helix 6.2 pCt. During the budding this quantity
decreases greatly, disappears even for 5. purpurea entirely (17 April)
but rises again quickly, when assimilation begins, to 3.7 pCt in leaves
and 3 pCt. in young shoots (21 May).

Of the absolute quantity of salicine in a branch with 300 buds

+ 36 pCt. disappeared from 24 March—17 April

se 18, 1" „ 17 March—21 May,
the assimilation, begun already before May 21, having given rise to new
salicine.

Experiments with branches placed in the dark in water*) showed
the following:

After the roots have been formed, a number of long etiolated shoots
bud forth, consuming by their development besides the fecula also
a great quantity of the salicine in the bark (+ 70 pCt).

At first the young shoots contain a great quantity 7.2 pCt., this,
however, keeps on decreasing; the absolute quantity calculated for
100 young shoots also diminishes :

for 100 young shoots long 18 mM. there is 28 mG. salicine

/ I I I nt DA Su " „15 # "

1) The quantity of salicine is at the same instant lower in branches with
catkins than in those without; the salicine diminishes more quickly.

2) These procentic values are calculated for dry weight.

5) These were branches of 6—10 m.M. diameter, the young shoots coming from
sleeping buds.
20%

( 298 )

These quantities are small compared to the entire quantity consumed
+ 330 mG. for 100 young shoots.

When the young buds were budding forth saligenine was found
in them, the branches were immediately killed in boiling water, the
extract after cooling down extracted with ether; so all influence of
enzyme could be excluded. It becomes very probable that the salicine
is analysed before the consumption, on account of saligenine being
found ; the quantity, however, is so small that if really the analysis of
salicine were to take place as indicated, and a decomposition to precede
the consumption, saligenine can only be an intermediate stage. Hither
the aromatic half disappears as such, or another aromatic substance
must be the definite product of the decomposition.

In the young leaves developing normally, salicine soon makes its
appearance again after having disappeared for a moment; we can
expect that this increase is connected with and due to the assimilation,
as etiolated shoots do not show it. In order to state whether the
leaves were really the place of a new formation and the light really
had a part in it, the quantity of salicine before and after darkening
was compared.

The quantity in the leaves was determined in the evening after
sunset and in the morning before sunrise (one specimen). Likewise
in the evening leaves were halved, one half with midrib left on the
plant, the other half analysed. The following morning the remaining
half was cut off from the midrib and also analysed). Provided that
a sufficient number, 100 or 200 leaves were halved, a comparison
could very well be made.

For a small-leafed specimen a 100 leaves

8 P. M. 7 Aug. 47.5 mG. glucose 87.2 mG. salicine

EAM B = eee " 60.2 / IJ
For a big-leafed specimen a 100 leaves

8 P. M. 7 Aug. 80 mG. glucose 177.7 mG. salicine.

4 A MESS) ein ed, DE ENA TT

So in both cases we see a decrease during an 8 hours’ summer
night of respectively 30 and 20 °/, of the salicine in the leaf in
the evening.

For experiments with entire leaves of one specimen :

8 Po M7 Aug. 467% salicine:
4 As Mas Sut) iy ea rde Ee oe
B ACME Br Mi Aen Petr

1) See Lotsy. Mededeelingen ’s Lands Plantentuin XXXVI,

( 299 )

Thus here too a decrease of 30 °/, during the night followed up
by an equal increase on the following day. If branches on the plant
are enveloped in black waxed paper the decrease amounts after
48 hours only to 35 °/,, no great difference with that of 8 hours;
increase, however, did not take place, so light proves to be a necessary
factor. The experiments of etiolating told the same.

If this quantity of salicine disappearing from the leaves was
removed to the bark, an increase would have to be observed there.
This was indeed the case, for branches rich in leaves the increase
of the quantity of salicine of the bark amounted in one night to
2.5 °/,; for branches with few leaves to 1.1 °/,.

From the etherextract prepared in the above described manner,
of the parts of Salix purpurea still another substance could be isolated
by means of subliming. According to the miero-chemic qualities this
was a substance resembling phenol and qualified by its compound of
lead and of lime, besides reaction with tetrachloorchinon as an ortho-
derivate '). The substance did not show Aldehydreactions. The further
micro-chemical qualities corresponded to those of the simplest ortho-
phenol, catechol. After a repeated crystallisation out of benzol the
melting-point proved to be 104°. Elementary analysis and determina-
tion of molecular weight confirmed the fact, that it was catechol.

As the material which furnished the substance was quickly killed
both in boiling water and in boiling alcohol and the etherextract
already showed the crystals before sublimation, influence of enzym *)
is not probable and formation out of resin is not possible.

Treatment with ferrichloride followed by additon of natrium hydro-
carbonate also furnished in the tissue the reaction of catechol. The
red colour was clearly visible in the unopened cells of the sections
of the bark, young etiolated shoots showed them faintly, older ones
more. Catechol is like salicine only to be found in the bark *).

The supposition was aroused that catechol might be the aromatic
substance, remaining there as definite product of decomposition of the
salicine. In order to test thé accuracy of this supposition, an investiga-
tion had to be made whether the quantity of catechol of the parts
of Salix purpurea were varying.

For a quantitative determination of the catechol the method of

1) According to an investigation of Prof. H. Benrens which will shortly appear,
communicated to me by Miss GRUTTERINK.

2) The black colour of the dying leaves is caused by the influence of a “tyrosi-
nase”’ on catechol.

8) Catechol was also obtained out of Salix Helix L., S. babylonica L., S. vitellina
L, Populus alba L., P. monilifera Ait, sometimes only very little.

( 300 )

DeGeNeER (Journal f. Prakt. Chemie 1879) could not be used on
account of a flavon-like colouring matter not closer examined, and
also precipitated by a basic leadacetate. So the method of Prof. BrHRENs
to determine Indigo was followed. The sublimate of a solution of
catechol of a known strength in absolute alcohol was compared with
that of the alcoholic solution of the remainder of the ether evapora-
ted dry. Now it was examined how much this liquid had to be diluted
to obtain an equivalent sublimate. The sublimation was performed by
means of the brass table described by Prof. Wisman. Under certain
precautions the determination could be accurately made to milligrammes.

The quantity of catechol of the leaves was in the evening 0.6 pCt. } with one

M ee Hoo pee ap ay mOrning0. 1, speciitien
pees with the
ri nm „vp » bark y y» » evening0.6 ,
; ; same
II I " i út I VA a morning0.4 " | ;
specimen.

So the quantity of the catechol here proved to change in reverse
order as that of the salicine. In the leaves the salicine diminishes in
the night, the catechol increases, and in the bark the catechol dimi-
nishes and the salieine increases. Is there any connection between
the extent of these changes?

For that purpose for one and the same object catechol was deter-
mined as well as salicine.

200 halves of leaves 8 P.M. 225 mGr. salicine (4.5°/,) + 32 mG. catechol (0.65°/,)
AN ies jn a) &eAoM. 162, ' (3.39), ) Adan 7 (1.05°/0)
So 63 mG. salicine less, 20 mG. catechol more.

The proportion of these values, given the degree of accuracy of
the determination of catechol, pretty well agrees with the proportion
of the molecular weights.

A comparison was also made of the change in salicine with that in
catechol for leaves budding forth in the dark.

17 Gr. bark before budding 351 mGr. salicine 36 mGr. catechol
Ly „ after 7 234 " Dy 1

budding etiolated shoots DD a y 4 " "

(a great increase in the bark, in the young shoots only a small
part of the catechol thus formed to be found) 64 mG. salicine was
used, 23 mGr. catechol was formed.

These two values stand in the ratio of 36 to 100, the molecular
weights in that of 38 to 100.

So it is very natural to assume here a decomposition of the salicine
into sugar and catechol with saligenine as intermediate stage (see

( 301 )

above). For this then a CH, group out of the lateral chain would
have to be decomposed, as saligenine is orthoöxybenzylalcohol and
catechol is the orthodiphenol.

Corresponding to this the quantity of catechol of the bark is large
in May(1.1 pCt), a greater part of the salicine then having disappeared,
much lower in July (0.3 pCt.) when the loss has been repaired *).
Where now has the decomposition taken place ?

PrerFer says Kap. VIII, Pflanzenphysiologie 2: Auflage: „vielleicht
dienen die esterartigen Verbindungen der Kohlenhydrate mit Phenol-
körpern zur Herstellung von schwer diosmirende Verbindungen bei
deren Zerspaltung im allgemeinen der Phenolkörper in der Zelle
intact verbleibt, um fernerhin wieder zur Bindung von Zucker benutzt
zu werden.”

The facts are excellently explained in the following way:

The decomposition of the salicine takes place in every cell, the
glucose is conveyed in the direction of the green parts, the catechol
remains in the cell and binds glucose, coming from cells situated
closer to the bark, to salicine.

Glucose is transportmatter and salicine is transitory reservematter.

The glucose being comsumed in young parts in greater quantities
than its supply is, catechol must be found, but only so much as
corresponds to the decrease of the absolute quantity of salicine.

100 young shoots 18 m.M. long 28 m.G. salicine, traces of catechol.
ROO 5 i SO. tM ght) 216 mG: i 2 m.G. "

6.4 m.G. salicine corresponds when calculated to 2,5 m.G. catechol,
when observed to 2 m.G.

This correspondence adds great strength to the hypothesis. *)

In the bark the loss of consumed glucose is not repaired, so
catachol increases greatly.

As for Aesculus, here it was especially the germination which
was studied. The glucosides found in the ripe seedlings being not
yet chemically determined, it was only necessary to base the method
of the quantitative definition on the quantity of sugar formed by
inversion. I had to trace whether the quantity of sugar bound in
glucoside decreased during the germination.

To this end the seedlings were ground and extracted with methyl-
alcohol, of this extract the alcohol was evaporated, and the watery liquid

1) [| here mean the quantity in the bark of thicker leafless branches where no
difference between night and day is observed.

2) Also the facts observed at the change of night and day can be excellently
explained in this way.

( (oa),

extracted with ether to get rid of oil and resin. The extracted
liquid served as definition of the reduction before and after inversion
by boiling it for 2 hours with HCl‘). ;

From the difference of this reduction the quantity of reducing
sugar originating from the glucoside could be calculated; it amounted to
13 pCt.

During the germination this quantity decreased in cotyledons by :
60 or 70 pCt. Fecula and albumen by 70 or 80 pCt. The germinating
plants contained only 1 or 2 pCt. of glucose bound in the shape of
glucoside, the consumption of the glucosided sugar during the germina-
tion could be regarded as proved by the 70 pCt. decrease of the
absolute quantity.

The localisation of aeseuline was observed by fluorescence of its
watery solution, to be seen when there are not too few sections.
Aesculine was to be found in ungerminated seeds only sporadically
in the plumule; when germinating it appears in greater quantity in
the stalks of cotyledons, not in the cotyledons themselves. Stalk and
hypocotyledon internodium contain aesculine when germinating in the
dark as well as in the light, so light is not necessary for the formation.

The stalks of the leaves show the aesculine only when developing in
the light and not in the dark; this seems to point to the fact, that the
aesculine of the normal germinating plant originates from two sources :
that it is formed for the greater part by reforming of substances out of
the cotyledons and side by side with this, that it is prepared inde-
pendently in the stalks of the leaves from substances assimilated by the
leaves. Experiments with full-grown planis, in the light and in the
dark, with coloured and with normal leaves made this the more
propable, but full certainty can only be given by means of later
quantitative definitions.

Studies on Gaultheria procumbens showed what changes took place
in the quantity of the gaultherine, the investigations have however not
yet been brought to an end. The method of quantitative definitions
was founded on the observation of the quantity of methylsalicylate
Which could be formed out of it. This was redistilled with vapour
out of the parts, caught in alcoholic potash and saponificated with it.
The kaliumsalicylate formed in this way was determined according to
the method of Mrssincer and VorTMANN ®). For smaller quantities the
colorimetric method of determination was used with Fe Cl,

1) After inversion and neutralisation the liquid was treated with leadacetate,

2) Messincer and Vortman, Zeitschrift f. Anal. Chem. 38 bl. 292.

Ber. d. deutschen chem. Geselischaft. Berlin. Bd. 22. 2313,

( 303 )

With Fagus sylvatica where Tarveer *) found methylsalicylate only
in the germinating plant, the latter method showed that it was also
present in the full-grown plant. Methylsalicylate is to be found
sporadically in the buds of the beech shortly before budding, during
that process it is found in the young leaves and shoots as well as
in the branches of the preceeding year. Young long branches are
richest in it, 0.02 pCt. As soon as the leaves have unfolded, this
substance begins to disappear again and is nowhere to be found in
a week’s time.

Further particulars to be looked for in the dissertation to appear
shortly.

Physics. — “Some observations on the course of the molecular

transformation.” By Prof. J. D. van per Waars.

As is well known, acetic acid may be considered as a mixture
of simple and double molecules and we find a decreasing number
of double molecules when we investigate the saturated vapour of
this substance at increasing temperature. The same applies also to
NO,. We are apt to conclude from these two best known instances
of molecular transformation that this course is the only one that
is possible. We may, however, easily convince ourselves that also
the opposite course may occur, and it appears to me that we may
conclude from figure (1) of the communication of Prof. H. W.
BakKrvis RoozrBoom in the Proceedings of the previous session, that
for the transformation of acetaldehyde and paraldehyde this opposite
course perhaps occurs.

Let us take the equation for the molecular transformation, as it
occurs Cont. II, pag. 29, namely:

vb UE -E) 2(H,—H,)
log en En +] — —
“ (1—2)? RT | I,

The quantity 1—v of this equation represents the quantity of the
substance expressed in grams which occurs in the form of simple
molecules, « therefore that which occurs in the form of double
molecules. If molecules were formed consisting of 7 simple mole-
cules, the equation would be modified into the following one:

(v—byr—la A
log ——_——- = + B.
(le) il,

It is true that we only find the equation in this simple shape if

1) Tattteur, Comptes Rendus A, Sc. Tome 132 p. 1235.

( 304. }

4

we make suppositions concerning the quantities ‚a and 5, which can
only be satisfied if the multiple molecules may be considered to be
mere complexes of simple molecules, which can be formed without
further radical modifications in the structure of the molecules them-
selves. But as I will apply the given formula only in the case of
saturated vapour at a pressure which is not very high, in which
case the influence of the quantities « and 6 may be neglected, we
may consider it to be sufficiently accurate for our aim.
We may deduce from it:

i dv de {1 n A
En ) ar is aT \ xz + Copies Te

For saturated vapour at a pressure which is not too high, we have:

—l
prik T (: nef r).
n

from which follows:

n—l de
dp dv i n dT
pdr vdT fi Rl
ee
n

: 1
If we substitute for — -

oA the value found above, we get the

equation:

la 1 T d ; A
REE EE Ce
dT nil ; 3
az (1—e«)(1—

Whether the number of multiple molecules in the saturated vapour
increases or decreases with the temperature, depends therefore on the
fact whether the value of the expression :

A
is more or less than =

T dp. 6 Ter
For a normal substance pat is approximately equal to 7 7:
For a substance in which molecular transformation takes place, the
factor 7 is to be modified and this factor will even vary more or
less with the temperature. But if a perfectly accurate numeric deter-
mination is not required, and if we only ask: Can both ways in
which ‚pr may be thought to vary with the temperature occur? then
we may state what follows:

( 305 )

“When the heat developed by the combination of 7” simple mole-
cules to a complex one is so great, that it far exeeeds the quantity
(n—1)7 Ti, — as is the case for acetic acid — then the saturated
vapour will at higher temperature be associated in a lower degree.
If on the other hand that quantity of heat is much smaller than
(n—1) 7 7. then the reverse will take place.”

When we proceed to saturated vapours of greater density and when
we approach the critical temperature, then this difference in the
course will no longer exist.

If we consider in the equation:

ET B de, r 1 n da A
n— 1) ——- — + — ——= —..
v—baT © ap l—w/) dT i!
ek)
the value of — Sa PT for the saturated vapour at all temperatures
vd A

between O and 7, we see that this quantity has a minimum value
for a certain value of 7. For very low temperatures it may be

7

ie
equated to 7 an and for the absolute zero it is therefore infinite.

But also for 77=T.,. it will be infinite, for by is infinite in the
critical point. The value of 7’ for which this minimum value occurs,
would for normal substances be the same fraction of 7. For sub-
stances with molecular transformation we find a different value for
this fraction. It may be calculated for many substances from the
experiments of SIDNEY Youne at least approximately.

Ed A
RT iT

Above the temperature for which — for acetic acid

also see is again positive. For substances which behave as acetic
di

acid therefore a minimum value of wv occurs. The fig. (1) of Bakuuts
ROOZEBOOM presents in fact such a minimum for paraldehyde, and
from this would follow, that this transformation is of the same type
as that of acetic acid. Yet it seems possible to me that an accurate
direct investigation would prove this minimum not to exist. If it
really exists, then it will probably occur at a much higher value
of 7%

But even if this transformation would also prove to be of the
same type as that of acetic acid, vet it seems not superfluous to
me to point out, that also the other type may possibly oceur.
The abnormality of substances as the alcohols, water, etc. is ascribed
to a possible molecular transformation, and yet the saturated vapour

( 306 )

of these substances appears to follow the laws of the perfect gases
the more accurately as the temperature at which it is investigated
is lower. So the density of saturated vapour of water at 100°,
appears to be 2'/, pCt. higher than would follow from the applica-
tion of the laws for perfect gases; whereas the saturated vapour of
water at ordinary temperature presents a density which does not
deviate noticeably from that, which follows from the laws of Borre
and Gay-Lussac. If for molecular transformation the type of acetic
acid were the only one which could occur in nature, then the
supposition that water is also subjected to this transformation would
involve that the deviation would be found to increase when the
temperature is lowered. It is highly probable that the deviation
of 2%/, pCt. of saturated vapour of water at 100°, which cannot
be accounted for by the ordinary deviation from the laws of
Borre and Gay-Lussac which also normal substances present, must
be ascribed to the presence of more complex molecules; but at the
same time we must then assume, that the heat of transformation
lies below the limit which we have indicated above.

The equation which we have used here, is taken from Cont. H,
p. 29 and there it had been obtained by the direct application of
the principle of equilibrium, according to which a given quantity of
matter at a given temperature in a given volume will arrange itself
in such a way that the free energy is a minimum. It is therefore
that we had to take a fixed quantiy of the substance, e.g. a unit
of weight, which might be divided into 1—# grams simple, and
z grams double molecules. When « varies, the total quantity of the
substance remains constant.

We may, however, also consider a mixture, consisting of a number
of 1—2 simple and « multiple molecules and then we may apply
the thesis that, when equilibrium is established the thermodynamic
potential for a molecular quantity of the multiple molecules must be
n times greater than that for the simple molecules. The linear function
of z, however, which in other cases may be omitted, must in this
case of course be preserved. If we then put:
$= MRT {u + (1-2) 1 (1-a) + ele) 4+ Tia (1-2) + Bal + y (1-2) 4+ de

then we have:

0
Sr 5 = MRT ju—ayp', + 1(1—a)} 4+ aT + 7,
EDT
0
and §-+ (l—z) 5 : — MRT {u + (1—a) wle + BT + 0.
pT
ds 5
From § + (1—z2) =n Se we deduce:
Oa »T der

( 307 )

a \ A
pr = (n—1) fu — eu’ — uws + B+ rik

This last equation yields the results we have obtained, in a still

log

simpler way than that which we have made use of originally. It
has moreover the advantage, that the usual signification of « and u,
as if is established in the theory of a binary system, may be kept
unchanged.

Reactions like that of acetaldehyde and paraldehyde, reactions
which we can bring about at pleasure by means of a eatalyzer and
in which the composition may be determined experimentally are of
course of the highest importance for the investigation of the course
of the molecular transformation. For reactions as that of acetic acid
the density is the only criterion for the degree of the transformation ;
and this criterion fails as soon as we work in circumstances in which
the deviations from the laws for the perfect gases are considerable.
The experimental investigation will therefore not be able to prove
the occurrence of a minimum in the number of the double molecules
in the saturated vapour of acetic acid. At the temperature at
which the theory predicts that minimum and which lies probably
between 0.8 7, and 0.9 7, the density of the saturated vapour
is already so great that it is nearly impossible to deduce reliable
conclusions concerning the course of the transformation.

Physics. — “Critical phenomena in partially miscible liquids.” By
Prof. J. D. van DER WAaLs.

I have read with great interest the communication of Prof. KupNEN
under the above title, which occurs in the Proceedings of the previous
session, and it induces me to draw attention to the following con-
siderations.

In my paper of March 25 1899 I started from the thought,
that the series of plaitpoints, which may occur at different tempe-
ratures, whether we arrange them to a plaitpoint curve or assign
a place to them in the 2, v plane, must form one or more continuous
curves — of course continuous in the mathematical sense.

When therefore the experiment yielded, e.g. for ethane and ethyl-
alcohol two separate plaitpoint curves, I have connected them by
means of a theoretical part.

If we wish to connect the two pieces of curves found to one
curve, we may perform this in two simple ways. In thefirst
place we may connect them in such a way that the curve is con-

( 308 )

tinuous also as to its direction. In the second place we may, between
the ends of the pieces which are experimentally determined, trace
a curve which presents in those ends abrupt changes of direction
and which has about the same course as the three-phase pressure,
though it lies everywhere lower than that pressure.

I then thought that the two pieces of the plaitpoint curve were
to be connected in the first manner. The experiment had shown
that the peculiarities which must then occur, namely the existence
of a minimum and of a maximum temperature, were possible and
really occurred in nature; at any rate the minimum temperature.
The peculiarity, on the other hand, which occurs, if we make the
connection in the second manner, namely the abrupt change of the
direction, was never observed. .

Now when we have made a choice and when we wish to examine
its meaning, all conclusions must of course be in accordance with
the choice we have made. Here | will mention the following
conclusions from the first way of bringing about the connection :
Ist. A mixture with minimum critical temperature exists. 2nd, A
mixture with maximum critical temperature exists. 38'¢. Plaitpoints
occur outside the borders of the three-phase temperature, which
cannot be observed, as they lie above the empirical w-surface.

In this case a plait must necessarily at a certain temperature be
separated from the principal plait, which at higher temperature (the
maximum critical temperature) has contracted to one point. In short
then the phenomenon quite corresponds to the description I have
given Cont. Il, p. 187. If therefore Kurnen accepts the way in which
the connection of the two pieces of the plaitpoint curve he has
determined experimentally, is brought about, then I cannot but consider
it to be inconsistent, if he raises objections to the interpretation.

But more important is the question whether the choice we have
made is the right one; whether, therefore, the connection between
the two pieces of the curve should not rather be brought about with
two abrupt changes in the direction. This has at the same time the
following meaning: Is the plaitpoint the course of which is indicated
by the theoretic curve, perhaps quite another plaitpoint as that whose
course is indicated by the experimental curve? Now I read in the
paper of KvrNEN p. 321 that he has obtained the figure I have
originally given, with the aid of other curves. But I think that this
must be understood in such a way that he has succeeded in pointing
out, that the two ends of the experimental branches may be connected.
The way in which the connection must be established can here, after
my opinion, not be decided. I have already doubted some time as to

( 309 )

this question. The first way of connecting requires that as well a
mixture with a maximum, as a mixture with a minimum critical
temperature occurs. And though I expressed in my paper of 1899
the expectation, that it would be possible to account for this, yet I
must acknowledge, that a further investigation has made me consider
the occurrence of a maximum critical temperature more and more
improbable.

After my opinion the question is decided by that part of the
plaitpoint curve KurNeN has determined experimentally, which starts
at the critical point of methylaleohol and which indicates the course
of a plaitpoint belonging to a plait which has its summit towards

ip.
, Is negative or at any

ap
the side of the small volumes. The fact that aT
a

Op
rate smaller than (55 quite agrees with the circumstance, that
3 Ü

do\. x
>, | 18 positive.
du

If this plait had its summit on the side of the large volumes, then
it would be possible to explain the course also for the case of ethane
and methylaleohol by admitting the existence of a maximum and a
minimum 7. As this is however not the case it seems to me that
we cannot but assume with KueNeN, that the theoretical part of the
plaitpoint curve indicates the course of a point, drawn i. a. by KoRTEWEG
(Archives Neérl. XXIV, p. 305, fig. 12) and which belongs to a
sideplait if we trace the connodal curve of the sideplait also in the
unstable region. The discontinuity in the direction of the curve
ensues then from the fact that the theoretic part represents the
course of another plaitpoint than the experimental part.

If we return to the case of ethane and methylaleohol then we must
admit that above 7’, the spinodal curve possesses a protuberance towards
the side of the small volumes, accompanied by a new connodal curve,
which if we trace it also in the unstable region, presents a new
plaitpoint. Or, what comes to the same: the existing plaitpoint splits
up into two plaitpoints. This second plaitpoint lies on the side of
ethane and in the beginning it will move with great velocity. At
higher values of 7 the sideplait extends and in consequence thereof
that part of the principal plait which has a plaitpoint on the side of
ethane contracts. At the moment that that part would vanish the second
plaitpoint has coincided with the plaitpoint which is indicated by the
point A (see fig. (1) of p. 319). This description differs in details
from that of Kuenen, but a great number of figures would be required

( 310 ) f

in order to show this difference clearly, but then also in order to
bring us into agreement.

For the case of ethane and methylaleohol the theoretical plaitpoint
belonging to the sideplait of the side of alcohol coincides at 7’, (see
fig. 2, p. 326) with the practical plaitpoint of the side of ethane. At
lower value of 7’ it is displaced in the «,7-plane towards the side of
alcohol and when the temperature continues to decrease it approaches
asymptotically to the plaitpoint with which it forms a #système
double hétérogène” (after the terminology of Korrewee). If we draw
this series of points in the plaitpoint diagram, it must of course satisfy
the condition which follows from the fact, that they le below the
three-phase triangle, namely on the side of the small pressures. At
low temperatures it lies even in the region of the negative pressures.

Fig. 2 of Kurnen p. 326 must therefore be completed with a
theoretic curve which starts at point A, retrogrades immediately to
lower temperatures and lies below the curve of the three-phase
pressure. The theoretical branch approaches to the same asymptote
as the highest branch that starts at C,. For the theoretic branch also

(ee) must be positive, and therefore we have:

dp Op j
IT ~ (55).

The rapid rising of this branch at low values of 7’ seems to be
contradictory to this explanation. But if we take into account that also

OT
approach to the limiting volume, this apparent contradiction disappears.
What is surprising, at least to me, is that these theoretic plait-

Op
( approaches to an infinitely great value for values of v which
v

points serve to make the course of the practical plaitpoints continuous.
But on the other hand the circumstance, that also for the course of
these theoretic plaitpoints a so important and at the same time a so
simple meaning has been found, confirms my opinion that now the
true description of the phenomenon has been given, at least for those
cases, in which the longitudinal plait has its summit on the side of
the small volumes.

But though the accuracy of the description of the phenomenon has
increased, we must acknowledge that the chance to find a satisfactory
explanation for the phenomenon is not greater than before; on the
contrary it has diminished. The circumstance in which a mixture of
two substances has a maximum and a minimum critical temperature
needs now no longer be inquired into. The question whether the

Ws

( 311 )

size of the molecule of the normal substance has influence on the
course, has also lost its direct importance. For mixtures of ethane
with an alcohol the separation between the two types lies between
methyl- and ethylalcohol; the question whether this separation takes
place between two higher terms of the alcohol series, if we take
instead of ethane a higher term of the series of carbonhydrogene
compounds, which seemed very important before is now no longer
of primary interest '). It seems to me that I have to return in many
respects tO my original meaning, namely that we have to inquire
after the circumstance which causes the spinodal curve to show a
protuberance towards the side of the small volumes. In mixtures of
a normal substance with an associating one this cause can perhaps

Op
be found in the circumstance that the quantity Ge can obtain ab-
U Dv

normous high values for such a mixture. As the equation:
dpdwp — (dp)?
Ov Ow? (5)
Op

applies to the spinodal curve, the value of — ay ay also be abnor-
vb

mously high in this case. If this is really the case an explanation
for the protuberance is given which is certainly satisfactory. Yet a great
distance exists between this observation and an adequate calculation.

In any case these experiments of KuerNeN, to which I hope that

he will add many others, are an important contribution to our know-
ledge of the critical phenomena of not miscible substances.

Physics. — “The influence of variation of the constant current
on the pitch of the singing arc” By J. K. A. Wurrumm
SALOMONSON. (Communicated by Prof. P. Zeman).

In the course of some experiments on the physiological action of
alternating currents of very high frequency, I tried the currents
generated by means of Depprerr's singing are. <A constant current
are between solid carbons shunted by a self-inductive resistance and

a condenser emits a note, the pitch of which corresponds with the

frequency of the alternate current generated in the condenser-circuit.

1) An experiment in order to investigate whether for propane the limit lies between
ethyl- and propylalcohol was already in preparation for a long time in the laboratory
of Amsterdam. But other labour which could not be delayed prevented each time
those who would undertake the investigation.

Proceedings Royal Acad. Amsterdam. Vol. V.

( 312 )

DvuppELL believed that the frequency was determined by the self-
induction and the capacity according the well-known formula :
p= 2aVel.

Paut Jannr thought the same and proposed, as DupperL had
already done before, to use the singing are for measuring small
coefficients of self-induction.

In the way proposed by JANrT, this seems to be impossible as the
frequency depends not only on the self-induction and the capacity
but i.a. also on the strength of the constant current.

I have investigated the variation of the frequency caused by varying
the constant current, the results being stated in this paper.

The experiments were carried out after Prukert’s method. The
P D at the solid carbons was measured by a Weston-instrument,
that showed the Volts of the constant current only, and at the same
time by a hot-wire Voltmeter. Lastly the current in the condenser-
circuit was measured by means of a hot-wire amperemeter. The
three readings being 4, EF, and /,, the frequency may be cal-
culated by

/

2
P = Sr res
Zacv EE,

c being the capacity of the condenser in farads.

The necessary correction of the instruments was known and has
already been applied in the tables. The arc-lamp used was a small
shunt-regulator by KörtinG & MATTHIESEN.

Series 1. Capacity 2,68 ml’. Selfinduction: bronze wire spiral of
80 windings; air isolation ; diameter 25 centimeter, height 50 centimeter.
The table contains in the

Ist column: Z, the constant current through the arc.

Qnd- oy E,‚ the constant current PD of the carbons.

ord hi KE, the hot-wire voltmeter reading.

Ath, E, the value of V #,2—E,? being the superposed
alternating volts.

oth ” /, the alternating current strength.

ee p. the number of complete alternations p. s. calculated

by PevKerT’s formula.

( 318 )

TABLE I.

h | A | Ly La fy) | p.
| |
1.9 | 37.0 | 4.0 | 37 | 4.8 4520
2.2 | 37.0 | 46.0 | 97.4 | 24 5230
2.6 37.5 | 43.0 | A bits Seek 5960
2.8 | 37.5 | 44.0 | 93.0 |. 2.4 6450
3.2 | 38.0 | 42.7 | 49.6 | 2.5 8000
3.7 | 38.0 | KO ERE 10390
LA 38.0 | 40.0 | 12.8 | 3.0 13980
| | |

Series 2. The same as in Series [. Capacity reduced to 1.68 mF.
TABLE II.

i E, By B is | p

‚Mr AD EEE ae 5 26 7 6200
2.4 | 39 B | 94.5 21 8130
2,8 | 39 a | 90.4 2.1 9820
3 38 12.7 | 19.6 2,3 11200
3.5 | 38.5 | 42 | 16.75 | 2.4 13590
B ol B MN ieee | 18.3 9.7 13980

Series 3. Capacity 1 mf. Selfinduction: coil of 160 windings
in 4 layers; wire 2 millimeters. Length of coil 8 centimeters, external
diameter 3.5 centimeter.

TABLE III.

|
frr Pt MERE nt a A ees
se | |
| |
1.9 8 41.7 | 98.7 | 24 14950
2.3 38 47 dee 8 17240
2.6 38 45 45 | 2.9 18820
| |
2.9 38 3 | 04 | 2.8 29900
3.3 | 37 12 19.8 3.3 26600
F Ge satay 42 19.8 3.5 98160
4A 38 | M | 15.4 3.4 | 35100
|

21#

( 314 )

Series 4. The same as Series III. Capacity reduced to 0.5 mF.
TABLE IV.

| | | |
iB | Ey | EB, | Fa | La | Pp.
] | | |
| | | j
1.9 35 MA ae ee pa IN ROE
24 | 36 | 2 |<16 | 2.51 | 36800
|
|
Bia 35 W- | 19.4 | 2.7 | 44300
Ol OD 39 a Whee 3 55590
3.4 35 Bi dod) 43180 84700
3.7 35 36.5 | 10.36 | 3.3 | 97700
| |
3.9 35 36.5 | 10.36] 3.4 | 100500

Series 5. Capacity 1 mF. Selfinduction: coil of 40 windings in
2 layers; wire 3'/, mm. Length of coil 8 centimeter, external dia-
meter 3.5 centimeter.

„TABLE V.

L Aol KERS 2 Ea I, p-
| | |
1.9. | 38 50.4 | 33.2 | 4.68 | 22400
| |
Do 38 | 50.4 33.2 | 5.16 | 24700
2.6 | 38 | 50.4 She 555 | 26700
2.9 | 38 | 4 26.0 5.20 31800
3.9 1316 | 46 26.5 | 6.45 | 37000
BiG WEN | ih | 93.8 6.15 41200
SU 338 43.2 | 22,8 6.24 | 13600
12 | 38 A | 45.4 | 5.70 59200

Series 6. The same conditions as in Series 5. The capacity reduced
to 0.3 mF.
TABLE VI.

HEN AES Be EL SP ER

| :
24 35 UE Be: eae A 61300
2.4 36 | 41.5 31 | 4.2 71900
9.9 5 12 939 | 4 | 91600
3 6 36 10.2 17.9 h A 430000

4.2 5 36.3 9:75 3.6 | 196000

( 315 )

Deppent. attained frequencies of 500—10000 complete periods p. S.
SIMON increased the number of alternations so much, that the note
emitted by the are ceased to be audible. He speaks of a limit of
380000—40000 vibrations. From my tables will be seen that I have
attained much higher frequencies, so high that I first distrusted them.
But as yet L have not been able to find any inaccuracy either in
the principle of the method or in its application. So T must think
that my numbers are exact, the more so as they seem to be confirmed
by a physiological estimate. With small frequencies, say up to 10000,
the pitch of the note may be easily estimated by the ear when we
produce two notes in rapid succession. In Series 1 I found that
increasing the current from 1.9 to 2.2 ampere caused the pitch to
rise about a “second”. By increasing from 2.2 ampere to 3.2 ampere
the successive notes sounded as with a quint-interval. The later eal-
culation of the frequencies from the galvanometer readings agreed
fairly well with the estimated increase of pitch.

The limit of audibility as calculated from the readings agreed
equally with the limit as determined by the aid of a recently gradu-
ated Ganton-whistle by Prof. EpELMANN, the graduation-table being
verified on different points by myself. I found as a limit for the
audibility about 48500 d.v.p.s. My are-lamp ceased to emit an
audible note when the frequeney of 42000 was reached. In the 6%
series no sound was heard at all. In the series 1, 2 and 3 the sound
was heard throughout. In the series 4 I heard the note distinctly
at 2.4 ampere; at 2,7 ampere I did not always hear the sound;
only every now and then I got the impression of a very faint and
high whistling sound. At 5.1 ampere I did not hear the sound. In
the 5% Series the sound was always present at 3.6 ampere and
sometimes at 3.7 ampere.

As these results agree, I think that the method is a correct one,
and that the higher numbers may also be relied upon.

The sound of the singing are may prove perhaps valuable in
physiological researches on sound. .

The highest frequency with my apparatus was attained with a
primary constant current of 4.2 ampere, /, = 36 Volt, 2, = 37.3
Volt, J, = 0.49 ampere, C = 0.03 m.F., Ea being 9.7 Volt and
p = 268000. Of course much higher frequencies may probably be
attained. But the resistance of my hot-wire amperemeter was rather
high, and I believe that therein lies an obstacle for my surpassing
this limit.

How are we to interpret the increase of the frequency caused by
an increase of the constant current? There is some analogy with

( 316 )

the rise in pitch of electromagnetically driven tuningforks when the
intensity of the currents is increased; and also with the rise of the
pitch of harmoniumreeds when the air-pressure is increased. Yet
there is already some difference in the origin of these last two
phenomena, so as to forbid anything more than considering the
analogy. The only allowed consequence is, that the electrical system
consisting of a capacity and a selfinduction does in this special case
not vibrate in its proper period and that this proper period might
only be expected to be brought about by a hypothetie infinitely
small constant current through the are.

Increasing the P. D. at the carbons seems to lower the pitch and
at the same time to increase the intensity of the sound; if the P.D.
rises too much the whistling ceases all at once. As I worked with
a constant E.M.F. of 110 Volts from an accumulator-battery, the
primary current strength was regulated by inserting resistance or
withdrawing it from the circuit. When without changing the resistance,
the P. D. at the carbons rises, the current falls off and so causes the
frequency to diminish at the same time. Yet by keeping the current
constant, by lengthening the arc and withdrawing resistance at the
same time an unmistakable lengthening of the period may be observed.

From the Tables 1—VI curves have been plotted connecting the
frequency with the current-strength.

It is not impossible, that a simple relation might express this
connection. Yet an experimental formula as

pHa+tbl+eP
is only possible when / is negative; as in this case there is a mini-

b
mum for /= >— this formula does not seem to be very plausible.

2
I have also tried a quadratic expression connecting the steadying
resistance with the frequency, but this did not give satisfaction.
At last I found as the most simple formula and agreeing best
with the observed results:

logp=adbl,
in which « and % are constants, p the frequency and / the constant

current intensity.
I found for series 1:

(SEP

u

A AE EE
ADE a
et hae |
Gee TME IES EE
A AREN

Bae
Ke
ke
Di
El
a
Ee

6
N
NE
34

es ke
28
Sane
IA S

ae

Ee

ee

ee

Ee
Et
La
BoE
Ae het
Bes
ae
BE

es
—

( 318 )

log p == 3.23522 + 0.2165 1.

] [ 7
if | log p (cale.) | log p (obs.) | p p (calc.) | p (obs.)
; — mn
1.9 | 3.64757 | 365514 | + 0.00857 1432, 4520
9.2 | 3.74159 | 3.71850 | 4 0.00698 5147 | 5930
9.6 | 3.79812 | 3.77595 | — 0.02987 G282 | 5960
2.8 | 3.84149 | 3.80956 | — 0.03186 6941 | 6450
39 | 3.99802 | 3.90309 | — 0.02493 | 8473 8000
3.7 4.03627 | 4.01662 | — 0.01965 | 40871 10390
4A 412987 | 4414364 | -+ 0.02077 | 43970 | 13920
! i |

BR eh
The mean error of log p being: WL =e = 0.00979 the error-
: ; b

factor of p is 1.053 and the mean error of p is 5.3 °/,.

Considering that 3 galvanometer readings are necessary which
individually ought to have errors of much less than 0.5 ®/,, but
which are to be taken all at the same time and therefore are
more inaccurate, a mean error of 5.5 °/, in the result, representing
an interval of less than a tone may not be called extravagant.

For series 2. I find: loy p= 3.47786 + 0.18453 J.

j | log p (cale.) | log p (obs.) £ p (cale.) | p (obs.)

4 of Ts aera 3.79239 | + 0.00083 6189 | 6200
2.4 3.92073 3.91009 — 0.01064 | 8332 8130
2.8 3.99454 3.99211 — 0.00243 9875 9820
3 0 4.03145 4.04922 | + 0.01777 | 10751 | 411200
3.5 4 A2371 4.13322 | + 0.00951 | 13296 13590
308 416062 4AM | — 0.01511 | 414475 | 13980
|
SEE
OW 5 = (o)° = 0.01228

the mean error of one observation being 2.867 °/..

( 319 3

Series 3. log p= 3.84563 + 0.17062 T.

me | log p {calc.) | log p (obs.) | P | p (calc.) | p (obs.)
1.9 | 4.46981 | 4417464 | 0.00483 | 44785 | 44950
2.3 | 4.23806 4.23654 0.00152 | 17300 17240
9.6 | 4.99997 | 4.97469 0.01465 | 19466 | 18890
2.9 | 4.34043 | 4.34635 0.00592 | 21900 29200
3.3 | 4.40868 | 4.49488 | 0.01620 | 95696 | 96600
3.6 | 4.45986 444963 0.01023 28831 28160
EA | 4.54517 | 4.54531 | 0.00014 | 35089 | 351C0

Eo
== > 3 eee QF
om = bas 2 (9)? = 9.01035

mean error of one observation 2.412 °/..

Series 4. log p= 3.80102 + OB Tee ys

1 ‚log p (cale.) | log p (obs.) p | p (calc) | p (obs.)

29 440220 | * 4.40140 — 0.00080 25247 25200
| |
2.4 A S6280 | 4.50585 + 0.09305 30542 36800
27 | 4.65532 4.64640 | — 0.00892 45219 | 44300
51 4. 78189 4.74468 | — 0.03721. | 60519 | 55550
3.4 187681 4.99788 + 0.05107 75303 84700
8 1.97174 4.98989 + 0.01815 93700 97700
od 503502" 5.00217 — 0.03285 108400 | 109500

BN.
Ont ee = (0)? = 0.02994

mean error of one observation 7.14 °/,.

( 320 )

Series 5. log p = 3.98960 + 0.17902 T.
Wat Tia Tease a oe fee PE ‘ oe cae | 3
I log p (cale.)| log p (obs.) e p (cale.) |p (obs.)
| | |

1.9 4.32974 4.33025 | + 0.02051 21367 | 22400
2.2 4.38344 4.39270 | + 0.009 | 24179 94700
2.6 445505 | 4 49051 | — 0.09854 98513 26700
2.9 | 4.50876 | 4.50243 | — 0.00633 | 32267 | 31800
3.2 4.56246 4.56820 | + 0.00574 | 36514 37000
3.6 4.63407 4.61490 | — 0.0197 | 43060 | 44200
3.7 | 4.65197 | 4.63049 | — 0.01048 | 44871 | 43600
4.2 | 4.7448 | 4.77989 | + 0.03084 | 55141 | 59200

———

om = ve = (0)? = 0.02024
mean error of one observation 4.77 °/,.
Series 6. log p= 4.31949 + 0.22466 J.

| ——

I log p (cale.)| log p (obs.) | ¢ | p (eale.) | p {obs.)
| = | |

2.1 4.79198 | 4.78746 | — 0.00382 6184 61300
2.4 | 4.85867 | 4.85673 | — 0.00194 | zoop 719.0
2.9 4.97100 | 4.96190 | — 0.00910 93540 91600
3.6 5.19897 | 5.41394 | — 0.01433 | 434360 | 430000
4.2 | 5.26306 5.29296 | + 0.02990 | 183957 | 196000

i
et 8 ve > (0)? = 0.01702

mean error of one observation 4.00 °/,.

The empirical formula represents fairly well the observed results
in the range of the experiment. But it does not give more than that,
I do not think that it may be used for extrapolating. This will be
directly seen, when we extrapolate for the intensity = 0. We cal-
culate for the frequency at the intensity = O in the 4" series: 6324 d. v.
and in the 3'4 series: 7009 d.v. Theoretically the frequency in series
4 should be exactly 2 times higher than in series 3.

( 321 )

A more exact method may perhaps give numbers from which a
better formula might be deduced, and which at the same time might
give us some insight in the phenomenon.

I have tried to get more exact numbers by means of the Kunpr
dust-figures but I did not succeed, though others might. Yet the
oscillatory discharge of a Leyden jar through an inductive resistance
easily gave regular dust-fieures. The reason why the Kunpt-method
proved refractory with the singing are, is not easy to be understood:
Lean only suppose that the intensity of the sound is not large enough.

Physics. — Dr. J. E. VeRSCHAF EELT. “ Contributions to the knowledge of
VAN DER Waals’ w-surface. VIL. The equation of state and
the w-surface in the immediate neighbourhood of the critical
state for binary mixtures with a small proportion of one of
the components”. Communication n°. 81 from the Physical
Laboratory at Leiden, by Prof. H. KAMERLINGH ONNES. ')

(Communicated in the meeting of June 28, 1902).

Introduction.

In Communication n°. 65 from the Physical Laboratory at Leiden *)
I have given the first results of a treatment of my measurements on
mixtures of carbon dioxide and hydrogen *) by the method which
KAMERLINGH ONNES *) alone and with ReINGANUM *) used for the
measurements of KUENEN on mixtures of carbon dioxide and methyl
chloride ®). They confirm KAMERLINGH OnNEs’ opinion that the isothermals
of mixtures of normal substances may be derived, by means of the
law of corresponding states, from the general empirical reduced
equation of statefor which he has given in communications nrs. 71 7)
and 74°) a development in series indicated in communication 59a.
In this empirical reduced equation of state

1) The translation of the first and second part of this article are treated as a
whole, hence some minor changes in text will be found.

2) Arch. Néerl., (2), 5, 644, 1900; Comm. phys. lab. Leiden, n°. 65.

5) Thesis for the doctorate, Leiden, 1899.

4) Proc. Royal Acad., 29 Sept. 1900, p. 275; Comm. 59a.

6) Ibid. p. 289; Comm., n°. 595.

6) Thesis for the doctorate, Leiden, 1892.

7) Proc. Royal Acad., June 1901; Comm., n°. 71.

5) Arch. Néerl., (2), 6, 874, 1901; Gomm., n°. 74,

( 329 j

where A, B etc. represent series of the powers of the reduced abso-
lute temperature ft, with co-eflicients which like 4 are the same for
all substances, we then put:

bs p v
aaa) ) = == en
Tir Pek Usk
Tk, por and vj standing for the eritical elements of the mixture
with molecular composition «, if it remained homogeneous, while

==

Tik
It must therefore also be possible to find expressions for the
critical quantities of a mixture — these are the elements ppt, Vzph
Ti of the plaitpoint and ps, var, Tr, of the critical point of
contact — in which only the co-efficients of the general empirical

reduced equation of state and further the quantities characteristic of
the mixture viz. Pir, Prk, Ver, occur, or the co-efficients of the develop-
ments in series of these quantities in powers of x. In the case of
mixtures with small values of #, it may, exclusive of exceptional cases,
suffice, to a first approximation, to introduce the co-efficients:
— a ata and p = x wa

Ty div Pk dx

A first step towards realizing this idea of KAMERLINGH ONNES has
been made by Kersom *) who took for his basis the general equations
by which van peR Waats in his Theorie moléculaire and following
papers has expressed the relation of the critical quantities and the
composition; he has found what these equations would become for
infinitely small r-values and has introduced into them the co-efficients

a

a and 2 mentioned above, besides others which might be derived from
the co-efficients of the general empirical equation of state. I have now
tried to work out this idea in a method which is more closely con-
nected to the treatment of the y-surface, namely by developing the
co-efficients of the equation of state and the equation of the 1p-surface in
the powers of zr. On account of the great complication involved by
the introduction of the higher co-efficients into the calculation, I have
confined myself to the lower powers of 2. However, the method
followed by me can also be used to find the co-efficients of higher
powers.

As I have confined myself to states in the neighbourhood of the
eritical point I could use instead of Kammriincn Onnzs’ empirical
reduced equation of state the more simple one which it becomes within
narrow limits of temperature and volume on developing the different

1) Proc. Royal. Acad., 28 Dec. 1901, p. 293; Comm., n°. 75.

:
j
4

( 323 )

terms in powers of the small quantities y—1 and ¢—1. According
to Van Der Waats’ method ') I wrote this new equation:

0) 0°9
NE (psf) A Parag yf
2 Op Op y
where the co-efficients ae aoa. ete. can be immediately derived from

those of the above mentioned empirical reduced equation of state.

1. The p,v, T diagram for a simple substance in the neighbourhood
of the critical point.

In order to limit the number of the continually re-occurring factors
as much as possible, I shall not write the equation of state of the
pure substance in a reduced form, but thus:

p =k, +k, (oon) +k, (ov)? + &, oor)? +.... =f). . (2)
where 4, /,, 4, ete. are temperature functions which can be developed
in powers of 7—7%,; as for instance:

k=, +k, (TT) + ks (LT) +. (2)
and it is evident that £,,—= pz while k,, and k,, are zero.

We might clearly find the equations of several curves in this
diagram, such as: the border curve, the curve of the maximum or
minimum pressures, the curve of the points of inflection ete. I shall
derive the former only, chiefly in order to apply to a simple case
the method of calculation to be used afterwards for finding the
pressure, volume and composition of the co-existing phases with
mixtures.

If v, and v, represent the molecular volumes of the vapour and of
the liquid, co-existing at the temperature 7’ under the pressure p,,
then these 3 unknown quantities will be determined by the equations:

pi A7 Pe AEN Ses he oe
and by Maxws.’s criterium

neef POR STe ate: A eee
Vi

The two unknown quantities v, and v, I shall, however, replace by the
i 1
two infinitely small quantities >(v,-+-v,)—x=# and zji P

is therefore the abscissa of the diameter of the border curve for
chords parallel with the v-axis, and g is the half chord.

1) Zeitschr. f. physik. Chem., 13, 694, 1894.

( 324 )
Equation (4) after division by 2 p yields:
1 1
Phy bh, PEED +g) $k, DEGO ELD GP) (5)
0

where for completeness I have not regarded the order of the differ-
ent terms. Also taking equation (3) once for v, and once for v, and
adding together, yields:
Phy bh, PEAP? +e") +h, DD HIG) HD" +6 DD HP") +...(6)
and subtracting and dividing bij 2 @ gives
O=k, HP HAB PHP) HAL DPL) . . . (YD

while the, at least to a first approximation simpler equation:
1
0 Sh + Rhy Dak, Cs ; 7) EEE

follows from (5) and (6).
The equations (6), (7) and (8) now determine the quantities P,‚p
and p,—pk; for we find:

bo

Bed hy, nn ry
=O ©)

80
D 1 1 k 2 ky, Pe T Ti) 1 (10
C — == a —_— - — . . .
"30 3 : 5 kyo ;

PPE Re (TT) ee
Along the border curve v = vr + ®+ p‚ so that we may write the
equation of the border curve:
0 = (v—»)? — (ver) B+ B*—g’,. . . . (12)
and to the first approximation this represents a parabola ’).
1) Just as v. p. Waats (Arch. Néerl. (1), 28, 171) from the reduced equation
St aelt
ob SEP fan es has derived 3 (v,—v,) = 2 V2 (1—+), I have also

~

derived 4 (eg +v)) from the same equation by means of the reduced formula (10)
and have found for it:
3 (v9 + 4) =1 47,2 (14),
whence, if p; and s, stand for the liquid and vapour densities :
4 (po + 6s) = pe [1 +0,8 AH]
From Amacar’s data for carbon dioxide I find:
A=} (92 + py) = 0,464 4- 0,001181 (Te — T),
or reduced 1 + 0,775 (1—t), and for isopentane (S. Youne’s data)
A= pr [1 + 0,881 (1—1)].
The above equation of state, therefore, represents the diameter numerically in a
satisfactory manner.
2) The same problem with regard to » has been treated by v. p. Waats (loc. cit.)
in a somewhat different way; only p is determined accurately by his method and
the border curve can be derived from his formulae only to a first approximation.

— ET

a

ee

( 325 )

2. The p, v, T diagram of a mixture with a small value

of « near the critical point of the homogeneous mixture.

From the consideration we have started from it follows immediately
that we obtain the system of isothermals of the mixture by moving
that of the pure substance to an infinitely small amount parallel to
itself so that the critical point (pp, vx) is brought on to the critical point
of the homogeneous mixture (par, Vee), and at the same time by
expanding it infinitely little parallel to its co-ordinates in multi-
Prk and the abscissae by 2E Moreover an isother-
Pk Uk
mal, belonging to the temperature 7 in the first system will belong

plying the ordinates by

to the temperature El T after we have moved and inagnified the system.
We put again:

p=l, +4, (eva) Hb, (oven)? + 1, (vver)’ +. - (13)

where /,,/,,/, ete. are once more functions of the temperature, thus:

=, +4, (LT) + bs (FT Tar)? +... . (13)

According to the derivation from the reduced equation of state

by means of Tir, por, Ver the co-efficients /,,, Ll, lo, 1, ete. are
only functions of «. Putting:

Trk = Ty 1 + ae Hate? +....)

Dak sxe DEAS ==: Baie Bie? Aep ila. i: coe est a
vak = Or (1 + ya Hy? +....)
where
pna, YaBB ete, ve 4)
we find
=P HB bnl (Bel eh (Bee
Bd klar] bek [1(30-2BeH
1,0 bk [1—(a-Be tl
L,p—hyol 1— (Ba — 4B) Han Joe
VERE Meiske U ars bP Ge

where all co-efficients / are expressed in co-efficients k as well as in
KAMERLINGH ONNES’ a's and #’s.

From the values of Tir, per, Vor, With mixtures of carbon dioxide
with small quantities of hydrogen for «= 0, «= 0,05 and « = 0,1, ')
I find:

1) Comm., n°. 65.

( 826.)

Tr = Ty, (A — 1,17 we + 1,58 «*)
par = pe (W— 1,624 42,4507). 2 2. . (16)
vp ==. vy (14-0022 —.0/95 2"), 4)
while from (14) would follow:
var = vy (1 + 0,45 « + 0,08 z°).

Although the agreement between the two expressions for v‚j is
not quite satisfactory, it yet by no means indicates that the law of
corresponding states does not hold; it may very well be a result of the
uncertainty of the critical data of the homogeneous mixtures, chiefly
of the v,,’s. Besides from the second formula for v,; I find:

for 2 = 0,05 vr = 0,00432 and for # == 0,1. 9,;= 000483
and these values deviate from those determined directly (0,00434 and
0,00444) not more than the amount of the error that can be made
in these determinations. Besides, since the law of corresponding
states does not hold entirely with pure substances, it is not likely
to do so for mixtures.

3. The p, v, 2, diagram for martures with a small value of a,
at a temperature differing little from Ty.

We shall now consider different mixtures at the same temperature
T'; the system of isothermals in the p, v, 2 diagram, at that tem-
perature is represented by the equation of state (13), where, however,
T must now be taken as constant and w as variable. We will now
put this equation in another and more suitable form.

Among all the mixtures there is one for which the critical tempera-
ture would be 7’ if this mixture remained homogeneous; the com-
position «7; of this mixture, and also the critical elements py, and
vr; are determined by equation (14). (In this equation we must put :
Vr PRS bii Dak = pTt and vr == V7}).

Hence we find to a first approximation
Kian eae 14 BT AE De (IT), oT = ae

It will be seen that to a first approximation the value vz is
either positive or negative according as 7'— 7), and «a have the same
or opposite signs, that is to say

a >> 0 eg |)

T>T,| em >; figs. Land? | em <0; figs. 3, 5, 9and11 |
| |
| |

T<Te vre <0; figs. Zand8 \ wr >0; figs. 4, 6, 10 and12 |

(T-T;).(17)

2) Comp. also Krrsou, luc. cit., p. 12.

( 327 )

Although from a physical point of view r can only take positive
values, in these considerations even the case x7,< 0 is not impos-
sible; for the point pry, vry has only a mathematical meaning.

In general, equation (13) may now be written thus:

p=m, + m, Vv —err) + m, (v— vz)? + m, (v—07i)? +...., . (18)

where m,, m, etc. are functions of « which can be developed in
powers of z—w7,; for instance:

Me, = Moo + m,, (L—A TE) + m,, (©c—ae7x)? +.... « « (18)

The co-efficients m are functions of the temperature which is here
considered constant; it will be obvious that mm, == pr» while m,,
and m,,==0. By equalization of (18) with (13) we can express all
the m’s in the 4’s, and in KAMERLINGH ONNES’ a’s and §’s; for we find:

kn : 5
Mao = kyo — De [na — (n + 1) B] (T — To) + ....

Mar = — kno [na — (n + 19] — hai Tra — (n+ 1)katijo(a— B) vr 4 … ete. (19)
so that to a first approximation :

LAE eee PPT 9) hall oy an
mM, = prB—k,, Tha, m,, =—-k,, The, m,, = -—k,, Tra-3k,,vi(a—B), etc. (19')

HARTMAN *) has given a diagrammatical representation of the p, v, z
diagram. This representation completely resembles a p, v, 7 diagram;
but this resemblance is not necessary. It follows directly from the
p,v, T diagram that £,, is positive, while %,, and k,, are negative;
in the p,v,x diagram m,, is negative, but according to (19), m,, and
m,, may be either positive or negative. The circumstance m,,<{0 does not
indeed influence the general shape of the diagram; it indicates that
the isothermals of the mixtures lie below those of the pure substance
as is the case at the upper limit (7 = 1) of Harrman’s representation °).
But while in the p,v, 7’ diagram the isothermals with maximum
and minimum pressure occur under the critical, the opposite may be
the case in the p,v,« diagram, if m,, and m,, have the same sign.
The four cases which may now present themselves, leaving out very
particular values of the coefficients, are given in the following table:

1) Thesis for the doctorate, Leiden 1899, p. 6; Journ. of Phys. Chem., 5, 425, 1901

2) From a mathematical point of view we may imagine the p, v, x diagram to be
continued outside the limits =O and x= 1. It is also obvious that z, if diffe-
ring little from 1, means the same as & infinitely small and that xz > 1 means
the same as x < 0.

22

Proceedings Royal Acad. Amsterdam. Vol. V.

( 328 )

Ty, 3 «EEE
m,, >9 or oh amd ke, ¢) ana 0 “or a he k,
a Pk a
2, >0 or a>0 figs. 1 and 2) | hes. 7 and 8 |

a |
figs. 9, 10, 11 and 12. |

m,, <0 or a<0 | figs. 3, 4, 5 and 6

HARTMAN’s diagram represents at the lower limit the case m,, >0
and m,, <0, at the superior m,, <0 and m,, >0. The case a >0
will in general occur when the second is less volatile than the first
substance; this for instance is the case when methyl chloride is
added to carbon dioxide’). On the other hand we shall find the case
«<0 when the second substance is the more volatile, when for
instance hydrogen is added to carbon dioxide (comp. formulae 16) or
carbon dioxide to methyl chloride *).

A p, v, « diagram based on observations has, so far as | know,
not yet been published. A diagram of this kind which I have drawn
from my measurements on mixtures of carbon dioxide and hydrogen
perfectly resembles the p, v, 7’ diagram after HARTMAN, so that in
the neighbourhood of pure carbon dioxide we must have m,, >0
-and m,, <0; according to formula (16) a is really negative, while
with &,, —1,61 (comp. Kensom Joc. cit., p. 14) I find m,, = 454,
and positive. For carbon dioxide with a small quantity of methyl chloride’)
a — 0,378 and 8 = 0,088, and hence m,, <<. 0 and m,, > 0; and for
methyl chloride with a small quantity of carbon dioxide, « = — 0,221
and B= 0,281 so that m,,>Oand m,,< 0. At temperatures between
the critical temperatures of the two pure substances, the p, v, « diagram
for mixtures of carbon dioxide and methyl chloride will probably
correspond to HarrMan’s drawing.

While two neighbouring isothermals (7, 7 + dT) never intersect

0p
in the p,v, 7’ diagram (the | - never being zero) this may be
Ps b o oT oO J

the case in the p, v, « diagram for two neighbouring mixtures

>

1!) Figs. 1—13 represent diagrammatically p,v,« curves for infinitely small values
of x and 7—T;, such as they appear in reality for finite values of x and T—T%.
They are moreover theoretically extended into the imaginary region x < 0. All
lines lying within the region of negative x are dotted; the isothermal =O is
represented by a dot-dash line. The line # — xe: (erroneously marked zr in figs.
1—12) would be the critical isotherm of the homogeneous mixture.

2) Comp. KAMerLINGH Onnes and Reincanum, loc. cit., p. 35.

3) Ibidem.

*) Comp. Keesom, Comm. n°, 79, p. 8.

——

-
eww een oid

J. E. VERSCHAFle neighbourhood of the critical state for binary

My, > 0; a Ze 0,

j. E, VERSCHAFFELT. “Contributions to the knowledge of van der Waals’ yf-surface. VII. The equation of state and the surface in the immediate neighbourhood of the critical state for binary
î mixtures with a small proportion of one of the components.”

0 0, RT ky a mt 1 1 Mer > Oa 0, RIK a nd, TZ Te Mor >

ig my, <0, «0, RI sk,

SU, RPP Gomer TS Ti. Mes S

Fig. 0, Fig. 11 ig. 12

Proceedings Royal Acad. Amsterdam. Vol. V

(wand w + de). If this point of intersection is situated at a finite distance
from the point prs, vrz, it lies outside the limits we are con-
sidering; but if it lies infinitely ‘near this point, then it practically
co-incides with it; then m,,—=0O and all the isothermals in the
neighbourhood will intersect each other approximately at the point
prk vrm This case is shown in fig. 13, where I have also supposed
a<0 and 7< 7. The isothermals intersect in pairs, and the curve
formed by all the points of intersection of two consecutive isother-
mals, also passes through the critical point (pry, v77) ; this is repre-
sented in fig. 13. The connecting line of the points of contact enve-
lops the isothermals; its equation is found by eliminating « from

. . bn
equation (18) and from —-==0, where we also put m,, == 0 ; hence

Ow
we find to the first approximation :
Tee; aoe Bote
P—PTk = — 7 —— Cere)’
4E’ bos

This parabola is turned upwards (as in fig. 13) if m,, is negative.

4. The w-surface.

In order to find from equation (18) the phases co-existing at the
temperature 7’, I shall make use of the properties of the y-surface
of van DER Waars. The equation of that surface is:

WES _f pdv + RT| « log « + A—2#) log (l—e) J,

where f is the gas constant for a gramme molecule, hence the
same quantity for all substances. Neglecting the linear functions of ,
we may write:

1 t 1
yy = - m, (v-v7p) — 5M (wor) - 3 m, (v-v7T;)* — 1 m, (v-v 7)? +...
1 1
+RT [wx loge + ae + a Fla RE et ian CaN ties RAPTOR a ao yo ANA

5. The co-existing phases.

The co-existing phases are now determined by the co-existence
conditions :

dw 0 Ow Ow
a =(5) | (Ge) (a) AR A Se HA

if u represents the thermodynamic potential :

22%

( 330 )

Instead of the third condition I find it however better to use an-
other which follows from all three, viz.
MESMER
where

0 0
M = w — (v—v7z) Se — (r—er7) = 2

Corresponding to a former transformation now I write
L(v, dv) — rrp =D and }(e,—v) =p

and equally

5 (wv, +2,) — &Tk = 5 and 3 (w,—2,) ror 5,

and I consider the infinitely small quantities ®, p‚ = and $ as func-
tions of the same variable, viz. p‚— prs Thus I find to the first
approximation *)

1 IP 7 he mm 2 4m, PPT:
| 01 oua gie at fie ae
male ert RE 13" 5m, \RT™) | me,

1 m’? 4;
fee | Nn tE | =

~ 2RTm,,| 3 RT 5 Mag
1 my, Pi1—PTk m*
jt — LI eee 23
2 =| Fate, | Me, RIm,, 5 (28)
1 ra Tk
gE AO Een
Mo,
Mor Pr TE
= EN LN Neo WEER Ted ee
and 3 Eep) a +en| (25)

where «7; and pr; may be replaced by their expression (17).
6. The plaitpoint.

In the plaitpoint the co-existing phases become identical. If we
represent the elements of the plaitpoint by «7,1, prp and vr: then

1) The four equations from which I derive the relations (22)—(25) are:

dp) (ow ee dy \ (dy ex Ow Ow
GG) GG) eral) GE)

The two first equations contain the expréssion log”; as all the other terms are
0,

: : 5 : &

infinitely small, this must also be the case with Jog —*, in other words, the ratio a
is zy

can differ only infinitely little from 1; § must therefore be of a higher order than =

HD
so that also log — may be developed in a series in powers of - BE,
©, ZHETk

“A> ae

ee

( 331 )

at that point = ep, —or = 0, B= erp er and § = 0, while
P1: =PTpt; thus we obtain, from the equations (22), (23) and (24),

ete ig) ie

8 Wera eli, 3 saat CA
Tpl = PT. SENT — 2 (27)

Nn m?,,+ RTm,, cy eh).

and
Mo, 2 Emms : :

OTpl—?Tk | a Mo TT ET .1)(28
5 eee tom weende Jee)

If er, prm and v7, are replaced by their expressions (17), the
elements of the plaitpoint are thereby determined to the first approxi-
mation as functions of the temperature 7; R7m,, may then be
replaced by Aim.

From equations (26) and (27) follows immediately :

Ee A 2)
LT pl — Tk

In order to see how this relation holds for mixtures of carbon
dioxide and hydrogen I consider the temperature 27,10° C. at which the
mixture w= 0,05 has its plaitpoint (pr, = 91,85 atm.) ; at that tem-
perature er: — 0,011 and pr, = 72,4 atm. so that Sag ee 500,

&T yl — ©The
in good agreement with the value 454 which I have found for m,,.

It follows from equation (26) that #7,: can be positive or negative.
As erk <0 is not impossible, this is equally the case with 27,1.
It is true that from a purely physical point of view the w-surface,
only exists between the limits «=O and «= 1 (in our case x > 0),
but from a mathematical point of view we can imagine this surface
to extend also beyond those limits ®). If we consider a temperature
lying above the critical temperatures of the two components of a
mixture, then there are, exceptional cases excluded (Hartman’s 34
type), no co-existing phases, that is to say the real y-surface does
not show a plait, although formula 26 shows that there is a plait-

1) If we take the value of zj. from the equation (26), insert it in (27) and (28),
and finally introduce the K's, a's and @’s, the formulae (27) and (28) become
Keesom’s formulae (25) and (2c) (Comm. n°. 75), while (26) corresponds to
Keesom’s formula (24).

2) Outside the limits x =O and x= 1 y is imaginary owing to the presence of
terms with log x and log (1—.x). Although this is the case the co-existing phases
beyond those limits are real, as the co-existence conditions contain the necessarily

1 —.t3

I OE Jog and. 1
real expressions (OQ — an Ol
p 1 g x a g jess:

(, 332) )

point on the imaginary part of it. If the temperature is lower than
the critical temperatures of the two components the plait occurs
between the limits «=O and «w—1, but, except for mixtures of the
second type, according to formula 26 the plaitpoint lies outside these
limits. Hence the case is physically not without significance, but the
plaitpoint cannot be observed.

Equation (26) may be written:

C "11 ry” 1
2 T pl == nmr (T—Ty), . . . . (26)
“~~ RT, k,,a—m>,, (

and this form shows that #7,; will be positive or negative as 77—T7,
and RT? kem’, have different or the same signs. R7?, k,,a>m?,,
is only possible if @a<c 0; R1°,k,,a< m*,, will always be the case
if a >0, but may occur with @< 0. The different cases that may

occur are shown in the following table.

RTM, ka Mn | RT7,k,, a < mo

|

Í a > 0 | 8570

O> are > erpl (Are > e791 > 0 | zap > 0 > an
Ly J} | > » land . .
| figs. 5 and 11 || figs. 1 and 7 | figs. 3 and 9

i]

| LT) > LT. > 0 IK) = LP > &TE | LTE SD LT pl |

Te [ag
See figs..6 and 12 || figs. 2 and 8 | figs. 4 and 10

|
|

1. The border curve in the p‚v‚,a diagram at the temperature T.
Ps Y /

Along the border curve v=v7,+P+ ¢, so that the equation of

the border curve may be written
0 = (o—o7,)—2 P (v — vry) +-P2—g?. . (30)

Where d> and g must be replaced by the expressions as functions
of p,. To the first approximation we can take therefor the expres-
sions (22) and (23) and neglect 7%; the equation (30) then repre-
sents a parabola of the second degree. The apex of this parabola does
not, as im the p,v, diagram of a simple substance eo-incide with
the critical point (pri, Vri), but with the plaitpoint.

Along that parabola

d°p 2M. model Bm kr Telg

dv? mt Rm, RT ke Mm

(31)

fi)

( 333 )

This expression is either positive or negative; that is to say that
the border curve may be turned with its convex side towards the
v-axis, while in the p,v, diagram for a simple substance the bor-

sh ne AD
der curve is always concave to the v-axis. aa will be positive if m
and R7",4,,a—m’,, have different signs, and will be negative in
the other case :

Vid lian ky, a = ME | RT; hi a me Mr

ml | figs. 5 and 6 | _ figs. 1—4 |
Be PSS RO ee
m,, <0} figs. 41 and 12 | fies!) 7-10 |

8. The projection of the connodal line on the x, v plane.

The equation of this curve has been given by Korrrwee *). In
connection with our preceding formulae it is most easily derived
from equation (380) by expressing p in terms of # and v by means of
the equation of state (18). I shall now bring it in a form analo-
gous to (30).

The border curve intersects the isothermal of the mixture « at
two points (p’,, v’,), and (p’,, v’,) which indicate the phases where
the condensation begins and ends. I again make :

gote) tm Dee
(p's + Ps) — pre = IF and 3 (p', — Pp) = 2,

and consider the four infinitely small quantities ®', gy’, 77’ and a' as
functions of 2.

By expressing that the two points are situated on the isothermal
(18) and on the. border curve (80), I obtain four equations from
which the relations we want can be derived. In this way I obtain
to the first approximation,

1 Rar: ae et ai Amf Mm,
Ben amat) (SRP NEN mn ihm) [et

01
1 [m,, fm’ 2 4m,,m
a. 5 we - = +. ma, + — Mas, _ Til saan UTk + . . e . (32)
2M5o| Moir 3 Np

IT = Ms (LTE nt Oe ne ee Va re)

and
RLM (GOTEN Phs ae eee]

1) Wien. Ber. 98, 1159, 1889.

( 334 )
Now we may again write for the equation of the connodal line
0 = (vor) —2 B! (vor) + PPE VE ere
To the first approximation along this curve
dij 2m,, AT, 2e Lua ge

a gal == IN. 7. El 2 F : he (37)
dv? mn, Rpm, RI, k,,ae—m,,

and this expression has the opposite sign to 7%, 4,,a—m*,,. Here
therefore we distinguish only two cases.

dr P
ARTE hee Pe alan F „<0, i.e. the connodal line turns its
av

concave side towards the v-axis (fig. 14);
dx :
Dee eR a Ne EM 13 a > 0O and the connodal line is convex to
LU

the v-axis (fig. 15).

9. The critical point of contact.

The characteristic of the critical point of contact is that there the
two phases with which the condensation begins and ends coincide.
If er, pr, and v7, represent the elements of that point we have there
D= o7,—017% 9 =0, Hpi prin =—Vand zun
and from (33) it follows that

RT m,,
OT, Sa Se ae
; mo + RT; m,,

BT Py a> AT > EE

that is to say to the first approximation the composition at the critical
point of contact is the same as at the plaitpoint (cf. 26). The diffe-
rent cases which may occur now follow.

A glee eile eee im tiea)

a). T>T 3 er, is negative and there is no connodal line inside
the region that can be observed. This corresponds to the position of
the border curve in figs. 5 and 11.

6b) T= Tr; e7.=0 and the formula (30) represents a connodal line
which touches the v-axis.

ce) T< Tr; xr, >O0 and there is a connodal line in the région of
positive 2, (see also figs. 6 and 12).

DAR Dragen el

a) F> Tr; er, >0 and the connodal line lies entirely within
the region that can be observed; (figs. 1, 3. 7 and 9).

b) T=T,; er, =—=0 and the connodal line touches the v-axis ;

ce) P< T,; er, >0 and the connodal line can only be completed

eaf ae

335 )

by prolonging it in the region of the negative w (fig. 2, 4, 8 and 10).
Equation (34) gives :
m*

PT: = PTk + Mo, (Tr — CTI) = PTL — EE RT, vrei ©)

so that also to the first approximation p7, = pri (comp. equation 27).
And from the equation (82) we derive in connection with (38):

UTr = OTE + : eae Se ae: (40)
AE B m,,(m?,,+RTum,,) RT. WW ez

from which by comparison with (28) we find

i m 11 Moy rm rr
Tr — UTpl = TL ze tm Gers en ee

The difference vr, — vr, may be positive or negative, that is to
say the critical point of contact may be situated on the vapour or
on the liquid branch of the border curve (or of the connodal line).
In the first case, as it is well-known, we have retrograde conden-
sation of the first type for all mixtures comprised between «x7, and
27,1, in the second case retrograde condensation of the second type:

TST lor, vry; rc. II; figs. 1 Bandd v7,v.¢c. 1; figs.7,9and11
| p /

ET or nn beses D, 2, ad zon rpuur.e.1Lfigs.8, LOandl2

Expressing that the plaitpoint and the critical point of contact lie
on the connodal line and subtracting the equations thus obtained
we find to the second approximation :

1 m?.. m?

4 Re i ae? Ths d . (42)
4 RT, Mao (mm? Ng Lait RT m,,)

this expression is positive if RT, ¢ > m?,, (fig. 14), and negative
if RP %k,e<{m?,, (fig. 15). In the same way we find by means
of the border curve

Ty —_ & 1B lige

ee Esta wre. (49)
Erp 4 RT; Mago (aios =~ RT: a Be
so that Mor Be, 0 et = a

Pe ihe tn pr < Pz: figs. 5 and 6! | PTr > pm igs. 11 oe 2

BEEN UL MS, pr > pri; figs. 14 pr oe PTyl; figs. 7 (feat |
als secs rl |

(To be continued).

( 336 )

Physics. — Dr. J. E. VerscHarreLT: “Contributions to the knowledge
of VAN per Waais’ y-surface. VIL The equation of state and
the w-surface in the immediate neighbourhood of the critical
state for binary mixtures with a small proportion of one of
the components.” (Continued). Communication n°. 81 from the
physical Laboratory at Leiden, by Prof. H. KAMERLINGH ONNES. *)

(Communicated in the meeting of Sept. 27, 1902).

10. The border curve and the connodal line in special cases.

1. When m,, = 0, ie. pr B=h,, Tra, all isotherms intersect one
another nearly at the critical point (pre, VT) as we have seen in $ 3;
according to the equations (26), (27) and (28) the plaitpoint coincides
in that case with this critical point. Besides from (31) it follows that
d*p : d*p
Pam this value however belongs to a only to the first approx-
imation (i.e. at the critical point itself), or the border curve is a
parabola of a higher degree than the second. In fact we find in

this case:

pes 1e A Mm Mao \m ont a ien d
gl gta ge), ge gan
Meso 9 Maa Mag
1 m,,m
11 $1
Pa PTR S| os we ee 5;
ELT

and therefore the border curve to the first approximation becomes a
parabola of the fourth degree; the equation of that parabola is:

Met 1 M,, Ma, :
P—PTk=——, 00 a (v—v x) ’
M 3 Mao
The connodal line, however, remains a parabola of the second
a 2}

. a*:
degree, on which en
dv? Tr ka

2. A second remarkable case is that where 27)m,,-+-m?,,—0; for
then the term p,—prz disappears from the expression for g? (equation
23), so that p becomes of the first order with respect to p,—pTk.
We then find :

1 (m,,m 0,.—PTk m i 2 mm
a a 01 ‘3 11 m , 1 t ot Paul 01 NEZ 01 40 a
en Eer a m RTim,,\ 3 0 EN a

Ol 30
and
5 2 2
ae en AD Moos OPE
Mao Me Ne Zei 5 RTE nn

BART. _ MMM Ì mn (Roem),
11 12 x

a, fd ym, DMs, x

1) Comp. Proceedings Royal Acad. of Sciences Sept. 1902.

(834 7

in the last term I shall express the co-efficient of (,—yr%)° for cori-
venience by A.

Substituting this in equation (30) we obtain to the first approxi-
mation an equation of the second degree, which now no longer
represents a parabola but an ellipse or a hyperbola. The coordinates
of the centre are:

i Mor 1 2 Me M40
= pTe and ve = vx, — ———{| =m -———— ET
den d RT ms, BAE on k

while the straight lines

p=prT and v=or + DP
are conjugate axes. With respect to these axes the coordinates of
the border curve are p and p,—pz, so that the equation of the
border curve with respect to those axes is:

m,
PK (pp) == t= — — (TT).
Mao i

In the same case the equation of the ee line is:

Pp, — Km’,, (weer) = — = *(T—T;,),
3 30
with respect to the conjugate axes :
e=eT, and v=v7y,.4+ DB;
Fees : : : 5 > Pi PTE :
where #' is obtained through substituting «—«7,; for — in @,

Moy

We must now distinguish two cases.

a. K<0O; the equations of the border curve and the connodal
line represent ellipses. Provided 4,, << Oand #,, <0 these ellipses are

real when 7’< 7}; they lie only partially — to the first approxi-
mation half — in the real part (wv > 0) of the y-surface. We find

two plaitpoints of which only one is in the real y-surface and two
critical points of contact co-inciding with the plaitpoints (at least to
the degree of approximation considered here, i. e. to the order
V(T—T;); the coordinates of these points are:

1 PRE
en ee a Kh, (1 — Tx)

30

Drie =P meld (LT
Pl Te — PT Kk, k)
Moy sale! ta kay ye Bi
UTyl = UTr — Ve : Hm, —_ (T—T}).
shee a Ae Moy Ms (RL; sE Kk t)

If 7—T7;, the border curve and the connodal line shrink to
one point, the critical point of the pure substance; and if 7'> Tj,
there is no longer a border curve nor a connodal line.

( 338 )

b. K>O; the border curve and the connodal line are hyper-
bolae; the asymptotes are:
p= +(p—pri)V K(bordercurvejandy'= + m, ,(«—« 7.) V K(connodal line).

If T>T;, p (or g’) is the real axis; only that branch of the
hyperbola which lies above the axis p= pry can be observed as
border curve; in the case of the connodal line it is only the branch
lying above the axis r= em which can be observed; again two
plaitpoints are found of which only one can be observed, and the
coordinates of which can be expressed by the same terms as used
for the ellipse. If 7 =—=7}, the border curve and the connodal line
consist of two straight branches meeting at the critical point of the
pure substance, which is therefore a double plaitpoint. Lastly, if
T< Ty, there is no longer a plaitpoint; we observe two branches
of the border curve and the connodal line lying to the right and
the left of the point prz, vr; each phase on one branch co-exists
with a phase on the other.

11. The border curve in the p, v, T diagram for a mixture

of composition «.

In equation (86) of the projection of the connodal line on the
a, v-plane, if we consider «© as constant and 7’ as variable, that
equation will express how the volumes of the phases, where the
condensation begins and ends depend for the same mixture on the
temperature. It therefore may be considered as the projection on the
v, T-plane of the border curve on the p,v, 7-surface for the mixture
of composition «.

This projection, can be written in the following form, corresponds
to (36)

0 = (vv)? — 2 ©" (var) + B'?—g'?, . . . (44)
where

1
Dii En (v',+0',) — vak = DH org vor = (to a first approximation)

<i LE m* 4, xi 2 mo 4m,, my,
—— Mm, ora ae jee as ‘p =F . TE = & +
RT; Ree SATE aa, be ee

we = m,,(m*,, 2
a le) = on ne En + Mo |H 3 Mei —
A mms | T—Tx 45
DT, ET ee
and
ih 2 m,, T—T x,
dr “ep? ZE ak ai ara 46
f 4 e, ) 4 RT rme, Ma GTE en

( 339 )
To this can be added
1 A ! rm ry
M= 5 WP ak Pre hi (T— Fae oe dee
and
x" = — Te Ba) colt Coe . (48)

To the first approximation equation (44) represents a parabola, of
which the apex determines the elements of the critical point of contact
for the mixture v. For we know that in the case of the critical
point. of contact v,=v',=v,,, so that g"=—0 and ® = vir— Var.
Hence it follows that’):

ns (49)
RT.
ym
Par = —— Pak ia RT. ke, U . . . . . . . (50)
1 m? Horde; x
Var = Vak + er, Oi (@—B) = = ma, ef RT zi a) | RT m., : (51)

In order to derive from this the equation of the border curve in
the p,v, T-diagram, we must express 7’ in terms of p and » by means
of equation (13).

Then we find:

OS (vu) — 2 O" (v— ver) + PI pl. . (52)

where

en END if Mor (= | mle EL a es Ti My mo, aa

2m le RT Silva De tie. ig

vji(a—B) 1 m or 4 m,,m,,
5 ke eT zi =p) + | (Se SUT AE Pen

hm, | p> gele
and

oe. Fea Ne one mee

ry le ry
Lem, km, aL
To a first approximation (52) is a parabola on which
be ke

kom:
be _o1 30 30
— 9°! 59 oT, — — 2
dv? Mr, FSi

ap

as in the case of the border curve of the pure substance.
The apex of the border curve is the point of the maximum co-existence

1) We obtain the same formulae if we replace in equation (26) xz» by its value
(17), put T= Ter and x7,= «x, solve Ty and substitute it in (39) and (40).

( 340 )

pressure *). Let Prom, Vim, Tm, be its coordinates, then we find by
putting yg” =0 and ®" = van — Vek

Pon =P — fe OS) NN
nin = tae + | mele —B gy (my ba — ST zi COR
TDi Gt J.
Hence to the first an PaP and N= Tar, but
vow — ta = — 5 ae le EEEN

for real mixtures, that is to say «>0O, the latter expression is neces-
sarily negative, so that the critical point of contact is always situated
on the descending (right) branch of the border curve. We cannot
call it the vapour branch, because here the apex of the border curve
is not the plaitpoint as in the p,v,.-diagram. The critical point
of contact is situated thus, because the critical isothermal touches the
border curve at that point, and because on that isothermal and hence
also at the critical point of contact 7, >> Tx (at least for real mixtures),

0
therefore <0 for the border curve. This corresponds to a diagram-
v

matical representation of a p, v, T-diagram for a mixture given by
KvuENEN *) and also with the experimental diagram for the mixture:
0.95 carbon dioxide, 0.05 hydrogen which I have given in my thesis
for the doctorate. In spite of the small value of zr, terms of higher
order appear to have such a great influence in the case of this mixture
that the apex of the border curve lies far outside the area investigated,
and the border curve at the critical point of contact is no longer
concave towards the v-axis but convex.

The plaitpoint elements for the mixture of composition z are found
by substituting 77, for ZY and « for x7,, in equation (26), by
solving 7: and substituting that value in (27) and (28). Then
we find

3
Tj ee ee

; RT py
tpt =e È zin dn en at d

RTym,,

km? km?
Pal Pl pee «| =p 2 Co. rk KO

Rm,

1) Comp. Hartman, Journ. Phys. Chem., 5, 437, 1901. Communications Leiden
Suppl. N° 3 p. 14.

*) Zeitschr. f. physik. Chem., XXIV, 672, 1897.

( 341 )

Mm, (2 1 m?,,m a
Vapl = Uxk + |e vy. (a—-) mG ot pt a 3 RT, mi, aon

30
which formulae, after some reductions, can be put in the form in
which Kersom has given them (Comm., n°. 75). Also the following
well known equation *) results directly from equations (59) and (60)

Pxpl— Pak = ky, (Fapt— T xk) Cele J eae baa” yee ce (62)
which also according to equations (49), (50), (55) and (57) holds for
the coordinates of the critical point of contact and for the apex of the
border curve.

From the coordinates of the plaitpoint of mixtures of carbon
dioxide with a small proportion of hydrogen *) («= 0, 0,05 and 0,1)
I derive the following formulae’

T pl T (1 — 0,30 a + a)
Papl = pe(1 + 4,42-+ 112?) Ae spare wan ta nd tO)

Vapl= vr (1 — 0,402 — 8 2?)

In connection with the formulae (16) I obtain directly from these :

Papl Prk
1 “cpl — Tar,

—1,66(1 + 2),

in good harmony with equation (62) (£,, = 1,61) ®). Using the value

k = — 513 ®), I moreover find that the formulae (59) and (60)
applied to mixtures of carbon dioxide and hydrogen become:
Prpi=T, (1+ 0,038 2) and pryi—pel +642); . (63)

hence the agreement with the formulae (63) is decidedly bad, as has
also been remarked by Krrsom (oc. cit., p. 13). We cannot,
however, draw any conclusions from this; it is improbable
that the inaccuracy of the data should cause this great deviation ;
but from the fact that terms of higher order produce such a great
influence in the mixture « — 0,05, we see that quadratic formulae
are very unfit for this comparison °), the more so as it appears from

1) Comp. v. p. Waars, Versl. Kon. Akad., Nov. 1897. It also follows directly
from the equation of state (13) in connection with (15), by expressing that the
elements of the plaitpoint satisfy this equation and by neglecting terms of a higher
order than the first.

2) VeRSCHAFFELT, Thesis for the doctorate, Leiden 1899.

3) Comp. also Kersom, Joc. cit., p. 14.

RN Er dr
*) Derived from ——- —- == — 32,2 (Keesom, p. 12).
Pv]: OWOT

5) By introducing the values for 2 =0,2 (comp. Verscuarrett, Arch. Neerl.,
(2), 5, 649 ete, 1900, Comm. n°. 65, and Keesom, loc. cit. p. 12) they certainly
will not become better.

( 342 )

Kersom’s caleulations (p. 13) that tolerably small variations in the
oe and ze
Accurate observations for mixtures with still smaller compositions are
therefore highly desirable. As the 7,,/, and also the coordinates of
the critical plaitpoint, are known with less certainty than the 77,1
and pp, 2 comparison of the theoretical and the experimental values

values of « and 2 greatly influence the values of

for these quantities is practically useless.
Again from the preceding equations Pryi= paer, T)i= Tr to a
‘first approximation, and

Vepl — Ver = — en CL Mon +m ji (64)
xp Lr — 9 RT am, RT’. | il u . . . e

Hence the plaitpoint may lie either to the right or to the left of
the critical point of contact; for positive « we have

| |
| Moy > 0 Moy = 0 |

|
| YE i
RI Ee > mo. | Vepl =d les WET | Vapl > Drs TEM |
| |
RPh EM or) Bayt Vars TC EE Wes EE ] |
es: |

If the plaitpoint lies to the left of the critical point of contact, it
may still lie either to the right or to the left of the apex, that is to
say either on the descending or on the ascending branch of the
border curve. In fact, according to (58) and (64) it lies:

m?*
1. to the right of the critical point of contact when m,, and RT: HM

have the same signs,
2. between the critical point of contact and the apex when
k

pees (SOA k m*
(EE tm.) dm 0 or ODM, (EE mand

3. to the left of the apex when

ko, (Mm? : :
My = En (Er A mo) SS 0 or 0 ee a (Fe ee ms) Je More
In the p, v, 7-diagram the plaitpoint has no geometrical meaning.
The expression that the coordinates of the critical point of contact
and the plaitpoint satisfy the equation (44) gives, to the second
approximation :

1 m*

2 2
sek BR gece aoe EE af ike ao
zpl 4 RTE ce siz m,) C (65)

80 11

dn en

( 343 )

e right side is necessarily negative ¢ ‘efore we always hav
Th ht sid ecessaril gative and therefore we always have
Tr > Tijs, which also necessarily follows from the meaning of the
critical point of contact. In the same way we find by means of
equation (52) :

tien mr m* Mok 1 /m*

01 01 01 Okee 01 wal

Papl Par 3 py. \ pan “fs Tei eh a Tomer ney ETT 4 Mii wv. (66)

a ie io ee (aed dah k ZN Lun

01

12. The condensation.

The line which indicates the relation between the pressure and
the volume during the condensation, the so-called experimental isother-
mal, extends between the two points p’,, v’, and p’, , v’, (the points
where the condensation begins and ends) but we can also imagine it
to extend beyond those two points, although there it has only a mathe-
matical meaning; for beyond those two points the quantity of one
of the phases would be negative. In order to find the equation of
the experimental isothermal we must seek at each volume for the
pressure at which the two phases into which the mixture splits, can
co-exist. For this purpose I return to the projection on the z, v-plane
($ 8) of the y-surface belonging to the temperature 7. If v,, xv, and
v,, ©, are the phases into which the mixture w splits when the volume
v is reached (v,>v>v,), the point v, # lies on the straight line con-
necting the points v,, 2, and v,, «, and hence we have this relation :

Sides AS NN eR SIRE 9

LUT s
where ®, Z, p and § have the same meaning as in $ 5. If p, is the
pressure at which the two phases 2, and 2, co-exist then we obtain
the. equation of the experimental isothermal by expressing the quan-
tities ®, =, p and § of equation (67) in p, by means of the equations
(22), (23), (24) and (25).

That this experimental isothermal passes through the two points
v’,, e and v’,, w follows directly from the way in which its equation
has been derived ; we also obtain it from the substitution of v’, , ©’, —

or v’,, #, — for v, «, which involves the substitution of v’,, 2’,
fore, Un ORP a SOE U, Oz...
By successive approximations (67) is brought to the form :
pg
01 .
P, = pre + Mo, (©—# TK) — aa (v—ory) a +....; « … (68)
I

if we consider only the three first terms, this is the equation of a
straight line, hence of that connecting the two phases where the
condensation begins and ends. In connection with (18) we find,
neglecting terms of higher order,
23
Proceedings Royal Acad. Amsterdam. Vol. V.

( 344 )

A
Pri =F (v—vTk) («—«x7%) + RT, (v—vT,z) « + m,, (v—v7z)’,

and according to (33) this may be written
pp, = koo (e— Te) [(0—PTe)* — Y")-

We see that in this form the experimental isothermal intersects
the theoretical at three points’), viz. v=vum+gq’, v=orr— gp!
and v= v7, (all to the first approximation) ; the two first points are
the points at which condensation begins and ends (®’ has been
neglected as being of higher order than g’), the third lies between
the two first.

When va + pf >v >> vr, that is to say at the beginning of the
condensation, p >p, and the theoretical isothermal lies above the
experimental ; when vz >v > vr: — gy, Le. at the end of the con-
densation, p > p, and the experimental isothermal is the higher *); this,
indeed, follows necessarily from the s-shape of the theoretical isother-
mal, and the approximate straightness of the experimental.

According to thermodynamics the two areas enclosed by the
theoretical and the experimental isothermal must be equivalent ®),

that is to say:
v's
f ep) dui):
v’,

+,’
(p—p,) d (v—vrx) = 0,

or

‘

ae
and this actually follows from the form, found just now for p—p,.
This has only been proved for the terms considered here; but obvi-
ously it must also be possible to prove this for terms of higher order.

13. The p, T diagram.

a. The vapour pressure curve of the pure substance. We have
found to a first approximation :
Pe, == Pleo eye ie
As &,, is positive, this straight line rises and terminates at the

1) Comp. for this Hartman, Comm., n°. 56 and Suppl. n°. 3 p. 25; Journ. Phys.
Chem., 5, 450, 1901.

*) Here the proof is only given for mixtures with small composition. For a general
proof comp. Kuenen, Zeitschr. f. Physik. Chem., XLI, 46, 1902.

3) It has escaped Brümcke's notice, who mentions this theorem in 1890 (Zeitschr.
f. physik. Chem., VI, p. 157) that it occurs already in a treatise of van DER WAALS
of 1880 (Verh. Kon, Akad., Bd. 20, p. 23).

( 345 )

point pi, Ty. Tr is a maximum temperature, so that this curve
lies in the third quadrant (S'O, fig. 16.)

2e EE R Za.
2
; S
P | Ja
Je PR
DO es ep a oe
1 2
76 FR i i

b. The plartpoint curve. According to equation (27)

ma. Aye Tir mf RT yh, T_T)
= = Tan Pk bot aang
PTP pi, me RT im, aT’). Bh ; mt LRT ( t)

This curve may have all possible directions. If we ae only real
mixtures (7 > 0), it extends only on one side of the point pr, ive namely
that corresponding to such values that 7-7 and m? od RT m,
have the same siens (according to equation 26’).

With regard to the position of the plaitpoint curve we distinguish
the following cases:

1. m, =90. pru= pr HA (TT), hence the beginning of the
plaitpoint curve will lie either in the direction of the vapour pressure

23%

( 346 )

curve of the pure substance or will co-incide with it as T > Tj, or
T< Tj, that is to say, according to (26'), as a is positive or negative.
In the first case (la), therefore, the plaitpoint curve will lie in the first
quadrant (OS fig. 16), in the second case (15) in the third quadrant
(OS'). We have noted that then the plaitpomt elements of a mixture
co-incide with the critical elements which the mixture would have,
if it remained homogeneous, hence the mixture behaves like a pure

dw
substance. This is the case ene 0 already discussed by VAN DER

v v
Waats'); in this case there is a mixture — here it must be the
pure substance itself — for which the vapour tension is a maximum
or a minimum, ‘and indeed it follows from the expression for p,—piz

' Op,
in this case?) that | — lk
Oz, /; 2,0

2a.m,, > Oand m?,, + RT, m,, > ihe —- eee k,, so that the plait-
d

point curve lies in the angle SO Y because 5 — 7’, must be also positive.
l

Zhan, > 0 and m’,, + hi; my = 0, ee = + o, and the begin-
(

ning of the plaitpoint curve co-incides with OY‘).

Thus we have here the second special case of the shape of the
plaitpoint curve investigated by vaN per Waars, i.e. where there is
a maximum or minimum temperature, here the critical temperature
of the pure substance. Really in this case ($ 10,2), as pry—p, is of
higher order than p7,i—pr,

hl 2 (PTpl—Pk)

gi

dT 1 et A eee ;
hence (; f ) = 0. T’> 7, that is to say 7; is the minimum plait-
PT pl k

point temperature, when A > 0; this is the case where the border curve
and the connodal line are hyperbolae (mixtures of Harrman’s third
type). And 7’< 7%, that is so say 7; is a maximum, when K < 0;
in this case the border curve and the connodal line are ellipses
(mixtures of the second type).

dpryl

Mor > 0 and m*,, + RT; m,, << 0. IT

< k, and because

1) Arch. Néerl., (1), 30, 266, 1896.

*) Comp. preceding communication, p. 267; to the first approximation == 2%.

3) Not with OY’, for, as in this case per pr and xr are infinitely small with
respect to Prpi—px and Erp: (§ 10,2), according to (29) prpi—pe == Mp, %, so that
for £ > 0, Pap: > pe.

( 347 )
T—T,. must also be negative the plaitpoint curve lies in the angle S’OY.
to, << Oand m?,, + RT, m,, > 9, zen < ko but T—T;, >0,
and hence in the angle SOY’.

3b. mm, <0 and m?,, + RT, m,,=90. The plaitpoint curve
touches OY’ 5). Compare moreover 25.

ie — Oana de dee in Oy se late k,,, but T—T;, > 0,
hence in the angle S’OY’.
d
From this it appears that ee can take all possible values. Accor-

ding to VAN DER WAaLs®), however, this is not true and the case
dpr,t pk !
a= = fe for instance could never occur. But it should be borne
in mind that this rule of van per Waats does not rest on an ex-
clusively thermodynamic reasoning, but also on special suppositions
about the form of the equation of state, which naturally corresponds
to special relations between the co-efficients introduced here, and as
a matter of course it is always possible that the numerical values
of the coefficients are such, that one or more of the cases considered
are excluded.

ce. The critical point of contact curve. To the first approximation
Ptr=prt,l, so that the critical point of contact curve to a first
approximation co-incides with the plaitpoint curve and the conside-
rations in 5 hold also for this line. Equation (43) shows moreover

that to a second approximation :
1 mk

Tr— PT oil = Sees Saco T—T;)’,
EE RP (nl RT )

from which it follows that the eritical point of contact curve lies
above the plaitpoint curve when m,, and 1? + R7).m,, have the
same signs; this occurs in the cases 2a and 3c just mentioned, hence
in the angles SOY and S'OY'. In the other cases the point of contact
curve is the lower. Moreover the two curves also co-incide to a
second approximation if m,, == 0 and even if m°,, + R7T).m,, =0.

apt, 4pTr
(2 er ve
to the second approximation.

== | although in that case p7,—pz7,i is not zero

d. The border curves. This position of the critical point of con-

t) Pipi < Dk for x >0; comp. preceding note.
2) Arch. Néerl., (2), 2, 79, 1898.

( 348 )

tact curve with respect to the plaitpoint curve corresponds to the
position of the critical point of contact with respect to the plaitpoint
on the border curves, represented in an exaggerated way in fig. 16.
To the second approximation those border curves are parabolae
which touch the plaitpoint curve and have a vertical tangent at the
critical point of contact, but to the first approximation they co-incide
with the axis which is conjugate to the vertical chords and the
equation of which according to (47), is:
P == Pak a5 Koy eS T xk) = Pzpl Se kos (T—T pI).

Hence these straight lines are parallel with the vapour pressure
curve of the pure substance and terminate, on the plaitpoint curve,
in the plaitpoint of the mixture to which they belong.

14. Continuation of § 9: the critical point of contact.

Mr. Kresom kindly informs me that the method given by him in
Comm. N°. 75 and which leads very easily to the constants of the
plaitpoint presents difficulties when applied to determine the constants
of the critical point of contact.

He however succeeded, by means of the method used by me in $ 9,
in deriving the constants of the critical point of contact from the
formulae '), given by Kortewee in his paper “Ueber Faltenpunkte”,
Wien. Sitz. Ber. Bd. 98, p. 1154, 1889, and proceeded thus.

It has been shown in Comm. N°. 59%, p. 367) that instead of
deducing the coexistence-conditions by rolling the tangent-plane over
the y-surface, we can also obtain them by rolling the tangent-plane
over a w-surface, the latter being deduced from the y-surface by
making the distance, measured in the direction of the y-axis, between
this surface and a fixed tangent-plane the third coordinate perpendicular
to z and v. We can go a step further in this direction by deducing
a y’-surface by means of KorTEWEG’s projective transformation *)

. on, _, (ou
var)" (Ge),

OH
vi
Here wy = WW — wry!
a! = £ — ET
v == v0 — VTpl

') The simplest way of proving that the case c; = «in Kortewee’s formula (4)
does not influence the present deduction, is by notin, that the area over which
the development is applied is infinitely small in comparison with xT',.

2) Proceedings Sept. 1900, p. 296.

5) See Kortewee |. c. equation 38.

(= ES: dy ;
9-0

it is also possible to obtain the coexisting phases by rolling a tangent-
plane over this '-surface. y” as function of z' and v’ presents
the form

WP =e, a? + d, a! v!? +e v'* (Kortewse’s equation 4).

Hence for the connodal curve Korrmwse’s deduction may be
applied, and we find for the equation of that curve

e .
seems testa (equation 8 1. ¢.).
m is now found from

m ay + i zl (equation 34),
Ox? JT 0x0v / pr

where the differential quotients are taken for the plaitpoint, so that
for a substance with a small proportion of one component, to the

first approximation
1 Op
MU a ie av .
MRT \ Ox) yg"?

Further we may put, leaving out terms of higher order, according

to equation (39)
ON amr (oe
ae (5)

da
Using the property that for the point of contact aes 0, this
f v

1
Pe ree OS
: 2MRT7,

yields:
Ow vy 0 ) = 0?
UTr— UT pl =a ET, k me > | i) + MRT), aa | UT pl
arro (5) & JvT ‘ cM
Dv

and

Gi

3 da) yr dp \? dp
Te dee ————— MRT;.| —— Ie rot.
ght paid 2 0°» jr : Gee) die
(MRT). HW

v®

der, der, TA gen d1 apl
he or 20: ==, or ——— ==, from which we
So that for «—0O qT AT a a C 5

dp... pz, : ape?
easily derive that also ae so that in the p7-diagram the
i aw Ax

point of contact curve and the plaitpoint curve touch at the ends.
We find further that with the same wv:

(37)
3 Ox 5 Op? 02 2
Raa ees! TRS MEN, Aar (OAN
f 2 0*p dp 0a) oT Oxdv Jr
(ety (a
dv? J\ dvd Tl’

from which p,,— pr, can be easily found.

If, as in Communication N°. 75 (Proceedings Nov. 1901), we
introduce the law of corresponding states, we find:

Physiology. — “On the structure of the light-percepting cells in the
spinal cord, Oll the neuro fibrillae mn the ganglioncells and O1
the innervation of the striped muscles in amphioarus lanceolatus.”
By Dr. J. Borkn. (Communicated by Prof. T. Pracr).

In connection with a former note?) I mean to describe here some
points of the histology of the central and peripheral nervous system
of amphioxus lanceolatus, especially to follow the neurofibrillae in
their arrangement and distribution in the cells and in the muscle-plates.

This paper is the outcome of observations begun in 1900 in the
Stazione Zoologica at Naples, but then not carried any farther, to
study the structure of the pigmented cells of the spinal cord. During

') Proceedings of the Royal Academy of Amsterdam. Meeting of April 19, 1902.

, 391 )

a stay at the Zoological Laboratory of Prof. Sr. Ap<rny in Kolozsvár
once again L took up the theme, with some excellently fixed material
I got through Prof. Aparny’s kindness. Finally the researches were
carried on in the Histological Laboratory of Amsterdam.

A. The structure of the light-percepting cells (eve-cells).

In 1898 Hesse *) showed, that the peculiar pigmented cells, which
are found in the spinal cord grouped round the ventral wall of the
central canal, and which after beginning at the third segment, are
arranged segmentally through the whole medulla, are each of them
composed of two cells, one of them a big ganglioncell without pigment,
the other a cupshaped cell, filled up entirely with dark brown pig-
mentgrains; the last cell covering the greater part of the firstnamed
cell and hiding it from view.

The big unpigmented cells Hessr called eye-cells, light-percepting
cells, the cupshaped pigmented cells he called the pigmenteup (Pig-
mentbecher), and the whole complex he compared with the cupshaped
eyes of the Planarians, that are equally composed of two cells, and
attributed to it the function of light-perception.

The arrangement of these two-celled eyes in the spinal cord is
strictly segmental. They begin in the fourth segment, with two eyes;
from there each segment is furnished with about 25 eyes. In the
region of the tail the number lessens, until a segment has only one
eve or none at all.

The eyes lying ventrally of the central canal are always looking
down, their line of vision, if we may call it so, being directed to
the ventral side of the animal, those at the left side of the central
canal look upward and to the right, those at the right side look down
and to the right.

The pigmenteup consists of one cell, the nucleus, when distinguishable,
Iving at the concave side of the cup.

The eve-cell is coneshaped, the base being covered by the pigment-
cup, the top being drawn out into a thin process. At the basal
side (turned towards the pigmenteup) the protoplasm. is differentiated
into a layer of fine small rods, placed at right angles to the cell-
periphery, and continuing in the protoplasm as a network of very
thin fibres. Another layer of minute rods may be seen close against
the pigmenteup. Between those two layers a clear space is formed,
Which is not caused by a shrinking of the cell.

W. kKravse') did not agree with the results of Hesse. He still
maintained that the pigmented cells in the spinal cord consisted

1) Zeitschr. f. Wiss. Zoologie. Bd. 63. 1898. p. 456.
1) Anat. Anzeiger. Bd. 14. Pag. 470. Zoöl. Anzeiger. Bd. 21. p. 481,

( 352 )

each of them of only one cell with the pigmentgrains lying only at
the periphery, just as Heimans and v. p. Stricut') had said in 1898;
by BEER *) and ScHNEIDER*) the description given by Hesse was taken
for right and confirmed.

As to the arrangement of the pigmentcells in the spinal cord in
the first place, the observations of Hrssr are not complete. They do
not simply lessen in number going from before backwards. In
young pelagic larvae there are to be seen very distinctly two groups
of pigmentcells, one in the cranial part of the body, the other in
the caudal half. Between those groups there are much less pigment-
cells in each segment. In later stages however these two groups
become fused, and then the arrangement is in the main as it is
described by Hessr.

As regards the position occupied by the pigmentcap on the eye-
cell, I can in the main confirm the observations of Hrssr. The
eyes at the ventral side of the central canal are always looking
down, those at the left are mostly looking upwards and to the right,
those at the right mostly downwards and to the right.

The histological structure of the eyes seems to me to be slightly
‘different from the one described by Hesse and SCHNEIDER.

The nucleus of the pigment-cell is never lying at the concave, but
mostly at the convex side of the cupshaped cell; sometimes the
nucleus is found in the middle of the pigment-cell, where often a
clear pigmentfree zone of protoplasm may be distinguished. According
to Hesse the pigment-cup consists always of only one cell. Now
sometimes in young animals, where the pigment is of a light-brown
colour and the nucleus may therefore be seen very clearly, I found
two nuclei in the pigment-cap, and so it seems to me that there are
sometimes two pigment-cells with one eye-cell. So the form of
the pigment-cap in fig. 3 seems also to point to the pigment-cap
being composed of two cells. As a rule, however, there is only
one pigment-cell in each eye.

In the eye-cell, lying under the pigment-cell, Hesse describes a
double row of small rods, lying close to the pigment-cell. This
double row of small rods exists, but the two parts of it are not
separate, but continuous at both ends, in whatever direction the cell
is cut through. So a flat oval body is formed, with a striated wall,
lying close to the pigment-cap (fig. 1.@), and following in its shape
the form of the cap. This body seems to me to be homologous with

') Mém. couronn. de |’Acad. roy. de Belgique T. LVI 1898.
2) Wiener med. Wochenschrift 1900.
$) Lehrb. der vergl. Histologie der Tiere 1902,

J. BOEKE. 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.

Fig. 1.
Pigment-cup and eye-cel
with vitreous bodies.

Fig. 3.
Pigment-cup and eye-cell with

Fig. 2 network of neurofibrillae.

Pigment-cup and eye-cell with Enlarg : 1200,

the network of neurofibrillae
Enlarg : 800.

ee ee ESS SSS
Fig. 4
\
\\ : 5
} X AST iva Sener
he 2 tr En . _

7 ij / ANN De |
fos is if ) sj) K = +

| ; \ j i
oP Cy 4 be 3. cross section through

< | \
| | Jd Ve. BA = Ted the muscle-plates.
ZEND JL nl | kaan 2
en
Belden ms
en EE |
f
Sey x
\ / a
Woe
My
Vi Fig. 6,
UY A. longitudinal
4 e
aS section.

Fig. 5. Arrangement of the neurofibrillae in a
section through a ganglioncell from the dorsal part
of the medulla. Fibrillae drawn with the
drawing apparatus in different optical sections.

Proceedings Royal Acad. Amsterdam. Vol. Y:

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PY NROLEIK TARTAR RG 9)

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( 353 )

the #Glaskörper” with a striated wall, as it is found in the eye-
cells of the Hirudines. As is the case with those eye-cells, here in
Amphioxus too the vitreous body seems to be filled with a granular-
looking substance (coagulation?) but this was not always clearly to
be seen.

Between this body («), that lies close to the pigmented cap, and
the nucleus (fig. 14) lying at the other side of the eye-cell, there
is in most cases to be seen another beanshaped body, that does not
possess a striated wall, but by a clearer tinction with protoplasmic
dyes and a more homogeneous substance may be distinguished from
the darker and more granular-looking protoplasm of the cell (fig. 14).

This body seems to be connected with the perception of light by
the eye-cell in the same way as the vitreous body described above.
The arrangement of the neurofibrillae in the eye-cells seems to point
to this conclusion. Entering the cell at the ventral side of the
nucleus, there, where according to Hesse the eye-cell is drawn out
to a point, the neurofibril forms a loosely built network round the
nucleus. From this network large neurofibrils ascend through the
cell and take the beanshaped body (4) between them (fig. 2, fig. 3).
Between this body and the pigment-cap these neurofibrils anastomose
again and form a second net, which seems to enclose the vitreous body
(a) with the striated wall. How the further course of these fibrils is
between the vitreous body («) and the pigment-cap I could not deter-
mine with any accuracy.

To obtain good results with the chlorid of gold-method of ApitHy
the sections may not be very much thinner than 10 a. Now for
the study of the eve-cells it is necessary to make sections of about
6 to 7 u, because in thicker sections the black pigment of the
capshaped cell embraces the greater part of the eye-cell and shuts
it out from view. It is therefore not possible to get those deep
black neurofibrillae, which may be seen so distinctly in the prepara-
tions of Aparny (the more so as the neurofibrillae of Amphioxus
are thinner than those of Hirudines); and even in sections of
6 to 7 u that part of the neurofibrillae-network, which is lying
beneath the pigment-cap is entirely concealed by the pigment-grains.
Probably the network is continuous and anastomoses at the other
side with the more ventrally lying network.

In what manner the neurofibrillae leave the eye-cell I could see
only in a few cases. The fibril seemed then to proceed horizontally
for some tinre but could not be followed any farther.

B. The neurofibrillae in the ganglion-cells.

On the neurofibrillae in the ganglioncells Ill say only a few words,

( 354 j

It would lead us too far to go into details about the arrangement
of the neurofibrillae in all the different types of ganglioncells, and
besides, that would not be possible without many plates and drawings.
I will therefore confine myself here to the following statements :

According to BerHe *) in most of the ganglioncells of the vertebrates
the neurofibrillae pass through the cellbody without branching or
breaking up into a network. Only in the spinal-ganglioncells and in
the cells of the lobus electricus of Torpedo marmorata Berne observed
networks of the neurofibrillae, and according to this author networks
possibly occur in the basal part of the cells of PurKinse in the
cerebellum and in the cells of the cornu Ammonis.

According to BOCHENEK ®) it is on the other hand probable, that
in the vertebrate ganglioncells the neurofibrillae form a very fine
network with small meshes. The very dense reticulum of neurofibrillae,
he was able to demonstrate in the ganglioncells of Herx, forms
according to BocHENEK an intermediate stage between the coarse net-
work in the cells of Hirudines and Lumbricus, and the very fine
network in the vertebrate ganglioncells.

In accordance with the statements by these two authors, we should
expect to find in the ganglioncells of Amphioxus either a dense reticulum
or a mass of disconnected interwoven very fine threads, passing from
one process through the cell-body into another process without
branching. This is not the case. In most of the ganglioncells the
arrangement and distribution of the neurofibrillae in the ganglioncells
resembles very much that which is described by Aparny in the
ganghoneells of Hirudines and Lumbricus.

Sometimes we find cells as the one shown in fig. 4, where the
neurofibrillae pass through the cell-body without interruption, but
this is only to be found in a few cases.

In the bigger ganglioncells, which are lying in the dorsal part of
the spinal cord and in the dorsal group of ganglioncells behind the
brain-ventricle, there is always a network of neurofibrillae branching
and anastomosing with each other. After having entered the cell in
most cases the neurofibrillae form a network round the nucleus
(partially distinguishable in fig. 5). From out this reticulum radial
fibrillae go through the cell body to the periphery (often branching
on their way) where they form a second network. With this network
are connected fibrillae, which pass through one of the processes of
the cell (out of the cell or into it?) — in short, a distribution of

1) Arch. f. Mikrosk. Anatomie, Bd. 55. 1900. P. 513.
2) Le Névraxe. Vol. Ill. Fase. 1, 1901. P. 85.

( 355 )

the neurofibrillae very much like that deseribed by Apatiy in the
smaller ganglioncells of Lumbricus. The fibrillae however in Amphioxus
ave thinner, and the reticulum finer.

In other ganglioncells there are not two networks (one round the
nucleus and one more at the periphery), connected with each other
by means of the radial fibrillae, but the neurofibrillae enter the
cell, form a network round the nucleus and leave the cell at the
other side, without there being any trace of a more peripheral
network to be seen.

A connection between different ganglioncells by means of the
neurofibrillae, I could not yet state with a sufficient amount of certainty.

In the colossal ganglioncells the #Kolossalzellen”, lying just in the
middle of the spinal cord, the arrangement of the neurofibrillae is
very peculiar. From out the colossal nerve-fibres, the axons of these
cells, a thick bundle of very thin neurofibrillae, arranged very regularly
and equally in the whole axis cylinder, enter the ganglioncell; in
the cell-body they pursue their way as a thick bundle that passes
round the nucleus, turns upon itself, forms a sort of vortex and then
seems to condense itself -into a few thick (composed of a great
number of elementary fibrillae) fibrillae. Where these fibrils go to,
I could not state accurately. In the axons the extremely thin neuro-
fibrillae are closely set and parallel to each other, and so a striking
resemblance is formed with the “sensorische Schläuche” of Hirudines
and Astacus. During the course of these nerve-fibres through the
spinal cord the neurofibrillae are seen to pass one by one every now
and then in an oblique direction through the wall of these nerve-
fibres; then they are lost in the nervous network without, and could
not be followed any farther. Perhaps they are connected there with
other ganglioncells, which should be in concordance with the character
of the colossal ganglioncells as connecting cells (“Schaltzellen’’).

(. The innervation of the striped muscular tissue.

According to Ronpe *) the motor nerves simply enter the muscle-
plates there where these end, and there is no trace of a motor nerve
endplate; according to HEYMANS and vAN DER STRICHT*®) however the
„motor nerves of Amphioxus terminate each in a shovelshaped end-
plate, that lies itself against the muscle-plate just as the motor nerve
endplates of the higher vertebrates do. According to their deserip-
tions and drawings the endplates of Amphioxus are thick shovel-
shaped plates without branchings, without further differentiations
(Golgi method).

1) Scunewer’s Zoologische Beiträge. Bd. Il, 1888.
*) Mém. couronn. par l'Acad. roy. de Belgique 1898,

(950)

Now Ap<ray and Rurrimi') were able to demonstrate in homo the
existance of “ultraterminal”’ nerve-fibres, that is to say nerve-fibres
which grow out from the branching and thickening of the motor
nerve known as “endplate”, and enter the muscle-fibre (this could
not be made out with absolute certainty) pass through it and in
many cases are connected with other endplates. Only a few cases
are described but they are sufficient to show that the so-called nerve
end-plate is not always to be considered as the real termination of
the motor nerves.

The following observations seem to point to the same conclusion.

The thin muscle-plates of Amphioxus (fig. 6@) present in longi-
tudinal sections a beautiful cross striation. Each isotropous disc (#)
is divided into two dises by a delicate, but distinct membrane of
Krausr; each anisotropous dise (g) is composed of two discs, separated
by a thin layer, that takes but a faint stain with chloride of
gold, the median disc of Hersen. In the middle of this transparent
portion there is sometimes to be seen an extremely deiicate line,
the membrane of HexsenN.

The membranes of Krause form, as is known, crossnets, which
bring the fibrillae of the entire muscle-plate in connection with each
other. In the adult animal real muscle-cells are not to be distinguished,
there are only the thin flattened muscle-plates to be found, which
however in hardened specimens sometime appear to be broken up
into rows of flat bundles of fibrillae. This is nothing but an artefact.

In longitudinal sections of Amphioxus in which therefore the muscle-
plates are cut in the same direction, but mostly appear not as plates
but cut obliquely as bundles of muscle-fibres (fig. 67), there are to
be found, in case the sections are coloured after the chloride of gold
method, in many places just there were the anisotropous and isotropous
dises meet, minute black dots, or small corpuscles; seen under a
microscope of the highest magnifying power these dots appear as very
delicate cross lines, thickened in the middle, running just between
g and 7. In these discs belonging to the same muscle-plate these
dots are lying in adjoining discs one just beneath the other, so that
rows of black dots running parallel to the myofibrillae are formed.
In each muscle-plate such longitudinal rows seem to be distributed
with some regularity. These black dots were always found only
at one side of the anisotropous disc, and, so it seems, always at
the same side of g, viz. at that turned caudal. The black dots lying
in the same muscle-plate in the same longitudinal row, are often

1) Rivista di Patologia nervosa e mentale, Vol. V fasc. 10, 1900.

|
:
k

(Sah)

found to be connected with each other by means of very delicate
fibrillae, which are running parallel to the myofibrillae. This could
be stated in many cases with great clearness. In some cases these
fibrillae were straight, in other cases more or less undulating. In
fig. 6a a longitudinal section through the muscular plates (cut
obliquely) is drawn greatly enlarged. The small dots and fibrillae
are easily to be seen.

In transverse sections the same rows of fibrillae and black dots
were also to be seen, and here they are seen to be distributed
more or less regularly on the muscle-plates (fig. 65). At both ends
of the black dot here too a delicate black line may be seen, extending
for some way along the muscle-plates but then being lost to view.
By playing up and down by means of the micrometer screw of the
microscope in cross sections too a longitudinal fibril may be made
out extending upwards and downwards from the black corpuscle;
this fibril is identical with that, which in longitudinal sections was
seen to run parallel to the myofibrillae and to connect the black
dots of a longitudinal row with each other.

So we find here in the muscle-plates of Amphioxus an apparatus,
which brings the anisotropous dises of the same muscle-plate in con-
nection with each other, which seems to be distributed with some
regularity over the whole muscle-plate, and which gives the staining
reaction of the neurofibrillae. Although I could not find the connection
of these fibrillae with the motor nerves, still these facts seem to
point to the conclusion, that we may regard these fibrillae and their
knobshaped thickenings at one side of the anisotropous discs as
representing the real innervation-apparatus of the striped muscle-fibres.
Sometimes I saw one of the longitudinal fibrillae near the place
of attachment of the myofibrillae to the myosepts bend off from
the muscle-plate; but it was lost almost immediately between the
myofibrillae in the neighbourhood and could not be traced any farther.
When we consider however the constant position of the small knob-
shaped thickenings at one side of the anisotropous disc, the fine often
undulated connecting fibrillae, the dark-purple tinction with chloride
of gold (Nachvergoldung Apituy) so characteristic for neurofibrillae,
then, I think, it is difficult to avoid the conclusion that they are
neurofibrillae.

This seems to me to be important from a general point of view.
Although the structure of the striped muscular tissue of Amphioxus
differs largely from that of the higher Vertebrates, yet the same type
of cross. striation, that is, the same structure of the myofibrillae, is
present in all,

=e

. Where now Hermans and VAN DER anion found: an
endplate identical with those of the higher vertebraten
of this structure can be seen an innervation of each anisotrop ous

can as I have attempted to show, there is room for the conclusion
in other vertebrates too the so-called motor nerve “endplate As.
ending of the motor nerve, but that from here neurofibrillae
the muscle-fibre, and that every anisotropous disc is innerva) ted.
truth of this surmise, however, must be Wen by further study is

Amsterdam, October 1902.

(November 20, 1902).

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING

of Saturday November 29, 1902.

EE

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 29 November 1902, Dl. XI).

GOM EE NTS.

J. J. Branksma: “The intramolecular rearrangement of atoms in halogen acetanilides and its
velocity”. IL. (Communicated by Prof. C. A. Lopry pr Bruyn), p. 359.

S. L. van Oss: “Five rotations in S, in equilibrium”. (Communicated by Prof. P. H. Scuoure),
p- 362.

J. WeEEDER: “On interpolation based on a supposed condition of minimum.” (Communicated
by Prof. H. G. van pe SANDE BAKHUYZEN), p. 364.

The following papers were read:

Chemistry. — „The intramolecular rearrangement of atoms in halogen
acetanihdes and its velocity,” Il. By Dr. J. J. Buanksma.
(Communicated by Prof. C. A. LoBry pr BRUYN).

(Communicated in the meeting of October 25, 1902).

In a former communication’) it was shown that the conversion
of acetylchloranilide in acetic acid solution under the influence of
hydrochloric acid proceeds like a monomolecular reaction. In continuing
this research the object was to study the influence of:

Ist. The dilution of the acetic acid with water.

2nd. The quantity of added hydrochloric acid.

3rd, The solvent (besides acetic acid, alcohols ete.). .

4th Different catalysers (HCI, H Br, H, SO).

5th. Different groups in the nucleus and their relative positions.

6. The temperature.

First of all the influence of the dilution of the acetic acid was
studied, varying proportions of hydrochloric acid being also added.
afterwards a few experiments were made in alcoholic solution.

1) Proc. Royal Acad. Amsterdam. June 29, 1902.
24

Proceedings Royal Acad. Amsterdam, Vol. V.

( 360 )

The modus operandi was as follows:

A definite quantity (8 to 4 grams) of acetylchloranilide was dis-
solved in respectively 100, 150, 200 and 250 ce. of 100 °/, acetic
acid; to this were added 10, 15, 20 or 25 cc. of 28,67 °/, hydro-
chloric acid and the mixture was finally diluted with water to

500 cc. The experiments were then conducted as described in the
4

previous communication; by applying the formula 4 = 3 1 —_— the
Ad
k’s were calculated; ¢ is expressed in minutes.
The following results have been obtained:
in 500 of solution. 10 15 20 25 e.c. hydrochloric acid.
on 7 Tr | B tu | 7 aT
ENG 100 | 0.00506 | 0.00973 | 0.0189 0.0241 |
| |
EE MEIER
=| 150 | 0.00846 | 0.0186 | 0.0318 0.0460 |
=a) ree Kal wes
en | | |
iB | 200 | 0.0157 | 0.0335 | 0.0588 |
o | | |
hd 1 | ! |
el | | |
S | 250 | 0.0359 0.0719 | | |
| | |
| | |
| reall | | | |
| 300 | 0.0836 | | |
hed SENTAAN | |
in 500 of solution. 10 15 20 c.c. hydrochloric acid.
BREA OAN Te |
S| 200 | 0.00883 | 0.0204 | 0.0341
ee Ee |
= | |
3 | 950 0.0158 | 0.0358 | 0.0591 |
Oo | | |

By means of these figures curves may be constructed either by
taking the figures from a horizontal row or those from a column.
The first row for instance shows how the velocity of reaction (con-
stant) increases in 20°/, acetic acid in the presence of a varying
amount of hydrochloric acid (10, 15, 20, 25 cc.) ete.

In this manner the different series may be represented by the
lmes UA, Bra “and? 1):

The first column shows how the velocity of reaction changes with
different concentrations of the acetic acid if the amount of the
catalyser is constant. These columns are represented by the lines
E, F, G and H. The alcoholic solution has been represented in
the same manner (A’, B’; C’, D’, E’).

These curves show:

1s*. That the velocity of reaction, both in acetic and alcoholic
solution, is decreased by addition of water.

( 361 )

dnd, That the velocity of reaction is much accelerated by increasing
the catalyser.

3d, That the curves all end in the origin of the co-ordinates
which means that the velocity of change in water without hydro-
chlorie acid is zero so that the substance is stable therein. [Always
on condition that light is excluded, (compare first communication) |.

On comparing the two tables it will be also noticed that the
velocity of reaction is greater in acetic acid than in alcohol; for
instance, in a mixture of 200¢.c. of acetic acid and 15¢.c. of hydro-
chlorie acid, k= 0.03385; when using 200 ¢.c. of alcohol and 15 e.e.
hydrochloric acid k = 0.0201 *).

If we compare the curves 4, I’, G and H we notice that on
decreasing the concentration of the catalyser, the curves begin to
approach the abscissa axis which again shows that, in the absence
of hydrochloric acid, the velocity of change in acetic acid or aleohol
is zero or in any case very small, which may also be seen from the

curves A, B, C and D.

A 100e.e. acet.acid with water to 500c.c. E10 e.e. HCI in 500 ec. solution.
B 150 » » > » ye yD) #415. 4 > DTE .
C 200 » » ) De Dee Gis D0 BEE DID aD )
D 950 » » » » ree DOD H 95 y » » ) > )
‘ |
(a
8 °
A
A
cc ICS
10 15 20 25 ccHCE

aceatic acid

1) If we calculate number of mols. of alcohol or acetic acid to a given number
of mols. of water we see that this difference in velocity of reaction is still greater.
24*

A’ 200 ¢.c. alcohol + water to 500 c.c. C 40 e.e. HCl in 500 e.e. solution.
B 250 » » a » » 500 » Dy EA) Ds no) » »
WD p DD at » »

10 15 Z0ecHCF

alcohol.

Mathematics. — “Five rotations in S, in equilibrium.” By Dr. S. L.
van Oss, Zaltbommel. (Communicated by Prof. P. H. ScHovre).

In a previous paper (these Proceedings, Vol. IV, p. 218) the investi-
gation of the elementary motion in S, was reduced to the consideration
of the elementary motion in 8S, by making use of a principle to be
read as follows: A system of rotations about planes all passing
through one and the same point is in equilibrium when their inter-
sections with an arbitrary S, are in equilibrium. Here we mean by
section of a rotation with any S, the rotation of the intersecting
space caused by its component about the plane orthogonally cutting
this S, in the intersection of the plane of rotation.

As an immediate result of this principle we can state the conditions
under which three to seven planes through one point can be the
planes of a system of rotations in equilibrium. Thus i. a. the con-
dition for four planes, that they must belong to a hyperboloidic
pencil, ete. ete.

We now wish to extend this principle in order to arrive by
investigation also at the case, that the planes do not pass any longer
through one and the same point.

It goes without saying, that if a system of rotations is in equilibrium,
its section with every S, must be in equilibrium. The question

( 363 )

here, however, is to find out how many of those intersections will
have to be examined before we can conclude about the system being
in equilibrium or not.

To this end we direct our attention in the first place to the case,
that a system @ has two sections in equilibrium, namely with the
spaces A and J.

If the section Q/A is in equilibrium, then 2 must necessarily be
reducible to a single rotation about a plane in A; likewise, if 2/5
is in equilibrium, then 2 can be reduced to a single rotation about
a plane in the space D.

So from the equilibrium of the sections it does not yet follow
that the system itself is in equilibrium, for the possibility remains
that it may be reducible to a rotation about the plane common to
the two spaces of intersection.

If, however, we can point out three spaces S, not passing through
the same point, their sections being in equilibrium, then the equilibrium
of the system itself is guaranteed. Let us now apply this result to
determine five planes which can be the bearers of a system of
rotations in equilibrium.

The neccessary condition which these planes must satisfy is that
they be intersected by three spaces S,, not passing through one and
the same point, in rays of a linear congruence. In other words: They
must intersect three pairs of straight lines, the director lines of these
congruences.

Now we know that in S, there are just 5 planes intersecting 6
given lines. They are the five “associated planes” of Srerr (Rend.
di circ. math. di Palermo, t. IL, 1888).

Now we have the necessary condition; we shall show, that it is
also sufficient.

Let 2 be a system of rotations about 5 associated planes, A an
S, so that 2/A is in equilibrium. If 2 were not in equilibrium itself,
this system would have to be equivalent to a rotation w about a
plane @ in A. If we reverse the direction of the rotation about this
plane, then the combination (€2—w) is in equilibrium. If we now
consider a second intersecting space B, not through e, then the planes
of @ are intersected in 5 rays of a congruence and the plane of @
in a line not belonging to this congruence. The section of B with
the combined system {£2—w would, however, have to be in equili-
brium. This is impossible, unless w is equal to naught, i.e. unless
2 is in equilibrium.

Nothing remains but to determine the ratios of the intensities of
the rotations of 2. This should be done as follows:

(364 )

We consider an arbitrary S, which intersects the planes of 2 mn
the axes of rotation of the section; the determination of the ratios
of the intensities belonging to them is a well known problem.

If, finally, we notice that between the intensities w and w' of a rotation
in S, and its intersection with a space <A the relation w' = w sin (Ao)
exists, then in this way the intensities of the rotations about the
five associated planes have become known quantities.

Mathematics. — “On interpolation based on a supposed condition
of minimum.” By J. Werper. (Communicated by Prof. H. G.
VAN DE SANDE BAKHUYZEN.)

For the reduction of the daily rates of the standard clock in the
Leyden Observatory I have developed a method of interpolation,
which may perhaps also be profitably used for other investigations.

The following is the problem we have to deal with: a variable
quantity, here the correction of the clock, is given for a series of
instants, during a long period, with unequal intervals; how can we
find an intermediate value of that correction at any moment.

First I tried to solve this problem with the limiting condition
that for all the intervals of time which enter into the caleulation
there is a smallest common divisor, which we take as unit of time.

1. Let S (clock correction) be the variable quantity, and g (rate) the
amount by which it increases during a unit of time. Let Sand ia,
be two successively determined values of S separated by m units

SES
: PUL DE : - ° .
of time, then — — is the average increase per unit; that increase
m

is represented by Q,. Hence the m quantities g, 9,.--.9Ji---9Jm Of the
i—=m

interval considered depend on the relation + g;= Sq — fee = m Qn
==

and a similar relation exists for each interval between two con-
secutive determinations of S.

In order to determine the quantities g, 1 put the condition that
the sum of the squares of the differences of the first order for the
whole period of observation should be a minimum. ‘This condition
of minimum was selected with a view to the special case where
we have to interpolate between the clock corrections, but I doubt
whether in all cases these interpolated values will be the most
probable ones. Leaving aside for the moment these considerations, I
go on developing the problem in hand. The quantities which cor-
respond to an interval of m units occur only in the following terms

int de ie

( 365 )

of the sum which according to this condition must be a minimum:

Widor (sdk ee oe + (9m — Im)" + (9g—9m)?
gp represents the rate preceding S, and g, the rate following Sg:
If to this quantity we add:

Zhn (9, + Ia al gien sia is + 9m—1 + gn)
their sum U will also be a minimum for the same values g, to gyn,
i=m .
i=l

These values g,.-.gm are found by means of the condition that
each derivative of U taken with reference to each variable shall be
zero. At the same time we must assign a definite value to 4, in

i=m
order to satisfy the equation gj = mQn.
i

Thus we obtain the following equations:
Ip HIN —I + hn = 9 |
Tee Te dende pd

Up alten Germ Ob = cts oe he ee

mm + 2 Iml — Im + Kp
Onl -- 2 In — Iq + bn 0"

Bij taking the sum of these m equations, each multiplied by 7 (m—1),
we eliminate 9, ,4i, gm, the coefficient of each gi of that sum being

i=m
equal to 2; hence the sum of the terms is 2 3 g:= 2 mQn.
=!
The coefficient of k is:
>: ety m (m-+-1) (m 4-2)
gl Uk ve €
Hence the sum of the multiplied equations is:
1 2
nn EO OE, m (m+ —_ ) HEA

_ 6p + 99 — 2 Qn)
mt 1) (m+ 2)
Then we determine the values of g; by multiplying the m equa-

tions by the terms of the following series:
mil), 2(m—i+1),...¢@—1)(m—i+1), i(m—i+1), i(m—i),..., 42, 71

whence km

( 366 )

and taking their sum; in the resulting equation all unknown quan-
tities g,..-Gm except gi are eliminated. That equation got by sum-
mation is:

1
— Ip (m—t+]) + (m+ l)gi — 19g + 5 i (m—i+1)(m+1) ky = 0

which yields:

m—itl i: i i(m—i+l1) ï
tewel he ene amer
md as oen Te Md 2 je
m re :
lence qd, = = 1 menses ee mk
ras MA Eilon EL Geeren ij
1 4 m 7
anc On ep = 09. = SU
: ml ep EED

The quantities g, and g, are still unknown and depend on the
quantities @Q of the neighbouring intervals; they may be derived
from them by means of successive approximation.

1 1
It gives some advantage to determine ->-(g,--g,) and 5 (Ym +99)

2 2
by approximations, because then we shall have to approximate
only one quantity for each S. The approximation may be made

—

1
in the following way: we put >(g)+9,)=c¢p and >(m+tyg=Co

then we obtain:

6
ki m* +2 (cy ae Ora 2 Qn)
om dt fa 2m? +1 a rn
INA ay wl c armenie EN 4
He A ea m(m?-+2)) * m(m? + 2) Me
3m m?—1 2m? +1
= — —__ Q, EN a 1 + ——— ] ¢,.
Ja m?+-2 Qn + m(m? +2) Te ( 45 er) 4

For the next interval of 7 units of time between the determinations
S, and S, we have the following equation :

2n? +1 n?—1

nett (te) te

i n° 4-2

As gy +4m=2¢, we obtain when finding the summation of the

two last equations a recurrent equation containing 3 consecutive

quantities c, so that c‚ can be expressed in c, and c,. This equation
can also be written thus:

( 367 )

2m? +1 2n? +1 m? —1 Sm
Ee TA TETE Cy a +, eater Cp 4+ -—— ae +
m(m?+2) — n(n?-+-2) m(m? +2) m?+2
on n?—]
lem eet eee tp Dey MI Ta ea, badly, oe ROL AG, en

nr? +2 n(n? +2)

For the first interval considered here the first of the equations
(A) is g,—9,+hn=0. This equation may also be written in the general
form by putting — g, + 29, — 9, + him = 0, thus assuming that the
value of y preceding g, and c belonging to the first observation are
both equal to g,. In the same way c belonging to the last observation
is equal to the last g of the last interval. Between each three
consecutive quantities c, therefore, a relation exists of the form (2)
and two other equations are added to the beginning and to the end
of this series, each containing only two values ¢ derived from the
formulae for g, and gy. Let cq and cy be the first two and Cy and
c- the last two quantities c, then we obtain by substituting ¢, for
Gn Cp and cy for cy the first condition, and by substituting c for
Jy =Cq and ce, for c, the last condition of the series which determine
the values c.

If the lengths of the ince intervals are represented by u and
y these equations are:

(2u*+-1) ca = + Qu — (u—1)
(2y7-- 1) ¢. = + 3n?Q, — (P°—1) oe,

The series (4) and these two equations determine all the quantities

c. If we solve them by approximation our purpose is soon gained ;
n Qin +m Qn

we assume to the first approximation cg = ————— and ¢, and cz

m+n
equal to the values of Q of the first and the last interval respectively.
From the equations (B) we derive the first corrections A, c,, A, cj,
ete. and A, ¢g is derived from the formula:
| 2m 41 2n? +1 m*—l n-—l

mm? +2) ' nn" +2) ag |

fee — A, « — ———- A, er.
eg FL (no) ea a cope Oe |

In this interpolation we determine g; and $; of an interval of m
units according to the formulae:

1 eq ml Cp—=C 1
n= (Gale tot ')— Ee kn + 5 ty + > Am ë

2m 2

1 . Wi ja l ,
8=5+(4-%&)i-(F ith se), Rr ke

2. Im the previous section the observed and the interpolated
quantities ‚S, occurring in the problem discussed, form a series of

( 368 )

discrete values corresponding to an arithmetical series of the argu-
ment: now I will remove the restriction of commensurable arguments
and will make this mode of interpolation applicable to a continuous
varying quantity and an arbitrary argument by putting for the
ratio of that series the infinitely small value df. The condition

pe

d?SN*
of minimum then becomes EE dt = Min:
(

a

The formulae for this continuous interpolation may be derived
independently, but it is shorter to derive them from the corresponding
formulae of the discrete interpolation developed above. For the present
I shall put for the lengths of the intervals between which we have

dS

to interpolate m’ and n’, for the derived values ae of the interpo-
lated function g’, to distinguish them from the letters we have used
in the former problem.

! !

nL u
Instead of m and 7 we have : and 7 fOP TE
dt dt

substitute the quantities g', dt, g', dt, g',dt, and for Q, and Q,, the

Cry we must

Bee SEN she
quantities ———* dt and “—— dt or Qndt and Qy dt.
m Nn

After dividing the relations (B) by df and omitting the infinitely
small values we have:

a OEE EE 1

== es G —_ — — == 1 = Pd — ed “

mn! Ja a! m7 Pai ni’
from which, after dropping the accents, we get:

et nQm + MQ, n(Qm — 9) m(Qn— 9)
ALT m+n 2(m + 7) 2 (m + 7)

to which we must add as first and last equations:

EE

u—G a
@ 3 B and ge =& + eg 5 AI

Ja — Q, +

6
For k„ we substitute — (gp +9’, — 2 Qn’) (df)*; for 7 we substitute
m

ae ; :
a if ¢ represents the time between the last preceding observation at
:

the moment for which we interpolate. These substitutions in the
formula for S, yield a formula for S,, which, after the omission
of infinitely small values and accents, is:

( 369 )

.

y ke ; JP: Yo
St = Sp + mt — ie Ge gg 2 Qn) = al +

Ip + ea 2Qn A
2m

m?

By substituting in the above formula m—t' for ¢, we obtain for S, a
formula developed according to the ascending powers of £, the interval
between the moment for which we interpolate and the moment of the
next observation. It is simpler to find the same formula by imagining
the interpolation to be made in the inverse direction, so that the quantities
g and Q change signs and the indices p and q change places. Hence:
Sm—t = S= Sj — ggd + = Z (Ip + Iq— 2Qm) — Eee fe le Ip+Iq—2Qn Ë

2m

m?

For S;, to be interpolated in the following interval we use:

3 edt Ig+Gr—2Qn i
St = Sq + Jt — De (Ig + Ir — 2Qn) ae Sy el + A ;

Therefore the formulae on either side of each observation are
different. If in the latter formula ¢ is negative and —‘? is substituted
for it, the resulting formula differs from the preceding one only in
the coefficients of the terms of the 3rd degree. The coefficients of
the terms of the 2nd degree have become equal by satisfying the
relation (C).

Therefore we also obtain the interpolated function if, by starting from
a value (S,) derived from observation, we represent the values of
S_, and Sp for the moments between that observation and the next
preceding one and those between that observation and the next
following one by the formulae:

S_t—= Sy — gat + gt? — Emt° and S= Sj + got + et? + ent®.
Taking this as basis, we find:

+97-3Qm +294 rt Agg H3Qh-gr 3 Ip 99-2 Qm e __ Ja Ir~2Qn

EERE ERE ear ae ne a n— :
q m n m? n°

z/d?SN* ef .
The integral if Wee) dt, which becomes a minimum through this
a
nterpolation, is equal to the sum of the integrals between two con-
secutive observations, and each of these integrals can be expressed
in the coefficients of the interval in the following manner:

a={(e)* geeen Ee sd OY

n aL

4
or: En rg (0g + eg er + €*,)-

( 370 )

For the total integral S /, we can also derive a simple form by
integrating partially:

z/d°SN? dS d°S "=d 2S
NE — —— | — ae ih
ij dt? dt dt? | dt dt?

a a a

Ne

d S
For the first moment a and the last moment z, ~~ —0, as follows
dt

from the first and the last equations belonging to (C). For each

PS
interval between two observations a is a constant quantity. Hence

dt
we find:

L = & 6 & (Sg — S-)
where the summation extends over all the intervals between the
observations. We can easily find a simple expression for the differential
quotient of / according to each of the observed values, which may be
useful when we want not only to interpolate for an intermediate moment
but when at the same time we have to determine the most probable
values of the observed quantities. For then the difficulty presents it-
self how to find the best method for diminishing the amount of the
minimum value / by applying corrections to the observations, of
which corrections the mean value is known.

In doing so heed must be taken that these corrections, being
errors of observation, shall satisfy the law which determines their
probabilities as functions of their magnitudes.

I have not yet reached a satisfactory solution of this problem.
The following remarks, however, on this subject seemed important
enough to be communicated.

3. Let L,, Lg, L, be the observed quantities, free from errors of
observation, and jf), fy, fr the errors themselves.

If we have developed the interpolation by means of the quantities
L and f separately, we obtain the formulae:

y= Lg + Got + Cg? + Ent?
hi= Ja Bet Jr Ag Danie et.
By means of the summation of these two formulae we get:
Si= Sg + ogt + eg t° + ent’.
WAR ED
dt? dt?

If we apply a partial integration to i dt, we get:

a

~
x

aL df aL df it
dt? dt ee dt

a a

dL df PdL df
or — — | — | —— — dt
/ dt dt? dt dt?

a a

In either case the integrated parts are equal to O, because at the

ok df
beginning and end —— and — are zero.
2 8 dt? dt?

In this way we find the relation:
2E, (haf) Zi En (Lig— Lr).
In the same way we find the relation:
> en (fo—fr) = J en (S,—S,).
By applying the corrections — f, the minimum /s becomes the
minimum J; = [s—f.

Es —f= = 6 (en—En) (Sy—fg Sr tf) ==
aa 0 Cp (Sg—S,) — 2 68, (Sy—S,) — 2 6 en (fg fr) in = 6 en (fa—=fr)
which expression by means of the latter relation may be reduced to:
Tyo fe ele ape Oe, ff

For infinitely small values f, the last term in the expression

; dls
given above becomes of the order /? so that we find De LA len— en).

q
This result enables us to determine the set of small corrections,
which, when applied to the quantities S, diminish Js by the greatest
amount. These corrections will be proportional to the abrupt changes

The variations in the interpolation coefficients g, c, ¢, resulting
from these corrections are found by repeating the interpolation,
with this sole difference that for the observed quantities ‚S we sub-

Ga
stitute the abrupt changes of Bi

As a rule a set of corrections of this kind will not show the
character of the errors of observation and therefore be dissimilar to
the set of errors which actually exist in the observed quantities S.
We may also determine a limit which should not be passed in the
rectification.

If the quantities f represent the real errors, we have:

Ig = IH 12 Ey (Af) + 28 & (ff)
The coefficients / of the interpolation formula between the

correct quantities S and the errors f being as a rule entirely
independent, we must assume that in 2 12 L, (f,—/;) the positive

and negative terms neutralize each other for the greater part. Hence
the difference /s — Jz, does not exceed 6 &, (7, — fr), the value -
of which depends only on the errors and the lengths of the intervals;
the mean value of this expression for every possible distribution of
the errors of the observations may be derived from the mean error
of those observations.

This is the utmost limit to which by means of corrections to the
observed quantities S we can diminish /s, lest the interpolation
curve found should assume a less sinuous form than would be
probable with regard to the results of the observations and their
precision.

Here follows an example of the computation.

The annexed table contains the interpolation coefficients of a part
(period 1882 June 8 to August 30), taken from a longer series of
observed rates of the clock Hohwii 17. Therefore the coefficients
at the limits of this period are not in accordance with the boundary-
conditions supplying the formula (C).

We compute the interpolated clock corrections by means of the
formula:

2
S= 8, +t (v + % Cy xs + u? e, i )

7 VL
Sy is the clock correction of the last preceding observation and
the coefficients gy, nej, n'en are given in the columns 5, 6 and 7;
they are expressed in the unit 0001. The values g, and nec, to
be used are placed a little above the horizontal line corresponding
to the length of the interval expressed in days, which interval
contains the moment ¢ for which we interpolate. Because of its
connection with the constant derivative of the third order of the
interpolation curve within each interval, the coefficient 17e, for each

interval has been placed on the horizontal line of that interval.

The 8 column contains the coefficients e and the 9% their differ-
ences 6 by passing from one interval to the other. For each of
these differences I have calculated the variation 46, of a given
6,, as the corresponding correction of the clock ‘S, increases by
+ 08.100 while the other corrections remain unmodified; they are

Og

given in the 10% column. By the increase AS, = — > 08.100

6;
the difference 6, becomes zero, so that by means of this Hees, we
obtain the same result as if in the determination of the interpolation
curve we had omitted the observation S,. Hence the correction of
the clock S, derived from this interpolation is equal to the observed

m,n.

Duration of the
intervals in days

or

Mean daily rates Q.

Pe

(Je)
~]
(Je)

A

(u +: ny =

Correction term

m( Qu—gr)+-1( Qn ~ Jp)

gy.
coefficient of 4.

2

coefficient of #2.

uC,

C

=

ve
|

ne.
coefficient of #.

e

=
—

| | Se |

/¢ | 4m |e

i Nash A GUIS in” ak
Pl
eee! SSN

bee SURO’

| s
ee AS 7.0\4+- 5.4 | —0.13
rage ia a ey ig
Fog e A ee
cain Oa Bt | 200
MOER POS ks
Een se BaP a:
ete: ten yak
—20 GH 26.0 | —0.08
et 29.3 | 0.08
Sagne baa AR
aeclee ta tiaee| (a
ery lie or sey |e er
ed 4.2 | —0.06
cast? 4,3 | $-0.07
|. 5.3 4.6 | -0.12
i at TI 6.4 | +042
ge me
ä 39. H67. | 0.09
hits —21 UH 85.0 | —0.03
mk vet 8.8-+ 2.9 | 40.04
Be gre het «| Sas
riot 10.6 | —0.10
CO tae bs 2.6 | 0.15
—2.5\4 3.8 | —0.07

S, diminished by res x 05.100. These differences Obs. —C

in seconds of time, are contained in the 11% column.
From the ee formulae I derived for these | 24 .

value Ig = > —n (¢q? + eger + ¢,?) = 69500, while for call th

ferent manners ut distribution of he errors of chbewratan tie 3 m

of all the values Zy= 6 €,(/)—/;), which values depend only o1
the magnitude of the errors and on their distribution is_
30500. In the computation the mean error of the observatic
been put 05.028, which value must be regarded as the smallest
can be assumed on the strength of other investigations. There
the sinuosity of the interpolation curve must be ascribed for a
part to errors of observation. |

(December 24, 1902).

OF THE

Vv OE OU IVE ae Vie

.

(ist PART)

om . AMSTERDAM, |
Fa . JOHANNES MULLER.
je | December 1902.

ta Ko

ATAU A AEE NMA
RADE AIEN APT:

of 15

\3

AM.

=

-KROBER & BAKELS.
AMSTERD mj:

4

DE ROEVER

‘

Se Z

Pal
cn vi
Nb

DN zi
veel eae
ADE led

Seen?

(AUNT

100139135