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THE AMERICAN MUSEUM

NATURAL HISTORY

Koninklijke Akademie van Wetenschappen
te Amsterdam.

PROCEEDINGS

RCT ION OF SCIENCE

WOE U MEE Ee

AMSTERDAM,
JOHANNES MÜLLER.
May 1899.

V aaa |
£1 40 | rf
WUSEUM MAO LK EN

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“.

APTN MOO

Royal Academy of Sciences. Amsterdam,

PROCEEDINGS OF THE MEETING

of Saturday May 28th 1898.

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 28 Mei 1898 DI. VII).

CONTENTS: „On the eyclographie space representation of Joachimsthal’s circles”, By Prof.
P. H. ScHoure, p. 1. — „On maxima and minima of apparent brightness resulting
from optical illusion”. By Dr.C H. Winxp (communieated by Prof. H. Haca) with 1
plate, p. 7. — „On the relation of the obligatous anaérobies to free oxygen”. By
Prof. M. W. BEIJERINCK, p. 14. — „On the influence of solutions of salts on the volume
of animalcells, being at the same time a contribution to our knowledge of their struc-
ture”. By Dr. H. J. HAMBURGER, p. 26. — „On an asymmetry in tne change of
the spectral lines of iron, radiating in a magnetic field”. By Dr. P. Zeeman, p. 27. —
„The Hall-effect in electrolytes”. By Dr. E. van EvERDINGEN Jr. (communicated by
Prof. H. KAMERLINGH ONNES), p. 27.

The following papers were read:

Mathematics. — „On the cyclographic space representation of Joa-
chimsthal’s circles.” By Prof. P. H. Scour.

1. In his ,Cyklographie’ Dr. W. Frepver has developed a
theory, in which any circle of the plane is represented in space by
one of two points of the normal, erected in its centre on the plane,
and having on either side a distance from this centre equal to the
radius. The ambiguity of this representation can be useful in the
distinction of the two senses, in which a point can move along the
circle. This is not necessary here.

According to the FIEDLERIAN representation the right cone, whose
vertex is a point P of the plane of the circles, whose axis is the
normal in P on this plane, and whose vertex angle is a right one,
corresponds to the net of the circles passing through P. Likewise
the pencil of the circles passing through P and Q has as image a
rectangular hyperbola situated in the plane bisecting P Q orthogo-

i

Proceedings Royal Acad. Amsterdam. Vol. I.

(2)

nally; of this hyperbola the line common to its plane and the plane
of the circles is the imaginary axis, the intersection of this line
with PQ is the centre, and the normal in this point to the plane
of the circles is the real axis. Or, put more generally: the circles
of a pencil are represented by a rectangular hyperbola, whose real
or imaginary axis is normal to the plane of the circles according
to the points common to the circles being real or imaginary, and
which breaks up into two straight lines, if these points coincide. And
the circles of a general net are represented oy a rectanguiar hyper-
boloid with one or two sheets, according to the cirele cutting the
circles of the net orthogonally being real or imaginary.

In different cases the FrEDLERIAN theory can give a clear and
concise idea of the position of ranges of circles. So a.o. the circles
having double contact with a given ellipse «. If this ellipse € be

9

a ye ee a? 2
represented by a +5 = 1,2 = 0, the ellipse Tm =p
and the hyperbola — Wok = 1, #=0 correspond to the two
U ed a~

ranges of circles having double contact with ¢. As is easily explained
these curves are transformed into the focal conics of ¢ by inverting
the sign of 2’.

In the following lines we study the surface that forms the image
of the twofold infinite system of JOACHIMSTHAL’s circles of «.

2. Through any point P of the plane of e can be drawn four
normals to «. The footpoints A, B, C, D of these normals may be
called ,conormal”. If the point diametrically opposite to A on & is
indicated by A', the known theorem of JOACHIMSTHAL says that
A', B, C, D are concyclic, if A, B, C, D are conormal.

This non-reversible theorem has been completed by LAGUERRE
in remarking that the circle 4'BCD meets the tangent fq in A!
to « for the second time in the projection Ov of the centre O of «
on tq’. Im other words:

If P describes the normal x, in A to e, the corresponding circles
A'BCD form a pencil, as all these circles pass through A’ and
Ow. This pencil being represented by a rectangular hyperbola, the
image in question is the locus of a simply infinite number of rec-
tangular hyperbolae. However, before we proceed to the deduction
of this surface, we investigate somewhat more closely the corres-
pondence between the points P of the normal mq and the centres
M on the line /,, bisecting orthogonally the segment A’ O',.

3. The relation between the points P and M on za and Ja’ is a (1,1)
correspondence, ie. these points describe piojective ranges. If P

(3)

is at infinity on »‚, this is also the case with M ou dy. So the
point at infinity common to ng and J,’ corresponds to itself, 1. e.
the projective ranges are in perspective. The centre of perspective
7, is immediately found as the point common to the joints ? M,
and FP, M, (fig. 1) of the pairs
of corresponding points (P;,4/))
and (P, M,). This point being
found, it is possible to indicate
the centre M of the circle of
JOACHIMSTHAL corresponding
to any point P of i.
Analytically the obtained
results are given back as fol-
lows. The coordinates of A
being acosp, bsing, the equa-
tions of the right lines mq, la,
P, M,, P, My are successively:

ar by 2 — Zar 2 by A
ie oOo — —— =", ly... ——— SS S60"
cos @p sin Pp cos P sii Pp
ar 2b — Zar by
a ae Se ESR ON pb tata ae pele
coop _ sin p cos p sin p
2
So the centre of perspective 7, has the coordinates — — cos p,
a

ra and this point describes the ellipse «’, the four vertices of

which are the four real cusps of the evolute of «. And the joints
AT, and A'T, likewise envelope ellipses, ete.
4. The simple relation between the lines ze and Ja proves

A d 4 : As 4,2
immediately that /, is normal to the ellipse —~ + aes — land
a”

that through any point M pass four of these normals /,,. In other
words, any normal to the plane of the circles meets four of the
rectangular hyperbolae and so contains eight points of the locus.
As the point at infinity common to all these normals does not lie
on one of the rectangular hyperbolae, the locus is a surface of the
eighth order. We confirm ‘his result by the deduction of its equation.

The cones that form the images of all the circles through A’ and
all the circles through Of are represented by

1*

(=)

(a — a cos p)° + (y — bsin p)° ee |
( ab? cos p EE ( a?b sin p y a he
U ee y — SE ie
b? cos? p + a? sin? pr ME pH a? sin? p

So these equations represent together the rectangular hyperbola
projecting itself in L/. Putting for simplicity’s sake u? for 2° + 4? — 2,
these equations can be reduced to

ur + b? He? eos? p — 2 ar cos p = 2bysingp)
ue (a?—e? cos? p) — 2 ab? x cos p + ab? = 2 a? by sin p {

So elimination of sin p gives for cos p the relation
cos p [(u® + a*) cosp —2ax]= 0,

which breaks up into

2 at
nom
Uit QE

As p is variable, the first condition cannot serve here. It cor-
responds in fact to this, that the two cones with the vertices A’
and O, coincide instead of determining together a rectangular
hyperbola, when A’ is one of the extremities of the minor axis
of e; whilst a similar treatment, in which the parts of cos@ and
sing are inverted, leads to the relation sin p = 0, corresponding in
the same manner to the coincidence of these cones, if A’ is one of
the extremities of the major axis of e. Substitution of the other value
of cos in the first of the second pair of cone equations gives the
result in the form

4 a? x 4b? y? ane
Crain NG arene
which really represents a surface of the eighth order.

Inversely this simple equation shows that the surface represented
by it may be generated by rectangular hyperbolae, by considering
it as the result of the elimination of w between

(1),

2 ax = (u? + a”) cos w |
2 by = (u? + 2) siny |
which represent for any constant value of w a rectangular hyper-
bola lying in the plane
2 ax 2 by

9

c

cos W sin W

(5)

For ~= p + 180° this equation transforms itself into that of Lr.
5. We signalize here some particularities of the found surface.
a. The intersection of the cone 2? + y?—2?—=0 with the plane
at infinity is a fourfold curve of the surface. For the substition of

x=p+<zcosi, y= qtesink

into the equation 1) yields an equation of the fourth degree for z.
It is reduced to a cubic equation under the condition

(p cos A + q sin A)? = a? cos? À + 6? sin? A
and te a quadratic equation for
p cos À + g sin À = 0.

So the four tangent planes in the point «= zeosÀ, y —zsin) at
infinity are represented by

veos) + ysink — z= +V a? cos? A + 6? sin? dD ,
reosA +ysmni—z=0,

the Jast of these counting twice. The deduction of the envelopes of
these planes for various values of À shows that the surface 1) is
touched at infinity by the developable surface or torse circumseribed
to the tangential pencil of quadries, to the four quadrics flattened to
conics of which belong the fourfold conic of 1) and the ellipse «;
moreover it is osculated at infinity by the cone 2 + y%—2?=0.
So this cone intersects the surface 1) in a curve in space of the
sixteenth order to which the fourfold conic of 1) belongs six times.

: ; : : . 4A x?
The completing curve in space lies on the cylinder —-+ — -=1,
a

in which 1) is transformed for u? —0; this cylinder meets the
surface 1) in another curve of the twelfth order, ete.

b, The intersection of the surface 1) with each of the planes
ZOX, ZO Y consists of four straight lines and a rectangular hyper-
bola counting twice. So y =0 yields the four lines + z= +a and
the hyperbola «#?—z*-++ a? =0, and likewise *=0 yields the four
lines y+2=+05 and the hyperbola y?—z*+ 02=0. So 1) con-
tains besides the fourfold conic at infinity still two double conics ;
moreover it bears eight right lines, viz. the four pairs of lines into which
the rectangular hyperbolae of the vertices of ¢ are degenerated,

(6)

c. The surface contains four separate double points, the four vertices
of «. By transporting the axes of coordinates parallel to themselves
to one of these points as origin and equalling the terms of the
second order to zero the equation of the corresponding osculating
cone is found.

d. The curve limiting the projection of 1) on the plane of the
circles is obtained by elimination of z between 1) and its differential
quotient according to 2. It consists of the intersection of 1) with the
plane of the circles and of the projection of a curve in space. The
first is the locus of the octuples of points common to the corres-
ponding pairs of circles of the two circle involutions

(w = asec)? + y? = a? ty? À \
a® + (y + b cosec hy? = b? cot? A J

and as such a quadricircular octavic; the isolated double points
in the vertices of ¢ excepted, all its points are imaginary. The
second is found by the elimination of u* between 1) and its diffe-
rential quotient according to x*, which, v being substituted for u?,
comes to the elimination of v between

4 a? a? 4 by?
(eta? (oP 7

4 a? 2 4b? 7?
vt a? vb?

=2rvt+ a4 02

By solution we find
(vazen, wWtLPPx=—4) cy?

and by elimination of v

2 2 4
Zary+(2byy=e ,

9
pe

; ; Ax Ay?
i.e. the evolute of the ellipse Sas cle =,
a

b2

be foreseen. For the normal at the plane of the circles in a point
of this evolute meets two immediately succeeding rectangular hy-
perbolae and is therefore tangent to the surface on either side of
the plane X OY. The curve of contact itself, of which this evolute
is the projection, is of the twelfth order. The cylinder of the sixth

This result was to

(7)

order, of which this evolute is a right section, meets the surface 1)
moreover in a curve in space of the order 24.

6. The found image 1) can be useful in different researches
about the system S of the circles of JOACHIMSTHAL. By determining
the number of points common to this surface and a rectangular
hyperbola, a parabola and a straight line, we find that the system
S has the characterizing numbers 4,8,16; in other words, it contains
four circles passing through two given points, eight circles passing
through a given point and touching a given line, sixteen circles
touching two given lines. In the same manner is proved that it
contains sixteen circles touching two given circles, etc.

7. If we are given a parabola instead of an ellipse, all the
circles passing through three conormal points pass also through the
vertex of the parabola. Here the found surface of the eighth order
is reduced to the right cone «?-+ y®=2*, of which the vertex of
the parabola 4° = 2px is the vertex. And the case of the hyperbola
ae is — 1, ==0 leads to the surface
re [hes ‘aid dat ; x

4 ara? 4? y?

(2 Pa)? IT

and is quite analogous to that of the ellipse.

Physics. — „On maxima and minima of apparent brightness resul-
ting from optical illusion.” By Dr. C. H. Winp. (Commu-
nicated by Prof. H. Haga).

1. If we see on a surface two zones of different (real) brightness
united by a transition-zone whose brightness decreases continuously
from the brighter down to the darker zone, this transitionzone
seems to be separated from the brighter zone by a still brighter line
(maximum of brightness) and from the darker zone by a still darker
line (minimum of brightness).

2. This phenomenon, which — as will be seen from what
follows — presents itself under very different kinds of conditions was
first observed by me in a drawing carefully and succesfully executed
by Mr. VAN GRIEKEN, of the firm van DE Weyer at Groningen,
by means of lithography. This drawing of which fig. 1 is a pho-
tographic reproduction (reduced to 1/, of its size), which unsatisfactory
as it is, yet enables us to observe the phenomenon, consists of a great
number of parallel lines of equal thickness drawn at intervals of 1
m.M. in two outer zones, at intervals of 0.4 m.M. in a middlezone,

(ES)

at continuously increasing distances in the transitionzones between
the lastnamed and the two firstnamed. (The law of increase of the
distances has been chosen so that the proximity of the stripes in the
transition zones varies as a linear function).

3. This phenomenon may be produced even more obviously and
in a simpler way by means of revolving discs, as are often used
in physiological optics. If we paste a piece of white paper of
suitable shape on a black dise and cause the dise to turn very fast
in its plane we may get on the surface any distribution of light
in which the brightness of the observed plane differs only for points
situated at different distances from the centre of rotation and so we
may compare it with the corresponding distribution of apparent
brightness. We can also photograph the discs first in rest, afterwards
in rotation, and then the first photograph gives an auxiliary figure,
from which the real distribution of light on the figure given by
the second photograph may be known.

Fig. 2, 3 and 4 show (reduced to + !/, of their real size) some
of the dises used by me; the outlines of the white parts of the
discs are partly radii pointing towards the centre of rotation, and
partly ares of spirals of Archimedes, for which, as is wellknown,
the variation of the length of the radius-vector is proportional to
that of its angle of rotation; at a rapid rotating of the discs .re-
presented by these figures we get in accordance with these curved
outlines transitionzones in which the apparent brightness varies as
a linear function. .

The maxima and minima of brightness on the limits of the tran-
sitionzones as mentioned in l., are clearly seen especially by direct
observation of the dises while rotating, but also by examining the
photographs taken of them. Fig. 5 and 6 are reproductions of such
photographs; fig. 5, corresponding to fig. 3, shows pretty clearly
the maxima and minima, alluded to above (being circles in this
case); fig. 6, corresponding to fig. 4, shows them hardly at all. The
reproductions of several of the photographs made by me proved so
inadequate that I preferred not to have them inserted here at all;
all those published, without an exception, show the phenomena in
question far less distinctly than the originals 1).

4. Now the question arises whether this optical illusion cannot
be classed among phenomena already familiar to us. Although I
dare not give a definite answer to this question I may be allowed
to offer the following considerations.

1) Before the assembly Prof. Haca has demonstrated the phenomena described by
me, as well by means of revolving discs as by photographs taken of them.

(9)

It is well known that two areas of different brightness, either
adjoining each other, or at some distance of each other standing out
against the same background, when viewed in one glance, influence
each other’s apparent brightness by contrast, so that the brighter area
causes the brightness of the darker area apparently to decrease and
conversely. Several psychologists LEHMANN !), EBBINGHAUS °), Hess
and PRETORI®), KiRSCHMANN *) and others have made this phenomenon
a subject of investigation and have brought to light some regularities
in its occurring; the laws that govern this phenomenon have however
not yet become completely known in spite of the important inve-
stigations of these scientists.

Now we should be inclined to suppose that the maxima and
minima of brightness described above are to be reduced to the
said effects of contrast. But then it would seem strange that
there should be no intensifying whatever of the lines, whenever the
transitionzone disappears between two areas of equal bright-
ness ; for we might expect that especially in this case there would
be a prominent maximum on the one side of the border and a pro-
minent minimum on the other side of it. But as it is, each of the
two zones shows almost uniform brightness (fig. Ta, which shows
the dise of fig. 76 while rotating) although it is not to be denied,
that in both areas there can be detected, towards the limits a slight
variation of brightness in the sense to be expected. Similar changes
appear a little more distinct in a zone of uniform brightness bounded
on the one side by a brighter zone, on the other side by a darker
zone as represented in fig. 8a (corresponding to fig. 8b); but although
in this case the contrasting influence of the neighbouring zones is
more visible, yet the phenomenon observed shows quite another
character than in the case of the presence of a transitionzone.

5. Presently we shall say a few words more about a possible
explanation of the optical illusion; first however I'll give some
further information about the conditions under which it appears and
about the laws which seem to govern it:

1°. In the case of a transitionzone with constant gradient of
decreasing or increasing intensity the maximum and minimum appear
exactly on the borders of the transitionzone; at any rate the devia-

1) LEHMANN, Wundt’s Philosophische Studien 3, S. 497, 1886.
*) Exspincuaus, Berl. Sitzber. 1887, S. 995.
*) Hess a. Prerorr, Von Graefe’s Archiv f. Ophthalmologie 40, 4.

4) KrrscuMann, Wundt’s Phylosophische Studien 6, S. 417, 1891,

( 10 )

tions, which might still exist, seem to fall within the limits of
probable error in the determination of the place of those lines.

2°. If we examine successively several drawings in which a tran-
sitionzone oceurs and which differ only in this regard that the
transitionzone gets narrower and narrower, we see the bright and
the black line growing finer and finer without there being any conti-
nuous increase in their distinctness; on the contrary the distinctness
diminishes when the transitionzones are very narrow and it seems
as if the narrowing transitionzone were a zone of almost constant
brightness, with sharply defined limits towards the other zones.
(Besides it seems to me that there is a general tendency to take
the middle part of a transitionzone in the above sense, for a zone
of uniform intermediate iilumination). This gradual fading away
of the limes at a narrowing of the transitionzone may easily be
seen by slightly extending (for instance 1/, cM.) the opening in
the middle of the rotating dise (fig. 7), by means of which the
dise is mounted on the axis, in the direction of one of the radial
borders of the white paper and then causing the dise to rotate, it
being mounted on the axis first as excentrically as possible after-
wards with gradually decreasing excentricity. Indeed we get in this
way a gradual narrowing transitionzone and at the same time the
experiment shows very clearly the just mentioned fading away of
the lines.

3°. Not only do the two lines appear when in the transition-
zone the brightness varies in a direction perpendicular to the border
of the zone with constant gradient, but also under quite diffe-
rent laws of intensity-variation as may be gathered from the
fact that also the photographs of the rotating discs show the lines
clearly; they are very prominent for instance when this gradient
is infinite on the brighter border and becomes finite and diminishes
gradually towards the other border, where it attains a minimum
differing from zero.

40, The lines can also be very conspicuous when the gradient
continuously approaches zero on the borders of the transitionzone.

5°. Lastly the lines appear in some cases even where the zones
of equal brightness on either side the transitionzone are replaced
by zones of which the brightness gradually decreases (resp. increases)
towards the transitionzone. It may easily be stated by means of
a rotating disc that the brightness between the two transitionzones
still may appear to have two maxima as in fig. 5, two minima as
in fig. 6 the real brightness having even a faint maximum, resp. a
faint minimum, in the middle between the two transitionzoncs.

Cia)

6. To return to the explanation of the optical illusion described
above, it seems not impossible to me that we should have to look for
it in the influences by contrast as mentioned in 4., starting for instance
from the hypothesis that each element of the field in general in-
fluences the observed brightness of any definite element under
consideration, an influence depending in a definite way on the
distance between the two elements and on the brightness both of
the „inducing and the ,reacting’” element. But then we are not
allowed, as we might be inclined to do at first sight, to assume that
this influence increases as continually the distance between the inducing
and the reacting element diminishes and as the difference in bright-
ness between these two elements increases. For the peculiarity of
the appearing of the lines mentioned in 5. sub 2°. would be
incompatible with an influence acting in this manner. Moreover
LEHMANN’s!) investigations have already brought to light that the
influence by contrast reaches its maximum at a definite value of
the proportion between the brightness of the inducing and the
reacting field. If we may as seems quite natural apply this law to
the contrast between any two elements of the field and if at the
same time further investigations might prove this critical” propor-
tion between inducing and reacting brightness to decrease as the
distance between these two elements diminishes, it may be con-
ceived that the optical illusion we have described and the ordi-
nary effects of contrast will be found to obey the same laws.
Accurate investigations will however be required *), especially con-
cerning the influence of the distance between two contrasting fields
on the amount of the influence, before we can arrive at exactly
formulating these laws.

7. Among the methods which may be used to produce the optical
illusion described I may still mention a very simple one: we send
a beam of light through a not too narrow slit, so that it fallsona
second slit parallel with the first, and receive the beam on a screen.
If the second slit is wider than the first, a middle zone on the
screen will be illuminated by all the elements of the first slit; on
either side this middle zone transition-zones will be found illuminated
by continuously decreasing parts of the first slit, and these zones will
pass into other zones not at all illuminated by light through the slit.

1) LEHMAN |. c. S. 525.

2) KrRSCHMANN announces in his treatise alluded to above the publication of his
investigations already partly made on this influence of distance; but the publication
seems not to have taken place yet.

( 12 )

The image on the screen will show very beautifully the bright
and dark lines mentioned in 1. On photographs taken of this image,
these lines are very clearly visible tuo; fig. 9, a reproduction of
such a photograph also shows them, but much less well-defined.

If the second slit is sufficiently narrower than the first, the image
on the screen will not show a part illuminated by the whole of the
first slit, yet there will be again a middle band of maximum
illumination across its whole extent; and for the rest the image on
the screen will show as a whole the same characteristics as in the
preceding case as to both real and apparent brightness. If the second
slit is gradually narrowing towards the lower part we see an image
projected on the sereen in which two straight bright lines appear,
these lines, parallel with the edges of the second slit, intersecting so-
mewhere, but remaining clearly visible beyond the point of intersection.

If we cause the light emitted from the first slit to cast a shadow
of a thin needle or thread, we get a silhouette with a middle zone
having over the whole of its breadth uniform minimum brightness
bounded by transition zones of uniformly increasing brightness
which on their outsides again are bounded by areas of uniform
maximum illumination. The maxima, and especially the minima
alluded to in 1. are again very clearly visible here, even to sucha
degree that in some cases the appearing of the minima might lead
one to speak of a doubling of the shadow cast by the thread.

In all these cases, if only the slits are wide enough, diffraction
plays no perceptible part.

8. If we illuminate the first slit of 7. by a X-ray tube instead
of by ordinary light, and if the rays are not caught on a screen
but on a sensitive plate we get on developing, negatives of which
the positives are exactly similar to the images described in 7.
Fig. 10 shows a reproduction of such a positive, corresponding to a
similar case as fig. 9.

Fig. 10 moreover shows a white rectangle, which covers part of
the drawing. This effect was obtained by covering part of the
negative, of which it is a reproduction, with a slip of paper during
the copying. I did so in order to point out that the disappearing
of the transition zone — which was effected on the spot in ques-
tion, at least for the greater part, by this slip of paper — is suf-
ficient to cause the line corresponding to it to vanish. Indeed the
bright line which in the other parts of the image is still visible,
however much it has lost of its clearness by repeated processes of
reproduction is no longer to be traced where the transitionzone
has been covered, which sufficiently proves the fictitious nature

Fig. 1.

|

Fig. 2. Fig. 3. Fig. 4. Fig. 5.

Fie. 6. Fig. 7a. Fig. 7b.

Proceedings Roy. Acad. Amsterdam Vol. I.

Ket ; LAE Mij ES

PA - Ly ,
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of the line. The same experiment may be made in the case of
fig. 9 by covering somewhere the transitionzone (for the greater
part) with a sharply ontlined piece of paper. That the disappearing
of the line is really due to the disappearing of the transition-zone and
not to ordinary contrast in consequence of the covering piece
of paper will appear if we take first a dark piece of paper and
afterwards a light one, both producing the same effect.

9. Although the optical illusion described avove may be produced
especially by the methods given here, yet it may be often observed
in a simpler way. In nearly all cases where we have an umbra
passing into a penumbra we may observe a dark and a bright line
as borders of the penumbra, and the optical illusion appears in all
the various forms described above and even more.

10. Attention has been drawn to the appearing of bright and
dark lines conjointly with a penumbra, as described in 7 and 8 by
SAGNAC (Journal de Physique VI p. 169, 1897). Formerly I did
not conclude from what he said on this subject that he took those
lines for the result of optical illusion only, although now it seems
to me, if not probable, yet possible that this has been the case.
That I feel justified to communicate my observations on this subject
somewhat extensively is owing to the great importance that, in my
opinion, must be attached to this optical illusion.

In the first place it has deluded many a physicist, who thought
that he observed diffraction lines or other important lines in cases
where now it is certain that no real maxima or minima of bright-
ness of any importance existed; so it has especially caused bright
and dark lines to be observed in X-rays-shadows the true nature
of which some have tried to explain in various ways, but no one
had yet sufficiently accounted for. (Ancther time I hope to return
to this subject).

In the second place it seems to me that this optical illusion may
under special conditions lead to the observation of the doubling of
bright or dark lines or bands where in reality there is nothing but
a broadening of these lines or bands together with the borders
growing less sharply defined (compare what has been said in 5. sub
5°), a thing that may occur f.i. when the optical system we use in
observing is not accurately adjusted (resp. accomodated), It may
be that in some cases this optical illusion must be held responsible
for doublings which have been observed and which have not yet
been explained in the right manner or not yet been explained at all.

In the third place the optical illusion may lead to errors in the
estimation of the place of the maxima and minima of brightness

( 14 )

in a system of bright and dark lines, as soon as the brightness in
the neighbourhood of the lines is not perfectly symmetrical with
respect to their centres.

At any rate we may conclude from what preceeds that we cannot
be too eritical while observing maxima and minima of brightness,
and that in many cases we shall even have to convince ourselves
of the existence or non-existence of real maxima and minima of
brightness corresponding to the observed maxima and minima.

Bacteriology. — On the relation of the obligatous anaérobics to
free oxygen. By Prof. M. W. BetsErincx.

The relation of the living cell to free oxygen is best to be judged
from the influence of this gas on the growth and on the mobility.
Of course, only the first method is of universal application.

As to the mobile microbes, some time ago I gave the name of
„figures of respiration” ') to the peculiar groupings, which originate
in preparations destined for the microscope, in consequence of the
access of oxygen only along the edge of the examined drop under
the cover-glass, the microbes being thereby enabled to seek that
quantity of oxygen which is best adapted to their respiration. Three
types may here be distinguished according as the microbes seek the
highest tension of the oxygen along the edge, a middle tension at
some distance of it, or the smallest tension in the centre of the
preparation. These types I called the aérobic, the spirillous and the
anaërobie type.

Further experience has shown that the anaérobic type, charac-
terised by the accumulation of the moving microbes at that spot

of the preparation where the oxygen tension is minimum, — com-
monly near the centre, — does not exist as a special type, but

becomes visible only under particular circumstances, and further,
that when the aération of the preparation is sufficiently small, all
anaërobies, examined till now, appear to belong to the spirillous
type, that is to say, they not only don’t fly those places in the
preparation, where a small oxygen tension still exists, but they even
seek them.

This tension, beneficient for the anaérobics, is however very slight,
whence follows, that by using only a moderate number of microbes,
consuming but very little oxygen, there may enter at the edge more
oxygen than is wanted. In such a case the tension, most approaching

1) Centralblatt fiir Bacteriologie Bd. 14 pag. 837, 1898.

(15 )

the required optimum, will be found in the centre. The accumu-
lation of the microbes will then also be localised to the centre,
causing the semblance of an anaérobic type as a special case. It is
clear, that if this is the right explication, the true representatives
of the second type, viz. the spirilli, must under certain conditions
also accumulate at the centre, namely then, when all the spirilli
together cannot absorb the total quantity of oxygen entering along
the edge of the preparation, and this is indeed easily to be observed,
by using a small number of spirilli and a large coverglass.

So, there is no sufficient reason to divide the mobile bacteria
into three types according to their relation to free oxygen, as I
formerly did, but only into two. It also seems to me that the
names for the types, already mentioned, are not quite applicable, and
that it is preferable to call aérophilous all organisms which seek the
highest oxygen tension !), and microaérophilous those which require
a lower tension. To this latter group then, belong the obligatous
anaërobies as far as now observed, and the aërobie spirilli with
regard to their mobility.

I am obliged here to speak of „acrobie spirilli”, as I have for-
merly shown that there also exists an obligatous anaérobic spiril,
namely the organism of the reduction of sulphates, Spirillum desul-
furicans. Though this kind is very mobile, yet the growth is so
slow, that I have not succeeded in collecting a sufficient number of
individuals to get distinct figures of respiration, — a difficulty which
exists also more or less with other obligatous anaérobics.

The conviction that free oxygen is beneficial to ali that lives,
and in the long run probably even necessary, is based on the
relation of the growth of the obligatous anaërobies to this gas,
and here the mobile forms as well as those which are not mobile
may enter into consideration. Before however describing the experi-
ments which seem decisive, I must fix the attention on the following
circumstance.

For alcohol yeast and the other facultative anaérobies, it must be
admitted, that the possibility of their temporary anaérobiosis, is
determined by the presence of a provision of oxygen in loose com-
bination with the living matter of the celi itself, by which combination
some cell divisions are rendered possible without the supply of new
oxygen. Consequently there must be a difference between aérated
and not aérated cells.

*) Here is only question of experiments in common air, not in pure oxygen.

( 16 )

If it is accepted that this relation holds also good for the obli-
gatous anaërobies, then it is to be expected that their provision of
oxygen will be much smaller than that in the yeastcell, so that it is
necessary to take much more efficacious measures to render the
influence of the oxygen visible in the former than in the latter case.
It is therefore desirable, in some cases even necessary, to use for
the experiments materials, taken from such cultures as have long
been continued in absence of air, by which the provision of oxygen has
been lessened. So far as I am now able to judge, strongly aérated
anaërobies are, as to their growth, aërophobie, 1. e. they grow best
there where the oxygen tension is minimum or zero. As contact
with air is in itself not sufficient to cause aération, — spores for
instance seem less fit to be aérated than vegetative cells, — there
now and then occur strange incidents which make the experiments
troublesome.

The way in which I arranged my growth experiments is as follows.

Material of the species to be examined, is introduced, in a not
aérated condition, and. if possible, in the state of spores, into the
culture mass still in fusion, in such a quantity, that the germs,
developped into colonies, may render that culture mass, after solidi-
fication, rather opaque.

If such a culture mass, from which the free oxygen is completely
withdrawn, is contained in a deep experiment-tube, where the air
can only find access from above, then, if the growth is favoured by
a certain oxygen tension, there must result at the very place where
this tension becomes optimum, an opaque and distinctly visible
niveau of colonies, which are greater than the colonies beneath and
above this niveau.

The easiest way for completely removing the oxygen, is to
sow simultaneously an aérophilous species, not acting injuriously on
the development nor disturbing the observation of the anaérobic.
Such an aërobie must have the following qualities: The oxygen
must be completely absorbed, without exciting so much growth in
the surface of the culture mass, that the colonies of the anaérobic
become indistinct. Besides, an easy recognition in the microscopic
preparation, and a simple separation of the aërobie and the anaérobic
must be possible.

In trying various species of microbes, I found some kinds of
yeast to be most efficient for the research of the anaërobies of putre-
faction and of sulphate reduction, as for these processes no carbohy-
drates are essential, in which case yeast does not grow strongly,
whilst it is distinetly recognisable under the microscope. Besides,

(17)

yeast can easily be separated from the anaérobics of proteine putrefac-
tion, because it dies at 50° & 60° C., whilst the spores of the latter
can be heated to 90° & 100° C. without dying. For the examina-
tion of those anaérobics which require sugar in their food, as for
instance the butyric ferments, it is preferable, for oxygen absorption,
to make use of certain blastomycetes (which grow and reproduce
like yeast, whilst alkohol fermentation is absent) or aërobic bacteria,
which don’t produce acid, nor liquefy gelatine. Good results were
obtained with a red blastomycete, isolated from garden-soil, and with
Bacillus fluorescens non liquefaciens.

It is good (but not always necessary), to place the prepared
experiment-tubes, in an exsiccator which is vacuated. For this vacua-
tion a KörriNG-waterjetpump with manometer will suffice, by which
at the same time the pression of the gas used may be measured.

Another very suitable method to state the influence of oxygen
on the growth, is to cultivate in the ,humid room” on the object-
bearer under the cover-glass, in a not too small quantity of the
nutritious liquid, but in such a way as to keep the preparation
thin enough for the microscope. In this way it is possible to observe,
in the same preparation, first the figure of respiration and afterwards
the growth.

The species of obligatous anacrobies which I have examined are
the following.

Butyricferment (Granulobacter saccharobutyricum). This anaérobic
is extremely common in garden-soil. Fit material for figures of respir-
ation is to be obtained as follows. Water with some kalium phos-
phate and magnesium sulphate and 5 or 10 pCt. glucose is boiled
in a little flask with so much fibrine that a thick paste is formed.
During the boiling an infection with garden-soil is practised, in which
only spores of bacteria remain alive. In the thermostate a vegetation
of aérobics develops first, which, by the absorption of the oxygen,
introduces butyric fermentation. Sometimes this fermentation will follow,
even in absence of aërobies, i. e. notwithstanding the entrance of air into
the mass of fibrine, thus showing that some aération is certainly no
bar to this process. If perhaps an aérobic grows too strongly, reinfection
in another flask with the same mixture, will suffice to make it dis-
appear and at length still to obtain an almost pure butyric fermen-
tation. If in the infection material there are too few spores,
as well of the butyric ferment as of aérobics, some aérobic bactery,
or a blastomycete must be purposely added for the absorption of
the oxygen.

In this way a culture is obtained containing only the ,oxygen-

2

Proceedings Royal Acad. Amsterdam. Vol. I.

(18 )

form” of butyric ferment, i.e. only mobile staves and no clostridia.
With them a figure of respiration may be produced consisting of
a single fine line of quickly moving little staves, situated at some
distance from the edge of the cover-glass and the meniscus of the
preparation, which places the microaérophily of this ferment beyond
all doubt.

If to the fermenting mass pure calcium carbonate is added, by
which the acid is neutralised, the growth of the bacteria becomes
much stronger, and the staves give place to clostridia rich in gra-
nulose, and which at length produce spores. Although the opaqueness
caused by the chalk, spoils in some degree the purity of the figu-
res of respiration, yet the experiment succeeds well enough, and leads
to the same result, i.e. proves that the clostridia of the butyric fer-
ment are microaérophilous in the same way as the oxygenform. With
boiled milk, *) in which a spontaneous butyric fermentation had origi-
nated, the above observations could equally be made. That the same may
be said with regard to the butylic ferment (Granulobacter butylicum)
formerly described by me?), I need hardly add here, as it was the
continued study of this very ferment, which rendered the here
described relations clearer to me.

Anaérobics of putrefaction of proteids. The most striking instances
of obligatous anaërobies are met with in the putrefaction of pepton,
or, generally speaking, of proteine substances. If one wishes to
isolate the microbes concerned, efficacious measures must be taken
for the exclusion of oxygen, as the quantity of air which these
ferments admit, without their growth being impaired, is certainly
much smaller than with the butyric and butylic ferments. Hence
here in particular it was of importance to study their relation to
oxygen.

Before entering upon my immediate subject, I think it necessary
to say something about the different species concerned in the process
of putrefaction, the literature on this subject being quite unsatisfactory.

Bacillus putrificus coli BrensrocK®) is an anaérobic, found back
by nobody, so that it cannot be typical for the putrefaction of
proteids. Besides, an exact microscopic examination shows that more

1) Milk, boiled in a not too undeep flask, will sometimes get into butyric fermen-
tation, even with free entrance of air, without the presence of aérobics.

2) Archives Néerlandaises I. 29, pg. 1. As this ferment produces much more
propyliculkohol than butylicalkohol it would have been better to call it Granulobacter
propylicum.

’) Zeitschrift für klinische Medicin, Bd. 8. pag. 1. 1884,

(19)

than one species must here be active. That however, the number
of typical bacteria should be very great, I think doubtful, for the
following reasons: The course of the process of putrefaction is quite
the same when the material, after infection with soil, is for some
moments heated to 90 à 100° C, as when this is not done. Hence
it follows that only spore-forming microbes are typical for the
process. The experiment shows further that exclusion of air acts
favorably on its course, so that all aérobic microbes appear to be
indifferent, except in so far as by absorption of oxygen, they favor
the development of the properiy so-called putrefaction bacteria.

By these two data the process was so much simplified from a
bacteriological point of view, that there appeared some chance of
further unravelling it. Though hitherto I have by no means entirely
succeeded, I think, nevertheless, that what follows holds good.

Three species of obligatous anaërobies are in particular concerned
with the putrefaction of proteids. In the first place Bacillus septicus,
secondly a group of extremely variable forms, related to the tetanus-
bacillus, and to which I will give the name of ,skatol-bacteria’’,
and thirdly, an immobile, well-characterised species, called by me
B. pseudopulcher. For separating these different species, I used a
culture gelatine of the following composition: Destilled water, 10 pCt.
gelatine, 3 pCt. pepton siccum, 0,05 pCt. dinatrium phosphate, 0,05 pCt.
magnesium sulphate, using at the same time yeast ora blastomycete
for withdrawing the oxygen. When put into a deep experiment-tube,
the anaërobies develop even with free entrance of air.

B. septicus PASTEUR, is, according to my experience, one of the
most spread species of bacteria, to be found wherever animal sub-
stances are tainting, and very common in dust and in the soil.
It is an easily recognisable and well defined species. A virulent
form of it goes in the German literature by the name of B. oedematis
maligni'). Material of the latter, occurring in the laboratoria,
I compared, also with a view to their relation to oxygen, with cultures
of B. septicus, repeatedly isolated by me from putrefying albumen
solutions, or fibrine, infected with garden-soil, but I could discover
no difference.

The skatol-bacteria are to be known by the globular spores
which are found in proteine putrefactions, in the swollen ends of
thin, commonly long staves. One of the forms isolated retained

1) A bactery, accepted by the medical men as a particular species, B. Chauveaui (of
the French) or B. emphysematos (of the Germans) is, in my opinion, only a variety of it.
Jk
ad

( 20 )

at first, even in the pure cultures, globular spores, whilst in other
isolations the spore-form proved not to be constant. The dimensions
of spores and staves are most variable. Motion, if present, is slow,
in pure cultures sometimes absent. Glucose, added to the above
mixture, gives rise to the production of gas. The colonies cause the
culture gelatine more to weaken than to liquefy; they are sometimes
colorless, commonly, however, surrounded with a brownish aureole.
The study of this species is difficult on account of the great vari-
ability in form and functions, which renders the experiments doubtful
and often suggests infection with allied forms, to which their com-
mon occurrence gives particular cause.

While skatolbacteria never fail in putrefying substances, B. septicus
may be absent and its place be taken by B. pseudopulcher. This
name was chosen on account of its resemblance to a common earth-
bactery, related to B. megatherium, and which I baptised B. pulcher 1).
Motion is never observed in pseudopulcher; the spores are oblong,
larger than in B. septicus, frequently to be found in long rows
within the threads, generally, however, they occur in short staves.
The colonies, which liquefy strongly, have a smooth surface, by
which they may be easily distinguished from B. septicus. They are
characterised by a heavy sediment, consisting of staves and spores.
This sediment is different, or wanting in B. septicus. The pure
cultures develop gases but not many stinking products. There is often
a distinct smell of cheese to be observed. The study of this bactery
is still imperfect and I mention it only because it might be taken
for B. septicus.

For the object [ have in view, I studied in particular B. septicus,
while I think, that there is not one indication in bacteriological
literature which suggests any benificient effect of free oxygen on the
functions of this bacillus. For the skatolbacteria on the other hand,
such indications exist. It seems at least according to some authors,
that certain varieties of the nearly allied and commonly obligatous
anaérobic tetanus-bacillus, are suscept to change into aérobies, a
transformation which I witnessed myself by other varieties isolated
from putrefying albumen. Moreover B. septicus is a „bona species”,
i.e. recognisable for everybody.

B. septicus 1s exceedingly mobile and generally consists of staves,
covered all over with ciliae. Spores grow easily, especially when
there is contact with air. They are more oblong than globular,

!) At present in trade by the name of valinit.”

( 21 )

mostly enclosed in the somewhat swollen ends of the staves, and
surrounded by a hollow space. Though this bacillus is evidently
polarically constructed, it moves spore-end or tail-end forward,
and may suddenly change the direction of the movement. Whena
little air accedes, the siaves may grow out into long threads and
the motion ceases.

With a total withdrawal of oxygen there is a disposition for the
formation of clostridia, but without a marked difference between
an ,oxygenform’” and a ,clostridiumform” as found in Granulo-
bacter butylicum.

If the nutrient matter is merely albumen or pepton, gases are pro-
duced, whose quantity increases more or less by the addition of glucose.

Fibrine and proteids produce volatile sulphides, sometimes in great
profusion ; production of merkaptan, too, !s observed under unknown
circumstances. The colonies liquefy the gelatine of the above com-
position; their surface is quite characteristically pointed, evidently
because many small shoots pierce slightly into the gelatine, before
the melting sets in. This may be compared with the behaviour of
anthrax, where, however, there is no melting at all. Commonly
whether spores or vegetative cells are sown out, only few germs
develop, which proves, that the nutrient matter itself, — even the
best I could procure, — acts in a high degree as a_,bactericid” in
relation to B. septicus. The growth is slow, even at brooding tem-
perature, when compared to allied aërobics.

Concerning the necessity of oxygen for B. septicus and the skatol-
bactery, I could state what follows.

B. septicus I observed as well with regard to the figures of
respiration, as to the growth. In both ways the microaérophily
could with certainty be stated. As this bacillus is extremely mobile,
and as the spores render the swarins of bacteria very opaque, the
study of the figures of respiration offers no difficulty.

A small number of bacteria accumulating in the centre of the
preparation, produce the impression of aérophoby. If on tke con-
trary, the bacteria are very numerous, a circular accumulation
is formed at some distance from the edge of the cover-glass and
the meniskus, pointing out the place where the tension of oxygen
is optimum. If we examine the inner field, i.e. the part surrounded
by the accumulation and totally deprived of oxygen, there, too, all
is in motion. This motion is however much slower, more staggering
and uncertain, than in the accumulation itself. I think that this
inner part is continuaily supplied with individuals from the accu-
mulation, which individuals, after some time return to the latter, to

(22)

take in a new provision of oxygen. Outside the accumulation, near
the edge of the cover-glass, where the pression of oxygen increases,
the number of bacteria diminishes quickly, together with the mobility
of the remaining ones. At the edge itself all is in complete rest,
and no motion sets in when the surrounding is freed from oxygen.
Still I have no reason to consider the resting individuals as dead;
I even think they function as an „oxygen filtrum’’, thus protecting
the more inwardly swarming.

If some grains of fibrine are introduced into preparations of
which the figures of respiration are being studied, and if placed at
e. a. 25° C. in a ,humid room’, a considerable increase of bacteria
may readily occur. Watching the process micros- and macroscopically,
we find the growth almost exclusively limited to the accumulation
parallel to the edge, which accumulation grows more and more dense by
the increase of the spores, whilst the central part continues as clear
as at first. Consequently, it may be taken for granted that 5. septicus
requires oxygen for its growth, as well as for its mobility.

On this occasion I wish to correct a mistake in my description
of Spirillum desulfuricans. I there stated erroneously !) that Spi-
rillum tenue, which is typical for microaërophily as to mobility,
is also mieroaërophilous with regard to growth, so that, when sown
in a fit culture mass, it shows its maximum growth, not at the
surface, but at a certain distance below it.

This has proved to repose on ,trophotropy”, signifying that growth
is more favored by the influence of the food than by the oxygen.
It occurs only when a bad culture ground is taken for the experi-
ment, and it is by the aérophily of the growing spirilli that it must
be explained. For the intense growth will cause at the surface a
rapid exhaustion, so that, if no abundance of food is present, and
if the food can only come up slowly from the depth by the process
of diffusion to the place of consumption, then, not the surface itself,
but a deeper Jayer will, under the joined action of oxygen and
food, be most favorably situated for growth and increase. Thus in
fact, Spirillum tenue is aérophilous as to growth and microaérophilous
as to mobility.

Beside to this peculiar form of ,trophotropy” in the growth, one
has to pay attention, when studying the figures of respiration, to a
phenomenon of almost the same nature with respect to the mobility,
and which may be called ,trophotaxis”. It consists in the accumu-

1) Archives Néerlandaises, T, 29, pag. 272.

(23 )

lation of the mobile microbes, which are more attracted by the food
than by the oxygen, not in the meniscus and at the edge of the
preparation, but at some distance. I observed this in an aérobic
species, which I have called Bacillus perlibratus, where trophotaxis
may become so strong, that microaérophily is mimicked, and was
erroneously described by me as such ').

With abundant food, however, nothing is to be seen of these
phenomena, so that by attentive observation microaérophily may
always distinctly be recognised.

I now return to the anaérobes of the putrefaction of proteids,
and in particular to the second important form, the skatolbactery.
Of this polymorphous form I examined, as already said, material
closely allied to the tetanus-bacillus, which material is strictly
anaérobic, and perhaps ought to be considered as the most character-
istie for the process of putrefaction in general. I isolated various
varieties and by means of growth experiments I was enabled to state
microaérophily. The mobility of my varieties was too insignificant
to be of use for the production of figures of respiration. When using
the above mentioned pepton gelatine as nutrient matter and Saccha-
romyces apiculatus for the absorption of oxygen, most convincing
„niveaus’’, of a light brown color and with much growth, originate
in deep experiment-tubes at a certain distance from the surface,
in the surface itself the transparent clear colonies of the apicu-
latus-yeast develop vigorously, the skatolbacteria not being able to
develop there.

The spore-formation seems here also to be favored by a small
quantity of oxygen. Certain it is that spores are the most profusely
formed in the niveau, and as their preduction goes parallel, first
io the weakening and then to the complete liquefying of the gela-
tine, it is clear that also the latter process must begin in the
niveau, to become only much later perceptible in the depth, and
without reaching the surface at all.

I wish to terminate this survey of the obligatous anaérobics,
studied by me, with the statement that the existence of micro-
aérophily could also be proved for Spirillum desulfuricans by means
of growth experiments.

This species is, in opposition to S. tenue, strictly anaërobie and
belongs morphologically to quite another group than the butyric-
ferments and the bacteria of putrefaction, which is clearly demon-

1) Centralblatt für Bacteriologie, Bd. 14, pag. 839, 1893,

( 24 )

strated as well by the vibrio- or spiril-form, as by the absence of
spores }).

If sown in pepton gelatine, with Mour’s salt and an aérobic bac-
tery (B. termo) for the absorption of oxygen, in deep experiment-
tubes, the microaérophily becomes visible by a black niveau”
of ferrosulfid, first formed at some distance beneath the surface
and thence, only slowly, growing towards the depth and upward.
When microscopically examined this niveau proves to be richest
in reducing spirilli, so that evidently not the function of the sul-
phate reduction as such, but the growth of the Spiri//um, active in this
process, is furthered by a low oxygen tension.

It is fit here to make a few remarks concerning the relation of
facultative anaërobies to free oxygen. By far the greater part of facul-
tatives is aérophilous. I mention for instance Mucor racemosus, all
alcohol yeasts, Bacterium coli commune, B. lactis aërogenes, Granu-
lobacter polymyxa, Bacillus tuberculosis, B. prodigiosus. If the pro-
duction of figures of respiration is possible, then the width of the
moving bacteria zone is very great, even in dense swarms, which
indicates a slow consumption of oxygen. ‘This is especially the case
with the fermenting species, as coli and aérogenes, and sometimes,
too, with not fermenting species, such as Bacillus tuberculosis ®).

Microaérophilous are among the facultatives, so far as I think I
can assert now, only the true lactic ferments, which may be brought
to two groups of which the most important representatives are:
Bacterium lactis (of buttermilk), and Bacillus longus (of cheese and
of the yeast industry).

As these forms have no motion and produce little living matter
in growing, the total quantity of absorbed oxygen is very small,
whence the experiments are difficult and subject to doubt. If
sown, however, in a proper solid culture mass, to which calcium
carbonate is added, in a deep experiment-tube, it may be observed
that, under favorable circumstances, at a certain depth below the
surface, the formation of acid is the most vigorous. This is caused
by the existence of a niveau, very rich in bacteria if compared with
deeper layers where less, as well as with those nearer to the
surface, where more oxygen is present. After some time, however,
so many colonies criginate, as well at the surface as in the depth,

1) As I think the only well-described instance of a spore-free obligatous anaérobic.

2) The mobility of Bacillus tuberculosis has first been seen by Mr. Mac Grinavry.
The figures of respiration are troublesome to obtain and only with quite young eul-
tures, as for instance of flesh bouillon agar, not older than 24 hours.

(25 )

that the microaérophily grows indistinct, without changing into
aérophily.

Recapitulating, and adding some instances not yet mentioned, I
come to this conclusion :

Aërophilous are: All aérobic bacteria (except some spirilli), most
facultative anaérobics, probably all cells of higher animals and plants,
most infusoria.

Microaérophilous are: The few hitherto examined obligatous
anacérobies, to which belong also the chromatia and other sulphur-
bacteria, and Spirillwm desulfuricans, Of the facultatives probably
all lactic ferments, besides some (perhaps many) species of monads,
and some infusoria.

Aérophilous with regard to growth, microaérophilous with regard
to motion are: Some true spirilli, perhaps also some monads.

Though nobody will be surprised that, in reason of the above
observations, I believe that all living organisms known at present,
require free oxygen for their existence, I am far from pretending to
have furnished the entire proof for that belief. It may even be asked
whether there is cause to speak of want” of free oxygen, and if
„use of it if accessible” were not more adequate.

With regard to the examined obligatous anaërobies I have only
shown that an extremely small quantity of free oxygen is propitious
to their growth and mobility, but not yet that in the long run they
would perish without it !).

I must however insist on this being positively the case with the
aérophilous facultative anaérobics, such as aleohol ferments, B. coli
commune, etc. If these are prevented from laying in a ,provision”
of oxygen, on which to live when this gas fails, the growth soon
ceases and, even with the best food, life too®). This fact is very
singular, for the extremely small quantities here concerned, are
nothing as to the development of energy.

Consequently it is not clear why the combined oxygen, which
abounds in the food, cannot here fill the place of free oxygen. With

1) Experiments in this latter direction have not yet given any sure results and
have only proved that, with apparently efficacious precautions, anaérobiosis without
access of air can long go on. So I could, without supply of air, make seven butylic
fermentations go on successively, but at the seventh there arose some doubt whether
the bacteria had varied or that an infection from without with butyric ferment had
occurred.

*) For this reason I formerly proposed to call these organisms „temporary auaéro—
bies”, but now that I am more and more convinced that also the vobligates” can
exist only temporarily without free oxygen, L no more attach much value to that term,

(26 )

the unknown signification of the latter it is, to be sure, quite
uncertain whether there must exist a minimum limit beneath which
the possibility of life is totally excluded; but as this limit does
certainly exist for the facultatives, one is by analogy inclined to
accept its existence everywhere, consequently for the obligatous
anaérobics, too. That is, for them also, to recognise free oxygen as
a necessity for existence.

This opinion has the more weight now that it has been proved
how easily may be shown that they not only wse free oxygen but
if possible, seek it and that it may promote even such important
functions as growth and mobility. .

Without doubt, this points to something more than use”, albeit
the term „want goes perhaps too far. As it is however a fact
that the obligatous anaérobics can produce thousands of new gene-
rations without a renewed contact with free oxygen, the hypothesis
demands the acceptance of a peculiar exciting action of the free
oxygen, stored up as a provision in the body of the bacteria.

This action cannot be compared to that of kalium, or of magne-
sium, or of the other elements necessary for life in small quantities.
In the first place, because the latter must be present in quanti-
ties of another order, quantities gigantic compared to that of the
oxygen provision; secondly and especially, because these elements
may be withdrawn from the most different chemical compounds.
The very necessity of the oxygen being free, causes the difficulty
of giving a definite representation of its function. Some light would
go up if it could be proved, that in the food a loosely bound
form of oxygen might occur, accessible to the anaérobies, and
Pasreur has indeed supposed that the oxygen, which is found in
beer wort, and cannot be separated from it by pomping or boiling,
makes the anaérobiosis of beer yeast possible.

Facts are however not in accordance with this hypothesis. Now,
as in the case of beer yeast and the other facultative anaérobics, we
are obliged to admit the existence of a store of free oxygen in
the cell itself, which, in a way hitherto unexplained, makes a
temporary anaérobiosis possible, analogy, supported by the observa-
tions here described, leads to the same conclusion for the obliga-
tous anaérobics.

Physiology. — On the influence of solutions of salts on the volume
of animalcells, being at the same time a contribution to our
knowledge of their structure. By Dr. H. J. HAMBURGER.

(Will be published in the Proceedings of the next meeting).

(21)

Physics. — „On an asymmetry in the change of the spectral lines
of iron, radiating in a magnetic field”. By Dr. P. ZEEMAN.
(Will be published in the Proceedings of the next meeting).

Physics. — The Haur-effect in electrolytes. By Dr. E. vaN Evrr-
DINGEN JR. (Communication N°. 41 from the Physical Labo-
ratory at Leiden, by Prof. H. KAMERLINGH ONNES).

1. The researches on the Harr-effect and the increase of resist-
ance in the magnetic field for bismuth, communicated to the
Academy in the Meetings of 30 May 1896, 21 April and 26 June
18971), and afterwards treated more at large in my dissertation,
induced me to put the question, whether these phenomena may
justify a choice among various theories about the nature of the
electric current and the resistance of metals. A first step towards
answering this question was the deduction of a formula for the
Harr-effect in electrolytes, with the aid of simplifying suppositions.
Indeed it is generally assumed that in electrolytes the electric current
consists in a convection of charges by the ions; the velocities of
this motion are known in many cases, hence all the data for the
calculation are present. This research, already begun in Chapter
VIIL of my dissertation, being concluded for the present, I wish
here briefly to communicate the results.

2. Several physicists have tried to observe the Harr-effect in
liquids. They succeeded indeed in observing differences of potential,
caused by a magnetic field in solutions of sulphate of zine and
copper which were traversed by currents, and changing their signs
on the reversal of the magnetic field or of the current. Whereas
however in most metals the Harr-effect is proportional as well to
the strength of the current as to the field, and in all metals the
difference of potential appears immediately on closing the magnetizing
eurrent, in the liquids this difference increases more than the current
and less than the magnetic field, and after the applying of the field
it grows slowly towards a maximum. Chiefly on account of the last
named fact Rorri*), Frorro®) and Curavassa *) refused to acknow-
ledge the differences of potential observed also by themselves as

1) Communications from the Phys. Lab. at the Univ. of Leiden. N°. 26,37 and 40.
2) Atti della R. Acc. dei Lincei 12 p. 397, 1882; Journ. de Phys. 1883.

*) Il nuovo Cimento, Ser. 4, T. 4, p. 106, 1896.

*) Elettricista 6, 1897.

( 28 )

proofs of the existence of the Harr-effeet in liquids, and attributed
those differences rather to ponderomotive forces, exerted by the mag-
netic force on the particles of salt, to differences of concentration
or to differences of temperature. The two physicists first mentioned
confined themselves to experiments, in which disturbances of this
kind were avoided, and the Hatt-effect had really disappeared ;
CHTAVASSA however also demonstrated ihe existence of differences
of temperature and of concentration, determined the influence of
these differences on the readings of the electrometer, and proved that
in a non homogeneous magnetic field vortical motions occur in the
liquid, which depend on the strength of the current, the magnetic
field ete. in the same manner as the observed apparent Harr-eftect.

BAGARD}) on the contrary believed to have avoided all distur-
bances in his experiments and was therefore convinced of the reality
of the Harr-effect in liquids.

The observations of CHIAVASSA were made in the same manner
as those of BaGarp; hence the greater part of the difference of
potential observed by BAGARD was very likely due to disturbances.
In the controlling experiments however, which were to prove that
whithout disturbances no difference of potential appears at all,
strongly concentrated solutions were always used; so it was still
possible that in the diluted solutions used by BAGARD a part of the
observed effect would remain even in the absence of disturbances.
Hence the question has not yet been solved by experiment.

3. We proceed to the theory of the phenomenon and for the
present confine our attention to the state of matters in the inner part
of the liquid, i. e. far from the lateral borders. If we put for the
KE. M.F. in the direction of the axis of X Ze, and for the velocities
of the ions caused by a slope of potential of 1 C.G.5. unit per cM.
U and V, then the velocities are

H,U and ZV

respectively in the directions of the positive and the negative axis
of X. We assume with Lorentz *) that an ion, moving with the
velocity » in a magnetic field of intensity H is acted upon by a
force represented by the vector product [v. .] for each unit of elec-

C.R. T. 123, p. 77 and 1270, 1896. Journ. de Phys. Sér. 3, T. 5, p. 499, 1896.

*) See f.i. Versuch einer Theorie der electrischen und optischen Erscheinungen
in bewegten Körpern. Leiden, 1895.

( 29 )

tricity. In real cases the numerical value of this product is small
as compared with unity; the variation in the direction of motion is
only slight; hence we are allowed to assume this force to be always
perpendicular to the axis of X. If the magnetie force is along the
axis of Y, the ions will obtain on additional velocity in the direc-
tion of the axis of 71).

These velocities will cause differences of potential and of concen-
tration. When the state of equilibrium has been reached it is not
necessary that the velocities should be zero, but it will be suf-
ficient if

1°. The velocities of positive and negative ions are equal.

20, As much of the dissolved material wanders back by diffusion
in the molecular state as is transported in the form of ions by the
said velocities.

For completing the image formed in this way we ought to ima-
gine at the borders of the liquid, or at all events outside the space
now considered, on one side molecules dividing into ions, on the
other side ions combining again into molecules. For the moment
we suppose the reaction-velocities for these processes to be infinitely
great.

We will now work out the two conditions.

If we call the E.M. F. in the direction of the axis of Z E,, the
ions obtain velocities in the direction of this axis equal to

(OH E,+ EU and (VHE,— EB) V.
Writing ej for the concentration of both ions and cg for the con-

centration of the salt, we may represent the velocities of diffusion
of the ions by

A de; , A dey 2
== el end == U
a dz cj, de
B dez
and that of the salt by NT
Cg dz

Here A js a constant closely related to the diffusion constant of
completely dissociated electrolytes; B has a similar signification for
the diflusion of a non dissociated salt.

1) A calculation which takes into account the irregular thermal motion of the ions
leads to the same results.

( 30 )

The first condition reads

A de Aude
(vin, tb Ua (Vik, bo Ji -(

cj de cj dz

the second
B deg

(
Sg Cy = | t
Cg dz IN Cy dz

Taking into account that the difference of concentration will be
very small, and that we supposed the reaction-velocities to be infi-
nitely great, we shall put cj = ke, & being a constant.

(2) may now be written

B de A de
— Ss (UHB. E Se)
cj dz ¢ dz
50

1de) (UHE, + E,)k

“de pede

Substituting this in (1) and writing a for — we obtain

Ak
B+ Ak

(UHE,+ E) (1—a)U={(VHE,— Ei) —a (UHE, + Ei) WV.

EAU V—a(U- Wi BH? — VE a (OE
5 VTE
Earls lenten

and
1 de, U(l —a) 4 V ja

EN SNE DD AVA
a de (

U(l—a)+ Vil +a)
The limiting cases are k= 0 and k=o .
First case (very slightly dissociated) a = 0.

JDA deo
ENDS EG ol 5 5 (@
7 U — 7) @)

7 dz
Second case (completely dissociated) a — 1.

H eden U+V
eee =F lll RT ey (2

cr dz

(31)

Both these results may be deduced directly. If ec, tends to zero,
no differences of concentration of the free ions are possible and the
velocities must be equalised by the action of electromagnetic and
electric forces alone.

The equation

(B, UH + E,) U=(E, V H — E,) V

immediately gives the relation (3).

In a completely dissociated solution on the contrary no molecules
of salt can go back by diffusion, so the velocities of the ions in the
direction of the axis of Z should both become equal to zero; hence

A de A de
Ope Be a2 Ogden — = aG
: a dz cy dz

from which the relations (4) follow immediately.

As a matter of fact, the reaction-velocities are not infinitely great.
By supposing these velocities to be equal to zero we may however
perceive that the result is not very much altered by this. In this
case no decomposition or combination occur; the concentration of
the molecules of salt is not altered, these have therefore no influence
at all upon the phenomenon. So we then find, whatever the real
degree of dissociation may be, the same result as in the case of
complete dissociation.

Hence it is very likely that the Harr-effect in liquids may ge-
nerally be represented by

ee H(U—V
E = — wH(U— V)
tt lying between 1 and }.

This result gives the rotation of the equipotential lines in the
inner part of the liquid. The question rises, whether this is what
has been observed in the experiments. In these namely the difference
of potential between two electrodes of metal is read; if these elec-
trodes are immersed in liquids of different concentration, another
difference of potential will appear, the value of which may be

( 32)

estimated by means of the formula of HELMHOLTz })

Here p, means the osmotic pressure for a concentration of 1 gram-ion
per cM®., e the charge of a gram-ion in electromagnetic units.

We take a definite case for this estimation, namely a solution of
sulphate of copper with the concentration cj = 3.105, the lowest
value we find among the numbers of KoHLRAUsCH °) for this salt.
We shail suppose that, in this case, applies the formula for com-
pletely dissociated solutions.

(Of Aik sis ll

so — (U—V)=155.10—-4%. Taking Zell volt or l0rCIGASE
H=104, we find ZE, = 0,78.

This is the difference in C.G.S. units between two points on the
axis of Z, 1 cM. apart.

The difference of concentration is determined by

1 UV
ns de; == Er H ee at .
Cy 2A

Comparing our formula for the velocity of diffusion with that of —
ale po U J A
NERNST®), it appears that A =2 Ti where — = force required to

u
move a gram-ion, with migration-veloeity u, with the velocity of
1 cM. per second through the solution.

We retain only the first term, so

i) U V
ee
Ci 2A

1) Wied. Ann. 8. p. 201, 1878. In this form the formula is given by Nernst, Zeitschr,
f. ph. Chem. 4, p. 129, 1889.

2) Wied. Ann. 50, p. 404. 1893.

%) Zeitschr. f. ph. Chem. 2, p. 619, 1888.

2 V U} Vv. Hee UV
eee Se peers
€ U+V 2 py € u
105 . 104 110

Se, 0,89.100. Sos 373.10—-l = 3,6

These calculations are sufficient to show that this difference of
potential is of the same order of magnitude as the Harr-effect.

If the electrodes are placed in little vessels communicating through
long tubes with the points on the axis of Z, as frequently occurred
in the experiments, then no difference of concentration exists at the
electrodes, and the last mentioned difference of potential disappears.

4. Comparison of theory and experiments.

For this comparison we choose the experiments of BAGARD with
a half normal solution of sulphate of copper. We find for this
solution, B UO Ir.

The experiments of BAGARD however in a field of 385 C.G.S.

give for a H a value of 13.107.
: E,

Taking the sixteenth normal solution in the strongest field, 962,
the theory gives 14.10—'8, the experiment 35.107.

If we moreover consider, that even the sign of the apparent effect,
which agrees here with the theoretical sign, in the experiments of
Cutavassa with sulphate of zine proved to be variable, it will
appear that we may safely conclude that the hitherto observed
galvano-magnetic differences of potential in liquids are not caused
by the phenomenon of Hatt.

Researches much more accurate than have been attempted till now *)
should decide whether the weak theoretical effect can be observed.
It may be doubted however whether the disturbances, which can
assume such large proportions, will ever be completely avoided.

5, So the result of this research is: for the present we can not

1) In the dissertation the factor 10° (ratio of volt and C.G.S, unit) has been
omitted. As moreover the accurate researches of Curavassa had not yet appeared
then, the experiments of BaGarp were, at that time, trusted more than they now
appear to deserve. Also mr. I’. G. Donnan at Holywood (freland) has noticed the
omission and has been so kind as to tell me so.

2) The smallest observable difference of potential was in the experiments of
Cutavassa 5.107° volts. The largest effect calculated above would give for a slope
of potential of 1 volt per eM in a field of 10000 C.G.S. units 1,4.107° volts.

(34)

yet use the phenomena in electrolytes in order to get a better insight
into the nature of the electric current in metals. In this respect
more may perhaps be expected from researches as those published
lately by Riecke!) under the title „Zur Theorie des Galvanismus
und der Wärme,” where relations are sought between the different
thermic, galvanic, thermo-magnetie and galvano-magnetic phenomena
in bismuth. I. a. Rrecke calculates with the aid of certain supposi-
tions U and V for bismuth and finds

T= 0052050 Va Onee

I intend shortly to publish the results of measurements of the
various phenomena in the same plate of bismuth, and to compare
those results with RrecKE's theory.

1) Gött. Nachr. 1898.

(June 24 1898).

Royal Academy of Sciences. Amsterdam.

PROCEEDINGS OF THE MEETING

of Saturday June 25th 1898.

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 25 Juni 1898 Dl. VII).

CONTENTS: ,,On chemical and microscopical examination of antimonial alloys for axle boxes”,
By Prof. H. Benrens also in the name of Mr. H. BAvcke, p. 35. — „The condition
of substances insoluble in water formed in gelatine”. By Prof. C. A. Lonry pe BRUYN,
p. 39. — „On the notion of the Pole of the Earth according to the observations of the
years 1890—1896”. By Dr. E. F. van DE SANDE BAKHUYZEN (communicated by Prof-
H. G. van DE SANDE BAKHUYZEN) p. 42. — „On a 5-cellar quadrant-electrometer and
on the measurement of the intensity of electric currents made with it”. By Prof. H. HaGa>
p. 56. (With 1 plate). — ,,On the influence of the dimensions of the source of light in
diffraction phenomena of FRESNEL and on the diffraction of X-rays”. (8d communication)
By Dr. C. H. Wixp (communicated by Prof. EL. Haca), p. 65. — „The galvanomagnetic
and thermomagnetic phenomena in bismuth”. By Dr. E. van Everpincen Jr. (com-
municated by Prof. H. KAMERLINGH ONNES), p. 72. — ,,On the deviation of DE ILEEN’s
experiments from vaN DER Waars’ law of continuity.” By Dr. J. VerscmarreLr
(communicated by Prof. H. KAMERLINGH OnNks), p: 82. — ,, The composition and the
volume of the coexisting vapour- and liquid-phases of mixtures of methylehloride and
carbonic-acid”. By Cu. M. A. HARTMAN (communicated by Prof. H. KAMERLINGH
Onnes), p. 83. (With 1 plate). — ,,Considerations concerning the influence of a
magnetic field on the radiation of light”. By Prof. H. A. Lorenrz, p. 90. — „On an
asymmetry in the change of the spectral lines of iron, radiating in a magnetic field”.
By Dr. P. Zeeman, p. 98.

The following papers were read:

Chemistry. — „On chemical and microscopical examination of
antimonial alloys for axle boxes.” By Prof. H. BEHRENS
also in the name of Mr. H. BAucke.

By the direction of the „Holl. IJz. Spoorweg-M4” several cushions
of Babbits-metal (82°/, Sn, 9°/, Sb, 9°/o Cu) were put aside for
chemical and microscopical examination. Alloys of this kind, when
slowly cooling from a melting heat, will split up into a nearly
amorphous mother liquor, rich in tin, into rectangular crystals (pro-
bably cuboidal rhombohedrons) of an a'loy of tin and antimony and
into a whitish bronze, forming radial clusters of brittle rods, com-
posed of hexagonal plates.

B)

Proceedings Royal Acad. Amsterdam. Vol. I.

( 36 )

The chemical examination of these components has been carried
out by Mr. BAveke, analytical chemist at Amsterdam, partly by
means of analytical, partly by means of synthetical methods, while
I have undertaken the microscopical and mechanical investigation
of the properties of Babbits metal.

For separating the products of liquation I proposed pressing of
the alloys in a semi-liquid state. This suggestion has been adopted
by Mr. Baucke and the method, worked out and perfected by him,
has given very good results. When Babbits metal in a pasty con-
dition is pressed between hot slabs of iron, tin will flow out, con-
taining 3°/, of antimony and copper and a hard, brittle cake will
be left, formed principally by the crystals described above. An alloy
composed of 90°/ tin and 10°/, copper gave a hard residue, from
which a remnant of mother liquor was removed by treating it with
hydrochloric acid and subsequently with caustic soda ley. Powdery
copper was washed away in a stream of water, and then analysis
gave 35.1°/, Cu, 64.8 °/, Sn for the composition of the cristalline
alloy, while the formula Cu Sn would require 34.9 0/, Cu and 65.1 Sn.
Repeated heating and pressing will drive out more tin, so that this
alloy may be said to comport itself in a similar manner as some
hydrated salts, e. g. crystallized sulfate of sodium.

In alloys with antimony the tin was found to be more strongly
combined. From an alloy, containing 10°/, of antimony, after heating
and pressing thrice, a residue was obtained, resembling closely an
alloy of 700/, tin and 30%, antimony. Purified by extraction with
hydrochloric acid and washing in a stream of water it was found
to be composed of 33.7 °/, Sb and 66.3 °/, Sn. Calculation from the
formula Sb Sn, gave 33.8°/, Sb, 66.2%, Sn. With 42°/, Sb an alloy
was obtained, showing prismatic crystals of higher melting point
between the cuboid ones of the compound Sb Sng. By hot pressing
and treatment with hydrochloric acid an alloy was isolated, answering
to the formula SbSn. Found: Sb 50.55, Sn 49.65 °/,; calculated :
Sb 50.37, Sn 49.630/,. In alloys, containing 80 °/) of antimony,
this element can be made to crystallize in a nearly pure state. Its
erystals are enveloped by a compound of prismatic form, probably
answering to the formula Sb, Sn. This point has hitherto not been
settled in a satisfactory manner.

Microscopical examination of cushions, that had done duty under
railway cars led speedily to the conviction, that their behaviour
depends on the frequency and size of rectangular crystals. In cushions,
marked as having been unduly heated by running, the rectangular
crystals of the compound Sb Sng were found poorly developed or

( 37 )

absent. By mechanical engineers I was told, that the alloy for
bearings must not be heated further than necessary for giving it
sufficient fluidity, then stirred and cast without delay in moulds
heated to the boiling point of water.

In Babbits metal, heated till its surface becomes smooth and bright
the majority of the crystals is not liquified. Castings, made of such
metal, without previous stirring, consist of tin, with about 4 °/, of
copper and antimony, while at the bottom of the melting pot a
hard porous mass is found, melting at the same temperature with
zinc. Made quite liquid, and then chilled, Babbits metal becomes
nearly amorphous, sonorous and very smooth when filed or turned.
Nevertheless it will stick to an axle, even when liberally lubricated,
and when heated to softening it is liable to recrystallization, crystals
being formed in a groundmass of liquid tin. Tinning of the axle,
sticking, and as an inevitable consequence heating will occur, when-
ever a heavily weighted axle is run in a box filled with such
metal. Finally recrystallization sets in and liquid tin is squeezed
out, the newly formed crystals accumulating around the axle. In
one case the crystals had formed a compact cylindrical layer, at
first sight puzzling, but now easily explained.

With a view to test this theory, experiments were made with
model cushion blocks, cast under varied conditions. The blocks were
fitted on a mandril of polished steel, running with a speed of 1600
revolutions per minute in a wooden casing. The apparatus was
contrived in such a manner, that the pressure on the mandril could
be varied at pleasure and the temperature observed on a thermometer
fitted into the blocks. The following table gives for some of the
experiments the pressures reduced to kilogrammes on the square
eentim. of the longitudinal section of the mandril and the mean
inerease of the temperature after a minute of running. Block I was
cast in a mould, cooled by running water, block II in a mould
heated to 100°, block IIT in a mould heated in molten zinc.

0.3kg.| 0.6 kg. | 1.2 kg. | 3.0 kg.

I 0.50 | 1.12 | 1,50 | 3.80

Il 0.64 | 0.74 | 0.75 | 1.64

Til | 0,65 | 0.72 | 2.62 | 4.64

3*

(38)

After the series of experiments with a charge of 3 kgr. block I
presented a running surface scarred by irregular grooves and scratches.
On block II the rectangular crystals stood out in a relief, similar
to that, produced by etching with hydrochloric acid. They were
smooth and bright, the interstices deadened by small scars or dimples.
On block III the particulars shown by I and II were found
combined.

An unexpected result was obtained by examining the metallic
sediment from the oil that had been used as lubricant. Mixed with
fine dust (essentially tin) were found: in sediment from block I
shavings, threads and angular fragments; in sediment from block II
spherical and egglike bodies (0.08—0.1 mm.), looking like small
drops of mercury; in sediment from block III spheroids and angular
fragments. A few of the spheroids from block II were subjected to
microchemical tests and found to consist of tin with a considerable
admixture of antimony.

These observations suffice to explain the slow increase of tempe-
rature in block II: the oil has been more evenly spread, owing to
the peculiar relief, developed on the running-surface of this block,
and at the same time a ball cushion has been formed, whereby
rolling has been brought in the place of sliding friction. Spheroids,
similar to those of block II were formed in experiments with model
bearings of magnolia metal (77.8 °/, Pb, 16.3%, Sb, 5.9°/, Sn) and
of aluminium brass, but not with bearings of common brass and of
grey cast iron. In this way I have been able to trace their origin
to cubical or polyhedrie crystals, scattered in a softer metal and
accompanied by smaller crystals of a hard and brittle alloy. In
Babbits metal fragments of the brittle rods of bronze act as a
grinding powder, undermining and rounding the rectangular crystals
of the compound Sb Sns, in the same way, as pebbles are formed
in the bed of a river. The tin comes in as a soft cement, possibly
its powder has also a favourable influence, augmenting the viscosity
of the Jubricant. Metal of coarse structure (cast in overheated moulds)
is not evenly eroded; the majority of the rectangular crystals, weakened
by cracks, are scarred and crushed, instead of being rounded and
loosened.

Further reasoning would be misplaced, as it may be expected,
that continued experiments and observations in the directions, pointed
out above, will speedily throw more light on the subject.

(39 )

Chemistry. — „The condition of substances insoluble in water
formed in gelatine.” — By prof. C. A. Lopry DE BRUYN.

The condition of matter called the colloid, is im many respects a
subject of interest. The physiologist, the physicist, the chemist take,
each in his department, an interest in the peculiar qualities of the
colloids. For to a great extent the processes of life take place in
a colloidal medium or between colloids; the part taken by colloid
bodies in osmose is generally known; every chemist knows a certain
number of examples in which some substances appear in a colloid
form, between liquid and solid-amorphous or as so-called colloidal
solutions.

An important study on the qualities of colloidal mixtures or
solutions, especially in a physic-chemical direction, we already owe
for many years to Mr. vAN BEMMELEN. In these important experi-
ments Mr. vaN BrEMMELEN has studied, besides other qualities, quan-
titatively the changes taking place in a colloidal mixture prepared
with water (a hydrogel) in varying the temperature or the relative
humidity of the surrounding atmosphere.

The observations of which I beg leave to give a concise survey,
do not refer in the first place to changes of a colloid mixture itself,
but to the influence exercised by a hydrogel on the physical condi-
tion of amorphous, insoluble substances, created in a hydrogel as a
medium. These observations are partly the result of former expe-
rience gained in the daily practice of the laboratory, as the non-
appearance of precipitates if in a qualitative analysis, say on metals,
there is an admixture of substances like gum; the non-precipitating
of chromate of silver in a gelatine-solution a.s. o. Such observations
are in my opinion not indicated with sufficient accuracy by stating
that the substances formed remain in suspension.

Experiences like those just mentioned were recalled to my memory
by a communication of Dr. Ernst COHEN in a meeting of the
„Amsterdamsch Genootschap.’ Mr. GAEDICKE had asserted in a
photographic journal that if equivalent qualities of Ag NO; and K Br
(somewhat more of the latter) are mixed in a gelatine solution of
5°/o, these two salts are only partially transformed, while this reaction
is complete in aqueous solution in consequence of the excessively
small solubility of Ag Br. This assertion of GAEDICKE will appear
strange to no one who performs this reaction; he will namely not
see a precipitate of Ag Br forming itself, but only a mild opal-
escence; while in aqueous solutions he will notice a strong troubling
arising. GAEDICKE rested his assertion on the observation (proved to

( 40 )

be incorrect by Dr. Conen) that when placing the mixed, solidified
Ag Br-gelatine in water, there appeared in the latter Ag Br-flakes ;
he ascribed their formation to the diffusion of non-transformed K Br
and Ag NOs; from the gelatine into the water, where the reaction
then takes place and the ordinary flaky Ag Br appears.

This opinion of GAERDICKE’s seemed improbable to Dr. COHEN;
and he has proved it to be incorrect by determining the conducti-
vity of the gelatine solutions before and after mixing. The reasoning
was simple; if the transformation is complete, the conductivity of
the gelatine solution (tested in a liquid state at 30°) must be equal
to that of K NO;; if no reaction has taken place, the conductivity
should be greater and reach the total of the conductivities of Ag NO,
and K Br in ratio to the imperfectness of the transformation effected.
The experiment decided in the former sense; the conductivity was
equal to that of K NO; alone and the hardly visible transformation
had yet completely taken place; the Ag Br is not dissociated into
ions, does therefore not conduct.

So we have here before us some examples of phenomena that
must strike the chemist; the apparent non-appearance of transforma-
tions and of precipitation when gelatine is present in cases in
which a strong precipitation is observed in water alone. I have
further extended these observations over a long series of reactions
in which precipitation takes place. It has appeared then that what
has been observed in different cases under peculiar cireumtances for
purely aqueous solutions viz. the interesting phenomenon that some
bodies (silicic acid, titanic acid, chrome- and ferrichydrate, arsenious-,
antimony- and coppersulphide, silver, gold, selenium) can remain in
colloidal solution, is a rule for solutions in aqueous gelatine. ‘The
colloidal medium keeps amorphous bodies which are created in it,
colloidally dissolved. This holds good for instance for the halogenous
combinations of silver, the sulphides, and many hydrates of the
heavy metals, for metallic silver, gold and mercury, for chromate
of silver, Prussian blue, copper-ferrocyanide, iodide of lead, peroxyde
of manganese a.s. 0. They all give transparent gelatines which solidify
on cooling, preserve their transparency, but often show an internal
reflection or fluorescence. Especially for the coloured bodies, which
I have cited here in the first place, the phenomenon is still remark-
able in so far as, by the very appearance of the color one need
not be in doubt about the question of the chemical change (as in
the case of Ag Cl or Ag Br) and need therefore not convince oneself
of its having taken place by determining the conductivity.

The modus operandi is nearly the same in all cases; deviations

( 41 )

in the concentration of some of the salt-solutions, required by the
precipitation of the gelatine itself, betray themselves. I started
with a 10 pCt. gelatine solution, which was filtered through a
sievefunnel!) when warm. By adding to this the same quantity
of the salt-solutions to be mixed (which were generally 4/19 à 1/99
normal) I got solutions containing 5 pCt. gelatine with the salt as
Mog or Myo normal. These still liquid solutions (temp. + 30°) were
mixed under strong stirring and cooled quickly to the point of soli-
dification. I then get a perfectly transparent gelatine, more or less
opalescent according to the concentration and the thickness of the
layer, which reflect a light internally and as it seems to me also
show fluorescence. The formation of colloidal silver, which as we
know, was first made by CAREY Lea in an aqueous solution, already
takes place in gelatine with Ag NO; alone, especially under the
influence of light; it appears in a very concentrated form after the
addition of some formaldehyde; it is then black-brown, still perfectly
transparent in thin layers and homogenous with the strongest mag-
nifying; only on the glass wall it deposes very slowly as a metallic
layer.

Without investigating the different cases more particularly, I only
wish to observe that I have not succeeded in keeping substances,
that precipitate crystalline or at all events crystallize very quickly,
colloidally soluted in a medium of gelatine. Calcium oxalate, barium
sulphate, ammonium- magnesium-phosphate and some other substances
form in gelatine miscroscopically correct crystals or crystalline
particles. In general it seems to me that from the many cases [
have investigated, this conclusion may be drawn that the visible
precipitation of amorphous bodies is prevented by gelatine, that of
crystalline bodies not or not so easily.

Now the question is which is the degree of division of the sub-
stance, the size of the particles which are prevented by their origin
in a colloidal surrounding to join to visible matter? It is here, in
my opinion, not a phenomenon of suspension or emulsion; these
terms are applied to microscopically visible particles; and therefore
I have spoken of colloidal solutions in a colloid. The size of the
particles is undoubtedly far beyond the limit of the microscopically
visible and therefore embraces the vast field extending between the
molecules themselves and the particles that are visible under the
strongest magnifier. According to the nature of the substances and

1) The gelatine contains a little chlorine (+ 0.1°/, H CI) and some sulphuric acid.
This must be taken into account in some reactions f.i. when forming Ag, CrO,.

(G42 )

the modus operandi (concentration of the gelatine and of the salts)
greatly different dimensions may be expected. Picron and LINDNER
who among others have proved the extremely small conductivity of
the aqueous colloidal solution of arsenious sulphide, admit four diffe-
rent ,grades” of division of this substance!). It will be found impos-
sible however to make clearly defined distinctions in this respect,
a gradual change in the size of the particles being much more probable.

The study of the phenomenon of the internal light-reflexion and
fluorescence, that shows itself more or less distinely in several sub-
stances formed in gelatine, may perhaps lead to further insight;
these optical phenomena are also found in bodies as milky colored
glass, that also contains invisible, extremely small particles. Others
however of the colloid solutions in gelatine are not only perfectly
transparent, but do not show any reflection of the light or fluores-
cence; it may therefore be admitted that the division of matter in
gelatine approaches that of bodies soluted in water. In view of
phenomena as those stated here, the idea of being soluted seems to
lose its sharpness of outline,

Equally interesting are the chemical reactions, which are the effect
of diffusion, on the substances formed in gelatine and in which one
may be passed into the other. If a Na Cl-gelatine is surrounded by
a Ago C, Oy gelatine the NaCl diffuses from the former gelatine into
the latter, the colloidal Ag, C, O, being not (or very little) diffusable,
while it is known (f.1. by experiments of GRAHAM and HuGo DE
Vries) that the salts dissociated into ions diffuse as quickly in
gelatine as in water. Now when the NaCl ions penetrate in the
bright red Ag, C, 0, the latter is converted into Ag Cl which, equally
colloidal in solution, remains transparent and spreads in the form
of a ring.

Astronomy. — On the motion of the Pole of the Earth according
to the observations of the years 1890—1896. By Dr. E. F.
VAN DE SANDE BAKHUYZEN. (Communicated by Prof. H. G.
VAN DE SANDE BAKHUYZEN.)

1. In treating the meridian-observations made at Leiden in the
last 20 years, it was necessary to arrive at a knowledge as exact
as possible of the change in latitude during that period and, before
investigating the Leiden observations in this respect, it seemed de-

1) Jo. >, Chem. Soc. GE, 137, 68, 63, FE, 568.

(43 )

sirable first to make endeavours to derive information from other
sources,

Since in 1891 the 14-monthly period in the motion of the Pole
of the earth had been found by CHANDLER, many computations
have been made on that subject by him. On the other hand the
chief series of observations of the last 50 years were submitted by
H. G. v. D. SANDE BAKHUYZEN !) in 1894 to a searching and
complete examination, in which the result of the Leiden observations
of the years 1864—1874 obtained by Mr. WILTERDINK’s *) elaborate
researches, as compared to those of the other observatories, proved
to be entitled to considerable weight.

Meanwhile a beginning had been made with special series of obser-
vations having expressly in view the investigation of the problem
of the latitude and soon important results were furnished by the
voluntary co-operation of a number of astronomers. More than once
Prof. AnBREcHT has summarised those results in the reports of the
“International Geodetic Survey” and of late an ample report has
been given by him about the state of the problem in Dec. 1897°),
in which he adjusted the whole series of the obtained results by :
continuous curve for the motion of the pole.

But a small part of these results could yet be used by H. G. v. D.
S. BAKHUYZEN and though it be true that CHANDLER has already
made many computations on this subject, yet often there is a lack
of judgment in the treatment of the observations, which in my
opinion justifies a new investigation covering now the whole of the
period of 1890—1897. The results I found being perhaps of some
importance apart from the particular aim for which I undertook
my investigation, I take the liberty of making them the subject of
a concise communication.

2. ALBRECHT could use the observations of 19 observatories, viz :
of Tokio, the Cape of Good Hope, 10 observatories in Europe, 6 in
America and finally Honolulu, a temporary observatory having been
erected there in 1891—1892. With a few exceptions the observations
have been made according to the Horrebow method. Not ina single
place however do they cover the whole period, so ALBRECHT had to
undertake extensive computations to derive in successive approxima-

1} Report of the Meeting of the Roy. Acad. Amsterdam, Febr. 1894 and also
Astr. Nachr. vol. 136 and 137.

2) Report of the Meeting of the Roy. Acad. Amsterdam, Dec. 1892.

3) Tu, Ausrecut, Bericht über den Stand der Erforschung der Breitenvatiation
m December 1597.

(42)

tions the mean latitude for each place and to join all the results
to a connected system of co-ordinates, by which the instantaneous
positions of the pole in respect to a mean one are represented.
ALBRECHT chose as co-ordinate axes the meridian of Greenwich and
one 90° westward, passing centrally over America, and finally he gives,
besides a curve for the motion of the pole, the said co-ordinates «x
and y for every tenth of a year from 1890.0 till 1897.5.

The curve of ALBRECHT is rather intricate and so we may take
for granted that his adjustment, performed undoubtedly with great
care, has strained the observations but slightly. Therefore I thought
myself justified in avoiding for my further computations the prolix
work of falling back upon the original observations, and in making
use of ALBRECHT’s x and y co-ordinates. Finally however I have
also compared my results with the original observations.

It being tolerably certain that the motion of the pole consists at
least in the main of a 14-monthly and a yearly motion, I have
examined.

1°. the 14-monthly motion;

20. the yearly motion;

3°. in how far the observations may be represented by the com-

bination of a constant 14-monthly and yearly motion.

3. The 14-monthly motion.

Leaving the results 1897.0—1897.5 out of consideration for my
computation, I had 70 z- and 70 y- co-ordinates at my disposal.
Assuming for the present 432 days for the length of the period we
find 6 periods = 7 years and 35 days. So the data allow of a good
separation of the two motions, but the mutual commensurability is
not so approximate that an easy determination of the elements
of both at the same time can be founded thereon. So I began by
deriving in 1st approximation the yearly motion and proceeded to
to use corrected z- and y- coordinates to determine the 14-monthly
motion.

The computation of the « and y was made quite independent of
each other and, assuming 432 days for the length of the period, I
united in both cases the 70 values to 8 means, which then formed
the basis for the computation of periodic formulae.

So I obtained:

t—2412439

x= + 0".151 cos 2 zr 132

( 45 )
Se
432

in which the epochs are expressed in Julian dates.
By these my 8 means are represented as follows:

y = — 0.143 sin 2 7

x obs. | 02¢6 y obs. | ,0—€
| |
02 SLOT — 07046 — 0”.003
es 5076 | Bid gp ts a 13
= EG on Dd ONE 4 18
= Die Es ah = AC eN ien 085 | — 22
= 164 | = 21 | os 036 | = 12
it A Je 10 TN sy, ne 28
ee donge. ¢ A ae ae a 7
4 120 we 15 | Ee 042 = 21

and

5

&

|S

n

= Ae
= + 0".013 WEA = + 0017
u

ALBRECHT assumes 0.04 as mean error of his co-ordinates,
according to which that of the mean of 9 values, with which we
operated here, would be 0".013.

We thus see that the amplitudes found for z and y are very
nearly equal and that the difference of phase amounts to 90° with
the difference of only a single day. The motion thus proves to be,
with considerable approximation, circular and to be direct, that is
with the rotation of the earth from west to east.

To determine the length of the period these results must be
united with the results of anterior observations. For that purpose I
did not retain the whole of the data used by H. G. v. D. SANDE
BakHUYZEN, but chose only the most certain results, namely those
from Leiden 1864—1874 and those from Pulkowa 1882—1892,
for which the mean errors are by far the smallest. So I obtained
as epochs of maximum of «,= epochs of maximum of the latitude
for Greenwich:

( 46 )

O—C O—Ch

Leiden 1864—68 Fundam. Stars 2403394 + 2 — 19

> 1864—74 Polaris 24033861) — 6 — 27
Mean 2403390 — 2 — 23

Pulkowa 1882—92 Vert. Circle 2410298 + 8 — 7
Observ. 1890—96 Summ. of Albrecht 2412439 — 6 + 13

Giving equal weight to the three results, we get:

Epoch of maximum 2408565
Reriod™ 3). en) Zololiedays

and the differences Obs.—Comp. contained in the last columer
but one.

This epoch of maximum falls in 4 days before the one according
to the results of H. G. v. p. S. BAKHUYZEN, whilst the length of
the period found by him was first 431.22, later 431.55. Had I
combined his mean epoch of maximum with my result then 430.36
would have been found for the length of the period.

This result again agrees well with the supposition that the length
of the period has remained unchanged for the last 35 years. In
that entire period it cannot have differed much from 431 days and
such a great variability as CHANDLER assumes is now already con-
tradicted by the observations. This appears, first in the differences:
Obs.—Ch. which I inserted in the last column of the above table.
In the second place however the consideration that just in the very
last years, according to both suppositions, the epochs must begin to
differ widely led me to investigate separately the three last years
of ALBRECHT’s summary. I operated only with the x co-ordinates
and determined from these the epoch in the same way as before.
This result, though necessarily less certain, an error in the assumed
yearly motion being now of influence, agrees however almost per-
fectly with that of the 7 years together.

I found :

Ep. of Max. Obs.—C. Obs.—-Ch.
2413299 — 8 + 27

1) These numbers deviate 3 and 4 days from those in the summary of H.G. v. p.
S. Bakuuyzen, as I interpreted the results of WitTeRDINK somewhat differently.

(47)

The error of the hypothesis of CHANDLER is thus already rather
considerable in 1895,

Let us now consider the amplitude. Uniting according to the
weights my results obtained by the z and by the y and adding to
them some values, formerly found, we obtain

Amplitude
Leiden 1864—68 Fundam. stars. 0".156
> 1864—74 Polaris 0.158
Pulkowa 1882—92 0.139
Final result of H.G. B. 1860 —92 0.168
Result 1890—96 0.148

We have to remark here, that the result of Pulkowa is probably
too small on account of the unequal distribution of the observations
of the individual stars, for which WILTERDINK applied a correction
in dealing with the Leiden observations.

So a change in the amplitude since 1860 is no more probable
now than it appeared before to H. G. v. p. S. BAKHUYZEN. On
the other hand we may not, as he already remarked, combine the
observations before 1860 with the later ones, certainly not so far as
the amplitude and perhaps not so far as the phase is concerned.
This might be reconciled with the conception of the 431 day-period
as a time of oscillation proper to the earth, when we assume !) that
from time to time sudden causes may change the mutual position
of the axis of rotation and the axis of inertia.

Finally I should like to lay down as most probable elements of
the motion of 431 days since 1860

Time of transit through the posit. axis of x 2408565
Reriodtatic en ese ee eae ten es eee AD days
Amplitude: pss iia a fe neds) nc? toa O AKD

consequently

07155 9 t—2408565
x == -+ 0.155 cos 2 77 4311

t—2408565

yo; 0'.155 sin 2 It EV

!) See also GYLDEN Astr. Nachr, Vol. 132. NO, 3157.

( 48 )

4. Yearly motion.

To the original #’s and y’s of ALBRECHT the values according
to the 431 day-motion were applied, in order to derive from
the residuals the yearly motion in 2nd approxination. I employed
for that purpose however values deviating slightly from those found
above as the most probable. For the amplitude I adopted 0".151, for
the period 431.0 and for the epoch 2412439 (or 2408560), which is
that found by me from ALBRECHT’s summary only.

Taking the means of the corresponding values for the different
years, I obtained for « and y 10 mean values, from which periodic
formulae, depending only on the sine and cosine of the single angle,
were derived, just as had been done in the 18t approximation.

The results found for the 7 years together deviated but slightly
from those which the 1st approximation had given, but I had now
also the opportunity of dividing the period into two and of deriving
the yearly motion from each half separately.

This seemed desirable, it being a priori very well possible that
this motion, probably caused by meteorological influences, might dif-
fer considerably in the different years.

So I found

from # from y
Fr t—261 5 t— 148
1890—96 «= -+ 6".116 cos 277 aa y = + 0".067 cos 2 2 365
1890 — 92 Oben 0".087 cos 2 2 ame
0— 2 = -+- 0.123 cos2n - spel in +0. cos 2 1 365
t—269 t—1638
1898—96 r—= -+ 0".113 cos 2 x an = + 0.058 cos 2 7 365

The epochs of maximum are expressed here in days from the
beginning of the year; if they are expressed in dates they are:

ty = Sept. 18 ty) = May 23
Sept. 9 May 6
Sept. 26 June 12

By the formula found for the whole of the period the means
employed are represented as follows:

xz obs. | 0—C | y obs | OSG
| |
EL NE) | 2000 07008
eh Oee ee Di lees Of a 6
EN ee De ee att 8
SO Gilly ak 7 | + 060 ie 4
=e 0G) En home ee a 13
4+ 025 0 eo 051 = 1
rs a 089 + 2 | + 024 + 7
TTE Be el, He 7
dee Bed Ml == 2
| |
le 0045 5 nen ha OO 0

EA a? DSA
| WELL = + 0.007
n

The mean residuals found by testing the mean values for the
half-periods have about the same magnitude.

For the entire period, as well as for both halves, the amplitudes
in « and in y prove to be considerably different. At the same time
the difference in phase clearly deviates from 90° = 91 days; it
amounts in the three cases to 117°, 124° and 105°.

So the orbit of the yearly motion of the pole is a rather excen-
tric ellipse, whose principal axes are inclined to the meridian
of Greenwich.

The motion of the pole in this orbit is very approximately a sim-
ply harmonic one. The mean deviations of the observations are here
even considerably slighter than in the case of the 431-day motion.

In order to investigate this elliptic motion more closely, I have
in the 3 cases turned the co-ordinate axes through an angle such
that they coincided with the principal axes of the ellipses. Doing this
it appeared in the first place that the major axes of the ellipses fall
east of the meridian of Greenwich and form with it the following
angles :

( 50.)
ellipse 1890—96 19° Kast.
» 1890—92 29° »
> 1898—96 10° »

Further we find for the components of the motion in the direction
of the principal axes:

4 t-Sept. 28 t-Sept. 28

1890~96 w= + 0".121 cos 2 j= 0.057 sin Bn —

t-Sept. 23 | 1-Sept. 23

1890—92 e= 40"13Ö cos? ae y = — 0",065 sin 2m a

t-Oct. 1 t-Oct. 1

1893-96 2=--0".114c0e2n ee yn — 0.0
365 365

So the motion is direct, like that of 431 days, and the times to
express the times of transit through the positive halves of the
major axes.

The motions found for the two half-periods do not differ so much
that there is any guarantee for a real difference existing. It is my
opinion therefore, that for the present we must assume as the most
probable orbit for the yearly motion of the pole an ellipse, whose
major axis lies 19° east of the meridian of Greenwich and whose
semi-axes amount to 0'.12 and 0”.06.

As early as 1894 CHANDLER had found!) an exeentrie orbit for
the vearly component; so on the whole I can fully confirm his result.
His ellipse however has a greater inclination (45° east of the meri-
dian of Greenwich) and also a somewhat greater excentricity (semi-
axes 0".16 and 0".05) than mine.

The results of absolute determinations of zenith distances are so
liable to systematic perturbations of a yearly period, that to my idea
they cannot contribute to a more accurate knowledge of the yearly
term of the motion of the pole.

The results obtained by the Horrebow-method too are certainly not
quite free from these perturbations and particularly there would be
reason to fear for them the influence of the inclination of the strata
of air either in or outside the observing room (see a.o. ALBRECHT

1) Astron. Journal, No. 323, 329 and 402.

(51 )

„Report ete.” page 11—12). Yet I believe, especially on account
of the good mutual agreement of the results 1890 —92 and 1893—
96, obtained by the cooperation of observatories partly different for the
two periods, that the results obtained are on the whole trustworthy.

To derive the yearly term H. G. v. pv. S. Bakuuyzen also exelu-
sively made use of the results then known of the Horrebow-obser-
vations, namely the series of observations of Berlin, Potsdam, Prague
and Strasburg made in 1889—1892. Of course only the « co-ordinate
ean be derived from these and, computing the corrections for the
small differences in longitude by considering the motion as circular,
the result is:

ke t—Sept. 12
pS se VO ges Lj SS
365

nearly coinciding with that which has now been derived from so
much fuller data.

Let us finally consider what may be said about the meaning of
the results obtained. In 1890 Rapau!) for the first time drew atten-
tion to the fact that by cooperation of periodic displacements of mass,
depending on the season, with the period proper of the axis of the
earth, then evaluated at about 304 days, motions of the axis of
inertia, caused by the above mentioned displacements, may be trans-
mitted greatly magmfied to the axis of rotation. By the relatively
small difference between the period of the perturbing action and the
period proper, we have to do with phenomena which can be regard-
ed as resonance and consequently the possibility arises that the
relatively small displacements of mass which may be brought about
by meteorological influences, may cause a rather considerable motion
of the axis of rotation. Shortly afterwards the matter was more
fully investigated by HeLMerT ?) who showed that the general el-
liptie motion of the pole of inertia causes motions of the pole of
rotation in orbits, which in the various cases may have every shape
from the circle with direct motion through more and more excentric
ellipses and the straight line, to ellipses with retrograde motion and
finally the retrograde circle. In the most favourable case (a direct
circular motion of the pole of inertia) the motion is transmitted mag-
nified about 6 times, in the most unfavourable case (a retrograde

1) Bulletin astron. T. VII, page 352.
2) Astron. Nachr. Vol. !26, N°. 3014.

Proceedings Royal Acad. Amsterdam. Vol. I.

( 52)

circle) reduced to about one half. If the motion of the pole of inertia
is not simply elliptic, but, more generally, expressible by a series of
periodic terms, these are transmitted more and more reduced to the
pole of rotation the higher the terms we reach. So in general to
irregularities in the motion of the former will correspond much
smaller ones in that of the latter,

All this remains not only true in principle, when we take the
period proper of the axis of the earth to amount to 431 days, but
also the numerical values remain about the same!). So it is pos-
sible and important to consider which motion of the pole of inertia
must be assumed to explain the yearly motion found for the pole
of rotation. Substituting my final results for 1890—96 in the gene-
ral formulae, we find as co-ordinates for the pole of inertia with
respect to the axes finally adopted :

t—Sept. 28

TEE
365

t—Sept. 28

== 04.082 32.2
y= sin 2 7 Bae

that is, the motion must be retrograde, the principal axes have
the same direction as those of the pole of rotation, but the major
and minor axes have changed places, and the motion of the pole of
inertia is but slightly smaller than that of the pole of rotation. We
would have found a more considerable proportion had the ellipse of
the latter been assumed less excentric.

So after all little has been gained for the explanation of the
phenomenon. Only it is perhaps more intelligible that the yearly
motion of the pole of rotation may be pretty regular, though a priori
the reverse be probable for the pole of inertia.

5. Comparison of the observed motion with the-sum of the two
adopted terms.

In the first place the « and y of ALBRECHT have been compared
with the computed values. I adopted for the motion of 431 days
the same elements which have served for the derivation of the yearly
motion, and for the yearly motion my final results for the whole
period. So I found the following differences between observation
and computation expressed in hundredths of seconds.

1) See also NewcoMB Monthl. Not. 1892, March.

(53 )

x Albrecht — « computed.
0 I 2 3 4 Wel 6 ri 8 | 9
| | |
EE A ET BE EE le ee,
91}— 8|— Al 1] Uik Giles Ede a Ol SE
EN EA PE ON PE PEEN 0 |
Gi [ee ee Aa 9 Olas, eee aetna 2.9 0
GAT AED ta. | GA ae Pee! ig) EADE AN 8 Oy) S= FOU ths
5 4 he a One TO rer | es ire 9 W's 0
CES pF rt SE EE EEE EN Je eT fe We
IH 6)/+ 5)+ 6/+ 3|— 2/— 6
y Albrecht — y computed.
aid hoi) |e oe ful cero, Tons Ied
———— sc ee,
neen Erde 9 |e | a 2.6
mr ed gis 4) tes f= a'| at, serleid
DE eeee vag See cetieeiong | SS Gils. Bye MY) Sh bba | Leg | ote 0
93 ere OEREN EE OM pea
94 0 old 3/4 SH 1/— IJ 21 0
OE NTB BE 0 AU Pe VICE
96 BM zelfde |l et ane gi | eltgriailio atd 4
Cf et Sl EE A |
Vf 24% = sono Vo AL = + 0"045 ,

whilst ALBRECHT assumes as mean error of his co-ordinates the value
0".04, differmg but slightly from the former. The residuals however
show more than once a systematic character.

In the second place the original results of observations — usually
monthly means — as they are communicated by ALBRECHT, were com-
pared with my formula, and for each observatory *) the mean devia-

1) If there exist for one observatory various separate series of observations, I reckon
them each separately as ALBRECHT does; besides as he I use only the observations
till 1896.5. So, if we leave out 4 very short ones, we arrive at 27 series. Neither did
I take into consideration the observations which ALBRECHT laid aside on account of
clearly appearing systematic error.

4*

(54)

tion of such a result was computed; by ArBrecHT himself the
comparison of the observations with his curve had already been
made. Moreover for every observatory ALBRECHT’s residuals as well
as mine were united to half yearly means, that is to say means of
these residuals were taken for each summer- and each winter-half year,
and finally from these, mean deviations for those half-vearly periods
were computed. !)

It would take too much space to communicate these comparisons i
extenso, so I shall restrict myself to a few results derived from them.

If we call A, and Ag the mean residuals of the single results
of observation as found by ALBRECHT and by myself, computed for
each observatory; A’a and A's the corresponding quantities for the
half-yearly periods, I find, taking the means of the 27 values of
each of these quantities:

Aa (mean) = + 0".061 A'a (mean) = = 0".033
Ag (mean) = + 0.071 A's (mean) = + 0.048

Among the 27 series Ag is smaller than A4 in 5 cases. (Pulkowa
2nd series, Berlin 1st s., Cape of Good Hope, Potsdam 24 s. and
Lyons) and larger in 22 cases; for the A' the corresponding numbers
of cases are also 5 and 22.

If I use only the 18 series with the smallest mean deviations
from ALBRECHT. I find

ea (mean) ==" = 7070511 A'a (mean) = + 0".029
Ar (mean) = + 0.061 A'gp (mean) = + 0.041

The fact that the Ag are in general larger than the A4 may
be attributed to real deviations from my formula and to systematic
errors of the observations, which for a part will have been trans-
mitted to the curve of ALBRECHT. As mean values for the sum of
those influences (deviation from my formula and partial influence of
the systematic errors), we find for all observatories together :

S (Apt Aa) (eae
VA ee j= — + 0",036

and for the eighteen most accurate series only :

= > EEN
yee Woes 47 aa AA) + 07.088,

So it appears: 1° that the combined influence of both cireum-
stances is very appreciable; 2° that influences are at work which

1) Means depending only on a single monthly result were neglected.

(55)

operate in a constant direction for rather long periods, 30. that
in the most accurate series of observations they appear in a less
degree. So it appears certain that systematic errors have been at
work, as indeed had already been found before (see above).

How great however is the share of those systematic errors? In
this respeet only the deviations of the various observatories compared
mutually for the same period can give us some indications and we
can use for this end the half-yearly means. If we look into these
more closely we often find considerable differences between observa-
tories situated close to each other, which must thus be due to
systematic error, but side by side with these we sometimes also
find criteria that real deviations from my formula may exist.

To show the first I have derived for the 4 observatories which
have furmshed observations during 6 successive half-vears (Potsdam,
Strasburg, Carlsruhe and Lyons), by comparing the result of each
one with the mean of the 4, the mean value of the total error of
observation in the half-vearly mean of an observatory. The result
found is + 0.049, that is a considerable amount and which,
as it agrees exactly with the value of A’ obtained above, would
as far as it goes tend to show that in this case!) systematic
errors of the observations alone may account for the deviations
from my formula.

On the other hand a case pointing to a real deviation from my
formula is offered by the summer of 1895. Here follow for the
European observatories the deviations from ALBRECHT as well as
from me:

O—A O—B
Kasan + 07.025 — 0".022
Prague = 10 — 48
Potsdam — 33 — 30
Carlsruhe — 104 — 170
Strasburg — 26 — 90
Lyons = 17 — 37

If a real deviation from my formula is indicated by this, it would
prove that the combination of a constant motion of 431 days anda
constant yearly motion does still somewhat fall short of the reality.
That the latter may be different in the various years is a priori
not improbable. It must be left to further observations, which will
have to be kept still more carefully free from systematic error, to
furnish more certainty upon this point.

1) The same criterion is not so easily applicable to other observatories and in other
years.

( 56 )

Physics. — ,On a 5-cellar quadrant-electrometer and on the measu-
rement of the intensity of electric currents made with it.” By

Prof. H. HaGa.

During the last years I was repeatedly obliged to measure with
accuracy the intensity of a constant current of about ten ampere.

From the many methods which might be used, I chose that by
which the difference of potential is measured between the ends of a
known resistance, inserted in the cireuit. As this method is excee-
dingly simple, capable of measuring currents of greatly different
intensities with an accuracy of !/,) percent, it seems desirable to
me to draw the attention to this method.

A good quadrant-electrometer is required. In 1893 Himsrept !)
described a 4-cellar quadrant-electrometer; the needles were sus-
pended by a silvered fibre of quartz; the damping was obtained,
by hanging two vertical magnets at the lower end of the small rod
which bears the needles, the poles to opposite sides, so that they
could move within an annular space in a piece of copper. The
magnets not forming a perfect astatic system, a small directing force
was left, because of which Himstepr was obliged to make the
whole apparatus moveable round a vertical axis.

It seemed to me that this difficulty might be avoided, by rever-
sing the Himsrept method of damping, that is to say by hanging
a hollow copper cylinder movable in a magnetic field *). A 5-cellar
quadrant-electrometer with this damping was constructed in the
physical laboratory at Groninghen. The principal part of this
apparatus is represented by fig. 1; the brass cylinder round the
quadrants and the cylindric case round the mirror are removed.

The base of the instrument is a brass plate five mm. thick on
three levelling screws; the four quadrants are placed on the plate,
insulated by glass columns; one of them may be moved micrometri-
cally. The terminals are attached under the plate, in order to protect
them from dust as much as possible. They are perfectly insulated
from the plate by ebonite, glass and shellac.

The whole apparatus for damping also is attached to the under-
side of the plate; it consists of a circular magnet three cm. high
(fig. 2), provided with the armaments a and 6; in the latter not-
ches have been filed, in which the poles of the magnet fit closely;

1) Wied. Ann. Bd. 50, p. 752, 1893.
2) Beiblätter, Bd. 19, p. 896, 1895.

H. HAGA. A s-cellar quadrant-electrometer.

Proceed. Roy. Acad. Amsterdam Vol. I.

fas kh
ie

; =
i) D cenTahh PARK

(57)

two brass plates c and d unite the
armaments and the magnet, so that
they form one whole. Another pair
of brass plates e and f are bent under
a right angle, the vertical parts are
soldered to ¢ and d; the horizontal
parts serve to attach the apparatus to
the under side of the plate. Also the
under sides of the armaments are
covered by a brass plate, in which
a copper tube is soldered, in which the
iron core & fits closely (fig. 1 and 2).
The hollow copper cylinder can move
in the annular space between the outer
part of the iron core and the inner
part of the armaments a and b; in
the middle of the plate is a hole as large as the space between the
armaments, so that a small aluminium tube may be siid over the
lower end of the aluminium rod, to which the needles are attached.
The tube bears an ebonite rod, which is screwed on the lid of the
hollow cylinder. In this way the cylinder is suspended exactly in
the centre of the magnetic field, the currents of air being excluded
by the brass plates round the armaments.

Moreover the apparatus bears a torsionhead and an arrangement
to move the needles in a vertical direction without their being dis-
charged. The length of the suspending fibre is 17 em.; the distance
between the lower and the upper plate is 13.5 em.

As to the sensitiveness of the electrometer, it depends on the
suspending fibre to a great extent. With a silvered quartz fibre of
55 « diameter a CraRkKcell caused a deviation of 760 mm. by
reversal, the needles being charged at 180 volt; distance of the
scale 2 M. In about half a minute the position of equilibrium was
reached after three oscillations.

As the total weight which the fibre had to bear, was 20 grams
(the hollow copper cylinder weighed 10 grams), a quartzfibre of 24 u
may also be used, through which the deviation would be increased
more than 16 times. The period, however, would be increased to
four times its former value.

If this very great sensibility is not necessary, a platinum wire!)
annealed in a candle-flame is to be preferred because of its

Fig. 2, WV, of the real size.

1) Hatiwacus, Wied. Ann. Bd. 55, p. 170, 1895.

( 58 )

greater convenience in use. The elastic hysteresis!) moreover is not
to be perceived, as is proved by the observations mentioned below.
The Wontasron wire of 25 «, supplied by Heraus can bear but 4
grams, a platinum wire of 50 « more than 30 grams; most of the
later measurements have been made with this platinum wire. The
time of oscillation (1/, period) is about 12 sec., and as the damping
was so regulated that the needles were in rest after three oscillations,
the observation could already be made after 36 sec.

In order to be able to regulate the damping, the hollow copper
cylinder is so long thinned and shortened, till (the whole iron core
being in its copper tube) the movement is aperiodic. By moving the
core downward, the required damping may be obtained, Every wire
has of course its own hollow copper cylinder which fits it best.

In using the quadrant-electrometer the charging-battery is of great
importance. If measurements are to be made only for a short time,
a ZAMBONI pile or a battery of water-cells, consisting of small
test tubes filled with water, in which copper and zine rods have
been put, is sufficient. If the charging-battery, however, must be
kept ready for use for some months, these arrangements do not
suffice any more; nor have I succeeded in reaching this by
replacing the water by paste of plaster or by gelatine with carbol.
I was very much satisfied with 300 LecLancHé-cells, supplied by
P. J. Kipp AND Sons, J. W. GrLray successor. In the following
measurements the positive pole of this battery was connected with
the needles, the negative one with the earth.

Table I contains the comparison of six CLARK-cells, constructed
according to the instructions given by Kane in Wied. Ann. Bd. 51,
p. 203, 1894, with a normal Crark-cell furnished by R. Furss,
at Steglitz near Berlin and tested by the Physikalisch-Technische
Reichsanstalt. This cell is called N, while the cells, here constructed
are marked A, B, C, D, E and F.

The negative pole of the cells remained connected with the earth,
the positive one with one of the pairs of the quadrants, while the
other pair of quadrants was kept on zero potential, the position of
equilibrium was determined. By reversal these two connections were
interchanged and this was continued till five observations were made.

1) German: Elastische Nachwirkung,

(59)

EAC BE Ey He Le

February 11th 1897.

Needles charged by 300 Leclanché cells: distance of the scale two metres.

Observed position of

Clark cell. equilibrinm. Deviation.
787.8 |
188.1 |
N. 18°.0 787.8 099.7
188.1
787.8
788.0
188.1
A. 18°.3 | 788.0 399.8°
| 158 2
| 788.0
787.2
187.2
B. 18°.2 787 .0 5399.9
187.2
787.1
787 .3
187.4
N. 787.1 599.8
187.3
787 .1
787.1
187.3
B. 18°.2 787.1 399.7°
187.4
787.1
188.2
788.1
A. 188.3 099.8
788.1
188.3
788.2
185 .3°
N. 788.1 399.8
188.25
788.0
186.0
785.9
C. 18°.0 185.9 600.0
785.9
185.9
784.9%
184.8
D. 18°.0 784.95 600.1
| 185.0

208

Clark cell.

E.

F.

118970

18°.0

18°.1

18°.2

18°.

18°.0

( 60 )

Observed position of

equilibrium,

791.

185.1
185.25

185.1
785.2

185.1
785.1

185.1
785.2

185.1
785.3
785.6

185.2
785.5

185.1
785.4
790.9

191.1
790.7

191.1
790.8
foe:

191.6
791.0

191.6
791.0

193.2
792.

193.1
792.5

193.1

193.0
792.7

193 1
792.5

193.2

192.9
792.4:

193.1
792.6

193.2
791.1

WON
791.3

192.05
791.2
791.9

192.0
791.7

192.0

Deviation.

600.1

600.1

600.3°

399.72

599.4

599.4

599.5

599.4

599.2

599.8

(61)

From these observations we deduce:

N. 599,8 N. 599,9 N. 599,7
A 5998 CG 6002 E 5993
B 5998 D 600,1 F 599,4

The difference of deviation, caused by N, must in my apinion,
be ascribed to the influence of temperature, in consequence of which
the potential of the charging battery was changed. If greater accuracy
is desired, it is necessary to keep the temperature of the charging
battery and of the CLARK cell constant; in these experiments the
CLARK cells were placed in glass vessels filled with paraffine oil,
and care was taken that the temperature could not differ much
during the night preceding the experiments.

From this series of observations is seen: 1°. that with this platinum
wire the elastic hysteresis may be quite neglected and 2°. that with
one observation a difference of potential of 1,4 volt may be measured
to at least Yo percent.

Another great advantage of this method is that the CLARK cell
does not yield a current.

If, without examining in how far the deviation of the electro-
meter and the difference of potential are proportional, we wish to
measure the intensity of an electric current, the resistance must be
chosen in such a way, that at its ends the difference of potential
is nearly equal to that of a CLARK cell, and this must be compared
with a Crakk cell. So a resistance of 0.14 ohm is required for
currents of about ten ampere; this resistance must be constructed
in such a way that the current cannot cause great differences of
temperature; therefore ten German Silver wires of '/2 mm. diameter
and about 1, M. long were arranged in parallel and placed in a
large basin filled with paraffine oil; because of the small tempera-
ture coefficient it is sufficient to know the temperature to within
three degrees without making a mistake greater than 1/1 percent.
The resistance itself was determined in the usual way with the
WHEATSTONE bridge. Many measurements of the intensity of cur-
rents have been made and ampere-meters have been tested with
this resistance !).

1) That it is necessary to test ampere-meters repeatedly is proved by the fact, that
on an ampere-meter of CARPENTIER a current of 10 ampere was marked in
March 795 with 12 amp.
January *96 7 1355 By
March ’97 „ 14 uy
October °97 7 16 „
Evidently the magnet has been losing its strength continually.

( 62 )

As it is, however, of importance to be able to use the same
resistance for currents of different intensity, it was investigated, in
how far the deviation of the electrometer and the difference of
potential between the pairs of quadrants are proportional.

To this purpose the current of two accumulators was conducted
through a resistance of 1050 ohm, viz. 400 + 300 + 200 + 100 +
100 +30 +20 ohm of a tested rheostat. By means of the side
plugs the difference of potential could be measured between 500,
400, 300, 200 and 100 ohm, in doing which the plug on one end
was always connected with the earth.

In order to eliminate the difference of the indication of the in-
strument between the positive and the negative potential of the
same absolute value, the current was led in both directions through
the resistance; the two CLARK-cells A and B were placed together
in one cylindric glass vessei, filled with paraffine oil; the negative
pole of A and the positive pole of B were continually in connection
with the earth and the others by turns with the electrometer.

The following tabie contains the observed positions of equilibrium
and the deviations, the smaller values of the deviation caused by
1 CLARK compared with those of table I are to be ascribed to the
gradual weakening of the charging battery; measured with an
electrometer of BRAUN the 300 LeCcLANCHÉ cells had no more than
320 volt. Distance of the scale was 2 meters.

TABLE II.
May 5th 1898. brl AE
Observed position of equilibrium. Deviation.
( 283.0
Clark B — 781.1 498.1
| 283.0 |
15°.1
( 781.6
Clark A + 284.8 496.8
| 781.6
203.8
866.0 662.2
203.8
[00h 4
866.3
206.4 659.9
\ 866.3

( 63 )

Observed position of equilibrium. Deviation.
eee ene
[798.2
| 269.7 528.4
798.0
400 Ohm
267.6
797.5 229.9°
\ 267.5
331.1
| 728.2 397.0
331.3
300 Ohm
728.8
332.7 396.1
728.8
( 866.2
500 Olm 206.3 659.9
| 866.2
660.2
| 396.0 264.0
659.8
200 Ohm |
395.1
659.1 264.0
395.1
| 458.9
| 590.9 131.9
459.1
100 Ohm a8
| 591.1
459.5 131.6
591.1
( 866.1
500 Okm 206.3 659.8
/ 866.1
( 282.0
Clark B — 780.6 498.5
| 982.2 |
( 781.2
Clark A + 284.2 497.0
781.2

The observation of the difference of potential at the ends of the
resistance of 500 ohm has been repeated a few times for one of
the two directions to find out, whether the intensity of the current
has changed during the experiment; it appears that it has remained
perfectly constant.

The results of this experiment have been collected in table III;
the two numbers between brackets represent the deviations caused
by the current in its two different directions.

(64)
TASB MENE We

| Difference of potential in volt. | Intensity of the

Deviation. | _ current
Observed. | Calculated. ADE,
Clark B — 498.1 Ì
497.5
Clark A + 496.8 |
( 662.2 )
500 2 661.1 1.900 1.905 0.003801
659.9 §
( 528.4 )
400 2 529.2 1.524 1.524 0.003810
| 529.95 §
( 397.0 )
300 a 396.6 1.143 1.143 0.003811
| 396.1 §
( 264.0 ) :
200 2 264.0 0.7617 0.7615 0.003811
| 264.0 §
( 181.9 |
100 a 131.8 0.3806 0.3810 0003805
| isi.6 . §
Clark B— 498.5) |
497.7 |
Clark A + 497.0 §

Because of the slight difference between the deviation of 1 CLARK
and the difference in potential at the ends of a resistance of 400
ohm, the proportionality between the deviation and the difference
of potential was assumed, from which 1.524 V. was derived;
accordingly the intensity of the current was 0.003810 ampere;
if we multiply this value with the value of the resistances — taking
the very slight corrections into consideration — we find the ,caleu-
lated” differences of potential. Under ,observed” differences of
potential the values have been given which are found in the sup-
position of proportionality between deviation and difference of potential.
It will appear that this proportionality ranges within pretty wide
limits. The same fact is also shown in the last column where the
intensity of the current is calculated by dividing the observed diffe-
rence of potential by the resistance. It is a matter of course that
the deviations are reduced to angles.

If care is taken that the angle through which the needles are
moving, does not exceed 7°3, (agreeing with the deviation 529 by

reversal) and that the deviations do not become too small, so that

(65)

the errors of the readings are less than }iooo of the deviation,
very different intensities may be determined with the same resistance
to at least '/;) percent. In this case the current was weak, and it
is clear, how with the quadrant-electrometer we may determine
among others the constant of mirror galvanometers without any
difficulty. If on the other hand we have a „Normal Widerstand”
of 0.001 ohm, as it is constructed by SteMENS and HAaLSKE for
instance, a current of 1000 ampere may be measured with the same
accuracy.

To conclude I shall point out a circumstance which may occur
in some cases with such measurements, and which may cause very
great mistakes, and has rendered a great many of my own experi-
ments worthless. In this laboratory 30 accumulators are coupled
in series, and different groups may be used in different rooms; in
my experiments the current, which passed also through the resis-
tance, mentioned on page 6, was taken from a group of 5 accumu-
lators; one end of this resistance was connected with the earth,
the other with the electrometer; when however in another room
another group of accumulators is used at the same time and part
of the circuit is in connection with the earth in that room too, or
is not quite insulated, the end, connected with the electrometer may
be between two points which are in connection with the earth, and
the true difference of potential is not measured. A mistake of this
kind is at once found when we change the direction of the current ;
moreover this mistake may be easily avoided by insulating the
cells used.

Physical Laboratory. Groninghen.

Physics. — „On the influence of the dimensions of the source of
light in diffraction phenomena of FRESNEL and on the dif-
fraction of X-rays.” (Third communication.) By Dr. C. H.
Wind (Communicated by Prof. H. Haga).

17. In my former communications on this subject), I have
pointed out (ef. Arts. 10 and 16) that the theory concerning the influence
of the widening of the illuminated slit, in the simple form at least
in which it was given there, cannot explain the fact that, when
the diffraction slit gradually narrows towards one end, the two
principal maxima continue to appear as two distinct bright or (on
photographic negatives) dark lines, even after the point of inter-

1) Versl. K. A. v. W. 5, p. 448 and 6, pe ios Uso

(66)

secting. According to theory there should be soon after the point
of intersection an area of nearly uniform maximal illumination in the
middle of the diffraction image, covering the whole region between
the two places where in fact the maxima are seen. This difficulty is
solved by the optical illusion, which I have described in the Procee-
dings of the May-Meeting. In cases like that mentioned — viz: those,
where a zone of uniform maximal illumination gradually passes on
both sides into zones of continuously decreasing illumination — there
are indeed two separate maxima to be observed on the borders of
the bright zone (cf. fig. 9 and 10 in the former communication),

18. This proves already that the optical illusion mentioned may
largely influence our observations of diffraction phenomena. As also
appears from some experiments, which I have lately made for this
purpose, this influence may even be so great, that the real distribution
of light in the diffraction images can hardly be deduced from imme-
diate observation in many cases. So, for instance, it has struck me
repeatedly that the diffraction image of a slit still shows the principal
maxima with great distinctness, even when the luminous slit has a
considerable width, whereas theory indicates the excess of intensity
in the maxima, compared with the field round them, to become
smaller and smaller, when the slit is widened more and more. As
we know now, that under the influence of the optical illusion
distinct maxima of brightness are observed even on the borders of
a zone of uniform illumination, provided that it passes into zones of
decreasing intensity, we may by no means wonder, if we see the prin-
cipal maxima apparently continue to be clearly visible, though their
excess of intensity become very small. We may ask however,
whether, because of the optical illusion, the place where we observe
our maxima of brightness be still the same as the place where those
maxima of illumination really occur. And without any doubt the
answer ought to be: no. Yet it may be presumed and experiments
have confirmed, that, as long as the principal maxima themselves
are of a considerable distinctness (excess of intensity), their apparent
place is only slightly influenced by optical illusion, that 1. 0. w.
the place, where our eye observes a maximum of brightness, is chiefly
determined by the principal maxima themselves. This explains why
some measurements of secondary diffraction images, mentioned in
my second communication on the subject, may have led to a taxa-
tion of the wave-length of light which was not quite wrong.

19. Another remark relating to my former experiments is this.
The maxima observed in the secondary diffraction images are of a
pure white, though we should expect them to be slightly coloured,

(67)

as their place, as deduced from the theory of those diffraction
images, is not quite independent of wave-length. We now easily
understand this particular to be also due to the optical illusion.
The differences of colour, which should really exist to some extent,
have intensities, which correspond to the real excesses of illumination
in the principal maxima and by no means to the much greater
excesses of brightness, which our eye perceives there.

20. Whereas our optical illusion leads in this way to the expla-
nation of some difficulties, it compels us on the other hand to give
up our former conclusion (cf. Art. 15), that the analogy between the
shadow images of X-rays and of ordinary light justifies the supposition
that the X-rays consist of undulations. The facts mentioned in my
former communication sufficiently show, that even without a trace of
diffraction the X-rays could produce shadow images, which present to
our eye the well-known bright and dark fringes. The photo a repro-
duction of which is given in that communication as fig. 6 shows in
originali a character which agrees perfectly with the (negative) X-shadow
images, obtained formerly by Fomm and others. Its dark fringes are
by no means less distinct than those of the X-shadow images men-
tioned; and on the other hand the latter show very distinct bright
fringes on their outer sides — though there may have been paid
little attention to these fringes hitherto —, these bright fringes being
exactly those corresponding to the bright circular lines in fig. 6.
Moreover it is by no means difficult — as I pointed out in Art. 8
of my former communication — to obtain the X-shadow images
with the characteristic bright and dark fringes by using slits
of a considerable width (cf. fig. 10 of that communication). This
however would contradict with expectations founded on the suppo-
sition of those fringes being caused by diffraction.

21. The optical illusion alluded to leaves, of course, beyond all
doubt the correctness of the theoretical considerations, communicated
before, on the influence of the widening of the luminous slit on
diffraction phenomena. Especially the simple method, developed in
order to take that influence into account, holds quite good as far
as concerns an exact interpretation of the diffraction images observed
and a calculation of the distribution of light, which may be expected
in diffraction images under given conditions *).

1) It is easy to see that my method for calculating the influence of the widening
of the slit on the distribution of light in diffraction images also applies, in principle
at least, to other diffraction phenomena than those of FRESNEL, e. g. to those of
FRAUNHOFER, and it is easy to conceive how this method is to be modified for
being applicable to such cases.

Proceedings Royal Acad. Amsterdam Vol, I.

( 68 )

The following question seemed rather important. What are the
different stadia through which the primary diffraction image, (pro-
jected by the edge of a screen f.i.), the luminous slit being gradually
widened, passes into the shadow image, belonging to a slit so wide
that diffraction has finished to be of any consequence; and how does
the diffraction image present itself to our eye in the different stadia
under the influence of the optical illusion mentioned. In order to
be able to answer this question I have photographed a series of
fifteen diffraction images of a rather wide slit, the luminous slit
having throughout the whole series an ever increasing width, but
the conditions of the experiment being left quite unaltered in any
other respect. The width of the latter slit ranged between such
limits, that the space through which the primary diffraction curve
must be displaced, in the construction of Art. 5, in order to obtain
a correct geometrical representation of the secondary diffraction image
we should expect, corresponded in the consecutive experiments to
displacements of the starting-point of the effective arch on the
spiral of Cornu, as by which the well-known quantity v of FRESNEL
varied from 0,2 (when the slit was narrowest) to 8,4 (when the
slit was widest). Applying the construction alluded to, I have on
the other hand drawn common-type graphicai representations of
the distribution of light in the diffraction images belonging to the
consecutive widths of the slit. It is not the place here for a de-
scription in details of the distributions of light expected and of
the distribution of brightness observed on the negatives; it may
be sufficient to remark that most of the plates of the series
showed a considerable difference between the distribution of light and
that of brightness, a difference even as concerns the general aspect
of the image. There is, however, not a total want of regularity
in these differences. I generally found that the eye perceives maxima
resp. minima of brightness in those places of the zoncs of continually
increasing intensity (transition zones), where — in consequence of
undulations of the primary diffraction curve — the rate of increasing
of the intensity changes considerably. For the rest the diffraction
appeared to come forth pretty clearly in the first plates of the
series (the luminous slit being rather narrow), so far as concerns
the general aspect of the images, whereas its influence further on
in the series decreases more and more and is at last scarcely
recognised. The latter remark is of some importance especially
with a view to the following considerations.

22. The leading idea of the whole investigation has always been
the desire to get an estimation of the wave-length of X-rays, or

( 69 )

at least a determination of a possibly low upper limit for such a
wave-length. With a view to this purpose Prof. Haca and myself
have continued the experiments begun by Mr. TiopeNs; in the
beginning, however, always with a negative result.

Finally two experiments have been made these last days under
the following conditions. In both of them the width of the luminous slit
was 6 = 49 and this slit received the radiation of an X-ray tube
(with self-regulating vacuum according to the newest system of MULLER
at Hamburg), placed in such a way that the anticathode made a
very small angle with the axis of the arrangement (cf. Art. 1) in
order to procure the greatest possible concentration of the pencil of
X-rays, terminated by the slit.

One of the ends of the diffraction slit was narrower than the
other, the latter being of a width of + 400 w, the other of a few
microns only. In the experiment A the distances were: a = 293,
b = 298 cM., in the experiment B: a= 605, 5 = 615 cM.

Both the slits as well as the sensitive plate were attached to
firm stands, fastened by means of plaster to columns of compact
lime-stone, which were attached with plaster to the pillars or the
stone floor of the building. The time of exposition was a little
more than 8 hours for the experiment A, 40 hours for the expe-
riment B.

After development each of the two plates clearly showed a thin
black line, sharpening towards one end and being the image of the
second slit.

By first observation there is no influence of diffraction to be
perceived on either of the plates, the borders of the black line
mentioned appearing almost absolutely sharp defined and the line
itself ending in a very sharp point. Closer observation, however,
shows on both sides a transition zone limited by a dark line on the
inner side, by a bright one on the outer side. Finally, by looking
earefully at the lines under a microscope, magnifying about 14 times,
I have been led to the following observations.

1°. On plate A the dark and the bright lines are pretty sharply
defined, much like those appearing in transition zones, where there is
no diffraction. The distance between the dark and the bright fringe
has for each of the transition zones an average value of about 67 u
over nearly the whole piate, while on the other hand the width of
the transition zones as calculated from the values of o, a and b
would amount to 50 w, in the supposition of rectilinear propagation.

Comparing the plate with the series of images mentioned in
Art. 21, one may feel inclined to assume that the difference between

5*

(70 )

those 67 and 50 w be possibly caused by diffraction; but at all
events it is certain that the image of the slit on plate A does agree
pretty well in its aspect with the images on those plates of the
series for which v > 2, 3, but does not agree with the other images —
a peculiarity which is quite compatible with the rather small value
of the difference just mentioned. Hence follows, however, as is easy
to calculate, that — if we may speak of a wave-length of X-rays —
we may assume:

As OLA

2°. The dark and the bright lines on plate B are less sharply
defined; the dark lines seem even to have passed into rather broad
bands with a gradual decay of darkness towards the outer side, the
image beginning in this way to resemble, as far as concerns its
general character, the former plates of the series of experiments
mentioned in Art. 21. It might even be considered, from its general
aspect, as being exactly similar to those of the images of the series,
for which v is about 1,5. If we might take this similarity for
granted, it would follow that

A == 08E

Influence of diffraction in this experiment is also made probable
to some extent by the fact that there have been found values for
the distance between the dark and the bright fringes in the tran-
sition zones, which range between 76 and 91 w over nearly the
whole plate and amount to 78 on an average, so as to point to a
distance actually bigger than on plate A; in this respect we should,
however, remember that the measurements could not be effected
with a high degree of accuracy. On the other hand the point of
intersection of the dark fringes on this plate correspond with a lar-
ger width of the diffraction slit than on plate A, which also seems
to point out an influence of diffraction. Nevertheless, though all
these particulars may be considered as possibly being caused by
diffraction, we ought to be aware it being by no means impossible
that they might have been caused by continual, though very slight,
vibrations of one or more of the stands, if only the manner in which
these stands have been mounted may have not quite prevented them
from any such continual motion.

30. In the neighbourhood of the point-end of the image of the
sht on plate A, my attention was repeatedly drawn to something,
that in my opinion may possibly be considered as a slight indication

REE)

of a fan-like broadening of the image of the slit, chiefly mamifesting
itself in a diverging of the two bright lines of the outer side. If
we might assume, that this fan-like broadening really exists and is
a consequence of diffraction, and further that such a broadening of
the image does not occur before the diffraction slit is so narrow as
to correspond at the utmost to a value 2 for the quantity v, we
should find by calenlation, as the diffraction slit has proved by
measurement to have a width of 2,3 w« on the spot where the
phenomenon is seen:

hes Ol

Though on one hand I am aware that what 1 have described as
seeming to be a fan-like broadening of the image of the slit is in
its appearance so utterly mean, that every one might feel justified
in not accepting my interpretation, yet it is on the other hand of
some importance, that this particular presented itself to my eye quite
spontaneously, I having had not the slightest expectation to observe
anything of the kind.

40, After having observed the phenomenon mentioned under 3°
on plate A, I tried to find something of the same kind on plate
B, and indeed I succeeded in finding a place which gave an indi-
cation of a phenomenon somewhat like it. The phenomenon being
even less distinct here than on plate A is in itself not astonishing
at all, as plate B on the whole seems to be much less affected
by the processus of insolation and development than plate A.
The spot where I believed to observe the fan-like broadening lies
higher here than on plate A, viz: on such a height as to correspond
with a width of the diffraction slit of about 50 ge.

If the reality of this phenomenon might be accepted, we might
deduce from it by caleulation:

LS OIL,

suppositions of the same kind being made as before.

It is in agreement with the above remarks that the image of
the slit extends considerably farther, at the point-end, on plate A
than on plate B and less far on both the plates than would corre-
spond to the real length of the diffraction slit. We may, however,
not attach too much importance to this fact, 1°. because plate B
shows on the whole a less intensive darkness than plate A, as has
already been said, and 2°. because the diffraction slit becomes so

( 72 )

exceedingly narrow on one end, that we could not expect much
effect of the insolation on the corresponding parts of the negative,
even if diffraction were to be excluded from before hand.

I do by no means intend to say that by what precedes the con-
clusion might be justified, that X-rays are diffracted and that they
have a wave-length of about O.1 à0.2 uw. Yet, as we have arrived
through two or three independent ways at results which agree pretty
well, those results — though each of them, the first excepted, may
separately be of nearly no value at all — if taken together make
me believe, that the conclusion mentioned may possibly be not very
far from truth. Moreover they make a further investigation in the
same direction desirable. As to the result mentioned under 1° I
think it may be accepted without any restriction !).

Physics. — Zhe galvanomagnetic and thermomagnetic phenomena in
bismuth, by Dr. E. van Eyerpineen Jr. (Communication
No. 42 from the Physical Laboratory at Leiden, by Prof.
H. KAMERLINGH ONNES).

In order to explain the galvanomagnetic and thermomagnetic
phenomena RiecKE®) assumes that a galvanic current is always
accompanied by a current of heat, and a current of heat by a gal-
vanic current. The basis of these hypotheses lies in WEBER’s theory
of the conduction of electricity and heat in metals; in this theory
also the conduction of heat is ascribed to the motion of charged
particles alone.

The velocities of the positive and negative particles are :
for a slope of potential of 1 C.G.S. unit per cM. wu and —v
for a slope of temperature of 1° per eM. Ip and gn.

In the magnetic field Z a positive ion with the velocity U is
acted upon by a force HU for each unit of electricity.

Rieckr assumes further that the velocities in the direction of this
force of the particles are zero in the state of equilibrium in the case
of the phenomenon of Hatt; the equilibrium is reached by the
combined action of a difference of potential and of temperature
between the sides of the plate.

In this way he finds for the coefficient of the galvanomagnetic

1) With great pleasure I acknowledge the assistance given by Mr. C. Scrourr in
the measurements, necessary for the experiments.
2) Gott. Nachr. 1898.

(73)

difference of temperature (i. e. the difference of temperature per linear
eM. for a slope of potential 1 and a magnetic field 1)

uv (u+t v)
ENEN MEM EN
UIn JV Ip

and for the rotation of the equipotential lines occurring in the
Harr-effect

9 9
Cia Ip

IOM gis” Psi «Ay LOS
U In + Ip )

In a similar manner he deduces:
Coefficient of the thermomagnetic difference of potential

(u v
Ugn + v Ip
Coefficient of the thermomagnetic difference of temperature (i. e.
the rotation of the isothermal lines)

40Gp— gm) _

Ge Ge Go (4
ugn Hv Ip

When these four phenomena have been observed, u, v, gp and gy
may be calculated. Proceeding to this calculation, RrECKE says: , Kine
thermomagnetische Temperaturdifferenz scheint hier (bei Wismuth)
nicht vorhanden zu sein.” Therefore he takes gp» = gn, which consi-
derably simplifies the formulae.

This remark however is not justified. As early as 1887 Lepuc’)
observed the rotation of the isothermal lines in bismuth; this obser-
vation was corroborated by the experiments of VON ErTINGSHAUSEN *).
The rotation however is not very large and hence one might think,
that RrECcKE's assumption does not remain far behind the truth.
In order to decide this question I have repeated the calculation with
the data used by Rrireke, augmented by von ETTINGSHAUSEN's
result for the rotation of the isothermal lines. The latter found
with a plate of bismuth, 2,2 cM. broad and probably *) 4,8 eM.

DC. R. 104, p. 1784, 1887.
2) Wied. Ann. 33, p. 135, 1888,
5) See von ErriNGsHaAusEN and Nernst, Wied. Ann. 33., p. 477, 1888,

( 74 )

long, when two opposite borders of the plate were maintained res-
pectively at 100° and at the temperature of the room, in a magnetic
field of 9500 C.G.S. a difference of temperature of 1/,° between
the two other borders. The slope of temperature in the middle of
this plate was probably no more than 10° per linear cM. Hence d

was about —6.10~7, and the four quantities must be calculated
from
sa— 29810 P tb=—T1610 CS 0132 dk

Eliminating g, and g, from the equations 1 to 4, we obtain

we t(btdvt+(bd—ac)=0.. (5) and u=v+(b+d) .. (6)
or
uw=ac—bd and u—v=b)4+d.

Only one of the two sets of values for u and », furnished by these
equations, satisfies all conditions

u = — 0,005.10® Ml ol Ome,
whence we calculate by means of the relations 3 and 4
nt KOE Gre OOS:

It is evident that gp and g, are not even approximately equal.
ae g g 5 5
The quantities Zand = which according to Rigckr’s theory are
u

proportional to the kinetic energy of positive and negative particles,
appear now to be

® 94105 2 — 0,0185.10°
v

u

2. An objection which may be raised both against this calcu-
lation and against that of Riecke is, that the various coefficients
were not determined all with the same sample of bismuth, and not
all in the same magnetic field. Indeed we know how different the
results of experiments upon bismuth from different sources may
prove to be; and though theoretically all the phenomena are propor-
tional to the first power of the strength of the field, practically this
proportionality is sometimes far from complete; VON ETTINGSHAUSEN
and Nernst f.i. obtained as constants of the Harr-effeet in mag-

(75)

netic fields from 1650 to 11100 values from — 10,27 to — 4,95.
Moreover in the formulae the value of the resistance of bismuth
must be used, which depends largely on the strength of the mag-
netic field. These considerations induced me to repeat the measure-
ments of the various phenomena with the same plate of bismuth
and in the same magnetic field 1).

In order to avoid as much as possible the disturbances which
might be caused in cast plates by irregularities in the cristalline
structure *), these experiments were made with a plate of bismuth
deposed by electrolysis in a solution of nitrate of bismuth.

During the experiments the plate was fastened on a little wooden
board under two copper strips, soldered to the copper tubes ser-
ving to supply or absorb heat and at the same time as electro-
des for the galvanic current through the plate. The thermo-electric
needles could be introduced between the plate and the wood at three
different, fixed distances from the copper plates, for which purpose
three grooves had been sawn in the wood. In measuring differences
of potential the copper wires of the thermo-electric couples (German
silver-copper) were used. The space between the plate and one of
the poles of the magnet was filled up with cotton.

A similar arrangement of the experiments was used by von
ETTINGSHAUSEN and NERNST in their research on the phenomena in
pure bismuth and in alloys of bismuth and tin ®), with this diffe-
rence, that as well the copper tubes as the thermo-electric needles
were soldered by them to the plate.

3. Measurements. Dimensions ot the plate: length 3,3 cM.,
breadth 1,15 cM., thickness 0,089 cM.

The experiments in which the thermo-electric needles were on the
middle of the plate are indicated by the letter A; those in which
they were placed on the side of the heated tube by B and the third
series by C. The distance between the two copper strips was 2,96
eM; the distances between the heated strip and the Ist, 2d and 3d
groove were respectively 0,65, 1,53 and 2,37 eM.

In judging the results, entered under B and C we should keep

1) See my communication in the Meeting of May 28, 1898, p. 53. Communications
Phys. Lab. Leiden, N°. 41, p. 13. pe

2) See my communication in the Meeting of April 21, 1897, p. 501 and June 26,
1897, p. 7), 72. Comm. NO, 37, p. 17, NO. 40, p. 8, 9.

5) Wied. Ann. 33, p. 474. If in the course of this research also the rotation of
the isothermal lines had been measured, it would have furnished good data for a
calculation,

(MAO)

in mind that the proximity of the well conducting copper strips
must cause a decrease of the occurring differences of temperature
and of potential.

Some observations were made in magnetic fields differing a little
from those mentioned below. The communicated numbers were then
obtained by graphical interpolation, just as the numbers of von
ETTINGSHAUSEN and NeRNST, entered under v. E. and N., which are
given for the sake of comparison.

a. Galvanomagnetic difference of temperature. The method of ob-
servation was the following: when the current through the plate and
the magnetizing current had been closed during about 15 minutes
and the temperature had become approximately constant, the deflec-
tions with both thermo-electric couples were alternately read at con-
stant intervals, f.i. 4 times that with the first and 3 times that with
the second. Then the magnetic field was reversed, after some minutes
the series of experiments repeated, thereupon the magnetic field
reversed again and a third series of experiments made. Afterwards
this whole series was repeated with the direction of the current
through the plate reversed.

Each series of 7 observations furnishes a mean difference of tem-
perature between the upper and the lower border of the plate. The
difference between the mean of series 1 and 3 and series 2 gives
double the galvanomagnetic difference of temperature. Finally the
mean was taken of the results with both directions of the current.

During these experiments water at the temperature of the room
was flowing through both tubes. But for this precaution a difference
of temperature of about 30° might arise between the two borders
where the current entered and left the plate, caused by PELTIER-
effect; in consequence of the rotation of the isothermal lines a sen-
sible error might be caused by this difference of temperature.

Current through the plate 3,0 ampères.

Difference of temperature in °C.

Magnetic field. es

r v. E. and N.
As 5 | ki (current 5,6)
|
1350 — 0,00 —
2730 + 0,03 + 0,02 — +- 0,95
4800 0,16 0,10 + 0,09 1,66
6100 0,29 0,20 — 2,12

(77 )
b. Harr-effect.

The observations were made by means of the method of com-
pensation }).

HArr-constant.
Magnetic field, EL

A B | C | ¥. E. and N.
| | |
13500 en A 12 ed | oes (105
2730 | 13,1 11,1 | men | 9,3
4800 | 12,4 10,2 | 10,2 | 8,0
6100 | 11,8 9,9 | 9,7 | 7,1
| |

c. Transverse thermomagnetic difference of potential.

For measuring this phenomenon the upper and lower borders of
the plate must be connected through the galvanometer ; as moreover
the current of heat cannot be reversed momentaneously, we are
obliged to observe the change in the deflection on the reversal of
the magnetic field. These reversals occurred every minute; the
readings were taken just before reversing.

In this measurement the rotation of the isothermal lines causes a
disturbance. Though the rotation is not considerable, yet the distur-
bances are not to be neglected; for on the reversal of the field the
sign of the difference of temperature between the borders is changed ;
moreover we have to do with a thermo-electric couple bismuth-
copper; in fact the disturbances assumed sometimes a value of 60
scale-divisions, which would cause an error in the difference of po-
tential of 1800 C.G.S. units.

The current of heat was obtained by conducting steam of 100°
through one of the tubes, and water at the temperature of the room
through the other tube. The slope of temperature, which we must
know in order to calculate the coefficient of this effect, is not the
same in different sections, in consequence of the loss of the heat
absorbed by the surroundings. Therefore I have measured the tem-
perature in the three places and found for A + 34°, B 50° and
C 28°. Thence the slope of temperature given below was deduced
by graphical interpolation.

") See communication of May 30, 1896, p. 47. Comm. N® 26, p. 1.

A | B IN C | v. E. and N.

Slope of temp. 14 | 28 8 | <4
Magnetic field. poses | | ~

Transverse thermomagn. diff. of temp. in C.G.8. units.

1350 — 1650 -— 3390 | — 900 =

2730 — 1300 — 5130 — 825 + 4900 4)
4800 + 1350 — 4020 | + 700 + 8600
6100 4+ 4480 — 1200 | + 2600 + 10700

In the graphical representation all observed differences of potential
have been inserted; the abscissae are strengths of the field, the
ordinates differences of potential, both in C.G. 8. units.

d. Transverse thermomagne-
= tic difference of temperature
(rotation of isothermal lines).

This difference of tem-
perature might have been
observed after the same
method as the galvanomag-
netic difference of tempe-
rature; just as the latter
it arises gradually. In con-
sequence of the heating of
the surroundings however
the temperature in the plate
was not so constant as in
the experiments without a
current of heat; moreover it
was desirable, with a view
to the correction of the
thermomagnetic difference
of potential, to measure the
rotation under quite the
same circumstances as in
those experiments. Therefore the variation of temperature on the
reversal of the field was here determined for each of the thermo-
electric couples seperately.

5000

2500

T
L

= 2500

') The breadth of the plate was here 2,2 eM.

(79)

4 | B | c

Slope of temp. 14 | 28 8
Magnetic field. Sahel: | |

Transverse thermomagn. diff. of temp. in °C.

1350 | — 0,04 | — 0,06 =

2730 0,09 | 0,12 = 004
4800 0,14 0,18 0,06
6100 0,16 0,23 0,07

4. Generally these results differ rather considerably from those
of VON ETTINGSHAUSEN and Nernst. The galvanomagnetic difference
of temperature is smaller and increases nearly in proportion to the
second power of the strength of the fieid instead of the first. The
Harr-effect is larger — larger even than has ever been observed
in bismuth — and increases more with the magnetic force. For
the thermomagnetic difference of potential we find in the weaker fields
even another sign than was observed before ; only in the stronger fields
the sign agrees again with the observations of von ETTINGSHAUSEN
and Nernst; accordingly the effect, when positive, increases more
than proportional to the first power of the magnetic force.

Probably the most important cause of this difference is the diffe-
rent purity of the bismuth; also the circumstance, that my bismuth
was deposed by electrolysis may have some influence.

The behaviour of the alloys of bismuth and tin may now serve
in order to indicate which bismuth is purer. Von ErriNGSHAUSEN
and N&RNsr experimented upon bismuth, considered as chemically
pure, and four alloys with increasing quantities of tin. They found:

a. The galvanomagnetie difference of temperature has a maximum
in the alloy with 1°/, of tin. In the alloys the increase is less than
proportional to the first power of the magnetic force, in bismuth it
is almost proportional to the magnetic force.

b. The Harr-constant is in the alloys much smaller than in
bismuth; the relative decrease with increasing magnetic forces grows
with inercase of the quantity of tin.

c. The transverse thermomagnetic effect is largest in bismuth; the
longitudinal thermomagnetic effect on the contrary has a maximum
in the alloy with 1%, of tin. The increase in the alloys is less
than proportional to the magnetic field; in bismuth it is nearly
proportional to that field.

Hence in respect to a and 5 my bismuth and the alloys differ

( 80 )

in opposite senses from the bismuth of von ETrINGSHAUSEN and
Nernst; also with respect to c, if we regard only the relation
with the magnetic force, whilst the discrepancy of sign is not found
in the alloys.

That indeed the bismuth of the physicists mentioned was not
completely pure is moreover proved by what follows: the temperature
coefficient of the resistance was found to be negative, whereas with
the electrolytic bismuth from HARTMANN and BRAUN according to
FrrMiNG and Dewar!) it is positive and just as in other pure
metals; the conductivity was 4,8.10~° instead of 8,6.10—% with
electrolytic bismuth, and the increase of resistance in a magnetic
field 8400 was 30°/, against 40°/, with the electrolytic bismuth
according to HENDERSON *).

Hence very likely the bismuth used by me was very pure. By
this result the confidence in the results of the experiments is aug-
mented; yet I willindicate a possible, though improbable disturbance,
which might account for the change of sign in the transverse effect.
It is namely possible that the thermo-electric needles did not follow
completely the variations of temperature of the plate, and that
therefore the disturbances caused by rotation of isothermal lines was
ereater than was calculated. If we consider however, that I found
for that rotation greater values than von ETTINGSHAUSEN found
with soldered thermo-electric needles, that after 1 minute the deflections
varied rarely more than one scale-division, and that my values for
the rotation would have to become at least 6 times greater in order
to render the effect positive in all cases, then it will be agreed that
this explanation is very improbable. I intend however to repeat one
of the experiments with soldered electrodes.

5. Before proceeding to the calculation of uw, v ete. from the new
data I wish to point out a remarkable discrepancy between RIECKE’s
theory and my observations.

According to formulae 1 and 3 the ratio of the coefficients of
thermomagnetic difference of potential and galvanomagnetic difference
Ip In
Ei

of temperature is equal to 5

9 gn
LE and — however are equal to
u 2)

1) Proc. Roy. Soc. 60, p. 78 and 425, 1896. A similar result I obtained with
bismuth from Oberschlema. (See my dissertation p. 99).

2) Wied, Ann. 53, p. 912, 1894.

(81)

1

° 9
oP Up Cp” and = fbn Ona
a 24

(see § 12 of RiEckn’s paper) where e denotes the charge in electro-
magnetic units, w, and w, denote masses and c, and ¢, velocities
of tke charged particles. Of course the product of these quantities
can never be otherwise than positive. Now for the galvanomagnetic
difference of temperature always a positive value, for the thermo-
magnetic difference of potential in weak fields however a negative
value was found. The regularity with which this phenomenon showed
itself, appearing f.i. from the graphical representation, proves that
there can be no question of errors of observation ; none of the known
thermomagnetic phenomena can cause a systematic error; hence the
negative sign of the thermomagnetie difference of potential in weak
fields is not to be reconciled with Riecke’s theory in its present
form.

But even if we will not insist upon this negative sign in the
weak fields, the positive value in stronger fields leads in connection
with the other quantities to conclusions, which give rise to the
question whether in the theory everything has been taken into con-
sideration.

For the calculation I chose the magnetic field 6100 and the series
of observations Ad. We find then

GOO LDS Sarl 0E ¢= 4 56:10-2 HS ORD

In the calculation of a and 5 for the resistance of the bismuth,
which has not yet been determined by me, was taken the value
which FLeminc and Dewar found in a field of 6100, namely
134.105 in C.G. 8. units.

The formulae 5 and 6 give
u = — 0,157.10—° v = 8,84.10-5
whence we deduce further

Gp— — 1,304 In = 0,046

so

= 8,3.10° = 0,0052.108

1 v

( 82 )

This result does not appear to me very probable.

6. I wish to defer a comparison between theory and experiments
entering into more particulars until also the longitudinal pheno-
mena: the conductivity for electricity and for heat, the change of
these in the magnetic field and the longitudinal thermomagnetic
effect have been investigated in this plate.

I think it probable that RrEckn’s theory will have to be modified.
Firstly also the variation in the magnetic field of the conductivity
for electricity and heat might be included in it. The observations
of these phenomena prove that the variation is much smaller for the
thermal conductivity than for the electrical conductivity. This indi-
cates, I think, that the theory wrongly ascribes the whole conduc-
tion of heat to the charged particles‘). It would be desirable to
try whether it is possible, taking this into account, to explain the
phenomena with the assumption that the kinetic energy is the same
for positive and negative charged particles, which seems at first
sight more probable. At the same time it might perhaps be recom-
mended to omit, in the deduction of the formulae for the four trans-
verse phenomena, the condition that the velocities of the particles
in the direction of the electromagnetic force should be zero, and te
replace it by a similar condition as was assumed by me in the
theory of the Harr-effect in electrolytes *). Finally it will appear
necessary to make some hypothesis in repiy to the question, what
happens with the charged particles when they reach the borders of
the metal. RrieckE himself indeed has observed *), that it is not
possible to formulate a complete theory of thermo-electricity with
the aid of his hypotheses whithout accounting for the conditions at
the junction of the two metals and forming an idea about the reci-
procal influence of ponderable molecules and electric particles.

Physics. — On the deviation of DE HEEN’s experiments from VAN
DER WAALS’ law of continuity. By Dr. J. VERSCHAFFELT
(Communicated by Prof. H. KAMERLINGH ONNES).

(Will be published in the Proceedings of the next meeting).
1) See my dissertation p. 114.

2) See communication of May 28, 1898, p. 48. Comm. N°, 41, p. 6.

5) $8 of his paper.

( 83 )

Physics. — The composition and the volume of the coexisting vapour-
and liquid-phases of mixtures of Methylchloride and Carbonic
acid. By Cu. M. A. HARTMAN (Communication N°. 43 from the
Physical Laboratory at Leiden, by Prof. H. KAMERLINGH ONNES).

S 1. Van DER Waats’ theory of mixtures has already given rise
to numerous observations. KUENEN f. i. has determined the isother-
mal lines for three different mixtures of methylchloride and carbonic
acid in the gaseous phase in order to construct the w-surface up to
the border-curve for different temperatures and to obtain data about
the values of aj, and Dis. The phenomena in the neighbourhood
of the plaitpoint have also been investigated by him for different
substances. Through this the shape of the connodal lines in the
neighbourhood of the plaitpoints has become fairly well known.

It was very desirable that now also a first plait crossing the w-
surface from one side to the other should be traced experimentally
with special indication of the coexisting phases. If at a given
temperature the composition and the density of these phases are
known we may draw the projection of the connodal line in the z-v
plane and in this figure we may draw the projections of the tangents
which unite the coexisting phases on the surface.

To obtain the data required for this has been the purpose of this
investigation. JI have chosen methylchloride and carbonic acid for
substances because many data about the mixtures of these two have
already been gathered by KUENEN.

§ 2. Fig. 1 may serve to explain the principle of
the method of investigation that has been followed.

The coexisting phases are contained in a wide reser-
voir A. At the upper end of the reservoir we may
isolate a definite volume of the vapour-phase by
shutting the cock B, and draw it off by means of the
cock By and receive this above mercury in a common
gas tube. The quantity of this is found by measuring
the volume, pressure and temperature of the gas and
the composition is found by having the carbonic acid
absorbed by potash.

In the same way we may isolate a definite volume
of the liquid-phase at the lower end of the reservoir.

The volumes of the liquid-space A and of the
vapour-space B have been determined by measuring
the volume of oxygen which they can contain at high
pressure.

6

Proceedings Royal Acad. Amsterdam. Vol. I

( 84 )

The equilibrium between the two phases is obtained by stirring
with the aid of an electro-magnetic stirring-apparatus, as has lately
been described by van ELpIK !) (see § 6). In this manner a perfect
equilibrium must be obtained within the wide reservoir. The cocks
A, and B, are wide open during the stirring. Care should be taken
that the composition of the substance in the space B should be the
same as that of the rest of the vapour-phase in Ff, and therefore,
after sufficient stirring (or while carefully continuing the stirring)
as much of the vapour as is contained in the space B must be
slowly blown off by slightly opening the cock Bz, after which the
cocks By and B, are saccessively shut. In tapping from the liquid-
phase the same is done with respect to the cocks 4, and Ag.

The spaces 4 and B are 0,0778 and 3,25 ¢.c.m., while the volume
of R is about 150 c.c.m. So we may assume that the change of the
composition of the liquid and of the vapour during the tapping may
be left out of consideration, if the tapping be done with the neces-
sary care in the way described above, and that the compositions of
liquid- and vapour-phases, found by analysis, indicate the composi-
tions of coexisting phases at the temperature and under the pressure
at which the tapping is done. I intend to connect with the present
apparatus the compound hydraulic pump for moving coexisting phases
(described in the Proceedings of the Meeting of May 27th 1897 p.
21) by means of which the permanent equilibrium between the phases
may be still better secured.

In order to keep the temperature constant, the apparatus is placed
in a water bath (see § 5).

The pressure of the coexisting phases is measured before and after
the tapping by means of the manometer connected with p (see § 4).
The average of both measurements is taken as the pressure to which
the coexisting phases belong.

When one measurement has been performed we may make a second
determination by tapping once more, and so on, as long as the
quantity of the liquid phase in the reservoir is sufficient. At each
successive determination we find a new value for the pressure to
which the new pair of coexisting phases belongs.

In this way a series of a certain number of successive determina-
tions was generally made at the same temperature.

§ 3. Description of the apparatus (fig. 2—4).

The reservoir R consists of a drawn brass tube (long 55 eM.
internally) closed at both ends by a plug screwed and soldered in

1) v. Evprk, Proceedings of the Meeting of May 29 ’97 p. 20.

EE

|
Ì
|
|
N
i
i
is
\
\
}
Y
t
+
i

os SB

ALT
CS LILIPAA LL Lh

Proceedings Royal Acad, Amsterdam. Vol. I.

EE

Tee
LQ (LE q
(& \g A

Ch. M. A. HARTMAN. Mixtures of methylchloride and carbonic acid.

=

if

a

EEL

EEN CA WE OEE CA KC OG LAAD TT

Ln Lr aA ACT A OT LI

( 85 )

it. The liquid-space A is contained between the needle points of
a double cock; the chamber of cock A; is connected with the reser-
voir by a brass overpipe a, which is provided with two nuts, and
in which a narrow steel capillary tube has been soldered which is
so long that the lower end of it reaches as far as the chamber of
A, and the upper end not only goes through the plug but emerges
nearly 5 m.m. beyond it.

Thus has been obtained that the communication of R with A
has as little volume as possible; while at the same time at the
lower end of the reservoir an annular space has been formed, in
which may settle particles from the walls or from the packings
which during the distilling of the gas might get into the reservoir.

A rim on the plug protects the capillary tube from being damaged
by the stirring-rod.

In the plug at the upper end of the reservoir three copper ca-
pillary tubes have been soldered.

One of these, 4, leads to the cock Bj; the vapour-space B consists
in a spiral made of a copper capillary tube (long 80 cM.) of the
same diameter. Care has been taken that the channel through which
the vapour streams out has the same diameter over its whole length
in order to prevent as much as possible the condensing of the vapour
by adiabatic expansion.

A second tube c leads to the cock Cz and serves to connect the
purifying apparatus with the reservoir. The third tube d connects
this reservoir with the apparatus for the measuring of the pressure.

§ 4. The measuring of the pressure.

Special care is required for this. By filling the tube which leads
to the closed air-manometer with mercury, we may prevent conden-
sation or evaporation in that tube caused by differences of tempe-
rature between that tube and the water-bath of the apparatus. But
then the mercury-meniscus on which the vapour presses must be
within the water-bath and moreover it must be visible in order to
enable us to read the difference in height with the meniscus of the
closed manometer.

Therefore the tube d has been connected through the cock C;
with the copper capillary tube e, which ends in the upper part of
the glass reservoir D, which is again connected with the mercury
in the air-manometer through the steel capillary tubes f, g and the
steel cock D,. With a view to greater accuracy two air-manometers
are used, the one for pressures from 4 to 20, the other for
pressures from 18 to 90 atmospheres, so that their indications may
be compared together.

6*

( 86 )

The pressure-cylinders of the two manometers are connected at
their upper ends with an hydraulic pump; from the latter and from
the tube h they are separated by cocks, so that each of them may
be put out of use separately. By means of the hydraulic pump the
mercury may be forced from one of the pressure-cylinders into the
capillary tubes 4, g and f, and so at the required height into D.

The difference in height of the mercury in D and in the mano-
meters is taken into account as a correction for the pressure.

The volume of D is so large that after a change of pressure the
mercury-meniscus in it always remains visible, without the hydraulic
pump being required continually.

S 5. The water-bath.

A constant temperature is obtained by causing water to flow
through the water-bath in which the apparatus is placed. Whenever
water from the main was used the temperature was regulated by
means of the same apparatus which was used by Dr. van ELDIK
in his investigations on capillary ascension !).

If the temperature of the water from the main was higher than
was required for the observations it was cooled by means of ice
and a circulation was brought about, on the whole agreeing with
that used by Dr. DE Haas in his researches on the viscosity of liquids”).

The water-bath is made so that the whole apparatus may be put
into it from above. For this the four cocks B, Bg, Cj), Cy are mounted
on a base-plate H, to which the cover K of the water-bath is
fastened. In the centre of this cover is an opening to let through
the tubes e and f; a rim surrounding that opening serves to fasten
a glass tube L in it. Besides in the four corners of the cover are
smaller openings in which the tubes b' and c’, the other end of
and a thermometer are tightly fixed by means of corks. At the
lower part of the base-plate is screwed an angiepiece with sliding
tube supporting the reservoir.

The water-bath itself consists of a rectangular box M, containing
the four cocks and a cylinder N, surrounding the reservoir. In the
front of the box are four openings with necks corresponding to the
steel pins of the cocks; when these have been placed into the water-
bath we apply brass lengthening-pieces to those pins and the ope-
nings are shut water-tight by means of corks. The double cock A
has a water-bath of its own soldered to it; an india-rubber ring
P (high 10 e.m.), which can slide along the cylinder, and when it is

1) van Erpik, |. c. p. 22. Comm. ete, NO, 39.
2) pp Haas. Dis. Leiden 1894, p. 8.

( 87)

tightly fixed completes the waterjacket. One of the glass side-walls of the
box M enables us in the case of a leak in the apparatus, to find out where
the gas escapes. As in the water-bath alone there are twelve connections
with overpipes and nuts, this measure is not superfluous.

During my observations at 9 to 10° the temperature in the room
exceeded that of the water-bath. In this case the water flows into the
apparatus through H# and can leave it through the pipe F’; we may then
expect the temperature of the water when flowing through to risea
little, but by no means to fall. Thus we prevent the liquid from
distilling from PR into D. Yet from time to time a small quantity
of liquid appeared on the mercury in D; however no perceptible
disturbance of the equilibrium between the two phases ensued, at
least the manometer showed no permanent change.

In case the temperature of observation should exceed that of the
room the same result may be obtained by letting the water in
through / and by causing it to flow off through H. G may serve
here to prevent the level from rising too much if F for the time
being does not lead off a sufficient quantity.

§ 6. The Stirring.

The soft iron stirring-apparatus consists in a little rod (long
15 m.m.) provided at both ends with a disc (broad 12 m.m.) and
moved electro-magnetically by means of a coil S, outside the water-
bath. A cylinder 7' of sheet iron fitting round the reservoir moves
together with the coil and serves to concentrate the lines of mag-
netic force in its axis. The current for this coil is supplied by four
portable accumulators.

§ 7. The analyses.

The composition of the gas-mixture, received above the mercury,
is determined by having the carbonic acid absorbed by pieces of
caustic potash (cylindres of 10 to 15 m.m. length). They must not
be too dry, else we are not sure that all the carbonic acid will be
absorbed. But on the other hand care must be taken that those
pieces are not too moist, as a separate experiment showed that the
methylchloride is dissolved by a saturated solution of caustic potash.
After some practice I soon succeeded in introducing potash in the
desired state of humidity into the gasometric tubes.

For some days the gas is left in contact with the potash. In order
to hasten the absorption the tubes are plunged as far as possible
into deep reservoirs filled with mercury, each consisting in an iron
gaspipe, closed at the bottom and carrying at the top a wide glass
basin. The absorption of the carbonic acid may also be hastened by
moving the tube in the mercury up and down,

( 88 )

Ín determining the quantity of gas in the tube the latter is sunk
into the mercury so deep that the measuring of the volume and of
the pressure of the gas may be done with the same accuracy. Fitting
tound the tube are elastic cylinders of thin sheet iron, provided
with sharp points, which are bent downwards. The needle is pointed
at the mercury surface, and the rim allows to read the divisions on
the glass tube. In doing this an india rubber stopper bearing a
glass water-jacket is fixed round the glass tube. By means of this
simple contrivance we know also the temperature of the gas to be
measured and so the volume may be reduced to 0° C and 1 atmosphere.

In determining the quantity of the liquid-mixture and of the
vapour-mixture drawn off, we also take into consideration the portion
of the mixture which remains in the spaces 4 and B after the
flowing off under the barometric pressure. Especially for the vapour
at low pressure this should not be disregarded.

As the measuring tubes were filled with mercury in the ordinary
way, there remained a small quantity of air in the theoretical vacuum ;
this quantity was determined and taken into account.

§ 8. Results.

The plait on the y-surface of carbonic acid and methylchloride

a
EEE HEE
| EEE

ane
aS

men

Pen
aten
En

a

Hus

NEEN
EEEN:

at 9°,5 has been investigated. As it was especially important to
learn as well as possible the character of the plait at one definite
temperature, corrections were applied for slight differences in order
to reduce all the determinations to the same temperature. The results
obtained as derived from the determination of ten coexisting phases
are only provisional; but vet they are sufficient to show us the
character of the plait as resulting from the observations. A graphical
representation of the results will be sufficient.

Fig. 5 gives the quantity of methylchloride contained in the mixture
(e of VAN DER WAALS) in function of the pressure in atmospheres (as
ordinate) for the liquid- and for the vapour-phase. Fig. 6 shows
further the value of the logarithm of the volume in function of a.
As unit of volume of a mixture we have chosen that at 0° C. and
1 atmosphere. For the sake of a convenient representation the loga-
rithm of the volume instead of the volume itself has been chosen
as ordinate (turned towards the bottom of the page). From this figure
and some lines drawn in it, which connect the coëxisting phases,
we may immediately deduce the projection on the z-» plane of the
connodal curve with the conjoint points of contact,

(90)

It is remarkable that the Jiquid-curve in fig. 5 should differ so
little from the straight line. So it seems that for these mixtures
at the chosen temperature the vapour-pressure of the hquid-phase
may be represented with near approximation by:

a Py (1—x) + Pt

in which P, and P, represent the vapour-pressures of the compo-
nents. If we compare this with the formula given by vAN DER WAALS),
it appears that the exponents in the latter differ little from zero.

Physics. — ,Considerations concerning the Influence of a Magnetic
Field on the Radiation of Light.” By Prof. H. A. Lorentz.

§ 1. The assumption that every molecule of a source of light contains
a single movable iou, which can be displaced in all directions from
its position of equilibrium and is always driven back to that position
by the same force, proportional to the displacement, leads to the
elementary theory of the phenomenon discovered by Dr. ZEEMAN.
Viewed across the lines of force, a single spectral line must, by the
action of the field, be tripled, and viewed along the lines of force,
be doubled; besides, the components of the triplets and doublets
must be polarised in a well known manner.

Whilst the first observations of ZEEMAN were consistent with this
theory, and he soon could confirm the theoretical predictions by the
observation of distinct triplets and doublets, yet it has become ap-
parent that the case is often less simple. Cornu proved, that f.1.
in the case of one of the sodium lines, viewed across the lines of
force, the central component of the triplet is doubled, so that in
reality a quadruplet is seen. MicHELSON and Th. Preston observed in
many cases not only a far more complicated structure of the central
component, but a similar structure of the outer components of the
triplet. According to these observations, the word „triplet” is
hardly applicable, though there is always an important difference
between the central part of the appearance in the spectrum (the two
central lines, f.i. of CoRNU’s quadruplet) and the outer parts; the
first is plane polarised, the plane of polarisation being perpendicular
to the lines of force, whereas in the right and left part the plane
of polarization is parallel to the lines of force.

§ 2. The facts mentioned evidently make it necessary to replace

1) v. p. Waars, Verslag Kon. Akad, May 28 °91 p. 416.

(91)

the elementary theory by a more complete one. Some time ago, I
examined !) therefore what phenomena are to be expected, if a mole-
cule, having an arbritary number of degrees of freedom and arbri-
tarily distributed electric charges, is oscillating about a position of
equilibrium.

Before returning to this subject, I will consider the conclusions
which may be obtained by arguments from symmetry, without ente-
ring into the details of the mechanism of radiation.

There can be no doubt, that we may consider the source of light
as a system of extremely small particles, oscillating partly with the
frequency of the light vibrations; in virtue of their electric charges,
these particles must excite in the surrounding aether periodically
oscillating dielectric displacements. These constitute the luminous
motion radiated by the source.

For briefness’ sake this entire system will be indicated by S.

We may now conceive a second system S', which is the image of
S, relatively to a fixed plane P. The meaning of this is as follows.

If A is a particle in S, there is in S' a particle 4’, which is
the image of A and of the same physical nature as this particle.
Especially, the mass and the electric charge are the same; or, to speak
more accurately, in corresponding points of A and A’ the same
material density and the same density of electric charge will be
found. Moreover, the particles A’ will be at every moment the image
of the particles A, or, as we may say, the motion of the ions in
S' will be the image of ihe motion in S. If this is the case, the
luminous motion in the aether in S’ will likewise be the image of
the motion in S, in this sense that the vector representing the die-
lectric displacement in S' is always the image of a corresponding
vector in S,

Of course all this will only be possible, if the forces operating
on the particles A’ are the images of those to which the particles
A are subjected. So far as the mutual action of the particles is
concerned, we may regard this as a consequence of the supposed
equality in physical nature. In order that the forces, originated by
the external magnetic field, may satisfy the same condition, we will
suppose that the vectors, representing the magnetic force in S', may be
derived from the corresponding ones in S by first taking their ima-
ges, and then reversing the directions of these images?).

1) Wied. Ann. Bd. 63, p. 278, 1897.
2) If the magnetic field is generated by electric currents, we may imagine the
required field in S' to be produced by currents, which are the images of the currents in S,

(92)

It will also be assumed that the properties of the image of the
source of light, as far at least as we are concerned with them in
really observable phenomena, are the same as those of the source
itself, so that the latter may be substituted for the image. Finally,
we suppose that the entire luminous motion in the aether is developed
by means of FouRIER’s theorem into simple harmonic motions; when
the total luminous motions in S and S' are each other's images,
the same will evidently be true of those parts of the luminous
motions, which have a determinate period 7’ — or rather periods
between two definite limits 7’ and 7 4d T.

§ 3. Let Q be a straight line, drawn from any point in the source
of light parallel to the lines of force, and let L denote the luminous
motion with a definite period T, existing at a distant point of Q.
By taking the image of the whole system, relatively to a plane
parallel to the line Q, it is easily seen that the image L'is exactly
the luminous motion, that would exist in the point considered, if,
the source of light remaining unchanged, the direction of the field
were reversed. Hence L' may very well differ from L, but, in all
observable properties, L' must remain unchanged, if the reflecting
plane be turned around the line Q as axis.

Whence it follows, that, if all vibrations of L are resolved parallel
to a line R, perpendivular to Q, the intensity produced by the com-
ponents must be independent of the direction of B. Indeed, R, and
R, being two lines perpendicular to @, and J, and Za the inten-
sities corresponding to them in the manner indicated, we may give
to the reflecting plane two positions P, and P, in such a way
that the image of PR, relatively to Pj, coincides with that of Rg,
relatively to Ps. Indicating by R’ the direction of these coinciding
images and by J'y the intensity corresponding to this direction of
vibration in L'— this quantity remaining the same, as was remarked
above, for every position of the reflecting plane — we may write
Ts ANd — hence lala:

In this way we come to the conclusion that the light propagated
along the lines of force, and having a definite period 7’, or, in other
words, occupying a definite place in the spectrum, cannot be polarised
plane or elliptically, neither completely, nor partially. It can only
be unpolarised, or circularly polarised; in the latter case the pola-
rization can be partial as well as complete.

The light would be unpolarised, if an influence of the magnetic
field did not exist at all. As far as we know, the components of the
doublets seen along the lines of force are completely circularly pola-

( 93 )

rised. From the above considerations it however appears that the
radiation might also be partially circularly polarised. We see at
the same time that, if‘in a given place of the spectrum the polari-
zation is righthanded, it must become lefthanded at the same place
by reversing the magnetization.

§ 4. Arguments of the same kind may be used when the ob-
servations take place across the lines of force. Now, we place the
reflecting plane perpendicular to these lines. The magnetic
field remains unchanged; consequently, the luminous motion must
have the same properties as its image. Hence the light, observed
in a given place of the spectrum, cannot be circularly nor ellipti-
cally polarised — neither completely nor partially. It must be either
unpolarised light, or plane polarised — wholly or in part — the
plane of polarization being parallel or perpendicular to the lines
of force.

It needs scarcely be mentioned, that all observations are in agree-
ment with this conclusion.

§ 5. A closer examination of the mechanism of radiation gives
us a relation between the light radiated along and the one radiated
across the lines of force. At least one conclusion concerning this
point lies at hand.

Let M be a single molecule of the source of light, and let three
rectangular axes OX, OY, OZ be drawn, the first along the line
of force. Let e be the electric charge in a point of the molecule,

having the coordinates x, y, 2; then we may call Sea, Sey,
2 ez — calculated for the entire molecule — the components of

the electric moment of the particle.

These quantities are continually changing, and will perhaps be
extremely complicated functions of the time. By means of FOURIER’s
theorem, we may however separate the parts that have a deter-
minate period 7. We will confine ourselves to these parts and
denote them by Mz, My, Me.

If now the dimensions of the molecule are very small compared
with the wave-length, then, the observer being supposed at a distance
of a great many wave-lengths, it may be deduced from theory, that
in all points of OY, light is produced merely by the variations of
Me and Mz, Me producing vibrations along, and Me across the lines
of force. Similarly for points of OX and OZ.

Suppose, that, when viewing across the lines of force, f. 1. from
a point of OY, in a given place of the spectrum light is seen

( 94 )

which is entirely plane polarised, the plane of polarization being
perpendicular to the lines of force.

Then, at the place in question, there will not be any luminous
motion produced by Mz, and, because the molecules are vibrating
independently of each other and hence light emitted by one can
never be totally destroyed by that originating from another, Mz must
vanish in all molecules. Of course the same argument applies to My ;
hence it follows, that no light can be observed from any point of
OX, that is to say in the direction of the lines of force.

BECQUEREL and DerSLANDRES have found!) that one of the iron
lines, when viewed across the lines of force, becomes a triplet, the
central and side components of which, as compared with those of
the ordinary triplets, have interchanged their states of polarization *).
The foregoing reasoning entitles us to predict, that only the middle
component of this triplet will be visible, when the phenomenon is
observed in the direction of the lines of force.

§ 6. In the paper cited above, I have established the equations of
motion for infinitely small vibrations of a molecule, having » degrees
of freedom, and placed in a magnetic field. I called pj, po, - -- Pn
the general coordinates, chosen in such a manner, that they are
Q in the position of equilibrium, and that they are principal coor-
dinates as long as there is no external magnetic force. I obtained
for the equations of motion

a py + bip — (erapa Heisps +... + e1npn) =, a
ay Pa + dg py — (carpi Heaps td +++ + ¢2npn) = 0,
etc.,

where a and 5 are constants, independent of the magnetic force.
The influence of the field is expressed by means of the terms con-
taining the quantities c, which are all proportional to the intensity
of the field.

They further satisfy the relations

Cris == —— Co) EE st (Cea)

To determine the possible periods of vibration, we put, according
to a known method, in (1):

1) Comptes rendus, 4 avril 1898.
2) The same phenomenon has been observed in the case of some iron-lines by
Ames, Harnart and Reese, Johns Hopkins Univ. Circular, Vol. 17, No. 135,

PA OF iy OP EN "Lene,
and eliminate ej, 42, . … … tn. If
bi bs bn
iet vt
ay ay ay
and
Cris
Sa
ay

P+ kj? eis l, eis l, inl
ear l, 2 — ka’, eal, ean l

, =0 : (5)
en l, €n.2 L, En.3 l, syine Bis Pk

In consequence of the relation (2), the development of the deter-
minant will contain only even powers of /?. Hence an equation is
obtained, of the zb degree in 2. From the circumstances of the
case it follows, that the roots of this equation are all real and nega-
tive; hence » pairs of imaginary values of / are obtained. If + ik’,
and —ik', are two of those values, there will be a mode of vibra-
tion with the frequency (number of vibrations in the time 2 7) 4’.

Evidently, without the field, the frequencies would become

ky, ky, . . . kn ’
and it is clear that, if there is a magnetic field, each of these
frequencies is modified into a value #’,, differing very slightly from 4.
In the cited paper I had restricted the development of (3) to

terms containing the products of two factors e. Denoting by J/ the
product

BFR) OR)... C454

and by J/,., the value, got from this by omitting the factors ? + 4,°
and ? +k, we obtain

IT ES = {2 ers Es.r IS — 0, . . . . . . (4)

( 96 )

where the sum is to be extended to all combinations of unequal
indices 7 and s.

I inferred from this equation, that a triplet can only be observed,
if three of the values k are equal, or, in other words, if the system
has three equivalent degrees of freedom. This will also be clear
when it is considered, that by a continuous decrease of the magnetic
field, the three components of the triplet may be made to coincide,
so that the simple spectral line, as seen out of the field, may be
considered as consisting of three coinciding lines. Applying the same
argument to Cornu’s quadruplet, it seems natural to suppose that the
lines, which are apt to undergo this modification, consist already,
under ordinary circumstances, of four coinciding lines, or otherwise,
that now we have four equivalent degrees of freedom, or four equal
values k.

Yet, the origin of a quadruplet cannot be explained by equation (4).
Indeed, if 4, ko, 43, ky are the frequencies having the same value k,
there are in each term of (4) at least two factors 2 + k®, Hence
the equation must still have two equal roots —k*, and besides only
two roots, differing very little from — k?,

er

S 7. It was however brought to the notice of the author by
Mr. A. PANNEKOEK that in this case equation (4) is incomplete,
because some of the terms neglected are of the same order of mag-
nitude as those retained, and that, by returning to equation (3), an
explanation of the quadruplet may be arrived at.

If kj? = ky? = hg = ky? =k?, certainly four roots of equation (3),
if not = — k?, will differ only very little from this value.

If 2 is one of these values (we need not occupy ourselves with
the other values of 2), then the four quantities @ + h?, ? + &,’,
2+ h2, 2 +h 2 will be small. On the other hand, the quantities

Paes PRS fo. Pee NG

will have values, which by no means become small. Since all the
quantities el are likewise small, the elements (5) of the determinant
will exceed by far all other elements, and we shall obtain a suffi-
cient approximation, when we take in the development of the
determinant only those terms, which contain all the quantities (5).
Evidently, the equation serving for the determination of the values
of 2, which differ only slightly from — k*, will therefore be

2 Jk? eis I, esl, eral

ear J, 2 - k?, eas 1, eoa 1

anil; Ae ease i CHA! i
earl, esn l, eis l, Pk?

If we develop this determinant, all terms, which have an odd
number of factors e‚‚l, are excluded by (2). Hence the equation
may be written

EHESS AR HE) HB=0,. 0. (6)

where A contains terms with 2 factors e,,/, and B terms with 4
factors of this kind. In all these factors /? may be replaced by
— k?. Consequently, A and B can be found, and A is now propor-
tional to the square and B proportional to the fourth power of the
intensity of the field.

From (6) we get two values of (/? + k*)?, which are both real and
positive, because, as was already remarked, real values must be
found for /?. Hence the solution of (6) may be represented by

OKEE AD ANT)
and

(PSE Wi BE an 20 ek B)

where «& and / are known, say positive, quantities. By reason of
what has been remarked about A and B, the values of « and (7
will be proportional to the intensity of the field.

Finally from (7) and (8) the following four values of /? are
obtained :

P=—-k tea, —k—ea, —k+ 7, —kK — 3,

so that in fact there must be seen a quadruplet in the spectrum. In
order that the four lines of this quadruplet may be perfectly sharp,
it is however necessary, that in a given magnetic field the quantities
«a and / are independent of the direction into which the molecule
is turned, or, what comes to the same thing, that, for a given po-
sition of the molecule, @ and ( are independent of the direction of
the magnetic force.

Mr. PANNEKOEK has also remarked, that a similar reasoning ap-
plies when an arbitrary number, e.g. p, frequencies / are equal.
In this case we come to the conclusion that, for a given position of the

( 98 )

molecule in the field, the simple spectral line must be separated into
a p-fold line, in such a way, that the position of the different com-
ponents is symmetrical to the right and left of the original line.
From this it follows, that if p is odd, one component remains at
the place of the original line.

It seems however very difficult to conceive a system, having
really, as is necessary for quadruplets, four equivalent degrees of
freedom, especially if in addition to this, it is required that the values
of @ and /? must be independent of the direction of the magnetic
force, relatively to the molecule. I have not been able to find out
a system, really fulfilling these conditions. It is true, it might be
argued that the very existence of a quadruplet proves the equality
of four frequencies, when there is no magnetic field, and hence that
the above theory of the quadruplet must be true, even though the
mechanism has not yet been found out. However I have some scruples
to be satisfied with this view of the case, for I think, it is not yet
quite certain, that the vibrations which produce light are really
to be described by equations of the form (1).

Physics. — On an Asymmetry in the Change of the spectral Lines
of Iron, radiating in a Magnetic Field. By Dr. P. Zeeman.

1. It is known that in the elementary treatment of the influence
of magnetic forces on spectral lines according to LORENTZ’s theory
it is sufficient, if only one spectral line is considered, to suppose
that in every luminous atom is contained one single moveable ion
moving under an attraction proportional to the distance from its
position of equilibrium. All motions of such an ion can be resolved
into linear vibrations parallel to the lines of force and two circular
vibrations, righthanded and lefthanded perpendicular to the lines
of force. The period of the first mentioned vibration remains un-
changed, those of the last are modified, one being accelerated and the
other retarded. The doublets seen along the axis of the field, the
triplets seen across it are in this manner simply explained and
also the observed polarisation-phenomena. Besides we must expect
according to the theory that the outer components of the triplet are
of equal intensity and likewise the two circularly polarized com-
ponents of the doublet. Eye observations as well as the negatives
taken by myself and others have always confirmed till now this
most simple symmetrical distribution of intensities. The question arises
cannot the external magnetic forces, sufficient to direct the molecular

( 99 )

currents assumed in the ionic theory of magnetism !), favour the
circular vibrations more than those along the lines of force ?). If
this be assumed we are also compelled to admit that the revoiving
of the ions takes place more in a given direction than in the
contrary. Hence then there must be a difference of intensity between
the two outer components of the triplet and between the two com-
ponents of the doublet. Although the ordinary magnetism of the
highly-magnetic substances has probably disappeared in the spark,
it seems rather natural to examine in the first place iron, nickel
and cobalt in search of a phenomenon in which the ,molecular cur-
rents” of AMPÈRE (or that part of these currents, which is pro-
duced by the motion of the light-ions) would manifest themselves
optically. However it seems to me by no means decided beforehand,
that other substances would not exhibit something of this kind. I
have however investigated in the first place iron.

The first results obtained were much promising. In the field used
several of the iron lines exhibited on the negatives a more intense
component at the less refrangible side of the spectrum. Further
inquiry has however shown that this seemingly positive result seems
to be of no value. I will give the results of my experiments
only in extract. Before describing them, it may be remarked, that,
if a directing influence, as mentioned, exists, we must expect that
the component at the less refrangible side must be intensified and
in the case of the triplet as well as in that of the doublet. The
sign of the charge of the ions cannot have any influence upon
this result.

2. Negatives were taken in the spectra of the third and second
orders obtained by means of a RowLaNnD grating (radius 10 ft,
14438 lines to the inch). More accurately was studied the part of
the spectrum between 3000 and 4000 A. U., when viewed in the
two principal directions across and along the lines of force. The vast
majority of the iron lines were, with the field used, resolved into
doublets, triplets, quartets etc. perhaps only three or four lines seemed
unaffected. Now I found in the case of a few lines inequality between
the outer components of a triplet across and of the corresponding

1) ef. Ricnarz. Wied. Ann. 52, p. 385, 410. 1894.

2) ef. Lorentz. Versl. Ak. Amsterdam, October °97, p. 213. [It was pointed out
by Lorentz in the article referred to, that the phenomena observed by Eaororr and
Grorerewsky can be explained, without any hypothesis of the kind mentioned by
the absorption, which the rays from the posterior part of the flame undergo in the
anterior part.]

7

Proceedings Royal Acad. Amsterdam. Vol. I.

( 100 )

doublet along the lines of force. On the negative the component at
the red side of the spectrum was darker, independently of a commu-
tation of the current. Of course the difference of intensity is depen-
dant upon the time of exposition. Upon some of the negatives the
difference was for a special line perhaps 50 or 100 percent.

However it was plain enough, that the outer components of the
triplets and also the two components of the doublets were, in the
case of the strong iron lines, of equal intensity. Now in the case
of feebler lines, let be one of them, perturbations will be possible
due to the overlapping of one of the components of a ,normal”
triplet or doublet and a feeble line, say but slightly affected by
magnetism. The Jatter line can 1° be present near / in the same
spectrum; or 2° belong to a spectrum of another order as the line
L; or 3° by the very presence of the field a special line may become
relatively to other lines more intense or a new line may be ori-
ginated. By taking negatives with different fields it will of course
be possible to evade difficulties from these three causes, at any rate,
if the supposed line is thin. We can however by taking also negatives
in absence of the field exclude 1, and by taking negatives in spectra
of different order or by cutting off any interfering spectrum in using
absorbents 2. Having done this, it appeared that also case 3 some-
times occurs; the intensity oe the iron lines relatively to the air
lines varies considerably and the mutual intensity of the iron lines
appreciably. New lines appear, at least lines absent on negatives
taken with the field off, became distinctly visible, while yet the
intensity of the field was insufficient to resolve the lines in
triplets etc.

The last mentioned perturbation is of course most treacherous.
Using however fields of varying intensities, I could avoid perturbation
3. Excluding however 1, 2, 3, only triplets, doublets etc. remained,
which, I think, can only be called quite symmetrical. Hence till now
there is no evidence for a directing influence of the magnetic field
on the orbits of the light-ions. ')

1) ef. Preston, Phil. Mag. Vol. 45, p. 333. 1898.

(August 9th 1898).

Royal Academy of Sciences. Amsterdam.

PROCEEDINGS OF THE MEETING

of Saturday September 24th 1898.

DEG

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 24 September 1898 Dl. VII).

CONTENTS: „Congealing points and points of transition in mixed erystals of two substances”,
By Prof. H. W. Bakuurs RoozeBoom, p. 101. — „On the influence of salt-solutions
on the volume of animal cells, being at the same time a contribution to our know-
ledge of their structure”. By Dr. H. J. HAMBURGER, p. 103.

The following papers were read:

Chemistry. — ,Congealing points and points of transition in
mixed crystals of two substances’. By Prof. H. W. Bak-
HUIS ROOZEBOOM.

In 1891 the author has laid down a theory on the building of
mixed crystals from solutions. This theory was applied to equili-
brium in systems of three substances.

Up to now no general rules had however been given for the
building of mixed crystals from fused mixtures of two substances.

The investigations in this direction had either been limited to
the influence of small quantities of the second substance on the
fusing-point of the first (van ’r Horr) or, as far as this had been
extended to greater concentrations, it had been done without any
theoretical guide and had led to false conclusions (KUsTER).

It is possible to plan a survey of the different cases of equili-
brium, which may present themselves between the fused mass and
the mixed crystals by making use of the condition of equilibrium
that the thermodynamic potential be a minimum,

Now Van RIJN VAN ALKEMADE has already stated formerly,
how in case of a continuous series of solid mixtures the potential

8
Proceedings Royal Acad. Amsterdam. Vol. I.

( 102 )

as a function of the concentration is represented by a similar curve
as that representing the potential values of mixtures of two liquids.
The problem therefore is to find out what cases may present them-
selves when these two curves are made to alter their relative
positions, in passing from higher temperatures to lower.

The result of this investigation is, that where a continuous mixture-
series exists, three cases are possible.

Case 1. The congealing points of mixtures of liquids of the
substances A and B, fall gradually from the congealing point of
B to that of A, in proportion as the composition of the fused liquid
is shifted in the direction of A. (in case of B's being the substance
haying the highest fusing-point).

Case 2. The line of the congealing points shows a maximum.

Case 3. The line of the congealing points shows a minimum.

In all the three cases there is the following connection between
the concentration of the fused and the solid mixtures:

The solid mixture contains, in comparison to the fused, a higher
percentage of that ingredient, at the increase of which the congealing-
temperature rises. In the maximum and in the minimum the two
concentrations are equal.

Important conclusions for the process of congealing and fusing
and for the fractionation of mixed crystals may be deducted from this.

If the mixture-series in the solid state is not continuous, it may
be deducted that two cases are possible.

Case 4. The line of the congealing points shows a break in a
transition temperature, situated between the fusing points of the
two components. At this point occurs a hiatus in the composition
of the mixed crystals.

Case 5. The line of the congealing points shows two descending
branches, meeting in a minimum point, below which temperature
every fusion congeals to a conglomerate of mixed crystals with two
different concentrations.

There may still appear further complications, should there exist
more than one solid modification in either of the components or
in both. Following the same lines that have led to the discovery
of the connection between temperature, concentration of solid mixture
and concentration of liquid, it is equally possible to find in what
manner the transition takes place from one solid state into the
other with different mixing-proportions both in case of homogeneous
and non-homogeneous mixtures. The number of peculiar cases is
here extraordinary, owing to the fact that in both components the
corresponding conditions may follow each other in different manners

( 103 )

and the transition-temperatures may lie at different distances from
each other.

The method given enables us to deduct the phenomena in each
particular case and promises to be an important expedient in solving
the complicated phenomena that appear in the congealing and the
consequent changes in alloys.

Physiology. — On the influence of salt-solutions on the volume
of animal cells, being at the same time a contribution to our
knowledge of their structure. By Dr. H. J. HAMBURGER.

My investigations concerning the connection which exists between
the power of salts to attract water and their power to extract
colouring matter out of the red blood-corpuscles, led to the hypothesis
that for every salt a solution might be found in which the cor-
puscles would retain the same volume that they have in their own
serum. This supposition proved to be correct and it could moreover
be shown that those solutions which left the volume unchanged
represented a precisely equal hygroscopic power.

The experiments referred to, made in 1884 and suggested by the
classic analysis of the phenomena of turgescence in plant-cells by
our countryman, Huco pe Vries, have been to me as well as to
others the point of departure for a series of researches which among
physiologists and pathologists have awakened a constantly increasing
interest in the new doctrine of osmotic pressure. To this result the
theory of electrolytic dissociation of vaN ’t Horr and ARRHENIUS
has of late contributed. And in combination with each other these
two theories are on the way to clear up many a dark point in the
domain of physiology. One might have supposed that in the
course of 14 years other animal cells would have been inves-
tigated in the same way as have been the red blood-corpuscles.
This, however, has not been the case. For various purposes in-
deed the hygroscopic power of fluids, such as blood, lymph, serous
fluid, milk, has been studied; to the serous and mucous mem-
branes, indeed, fluids of different osmotic pressure have been offered
for absorption, in order to deduce from the change in this osmotic
pressure data for the knowledge of the resorption process; but
the influence of salt solutions on any other than the red blood-cells
has not yet been investigated. And yet for more than one reason
this is to be desired. In the first place in order to control the
inferences that have been drawn from the observations made with red

blood-corpuscles, and to decide many differences of opinion which
g*

( 104 )

exist on them; but also with a view to the questions for the solu-
tion of which the red blood-cells are not serviceable, because they
are known to lose their colouring matter very easily.

For years then it had been my desire to extend my researches in
the above direction, yet, extremely simple as my plan was in prin-
ciple, I was checked by the difficulty of obtaining a sufficient quantity
of isolated cells, which, with the means, then at my disposal, would
have enabled me to determine their volume.

This difficulty has now been overcome by the use I can make of
little tubes which I constructed last year to compare the volume of
bacteria in two cultures, and which admit of experiments with
small quantities '). We have, as yet, investigated four sorts of cells,
white and red corpuscles of different animals, spermatozoa of the
frog and the intestinal epithelium of the horse and the pig.

We shall treat of the intestinal epithelium on some future occasion.

Phenomena of a peculiar nature, which have manifested themselves
while studying it, make a further research necessary.

White blood-corpuscles.

These were obtained by leaving horse-blood, in a closed bottle
defibrinated with pieces of glass. The red corpuscles then for
the greater part precipitate, while the white all remain suspended
in the fluid above. Their number is comparatively small. Now in
order to obtain a fluid abounding in white blood-corpuseles, 1/5 L,
of turbid fluid was centrifugalized, 470 ec. of the clear serum
eliminated and the precipitate equally divided in the remaining
fluid. Of this fluid about !/, c.c. was measured off and placed in
test-tubes with 15 c.c. of different salt solutions. After repeated
mixing, and after half an hour or a little longer 5 ce. or more
were placed in the above mentioned little funnel-shaped tubes and
centrifugalized till (the rapidity of revolution of the centrifuge not
varying) the level remained constant for fifteen minutes.

Fluids. Volumes of precipitate.
ennn eenn eener
Na Cl solution 0.7 pCt. 46.25
Serum (isotonical with NaCl 0.9 pCt.) 41
Na Cl solution 1 pCt. 39.25
Na Cl solution 1.5 pCt. 33.5

1) Report of the meeting of the Royal Academy of Sciences, April 21st 1897,

( 105 )

A regular diminution of volume is seen.

Meanwhile among the whiteblood-corpuscles there were a number
of red ones. In the case under consideration 569 red ones were
counted to 109 white, and the question now was whether, and to
what extent the red ones must be considered reponsible for this
result. In order to get an idea of the share that each had contri-
buted to the volume, let us for a moment suppose that the diameter
of the white corpuscles amounts to double that of the red ones, and
moreover that the latter are not discs but globules. In this case the
red corpuscles would represent a volume of 569, and the white 872.
This calculation tells undoubtedly to the advantage of the red cor-
puscles, seeing that the diameter of the white is more than double
that of the red, while the shape of the latter is a dinted dise and
not a sphere.

In order now to inquire what share in the contraction and
expansion must be assigned to the influence of the red corpuscles,
the above experiment was made with red corpuscles only. If we
arrange the figures obtained, and the percentage alterations in volume
proceeding from them, in a table, which at the same time contains
the results just obtained, a striking agreement is evident.

Percentage volume-increase,

7 |
Volume of | Volume of | calculated with respect to

| Precipitate | we pnt | the volume in serum.
Fluids. hea together. |

See former Red blood Mixture of

voile table. | corpuscles. {red and white.
| |
Na Cl-sol. of 0.7°/,. 43.5 46.25 + 18°/, +- 12.8°/,
Serum (isot. with Na Cl. 0.9°/,.) 38.5 41 — —
Na Cl-sol. 1°/,. | 36.75 39.25 5 4 sep 5 | = 4. 24/,
|
Na Cl-sol. 1.5°/. 31.75 33.5 — 17.5°/, | — 18.39,

From this table it appears that the alterations in volume of red
corpuscles are exactly similar to those exhibited by the mixture of
white and red, whence it follows that the red and white blood cells,
caeteris paribus, expand and contract in an equal measure.

This remarkable result, which, as will presently appear, was
confirmed by many other experiments, was made the point of de-
parture for the investigation of which an account now follows.

Though, as may appear from the introduction, it was originally
my intention to study the influence of the solution of different salts
on the volume of cells, I have hitherto occupied myself only with

( 106 )

Na Cl solutions and mixtures of serum and water, considermg them
quite sufficient to answer the question which at the outset inte-
rested me most. Whence arises the equality of expansion and con-
traction of red and white corpuscles? A question which immediately
led to another, viz., why are the cells expanded by hypisotonie and
contracted by hyperisotonic solutions ?

Now we may with Scuwarz consider the contents of the cell
(exclusive of the nucleus) as a homogeneous mass, or with REMAK,
Kuprrer, FLemMime, Birscuni and many others, as aprotoplasmic
mass intermingled with fluid. What must happen then in the former
case, if in a NaCl solution of 1.8 °/, we immerse a cell of which the
homogeneous contents corespond in hygroscopic power to a Na Cl
solution of 0.9 °/,? This mass will then contract to one half. If it
is placed in a NaCl-solution of 14 °/, the expansion must amount to
1.5—0.9

0.9

in a NaCl-solution of 0.7°/) the expansion must then amount to
a X 100 = 22°/,. What appeared though? That the con-
traction as well as the expansion amounts to much less, viz., respec-
tively 17.5 and 13 °/, (ef. former table). This leads us to the conclusion
that in the red and white corpuscles there must be a substance,
which has either no part in the hygroscopic power, or a smaller
one than the other ingredient, and the question then presents itself
to us, how are we to suppose these substances to be arranged.

Of the different hypotheses which in this respect have been formu-
lated for cells in general, there is only one which has appeared satis-
factory to us. And this is the hypothesis of Bürscnur }).

According to this hypothesis the cells consist of a protoplasmic
net the closed meshes of which lie close to each other, and
the contents of which is a fluid. From the fact that the percen-
tage of the contents of the cells in hygroscopic matter, notwith-
standing that salt-solutions of different degrees of strength are
brought in contact with it, remains the same, we may suppose that
the protoplasmic net is not permeable to salts, but only to water *).
We may further suppose that only the fluid contents represent the
hygroscopic power of the cell.

X 100 = 66°. If on the other hand, we place it

1) Cf. Biirscutr, Untersuchungen über mikroskopische Schäume und das Protoplasma.

*) If the blood-corpuscles are considered permeable to salts, a change in the
isotonic relations must then take place, for by this only is the immutability of the
water-attracting force of the contents of the meshes guaranteed. For what follows,
however, it is indifferent which of these two conjectures is correct. The one men-
tioned in the text is certainly the simplest.

a dende

eee,

( 107 )

Tt is thus only the fluid contents which produce the expansion and
contraction of the cell by hypisotonie and hyperisotonie solutions.

If this conjecture is correct, then in the amount of expansion and
contraction of the cells there must lie a measure for the compara-
tive volume of the two ingredients, and the result must then depend
to a great extent on the concentration of the salts employed.

Under this impression we began to effect a number of determi-
nations of the volumes of the network-substance in white blood
corpuscles.

The white corpuscles used for this purpose were almost entirely
freed from the red by simply leaving the fluid rich in leucocytes
which was obtained by the method above described at rest for an
hour. The red corpuscles were then precipitated and in the fluid
above were only the white.

Let us discuss the first series of experiments somewhat more in
detail. Equal quantities of white corpuscles are mixed with Na Cl
solutions of 0.7, 0.94 (isotonic with the serum) and 1.5°/9. After
centrifugalizing equal quantities of these solutions, the volume of
the white corpuscles respectively amounts to 41, 35.5 and 29.5.
In order to calculate the volume of the protoplasmatic net by means
of these two last figures, we may reason as follows : Suppose p to
be the volume of the protoplasm of the network substance, then the
volumes of intra-cellular fluid amounts respectively to (35.5—p)
(29.5—p). Seeing we must take for granted that the percentage of
hygroscopic matter in the intra-cellular fluid remains the same, the
following equation must hold.

(35.5—p) 0.94 = (29.5—>p) 1.5
p= 194

From the following figures obtained with the NaCl solutions 0.7

and 1.5°/, the equation results
(41—p) 0.7 = (29.5—p) 1.5
DE

It appears, therefore, that the quantity of protoplasmic network
in both cases is nearly equal.

The mean is 19.45.

If we now take into consideration that the total volume of the
white blood-corpuscles in the solution of 0.94 which is isotonic with
serum, amounted to 35.5, we then find a percentage of

eee a 26 100 645s
taken up by the protoplasmic network.

( 108 )

The network-volume of the same white blood corpuscles was
further investigated with the aid of mixtures of serum and different
quantities of water.

Volume of white corpuscles

(1) in undilated serum 35.15
(2) in serum mixed with 20°/, water 39

Bema dein bt yo 40e EE
4 ” ” ” ” 50 ” ” 43.5

From (1 and 2) we obtain the equation :
120 (35.75—p) = 100 (39—p)
p=19.5
From (1) and (3) we obtain the equation:
140 (35.15 —p) = 100 (41.75 —p)
p= 20.6
From (1) and (4) we obtain the equation.
150 (35.75 —p) = 100 (43.5—p)
p = 20.3
It will be seen, that the figures which are found for p agree

19.5 + 20.6 + 20.3

very well with each other. The mean is 3

= 20.04,

‘ 20.04
KR Re
i. e. caleultated at 85.15 ae ae

responds well with that obtained by the NaCl solutions.

The observation might be made, that the numbers 54.5 or 56
cannot give the exact volume of the protoplasmic network as by cen-
trifugalizing only the precipitate and not the real volume of blood-
corpuscles is determined. I have, however, convinced myself by
experiments, that this has no perceptible influence on the percentage
of the network substance.

This may be clearly observed inter alia when by means of acce-
lerated velocity of the centrifugal machine we compress the precipitate
a little more.

The percentage of p is hardly or not at all changed by it. It
must, moreover be borne in mind, (I) that for one experiment all
fluids are centrifugalized at the same time and (II) that the figures
of the last experiment, 39, 41, 75, and 43.5 are a little greater
than corresponds with the real volume of the cells, because there is
still fluid among the cells, the same is the case with the number
35.75 with respect to which the percentage has been calculated.

A second observation may be made viz, that in the calculation we

X 100 = 56°/,, a number that cor-

( 109)

have overlooked the influence of the volume of solid substances
dissolved in the intra-cellular fluid. The figure that has been obtained
for the volume of the protoplasmic net might perhaps by this have
to be a little modified.

It appears difficult to me to state exactly what degree of accuracy
has been attained by our determinations. For our object, however,
the absolute values are of but little moment. Meanwhile, as will be
observed, the correspondence between the ciphers obtained is striking:
I should be surprised if they deviated much from the exact number.

We now subjoin a table, comprising some of the experiments
just described, and in which the percentage volume of p is calculated
in the way that has been indicated.

( 110

)

Mle il. diit IV. V.
Volume obser} Volume of the proto- | Mean vol- Mean percentage
P ume of the) of protoplas-
3 ved of white : :
Fluids. bland plasmic network protoplas- | mic network
corpuscles mic in the
P ; (7) network ‚white corpuscles.
calculated from
a. NaCl sol, 0.7°/, 49.25
b. ry 0.98°/o 42.75 23.9 aande )
24.1 56.3°/,
ce ” meel blik 35.75 24.3 bue )
a. NaCl sol. 0.5°/, 40.25 (19-4) ane (63.6 °/,)
b. ” PE Wiis 35 16.7 bud )
16.55 54.3 °/,
” n 0.94°/, 30.5 16.4 cud j
d. 7 " 14955 25.25
a. NaClsol. 0.25°/, 30.5 20.46 and (20.46) (ss Of)
b. ” „ 0.5°/, 29.25 (15.8) bud (15-8) (67-9 Of)
c. 7 O7; 26.50 12.4 ene |)
12.5 53.7°/,
Gh cee 7 OCI: 23.25 12.6 ace al
Ch ” ze U 19
a. NaCl sol. 0.25°/, 37.75 (18.72 and (18-72) (78 9/0)
b, ” n 0.5°% 30.25 (16.18) bow d (26 18) (63.2 °/,)
c " i EUS 27.25 13.2 ene |)
13.35 55.6%,
d. „mn 0.9%, 24. 13.5 d me }
e " nw 1.52 19.75
4, serum. 34.75
b. serum + 20°}, water 37.75 19.75 auh
c. serum + 40°/, water 40.75 19.70 ane 19.73 56.7 Uo
d. serum + 50°/, water 49.25 19.74 and
a, serum. 33
b. serum + 20°/, water 36 18 aunt |
c. serum + 40°/, water 39 18 an ec 17.83 54 °/,
d. serum + 50°/, water 40.75 17.5 and |

(111 )

_ From this table it follows:

1. That the volume of the net-work varies between 56.7 and
53.7 pCt. of the whole cell-volume.

2. That, where a solution of NaCl of 0.5 pCt. is employed, a
solution which with horseblood causes colouring-matter to issue from
a portion of the red corpuscles, the figure for the net-work is found
to be greater than where solutions of 0.7 and 1.5 are applied.

What applies to NaCl 0.5, appears to be in a still greater measure
the case, when a NaCl-solution of 0.25 pCt. is employed. In the
table the numbers bearing on this are indicated in small ciphers.

This result may be thus explained:

By a very weak salt solution the volume of the intra-cellular
fluid increases so considerably that, in consequence of the great
tension, the protoplasm becomes permeable and allows the contents
to pass through it. Consequently the expansion cannot be so conside-
rable as according to the calculation a NaCl-solution of 0.5 or 0.25
would have to produce, and the equation must, therefore, yield too
great a p. According to this view of the matter there is a perfect
agreement with what we observe in the red corpuscles; there the
issue of the fluid contents of the cell is rendered visible by means
of free haemoglobin.

As to the way in which protoplasma and intra-cellular fluid are
arranged in the white corpuscles, we do not learn much from the
experiments communicated. We may indeed explain the phenomena
by considering the cell to consist of a protoplasmic net of closed
meshes; but we may also imagine it to be built up of a closed husk,
within which is a fluid divided among protoplasmic strands, which
do not form closed meshes. In the latter case, however, we must
take it for granted that the external husk is only permeable to water
(cf. note on page 106).

In order now to make a choice between the two hypotheses, I
measured off two equal quantities of white corpuscles, and for an
hour vigorously shook one quantity with a large (number) of sharp
pieces of glass. By this means a considerable quantity of white
corpuscles were bruised and torn.

When now equal portions of the bruised and not-bruised white
corpuscles were treated with different salt solutions, the contraction
and expansion appeared for both sorts caeteris paribus almost
the same.

The result obtained, as far as I can see, is not to be otherwise
explained than by taking it for granted, that every average part of
the white corpuscle, again of itself, consists of a closed net of meshes.

( 112 )

From simple histological experiments into which I do not propose
to enter now, we learn the same.

Red Corpuscles.

The same experiments that we made with white corpuscles (omitting
of course the bruising experiment) we also made with the red.
It may suffice to give again some of these experiments in a table.

HORSEBLOOD.
i LE III. IV. Vi.
Volume obser- Volume of the | Mean volu- |Mean percentage
me of the | of protoplas-
Fluids. ved of red protoplasmic protoplas- | mie network
mic in red
corpuscles. network. network. corpuscles.
(ee Se en eene eenn
calculated from
a. NaCl sol. 0.7°/, 41.75 aande UO )
19.8 55°/,
bau 610-9401 36 Ode oo |
IC: y n 1.5/5
a. NaCl sol. 0.7°/, 43.5 ane 20.6 )
19.98 53.3°/,
Deen on OR 37.5 bone 19.9 ||
Os i ip Wake 31
a. NaClsol. 0.7°/, 42 ame LO )
20.15 54,5°/,
b. / A Ohe 37 b me 20.6 \
Cc. I ” IADS 30.25
a. serum, 34.5 anv 18.25
b. serum + 20°/, water. 37.75 ane 18.8 18.51 53.6°/,
ce on nw 40% vw 40.75 and 18.5
Gs. wit WBO 42.50
a, serum, 35.75 a nb 19,5 |
dv. serum + 20°/, water. 39 auc 20.1 19.93 55°,
e wv nw40% w 42 aud 20.24 |
th he rp SUIS) 7 43.5
a, serum. 36 amb 19.75 |
dv. serum + 20°/, water. 39.25 auc 19.75 |; 19.83 55°,
Cc. u u 40°/, u 49.5 and 20 |
d. u uv 50°/o u 44,

(113)

Here too it appears, that in the different experiments the per-
centage relation between protoplasm and intracellular fluid shows
but little deviation, and corresponds in a most striking manner with
what was found in the white corpuscles of the same animal.

We were now interested in ascertaining what results the blood-
corpuscles of a rabbit would yield.

We took some blood from the ear and defibrinated it. After care-
fully filtering off the fibrine, it was mixed with salt solutions in
the same way as the corpuscles of the horse. In the following table
are found some of the results obtained The number of white cor-
puseles after defibrinating is, however, so small, that we are almost
justified in considering the result as proceeding exclusively from the
red corpuscles.

RABBIT-BLOOD.

— SNN
Volume of Volume of the _ {Mean volu- | Mean percentage
me of the of the
Fluids. corpuscles protoplasmic protoplas- protoplas-
mic mic network
observed. network. network. | in corpuscles.
(calculated from
a. NaClsol. 0.7°/, 43 aande 20.2
b. u Ld 0.85°/ 5 | \ /
(isot. with blood serum). a eA Mosk ae Dis
c. NaCl sol. 1.2°/, Ba bud 19.3
d. DG dE 30.5
a. NaCl sol. 0.7°/, 44.25 ame 19.6
EO Ue 40 ge 4719.92) 1905 48.70
(isot. with blood serum). Testi’ ? : To
c. NaClsol. 1.2°/, 34. br d 19.1
d. aay MESO fe 31.25
a. NaClsol. 0.7°/, 40.5 AG Wtf
vu «» (.86°/ ' P
(isot. with blood serum). 36-25 and 18 17,98 a ele
NaCl sol. 1.2°/, 31 bud 18.1
d. (Dr Naf 28.5

These experiments indicate a smaller volume for the protoplas-
matie network than was found in the horse.

In the third place we communicate a few determinations with
the blood-corpuscles of the frog.

( 114)

FROG-BLOOD.

Volanesbe Volume of the Mean volu- (Mean percentage
Ls | rediblegde i me of the | of protoplas-
Fluids. |_corpuscles protoplasmic protoplas- | mic network
observed. me | in red
network. network. corpuscles.
a. Na Cl sol. 0.35°/, 44,5 ade a 28.7
p Wake 38 bv d 29.25 28.78 15.7°o
c. 1d WSs 36.75 are 28.9
gris Bree 34.5
a. Na Cl sol. 0.35°/, 41.75 and 27.9
b. gp NORG ES 36 bad 27.8 27.5 use
SP OOR 34.25 ae 26.8
d SZ 32.75
a. NaCl sol. 0.35°/, 45.5 ane 27 |
b. ie An OK 37.5 bud 27.5 27 72°/,
oh PT ORF 36 AN 26.5 |
de sf ne IY, 33.5
a. NaCl sol. 0.35°/, 40.5 and 25.14
Di es 0:69), 34.25 beed 24.83 25.16 73.49fo
gn nk ve COME 33 au 25.5
Tito be oS 30.5

If, on one hand, we compare the protoplasmic network in the horse
and rabbit with that of the frog on the other, we are struck by
the fact, that in the frog the volume of network is so considerable.

On further consideration, however, this point agrees with what
we observed in 1886. It then appeared, that while we may dilute
horse-blood serum with from 60 to 70°/ of water before colouring-
matter issues, frog-blood serum will bear 2009/, and more of water.
This would not be possible, if there was as much intracellular fluid in
these blood corpuscles as in those of the horse’s, for the expansion
would have then become much too strong.

Spermatozou of the Frog.

In conclusion I will describe a few experiments, which served

a

(115 )

provisionally to ascertain whether cells, the nucleus of which con-
stitutes the main mass, would conduct themselves like those we had
examined. An excellent subject happened to present itself viz. imma-
ture spermatozoa of the frog; only a few stirred.

Valeo: Volume of the Mean volu- a ee
: (sesso oer thel 5 me of the, of protoplas-
Fluids. sad blood. | protoplasmic | protoplas- | mic network
oe network. ak papas,
a. NaCl sol. 0.35°/, 69 aand d 48.2
a ve LOK OCTS 61 bud 47.25 48.13 78.8°/,
Oe WEEE 59 amc 49
Bean eg 55.5
a. NaCl sol. 0.35°/, 70 ard 42.3
n__n 0.6% 58.5 | bad | 429 || 49.83 73.2°/o
a Oo OGS 57 anc 44
is AYE 52
a. Na Cl sol. 0.35°/, 62 and 44.3
i wi 056 55.5 bud 43 44.1 79.4°/,
0 # 0.7/6 53.5 anc 45
Bel 50.5
a. NaCl sol. 0.35°/, 72 avd| 44.3 |
b. » # 0.6°/, 60.5 bad 44.2 | 44.5 73.5°/,
Gm of Leer 58.5 Geet 45 |
(5 are ne 54 |

We see therefore, that the spermatozoa give nearly the same
cipher as the blood-corpuscles of the frog.

In how far a correspondence will prove to exist between the
quantative proportion of protoplasma and intracellular fluid in different
cells of one and the same individual, we shall have to learn from
further researches.

CONCLUSION.

1. Besides the red blood corpuscles, the white and the sperma tozoa

(116 )

also exhibit contraction by hyperisotonic and expansion by hypiso-
tonic solutions.

2. The observation, that the amount of this expansion and con-
traction is much less than it would be if the cells in question
consisted of a homogeneous mass, leads to the conclusion, that the
cells must consist of two substances, one representing the hygros-
copie power of the cell, the other, which has no share, or only a
slight one in the hygroscopic power.

3. By the quantitative determination of the expansion and
contraction which the cells undergo under the influence of NaCl-
solutions of different concentrations, or of serum, mixed with dif-
ferent quantities of water we have a means of fixing the percentage
proportion between the two constituents of the cells.

From the experiments hitherto made it has appeared, that in the
white blood corpuscles of the horse the volume of protoplasm-sub-

stance amounts to 56.7°/>—53.1%/,
For the red corpuscles of the horse 55 0/,—53 P,
se pre a of the rabbit 51 0/,—48.70/,
A ee 2 of the frog 16.4°/,—12 J,
+» » Spermatozoa of the frog 79.4°/,—73.2°/)

If we injure the white bloodeorpuseles by mechanical means,
the expansion and contraction under the influence of salt solutions
appears to be almost unchanged. The results obtained are with
difficulty otherwise to be explained but by supposing, that these
cells consist of a network of protoplasm, the closed meshes of which
contain a fluid that exclusively represents the hygroscopic power of
the cell.

Consequently Bürscurr’s theory of the ,Wabenstructur” of the
cells receives, at least for the leucocytes, from physiological experi-
ments a powerful support, which seems not to be superfluous in
face of the objections of an histiological nature which have been
urged against the arguments in its favour.

(October 14th 1898).

Royal Academy of Sciences. Amsterdam.

PROCEEDINGS OF THE MEETING

of Saturday October 29th 1898,

—DECo

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 29 October 1898 Dl. VII).

CONTENTS: Report on the 2nd International Catalogue Conference. By Prof. D. J. Korrewec,
p- 117. — ,,Attention and respiration”. By Prof. C. WiNkrer, p. 121. (With 5 plates.) —
yA simple deduction of the characteristic equation for substances with extended and
composite molecules”. By Prof. J. D. van DER Waars, p. 138. — ,,The rate of sub-
stitution of a nitrogroup by an oxalkyl”. By Prof. C. A. Lopry pre Bruyn and Dr.
A. STEGER, p. 144. — „On some anomalies in the system of MexpereJerr”. By Prof.
Tu. H. Benrens, p. 148. — On the action of methylie alcohol on the imides of bibasie
acids”. By Prof. S. HooGEWerRFF and Dr. W. A. van Dorp, p. 151. — ,,Description
of an open manometer of reduced height”. By Prof. H. KAMERLINGH ONNES, p, 154.—
„Cup-shaped red bloodcorpuscles (Chromoeraters)”. By Dr. M. C. Dexuvuyzen (Com-
municated by Dr. P. P. C. Hoek), p. 154. — „Some remarks upon the 14-monthly
motion of the Pole of the Earth and upon the length of its period”. By Dr. E. F. van
DE SANDE BAKHUYZEN (Communicated by Prof. H. G. van DE SANDE BAKHUYZEN),
p. 157. — „The influence of pressure on the critical temperature of complete mixture”,
By Mr. N. J. van per Lee (Communicated by Prof. J. D. van per Waars), p. 158.

The following papers were read:

International Catalogue. — Prof. D. J. KorreweG reads the
following Report:

The interest, which many members of our Academy have shown
in the issue of the second International Catalogue Conference, held
in Londen from Oct. 11 to 13, as well as the circumstance that
our Academy has declared itself willing to contribute towards the
part, which the Netherlands are to take in the work, being well
executed (see the Proceedings of the ordinary meeting of Nov. 28
1896), have induced me here to give a short account of what has
been done since the holding of the first conference, in July 1896.

9
Proceedings Royal Acad. Amsterdam, Vol. IL,

( 118 )

To some extent this account is to be considered as a sequel to
my communication, published in the Proceedings of our meeting of
Sept. 26 1896. As I did then I shall now again confine myself
as much as possible to those points that may be considered to be of
more lasting interest to science.

The former conference had addressed itself to the Royal Society
requesting that this Society might appoint a committee for studying
and reporting all questions regarding the Catalogue that still remai-
ned unsettled.

In compliance with this request a copious report, dated March
30 1898, was sent to the different governments and to the dele-
gates of the former conference. These last were requested to state
their personal remarks in an inofficial manner.

This report, which we will call the Report of the Royal Society-
Committee, contained in the first place further proposals regarding
the international organization to be introduced. One of these con-
cerned the instituting of an International Council and of Internatio-
nal Conventions, besides the Central Bureau in London and the
National or, as they are now called, Regional Bureaux, the esta-
blishment of which had already been resolved upon by the first
conference and which are to do the regular work of composing the
Catalogue.

The International Council, formed by delegates of the Regional
Bureaux, one for each, was to meet at least once in every three
years in London and was to constitute the governing body of
the Catalogue. It has however to submit to the decisions of the
International Conventions, which shall be held in 1905, in 1910
and after that every tenth year, the members being appointed by
the governments participating in the organization.

A further proposal tended to institute for each science an Inter-
national Committee of Referees, consisting of five members, appoin-
ted by the International Council. It is to this Committee that the
director of the Central Bureau shall have to apply on the arising
of difficulties in the application of the classification-schedule, drawn
up for that particular science. Changes of and additions to the
schedule, which the Central Bureau deems desirable, are submitted
to its approval, while it has the right independently to introduce
such changes and additions.

In the second place the costs of the enterprise were estimated in
this report.

This was done on three different suppositions, firstly, that only

(119)

a Bock-Catalcgue shall be issued; secondly, that moreover a primary
Slip-Catalogue shall be edited, with this restriction however that
but one slip has to be issued for each publication (book, paper ete);
thirdly, that a secondary Slip-Catalogue shall be composed in which
each paper has to be represented by one slip for every subject treated
therein, so far as these subjects give rise to different entries in
the Book-Catalogue; every effort being made however to prevent
an excessive extension of the number of slips pertaining to one
paper.

As a result of the committee’s estimates and calculations it ap-
peared that on the fist supposition the receipts probably will cover
the expenses, if not at once at least after a certain period; that
this may be the case even on the second supposition; but that it
can hardly be expected on the third supposition.

In the third place the report of the Royal Society-Committee
contained classification-schedules, worked out for most of the sciences
that have to be treated in the Catalogue.

In these schedules, the construction of which differs considerably
for the different sciences, according to the particular demands of
each science, ample room has been left everywhere for changes and
extensions, that may be desirable in future. The registration-symbols
and numbers only play a subordinate part. They are technically
indispensable to the work of the Central Bureau and for arranging
the slips of the Slip-Catalogue. Acquaintance therewith however
may be considered as wholly or to a great extent superfluous to him
who uses the Catalogue.

When too many entries should come under the same heading, a
further sub-division may be attained by the introduction of ,signi-
ficant words” which may afterwards, if desirable, be transformed
into new headings. In this way a natural growth of the classifi-
cation will be arrived at, keeping up with the development of science.

Taking into account this in my opinion very suitable construction
of the book-catalogue and the circumstance, that the instituting of
Committees of Referees seems to me a sufficient guarantee that the
needs and demands of the real scientific workers in the different
sciences will be decisive, I complied with the above-mentioned
request of the Royal Society-Committee by stating that my personal
opinion was in favour of the project in general. At the same time
I subjected the mathematical schedule to a closer examination and
added some remarks on the classification-schedules of more general

tendency.
Q*

( 120 )

In the second conference now held, this Report of the Royal Society-
Committee was made the base of the deliberations, in order to come
as much as possible to a decision on the subjects contained therein.

Amongst the conclusions so arrived at I have to mention in the
first place those concerning the international organization.

The establishment of an International Council and of International
Conventions, constituted as proposed by the Royal Society-Committee,
that is to say as described above, was accepted by the conference.

The instituting of the International Committees of Referees on
the other hand was referred for consideration to the International
Council when constituted.

In the second place resolutions were passed on the arrangement
of the catalogue.

Notwithstanding the greater costs that will be incurred by it,
the maintaining of the slip catalogue, besides the book-catalogue, was
urgently insisted on from many sides. The resolution taken by the
former conference of editing the catalogue in both forms was unanimously
confirmed. It was however deemed necessary to make the finantial
prospects of the enterprise, which cannot at present be rightly
estimated, decide on the question whether only the primary slip-
catalogue or also the secondary one will have to be issued.

This last course was thought very desirable in itself, as it offers
the only means of collecting and keeping together the complete slips
for each particular branch of science. The hope was expressed that
a suitable arrangement of the secundary slips might greatly reduce
the large difference of cost which, according to the report of the
Royal Society-Committee, would exist between the two forms of the
slip-catalogue.

As to the classification-schedules in the third place, it was resolved
that separate schedules shall be composed for the following sciences:

Mathematies; Astronomy; Meteorology ; Physics; Cristallography ;
Chemistry; Mineralogy; Geology (including Petrology); Geography
(only the Mathematical and the Physical part); Paleontology; Ana-
tomy; Zoology; Botany; Physiology (including Pharmacology and
Experimental Pathology); Bacteriology; Psychology; Anthropology.

For the rest the assembly confined itself to draw up some very
general rules for the construction of these schedules, the further
development of which is left toa provisional International Committee,
which probably shall appoint experts for every branch to assist in
the working out. In many cases certainly the provisional classification-
schedule, added to the Report of the Royal Society-Committee, may
serve as a base.

( 121 )

Appointed at first to judge of and to fix the classificaticn-schedules,

the Provisional International Committee has at the same time been
invested with the extensive power of taking resolutions on different
questions left undecided by the conference, regarding the construction
of the catalogue. This committee will have to frame a report, not
later than July 31st 1899; which will be incorporated in the deci-
sions of the conference.
- It cannot be denied that the task of this International Committee
is a heavy one. In order to render it somewhat easier and to give
to all opinions an opportunity of making themselves heard, the de-
legates have been charged with the formation of local committees,
each in his own country, to consider the questions left undecided
and to report there on to the International Committee within six
months.

In my opinion these committees will indeed be able to do useful
work. For if it might appear that there was but little difference of
opinion on matters of importance, the decisions of the International
Committee would certainly be facilitated. The clear exposition of the
different questions in the report of the Royal Society-Committee raises
a well. founded expectation that such concordances will take place.

I venture to express the hope, that the Committee of our Academy,
which has already formerly occupied itself with the International
Catalogue, will by its cooperation enable me to fulfil this part of
my charge.

Conformable to the above the President promises again to con-
Pp 8

vocate the Committee which has on former occasions given advice

on the International Catalogue.

Physiology. — Prof.C. WINKLER on: „Attention and respiration”.
S 1. Introduction.

The present physiology of the cortex of the brain justly attaches
great importance to the idea of association. Since it has been proved
that different functions may be ascribed to different parts of the
cortex of the brain, it has become necessary on anatomical grounds
to suppose connections between those parts, moreover to assume on
clinical grounds, that in psychical processes these connections are used.

( 122 )

The physiology of the cortex of the brain is compelled to ac-
cept the theory of so-called parallelism between physiological and

psychical processes — for without this theory all physiology as a
foundation of psychology is impossible — it is therefore required

that a special physiological modification in the central nervous
system correspond to every special psychical process. At once
however, a difficulty arises. j

Through self-observation, psychology knows a succession of diffe-
rent conscious states, but no more. It teaches nothing concerning
the way, in which this succession occurs. Physiology, therefore, has
to explain the way, in which this succession takes place.

For this it uses the idea of association. It assumes that a phy-
siological modification in one group of cells can propagate along
fibres to another and bring about a new modification there. If it
is true, that in general only modifications in cells may be accom-
panied by conscious parallel processes, and not the processes pro-
pagating in the fibres, the fact that self-observation knows succession
and no more, is not strange. But the idea of association has a wider
application.

It is its task to point out what special phsysiological modification
corresponds to every special conscious condition.

The characteristies of the former may be determined in different
ways, either by the place occupied by the cell-group which is modi-
fied, or by the combination of two or more co-acting cell groups.
By means of association this combination is possible in numberless
variations.

To physiology taken in this sense, which aims at combining a
succession of conscious conditions with an association of physiological
parallel processes, the name of association-physiology has been given.
It is of course, rigorously a science of matter. It does not suffer itself
to be led astray in its views by the existence of conscious parallel
series. It states their existence, but keeps silent about their nature.
It treats conscious life as the life of an automaton, who perceives
scarcely anything of the processes going on in him, but who reacts
to some, by far the fewest in number, with the corresponding con-
scious parallel series.

At all times a difficulty has presented itself to the association-
physiology. It cannot be contradicted that self-observation, in our wan-
ting to make movements, in our being attentive and in many
other conscious processes gives the impression, as if we were active
agents in the conscious processes. Waence this feeling of boing active ?
How is it to be explained that self-observation misleads the subject

( 193 )

about the part it plays, though to the association-physiology the subject
appears as a passive, successively perceiving and imaginating subject?

A better knowledge of the psychomotor area of the cortex has
solved this question fairly satisfactorily. A number of clinical ob-
servations have shown that perception and remembrance of a once
performed movement of the muscles as well as the movement itself,
depend upon the psychomotor area remaining intact.

A number of physiological experiments SESE proved, that every
modification of a definite centre in this part of the brain — e.g.
one caused by an electric current, — flows to a special group of muscles
and brings about a special Data of movements.

If the supposition is admitted that the modification brought about
in the cortex of the brain is no other than the one originating
under physiological conditions, the latter, whose conscious parallel
is known to our self-observation as remembrance of the same com-
bination of muscular contraction which is to be performed, will give
rise to the error of the subject. The subject sees that on the remem-
brance of such a combination of movements, the movements them-
selves invariably follow and concludes that the former causes the latter.

The physiological modification, however, remains the cause of the
muscular’ contraction. Its conscious porate series, unexplained,
perhaps unexplainable, does nothing. The subject, as long as it is
taught by self-observation only, fancies that it is active, that it
possesses a feeling of effort.

When we speak of a will to move, we mean the remembrance
of a movement of the muscles, which is to be performed, whose
physiological parallel series brings about this same movement, while
the subject fancies that the remembrance is the cause.

All remembrances of movements of the muscles have this cha-
racter of activity in common and it is also found in many com-
pound psychical processes.

When many impressions from sources of light bring about visual
perceptions, there is generally but one which we retain, or as
WILHELM Wunpt expresses it, of which we have the apperception,
compared with the many sensations of which we have the perception.
We direct our attention to that one actively, as it seems to us. It
has a chance of being distinctly remembered, while the others pass
by unnoticed, are forgotten.

Here too, a feeling of being active. If we did not possess this
gift of apperception, if we could not, even in appearance, detain an
image actively, our thinking would be a whirl of successive images
(vecollections), as may perhaps occur in the brain of a maniac,

( 124 )

Direction of our thoughts in one sense, would be impossible.

It is the question if, in this exertion of the attention which ap-
pears so undoubtedly active to the self observation, the remembrance
of movements do not play a similar part, as was the case with
the will to move.

Can the subject actively, by the association of psychomotor cell-
groups with the modifications which are accompanied by conscious
remembrances in the observing regions of the cortex, be made to
fancy, that he fixes his remembrance?

To answer this question, it is necessary to know beforehand,
whether there are contractions of the muscles, and if so what con-
tractions, through which the man who fixes his attention is diffe-
rent from himself, as he is when he is not attentive.

For every modification of the psychomotor area must necessarily
flow to the periferie muscles. Even if it is not very strong, it must
bring about some modification in the corresponding group of muscles,
though it be only a beginning of contraction, an increase of the
tension of the muscles.

It will appear — and this I want to show in my exposition ---
that the attentive man distinguishes himself from one not attentive
in various respects by changes of a motor nature and that this
remarkable combination of movements may be reproduced from one
single point by electric stimulation of the cortex of the brain of
a dog.

SIL The variations in the volume of the brain during

psychical processes.

Before entering upon my real subject, I must dwell for a moment
on the modifications, which occur in the brain when at rest or
during conscious function. Many years ago Mosso has proved that
the volume of the brain varies continually. Sometimes people have
a defect im the bones of the cranium. Then the brain, covered
only by the membranes on that place, is fit for observation. If the
movements of the brain in half-sleep are registered — movements
visible even to the naked eye — it appears that the brain regu-
larly varies in volume according to the varying quantity of blood
it contains. We see then:

1°, Oscillations caused by pulsation, because every contraction
of the heart urges blood in the scull.

2°. Oscillations caused by respiration, because at every expira-
tion the blood can flow less easily from the brain.

(125 )

3°. Special oscillations of vo-
lume, which are longer and occur at
irregular periods; their cause is less
clear.

Oscillations of the volume of the brain
caused by pulsation and respiration
in half-sleep.

a. tracing of the volume of the brain.

4, tracing of the respiration. The des-
cending line is that of the inspiration.

c. tuning fork, 2 vibrations per second.

d. abscis.

(Laurens. June 18th 1898. Defect
of the scull caused by tuberculosis
of the os parietale.)

a4
v
Co)
=
7)
:
—
SD
N=
=i
Ss
=
x
2
o
ee)
le}
o
=
=
©
>
o
=a
re)
=|
=)
ui
o
°
=
on
>
a
i)
De
~~
PD
o
=
re)

Figure I is an example of the two
first mentioned, in fig. II and III the
last mentioned are very clear.

Whenever a sensation of sound
draws his attention, whenever the
person performs an intellectual pro-
cess, e.g. the solution of a sum, the
hyperaemia of the brain increases;
it decreases as soon as the exer-
tion stops. The long last-mentioned
oscillations continue for some time
afterwards, to be of much greater am-
plitude and of much longer duration
than before the exertion took place (see
fig. III). On the other hand the oscil-
lations caused by respiration become
less visible during the exertion; after
the exertion, however, they become
very distinct.

At last the oscillation caused by
pulsation changes too. It becomes
quicker. Moreover the long oscillations
are influenced to a certain degree by

|
2
|
=

g fork. 2 vibrations per second.

tracing of the volume of the brain.

tunin

a.

\

UUM

b.
(Grausz, Febr. 2nd. 1898, Defect of the scull in the os parietale after amputation of the Gangion Gasseri.)

(126 )

VAY AYA A v\ i NANA We

Oscillations in the volume of tl
ig. UI. 1. At 4 there is a knock at th

In all tracings a = that of the volume of the brain,

VAAT RENATA ú
4

74

ve brain duri
e door. Fig

4 = that of the respiration, ¢ = that of the tunin

1e intellectual labour. (By GRAUSZ. See
TIL 3. from 4—B a sum 12 x 4 = 48 is being solved.
Fig. UI, 3. from 4—B a sum 3 X 3 X 3 X 3 = Sl is being solved.

NEN

IL.)

g-fork with 2 vibrations p. sec.

(127 )

the oscillation caused by pulsation. At the moment when the curve
of such a long oscillation rises high above the abscis, the duration
of the oscillation of the pulse is long !). The increase of the volume
of the brain is preceded by acceleration of the pulse, as appears
from the graphical representation in fig. IV and from the figures
in the note.

Fig. IV. Graphical representation of the duration of the pulsations in seconds,
compared to the elevation of the tracing of the volume of the brain
above the abscis at every pulsation,

A. Height above the abscis of the volume of the brains in mM.
B. Duration of the pulse in seconds, - - - - - (Grauzs, see fig. IL.)

So it is clear, that in registering the pulsation of an artery, we
must find the same acceleration and retardation, which returns at long
irregular intervals and is not dependent on the respiration.

1) If we measure the height above the abscis of the long oscillation, when the
cylinder rotates quickly, and the duration of every oscillation of the pulse which
corresponds to that height, we find :

Height Duration of Height Duration of Height Duration of Height Duration of
above abscis pulsation above abscis pulsation above pulsation above _ pulsation
inmM. in seconds. inmM. in seconds. abscis. inseconds, abscis. in seconds.

5.00 0.62 4.25 0.65 1.75 0.675 4,50 0.65
5.25 0.62 3.50 0.725 2.50 0.65 4.50 0.625
5.00 0.62 3.00 0.75 3. 0.625 5.00 0.625
5.25 0.65 2.25 0.775 2.75 0.65 5.00 0.65
4.75 0.675 1.75 0.77 3.00 0.625 4.25 0.65
2.00 0.77 3.50 0.625 3.75 0.65
1.75 0.77 4.25 0.625 3.75 0.65

4.50 0.6 3,50 0.65etc,

( 128 )

If we take into consideration that even these single facts prove,
that every increase of the volume of the brain is attended by quick
pulsations, we shall find that a great deal may be learned from
the study of the pulsation of the artery, when the brain is at work.

This will be my first investigation.

§ 3. The influence of the exertion of attention on the heart,
the respiration and the extensor muscles of the hand
and the neck.

If we examine the influence which the exertion of attention has
on the heart and consider it separately for a moment, remarkable
facts will be found.

First a few words about the arrangement of such experiments.

As an example of a strong exertion of attention, which is very
slightly if at all attended by feelings of pain, the solving of a sum
is taken. The intellectual labour which is not attended by feelings
of pain or pleasure as suggested by the French authors is taken as
starting-point. The person used for the experiments is laid on a
couch. When he himself is perfectly calm and all around is quiet,
the pulse and the respiraton are registered. It has been arranged
that a number, generally of two figures, shall be called out to him
at a given moment, and that he shall continue to multiply this
number with itself, till a signal tells him to stop. He is to calculate
without using expedients. He works therefore with visual repre-
sentations, with remembrances of visual representations of numbers.
Generally the experiment lasts + half a minute.

The result, whether right or not right, is not pronounced by the
calculator; it must be dismissed at once from his mind. For many
experiments have proved, that the correctness or incorrectness of
the result is of no importance to my purpose; the rest or unrest
after the labour is. .

In such experiments the pulse and the respiration may be registered.

The person to be experimented on lies calmly, the cylinder rota-
tes quickly. Three levers note down. The pulsation of the arteria
radialis, the respiration and a tuningfork, which makes ten complete
vibrations a second, are registered with air-transport. The latter
enables us to read the time accurately down to the twentieth parts
of seconds, independent of the irregularities of the clockwork of the
cylinder. The tuning-fork is kept in continual vibration by an
electro-magnet.

( 129 )

In this quiet half-sleep we see what follows:

Towards the end of the respiration, which has become calm, the
pulsations are of a long duration. When the inspiration begins, they
are shorter. Towards the end of the inspiration and during the
beginning of the expiration the pulsations are at the quickest.

When the expiration has reached its maximum, they are very long;
the same thing begins over again just before or after the beginning
of the inspiration.

It is not necessary to dwell on the influence of the respira-
tion on the duration of the pulse and the pressure of the
blood, which is fairly well-known. It appears, however, also, that
the duration of the pulse varies at irregular intervals. Independently
of the respiration, which never loses its influence, the pulsations
become quicker or slower at irregular periods. These particularities
must not be overlooked.

When we have registered long enough to have a sufficiently trust-
worthy starting-curve (see fig. VII) in half-sleep, a number is called
out to the person. Even if he does not calculate, this call is sufficient
to bring about a slight, passing acceleration of the pulse. If howe-
ver, he calculates, the acceleration sets in at once. It increases,
according to the increase of exertion. When after half a minute
the signal „stop’ is given, the acceleration of the pulse continues
for some seconds. After that, a shorter or longer amphibole stadium
follows, in which there is neither acceleration nor retardation. Finally

AN vv Avi VVA

NS

Vig. V. Three series of pulsations one above the other.
In all three: a. is the pulsation of the arteria radialis.
hb. is the tuning-fork of 2 vibrations per second.
The lowest series, with 28 pulsations in 20 seconds before
The middle series, with 29 pulsations in 20 seconds during the sum,
The highest series, with 25 pulsations in 20 seconds after
(J. pe Vve, April 1898, Reduced to '/; of its size by means of photography.)

( 130 )

and sometimes for a very long time, a compensatory retardation
follows ') (see also fig V and VI).
All this occurs by oscillations. The influence of the respiration

1) Here is an example in figures: Experiment March 1898, J. pr Vrrrs, Pulse and
respiration noted down during quick rotation. Duration of the pulse in seconds.

0.875 0.625 0.775 0.875 0.925 0.9
0.8 0.625 0.825 0.8 0.9 0.9
ee 0.625 0.8 0.85 0.925 0.925
DE 0.625 0.85 0.875 0.95 0.975
0.8 0.65 9.875 0.875 0.925 0.975
0.85 0.695 0.825 0.8 0.9 0.9
0.85 0.625 0.825 0.875 0.9 0.925
heid 0.65 0.82 0.9 0.9 0.95
0.875 0.675 0.875 0.975 0.9 0.995
0.85 0.7 9.875 0.9 0.950 0.95
0.875 0.725 0.875 0.875 0.925 0.95
0.900 0.75 0.85 0.9 0.985 0.995
0.875 0.75 09 0.875 0.9 0.995
0.85 0.85 0.875 0.875 0.9 0.925
0.85 Hoz 0.825 0.85 0.875 0.9 0.925
0.85 0.85 0.85 0.925 0.9 0.9
0.75
0.85 0.85 0.875 0,995 0-925 0.95
0.875 ce 0.85 0.85 09.9 0.9 0.975
OS) ae 0.8 0.925 9.925 0.875 0.9
0.825 0.8 0.99 0.925 0.9 0.9
0.675
0.85 0.775 0.9 0.925 0.925
0.65 :
0.825 Ho cs 0.825 0.950 0.9
amo ores 055, PNO 0.925
Diss 0.95
Ln
0.925

="

Prof, C. WINKLER, „Attention and Respiration.

Fig. Vl. Graphical representation of the duration of the pulse in quiet halfsleep, during and
after the solving of a sum done by
As sum 7 to be multiplied by itself was chosen. The result 2261 was incorrect.

The duration of the pulsations has been given in hundredth of seconds. At every ssteric the in-
spiration begins

Besides the influence of the respiration other oscillations in the duration of the pulsations are
also perceptible, During the sum the duration of the pulse becomes shorter, this continues even for
some time alter the sum, afler that every pulsation lasts longer than before. The reaction is still
going on. (Dr Vre, March 1898).

Proceedings Royal Acad, Amsterdam. Vol. I.

Re
B een nnen eaten tlg ne nere Fer ven on hfd lee orale Bs Hoe orn de Be nen Remie) neen aval
TET
5
.
4
——
a
—
=
—s 5
en

Fig. VI. Three series of pulsations one above the other during quick rotation of
the cylinder.

In all three a — the pulsation of the arteria radialis, 4 — the respiration
e = the tuning-fork of 10 vibrations per seconds, d = the abscis.

The highest [ has been taken before —, the middle IL during —, the
lowest III after the sum.

The figures give the duration of the pulse in '/.) of seconds (half vibra-
tions of the tuning-fork). Those along the upper border give the duration
of pulsation. Those along the lower border give the division of the length
of a pulse by the dicrotism.

(Prof. Saurer, March 1898.) Reduced to '/, of its size by means of pho-
tography,

is more clearly noticeable after the sum than before, and also the
longer oscillations return. (See the graphical representation fig. VII
for the different oscillations, the acceleration, the amphibole stadium
and the compensatory retardation as consequences of exertion).

The acceleration of the pulse under such circumstances has, ho-
wever, been known since THANHOFER. The compensatory retardation
has not had due acknowledgment. And yet, compare fig. V, it may
be very considerable.

But this is not all that happens. During the sum the blood-
pressure in the radial artery seems to increase, at least the curve
rises, and at the same time the form of the pulse-curve chan-
ges somewhat. Though the shortening of the duration principally
influences the diastole of the heart, yet the dicrotism moves a little
nearer to the top when the pulse is short, than when it is long.

At Jeast in an absolute sense. Comparatively, however, the dicro-
tism has moved farther from the top. Compare fig. VI.

Summa summarum. During the exertion of the attention the pulse
is accelerated. After that it becomes slower. The acceleration sets
in at once, at least if the other influences on the duration of the
pulse are taken into account.

Let us now turn to the respiration. This is registered by the

( 132 )

pneumograp of Marey. The descending line represents the inspira-
tion, the ascending line the expiration in every curve which has
been obtained in that way. The arrangement of the experiment is
the same as before.

During the sum, the respiration becomes quicker and more super-
ficial, after the sum slower and more extensive (fig. VIJI—XIID.

The first expiration can be lengthened, but it reaches rarely
the height of the preceding expirations. The shorter duration of
the next respirations, however, is principally dependent on the
shorter duration of the expiration!), while the lengthening of the
expiration after the sum is characteristic (fig. IX and X). It exists
even then, when the duration of the respiration is little or not
lengthened, because a slight shortening of the inspiration continues
after the sum.

A tendency to deep inspiration with limitation and specially
shortening of the expirations is characteristic of what happens during
the sum. Not with everybody, though. Sometimes the deeper inspi-

1) The counting fig. 8, 9, 10 shows this clearly:

ki ï 1 i

Fig. 9. Fig. 10.
Before During | After Before During After
the sum. || the sum. | the sum. the sum. the sum. the sum.
| |
psletillst|/et|ls+t|/eSl=b| eS] Slet eS] eS
Bs 4s Be Eyer IN Jeb we Bs aS SS Ke Bis Xe,
£5 Ee Ie (So || Be | So | Ber Be | Kou Solcon
oF | oP oF oF oF 5E or SP || ob oF © B sE
He} FS Sion er ato Bo Bo Bo Fo Bo Fo Fo
En ec n mn | ol =e a lac) mn = hac Fe
1. 8sec.|2.5sec.||\0.6sec. 1. 9sec. |l. 1sec.,3. Ssec |L. 2sec.|2.4sec.||0. 9sec,|1 .7sec.||0. Isec./2. Gsec.
| H |
1.47 |2.6 » IL. 7 |2.2 7 |/1.2 » le w $0.9 » (2.4 7 0 8 » |L.8 » |.» (2.9 7
| | | | |
137 18. „Ile {1.84 (1.34 (3.3 7 (i1 » (2.6 « (O8 » 18.2 9 ID nae
| | |
1.3 7 (3.2 il. w 1.9 1.3 w 13.6 ¢ [1.1 » 2.5 » |10.8 vld » 10.9 » 12.6
| [1.2 » [1.9 7 1.5 » |8.4 741.1 » 22e 10.9% (1.2 7 ll. #189 «
| WEE 22 1.2 „ \38.9 ” 10.9 » |1.5 w IL nw \29u
| | |
| 0.8 w 1.7 » {1.2 » 12.6 w
110.6 » 1.4 4 10.9 w 12.4 „
| | | |
| 0.6 wl. w
| 0.6 » \2.1
i | |
On an average!|On an average On an averagefOn an average |On an average |On an average
1.3sec.|2.8sec.||1. sec./2. sec.||1.3sec.|3.6secJ1. sec}? 4sec. ee 0th 2 ew
\

| respiration (the ‚descending line is the inspiration).

AAN

5

13

MAIN

3.3

13

|

adem

. XI. Durine the sum, the expi-
WAN. ration, which is lone at first, is conti-

nually interrupted by quicker inspira-
tions. [t becomes less and less extensive
and makes place for deeper inspiration.
After the sum lengthened expiration.
(VAN per Praars, July 1898).

Fie. XII. During the sum, nothine
but exceedingly quick and superficial
respiration. Then slightly longer expi -
ration. Ciphers as above. Sum SS X 83.

(Dr. Rurrmea, Sept. 1898).

Fie. XIIL, During the sum the
respiration becomes quick and super-
ficial, with somewhat deeper inspiration
than before. After that long expiration
and deep inspiration. Sum 32 X 32.

(UTERMÖHLEN, Sept. 1898).

+rot U, WINKLER; „Attention and Respiration.”
s of the respiration during the sum from o—J,

> 2 = the pulsation of the arterin radialis, 2 = the abscis. 3 — the tuning-fork of 5 vibrations per second. & — the respiration (the ‘descending line is the inspiration).

Wan

PAR ea meen |
NNN NN A
los

MH, 1glt zele 16], 29) 1 Agt 2blog 24)

WTA
KAAL ANN ANIM AN WENN

fe XT NNW H
2 XI. Di
A 1 1 & 6 t
in seconds. Sum 76 % 76. (WINKLER, Alter the si
July 189 Vax per Puaars, July 1893)
k xu. I tS
: ipa rf il i © expi
fionelengthened
59 59. (Wranvr
(304 | ree ln | las sul
sala 45 fib ig | jajsujosilocifreyerforebonifotrfosifelarpbaybbna.S['o 32 (ik HIS 3.8 |
4 | i
[ and deep inspirat
ned. Ciphers Sum 47 x 47. B (UrFesömveN, Sep
(Kvers, July 1898), A

ANNANNAANAANANANAAA PONSEN ENEN NAA
\

iw

Proceedings Royal Acad. Amsterdam. Vol, I

( 133 )

ration is wanting and gives place to an enormous acceleration of the
superficial respiration (see fig. XII). Sometimes there is a form
intermediate between the two (see fig. XIID.

Summa summarum. During the exertion the respiration, specially
the expiration, is shorter and more superficial ; both inspiration and
expiration are diminished in the beginning, but give gradually way
to a stronger position of inspiration of the thorax. Then a compen-
satory retardation of respiration follows, specially of the expiration,
with an inclination towards more extensive expiration and longer
intervals.

During such a sum, however, the lumen of the periferie blood-
vessels changes also. HArLION and Comte have invented a simple
instrument to register the volume of the fingers, the so-called capil-
lary pulse of the fingers. A caoutchouc cylinder is placed firmly
along the fingers in the hollow of the hand, while the whole hand
is covered by a solid glove. Every change in the volume of the
fingers under the influence of the working of the heart or the respi-
ration, is imparted to the caoutchoue and can be registered.

And now, just as Bryer and Courrier have already pointed out,
it appeared also to me, that sometimes after a preceding extension,
the volume of the fingers decreases during the sum (see fig. XV).

Binet and Courrier think rightly, that this is partly the con-
sequence of a spasm of the blood-vessels in the fingers. In fact,
when we try to find out with Mosso’s sphygmomanometer, as they
also did, how it is with the blood-pressure in the capillaria, the
result is, that the pressure of the blood increases in the capillaria
during the sum.

If according to the particular arrangement of this instrument we
start from a very slight opposing pressure (in casu 30mM. He.), a
curve is traced during the sum, which does not only ascend, but
shows increasing deviations (see fig. X Vla); and if we start from the
optimum of the opposing pressure (in casu for myself = 50 mM. He.)
the tracing rises, while the deviations decrease (fig. X VIA).

So the volume of the finger becomes smaller, the pressure in
its small blood-vessels increases. There is undoubtedly a spasm
of the vessels in the perifery. Besides the spasm of the vessels
another influence works on the volume of the fingers. The deep
inspiration empties the blood-vessels and has certainly some in-
fluence on the descending of the curve which the volume of the
fingers traces during the sum. In the third place it is not impossible
that in the arrangement of the experiment as done by HALLIon and

10

Proceedings Royal Acad. Amsterdam. Vol. I,

(134 )

Comte and Bier and Courrier, a slight extension-movement of
the fingers causes a release of the cylinder. If this were the case,
a descending of the tracing registered in that way, would be found.

It was natural to register also the extensor muscles of the hand
and the fingers. This may be very fitly done with an air-cushion.
In this case, the local capillary pulse is of course noted down, but
every local expansion of the muscles will occur as a rising in
the curve.

Such a rising takes place. The influence of the spasm of the vessels,
which exists in the perifery, as we saw before, should be noticeable
here, and the tracing should descend. But on the contrary the tracing
very considerably ascends as fig. XVI and XIX show.

The objection, that an air-cushion does not work as a volume-
writer, but as a sphygmomanometer, is not justified. This is also
to be seen on the curve traced. The deviations remain as large as
before in spite of the enormous rise of the curve during the sum
(fig. XVII and XIX).

When an air-cushion is placed at the same time on the flexor-
muscles of the hand and the fingers, and is made to trace the slight
deviations, we see hardly a change, at the utmost an indication of
a slight falling of the line, which is to be regarded as a conse-
quence of the spasm of the vessels.

It is then unvariably a volume-pulse which is noted down, and if
we place an air-cushion on the muscles of the calf (fig. XIX),
exactly the same volume-curve is obtained, as we know since BInEr
and Courrier for the fingers, and which is represented during
the sum in fig. XV. There is only one explanation left: the
extensor muscles of hand and fingers are contracted to some
degree, or rather, for the movement does not manifest itself in
a change of place visible to the eye, the tonus of the extensor
muscles of hand and fingers has become greater. In consequence the
curve which has been traced during the sum by the air-cushion
placed over these muscles rises,

If finally we place the air-cushion on the neck, an observation
like the one on the extensor muscles of the hand can be made. The
curve, which is here of course very much influenced by the respi-
ration, and which is registered by the air cushion as rising by
inspiration, but falling by expiration, rises during the sum. Some-
times the head is even visibly thrown backwards. (see fig. XX).

Summa summarum. The tonus of the extensor muscles of the
hand and neck is augmented.

If we take all this together, the question arises, if all these

Fig. XIX. Tracing of the local volume registered with air-cushions above the exten-
sor mnscles of the lower part of the arm and above the muscles of the calf.
A that on the extensor muscles of the arm,
B that on the muscles of the calf.
During the sum, the air-cushion on the muscles of the calf notes down the usual

volume-curve, as is represented in fig. XV for the fingers. The curve on the eatensor

muscles rises as a consequence of the tension of the mascles which takes place.

(Wrarpr Beckman, Sept. 1898).

Fig. XX (Winker, Sept. 1898). Fig. XXa (Wrarpr BECKMAN,
Sept. 1898). Fig. XX4 (LANGELAAN, Sept. 1898). Tracings registered
with immovable air-cushions on the muscles of the neck. The tracing
rises at every inspiration, because the head threatens to be throwna
little backwards through the tension of these muscles. This happens

in a far greater measure during the sum,

Fie. XV. Change of the volume of the fingers registered with the
| saoutchoue air-cylinder of HarrroN and Comrr,
| During the sum (multiplication: 17 and 19) this curve goes
| down after a short slieht rising. The volume of the fingers decreases
| accordingly (WINKLER, June 1898),
| Fie. XVI. Change of the pressure of the blood in the capillaria
registered with Mosso’s sphygmomanometer. In fig. XVla the oppo-
sing pressure is + 30 mM, Hg,

During the sum the tracing rises and the deviations increase. In
fig. XVI/ the opposing pressure is + 50 mM. He., that is the op-
timum, with which the greatest deviations are obtained. During the
sum the tracine rises, but the deviations become smaller. So the
blood-pressure increases during the sum, (WiNKkrer, Sept. 1898).

Prof. GC, WINKLER, „Attention and Respiration.”

lig. XV—NIX. Changes in the extremities during the sum

Wig. XV. C f the fingers registered with the
ORE sail Goer
Dies kt (multi, 17 1
d N zn, T v of t fi
accordingly (Wiykter, J 1898
Fig. XVI. Change ; » of the 1 in the capillaria
s e ) mM. Hg
Fig i Va. the t 1 the de In
Bd j . t 50 mM. Hz, t =
mum, with if at ned. Du
ANNM | aen y Ee Yee Ola chs eo Mme
ATUL ina Wild fii ; MN blood-pressure increases during t Wirvkzen, 5

Proceed oyal Acad, Amsterdam. Vol. I

Prof. C. WINKLER: „Attention and Respiration.”

Fig. XX.
eee Side-view of the scheme of the cortex
Ee =S : ‘ N a 2 :
an | . of the brain of a dog. The ciphers in-
STATER re : 5 5 :
aor i 6 SEE dicate the squares, which were successi-
sie SSS
See ae : : :
Ed 1713 En vely stimulated with the induction cur-
Qua 8 oh aerial Ee rent When 15 and 16 are stimulated
ir sei Ee \T Fe - - . z
a Se we see deeper inspiration or less extensive
SSN expiration, or quicker superficial respi-
ration.
a
Fig, XXI.
AE paterebes \
7 KD € te
At tzt
/ a { Ne < 7
ay, Ano: \ A Side-view of the scheme of dog’s
Ne eN | F :
DE Re F Vv \ brain. (as above).
x sd “| © \
CUA BS = =
ee js 3} =
RX .
Ney ya jl v 5 ~
DEE) — A 2 a
2 A AAN

NG a

Fig. XXII.

Side-view of the brain of a dog. If
the place, indicated by a circle, is stimu-
lated with an induction current, the in-
spiration becomes deeper, the respiration
quicker, the expiration less extensive and
the pulsation quicker. After the stimula-
tion the expiration is lengthened, the
pulsation slower than before. By stimu-
lation with a moderately strong induction-
current we find stretch-movements of the
fore leg and lifting up of the head.

Front-view of the same brain of a dog.
The circle agrees with point 16 of the

schemes above.

Proceedings Royal Acad. Amsterdam. Vol I.

( 135 )

changes cannot be regarded as consequences of changes of respiration.

In fact, leaving the periferie contraction of the vessels out of
account, there is much to be said in favour of this conception.
Inspiration and acceleration of the pulse, expiration and retardation
of the pulse belong together and it is scarcely possible that the
tendency to inspiration should not be accompanied by acceleration
of pulsation during the sum, whereas the long respirations after it
must be attended by retardation. As to the stretching of the muscles
of hand and neck, every one can observe in himself, that a strong
inspiration is attended by these movements.

So my exposition comes to this, that the popular saying that one
who listens very attentively, listens with suspended breath is not a
very incorrect expression. I know, however, very well, that the
movements here described, are not the only things, which happen
during the exertion of attention.

§ IV. All the movements described here, may be brought
about experimentally by stimulating a certain area
of the cortex of dog’s brains by means of
an induction current.

When we try to find out whether the movements mentioned above
can be brought about experimentally, it is obvious, that we must
turn to the cortex of the frontal lobe of the brain. We are brought
to this on clinical grounds. Patients suffering of the cortex of the
frontal lobe on both sides show an inability of detaining an image;
they are often confused maniacs; they are so no less by their
inability of remembering events. Both phenomena point to a marked
disturbance in the power of apperception.

I began therefore a methodical investigation with Mr. Wrarpr
BeckMaNn who will discuss the literature!) on this subject and a
number of details of the experiments. The question was, whether
the functions of respiration could be modified by stimulation of
the cortex of the frontal lobe of a dog’s brain.

To this purpose the cortex was stimulated with a secondary induc-
tion current with electrodes, at a distance of two mM. from one another.

Four Leclanché-cells feed the induction coil, a sledge of Du-Bots
ReyMonD, and the current can be scarcely felt on the tip of the

1) I leave it to Mr. Wrarpr Beckman to point out the agreement and the diffe-
rences of our results with the investigations of Hrrzic, Munk, Krauss, Semon,
Horstey and SPENCER.

10*

( 136 )

tongue when the secondary coil was 11 eM. from covering the
primary.

A Desprez-signal indicates the moment of stimulation on the
cylinder, while the respiration is registered with the pneumograph
of Marey and the arteria femoralis with an instrument borrowed
from the tonometer of Talma.

At eight o’clock in the morning the dog gets from 30—50 mGr.
morphia, depending on its size. In narcose with ether the frontal
lobe is exposed as far as the dura mater, according to the well-
known method.

After a long time of rest and when the respiration is no longer
disturbed by the morphia, the experiment begins about one or two
in the afternoon.

The surface of the brain, representations of which will be found
in fig. XXI—XXIV, is divided into a number of squares, so far
as it is required for our purpose. The size of these squares are
determined by the topography of the cortex.

After having determined the different centres on the cortex by
stimulating a well-known area of the motor region, the animal
breathing calmly, it is first found, that there are a number of centres
from which it is impossible to bring about any change whatever in
the respiration.

It appears however, that constant changes may be brought about
regularly after stimulation of a few points indicated by 15 and 16
in the scheme. This point lies in the transition from the gyrus
sigmoideus (prae-cruciatus) to the frontal lube and in the second
lateral gyrus near the place, where the fissura coronalis approaches
the fissura praesylvia closely. As soon as we stimulate with an
exceedingly weak current e.g. with 11 cM. distance between the
coils, some quick inspirations are seen to be brought about as in
fig. XXIV. If we stimulate with a current somewhat stronger, the
inspiration becomes somewhat quicker and is accompanied by acce-
leration of pulsation (see fig. XXV). A moderately strong stimulation,
e.g. of 9 cM. distance, causes a stronger spasm of inspiration with
strong acceleration of pulsation, whereas the current also irradiates,
and causes stretch-movements of the muscles of arm and neck (see
fig. XXVI), which were distinctly visible, so that it was unneces-
sary to register them. In fact the respiration (inspiration) centre
mentioned, lies between the centre for stretching the muscles of the
hand and that for lifting the neck.

This acceleration of respiration with deeper inspirations, eventually
restraining and shortening of the expiration is always followed by

A LI ~
PT TN

MAEKAA VUUT iT

AANNAME AANKAN

CLAN PAD A AAA Pfff
KEER CAAAAMANERARAA

tion
At c
tex

tion
cM.)
tion

tenir An U Il hh Sho hk REP RISA Rf
Lj - ee
7 4

a

Og ERA Pach!
(oe oF

ie PA / r E a
AVR MAN AWWA eV NAA AANV
ikheb ek ende Aes ke

t

takes

Prof. C WINKLER, „Attention and Respiration”.

a of respiration and pulsation during the stimulation of point 16 (see fig. XX—NXIV) of the cortex of the brain of dogs

XXIV—XXVINT. Chan,

In all curves the abscis and the time have been registered. Time by a tuning-fork with 2 vibrations per secund.

NUAN ONANISM SRREN

a 5
gk
Fig. XXVII AANSLAAT NANA
Thy
a 5
1 (July, 15th 1898
15 ond 16
JONOEBEVOVEN IAA PANAMA YASS MANNA ANNAN ANALE
re lu S
1 ong a 8 fn : - 5 a
Tas I \ po \ i= Nae Mis,
5 ie ) gama MMVII YOAV YY CO Se
lengthening of expiration and ‘ \ .
fi ee mA. . ie D Ree Cer pees Tee
XVII 3 L 3 5
ra] 1898). At
16 h the jon current
dur ndicated by the signal ~ f Ls
In every f the resp both N NN " ‘i AIAN AMRMAANIA ASANTE RE
and expin leep P \ \ i :
inspiration and scceleration of the
pulse well os quicker respiration

toynl Acad. Amsterdam. Vol, L

(137 )

long expirations, nay even by the expiration-position of the thorax,
and at the same time a distinct retardation of the pulse is seen to
follow as a consequence of that stimulation. The influence on the
respiration of electric stimulation of this point 16 is perfectly con-
stant, and can be brought about in all phases of the respiration,
as fig. XXVIII proves. There is always stronger inspiration ete.

Summa summarum. Ly stimulation of a very small region in
the frontal lobe of a dog’s brain, acceleration of respiration, ten-
dency to deep inspiration, acceleration of pulsation, contraction of the
extensor-muscles of hand and neck may be brought about, followed
by retardation of pulsation and long expiration.

The movements expressing attention are consequently localized on
a comparatively small area of the cortex of a dog’s brain and may
be demonstrated experimentally.

S V. Conclusion.

Let us now return to the theory of the parallelism between phy-
siological and psychical events.

I have shown in a series of arguments, that any man, fixing
his attention, performs a constant series of movements. I do not
mean to say that these are the only movements, through which
the attentive man differs from himself, as he is in a not attentive
state. I am convinced that there is a great deal to be done in this
direction. But the movements described here form a sharply defined
group. I believe that they ail depend on a modified respiration.

Self-observation teaches us, that we turn our attention actively
to a perception. We are justified in assuming that representations
of movements possess an active character for the self-observation.
We find attentively examined representations also connected with the
representation of movement, and in consequence provided with the
same character.

The physiological process parallel to attention, from the point of
view of the association-physiology may be explained by the existing
complexes of movements. A special complex of movements may be
produced by means of an electric current from the cortex of a dog’s
brain. It is on a larger scale exactly the same combination of
movements which is found in the attentive man.

When a physiological change whose parallel series is e.g. a visual
representation, propagates and brings about a new change in the
psycho-motor inspiration centre, there is for the self-observation, a

( 138 )

visual representation + a representation of a respiration-movement,
performed in a special way. Self-observation calls this complex the
apperceived or the attentively observed visual representation.

Though psychology cannot be treated now experimentally, yet the
theory of physiological parallel processes justifies the opinion that
attention and representations of movements originated by special
respiration movements, are closely connected. Closer investigations
on monkey’s brains will be necessary. The other movements expres-
sing attention will have to be submitted to a systematical investi-
gation in the same way, to throw further light on the problem
treated in this paper.

Physics. — „Simple deduction of the characteristic equation for sub-
stances with extended and composite molecules”. By Prof. J.D.
VAN DER WAALS.

If the quantity of substance inclosed in a certain volume is con-
sidered as consisting of material points, which may also be done
with extended molecules, composed of atoms, the equation

d = mr?
— -—l/, 2 (Xx + Yy+ Ze)... . (a)

dt?

bm ee

holds, provided that the quantities occurring in this equation be
applied to all material points.

If groups of these material points are united to separate systems,
as is the case with molecules, which cannot be considered as one
single point, the equation mentioned above, becomes:

dE mr EE pre
Tym VA4 EE lu VP = VY, - EE Fha it?
9 dt”

— WE (Xa, + Vy; Ze) U EE (Xe, de Woe ee

in which the index relates to the centres of gravity of the systems,
and the value 7 indicates the value of a quantity relatively to the

centre of inertia.
For the stationary condition of the centres of gravity as well as
of the systems themselves, this equation is simplified to:

= Yom V2? + EE Nou V2 = — Yq = (Xz, + Vyz + Zee) —

wa, SD (Nr Vy, HZ) US Oe

( 139 )

The condition which is required for considering a group of points
as a system is, that these points keep always together, whatever
may happen and that the quantity 22 wr,” keeps constant.

For the term — 3/, = (Xx. + Yy- + Ze) we may write 3/. (N + Ni) v,
so that the latter equation may be written:

Zom V2 4+ EE No pe VP =P (N + Niv —
WEE (Xz, + Vy, - Ze) ete (d)

In these equations collisions taking place between material points,
cannot furnish a value, as in every point where a collision takes
place, there are two forces of opposed direction, which, working
at the same point, destroy each other. The forces in the term
U EE (Xr, + Fy, + Zz,) are simply the attractive forces between
the points of the system and possibly also the attractive forces which
are exercised on a system by the surrounding ones.

It is true that in transforming —1/,2(Xzr,+ Yyz+ 22.) to
(NH Nj)v it has been assumed for these latter forces, that for
a system, which does not lie near the surface =X is equal to 0,
but from this does not follow that =Xz, is equal to 0.

If to the moving systems themselves the virial equation is applied,
we get the equation

EEV EEK + yt Ze) «©

provided that in X', Y'and Z' all forces, also those which exist on
the surfaces as pressures, are taken into account. These systems
move in a space, in which the pressure is N +4 AN, per unity of sur-
face, and if we were justified in considering the pressure as really
exercised on the surface of every system, the value furnished in the
second member of the equation would be equal to % (V+ 4) bj,
if we represent the volume of all the systems together by 0).

As this pressure, however, is transferred on every system by the
collisions with the other systems, in calculating this value, we
must consider that pressure as exercised at a distance twice as
great, so on the surface of a volume, whose lineal dimension is
twice that of the sytem; at least for spherical systems. Of the
value obtained in this way, the half is to be taken, because a
pressure exercised by the first system on the second is at the same
time a pressure, which is exercised by the second on the first. The
equation (e) becomes then if we put b= 4b,

( 140 )

SEN u V2 = 3/5 (NA Nb = Yo EE Beet Vr Aerden
If (f) is subtracted from (d) the well-know equation is obtained
Sla (N + Ny) (@ — 6) = !/g = m Vz.

The equation (f) may be considered to contain the condition for
the stationary state of the molecules themselves. In the form given
it is, however only applicable, if the molecule is supposed to be
composed of material points, which do not form again separate
systems. If the latter is the case, the equilibrium of every separate
system will give rise to a new equation, which, however, will not
change the equation 2/2 (N + jy) (v — b) = 1/2 Em VA.

For a mixture consisting of zj + #9 molecules, we find the virial-
value of the surface-pressure of all the molecules together through the
observation, that the amount of the pressure on the unity of surface
for the two kinds of molecules is proportionate to the numbers
which are found in unity of volume and therefore also proportionate
to m and vg. For collisions with a molecule of the first kind, a

js ny =
surface- pressure amounting to ——~— (V + Ni) must be assumed, and

ny + Ny
for collisions with molecules of the second kind a surface-pressure of
Ng 7 7
mA Va):
my, + ng

We find for the quantity with which °/,(4 + Ni) is to be multi-
plied in order to indicate the value of the virial of the pressure,
which is exercised on the surfaees of the moving systems, the same
value as Mr. Lorentz (Wied. Ann. 1881, Bd. XII, Heft 1) has
found, viz.:

Zaar (642 mj? +-.do° No? + 2 68 nj No)

nj + Ng

bi

It is easy to deduce, by the preceding way of obtaining the characte-
ristie equation that the value of b is equal to 4 times the volume of
the molecules only in ease of infinite rarefaction, and that if must
be smaller in case of less great rarefaction; it is not even difficult
in that case, to give a first approximation of the way, in which 6
depends on the volume of the substance. By the calculation of the
equation (/) we find the value of the virial of the pressure on the
moving systems to amount to half the value of the virial of a pres-
sure N -+ Nj, exercised on as many surfaces as there are systems,

(141 )

but the systems are supposed to be limited by a spherical surface,
described with a radius, which has twice the length of the radius
of the systems themselves. Let us call these larger spheres: distance-
spheres.

All these distance-spheres are supposed to lie quite outside one
another and to have no points in common. As the volume of all
these spheres together is 8 times as great as the volume of the
molecules, the case that all these spheres lie outside one another is
by no means possible, if the volume is smaller than 2 0.

But even if the volume is so Jarge, that the distance-spheres
would le quite outside one another, if the molecules are supposed
to be spread in the space at regular distances, a great number of
distance-spheres are sure to cover one another in consequence of the
fact they are spread quite irregularly. Now the question is, in how
far the computation of the value of the virial of the pressure
N + N, is to be modified in consequence of this fact. If we have
some molecules, lying in such a way that the distance-spheres inter-
sect, we have not two entire spherical surfaces on which pressure
is exercised but a surface consisting of two parts of spherical sur-
faces. The pressure within the space enclosed by them, is the same,
as if it consisted of two separate parts, but the value of the virial
of the pressure for the two molecules together amounts to twice
3 WN + N)(b—S), if B is the volume of a distance-sphere and S
the volume of the segment which is cut off from a distance-sphere
by the plane of their intersection. In other words, we must take
into account only that part of the distance-sphere that reaches up
to the plane of the intersection, instead of the whole distance-sphere.

We come, accordingly, to the same result which I had obtained
in another way before (Verslag Kon. Ak. van Wetenschappen Am-
sterdam, 31 October 1896).

A second approximation is also mentioned there, and though the
determination of the value of that correction leads to such long
calculations, that as yet I have not brought them to an end, vet I
will make some remarks on the way in which this value might be
obtained.

If A, B and C are taken for the instantaneous position of the
three centres of the distance-spheres and M for the centre of the
circumscribed circle, the mean value of the volume limited by the
surface of the distance-sphere A and the two planes FM and
AMD, will represent the second correction.

If we put AM=a and LAMG=C, and the radius of the
distance-sphere = #, the value of the volume £MD will be

( 142 )

oa SGA Paras ee

AS

Re
TE == 2/s Rs Bo tg lv cy —

— asin C (ze =

a? = = foe VR — a?)

a cos C

a sin C a cos C\/(R? — @®)
3

If C moves on the circle ABC, the centre of which is M, «and
C remain the same and consequently Z keeps its value also.
Let provisionally, the distance of A and B remain invariable and
let C move arbitrarily, then M moves along the line FG. If we call
the heigt of M above AB equal to A, Z may be considered as func- .

2
tion of k by observing that @? = 1? + 5 (r the distance AB) and

Hie . .
sin C= 5— . If the whole figure is turned round line 48, and if
<a 4

(143)

the whole space, in which C may be found is divided into volume-
elements AV, we have to determine

N
yi IAJ.
v

As 7 is known as function of 4, AV must also be given as de-
pendent on h.

If we represent the angle which CM forms with FG by p, the
annular volume-element, in wich C lies, is to be represented by

22 dp dh(h + a cos p)°.

If we take p between 0 and the value which it has, when C lies
on the distance-sphere of A, twice the value of this integral is to
be taken.

As the value of @ is quite determined by 4, when C lies on the
sphere of A, the integration must be done with respect to 2, and the
limits are to be determined, between which 4 is to be taken.

72
The highest value of k is of course / (2 ~ 5): the lowest

value may be found from

tav (i# +7) =y(m- 5)

or
a}
zen
2
= =
2y(e-—)
rf
The lowest value, however, cannot descend below — // (ze = 7)

which would be the case if r > &y/3. This is the cause that the
integration, must be done in two tempo’s, and that we have to
calculate

RV 2R V(e-*)

4
| dr fa — [a | dh

R RV 3 V (a4)

( 144 )

Chemistry. — „The rate of substitution of a nitrogroup by an
oxalkyl”. By Prof. C. A. Lopry DE Bruyn. With reference
to Dr. A. STEGER’s dissertation.

Up to this moment no investigation had taken place of the velo-
city of substitution of the atoms or atomgroups, immediately connected
with the benzene molecule by other groups; yet such an investiga-
tion was of importance for the knowledge of the qualities of the
benzene-nucleus and the influence of the different places on each
other. A reaction which was excellently fit for this purpose I had
formerly met in a comparative study on the three dinitrobenzenes
viz. the substitution of one of the nitrogroups in ortho- and para-
dinitrobenzene by oxymethyl or oxyethyl ') according to the equation:

NO,
NO,

OCH, (C, Hs)

Cs Hs NO

+ Na 5) CH, (C, H;) = Cs Hy, + Na NOs.

A preliminary experiment had already shown me that the para-
dinitrobenzene at 0° is more speedily substituted with natrium-
methylate than ortho-dinitrobenzene.

Now Mr. Stecer has studied quantitatively the four above
mentioned reactions at temperatures of 25°, 35° and 45°; besides
the influence of concentration, that of the presence of a natriumion
and that of the gradual adjunction of water were also examined.
The results of this study, published by Mr. STEGER as a dissertation,
are of general interest, to which I think I may draw attention.

In the first place then it is now proved that the velocity of
substitution is greater with paradinitrobenzene than with ortho-
dinitrobenzene ; for both the transposition takes place more speedily
with natriumethylate than with natriummethylate, a phenomenon
that agrees with the observations of others. The conduct of ortho-
and paradinitrobenzene is not the same for the two alkylates, a
difference that may be brought back to the influence of the two
alcohols that served as solvents. The influence of the temperature
however, being different for the two dinitrobenzenes, was equal for
each of them towards the two alcoholates.

The question as to the influence of the concentration on the ve-
locity of reaction was important with a view to an investigation by
Heeur, Conrad and BrtckNeR”*) on the velocity of aetherformation,

1) Recueil 13 (1894) 101, 106.
2) Z. f. phys. Ch, 5 (1890) 289.

( 145 )

consequently of reactions which were perfectly comparable to those
mentioned here; for they run on the equation:

CH; J + NaO CH; — CH, O CH, — NaJ, ete.

Said investigators had proved that in the process of the aether-
formation the reactionconstant increases with the dilution. To us
it is evident (which in 1890 could not yet be the case with H.,
C. and Br.) that we must here think of the influence of the elec-
trolytic dissociation increasing in proportion to the dilution, that is
to the inerease of the oxalkylions') and to write the following

equation :
CH; J + Na + OCH; = CH; O CH; + Na + J
or, the natriumion not taking part in the reaction
CH; J + O CH; = CH; O CH; + J.
The reaction studied by Mr. Steger would then be represented by

Co Hs (NO2)? + O CHs = Cy Hy NO. O CH3 + NOsv.

But then it came out, remarkably enough, that in opposition to
the process of aetherformation the constant of the last named reac-
tion was not changed by the concentration.

The question that now naturally offered itself as a consequence
of this result was this. If a regular influence of the dilution, as
required by the electrolytic dissociationtheory does exist in the aether-
formation and does not exist in the substitution of the dinitroben-
zenes, What is then in both reactions the influence of the addition
of a substance with the same ion? If a sodium salt is added, the
increase of the concentration of the natriumions will keep back that
of the oxalkylions and consequently cause the reactionconstant to
fall. By H., C. and Br. this question had been studied cursorily
and unsatisfactorily only.

When investigating the velocity of the aetherformation while
adding increasing quantities of Na J, it was now shown, that the
reactionconstant, in accordance with the iontheory, decreases in re-

1) Neither CH, J nor C; H‚ (NO)? conduct the electric current in alcoholic solutions.

( 146 )

gular gradations. On the other hand however the experiment showed
that for the transposition of orthodinitrobenzene a change in the
velocityconstant by the addition of a sodium salt is not noticeable.
Consequently we arrive at the conclusion, improbable in itself, that
of two for the rest perfectly homogeneous reactions, one is under the
influence of the electrolytic dissociation while the other is not. More
acceptable seems to be the supposition that the theory of the electrolytic
dissociation cannot be considered as an element of explanation in
all reactions in solutions containing electrolytes and that the trans-
positions between substances, which both or one of which behave as
an electrolyte may still depend upon other causes than the nature
and concentration of the ions.

To the problems to which we are led by this result, one of the
foremost is: what change the conductiveness of alkylatesolutions
undergoes by dilution.

The study of the reaction we treat of here, has still been extended
for orthodinitrobenzene and this has also afforded some results which
are not unimportant. Some ‘observations of an earlier date had
shown that the addition of very small quantities of water sometimes
greatly alters the qualities of alcohols. Consequently we resolved
to equally investigate that influence on methylic and ethylie alcohol.
The result was unexpected in many respects. In the first place we
saw the reactionconstants continued to exist, even in mixtures of
alcohol and water with up to 50 pCt. water. Now it is generally
supposed that sodium-alcoholate with only a little water is already
transformed, at least partly, in natron and alcohol. If natron had
been present we might have expected the formation of nitrophenolate
and consequently the two following reactions taking place simulta-
neously:

Cz Hy (NO,)? -b Na O Cy Hs = Cs Hy NO, O Cy H; + Na NO,

and

C; H, (NO,)? + Na OH = Cy Hi NO, OH + Na NOs.

In the latter case a second mol. natron should have formed the
natriumnitrophenolate and consequently the concentration of the
natron should be equally diminished. In case of the two reactions
running simultaneously an equal velocity might not be expected. With
this difference in velocity the equilibrium between Na OH and
Na OC, H; had to be equally altered and so, besides the three men-
tioned reactions there, should appear a fourth:

Na OC, Hs + Hy 0 S Na OH + C, H; OH.

(147)

If all these reactions should take place simultaneously, there could
be no question of a constant. And yet, as mentioned above, there
were found constants for the two aleohols, even for alcohols diluted
with an equal weight of water. The explanation proved to be easy.
In opposition to the generally adopted idea, it was shown that the
sodium in methylie alcohol diluted with 50 pCt. of water was mostly
bound to oxalkyl. The same may aiso be proved by a quantitative
estimation of the natriumnitrophenolate formed, which was pos-
sible along the colorimetric way owing to the yellow colour of that
salt. The quantities formed of it, proved to be very small and
amounted only to a few percent for 50 pCt. and 60 pCt. ethylic
alcohol.

There also came out another peculiarity viz. this, that the addition
of water causes the reactionconstant in methylic alcohol to rise from
0.0169 to 0.0249, in ethylic aleohol to fall from 0.0261 to 0.0104.
For a percentage of + 12 pCt of water the constant of the two
alcohols is the same. It was now highly to be regretted that the
constantly decreasing solubility of orthodinitrobenzene in the diluted
aleohols did not allow to continue the experiment down to water.
The two curves that may be constructed with the constants and the
percentage of water must necessarily meet in one point, the one
that would indicate the reactionconstant for aqueous natron, that
is in absence of the alcohols. Yet we were able to extend our
tests so far that we have shown for the still more diluted alcohols
how much nitroanisol and nitrophenetol and how much nitrophenol
were formed when boiling dinitrobenzene with natron that contained
40, 20 and 10 pCt. of the alcohols. The result of these tests —
see below — shows that even in the strongly diluted methylic
alcohols the formation of the methoxyl-compound forms the principal
reaction, while in ethylic alcohol a considerable quantity of nitro-
phenetol is created nevertheless.

Methylic alcohol, b. pt. ‚time _ dinitrobenzene, _oxalkyl-comp.
400/, gite Sh. | 3.03 gr. 2.7 gr. + 96°/,
20 » 89° >-| 301 » Bays + 88 »
10 » 94° iG Re es 2:0) a + 70 >

Ethylie alcohol

40°, 86° Sh. | 32 » Zend + 63 >

20 » 92° WG) eel GH 55 1.15 » ZE ¢;

( 148 )

In continuing these experiments it will in the first place be our
purpose to make out ifin the aetherformations, taking place in aleohols
diluted with water, the same conduct appears as in the transformations
of the dinitrobenzenes treated here. Further we shall try to find
substances the transformations of which adapt themselves to a
quantitative study, both in aleohol and water and in any mixture
of these two solvents, with simultaneous estimation of one of the
products.

Chemistry. — „On some anomalies in the system of MENDELEJEFF”’.
By Prof. Tu. H. Benrens.

In his fourth paper on isomorphism („Beiträge zur Kenntnis des
Isomorphismus”’, IV, in „Zeitschr. f. physik. Chemie, VIII, 1) Mr.
J. W. Rereers has denied the existence of isomorphism between
tellurates and sulfates and has given to tellurium a place between
Ru and Os (Fe = 56, Ru= 104, Te = 128, Os = 195). His views
are founded on two facts: on the absence of compound erystals, com-
posed of Ky SO, and Ky Te O, and on the existence of isomorphism
between chlorotellurates, chloroplatinates and chlorostannates. In the
second place the anomaly in the differences of the atomic weights
of Sb, Te and J is mentioned and likewise the analogy between
H, Te and H,8, but the principal weight is attached to the con-
clusion deduced from isomorphism. His first assertion is drawn from
experiments with K,MnQO,, a compound, forming green crystals
with K,SO,, but not with K,TeQO,. It has been confirmed by
experiments with Age CrO,, by which compound growing crystals
of Ag, SO, are stained from amber yellow to a fiery red, while it
does not enter into crystallizing Ag, Te Os.

Where Mr. Rereers has made use of isomorphism between chloro-
tellurites (he writes: chlorotellurates) and chloroplatinates, to sub-
stantiate his second assertion, his argumentation is less stringent,
as he has not given experiments of his own. The base of his second
assertion must therefore be thoroughly tested.

No compound crystals were obtained with Te Cl, and Pt Cl4, the
solubilities of the two compounds K, Pt Cl, and Ks Te Cl, differing
too much. With Css Sn Cl; and Cs; Te Cl, and with Cs, Os Cl, and
Cs, Te Clg better results were obtained. Beautiful compound crystals
were produced by adding Cs Cl to mixed solutions of Te Cl, and
Ir Cl,, strongly acidulated with hydrochloric acid. In this case the
compound crystals were light brown, while the one of the compo-
nents is yellow, the other red-brown,

( 149 )

To ascertain, if Te comes more near to Sn or to Ir and Os
experiments with several acids were tried, with a somewhat starting
result. Tellurium dioxide is dissolved by K HC O4, forming well
developed microscopical crystals of a double oxalate, resembling
erystals of potassium-zirconium-oxalate in form, dimensions and
manner of formation. :

Here the question arose: How far may the isomorphism of the
compound Ky Sn Cl; with analogous compounds of other tetrachlorides
extend? In the first place the behaviour of Pb Cl, was examined. With
strong hydrochloric acid, cooled by ice, PbO, gives a yellow solu-
tion, from which Cs Cl precipitates dark yellow oetahedrons, while
in a solution, mixed with Sn Cl,, bigger erystals of light yellow
colour are formed. From mixed solutions of Sn Cl, and Pt Cl, no
compound erystals could be produced, while mixed solutions of Sn Cl4
and Ir Cl, gave a complete series, varying in colour from dark red
to a faint reddish yellow. Crystallization of pure chloroiridate is
prevented by means of a strong dose of hydrochloric acid and
heating, before adding rubidium chloride. At ordinary temperature
only a few compound crystals are formed, and these are faintly
tinged. Fractionating by repeated additions of RbCl is to be recom-
mended; it facilitates the preparation of a complete series. Mixed
solutions of Sn Cl, and Os Cl, are not so easy to manage, besides
the variation of colour (from colourless to light brown) is not so
striking. Finally experiments were made with MnCl, prepared by
dissolving MnO, in cooled hydrochloric acid. From this solution
CsCl precipitated dark red octahedrons, resembling crystals of the
compound K,IrCl;, while from solutions, mixed with Sn Cl,
compound crystals of all shades between a dark red and a faint
reddish yellow were obtained, perfectly imitating the series produced
from mixed solutions of Sn Cl, and Ir Cl,

These last experiments are particularly suggestive. The isomor-
phism of K Mn 0, and K Cl O, is the principal argument for placing
Mn near Cl in the seventh group of MENDELEJEFF; on account of
the isomorphism between Ky Mn O, and Ky SO, it might be placed
in the sixth group; reasoning from the experiments with the tetra-
chlorides of Mn and Sn would bring it into the fourth group; from
this it must be removed to the third group if you start from the
isomorphism between common alum and manganum-alum; finally,
if you fix your attention to the crystalline forms of manganous
oxalate and of the doubie phosphate of ammonium and manganum,
Mn must have its place in the second group, next to Mg. The
compounds of chromium exhibit a similar protean behaviour.

11

Proceedings Royal Acad. Amsterdam. Vol. I.

( 150 )

With a view to isomorphism chromium might be placed in the
eventh, the sixth, the third, and on account of chrom-ammonium
in the eighth group. For tellurium you have choice between three
groups. If the principal weight is accorded to the analogy between
H, Te vand H,S, it must be placed in the sixth group; if you
follow Mr. Rereers, in putting the isomorphism of Ks Te Cl, with
K,OsCl, and KyIrCly upon the foreground, a place must be
found for it in the eighth group; if the attention is fixed on the
somorphism of Cs, Te Cl; with Cs, Sn Cl, and on the analogy
of potassium - tellurium- oxalate with potassium - zirconium - oxalate,
it may be put into the fourth group. Meanwhile it may not
be overlooked, that Te owes its place in the sixth group solely
to the analogy of H,Te and H,S; that, to fit into this group,
its atomic weight ought to range below 126 (Sb = 120, Te = 123(?),
J = 126.5) and that the atomic weight of Te stands likewise
in the way of a migration to the fourth and to the eighth group.
In the fourth group no place is open next Sn for an element
having an atomic weight about 120 (Sn = 117.4, Ce = 141), and
if Te should be placed in the eighth group, between Ru and Os,
search would have to be made for seventeen new elements in this
group. The difference between the atomic weights of two acknow-
ledged membres of this group, taken in a vertical column, amounts
to 45—48; between Ru and Te it would be half as great (Ru= 104,
Te = 126—128), thus: three unknown elements, filling the gap
between the first and second file, eight between the second and
third (Ra = 104, Os = 195) and six below the third (Pt = 195,
U = 240). Not impossible, but certainly not probable. Probably,
if Mr. Rereers had been acquainted with the isomorphism of
Cs, Mn Cl; and Cs. Sn Clg, he would have stopped at the statement,
that isomorphism between tellurates and sulfates does not exist,
and would not have proceeded to seek a place for tellurium in
the eighth group with a difference of 22 between two consecutive
atomic weights instead af 45.

The weight of isomorphism in chemical speculations must be
further reduced than has been done by Mr. Ruvarrs. The hypo-
thesis, that isomorphism among a group of compounds does point
to isomorphism of the elements which these compounds have in
common, is abandoned by most chemists, but isomorphism between
sulfates and chromates, between phosphates, arsenates and vanadates,
stated without restriction, is even objectionable. In alum trivalent
chromium can take the place of aluminium, while sulfuric acid
cannot be exchanged for chromic acid, and yet this exchange can

( 151 )

easily be made in sulfates of univalent and bivalent metals, without
altering their crystallization. In double arseniate of ammonium and
calcium phosphoric and vanadie acid cannot fill the place of arse-
nicic acid, while in lead-apatite the three acids can be exchanged
without any visible change in the form and structure of the crystals.
Here isomorphism is restricted to small groups of compounds, whose
limits are narrow and sharply defined; in other cases the limits of
isomorphous groups are very wide, wider than generally admitted.
Take for example the double arsenate of ammonium and calcium,
(NH), Ca As O4 + 6 Hs O. In this compound Ca can be exchanged
for Ba, Sr, Pb, Mg, Mn, Fe, Co, Ni, Zn, Cd and Cu. Nearly the
same extension of change is found in triple acetates of the type:
Na Mg (UOsz)3 (Cy Hs Op) + 9 Hy O. They form rhombohedral
erystals, imitating the regular (tetrahedric) crystals of the compound
Na (UO,) (Cy H3 O.)3. Speculation on a possible connexion between
the wide range of isomorphism in complicated double and triple
compounds with their constitution leaves the impression, that their
form is ruled and fixed by constantly recurring nuclei of great
volume, or, with other words: that isomorphism and morphotropism
have a cause in common. The nucleus of the triple acetates is the
compound Na (UQg) (Cy Hs 0»)s. Morphotropism plays here a pro-
minent part, accompanying isomorphism and producing a striking
imitation of regular forms in rhombohedral crystals. Obviously a
connexion exists between these phenomena and the combination of
isomorphism and morphotropism, found in some families of minerals,
e.g. the pyroxenes, where exchange of Mg for Ca, of Ca for Zn
or Mn does change the system of crystallization, while the general
shape or habitus of the crystals remains unchanged.

Chemistry. — „On the action of methylic alcohol on the imides
of bibasic acids”. By Prof. 5. HooGewerrer also in the name
of Dr. W, A. vaN Dorp.

In April of this year we have placed in the Recueil des Travaux
Chimiques des Pays-Bas et de la Belgique a short account, which
shows that, by heating the imides of bibasie acids with methylic
alcohol containing muriatic acid, the methylic ethers of the amido-
acids, corresponding to the imides, are formed in some cases,

At least this was observed with the phenylimides of succinic acid
and maleic acid, also with those, substituted in the radical of the
acid. For example the phenylimide of maleic acid with methylic alco-

Als

(152)

hol containing muriatie acid forms the ethereal salt according to
the equation

CH—COo CH—CO. NHC, Hs
I >NOH; + CH,OH = || ;
CH—CO CH—CO. OCHs

On a closer study of this reaction we have found that the co-
operation of the muriatie acid may be promotive in some cases to
the formation of the methylic salt, but is not required for it.

Several imides investigated by us are transformed partly in the
ethereal salts of amido-acids, when heated with absolute methylie
alcohol without the addition of methylie alcohol containing hydro-
chlorie acid. It is best to work in sealed glass tubes at temperatures
between 150°—200° C. and sometimes higher still; but methylic salt
formation also takes place when the imides are for a long time
boiled with methylic alcohol.

We could show besides in some cases that these ethereal salts,
when heated with methylic alcohol, are partly transformed again in
imides and methylic aleohol. Perhaps these reactions are reversible:

imide + methylie alcohol = methylie salt of the amido-acid,

This point will be investigated.

BeRTHELOT and PAN DE Sr. GILLES in their classic papers on
the formation of ethers from acids and alcohols say, that the maximal
quantity of ethereal salt that can be formed is but slightly depen-
dent on the temperature. This seems equally to be the case, at least
sometimes, in the case of the formation of the ethereal salts of amido-
acids from imides.

We have prepared the ethereal salts of the corresponding amido-
acids from the following imides by heating with methylic alcohol:
succinimide, succinphenylimide, succinparanitrovenzylimide, malein-
phenylimide, phtalphenylimide.

CH,—CO
Succinimide | > NH, when heated for three hours in
CH,—CO
sealed tubes with the octuple weight of absolute methylie aleohol
at a temperature of 170° C., gives the methylie salt of the succino-
CH,—CO—NH,
amido-acid | in large quantity.
CH,—CO 0 CH;

We prepared this ethereal salt, which we did not find mentioned

in literature, also by letting methylie iodide act upon the silver salt
of succinoamido-acid, and convinced ourselves that both compounds
are identical. If the imide is boiled with methylie alcohol, ethereal
salt formation takes equally place, though slowly.
CH,—CO
The transformation of the succinphenylimide | >NC¢,Hs in
CH,—CO
CH,—CO—NH C, Hs;
the ethereal salt of the amido-acid | :
CH, —CO—CO OCH;
place easily if methylic alcohol containing muriatic acid is used, seems
to be more difficult when this alcohol alone is employed. We had
to heat up to 240° C. in order to obtain a satisfactory result. We
consider our work with this imide as not yet finished.
CH,-—CO
If the succinparanitrobenzvlimide | >N CHC; Ha NO, is
CH,—CO
heated with a septuple quantity of methylic alcohol for some hours
CH, CO. NH. CH,. C,H, NO,
at 170° C., a small quantity of the ester |
CH,.CO OCH;
is formed. Experiments on ethereal salt formation at lower tempe-
ratures were not made in this case. On the other hand this methylic
salt, when heated to 170° C. with methylic alcohol, is for the greater
part transformed in the imide.
CH—CO
The maleinphenylimide || >NC,H; (1 part), when heated
CH—CO
with methylic alcohol (7 parts) at 170° C., is transformed partly in
CH—CO—NH C, H;
the methylic phenylamidomaleinate || . The same
CH—COOCH;
reaction takes place already, though slowly, when the phenylimide
is boiled with methylic alcohol.

which takes

CO

>NC,H;, when heated with

CO

methylic alcohol on a waterbath in a flask connected with an

inverted condenser, or at a higher temperature in sealed tubes,

produces small quantities of the methylic phenylamidophtalate
/CO—-NHC, H;

The phtalphenylimide C, He

C, H . The fact of this ethereal salt being unstable

4
CO O CH3

against methylie alcohol we learn at once, when trying to crystallize

( 154)

it from this solvent. The warm solution soon deposits some phe-
nylimide.

To conelude we have found in comparative experiments that the
imides form the ethereal salts of amido-acids much easier with me-
thylic alcohol, than with aethylie- or propylie aleohol. The greater
ethereal saltforming faculty possessed by the former alcohol!) shows
itself equally in these experiments.

We herewith tender our best thanks to Messrs. VAN BREUKELE-
VEEN and vaN HAanst, who assisted us with great zeal in the
present investigation.

Delft/ Amsterdam, October 1898.

Physics. — „Description of an open manometer of reduced height”.
By Prof. H. KAMERLINGH ONNES.

(Will be published in the Proceedings of the next meeting).

Zoology. — ,Cup-shaped red bloodcorpuscles. (Chromocraters)”.
By Dr. M. C. Dexnuyzen. (Communicated by Dr. P. P. C.
Hoek).

The red bloodeorpuseles of the lamprey (Petromyzon fluviatilis)
when examined living or after fixation, exhibit a remarkable shape,
which has escaped the attention of investigators. They are bell-or
cup shaped cells. Their body contains a rather deep cavity which
may be called an „oral invagination’. The rather wide opening is
round, but owing to the facility with which the cells change their
shape, may become a split or a triangle.

A second less evident ,aboral” invagination is found at the aboral
pole, in a somewhat eccentric position however. Seen from above
one of the poles, the cell is somewhat oval, almost round. No
wonder that such a shape is not recognized, when the blood is
spread out in a thin layer, dried and then preserved.

There is scarcely an object imaginable better calculated to make
the objections evident which must be alleged against the usual
methods of drying for the purpose of investigating the blood.

True amoeboid properties are wanting; some of the damaged cells

1) Vid, MersenuwkrN, Lieb. Ann. 195, p. 357.

( 155 )

however do indeed remind us of the thorn-apple shapes of the red
blood-corpuseles of mammalia and amphibia.

The nucleus is ellipsoid. It lies in the proximity of the aborat
invagination, and appears to be connected here with the boundary
layer of the body of the cell by means of the microcentrum, the
group of centrosomes.

The retraction sometimes tapers off rather sharply. The bottom
of the deep oral invagination also appears to be connected, though
much more loosely, with the nucleus.

Under injurious influences the mouth may disappear and the cell
become globular, or the bottom of the oral invagination be thrust
outwards like a bag turned inside out, so that a (clear) vesicle is
extruded from the oral ring, or the nucleus may be ejected from
the opening of the mouth. In preparations where the boundary layer
of the body of the cell presents itself as a sharply defined mem-
brane, a ring is visible round the mouth, viz. the oral ring. Round
the aboral invagination we observe in such preparations, though
less frequently, an aboral ring. What kind of peripheral, oral and
aboral differentiations, preformed in the living cell, lie at the bases
of these images, we cannot as yet say.

These cells may be called chromocraters, a word derived, by
analogy with the term chromocyt in zoology, from the Greek zorg,
a cup.

The desirability of proposing this new name arises from the
circumstances that the chromocratere proves to be a red blood-corp-
uscle occurring in widely divergent groups of animals. It may
be a thing of importance in phylogeny and in mammalia an inheritance
of great antiquity.

The common red blood-corpuscles of mammalia (rat, cavia, rabbit)
pass through a stage, in which they are nucleated chromocraters,
and that as mature erythroblasts or normoblasts, when the nucleus
is already pycnotically degenerated, which cells eject their nucleus
through the oral invagination.

They then become cup-shaped erythrocytodes (known already to
RINDFLEISCH !) and Howe. 2)): e.g. enucleated chromocraters with
deep oral and less deep aboral invaginations.

In the full-grown red blood-corpuscles of man viz. in the tips of

1) Rinprietscu, Ueb. Knochenmark und Blutbildung. Archiv f. mikrosk. Anato-
mie. XVII. 1880.

2) Howern, The life history of the formed elements of the blood, especially the
red bloodcorpuscles; Journal of Morphology. IV. 1890,

( 156

the fingers it may also be shown that the two invaginations of the
bi-coneave discs are not morphologically equal. Their chromocrateric
nature may be rendered visible by „fination” of the out-flowing
blood in osmie acid (according to an observation by Mr. H. W.
3LOTE, assistant at the Leyden Laboratory of Physiology).

We will by no means assert that all nuclei are eliminated by
ejection; there seems to be no reason to question the statements
made by trustworthy writers of cases in which the nucleus is destroyed
by intracellular degeneration.

In the freshly fixed thighbone-marrow of a Cavia in an advanced
stage of pregnancy, a round corpuscle, corresponding in all respects
to the pyenotic nucleus of mature normoblasts, was observed in
nearly all leukocytes next to the polymorphous nucleus.

Moreover the ejection of the nucleus already figured by RINDFLEISCH,
may be easily observed e.g. in the thighbone-marrow of a rabbit
three weeks old.

Now chromocraters, corresponding in shape to that described of
the Lamprey, were also observed by me in Phowichilidium femora-
tum, a Pycnogonid abounding in the port of Nieuwediep. Also just
the same typical exterior of the aboral invagination, sometimes sharply
tapering and pointing to the adjacent nucleus. The ejection of the
nucleus through the oral opening of a somewhat damaged cell has
also been observed.

1 myself have observed chromocraters only in mammalia, lampreys,
and the species of Pyenogonid just mentioned. Now we find in
zoological literature descriptions and figures by different writers, who
probably have seen chromocraters but owing to the difficulty of
obtaining living specimens of the sometimens scarce material, their
statements could not as yet be controlled or verified.

Unknown to each other the writers observe with surprise and
more or less incidentally, that they have seen bloodeells which
were cupshaped.

Dourn in his Monograph of the Pantopoda of the Gulf of Napels
says, that in nearly all Pyenogonids he had seen bloodeells which
he called, „Ballons”. ,Sieht men sie im Blut circuliren, so erscheinen
sie Belen wie ovale Ballons aus Seidenpapier die nicht mit Luft
voll erfüllt sind.”

GRIESBACH') has figured the haemoglobine-containing cells of Pec-
tunculus glycimeris, a Lamellibranch Molluse. „Sie sehen mützen-

') Griesbacu, Beitrige zur Histologie des Blutes. Arch. f. mikroskop. Anatomie.
XXXVII. 1891.

re

(157 )

förmig aus, sie lassen sich vergleichen mit einem eingedrückten
Gummiball, sie ähneln dem Hut eines Pilzes und durch die ein-
gedriickte Stelle sieht man deutlich den Kern hindurehschimmern.”

From the figure I think I may conclude that we can here have
to do with hardly anything else than with chromocraters, at least
with cells which have a great many properties in common with
those we have described.

Erste in his Monographie der Capitelliden has figured at least
dish-shaped red bioodcells in Chaetopod worms (Notomastus). Nor
should we omit to mention the figures and communications of
Cuknot)!) concerning Cucumaria Planci, an Echinoderm, and of
Sipunculus and Phascalosoma (Gephyreans).

That the same very characteristic species of cell, possessing a shape,
the appropriateness of which is at least very questionable, the sig-
nificance enigmatic (unless the calyxiform bloodcells of the Gephyreans
he congenial with chromocraters) should occur among such widely
divergent groups of animals as Pyenogonids, Petromyzontes, Molluses
(perhaps) and Mammalia, justifies, in my opinion the conclusion, that
the chromocrater is a heritage from the common ancestors of the above
mentioned groups of animals, that is from worms. In the ontogenesis
of the red blood-corpuscles of mammalia the ancestral calyxiform
nucleated blood-cell again appears for a short duration.

This investigation was carried on in the Physiological Laboratory
of Leyden and at the zoological station at the Helder.

By the communications of GrGrio Tos?) our attention was
directed to the Lamprey.

Astronomy. — ,Some remarks upon the 14-monthly motion of the
Pole of the Earth and upon the length of its period”. By
Dr. EK. F. van DE SANDE BAKHUYZEN (Communicated by
Prof. H. G. VAN DE SANDE BAKHUYZEN).

(Will be published in the Proceedings of the next meeting.)

1) Cuinot, Etudes sur le sang ete. Arch. d. Zool. expérimentale et générale.
IX, 1891.

2) E. Gierro Tos, Sulle cellule del sangue della lampreda. Accad. reale della scienze
di Torino, 1896.

( 158 )

Physics. — „The influence of pressure en the critical temperature
of complete mixture’. By Mr. N. J. van per Lem. (Com-
municated by Prof. J. D. VAN DER WAALS.)

In 1886 (Wied. Ann. Bd. 28) Mr. Arexnsew published investi-
gations, undertaken to find out the influence of temperature on the
mutual solubility of two liquids which are but partly soluble in
each other. A temperature proved to exist, above which mixture in
all proportions takes place (critical temperature of complete mixture).
The existence of this temperature had been already supposed before.
In 1880 (Verh. Kon. Ak.), Prof. vAN DER Waats had pointed out,
that the pressure too, must play a part in this phenomenon, and
he had found that in a mixture of ether and water, the meniscus,
parting the two phases, becomes flatter by higher pressure. Though
this might be considered as a proof that the two phases approached
each other as far as composition is concerned, complete mixture is
not attained. Mr. ALEXEJEW seems to have been induced through
this treatise, to examine also the influence of pressure for the mixtures
investigated by him, but with a negative result. (I have not been
able to consult the description of these last experiments. I know
them only from citations). By the theory of the surface w (J. D.
VAN DER WaAALs: , Théorie moléculaire d'une substance composée
de deux matières différentes. Arch. Néerl. T. 24 or Versl. Kon. Ak.
23 Febr. 1889) the influence of the pressure on the mutual solubi-
lity was also examined. In 1894 Mr. J. pe Kowatsky published
the description of his investigations (C. R. T. CXIX p.512) concer-

ning this theory. No influence of the pressure was found — not
even by very high pressures — except for a triple mixture of

aethylaleohol, iscbutylaleohol and water. A pressure of 900 atm.
made the liquid homogeneous at a temperature of about 3° below
the temperature of complete mixture. Of late Mr. Kropsre (Zeitschr.
f. phys. Chem. 24. 617. 1897) has found a perceptible influence of
the pressure for mixtures of ether and water by a pressure of 100
atmospheres, without, however, determining its degree.

The purpose of the experimeuts which will be described here,
was, to find something about the influence of the pressure on the
mixture of liquids.

Of all the mixtures examined by Mr. ALEXEJEW the pair water
and phenol seemed best fitted for these investigations. The critical
temperature of complete mixture is about 67°. The phenol used
was from Merck & Co. and was tested beforehand by determining
the fusing-point. It was preserved in the dark in sealed glass tubes,

( 159 )

each containing about the quantity necessary for one experiment.
The proportion of the mixtures was regulated by putting together
quantities of a given weight of the two substances. As the deter-
minations were made for mixtures whose temperature of complete
mixture was near the critical, the liquids were divided into two
phases at the temperature of the room. Therefore the mixture was
well shaken, so that an emulsion was obtained. A certain quantity
of this was quickly poured into a capillar funnel, with which the liquid
was brought into the observation-tube. This tube consisted of a
straight tube of thick glass with about 3 m.M. inside diameter. It
was fused together at one end, widened in one place just as the
CAILLETET-tubes are, and cemented in a brass mounting. After a
sufficient quantity of the mixture was poured into this tube, the
stirring-contrivance was applied to the liquid, consisting of a
magnetised needle, round which a closely fitting glass capillar was
slided, which was then fused together on both ends and provided
with glass balls to prevent its sticking to the glass walls. To bring
this bar in motion an electro-magnetic stir-apparatus was used,
like the one described by A. vaN Expik (Versl. Kon. Ak. 1897).
After the stir-apparatus had been put in, the air-bubbles were
removed as much as possible, and then the mercury was put in the
tube. For this a not too great quantity was first carefully put in
at the top of the tube. If care was taken that the mercury had but
very little velocity, it kept sticking high in the tube, in consequence
of the capillarity. After that it was easy to make it glide along a
capillar down to a few eM. above the surface of the mixture. Now
mercury could be poured in by means of a capillar-funnel, in which
air-bubbles could be avoided. At last the whole mercury fibre could
be lowered, till the lower end reached the surface of the mixture.
After the tube had been completely filled with mercury, it could
be turned upside down and placed in a steel vessel, which was in
connection with the forcing-pump. Within this steel vessel a glass
vessel filled with mercury, was placed in such a way, that the lower
end of the glass tube was below the surface of the mercury. The
space was further filled with glycerine, and the glass vessel closed
with a brass nut. To have it hermetically closed, rubber rings
are used,

The pressure could be kept constant with this instrument for a
considerable time and could be read by a metal-manometer, a new
one specially used for these experiments. This manometer had been
tested, before it was received by us. As the influence of the pressure
proved to be very slight, little differences of pressure were not paid

( 160 )

attention to, and it was not necessary to use a more accurate in-
strument. This slight influence, which had been expected beforehand
from the theory and in connection with the experiments before-
mentioned, made it necessary to make the observations near the
temperature of complete mixture, Here the difficulty presented itself,
that the heat which would be developed by compression, might be
the cause that the temperature, which had first been below the
temperature of complete mixture, would rise above it. In this case
mixture would not be the direct consequence of the pressure, There-
fore it was of great importance to make an arrangement by means
of which it would be possible to keep the temperature round the
elass-tube constant for a considerable time: for in this way it wouid
be possible to remove the disturbing influence mentioned before. The
attempts to get a suitable thermostat, led to the following arrange-
ment agreeing in many respects with the one described by W. WaTson
(Phil. Mag. Vol. 44 July 1897): a glass cylinder, 30 eM. high and
with a diameter of 5,5 cM., is closed on beth ends with caoutchoue
stoppers. These stoppers are pierced in the middle, so that a glass
cylinder of the same height as the former and with a diameter of
2,6 cM., can be placed concentrically with the other.

The annular cylindric vessel obtained in this way, is placed so
as to have its axis vertical. Two holes made in the higher stopper,
give an opportuniiy of adjusting two glass tubes. One of these is
closed with a tap and serves to bring the liquid into the vessel.
The other is (the glass tubes being in close contact) connected by
means of a rubber tube with another glass tube placed vertically,
which leads throngh a cooling-apparatus, and is bent horizontaily
just above it. It leads further to a T shaped piece to which are
fastened 1°. an open manometer 2°. another T shaped piece. One
arm of the latter T shaped piece has a rubber tube with a squeezer.
This squeezer is so constructed that by means of a screw the ad-
mission of air can be nicely regulated or entirely stopped. The
other arm leads to two large closed bottles, having together about
40 LL. contents, and from there to a rubber tube (with a squeezer),
which brings about the connection with a waterairpump. In this
way the vessel is connected with a Jarge space, in which the
pressure can be lowered. The regulating of this pressure, read
by means of the open manometer, can be easily done by the two
squeezers mentioned. Then a small quantity of mercury is first
brought into the vessel, enough to cover the bottom, and to
preserve the eaoutchoue in this way, and on it a quantity of aethyl-
alcohol, which can be made to boil under various pressures. The

( 161 )

heat required was furnished by an alternating current, easily obtai-
ned by the installation of Electra which is found in the laboratory.
This current is led through a spiral, wound round the inner cylinder
of the boiling-vessel, the ends of which have been sealed through
the glass of the outer cylinder. A necessary condition for the remai-
ning constant of the temperature proved to be that the spiral remained
entirely merged in the liquid.

The glass forcing-tube containing the mixture was then placed
nearly in the axis of the inner cylinder with a thermometer and
the tube of the electro-magnetic stir-apparatus near it. The space
was then closed with wads on both sides. The thermometer was
quite inside that part of the inner-cylinder, where the temperature had
proved to be the same throughout. Therefore correction for the sticking
out of the mercury was not necessary. Within the same space the
mixture which was to be examined and the tin tube were placed.

The mixture was now brought to about the temperature of com-
plete mixture, which took about an hour. Then the temperature
was made to rise a little under continual stirring; after a moment's
rest it was made to rise again ete., till the cloudiness (the proof
of the presence of two phases), had quite disappeared. Then the
temperature was read. After that the temperature at which the
cloudiness reappeared was determined in the same way by cooling
the mixture. By repeating these observations a few times, the
temperature of complete mixture could be very accurately determined.
(The thermometer was verified at the Reichsanstalt). In the same
way the temperature of complete mixture by greater pressure was
determined. The results of these observations follow:

22%, 2 = 0.05
pressure : norm. 30 60 90 120 150 180 atm.
temp. of compl. mixt.: 66.7 66.7 66.9 67 67.1 67.2 67.3
S405 2 = 0:09
pressure : norm. 30 60 90 105 130 atm.
temp. of compl. mixt.: 67.6 67.6 67.8 67.8 68 68.1
Ro eo Osll
pressure : norm. 60 90 atm,

temp. of compl. mixt.: 67.3 67.5 67.7

EN te = Oat
pressure : norm. 60 90 120 atm.

temp. of compl. mixt.: 64.8 65.1 65.3 653

490, == 0.16

pressure: norm. 30 60 90 120 150 180 atm.
temp. of compl. mixt.: 65 65 65.1 65.2 65.3 65.5 65.6
Dor AS
pressure: norm. 30 60 90 atm.

temp. of compl. mixt.: 61.2 61.2 61.3 61.3

(The percentage of phenol has been given here. In the theory
of the surface w we suppose that the quantity of one of the liquids
is M,(1—2) and of the other M; r, in which M, and Ms, represent
the molecular weights. Here 4/, = C; H; OH.)

These observations prove, that increase of pressure causes the
temperature to rise. Considered in connection with the theory of the
surface w, they show that the longitudinal plait (second plait) has a
plait-point on the side of the greater volumes and that at that plait-
point it turns its hollow side towards the «-axis. As moreover, it is
possible to prove in general theoretically, that rise of temperature
makes the plait move in such a way that the projection of the
connodal line on the XV plane falls within that of a preceding
connodal line, it follows from this, that the longitudinal plaits
(second plaits) will be moved to the side of the z-axis if the tem-
perature rises. At a certain temperature the two connodal lines
will intersect. Then we have three co-existing phases. When the
temperature rises, the two points of intersection approach each other,
in other words, the phases begin to resemble each other more and
more. At last the two curves touch; there is only one liquid phase
left, co-existing with the gas-phase. This temperature is called the
temperature of complete mixture. This, however, is but one of the
many critical temperatures of complete mixture, for at a higher tem-
perature it is possible, by increasing the pressure, to get two liquid
phases, which can become perfectly equal in composition and mole-
cular volume. In this case also, there is a critical temperature.
So the critical temperature rises through increase of pressure in
the mixture examined.

( 163 )

If once more the case that two connodal lines intersect is examined,
it is easily seen, that the two intersection-points are nodes of the
longitudinal plait (second plait). When the temperature rises they
approach each other, and when the curves touch, the point of contact
may be considered as two nodes having fallen together. From this
follows, that when two connodal curves touch, the point of contact is
a plait-point of the longitudinal plait (second plait). The spinodal
curve of the longitudinal plait will therefore also touch the spinodal
curve of the transverse plait (first plait). A consequence of this is,

: | 4
that the differential coefficient ae (see T. M. p. 15) must be O in
Ly

this case which points to a maximum or minimum of the line
p=J\(%), that is the curve, which represents the relation between
the composition and the pressure of the saturated vapour of the
mixture.

To test this conclusion experimentally, some pressures of vapour
were measured according to the method denoted by LEHFELDT
(Phil. Mag. July 1898), the results follow:

4.85, «z= 0.01 | 10.1% x=0.02 | 18,90, «= 0.04
Ye Ean miele IN Bane Me ae Pe ine mel
72.4 263 77.2 321 72.2 260
73.9 280 | 773 323 72.3 262
74.9 201 | 77.5 325 | 729 269
75.1 294 81.9 388 73.7 277
76.1 306 | 85 438 75.5 299
77.4 323 | 75.7 301
78.5 338 | 76.5 312
79.9 357 | 77.7 328
81.6 382 amena9 331
83 403 | 78.9 344
83.8 416 | 79.6 353
85.4 AAS | | 80.5 367
86.6 464 | 81.6 384
87 471 83 105
84.4 428

Ts

a = 0:39
P. in m.M.

( 164 )

z= 0.17
P. in m.M.

251
253
264
277
289
306
321
337
351
378
386
401
417
448
462
468
470

op == (05)

P in m.M.
212
215
229
234
253
274
287
323
381
382
389

_

(165 )

From these figures the following values were found by interpoia-
tion for the curves p= fì (7). (The pressures for pure water are taken
from the tables of Laport. A slight correction ought to be made
in the figures mentioned, which is, however of no influence on the
general course of the pressure curves).

0 0 289 314 340 369 400 433
5 001 293 318 344 373 403 436
10 0.02 294 319 345 374 405 438

x “A05, 438
34 0.09 204 319 346 275 406 440
51 0.17 294 319 345 374 404 438
77 0.39 268 289 310 336 364 397
84 0.5 201 223 245 267 290 311

Though its exact place cannot be determined from these figures,
yet it appears that there is a maximum, which corresponds nearly
with value 34 pCt. (c= 0,1), so nearly with the composition by
the critical temperature of complete mixture of three phases.

(November 25th, 1898.)

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4

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING

of Saturday November 26th 1898,

ee

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 26 November 1898 Dl. VII).

CONTENTS: „„Haematopoiesis in the placenta of Tarsius and other mammals”. By Prof. A. A. W.

Husrecnt, p. 167. — „On a Contagium vivum fluidum causing the Spot-disease of
the Tobacco-leaves”. By Prof. M. W. BrIJERINCK, p. 170. — „On congealing- and

melting-phenomena in substances showing tautomerism”. By Prof. H.W. Baknurs Roo-
ZKBOOM, p. 176. — ,,Variation of volume and of pressure in mixing”. By Prof. J. D. van
DER Waars, p. 179. — ,,Equilibriums in systems of three components. Change of the
mixing-temperature of binary mixtures by the addition of a third component”. By
Mr. F. A. H. SCHREINEMAKERS (Communicated by Prof. J. M.van BEMMELEN), p. 191. —
„On the accurate determination of the molecular weight of gases from their density”.
By Prof. J. D. van per Waars, p. 198. — „Some remarks upon the 14-monthly
motion of the Pole of the Earth and upon the length of its period”. By Dr. E. F. van
DE SANDE BAKHUYZEN (Communicated by Prof. H. G. van DE SANDE BAKHUIZEN)
p- 201. — ,,A standard open manometer of reduced height with transference of pres-
sure by means of compressed gas”. By. Prof. H. KaaeERrrINGH ONNes, p. 213. (With
one plate.)

The following papers were read:

Zoology. — „Haematopoiesis in the placenta of Tarsius and other
mammals.” By Prof. A. A. W. Husrecur.

The various authors who have investigated in the course of the
last thirty years the first origin of the mammalian red blood-cor-
puscles have come to conclusions that are far from unanimous.
This can in part be ascribed to the wish to look upon the red
blood-corpuscles without nucleus of the full-grown mammalia as
morphological elements, that are equivalent with the nucleated red
corpuscles of the lower vertebrates and of mammalian embryos.

12

Proceedings Royal Acad. Amsterdam. Vol.

( 168 )

Against this view SCHÄFER, SEDGWICK-MiNor and RANVIER (whose
experimental proof has however a year ago been disposed of by
VOSMAER) protested. The two first-named lock upon the non-nucleated
mammalian blood-corpuscles as plastids, that are formed in cells in
an analogous way as are the chlorophyll-granules in vegetable
cells. The majority of the remaining investigators consider the non-
nucleated mammalian blood-corpuscles as cells from which the
nucleus has either been extruded (RINDFLEISCH, VAN DER STRICHT,
Bizzozero, SAXER, KosTANECKI, HoweLL, MoNpino), or in which
the nucleus gradually disappears within the bloodcell (KörLLIKER,
NEUMANN, SANFELICE, SPULER, Léwit, ELIASBERG, FREIBERG, GRUN-
BERG, ISRAEL, PAPPENHEIM). Dissp, summarizing the results obtained
up to 1895 writes as follows: , Kine sichere Entscheidung der Frage
nach dem Modus der Entkernung der rothen Blutzellen erscheint
einstweilen unmöglich, da die directe Beobachtung des Vorganges
der Entkernung im strömenden Blut unthunlich ist.”

On comparing the maternal and the embryonic blood-corpuscles
as they circulate in each other’s immediate vicinity in any section
of the preserved placenta of various mammals in various stages of
development we are struck by two facts. Firstly the nuclei of the
embryonic blood-corpuscles differ in many respects from the nuclei
of the very earliest bloodcells that arise in the area vasculosa.
Secondly it is the first-named nuclei” and it is not the corpuscle
that encloses them, which resemble both in size and very often in
staining properties the non-nucleated corpuscles of the mother, so
that the question imposes itself whether, if indeed the nucleated
embryonic mammalian blood-corpuscles change into non-nucleated
corpuscles by extrusion of the nucleus, it might not much rather
be this so-called nucleus (which differs notably from a normal
nucleus) which wijl correspond to the definite non-nucleated corpuscle,
than the vesicle from which it has been expelled.

The observation of quite a different series of phenomena in the
placenta cf Tarsius spectrum leads to a confirmation of this hypo-
thesis. They render it probable that during the development of the
Tarsius-placenta part of the cell-material which is actively concerned
in this development, becomes converted into blood-corpuscles that
are set free in the circulating maternal blood which bathes it. These
bloodeorpuscles, entirely corresponding to those which we encounter
everywhere in the maternal bloodvessels, do not take their origin out
of the cytoplasma but out of the nucleoplasma and do not consist
of chromatin so characteristic for the nucleus, but rather and prin-
cipally of nucleolar matter which plays a part in many cell-nuclei

( 169 )

by the side of the chromatin. Haematopoiesis occurs in various
ways in the Tarsius-placenta. Every now and then we notice a
nucleolar body (the nuclear membrane surrounding it becoming
partially indistinct and then disappearing) being set free and mixing
up with circulating blood-corpuscles from which it cannot possibly
be distinguished. Besides this simpler mode of origin we find
another in which large-sized, so-called gianteells with lobulated
and gemmating nuclei play a part. Numerous nuclear fragments
are set free from it, the nucleus itself vanishing in the process.
The fragments are of equa! size, behave in a corresponding way
towards the most different staining reagents and might be designated
as „haematogonia”’. All the intermediate stages between these hae-
matagonia and normal blood-corpuscles were observed and similarly
their development out of the enlarged nucleus and not out of the
cellplasm could be demonstrated. Tf are not only maternal but also
embryonic trophoblastcells which partake in this haematopoiesis
under similar phenomena of proliferation; the blood-corpuscles thus
formed are also caught up by the maternal blood and circulate
with it.

A destructive significance cannot reasonably be given to the giant-
cells in the Tarsius-placenta: they are decidedly constructive ele-
ments, which furnish not only blood-corpuscles, but also the walls
of bloodlacunae. This double part is often played by solid strands
of cells in lower vertebrates.

It deserves attention that the participation of giaptcells with
characteristic proliferating nuclei in the formation of blood in the
bone-marrow, the liver and the spleen of mammals was expressly
recognized by NEUMANN, K6LLIKER, PEREMESCHKO, KUBORN, SAXER,
ELIASBERG, FREIBERG a.o. Many of them look upon the prolife-
ration of the nuclei of these giantcells (which are perfectly distinct
from those other giantcells, the osteoclasts which occur in their
immediate vicinity in the bone-marrow) as the first step in the
formation of blood-corpuscles, although none of them has expressed
the opinion that these latter should not be looked upon as cells but
as nuclear derivates. As soon as we do this, on account of what
we have observed in Tarsius, light is also thrown on the develop-
ment of the fullgrown non-nucleated corpuscles out of embryonic
nucleated ones, a phenomenon which as above indicated is undoub-
tedly comparable to it.

Similar haematopoietic processes are noticed in the placenta of
Tupaja, which differ in detail but agree in general outlines with
what has here been described for Tarsius.

oe

a

CO 7

Whether blood is also formed in the placenta of other mammals
must be carefully looked into. Corpuscles are figured, mixed up
with maternal blood-corpuscles, by Nour for the bat’s placenta, by
Maximow for that of the rabbit, by SreGeNBEEK VAN HEUKELOM
for that of man, with which I feel inclined to identify my ,haema-
togonia” and of which the first and last-named author decidedly state
that they are distinguished by certain characters from polynuclear
leucocytes.

Neither of them, however, refers what he has observed to hae-
matopoeisis.

In point of fact MASQUELIN and Swan (1880) and FROMMEL (1888)
have already stated that blood is formed in the placenta respectively
in the rabbit and in the bat. Their observations have up to now
convinced but few and do not correspond in their details with my
own. What I have myself observed in the rabbit, the hedgehog, the
shrew and the mole has never emboldened me to conclude to the
existence of haematopoietic processes in the placenta: it was not
until I had examined the Tarsius-placenta in which the phenomena
are so extraordinarily lucid that I was forced to draw the con-
clusions of which a rapid sketch was given above, but which is in
no way meant to be a generalisation. Ungulates and Lemurs,
certain Edentates (and probably also the Cetacea) undoubtedly miss
a similar haematopoiesis. Its strong development in Tarsius is
perhaps connected with the unfavourable relation in which the small
and delicate mother finds itself placed with respect to the compara-
tively large foetus, while moreover each parturition is generally
immediately followed by a new pregnancy, a circumstance which
however exhausting its effect may be upon the mother is decidedly
most favourable to the collector of embryological material.

This short account will soon be followed by a full description
with plates and figures, which will appear in the Report of the
Zoological Congress that was held at Cambridge in 1898.

A discussion followed in which Prof. Mac GiLLAvRY and Prof.
Hurrecur took part.

Botany. — „On a Contagium vivum fluidum causing the Spot-
disease of the Tobacco-leaves”. By Prof. M. W. BeijeEriNek.

The spot-disease of the tobacco plant, also called mosaic-disease,
consists in a discoloration of the chlorophyll, spreading in little
spots over the leaf and afterwards succeeded by the partly or entirely
dying away of the tissue which originally composed the spots. Com-

er

Cum 9

monly the discoloration first manifests itself near the nerves of the
leaf by a considerable increase of chlorophyll; afterwards the inter-
spaces between the dark green spots are affected by a bleaching-
process, which mostly does not go farther than to give a yellow
hue to the sickened parts, but which in some cases, causes variega-
tion. The dark green spots grow in the beginning more intensely
than the rest of the leaf, thus becoming blown-up protuberances
rising from the upper surface of the leaf. This, however, occurs
oftener with artificial infection experiments than on the tobacco fields,
where the diseased leaves remain flat. The third phase of the disease
consists in the locally dying of little spots irregularly spread over
the leaf; they get soon brown, are very brittle and even the culling
of the leaf may change them into holes. They make the leaves
valueless as wrappers of cigars.

Professor ADOLF MAYER pointed out in 1886 that this disease is
contagious. He pressed the sap out of diseased ptants, filled with
it little capillar tubes, put them into healthy plants and after two
or three weeks he found these to be likewise attacked by tlie disease.

In 1887 I endeavoured to solve the question whether any parasite
might be found as cause of the disease. It was clear that, if this
should really be the case, there could only be thought of bacteria,
for microscopic observations had not indicated the least traces of
microbes. The bacteriologie culture-methods proved that aërobic
bacteria could not come into consideration for they failed as well
in the tissue of the healthy as of the diseased plants, and the
same holds good regarding the anaërobies. So, it was certain that
here was an instance of a disease caused by a contagium fixum.
This consideration induced me in 1897 to conduct new infection
experiments in order to become better acquainted with the charac-
teristics of the contagium. The chief results of these experiments
are the following.

In the first place it was proved that the sap pressed from diseased
plants and filtered through very dense porcelain was absolutely
devoid of bacteria, without losing of its virulence. Attempis made
to point out in the filtrate aérobics or anaërobies again did not
give any result.

In order to answer the question whether the virus ought to be
considered as corpuscular or as dissolved or liquid, some parenchyma
of diseased plants rubbed fine was spread over agar-plates and then,
left to diffusion. A virus, consisting of discrete particles, would
needs remain on the surface of the agar and consequently be in
the impossibility of rendering the agar virulent; a virus, really

dissolved in water would, on the contrary, be able to penetrate to
a certain depth into the agar.

After about ten days’ diffusion, a time which I considered suffi-
ciently long in accordance with that wanted for the diffusion unto
a eonsiderable depth of diastase and trypsine, the surface of the
agar-plate was first cleaned with water and then with a solution of
sublimate; then the upper layer was removed by means of a sharp
platinum spatula. {n this way the inner part of the agar might be
reached without its having any contact with the particles adhering
to the surface. Infection experiments performed with these deeper
layers caused as well the disease as the porcelain-filtrate. So, there
seems no doubt left but the contagium must be fit for diffusion and
consequently considered as fluid.

The infection experiments were performed with the expressed sap
by injections with the syringe of PrAvaz. The most proper place
for injecting 1s the stem, and in particular the youngest parts which
are still in growth. The nearer the place of injection is to the
terminal bud, the sooner its consequences show themselves. This is
evident from the experience that only those leaves are susceptible
of infection which are still in growth and in the phase of cell-
multiplication, meristems being by far the most susceptible. By
making use of this fact and injecting the virus cautiously quite
near to active meristems, I was of late enabled, three days since
the injection, already to observe the first symptoms of the disease,
whilst otherwise they must be waited for two or three weeks longer,
Full-grown leaves, and even leaves whose cells are still in the phase
of elongation but no more in that of multiplication, are unfit for
infection.

As the quantity of virus, sufficient to produce a large number of
diseased leaves, is extremely small, and as the juice of these leaves
will serve to infect an unlimited number of plants, it is clear that
the virus must increase within the tissues. In accordance with what
is said before, this increase occurs in and with the dividing cells,
the full-grown tissues of the plant not allowing any such increase.
This quality of the virus reminds, to a certain extent, of the action
of the cecidiogenous substances, which likewise exert their influence
in those parts of plants only, which are still in a state of growth
and cell-multiplication. Out of the plant it scems impossible to bring
the virus to increase. This conclusion must be drawn from the fact
that bougie-filtrate mixed and long kept with a certain quantity of
the filtrate of juice of a healthy plant, not only does not increase
but even loses in virulence in the same degree as if it had been

( 173 )

diluted with pure water. It is not difficult to convince oneself of
this, for the quantity of the virus employed is of great influence
upon the symptoms and the course of the spot-disease. If a consi-
derable quantity of virus is at once introduced into the plant, the
first diseased leaves, which develop from the bud, not only show,
besides the usual symptoms, a remarkable relaxation and suspense
of growth, by which they remain much smaller than normal leaves,
but also deep, irregular pinnate or palmate incisions in the margin
in consequence of some lateral nerves remaining short. As the
chlorophyll-tissue thereby develops very imperfectly and as, especially
near the nerves, the formation of chlorophyll may be quite deficient,
these leaves get a peculiar striped appearance and by their shape
belong to the true monstrosities !). When a small quantity of the
sap is used such deformations don’t appear at all, so that it seems
to me that an increase in virulence of the sap under the said circum-
stances would not have escaped me.

Consequently I consider it as certain that the virus can only be
reproduced in the manner described, with and through cell-multi-
plication of the plant. In my opinion this fact must be related to
the fluid or dissolved state of the virus, for, with regard, to a
contagium fixum, were its particles ever so small that they escaped
all microscopic observation, there is no plausible reason why it
might not augment, like parasitical bacteria, out of the fosterplant.
It does not even appear impossible that a microscopically invisible,
but notwithstanding corpuscular contagium, might occasion visible
colonies on culture gelatine. A fluid virus, fit for diffusion like that
of the spot-disease, would penetrate into the gelatine or the agar
and, if it were fit for reproduction, it would then alter the chemical
nature of the nutritive substances, which might perhaps be observed
by a change of colour or of refrangibility in the plates. When
„sowing”’ the virus on malt-extract gelatine, and on plates obtained
from some plant-infusion with 2°/, canesugar and 10°/, gelatine, —
according to my experience excellent culture masses for bacteria com-
monly occurring on plants, — such alterations could in no way be
observed. Moreover, though reproduction or growth of dissolved matter
is not quite inconceivable, yet, it is difficult to imagine in what way
such a process might be achieved. A division-process in the molecules
causing their multiplication, meets, to my mind, with great difficulties ;
even the conception of „molecules which take food”, would seem to
me vague, if not inconsistent. The increase of the contagium now, is

1) On one of my plants such a leaf had taken the form of an ascidium,

( 174 )

on the contrary, partly explained by the circumstance that it must
first be bound to the protoplasm of the living cell itself, and so
carried on into the reproduction. In any case, two enigmas seem
by this fact to a certain degree to be reduced to one ').

If the ground in which the tobacco-plants grow is infected with the
virus, one sees, after some time, the disease appear in the terminal bud.
The time of the incubation varies very much and depends on the
size of the plants. In smaller plants I remarked the first symptoms
of the disease in the new-formed leaves of the terminal bud two
weeks after the infection; in bigger ones after three to six weeks.
Root and stem are in this case obliged to convey the virus often
to considerable distances. Various observations prove that this con-
veyance goes, by way of exception, along the xylem, which conducts
the water; usually, however, it seems to follow the so-called descending
sap, and then it probably goes along the phloem.

That the first mentioned way may be followed, must be concluded
from the order of succession in which the symptoms of the disease
appear when a great quantity of the contagium is introduced into
the stem, for in this case those parts of the young leaves get first
diseased which are exposed to the strongest evaporation, such as
the tops and margins which reach freely out of the bud. The con-
veyance of the virus along the phloem may be concluded from the
following observation.

If one infects the middle-ribs of full-grown leaves, or of leaves
whose cells are in a state of elongation but no more of cell-division,
the leaves themselves continue healthy, but the virus turns back to
the stem, thence, in the usual way, to infect the meristems of the
buds and the youngest leaf-rudiments. This return of the virus from
the leaf down to the stem must undoubtedly be by the way of the
descending sap, that is along the phloem.

1) Perhaps, basing on these considerations, one may think of the possibility that
enzymes, in a manner agreeing with that of the contagium fluidum, are reproduced
in the cells, and might thus, to a certain extent, be considered as independently
existing. Concerning this point I wish to observe the following. Pressed yeast, culti-
vated. in nutriment containing diastase, takes from it a notable quantity of diastase
which it is difficult completely to remove from it by washing. If, however, this yeast
continues growing in a medium free from diastase, then the diastase soon totally
disappears. That this might be attributed to incongruence between the protoplasm of
the yeast-cell and the diastase-molecule, so that a persistent union might possibly be
effected by other microbes or by means of the tissue-cells of higher organisms, is not
probable, the yeast-cell being not absolutely free from diastatie substances, containing,
for instance, some elucase. For the moment, therefore, I must consider such a con-
clusion as unavailable,

From out the root, infection is possible even with plants of two
or more decimeters in height. If for this purpose woundings of the
root are necessary, is not yet clear; probably roots may absorb the
virus from the ground even through their unhurt surface. As infec-
tion only occurs in the buds and meristems, the number of healthy
leaves found at the bottom of the plant, indicates in some way the
date of the infection, in case the virus has entered through the root

Without any loss of virulence the virus may be dried and in tha
state exist through the winter, for instance in the ground; part,
however, gets lost then, just as is the case with many bacteria and yeast
species. The leaves, too, keep their virulence when dried, so that
the dust of the brittle leaves helps, no doubt, to spread the disease.
Precipitating the virus with strong alcohol from its solution and
drying the precipitate at 40° C., it remains virulent.

As was to be expected, the virus in moist state is rendered in-
active, not only by boiling temperature, but already at 90° C. The
lowest deadly temperature I have not been able to fix; I think it
will be found between 70 or 80° C.

Above I alluded to the formation of characteristic leaf-monstrosi-
ties when a large dose of the virus is injected. Another, but rarer
effect of artificial infection, is variegation or albinism. Hitherto I
obtained this effect in too few plants, than that I should be able
to point out how it may be expected with certainty; but I have
some hopes that further experiments will enable to produce it
at will.

That albinism, or at least one of the forms in which it appears,
shows a certain relaticn to the leaf-spot disease, may be allowed
already at a superficial view of the latter. However, until now, we
are obliged to admit that an important difference exists between
them as to the way of transferring the infection. In so far as may
be concluded from the relatively few experiments concerning this
point, infection for albinism requires a direct uniting, by means of
grafting or budding of the variegated with the green plant. In-
fection, on the contrary, of green plants with the crushed tissue of
variegated varieties, seems never to produce any results. My above
mentioned plants, however, indicate that there must exist another
way alang which variegation may be calied forth, namely by a virus
existing outside of the plant.

Probably there are various other plant-diseases, which originate
in a manner alike to that of the spot-disease of the tobacco. The
disease of the peach-trees in America, described by ERwin Smita
under the name of „Peach Yellows” and „Peach Rosette” (U, S,

(116 )

Departm. of Agriculture, Farmers’ Bulletin N°. 17, Washington 1894)
are, according to the description, undoubtedly caused by a conta-
gium fluidum, but it is still dubious whether the infection is only

transferred by grafting and budding, or, — which is more pro-
bable, — also by a virus existing outside of the plant.
Chemistry. — „On congealing- and melting-phenomena in substances

showing tautomerism”. By Prof. H. W. Baknurs ROOZEBOOM.

The latest discoveries on tautomerism, which have shown, that
tautomeric substances in the liquid state must be considered as
mixtures of two kinds of molecules of different structure, have raised
the problem how to explain the complicate congealing- and melting-
phenomena of such substances, in case both forms or one of them
can appear in the solid state.

Some remarkable investigations on this subject have of late been
made by Bancrorr and his disciples, which were a continuation
of a theory of Dunem.

At an attempt to unravel the investigations of CLAISEN on this
subject, the reader had come to the same conclusions, which may
be united to a perfectly clear graphic sketch.

Bancrorr having already published this, there would be no reason
to revert to the subject, if not all examples chosen by him, referred
to cases in which all the melting- and congealing-points were found
in the region of temperatures in which equilibrium is still obtained
between the two forms in the liquid state.

In such a case we generally have the disadvantage of there being
no certainty about the mixing-proportion of the two substances at
the moment of melting or congealing. Consequently it is impossible
to give quantitative representations.

To arrive at a good understanding of the phenomena, it is there-
fore desirable to begin with a deduction of the conduct of tautomeric
substances, the congealing temperatures of which are below the
temperature-limit where in the liquid state transformation between
two forms is still possible.

If we call the two forms @ and (9, we may build up a sketch
in which the mixing-proportion of « and / is measured on the
horizontal axis of 0—100 aud the temperature on the vertical axis.

According to the supposition made above, the congealing appears
in the ordinary and simplest form of the congealing of mixtures
of two substances i. e. starting from the melting points A and B
of the two modifications, we have two melting-lines AC and BC

(171)

meeting in the point C, below
which every liquid mixture
congeals entirely to a conglo-
merate of @ and / crystals.

We now suppose that at
higher temperatures not all
mixing-proportions in the liquid
state are possible, but equili-
brium appears, giving at each
temperature a definite mixing-
proportion of @ and £. We
represent these mixing-propor-
tions by the line #G which
is arbitrarily drawn as rising
from left to right, representing
the case in which the transition
af} takes place with absorp-
tion of heat.

The reverse is also possible,
or it may be a vertical line if
the heat is zero.

On the left of the line ’G
is the region in which the
transformation @ — /? takes

concentration 2 place, on the right that of the

transformation @ — /9,

Now in ease both transformations do not take place at lower
temperatures, the supposition naturally occurs to us — on analogy
of many other phenomena of recent date — that the transition from
the region of reciprocal equilibrium to the region of no equilibrium is
formed by two regions of one-sided equilibrium, as may be represented
by splitting up the line GF into two lines #Y and FZ which
end below certain temperatures on each of the axes.

If I now heat the solid modifications only a little above their
melting point, they will be in a condition to congeal again at the
same temperatures at which they melted. But if I heat them to a
higher temperature, keeping them for some time at a temperature
belonging to the region of one-sided or reciprocal equilibrium, a greater
or less transformation in the liquid will take place between the two
modifications, varying afterwards according to the velocity of cooling.
The manner of proceeding of the congelation after return to this
region will depend upon all these circumstances.

«

(DE >

From the sketch the following conclusions may be drawn:

Case I. The substance « or 7 is heated for a considerable time
after melting at a temperature situated above that of point F, Then
the liquid is slowly cooled.

No matter what the heating-temperature was, and whether we
started from « or from /2, the congelation now begins in point HZ U),
deposing solid @, until it is completed in C, deposing solid @ + /.

Case II. The substance « is heated for a considerable time after
melting at a temperature situated below PF, being afterwards slowly
cooled.

The first melting point is now variable, always lying above M,
and that the more so in proportion to the heating having taken
place to a lower temperature. The first deposit is solid @, the con-
gealing ends in C.

Starting from /%, and in proportion to the heating having been
lower than J’, the first congealing point will be at first below 4,
deposing @, then falling to C, then rising along CB deposing /.
C remains the final congealing point.

Case III. The substance @ or / is heated for a considerable
time after melting at a temperature above F, but afterwards quickly
cooled.

The first congealing point is situated to the right of H, no matter
whether « or /? be the starting point, and this the more so in
proportion to the heating having been greater and the cooling quicker.

The starting pomt of the congelation may even move past C,
so that /? becomes the substance first deposed, provided the line
FG yunning sufficiently to the right. C remains the final con-
gealing point.

Case IV. The substance « or / is heated for a considerable
time after melting at a temperature below F being afterwards quickly
cooled.

The results both for « and /} are tne same as in Case II.

Case V. If the heating does not last long enough to reach the
final equilibrium in the liquid state, the same result as in Case II

1) The point A lies vertically under 7, or better still under the point of #2 on
which a vertical tangent may be drawn to this curve,

OO Sa

will be obtained in case of a quiek cooling — independent of the
situation of the heating-temperature.

The velocity of cooling as mentioned in Case III—V, is supposed
to be such that the liquid finds no occasion to alter its mixing-
proportion @/f acquired at a higher temperature. Should the velocity
of cooling be less, this only results in the differences between the first
acquired congealing-point and point 4 being smaller than in a case
of very quick cooling. The deviations remain however in the same
direction.

It is therefore possible to determine with perfect accuracy the
apparently curious phenomena of congelation, with a knowledge of
the lines GF, FD and FE. On the other hand it would be pos-
sible, from observation of the congealing temperatures, after the
substance @ or {5 having gone through a sharply defined way, to
conclude to the situation of different points of these lines, conse-
quently to determine their direction, if this were not possible along
other ways.

The phenomena described here, may appear not only in tautomeric
substances, but in all substances which in the liquid state, give two
modifications that are apt to transformation.

Consequently many optic isomers that show equilibrium at higher
temperatures, come under this head. There however the matter can
often become complicated, it being possible that after the transfor-
wation of the d or the /-form, the racemic form deposes in the solid
condition. It is however easy to take this into account.

Physics. — „Variation of volume and of pressure in mixing’.
By Prof. J. D. VAN DER WAALS.

The supposition of Mr. Amacar (C. R. 11 Juillet 1898), that in
a mixture every gas can be considered to occupy the volume which
it would occupy separately under the same pressure and at the
same temperature, comes to the same thing as supposing, that
mixing under a constant pressure does not cause variation of
volume, and that there would be no question of either positive or
negative contraction. As at great densities (of liquids), mixing is
generally accompanied by contraction, the thesis, also in case of
slight densities, can only be meant as an approximation. For slight
densities this thesis can be tested by means of the characteristic
equation of a mixture.

( 180 )
For a molecular quantity of a mixture, consisting of m, (1—«)

and m,« unities of mass, the equation holds:

po Mi ed =) En

v—by v

or by approximation

1

po== MRT — — (a, —b, MRT). .. ~ Soe
v

For each of the components
1 lg

po = MRT (a bh MRT) VEN

vy,
would hold for a molecular quantity, and

1
poy = MRT — — (a, — 6, MRT) NEN
Vv,

2

If we put v=», (1 —e) Jor J Av, and take into consideration
that ara, (l—e) + 2a,e(l —2) +a, 2°
and brb, (1 —2)?+ 26,,2(1 —2)-+ b, 2?

1—.) (a, —b, MRI)
+

v

1
pAn = — — (ar — be MRT) +
v 1
x(a, —b, MRT)
KEE

Vs

2

by subtracting the sum of (1—2) times equation (2) and 2 times
equation (3) from equation (1).

As pv as well as pv, and pe, are equal to MRT by approxima-
tion, we may put

MRT Ay = {a, (l—2) + a, « — [a, (12)? + 2a,, (le) + a, 27] }

— MRT {b, (le) + b, x — [b, (12) + 25,, x (ler) + 6, 1}
or
MET A, = — #(1—z2){ [2 4,, —'a, al —[20,, — b, —0 ae

or

(181 )

Ch ae AGE ¢
LS =e (1— 2) | MRT = (0, +. b, —2 1) . . (4)

From this equation (4) follows: 1°. that the absolute value of
the variation of volume at a given temperature is independent of
the pressure, under which the mixture takes place, of course only
as long as it does not surpass the limit, below which the calcu-
lations mentioned are sufficient approximations ; 2°. that the maximum
value of this volume variation is found for «= }; so if the sub-
stances to be mixed have the same volume. For air, which is
composed of oxygen and nitrogen, the volumecontraction will amount
to no more than !°/,; of the value, found when equal volumes of
oxygen and nitrogen are mixed. The quantities must, of course, be
chosen in such a way, that in both cases the total volume of the
components is the same; 3°. that it depends on the value of the
expression :

Nae ieee eet aby) CS a ee
1+ «at 7 .
whether negative or positive contraction takes place.

As in the characteristic equation the volume, occupied by the
molecular quantity under the pressure of one atmosphere and at 0°,
has been taken as unity of volume, the quantity A» is also expressed
in that unity.

It is true that the unity of volume in the three equations (1),
(2) and (5) is not absolutely the same, on account of their different
degree of deviation from the law of Boy, but the influence of
this fact may be neglected in these calculations, as the deviation
it causes, is a small quantity of higher order.

If we proceed to the discussion of the expression (5), we see in
the first place that b, + 6, — 2b,, =0 comes to the same thing as
assuming the co-volume of a mixture equal to the sum of the co-
volumes of the components.

The circumstance, that it is easier to arrange arbitrarily formed
bodies, which take up together a certain volume, in a given space,
when the bodies are different in size, than when they are all of
the same size, makes it probable, that the co-volume of a mixture
of molecules of different sizes will be smaller than 4 times the real
volume. In the deduction of the characteristic equation, in which,
however, the molecules are thought as spheres, this has been proved,

( 182 )

and %/, (bb, PL) (bb, 4 Bb,) 1) has been found for the value
of b, + 6, —26,,, an expression which is always positive. On the
other hand, this expression, which is equal to 0, when b, =b,, and
which is positive, as well when J, > b, as when b, <b,, shows
that for a small difference in size the value of 0, + 6, —2b,, is
very small. If we might neglect it, it would only depend on the
sign of 2a,,—a,—a,, whether mixture would cause contraction
or not.

When 24,, — a, — a, is positive, mixing is favoured by the mo-
lecular forces. For if we suppose the two gases before the mixing

i N a ay :
separated by a mathematic surface, — and — are the forces which
v. al v rd
1 2
2a
: ; Hae ; :
oppose mixture, and ——— is the force, which draws the two sub-
Uv, Ve.

1 2
stances through the bounding surface. In this case we may put
=v,, and the sign of 2a,,— a, — a, proves to be decisive.

In general we are justified in expecting, that when mixing is
favoured by the molecular forces, and when in consequence of the
mixing a smaller molecular volume must be subtracted from the
external volume, both circumstances cause positive contraction (ne-
gative value of A»).

If (a, +4, —2a,,) and (6, +4, —26,,) are both positive, a
temperature exists, below which A, is positive and above which
Ay» is negative, just as is the case for the deviation from the law
of Boyne for a simple substance. But in general we may expect
that — A» (volume contraction) will be small and that the thesis
of Mr. AMAGAT will hold true with a high degree of approximation,
at least in all cases, in which the properties of the components
differ little. In the first place because a, + a, —2a,, and 6, +b, —2b,,
are both equal to 0, if the substances are the same, and we may
therefore put, that when the difference is small, the value of these
quantities will be small, compared to each of the terms, of which
they consist, e.g. a, +4, — 2a,, is small as compared with a, or a,,
and l, + 6,—2b,, is small as compared with 6, or b,. Secondly
on account of the factor «(l1—z); for air this factor amounts to no

v
0

4
more than — .

25
Our equation cannot be tested at the values which Mr. AMAGAT
gives for air of the ordinary temperature and which begin at a

1) Théorie Moléc. Arch. Néerl. Tom. XXIV.

emd dn

( 183 )

pressure of 100 atm., as the equation is not sufficiently approxima-
tive, and because Mr. Amacat himself comes to the conclusion,
that the deviation found does not exceed the possible errors of
observation. It were desirable that similar experiments were made
with equal volumes of substances which differ much in physical
properties. In testing, the equation (4) should be replaced by another
which would hold with a higher degree of approximation. If
the volumes 2, v, and ev show a marked difference, the term
a, +a, — 2a,, should be replaced by:

an expression, which at a feeble density may be considered as equal
to a, a, — 2a,,, but which approaches

b b (> ape gek)
NDR De De Be

if the density increases.

We have no right to expect, that the value of A, will remain
perfectly constant at various degrees of density (which would follow
from the approximative equation), and at any rate the reservation
is to be made, that always either two gas-phases or two liquid-
phases are to be mixed. We may however expect, that the value
of A» will keep within certain finite limits, and that therefore, that
which may seem large as compared to two small volumes (liquid
volumes), may be neglected if compared with very large gas volumes.

Mr. Kuerrex (Dissertation 1892, Leyden) has made observations,
from which the quantity A» may be determined for mixtures of
of CO, and CH, Cl and has found it positive. It is to be regretted,
that he has not tried to determine the value of A,, but that he
gives the increase of pressure, which is to be applied, in order to
reduce the volume of the mixture to the sum of the volumes of
the components. Intricate calculations are necessary for finding our
result confirmed, namely that A» is not 0, but that it has a value
of the same order of greatness all throngh the course of the isotherme.
If he had restricted himself to the determination of Av, he would
undoubtedly have come to the conclusion, that A, is quasi-constant,
and he might have given an approximative rule, which I now feel
obliged to ascribe to Mr. Amacar, though AMAGAT’s rule A, = 0
must be replaced by A» is nearly constant.

13

Proceedings Royal Acad. Amsterdam, Vol. I,

( 184 )

1 shall not carry out the intricate calculations, which would be
necessary to calculate A» from Mr. Kuxrnen’s observations of the
increase of pressures, but I shall restrict myself to an approxi-
mation, sufficient to conclude that the different values of A» in
Mr. KueNeN’s experiments must have been quantities of the same
order.

From
MRT a
p= a
v—b uv?
follows
dp MRI 2a
do (v—b)j? v8
and
I —2b MRT
== MR Tee pe — a ie
dv v'

by approximation.

_ (1 + at) (Ap)

So we can calculate the quantity Av from A, =
ip

Variation of pressure in mixing.

Atmosph. Mixture. T. 433.0 403.0 373.0 343.0

10 Sih 10.06 10.07 10.08 10.08
1/3 10.04 10.05 10.07 10,10
Vn -- 10.06 10.07 10.09

30 JA 30.67 30.85 31.20 —
1/, 30.56 30.81 31.25 pe
Nh — 30.78 31.06 —

50 51, 52.4 54.4 Sy Bis
1), 52.1 54.3 Bs, L
u, a 53.1 a oe

If we take 7 = 403° ande = */,, as an example from Mr. KUENEN’s
table, which I have reproduced here, we find at

(eh)
p= LOP A Ay = O20 O80
p= 30 Ay = 0,0014

p90 An == 90,0026

Also from Mr. KurNeEN’s values, about which he himself remarks,
that they show but little regularity, we get the impression, that
the exact determination touches the limit of the errors of observation.

From the observation at 433° we find if «= */,

p= 10 Ay = 0,00095
p= 30 An —0,000 18
D= 50 Ay = 0,00152

According to the formula (4) A, must be smaller at a higher
temperature, which is also confirmed by the calculated values; for
the rest the increase is not so quick at 433° as at 403°. But I
repeat, what I said before, that though the approximative formula
gives a constant value for Av, we want more accurate formulae, to
indicate the real course.

Let us compare, in order to judge about the degree of approxi-
mation, with which the thesis of Mr. Amacar holds true, the cal-
culated quantity Av with the value of Ap. By A, we represent the
difference between the pressure of a mixture and that pressure,
which we should find if the law of Dauron held good.

If we take in a volume v first 1 —z molecules of the first sub-
stance and if we call p, the pressure, after that « molecules of the
second substance, with the pressure p,; and finally a mixture with
pressure p, then Ap=p—(p, +).

: . v .
In the first case the molecular volume is em: the second case
—wv

v SN : :
—, and for the mixture v. So we have the three following equations :
v

13*

( 186 )

_ MRI (1—2z) a, (1—2)?
Zi v—b, (l—r) a v"

and

ME, MRT «x a, wv?

Ps = —_—— —
v—b, © u?

and from this by approximation

2 MRT, « (1—a) — 2a,, «(1—2)

vw

Lo Pe Pas

or

(1 + at) by, me

Ap = 2 Ee (1—2).

If we first restrict ourselves, when discussing the value of Ap,
to this approximative formula, which is sufficiently accurate under
a small pressure, we see 1°. that Ap varies greatly with the density,
that it is even proportional to the square of the density; 2°. that
Ap depends on the composition of the mixture in the same way
as Av, and 3°. that the sign of Ap depends on the sign of
(1+ at) b,, —a,,. This expression cannot be considered as small,
and does by no means disappear, when the two components are
the same.

In this case b,,=b, and a,, =a, and the value of Ap is also
of the same order as the deviation of the pressure in the investigation
of the law of Boy, and varies also inversely as the square of
the volume. Also for Ap there is a temperature, at which it is 0,
just as is the case with p —p’, if p' is the pressure according to
the law of Boye and p the observed pressure. Below this tempe-
rature Ap is negative, above it, on the contrary it is positive. The
agreement of the course of A, with that of p—p', when the volume
gradually decreases, is nearly perfect.

When the volume is continually decreasing, a maximum value
for p—p' is found in those cases, in which this difference is
negative for a large volume, and in this case a volume may be

LET }

reached, at which p— p' has descended again to 0, reversing its
sign when the volume is still more diminished. The same holds
true for Ap!).

In order to show this, the approximative value of equation (5)
does not suffice. A more accurate value of Ap is:

= all) ze Glow) ED) ha)
Ap — 2x (1 dE (1 JL ar) (1 bz) (v—bz) lob, (1—2)] (v—b,2) y? \ 9
if we represent by f the quantity

[br — b, (I—2)]? |
2b,,

(6, +5) © (le) +

If we calculate p — p', we find

,_ Gta) (1—d)b at) a
u v (v—b) oy

je
If a>(1+a)(1—0)b(1 4+ at), p—p' is negative, when the
volume is large, but positive when
b

1 Hoi + a) (1 — 6) (1 — at)

vS

A, has, it is true, a more intricate form than p —p'. But this
is more in appearance than in reality.

If a,b, (1 + az) (Ll — bz) (1+ at), Ap is negative, when the
volume is large, but positive when v does not differ much from 0,.
It has in reality no significance that the sign would be again re-
versed for other values of v also, e.g. between bz and b, (1 — 2),
because in a volume smaller than 6, the mixture could not take place.

A series of values for A,, which Mr. Kuenen gives from his
observations on mixtures of CO, and CH, Cl and which we repro-
duce here, may be used to test the properties of Ap pointed out here.

1) These results have already been deduced by Maraures from the observations
of ANDREWS. Wien Sitz. Ber. 1889, Band XCVIIL Seite 885. See also B. GALITZINE,
Wied. Ann. Band XLI,

Deviation from the law of DALTON.

Vol. T. 433.0

0.015: 8/7 SAAB 2560

0.030 3, 44.5 —1.6

0.045 3/, 31.58 —0.78

0.060 2, 24.46 —0.46

Is Fi

A=p— (pi +22).

In the approximative equation (5) the value of A, does not vary,
when we interchange x« and 1 — z. In the more accurate equation
this is no longer perfectly true, but the asymmetry is only per-
ceptible for very small volumes.

Mr. KUENEN finds, at T= 403°,3

if v = 0,06

if vp = 0,045

ifv = 0,03

rs OON)

At lower temperatures the agreement is less perfect than is the
case for the three first mentioned volumes in the above table; but

I

373.0
p A
50.0 —8§.9°
60.0 —11.9
Qsog t= e's
Se 26
37.0 —3.7
39.5 —2.5
25.46 —1.22
26.55 —1.78
97.69 —1.16
20.06 —0.70
20.66 —1.04

21.30 —0.66

Ap = — 0,55 Atm.
Ap = — 0,56

Ap = — 0,93

Ap = — 0,96

Ap = — 2,1

Ap = — 2,0

Ap = .— 7,4

Ap = — 6,8

( 189 )

in general more perfect than in the case of the last volume. The
rule that A, is proportional to #(1—~) involves that for «= /, a
value must be found that is */, times larger than that for c= '/, or
*/,. From Mr. Kuenen’s value a greater proportion is generally found
for it. At 7=403°,3 the proportion found in the case of the four
0,89 1,52 3,2 9,9

; ; and ——; so values
0,555 0,954” 2,05 7,1

varying between 1,6 and 1,4.

before-mentioned volumes is

IES) st RTS 1,04

’ ’ and ;
8,875 2,55 1,19 0,68
so they are varying between 1,5 and 1,35.

But at T= 343°, we may consider the proportions found as
equal to ‘/,.

According to the remarks, deduced from equation (6), the depen-
dence of A, on the volume must be expected less great than pro-
portional to the squares of the density. This may be considered as
being confirmed by the values, given by Mr. Kuenen. So Mr. KUENEN
Ansa ie —HO-o. A; —O0.8l and at »1—. 0:03 Aj—=2)9) and if
v= 0,045 Ap = 1,38 etc.

The dependence on the temperature, for which according to equa-
tion (5)

At T= 373°, the values found were

eo Ga
v?

on Ap), —(— Ap), = = v(1—z)

would hold, and according to which formula for the same value
of « and » the differences of the observed values of A, would be
proportional to the differences of temperature, is not confirmed by
KueENEN’s figures. But in all this we must not overlook the fact
that the Ap’s are already differences of observed quantities and not
the observed quantities themselves, while {(—A »)z,—(—Ay,)z,} are
again differences from these differences. It is therefore to be regretted,
that there are so few observations, which may be used for this
investigation, and specially that Mr. Amacar has not been able
to continue his investigation of the mixture CO, and N, ’).

If we try to calculate a value for ¢,, from the observed value of
Ap, e.g. from the observation with v = 0,06, ©= %/,, T= 373,
which gives Ap=—0,7, this can of course, only be done by

1) C. R. Acad. des Sciences, 11 Juillet 1898.

£ 190)

assuming a value for J,,. If we assume 0,0024, a value which lies
between 4, =0,0020 and b, =0,0029, while an error in this value
will have comparatively little influence on the value of a,,, we find

a,, = 0,7 X 0,0036 X /, + 0,00328 = 0,010 .

From Mr. Kuenen’s values for the variation of pressure (— Ap),
we find the following value for a,,, which has been calculated by
means of the approximative equation.

T — 348 » = 0,06 » = 0,045 » = 0,03
e=, 0,0105 0,0117 0,0101
c= '/, 0,0112 0,0109 0,0104
a= */, 0,0116 0,0114 0,0110
T — 373

e=, 0,0096 0,01086 0,0100
em /, 0,0096 0,0104 0,0097
a= |, 0,0093 0,0099 0,0095
T — 403,3

r= /, 0,0088 0,0086 0,0086
e= 0,0099 0,0097 0,0093
e=", 0,0089 0,0087 0,0084

For the calculation of a,, from the results at v = 0,015, given
by Mr. Kuenen, the approximative equation is no longer sufficiently
accurate.

For these values of a,, we see the same not yet explained phe-
nomenon, generally observed for the values of a, and a,, namely
that they increase at lower temperatures. The advantage of the
equation which has served to calculate them, is that it is indepen-
dent of possible changes, which might have occurred in the values
of a, and a, through change of temperature. So the accurate deter-
mination of — Ap is as yet the best means of supplying at least
one relation between a,, and b,. The variability of a,, with the
temperature, would therefore be no reason to doubt of the values
found for a,,. There is, however, another circumstance, which makes

(191 )

me doubt, and that is, that according to the results obtained by
me formerly (Verslag Kon. Akad. 27 Nov. 1897) a, + a, — 2a,,
a, + 4%

9 )
&

and this

would be negative for CO, and CH, Cl or a, >
would require a greater value for a,, than would be found from

Mr. KueNeN’s values for — Ap. In order that a,, > a om should

=

hold good, e.g. at 7 == 343°, a,, would have to be greater than
0.00126, while from the calculation of — Ap, a,» is found to be
at the utmost 0,0116. That from Mr. Kuenen’s observations

ree a follows, is confirmed by the observation, that mixing
of CO, and CH, Cl gives increase of volume.

If this is really the case, it would prove that I ought to have
expressed myself with still greater reserve than I did in my: “Ap-
proximative rule for the course of the plait-curve of a mixture” !).
Though I have drawn the attention to the fact, that the real plait-
curve will deviate from the curves drawn, yet I had thought, that
the deviations would not be so great, as to make the different types
no longer to be distinguished. Yet so great a deviation really
oceurred in this case.

If we look back on the two rules discussed here: A, = 0 and
Ap = 9, we are induced to qualify the first rule as an approximative
law. Throughout the course of the isotherme, from an infinite volume
down to the smallest possible volume of the substance, there may
be deviation, but the deviation remains within finite limits. The
second rule hoids perfectly good for infinite rarefaction, but it
would be utterly impossible to apply it also to liquid volumes.
Such a law may be qualified as a loi-limite. Considered from this
point of view, the law of BoyLe too is not an approximative law,
but only a loi-limite.

Chemistry. — Prof. VAN BEMMELEN reads a paper of Dr. F. A.
H. SCHREINEMAKERS on: ,Equilibriums in systems of three
components. Change of the mixing-temperature of binary mix-
tures by the addition of a third component.”

Among the different systems composed of the components 4, B
and C we suppose the case, that in two of the binary systems f.i.
A—B and A—C two liquid phases can appear, but not in the system
B—C, An example of this we find fi. in the system formed of:

1) Verslag Kon. Akad. Nov. 1897.

( 192 )

water, aleohol and succinonitrile, two liquid layers only appearing
in the binary systems water-succinonitrile, and alcohol-succinonitrile
but not in the system water-alcohol. A second example, which Dr.
SCHREINEMAKERS has now subjected to an investigation is the system:
water, phenol and aniline; in the system phenol-aniline there do not
appear two liquid layers, in the systems watcr- phenol and water-
aniline there do. Yet the isotherms acquired in both systems are
entirely different as shown in figures 1 and 2. In fig. 1 the letters
W, A, N indicate the components water,
alcohol, succinonitrile ; in fig. 2 the com-
ponents are water, aniline and phenol,

indicated by the letters W, An and Ph.
(de In both systems we shall only consider

N

AD part of the appearing equilibriums viz the
Wi A appearing liquid phases that can be in
Fiat equilibrium with each other; the equili-
ij briums in which solid phases appear are
Ww not considered here.

Let us begin with the system: water,
alcohol, succinonitrile; at temperatures
above 56°5 only homogeneous liquids are
possible and no separation into two layers
can appear. The ¢-surface in fig. 1 above
the triangle W A N is consequently in
every point convex-convex downwards.
Here and in future we only consider the
sheet of the ¢-surface that belongs to the liquid phase }). When
the temperature falls there appears at 56°5 a plaitpoint and at
lower temperatures a plait is developed ending on the plane WNC
and continually extending in case of a fall in the temperature. In
fig. 1 d is the projection of the plaitpoint at 56°5 ; the different
lines drawn, each of them ending in two points of the line W WN
are the connodal lines at the different temperatures ; they are all
situated in such a way, that those belonging to lower temperatures
lie outside those of higher temperatures. In case of a fall in the
temperature the plait from the side W MN extends more and more.
At + 32° there appears however a second plait on the C-sufrace, origi-
nating in the plane A N ¢, in a point, the projection of which is
indicated by ¢; consequently we now get at a lower temperature

') Vid. J. D. vaN per Waars, Proceedings of the Royal Academy of Amsterdam
1897, 209.

( 193 )

besides the connodal lines ending on the side W N, also connodal lines
ending on the side N A. Both plaits extend more and more when
the temperature falls and the two connodal lines approach each other
continually ; the crosses on the dotted line d e indicate the plait-
points of the different connodal lines. We are therefore led to
suppose that in the end the two plaits merge into each other; yet
it was imposible to demonstrate this experimentally, because, in
consequence of the appearance of the solid phase succinonitrile, the
left connodal line below = 5°5 and the right one below + 4°5
indicate only less stable equilibriums.

Quite different are the phenomena in the system water, anilin and
phenol in fig. 2. Here there appears namely but one plait on the
¢-surface. Above 167° a separation of a liquid in two layers can
never occur in this system; the ¢-surface is in every point convex-
convex downwards. At 167° there appears a plait-point on the side
W An ¢, its projection being e. As the temperature falls the
plait extends and we get connodal lines as in fig. 2, in which
the crosses again indicate the plaitpoints. The plait continues to
extend and reaches at 68° the plane W PA¢ in a point, the projection
of which is indicated by @; the connodal line has a form like the
one which in fig. 2 touches the side Ph W in point d. At still lower
temperatures the plaitpoint on the ¢-surface disappears; the plait
extends from one side to the other, so that two entirely separate
convex-convex parts are formed. The connodal line now has fallen
into two parts, separated from each other, both ending on the sides
Ph W and An W. At further lowering of the temperature the con-
nodal line keeps its form; the two parts move however continually
farther from each other and at last some of the points represent
less stable states, as solid phases, viz phenol and a combination of
phenol and aniline are formed.

The preceding investigations have led to a theoretical and expe-
rimental investigation of different curves; in these pages a survey is
given of some of the experimental investigations.

Let us take the connodal lines of fig. 2; below 68° no plaitpoint
appears on them; at 68° it appears in point d and the temperature
rising it moves along the line de from d to e where it disappears
at 167°. It is however very difficult to realize these plaitpointeurves
experimentally; neither has this been done in the different systems
investigated by Mr. ScHREINEMAKERS. He has however determined
another curve, which will not much deviate from it in the two
systems mentioned above. It is the line of the critical mixingtem-
peratures which coincides with the former in at least 2 points,

( 194 )

viz. in the points d and e: the critical mixing-temperatures of the
binary systems.

If we start with a mixture of phenol and aniline, adding water
to this binary mixture, two liquid phases are formed, passing into
one when heated; this mixing-temperature depends upon the quan-
tity of water added. The highest mixing-temperature we are able to
reach by the addition of water, may be called the critical mixing-
temperature of water with the said binary mixture. In varying
the proportion of phenol and aniline in the binary mixture, another

critical mixing-temperature
5, 3 will be obtained by the ad-
Ek dition of water.

In fig. 3 is shown on the
X-axis the eomposition of the
binary mixture; on the Y-axis
the critical mixing-tempera-
ture of this binary mixture
with water. We then get the
lme de in which d indicates
the critical mixing-tempera-
ture of phenol with water,
and e that of aniline with
water. The line de may be
drawn according to the table
given below.

Critical mixing temperature.

Molec. anilin on 100 Molec. phenol + anilin.

Composition of the binary mixture

in Molee. aniline on Critical mixingtemperature
100 Molec. after the addition of
Phenol + Aniline. water.
0 oe Vere MRR tad ea AE 68°
LT SB aed sets de EE ee ER
Zoi did EY gu. cabo et feted Peles . 114°—115°

SHS ei 4 5m or alt ret oen LAP ordt. WR
50 apen OLE Wie sk sen cs ae Nett)
O2S ied krk. eve ee om PAT ey, NER
DOT Eel Mitra opeet a We erdee he A A UNE S
MAD IA ESR oom BTO rte to OE

100 ON EA BE aso. vo, CULO

For each of the binary mixtures of phenol and aniline, given in the
above table the mixing-temperature is determined by the addition of dif-
ferent quantities of water and the critical temperature deducted from it.

We see therefore that the critical mixing-temperature of the binary
mixtures increases in proportion as they contain more aniline —

( 195 )

decreases on the contrary in proportion as they contain more phenol.
The extreme limits are 68° and 167°.

Dr. SCHREINEMAKERS has also investigated how the critical mixing-
temperature of water with phenol is changed by the addition of
sodiumehloride. In the following table the results are given.

Composition of the binary mixture Critical mixingtemperatures
in Molec. NaCl on 100 Molec. after the addition of
(H, O + Na CI). phenol.

0 NTO VELE flrs: ach siete ex WA tee 68°

OESO LME each teenie. colar; Oh ese Re me 70S
VIE Ol Ree i cs cg Ok Chem TT CE CF ALES
PAV he ooh SON Oe) Gell NOORDER cman IS

If we now indicate in fig. 3 on the X-axis the binary mixture
viz. Molec. NaCl on 100 Molec. (Na Cl + H,0), and on the F-axis
the critical mixingtemperature of those mixtures with phenol, we
get the dotted line df, rising very quickly. A similar line also
exists in the system investigated by SCHREINEMAKERS of water-
succinonitrile and sodiumehloride.

By the addition of aniline or NaCl we therefore get a rise in
the critical mixingtemperature of phenol with water; the same
occurs also if the pressure is augmented, as lately shown by Dr.
N. J. van DER Lee). A fall in the critical mixingtemperature can
also occur, as Dr. SCHREINEMAKERS found with alcohol.

A line quite different from that in fig. 3 is found by Scureine-
MAKERS in the system: water, alcohol and succinonitrile.

, If we start from the bi-

56 d De 4 nary mixture water and

ij alcohol, we can again get
two liquid layers by the
addition of succinonitrile.
In fig. 4 the composition
of the binary mixture:
water and alcohol is read
on the z-axis, while on the
y-axis we find the critical
mixingtemperature by the
addition of succinonitrile.
The course of the line dd'e'e

; is known from the following
Molec. alcohol on 100 Molec. water 4- alcohol. table:

Critical mivingtemperature.

") Dissertation, The influence of pressure on the critical mixingtemperature. Am-
sterdam 1898.

( 196 )

Composition of the binary mixture in Critical mixingtemperature
Molec. Alcohol on 100 Molec. after the addition of
Alcohol + water. succinonitrile.

Oh VOP Ro POE edo Dd

DAE AL
WZ lt ee POND a REN ROE
ID Ora Mins A) irene emer oes tte It

30.A1NPornt Ad ese Gee hen og VPS
G6.6 Point ver) (eas 3) eels RS
(hie Si ease eo ere ok eo us oo Ag: JI

846 reren bs cit Ven valk vena bears ES TE Rn
100 Ee Point ANAAL HA CE ERS KE

Of the dotted line d'e' only a small part could be realized; the
greater part it is however impossible to determine. Yet we are led
to suppose that the line d'e will run as drawn in the figure viz.:
with a minimum-temperature at + 3° coinciding with the point in
which in fig. 1 the two connodal lines merge into each other. The
difficulty of determining the course of the curved line lies in the
fact of the two liquid-phases presenting there less stable equilibriums ;
the few cases in which Dr. ScHREINEMAKERS succeeded in obtaining
them, were insufficient to deduct the critical mixingtemperatures
from.

Besides the question of the critical mixingtemperatures of ter-
nary systems, we can set ourselves many other problems one of
which I shall discuss.

Take a binary mixture viz. one of water and phenol; the mixing
temperature of such a mixture depends upon its composition; f.1. the
mixingtemperature of a mixture containing 10.9 pCt. of phenol is
+ 46°. This mixingtemperature is altered not only by pressure,
but also by the addition of a third component; it may be raised or
depressed. An example of a rise Dr. SCHREINEMAKERS has determined
experimentally by taking as a third component aniline; he found
that the mixingtemperature began by rising from 46° to about
163°, to fall again after a further addition of aniline. In order to
draw this line in fig. 3, only the components phenol and aniline
of the ternary mixture are considered. Owing to the proportion of
water and phenol being constant in all the mixtures, the entire
composition is known. We have:

( 197 )

Molec. aniline on 100 Molcc.
phenol + aniline. Mixingtemperature.

ORR Mes ai BD a reen u 40,
BODE a boto Be oe oo oo AE
GRO a) AE Aere et PAD
LR EE One
SONOR ARNE Ne nente trent sins ROO
OS dt ob) oe on dool ton Kie
ED AME da NE LOL Oo
GEOON teen ea en Ed
ATD eene: Nash ene bonte lA

If in fig. 3 the number of Molec. aniline on 100 Molec. Phenol
+ aniline is indicated again on the X-axis, and on the Y-axis the
mixingtemperature, we get a line ghk as is drawn in fig. 3 which:
1° starts from g to a higher temperature, 2° touches the line de
3° reaches its maximum temperature in 4 and 4° further on bends
down to lower temperatures.

The preceding line ghk is for a mixture containing 10.9 pCt.
Phenol and 89.1 pCt. water; for mixtures of other compositions we
also get other lines. F.i. if we take a mixture of 63.7 pCt. phenol
and 36.3 pCt. water, it has just like the former its mixingtem-
perature at + 46°. When adding aniline we then get the following:

Molec. aniline on 100 Molec.
phenol + aniline. Mixingtemperature.

0 Poe el cette ty) Natomas “Gyan HOR
POA OU See Se tae Ral nog way ete rare to ee
EEEN POE RDE kT CE IID Oa:
CET A ENE mek OS EEEN ac tens Alig
GUERRA
CO aya TEIL EME va Van WL mies VAE LOSS
AETR ee) en te enen Mee
(EED or
These values are indicated in fig. 3 by glm, which like g hk

begins at g, reaches its maximum temperature at /, and then bends
down to lower temperatures.

(198 )

So we have now got two lines, both starting from point g in
fig. 3. From each point below d two more such lines may be
drawn; but from d itself but one. To find this we must set out
from the critical solution of water and phenol. But this is not
exactly known. Dr. SCHREINEMAKERS took a solution, containing
35.77 pCt. phenol wich certainly lies near the critical one. He
found:

Molec. aniline on 100 Mol.

phenol + aniline. Mixingtemperature.

0 DENN. oi
2046 NTL A fide St en Ae EDER
DEISBAEN Dr ontdoen, EN
5008 wa Sol rok re Aiel or tea oc REN
6869, Nay odt ge Arash A BD EROL
(BOSS NVS TEE EERE EK OI ee cea
SOS eon en Piece MG wee EEN

BT s20 9 rnaar zien See get en et ee ER te

The line that may be deducted from this table is however not
given in fig. 3; as far as it is continued, it is entirely above ylm
but intersects Ak in a point situated between g and the intersection
of the two curves ghk and de.

Physics. — „On the accurate determination of the molecular weight
of gases from their density.” By Prof. J. D. vaN DER WAALS.

From the equation:

(+ apo) (0b ey) = = 1pm No?
o?
follows
= Ig m N 82 = po vo (1 Ha) (L—5)

and
=1/,m N 8? = py v% (1 Ha) (1—6) (Ll Hat) .

If the quantity N is equal for two different gases, it follows
from the thesis that at the same temperature !/ ms* is the same,
that for the two gases py) %)(1-+)(1-b) has also the same value,
and therefore also vp (1+ a) (1—b).

( 199 )
If the whole quantity of the substance is equal to the molecular

L e
weight, v = — , so that the equality of vo (1 He) (1—b) may be written
Ar

= (1 +4) (10) = (1 + a) (1-0)
ay ay

or
, dy an
OME LO Se EEn
(tale (hes), « HBr (3)
: dy 3 :
The quantity ———-—_—~ js the normal density, which would
GESTE) «(lh 5)

also have been found at 0°, if the law of Boyur had been true.
Let us represent it by d,.

If we determine the density of a gas at 0° and under the pressure
py-(at which the quantities a and b have been determined), we have
only to divide this density by (1 + a) (1 —b), to find the normal
density, and to this the molecular weights are proportional.

If the density is determined at another temperature and under
another pressure, a volume v, is calculated from the pressure, the
temperature and the volume read, making use of the formula:

pr
ltat

= !
SS

Fy = m1 5
By means of this volume a density (d) — — is found, and we
v
0

have to investigate in what proportion it stands to d,.
Let us calculate for this purpose the proportion of v, and »,'
From

_ Povoll +a)(L—b)(l+ at) — apor,?

2
v—bu, v

follows
a Uy

v
kk ¥
—bry lat ° v

ee = (1 + a)(1 —d)r%
1-+ at po v

or

} a Vo,

Pato men

If we restrict ourselves to very large volumes only, so to obser-
vations under a small pressure, we may put

14
Proceedings Royal Acad. Amsterdam, Vol. L

( 200 )

© he Vo ( a 2
(1 + a) (1 — b) 2% v (EHL Ha) |
or
ds ES Pv a aa
dy Pov (Ll +a) (1—d)(1 teat) (14 a)(l1—d+at) |
dy, En p ( a )

Seike AE
a, pol FAD Fed FOD ed §

R 5 : re 1
If we take for p a certain fraction of the critical pressure e.g. ay

as Lepvuc does ,Annales de chimie et de physique, Sept. 1898”
” } dv | ) p ?
then

7 cee. p 1 a
Ds Sen En mn OE == 5
76 (OMR me Po dOr 206?
and
dy ay eel a a i
ae 76 275 (1 +-c)(I—b) (U + ot) (610 jk

By means of the critical temperature

8 a
1 Jet, = -
MENENS
we find
den eee e ie Bn
do TORE NS ze
or
In IAD jk
ed SAO CHEN = & a 1)
do TAB ST
Th 8 3 Z ; 8 6
For = . the correction is 0 and the density found is the

Ei 27
normal density. At this temperature a gas follows the law of
BoyrLe, of course only under a slight pressure.

Tr 8
For a <a

case with hydrogen at 0°. In this case ¢, > (d)'. Then the value

27 one : 3
57 or Oras Tj. the correction is negative, as 1s the

d, D 27 ah nl °
of a y has a maximum for 7 = mt Tr. For hydrogen at 0° the
do

( 201 )

value of 7 las already surpassed this limit. The fact that such «
maximum value exists may be understood, if we consider that a
gas under a constant pressure is ever more rarefied, when the
temperature rises — so that at 7 = infinite, a En

2

would require an infinite volume, and correction would be un-
necessary.

The condition for the observation under a pressure of == without

the vapour being saturated is, that 7 must not descend below a

ry

tel Bal, : Ty;
certain limit, which we shall put at Lens
i
: Die N dy, }
For a = 1,6 we find (i y = 1—0,0116, so that the normal density
cd
0
is more than 1 pCt. smaller than that which is furnished by the
observation.
! ; } Ty. Nl 5
If the assumption of a =a wp agrees better with the observations,

than the supposition that a is constant, we should have to put:

zl 0,001645 (5) EAS, 1|
ETE DEWET healen

p=

E ¢ Tr 3
in which case for En the normal density would be more

than 2 pCt. smaller than would follow from the observations.

Astronomy. — „Some remarks upon the 14-monthly motion of the
Pole of the Earth and upon the length of its period”. By
Dr. EK. F. van DE SANDE BAKHUYZEN (Communicated by
Prof. H. G. VAN DE SANDE BAKHUYZEN).
(Read in the Meeting of October 29!» 1898).

1. In the recent N°. 446 of the Astronomical Journal another
essay is given by Dr. CHANDLER on the motion of the Pole of the
Earth, in which he discusses the observations performed in the years
1890—1898 and employs the older series to investigate anew the
length of the 14-monthly period. On this last point he contends the
opinions formerly emitted by H. G. vay Dr SANDE BAKHUYZEN
and recently by me (Proceedings of the Royal Academy, Amsterdam.
June 1898). To this latter paper he devotes a note ranning as follows:

ylhe memoir last referred to did not arrive until the present

14*

( 202 )

„artiele was written, but I interpolate this statement with regard
„to it in order to enable astronomers to decide as to the justness
„of the views therein set forth. Both of the gentlemen of the Leiden
„observatory strenuously maintain that the mean period is more than
y431 days, and that it is invariable. The formula V” (that is the
result given by E. F. v. p. S. B.) „is deduced by a peculiar and
„arbitrary treatment of the results of observation, its initial epoch
„being based on the Leyden observations alone, on the alleged
„ground that its errors are far smaller than those of all other series,
„Which are rejected. I must however deny the propriety of assigning
„a weight of zero, relative to Leyden, to the extensive and precise
„series at Pulkowa between 1863 and 1882 with the Vertical Circle
„and Prime Vertical Transit.”

I shall now take the liberty to add on my part some remarks to
these opinions of Dr. CHANDLER. At the same time I shall make
use of the opportunity to consider the problem of the length of the
14-monthly period somewhat more closely, which consideration will
naturally lead to the discussion of the results on this point arrived
at by CHANDLER in his last paper.

2. In the first place in regard to the grievances raised by
CHANDLER against my manner of treatment I will grant at once
that, by not using the results obtained at Pulkowa in the years
1863 to 1882, I would have committed a gross error, if it had been
my purpose to include in my investigations, in an independent way,
the observations before 1890. This however was in nowise the case.
It was simply my intention to submit to a discussion only those
obtained in the period 1890 to 1897; but as from these alone the
length of the 14-montbly period could naturally be derived with
but slight accuracy I had recourse to the results formerly deduced
and compiled by H. G. v. D. SANDE BAKHUYZEN. It seemed unde-
sirable however to use all these results. In the first place, for
reasons to be stated hereafter, I thought it necessary to exclude
those of an epoch before 1860. Further consideration then led me
to restrict myself, in the deduction of a provisional result, as far as
concerns the observations between 1860—1880, wholly to the Leyden
results. 1 determined on this course because these proved to have much
smaller mean errors than all others of the same time, in as far as
they had been treated by H. G. v. D. S. BAKHUYZEN, whilst moreover
these Leyden results proved to lie about midway between the others ;
so that by including these the final result could not be modified
to any considerable amount.

I might perhaps have pointed out still somewhat more clearly the

(203 )

entirely preliminary character of my result for the length of the
period, if I had not thought my meaning sufficiently evident. At all
events I assuredly think that, in formulating my result, I have not
lost sight of the prudence necessary under these circumstances. Thus
I give, beside my result of 451.11 days, also the one which would
follow if the mean epoch found by H. G. v. p. S. BAKHUYZEN
were combined with mine, viz. 430.36, whilst finally I observe that
for the last 35 years the length of the period cannot have differed
considerably from 431 days and that such a great variability as
CHANDLER assumes, is now already contradicted by the observations.
So I believe I may state that the words of Dr. CHANDLER: ,stre-
,nuously maintain that the mean period is more than 431 days,
,and that it is invariable” show but very inaccurately the stand-
point taken up by me?).

Let this suffice to answer CHANDLER’s observations about the
treatment followed by me; his remarks concerning the facts themselves
will be presently considered.

3. Before discussing the results furnished by my later computations
on tke length of the period, I will concisely state the results arrived
at by CHANDLER in 1894 (Astr. Journ. N°. 322) and those lately
deduced by him. His formula of 1894 gave as Epochs of minimum
in the 14-monthly motion :

T = 24023274 + 4281.6 EH 554 sin F |
in which, with a sufficient approximation » (1)
W — (t—1865.25) .5°.48 — E X 6°.43 |

From this there results for the length of the period, osculating
for the epoch Z:

P = 4284.6 + 64,2 cos (EX 6°.43). . . . . (2)

So the length of the period may vary from 434°.8 to 4227.4 and
the cycle of this change embraces 56 periods or 66 years. The
maximumlength would have been reached in 1865, the minimum-
length would take place in the present year 1898.

In his last paper CHANDLER starts with this formula and tests it
by the observations of 1890 to 1897. He does not use the x and y of
ALBRECHT, but values derived by himself, which however agree with

1) Neither are his words accurate, where they concern H. G. v. p. S. Bakaoyzen.
See a.o. Astr. Nachr. N°. 3275, page 163 at the top.

( 204 )

the former in their general course. The length of the period with
which he starts thus amounts to about 423 days and from the
observations a correction is found for it of + 5 days, which however,
as CHANDLER observes, must be quite uncertain, it not being sure
that the length of the yearly period is exactly a year. Meanwhile,
later on, a correction of + 4 days for the length of the period is
assumed beside such a one of + 8 days for the mean epoch and,
as CHANDLER thinks it proved that the length of the period is
variable, he accounts for the correction by a quadratic term added
to the formula of the epochs which thus becomes:

T = 24126464 + 4274.0 KH — 04.08 £2. . . . . (3)

where the initial epoch is placed 24 periods later than that of the
preceding formula.

Tested by the older observations this formula proved to satisfy
fairly those since 1835, but not at all those of Ponp, which leave
for the epoch a deviation of 166 days. Although formerly CHANDLER
set great store by Ponp’s observations, it yet seems that he desires
io have the elements of formula (3) regarded as ,the revised elements”
he wished to determine. It is true that a doubt about this conclu-
sion arises by reading in the ,conclusions’’ which, in another part
of the paper (p. 107), are derived from ,substantially all the competent
testimony available” (b) „that the mean period since 1825 is 428 days
„within a small fraction of a day’, whilst formula (3) gives us for
this quantity 4317.6, and (d) that the hypothesis of a change in the
period uniform with the time is incompatible with the observations
before 1860, whilst in conclusion (¢) a change per saltum between
1850 and 1860 is called also incompatible with the facts. Leaving
this for what it is, I shall in what follows, indicate formula (3) as
CHANDLER 1898.

The differences between the epochs computed according to this
formula apd to that of 1894 are rather small between 1870 and
1894, but increase rapidly beyond these limits. So we find for
Cu 98—Cu 94 in 1830 — 126 d., in 1860 + 38 d., in 1898
+ 25 d. and in 1900 + 32 d.

4. In the first place I investigated more closely what the obser-
vations from 1890—97, taken by themselves, can teach us about
the length of the 14-monthly period. In my former paper I examined
the # of the three last years only; now I did the same for the three
first years and then I acted in the same way for the y.

I thus obtained the following results for the mean epochs of

(7205 )

maximum, to which I add those for the whole of the period 1890—96,

Observ. Obs. —E. B. | Obs—Ch.94 | Obs.—Ch.98

=
1890-1896 | 2419439 Ee 4215 EE
1s90—1892 | 9419006 227, oe} 0
1894—1896 | 2413300 == + 98 Ti
y
1890—1896 | 2412438 | —7 + 12 te
1s90—1892 | 2412007 AG + 4 ey
18941896 | 2413298 ig + 26 1 i

If we derive the length of the period from those couples of par-
tial results, lying three periods apart, we shall find:

from « 4314.3

„ y 430.3

The surprising agreement with the results obtained from great
intervals of time had of course to be regarded as partly accidental.
Now in order to investigate more closely what accuracy might be
arrived at, I fell back on the original values for the coordinates «
and y as they have been derived by ALBRECHT. In my preceding
paper I gave on page (53) 12 a comparison of these values with those
computed by my formula. In entirely the same way I now made
comparisons with formulae in which 423 and 428 days were suc-
cessively assumed for the length of the 14-monthly period, but which
agreed for the rest, mean epoch included, (which mean epoch coin-
cides approximately with 1893.0) with those employed for the former
comparison. These lengths of the period were taken from CHANDLER’s
two formulae.

I shall not here communicate these comparisons themselves, but
shall give only the sums of the squares of the deviations and the
mean values of the latter, repeating also the values formerly found
with the tengih of the period 431¢ ;

( 206 )

Period Nn M. dev. = Ay M. dey.
451 1207 = te Oa 0:40) 1582 + 0.046
428 1322 tE (0 .042 1651 + (0 204%
423 1699 === (0) (027 2083 OUDE
: 1708 a 0 .047 1976 == 10205i

We see that a 428 days’ period satisfies the original observations
almost as well as a 431 days’ period.

On the other hand a 423 days’period leaves considerably greater
errors, which are but slightly diminished by deducing anew also the
yearly motion, as is shown by the numbers given in the last place.

So our result is, that the observations from 1890—97 prove in
themselves a 423 days’ period to be improbable; but much farther
than that we cannot go.

5. In the second place I had recourse again to the older series
of observations, but, before discussing this investigation, I will state
that, now again, it lays no claim to completeness. I have only again
combined the results of observations treated already by others, with
each other and with my results for 1890—1897 and from these I
have drawn such conclusions as seemed most probable to me. The
observations of Pulkowa 1863—1875 only make an exception, as
for these I made a computation myself founded on the results arrived
at by IVANOFF in two important papers. ')

First came the question how far we may go back in the employ-
ment of older observations and this again depends upon that other
question, whether we assume in the 14-monthly motion a lasting
continuity, or whether we do not exclude the possibility that more
or less sudden changes may take place.

As is already remarked, CHANDLER includes amongst the conclusions
formulated in his last paper, also this one, ,that a change per saltum
„between 1830 and 1860 is incompatible with the facts”. To me
on the contrary it seems that there is every reason to assume the
possibility of such a change between 1840 and 1860.

This statement is based in the first place on the values for the
amplitudes as they have been found before 1860 and after that

1) A. Ivanorr, Variations de la latitude de Poulkovo déduites des observations
1863—75. (Mélanges math. et astr. T. VII.) St. Pétersbourg 1894.

A. Ivanor, Recherches définitives sur les variations de la latitude de Poulkovo
(Bull. Acad, Pétersb, Serie V. T. ID. St. Pétersbours 1895.

( 207 )

time, and which follow below. Here and there I have inserted the
results of two different treatments of the same series of observations.

Series of Observations. Amplitude. Authority.
Greenwich Mural C... 1825—1836 0" 126 Ch. A. J. 315
Greenwich Mural C... 1836—1850 0 .060 Ch. A. J. 320
Pulkowa Prime Vert. . 1840—1855 0 .035 vow » 296
Pulkowa Vert. C..... 1840—1849 0 .056 Hi GB) ALN. 3275

u ees r ” 0 .08 Ivanof Rech. déf.
Greenwich Tr. C..... 1851—185$8 0 .069 H.G. B. A. N. 3261

Greenwich Tr. C..... 1858—1865 175 HH. G. B. A. N. 3261

Washington Prime Vert. 1862—1867 „126 r i
Leiden Fund. Stars... 1894—1868 „156 Result Wilterdink.
Hie EOMATIS Vie cece ars 1864—1874 „158 4) ” ”

Greenwich Tr. C..... 1865—1872 H.G. B. A. N. 3261

EL (ey fe fer Sy tS oS)
vo
oo
w

Pulkowa Vert. C. Pol. 1863—1870 „226 7 rs
” ” „_ 1871—1875 „179 u 7
v w Allthe St. 1863—1875 „127 Tvanof Rech. déf., B, ¥. B
7 Prime Vert. . 1875—1882 0 .236 2) Ch. A. J. 297
7 Vert. C..... 1882—1891 0 .145*%) | Nyrén Bull. Pét. T. 35
7 ss 7 a 0 .139 H.G. B. A. N. 3261
Greenwich Tr. C..... 1880—1891 0 .141 Ch. M.N. 53 119
Madison ot 1883 —1890 0 .152 Ch. A. J. 307
Ly OTS istole rete cle 1885—1893 0 .175 ” „ 334
Summary Albrecht. ... 1890—1896 0 .148 E. F. B. Ac. Amst. 1898.
„ 1890— 1892 0 .167 Result E. F. B.
v 1894 — 1896 0 .131 4) r 7

1) These results deviate slightly from those communicated by H. G. v. p. S. B.
in A. N. 3261. The investigation of WrirerpinK will be shortly published by
him in detail.

*) The result 07.33 given by Nyrin for 1875—1878 in Bull. Pétersb. Vol. 55 is
certainly too great, as it is influenced by the yearly motion.

*) Result for the entire motion, upon which however the yearly motion seems to
have had but slight influence.

*) Results now deduced by me for the partial groups,

(208 )

This summary shows pretty clearly that the amplitude was
found to be considerably smaller in the years 1836—1858 than in
the following period. For a number of series the mean errors have
been deduced (see A. N. 3261) and the consideration of these
strengthens the conclusion which admits as probable the reality of
the observed difference. On the other hand no variability of the
amplitude is to be found after 1860 and we may conclude at least that
the observations make a more or less sudden change between 1850
and 1860 much more probable than a periodic or continually in-
creasing one. Now the dynamical theory of the rotation of a sphere
not absolutely solid, either as a whole or in some of its parts, leads
to the same result. It teaches us,!) that with slow secular displace-
ments of mass the axis of the greatest moment of inertia is entirely
followed in its motions by the axis of rotation; that with periodic
displacements the axis of rotation will get a motion of the same
period as that of the axis of inertia, which is added to its own
motion, but that in the case of sudden displacements of mass the
axis of inertia is the only one to shift its position, so that the
opening of the cone, described by the axis of rotation around it,
changes, introducing thereby a discontinuity in the motion of the latter.
The amplitude changes and in general also the phase, but after that
the motion continues in its old period.

May we however be led in this problem by a dynamical theory?
CHANDLER denies this strenuously. He thinks it has proved itself
a blind guide in this case, and that he who would follow it would
betray reprehensible conservatism.

It is a fact that misplaced conservatism has frequently delayed
the development of science and, if it were still necessary, the
beautiful discovery of CHANDLER himself of the motion of the Pole
named after him, would prove once again that an unprejudiced in-
vestigation of the observations, without being guided by any theory,
can lead a problem in the right paths and render an important
service to science.

But on the other hand we are justified I think in not granting
the conclusion that the most simple theory is erroneous or incom-
plete, before such a theory is shown to be decidedly incompatible
with the observations.

At the same time a theory, even a somewhat imperfect one, if it
be only based in general on correct foundations, is certainly entitled

1) See a. o. Hrrmerr. Die math. und phys. Theorieën der höheren geodiisie,
Vol. 11 page 417.

( 209 )

to some eonsideration in those cases, where the observations cannot
as yet furnish the necessary information. Such a case being before
us we are justified in not wholly disregarding what it teaches.

6. According both to observation and theory therefore a more or
less sudden displacement of the axis of rotation between 1850 and
1860 must be regarded as possible and so I think that for the
present only observations after that time may be employed to deduce
the length of the period.

In the following table all the epochs of maximum after 1858, that
have been determined, are brought together, at least those which were
accessible to me and which seemed more or Jess trustworthy. In the
first place all the results of H. G. v. p. S. BAKHUYZEN have been
inserted, together with those of WiILTERDINK for Leyden; further
several ones deduced by CuaNDLER, then my result from the obser-
vations 1890—1896 and finally an epoch of maximum deduced by
me from all the observations with the vertical circle at Pulkowa
1863—1875, as they have been treated by IvVANorF.

Series of observations. KE. Epoch. | Weights. | O.—E.B.I.} Auth.
|

Greenwich Tr. C....1858—65 | —18 | 2400745 1 — 60 H. G. B.
Washington Pr. Vert. 1862—67 | —l4 2506 1) 2 — 24 ”
Pulkowa V. C. Pol. .1863—70 | —13 3035 1) 2 + 74 ”
Leyden Fund. stars..1864—68 | —12 3394 2 + 2 Wilt

v_ Polaris … … 1864—74 | —12 3386 al Peale ”
RO vos is | sassy IM cas | neve
Pulkowa Vert. C....1863-75 | —0 | 4277 4 +23 |Iv,E.F.B

2 V.G. Pol. 187175 | — 8 51461)| 2 30) EG

» Prime Vert. 1875—82 | — 3 7290 2 + 18 Ch

me verten Cs cies 1882—91 +3 9867 A + 8 BGB,
Greenwich Tr. C....18SSO—91 | + 3 9870 1 + 11 Ch
Madison ........... 1885—90 + 5 2410704. L — 16
yi te, AET 1885—93 | +76 11512)| 2 0 3
Summary Albrecht. ..1890—96 | -++ 9 2439 6 — 6 E. ¥. B.

1) CuanptER also discussed these series of observations; his results deviate resp.
only + 4, +5 and —5 days.

2) Gonnesstar, whose observations of 15 polar stars have been employed here, found
himself an epoch 3 days later. Bull. Astr. Vol. XI. Afterwards a formula with 4 terms
hus been deduced by him. C. RK. T. 124, page 930,

( 210 )

For that purpose I employed his table on page 269 of the ,Re-
cherches définitives” and resolved the 14 equations founded there-
on without paying regard to the weights assigned. The epoch
obtained by me agrees entirely with the epoch deduced from a
curve by Ivanorr himself.

The column E contains the rotation-numbers of the maxima; for
the initial epoch was taken the mean maximum epoch of my prece-
ding paper. The following column contains the epochs of
maximum reduced to Greenwich and against these the weights have
been inserted which I assigned to those results. It was difficult to
determine these weights accurately on account of the evidently con-
siderable systematic errors. It was not allowed to take as their
exclusive measure the mean errors derived from the agreement of
the observations of a single observatory infer se; so they have been
determined according to a rough estimation. I adopted the values
assumed by H. G. v. pv. S. BAKHUYZEN, and for the remaining
series I acted in an analogous manner. The column Obs.—E. B. I.
contains the deviations from my formula deduced in the preceding
paper and the last contains the authorities from which the several
results were borrowed.

I at once omitted the series of Greenwich finally not included by
H. G. v. p. S. BAKHUYZEN in his computation, their results being
already contained in those of the other series. On the other hand
I have inserted, besides the epoch deduced from Ivanorr’s results
for all the observations with the Vertical Circle at Pulkowa 1863—
1875, also those deduced by H.G. v. p. S. BAKHUYZEN, from Polaris
only, as observed resp. by GyLpEN and Nyr&n. True, the former
result is founded on a much greater number of observations, but it is pos-
sible that the mixing up of the results of both observers has done
more or less harm, a point which Ivanorr himself also discusses
in his first paper page 516.

I have now tried to correct my first formula with the aid of the
results compiled in this way, and have rigorously resolved for that
purpose all the equations they furnished, having due regard to their
weights. At first sight the differences Obs—E.B.I seem to betray a
non-linear course, but on closer examination this proves to be only
apparent, at least for the greater part, and on account of the occasio-
nally considerable differences between close-lying epochs I thought
I was not allowed to depart even now from the simple supposition
of a constant length of the period. I made two solutions: including
the first time the result according to Ivanor and omitting those of

( 211 )

the Polaris-observations of GyLDEN and NyREN and the second time
including the two latter results instead of the former !).

So I obtained:

1st solution: A epoch + 04.1
A length of the period + 0 .06
2nd solution: A epoch + 44.7

A length of the period — 0 .45

We see that it makes rather a considerable difference whether we

(Obs—E.B.la. Obs—E.B IIb. Cage Oe eeure

i

Greenwich Mural C..... 1825—1836) +142 d. | +116 d.| + 44d. | +163 d.

7 un 1836—1850?) + 22 0 + 2 + 7
Pulkowa Prime Vert... . 1840—18552) — 9 — 30 — 23 | — 27
ve Vert. C....... 1840—1849%) — 50 — 71 — 59 — 70
Greenwich Tr. C....... 1851—1858") —92 | —108 — 82 —127
|
Greenwich Er. Co, 1858—1865 — 59 — 73 — 61 — 98
Washington Prime Vert. 1862—1867 — 23 — 35 — 38 — 61
Pulkowa Vert. C. Pol.. 1863—1870 | + 75 + 63 + 56 + 37
Leyden Fund. Stars..... 1864—1868 + 3 — 8 — 19 — 34
meee POlavishate cme 1864—1874 — 5 — 16 — 27 — 42
Greenwich rs Cyes2-- 3 1865—1872 + 44 + 33 +- 22 ln
Pulk. Vert. C. All the St. 1863—1875 + 23 + 14 — 5 — 13
u 7 Pol. 1871—1875 + 30 +. 22 — 3 — 4
” Prime Vert... 1875—1882 + 18 + 12 — 18 — 7
" Viert Cristy... 1882—1891 + 8 + 5 — 12 0
Greenwich) Tr Cr... . 1880—1891 + 11 + 8 — 9 3
MEEO Dorade sn Ooo 1883—1890 — 16 — 18 — 25 — 19
TGYOW sss arne otenene . 1885—1893 0 — 2 — 3 0
Summary Albrecht..... 1890—1896 =— — 7 + 13 + 6

1) I also made a solution in which the length of the period was assumed as un!—
formly variable, but [ do not mention it here, as the result seemed wholly illusory,

*) According to CHANDLER.

5) According to H. G, VAN DE SANDE Baknuyzun.

( 212 )

follow one way or the other in reference to the observations of
Pulkowa.

For the initial epoch and the length of the period itself we obtain
in the two cases:

Ila 2408565 431.17 days.
115 2408570 450.66 _„

Although after all the first solution seems preferable, I have given
below the deviations of the observations from both, besides those from
CHANDLER’s two formulae of 1894 and of 1898. In order to show in
what relation the results of the observations before 1858 stand to
those of later years I also include the former.

The consideration of the deviations for the observations 1858—
1896 shows that the agreement for CHANDLER’s formulae, notwith-
standing their greater intricacy, is not better than that for mine.
If, in order to compare in this respect EB. Ia with Ch.94 and
Ch.98, we omit, as is only just, the two Polaris-series of Pulkowa,
we shall find that the sum of the squares of the residuals multiplied
by the weights is even smallest for E.B.lla. The distribution of
weights, however is of very great influence on these results.

With regard to this period (1858—1896) therefore I should like
to give as the results of my investigation :

1°. For the present there is no sufficient reason to assume in the
14-morthly motion since 1860 a non-uniform velocity.

2°, The length of the period in these years has not deviated
much from 431 days.

These results clash entirely with those of CHANDLER’s last paper
and little change has been brought about in the conclusions, at
which I arrived in my previous communication agreeing in the
main with the anterior results of H. G. v. D. S. BAKHUYZEN.

The epochs according to both solutions Hla and 114 coinciding about
1893 and no reason existing not to adopt for the length of the
period the round number of 431.0 days, lying between both solu-
tions, I assume for the present as final result:

Elements II of the 14-monthly motion since 1860.

Epoch of maximum for Greenwich . . . 2412446
Length, of thesperntod denn sean 431208

Ara p lit ude MERA e= AES, 0.”156%)

1) Mean value deduced from the previous summary.

prm

( 213 )

In the second place with regard to the period before 1858, I
think as yet little can be said about it. Whilst the much smaller
amplitude found in this period makes it fully justifiable in my
opinion, not to connect the results for that period with the later
ones, I dare not deduce anything from the observed epochs them-
selves. The results 1836—1858 are very uncertain on account of
the small amplitude and I cannot give an opinion about the
certainty of the results of the observations of Ponp.

Physics. — Communication No. 44 from the Physical Laboratory
at Leiden by Dr. H. KAMERLINGH ONNES. „A standard open
manometer of reduced height with transference cf pressure by
means of compressed gas.”

(Read in the mecting of October 29th 1898).

SL. The Principle. Im order to make aceurate determinations
of high pressures to about 100 atmospheres, open mereury-mano-
meters are indispensable. If we deduce the pressure from the com-
pression of any kind of gas in a closed manometer by making use
of the equation of condition of this gas, determinations with open
manometers form the basis of the measurements and in making
accurate measurements it will prove desirable to test if possible the
indications of the closed manometer by comparing them with those
of the open manometer. But wherever we want to determine the
pressure with greater accuracy than is secured by the equation of
condition of the gas with which the closed manometer is filled, there
is no other way than making the measurements by means of an
Open manometer, and that with an apparatus which admits of a
high degree of accuracy.

The frequent use made of closed manometers !) for the experiments
in the Leiden laboratory and the necessity to measure the pressure
with great accuracy in the case of some determinations (especially

1) If we can measure a range of pressures in a comparatively short time with great
accuracy the graduating of closed manometers after we have filled them becomes so
simple that we may omit the measurements from which in other cases the value
of the scale is deduced. In principle a closed manometer graduated in this way, as
a measuring-apparatus is equal to the metal-manometer, but it is preferable to the
latter in so far as its indications when the necessary corrections are applied, are
perfectly reliable and probably much more sensitive. The graduating of the closed
manometer after its construction relieves the observer from those determinations that
take up much time and are very uncertain. The accuracy which can be attained in
closed manometers to 100 atmospheres is sufficient for the gauging of ordinary metal-
manometers, which in order to be reliable must be tested repeatedly and which are
specially used as indicators of operations when employed in accurate measurements.

(214)

to pressures of about 60 atmosphercs), made an alsolute manometer
a real want for a long time past. It it impossible to place there
open large manometers with a single continuous mereury-column fol-
lowing the example of REGNAULT, CAILLETET and AMAGAT. Only in
special cases there will be an opportunity for doing this and generally
one will have to have recourse to the principle (first applied by
Ricmarps in 1845 and afterwards by others) to shorten the open
manometer by dividing it into several not very high manometers placed
side by side in which the pressure to be measured causes the column
of mereury in the first manometer to rise, while a pressure is applied
above the mereury which pressure again is measured by transferring
it to the second manometer where it causes the mercury to rise
under an excess of pressure which is measured by the third mano-
meter, ete. RicHAaRDS and his followers have the pressure transferred
by water. This means is also given by TrieseN ') and his design
has been taken as a basis in constructing the normal-manometer of
the Physikalisch-Technische Reichsanstalt, an apparatus which though
made after the principle of those formerly mentioned fulfills far
higher eonditions by its whole construction.

In the (diagrammatic) serpentine syphon of upright and reversed
U’s when in equilibrio the upper fl parts contain water, the
lower U parts contain mercury and if a pressure is applied to
one end, all the menisci are set in motion at the same time, so
that the pressure might be deduced from the moving of one of
the menisci. Adjustments however are made on all the menisci sepa-
rately, and in this way only, as Wiese rightly remarks ®), a
standard instrument is obtained. Yet the moving of all the menisci
together has been one of the difficulties which checked the operations
with the standard-manometer in the Phys. Techn. Reichsanstalt.
For there, although the apparatus was intended also for determinations
of higher pressure, they have contented themselves with attaining
20 atmospheres, a limit not even high enough for tcsting the mano-
meters of the Government Survey of Steam Boilers in this country by
direct comparison with the absolute manometer. (Among the manometers
which I have tested by means of the open manometer for the Chief
Government Surveyor of Steam Boilers, there were some to 30 atmo-
spheres; among those tested by me for the Chief Constructors of H. M.
Navy there were some to 60, and others even to 100 atmospheres).

1) Zeitschrift f. Instrumentenkunde. 1881, p. 114.
2) Compare his interesting paper in the Zeitschrift fiir Comprimirte Gase 1897,
p. 98, 25, $2, 101.

(215 )

Another defect of the Reichsanstalt-apparatus is that both the
weaker and the greater pressures are indiscriminately measured in
tubes of such a size of bore as is required to resist the greatest pressure
that those pressures whether great or small are deduced from the and
equilibrium of one and the same number of columns of liquid of
the same length, and adjustments on one and the same number of
mercury-menisci. And so in the case of low pressures the uncertainty
resulting from the correction for capillary depressions and for the
temperature and the reading error are unnecessarily great. For the
purpose mentioned in the beginning, this apparatus which for the
rest serves to test metal-manometers is of no value.

When I reflected for the first time upon the problem how to
measure regularly with an absolute manometer pressures, even greater
than those determined by ReGNAULT on the tower of the Collège
de France, at the Leiden laboratory where I could not dispose of
a great height, the shortened manometers mentioned above were
unknown to me. I have considered the transference of pressure by
means of a liquid which allowed of contact with steel and mercury,
yet after all I did not make use of this means. At first sight it
seems that the division of the manometer into separate manometers,
in which the pressure is transferred from the one to the other by
means of compressed gas offers more difficulties than the transference
of the pressure by water sv simple in its principle. Yet it seemed
to me that these difficulties, at least there where the experimentalists
are accustomed to work with gases under high pressure, could be
easily surmounted. Especially the ordinary steel bottles filled with
gas under high-pressure may be utilized to bring the required tension
into the space between the two succeeding columns of mercury, by ad-
mitting gas into the connecting-tube of the manometers and this with
great accuracy with the aid of finely-regulating high-pressure-cocks.

By adhering to this idea I have already succeeded so far that in
a room of the laboratory pressures to 60 atmospheres can be deter-
mined by one direct measurement with an apparatus constructed
according to this principle and consisting of 15 partial manometers
connected together. Seven of the partial manometers connected
together may be used as a differential manometer of 28 atmospheres
under a pressure of 100 atmospheres, so that after having deter-
mined at once directly the pressure of 60 atm. one can, with this
pressure as a basis by means of a second determination with a
column of mercury of 28 atm. attain a pressure of 88 atm. and
again proceeding from this pressure attain 100 atm. by means of a third
determination. This apparatus (represented in fig. I) is constructed

15

Proceedings Royal Acad, Amsterdam. Vol. 1,

( 216 )

by the ordinary means offered by the laboratory. It can easily be taken
to picces and cleaned, leakages can easily be detected and repaired
and it admits of a high degree of accuracy in reading. Even in use
it answers expectations better than I dared to expect. It now seems
to me that a shortened manometer consisting of a tube of every-
where equal bore which is alternately filled with water and mercury
would offer more difficulties and admit of less accuracy than this
apparatus consisting of parts which each can be used either as
manometer or as differential manometer, ef which each has a size
of bore agreeing with the pressure te be determined therein, and to
which more partial manometers for higher pressures can be added
without any alteration being made in those which exist already.

2. The separate manometers. At first I had thought of using
tubes of 12 atmospheres length and to fasten these on a wall of a
staircase. On nearer consideration of several sources of error in the
observations it seemed to me desirable however to arrange the whole
apparatus at least to pressures of 60 atmospheres in one and the
same room along the wall. Quick reading, so desirable in many
respects, was only possible when the single tubes were not longer
than 3.14 M. so that the height of the mercury in the tubes could
be 3.04 M., corresponding to 4 atmospheres.

Every separate manometer consists of one single piece of glass,
made of tubes sealed together, which can be properly cleaned and
dried. The mercury once brought into the manometer-tube remains
there and has contact only with the carefully cleaned glass and the
dry gas which causes the pressure. Where a meniscus is to be
adjusted the manometer-tube should be wide enough for sufficiently
obviating the uncertainty resulting from the capillary depression,
and for the rest so wide as the pressure which the separate
manometer shall have to resist will admit of. The manometer is
on both ends provided with suitable contrivances by means of
which it may be connected with the other paris of the apparatus,
and the tubes of which it consists are bent in such a way that
these joints together with the others can be brought very near to
each other at the bottom of the apparatus near the stopcocks.

I used three different types of glass tubes. The first type is repre-
sented by tube A in fig. 1. One leg of the U-shaped wider tube
(12 m.m. diameter) is half the length of the other, to both legs
capillary tubes have been sealed on which are bent downwards and
reach below the lower part of the U. Tubes of this kind A may
generally be used where we want to read a whole range of positive
pressures’ from 0 to 4 atm., (from o to m,'—m,) on the same tube.

( 217 )

One might construct a manometer entirely with tubes of that type,
each for 7 atmospheres, in which the additional pressure above x7
atmospheres might be read on a tube proof against » 7 atmospheres,
while each of the x preceding tubes were adjusted on a difference of
pressure of r atmospheres but this manometer when adjusted to a
high pressure, would contain more compressed gas than is necessary.

This is not desirable, for with unaltered section of the tubes at
the place of the mereury-menisci, and with unaltered distance
of the latter, change of temperature in the gas confined between
the two columns of mercury, will bring about a displacement of the
menisci which will be the stronger as the volume of the confined
gas is larger. So we must try to limit as muchas possible the volume
of the space filled with gas. This is also desirable in order not to
waste any gas during the operations; which gas, with a view to the
preservation of the apparatus and in order to enable us to apply the
corrections with exactitude must be perfectly dry and pure; finally
because the effect of a possible explosion of a tube filled with gas
at a high pressure, is in proportion of the quantity of the gas
compressed therein.

In order to economize gas we use the second type represented
by the tubes Bj, Bs in figure 1, which is also easier to be handled
than A, These tubes consist of a wider upper cylindrical vessel,
b and a lower cylindrical vessel, a, in which the mercury-menisci
are adjusted, of a capillary y, (comp. fig. 2) through which the mercury
rises and of the connecting capillaries f, and 4, bent downwards.
The diameter of both vessels is such as would be chosen for a
manometertube of class A, intended for the same pressure and
smaller in proportion to the augmentation of the pressure for which
it is destined. The following are the diameters of manometers for:

Atmospheres Inner diameter Outer diameter
12 9 mM. 12.8 mM.
20 8 13.5
32 6,5 13.5
60 6,5 15.5

In order to be able to take the lower cylinder as short as possible
we choose a narrow capillary for the ascension of the mercury, in
doing this however we must take into account that this has a
great influence on the motion of the mercury and makes that the
adjusting requires more time. As the co-efficient of friction of mer-

15*

( 218 )

eury is much greater than that of gas, one might take the capillary
through which only gas flows, narrower than that through which
mercury flows, without causing thereby considerable delay in adjust-
ment. As the dimensions of those capillary tubes however do not offer
any difficulties, and it is not desirable to take them narrower than
is strictly necessary (comp. § 7) I used capillaries of nearly the same
section both for gas and mercury.

The section of the capillary tubes is from 0,75 m.m?, to 1.37 m.m*.
The length of the upper cylindrical vessel is 8 em. This length
Jeaves more than sufficient room in adjusting the meniscus, without
the accurate determination of the height of the mercury being damaged.
The cylinder may not be shorter because when the mercury rises,
danger might arise for the mercury to overflow which would cause
all the other manometers to overflow likewise. The whole apparatus
would temporarily become unfit for use and even the joints on the
board to which the stopeocks are fixed might be endangered.

The length of the lower cylinders is calculated after the available
capillaries and the upper cylinders. It has been taken into account
that when the lower cylinder contains so much mercury as necessary
to fill the whole capillary and the whole upper cylinder, a space
of 4—5 e.m. long remains above the mercury. If this precaution
had not been taken, gas bubbles that might rise (in blowing off
the manometers) would cause the mercury to overflow, which as
mentioned above must be prevented carefully.

An open manometer cannot consist of tubes of the type B only
as in these we can only adjust at a fixed difference of pressure
(position of the mercury nearly in the middle of the upper cylinder).
With » of these tubes, each measuring a difference of pressure of r
atmospheres one can adjust accurately at zr atmospheres only. For
adjustment at the additional pressure above zr atmospheres we want
another tube, viz. the tube 4, the first in the plate.

In constructing shortened manometers we can very succesfully
avail ourselves of tubes of the third type, C (comp. fig. 1). These
are distinguished from the type A by their having the two branches
of the U equal in length so that we may adjust both positive and
negative differences of pressure, according as we adjust either at
rj on the left and 79 on the right or conversely at 7; on the right
and at 7, on the left. Suppose that we have adjusted the tubes
A and Zi to Bs together at 35 atmospheres and that we want to
measure the pressure of 34.8 atmospheres, this can be obtained, (the
adjustment in all preceding tubes remaining unaltered), by adjusting
the mercury in tube C at — 0.2 atmospheres difference of pressure.

ee

(219 )

The tube shown in fig. 1, serves to adjust at positive and negative
differences to within !/, atmosphere.

§ 5. The connections and the stop cock board. In the apparatus
represented here, tube A at one end has contact with the atmosphere
by means of a drying tube Q, coated with P; O; by which it is protected
from moisture. And so in this case an india-rubber tube is suffi-
cient connection. At the other end however the ordinary contrivance
which is found at both ends of all other separate manometers has
been fastened. To the thick-walled glass capillary (comp. fig. 4) p, a
steel capillary g has been cemented which carries an overpipe W
with a nut U. This nut is screwed (comp. fig. 1) on the correspon-
ding tap (of Tj) of the stop-eock board; the steel capillary gives
elasticity to this joint. The communication between the other

manometers is also obtained by screwing the connection-nut on to

the T-pieces, 7, on the stop-cock board. The horizontal branches
of the T-pieces form the connection between the successive
manometers, the stcel stop-cocks in the vertical branches of the
T-pieces form the communication of the space between the lower
meniscus in one manometer and the upper meniscus in the next
manometer with the main feeding tube 4, from which when brought
to a sufficient pressure, gas can be admitted in that space in order
to apply the desired pressure on the columns of mercury.

This main feeding tube (of copper with brazed on branches)
is filled by the bronze stopcock X through the steel cross-piece V
from a cylinder with gas compressed at a sufficient pressure — dry
air or oxygen or hydrogen, for Jower pressures sometimes dry
carbonic acid — which gas passes over P.O; (in the drying tube
1) before entering the apparatus. The cross piece N enables us at the
same time to make communication between the manometer and the
apparatus in which we want to measure the pressure; such an apparatus
in the drawing being a metal-manometer as represented by MZ. This
metal-manometer and the stop-cock Z are also used to measure the
pressure in an apparatus which is joined to 7, before causing com-
munication between this apparatus and the open manometer by means
of the stop-cock Y.

4. The adjustment at a given pressure. The admission of the
compressed gas in the different spaces in the manometers must be
performed with the greatest caution. In the first place we have to
prevent the overflowing of mercury from one manometer into the
other; we have alluded already to the disagreeable consequences of
this. Then we must remark that when we cause mercury to rise in
one of the manometer-tubes Bz f. i, and admit therefore (keeping the

a

( 220 )

stop-cock Ay shut) pressure into the lower cylinder, the gas in the
closed space between the upper meniscus in Bz and the lower meniscus
in the preceding manometer will be compressed and consequently
the lower meniscus in 4, will be further depressed. A similar
displacement is repeated in all preceding manometertubes at the
adjustment of each following manometertube. If finally we want
to get the desired adjustment in all cylinders we must begin because
the spaces between two manometers are not provided with separate
stop-cocks for drawing off so as not to add unnecessarily to the num-
ber of stop-cocks and connecting pieces, by causing the mercury to
rise in the manometer to less than the required height i.e. only so
far that it will be brought to the required height by the following
adjustments in the other tubes. In order to facilitate the filling these
heights have been indicated by distinct marks (comp. zj, #2 in fig. 1).

In order to bring the apparatus to a given pressure, (at 46!/4
atmospheres f.i. as in the drawing) we must find out which multiple
of the whole height is nearest to that pressure, how many tubes
of the type B we shall have to use therefore and which additional
pressure has to be adjusted in A.

Then all stopcoeks except Aj, KA and X, are opened wide and
gas is carefully admitted through X until the difference of level in
A has the required amount (in this case 2!/, atmospheres) within
about 6 e.M., after which X is shut. In all the other manometer-
tubes the pressure rises to the same height, but the position of the
mereury remains unaltered during this process. Then shut A, and
open X carefully until the mereury in B, has reached «,; shut
Ky (« is shut) and admit gas through X until the mereury in By
has reached 2, ete. until the mercury in Bi, has reached #5, shut
X and Kj, and admit pressure through X till the topsurface of the
mercury in Bj, in this special case is just in the middle of the
upper cylinder. Then the menisci in all the preceding manometer-
tubes are in a proper position.

A given pressure can always be adjusted accurately within a
small fraction of an atmosphere.

If differences should remain or arise between the pressure adjus-
ted and the pressure we want to determine, we can take away these
differences by means of the differential tube C which in the
case represented here was not used. Ajo to Ay; are left open,
Ky, is shut and more gas is admitted through X, but at the same time
we draw off through A A just as much as to leave the menisci in By,
in the same position, and then the desired difference of pressure in
C is adjusted. After this X and A A are shut,

( 221 )

In order to stick to the principles of the construction of our ap-
paratus we should have at hand C tubes of different sections and we
should always have to join on such a tube as agrees most with the
pressure to be measured.

From what preceeds it appears that when we have adjusted at a
certain pressure and we want to pass to another this can be done
easiest by 4 atm. at a time. In order to rise 4 atmospheres we must
let the last tube Bj, go back to the mark #j, by drawing off through
KA, shut KA and Ko and admit gas through X until the required
adjustment in Bjo is attained. In order to let the mercury fall 4
atm. we must act conversely, viz. draw off through KA till the
mercury in Bjo has fallen; shut A A and open Ajo and again admit
gas through X until the mercury in Bj, has reached the middle of
the upper cylinder.

If we want to pass over to pressures higher by a fraction of 4
atm. say 2 atm. then we must proceed more cautiously; as a rule one
should work with all stop-cocks shut, because all menisci will vary
at a higher adjustment in A, but it will often be sufficient to bring
A almost to the desired new pressure through the stopeock A, and
to bring the other menisci to a proper position by admitting a higher
pressure through X, if only we have left unimpaired the reserve
space in the upper cylinders. In none of these cases the adjust-
ment will offer any difficulties.

It is however more difficult to let the pressure fall by differences
of less than 4 atm. We then must first adjust at 4 atmospheres lower
und must raise the pressure to the desired pressure by adding the
remaining difference, if the position of the mercury in tube 4 per-
mits. If not, we shall have to empty the main tube, to blow off the
manometers, and to raise the pressure anew from 0 to the desired
pressure. For in the tube A we can only adjust at a rising pressure,
because at a falling pressure mercury would overflow from the upper
receptacle Bj.

If we should wart an apparatus in which we can adjust with
the same rapidity at rising as at falling pressures, this should
consist entirely of A tubes and we should have to read the addi-
tional pressure above the multiple of 4 atmospheres on the tube
containing the highest pressure. Or we should have to add to a
manometer consisting of B-tubes a differential tube C of 2 atmospheres,
or two tubes C of 1 atmosphere each to which as in the case of
the separate manometers a special supply-stopeoek has been joined.
The remarks made previously concerning the diameter apply to
these tubes unless one should be satisfied for all pressures with

( 299 )

reading 2 (or 4) menisci in tubes calculated for the highest pressure.

The standard-manometer as a matter of course is used to determine
pressures, that are carefully kept constant for a long time, and by
preference by repeated readings from one and the same adjustment.
And so there was no reason for using the above-mentioned auxi-
liary means.

5. The reading. ‘The position of the menisci is read on tubular
measuring rules, suspended between the manometer tubes in rings
of CARDANUS co, ¢) +--+ ++, Which rules besides promoting the
accuracy of the measurements, have the advantage of being easily
applied to the apparatus and removed from it. The measuring
rule used with the manometer of type A in which adjustments are
made at different heights is a brass tube graduated in m.m. over its
whole length. The measuring rules used with tubes of the type B are
ordinary brass tubes to which only at both ends short graduated
scales « are fixed. We adjust at the menisci in the tubes B, all of
which are at an elevation of nearly | M. or nearly 4 M. above the
ground with the aid of two theodolites. One of these is placed on
an isolated observation pillar in the room, 4 M. in front of the
wall against which the apparatus is fixed. Vertically above this
one a second theodolite is placed on a table (3.5 M. high) resting
on the same pillar. Next to this isolated elevation or observation-
tower steps provided with a platform, such as are generally used
for observing purposes in the laboratory, are placed.

In this our case it was very difficult to make the menisci clearly visible
in the way in which it is generally done viz. by sliding along the tubes
a piece of black paper tubing until the rim of this piece of tubing
almost touches the meniscus and the meniscus stands out as a dark
reflection against the bright background (white paper), especially because
in order to protect the observer when he opens or shuts stopeoeks, or
looks for leaks and his eye is very close to the apparatus, sheets of
plate glass P (fig. 1) have been placed in front of the manometer
receptacles. The sheets of plate glass are supported by clamps fixed
to beams r which are screwed on to the wooden strips / fixed every-
where alone the walls of the laboratory for fastening purposes.

Mr. J. C. SCHALKWIJK, assistant at the laboratory to whom
IT am much indebted for the care bestowed upon the apparatus,
has hit upon the idea to place behind the meniscus a drawing of
black teeth against a white surface (comp. fig. 2 and 3) which is
reflected on the meniscus. The coming together of the reflection
of the teeth on the meniscus with the drawing of the teeth enables
us to determine accurately the place of the top of the menisens,

ee er en eee nn
Sm — ee — - a

i
at rn ee

SSS

—
is. a 2s
nn u zE

el
ie)
2
Ei
3
=
:
Ss
5
2
a
i
Z
5
3
Ei
:
4
:
[|
8
ei

| Proceedings Royal Acad. Amsterdam. Vol. L,

(223

The method of adjustment of Mr. SCHALKWIJK will prove very useful
in many other cases. ;

The illumination is obtained by means of incandescents lamps
which are moved along at a suitable distance of the apparatus.

In order to read the position of the mercury in the tube A or in
the small tube C, we can, if perfect precision is not necessary and we
therefore need not take the readings by means of a levelling teles-
cope, utilize indicators fixed to pieces of tubing, which can be moved
to and fro round the glass tube.

§ 6. Remarks on the constructing of the manometer. The appa-
ratus is constructed by Mr. G. J. Fri chief of one of the instru-
mentmakers workshops of the laboratory, whose able help was of
great value. Although the single pieces of manometer-tubes are
very large the constructing and handling especially of the type
B did not offer great difficulties. But it need hardly be men-
tioned that all the operations have to be done very carefully
and cautiously, if so complicated an apparatus as the manometer
is not to have any leak or other defect. To persons who want
to construct such an apparatus the following remarks may be
useful. In order to make a tube of the type B the separately blown
cylindrical vessels with short capillary tubes (about 15 e.M.) bent
in the proper form (comp. fig. 2) are put together with the other
parts either suspended from pulleys or placed on stands, provided
with proper india-rubber tubes in which we can blow, and sealed
together by means of the hand blow-pipe (fed by a water blow
pump). In this way tubes of any length can be sealed together. As
the manometertube of the type B, consists principally of capillary
tubes it forms a very elastic whole. It is mounted on a loose board
between cork by means of clamps, cleaned with boiling, and dried
with the same precautions as the glass used for the thermometer
described in the Proceedings of Mai 30th '96, p. 40!). During the
boiling the tube with the auxiliary board are placed in a sloping po-
sition, entirely filled and with both branches plunged into small basins,
and heated by means of a BuNsEN-flame regularly over its whole
length. After the drying the ends are provided with the steel caps,
p, (prepared beforehand) to which the steel capillaries (treated as
the thermometer capillaries comp. Proceedings May 30th ’96, p. 41)2)
with the overpipe W have been fastened (fig. 4). The steelcapillary
(comp. Proceedings Dee. ’94, p. 168)%) (long 35 eM.) has been

1) Comm. of the Phys. Lab. at Leyden 1896, n°, 27 p. 8.

2) Ibid. p. 9.

3) Comm, of the Phys. Lab. at. Leyden 1894, n°, 14 p. 8,

( 224 )

screwed as ].c.p. with marine-glue into the cap and into the over-
pipe, and after this the joint has been soldered with tinmans solder
in order to shut up the soft marine-glue firmly while the seam is
protected from the action of the mercury.

The fastening of the steel caps to the glass capillaries which are
widened towards the ends requires special care (comp. the cementing
of thermometer-capillary, Proceedings May 30th 1896, p. 41)1). It is
done as then by means of red sealing-wax, that answered the pur-
pose better than several other mixtures that have been examined
since that for this purpose. In addition to the precautions in the case
mentioned l.c. we had to prevent the sealing-wax from having
contact with the steel capillary until all tbe air has escaped, as
else the passage for the air would be blocked up, which would
cause a defective closure.

We continued the pushing on of the cap under moderate heating
as when cementing the volumenometer cap (l.c. p.) until the sealing
wax became visible between the steel capillary and the glasswall.
In this way we succeeded in getting perfectly tight connections,
only the joint between the glasscapillary and the steeleapillary
would sometimes give rise to defects and as the reliability of this
joint is of great importance to the usefulness of the manometer
we are still trying to get a better connection. After the joints
have been made the manometertube is ready to be tested by pres-
sure in order that we may detect leakages. In order to fill the
manometertube with mercury we cement a small thin-walled glass-
capillary the point of which has been sealed, on the end of the
steeleapillary which projects beyond through the overpipe, then we
exhaust the manometer by means of the mercury pump and the
point is broken off under mercury. By admitting air we then can
expel as much mercury as is desirable.

Each manometertube is fastened on a separate board /2; by means
of 4 clamps & (comp. fig. 5) between cork and this board is serewed
on to a board /2, which is fastened to the wall by means of fixing
it to a strip L.

The T-pieces on the board on which the stopcocks are fastened, are
forged of steel and have been pierced afterwards. The high-pressure
stopcocks (the ordinary Leiden pattern) are also entirely made of steel
in order not to be attacked by the mercury which might accidentally
get into the horizontal connection-canals of the T-pieces; they have

1) Comm. of the Phys. Lab. at Leiden 1896. NO, 27, p. 8.

been placed higher than these connection-canals so as to make it
more difficult for the mercury to get into them. The footplates of
the stopcocks are fastened by means of wood-screws on the stopcock-
board. The connection of the stopcocks with the steel T-pieces is
obtained again by marine-glue fastened by soldering-work; al these
parts and the coupling by nuts and taps proved perfectly reliable.
After the manometertubes have been connected, the whole apparatus
is exhausted through the stopcock A, (at the same time coupling
the left side of A to the airpump) and is filled with gas from the
main feeding tube.

When there are still leakages in the apparatus after this has been
performed, these are shown by the motion of the mercury columns
when the manometer is brought to pressure. They are then detected
by passing a pencil with soap-water or oil along the suspected
seams, and generally they can easily be repaired without removing
any of the separate manometers from the apparatus (which however
would not offer the jeast difficulty owing to the elasticity of the
glass capillaries, the flexibility of the steel capillaries, the mobility
of the boards and the suitable position of the joints).

7. Corrections. In computing the pressure from the read height
of the mercury the ordinary corrections for open manometers must
be applied.

I need not dwell upon the well-known small corrections which
the theodolite-readings (comp. § 5) might require, from the telescope
being not perfectly level in the way of reading which is followed
here; I will only suggest that the correction for the capillarity may
be applied by determining the height of the meniscus by means of
the reading telescope. We have however not yet much experience
about that correction and till now we tried to equalize the two
menisci in one and the same tube as much as possible by knocking.
There are however two corrections resulting from the peculiar con-
struction of the apparatus on which I shall have to make a few
remarks.

The first correction is that for the difference of pressure in the
compressed gas near the lower meniscus in the one and near the
upper meniscus of the next manometertube. If the corrections must
be very small we might use for the supply of pressure compressed
hydrogen, this may be of advantage for very high pressure, at 60
atmospheres or 45600 m.m. the correction for all hydrogen columns
together is not more than about 9 m.m., at 100 atm. or 76000 m.m.
not more than 21 m.m. so that these corrections have only to be
applied to measurements, which are very accurate. But as the slightest

contamination of the hydrogen has a great influence on the correction,
this gas can only be applied when one disposes of a compression-
pump as constructed at the Leiden laboratory (Proceedings, Dec. ’94,
p. 168)!) by means of which the hydrogen can be re-compressed without
its becoming impure. Compressed air at 60 atm. (about 120 m.m.)
gives a correction which can be appiied with perfect certainty.

In the case of lower pressures we can use commercial carbonic
acid from cylinders, if only one takes good care to dry it. Ata
comparison at about 48,6 atm. we read on the manometer, after
having applied all the corrections except those for the connecting
tubes between the separate manometers, a total column of mercury
of 369433 m.m. The correction for the carbonic acid columns was
but to — 1448 mm.

After the correction for the columns of compressed gas in the mano-
meter has been applied we must still take into account the column
of the gas between the level of the last meniscus of the manometer
and the level of the place at which we want to measure the pressure
in the apparatus. The determination mentioned above referred to
the pressure in apparatus which were placed in a distant room;
these were connected with the manometer by a conduit (40 M.
long) filled with carbonic acid; the difference of level amounted to
0,65 M. and the correction was -+ 6,2 m.m.

A second correction peculiar to this apparatus, must be applied
when the mereury in the manometertubes stands not perfectly still, as
even the slowest motion of it through the narrow tubes requires a
measurable pressure. If a velocity of 0.1 m.m. in a minute is ob-
served at the menisci in one of the separate manometers, this agrees
with an excess of pressure and with a correction of about 0.1 m.m.
For the streaming of the gas this correction would be uncertain as gas
may overflow without this being perceived at the movement of the
menisci. Therefore the tubes along which the gas flows from the one
manometer to the other may not be too narrow. The diameter of the
steel eapillaries is 0.6 m.m. They don’t add to the friction more than
the glass capillaries and these are taken comparatively wide (comp.
§ 2) so that when the apparatus is in a good condition we need
not pay attention to the motion of the gas.

Usually the filling of the tubes is done very slowly, the filling of
each tube takes about 4—5 minutes. Each time at the closing of the
stop-cocks the equilibrium is fairly well attained. If however a small

') Commun, fr. the Physical Laboratory at Leiden, 1894, N° 14 pg. 7,

excess of pressure had to be applied it appeared that even in the
remotest tube the mereury soon stands still. After the adjustment
is made we usually wait 10 minutes to make sure that no further
change occurs. During that time several readings can be prepared
or taken, amongst others those of the 8 thermometers, indicating
the temperature.

As the temperature during the observations is kept as equable as
possible, and as the cylindrical vessels have been taken as short as
possible (comp. § 2) the movement of the menisci of the mercurv-
columns through the alteration of temperature of the gas, after the
adjustment has been made, is very slight.

(December 21th, 1898.)

« > oT A = a ie se ® y on A Lj
Pp ae feaie : ’ i : nà B,
2 YT ad j i. A P

t hal ws at eatery, 70 Ae 1e
Phi! - aat Saale eae |
ere ne ie one AO ee Be
J ‘ 1 zt Ere Cerva bi here afs rf at)

ad
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> |
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.
; > AR
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ay
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7
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Rn

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING

of Saturday December 24th 1898,

Ce

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 24 December 1898 Dl. VII).

CONTENTS: „On mixed crystals of nitrate of kalium and nitrate of thallium.” By Prof. H. W.
Baxuuis RoozeBoom, p. 229. — „Variation of volume and of pressure in mixing (II).”
By Prof. J. D. vaN DER WAALS, p. 232. — ,,Measurements on the course of the isotherms
in the proximity of the plaitpoint and particularly on the course of the retrograde
condensation in a mixture of carbonie acid and hydrogen.” By Dr. J. Verscuarrerr.
(Communicated by Prof. H. KAMERLINGH ONNES), p. 243. — ,,Measurements on the
magnetic rotatory dispersion of gases” By Dr. L, H. Srerrsema. (Communicated by
Prof. H. KAMERLINGH ONNES), p. 243.

The following papers were read:

Chemistry. — „On mixed crystals of nitrate of kalium and nitrate
of thallium”. Dissertation written by Dr. C. vay Eijk and
presented by Prof. H. W. Bakmurs RoozeBoom who reads
on this subject as follows :

Some time ago (vide Proceedings of the meeting of the Academy
of 24 Sept. last, page 101) speaker has given a theoretical develop-
ment of the course of congealing of a molten mixture of two sub-
stances, from which mixed crystals are deposited when cooling and
of the course of transformation of such crystals, in case one of the
two components or both of them pass into another solid modification.

Nitrate of kalium and nitrate of thallium now are the first
examples of a system of two substances, of which we have acquired
a general survey of the course of these two phenomena over the
entire field of concentration, and in which the observations agree
in all respects with the course deducted theoretically.

16

Proceedings Royal Acad, Amsterdam, Vol, IL,

( 230 )

Let us first con-
sider the congelation
(see figure).

The _congealing
temperature falls in
mixtures of 0 —31.3
mol.pCt. K NOs from
206° (melting point
of T1 NOs) to 182°
(AC). From these
liquids mixed erys-
tais are deposited,

containing more

TINO; than the
liquid, namely 0—20
pCt. K NOs (AD).
These are heavier
than the liquid.
Starting from KNO;
the congealing tem-
perature falls equally

from 339°—182°
(BC) while from the
molten mass of 100—
31.3 pCt. K NO;
mixed crystals are
deposited containing
100—50 pCt. K NOs
(BE) being therefore
richer in K NOs.
These crystals are
specifically lighter
than the molten mass.

The congealing
both in points of
AC and of BC takes
place in such a tem-
perature-interval, as
comprised between
the points of AC
and AD or BC and
BE showing the same

(231 )

concentration. At the minimum congealing-point C the liquid of
31.3 pCt. K NO, solidifies to a conglomerate of two kinds of mixed
erystals, one with 20 pCt. and the other with 50 pCt. K NOs.
Notwithstanding both kinds belong to the rhomboedrie system, the
mixing series is not continuous.

Below 182° three different conditions are therefore possible in the
solid state: homogeneous mixed crystals («) of 0—20 pCt. K NOs,
homogeneous of 50—100 pCt. K NO, (@') and conglomerates of the
limit-erystals of 20 and 50 pCt, in variable relations, in accordance
to the composition of the fused mass, taken as a starting point.

The mixed crystals, either homogene or conglomerate undergo in
case of further cooling, transformations from the rhomboedric to the
rhombic form.

For K NO; that transition was known at 129°.5 (6).

For TINO, Dr. van Erk found for the transition temperature
144° (/).

The determination of these temperatures for these two substances,
and for their mixed crystals, was effected either by observing the
delay in the rise or fall of the temperature, effected by the heat of
transformation, or by determining the temperature at which the
transformation becomes noticeable by the refractive power or the
exterior of the crystals. These latter observations are made both
microscopically and with the naked eye.

Between 182° and 144° no transformation takes place; we have
only found, from the course of the transformation at a lower tem-
perature, that the limits of the homogeneous crystals a and «'
diverge somewhat more at a falling temperature. At 133° these
limits have become: 20 pCt. and 69 pCt. K NOs.

The transformation-temperature of the homogeneous «-crystals falls
with increasing K NO; proportion from 144°—133° (line /H); the
correct position of line Hs, indicating the rhombie /3-crystals
formed, is however not known. The transformation temperature for
all conglomerates of @ and @' mixed crystals is at about 153° and
from the fact that this temperature remains constant between 20
pCt. and 69 pCt. K NOs the situation of the points MZ and UH, is
deducted and the course of the lines DH and EA).

At 133° all the rhomboedric «-crystals of the conglomerate are
transformed in rhombic /-crystals.

Below 133° the conglomerate consists therefore of - and «’-
crystals. The limits of these two kinds are proved equally to change
in case of a further fall in the temperature (lines HJ, and H, J)

16%

( 232 )

namely both to a higher K NO, proportion so that these limits have
become at 108°.5: 40 pCt. and 84 pCt.

The homogeneous rhomboedric «'-erystals only begin below 129°.5
to be transformed in rhombic mixed crystals /’.

For crystals of 100—84 pCt. K NO, the transformation tempe-

rature falls from 129°.5—108°.5 (GJ). At 108°.5 the composition
is attained, also possessed by the @' mixed erystals, which were
already present in the conglomerate with /-crystals from 133°. Below
108°.5 all the «'-erystals in the conglomerates are now transformed
in rhombic ones. The transformation is completed at this tempe-
rature.
In consequence of the discontinuity of the mixing-series there
remain however below 108°.5 still 3 mixing-types of rhombie crystals
viz. homogeneous /? and /2" crystals and conglomerates of both
limit-crystals.

The limits of mixing and consequently the composition of the
two component parts in the conglomerates, being at 108°.5 + 40
pCt. and 84 pCt. K NO,, diverge still more with falling tempera-
ture, so that they have become at 10°: 15.5 pCt. and 96.5 pCt.
(J, K and J, K).

At the lower temperatures these limits are easily found, by deter-
mining the limits of the mixtures in the crystals that are deposited
from aqueous solution.

Physics. — „Variation of volume and of pressure in mixing (LI):”
By Prof. J. D. van DER WAALS.

For a simple substance we may calculate how much its volume
under a given pressure and at a given temperature differs from that
which it would have occupied, if it had perfectly followed the law
of BoyLe.

Let us call the real volume v, and that which it would occupy
according to the law of Boye v', then the quantity to be examined
is v —v. Let the quantity of matter be equal to the molecular
weight.

From

MRT MRT a

D= = = =

v vu—b ve

follows
v
y=
b a 1

Tb AHO + eo

(233 )

a
If we put =a’, we find
Ee (AKTE oe it
' b v
a— mmm,
3 Ms v—b_a'v(v—b) — br?
v— v= 5 al = v? — a'(v — dD)
2 ae
or
ab
a’ —b — —
ie
»—v= : 7
a ao
Tease = fee
v Uf

If »=o we find for the increase of volume in consequence of
the causes which make a substance deviate from the law of Boye,
the value a’ — b.

If we had not solved the problem in general, but had restricted
ourselves to a first approximation, we should have found this
special value (a' — 6) as apparently the general one. So in my paper
on „variation of volume and of pressure in mixing” I have found
for Av

rn a + az — 2 ag
((1 + az) (lL — be) (1 + a@t)

= (hy $0 — 2b)

but only because the value of A, had been determined by approxi-
mation — and the question is not without interest, can the real
course of A, be determined? For the quantity © — v for which the
accurate value has been found above, this may of course be done
— and it will be possible to show that a similar course is to be
expected for A,.

If we proceed to the discussion of,

ab

a—b—
; ds v
v EN aw
v ve

U

b . ’ al ©
we first observe that for v = ler the quantity » —v= 0. This
a —

is the same value for which the quantity p —p', treated in my
former communication, is equal to 0.

Two cases, however, are possible, if beginning with >= we
diminish the volume gradually.

When diminishing v, the value of v'—v may either decrease
continually down to 0, or it may first increase to a certain maxi-
mum, and then eae Which of the two cases occurs will depend

a 7 . .
on the vatue —. If we put by first approximation

)

ab a
i («' — en) (1 4. en)
v v

or

v —v=a—b+ Aen

v

we see, that when a’ > 2d, © —v ee oe to increase and vice
versa. The condition a’ > 2 6 leads to a. When Tie a

v' —v will begin to increase and vice versa. “the condition hy the
limiting value of v'—v being positive, is a’ >b or ET,

Our result is therefore that for half of the temperatures, at which
v'—v is positive, this quantity will begin to increase still more.

This result will be modified to some extent, if we take also the
variability of b with the volume into account, — for this particular
problem it is sufficient to know the first correction term — but as
long as the accurate value of 6 is not known, it may be better to
consider b as invariable —, also because the laws found in this
supposition are generally much simpler. Not before a sufficient
number of reliable observations are at our disposal, at which the
result of this and similar calculations may be tested, it will be
possible to investigate, whether this and the following calculated
correction-terms of b can account for the deviations.

If we consider b as independent of the volume, we find by diffe-
rentiating o' —v, that a maximum is found at

v a

es al —2d-

In order to find » positive, a’ must be greater than 2 b, which agrees
with the preceding result.

j ae
If we substitute this value of — in v' — v, we find for the maximum

value of v' — v

: b b
(v me V) max. == 4b a0 32 T 7
audi 27 Toe

As a matter of course it is better to restrict ourselves to tempe-
ratures above the critical. Below this temperature v'— v is not
single-valued and the inquiry after the value of v'—v for such
points on the theoretical isothermal as for which the pressure
would be negative, has no sense. If we take as utmost case 7 = 7%,

: , Dit
the maximum value ©’ —v has risen to — b.
J

For the value of the proportion of the maximum amount of v' — »
and the initial value, we find

32 7 27 Tr
eee!
27 Tr Se

Path A ,
T to be taken between Ta Tr and 7. This proportion which at

27 . nun
ET Tj, is equal to unity, reaches the value of 2.27 at T= 7.
1

Now we can imagine the course of v'—v at all temperatures

above the critical.
27 A EN, : 5
WAR tor FESS = Tj the limiting value of v' — v is negative and equal

to b (= —_— — 1) , so contained between —?/ and 0. For decreasing

value of v, the quantity descends to the value —h at v=b. There
is neither maximum nor minimum.

27 seathc : SiC
2°. for 7 between E Tj, and iG Tr, the limiting value is positive

and keeps between 0 and 5. For decreasing value of v, v' —v

descends down to —b. So there must be a value of v, at which

ve’ —v changes its sign. This value of v has been calculated above,
!

ab ‘ : /
and has been found to amount to — ar € for which we may write

t
a-—

v= (——_——_

8 oe

27 Ti

This value for » lies between oo and 26,
As in the preceding case there is no question of a maximum
value.

27 :
3°. for 7 between Te Tj, and 7, the limiting value of © —v is

contained between b and 2%/, 5. When the volume decreases, v' — v
begins to increase, till a certain maximum value is reached, which
amounts, however, at the utmost to 2.27 times the limiting value.
It decreases afterwards, reaches the value 0 and ends with — b.
40, for values of 7 < 7; only those values of v have to be con-
sidered, which lie beyond the limits of coexisting gas- and liquid-
volumes, and v'—v loses even its theoretical signification for such
volumes for which the pressure on the theoretical isothermal is ne-

27 ;
gative. For T= Ee Tj, the isothermal touches the p-axis at v =2b.

There the quantity v'—ev is infinite, because if p=0, v' is also infinite.
But this does not mean at all that for the volumes which may be
realized at that temperature, v' — v will increase to a high amount.

27 Î
Let us take e.g. facie T,. In order to find the highest value for

v' —v, we have to determine the value of v for saturated vapour and
to substitute that value of » in the formula

a b
a’ — 6 — ——
v
VUE rs
il a ab

b 1 :
Let — be taken equal to =, — and as at this temperature aib

v a0
we find :
4
| — 35
» — v = 6 —— EER
(1 a5

so a value which is not much higher than the limiting value. If

( 237 )

we follow the border-curve from T= 7; down to very low tempe-
ratures, at which the vapour volumes are very large, a large pro-
portion may be found in the beginning, but very soon that proportion
must become nearly equal to unity.

By means of the knowledge of »' — v, we may conclude to the
course of A,, the increase of volume when two substances mix under
constant pressure. If we call the molecular volume of the first
component under a given pressure vj, of the second component vz

: MRT
and of the mixture v, then wv, and 2’, and v' are equal to — —
P
and so equal to each other.
For A, = v — (1 — 2) vj — z vg we may therefore write

Av = (1 — 2) (oy) — m) + 2 (0's — v9) —(' — 0),

and so we find A, from the values of v' —v for each of the sub-
stances.
For tv) =7=v—o we find

Av = (1 — 2) (aj — bj) + 2 (@'2 — by) — (ar — bx) -

If we put (1+ a) (1—4), (1 + a) (1 —by) en (1 +42) (1 — bz)
equal to 1, we obtain equation (4) of my former communication
(Proceedings Nov. 1898, p. 181). There also the same approximation
is applied in equating px, pr. and pv. But from the result now
obtained, it appears clearly that

+ ag — 2 ayo

— FT (41 —_— ly — ) |
a(1—z) / TEE (bi + ba 2 bi)

is only the limiting value of A, for infinite rarefaction and we are
led to the question, whether something further may be deduced with
regard to the course of A» under increasing pressure, and whether
it may be possible to account for the fact that the values for A,
which may be deduced by means of KUENEN’s observations, do not
show that symmetry which follows from the factor «(1 — 2) and
which appears so clearly from this observations of A,. -

If we substitute the values found for © — vj, vg — vz and v'—v
we find

( 238 )

a, by fj a's by fi ay by
alee bye Sign ples alge de
Vv) Vg v
N= (1 == «) —— Seat Er EL En So
1 ay a’, bi da ag by On ehs
en À 9 hae ERN Tren 75
vj Vi” Va Vg” Vv vw

in which 2, vo and v represent the volumes, occupied by the com-
ponents and by the mixture under the same pressure. As long as
we restrict ourselves to large volumes, we may take vj, v and v as
being equal to each other, and then we find for the second term
of A, (which must be divided by v) the value:

Mm) a)! (ay — 218) Pea’, le — 20.) a (a R

The sign of this quantity for the different values of 2 will decide
whether A,, when the value of wv is decreasing, will decrease or
increase and the value which this quantity possesses, will be decisive
as to the degree of this variation. This quantity disappears for
z= and «=1, and must therefore have «(1 — 2) as a factor. If
the remaining factor were independent of 2, there would again be
symmetry in the values of A,, also when the volume decreases. If,
however, this factor depends on x, there remains symmetry in the
limiting value of A», but this symmetry must disappear sooner or
later, when the pressure increases. The remaining factor has the
following intricate form, which I shall give in the five parts, into
which it may be divided:

(8 —32@-+ 2?) a')(@, — 26) ele MENE)
+ (1 + @ + 2?) a'g@’g—2b). «en - = (B)

—2(1—2) | a'yg (dj — 2 bj) + ay (dio — 2

[8
ed
ES
2
—
Vern
.
.
a
>
J
—

—2 2 | a'y9 (a'g — 2 bg) + a's (ap — 2 bol - + ©)

— «(1 —2) | Aan (dia — 2 bya) + hyp — 2 b3) + ag (a's — 2) | (@)

If we put a+ a'9—2a},>=Aa and bj + be — 2 b19= Aa, the
sum of these five terms may be brought under the following form:

(1259 ))
(a'g—a@)) (a'g—bg) — (a, —b) | + 2 Aa {(1—2) (a' —b) + #(a'g by) | —
—2, (1 — aja, Heras — 2x(1 — 2) Aa (Aw — 2 As).

r(l rz
So this quantity taken ae times represents the first correc-
v
tion of A,, whereas «(1 — x) (Aw — Av) represents the limiting
value of this quantity — so that for « near zero the value of
Av is equal to

(a'9-a’)) (a'g-be) — (a'\-b)) | + 2 Aa (a) -b))-2 Ad d))
2) (AAD $$ Ee. f

vi wrd
and for z near 1 equal to

(a'y-a)) (a'y~by) — (a';-by) | + 2 Aa (a's -ba) -2 As Cs)
alle) (AA+ ; uae

Vg

2

So there is a distinct asymmetry, as soon as a’, — bg is sensibly
greater than a’; — bj, but the different cases that may occur are so
numerous, that it is better for the present not to enter into a further
discussion, as the experimental data are wanting.

Yet it should be observed that the asymmetry is not so great as
to account for the circumstance that Mr. KUENEN’s values for (A;)' ')
at e= e=lg and «=!/, differ so little, while with scarcely
an exception the highest value is given at z= °/,.

As, however, the accurate value of A, requires too intricate cal-
culations to draw general conclusions from them, we shall have
recourse to the graphical representation, in order to give at least
an idea of the course of this quantity.

Let us consider for this the formula :

Av = (1 —2) (oy — 01) + 2 (0's — va) — (v's — 2),

from which appears, that A, may be considered as resulting from
three separate quantities, viz. ©) — vj, v'g — va and v' —v. Each of
these quantities, which have been discussed before, may be repre-
sented by curves as have been drawn in the following figure.

1) Proc. Noy. 26th 1898, p. 184.

( 240 )

W,

In this figure » and v'—v have been taken as axes. The origin
is in point 0. At T= v'—» is equal to —b for all values of v.
In the figure this has been represented by a line parallel to the
v-axis. If the variability of 5 with the volume could also be taken
into account, this straight line would naturally have to be changed
into a curve, which approaches asymptotically the position given
here when the volume is large and which has come sensibly closer
to the v-axis at the smallest volume possible. But then every curve
had to be modified, specially in the region of the small volumes.

Under an infinite pressure the value of v'—v is equal to —b at
all temperatures. Hence all curves pass through the same point.
According as the temperature falls the curves begin higher at

27
v=o. The curves drawn are those for 7= 3 7). (the temperature
at which a substance obeys the law of Boyue, if the volume is

27 oR SI ;
infinite); for 7 = a5 T;, (the limiting temperature at which v'—v

begins to show a maximum value), for 7=%/s; 7, and T= Tx.
The maxima lie on an equilateral hyperbola, which has » = 26
and v'—v = b as asymptotes. ; (atd
When the volume is rather large, the different curves do not
differ sensibly from straight lines parallel to the v-axis.

( 241 )

As soon as 7 descends below 7, the quantity »—v can become
very great; this happens, however, between such values of v, as lie
within the border curve, and which therefore cannot be realized.

If for the two substances, of which the mixture is to be composed,
such curves are construed, whose dimension and form will depend

'

on b and =: a point of the mapping of (1—z) (x'—v)) + 2 (wy —v3)

may be found by connecting two points of those curves by a
straight line, and by dividing that straight line into parts which
are in inverse: ratio to z and 1—«, The two points chosen must
always belong to values of v, and v2, which occur under the same
pressure. The curve obtained in this way will approach v,'—v, the
nearer, the smaller « is, and may to some extent be considered as
a mean curve. When v’—v has been construed, Av may be found
by taking the difference of the ordinate of the resulting curve of
the two first mentioned and of the last mentioned, always for such
values of v, as occur at given p.

Though it is true that the course of A, does not follow in parti-
culars from this way of construing, yet some general rules may be
derived from it. As has been observed before, we find for v = oo
again the former value, viz. «(1 — #) {Aa — Az}. For the limiting
value on the other side we find:

— A, =); (la) + bg ab, = (le) Az,

so a contraction. In all these cases, in which Aa'—Az is positive,
a pressure must exist, under which mixture without variation of
volume takes place. If the volumes are very great so that v,'—r,
vty’—v; and v'—v remain invariable, A, too will not vary much in
absolute value. The variation may however be considerable relative
to the limiting value. But it appears at any rate, that if none of
the three substances, viz. the components and the mixture, remain
considerably below the critical temperature '), the absolute value of
A» remains within finite limits throughout the course of the iso-
thermal.

If we try to calculate (4,)' directly, viz. the increase of pressure
on the mixture, in order to keep the volume equal to the sum of

1 By the critical temperature of a mixture is understood that temperature which
is caleulated from a, and Jz in the same-way as for a simple substance,

(242)

the separate volumes, we find for it the following expression :

Adler}
x (1 — z) 7

Otte 2 (G aa )+ bl 1)

Ge iy Je eee
(or — by) (L — 2) + (eo — bo) @ ea

Vg vj
a — +ag — — Zag
hl Ug

vj (1 — 2) + v2

For volumes which are not too small, which do e.g. not descend
below 0,03, we might put by approximation

(Ap) =

xv (1 — 2) (GS
2e}?

RE. —
[vj (1 — 2) Hv Sata Vo »)

~ (by + — 2b.) (1+ any.

If v, and vs are left the same and only the value of 2 is changed,

2 v al
(Ap) is a maximum if i = . This leads to the rule, that
yn Vg

the maximum value of (A„)', which for small values of p is found
in mixtures for which # = !/,, passes, when the pressure increases,
towards mixtures, in which that component is in excess which is
most compressible. As A, reverses its sign, when the volume is
very small, this must also be the case for (A) .

If a—b,(1+e@t)=0, the first component follows the law of
Boye. In the same way the second component, if ag—by(1 + at)=0.
If arb (1 + @t)=0 the law of Dauron holds good. And finally
if (a + ag — 2 ayy) — (by + bg — 2 dyn) (1+ @t)=0 , there is no
variation of volume, and the law of Amacar holds true. All this
only in the supposition of large gasvolumes. Let us call the tempe-
ratures, at which these four relations are fulfilled: ta, to, tc and ty.
If ta >w >t, then tate. The supposition ta >ts > te is fulfilled,
if the two components can form mixtures, the critical temperature
of which lies below that of the components !). Then ¢ is the lowest
of these four special temperatures.

1) Moleculartheorie. Phys. Chem, V. 2, p. 149.

( 243 )

On the other hand ¢, is the highest of these four temperatures,
if there should exist mixtures, the critical temperature of which is
higher than that of the components. In general the following rela-
tion exists between these four temperatures:

by ta + dg ty = 2 biete + (bj + by — 2 bio) ta .
If we call ¢, the temperature that fulfils the condition that
(bj + bo) tn = by ta + ba tos

tm lies always between ¢, and tg, while the distance between tn
and ¢. is smaller than that between ¢,, and t,.

Physics. — „Measurements on the course of the isotherms in the
proximity of the plaitpoint and particularly on the course of
the retrograde condensation in a mixture of carbonic acid and
hydrogen.” By Dr. J. VERSCHAFFELT (Communication N°. 45

from the Physical Laboratory at Leiden, by Prof. H. Kamur-
LINGH ONNES.)

(Will be published in the Proceedings of the next meeting.)
Physics. — „Measurements on the magnetic rotatory dispersion of
gases.” By Dr. L. H. Stertsema (Communication N°. 46
from the Physical Laboratory at Leiden, by Prof. Kamer-

LINGH ONNES.)

(Will be published in the Proceedings of the next meeting).

(January 16th 1899.)

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KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING

of Saturday January 28th 1899,

Ce

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 28 Januari 1899 Dl. VII).

Contents: ,,Brackish water-deposits of the Mélawi in the interior of Borneo”. By Prof. K. MARTIN
p- 245. — „On Hydrogel of oxide of iron (ferric-oxide”). By Prof. J. M. van BEMMELEN
p- 249. (With one plate.) — „The equilibrium of systems of three substances, in which
two liquids occur”. By Mr. B. pe Bruyy. (Communicated by Prof. J. M. van
BEMMELEN), p. 253. — ,,The representation of the screws of Barr passing through a
point or lying in a plane, according to the method of Carorarr”. By Prof. J. CAR-
DINAAL. p. 258. (With one plate.) — „On the vibrations of electrified systems, placed
in a magnetic field. A contribution to the theory of the ZerMaN-effect”. By Prof.
H. A. Lorentz, p. 263. — „On trinodal Quartics”. By Prof. Jan DE VRIES, p. 263. —
Calculation of the second correction to the quantity b of the equation of condition or
VAN DER Waars”. By Mr. J. J. van LAAR. (Communicated by Prof. J. D. vAN DER
Waals), p. 273. — ,,Measurements on the system of isothermal lines near the plait-
point, and especially on the process of the retrograde condensation of a mixture of
carbonie acid and hydrogen.” By Dr. J. VeurscnarreLt. (Communicated by Prof.
H. KAMERLINGH ONNEs), p. 288. (With one plate.) — ,,Measurements on the magnetic
rotatory dispersion of gases”. By Dr. L. H. Siertsema. (Communicated by Prof.
H. KAMERLINGH ONNES), p. 296. (With one plate.)

The following papers were read:

Geology. — „On Brackish-water deposits of the Melawi in the
interior of Borneo”. By Prof. K. MARTIN.

It is more than forty years since the mining engineer R. EVERWIJN’s
geognostical expeditions in the , Wester-Afdeeling’”’ of Borneo. Since
that time several explorers have been occupied with the geology of
that country and nevertheless all our present knowledge of the geolo-
gical formation of West-Borneo is still based on incoherent data only
of which we do not even possess a rough geognostical sketch map.

During the last years the mining engineer N. Wing Easton has
been intrusted to make a closer investigation o this country and

Ui

Proceedings Royal Acad. Amsterdam. Vol

( 246 )

from the examination of the fossils forwarded by him to Leyden it
was possible to point out inter alia the existence in Borneo of a
jurassic system !).

His last consignments from the basin of the Kapoeas contained
sedimentary rocks with hundreds of fossils upon which I wish to give
some preliminary information. Of the objects to which I wish parti-
cularly to draw attention only a few have been coliected at the
main river somewhat below the mouth of the Melawi whereas the
greater portion were found in the region of the last named important
left branch of the Kapoeas. The localities are situated either on the
said Melawi or on its tributaries the S.?) Kajan and the S. Tebidah
which flow into the 8S. Kajan. Taken altogether the fossils have been
collected in ten different places and an examination of important
material containing numerous organic remains from most of these
localities was possible. This examination however proved to be rather
difficult, the objects being as a rule exceedingly brittle thus requiring
to be prepared with the greatest care which could only be done
with the aid of a needle.

The fossils are embedded in clay some of which contains calcium
carbonate and turns into marl; in some cases they also form the
organic centres of marl concretions. In other cases the clay becomes
sandy and often it serves only as the cementing material which keeps
the thick mass of fossils together. Shell-breccia are numerously
represented.

Among many hundred speeimens of shells and periwinkles obtained
from this material, only seven species can be named viz. Arca mela-
viensis spec. nov., Cyrena subtrigonalis P. G. Krause, Cyrena sub-
rotundata P. G. Krauss, Corbula dajacensis P.G. Krauser, Melania
melaviensis spec. nov, Paludomus gracilis P. G. KRAUSE spec., and
Paludomus crassa P. G.KRAUSE spec., but the greater part of these
species vary so much as to render the determination very difficult.
The material collected by G. A. F. Monencraarr at the upper
Kapoeas especially at the 5. Pinoh and the S. Lekawai (also branches
of the Melawi) on being examined by P. G. Krause was found to
contain also the above mentioned species; but the material at his
disposal for his researches being defective in several respects, he has
not been successful in giving a complete determination of some species
(Area and Melania) while to others he has given different generic
names (Paludomus).

Having compared the petrifactions of the different localities in the

1

)
2)

See: Sammlg. d. Geol. R. Museums in Leiden. Bd, V, (hk rausr, Martin, Vocer).
S = Soengui, Malayan name for river,

ee

(247 )

collections of MoLENGRAAFF and WinG Easton it becomes evident
that in the basin of the Melawi a deposit oceurs which taken as «
whole is of the same age. This deposit evidently corresponds with the
formation stated by Everwisn to be tertiary, his statement however
was not sufficiently proved. The fauna of these beds exhibits diffe-
rent facies which is due in all probability to the quantity of salt
having varied during the process of formation and also having been
present in greater or lesser quantities in different localities. A num-
ber of species (Melania and Paludomus) living in fresh water have
been found amalgamated with the species of Cyrena and Corbula
which are prevalent amongst these fossils and were inhabitants of
brackish water as also the species of Arca which may have lived
in close proximity to the sea. This amalgamation would chiefly take
place during the rainy season.

It is exceedingly difficult to settle the age of the strata in regard
to the character of the fauna as sketched above. A direct determi-
nation based solely on the occurrence of the species is impossible as
none of the above mentioned species corresponds with any described
species either from India or the Malay Archipelago. Neither is it of
any use to compare these fossil species with the terrestrial shells of
Nias described by Woopwarp and which up to the present time
have been considered by others to be tertiary. During a recent visit
to London I have had an opportunity of studying these Nias forms
and feel assured that they decidedly are not tertiary but are, as
WoopwaArp supposed, of a more recent date.

A comparison with the ,intertrappean beds” of India, which con-
stitute a connecting link between cretaceous and tertiary, seems to be
of the greatest importance. Their fauna still allows relations to be
traced to the Laramie-group of North America and similar relations
also exist between the Laramie-group and the upper cretaceous of
Ajka in Hungary; consequently this fauna was not from a geographical
point of view so well differentiated in those days as at the present
time. The fauna of the Melawi beds does not show any features to
correspond with that of the ,intertrappean beds” the Laramie-group
ete., on the contrary containing only still living Indian genera amongst
which is the genus Paludomus it resembles very closely in character
that of the present day.

Separating from Paludomus the genera Pyrgulifera Meek and
Cosina Stache which certainly do not belong to it, there remains
only a single group which must be considered one of the most
characteristic of the Indian fauna. The occurrence of the genus Pa-
ludomus is restricted to this area, being found in India, Further

iy

( 248 )

India, Sumatra and especially in Ceylon and Borneo. Amongst the
still living Bornean forms there are found some species closely allied
to the fossil ones; P. gracilis in particular closely resembles P.
Hveretti Smith from Sarawak.

Setting on one side its dissimilarity to the fauna of the „inter-
trappean beds” and on the other its resemblance in one highly
characteristic point to the fauna of the present day we may conclude
that the Melawi deposit must be of more recent date than the said
Indian strata, which constitute a transitional formation between
eretaceous and tertiary. For the above reasons the Melawi deposit
cannot be older than tertiary but may be of eocenc age as, not one
of the seven aforesaid species is known to belong to the present
fauna and may be considered as extinct, the habitus of two of
these species (Melania melaviensis and Cyrena subtrigonalis) is more-
over somewhat aberrant when compared with still living forms.
Meanwhile a more exact determination of its age than ,tertiary”
cannot be given with any certainty and it is for this reason and to
avoid all misunderstandings that I propose to call this deposit by
the generalizing name of ,Melawi group” in reference to the region
where it has originally been found.

From the material which has been examined, the Melawi-group can
be traced from the 8. Tempoenak below Sintang eastwards along
the Melawi as far as the S. Lekawai and also on the 5. Kajan toa
certain point somewhat above Maboek *). This tertiary (eocene ?)
brackish-water sediment can only have been formed with the assis-
tance of rivers and brooks which perhaps belonged to the same river
system that is now represented by the Melawi and its tributaries and
accordingly the beds of these streams may have been cut out of
the sediments which they themselves have contributed to form.

1) At present it is impossible to trace a further extention of the Mélawi-group. I can
only state that I have also received through the agency of WiNG WasroN a consignment
of petrefactions from the river Silat (flowing into the Kapoeas near Silat above Sintang
which contains a fauna differing from that of the Mélawi-group.

Particularly numerous amongst which are the remains of Viviyara which is repre-
sented by at least two different species and there also occurs a species of Corbula (s. str.).
The latter seems to be quite distinct from C. dajacensis
while amongst the species of Vivipara, a highly characteristic
form is found which I propose to name Z. Hastoni. The
figures of two specimens of this new species are inserted here.

A yery remarkable characteristic of this species is the pre-
sence of sharp and prominent keels, one of which situated at the angle of the whorls
projects very strongly.

It is possible that this deposit of the river Silat is older than the Melawi-group,
but certainly it is not older than cretaceous,

( 249 )

Chemistry. — „On Ilydrogel of oxide of iron (ferric-oxide)”.
By Prof. J. M. van BEMMELEN.

In the Recueil des Travaux Chimiques des Pays-bas !) Mr. Sprina
stated some time ago that he had prepared a hydrate of oxyd of
iron: d'une composition définie. He had got it by allowing to dry —
by exposure to the air — the gelatinous precipitate produced by
ammonia in a diluted ferri-solution and that after having washed
it out. After 72 days the equilibrium became stable, and after 5
months it was found to be unchanged. It answered to the composi-
tion Fe,O;. 4 H,O. Above sulphuric acid it lost water so that after
3 days the composition was Fe, O, 1.78 H,O (calculated by me).

Formerly, in 1888) and 1892, I have communicated, that the
gelatinous oxide of iron had no stable composition, but was an
absorption-alloy of Fe, O, with water. I had also found the number
+ 4,0 H,O in one of my preparations, but I considered it as an
alloy, that only answered to a whole number by chance. The opinion
that a fixed hydrate had been obtained, is contrary to the nature
of hydrogels. For the composition is continuously dependent on: 1“.
the structure of the colloid, which in its turn depends upon the
circumstances of the gel-formation; 2"°. the modifications that the
structure has undergone by the further treatment ; 3°". the concentration
of the gaseousphase, with which the gel co-exists; 4°. the temperature.

Owing to my having determined the composition only with a few
vapour-tensions, SPRING’s communication led me to determine the entire
isotherm at 15° viz. of dehydration of rehydration and of rede-
hydration and to examine carefully how the Hydrogel behaves when
exposed to the air, the vapour-tension of which is continually changing.

Accordingly I prepared again a Hydrogel from a highly diluted
ferric-solution *) and worked with it at once, while it was still
quite fresh. Besides I determined the same curves for the prepara-
tion already investigated by me in 1882, which had now grown
16 years older (III); and in the third place for a preparation made
in 1891, which had been under water for seven years (II). These
determinations were made in the same manner as formerly for the
hydrogel of SiO, and of CuO*). On the graphic sketch I have

1) 18.222 (1898).

*) Recueil VIL 106—114. J. f. prakt. Ch. #6 —529.

5) 1 Part Fe,O, on 66 p. water = 1 Mol. Fe, O, on 585 p. water.

*) Vide Verslag Kon. Akad. of 28 Janr, 1893 and 29 June 1895. At present the equili-
briums are determined at vapour-pressures of 12°—11"—10°—10—9!— 817?
—43—2—0° m.m. both for A and for Z | and Z 4.

6°—5

( 250)

made use of the same signs (see fig

eV 108 the curve of
dehydration of water, 4 f for that of the rehydration of water
and Z| for that of the redehydration of water. The equilibrium
at a certain vapour-tension was only gradually approximated on
A |, the more slowly in proportion to the latter’s differing less
from the tension of saturated vapour (12.7 m.m.). At 12? m.m. a loss
in | month’s time was still noticeable after 5 months; at 9 m.m.
the loss in 1 month’s time was no longer noticeable after 3 months ;
and at 0° m.m. after one week. On the contrary the equilibrium
in Z and Z was obtained within 1—2 days, except on part of
Z| (from point O to O,) where the phenomenon of Hysteresis
showed itself again.

From the figure we see that the curves agree with those for the
Cu O- and the Si Og-hydrogel.

The proportion of water at 15° is greater than that of these two
(I only give here that at 12° and at 0 m.m. vapour-tension).

122 m.m.| 0° m.m.
Fe, OF a5 95 1 51
Cun EE 1.1
510; | 26 0.25

| ]

but is equally continuously dependent on the vapour tension.

Point O, which shows a break in the continuity in silicie acid (in
consequence of a transformation in the gel and the diminution of
the power of absorption resulting therefrom) and at the same
time the turnpoint of the process of de-hydration, this point is not
so clearly seen in the hydrogel of Fes Os. But it betrays itself in
the following manner. If the gel, arriving in any point of the line
A J, is provided again with water from this point (by the exposition
to a higher vapour-tension up to 127 m.m.) it only absorbs +
0,2 H,0; comp. for this on fig. 1 the lines A f, starting from the
points a, b, e, d. This rule however only holds good if the propor-
tion of + 3,5 H,O is not yet reached; beiow this the gel absorbs in
ease of rehydration so much water, that the proportion in tension
of saturated vapour amounts to + 5,6% It is therefore about here
that the possibility of reversing the further process of the dehydra-
tions begins, and there is a point which answers in that respect
to the turningpoint O in silicic acid. At the end of the dehydration
in point O, (vapour-tension = 0° m.m.) the appearence of air-bubbles

7 moder

“uur UL UOISUD

S S

Se

9 |
8
7
. :
4 |
5 /
jp a
7
0

Proceedings Royal Acad,

Isothermen bij 15°... .. — Isotherms at 15°.
WRONG cys 6 oo) 0 tom — fresh.
7 jaar onder water..... = 7 years under water.
IG PANO Goo boo or = 16 years old.
5 : 8 tension of saturated
Verzadigde Waterd. Spann. = !

| vapour.
Watergehalte (molec.) . . . = Molecules Water.

J. M. van Bemmeten, On Hydrogel of Oxide of Iron (ferric oxide).

Me Poble bij if

Tsotiermen bij 15°, . . ., — Isotherms at 15°.

7
Sp
e
Lr
ge
3
ji
©
5 st Nersolijn ersten aan se ent
| i & 47 IE ~[posroudermater! ‘7 jnor onder water, 7 years under water:
BS su rh
me ll U laad 16 jnarvoud . . 16 years old,

Nasi Waters) Span

2 | tension of saturated:
Veraaligd: Waterd, Spann, = | Tacit

50

=> Wares, gehalte (OV, )

yoo m0

Watergelilte (moleo,) . „ . = Molecules Water.

Proceoilings Royal Acid, Amsterdam. Vol, te

( 251 )

on the immersion in water is only observed in a slight degree U.
It must therefore be inferred that but few cavities are formed during
the dehydrations on the branch O—O,. This phenomenon is how-
ever much better noticed in the gel II (see below). The final curve
of the rehydration Zf again has the points O, and Os, which
appear at the redehydration of water as in the case of silicic acid.
For the rehydration curve Z| does not converge, neither with
Z{ nor with A |. It is true that the difference for the branches
03 Os and O, O, is slight, but just as with silicic acid, the branch
Oz O is vastly divergent from O; Oj. The same hysteresis-phenomenon
appears. Line Z f, especially the branch O, O, can only be realized
in the direction f (rehydration), the line OO, in the direction
) (dehydration). An intensified power of absorption is created on
Zf, that leaves its influence on Z |. At the redehydration (Z |)
a point O appears, showing the same phenomena as in silicie acid.
Starting from this point O, the equilibrium is obtained very slowly
on the branch 00); a weakening of the power of absorption takes
place, that leaves its influence behind, so that at the rehydration
it is not the branch OO, that is run back, but the branch QO, Os.
As a result, here as with silicic acid return-curves may be realized
within the figure OO, 0,0, if rehydration or redehydration
takes place, starting from a point on the line O O, or on the line
0, Os. Two of these intermediate curves, one of the dehydration
|) and one of the rehydration 4, are indicated in the figure by
dotted lines.

Modifications. The modification caused by time, by which the
power of absorption is weakened, is also the same as with silicic
acid. The figure shows this for a Gel, that has grown 16 years
older (curve A | of IIL). The proportions are lower again than
were found before, when the same substance was seven years older
than at the first determination. The fact of the Gel having been
under water for seven years has also weakened the power of ab-
sorption (curve A | of II). For the sake of clearness the curves
ZY and Z| have been omitted. They differ very little from the
A | line, and only diverge from it at higher vapour-tensions (at
about 10—1i1 m.m.), as is shown in the foilowing table:

1) In silicic acid many cavities are formed, which condensate a considerable vo
lume of air. Vide Verslag Kon. Akad. of April 6, 1898, p. 498— 506,

| ILL (16 years old). Il 7 years under water.
Ly» the it Z Z
m.m, Mol H,O Mol H,O
9 | 1.55 1.5 IE | L5
10 | 1.6% 1.68 1.68 | 1.73
107 War 1.77 1.85 | iat?
nas 2.25 2,47 3.02 | 4.5
12? 3.35 3.53 6.7 | wee
127 saturated. an Sh) 8.6 2)
eS SE en a = == a = =
| ') Obtained in the course of 2) After 8 davs
some months. | ) B drek

The same phenomenon presents itself as with silicic acid. The
more it is modified, the more water it can absorb at the higher
vapour-tensions. The hysteresis is removed to that region. The
Gels IL and III at rehydration can absorb up to more than
8 Mol. HO, while I can come no further than to + 3.6°.

It is highly remarkable that III requires months for it, II only
days. This too points to a difference in structure. Now it is very
remarkable that Gel III does not show any air-bubbles escaping
at the point Oo, when immersed in water, while Gel IL does. In
Gel If there appear immediately on the surface and at the rims
of the transparent (so exceedingly thin) films at numerous places
smaller and larger air-bubbles. Consequently the gel contains cavi-
ties, but their joint volume is not by far so great as in silicic acid.
In connection herewith seems to be that II absorbs pretty quickly
a considerable amount of aqueous vapour at a vapour-tension of 12
m.m., while III, which contains no cavities, does this so extremely
slowly.

It results from the above that no chemical hydrate can be obtai-
ned by drying the Gel by exposure to the air, and that moreover the
composition must change with the change in the vapour-tension of the
air. This was also proved by daily weighing a quantity of I exposed
to the air (freshly prepared and pressed between two porous plates)
for half a year. In the beginning it contained + 18 Molec. H,O
on 1 Molec. Fes 0, and contained therefore much water inclosed.
With decreasing velocity the proportion had fallen after 9 days to
5,4 H,0; from that period it eame sensibly under the influence of the
changes in the vapour-tension of the air, so that it decreased irre-
gularly in weight and sometimes inereased. After 1!/, month the

;
‘
f

( 253 )

proportion had fallen to 4,64 H,O, and for the next three months
this proportion varied according to the vapour-tension of the air,
between 4,64 and 4,55 H,O. Unaltered weight, rising or falling
were found to agree with the indications of the hygrometer (of
KLINKERFUES’. Meanwhiie a little decline was observable. If the
vapour-tension of the air, which in that time varied between 10
and 8 m.m. had fallen to 7 m.m. and had remained stationary
for some time, the composition + 4 H,0O would have been
attained. For this amount has been obtained in the Gel I after
some months at thaé vapour-tension. That composition would have
risen but little if the vapour-tension of the air had become again
greater.

That the composition depends on the temperature, that the power
of absorption is weakened by heating to higher temperatures, and
is destroyed at incandescence, all this I have already communicated
before +).

Dr. KroBBie and I have only succeeded in observing the transition
of colloidal ferric oxide to a erystalloidal chemical hydrate in case of
monohydrate*), by the influence of water at 15° on the hexagonal
crystals of the chemical compound Fes0s. NagO, in which Na, 0 is
gradually replaced by HO without the crystalline structure (form,
transparency, power of polarisation) being modified. Nature provides
us with the crystalline Monohydrate: Göthit, that can bear heating
to + 280° without losing water and without passing into the amor-
phous state *).

Chemistry. — Mr. van BEMMELEN presents in the name of
Mr. B. pe Bruin a paper on an investigation held in the
Inorganic Chemical Laboratory of the University of Leyden,
concerning : „The equilibrium of systems of three substances,
in which two liquids occur”.

In systems of three components, in which two liquid phases
occur, the following cases may be distinguished:

1st. the components A and B form together two liquid phases;
equally so the components A and C and B and C.

gnd, the components A and B and A and C form two liquid
phases, but the components B and C do not, at least in stable
conditions.

1) Recueil %. 111—113, Zeitschr. anorg. Ch. 28. 24.
2) J. f. pr. Ch. #6. 523—529.
3) J. f. pr. Ch. 46. 521.

( 254 )

3, only the phases A and B form two liquid phases; A and
3 or B and C do not do so, at least in stable conditions.

40, the components in pairs never give two liquid phases at
least in a stable condition.

Examples of the first three cases have been investigated by
SCHREINEMAKERS }); purpose of this investigation was to examine
also an example of the last mentioned case. Not until the inves-
tigation was nearly finished, did there appear an essay by SNELL
on potassiumchloride, acetone and water, by which an example of
the fourth case is given ®).

Mr. pe BRUIJN examined the equilibriums in the following systems:

Ammoniumsulphate, ethylaleohol and water.

Potassiumearbonate, methylaleohol and water.

Potassiumearbonate, ethylaleohol and water.

Sodiumsulphate, ethylaleohol and water.

Guided by the theory of ScHREINEMAKERS on equilibriums in
systems of three components, in which two liquid phases occur, he
succeeded in making a sketch of the equilibriums in the systems
examined. The composition of the phases is represented in the
usual manner by means of a triangle; if the temperature-axis is
placed vertically on the plane of the tiangle, we get a represen-
tation in space.

I. The system: ammoniumsulphate, ethylalcohol and water.

Above + 8° the general form of the isothermals is as given in fig. 1.
The isothermal consists namely of three parts: RO, OPB and BQ,
meeting in O and B in an angle. RO and BQ indicate all possible
solutions, that can be in equilibrium with the solid (NH), SO,
OPB is the connodal line with the plait-point P; it indicates
therefore the solutions that coexist; the points O and B are the
two liquid phases which are not only in equilibrium with each
other, but also with solid (NI), SO,. In case of a change in the
temperature the different parts of the isotherm are displaced; at a
higher temperature “OZB increases; at a fall in the temperature
/ OZB diminishes till at + 8° the lines OZ and ZB coincide.
The points O, B and P coinciding at this temperature, the iso-
thermal consists at this and lower temperatures of only one curve
RO and BQ coming in each other’s prolongation; there remain
therefore only the equilibriums of solid salt with solution, Mr. DE
3nuIJN has determined such an isothermal at 6,°5. Two liquid

1) Zeitschr. f. phys. Chem, #8 543 26 237 28 95 (1898) 23 417 (1897).
2) Journ. of phys. Chem. 2 457 (1898).

rg

(AD)

phases are no longer possible in a stable equilibrium. It is true
that Mr. pr Brutsy has noticed them several times, but they
disappeared at the appearance of the solid phase.

Mr. pe Bruin has also deter-
mined several isothermals at higher
temperatures, where the isothermals
have forms as in fig. 1. As to
the connodal lines for the difte-
rent temperatures, it was proved,
that they intersect each other in
different manners or cover each
other within the limits of the faults
of analysis. In order to further
investigate this point several sec-
tions were determined, in which the proportion of water and alco-
hol was the same, but the quantity of (NH4).SO4 varied. In accor-
dance with the situation of the connodal lines with respect to each
other Mr. De Bruijn found the following facts. If the proportion
of (NH, SO4 is taken for the ordinate and for the abscis the
temperature at which two liquid phases become homogeneous or a
homogeneous liquid phase is divided into two others, we get, with
a greater proportion of alcohol, lines rising with the temperature ;
with a smaller proportion of alcohol, lines falling with the tempe-
rature, between the two, lines showing a maximum, which moves
toward a higher temperature with a greater proportion of alcohol.
From these different sections follows in accordance with the iso-
thermals given, that it is possible to have solutions of (NH 4),SO#
in water and alcohol that are homogeneous at a certain temperature,
but divide into two layers both in case of a rise and ofa fall in the
temperature. Mr. pr Bruin has made several of these solutions.

IL. The system: Potassiumearbonate, methylalkohol and water.

Ze Next to the two liquid phases
there appears in this system as
a solid phase the hydrate (K,COs),
(HO), (at lower temperatures per-
haps a still higher hydrate). The
isotherm has here the form of fig.
2. RO and BS indicate the solu-
tions that can be in equilibrium
with (K,COs;),(H,0),; SQ the
solutions in equilibrium with

Tag,

(250)

K, CO; ; OPB is the connodal line with the plait-point P; with each
liquid phase of part OP one of PB can be in equilibrium. Mr. pr
Bruin has determined the situation of the connodal line OPB at
different temperatures. Just as in the preceding system the points
O and B approach each other when the temperature is lowered ; in
the preceding system they met at + 8°; in this system however no
earlier than at + —33°.

Ill. The system: Potassiumcarbonate, ethylalkokol and water.

The isotherm has here the same form as in the preceding system.
The composition of the two liquid phases in equilibrium with the
hydrate was determined at temperatures of — 18° to 75°. The propor-
tion of salt rises with the temperature, that of alcohol changes less
than the amount of the faults of analysis. That a change in the composi-
tion of the two liquid phases does however decidedly take place when
the temperature is changed may be deducted from the observation, that
such homogeneous solutions divide into two liquid phases at a change in
the temperature. Different pairs of conjugated points were determined
on the connodal line at i7° and at 35°. The connodal lines for dif-
ferent temperatures intersect here too. Sections, as in the case of
ammoniumsulphate are not determined here; from a single observa-
tion made by SNELL it may be deduced that these sections will not
show a maximum here but a minimum.

A great difference in the conduct of methyl- and ethylaleohol is shown
by what follows. At 17° the upper layer contains in equilibrium with
the solid phase 91,5 pCt. ethylaleohol and 0,06 pCt. K.COs ; the lower-
layer 0.2 pCt. ethylaleohol and 55.2 pCt. Ky CO. The ethylaleohol and
the potassiumearbonate form therefore each of them, with part of the
water, a liquid in which the other eomponent hardly occurs. In the
system K,CO;, CH,OH and H,0 the upper layer contains however at the
same temperature 69,6 pCt. methylalcohol and 6,25 pCt. K,CO,. the
lower layer 5,7 pCt. methylaleohol and 48,4 pCt. KgCO;. Another great
difference in the conduct of methyl- and ethylalcohol in these systems
is the following. In the system with ethylalcohol the temperature has
hardly any influence on the position of the points O and B; the
proportion of water and alcohol remaining in two liquid phases, that
are in equilibrium with the solid hydrate of K‚ CO3, nearly unal-
tered from — 18° to + 75°. In the system with methylalcohol the
temperature has on the other hand a great influence on the propor-
tion of water and methylalcohol, the latter being more miscible in
presence of the solid salt than water and ethylaleohol,

7

( 257 )

IV. The system sodiumsulfate, ethylalcohol and water.

In this system Mr. DE BRUIJN
investigated besides the stable
equilibriums also some less stable
ones. Fig. 3 indicates the gene-
ral form of the isothermals below
32°5; the drawn curves RS and
SQ show the stable equilibriums,
the dotted curves LU and MN
the less stable ones. RS indicates
the solutions that can be in equi-
librium with sclid Na,SO,10H,0; SQ the solutions in equilibrium
with Na, SO4.S is the solution in equilibrium with Na, SO, 10 H,0
and Na,SO,. At a rise in the temperature the point S moves to the
left and upwards and at 32° joins R in V, this point indicating
the composition of the aqueous solution that can be in equilibrium
with solid Na,SO4 10H,O and Na,SOy. When the temperature rises,
the line RS therefore dwindles, while SQ is prolonged ; at 32°5
RS disappears and only SQ is left, while S falls on the line WZ.
Mr. pr BRuIJN has determined these isothermals for different tempe-
ratures experimentally.

Besides the stable equilibriums mentioned above viz. Nag SO, 10 H,O
+ solution and Nas SO4 + solution Mr. pr Bruisn also determined
the less stable system Nas 504 7H,0 + solution. The solutions
in equilibrium with the hydrate Na SO, 7 H,O are represented by
line LU (fig. 3). The latter being situated entirely above the curve
RS, the solutions pass into a solution of RS, if the less stable con-
dition ceases to exist. .

If it was possible for two liquid phases in stable condition to
appear in the systems of equilibrium mentioned above, this is no
longer the case here. But on the other hand it is easy to get
these systems, if care is only taken that neither Na, SO nor
Nas 504 7H, O, nor Na, SO4 10 H,0 can come in contact with the
two liquid phases. Consequently Mr. br BRUIJN has succeeded in deter-
mining the connodal lines for different temperatures; care being
however taken to prevent the liquid phases to come in contact with
the air. If the latter happened or if only a particle of NaSO,.
10 H,O was introduced, the crystallisation of Na,SO,.10 H,O fol-
lowed at once, and the two layers passed into one. That this must
necessarily be the case is shown by fig. 3, the connodal line MN,
determined by Mr. pr Bruin being situated not only above RS,
but even above LU.

( 258 )

Mathematics. — “The representation of the Screws of BALL pas-
sing through a point or lying in a plane, according to the
method of Cavoraul.” By Prof. J. CARDINAAL.

1. This communication must be regarded as a continuation and
enlargement of a lecture delivered at the 70 Congress of the “Ge-
sellschaft deutscher Naturforscher und Aerzte” at Dusseldorf (Sept.
1898) and published in the last “Jahresbericht der Deutschen Ma-
thematiker-Vereinigung”’. There the method applied in the following
pages has been considered in its relation to the “Theory of Screws”
by Sir R. St. BALL, so I think I can suffice by beginning with a
few brief indications indispensable for the understanding of the pur-
pose of the communication.

2a. The motion of a body considered here is the motion with
freedom of the 4t degree; the screws about which motion is possible
form a quadratic complex, consisting of all screws reciprocal to a
given eylindroid CS,

b. We construct the screws passing through a point P and be-
longing to the complex by drawing perpendiculars through LP to
the generatrices of >; each of these perpendiculars moreover inter-
sects two generatrices of (>, equidistant from the middle plane (con-
jugate lines). The locus of these serews is the cone P*.

c. In a similar manner we construct the screws situated in a
plane a. They envelop a parabola z?.

3. The representation of the rays of a quadratic complex has been
treated among others by R.Srurm and Caporatt. We find it inserted
at large in Mr. Sturm’s “Liniengeometrie’, III, pages 272 — 282.
The special complex formed by the screws alluded to belongs to the
type treated on pages 438—444. Although the results laid down in
the following correspond with those obtained there, as could be
expected, there is a great difference in the investigation; this diffe-
rence can be circumscribed as follows :

ist. The proofs are here deduced immediately from the theory of
Barr, whereas with Sturm they follow as special cases out of the
complex. 5

2nd. The constructions, more particularly a principal construction,
are really executed.

4. Fig. 1 represents the axonometrical projection of a cylindroid,

whose construction is understood to be known. ‘The nodal line d
coincides with the axis OZ; we suppose further that the rotation

( 259 )

of the generatrices has begun in the plane ZO Y; on the line
O—() the maximum pitch g has been measured out; on the following
lines J—1, JJ—2, ete. the succeeding pitches are now continually
measured out from the nodal line, the measuring ceasing in the
position where the rotation amounts to 180°, thus the whole
height of the eylindroid having been described on both sides of the
centre O. To explain this we make use in the first place of the
circle, which has served to find the length of the pitch of any
generatix, drawn on half the scale of the principal figure, where the
length of any generatrix (e. g. IT—2) is indicated with its corres-
ponding angle of deviation.

In the second place we see axonometrically constructed the pitch
curve projected on XO Y with the projections O—0, 0—1 ete. of
the generatrices. Further is drawn the perpendicular A B to //—4
passing through A on a=1—T7. According to 20 this is a screw,
so it meets the line a’ = J—5 conjugate to 1—7.

Remarks. a. The projection of the above mentioned pitch curve
lies entirely on one side of the axis 0 Y. Evidently this is half the
figure we obtain in constructing the curve with the equation:
yo =a-+ 2rcos?O. It is merely a consequence of our peculiar manner
of measuring that by the followed construction only half the figure
is obtained.

b. In the constructed figure all the pitch values have the same
sign: if this were not the case, the figure of the projection would
be changed, the curve half drawn, half dotted would show a double
point, so the entire projection a fourfold point. This last has now
become isolated.

5. Fig. 2 represents the parallel projection of the principal curve
of the representation of CAPORALI and must be considered in con-
nection with fig. 1. On the generatrix a of C® a point A has been
fixed. Through A the screw A A' B has been drawn, being one of
the rays of the pencil through the centre A in the plane 4 «a'= a.
A, as pole of @, determincs with « a linear system of the 3¢ order
of linear complexes.

With these figures we suppose that C? lies in the space >, the
principal curve in the conjugate space >,. To any linear complex
in = a plane in 2, corresponds, to any screw a point. The prin-
cipal curve is the locus of the points in +, to which corresponds
in + not only a single screw but a pencil of screws. <Ac-
cording to these conventions and to the indication sub N°. 1

( 260 )

we can pass to the analysis of the principal curve. It consists of
the foilowing parts:

a. The conic K? in plane 0,, locus of the points corresponding
to pencils of screws having a ray in common with the pencil (A, «)
and whose planes are parallel to the nodal line d,

b. The conic K?, in plane v,, locus of the points corresponding
to pencils of screws having in common a ray with (4, @) and con-
sisting of parallel rays.

c. The line L=Da Du, intersecting K?z and K?,, locus of
the points corresponding to pencils of screws whose vertices lie on
«a and whose planes pass through a.

Both conics have two imaginary points in common; the planes
O, and v, are the loci of the points corresponding to screws pa-
rallel to d and to those in the plane at infinity. They have not
been indicated here.

In the figure have further been constructed the vertices 7, and 7 of
the two quadratic cones, determined by K?/ and K2,. The line

ad

connecting 7, 7; meets Ò, and v, in My and M,.

6. Now the forms of =, corresponding to the cones and parabolas
of XE can be found. It is evident that we shall get curves in Zj.
Let us take a vertex P and construct a cone of screws P?. The
construction gives rise to the following remarks:

a. Let us imagine through (A,«) a zero system, formed by two
reciprocal systems of points and planes with the property that any
point lies in its corresponding polar plane (“Nullsystem” of Morsrus),
with a linear complex @ situated in it; the polar plane of P inter-
secting cone P? in two generatrices, the corresponding plane ©, inter-
sects in two points the curve P,? corresponding to P?; so Pj? is
a conic.

b. One screw of P? intersects a and a’; so P,? meets /, in one point.

c. One screw of P? is parallel to d; so P,? intersects 0, in one

point not situated on Ky.
__d. It is very important to determine how many screws of P?
belong to the pencils of parallel screws having one screw in common
with (A,@). Let us bring a plane parallel to @ through P; two
screws of P? m and », are parallel to the screws m’ and »' of
pencil (A, @); from this we conclude that m and me’ are perpendi-
cular to the same generatrix of C%; so they belong to the same
pencil of parallel screws, viz. to a pencil having with (4, @) one
screw in common. The same can be said of x and n'; so P,? inter-
sects the conic A? in two points.

( 261 )

e. Further we must determine how many screws of P? belong
to pencils of screws, whose planes are parallel to d, having with
(4, @) a screw in common. Therefore it is necessary to determine
the points common to screws of P? and the screws of (4,«@) lying
at the same time on a generatrix of Cà. Let us first consider the
section of plane « with C%; it consists of the line a’ and a conic
A?. In the second place we must notice that the feet of the per-
pendiculars through P on the generatrices of C$ form a conic B?,
iying in a plane having moreover with C a right line 5 in common.
Both degenerated cubic curves A? + a’, B? +b, intersect in three
points. As the lines a’ and 5 cannot intersect, those points lie in
such a manner that a’ meets once B?, b once A? and A? once B®.
Now the last point Z is the only point of intersection satisfying
the above condition; so P,® intersects K?g in one point.

7. The curves corresponding in 2} with the screws, enveloping
the parabolas in the planes 7, are determined in the same way.
We shall show this briefly.

a. Out of the pole of zr with regard to the zero system through
(A,a@) two tangents can be drawn to the parabola z?. So the cor-
responding curve 7? is a conic.

b. One screw in zj? meets « and a’; so zj? intersects l in one
point.

c. One screw in z lies at infinity; so 7)? meets the plane v;
in one point, not situated on K2,.

d. One screw of pencil (A,«) is parallel to the plane zr; both
belong to the same pencil of parallel screws; so ,? has one point
in common with K2,.

e. The line zr common to @ anda meets C® in its point of inter-
section with a’ and moreover in two points / and N. Through M pass
two tangents of 7? One of these tangents contains a point lying
on the generatrix m’ of C%, conjugate to that on which M is situated;
the other one is perpendicular to m itself. The latter tangent deter-
mines with the screw A M a plane perpendicular to m; consequently
in that plane there is a pencil having a screw in common with
(A,@); this pencil belongs to those, whose plane is parallel to d.
The same reasoning can be applied to MN. Consequently the corres-
ponding conic z,*? intersects the conic AK? in two points.

8. So the conics P,? and 7,2, having four points in common

with the curve K?, + K2q +l, their number in >, would amount
to oo*; there being however in = only «©? cones and curves of the
18
Proceedings Royal Acad. Amsterdam, Vol. L.

( 262 )

complex, there must be a closer definition of the conics. This is
also evident from the following. All cones P? of the complex belong
to zero systems of a special kind. The line connecting P and A
defines such a special linear complex of rays; it censists of all rays
intersecting PA. All these systems have the point A in common;
the net of rays through A contains the rays common to these
systems and finally the screws common to all consist of the pencil
(A,@) and the pencil through A perpendicular to a. Hence it
follows:

All zero systems in which the screws of the cones of the complex
are situated have in common the pencil through A perpendicular to
a, to which in =; a point Cg on K? corresponds (compare STURM,
III p. 276).

In a similar manner is proved that the pencil of screws common
to all zero systems of the curves of the complex is the pencil of
parallel screws lying in @, to which pencil a point C, in 2; on
K?, corresponds.

9. Now a construction will be deduced to find the points Cg
and C,. It is evidently sufficient if we consider the point of inter-
section of a plane, in which one of the conics P,? or m,° is lying,
with Ag and K?,; specially that point of intersection which is not
at the same time a point of P,? or m,°, for which we can choose
in = a special cone or conic.

Let us take P on the nodal line d in the point where the
generatrices with maximum and minimum pitch g and # meet. Cone P?
breaks up into two planes through d; one plane is perpendicular to
g, in which a pencil of screws lies with P as vertex, ali screws
having a pitch equal to that of &; the second is perpendicular to
k, which also contains a pencil of screws having a pitch equal
to that of y. To each of these pencils a right line corresponds in
=}; the first belongs to the cone 7%, the second to the cone 72, ;
further a screw of the degenerated cone P? coinciding with d, the
corresponding plane of ©) passes through 44 7, Tp ; so it intersects
K? still in a point, the point Cg that was to be found.

10. From the preceding we easily deduce the construction of the
point €,. Let us bring plane z through g and k. The parabola
m* breaks up into two pencils of parallel screws consisting of
rays perpendicular to g and of rays perpendicular to 4, the first
having the pitch &, the second the pitch y. So the corresponding
plane in 2} passes through two generatrices of the cones 7% and

5

SES ee

J. CARDINAAL, The representation of the screws of BALL passing through a point or lying
in a plane, according to the method of CAPORALI.

Cylindroid,

Piteh-Construction 1 a 2.

Proceedings Royal Acad. Amsterdam Vol

( 263 )

7%, and both pencils contain at the same time the ray at infinity
of the plane g* The latter is a line through which the bitangen-
tial planes of C® pass; the point in =, corresponding to it is D,. So
the point ©, is found by constructing the plane 7? ,7*, D, and
determining its point of intersection with A“, .

Physics. — „On the vibrations of electrified systems, placed in a
magnetic field. A contribution to the theory of the ZEEMAN-
effect”. By Prof. H. A. Lorentz.

(Will be published in the Proceedings of the next meeting.)

Mathematics. — „On Trinodal Quartics”. By Prof. JAN DE VRIES.

1. If we consider the nodes D,, Dy, Dz of a trinodal plane
quartic as the vertices of a triangle of reference, that curve has an

equation of the form :
Vg = ayy 9? ag + Gag 7g” By” + gg A 79 H
+2 mg #3 (ano 73 Haag 4+ 431%) =O. . (1)
The equations
PD, = b, 1973 + bo aga, + b3%,%=0,..- « « (2)
Py =e) Xo tg + Cg ag 71 + eg] %yg=—0.- . « « (3)

then represent two conics passing through the nodes.
If the coefficients of these equations satisfy the conditions

Stim LINSSEN Una cre pelo ce: oo (é)

it is evident from the identity
Py, WP, —— Ti =] TX = (by Cz + bz Cy — 2 a9) Hg oO o (5)
that the two new couples of points common to J, and each of the
two associated conics d, and W, are situated on the right line

corresponding to the equation

> (bi Cg aL bs (a 2 a9) Tg = 0 . . . . . (6)

( 264 )

Eliminating with the aid of (4) the coefficients ¢,,¢,¢, we shall
find for the chord common to @, and 7, the equation

SS (a), bo? — 2 Q9 by bg ae A29 b°) bg Da ZE 0 e . . (7)
2. ff the coefficients b and e are submitted to the two conditions

Dy Cy == Gay, Daos = dage EE

only, it results from
Py ¥, == IP == Lg Ls Os ’ . . . . . . (9)

that it is possible to bring a conic through the nodes D,, D3 and
the couples of points B,, By and C,, C, commou to FT, and each
of B, and ¥,.

The equation of this conic is

$25 = (bj cy — am) ages + ay FE (by ea + bg cy — 2 ayy) ag = 0. (10)

We shall call d, and ¥, complementary with regard to Ds, D3.

If C,, C, are fixed and the conie (2, varies, the variable pair
B,, By describes an inyolution 7,2 determined on it by the pencil

== 0;

Evidently the variable chord B, B, is represented by (7), where
in connection with (8) only 2, is variable. Substituting b,c. and
bs cz for agg and azz into (7) we shall find for B, B, the new equation

(ez rg + € 73) by + [ (43 ea + bz Ca — 2 433) mj — 2 ay3 ta — 2 ay9v3] by +

+ ay, (bg zo + bg az) = 0, 2 p (11)

which is quadratic with regard to bj. So the curve of involution is
a conic 2 with the equation

dan (bg rg + Dg zo) (ea ag + €319) = [ (boeg Jbz ea) er — 2S aygag]?. « (12)

From the symmetry of (12) w.r. to the quantities b and c it is
now evident that $ is at the same time the envelope of the joming
lines of the pairs C,C, of the involution /,* which is generated
when B, B, are fixed and 2, is variable. These two complementary
involutions are characterised moreover by the property that each
pair of J,” can be joined to each pair of 7.2 by a conic containing

dn nn eee

( 265 )

also Ds, D;1). In particular every chord B, B, determines one pair
of the 7,2 and reversely.

3. In connection with (8) the curve of involution is fully
determined by ‘the value of (0). + bse). Substituting 24 for this
parameter we can represent 52 by the equation

jj (agg wo? + 2 katy rg + agg 13°) = (EF aag — ky), « (13)
which is quadratic w.r. to the parameter &; therefore the conics 9»
form a system with index tio.
Generalizing for shortness the equation (13) to

Pe OOK R= O 5 eee a (td)

where P, Q, R denote known quadratic forms, the envelope of the
system is given by

PIR ONS Oe nS A cS)

By mere reckoning this equation proves to be identical with (1);
so the envelope of the system (14) is the given trinodal 7,
Out of the identity

(P2+2Qk+RR—K(PR—Q@=(Qk+ Ry? . (16)

follows, that each conic #57 touches the curve £, in the points
common to fy and Qk+ R=0, or, what comes to the same, in
the points common to the conics Qk + R=0 and Pk+ Q=0. So
the four points of contact of J, with the conic He Indicated by
kj are also situated on

AEO EN OE a J. Cl

The equation (17) being symmetrical in the parameters %, and
ky the conic represented by it will also contain the points of con-
tact of the conic 9 indicated by fh.

Hence we may conclude that each conic of the net

1) In a paper published in Vol. XIV of the „Nieuw Archief voor Wiskunde”
(pages 193—200) I have pointed out that suchlike complementary systems of pairs of
points present themselves on the binodal quartics. Likewise the special involutions
of $ 5 have their analoga on these curves.

( 266 )
Pika Oey R=) > oh ANN

contains two quadruples of points of contact of four times touching
conics 5.

‘he corresponcing parameter-values follow out of:

The corresponcing paramet lues foll t of

v ky ky = A and wv (hy + hy) = Lee

4. To determine the pairs of line belonging to the system we
substitute %: 4 for * into the condition that the discriminant of (13)
disappears. After reducing we find

(dog A — 4)? A? (agg agg A2 — p= 0 mn en (19)

Evidently for A—0 we have the right lines DD; to be counted
twice; for z= AV ago a33 we have the four times teuching conic

(aag — Wago 233) mt + 3 2g + Up= & (72V ar G33 He, War dap). (20)

breaking up into two double tangents.
Likewise # = — AV ao az, gives two double tangents.
Finally # =a, 4 produces the conic

(an 492—4}9”) as” + 2 (ay) aag —M%49 013) 2 23 + (an a33—4)3”) a5? = 0, (21)

composed of the two tangents drawn through D, to the curve I.

On any right line / the conics ®, determine a (2,2) — correspon-
dence; the point of section of 1 with D, Dz belonging to the coin-
cidences of ‘this system, there are three curves Î, touching a given
right line. These agree with the three manners in which the points
common to l and J, can be divided into two pairs. Each of these
pairs determines an involution, i. e., a curve $5. This contradicts
in appearance only the fact that an Z? is determined by 2 pairs,
for the two points lying in D, form a pair common to all 72.

Evidently a system of four times touching conics is conjugated to
each pair of nodes of Jy.

5. If the conics d, and ¥, alluded to in § 2 are identical, it
follows out of the equation

Dj? — I, == Tg Pz 0, . . . . . . . (22)

that the conie .Q, drawn through D, and D; touches the curve 74

( 267 )

in both points common to £, and the conic @, passing through the
three nodes.
It is therefore rational to put

== SAC Gin, US (Ta ee ee P8))

Of the two systems pointed out hereby we shall consider only the
system determined by the upper sign. All conics @, belonging to
this are defined by

D= Vase a 13 Arde À za 13 Aan = Wao (245)
So we get
Dg = (LA?) ayy 9 7g H 2 (ao  Van aag) on 13 +
2 (arg A War aag) 71 2 + 2 (49g — W agg agg)? = 0, (25)

which proves that these conics drawn through MP, and Ds, touching
two times elsewhere, form a system with index two.

For the connecting line of the points of contact B,, By, we find
with the aid of (6)

(1 +A?) (ep V ayy gg + 23 Wan agp) = 2A (ZS aja rg V agg ays) « (26)

So these chords of contact form a pencil whose vertex is the
point common to the lines

ty V ay, ass + 23 V a4, ass dag = 0, are tet . (27)

Each ray bears two pairs of the involution formed by the pairs
B,, By. The values of 4 corresponding to the pairs borne by the

ray
te (eo Wan agg Hes Wan dap) + (FE aya ty — mi Was agg) = 0. (28)

are found out of
EN ER EN Te A 2E
For «= + l we get two rays d, and dj, on which the two pairs

coincide; so these are double tangents.
Likewise is proved that the negative sign in (23) produces a

system of conics of double contact drawn through Ds, Ds, whose
chords of contact pass through the point of intersection of the
remaining double tangents d, and ds.

6. The conics through D,, D, touching ©, in B, determine an
12. Of its two double points one, Bs, is joined with B, by means
of a ray passing through the point (dj d;)=D),; the second Br
lies with B, on the ray through Do; = (d,d3). Now B, is a double
point of the complementary 72; let us indicate the second double
point by Br. As any pair of the first involution can be united to
any pair of the second by a conic containing Dy, Ds, there are two
twice touching conics £2), touching 7, in By, B, and By, Bm.
Hence Br B, passes through Do; and By Bry through Do

So in I’, an infinite number of quadrangles may be inscribed,
one pair of opposite sides passing through Doy, the other through Das.

Their vertices form the groups of a biquadratic involution,

Each couple of pairs of the involution (B, By) collinear with
Do, lies in a conic containing the nodes D,, Ds. This follows readily
from the equation

an Dy — riva agg + 2) ta V agg + Ay ao 3 411) (aj ta agg HT Ta Aga
f Ag rors Wan) = an wars {2 (aag — Waag 433) 4° +
+ [2 arg — (Ay + Ag) Wan agg an za 4
[2 arg (Ar Ag) Wan agal en eat (l —Ay Ào)ro as agg 433} « « (30)
To find the equation of the conic joining Dy, and D; with the

vertices of one of the above mentioned quadrangles B, B, By Bir
let us consider the following identity

U(r TV A33 +213 V ay. -Ayarnitg Van) (rra aggre aapt Aaeatsi/ an) +
Ho (ej rg agg tg V a9 fy Lo 3 Way) (#1 wa V 33 —2 3 V A32 +

Hf fg #93 Wan) = O41 (FS ajy 9? es HLT age r2e) « « « (31)
We easily find that this is satisfied if we put
ge = V agq 433 + dag) : 2 Wazgazs and o = (Waz agg — agg) : 2 V dag a39.

By substituting the value of A 4 A, following out of (31) into
the equation of the conic indicated in the part on the right side of

( 269 )

(30), we find that the conic (D, D; B, By By By) is represented by
An Ea = Ajo @ Fo — Ayes Tj Tz — VY Tg Tz == 0 . . . (32)

Here v is a new parameter dependent on A, A, whilst A ; denotes
the minor corresponding to a in the determinant formed by the
quantities aj.

Of the biquadratic involution formed by the points B the qua-
druple »=0 is the only one, the points of which are collinear.
So the right line Do, Do; has the equation

An mj — Ayn tg — Aygag=O0. . . . « . (33)
By remarking that the third diagonal point A of quadrangle

B, B, By Bu is the pole of Do, D2; with respect to the conic (32),
we easily find that the coordinates of A are determined by

N en)
2 Ajo Ans — Any An Ais Ay Aig

Thus the locus of A is the right line
Adr tric ad OC oO soso oc o (39)
7. The relation
an (San MQ? as + 2 rj 2g 23S ag3 ey) = (an 273 $+ AQX 73 0132142) +
+ ty? [ (ay) 433443”) rq? + 2 (an dag — Cg A13) 2923 + (andag— ang) 3°] . (36)
proves that the tangents of I, passing through D, are represented by
Agg to” — 2 Agg ra #3 + Agg = 0, « . « « (87)
whilst their points of contact R,, Rr are determined by the conic
Q1 = AH Fy 3 + Ay9% 73 + ayg% t=O. « « « (38)
Out of the equation

Og = a9 Tg 3 — LET) Tj 3 — A23 £j Tg == . . . (39)

( 270 )

of the conic (D, Dz Dz Ry Rn) is found (according to § 2) the
equation

Arg tg Hagg 21 %3 + 03310 = 0 . . «. « (40)

for the pencil of conics complementary to g, with respect to Dy, Ds.
Consequently to this pencil belongs

03 = Az To 73 + Gog 7] 73 + A932) %g=0 . . . (Al)

The points Dao, Dz, Ry, Ru, Ry, Ry can be joined by a conic.
By applying (10) we find that this conic is indicated by

093 == Ay xy = A75 Lj Lg — A73 Tj 73 -+ A33 Lg lg = 0 . (42)

So it belongs to the pencil represented by (32). This was easy
to foresce, the pairs of tangents through D,, DV, furnishing one of
the inscribed quadrangles alluded to in § 6.

In a similar manner by considering the pencil complementary
to g, we deduce that D,, D3, R, and Rr lie in a conic with the

x

pair of points c', C" determined by
Uy 93 ttz + Ago Ag) #3 @y + 33 dorma. « « (48)

Hence out of the symmetiy of this equation follows that C!, C!
are also joined by conics with the quadruples D,, Ds, Rs, Ri
and Dj, Ds, Ry, Rit.

For the conic (Dz Dz R, Ry C' C") the equation

71 = (412 Arg + ag Ais) 1? + (ang Áo — ag Aga) 2+
+ (412 Arg — 413 Ags) 21 73 Han Aog gg = 0 . « (44)

is furnished by (10).
According to a wellknown property the six antitangential points
R lie in a conic. This is confirmed by the identity

9 a 9
Ag” Tp, — 03/1 = xy (Pie EE (45)
where gj93 represents a quadratic form.

But moreover (45) proves that this conic has still the points C'
and C" in common with TD.

S. According to the identity

Ty = (433 9” A 2 agg tg ng 4 daa 23°) % + (an 72 23 +

+ 2 ay a 73 + 2 agra) roes (46)
the tangential points 7, and 7r of D, lie on the conic
Ty = ay fast Zager + 2ejgrj%—=O . . « (47)

It is complementary to the conic (43); so there is a conic a
passing through Ds, Ds, Ti, Tr, C°, C".

It is similarly proved that Ds, Ds, Ts, Tu, T3, Tun lie in a
CONIC Taz.

And now again we can form an identity

À ne ok T93 Ei = Ti T123 : . . . * ° (48)

out of which follows that C' and C” are also connected with the
six points 7 by a conic 793.

Thus the conic mjg of the six tangential points and the conic
Qi; Of the six antitangential points intersect in two points lying
on Ty.

Mr. Britt has pointed out that also the six points of inflection
are connected by a conic @ (Math. Ann. XII, 106), intersecting
Tr, still in two points belonging to the conic 7.3; (Math. Ann.
XIII, 182).

Out of the preceding follows that the complementary points are
lying on three remarkable conics 9)93, 7j23 and @.

9. Evidently there are four conics dg, coinciding with their
associates, each determining the points of contact of a double tangent.
They are represented by

Oy = 234) + 83% Vaag + 21 MY O33 = 0,
Oy = — 79 3a +13 eVa + 2) zo A33 = 0,
(49)
Og = ran — yt} Vaag HA My G33 = 0,

Os = 731 $3 1 VQ — meal. |

(212)

By applying (6) the equations of the double tangents d,, d,, dy, ds
can be easily found. Of course they can also be deduced from (26).
There are two identities of the form

DORE ty Eps |
(50)
Did Og = 2 Ez 5193 |

do and 05, 0; and 0, being complementary w.r. to D, and Do;
hence it follows that D, and Dy are connected with the points of
contact of dy and ds by a conic Ey =O and with the points of con-
tact of dy and d, by a conic §.=0.

Furthermore the identical equation

a33 rT, = Ens En == 2 ov . . . . . . (51)

furnishes the proof of the wellknown property that the eight points
of contact of the four double tangents lie in a conic

F = = Aj, 2,7 — 2 J ais agg 2} pS eon ao (5%)

We easily see that the points of contact of dj and d, determine
with the node D; a conic with the equation

Mae = dy dz — (q+ Van A22) S19 = (42+ Way) 499) Os

— (Aj) 2)? — 2 jy ty tg + Ago ty”) = 0 . (53)

Out of the second form of 1} now follows that it also contains
the antitangential points of Ds.

In the same way we can show that Ds, is joined by a conic to
its antitangential points and the points of contact of d, and d,.

The six points R lying ina conie ¢493, whilst Ds =(R, kyr, Ry Ry,
Da = (Ry Rr, Ry Ky) and Do, = (Ry Ru, Rz Rix), the inscribed hexagon
R, Ry Rk, Ri Ry Rij has the double tangent d, for its line of
PascaL. Similarly is proved that the remaining three double
tangents are lines of Pascan for three other hexagons formed out
of points R.

( 273 )

Physics. — , Calculation of the second correction to the quantity b
of the equation of condition of VAN DER Waars.” By
Mr. J. J. van LAAR. (Communicated by Prof. J. D. VAN DER
WAALS.)

In a paper, published in the Proceedings of the Meeting of the
Section for Mathematics and Physics of the Royal Academy of
Sciences 29th of Oct. 1898 (appeared: Nov. 9 1898), Prof. van
DER WAALS has pointed out among others how a second correction
to the quantity b of his equation of condition might be found. The
integrations necessary to it, proving to be extremely tedious and
lengthy, have not been calculated at full length.

I then tried to work out these integrations; I shall communicate
in short the results found, referring, with respect to the various
mathematical developments which led to my results, to a more
extensive treatment that will shortly be published elsewhere (in the
“Archives du Musée Teyler’).

The form to be integrated!) ran as follows (see pages 142—145
of the cited Proceedings):

INK
O5 „2a(h + acos 0) dh dO X part of segment,

in which that part of segment is found to be:

J

oe ; roe ( VR —@
ls a® sin p cos py) R? — a? + 2/, RS tan”! \ tan PE) =

IVE

a COS (p

— asin p (R? — 1/3 a? sin® p) tan

If we now first perform the integration with respect to 4 between
the limits 0 and 4, where 0, is given by the circumstance that the
centre C of the third sphere cannot lie within the two spheres A
and B (see fig. on page 142), we have to integrate:

01
2 (a + a cos 0)? dé,
0

1) The angle AMG indicated as C by Prof. v. p. Waats has here been called ¢,
whilst the angle indicated as p has here been called §.

( 274 )

giving after some reduction

[ue Iga) 0, + (2 ah sin 0, + Wo a® sin O, cos |

If we now call the angle CMA, point C lying on the sphere A

2 w, we have evidently, 0, being = 180 — p —2w
sin0,= sin(p td 2w) == — sinpoos2y + cospsin2 w
— cos p cos 2 w + sin p sin 2 yp ,

cos 0) = — cos (p + 2y)=

or as
; bats Up ie h liar
sin ~ = cos P = — tan Pp =
a a h
il 5 4
cos2 w= — (a —!/, Ry,
a

Ws Ya — RI
a
lp 7 (a? — Yq B) + h Ry/a? — Uy Re

1, R
le sin 2y =

also sin 0, =
1 9 > ED

cos 0) = — | — h(a? — Uy RP) + Vor Ry/a? — "/, KR? |

a a

so, taking into consideration the relation
a? — 1, r°,

=

fter reduction, we find:

1
Zah sin Oy + 3 a? sin O, cos O, = oie EE ra — "yr? (Bat — 1/5 RE) +

(1)

+ RYa— Yj, R? (Bet + U a? (RP — 12) — lf, RP )|

(4 Yy a?) Oy attent

0, being equal to (180 — p) — 2w
Now the form to be integrated is
a - el X part of segment X dh

7

( 275 )

To simplify still further we put:

linn Bh a= WR,
so that
h=RVy— nr?
and
pt Aen
dh = “Io Vr

The above mentioned expression for the part of segment passes into :

Is [rn LP) (YP) +2 tan! (n = ss

=
— n(3—n?®) tan! Vo we +):

=p
(1) becomes

1 en
Hp [ny ni Er nl EA

(2) becomes

V9 he (3 a —2 n°) [tan ee. tun—! ZE Slt
Vy

so that our integral is now, writing everywhere « for y°, trans-
formed into:

N
=O [(A + B4 C+ Dan

c 2 B Le
where (paving attention to dh being equal to 1/, Pe

Va —n?
Nee (dn jn
MAT: le (Bz 2) TE re) ‚er (1-4n?) n° En
u De ze |
Bn en oe ! kl
= — 27 — in
n(3 )/ a tan ae an =
N
Ga " (3.22 = If) 322 + 1/, (1 — An?) — aye — Zi x
a x x — n?
l—ez lr |
SK > tan! (n bes ) — n (3 —n?) tan-! | ;

Sr — Anr —n Ja
DS == | ND
Va —n? | Va — nv? Va — 1), x |
1x le
x [2 tan—] ( n Val 5 — n (3 — n?) tan”! V/a |
en? x — n?

In the integrations following now we shall for the present not
pay attention to the limits for 2 (or x). To simplify the notation
I still propose the following abridgments :

DAG l= ;
= 2 =

9
Hi pS Hi

VAD Der VD Wer!

We then easily find for the five parts of the integral i A du:

A, =3 mf pda =), n* | (2e — (1 + n°) ) p — (lL—n’*)? tan! |
(3)
1+ n?

n

tan—! ne |

ca
A, = — 1/5 we fe darom 5 — 2 tan led
22 7)
A3 „fr dz = San le a?) p'—*/16 tan! |
Ay = '/,n (1-4 n°) Pae= 1/4 (1-4 n°) lp’) tan le! +tan—! ye ‚ (4)
a“

U !
p
A, = — zn dx = n3 lias —2tan— 2! + 5/, tan! VY, 2’
2 x

as is to be verified by means of the relations.

22—(1 2 Di pres
dp = —'/y dt hd de dp! = — U I dix
Pp P
lx dz
dtan—!z = —1}/, a d tan—! 2! = — Ui
P Pp
dx dx
dtan-laz= — ange dtan—! Y/, 2! = —Y,—
2 vp up

(Cat)

Furthermore, as

fs a? n°) V le dv = — 2 a n°) (1—2)"/2 = 3/5 (1 =|

—n n da I, ; da
d tan! = din =

Sa — — = /4 ==
Van? 2% Wan? Vals rVaÏa

we find for both parts of | Bde:

Bn a n°) (le) — 35 la) nn
Van?

_ ( 3} 7 8) A ( 3 om 4 18 A ;
in pen CO ora eer et 5 A emd nn el Fee En Tee
n | 10 v 50 60 n \p mn 9 1 60 n ) an ot

SE las -
+ EN eer n ) tan— nz

1/
Bs a B) (1 2)ls — 4), att) tan—1 —_!2

EE
V alg

ne

3 19 Zn A 271 ie ae Ees
— Nn den 5) (en — 2) tan Ee

1 1
+8 ‘= ae n?) tan! ize’ |

The integration of the four parts of fe de is already more difficult,

Comparatively easy are C, and Cy:

5 A 5 5 ui is
C, = — n° (8—n?*) 5 tank 2d =
x

1 1 3
= — n?(3—n’) |—*e p+ bami, (1-2) | tan—1z—— tan Ine | |
i 2x i j 2n i \

+ 3 2—}/,
Cy = 2n | tan! nz . de =
aw

) 1 n°
=2n B= Sn tan we + ( Sed —— ——— ) tan ne]
An 2e sd

Proceedings Royal Acad. Amsterdam. Vol. I.

( 278 )

To integrate C, we add to this integral :

9 2 Is
-— n(3—n*) —— tan! z.du ,
: en”

which afterwards will be subtracted from Ds. So C, becomes:

"Aat Up x (1—4 nr?) —n? Un
Ci = — 1 ef semis Ë = sei se Vee = (nim sed

We Wi ne

But now we find:

A a2 + U r(l—An?)-n? al), ; — |
aus Es je ) — = dnd En en (wr?) | 5
Pred dn
so that we get (the various developments — as was said before —

will be published elsewhere):

Mel) ITE
Ie
a

iel (B—n)|
IP Uytant dta a. (2)

Likewise to the integral C, is added:

C4
ay tan—! nz. dz ,

v—n?

which shall directly be subtracted from D,. For

APH Upell dn) zij
Cas 2 [- = ad 5 { = Ee DE a Lay = tank Med

Mi dT

we find in quite the same way as for C3':

Ala ye Sas, we a
id = iB Sn ) (@—n?) tan ne +
} 1
+2n 5 5 —2tan—)2'+ = tan—1 1/, il . (8)

( 279 )

~3 r—2 n? ——
As | Wane is equal to2«V«—n*, we shall find after
gn?

rious reductions successively for the 4 parts of he D de:

= 5 . 3 r—2 ne — Nn
D = — n(S n°) — tan ———— tan le. de =
Van? V v—=n?
eet nn
= —n(3—n®) | Zer a—n? tant ——— tan—! z —

- Va u?

ra=

== —n rf eeen . ij
—?/a(e-+2)V 1e tan! We —= + ?/gnp—n(a—3/o—*/gn?) tan lets tante (9)

vn”

Likewise:
DD —n
Dj : tan”! == tans nz sde
Var? V «—n?
— —n Eon. —n
= 2 | Zee n? tan—!—_ tan | nz — 2 ni sitar —
2 »
an? Van?

The integral D3, viz.

Ds; = 2n(3—n*) |

TO tan—| Se de

Var "4

3 wv
Va

9 2 1
mf) la
tan Ì =
n?

can first be reduced to

1 /
Ds — 2 1 (3—n*) [2 & War? tan! — Lv tan! a +
Val

2

Pm x 1/

1 ad

+ Ys jy tan le. de | ———tan—! —_=~_ de.
din Js lr 4

V

U 1/

=e
But as i iA y tan—! z.dx can be transformed into
4

mend

zen — My —————
ID tan 12. de + 2V (w—1/,) (a—n?) tan! z — p'—3/,tan— 2’,

9
nd

ios

( 280 )

* tan—) 2.dx ;

we subtract from Ds; the part 2(3-n?) <-!/, ih en
Pm! n?

which part, as we saw above, was already added to C3. After
various lengthy developments we find at last:

Dz = 2n (3—n?) l2 aan? tant tan— z —
Via
. Le is
— */3(« + 2)V 1—atan—! Vet + Y («—Y,) (er?) tan— z
wv

ae Ce eas 4
Fag ery Omics Tie oP se | ot ve, OR)

*3 rn? My

tan—! nz . dz,

J Vin =,

tan—! nz. de into

after transformation of the integral A

aa

=p zn
I/y |- | tan Ine. de + 2 V(r—l/4) (an?) tan—! nz —

tN

— 2ntan— z' + n tan—! Woe!
2 5)

and subtraction of the integral already added to C,:

gls
a Va OUTE WP odd 5

vn?

we find:

= 1 ij,
— 9
Dy it E BY x—n2 tan ——— tan! nen! 1 Stan!) =

Vi Va!
FV (a—1/4) (en?) tant nze—2ntan—! 2! 4-3/g n tant . (12)

If we now join all the similar terms, we shall find for

fu SEE GERD:

en —< ————: a,

( 281 )

the following:

] n? E
= eu ae (Geese ate (Cia )) | V (l—2) (¢—n*) --

au. = sia + S/n 2 + Us w(9—10 n2) | V (l—a) (e= U)
+ [= 28 =n) (2 + 5) — LE + an) +
dmt) (——2) Eej om Wis +
= 2 (——2) GT eH |r (» haa
—— oF tan”! Vn Eb oe on u +

mr = 1p.
+ Any lallen?) Lee — 7 —2 tan—! ———

(13)

Van? V =r)
1
+22 Wen? (= ——_— 2tan—! — fa ) DG
Van? Vals
1e Ia
x | Bean (1 eS tE ) tan! Ve =|
2—n

Let us now introduce the limits for 4. These are (see the paper
of Prof. v. p. Waaxs) for values of r lying between & and A3

Res 1 re

Jar me Ee
SS and WR?! ne :
2Y R2—1/, 7? la

whilst for values of » between Ry/3 and 2 ZR they are:

—YR—Y, and VR lr”.

So with our notations we get (h = RV 2—n?);

For n= 1), to Wo V3: |
Va f t EES : to 1);\
vn? fr ‚o /\|—n2 (a fr SSS (0) 3

tn” from WA v n (: from (a) ) |

For n= 1/1/38 to 1: |
Van? from —Y1—n? to Wl—n? (a from 1 to 1). |

Substitution of these limits in (13) gives, paving attention to the
circumstance that wherever Ve—n? appears in tant, the value of

= ——
~

tan js equal to w for Van

= —VJ—nx?, when at the same
time V1—x (which becomes 0) appears in the numerator:

Iq (n == Yo to YoV3) = — Oly + Son? — 9/5 nt) V3—4 a tE
Ju (7 4 9 6 { 1 V3—4 n® u¢ 47 ) WV 3—4n*
NTA EO ON Pees Oe a aS le
(7 bs nf) tan TD 10” an 12,2
zl V3—An? 39 V3—4 n?
+ En SS = HS)
5 n 10 In
(14)
Te Bret 9 6
nn WE V3 to N= 7 l= 10 n + A i 5 nt JL = ne] JE

+ Yom 3 (2—38 n + n3)Vl—n? +

fa 28m + Wh) Va (tant 2 — Wy m)

} 1),
tin SSS SS an
Van? r—l/
: D 1 Sea 1—2 n?
disappears for 2 = ———— ( = ee
4 (ln?) 2V1—n?

The expressions found for 7, and J, have been verified by me in
various ways aud every time found true. They are both still to be

5
multiplied by 1/3 a Zé aa Before passing to the second integration

with respect to 2, we must calculate a complementary term for the cases

( 283 )

(not mentioned in the cited paper) in which point M falls outside the
segment and an entire segment is ineluded by a third sphere. It is
easy to see that that complementary term is obtained out of

i 2 | | rl 2 ar (h + a eos 0)? dh dO X segment,

which produces after some reductions,

Segment being equal to 1/50 (2 K°—3/, R? x 4-1/5 93) = 1/5 7 R3(2—3.n +-n3):

Z n(3 2
ip bee ie pr esntof | B:
Race: 1/,a(1—4.n2)—n? zl, 3a-2n2 =1 1, j
hel ) Ae En is (ton : tant ) | dv.
x rn V zn? V x—n? Vial, 7 4

Of this integral we mention only the result taken between the

limits We — 2? = os to

eco pce 1
VY r—n? = — j/1 — nv? (> from ———— to Ì ) :

It is evident that this integral relates only to the second tempo

(n=1/,.//3 tol) .
We find:

7

1 2 A
I= Yin? Lo (2 —3n-+n3) faro — hy (I= 23) —

—2y1—rn? C= — Ì/; z)|. 56, (05)

by which most remarkably the above named value of J, is
considerably simplified and, with the omission of the factor

Nees

77) Passes into :

47

A 1 6
nala it tt | ene (LG)

( 284 )

If we now multiply by

co
al
>
=
a
A
~
=
~

4 N A
dun dr Xr ark

we have still to integrate:

Yo/3

1
Dn Vie ‘ 5
iS eh? 7e Ian? dn + H+ 1") n? dn|
1, Is

This integration we break up into parts again.

1/3
Iz
furnishes:
py ee 89 83 SN ga
= (Gre n mok n 520 n° + a0" Vv — An? +
la v/3
2205 VERE
= tan! | ’
16384 2n
Is
as is to be verified by means of the relations:
— An dn V 32477 — Ard

1/3 A= dittim = = > *
ld a 2n V3 — 4 n*

Introduction of the limits gives further:

: 2169 eee re
an 5c 10384 V rosen (°° VO

In the second place, see (14) and (16):

ia V3
Pr LU ij

JL
Ts = fa ns— Ant + 6/. n°) tan! “ aR aR at fe nf —4 616). n°) ,
eed TL a
US Va vs

( 285 )

V3 —4n* 5
INE ne PER takes for n= l/,p/3 the value a, we find by
RL ~
means of
ei VA n 2n dn

me EA eae

and, paying attention to the relation tan! 2/2 = a—2 tan! 2:

5719 127 169 1
fi i Ja + ( -- ) tam 2 —

ne \05256) | 17.82 15.128 7.16
YoV3
WT, GE ee nO
{ LS aL re
kj (L—n)V3 — An?
In the third place :
fu ay
nV3— 422 ee
Te =| = n— 5”) tan! a 5 i : mf (5 ETT na dn.
ve V3

NV%—4n* 3— An? dn

With d tan! —— = - ;
1 — 2 n? le NVE

we easily find:

16
37 V3 —42% ——— nt nl

7
en
; 0 m -- ED an—! 4 dn (19)

co

2
/2

For

2V3

21 A 2 39 Saas 2
Jin =|) l= n° tan! Ann aR n° tan! El dn
1,

we find by means of

Vs An? —2dn

de VA An? — dn
2 SAT

d tan ==

n (ln?) 3—4n

= 9) Chai

( 286 )

7 21 21 : 2) 39 mee
(dan 72.) tan 72
: ( SLA CL es Rae en

wV/3 a 4 ze 4 (1 2
DV: ne en — n°)

a —d
(1—n))/3 —

where again in the first part I made use of the relation
tan-1! 2 1/2 = a—2 tan! 1/2,

If we then join the terms obtained, we shall get besides the fore-
most factor

2169 ( 383 «127
= WETEN REE TE ) a
F 2205 559 Len
( 16384 * 15.128 — 716 ) ae (20)

Ys

+{= Shan? + 25). mt — 16/. nb 1 8/, m8 — 4/,, nld
%

(ln Ar a

For the integrating of this last integral we again refer to the
more lengthy paper; it is sufficient to mention the result for J.
I only draw attention to the fact that after having successively
determined

nek dn
JV3— An?’

where k= 1, 2, 3, 4, besides

n° dn E
ervan

all the above-named integrals are found by parts. So is e.g.

n* dn es n° dn * n= dn
Je — n°) V3 — An? = (5 — n°) V3 — An? ee V3—4n? *

ete. The result now becomes, after multiplication by the foremost

(287 )

factor and by N for all N spheres:

Tk

9
3 v2 Hen:

32 N3r 73 153
| ve if
7.45.64 75.256

teel fe
TEE. vel 5)

If for a moment we call the expression between brackets @, this
may be written:

4 ,\3 NS 9 @
(Ger) Mx tt

For the double volume of the MN spheres of distance remains
also, after paying attention to the 1 and 2" corrections:

17 N?
N .*/, 0 RS — (4), 77 RS)

13

9 @ NS
= TE ai ie pc
6a 7 + (lg 77 3) EET

17 8b 9 @ 642?
== We a =|:

64 V'2n ve
N .4/, 2 R3 being equal to 85. If now 4b=5,, then in

17 b OROSAN
Oy es | eae ene |
es | eer

7 . J . @
the 2"! correction sought for evidently becomes equal to 18 —, so:

7

P= Ë [va 153( tan! V2—l/
ETE toe i 3 (tan 2—Yan J],
or
(== | 73 V2 4 81.17 (ton vak x )| 119.22)

this being our definite result. The value of this is, exact in 4
decimals,

fB = 0,0958,

so almost 1/5, whereas the 1° correction was fully 1.

288 )

Physics. — „Measurements on the system of isothermal lines near
the plaitpoint, and especially on the process of the retrograde
condensation of a mixture of carbonic acid and hydrogen”.
By Dr. J. VERSCHAFFELT. (Communication N°. 45 from
the Physical Laboratory at Leiden by Prof. TH. Kamer-
LINGH ONNES).

(Read in the Meeting of December 24'» 1898).
Sri:

In one of his first communications on the process of the retrograde
condensation KUENEN has given some measurements, from which the
course of the ratio of the volume of the liquid-phase to that of the
vapour-phase along one definite z-line (VAN DER WAALS’ w-surface)
may be deduced. It was desirable to get a general view of the
process of condensation along different #-lines on one and the same
w-surface (especially between the « at the critical plaitpoint and the
rv at the critical point of contact) or, what comes to the same in
this case, to get to know, for a definite composition of the mixture,
the process of the condensation along lines belonging to w-surfaces
for different temperatures, near and especially between the tempera-
ture of the plaitpoint and that of the critical point of contact for
this definite «.

An opportunity for making measurements on this subject was
offered by a more ample investigation on isothermals of mixtures of
carbonic acid and hydrogen which was undertaken by myself !).

§ 2. Method.

The pure hydrogen was prepared by means of the apparatus used
in filling the hydrogen-thermometers for the measurement of low
temperatures, and formerly described ®).

The pure carbonic acid was obtained from the commercial liquid
gas, following the method first applied by KueNeN *) and now re-
gularly used in the Physical Laboratory at Leiden. The way of
preparing the mixture and the apparatus used were mainly the same
as those formerly used bij KUENEN in a similar investigation (see
the annexed figure).

1) Compare KAMERMNGH Onnes, Versl. Kon. Akad., Dec. 1894, pg. 179.

2) KAMERLINGH ONNES, Versl. Kon. Akad., May 30th 1896; June 27th 1896. Comm
fr. the Phys. Lab. of Leyden, N°. 27.

*) Diss. Leiden, 1892,

( 289 )

Fig. T.

Even small quantities of hydrogen, added to the carbonic acid
cause a great increase of pressure when the latter gas is condensed.
In order that the end of the condensation can be reached without
danger to the glass tube, the experiments were made with a mixture
containing 5 mol. feces on 100 mol.

The volumes of the mixture were measured in a manometer- inbe
of about 0,05 e.m.? in section, on which a graduated scale in m.m.
had been etched tested carefully by a kathetometer. The calibration
was made by filling the tube with mercury and by causing this
liquid to flow out in small quantities; the columns of mercury thus

(290 )

run out were weighed and afterwards measured by the kathetometer.

Perfeet equilibrium of the phases was secured by stirring with
an electro-magnetic stirring apparatus, first used and deseribed by
KUENEN '), afterwards applied by van Erpik?®) and HARTMAN ®).
In measuring the volumes, the contents of the stirring-red had to
be taken into account. This volume was calculated from the shape
of the stirring rod; this was very regular, and consisted in an
almost perfectly cylindrical part 28,5 m.m. long and on an average
of 1,450 m.m. in diameter, and two globules, one on each end, of
2,300 m.m. and 2,383 m.m. diameter respectively. From these data
the volume of the stirring-rod was found to be 60.4 m.m.*.

The compressibility of the mixture was compared with that of
pure hydrogen. To this end the experimental tube was connected
with another manometer-tube on which, like on the former, a gra-
duated scale in m.m. had been etched. The scale was tested by a
kathetometer and the manometer was carefully calibrated. This tube
however was much narrower than the first, its section beiag only
about 0,006 c.m.*. It was filled with a known quantity of pure
hydrogen.

From the specific volumes of the hydrogen, the pressures were
calculated by means of the formula

p (v—0,000690) = 1 + 0,00370 ¢ 4)

borrowed from AMAGAT’s latest observations on the compressibility
of hydrogen °).

Volumes and pressures were carefully calculated to within 1/;099,
as in these experiments po higher degree of accuracy was to be
expected.

The two glass manometers were screwed in the usual way into
two steel cylinders, which were partly filled with mercury, and for the
rest with glycerine which transfered the pressure from a compres-
sion-pump. The lower ends of the cylinders were connected by a
steel tube filled with mercury; at their higher ends they communi-
cated by means of a brass tube with T-piece for joining on to
the compression-pump.

By connecting the cylinders at their lower ends, a contrivance

1) loc. cit.

2) Versl. Kon. Akad., 29 May 1897; 21 June 1897. Comm., N°. 39.
3) Versl. Kon. Akad., 25 June 1898. Comm, N°, 43.

4) For explanation see a following communication.

5) Annales de Chim. et de Phys., 6e série, t‚ XXIX,

( 291 )

recently introduced by HARTMAN!) a difference of the levels of the
mercury in the two cylinders is avoided, a difference which we
should have to take into account without being able to determine it
with sufficient certainty. The only thing now left to be taken into
account was the hydrostatical difference of pressure caused by a
different height of the mercury in the two tubes, and of the diffe-
rence in capillary depression caused by the difference in diameter
of the two tubes. An experiment made on purpose showed this
difference to be about 7 m.m., a quantity which could be neglected
as being smaller than the possible error of observation in the mea-
surement of the pressures.

Suitable temperatures ranging between that of the room to a
little above the critical temperature of carbonic acid, were obtained
by means of an apparatus first used by vAN ELDIK, and at the same
time with me by Harrman. The bath was constructed in a way
as described by me in a former paper and as it was used afterwards
by van Expix. Whenever small fluctuations of temperature occurred
the observations were reduced to one and the same mean temperature
by making use of an approximated coefficient of temperature which
could be deduced from the uncorrected experiments.

§ 3. The isothermals.

In table I the results of the determination of isothermals are
communicated. The pressure is expressed in atmospheres, the
volumes have been measured by taking as unit the theoretial volume,
viz.: the volume that would be occupied by the same quantity
of the mixture at a temperature of 0° C. and under a pressure of
1 atm, if it followed the laws of a perfect gas”).

The reduction to 0° C. was made by means of the coefficient of
expansion of carbonic acid 0,00371%), the reduction to 760 m.m.
by means of Boyre's law which in the range of pressures here
coming into account was sufficiently accurate.

1) loc. cit.
2) For further explanation see a following communication.

*) See a following communication.

(s 2925)

PARE NE 1D) 1 3) Mixture 0,0494. Isothermals.

Temp. | VMG. |pressure. || Temp. | DE Pressure. Volume. | press,

15°.30 274.9 | 3] .41 | 26°.80 06480, 79,30 04.063) 92.15
2471 |. 34.19 | ae 06050) $0.95 03750) 95.10
2074 | 39.12 | 05704) 82 03390) 100.6
1688 | 45.08 | | 05830) 83.90 || 02895 111.8
102 52575 04197) 90. 06480) 79.95
1187 | 55.35 | 04163} 90 | 06095) 81.55
1152 | 56.95 | 04098) 91 05710} 83.20
1110 | 57.20 | 03979] 92 | 05540] 83.90
1074 | 57.55 | | 03950) 92 | 05880) 84.60
09180) 59.25 | 03403) 99 | 04975) 86.60
07240) 62.15 03013) 109. | 04645] 88.45
05275) 67.75 | 970.10 05710 82 04573| 88.95
03539) 80.55 Mell 05345] 84. 04445) 89.60
02543) 102.9 | 04205) 90 04410) 89.80
02500) 108.1 (Dl, Dl 04063) 91. 04396) 89.95
02471| 111.3 | gags! 92.20 | 04297] 90.55
02498) 117.0 | 03992) 92 04255) 90.85

21°.50 2071 | 40.63 | 03963) 92 04573) S9.35
1880 | 43.56 03928) 93 04184) 92.05
1691 | 46.97 | 03915] 93 03788] 96.00
1495 | 50.90 | 03716) 95 03319/103. 4
1302 | 55.45 || 27°.30 2079 | 41 03051/111.2
1112 | 60.40 | 1688 | 48 | 02952/115.5
09190] 65.95 | | 1305 | 57.80 || 32°.10) 2074 | 42.98
08450, 68.00 09190) 69 | 1880 | 46.36
07240) 70 30 | 06470, 79.8 | 7686 | 50.25
05285) 76.00 | 06120, SI. 1404 | 54.65
03629, $8.00 | 05700, 83 |__1302 | 59.90
02s32| 102.9 | 05330) 84, 1106 | 66.05
02782) 105,2 | 04946) 86, 09190) 72.95
02732) 107.7 | 04523) 88 07235| 81.35
02675) 112.6 | 04255) 90. 05310, 90.90
02612| 118.4 | 04219) 90.8: 04190] 99.40

26°.80 09125) 69.80 04197] 9. 03377|111.9
07220| 76.60 || | o4205] 92.

1) By corrections afterwards made, and which will be diseussed in a following

4 | —
;
. process of the retrograde condensation of a mixture of carbonic acid and hydrogen.

javana):
AB ARBO i

Zeja nn nnn
Za OEE

GERE AZEAZEE SEKEe

jo;

El

|

|
DE

zee.

[
rE

goer,

goor.

Be
eI
2000

5 &
H

Baan
pee

HEE
itt
HE:

J. VERSCHAFFELT, Measurements on the system of isothermal lines near tho plaitpoint, and especially on

HE
BEERS

500

m

Be

|

a
(el a a

100:
‘Proceedings Royal Acad. Amsterdams. Vol.

SESRRRReee
5

gar

( 293 )

Fig. I shows the system of isothermal lines!). At temperatures
below 27°.50 I observed separation into two phases; 27.50 is the
temperature of the critical point of contact of the mixture. The
isothermals of 15°.30 and 21°.50 show distinctly a discontinuity in
slope resulting from the separation into two phases.

In the diagram the points where condensation begins and ends
are connected by a curve, which forms the limit between the area
where there is only one phase and the area where there are two.
The common tangent to the border-curve and the isothermal is
not horizontal as in the case of a pure substance. As for the
course of the border-curve at still smaller volumes, it is bound
to show a point of inflection somewhere and to be reversed
finally towards the axis of the volumes. In the figure however the
convex side is turned towards this axis, so that the reversing will
probably occur only at a very high pressure. I observed that at a
temperature of 27°.10 at a decrease of volume the meniscus became
more and more indistinct and disappeared at last in the middle of
the tube as a mist when the volume 0,004063 and the pressure
91.85 atm. were reached. And so this point is the plaitpoint for the
composition « —0,0494. The critical point of contact cannot be deduced
with accuracy from the experiments themselves; the best way is to
find out from the figure the point of contact of the critical isothermal
and the border curve. In doing so we find with pretty great certainty
the elements of the critical point of contact for the composition
= 0,0494; ¢=27°.50; v = 0.0048; p = 87.4 atm.

The value of the coefficient of pressure for different volumes can
be determined from the isothermals above the critical isothermal. These
coefficients of pressure within the narrow limits of the temperature
may be considered as constant, and the observations at large volumes
point to this fact. These coefficients of pressure are:

dp
v = 0.0338 Ss = 0.138
dt/v
281 0.170
225 0.216
203 0.245
150 0.283
158 0.336

communication, the numbers here given and others occuring mm this communication
do not exactly agree with those published in the dutch communication, The volumina
underlined are those where separation in two phases takes place.

1) Fig. 1 has been constructed at an arbitrary scale. The exact one we obtain by
multiplying the abscissae by 1,127, and the ordinates by 0,99.

20

Proceedings Royal Acad. Amsterdam. Vol. I.

( 294 )

pear @

= 0.0338 OS

dt/»

135 0.409
112 0.515
101 0.58
090 0.68
079 0.83
06S 1.00
056 1.22
045 1.50
034 2.40

With the aid of these coefficients of pressure the unstable parts
of the isothermal lines were extrapolated and mapped on the figure.
Only for 15°.30 and 21°.50 the extrapolated parts deviate suffi-
ciently from those observed, to be clearly distinguished. As in
the case of a pure substanee the two curves intersect and the areas
thus included must be equal as in the case of a pure substance !).
We can immediately see on the figure that this condition is satisfied,
in so far as we can judge by examination only. A more accurate
test by measuring the areas is useless on account of the uncertainty
of the extrapolation we have made.

S 4, The course of the condensation.

Below the temperature of the plaitpoint the process of the conden-
sation was normal: the quantity of Huid was constantly increasing
while the volume was decreasing, so that finally the whole space
was filled with liquid. Between the temperature of the critical point
of contact and the plaitpoint-temperature retrograde condensation was
distinctly observed.

In order that we might represent the process of the condensation
graphically, I measured volumes of liquid belonging to definite volumes.
The results of these measurements are given in Table II.

This table is graphically represented in fig. 2. There we can dis-
tinctly see the normal course of the condensation below the plaitpoint-
temperature 27.°10; the lines of condensation are constantly rising
and end in points lying on a straight line with a slope of 45°: at
these points the volume of the liquid is equal to the total volume.
Above the plaitpoint-temperature the condensation-line rises first
but finally returns with great rapidity to the axis of abscissa; the
course of these condensation-lines is therefore very asymmetrical, and
even more so the closer we get to the plaitpoint; in approaching

1) See Biimckn, Zeitschr. f. physik. Chem., VL, p. 157.

( 295 )

iP AC Belo Es
Mixture « = 0.0494. Condensation lines.

Ii
ee

| | | | I | | “a
15°.30/ 1111 00015|! 26°.80 05700/ 00076|| 27°.30 | 04572) 00644
| 1074 00056 ogss0 ae | ae 04523) 00758
09190, 00388) 04197, 01592, | G4418) 00799
07235] 00875) 04163) 01585)| 04374) 00786
05975| —01498|| 04028] 01798) 04331} 00877
03539 e200 03979 01956 04298, 00644
02543] 02543, 279.10 | 05120} 00393 04318, _ 00174
21°.50| 08450 ooo "> | 04524, 00966 | 04283) 00438
07285, 00446, (il.p)) 04073] 01486) 04297] 00883
(5285 01231 270.30 05330, 00057/) | 04255} 00190

036co] 02115 | 04948) 00376)

| Pee | |

the plaitpoint from below the condensation-lines in the last part
become more and more steep. As for the condensation-line of the
plaitpoint-temperature itself, this terminates in the point with the
abscissa 0,004073, and the ordinate 0,001486. We may however
also consider the perpendicular through that point as forming part
of this condensation-line, and then the steepness of the acclivity on
the one side and the steepness of the declivity on the other side are
easier to be understood.

Finally I give the volumes and pressures at the beginning and
the end of the condensation as read on figures 1 and 2.

Beginning of the condensation. End of the condensation.

Temperature. Volume. Pressure. Volume. Pressure.
15°.30 0.01111 57.20 0.002543 102.9
21°.50 0.008545 67.90 2892 100.0
26°. 80 5850 81.75 3833 93.20
27°.10 (pl. p. t.) 5625. 83.00 4063 91.85
27°.30 540 84.6 427 90.5
27°.50 (er. t.) 48 87.4 48 87.4

These data when brought in connection with those for other mix-
tures may serve for mapping the binodal curves on the w-surfaces, and
for constructing the p- t- 2-diagram.

( 296 )

Physics. — „Measurements on the magnetic rotatory dispersion of
gases.” By Dr. L. H. Stertspema. (Communication N°. 46
from the Physical Laboratory at Leiden by Prof. H. KAMER-
LINGH ONNES.)

(Read in the meeting of December 24th 1898.)

1. Description of the apparatus. The figures given here are intended
to complete and to illustrate the description ') of the apparatus used
in the investigation.

Fig. 1 shows a general view of the whole apparatus and of the dif-
ferent electric circuits, fig. 2—5 show the two nicolbearers in section.
For the description of these I refer to the communication of March
1896, for the coils to that of June 1893, for the optical apparatus
and several other details to that of January 1895. The description
of the mirror-reading of which fig. 6 gives a general view, and
fig. 7 and 8 represent some details, may also be found in the latter
communication. Fig. 9 represents the high-pressure tubes with the
manometer, fig. 10 shows one of the high-pressure stopcocks that
have been used. Fig. 11 represents a section of the system of tubes
for the circulation of water together with the thermometers.

EXPLANATION OF THE FIGURES.

Rigs 1. General arrangement of the apparatus. A collimator, B smaller nicol-
bearer, C and U coils, “ greater nicol-bearer, / # experimental tube,
G screw for the rotation of the smaller nicol-bearer, which is connected
with it by the steel wire H H, guided by the pulley O; Z weight for
pulling back the nicol-bearer. Z vertical graduated glass scale on which
the rotation of the mirror N is read in the telescope K by means of
the intermediate mirror J/, P prism and Q telescope of the spectro-
meter, X switchboard where the currents are supplied, y arc-lamp, the
motor of which is fed through a thinner wire originating from terminal 3,
g resistance and 3 amperemeter in the arclamp-circuit, ¢ switch for trans-
ferring the current from the coils to the resistance Y or for breaking the
current, à commutator for reversing the current in the coils, Z switch
by means of which the whole apparatus can be switched out except
the shunt 7, which sends a derived current to the galvanometer 7
with the stop-commutator U,

Fie. 2—5. Section of the two nicol-bearers. a nicol, mounted in a cylinder g, and
kept in its place in the nicol-bearer mz by means of a ring 4 with adjusting
screws, / experimental-tube, on to which the tube with flange » has
been soldered and which is fastened to the nicol-bearer by the nut g
with the stuffing-ring ¢, e connecting nut for the high-pressure conduit,
h level, o flange with six bolts and nuts p, ¢ glass plate with nut d
and leaden-stuffing ring 7, which is prevented from being forced out by small
rings s, « handle to which the steel wire 4 (comp. # fig. 1) is fastened.

1) Verslag Kon. Akad. 1893/94, p. 31; 1894/95 p. 230; 1895/96 p. 294, 317;
1896/97 p. 131, 182; Comm. Phys. Lab. Leiden N°, 7, 15, 24, 31,

nn EO

L. H. SIERTSEMA : „Measurements on the magnetic rotatory dispersion in gases.”

A

weedloge Royal Acad Amsterdam Vol, 1,

ge

(297 à

¢

Fig. 6. General arrangement of the mirror-reading. K telescope, L graduated
glass scale, illuminated by the mirror-strips Q, M intermediate mirror,
N reading mirror.

Fig. Tand 8. Mounting of the mirror on the nut in the flange of the smaller nicol-
bearer, d nut, X and F two rings, Z fastening-screws, N reading-mirror.

Fig. 9. High-pressure conduit. F cylinder with compressed gas, 4 high-pressure
stopcock for closing the former, B stopcoek for closing the mano-
meter, C and D stopeocks for drawing off the gas, / connection with
the experimental tube.

Fig. 10. High-pressure stopcock. See A, B, C and D of the preceding figure.

11. Sections of the tules for the circulation of water together with thermo=

meters. id tubes in sections, #, supply, 7 outlet, 7, and 7, thermo-

meters, 7, and m, nuts.

Fig. 12. Curves of the rotatory constants. See further on.

2. Formulae for interpolation of different forms. It has been
stated in a previous communication!) that the different theories of
the magnetic rotation lead to two forms of formulae for the rotatory
constants of @, viz.

Cue te
SS SS — . . . . . . . . I
oO 7 T 53 TT ( )
D= Pp + ie See kod oe BOER (LEG)

With a view to the fact that in the case of oxygen we obtained with
the first form a better accordance with the rotatory constants ob-
served than with the second form), we have published in the later
communications only formulae for interpolation of the form (I) with
two terms. In the meantime the continuation of the calculations
showed that for nearly all gases the form (II) with two terms was
more satisfactory. The contrary proved to hold only for oxygen and
for the mixtures of oxygen and nitrogen, among which we may
mention in the first place air, further a mixture with 87.8 percent
oxygen, on which some observations have been made in the be-

1) Versl. Kon. Akad 1894/95 p. 237; Comm. Phys. Lab. at Leiden N°. 15, p, 27.
3 " p. 238; 7 ” ” ” INOS by pees

( 298 )

ginning |), and a mixture with 26.0 percent, on which only a few
observations have been made not published hitherto. For these
mixtures form (II) required three terms, as was the case with
oxygen.

For judging of the accordance of the formulae we have always
calculated the probable error of an observation of the weight one,
according to the rules of the method of jeast squares. In the
two first columns of the following table these probable errors are
to be found. They are computed by taking three terms in the form
II for oxygen and mixtures containing oxygen as said above, and two
terms for the other gases, and belong to the rotatory constants
expressed in minutes, multiplied by 10° and for the pressure and
«the temperature mentioned in the observations.

PRO) BA Boba HOR RO Ris:

Form of formula for interpolation: I Il IIL
Oxygen 58 5.4 5.0
Mixture with 87.8 percent O 6.9 78

7 “u 20 4 O 3.9 3.0
Air 319 2.7 dd
Nitrogen ON 7.4 tell
Hydrogen 89 47 4.9
Carbonie acid I 0.147 0.122 0.106
7 „ 112) 0.184 0 081 0.047
Nitrogen monoxide 5.4 3.0 2.2

An investigation of the errors, which are to be anticipated in the
different adjustments and readings, always yielded for the error to
be expected in the rotatory constant numbers larger than those of
the table given above, c.g. for oxygen 11 in the violet and 6 in
the red. With a view to this fact the accordance for all formulae
mentioned may be considered satisfactory. Yet in the gases without
oxygen the errors of the form (II) with two terms are always
smaller than those of (1), so that if in choosing between the
two forms we had to consider this only, we should prefer for these
gases the form (II). But it is not excluded that other forms of for-
mulae for interpolation should yield a still smaller error. This
appeared to be the case with the form

) Versl. Kon. Akad. 1894/95, p. 236. Comm. Phys. Lab. at Leiden N° 15, p. 26.
2) Observations with gas from two cylinders of unequal purity.

—

Baas |

( 299 )
b
DA ed

which gave the errors given in the third column of the table.

3. Law of mixtures. When we wish to apply the corrections
for impurities in the gases investigated, we have to assume a law,
from which the magnetic rotatory constant of a mixture can be
calculated from the constants of its constituents. In a former com-
munication ') a simple law has been assumed, without any conside-
ration of its theoretical basis.

We can deduce this law from the supposition that the magnetic
rotation is an additive property, and that the rotatory constant of
a mixture is therefore equal to the sum of a number ef terms, to
which each molecule contributes one. Let the condition of the mix-
ture be determined by the pressure p, by the temperature ¢ and for
the rest by assuming that in the unit of volume «N grammolecules
of one component are mixed with (l — )N of the other. Let
G'p,t,2 be the amount which a grammolecule of the first component
contributes to the rotatory constant, and g”p,11— the same for the
other component and let Nop, be the rotatory constant of the
mixture, then we find that

iOpen Nt Op, tue + N(L — 4) Opt, 1e
and therefore
Opt = On, ye U HO ne

The quantities opte, introduced here, which we might call
molecular rotatory power, will depend on the condition of the
molecules determined by p,t and ye. The way in which they depend
on these variables cannot be deduced from the observations without
the aid of a molecular theory, except in the case when « =0 and
we have therefore to deal with simple substances.

In applying this law we assume these quantities g to be constants
and then we can deduce them from those for the simple gases. Let
rand r" be the rotatory constants for the two gases at the pressure
p and the temperature ¢. Let further « and y be the volumes of
the two substances which we should have to mix in order to obtain
the unit of volume of the mixture, all these volumes being measured

1) Verslag Kon. Akad. 1894/95, p. 236. Comm. Phys. Lab. Leiden N°. 15 p. 26

( 300 )

at the pressure p and the temperature t. Then we may deduce
from the foregoing Jaw that

' Lik
n=ardyr

which expression agrees with the one assumed before. It may be
remarked that the quantities 7, 7’, 7", « and y are taken at one and
the same pressure p and one and the same temperature ¢, and moreo-
ver that on account of discrepancies from DaLTON’s law + may
differ from 1.

This law of mixtures deduced for gases, agrees, if the molecular
rotatory power is considered to be constant, with that which has
been adopted by Jaun'), Wacusmuru 2) and others for mixtures of
liquids and saline solutions.

4. Results. Bij applying the above-mentioned law of mixtures
we can calculate the rotatory constants ef the pure gases, as has
been shown before. The following table gives the coefficients of
the formulae

C C3 Cr dy
Dii SS fl —— ae 3 te
OS Sak aw ae aes = @)
Co C, Cy \ Ce dy
7 = —— = == 1 a 7 a aL
Sea aes (4 7e) al u el B

which represent the rotatory constants @, expressed in minutes, and
multiplied by 10°.

T ] ip TT

| pressure | temp. | C, | C; | d, | Cy C, Cs ds
| ne | I : —
Oxygen pe Kg. | 70.9 272.8] 19.15 0.0704) 296.7|— 48.03 |4 204 |
mixt. with 87.8°/,0) #1 » | 17°.0f 240.6) 23.30/0.097 || 249.1)/—30.57 (2.521
ny 6.070} » » | 179.6] 20.7) 40.98/0.904 || 210.1|— 7.71 (0,805
air ot 13°.0) 191.5) 46.19/0.241 | 216.3/—12.57 [1.410
nitrogen n mn | 14°.0) 171.2) 52.86/0.309 | 183.6 2.27 0.0124
hydrogen | 85.0 „ | 9°.5| 138.8) 45.1910.325 || 151.5] 2.38 0.0157
carbonic acid 1 atm. | gesl 2.682/0.8305/0 310 || 2.894) 0.0887 0.0116
nitrogen monoxide} 30.5 atm.| 10°.9 deel 22.95/0.303 || 81.26) 0.820 0.0101

1) Jann. Wied, Ann. 43, p. 284.
2) Wacusmutu. Wied, Ann. 44, p. 380,

( 301 )

The numbers given differ slightly from those communicated before !)
on account of a general revision of the calculations.

The law of mixtures may further be applied, as has been done
before *), to the mixtures of oxygen and nitrogen and the observed
rotatory constants may be compared with those computed from the
components. This comparison will prove very satisfactory in the
case of air, but less so in the case of the two other mixtures.

In fig. 12 curves are given showing the relation between
magnetic rotatory constant and wave-length, which are drawn by
making use of the values calculated from some of the communicated
formulae for interpolation. They prove clearly that the dispersion
of the magnetic rotation for all gases, oxygen excepted, is pretty
much the same. If we consider the large coefficient of magnetisa-
tion of oxygen, it becomes evident?) that the magnetic rotatory
dispersion depends on the magnetic properties of the substance, a
fact to which H. Becqueret has drawn the attention *).

It is a striking fact that the order of the gases examined, when
they are arranged according to the values of the coefficients d, and
dy, should be the same as the one found for the coefficients of
magnetisation. This appears from the annexed table:

d, de Q. 10° 2)

oxygen 0.0704 | —0.056 | 0.662

|
|

nifrogen monoxyde, 0.303 | +0.0101 | —0.158

nitrogen 0.309 0.0124 | —0.165

carbonic acid | 0.310 0.0116 | —0.172
|

hydrogen 0.325 0.0157 | —0.176

1) Verslag Kon. Akad. 1896/97, p. 132. Comm. Phys. Lab. Leiden N°. 31, p. 56.

2) Verslag Kon. Akad. 1895/96, p. 301; 1896/97, p. 132; Comm. Phys. Lab. Ley-
den, NO, 24 p. 10, N°, 31 p. 6.

*) H. BecQurreL. Ann. de Ch. et de Ph. (5) 12 p. 85. Comp. also Verslag Kon.
Akad. 1893/94 p. 31; Comm. Phys. Jub. NO. 7 p. 9.

*) The extraordinary large dispersion, observed by BrcQverer in substances with
negative magnetic rotation drew my attention to the negative constant which QuincKE
(Wied. Ann. 24. p. 615 (1885)] found in amber. A fresh measurement with a piece
of transparent, light brown amber of 1.78 cm. thickness actually showed negative
rotation. Yet it appeared that the emerging ray of light, even without the action of
the electro-magnet, was strongly elliptically polarized. In connection with the theore-
tical investigations on the magnetic rotation in doubly refracting bodies (Gour,

( 302 )

The fact that d, is almost the same for all gases with small
coefficients of magnetisation seems favourable to Mascary’s formula
which leads to a formula for interpolation of the form (1); coeffi-
cient vy in this form is related in a simple way to d,, and is accor-
ding to JoUBIN’s investigation *) in a high degree dependent on the
coefficient of magnetisation.

If we express the rotatory constants in circular measure instead
of minutes, we obtain the following coefficients

10.10 @ = C2 — EE CG ie

balken OF | Cs) | d, | Ca! | C,! Co! dy

ETT | | | |
Oxygen |109 Kg.| 7°.0) 792 58.7/0.0704!| §63/—139.7 |12.49
mixture with 87.84, O| » » 78.01 zool erzelonoor | 725|\— 88.9 | 7.33

” n 26.07 O)] v u 70.6! 5841119.1/0.204 | eli 22 43) 2.342
air | |13°.0) 567 184.4)0.24 | 629|— 36.57) 4.10
nitrogen y |14°.0) 498/153.8 0.309 || 534 6.60 0.0124
hydrogen | 85.0 Kg.| 99.5} 404 [131.510.3295 | 441) 6.92 0.0157
carbonic acid | 1 atm. | 69.5) 7.80/2.416/0 310 |) 3.49 0.0980 0116
nitrogen monoxide 305 atm 100205 66.8 0.303 (2304 2.385 0.0101

For practical use the following tavle may serve, which gives the
Pp Ors ) 5
magnetic rotatory constants for different wave-lengths, expressed in
minutes and multiphed by 10°.

Wiener) this result may easily be explained without assuming a negative rotatory
constant. Lt is not improbable that QuiNcKe’s result may be accounted for in a
similar way.

*) According to a formula for interpolation (LL) with two terms, which is not
mentioned in this paper.

2) QuiNcKe’s constants relutive to air. TöeLeR and Hennig. Wied. Ann. 34, p. 790
(1850).

*) Jousry. Thèse Paris 1SSS, p. 24. Ann. de Ch. et de Ph. (6) 16, p. 78 (1889).

( 303 )

5 T = 5 ] | .
| mixture | mixture nitrogen

A oxygen | _ with with | air | nitrogen | hydrogen) oxygen Gnas

| \s7 8°/, Ol26.0%, O|
| | | |

pressure | 100 Kg. | 100 Kg. 100 Ke. | 100 Kg. | 100 Kg. | 85.0 Kg. | 1 atm. [90.5 atm.

temp. oes erdee PATE 137.0) 1490 | “9°.5. || VOEG ENNKTEEND

0.493) 908 | 877 | 1074 | 1062 | 1097 | 921 | 17.98 | 480
431| $75 | 849 | 1033 | 1020 | 1054 854 | 16.56 | 461
454| 799 | 779 | 930 | 914 O44 791 | 14.83 | 413
486 | 721 695 812 797 815 684 | 12.86 | 359
517| 663 | 634 | 790 707 719 600 | 11.30] 315
597| 646 | 616 694 682 691 576 | 10.86 | 303
555| 604 570 628 618 620 | 517 9.75 | 272
589| 559 22 | sl 553 548 456 8.62 | 241
619) 523 | 487 | 510 504 495 412 | 7.78 218
656| 484 449 | 457 | 459 439 365 | 6.91 | 193

eo | 0.531 | | | 0.559 | 0.563 | 0.570 | 0.838 | 0.616

In the last line of this table the values of the molecular rotatory
power for Na-light divided by that of water, are given according
to the example of Perkin !). Although it appears from his investi-
gations and those of others that the calculation of the molecular
rotatory power of a chemical compound as the sum of that of its
atoms does not hold good throughout, it may be interesting to
compare PeRKIN's atomic rotations with those resulting from our
observations. From the above-mentioned values of the molecular
rotatory power foilows for 1 atom:

00205
N= 0:281
He 0235

Perkin finds for oxygen 0.194 or 6.261 according to the way
of composition, and for hydrogen 0.254, numbers as we see of the
same order. PeRKIN's number 0.717, calculated for nitrogen in amines

1) Perky. J. of Chem. Soc. 45, p. 421 (1884), and following volumes.

( 304 )

does not agree with our number; neither is our value of N,O to
be composed from PRRKIN’s atomic values.

If following Perkin we take in CO, for 1 atom carbon 0.515,
we find Os = 0.323, which would be more agreeable to the value
0.39, which Hiyricus!) deduced from organic acids. Taking everything
together the agreement is fairly well, except for nitrogen.

*) Hiyricus. C. R. 113, p. 500 (1891).

(February 254 1899.)

.

q

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING

of Saturday February 25th 1899.

IIET

o
(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 25 Februari 1899 Dl. VID.

Contents: „On the orthoptical circles belonging to linear systems of conics.” By Prof. JAN DE
VRIES, p. 305. — „On solubility and melting point as criteria for distinguishing racemic
„combinations, pseudoracemic mixed crystals and inactive conglomerates.” By Prof.
H. W. Bakuvis Roozesoom, p. 310. — ,,A geometrical interpretation of the invariant

2 - pe 2 P > .
Tl (ab)? of a binary form a™” of even degree.” By Prof. P. H. Scnourte, p 313. —
n+l
„On the deflection of X-rays.” By Prof. H. Haca and Dr. C. H. Winn, p. 321. —
Prof. B. J. Srokvis presents the dissertation of Dr. G. Berraar Spruyr: „On the
physiological action of methylnitramine in connection with its chemical constitution,”

p- 321. — „On a simplified theory of the electrical and optical phenomena in moving
bodies.” By Prof. H. A. Lorenrz, p. 323. — ,,SroKkes’ aberration theory presupposing
an ether of inequal density.” By Prof. H. A. Lorentz, p. 323. — ,,Measurements on

the system of isothermal lines near the plaitpoint, and especially on the process of the
retrograde condensation of a mixture of carbonic acid and hydrogen.” (Continued). By
Dr. J. VeRSCHAFF «LT, (Communicated by Prof. H. KaMERLINGH Onnes), p. 323. (With
one plate). — ,,Measurements on the change of pressure by replacing one component
by the other in mixtures of carbonie acid and hydrogen.” By Dr. J. Verscnarretr,
(Communicated by Prof. H. KAMERLINGH ONNES), p. 328. —,,On the velocity of electrical
reaction.” By Dr. Ernst Cowen, (Communicated by Prof. H. W. Baxuuts RoozeBoom),
p- 334. — Prof. A. P.N. FRANCHIMONT presents the dissertation of Mr. L. T.C. Scury:
„On synthetically prepared neutral glyceryl-ethereal salts — triacylins — of saturated
monobasic acids with an even number of C-atoms,” p. 338. — „On the Vibrations of
Electrified systems, placed in a Magnetic Field.” By Prof. H. A. Lorentz, p. 340.

The following papers were read:

Mathematics. — „On the orthoptical circles belonging to linear
systems of conics.” By Prof. J. pe VRIES.

1. The locus of the points through which we can draw ortho-
gonal tangents to the conic

a Ë
Say at al

Proceedings Royal Acad. Amsterdam, Vol. I.

( 306 )

is the circle represented by
e®+tyo—(At+ BC.

This orthoptical circle (Moner’s circle) is real for the ellipses
and the hyperbolae situated in the acute angles of their asymptotes,
and imaginary if the hyperbola lies in the obtuse asymptote-angles;
it degenerates into a point for the rectangular hyperbola (A+B=0)
and for the system of two right lines (C=0). With the parabola
it is represented by the directrix.

The orthoptical circle being concentric with the conic to which
it belongs, the centres of the orthoptical circles @ of a pencil of
conics lie on the conic y, containing the centres of the pencil.

If now, following Mr. FIgEDLER, we represent each circle by the
vertices of the two right cones of which it is the base-circle, the
system (@) is represented by a skew curve of the 4 order (2,
Indeed, each plane perpendicular to the plane V of the orthoptical
circles intersects the conic in two points and bears two pairs of
poiuts representing orthoptical circles.

The skew curve 2, being intersected in four points by a plane
parallel to V, there are in (@) four circles with given radius.

So the system (@) contains four point-circles; it is evident that
we find these in the double points of the three degenerated conics
and in the centre of the orthogonal hyperbola belonging to the
pencil.

2. The system (@) contains two orthoptical right lines, viz. the
directrices of the two parabolae in the pencil. Each of these lines
is represented by two planes inclined to the plane V at angles of
45°, i.e. parallel to four generatrices of each rectangular cone 4/3
having its vertex in a point P of V and placed symmetrically with
respect to this plane.

The cone 11, bearing the images of all the circles through P, and
the above named four points at infinity representing two right lines
not passing through P, the remaining four points of intersection
of I, with Q, will represent two circles (@) intersecting in P.
Therefore :

The orthoptical circles of a pencil of conics form a system with
index two.

This can also be shown as follows. The tangents through P to
the conics of the pencil are arranged in a (2,2)-correspondence,
each ray through P being touched by two curves. Tais system has

( 307 )

two pairs of rays in common with the involution of the lines,
intersecting in P at right angles; so through P pass two circles @.

Two planes intersecting the plane V in the right line / at angles
of 45° have four pairs of points in common with the curve (24.
This shows that Z is touched by four orthoptical circles. Their
points of contact are the coincidences of the (2,2)-correspondence,
determined on / by the system (©).

3. If we represent the form
Hy +ax+ by +e
by C, the system (@) is represented by the equation
Ch A0.

The power of the point (#, 4) with regard to the circle indicated
by a definite value of 2 is then represented by
HENNEP
ft 27 23

This expression becomes independent of À if we assume the radi-
cal centre of C, Co, C3 for («, y). So all the circles @ have a com-
mon radical centre or, in other words, all orthoptical circles cut a
fixed circle 4 at right angles.

As 4 must bear the point-circles of (@) we may conclude to the
following theorem:

The circle through the diagonal points of a complete quadrangle
contains the centre of the orthogonal hyperbola determined by the ver-
tices of the quadrangle. Through its centre pass the directrices of
the parabolae which can be drawn through those vertices.

Considering the obtained results as a property of the rectangular
hyperbola it can be expressed in the following terms:

The diagonal points of each complete quadrangle inscribed in a
rectangular hyperbola can be connected by a circle with the centre
of that curve.

4. All circles @ being orthogonal to the fixed circle / their
images lie on the orthogonal hyperboloid of revolution with one
sheet cutting V in / at right angles.

So the image , is the section of this hyperboloid with the eylin-
der, which is orthogonally cut by V in the eonie 7.

21*

a

( 308 )

When the base points of the circle form an orthocentric group ?)
all the conics are rectangular hyperbolae; so the system (@) consists
entirely of point-circles.

The orthogonal circle 4, bearing them, passes through the diago-
nal points of the complete orthogonal quadrangle and coincides with
the circle of FEUERBACH (nine-points circle), containing as is known
the centres of all the orthogonal hyperbolae through the vertices and
the orthocentre of a triangle.

5. According to the method of FirpLer the orthoptie circles
of a net of eonies will be represented by a surface, intersecting the
plane V of the net in the locus of the orthoptical point-circles.

Any point P determines a pencil belonging to the net, one of
the base points of which is P; so through P passes an orthogonal
hyperbola. From this follows, that the orthogonal hyperbolae form
a pencil situated in the net. As was said above the orthoptical
point-circles of this pencil lie on the circle 4, passing through the
diagonal points and the middle points of the six sides of the qua-
drangle of the base points.

The remaining point-circles are centres of pairs of lines and
form the cubic curve, called the HessraN of the net.

Three pairs of lines of the net belong to the pencil of orthogonal
hyperbolae and consist of orthogonal right lines. The double points
must lie on the HessIAN as well as on the circle 4; so these curves
must touch each other in three points.

Both loci of point-circles forming together a curve of the 5t order,
the image of the system of orthoptical circles is a surface of the 5 th
order Sz. A

Each right line of V is touched in each of its points by one conic
of the net; each right line determines the direction of the axis of
a parabola belonging to the net. From this follows, that the point
at infinity of each right line cutting V at angles of 45° is to be
regarded as the image of an orthoptical right line.

So the points of contact of the asymptotes of the rectangular
hyperbola representing all the circles through two points belong to
the ten points common to S; and that hyperbola. The remaining
eight points of intersection representing four circles it is evident
from this that we can draw four orthoptical circles of the system
through any two points.

1) That is to say: four points, each of which is the orthocentre of the triangle
having the others for vertices.

( 309 )

6. It U, and U, represent the differential quotients of the qua-
dratic function U with regard to z and y, the centres of the conics
of the net

OLAV + uW=0
are indicated by the relations

Us +iV2+ uWe=0,
Uy + AVy + eW, = 0.

So in general any point («,y) is the centre of one conic. On the
other hand any of the four points determined by

WER: 0, = Ven: Vi W.: W,

is the common centre of an infinite number of conics. For each of
these points the above mentioned linear equations are dependent of
each other, so that 4 and w are connected by a linear relation; so
in this way a pencil of conics is characterized.

Consequently the surface S; contains four right lines perpendi-
cular to V.

7. Let us now consider the orthoptical circles belonging to the
conics with four common tangents. Any right line through the point
P determining a conic of the tangential pencil, the tangents through
P form an involution. This contains only one pair of rectangular
rays; so P lies on one orthoptical circle.

The wellknown property according to which the centres of the
tangential pencil lie in a right line, also proves that the orthoptical
circles of a tangential pencil form a pencil.

According to the cireles of that pencil passing through two fixed
points or intersecting a fixed circle orthogonal or touching each
other in a fixed point, the system (@) will be represented by a rec-
tangular hyperbola with its real axis perpendicular to V or situated
in V, or by two right lines cutting V at angles of 45°.

So the system (@) contains no more than two point-circles or, in
other words, the tangential pencil can contain only two rectangular
hyperbolae.

A conic of the tangential pencil degenerating into two points, the
line joining these points is the diameter of the corresponding @. In
connection with the statement above the wellknown property results
from this:

The circles described on the diagonals of a complete quadrilateral
as diameters belong to a pencil.

( 310 )

8. Finally we consider a tangential net.

Two right lines through P which intersect at right angles are
touched by one conic of the net. If the right angle included by
these lines turns about the vertex P the pairs of tangents drawn
through Q to the variable conic form an involution. For every ray
s, drawn through Q, determines a tangential pencil belonging to the
net, having the pairs of an involution (7, 7’) in common with the point
P. The eonie touched by the orthogonal pair (7, r') has a second
tangent s through Q, forming with s a pair of the involution indi-
cated above. The orthogonal pair (s, s') determining a conic for
which # and +’ are at right angles to each other, we can draw but
one orthoptical circle through the points P and Q.

According to the circles (@) possessing an orthogonal circle or
intersecting a fixed circle in two diametrically opposite points or
passing through a fixed point, the obtained net of circles is repre-
sented by an orthogonal hyperboloid of revolution with one or two
sheets or by an orthogonal right cone.

Chemistry. — “On solubility and meltingpoint as criteria for
distinguishing racemic combinations, pseudoracemic mixed crystals
and inactive conglomerates.” By Prof. Baxnuris RoozeBoom.

Though several times attention has been drawn to the phenomena
of solubility and melting in order to distinguish between the types
mentioned above, no certainty has been attained as yet.

1. Solubility. We only get a clear insight in the phenomena of
solubility by drawing attention to the number of solubility curves
obtainable at a given temperature.

If Oa is the proportion of the
? B saturated solution of the dextrosub-
stance D, and Ob the same for the
laevosubstance L, these t wo are equal

at the same temperature.
3y adding L to the D-solution
SJ] and vice-versa we now get, if no
racemic combination appears at the
temperature used, nothing else than
two solubilitycurves, starting from
0 d a the points a and 5 and meeting in
Fig. 1. c. Their precise direction depends on
the manifold actions that can take place in the solution. From
the perfect equivalence of L and D it results however necessarily
that ¢ must always lie on the line OB, which halves the angle of

s

(311)

the axes, so that the solution which is equally saturated with L
and with D is inactive, no matter how great the excess of L or D
with which it is in contact.

If at another temperature a racemic combination is possible, we
get three solubility-curves de, efy and gh. The second regards the
solutions of the combination; here f represents the pure solution, ¢
and g those which are acquired in presence of an excess of Dor L.

At the transition temperature the curve in the middle disappears
(point A). Here too the solution is always inactive. If therefore an
inactive substance is a conglomerate (by which I mean a solid mix-
ture in which the components lie side by side separately) of L and
D, we shall never get as a saturated solution anything else than
point c; if the substance is a combination we can get three solu-
tions, as we dissolve it alone or with an excess of L or D.

Phenomena observed at evaporation. On this subject experiments
have lately been made by Kippina and Porp. From the figure of
the solubility-curves it is easy to deduct, in the graphic manner first
instituted by ScHREINEMAKERS, that in case of the evaporation of a
solution containing an excess of D or L, the solution arrives at last
in point ¢ — that is to say becomes inactive in case no racemic
combination exists at the temperature used. If on the other hand
this combination does exist — we arrive with an excess of D to
a final point in e, with an excess of L in g.

In this manner it would be equally possible to make out what is

deposited: conglomerate or combination — if in these evaporation
experiments care were always taken that the necessary crystallisa-
tionnuclei were present — a circumstance to which K. and P. have

paid no attention.

Partially racemic combinations. These have lately been discovered
by LADENBURG and been studied with a view to the solubility in
D- and L-strychninetartrate.

The symmetry of fig. 1 disappears in that case owing to the
unequal solubility of the two components. Consequently point A
will generally lie no longer on OB. It results therefrom that the
combination, even before its transition-temperature is reached, already
possesses a temperature-interval of partial decomposition. So Mr. LADEN-
BURG is wrong in the opinion that this combination in its transition-
temperature must furnish a solution, containing an equal amount of
D- and L-tartrate.

At temperatures situated in the decomposition interval, we now
only get two kinds of solutions in case the combination is dissolved
alone and with an excess of D or L.

( 312 )

Pseudo-racemic mixed crystals. As I demonstrated on a former
occasion, mixed crystals must be considered as one solid phase. For
mixed crystals formed of optical antipodes, if they exist, it will per-
haps be possible to appear in every proportion. In such a case we
should only get one solubility-curve in fig. 1, connecting the points a
and 6 and being symmetrical again.

If at lower temperatures, a racemic combination should appear,
the continued mixing-series would be broken by it. The sketch of
the solubility curves would consequently be altered in so far that
the lines WA and CA would pass into one continuous curve. The
evaporation phenomena would equally be altered.

II. Melting points. The opinion exists
that a higher melting point is a proof of a
racemic combination when compared with the
melting point of the antipodes. Uncertainty
exists when the melting point of the inactive
E F substance is equally high or lower.

Here too, it is only the study of the
melting- and congealingeurves along their
entire lengths, that can give us sufficient

L D certainty.

If no combination, nor mixed erystals exist,
fig. 2 must give the groundplan for the
congelation. ‘The mixing proportions of L
and J are indicated on the horizontal axis,
the temperature on the vertical. A and B
are the melting points of L and D. AC is
the congealing-line for liquids depositing L,
BC for such as deposit YD. Every mixture
congeals at last in C to an inactive conglo-
merate of L and D. If on the other hand
there is a racemic combination, two types
are possible, represented by fig. 3 and 4.
In these C is the melting point of the com-
bination, which is higher or lower than the
melting points A and B. Independent of
this fact, the congelation now leads to three
curves, the one in the middle representing
the case that the combination is deposited.
It has two branches.

If, to end with, there is a continual mixing-
series, there will be but one congealing
curve. But the latter need not be, ina repre-

sentation as the one used here, a horizontal line connecting A and
B-as was the opinion of Krpprna and Pope, but may quite as well
show a maximum or a minimum, which then however lies at 50
pCt. I even suspect such to be the case in camphersulfonie chlorid
and earvontribromide.

According to these views, neither a higher nor a lower melting-
point furnishes a proof on the nature of an inactive substance, but
the study of the entire melting-line does.

A single curve serves in case of mixed crystals, two curves in
case of an inactive conglomerate, three in case of a combination.

Other remarkable phenomena may still present themselves, in
case transformations of the combination, mixture or conglomerate
appear after the congelation.

Mathematics. — “A geometrical interpretation of the invariant
IT (ab)? of a binary form a?” of even degree’. By Prof.
n+1

P. H. ScHouTE.

With regard to the creation of the beautiful theory of the in-
variants undoubtedly very much is due to SYLVESTER as well
as to ARONHOLD, Boor, BRIOSCHI, CAYLRY, CLEBSCH, GORDAN,
Hermite and others. As early as 1851, indeed, he developed in his
treatise: “On a remarkable discovery in the theory of canonical forms
and of hyperdeterminants” (Phil. Mag., Vol. IL of Series 4, p.
391—410) the foundation upon which the theory of the canonical
forms is based. The principal contents consist of the proof of two
theorems. According to the first the general binary form of the odd
degree 2n—l1 can always be written in a single way as the sum
of the 2n—lst powers of „ binary linear forms; according to the
second the binary form of the even degree 2 can be written as
the sum of the 2x‘ powers of » binary linear forms — and in
that case in a single way too — only when a certain invariant
vanishes. For this invariant with which we shall deal here compare
a.0. GUNDELFINGER’s treatise in the “Journ. f. Math”, Vol. 100,
p. 413—424, 1883, and Satmon’s “Modern higher algebra”, 4% ed.,
p. 156, 1885. So the theory of invariants of a certain form of any
kind is ruled by the question about the minimum number of ho-
monymous powers of linear forms by which it can be represented.
(Compare a.o. Reyr in the “Journ. f. Math’, Vol. 73", p. 114—122).
With this the theory of involutions of a higher dimension and order
are closely allied. Likewise theorems ere deduced from it relating to

( 314 )

hypergeometry. For all this we refer to two important papers by
Mr. W. Fr. Meyer. The first, published at Tübingen 1883, is entitled;
“Apolarität und Rationale Curven”’; the second, inserted as “ Bericht
über den gegenwärtigen Stand der Invariantentheorie’ in the 1s Vol.
published in 1892 of the “Jahresbericht der Deutschen Mathematiker-
Vereinigung’’, is an invaluable report about this branch of Mathematics.
On page 365 of the former work a theorem appears under 74
which is closely connected with our subject.

It goes without saying that it must be possible to reach con-
versely the above quoted theorems of SYLVESTER and the higher invo-
lutions connected with them starting from the theory of poly-
dimensional space. Indeed, Mr. Crirrorp has stated already in
1878 in his important treatise “On the classification of loci” (Phil.
Trans., Vol. 169, part 2nd, p. 663—681) that in this direction a
geometrical interpretation of any invariant of a binary form is to be
found. So in trying to determine a certain locus in space with an
even number of dimensions I have fallen back upon a geometrical
interpretation of the invariant of SYLVESTER; however examining
the above mentioned literature I soon discovered that this interpre-
tation had already been found.

Yet I wish to publish my study. In the first place because it may
prove that the geometrical way is at least equally simple as the
algebraical. Secondly on account of its containing a method of eli-
mination I have as yet nowhere met with in this form. Thirdly
because it is not quite impossible that entirely corresponding inves-
tigations may lead to a geometrical interpretation of other general
invariants }).

1. A curve allows of a twofold infinite number of chords, con-
taining together a threefold infinite number of points. If this curve
is situated in the space S* with three dimensions these points will
fill the whole space and one or more of these chords will pass
through any given point. If the curve is situated in the space S*
with four dimensions the locus of the points through which chords
pass, ie. the locus of those chords themselves, is a curved space of
the third order. The point from which we start here is the investi-
gation of this curved space for the simplest possible case, namely

6 D 3 . On > nD 5

1) I think e.g. of the invariant (ad)” (ed) (ae) (ld) of a general binary form gna

of odd degree (compare SALMON |. ¢., p. 129, problem 24) forming an extension of

the discriminant of az’, of which as yet no general algebraical interpretation seems
known.

(315 )

that of the normal curve of the space S* that is of the rational C, of
the fourth order, represented by the equations:

where zo, 21) #2, 25, a, are the homogeneous coordinates of the
point Z of the curve belonging to the parameteryalue A.

2. If A, and 4A, are the parametervalues of any two points Zj
and Zy on Cy, the coordinates of any point A of the line joining
LE, and Ly are given by the relations

ii) ase + P2

mn = pydy + pads

ty = py Ay? + Py Ag? Sy tor NLD)
as = py Ay? + py Ag?

&4 = pr Af + pa dot

and now by eliminating the four quantities 4), 42, pi, py we find
the equation of the locus required.
The result of this elimination is the cubic curved space
To Tj To
Fiene 0 A sens « (8)

quit ck
For if
Pi + Pa pi da + pede pi Ay? + pa Ag?
Pid, + pods Py Ay? + pa Ag? Pr Ay? + pg Ag?
Dray? + po he? =p A+ poke? =p. Ag* + po Ag*

is written down, it is immediately evident that every combination
of partial columns vanishes after easy simplifications, two of the
three columns being equal to each other’).

1) As I already stated above, [ nowhere met with this simple deduction of the
invariant of SyLvrster which can be pursued through all spaces $2", In the original

( 316 )

3. The osculating space belonging to the point L of C4 has for
equation

ay At — Ax M4620 —4ea,d4+a,=0 . « . (3)
So the coordinates «,, 2), #2; «3, v4 are the coefficients of the form
ag (— A)* + 4 ay (— A)? + 6 ay (— A)? + dag (— A) 4 24

of the fourth order in (— A), bare of the binomial factors.

So the result (2) can be written as j = 0 and represented symboli-
cally by (be)? (ca)? (ab)? = 0 (see a. 0. CLEBSCH-LINDEMANN's “ Vorle-
sungen über Geometrie’, I, page 229). From this ensues at the same
time that any point of the obtained locus is distinguished moreover
from any point taken at random in the space S* by the property that
the four osculating spaces of Cy passing through it belong to four
harmonic points of the curve. We shall point this out more directly.
We suppose in the formulae (1) the quantities A), 42,~1,p2 to be
given; then by substituting in (3) the values ensuing from this for
vz we shall find

Pi (A—A,)* 4- Pa A—Àg)* =S) « ane ears (4)

as the equation which gives us the parametervalues of the four
points L of Cy, whose osculating spaces intersect in the point A
of the line Z, Zz given by (1). If for convenience’ sake we take the
points Lj and Ly as base points with the parametervalues 0 and oo,
this equation can be reduced to A*—1—0 and the roots 1, —1,
V—1, —V—1 show immediately that the pairs of points belonging
to (1,—1) and V—1,—V—1) separate each other harmonically,
whilst each of these pairs behaves in the same way with reference
to the pair of base points Zj Ly belonging to (0, %). By this, not
only the harmonie position of the four points (4) has been indicated
but moreover the following theorem has been proved:

“Any two points Lj, 2, on Cx determine on this curve a qua-
“dratic involution Z, of which they are the double points. If ot
“this J, we join two pairs separating each other harmonically we
“get the biquadratic involution J, represented by the equation (4)

work (Phil. Mag. Le.) first a binary form of odd degree is discussed and the
invariant belonging to forms of even degree are reached at the end by a round-about
way. In SALMON (1. ¢.) and otherwhere the determinant is regarded as an extension
of the covariant of Hesse built up out of second differentialquotients, here differen—
tialquotients of the 4th order, etc.

( 317 )

“characterized by the particularity that each of the two points
“L,, Ly counted four times represents a quadruple of it. The oscu-
“lating spaces belonging to the points of any quadruple intersect in
“a point A of Z,Z,. And if this quadruple describes 7; , the point
“A generates on Lj Lj a series of points in projective correspondence
“with Zu”

Moreover we easily find !):

“If A and A’ are two points of the line 2,2, harmonically sepa-
“rated by Zj and Ly, the quadruple of 7, belonging to A has the
“combination of Lj and Zy with the quadruple of Z, belonging to
“A' for its sextic covariant 7. And combination of the quadruples
“belonging to A and A’ generates an involution of the eighth order.”

The indicated /s is represented by the equation

py (A — Ay)> — pa? (A — Ap) = 0;

so it is characterized by the particularity that each of the two points
Ly and Ly counted eight times represents an octuple of it.

4. We now pass to the space S® and there we determine the
locus of the planes having three points Zj Le L3 in common with
the normal curve C;

of that space. This is obtained by eliminating the six quantities
iy Ao» 43) Pry Pas Pz between the seven relations

p= py dy! + pg Age padt «ce «so (8)

where & must take the values 0, 1,...5, 6. In quite the same way
as above we find here the curved space S4 with five dimensions of
the fourth order represented by

vy vy) V9 Us

|

| % Up) v3 C4 | F
oP) Ts vy ts |

| |
ve Ly ts TG

1) In fact, the form 7’ of a,4 + aat is a wa (wf F a5"),

( 318 )

The first member of this equation is again an invariant of the sextic
Eft (— Je +- 6 vj (— A) = 15 Bo (— At + ome! va +. 6 Ls (— A) -- Los

which made equal to nought indicates the osculating space belonging
to the point L.

Now we find in the ordinary manner by passing to the use of
symbolic coefficients and by noticing their mutual equivalence that
the indicated invariant may be represented by (ab)*(ac)?(ad?) (be)?(bd)*(cd)”.
Naturally if the invariant!) vanishes there is a connection between
the six points of C; whose osculating spaces pass through the point
A of the plane Zj Ly Zs indicated by the formulae (5), for substi-
tution of the values following out of (5) for the seven coordinates
az in the equation of the osculating space of the point ZL gives

py (A — Ay)® + po (A — Ag)® + pz (A— Ag)’ = 0. . . (6)

So we have the following theorem :

“Any three points Zj, Lo, Lz; on C determine on this curve an
“involution J, of the second dimension and the sixth order of which
“each of the three points counted six times represents a sextuple.
“The osculating spaces belonging to the points of any sextuple inter-
“sect in a point A of the plane Lj Lo Ly; if the sextuple describes
“7,2, the point A generates in the plane Lj Ly Zg a plane system in
“projective correspondence with J,?.”

The considered invariant of a,° is indicated by SYLVESTER as
“catalecticant” because its vanishing is the condition under which
az> can be represented as the sum of three sextic powers; in con-
nection with this an az° allowing this reduction is called a “meio-
eatalectic”’ sextic (Phil. Mag. |. ce. page 408).

5. Finally we examine in the space S” the locus of the linear
space Sn! having 2 points Z,,Z,...Z, in common with the
normal curve C5, represented by

SS

1) If according to the common notation f=az° and L=(f, f)'= (eb) a2? be? =
the fourth transvectant of f with itself, then the indicated invariant is the fourth
transvectant (4% 4) of Z with itself (see GORDAN-KIRSCHENSTEINER “Vorlesungen über
Invariantentheorie”, Vol 2, page 286).

For the following case /=az* we have got to deal with an invariant of the fifth
order in the coefficients. There being (see a.0. VON GALi’s two papers in the “Math.
Ann.” Vol 17, p. 31—51 and 139—152, 1890 on “Das vollständige Formensystem einer
bintiren Form achter Ordnung”) but one invariant of this kind, our invariant must in
this case correspond to the one indicated by the sign /#x,

( 319 )

__Tan—l __ Tan
ia. j2n—1 = }2n É

For this the 2 quantities Aj, 49, . . « Any pis Pa « « + Pn must be
eliminated between the 27” + 1 equations

R= Spd, . Pee nome (CU

where successively 0, 1, ...2n—1, 2m has to be substituted for 4.
In the indicated way we shall get the result

Xo Ti Gr oe 0 Gine Lx
|
| & Vg T3 tre En +1
v9 v3 T4h ee En +1 Tr +2
—OPN(S)
T—1 En Tr+1 + + T2n—2 LIn—1
Un Un +1 LnH2 + + LIn—1 Tan

}

Likewise in this general case the left hand member of this equa-
tion represents an invariant of the binary form of the 2nth degree
in (—2), which made equal to nought indicates the osculating space
belonging to the point Z of 4. In symbols this invariant is indica-
ted by LNG b)? where J/ is the general sign of multiplication and

where the index x + 1 points to the fact, that the multiplication
must be extended to the 4(n +1) factors (ab)? which can be
formed of x + 1 set of coefficients a, b, c‚ .. .}).

By substituting the values (7) in the equation of the osculating
space we find

in

eT ri Bc ce) fok vo (EN
=a

that is to say:

*) Probably the general notation m (a)? makes its first appearance here. At
- n+l
least I found everywhere the notation in the form of a determinant and nowhere
a symbolic representation nor a reduction to transvectants.

( 320 )

“By taking on the normal curve Co, the m points Zj, Lg,... Ln
n—l

“arbitrarily we determine on it an involution J of the dimension

2n
“n—1 and the order 2n, of which each of those # points taken 2n
“times forms a group. The osculating spaces belonging to the 2n

“points of any group of that involution intersect in a point A of
3 n—l deo . . . .
“the linear space S, , containing the » given points; if this group

B 2 > Dl e . n==l A
“describes the involution J; the point 4 generates in S , a linear

. . : : n-—1
“system in projective correspondence with 4 .”

As far as I am aware of up to now a polydimensional interpre-
tation suiting all values of m is known of three general invariants,
namely of the discriminant D, of the invariant (ab), and of the

a n . .
invariant of SYLVESTER dealt with here. If 2_, is again the equa-
tion of the osculating space of the normal curve 7 = Àk, (k= 0, 1,...n)
in the space with # dimensions, corresponding to the parametervalue

A, then D=0 represents as is known the curved space Sale
with n—1 dimensions of the order 2 (n— Ll) which is enveloped by the
osculating space if A varies; leaving alone the supposition n = 2, which
has no sense, we get that n=3 gives in the ordinary space the develo-
pable surface having the cubic normal curve of that space as cuspidal

line. According to CLIFFORD (l.c) (ab)?r = 0 is in the space s”
the quadratic curved space Se with 2n—1 dimensions repre-
senting the locus of the point lying in a space Se with the points
of contact of the 2 osculating spaces of the normal curve of that

space Se passing through this point; whilst the corresponding inva-

3 D nl % :
riant (ab)2"-! of the normal curve of the space Ss” vanishes iden-

tically and the indicated particularity presents itself there, compare
the case of the skew cubic in our space, for any point.

For the case »=4 the invariant (ab)f=0 is identical with i=0
(CLEBSCH-LINDEMANN l.c.) and at the same time the condition that
the four points of contact of the osculatingspaces through any point
of the locus form an equianharmonic quadruple. Moreover D is a
linear combination of # and j?, from which finally ensues that any
plane cuts the space D = 0 according to a curve of the sixth order,
having the six points of intersection with the surface of intersection

of both spaces i=0,j=0 for cusps; in each of these points the
section of the plane with the osculating space of j —=0 form the
cuspidal tangent. As is known the space D= 0, also by the aid of
its double surface i= 0, j= 0, divides the space S* into three parts
containing the points for which the number of the real osculating
spaces passing through them is successively 4, 2 and 0.

Physics. — Prot. HaGa made, both on behalf of himself and Dr.
C. H. WinD a communication: „On the deflexion of X-rays”.

Deflexion of X-rays was proved on the experiment being arranged
as follows:

The RÖNrGEN-tube was placed behind a slit 1 em. high and
14 microns wide; at 75 em. from the latter was the diffraction slit,
which gradually diminished in width from 14 to about 2 microns.
The photographic plate was placed at 75 cm. from the diffraction
slit. Time of exposure from 100 to 200 hours. The image of the
slit first became narrower and then showed an unmistakable broa-
dening. From the width of the part of the diffraction slit corres-
ponding to this broadening and the character of the broadening an
estimination can be made of the wavelength. It appeared that X-rays
exist of about 0.1 to 21/. ANGSTROM units, comprissing 4 octaves.

(A detailed paper will appear in the Proceedings of the next meeting).

Physiology. — Prof. Sroxvis presented for the Library the
inaugural dissertation of Dr. G. BELLAAR SPRUYT: „On the
physiological action of methylnitramine in connection with its
chemical constitution.”

At different occasions our member Prof. FRANCHIMONT exposed
in our meetings his views about the chemical structure of nitra-
mines, especially of methylnitramine. Till yet the question about
the intimate chemical constitution of these compounds, in reference
to the manner, in which their nitrogen is linked with the other
elements, is an open one. Whereas some authors believe, that the
nitrogen of nitramines is linked with hydroxyle, so that the whole
compound is a species of nitrite: H—O—N=O, Prof. FRAN-
CHIMONT rejects this view, and considers it linked in a cyclical

0)
as As Prof. FRANCHT-

O
way, for instance HN? | or H—N
| NO SO
MONT considered it of some value to study the physiological action
of nitramines, to the aim of throwing more light on the open
22

Proceedings Royal Acad. Ainsterdam, Vol. L,

( 322 )

chemical question, Dr. Spruyr took the matter in hand in the
Pathological Laboratory of Amsterdam. In applying to nitramines
and nitrites the well known law of the relation between chemical
constitution and physiological action, which is best expressed in
this formula: “compounds of homologous chemical structure possess
homologous physiological action,” we may conclude, that if nitra-
mine should belong really to the group of nitrites, its physiolo-
gical action must be also that of a nitritecompound. The physiolo-
gical action of nitrites is a well known one. They are all toxic
substances. Dr. Spruyr considered it as a first step in his researches
to state the physiological effects common to all nitrites without
exception, to the nitrites as well derived from alcoholic radicals,
as to the simple alkali-nitrites. As such he found invariably:

1st the formation of methaemoglobine out of the haemoglobine of
the blood in the living body as well as in the blood “in vitro”;

2nd dilatation of the arteriolae, and rapid sinking of the arterial
bloodpressure ;

3rd injurious effects on the intensity of the contraction of the
isolated frog’s heart, as fast as the nitrites circulate with the blood
through it;

4th paralysis of the nervous system in frogs, convulsions in
mammalians.

In experimenting on frogs and rabbits with methylnitramine-
natrium, dissolved in a physiological salt-solution, Dr. SPruYT never
found one of the essential phenomena, which are produced by
nitrites. The methyl-nitramine-natrium compound behaved itself in
the animal body and its liquids on the contrary as a fast indiffe-
rent substance.

If we consider, that nitrite of amyle C? H'Y—O—N=O is one
of the best known nitrites, with an eminent toxic action, in which
all the physiological effects of nitrites are represented in the most
typical way, and if we pay attention at the same time to the
remarkable fact, that Scrapow in his study of the physiological
action of nitropentan, which is an isomeric compound of nitrite of
amyle never met with one of the essential phenomena, produced
in animals by nitrites, the conclusions, which Dr. Spruyr arrived
at, are easily conceived. ‘These conclusions are: that the study of
the physiological action of methylnitramine makes highly probable
the opinion of FRANCHIMONT about its chemical structure (nitrogen
linked in a cyclical way), and is in direct contradiction with HANTscu’s
hypothesis, that it should contain nitrogen linked to hydroxyle, and
belong to the nitrite-group.

( 323 )

Physics. — „On u simplified theory of the electrical and optical
phenomena in moving bodies”. By Prof. H. A. Lorentz.

(Will be published im the Proceedings of the next meeting).

Physics. — „SroKes’ aberration theory presupposing an ether of
inequal density”. By Prof. H. A. Lorentz.

(Will be published in the Proceedings of the next meeting),

Physics. — „Measurements on the system of isothermal lines near
the plaitpoint, and especially on the process of the retrograde
condensation of a mixture of carbonic acid and hydrogen”.
By Dr. J. VERSCHAFFELT. (Continued). (Communication n°. 47
from the Physical Laboratory at Leiden by Prof. H. Kamer
LINGH ONNES).

§ 5. The course of the plaitpoint curve.

Two other mixtures e=0,0995 and «=0,1990 were investigated
in the way described in § 2. But in the case of these two
mixtures the investigation could not be made so completely as in
the case of the first mixture. For = 0,0494 we could trace the
isothermals pretty far above the plaitpoint-pressure ; but for # = 0,0995
the plaitpoint was situated towards the end of the series of observations,
and for «== 0,1990 the observations could only be made till near
the critical point of contact. By means of these observations, the
results of which are communicated in the tables III and IV, we
can derive some information regarding the course of the plaitpoint
curve in mixtures of hydrogen and carbonic acid in the neighbour-
hood of pure carbonic acid.

22*

Mixture z= 0,0995.

( 324 )

TABLE HI.

Isothermal lines.

deepal ong (Pressure. | Temp. | OE (Pressure. | Temp | vole Press.
169,90| _ 2774 | 32.24 || 29°.80 07185) 81.60 || 25°.00 03974/110.8
| e400 | 35.98) CP 06495} 85.05 || 23°.45 | 06685) 86.85

| yvi99 | 38.90 | | 05955) 87.80 pes 06070) 90.50

2066 | 40.80 | | 05895] 91.95 | 04918) 99.45

1874 | 43.91 | | 05260) 92.45 04580/102.9

1683 | 47.51 | 04171) 104.1 04196/108.2

1490 | 51.65 | 03619) 114.6 03776/115.3

1296 | 56.60 || 240,90 | 09145| 73.45 || 26°.05 2069 | 42.82

i108 | 69.95 OPEN) | ozaas) 82.50 1873 | 46.97

1067 | 63.50 06700) 85.40 1685 | 50.20

1029 | 64,85 || 06470) 86.65 1486 | 54.90

09940, 66.00 || | 06120, 88.60 1300 | 60.25

09565) 67.30 | | 05685| 91.60 1107 | 66.85

09145) 68.30 | 05270| 94.30 09185) 74.50

08800) 69.10 04902) 97.45 07240) $4.20

08360) 70.25 04566) 101.1 05300, 96.90

07990| 71.35 04171) 106.3 04566 103.9

07165) 74.00 | | 03904! 110.8 03806/115.8

05240) 84.20 || 03821) 112.2 || 39°.30 2052 | 44.58

03551 106.9 | (il. ») 03738) 114.2 1870 | 47.93

03284 118.6 || 250.00 07260) 83.25 1675 | 52.20

22°.80| 2061 | 42.20 06685] 86.40 1479 | 57.15
1877 | 45.40 06090] 89.95 1297 | 62.85

1683 | 49.26 05700) 92.60 1109 | 96.95

1480 | 53.90 05330| 95.30 09145| 78.60

1293 | 59 10 04948) 98.45 07220) 89.70

1110 | 65 15 || 04551) 102.5 052551105. 4

' 09145) 72.55 04376| 104 7 (4249/1181

( 325 )

PA Bele?) IVE
Mixture x= 0,1990. Isothermal lines.

| Volume ll Volume Volume

Temp. | 0,0. Pressure emp 0.0. Pressure. |, Temp. 0.0 | Press.
| | || | eel
| U
15°.35, 2960 | 81.34 |) 159.35 | 018 105.9 || 22°.80 1316 | 63.20

| 2700] 33.84 || zl _04559| 117.4 | a 1082 | 72.85
2493 | 37.97 || 20°.90 | _ 07810 89.15 | 09025! 82.45
2142 | 41.26 07465| 91.75 07115, 96.05
2031 | 43.03 | 07108 94.55 | 05255/116.0
1844 | 46.58 | 06735| 97.70 | 05140/117.6
1053 | 50,55 | | 06835] 101.5. | 05070 118.8
1461 | 55.70 | 05965) 105.L | |___04965/120.6
1276 | 61.55 05575, 109.6 | 31°.80 2018 | 47.00
1090 | 68.90 | 05210 114.2 | 1838 | 50,90
1051 | 70.85 | 22°90 06715, 99.05 | 1651 | 55.50

| 1016 | 72.10 || 06340 102.5 | 1465 | 61.15
09745| 73.95 | | 05965) 106.4 | 1275 | 68.20
09385) 75.50 | | 05585) 110.9 | ica 77.00
09020) 77.75 | | 08940| 115.4 | | 09020) 88.10
08605 79.75 | 920.80 2030 | 44.79 | | 07105,104.1

| 08275) 81.40 || 1833 | 48.78 | 05965 117.1
07860, 83.60 | 1651 | 53.00
07125) 88.20 | 1461 | 58.35 || |

I| |

For the three mixtures the volumes and the pressures at the be-
ginning and the end of the condensation were read on the p-v-t dia-
grams, constructed by means of the data in the tables I, III and IV,
and of which only one was given in the previous communication ; these
volumes and pressures are given in table V. Only for 7 =0,0494
the end of the condensation was observed for temperatures at some
distance from the critical point of contact; for «= 0,0995 the
increase of pressure during the condensation was so great that for
temperatures a little below the plaitpoint-temperature observations of
the end of the condensation could not be made. In the case of the
mixture «= 0,1990 no observations could be made on the liquid-
branch of the honde -curve,

—
bo
ler]
—

UA B a WV,

Border-curves.

‚ Begin. condensation. | End condensation.

Volume. | Pressure. | Volume. | Pressure.
|

| | } |

|
Temp. | : =
|

a= 0,0494:
15°.30| 0.01111 | 57.20 | 0.002543 | 102.9
|
21°.50 0.008545 | 67.90 2892 | 100.0
26°, 80! 5850 | 81.75 3833 | 93.90
27°.10) 5625 83.00 4063 | 91.85
(DLD, 1) |
97°30 540 84.6 427 | 90.5
270.50 48 87.4 48 | 87.4
Crp. of cont.)
temp.) | |
x= 0,0995

16°.90 0.009440 | 67.80
22°.80/ 6890 | 83.20
24°.20 6255 | 87.90 | 0.003737 | 114.3

(Dl, p, t) | |
95°.00| 565 | 92.9 | 412 | 108.4
95°45) 47 | ao. | 47 (or

(erp. ofcont, | |
temp.) | | | |

v = 0,1990

150.38] 0.008795 | 79.10

20° 90 6335 | 101.5

22° 20 560 | 110.9
+99°.8] +50 |+190

(er.p. Of cont,
1emp.)

Fig. 4 shows a graphical representation of table V. In this dia-
gram t is abscissa, p ordinate and x parameter. As will be known this
diagram consists of the vapour-pression curves of the two pure sub-
stances, connected by the plaitpoint curve; in between are the loop-

Dr. J. VERSCHAFFELT, Measurements on the system of isothermal

lines near the plaitpoint, and especially on the process of the

retrograde condensation of a mixture of carbonic acid and hydrogen.

Proceedings Royal Acad. Amsterdam. Vol. I.

yes

1 tS eget

ad = or ee

} torr
am, SUNT eee (Mid: AND
A) vuole

polis Ree EWG.’

=
an ry
‘
i
K |
wd
/
Î
q
“ ;
i
Es
a)
{ pe Ln
er _ ke
.
‘
4 sf
a
5 A
al
7 Pa
aia
5

( 327 )

shaped border-curves of the mixtures which touch the plaitpoint
curve in the plaitpoint. In the critical point of contact the tangent
is parallel to the p-axis.

In this figure I have also drawn the vapour-pressure curve
of pure carbonic acid, as determined by AmaGat!). By con-
necting the plaitpoints with the critical point of carbonic acid:
t= 31°,35, p = 72,9 atm., we obtain a part of the plaitpoint curve.
This plaitpoint curve rises steeply. It is probable that it also rises
steeply from the critical point of hydrogen: ¢ = — 234°,5, p = 20
atm. *).

The course of the plaitpoint curve found thus agrees with Kunp?’s 8)
observations on the influence of the pressure of compressed hydrogen
on the surface-tension of liquids in contact with it, if they are
understood as VAN ELpik *) has explained in his doctor-paper. Van
Erpik points out that the pressure at which the surface-tension
would become zero is the plaitpoint pressure which corresponds to
the temperature of observation. Moreover he has investigated the
law of the surface-tension as a function of the pressure. He con-
eludes that the plaitpoint pressure for hydrogen and ether at the
ordinary temperature would be no less than 750 atm, from which
follows a steep rising of the plaitpoint curve for ether and hydrogen
on the etherside.

The experiments communicated in this paper are not the first
that have been made on the critical phenomena in mixtures of hy-
drogen and carbonic acid. CAILLETET®) has made experiments with
a mixture containing about 5 mol. of CO, on 1 mol. of Hy. They
were undertaken in order to show, with a view to JAMIN’s expla-
nation of the critical phenomena, that by increase of hydrogen-pres-
sure the carbonic acid is bound to disappear. CaILLeTer has found
that this really occurred and this at a higher pressure as the tem-
perature was lower; for instance at 245 atm. at 15°, and at 153
atm. at 25°. But when we have to construct the border-curves and
the plaitpoint-curve we can set no value upon these observations,
as CAILLETET did not secure the equilibrium of the phases by
stirring; and only since KUENEN ®) has avoided the appearing of

1) Comptes rendus, 114, p. 1093, 1892.

*) See OrszEwsKr, Wied. Ann., 56, p. 133, 1895.

*) Ber. d. Kon. Acad. v. Wiss. Berlin, 21 Oct. 1880.

4) Van Erpik, Dissertation, Leiden 1898. Communic. Leiden Ne. 39,
?) Comptes rendus, 96, p. 1448, 1883.

*) KueNeN, Dissertation, Leiden 1892, Communic. Leiden N°, 4,

( 328 )

phenomena of retardation, the experimental investigation of the eritical
phenomena in mixtures has led to reliable results. That phenomena
of retardation give rise to important deviations is shown by the fact
that CaILLerer has observed condensation at 25°, whereas my expe-
riments show that the critical point of contact of his mixture after
equilibrium of the phases has been obtained, ought to be found at
about 23°.

Physics. — , Measurements on the change cf pressure by substitution
of one component by the cther in mixtures of carbonic acid and
hydrogen”. By Dr. J. VERSCHAFFELT. (Communication NO. 47
from the Physical Laboratory at Leiden by Prof. H. Ka-
MERLINGH ONNES. (Continued.))

S 1. Change of pressure by substitution.

Tables VI—X contain the results of the determination of isothermals
in mixtures with a still larger quantity of hydrogen than those
treated of in the former communications. In these mixtures no conden-
sation-phenomena appeared in the area observed; and so they cannot
reveal to us anything more about the further course of the plaitpoint-
curve, but in connection with the results communicated before, they
show us in what way, at a given temperature and a given volume,
the pressure of the mixture depends on its composition.

With the aid of all the determinations communicated we have
first calculated the coefficients of pressure, the values of which for
different compositions and volumes are given in Table XI. Then
we have calculated for one and the same temperature (18° C.) the
isothermals of the different mixtures and represented them in anew
diagram, the p-—v-« diagram. On this diagram we have read the
pressures belonging to one and the same volume for different mixtures :
table XII contains the values read in this way for some volumes.

As will be explained in § 2 we have chosen the units of volume
for the different mixtures so that 1 e.m.° of each mixture contains
the same number of molecules, when the volumes of these mixtures
expressed in the units accepted for this purpose, have the same
value. Table XIE therefore shows the change in pressure when,
starting from one of the two substances in pure condition, we gra-
dually substitute the molecules of this substance for an equal number
of molecules of the other substance.

( 829 )

The character of this „change
of pressure by substitution” is il-
lustrated in the annexed figure: in

this diagram the abscissae repre-
sent the compositions, and the
ordinates the pressures for the
volume 0,020 and at the tempe-
rature 18°C. From this figure it
appears that this change of pres-
sure is not proportional to that of
the composition, the pressure is
always greater than would follow
from a linear relation; if only a

kern
ak LI DE Liss small fraction of the number of

a as Qt as oF as B yp 4s ag 40

hydrogen molecules is substituted
by an equal number of carbonic acid molecules hardly any change
in the pressure takes place.

Table XII shows clearly that neither the coefficients of pressure
undergo any material change, when the number of hydrogen mole-
cules substituted by carbonic acid molecules is only a small fraction
of the whole number of hydrogen molecules.

§ 2. The unit of volume.

It was desirable to express the volume for each mixture in a
special unit of volume, chosen so that one c.m.” of each of the
mixtures contains the same number of molecules when its volume,
expressed in this unit, has the same value. We can do this by taking
for each mixture as unit of volume: the volume which the quantity
of substance used would occupy at 0° C. and 1 atm., if the mixture
behaved like a perfect gas. This volume I will call the theoretically
normal volume; it is obtained by multiplying the volume generally
called the normal volume viz. the volume which is actually occupied
by the substance at 1° C. and 1 atm., by a factor expressing the
deviation from AvoGaDRo’s law.

In connection with Avocgapro’s law this measure for pure
substances has been proposed by KAMERLINGH ONNES in 1881. At
the same time he pointed out the desirability of expressing hence-
forth the molecular quantities also in absolute measure. In order
to determine the deviation of the normal volume of hydrogen from
that which is to be used in applying AvocaApro’s law, he employed
VAN DER WaAALs’s law and the value 0,00050, deduced by vAN DER

( 330 )

Waars for a—b (Continuiteit p. 91) from Rea@navutr's observations.
And so he obtained in KG. M.S. the equation

(> + =) (v—b) = 2262000 (1a) ,

which he thought fit for determining the deviation of the gases
from AVOGADRO’s law !).

In the case of hydrogen we shall however use AMAGAT’s obser-
vations below 200 atm., which we have also used in determining
the pressures. With sufficient approximation they yield for the
isothermal of 0° C., ;

p(v — 0,000690) = 0,99931 8),

when the normal volume is chosen as unit. Hence in order to
obiain the theoretically normal volume we must multiply the volume
at 0° and 1 atm. by 0,99931.

From the weight of 1 liter of hydrogen: 0,08955 gramme at 0°
and 760 m.m. mereury, 0° C. and 45° latitude and the molecular
weight of CO,: 43,89, we deduce the weight of a liter carbonic
acid to be 1,9652 gramme under the same circumstances ; REGNAULT
found for this 1,9771, which means a deviation of 0,0060 from the
theoretical value with respect to hydrogen. The density of carbonic
acid is therefore 0,0053 higher than the theoretically normal density,
so that in order to find the theoretically normal volume of pure
carbonic acid we must multiply the volume at 0° and 1 atm.
by 1,0055.

An observation made by Braun *) gives us some information on
the deviations of AvoGapRo’s law shown by mixtures of carbo-
nic acid and hydrogen. He has found that when we mix two
equal volumes of hydrogen and carbonic acid under a_ pressure
of about 71 e.m. mercury, the pressure rises 0,097 em. thus
0,0014. And so we may accept that when taking two equal
volumes of hydrogen and carbonic acid we obtain by mixing a

1) The problem in general has been treated by v.v. Waars in his communications
“On the accurate determination of the molecular weight of gases from their density.’
Proc. Noy. °98 and “Variation of volume and of pressure in mixing IL.” Proc, Dee. ’98

2) See KAMERLINGH Onnes. Verh. Kon. Akad. v. Wet. 1881, Algemeene theorie
der vloeistoffen, p. 5—7. Abstract: Arch. Néerl. t. XXX.

®) Wied. Ann., 34, p. 948, 1888. KUENEN has pointed out a similar change of
pressure in mixing compressed gases by stirring.

double volume under a pressure of 1.0014 atm. Let » be the number
of molecules which one volume of a perfect gas would contain at
0° and 1 atm., so that 0,99931 „ is the number of molecules of
hydrogen and 1,0053 # the number of molecules of carbonic acid,
then it is easy to see that one volume of the mixture at 0° and
1 atm. must contain 1,0009 x mol. And so in order to find the theo-
retically normal volume of a mixture consisting of an equal number
of molecules of hydrogen and carbonic acid we must multiply the
volume at 0° and 1 atm. by 1,0009.

Let, as in Vv. D. WAALS’s paper, x be the proportion of the number
of hydrogen-molecules to the whole number of molecules, then we
can represent the deviation from AVOGADRO’s law by the numbers:
1,0053 for z=0, 1,0009 for z—=0,5, and 0,99931 for z=1. The
deviation for intermediate mixtures can be found with sufficient ap-
proximation by applying a parabolic formula of the form y= a+ be+ce?;
and then we find that the deviation may be represented by

y = 9,99931 + 0,0060 (1—z)? .

According to this formula the influence of small admixtures of
carbonic acid with the hydrogen is very small, a fact to which the
attention will be drawn later on.

For the reduction to 0° C. we had to use the coefficients of
expansion of the mixtures. As a first approximation I might have
calculated the coefficients of expansion with the aid of a linear
formula from the coefficients of expansion of the pure substances:
0,00366 for H,, 0,00371 for CO,. But led by the previous result
regarding the deviations from AvoGapRo’s law I thought it probable
that the dependence of the coefficient of expansion on the compo-
sition « would show the same characteristics; and so I was obliged
to put it thus:

ap = 0,00366 + 0,00005 (1—2)? .

In determining the theoretically normal volume of hydrogen it was
mentioned that by starting from different experimental data we
arrive at different deviations from AvoGApro'’s law.

This is even more so in the case of carbonic acid. If by the side
of the number 0,99950 for hydrogen formerly accepted by KAMERLINGI
ONNEs we also borrow from v. p. Waaus’s Continuiteit (p. 76) the
number 1,00646 for carbonic acid (deduced from ReaNauLt’s iso-
thermal lines) and if we substitute this for ReaNauLt’s determination

( 332 )

of the density of carbonic acid we should find for the mixture 1/,
hydrogen—!/, carbonic 1,00158, whence :

y = 0.99950 + 0,00136 (1—r) + 0,00560 (l—z)? .

From the point of view of a consistent application of VAN DER
Waats’s law a calculation of the theoretically normal volume of
the carbonic acid from the normal volume and the compressibility
would be preferable to the method of calculation followed by me.
But then the proportion of the weights of one volume of carbonic
acid and hydrogen in the state of perfect gases and the molecular
weights would be discordant, and it are the latter which we want as a
basis for our choice of units of volume (with a view to v. D. WAALS’s
theory of mixtures), The influence of the differences yielded by the
calculations from the different data is not such as to render doubtful
the character of the change of pressure when substitution takes place,
but still in my determinations the discrepancies differ little from the
errors of observation. From this we see once more the necessity of
accurate observations with perfectly pure substances in order to make
progress in the knowledge of the laws which govern the gaseous state.

TABLE VI. « =0,3598. TABLE VIL. «= 0,4993.
Ma 1 oa
2810 | 34.44) 36.85 3168 | 32.11) 33.84
2585 | 37.17 39.80 2975 | 34.09) 35.95
2442 | 39.15) 41.96 9895 | 35.78) 37.78
2299 | 41.38 44.38 2667 | 37.85) 39.97
2159 13.77 46.95 9519 40.08 42.36
2014 | 46 54 49.99 2355 42.60) 45.07
1869 | 49.70) 53.45 2206 | 45 34 47 97
1724 | 53.35) 57.40 9045 | 48.71) 51.55
1587 57.38 61.80 1889 | 59.35| 55.50
1480 | 60.90 65.75 1736 | 56.80! 60.20
1340 | 66.35] 71.75 1624 | 60.45| 64.05
1907 | 72 40) 78 45 1468 | 66.35 70.40
1067 | 80.30) 87.25 1523 | 73.08) 77.65
09255 £9.90, 98.30 1172 "81.85: 87.10
07940 101.60 112.0 1017 | 93.15 99.50

| |
06510/115.3 08694107.3 114.9

( 333 )

TABLE VIII. TABLE IX. TABLE X.

z= 0,6445. x=0,7963. x=0,8972.,

at es Pain ed Een Wit dd
“2079 | 34.85) 35.89) 36.85 3293 | 32.61 3234. | 33.46
2745 37.76 38.79 39.95 2999 | 35.81 2989 | 36.29

2600 39.90 41 00, 42.13 2723 | 89.47 2840 | 38.15

2446 | 42.35) 43.53) 44.80 2474 | 43.49 2692 | 40.31

2294 | 45 10 46.34 47.88 2253 47.78 2532 | 42.94

143 | 48 21) 49.60, 51.00 2032 | 53.00 2384 | 45.72

1989 | 51.90) 53.35, 54.95 1840 | 58.60 2217 | 49.22

1836 | 56.05 57.60) 59.39 1630 | 66.20 2076 | 52.65

1686 | 60.90) 62.65 64.55 1484 | 72.95 1904 | 57.50

1576 | 65.20) 67.05, 69.05 1335 | 81.35 1764 | 62.25

1433 | 71.45) 73.60, 75.80 1212 | 89.65 1635 | 67.40

1284 | 79 50) $2.00) $4.55 1090 100.1 1485 | 74.55

1140 | 89 20203 94.85 09650 113.2 1336 | 83.15

09935/102 2 105.5 108.9 1173 | 95.20

08495 119.2 | 1028 ‘109. 5

TABLE XI. Coefficients of tension. (15°—30° C.)
Volume | ET EET RO —

0,0 ia 00600. 04910. 09950. 19900. 35280. 4993 9. gaas. 79680. 8972,1.0000

0.162
175
190

(0.159 (0.156 0.150 lo.142 [0.134 |
172 | 168, 163 | 155 | 146
186 | 183\ 177 | 168 | 159
204 | 199 | 193 | 183 | 174
223 | 218 | 211} 201 | 191
249 | 242 934 | 223) 212 |
285 | 276) 265| 250) 237
333 | 321 306 | 286 | 270
sds | 381 360| 331| 312 |
481| 461 431) 395| 373
500 | 566 433 | 495 | 464

0.130

141 |

154
168
185
204
227

256

296
353

138 | 136
150 | 148
163 | 161
179 | 176
197 | 194
221 | 216
249 | 244
286 | 281
339 | 331

436 | 415 | 405

(0.127 0.126 0.126

135

( 334 )

TABLE XII. Pressures at 18°.

Compositions «=

Volume ; 7
| | | : |
o. 0-0000)0.04940,0995(0.19900.3598 0.4993 0. 6445 0.7963 0.8972 1.0000

| | |

30 |28.901)) 29.68) 30.37 31.33) 32.70 33.81] 84.77 35.80 36.19 36.31
29 (29.73 | 30.43 31.83) 32.95) 38.75 34.92) 35 95) 37.09 37.46 37.59
28 80.58 | 31.35 32.95| 33.24) 34. Sb 36.12) 37.19) 38.43) 38.83, 38.97
27 131.45 | 32.32 33.93| 34.34) 36.04 37.39) 38.56) 39.81 40.29, 40.45

26 32.40 | 33.33) 34.28 35.53 37.32 38.80] 40.05] 41.33 41.87 49.04
25 [33.36 | 34.40] 35.37] 36.77) 38.64) 40.23] 41.64] 42.98) 43.69) 43.77
24 [34.38 | 35.53 Bees) eats) lila l 41.80) 43.33) 44.80 45.48) 45.65

39.43) 41.72) 43.571 45.17| 46.73) 47.48) 47.70
22 36.55 | 38.00) 39.11 40.01 43.40 45.46 47.18) 48.90 49.67 49.94
21 37.75 | 29.40) 40.55 42.50, 45.26, 47.50) 49 39| 51.20, 52.15 52.40
40.85 42.10) 44.26 47.30] 49.65| 51.80| 53.75) 54.80 55.10
19 40.40 | 49.40 13.76, 46.15 49.49 52.10, 54.45) 56.65) 57.80, 58.10
18 /41.90 | 44.02] 45.56 48.22 51.90] 54.95] 57.45] 59.85) 61.18) 61.50
17 |43.43 | 45.70| 47.47) 50.40) 54.60| 58.00) 60.75) 63.45] 64.90] 65.25
16 |45.00 | 47.59] 49.55 52.80] 57.50 61.30| 64.55| 67.45] 69.10) 69 50
15 46.64 | 49.45] 51.85] 55.45] 60.80] 65.00) 68.75] 72.10) 73.85] 74-35
14 [48.35 | 51.65] 54.30] 58.40) 64.60] 69.30] 73.35 77.50 79.25 79.95
13 [50.05 | 54.00] 56.00) 61.75, 68.80) 74.30, 78.80) 83.55) 85,65 86.45
12 (51.85 | 56.40) 59.85) 65.60) 73.60) 80.00) 85.30) 90.85) 93.10) 94.10

|

11 (53.65 | 59.00) 63.05 69.75) 79.10) 86.75) 93.00 99.25102.0 103.1

10 [55.50 61.65) 66.55) 74.25 85.40) 94.40/102.1 |109.6 112.9 114.3

Chemistry. — „On the velocity of electrical reaction”. By Dr. ERNST
COHEN, (Communicated by Prof. H. W. BAKHUIS ROOZEBOOM).

1. If two elements, arranged as follows.

Electrode, rever- | Saturated solution of a | Electrode, rever-
sible with respect | salt S in presence of the | sible with respect
to the anion. ‚stable solid phase of the | to the cathion.

| salt.
and

1) This column has been deduced from isothermal determinations of pure carbonic
acid, not yet published.

( 335 )

Electrode, rever- | Saturated solution of the | Electrode, rever-
sible with respect salt S in presence of the ‚sible with respect
to the anion. metastable solid phase of the to the cathion.

| salt.

are coupled up in opposition to each other, a transition element of
the third kind!) is obtained.

If the salt S is zine sulphate, the combination in question may
be composed of two CLARK-cells; in the one Zn SO, 7 H20, in the
other Zn SO,.6H,O forms the solid phase provided that the tem-
perature lies between the cryohydratic temperature of ZnSO,.6H,0
and the transitionpoint (59°).

2. The electromotive force E of this transition element is the
measure of the maximum work which the reaction occurring in the
element at the temperature 7 can perform.

In a later communication I shall show how £ may be calculated
by thermodynamics.

Experimentally, ZE may be directly determined or it may be cal-
culated from the measurements of JAEGER ®), who has measured the
E.M.F. of Cuarx-cells at different temperatures, Zn SO,. 7H, O
(the stable phase) or Zn SO,.6 HO (the metastable phase) being
present as the solid phase between 0° and 39°.

In this way the following numbers are obtained:

Temperature. ZMF. of the transition element.

— 5°,0 16.2 Millivolts.
0°,0 14.9 3

+ 5°,0 13.5 3
9°,0 1223 ‘3
15°,0 10.3 En
250 6.4 eN
30°,0 4.2, 5
35°,0 ne
39°,0 0 =

3. The velocity with which the reaction which occurs in the

') See Conen, Zeitschrift für phys. Chemie, Bd. 25 (1898). S. 300,
2) WIEDEMANN's Annalen, Bd, 63 (i897), 354,

( 336 )

transition element proceeds at the temperature 7 is represented by
the equation
E

kn tee

where (WW) is the sum of the interval resistances (at T°) of the
elements of which the transition element is composed, and Z the
electromotive force of the transition element at 7°.

I have shown!) that the internal resistance of a CLARK-cell at
TO is proportional to that of the zine sulphate solution, saturated
at 72.

Let the measured resistance of a saturated solution of

Zn 80O,.7H,0= W,

and that of a saturated solution of ZnSO,.6 HO at the same
temperature =W,. Then

= (W)ro= (py Wire + (py Wo) ro ,

where pj and ps are constants depending on the capacities of the
CLARK-cells used and of the vessels in which the resistances of the
saturated solutions were determined.

If the same vessel is used for all the measurements, the equation
may be written

=(W)r, = p(Wi+ Wo):

If we call Q, and 2, the specific resistances of the saturated
solutions of Zn SO,.7H,O and Zu SO,.6H,0O at T° and z the
resistance-capacity of the vessel employed in measuring W, and W,
then

Or Wi

(2, wee Wo
2 E
and je ee ee a
PED )

2 ($2; + £29)

iE

Or Ke

~~ Q) + Qs

1) The paper relating to this will appear shortly in the Zeitschrift fiir physikalische
Chemie.

( 337 )

The values of the electrical reaction velocity constant, K,, are
placed in the last column of the following table, which contains
the results of the observations.

vi B (Millivolts) W, Wa n= ——=
— 5° 16.2 445.9 524.1 0,0167
0°,0 14.9 384.2 452.2 0,0178
+ 5°,0 13.5 337.0 396.3 0,0184
9°,0 12.3 305.75 360.35 0,0185
15°,0 10.3 271.60 315.50 0,0175
25,0 6.4 236.40 274,25 0,0125
30°,0 4,2 225.10 248.85 0,0088
35°,0 1.9 218.50 228.35 0,0042
39°,0 0 215.0 215.0 0

The observations cannot be continued below — 5° because the
eryohydratic temperature of Zn SO,. 7H, O lies at about —6°.

Representing the values of A) graphically as a function of the
temperature the following curve is obtained.

Blectrical Reaction velocity.

=S 2 25 30° CEP

5
Temperature.
23
Proceedings Royal Acad. Amsterdam Vol I.

( 338 )

From this it is clearly seen that starting from 39° the velocity of
electrical reaction rapidly increases, reaching a maximum at about 9°
and then diminishing again.

It is worthy of note that the curve, which here represents the
velocity of electrical reaction at different temperatures, possesses the
same form as that representing the rate of crystallisation of many
substances at temperatures below the melting-point !). I shall take
up this subject more fully later, as also the study of the velocity
of the following reactions:

Zn+ CuSO, =Cu + ZnSO, (DANIELL-element).

Zn + Hg SO, = Hes + Zn SO, (CLARK-element).

Zn +2AgCl = Ag, Zn Cls (WARREN DE LA Rur-element).
Zn +2HeCl = Hes + ZnCl, (Heumuourz-element).

Amsterdam, February 1899.

Chemistry. — Prof. FRANCHIMONT presents to the library of the
Academy the dissertation of Mr. L. T. C. Scurey entitled:
„On synthetically prepared neutral glyceryl-ethereal salts —
triacylins — of saturated monobasic acids with an even number
of C-atoms” and elucidates it in the following words:

Since CHEVREUL’s experiments in the first quarter of this century,
fats, at least animal fats, are considered as mixtures of glyeeryl-ethereal
salts, on account of the products formed by them after treatment with
solutions of bases; but it is extremely rare that a glyceryl-ether has
been extracted from it in a pure form. The difficulties attached
to such separations have as yet not been sufficiently overcome.

About the middle of this century some of these glyceryl-ethereal salts
have been made synthetically by BerrueLor and others, but generally
they did not obtain them in a pure condition. Now Mr. Scury has,
with a view to the acids said to have been obtained from butter, made
synthetically eight glycerides, called by him, in order to prevent
confusion with polyglycerinderivatives, triacylins and has determined

See GERNEZ, Journal de physique (2) 4, (1885) p. 349. Tamman, Zeitschrift
fiir phys. Chemie, o, a. 23, #26 (1858). vy. *r Horr, Vorlesungen über theor, und
phys. Chemie (1898). 5, 226.

( 339 )

their density, refractive power and meltingpoint. Of these eight, three
were entirely unknown viz caproin, caprylin and caprin ; three: buty-
rin, palmitin and stearin had formerly been prepared synthetically,
but the former two certainly not pure; two: laurin and inyristin had
only been obtained from natural products, but neither quite pure.

The method of preparation adopted by Mr. ScHey consists simply
in heating glycerin with an excess of the acid up to a temperature
at which neither the glycerine, nor the acid, nor the ethereal salt
suffer decomposition and under circumstances in which the water
formed is immediately drawn off as completely as possibly e.g. by a
slight current of air and under diminished pressure in the apparatus,
this being followed by fractional distillation in vacuo or erystalli-
zation from different solvents, until one of the properties mentioned
underwent no further noticeable alteration by this treatment. ‘This
fact led to the conclusion of the purity of the product; Mr. Scuey
attaching little value to elementary analyses in these cases, they
have not been made.

The determination of the specific gravity was always done by
weighing a certain volume of the substance and an equal volume of
water at the same temperature; the exactness acquired in this way
holds good up to one or two unities of the 4 decimal.

The refraction-index was determined for sodium light with a refrac-
tometer of PuLrrich with which generally the 4 decimal is certain.
The determination of the meltingpoint has not been so exact, but
that differences of one or two tenths degrees may occur.

Mr. Scuey has not only determined the three properties of his
products, but also of the original substances (the acids), which were
purified to the highest possible degree, except the two highest acids,
which Dr. L. B, O. pr Visser of Schiedam had kindly procured
him in a very pure condition. Of the eight triacylins prepared,
tricaprin offers the highest guarantee of purity because it crystallizes
best of all and was obtained in great, clear, well-formed erystals ; the
lower terms are at the ordinary temperature liquids of which tribu-
tyrin alone has an intensely bitter taste.

Finally Mr. Scuey treats of the methods by which it is possible
to calculate, appreximatively at least, density and refractive power
of these substances. The calculation with the numbers determined by
others for the atomicvolumes (even TRAUBE’s with the co-volumes)
and for the atomicrefractions, gives results differing pretty much from
those found by him. He here points out the little certainty offered
by the generally accepted values for atomievolumes and atomic-
refraction,

23*

( 340 )

Another method of calculation already indicated by BERTHELOT
in 1856 viz. from the molecular-volumes and the molecular-refrac-
tions of the substances that have interacted, at equal temperatures,
led to better results. It has already been remarked by others, that
the ethereal salts of the fatty acids in general often seem to be formed
without great change of volume and this seems equally to be the
case with triacylins. For caprin the result of this calculation of the
molecular-volume even perfectly agrees with the one really found;
it does not result therefrom that this should necessarily be the case
with the other terms as well, and in the subjoined table given by
Mr. Scuuy their deviations are shown.

A third method of calculation starts from what is found for one
of the terms and as all of them rise or fall with an equal diffe-
rence of composition, it takes into account the average value of this
difference. Starting from caprin, as the purest product, the values
calculated on this base and those for molecular-volumes and molecu-
lar-refraction concurred pretty well, as will be seen from subjoined
tables.

As to the meltingpoints it was found that they weve quite or
nearly quite equal for capric acid and for tricaprin, while for the
lower terms of the triacylins the meltingpoint is below that of the
acid, for the higher ones on the other hand above it, which does
not agree with what BerrueLOT thought to have found.

This work will be published in the Recueil des Travaux Chimiques
des Pays-Bas et de la Belgique.

Physics. — „Ou the Vibrations of Electrified Systems, placed in a
Magnetic Field”. By Prof. HW. A. Lorentz.

(Read in the meeting of January 28 1899).

S 1. Many spectral lines show the ZeemMan-effect according to
the well known elementary theory, and are thus changed into
triplets or, if viewed along the lines of force, into doublets, yet there
are a rather large number of cases, in which the phenomena are more
complicated. Cornu!) found that the line 2, becomes a quartet,
whose outer and inner components are polarized, the first parallel
and the latter perpendicularly to the lines of force. Similar quartets
have been observed in other cases. Sometimes’), in triplets and quar-

1) Cornu, Comptes rendus, T. 126.
2) Becauunen and DesLANDRES, Comptes rendus, T 127, p. 18.

( 341 )

tets, the inner and outer lines have interchanged their ordinary
states of polarization. Finally Mrenrerson, Preston!) and other
physicists have seen a division of some lines into 5, 6 or even more
components.

I shall examine in this paper, to what extent such multiple lines
may be explained by appropriate assumptions concerning the way in
which light is emitted. Of course I am perfectly aware of the possi-
bility that my interpretation of the facts will have to be replaced
by a more adequate one. The special form of my hypotheses has
the less value, as in the only case in which I have endeavoured
to account for all the peculiarities of the phenomena, I have suc-
ceeded but poorly, at the best.

§ 2. Since the components, into which a line is broken up by
the magnetic force, are in many cases as sharp as the original line
itself, it must be admitted that the periods of all the luminous par-
ticles of the source of light are modified in the same way. This is
only possible in two ways. Either, in the magnetic field, all the
particles must take the same direction, or the modification of the
periods must remain unchanged, into whatever position the particles
may be turned. The first assumption leads however to some diffi-
culties 2). I shall therefore suppose the luminous particles to be
spherical bodies, having the same properties in all directions. This
may be true, even though the chemical atoms be of a much less
simple structure; indeed, the vibrating spherical ion may very well
be only a part, perhaps a very small part, of the whole atom ®).

It has been shown in a former paper®) that a triplet may be obser-
ved if, among the principal modes of vibration of the system, there
be three, for which, outside the magnetic field, the time of vibration
is the same, or, as we may say, if the system have three equiva-
lent degrees of freedom. Afterwards Mr. PANNEKOEK ®) remarked
that a quartet may appear if there be, in the same sense, four equi-
valent degrees of liberty, and in general, a z-fold line, if of the
principal modes have equal periods.

Now, spherical systems, vibrating in one of their higher modes,
have indeed more than three equivalent degrees of freedom.

1) Micuenson, Phil, Mag., Vol. 45, p. 348. Presvon, ibidem, p. 325.

2) See Lorentz, Verslag der Verg, Akad. van Wetensch. VI, p. 197, and Arch.
mvGiey lin Bs lo 5 ph by.

*) See Lorenz, Verslag der Verg. Akademie yan Wetenschappen VL, p. 514.

4) Wied. Ann. Bd. 63, p. 278.

*) Verslag der Verg. Akademie van Wetenschappen VII, p. 120. Proceedings Royal
Acad, Vol. I, p. 96

( 342

Ne

§ 3. I shall consider in the first place an infinitely thin spheri-
1 shell of radius a, charged, in the state of equilibrium, to a
uniform surface-density o. The surface-density of the ponderable
matter itself will be denoted by g. We shall suppose that the points
of the shell can only be displaced along its surface, that the elements
earry their charge along with them, and finally that, after a displa-
cement, each element is acted on by an elastic foree, which is
brought into play merely by the displacement of the element itself,
and not by the relative displacement of adjacent elements.

When the motions are infinitely small, the elastic force may be
taken proportional to the displacement a. Let it be

Ca

— k a

per unit area, the constant #° having the same value all over the sphere.

The only connexion between the different parts of the shell will
consist in their mutual electric forces. If the wave-length of the
emitted radiations be very large in comparison with the radius of
the sphere, we have merely to consider the ordinary electrostatic
actions, depending solely on the configuration of the system. Hence
there will be no resistances proportional to the velocities, and con-
sequently ro damping. In fact, it is well known that the damping
which, in some degree, must always be caused by the loss of
energy, accompanying the radiation, may be neglected when the
wave-length is very much larger than the dimensions of the vibra-
ting system.

§ 4. In the absence of magnetic forecs the shell can vibrate in
the following way.

Let Y7 be a surface harmonie of order 4. Then the displacement
of a point of the sphere is

p EE a as (U)

Here / is the direction in the surface in which Y, inereases most

< fo) Yn 2 : ; 5 .
rapidly, and Si is to be regarded as a vector in this direction J.
y, 3 2

The coefficient p is the same all over the sphere; it has the form

g cos (tl €), . « aa aiase) Semen)

so that xj, is the frequency of the vibrations.

(343 )

In consequence of the displacements (1), the electrie density will
have changed from 5 to

oO
54 h(h L 1) oa Vigne

a

Hence, there will be an electric force

SA ao
2h4+1 a fo)
(V = velocity of light) along the surface and, as the density

differs from & by an infinitely small amount, we may write for
the force per unit area

LE Cece
AV

ZEE eae ae
The equation of motion becomes
EO orn , b(k +1) 6% 9 Yn
IPP A ee)
ol o/ 2h4+1 a ol
and the frequency vj is determined by
h(h-+1 o°
NG)

24+ 1 a

Thus, we see that the frequency is the same for all motions
corresponding to a harmonic of order 4, no matter what particular
harmonie of this order may be chosen.

If we put 4=1, we obtain the frequency of the slowest vibra-
tions; ‚== 2 corresponds to the first of the higher types of motion,
and so on. However each of the different types includes a certain
number of different modes of motion.

In the motion we have considered there is a kinetic energy

Ca Ya?
One | En dao,

do being an element of the sphere, and the integration extending
all over the surface.

In virtue of the properties of spherical harmonics we may also
write

The potential energy is given by

v

AE 78 Vin?
US eneen Ze | Yi? dao AAR py? Gen lo =
i eae Pr MA | zi)

6 79 he (h zE ie 5? 1 1 9 9 9
= te tE D Pp [Ve do.

If we put

I? (h 1)? o° he
2 “ —-+A(h+1)—
2h-+1 a Mor 2

Aly, = tl ijn I
and
0.
By = h(h +1)
a”

these formulae may be replaced by

Te | Hij de

and

WAnps Í Y do.

§ 5. We shall now take for 4 a determinate number and consider
only vibrations corresponding to harmonics of this order. These
motions of the common frequency », may differ from one another by
the position of the poles of the harmonie Y;. Moreover, vibrations
depending on different functions Y, may be superposed with any
amplitudes and phases we like.

However, not all of these modes of motion are mutually independent.
Since any surface harmonic of order h may be decomposed into
2 h + 1 particular harmonics of the same order, there are only
2h + 1 equivalent degrees of freedom, for which the frequency is
nj. As for those 2 4-+ 1 fundamental harmonics, as we shall call
them, they need only satisfy the condition that none of them can be
expressed in terms of the other ones. After having chosen these
functions, which I shall denote by

Yi, ’ Vig ’ V5 ete,

( 345 )

We may write for the displacement in the most general case we shall
have to consider

3 Vig d Vis d Ya
Er = #45 — a. IS =
TE NT Cera

cS) Hien ea o (@
where each term represents a vector along the surface in the manner

indicated in § 4, so that / has different meanings in the different terms.
The potential and the kinetic energy will now be found to be

U= Say py” + 4 gg pro” + 4 agg py” + ete... +
+ dje Pi Po + %3 Pi ps + ete,
T= ¥ dy) Py? + Ebi? + 4 bsg Bs” Hete... +

+ D2 Pi be + biz Pi bs + ete,
where

,
ro =z 7
Uuu == A, | } le Af Uu, = As f Pus Vis do,

ev

a

rde Ean do, Dine [re Hir do.

wv

As long as we limit the investigation to the vibrations of order h,
we may ignore the other degrees of freedom; we may then consider
the 2 h +- 1 coefficients pj, pz, ps . . . as the general coordinates.
The equation of motion for the coordinate p, will be

a ask dU
ew

it will take the form

d ,oT aU
NEO ee ONE
dt a Ou TC @)

if, besides the forces which we have considered thus far, there are
other forces whose general components are Qu.

§ 6. If an electrified system be vibrating in a magnetic field, its
parts will be acted on by electromagnetic forces proportional to the

( 346 )

charges. Per unit charge these forces are given by the veetor product
of the velocity and the magnetic force in the field.

Let there be a made of motion A, with frequency 1, before there
is any magnetic force, and let F be the electromagnetic forces arising
from this motion as soon as the field is produced. The direction of
these forces will obviously change with the frequency , and to deter-
mine their action on the system is a problem of ,resonance’’ or of
„foreed vibrations”. In general, the system will respond to the forces
F by a motion in several of its other fundamental modes. In fact,
any particular motion B will certainly be excited if only the forces
F do a positive or negative work in an infnitely small displacement
corresponding to that mode B.

Since the electromagnetic forees are perpendicular to the velo-
cities, the forces / will do no work if the infinitely small displa-
cement belong to the mode A itself. A direct influence of the forces
F on the motion A which gave rise to them is thereby excluded.

As to the other modes, all depends on their frequency. If the
frequency »’ of a motion B be considerably different from , the
forced vibration B, if it exist at all, will be very insignificant, for
experience shows the forces F to be very feeble as compared with
the other forces acting in the system. As well as the forces F
themselves, the amplitude of the forced vibrations B will be pro-
portional to the strength H of the field. Hence, the electromagnetic
forces F', which exist in consequence of the vibration B, will be
of the order H?, and it will be permitted to neglect their reaction
on the original motion.

The case is quite different as soon as the frequency of B is
equal to that of A. The amplitude of the new motion B will then
rise to a much higher value; as may be deduced from the equa-
tions of the problem, it will reach the same order of magnitude as
the amplitude of A itself. The influence of the forces /” on the ori-
ginal motion will likewise be much greater than in the former case.

One may see by a simple reasoning that this influence will
consist in a modification of the period. Since the forees F have
the same phase as the velocities in the motion A, there will be a
difference of phase of 1/, period between them and the displacements
A. On the other hand, the displacements in the motion B have
the same or the opposite phase as the forces /’, and the phase of
the forces £' will differ by '/, period from that of the displacements
B. These latter forces will therefore have the same or the oppo-
site phase as the displacements A, and this is precisely what is
required, if they are to change the frequency of A,

( 347 )

We see at the same time that the simultaneous motions A and
B will differ in phase by !/, period. This is the reason why cir-
eularly polarized light can be emitted in the direction of the lines
of force.

§ 7. The foregoing reasoning shows that, in the magnetic field,
the vibrations of order % will never be perceptibly modified by
the vibrations of different orders. We may therefore continue to
consider them by themselves. Now, the meaning of the term Q,
in equation (5) is this, that Q. dp, is the work of the electromag-
netic forces corresponding to the infinitely small displacement deter-
mined by dp,. But the electromagnetic forces are linear functions
of the velocities; consequently, Q, will take the form

DZ EEE

The coefficients « are easily calculated. Let the centre of the
shell be the origin of coordinates, the axis of 2 having the direction
of the magnetic force H. Then, if 7 be the distance to the
centre, and

Wy =r Yin

the solid harmonie of degree A, corresponding to the surface har-
monic Ys, I find

ry Ys 2, |
Hoke IW. 3Ww W.|
En = a3 | en ALP EON ven et “SP ACR)
qzh+2 f Ou dy dz |
UWE COW die, |
du ‘ oy ; dz

I shall suppose that the axis of y points to the place the observer
occupies when viewing the phenomena across the lines of force.

It will sometimes be found convenient to distinguish the funda-
mental harmonics by suffixes, indicating the position of their poles.
Thus Y, will be the surface harmonic of the first order whose pole
is determined by the intersection of the axis of « with the sphere;
Y,, the harmonic of the second order, having its poles on the axes
of « and y, Yer the zonal harmonic, whose poles coincide on the
axis of x. If these notations be used, the suffix which indicates
the order of the harmonic may be omitted,

( 348 )
By (7) we see that
Eup = 9 ’ Erp = — Euve

la al Y . S .

These relations would hold for all electrified systems, vibrating
. . 5 i=]
in the magnetic field.

§ 8. We shall begin by examining the vibrations, depending on

harmonics of the first order.
Let the fundamental harmonies be

Then:

p= pr Ho, £13 == &3 = 0 ,

and, if we replace au, bm and #2 by @, i, 4,

fy Py =— @ pi kade RE)
(fi Papa ED - = =)
Pz — © Ps

From these equations we conclude that, for 7= 0 and = 0,

all vibrations have the frequency 7, given by

which follows also from (3).

When there is a magnetic field, the vibrations corresponding to
Y. will still have this frequency ™, but besides these there will be
two motions with a modified time of vibration. In order to find
them, we may suppose that p, and p, contain the factor eit multi-

( 349 )

plied by quantities independent of the time. Then, neglecting
quantities of the order vf H?, we may satisfy (8) and (9), by as-
suming either

p= + iP» n= dn
or

Py= ip, n=n—n.

In these formulae

F € Ho
Ly SSS SS SS 5
2% 40

or, writing e for the total charge 47a?5, and m for the total

mass 4 7ra°g,

)

He
4m

oy =

In the two modes of motion, which correspond to py=+ip,, and
Pz = —tp,, and the expressions for which are got in the ordinary
way by taking only the rea! parts of the complex quantities, the
coexisting Y,- and Y‚-vibrations will show a difference of phase of
1/4, period. This difference will have opposite signs for the two modes.

The vibrations corresponding to surface harmonics of the first
order may be roughly described as oscillations of the entire charge
in the direction of one of the axes of coordinates, or, to speak more
correctly, in these vibrations there exists at every iustant an „electric
moment” parallel to one of the axes. Thus it appears that the mode
of motion we have now examined closely resembles the one that is
assumed in the elementary theory of the ZeemAN-effect and it is but
natural that we should again be led to the triplets and doublets of
this theory. Only, for equal values of e and m the change x’; of
the frequency is half of what it would be in the elementary explanation.

S 9. In investigating the vibrations of the second order we shall
introduce two new axes OX' and OY, which are got by rotating
OX and OY in their plane and the first of which bisects the angle
NOY, We shall take for the fundamental harmonics :

Yor = Yan Yoo = Yury, Yo3 Yan Yor Vijn Yo; Ye

We may really do so, because any harmonie cf the second order

( 350 )

may be decomposed into these five functions. Now we have the
o lowing solid harmonics

and, putting
Is IU a Ay = 2; Is TU a? By — Pa 3] Tt H = € 5

the following values of the coefficients :

yy = Ayr Aga — Gas — 9 oy (ps == A
by, = bog = Daz = aa = 3 Po, bz, = 4 fa
Eg = + 2 &, En = — 2 &
oa. —— as 9, E13 = — Ey:

All coefficients that have not been mentioned here have the
value 0.
The equations of motion become

3 35 py = — 3 3p, edge EN

3 [3 Po = — 3 Ay py — 2 ey Pj) | ene eee

Bebe Sorte «. .

3 Po ps = — Oho ps — fgg . . 2 en
[Py 25 = — Ps:

It appears that, in the absence of a magnetic force, ail vibrations
) 5 ?
of the second order will have a common frequency #2, given by

When the shell is placed in the magnetic field, it will be only
for the Y-.-vibrations that this freyuency remains unchanged, and
there will be four motions with a slightly increased or diminished
frequency.

a re ee So

( 351 )

Operating again with expressions that contain the factor e™, we
can satisfy (10) and (11) by the values

Pati 1+ Bnn,
and likewise by

p2=—tpy 9 n=ng—n;',
the change in the frequency being given by

ae cone He

ie 3 (72 rai 60 RTG

1
Ng

In both eases we have to do with a combination of a Yux,- and
a Yry-vibration, the two vibrations having equal amplitudes, and
differing in phase by 1/, period.

From- (12) and (13) we deduce the possibility of two similar
combinations of a Yz.- and a Yy-vibration; the frequency is

nz + Àns,

for one combination, and

for the other.

S 10. Similar results are obtained by supposing that a charge
is distributed with uniform volume-density 5 over a spherical space
and that each element of volume, after having undergone a dis-
placement a from its position of equilibrium, is acted on by an
elastic force, proportional to the displacement. Let #a be this force
per unit volume, g the uniform volume-density of the ponderable
matter, and let us suppose that this density is invariable and that,
besides the charge o, the sphere contains an equal charge of opposite
sign that is immorable. Then, outside the magnetic field, a motion
represented by

evene + vO

may take place.

By / I have now indicated the direction in space in which the
solid harmonie Wz increases most rapidly, and the differential coeffi-
cient is to be understood as a vector in that direction. The factor p
is still of the form (2), and for the frequency I find

onp =htddn VV? ee ä
2h+1

This formula is of some interest in connection with an important
phenomenon that presents itself in the series of spectral lines. If,
namely, the number 4 is made to increase indefinitely, the frequency
nj approaches to a determinate limit.

It appears from (14) that in the present case, as well as in the
former one, each type of motion corresponds to a certain spherical
harmonic. Hence, all the reasonings of the foregoing articles may
be repeated with only a slight modification.

I shall not dwell at length on this subject; suffice it to say, that
in the magnetic field the vibrations of the first order have the
three frequencies

He

nj and xj + —,
2 m

whereas the frequencies of the motions of the second order are

He He
My , ME — and nt.
2 m 4m

In these expressions e again denotes the total charge, and m the
total mass.

§ 11. The fundamental electromagnetic equations for the sur-
rounding ether enable us to determine the vibrations emitted by
the systems whose motion we have examined. The expressions for
the components of the dielectric displacement will contain terms
inversely proportional to the distance 7, but also other terms varying
as the second and higher powers of r—!. Now, it is clear that
only the terms of the first kind are to be taken into account when
we treat of the emission of light. If these terms are calculated for
the vibrations of the first and the second order, they are found in

. u a . . .
the latter case to contain the factor aye being again the radius

of the sphere, and 4 the wave-length of the emitted radiations. If,
therefore, the displacements on the sphere itself in the Yz-vibrations
were of the same order of magnitude as those in the Yj-vibrations,
the light produced by the first would be very much feebler than that
which is due to the latter, All determinations of molecular dimen-

( 353 )

: a, zal datk
sions tend to shew that 5 38 an excessively small fraction; if it

were otherwise, there would be so much damping that the spectral
lines could not be as sharp as they are.

Now one might believe that on the sphere itself the amplitude of
the Y-vibrations were so much greater than that of the Y,-vibrations,
that the motions of the second order could produce a perceptible

amount of light, notwithstanding the smaliness of the factor —. As-

suming this for an instant, improbable though it seemed, and deter-
mining by my formulae, for the shell as well as for the solid sphere,
the properties of the emitted rays of light, I was led precisely to
Cornu’s quartet if I supposed the observations to take place across
the lines of force, the middle line of the quintet vanishing alto-
gether. This seemed very promising at first sight, but, considering
the radiation along the lines of force, I found that in this case it
ought to be the two inner lines of the quartet that remained, and not
the outer ones, as observation has shown to be the case. This suffices
to banish all idea that the influence of the factor = might be com-
pensated by a large amplitude in the sphere. We cannot but take for
granted that the vibrations corresponding to harmonics of the second
order are incapable of radiating. This is due to the circumstance
that in adjacents parts of the sphere there are equal and opposite
displacements of equal charges.

Of course, the vibrations of still higher orders will be equally
incapable of producing rays, and similar remarks will apply to sys-
tems of a totally different nature. Thus, the higher tones of a
sounding body whose dimensions are very much smaller than the
wave-length, will be very feebly heard, and it is for a similar
reason that the tone of a tuning fork has to be reinforced by a
resonance case. After all it seems very probable that the light of a
flame is in every case caused by vibrations in which there is a
variable electric moment in a definite direction, and which may in
so far be called of the first order, though they need not depend
precisely on a spherical harmonic. If this principle be admitted, it
may be shown that, along the lines of force, only those components
remain visible which are polarized in the direction of these lines
when viewed across the field.

§ 12. Seeking for some means by which the vibrations of the
second order might be made to reveal themselves in the spectrum,
24

Proceedings Royal Acad. Amsterdam. Vol. I.

( 354 )

and by which therefore the multiple lines in the ZeEMAN-effeet migh
perhaps be explained, I have been led to the assumption that in a
source of light there exist not only the primary vibrations we have
so far considered, but also secondary vibrations which are produced
in the way of von HeLMHOLTZ's combination tones. This assumption is
by no means a new one. Many years ago, Mr. V. A. Junius!) has
remarked that the many equal differences existing between the fre-
quencies of different lines of a spectrum, seem to indicate the presence
of such secondary vibrations. Indeed, it seems difficult to conceive
another. cause for the constaney of the difference of frequencies
which is found e.g. in the doublets of the alkali metals. It ought to
be remarked that secondary vibrations, the word being taken in its
widest sense, may arise in very different ways. The displacements

may be so large that the elastic forces — and in our spheres also
the electric forces — are no longer proportional to the elongations.

Or, perhaps, the vibrations will cause the superficial density of the
charged shell to vary to such a degree, that the convection current
cannot be reckoned proportional to the velocity and the original
density. Moreover, two vibrating particles may act upon each other
and each or one of them may thus be made to vibrate as a whole.
This case would present itself e.g., if there were two concentric
spherical shells, each of them capable of vibrating in the way we
have examined. They might have different frequencies, or even one
of them might have the frequency 0; i.e., one sphere might be
charged to an invariable density proportional to some surface harmonic.

It is not necessary to make any special assumption concerning the
mechanism by which the secondary vibrations are produced. It will
suffice to assume that the system is perfectly symmetrical all around
the centre of a particle and that, if in one primary vibration we
have to do with expressions of the form:

g cos (nt Je), «<A

and in a second one with similar expressions :

q' cos (nt FE), det EN

the derived vibrations will depend on the product

1 V. A. Junrus, De lineaire spectra der elementen. Verh, der Kon. Akad. v.
Wetensch, Deel 26.

EE .

( 355 )
q q' cos (nt + e) cos (n't Hc!) = 4h qq cos[(n—n')t +(e —e)] +
4qq'cos[(n-+n/)t + (c+ e)].

Of the two vibrations, I shall only consider the one whose fre-
quency is n—n’,

§ 13. It is easily seen, and may be verified by working out some
example, that we can obtain a secondary vibration of the first order,
i. e. one which really emits light, by combining a vibration of the
second order with one of the first order, these primary motions being
executed either by the same sphere, or by two concentric shells.

Let us now imagine the three vibrations corresponding to the
functions Y.., Y, and Y., and the five vibrations determined by Y,,,
Ve =H(Y yy Yee), Yaz, Yyz, Yes. Let the factor p that has been intro-
duced in §4 be of the form (15) for one of the former vibrations, and
of the form (16) for one of the latter. By considering the symmetry
of the system, it may be shown that a secondary vibration in the
direetion of one of the axes of coordinates can only be produced by
the combination of these two, if, among the three indices of the two
harmonics, the one that corresponds to the axis considered, appear
an uneven number of times. Thus the mutual action of a Yr,‚- and
a Y,-vibration will call forth only a vibration in the direction of OY.

Another question is to determine the amplitudes of the derived
vibrations taking place along OX, OY and OZ. In every special case
the amplitude must be proportional to qq’; we may therefore denote
it by multiplying gq’ by a certain amplitude factor.

These factors are not independent of one another; they may all
be expressed in terms of one of them. To understand this, it must
be kept in mind that, if the first of the two combined primaries
a and b be decomposed into some components, say into aj, ag, etc.,
the secondary vibration {a, b} may be considered as the resultant
of {a;,b}, tag, bj, etc. If we denote the amplitude factors by

Yan, Yels, ete., the last index indicating the direction of the
secondary vibration, we shall have

LY;

yy Yel = ye Yz|x ’

anid
pe, HE + [Yay ee + Piers AES 0.

The last formula is a consequence of the relation

ve slg Ate ya Ut

Let us put

Then
[Yay Melk = — 44%, [En Melk: == — 34%,

so that the amplitude factor is now known in all cases in which the
harmonic of the second order is a zonal one whose pole coincides
with that of the other harmonic or is 90° distant from it. All other
cases may be reduced to these two by suitable decomposition of the
harmonics. In this way I find the values of the amplitude factors
inscribed in the following table; the letters x, y, z again serve to
indicate the direction of the secondary vibration.

"ey Yay Ye, i Yes
Pe HUD UD) HUD Oe
Vn ln te) 0 + 3/42(z) — hz (y)
Y 0 0 LACIE ELAN) ee

§ 14. In the magnetic field there are three modes of motion of
the first order, whose frequencies are

my st ma, my n'y 4 ye. le eC)

We shall call the amplitudes of the variable pj (§ 8) in the first
two motions, and that of the variable p, in the last one

Gia Toe WOERD

Then there are five motions of the second order, having the
frequencies

mgt n'g, ng gs Ng Eng, ng — Alg, Mm « « (18)

Let

respectively be the amplitudes of p, ($ 9) for the two first motions,
of pz for the third and fourth, and of p; for the last vibration.
We shall now take as an example the combination of the first
of the vibrations (17) with the first of (18).
The motion of the second order consists in a Y‚,- and a Yyy-
vibration for which we may respectively write

(357 )
q' cos [ (na + n'a) t He]
and
qr cos [ (ny + n'g)t He + $7).

On the other hand, there are at the same time a Y,-vibration

gy cos [(m + m')t+e},
and a Y,-vibration
gr cos [(m + m)t-fe+ 3m].

Consulting the small table of the last Art., I find a vibration

3/4 #9191 cos [ (ng — ny + ng’ —m)t he —e—$ a] —
— Sagan eos [(mg— my + mo —m/)t+e’—e + 3a] =
= 3 aq qr cos [ (ng — ny + ng — m')E+e —e— ha]

parallel to OX, and a vibration

Sa qa gn ¢08 [ (my — my + Mg! — mt He —e] +
+ 3/4491 91' cos [ (ng — my + ng’ — mt He —e] =
= 3/9 #9, gr cos [ (mg — ny + ng! — ny') t He —e)

in the direction of OY, Hence, across the lines of force we shali
see light whose vibrations are perpendicular to the lines of foree and

: : . 9 9 2 s
whose intensity may be put proportional to ae qi? n°. Since there

is a difference of phase of '/; period between the two secondary
vibrations, both together will produce circularly polarized light along
the lines of force.
By similar reasoning it is found that the second of (17) and
the second of (18) do not produce any secondary vibrations.
Examining all the 15 combinations, I find the following results,
as regards the radiation across the lines of force.
A. There will be seen in the spectrum the following lines, whose
vibrations are parallel to the lines of force.
1. A central line whose frequency is ng—n,, and whose in-
tensity is proportional to

q3° q's” [12].

( 358 )

2. Two side lines, each at a distance of 4 n9'—n;' from the
) 2 2 1
preceding one. Their intensities are

9 9 19 9 9 19
a q° gs * [9] and ee qa” [9].

B. The following lines will be produced by vibrations perpen-
dicular to the lines of force.
1. Two lines at distances n'—n,' from A,1. Intensities:

9 ae Af) 9 DR
oe [9] and 49 q2 [9] -

2. Two lines at distances 47's from A, 1. Intensities:

9 a? [5] ae are =|
16 % G3 my an 16% qa 5):

3. Two lines at distances n'; from A, 1. Intensities:

1 aes 3 Lig Ak
pave [S]oa Larve [S)

In the observations along the lines of force, the lines B only
will be seen, with the same relative intensities. They will then be
circularly polarized.

Of course, the source of light will contain innumerable molecules
for which the quantities g and g' will have widely different values.
Assuming that both the vibrations of the first and those of the
second order take place indifferently in all directions, and that even
a particular vibration of one kind may be equally accompanied by
vibrations of the other kind in all possible directions, I find for
the relative intensities the numbers inclosed in brackets.

Perhaps the way in which the ions are made to vibrate will be
unfavourable to the existence at the same time of certain particular
vibrations of the first and the second order; some of the derived vibra-
tions would then have a smaller intensity than the one indicated.
As to the middle line 4,1, it must always be weakened by ab-
sorption in the exterior parts of the source. Yet, in the case of
luminous particles of a symmetrical structure, it seems impossible
that this central line should ever vanish altogether.

§ 15. If there were no ZEEMAN-effect for the vibrations of the
first order, we should have #', = 0, and the lines B,3 would form

( 359 )

a single line in the middle, whose intensity would be 3. If in this
case, for one reason or another, this line B, 3, and the lines 4, 1
and B, 2 were to disappear or to become imperceptible, we should
only see A,2 and B,l and this would be a quartet as has been
observed by Cornu.

The case n'3 = zn, (§ 9) is likewise of some interest. B,1 and
B,2 would then form a single pair, each of whose components would
have the intensity °7/.. The distance of these strong lines would be
half that of the lines 4,2, and, if it were not for A,1 and B,3 we
should have «a quartet, the outer components of which would be
polarized perpendicularly to, and the inner components in the direc-
tion of the lines of force. Quartets of this kind have been really
observed.

S 16. The following remarks remain to be made.

1. Since the frequency of the secondary vibrations is wholly
determined by that of the primary ones, we need not trouble our-
selves about a direct ZEEMAN-effect in these secondary vibrations.

2. Any explanation of the spectral lines must account for their re-
versibility. Consequently, the foregoing theory, which attributes some
lines to derived vibrations, will hold only, if a system can be made
to vibrate by the action of forces, whose period corresponds not to
a primary, but to a secondary vibration of the system. I believe
this to be really possible, but for want of space, I shall not now
insist on this point.

3. If one wishes to apply the above considerations to vibrations of
an order, higher than the second, one soon perceives that it is
impossible to obtain a motion of the first order by combining these
higher modes with vibrations of the first order.

Vibrations that are capable of radiating may however be derived
from two vibrations whose order differs by unity. If now the primary
motions showed the peculiarity that has been mentioned in § 10
and has been observed in the series of spectral lines, this peculiarity
wonld also present itself in those derived vibrations whose frequency
is the sum of the frequencies of the primaries; it would not exist
in the secondary vibrations corresponding to the difference of these
frequencies. I must acknowledge however that this conception of
the series of spectral lines seems hardly reconcilable to the fact of
so large a number of lines becoming simple triplets in the magnetic

field.

(March 22th, 1899.)

he ERG ake Dh

| eat A nakrkt ke aa
j t har Ue Ì
ay 1 aA)
ie LN ee nit
prea ‘

! veg
à AE aat
1 i | Af oe
aft el Pity
i i hay
£ iE)
vy
‘
Î
bind CA
7a
au } CA AE
? Glad eN
. NN j Ln i ~~ .
Fes liteil gt
‘ ihe!
ey Ae ie OT P
Tay «dt " ih OTT) tay ei ts!
an ' i A eh th Aly CAR
= gt CRY Bh PAS. ES

BN val A fi

Ne dn dn SE t~—‘S~S

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING

of Saturday March 25th 1899.

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

Afdeeling van Zaterdag 25 Maart 1899 Dl. VII).

Contents: „The effect produced upon respiration by faradic excitation of some nerve-tracts”.
By Prof. C. Winkrer and Mr. J. Wrarpr BECKMAN, p. 361 (With one plate). — „The
influence of salt-solutions on the volume of animal cells”. (2nd Communication.) By
Dr. I. J. HAMBURGER, p. 371. — ,,An anomaly in the course of the plaitpointeurve in
a mixture of anomalous substances”. By Prof. J. D. van DER Waars, p. 385. — „On
variation of volume and of pressure” (III). By Prof. J. D. van DER Waars, p. 390. —
„On the characteristic equation of y.p. Waars.” By Prof. L. Borrzmaxn (communicated

by Prof. J. D. van per Waats), p. 398. — ,,The galvano-magnetic and thermo-mag-
netic phenomena in bismuth” (2nd Communication.) By Dr. E. van EvERDINGEN Jr.
(communicated by Prof. H. KaMmERLINGH ONNES), p. 404. — „On the velocity of elec-
trical reaction” (II). By Dr. Ernst COHEN (communicated by Prof. H. W. Baxuurs
RoozeBoom), p, 417. — „Diffraction of RöNtceN Rays”. By Prof. H. Haca and Dr.
C. H. Winn, p. 42u (With 2 plates). — „Simplified Theory of electrical and optical

phenomena in moyirg systems”. By Prof. H. A. Lorentz, p. 427. — „STOKES’s Theory
of aberration in the supposition of a variable density of the ether”. By Prof. H. A. Lorentz,
p- 443. — „On reducible hyperelliptic Integrals”. By Prof. J. C. Krurver, p. 448.

The following papers were read:

Physiology. — ‘The effect produced upon Respiration by faradic
excitation of some nerve-tracts’. By C. WINKLER and J.
Wrarpr BECKMAN.

In one of the previous meetings!) of the Academy, we made a
communication about the results of our experiments upon the chan-
ges of respiration, occasioned by faradic excitation of the cortex of
the frontal brain in dogs. We then demonstrated, that a defined spot
(our point 16)*) answers to that excitation by increasing the func-

") C. Winkrer, Attention and respiration. Proceedings of the royal Academy of
Sciences. Amsterdam. Saturday, October 29th 1898. p. 121. ’
*) Ibidem, cf. Fig. XX—XXIII,

bo
or

Proceedings Royal Acad. Amsterdam. Vol. I.

( 362 )

ions of the inspiratory centres, which are supposed to exist in the
medulla oblongata.

Strong currents call forth a forced permanent inspiration (occa-
sionally a deep inspiration foliowed by lengthening (suppression) of
the expiration). Weak currents cause acceleration of respiration.
Often, both these effects, may be observed combined.

So with respect to this problem, we took the side of Murk !)
and SPENCER *) against Hrrzi *) and Francois FRANCK *).

During our experiments we found that a regular respiration was
to be considered extremely rare, with the animals at our disposal.

Acceleration of rhythm, variation of amplitude, superficial inspi-
ration alternating with a deep or a very deep one, all these appa-
rently spontaneous disturbances were often observed, and may oeeur
without any electric stimulation of the cortex. They were a hin-
drance to our experiments.

Two circumstances could be considered to be the cause of the
irregularity in the respiration of our animals; the narcosis, which
could not be dispensed with, as a painful operation had to be per-
formed, and the serious operation, necessary for the exposure of the
cortex of the brain. Both influence the respiration, increasing the
action of the inspiratory functions.

The influence of morphia-narcosis.

All the animals experimented on, were operated in ether-narcosis,
after the injection of a small quantity of murias morphici
(+ 0.005—0.010 Gr. pro kilogramme weight of the animal).

It may be true, and we also stated the fact, that the irregular
respiration may be made into a regular one, in rhythm and in amplitude,
by means of ether, but we did not dare make use of this poison, con-
sidering the uncertain influence exercised by it on the excitability of
the psycho-motor centres of the cortex.

On the other side it is a well-known fact, that ether-narcosis passes

1) Herman Monk. Ueber die Functionen der Groszhirn-Rinde. Elfte Mittheilung.
1890. S. 159. (Gelesen in der Gesammt-Sitzung der Königlichen Akademie der Wis-
senschaften zu Berlin, am 20 Juli 1882).

2) W. G. SpeNcer. Philosophical Transactions of the Royal Society. London 1895.
Vol. 185. p. 609. The effect produced upon Respiration by faradic excitation of the
cerebrum in the monkey, dog, cat and rabbit.

*) Epvarp Hrrzic. Untersuchungen ueber das Gehirn. Berlin 1874 S. 84.

*) Francots Franck. Legons sur les fonctions du cerveau. Paris 1687, p. 126—162.

( 363 )

off quiekly and our experiments began at the earliest, an hour after
the cessation of the narcosis.

As for our experiments, a discussion of the influence of ether can
therefore have no value.

It was a different case, with the small quantity of morphia which
we injected four hours before the beginning of our experiments.
Our reason for doing so was partly to keep the dogs a long time
quiet (insensible to pain), partly to use its influence for the stimu-
lation of the cortex as morphia increases the irritability of the psy-
cho-motor centres to a certain extent.

The influence of morphia on the respiration was evident in ali
the tracings we cbtained of our animals. In consequence of the very
moderate dose of morphia which was used, the respiration may be
somewhat slower and deeper than before, but (and this is a charac-
teristic feature in the tracing of the respiration in morphinised dogs),
every now and then, in some cases frequently, the regular tracing
is interrupted by a quick and very deep inspiration, followed by a
slow and prolongated — a suppressed — expiration (Fig. 1).

This long and deep sigh which we called the morphia-sigh, we
always met with in the tracing of the respiration of morphinised dogs..

Sounds in the neighbourhood, e. g. the clapping of hands, the
rattling of the hammer of the induction- apparatus, may call it forth.
Often, in the majority of cases even, it seems to come, without any
exterior influence.

Another irregularity, which is closely connected with the typical
one we described, is the following:

Short inspirations, not very deep, but quick, are noticed in the
tracing, during the prolongated expirations, characteristic to the sigh.
They change the aspect of the sigh. It seems, as if a secundary type
of respiration with a quick rhythm, is superimposed upon the ordinary
type. This superposition may be seen at the very first in the expiration-
phase of the morphia-sigh, but often the quick respirations appear in
the expiration-phase of several respirations, sometimes even in every
one of then. (Fig. 2.)

Both changes, the deep inspiration with lengthened expiration,
and the quickened respiration, at first only noticeable during the
period of expiration, speak in favour of increased inspiratory functions.

They are of the same nature as the inspiratory effects, observed
during the excitation of our point 16 of the frontal part of the
cortex !). As we mentioned before, it is known that morphia increases

1) ©. WINKLER |. c. p. 158 and fig. XXV, XXVII and XXVIII.

no
or
*

( 364 )

somewhat the excitability of the psycho-motor centres *), We stated,
that ether, in diminishing the irritability of those centres *), causes all
those irregularities to disappear.

We also observed that acoustic and optic impressions were in many
cases the perceptible causes of these sighs, and it is known in human
pathology, that a general stimulation of the human cortex (menin-
gitis, tumour of the frontal lobe) may occasion similar sighs.

So there is room for the opinion, that morphia exercises the same
influence on the point 16 of the frontal cortex as on the other
psycho-motor centres, and that our experiments were made on dogs,
whose inspiratory functions were increased by a tonus, proceeding
from the cortex of the brain. We notice at the same time two diffe-
rent effects upon those inspiratory functions, 1° the deep inspira-
tion, 2° the quickening of rhythm.

The influence of the operation.

Of still greater importance is the effect of the operation on the
animal, after the increasing (by morphia) of its sensibility to influences
which promote inspiratory effects.

Nerves (the optic Nerve and two branches of the trifacial Nerve)
are exposed and cut through, and so are stimulated mechanically.

This stimulation changes the respiration.

Effect of the faradic excitation of the optic Nerve

upon the Respiration.

The tracing of the respiration registered during the faradic excita-
tion of the optic Nerve (fig. 3 N. opt.) is a very characteristic one.

When stimulating with a very weak current (12 cm. distance
between the two coils) a quick and very deep inspiration is produ-
ced, immediately followed by a lengthened, suppressed expira-
tion. The stimulus not being of too long duration, the suppression
of the expiration lasts as long as the stimulation, and sometimes
even longer.

After stimulating with moderate currents (10—6 em. distance
between the two coils) the tracing of respiration is that which is
reproduced in fig. 3. A series of quick respirations is superimposed

1) Hirzie |. c. p. 38.
2) Hirzie |. ce. p. 39.

( 365 )

upon the tracing of the deep, sigh-like respiration, mentioned above.
Always the deep inspiration sets in at the beginning, the suppression
of the expiration lasts till the stimulus ceases. Usually the stimulation
causes also stretching of the neck.

It proves that it is necessary to control the tracing of the thoracal
movements (registered with the pneumograph of Margy) by the
tracing of the changes which the pressure of the air in the trachea !)
undergoes. The quick respirations then appear as violent gasps,
causing very extensive movements of the lever, inspiratory as well
as expiratory.

The stimulation ceasing, the inspiratory effect still continues. After
a strong stimulus a few quick respirations take place followed by
deep inspiration.

The effect of the excitation of the N. trigeminus upon
the Respiration.

Equally characteristic is the effect of the excitation of the first
branch of the N. trigeminus upon the respiration.

We examined the N. frontalis and the N. lacrymalis of the ramus
ophthalmicus Nervi trigemini (Fig. 3 r. lacr. N. V.). As yet we
will not speak of the N. ethmoidalis and the N. naso-ciliaris.

Even the weakest currents (12 em. distance between the coils)
cause quick, violent gasps, inspiratory as well as expiratory, such
as we mentioned previously, in speaking of the optic Nerve. The first
of the guick respirations may be an expiration, in general this is
not the case. The tracing now obtained, forms however a perfect
contrast to that of the respiration produced by the excitement of the
optic Nerve; the effect is not characterised by the sigh, the maximal
inspiration followed by suppressed expiration does not exist. On the
contrary, the inspiratory position of the thorax slowly increases. The
stimulus having ceased, the slowly extended, but now distinctly inspi-
ratory position of the thorax changes suddeniy and makes place for
a forced expiratory position, though the quick respiration continues

1) For this purpose the vertical tube of a hollow T-canule is introduced into the
trachea. The air enters freely through one horizontal arm, the other is connected with
Marey’s drum. The tracings show only the quick changes of pressure of the air
in the trachea, Continuous conditions, such as a permanent inspiratory or expiratory
condition of the thorax are registered as zerolines, and slow variations of pressure,
even if they are noticeable, are registered (one of the legs of the T-canule being open)
in an incomplete manner.

( 364 )

somewhat the excitability of the psycho-motor centres *). We stated,
that ether, in diminishing the irritability of those centres *), causes all
those irregularities to disappear.

We also observed that acoustic and optic impressions were in many
cases the perceptible causes of these sighs, and it is known in human
pathology, that a general stimulation of the human cortex (menin-
gitis, tumour of the frontal lobe) may occasion similar sighs.

So there is room for the opinion, that morphia exercises the same
influence on the point 16 of the frontal cortex as on the other
psycho-motor centres, and that our experiments were made on dogs,
whose inspiratory functions were increased by a tonus, proceeding
from the cortex of the brain. We notice at the same time two diffe-
rent effects upon those inspiratory functions, 1° the deep inspira-
tion, 2° the quickening of rhythm.

The influence of the operation.

Of still greater importance is the effect of the operation on the
animal, after the increasing (by morphia) of its sensibility to influences
which promote inspiratory effects.

Nerves (the optic Nerve and two branches of the trifacial Nerve)
are exposed and cut through, and so are stimulated mechanically.

This stimulation changes the respiration.

Effect of the faradic excitation of the optic Nerve

upon the Respiration.

The tracing of the respiration registered during the faradic excita-
tion of the optic Nerve (fig. 3 N. opt.) is a very characteristic one.

When stimulating with a very weak current (12 em. distance
between the two coils) a quick and very deep inspiration is produ-
ced, immediately followed by a lengthened, suppressed expira-
tion. The stimulus not being of too long duration, the suppression
of the expiration lasts as long as the stimulation, and sometimes
even longer.

After stimulating with moderate currents (L0—6 em. distance
between the two coils) the tracing of respiration is that which is
reproduced in fig. 3. A series of quick respirations is superimposed

1) Hirzie |. c. p. 38.
*) Hiraia |. c. p. 39.

( 365 )

upon the tracing of the deep, sigh-like respiration, mentioned above.
Always the deep inspiration sets in at the beginning, the suppression
of the expiration lasts till the stimulus ceases. Usually the stimulation
causes also stretching of the neck.

It proves that it is necessary to control the tracing of the thoracal
movements (registered with the pneumograph of Margy) by the
tracing of the changes which the pressure of the air in the trachea !)
undergoes. The quick respirations then appear as violent gasps,
causing very extensive movements of the lever, inspiratory as well
as expiratory.

The stimulation ceasing, the inspiratory effect still continues. After
a strong stimulus a few quick respirations take place followed by
deep inspiration.

The effect of the excitation of the N. trigeminus upon
the Respiration.

Equally characteristic is the effect of the excitation of the first
branch of the N. trigeminus upon the respiration.

We examined the N. frontalis and the N. lacrymalis of the ramus
ophthalmicus Nervi trigemini (Fig. 3 r. lacr. N. V.). As yet we
will not speak of the N. ethmoidalis and the N. naso-ciliaris.

Even the weakest currents (12 em. distance between the coils)
cause quick, violent gasps, inspiratory as well as expiratory, such
as we mentioned previously, in speaking of the optic Nerve. The first
of the quick respirations may be an expiration, in general this is
not the case. The tracing now obtained, forms however a perfect
contrast to that of the respiration produced by the excitement of the
optic Nerve; the effect is not characterised by the sigh, the maximal
inspiration followed by suppressed expiration does not exist. On the
contrary, the inspiratory position of the thorax slowly increases. The
stimulus having ceased, the slowly extended, but now distinctly inspi-
ratory position of the thorax changes suddenly and makes place for
a forced expiratory position, though the quick respiration continues

1) For this purpose the vertical tube of a hollow T-canule is introduced into the
trachea. The air enters freely through one horizontal arm, the other is connected with
Marey’s drum. The tracings show only the quick changes of pressure of the air
in the trachea, Continuous conditions, such as a permanent inspiratory or expiratory
condition of the thorax are registered as zerolines, and slow variations of pressure,
even if they are noticeable, are registered (one of the legs of the T-canule being open)
in an incomplete manner.

for a time. Then generally one or more sighs follow, after which
normal respiration is restored.

The N. infra-orbitalis rami supra-maxillaris N. trigemini answers
to the excitation by a change of respiration different from that
produced by stimulation of the N. opticus, but also differing
at least in some measure, from the effect of the excitation on the
first branch of this Nerve. The effect, even when but very weak
currents are used, is always the same, a strong permanent inspi-
ratory situation of thorax, accompanied by very quick respiration
(Fig. 4). The tracing of the respiration differs, in this case, from
the maximal sigh-like inspiration produced by stimulating the optic
nerve, by its permanence, and by the after-effect, which is a forced
expiration and long duration of the quickened rhythm. It differs also
from the tracing produced by excitation of the first branch, the
quickening here taking place in a more marked manner and during
permanent deep inspiratory position of the thorax, and the after-effect
also being more marked and lasting longer.

These facts prove, that the effect of excitation of the N. opticus and
of the N. trigeminus on respiration cannot be so simply formulated
as CHRISTIANI!) did by saying that excitation of the optic Nerve
produced an inspiratory, that of the N. trigeminus an expiratory effect.

Faradic excitation of the three nerves mentioned, always accelerate
the respiration, that is to say, each of them exercises the same
influence on the second of the inspiratory effects above mentioned,
but each of them has a somewhat different effect on the first of
the so called inspiratory effects 1. e. on the deepening of the inspiration.

The faradie excitation of the optic Nerve cails forth the maxi-
mal deep inspiration, directly followed by lengthened expiration,
suppressed as long as the stimulus lasts — what we have called
sigh —, that of the first branch of the N. trigeminus produces none
or very little effect, it increases slowly the inspiratory position of
the thorax, that of the second branch of this Nerve maintains the
thorax in a permanent and maximally extended state.

The different tracings of respiration, obtained during excitation of
the nerves, make it advisable to suppose that two different inspira-
tory effects, acceleration of rhythm and deepening of amplitude, exist.

The deepening of the amplitude however may appear in two forms 1°,
as the quick, maximally deep inspiration followed by a suppression

1) Anrnur Cnristiant. Ueber Athmungscentra und centripetale Athmungsnerven.
Monatsberichte der königlich preussischen Akadeinie der Wissenschaften zu Berlin,
1682. (Sitz. 17 Febr. 1881). S. 213.

( 367 )

of the expiration — our sigh —, 20 as a permanent and maxi-
mal inspiratory position of the thorax (SPENCER’s over-inspiratory tonus).

The excitation of these nerves makes it possible to distinguish and
separate the two inspiratory effects. The optic Nerve, when excit
ed with a very weak current only produces the rise of the sigh,
the excitation of the first branch of the fifth Nerve in that case
quickens respiration. Somewhat stronger currents generally call
forth both effects (SPENCER’s over-inspiratory clonus) together. A
very strong current may give in both cases a permanent inspiratory
effect. At the same time the tracing of respiration during the exci-
tation of the optic Nerve, can in no case be confounded with one,
written “during the excitation of the first branch of the fifth Nerve.

If the cortex of the brain is excited at the point 16 of our dia-
gram the same order of effects is produced. Weak currents cause
acceleration of rhythm, !) moderate currents deep inspiration, length-
ened and suppressed expiration, often with a quick rhythm of res-
piration superimposed in the tracing, *) strong currents may produce
an over-inspiratory tonus. °)

The same effect is produced as soon as the side wall of the
third ventricle is stimulated. We fully confirmed CHrIisTIANT's
results on this subject, as opposed to those of KNouL*). The
excitation of a spot in the side wall of the ventricle, situated under
the commissura posterior, produces inspiratory effects. Again weak
currents cause acceleration of rhythm, moderate currents cause deepe-
ning of inspiration combined with acceleration, strong currents pro-
duce a forced, permanert inspiration (Fig. 5). It seems probable too,
that in this case, no centres are excited, but nerve tracts ori-
ginated from the cortex cerebri in the region of point 16 of our
diagram.

Our operation often causes the accelerated type of respiration, by
mechanical excitation of the Nerves. This is nearly always the case, if
it is necessary to remoye the contents of the orbita, in order to make
room for the exposure of the frontal and basal parts of the brain.

The ophthalmic artery and the ophthalmic vein must be tied and
often it is impossible to tie the ligature, without taking the optic

1) Winker |. c. fig. XXIV.
*) Winkter |, e. fig. XXV and fig. XXVIII,
3) WINKLER Ì. c. fig. XXVI and fig. XXVII.

*) Prof. Ph. Knoun. Beiträge zur Lehre von der Athmungs-Innervation. 6te Mitth.
Zur Lehre vom Finflusz des centralen Nervensystems auf die Athmung. Sitzungsber.
d, K, Ak. d. Wissensch. in Wien, Bd, XII. Abth, IIT. S. 283,

( 368 )

Nerve and the first branch of the N. trigeminus into it. If this
happens, one may suddenly see the regular rhythm which existed
before quickened not only, but the acceleration of rhythm may be
superimposed upon the existing rhythm (Fig. 6).

Then a very typical tracing of respiration is obtained. Not always
the superposition of the quick rhythm takes place so completely, often
the acceleration covers the former type partially, and if the sighs,
mentioned before, interfere with the two rhythms of respiration des-
cribed, the tracing may become of an extreme irregularity. In such
cases it is impossible to experiment on the changes, which respira-
tion undergoes during the stimulation of the cortex.

The effect of the excitation of bulbus, tractus and lobus
olfactorius upon respiration.

If the consequences of the narcosis and the operation are known,
and the tracings obtained in such abnormal conditions understood,
it may be possible to study the strange effets, which the excitation
of the bulbus, the tractus and the lobus olfactorius produces upon
respiration.

Munk, DANILEWSKY, ') Unverricut *) and others obtained expira-
tory effects on stimulating different parts, principally the basal parts
of the brain. SPENCER mentions the effects after stimulating the
lobus olfactorius in a most accurate manner.

Our results differ in many points from the results reported by these
authors. In a single point our experiments agree with, and confirm
the view of SPENCER viz. with regard to the existence of a well
defined spot on the lobus olfactorius, stimulation of which produces
slowing of respiration and arrest of the respiration in expiration,
even if weak currents are used.

In our diagram (Fig. 9) this point is indicated by the letters
f and g. It is found on the lobus olfactorius, on the border of
the fissura rhinica, exactly behind the place where the fissura prae-
sylvia touches the fissura rhinica.

But our experiments teach us more. The same effect may be
obtained from the tractus and also from the caudal end of the bulbus
olfactorius. However, we can state, that it can only be produced
from the basal surface of the olfactory bulb, and from the basal

1) DANILEWSKY. Experimentelle Beiträge zur Physiologie des Gehirns, Prrücer’s Arch.
f, Phys. Bd. XI. 1875. p. 128.

2) UNvermicuT, Experimentelle Untersuchungen über die Innervation der Athmungs-
bewegungen. Verhandlungen des Congresses für Innere Medicin, Wiesbaden 1888.

( 369 )

parts of the tractus. Therefore it is easier to find it at the points
f and g of our diagram, where the tractus and lobus olfactorius
reach each other, instead of exposing the basal surface of the brain,
which is much more difficuit.

Perhaps this is the reason why Spencer does not state, that the
expiratory effect, we now shall describe, may be produced by exci-
tation of the olfactory bulb.

There is still another point, wherein our results differ from those
of SPENCER. This author obtains “arrest” (and it sometimes takes
place in inspiration, sometimes in expiration) at the beginning of
the excitation with rather strong currents, and as soon as the sti-
mulation stops, the “arrest” ends.

We observed, that even weak currents (10 c.m. distance between
the two coils) and even better currents of moderate strength (8 —6 c.m.)
exciting the points f, g, or the basal middle part of the tractus and
the bulbus olfactorius, produce the following effects.

The respiration may become slower (Fig. 7). In general however,
after a few slow respirations, the thorax gains the position of expi-
ration, and at last “arrest in expiration” takes place. This arrest
may occur before the stimulus (during 10 seconds generally) ceases,
but more often this arrest begins only a few seconds later. It may
then last half a minute and longer. The current not being stopped,
the arrest sets in, and may last for 1 or 2 minutes; ultimately
deep inspirations set in.

If the currents last 10 sec. only, the arrest often begins after
they have ceased, is prolonged 15 to 45 seconds, and then a few
superficial respirations appear (often only visible in the tracing of
the trachea-respiration), the thorax meanwhile taking an inspiratory
position. This period may be indicated by a few inspirations only,
(Fig. 9) at other times the thorax abruptly takes an inspiratory
position and remains a long time in it, some irregular and super-
ficial respirations coming between (Fig. 10), and often the thorax
reaches its inspiratory position only very slowly after a greater
number of irregular, superficial, gradually deepening respirations
(Fig. 11 upper tracing). At the end one or two deep sighs appear,
followed by very deep and slow respirations. 15 minutes and more
may elapse before all has returned to the normal condition.

The arrest and the described mechanism of compensation of the

arrest — as we have called this after-effect, because it may be supposed
that deepening of the inspiration, compensates the arrest in expira-
tion — may be ealled forth, by exciting the points fand g with the

utmost constancy. With no greater constancy are the movements in

( 370 )

the opposite fore-leg caused by faradisation of the psycho-motor
centre of the foreleg.

Occasionally the compensation-movements may be seen, even
without the pre-existence of the arrest itself (Fig. 11 lower tracing).

Exceptionally, the mechanism of compensation is not ‘brought
forth, and in two cases the dog died from the shock, respiration
being arrested in expiration. In the cases, in which this event took
place, the inspiratory functions had been injured by preceding expe-
riments of long duration.

It is clear, that these expiratory effects are due to the stimu-
lation of the olfactory bulbus, tractus and lobus, consequently of
a nerve-tract, not of a centre. It may be conceived, that the dog,
as soon as strong olfactory impulses reach him, arrests the respira-
tion in expiration, to prevent his smelling more. Then prudently,
with irregular, superficial respirations, the thorax is brought into an
inspiratory position and as soon as the danger seems past, he restores
his respiration with deep sighs and long, deep inspirations. The
tractus olfactorius answers faradic excitation by expiratory effects.

The difference between our results and those of SPENCER, which
will make further experiments necessary, may perhaps be due to
the fact, that Spencer worked with ether-narcosis.

DESCRIPTION OF FIGURES.

Fie. 1. Morphia-sigh of a dog.
1 is the zeroline.
2 is the tracing of a tuning-fork of 2 vibrations per second.
3 is the tracing of the movements of the thorax registered with the pneu-
mograph of Margy.
4 is the tracing of the respiration registered from the trachea.

Fig. 2. Morphia-sigh with quickened respiration superimposed upon the phase of
expiration.
1 is the zeroline.
2 is the tracing of a tuning-fork of 5 vibrations per second.
3 is the tracing of the movements of the thorax registered with the pneumo-
graph of Marry.
4 is the tracing of the pulsation of the arteria femoralis.

Fie, 3. Effect upon respiration during faradie excitation of the optic Nerve and
during that of the first branch of the fifth Nerve.
1 is the tracing written by the electric signal, noticing the moment of
excitation,
2 is the tracing of the tuning-fork of 2 vibrations per second.
3 is the tracing of the movements of the thorax registered with the pneumo.
graph of Marny.
4 is the tracing of respiration registered from the trachea (in all the
following figures, the ciphers 1—4 have the signification here mentioned).

©, WINKLER and J. WIARDI BECKMAN. The effect produced upon Respiration by faradic excitation of some nerve-tracts

“tt , 3 f sei
sn WN MT iy)

Fig. 10.

Fie.

Fig.

ig. 11.

or

~)

5 UO

atl.)

At N. opt. the optic Nerve is stimulated, At 7. lacr. N. V. the firs;
branch of the fifth Nerve. The signal causes the rise of the zeroline as long
as the faradisation lasts. The distance of the coils in exciting the optic
Nerve was § cm., in exciting the 7. lacrymalis it was 12 em.

Effect upon respiration during faradisation of the second branch of the fifth
Nerve.

The tracings 1 and 2, does not exactly part from the same point as the
tracings 3—4. The rise of the signal takes place at a moment that the
tracing 3 and 4 have already passed. Tracing 1 and 2 must be read, placed
somewhat more to the right side.

Effect upon respiration during faradisation of the wall of the posterior end
of the 3 ventricle.

In I, IZ, Ill and IV the stimulation takes places with increasing currents
(Distance between the coils of 9, 7, 5 and (4 em.).

Effect upon respiration of a mechanical stimulation (ligature) of the Nerves,
which reach the orbita.

The slow respiration existing before, immediately varics. There exists a
type of respiration, wherein two different rhythms can be recognised. The
one is slow and the other, quick one, is superimposed upon it.

. 1-11. Effect upon respiration during and after the stimulation of the olfactory

tract and of the lobus olfactorius.

During the faradisation of the olfactory tract respiration becomes slower.
(Distance between the coils 6 em.).
Faradisation of the lobus olfactorius (Distance between the coils 8 em.) ing.
Arrest in expiration, follows the stimulus, A few irregular respirations bring
the thorax in an inspiratory position. Deep and slow inspirations follow,
Idem in point e. Slowing of respiration, increasing of the expiratory state,
arrest in expiration. Afterwards arrest in inspiration, deep sighs and finally
deep and slow respiration, lasting a very long time.
Upper tracing. Idem in point g (7 em. distance between the coils). Slowing
of respiration, arrest in expiration, afterwards irregular and superficial respi-
rations extending the thorax, sighs, and finally deep and slow respiration.
Lower tracing. Idem in point g (10 em. distance between the coils),
Without a precedent arrest in expiration, the described movements of inspiration
appear nearly at the same time after the stimulus, as in the upper tracing,
Diagram of the brain of a dog, showing the lateral parts of the rhinencephalon
which were stimulated. After faradisation of the point f and g the expiratory
effects are noticed.

Physiology. — “The influence of salt-solutions on the volume of

animal cells’. (224 Communication). By Dr. H. J. HAMBURGER.

At the May-meeting of last year was discussed the influence
of salt-solutions of the volume of red blood-corpuscles, white blood-
corpuscles and spermatozoa. We can now communicate the result of
similar experiments made with epithelium-cells, derived from four
different places: the intestines, windpipe, urine-bladder and the
oesophagus.

( 372 )

The epithelium was invariably obtained by carefully scraping it
from the organ of an animal just killed. The scrapings were distri-
buted in a little fresh blood-serum or in a Na Cl-solution of 0.9°/o
and afterwards filtered through a small filter of unprepared gauze,
in order to have the cells as far as possible quite free or in small
aggregates. Equal quantities (+ 1/, cc.) of the fluid thus obtained,
were measured off and inserted in test tubes in which were equal
quantities of the salt-solutions, to the influence of which the epithe-
lium cells were to be exposed. After exposure for half an hour
equal quantities of the mixtures were put into funnel-shaped tubes
to be subjected to the influence of centrifugal force. When the
level of the sediment had become fixed, the volume of the epithe-
lium-column was considered to be determined. If after being centri-
fugalized for a short time, the small column of cells did not appear
to be quite homogeneous, by far the greater part of the clear fluid
was pipetted off, the small column with the remainder of the fluid
stirred by means of a platina wire into a homogeneous mixture and
again centrifugalized. If this was necessary with one of the tubes,
the same was done with the other three.

I. INTESTINE-EPITHELIUM.

Experiment I.
‘
Epithelium of the small intestine of a horse, at about one meter’s
distance from the pylorus.
The epithelium is distributed in a little blood-serum of the same
animal.

Salt-solutions employed Volume of the epithelium

Na Cl-sol. of 0.7 °/ 35.5
ORO 34
ees yay 33
Pe ieee 29

It will be seen that the volume of epithelium regularly decreases
with the rise in the concentration of the salt-solution.

1) Cf. Verslag der Vergad. Kon. Akademie, April 21 1897 and May 28, 1298,

( 373 )

A priori, another result might have been expected. The intestinal
mucosa may be considered as a resorbing organ par excellence, and,
as experience teaches us, diluted NaCl-solutions pass through it with
the greatest facility. Hence it seemed obvious that when scraped — off
intestinal epithelium would be distributed in large quantities of NaCl-
solutions of different concentrations, the cells would be saturated
with these solutions, so that there would soon be no more question
of a difference in osmotic pressure between the contents of the cell
and its surroundings; in other words, it was to be foreseen that the
volume of the intestinal epithelium would not be affected by the
influence of salt-solutions of different concentration.

The following experiment, made in the same manner and with
the same sort of epithelium, was to give results quite different from
those of the first experiment.

Experiment II.

Epithelium of the small intestine of a horse, at about half a meter’s
distance from the pylorus.

The epithelium is distributed in a little blood-serum of the same
animal.

Saltsolutions employed. | Volume of epithelium.
NaCl-solution of 0.5%, | 106
” v 7 07°, | 103
F ” r oat | 103

“ Ua a“ 1853 | ] 05

In this experiment the volume of the epithelium remained unchanged.

The difference in the results of the two experiments made a
number of similar experiments necessary.') They confirmed and
enlarged the knowledge we had obtained from the two first:
occasionally it appeared that, as in experiment I, the volume of
epithelium was greatly under the influence of the concentration ; in
by far the most cases, however, the concentration exercised no per-

1) A full and detailed description of the experiments, hereby made, would require
more space than we can here afford; that is also the case with other particulars. They
will, however, be inserted in the Archiv f, Anat. u. Physiol. Physiol. Abth,

(314 )

ceptible influence. This result was obtained not only with NaCl-solu-
tion, but also with grape-sugar and with mixtures of serum and water.

Seeing this difference in the results, obtained with the same
sort of epithelium, only two possibilities suggested themselves: either
the method of investigation was not to be relied on, or the epithe-
lium, though drawn in the different cases from the same spot, was
not always in the same condition.

The first possibility had to be rejected; 1. because in one and
the same experiment the results with salt-solutions of different con-
centration corresponded, not only two to two, but also mutually, and
that, indifferently whether the result did, or did not, indicate an
influence on the volume; 2. because the method with the red and
the white corpuscles, the spermatozoa, and also with the bladder-
and oesophagus-epithelium obtained by seraping, had yielded uniform
results.

There is nothing left but to assume that the epithelium is not
always in the same state of permeability.

With respect to this we may form two conjectures: we may sup-
pose that it is merely a question of time, in other words, that in
those cases in which the volume of epithelium appears to be influ-
enced by the concentration of the salt-solutions, the cells after half
an hour’s immersion are not yet, or but very imperfectly saturated
with the solution, whereas the osmotic equilibrium has already been
established. Under these circumstances more salt-solution might,
after half an hour’s action, have penetrated into the cell, and the
concentration of the salt-solution would in a less degree cause its
influence to be felt on the volume of the cells.

This, however, proved not to be the case.

Jonsequently we must consider the second possibility, viz, that we
have to do with a modification in the state of the epithelium which
continues till it is removed by some agent, a chemical one, for instance.
And indeed, we sometimes succeeded in bringing epithelium from
one state into the other; and that, by means of Mg SO4, which is
known to be able to bring about a modification in the resorbing
power of the intestine, and also by the addition of traces of an acid.
I say purposely ,sometimes”, for now and then we failed.

For the rest, the conditions under which the intestinal epithelium
passes from one state to another and what changes, the cell thereby
undergoes, have hitherto remained unknown to us }).

1), 1 may here observe that this result is by no means a contradiction of the views
1 formerly expressed, viz, that the resorption phenomena, hitherto known, may be
explained physically. At the time I stated emphatically: I do not think of asserting

(375)

Involuntarily we are reminded here of what HerpENHAIN observed
in the live animal with respect to the power of the interstitial sub-
stance between the epithelium cells to allow methyleneblue to
pass through it: in the same field he saw amidst cells whose inter-
stitial substance was coloured blue, others whose interstitial substance
had remained absolutely colourless. 1).

In the most recent times they have tried in the Zürich laboratory
to answer the question, whether in the intestine, besides the inter-
stitial substance situated between the epithelium cells, the cells them-
selves allow dissolved substances to pass through them. *)

The investigations described above have, in my opinion, given an
answer to this question. For, save in those exceptional cases, in
which the seraped-off epithelium appears to be in a peculiar condition,
the volumina of cells, influenced by salt-solutions of different concen-
tration for half an hour, exhibit no mutual differences.

Now this phenomena might be explained by the supposition, that
the epithelium cells are quite indifferent to the salt-solutions, that is
to say, that they allow neither water nor salt to pass through them ;
but the supposition that they would not allow water to pass through
them is immediately disproved by the fact that when, immediately
after mixing them with salt-solutions, we centrifugalize them, and
thus do not wait half an hour before doing so, a difference in volume
is distinctly observed, viz., the volume increases as the concentra-
tion rises.

The cells then, must be permeable to water. Yet the fact, that
the volumina of the epithelium cells after a longer immersion in
salt-solutions approach nearer and nearer to each other, forces us no
less to conclude that the salt-solution penetrates, as such, into the cell.

Our experiments teach us something, also with respect to the
permeability of the cel/-nucleus. They teach us that it is most pro-
bable that, beside the body of the cell, the cell-nucleus of the intestinal
epithelium also allows salt-solutions to pass through it. For, just

„that life neither can, nor will exercise an influence on the resorption process.”
„Under physiological and pathological conditions finely-shaded changes may unques-
„tionably manifest themselves in living membranes, exercising no small influence
von the physical process taking place in them, but by which these processes do not
veease to be purely physical.” (On The significance cf respiration and peristaltic
for the resorption in the intestine.” Verslag der Verg. Jan. 2%th, 1896, note).

1) Hpmenuary. Beiträge zur Anatomie und Physiologie der Diinndarmsclleimhaut.
Pfliiger’s Archiv, Supplementheft. 1888, S. 49.

*) R. Hoser. Ueber Resorption im Dünndarm. Zweite Mittheilung. Pfluger’s
Archiv, B 74, S. 269, 1899.

(376 )

suppose that the nucleus of the intestinal epithelium was per-
meable eaclusively to water, its volume ought to be modified
by the concentration of the surrounding salt-solution, and the cell
in its entirety would experience the influence. What do we observe,
however? That the total volume of the cells is independent of the
concentration of the surrounding salt-solution. Hence, it follows that,
considering the relatively great share the nucleus has in the volume
of the cell, the nucleus has also allowed the surrounding salt-solu-
tion to pass through it.

However, if the nucleus were quite impermeable, even to water,
the total volume of the cell might still have been independent of
the concentration of the surrounding salt-solutions. Considermg howe-
ver all we have seen concerning the influence of salt-solutions on
the volume of spermatozoa, red and white corpuscles, bladder- and
oesophagus-epithelium, the impermeability to water is highly impro-
bable, and can hardly be supposed, if we consider the part, played
by water in the vital processes of the cell.

II. CILIARY-EPITHELIUM.

The second sort of epithelium we have investigated is ciliary-
epithelium from the trachea. The advantage of this is, that during
the whole experiment, we can ascertain whether the object is yet in
a live state. After the cells had been, four hours and even longer,
in contact with the salt-solutions, cilia were or could be set in move-
ment. Also after centrifugalizing ciliary movements could be produced.

Since the experiments were performed in the same manner as
with the intestinal-epithelium, it will suffice to record the results.

Experiment XXI.

Ciliary-epithelium from the trachea of a horse just killed.

The epithelium is distributed in a little Na Cl-solution of 0.9,/°.
Immediately afterwards equal quantities of it are brought into con-
tact with 15 c.c. of a solution of NaCl 0.7°/, and 1.2°/5. After
half an hour’s immersion, 8 c.c. are centrifugalized.

Salt-solutions employed. Volume of the epithelium.
NaCl 0.7°/, 98
09°, 98
7 12 | 85

( 377 )

If we compare the numbers, obtained after an immersion in NaCl
0.70/, and 0.9°/, it appears, that the difference in concentration has
exercised no influence on the volume of the cells, but it has with
respect to the Na Cl-solutions 0.9°/, and 1.20/,.

It was possible that the Na Cl-solution 0.9%, and 1.20, had
therefore caused some contraction, as half an hour’s immersion had
been insufficient to effect a complete exchange between the contents
of the cell and its surroundings.

Under this supposition it seemed to us recommendable to centri-
fugalize the now remaining, but already two-hours old mixtures.

Salt-solutions employed. | Volume of the epithelium.
NaCl-sol. of 0.7°/, 86
a es x LOD), 86
nele 83

While thus after half an hour’s immersion the difference in volume
of the epithelium, lying in 0.9°/, and 1.2 °/) Na Cl-solution amounted to
98—85 7 = age A
ga, xX 100 = 13°, this difference, after two hours amounts only to
86—83
SER X 100 = = 49,.

It appears thus, that after a sufficiently long immersion of the
epithelium in salt-solution, the difference in concentration exercises
no influence on the volumina.

Of the many experiments, made in this direction, I will add two.
Experiment XXII.

Epithelium from the trachea of a horse just killed, distributed in
serum and afterwards in salt-solutions.

Salt anlutions ; Volume of the epithelium after an eon in salt-solutions for
employed. | 1/, hour | 2 hours | 4 hours
: ee
NaCl-sol. of 0.7°/, 68 66 62
oo JONS | 63 64. 61
wan Wa © 199} 57 59 | 57
Pee ee tE 54 | 57 57
26

Proceedings Royal Acad. Amsterdam. Vol. I.

( 378 )

It will be seen that the longer the epithelium is left in contact
with the salt-solution, the less is the difference in volume. In this
case a contact even of two hours is not sufficient to effect a complete
exchange between the contents of the cell and its surroundings. At
the end of the experiment, we can, by putting a preparation in a
gas-camera and passing CO, through it, still set the cilia in movement.

Experiment XXIII.

Volume of the epithelium after an immersion in

Salt-solutiors salt-solutions for

|
Te | !/, hour 2 hours 3 hours
EEN eee
NaCl sol. of 0.7°/o | 90 | 83 80
Do 7 OEP | 86 79 81
In DP NEE | 78 76 78
er 4 159). | 74 75 78

From this experiment we learn that, after half an hour’s immer-
sion, the volumina still differ, but after two hours only very little,
and as little after three. After two hours thus the exchange
between the contents of the cell and its surroundings is almost
completely accomplished here.

At the end of the experiment the epithelium was still alive.

From these experiments, then, we may conclude that the ciliary-
epithelium in a live state allows Na Cl-solutions to pass through it,
though not so rapidly as does the intestinal epithelium.

This permeability of the isolated epithelium, which, although con-
siderable, will of course be more intense in situ, is quite in accor-
dance with the clinical experience, that remedies injected intratra-
cheally are very rapidly resorbed. About the permeability of the
nucleus, can be said the same what has been observed with respect
to the intestinal epithelium.

Ill. BLADDER-EPITHELIUM.

If with the intestinal- and tracheal-epithelium we had to do with
cells which might be expected to be easily permeable to salts, the
reverse was to be expected of bladder-epithelium. The bladder,
indeed, would very badly answer its purpose, if it possessed a great
permeability for dissolved substances.

( 379 )

As is well known, the urine-bladder is lined inside with a fourfold
layer of epithelium cells. In a pig-bladder these may be easily elimi-
nated. It proved however to be necessary to wash the bladder out
well, because not infrequently in the pig, and commonly in the
horse, sediment is found on the mucous membrane.

Experiment XX XI.

Bladder epithelium of a pig just killed; distributed in a little
Na Cl-solution of 0.99.

Equal quantities of this are left for half an hour in contact with
Na Cl-solutions of 0.7%, 0.99/,, 1.2°/, and 1.5%). After being cen-
trifugalized for about two hours, the contents of the tube are well
stirred up by means of a platina wire, left an hour to themselves
and again centrifugalized.

Salt selufions Wolume jaf En after injection of
employed. 1/, hour 1’, hour
NaCl-sol. of 0.7°/, 78 78
pe ne 0:9), 70 70.5
nn np 19 62.5 62
wow ze ors 58 | 58

From this experiment it appears, that the volume of epithelium
decreases regularly and also considerably, with the rise of the con-
centration of the salt-solution, and that the figures obtained after
an hour and a half’s immersion are found to be the same as after
an immersion of only half an hour.

On the ground of similar observations, made on red and white
corpuscles and spermatozoa !), we came at the time to the conclusion,
that the cells consist of two substances, which behave differently
with respect to hygroscopic power; one, the protoplasmatie, which
has no share in the hygroscopic power of the cell, and the other,
the intracellular fluid, representing the whole hygroscopic power of
the cell. It was then possible by a simple calculation to determine
the proportion of the volumina of protoplasmatie to intracellular

1) Proceedings Royal Academy Amsterdam, May 1898.
26*

( 380 )

substance. And the figures obtained with the same species of cell
by means of different salt-solutions agreed well with each other.

If we calculate this proportion also here (1st column), considering
the NaCl-solution of 0.9°/) as the physiological one, we find for
the volume of the protoplasmatic substance with respect to that of
the whole cell

from a andd... . 57.8%,
irom) @) and) <6... DSE
from: sb and ds. =. nel?

These figures correspond well to each other and, joined to other
experiments yielding the same results, which we must omit however
to describe here, justify the same conclusion which, at the time, we
arrived at with respect to blood-corpuscles and spermatozoa.

But not only is there considerable agreement among the figures
obtained for the volume of protoplasmatic substance of the bladder
epithelium of different pigs and horses, but it struck us that these
figures deviated so little from those, which we had found with the
red and the white corpuscles of the latter animal (Proceedings ee
Academy Amsterdam, May, 1898). ;

Hence the idea eend to us that we should once more try
simultaneously with the same animal to determine the volume of
protoplasma-substance in bladder-epithelium and blood-corpuscles.

As will appear from the following experiment, the agreement was
striking, indeed.

Experiment XLI.

Bladder-epithelium of a pig and defibrinated blood of the same
animal are mixed with Na Cl-solutions of 0.7°/, and 1.5°/,, and half
an hour afterwards both pairs are simultaneously centrifugalized.

Volume of Contraction by
sediment NaCl 1.59,
a. NaCl-sol. of 0.79/ 96 96—69
od Bladder-epithelium | —gg “100281,
Mn ARE | 69
c. NaCl-sol. of 0.7°/ 134 1134—96
a Red corpuscles. jz, * 100 = 28.2°/_
nn 1 Ab}, ) 96

( 381 )

Consequently there is a very striking agreement between the
contraction of the bladder-epithelium (containing the nucleus) and the
red biood-corpuscles (void of nucleus), effected by the same salt-solution.

Influence of Urea.

Considering the above-described behaviour of bladder-epithelium with
respect to NaCl, it appeared further of importance to me to ascer-
tain whether this applied to urea, a substance which is present in
large quantities in the urine of omnivora, and which according to
determinations of the freezing-point made by me, constitutes in man
more than a third part of the hygroscopic power of the whole of
the urine.

The question interested me, especially from a general physiological
point of view. As is well known, GRIJNS and Körper observed that
red blood-corpuscles let urea easily pass through them. And I should
not be surprised if that were the case with most of the other cells
too. It could not but appear fitting to us, that the cells should be
able to get rid of urea, the principal final product of albumen analysis.
But it would certainly appear unfitting, if the urea should be able
as easily to penetrate through the wall of the bladder. In that case
the bladder would answer very badly to its purpose as a reservoir
for the refuse products, of which the urea constitutes an important
part, and one not without danger to the organism.

The question then arose: does the bladder-epithelium, in contrast
with the red-blood corpuscles possess the power of refusing a pas-
sage to the urea? In order to answer this question we prepared
urea-solutions, isotomic with NaCl 0.7, 0.9, 1.2 and 1.5°/o, caused
them to act on the bladder-epithelium, but obtained only a compa-
ratively slight influence on the volume. On a longer action the
difference between the volumina was 0; in other words, in four
different solutions the epithelium exhibited the same volume; the
urea-solutions had thus penetrated as such into the cells,

Formerly we had observed that red-blood corpuscles are destroyed
in pure urea-solutions!); perhaps the epithelium was injured too by
such solutions. We, therefore, resolved, instead of pure urea-solu-
tions to take mixtures of NaCl and urea-solutions, which were, two
and two, isotonic with each other, the more so, because in the urine
there is much NaCl besides urea.

Here is an experiment that speaks distinctly.

1) Archiv. f. Anat. u. Physiol. Physiol. Abth. 1896, S. 481.

—
med
mS)

ed

Volume of the
Solutions employed.
epithelium

|
a. NaCl-solution of 0.7°/, 85.5

|
b. 75 ee NaCl-sol. of 0.7°/, + 25 ee ur. sol. isat. with NaCl07°/, | 102
c. NaCl-solution of 1.5°/, 61
d. 75 ee NaCl-sol. 1.5°/, + 25 ce ur. sol. isot. with NaCl. 1.5°/, 70

Had the Na Cl-urea-solution 6 acted like the Na Cl-solution a,
with which it was isotonic, the volume would then have become,
not 102, but 85.5. And had the Na Cl-urea-solution d acted like
the Na Cl-solution ec, with which it was isotonic, the volume would
have become, not 70, but 61,

But the volume of 5 corresponds exactly to what would have
been found, if 75 ee. Na Cl-solution 0.7°/, had been diluted with
25 e.c. of water, instead of with 25 ee. of urea-solution.

The same applies to d with respect to c.

The urea has thus distributed itself equally over the cell and its
surroundings, without curtailing the power of the epithelium to
resist NaCl. For the calculation of the volume of protoplasma-
substance from d and 6 (supposing the urea-solution added, be eon-
sidered as water) and from ¢ and a give the same figures.

We are, therefore placed before this question: What is the reason
the urea so easily enters the scraped — off epithelium, whereas the
intact wall of the bladder appears to exhibit if not an absolute, yet
but a very slight permeability to urea.

With the answering of this question I am now engaged.

IV. OESOPHAGUS-EPITHELIUM.

We now wish to examine another species of epithelium of which,
as was the case with bladder-epithelium, an impermeability to salt
was to be foreseen.

For this purpose we tricd the epithelium of the oesophagus, which
for resorption has no more significance than has the bladder. What
we scrape off here consists of great flat cells in which are found
no inconsiderable number of round and oval grains which make the
impression of being bacteria, and which may also be deeply stained
with alkaline coloring matter.

The experiments performed in precisely the same way as those

( 383 )

with the other species of epithelium, taught us that there is, as is
the case with bladder-epithelium, a regular connection between the
volume of the cells and the concentration of the salt-solution used.
There was, however, considerable difference in the amount of the
alterations of volume under the influence of salt-solutions in different
oesophagi of the same species of animal.

On studying our notes, however, it was soon obvious that a slight
dilation or contraction was always accompanied by the presence of
many grains in the cell.

And so the idea occurred to us that these grains were answerable
for the relatively slight changes in volume.

With this hypothesis in view, we made some comparative deter-
minations with oesophagus-epithelium and blood-corpuscles of the same
animal, and we found a striking correspondence between the mag-
nitude of the changes in volume of the two cells produced by the
same salt-solutions; but only in the case that the microscope showed
a small quantity of grains in the epithelium.

As an instance of this we communicate the following experiment:

Experiment LH.

Oesophagus-epithelium of a pig and defibrinated blood of the
same animal are mixed with NaCl-solutions of 0.7°/, and 1.59/,,
and both pairs are simultaneously centrifugalized half an hour
afterwards.

Volume Contraction of NaCl
of epithelium. of 1.59/,
a. NaCl-sol. of 072} oesophagus | 82.5 Es, NE Cee
5. er 15°). | epithelium. 59 2.
c. NaCl-sol. of 0.7°/,) red Deed: 90 90—64.5 ann
\ corpuscles 90 x Tat aig
CR oe dele pay Aa 64.5

The change of volume of the oesophagus-epithelium corresponds
in a striking manner to that of the blood-corpuscles.

The experiments, then, have successively taught us that in white
blood-corpuscles, spermatozoa and oesophagus-epithelium the proportion
of the volume of the protoplasmatic substance (including the chro-
matine-threads of the nucleus) ta the volume of the intracellular

( 384 )

(includiug the intranuclear) substances, is the same as in the cor-
responding red blood-corpuscles.

We may ask ourselves whether we have not here to do with a
general phenomena which, consequently, also applies to the other cells.

Before we are justified to answer in the affirmative, we should
of course have to investigate 2 number of the other cells. Most of
them however don’t admit of this. Cells such as the intestinal and
the tracheal-epithelium, which allow salt-solutions of all concentra-
tions to pass through them and thus neither contract nor dilate, are,
as is obvious, excluded.

Summary.

The principal results to which the preceding investigation has led,
are as follow.

I. Of the four kinds of epithelium examined, the intestinal-epithe-
lium and the ciliary epithelium of the trachea undergo no modification
of volume under the influence of Na Cl-solutions of different concen-
tration; they allow the Na Cl-solutions easily to pass through them.
And this is the case, not only with the body of the cell, but pro-
bably also with the nucleus.

II. The fact, that the ciliary-epithelium, at the end of the expe-
riments, is found to be still alive, increase the value of the results,
not only with respect to the ciliary-epithelium itself, but also with
respect to the intestinal-epithelium.

III. In contrast with the intestinal and the ciliary-epitheliam, the
bladder- and oesophagus-epithelium exhibit a contraction by hyper-
isotonic and a dilation by hypisotonic Na Cl-solutions.

IV. From the amount of this contraction and dilation may be
calculated the proportion between the volume of protoplasma substance
and the intracellular contents.

This proportion, for the oesophagus-epithelium as well as for the
bladder-epithelium, appears to correspond to that in the red blood-
corpuscles of the same animal.

VY. Urea-solutions, in contrast with NaCl-solutions, leave the
volume of the isolated bladder-epithelium unaltered, From mixtures
of urea- and Na Cl-solutions indeed only the urea-makes its way through

( 385 )

the cells, whereas exclusively the Na Cl-solution exercises an in-
fluence on the volume in consequence of its concentration.

This does not seem to be in accordance with the function of
the bladder as a reservoir for the refuse products, of which the urea
constitutes an important, and for the organisation a very injurious part.

There must be factors then, which counteract the resorption of
urea in the wall of the bladder.

Physics. — “An anomaly in the course of the plaitpointeurve in
a mixture of anomalous substances.” By Prof. J. D. vaN
DER WAALS.

In the „Zeitschrift für physikalische Chemie XXVIII Heft 2”
KUENEN and Rosson have communicated observations on the mutual
solubility of liquids, which give occasion for a short remark. In
mixtures of ethane and ethylalcohol or one of the following alcohols
they found, that the plaitpointeurve consists of two isolated bran-
ches, which intersect, and end on the curve which indicates the
pressure of the three phases. In the following figure their result
has been represented schemetically.

P

Je

Fig. 1.

Let C, be the critical point of ethane, C, that of alcohol, then
C, indicates the point, in which the plaitpoint, originating in C
can be observed no longer and it seems to serve as terminating point
of the pressure of the three phases. Then C3 indicates the point,
in which the plaitpoint, originating in C, cannot be observed any

( 386 )

longer, because it disappears there above the triangle of the three
phases-pressure. It appears then as the beginning point of the three
phases-pressure.

Led by the thought that if the temperature rises a plaitpoint can
only appear on the surface w, if a plait splits into two parts or can
disappear, if two plaitpoints fall together, and that therefore a branch
of a plaitpointeurve can never end in any other point than in the
critical points of the components or in a point at an infinite dis-
tance. I have occupied myself with the question how the two sepa-
rate branches can be joined into one curve. The simplest way of
doing this is by joining the two branches, as is indicated by the
dotted line in the figure.

The vertical lines, between which the closed part of the curve lies,
represent then a maximum and a minimum temperature. The mini-
mum temperature is the temperature at which the transverse plait
splits into two parts and from which a plaitpoint starts to the
right and to the left towards the critical point of the components.
The greatest irregularity of the point, going towards C, the critical
point of alcohol, is that in its course it approaches a little nearer
to the side of the small volumes. But the point, describing its way
to C, has greater irregularities. At the maximum temperature it
meets another, which has come from the opposite direction, starting
from C, and at their meeting its movement ends. The three branches
mentioned however, form a continuous curve on the vr-plane.

At a given temperature, between the minimum and the maxi-
mum temperature, the projection of the spinodal curve consists of
two separate parts. One part forms a small closed curve round the
point where the meeting will take place; the other part has an
almost regular form.

But the two plait-points, which belong to the first part, are quite
covered by the ruled surface of the connodal curve of the second
part. Moreover the peculiarity presents itself that there is a great
distance between the spinodal and the connodal curve- a distance
great enough to contain the closed branch of the spinodal curve.
After I had convinced myself that an exact description of the pheno-
menon has been given in what I have said before, the question was
to be solved, how this would agree with the fact, which I had
remarked before. I have remarked (Molekulartheorie V 2) that for
a mixture of two substances there can only be question of a maxi-
mum or of a minimumtemperature, but that the existence of the
two at once is excluded. I think that we must look for the expla-
nation of this in the fact that in the experiments of KuwNEN and

( 387 )

Ropson one of the components is an anomalous substance. It is
almost generally accepted, especially because they do not follow
the law of the correspondent states, that alcohols when in the liquid
state possess complex molecules. At *= 1, i. e. for pure alcohol,
the association into complex molecules is perfect or maximum. But
when 2 is very small the dissociation into simple molecules is
nearly perfect. Under these circumstances the critical temperature

is not determined by the course of =e alone.

z

The critical temperature would be proportional to this quantity,
if the molecules of alcohol also in a rarefied solution continued to be,
what they were in the dense state when the substance is taken pure.

Now in general the critical temperature of smaller molecules will
be lower than that of more complex molecules. Starting from ethane
the temperature would have to rise considerably till it reached that

a. .
of alcohol according to the course of i In consequence of the dis-
z

sociation of the alcohol molecules the course will be determined by

ay . : . - .
i fe where f is smaller than unity. If z is near unity this factor
C4

too will not differ much from unity. For values of 2 which do not
exceed 4, an idea of the value of this factor is obtained by equating

it to = Now it is easy to see that even ne had no mini-
“ zx

mum or maximum, there would be numerous cases, in which the

factor f causes such a maximum, and this would involve that there

was also a minimum.

If the true interpretation of the phenomenon is to be found in
this, a course such as KUENEN and Ropson have found for mixtures of
alcohol, can never be found if the substances do not associate. But
the reverse may not be stated. What appeared as a longitudinal plait
in KuvENEN and Ropson’s experiments, was in reality nothing but
a somewhat modified transverse plait. The following phrase already
refers to such a modification: (Mol. Theorie p. 172) „Es zeigt sich
dann aber, dass in diesem Falle die beiden Falten auf ihre Bildungs-
weise anders angesehen werden miissen u. s. w.” In the figure on
p- 173 the spinodal curve has, however, not been traced correctly.
The bulging to the right of P should not be there. It should be
replaced by a small isolated closed curve, which has separated from
the other parts at the minimum temperature.

It is not without interest to remark that the mixture of ethane
and methylaleohol behaves so differently. To find the probable cause

( 388 )

of this deviation I have construed the locus of the point for which
7 and a = 0, as has been done in “Een benaderde loop voor de
plooipuntslijn van een mengsel” (Verslag der vergadering Kon. Akad.,
27 Nov. 1897). Now we had also to take into consideration, that
one of the substances is abnormal. The influence of this property
can only be calculated in a very incomplete manner, because the
way in which association of the molecules takes place in such an
abnormal substance, is not known. In consequence the result which
I have obtained by this wholly approximative calculation may only
be accepted with great reserve.

The locus mentioned may occur in two different forms, which
depend on the fact whether in the gaseous state the molecules of the
abnormal substance are larger or smaller than the molecules of the
substance with which they are mixed. If they are larger the curve
has a loop which hangs down as in the figure (1). That the
molecules of Cy Hg O, C, Hs O, ete. are greater than that of
Cy Hg will not be doubted. If on the other hand the molecules
of the abnormal substance in the gaseous state are smaller, the loop
is turned upwards. To all probability, however, the molecules of
CH,0O will be smaller than those of Cy Hy. In this ease the follo-
wing schematical figure may make clear the provable course.

B
: ae

Fig. 2.

Let A be the critical point of ethane, B that of methylalcohol.
Let EC be the pressure-curve of the three phases and C the point,
in which the plaitpoint-curve, originating in 4, meets the three-phase-

( 389 )

pressure-curve. In this case point D, which lies on that branch of
the plaint-curve that originates in B above C, is the last of the
plait-points that may be realized if the phenomena of retardation
are excluded. From this follows, that however much we may lower
the temperature, the pressure of the three phases will continue to
exist. The points between C and D, marked on the curve, indicate
plait-points of such values of 7, at which they lie above the derived
surface, resting on the connodal line which encloses the two separate
branches of the spinodal line. From the phrase of Kurnen and
Rosson, p. 357: “Oberhalb 35,37° ist nur eine Falte vorhanden, deren
Faltenpunkt wir bei Methylalcohol nicht erreichen konnten, weil Druck
und Pemperatur zu hoch waren” seems to follow, that point D of
our figure 2 must not lie above C, but that it would have to be
taken more to the side of B. As there remain so many uncertain-
ties, it is to be regretted, that in the case of methylalcohol they
have not been able to carry out their investigation. We must not
attach greater value to fig. 2 than that it has led to the supposition
that the cause of the difference in behaviour for mixtures of ethane
and methylaleohol must be found in the smallness of the methyl
molecules !).

I shall avail myself of this opportunity to make the following
remark about what is really properly to be called “longitudinal plait.”

In a mixture of normal substances a relation may exist between
the quantities aj, aja, ao. bj, bja and by, of such a nature that there
actually exist two plaits, each of which possesses a connodal curve
of its own. At a same temperature both may be proved experi-
mentally. Then the principal direction of the transverse plait is
// v-axis and the principal direction of the longitudinal plait is
// v-axis. But in this case the plaitpoint of the longitudinal plait
lies on the side of the large volumes. This has been proved
theoretically by Prof. KorreweG in the special case of sym-
metry and a similar case has been worked out experimentally by
Mr. vaN DER Lee. (Proc. Royal Acad. 1898). Theory has uot yet
been able to decide whether this plait may be again closed if the
volumes are much smaller still, or whether it continues to diverge,
even when the limiting volumes are reached. If the latter should

2

dp dp* .
1) The geometrical locus of the points, for which a and = is equal to 0, cannot
av av-

teach anything about the plaitpoints of the real longitudinal plait. Moreover I do
not share Mr. Kurnen’s expectation that also for methylaleohol the plait is the same
as for the following aleohols. L expect that the course of the plaitpoint-curve of a
mixture of methylaleohol and ethane shows great resemblance to that of a mixture
of water and ether.

( 390 )

be the case, a plait, which appears as a longitudinal plait, but
which has its plaitpoint on the side of the small volumes, as in
the observations of KUENEN and Rosson, is not a longitudinal plait,
but a somewhat modified transverse plait. If then in the liquid
state complete mixture does not take place under all circumstances,
the phenomenon is to be ascribed to other causes than in case of
a real longitudinal plait.

If further investigations confirm what has been said, we should
have to find the cause in this case in the fact that at least one
of the substances is abnormal.

Physics. — “On variation of volume and of pressure’. III. By
Prof. J. D. vAN DER WAALS.

In order to be able to judge about the extent of the variation of
volume and of pressure in mixtures of two substances, it will be
necessary, to find for the different proportions of mixing the pres-
sures at which the number of the molecules is the same for the
two substances, if the volume and the temperature are also the
same. If there were no deviations from the law of Boye, the pres-
sures required would be equal. Assume that for a mixture the cha-
racteristic equation is :

ay
(p+) (ete) = MRT,

at a given temperature the 2nd member of this equation has a con-
stant value for mixtures with the same number of molecules, and
so we may find the pressure which satisfies the preceding condition
in solving the value of p from this equation, if the value of v is
constant. Take as uvity of pressure 1 atmosphere and as unity
of volume, the volume occupied by a molecular quantity of the
mixture under that pressure. The value of the second member is then

(1 + az) (1 — be) (1 + @ i),
for which we may write with a sufficient degree of approximation
(1 + ax — be) (l Hat).

If we write p, for the value of the pressure taken as unity, and

( 391 )

(v))r, for the volume occupied by a molecular quantity at 0°, the
characteristic equation is

[p+ ar atl (ete (epe| = po (ee (hae) (Ite) (bad),

from which we deduce that the conditions that in 1 cM®. the same
number of molecules be found are, that we have different mix-
tures with the same value for v, the same value for ¢ and that we
have that value of p, for which the first member and therefore aiso
the second, is the same. The simple result is that the quantity of
the different mixtures is to be chosen in such a way that
(v)x (1 + ar) (1 — bz) has the same value for them all.

As po (% 2 (1 + az) (1 — be) (1 Hut) is the limiting value of the
product pv, the preceding condition is also fulfilled, when this limiting
value is the same for the different mixtures.

In the two preceding proceedings of the Academy Mr. J. Ver-
SCHAFFELT has published observations about mixtures of carbonic
acid and hydrogen. In order to determine the volumes, which contain
an equal number of molecules, the observer has followed a course
which agrees with the determination of (eo)z (1 + ar) (1 — bx). He
is of opinion that the investigation of the limiting value of pv would
not serve the purpose. I think that this conclusion must be drawn
from his remark p. 332. „From the point of view” etc.

Be this as it may, I shall prove that both ways may be followed.
At the same time I shall investigate, in how far his observations
agree with my characteristic equation. But first a remark about the
accurate form of the characteristic equation, or rather about the
value of the quantities a, aud dz.

I have always taken for them the following expressions:

dz = ay (le? + 2 ayy x (le) + ag 2?
and bz = bj (1—a)? + 2 bj. a (le) + b3 2°.

It is easy to see that if we want to be perfectly accurate we
must put:

dz (vo? = ay (%)2 (La)? + 2 ayq (vh (edet (Le) $ ag (09)3 2°
and bj (wvo)z = bi (vo) (L—a)? + 2 bijz V (%); (%)g v (ler) + bg (vo) 2?

lf we were allowed to equate (vo, (%)2 and (vo)z, there would

( 392 )

be no difference between the two values of a, and be; and at any
rate the difference will be scarcely noticeable, if the observations
on the mixtures do not reach the highest degree of accuracy. But
to know the accurate form is necessary in the first place for the
sake of perfect accuracy of the theoretical considerations, and in the
second place in his observations Mr, VeERSCHAFFELT seems to have
aimed at and perhaps reached that high degree of accuracy, at
which differences between the two sets of values of az and bz might
be of influence.

Let us now proceed to investigate in how far Mr. VERSCHAFFELT
has succeeded in determining the volumes which contain an equal
number of molecules under a pressure of 1 atmosphere.

He puts for this:

y = 0,99931 + 0,006 (l—e)? .

From this formula we obtain the value 0,99931 for hydrogen
(© = 1), the value 1,0053 for carbonic acid ( = 0) and the value
1,00081 for «=4. By means of these three values, taken from
observations, he has calculated his formula, assuming that y might
be put under the form a + br + cx’.

According to the theory the factor, with which (vo)r is to be
multiplied in order to obtain the volume, which contains the same
number of molecules, must be equal to:

(li a.) (1 be) = eae ee

If we take the latter form, viz (1 + az— bz), we make already
use of an approximation. But even with this approximation we find :

dl be? ay (lx)? 9 a (1-2) aw |
y=l (lar —bz) aan hie ( +-a,—b})(1-a9—-by) Re (1+-ag-by)? *
bj (Lee)? x (1-2) a
(1+az bz) ioe als Veren Ere | ,

so that we must make use of another approximation to get a form
like y=a-+ be + ce®, All this may cause deviations, but the error
which is committed by assuming this form, will remain but insigni-
ficant. My objection to the formula:

y= 0,99931 + 0,006 (1—2)2

has another ground. Mr. VeRSCHAFFELT himself remarks, that if he
had made use of other experimental data to determine the values
of a, b and ec, he would have found the following formula:

y = 0,9995 + 0,00136 (l—e) + 0,0056 (l—z)?.

But he uses the former — and now [I shall show that the latter
agrees to a great extent with what his own experiments teach, and
that the former certainly cannot be true.

When two gases are mixed in different proportions — and one
of the gases (carbonic acid) deviates in one direction from the law
of Boyue, whereas the other gas (hydrogen) does so in the other
direction, we may expect the existence of a mixture, which follows
the law of Boyre. What may be brought about by change of tempe-
rature in case of a simple gas, occurs here by change of the mixing
proportion. For such a mixture y=1. From the formula

1 = 0,99931 + 0,006 (L—a)?
follows «= + °*/;. From the formula
1 = 0,9995 + 0,00136 (1—x) + 0,0056 (Le),

follows «= 0,8.
Mr. VeERSCHAFFELT has made observations for «= 0,7963 and
«== 0,6445. The products pv for «=0,7963 are respectively

1,0740, 1,0756, 1,0764, 1,0749, 1,0748.

At v=0,02 pv has still the value of 1,0750, and not before
v= 0,01 it has reached the value of 1,0960.

From these values of pv we may conclude that the mixture has
nearly that composition, in which it would follow the law of Boye
in great volumes. From the long series of larger volumes, in which
actually constancy of this product has been found, we might deduce,
that the mixture deviates still in the direction of carbonic acid —
and that therefore z should have a somewhat greater value in order
to form a mixture, which follows the law of Boyne only in very
large volumes, but yet shows an increasing product from the be-
ginning.

If we take the value of pv that belongs to the mixture, in which
«= 0,6445, we find:

1,0451, 1,0425, 1,0413, 1,0411, 1,0413, 1,041,

27
Proceedings Royal Acad, Amsterdam, Vol. I.

( 394 )

while at »=0,002 the product is diminished to 1,036 and at
v=0,01 it descends still more down to 1,021. From the former
series of values we might still be in doubt whether this mixture
also possibly follows the law of Boyrr, but the value at v = 0,01,
which has perceptibly decreased, decides, and shows convincibly,
that this mixture still deviates in the direction of carbonic acid.
My conclusion is therefore that for the mixture for which y= 1
the value of « cannot descend below 0,8.

In such a mixture the product pvr=(l tat), or (¢=18°)
pe = 1,06606. For this value we found above 1,074. This would
lead to the conclusion that if Mr. VeRrscHAFFELT equates the volume
to 0,03, it is in reality no more than 0,02983. As a similar diffe-
rence is also found for the following volumes, it would point to
the fact that he has taken the unity of volume in this mixture
+ 1 pCt. too large, an error which surpasses the amount of the
above diseussed corrections. If we would not acknowledge this error,
we should have to take as the mixture for which pp =1-+e@t one
for which « is smaller, which is contradicted by the experiments
on compression, as has been shown before.

Put 35,80 as the value of the pressure, which a gas would exer-
cise, if it should follow the law of Boyre. For every series of
observations if the volume «= 0,02983, we find in Table XII,
p. 334 indicated the pressure which is to be subtracted from 35,8,
to find the influence of the deviations.

If we put

gm lor t
(35,8 — p) = (eee

ve

?

the value of az—bz(1--@t) may be calculated for every mixture from
this approximated equation. If we calculate a,—b,(1-+ e@¢) (for
carbonic acid) we find 0,00614 and — 0,000454 for ag—b (1 + &t)
(hydrogen). By means of these values we may determine the
constants for y=a- be + ce*, if we make also use of the cireum-
stance that the value of y=1 is to be found for «=0,8. Then
we find:

y = 0,999546 + 0,001189 (1—2) + 0,005405 (1—a)? ,

an equation which closely resembles that one, which Mr. VERSCHAF-
FELT thought, that he ought not to make use of, and which yet
has been deduced from his own observations only. In the following
table we find the value of y for values of «= 0,1, 0,2 ete.

ENOR reren det y = 1,00614
OD Yee 1,00499
(ts ee ee 1,00396
OENE Ste 1,00303
1 mad te See 1,00220
OEE eg. 1,00149
er By che tes. 1,00089
en EN 1,00039
Ole take ae ae oth EE 1
Om EES 0,99972
slg a eT Ow nia akon 0,99954

By application of the approximated formula
(35,8 — p) v? = ar — bz (Ll + at)

we find from the series of observations

Ce Er Se eno wo a dee y = 1,00483
= OND 6 2 wen oe aten Het 1,00398
CU EET ac satis mee ot Eee 1,00276
Ce OER egte ala oneal cae 1,00177
TE OIGREON AP or seas Neb ss te 1,00093
GOB ho) siete) AE 1

a OOF Bera VA de te 0,99965

Only at «=0,5 a deviation of importance is found.
For ¢= 18° we may calculate from

az—bz (1 + wt) = — 0,000454 + 0,001189 (1—2) + 0,005405 (1—ay?
the value ajb (1 a a t) == 0,0001375 and
Gl ag Zen NP SUE en 0,005404

According to this value of a2—0,) (1+ «t) the deviation!) from
the law of DALTON would be in the usual direction, i.e. in such
a way that the pressure of the mixture at larger volumes is smaller
than the sum of the separate pressures, whereas at smaller volumes
the sign of the deviation is reversed. In consequence of the small
value of a g—bj. (1 + @t) = 0,0001375, the deviation will be but
slight. We may examine whether this is confirmed by the observa-
tions of Mr. VerscHAFFELT (table XII), if «= 1/9. So for v= 0,03

1) See Proceedings of Noy. 1898. N
271%

( 396 )

pi = 28,9 and pp = 36,31. If an equal number of molecules of car-
bonie acid and hydrogen so that # =!/z, are mixed in the same volume
»== 0,03, the volume contains twice as many molecules, so the same
number in v=0,015. For this volume Mr, VeRSCHAFFELT finds
p=65. The value of p; + pz = 60,21.

In the same way

at v=0,028 p,=30,58 p,=88,97 p,+-p,—69,45 andat v>=0,014 p— 69,30
» v=0,026 p,=32,40 p,=— 42,04 p,+t+p,—74,44 andat v—=0,013 p=74,20
v v=0,024 p,= 34,38 p,=45,65 p,+-p,=80,03 andat v=0,012 p— 80,00
„ v=0,022 p,=36,55 p.=49,94 p,-+p,=86,49 andat v>=0,011 p=86,75
y v=0,020 p,=39,08 p,=55,10 p,tp,=94,18 andat v—0,010 p= 94,40

So in the case of carbonic acid and hydrogen, the quantity
ayg—0y9 (Let) is not large and (a, + ag — 2 ay2) — (bi 4 by — 2 hija)
(1 Het) small, but the contrary. The latter may be expected for
substances which differ much in physical properties.

In my communications under the same title, in the proceedings
of November and December 1898, I have discussed two rules of
approximation for mixtures, viz. the law of DALTON and that of
AMAGAT. As a third rule of approximation the following rule might be
given: In a mixture a substance exercises the pressure that it would
exercise if the other molecules were substituted by molecules of iis
own kind. Let us call the pressure which the first mentioned gas
would exercise, if all the molecules were of the same kind pj, and
that of the second gas pa, then this rule of approximation comes
to the same as putting

p=pi(l—e) + paer.

From the graphical representation of Mr. VERSCHAFFELT p. 329
it appears that for earbonie acid and hydrogen p— [pi (l—e) + pga]
is positive.

From the characteristic equation we may ceduce for this difference:

—2 a5) —(b g—2 bo) (A
pep (Ia) o= ae + 4 —2 a9) — (bj + bo 12) A Het)

9
vw

b
for all volumes large enough that we may put 1 + — for = 5
v a

So we see that for large volumes this third rule of approximation
is exactly the same as that of AMAGAT.

At a given volume p is a function of « of the second degree
and the maximum deviation will be found at == !/z.

(397)

For v= 0,024 the following table gives the calculated and the
observed values of the pressure.

In the formula p= pi (1—2) + pe + Aer (l—z) we have taken
A as equal to 8.

z 0 0,05 Ol 02 0,352 05 06445 08 09 1
p _caleulated 84,38 35,32 36,22 37,91 40,18 42,01 43,47 44,67 45,24 45,65
p observed 34,38 35,53 36,54 38,04 40,12 41,80 43,33 44,80 4548 45,65

For the value of A which might have been calculated by means of
the relation

(a + ag — 2 ayy) — (bj + bg — 2 by) (1 Hat)

A
v>

RS

1’

we should have found about 9,5, if Aa —As(1 + zt) = 0,005405
(see p. 395).

The value of p, putting A=9,5, agrees nearly perfectly
for smalk values of x and 1—za, but in this case the differences
are larger again for values of 2 near }/. From 4 =8 would
follow Aa—A, (1 + at) = 0,00461 !).

From all this follows that absolute agreement between the theory
and the observations of Mr. VERSCHAFFELT does not yet exist. But
the differences remain below 1 pCt. It would be premature to try
to decide as yet whether the differences are to be ascribed to the
theory or to the experiments. Yet we may say that in these obser-
vations the differences are smaller than in those that I have tested
before. And the fact that up to now the differences grow less as the
observations grow in accuracy, seems to plead in favour of the theory.

') In calculating the coefficient in the equation
y = 0,999546 + 0,001189 (1—z) + 0,005405 (1—2)2

we have made use of the data for carbonic acid and hydrogen, and of the supposition
that y= 1, if «= 0,8.
If we take y=1 for #— 0,82, the coeflicients become

y = 0,999546 + 0,001618 (1—a) + 0,00497 (1—2)° .

These values of the coefficients seem more probable to me; moreover in this case
the values of the two tables on p. 395 agree still better.
With these coefficients is

4,,—b,3 (L 4- zt) = 9,000355

(a, + a, — 2 ays) — Abe — 2 4,,) (1 2 f) = 000497 ,

and

( 398 )

Physics. — Prof. vay DER WaarLs presents for the Proceedings
of the meeting a paper of Prof. L. BOLTZMANN, foreign
member of the Academy,: “On the characteristic equation of
v. D. WAALS,” with an accompanying letter from which the
following extract has been taken.

Vienna, March 2nd 1899.
Dear Sir,

Mr. van LAAR has sent me from Utrecht a calculation which he
undertook at your demand. From this I have calculated the next
correction term of your formula in the same way as I have foilowed
in the second part of my gas-theory, and I take the liberty of sending
the MS. to you. The result will differ in some respects from the one
you obtained, but I should consider a discussion about it very inte-
resting on mathematical grounds; not so much on physical grounds,
as the further correction terms are certainly not calculable. Under
slight pressures the observations are too inaccurate for this term to
be usefal, while for high pressures more approximation terms would
be required. Moreover no observations have been made on //g-vapour,
argon, helium, where spherical molecules may be presumed. I should
be pleased if you would lay my MS. before the Amsterdam Academy
of Sciences and I should like it to be printed in its Proceedings,
because I think this the best way to attain my purpose, viz. to
incite those who are interested in this question to a discussion which
might be useful ‘to science. . Sn

Yours truly
Lupwia BOLTZMANN.

At the demand of Prof. van DER Waars, Mr. van LAAR has
calculated a formula which may be used for the calculation of a
further approximation term in the former’s formula. I shall show
how Mr. van Laar’s formula may be used for the further deve-
lopment of my calculation relating to this subject, and make use of
the same notations as in the second part of my “Lectures on Gas-
theory”, which I shall always briefly quote as l.c.

I. Caleulation of the space left for the centre of a new
molecule to be introduced into the gas.

Let V be the volume of a vessel, in which there are found » very

(399)

small, rigid spheres (molecules), all of them having the same pro-
perties and of the mass and the diameter 5.

We represent by D, the first approximated value of the space D
left for the centre of a molecule new added into the gas. This
molecule has the same properties as the others. Then D,= V. As
a second approximation we must subtract from this the volume of
the distance-spheres of all the x molecules. The term distance-sphere

stands here for a sphere concentric to the molecule and with the
2 ; 3
=b and

; 4
radius 6, so having a volume of ee If we put
m

the total mass of the gas mn = G, then the sum of all the volumes
of all the x distance-spheres is 2 Gb and the second approximated
value of D is therefore

DOE sido) oral vou ee (1)

For the third approximation we must take into account that not
the sum of the volumes of all the distance-spheres is to be subtracted
from V, as here and there two distance-spheres cover each other
partially, and that then the space which is common to them, is to
be subtracted but onee. So we must add to DP, the sum 7 of all
spaces which two distance-spheres have anywhere in common.

We find the volume 7 in the following way: We construe round
the centre of every one of the x molecules a spherical shell con-
centrical with the molecule, with an inner radius 2 and the very
small thickness de, which spherical shell we shall call S. The
volume 2, which is the sum of all the spherical shells S construed
in such a way, is 4ana?dr. The number dn of the centres of the
molecules which are found in any of these spherical shells is to
the total number of the molecules in the first approximation as ZR
is to the volume of the vessel V, so that we get

Uig uss Clin DOG BNE ae onde to (4)
or

Aan? ea? de

dn =

The last expression gives the number of molecules whose centres
lie at a distance between « and «+ de from the centre of any
other molecule. The number of the pairs of molecules, whose centra
have a distance between these limits, is }dn. As soon as « is
between o and 2e, the distance-spheres of the two molecules of

( 400 j

the pairs in question will have a lens-shaped space of the volume
= 7 8 0 2
Se (ND oF — 12.67% ¢ 2 a3) on EN

in common (le. p. 166)1). The sum of all these lens-shaped spaces
which occur with all possible pairs of moiccules, is represented by
Z. Therefore

2 2 17 G20?
ze [kim rs dr (16 08 — 12 Pea = te

and
D= Vb

The value of D, in which the approximation has been worked
out one term further, is cailed Dy. To find it, we must first sub-
tract from Ds the sums of all volumes which belong to the distance-
spheres of three molecules at the same time, and which is according
to Mr. van LAAR

2B Gb

Ve

in which 7 is the quantity which he has calculated and which he
has also represented by /? on the last page of his discussion.
Secondly however we have also to add a correction term to Z, which
we shall represent by ¢, so that
wer pee _ 372" ee
16 V Va
We get the correction term ¢ by the following consideration. The
proportion (2) is only right as a first approximation. If we try to
obtain to a greater accuracy, the last term of the proportion should
not be represented simply by V, as the whole volume of the vessel
is not at the disposal of all the x molecules. In the same way a
correction term is to be inserted in the last member but one of the

1) Compare also: VAN DER Waats, Amst. Acad. 31 Oct. 1896 and 29 Oct, 1898,

( 401 )

proportion, while also a part of the volume, represented above by R,
will fall in the distance-sphere of other molecules.

Next we may state the following rule. According to proba-
bility the relation between the number represented above by dz and
the total number x of the molecules will be the same as between
that part Zj of the space ” which is left for the centre of a new-
added molecule and the whole space which is left inside the vessel
for the centre of a new-added molecule. *)

According to formula (1) the last mentioned space is V — 2 Gb.
The last term of the proportion (2) should therefore be represented
by V-—-2Gb instead of by V. Lj is still to be found. For this
purpose we construe inside each of the above considered » spherical
shells with a radius 2 and a thickness dr, which we have called
the spherical shells S, a coneentrical spherical shell with an inner
radius y and a thickness dy. The latter spherical shells we shall
call the spherical shells 7. he sum of the number of the centra
of molecules, which lie in any of the spherical shells 7 is, analo-
gous to the equation (3)

4 arn? y° dy

en
a =

(8)

The part

= Gy)
vl
of the surface lies within the distance spheres of every separate one
of the molecules ; thence the part
o* —(«— yp
y

of the inner space of the spherical shells in question with a radius
# and a thickness dz, as an easy calculation shows. That part of
the volumes of all the spherical shells S which is covered by the
distance spheres of all the dy molecules together is therefore @ dy,

If no molecules were to be found inside the spherical shells S,
we might integrate this expression with respect to y from z—o@ to

z-+o and
16 7? n? 2? 6 2hG4
[emer dx = Ann aide ae (LO)

(9)

o=nwrdr

33 114 V
would follow.

1) For a fuller exposition of this rule comp. Le. § 61.

( 402 )

Then the space of the sum of the volumes k= 472% dx of all
the spherical shells S together, which is enclosed in the distance
spheres, would be to this total space 2, as the whole space 2 Gb
occupied by the distance spheres of all the molecules of the gas to
the whole volume of the vessel V, which was to be expected a priori.

In every spherical shell S, however, a molecule is found, so that
the centre of another molecule cannot come closer than at a distance
5 from the centre of the spherical shell. Therefore we have to
subtract from the value (10).

{ Am? n2 a? de ( x3 46°
.

On 7 — — a6" + 5) —=4nna dry,

yr?

in which

Instead of the last term but one in the proportion (2) we have
therefore to put

Anne? de (1 pee Se 7) B

B A ZON '
As we ought to substitute V (1 — Ze) for the last term, it

comes to the same thing as if the last term were left as it is,
and-as if

Anna? de (l + 7)

were substituted for the last term but one, at least if terms of still
higher order are neglected.
We obtain therefore for dx the correction term

dv =y dn

and for Z the correction term

og
èn?

== { Ky dv = | a? dx (v2 —12 0? + 166°)? =

72 I

2357 ani 69 2357 GSUS

22680 V2 — 6720 V?

rs

( 403 )

By the substitution of these values, formula (7) becomes :

D= VGL +

en (257 ‚nF
is 7 + Gm

EN (8 2857) GEL 4
Be aye ca =| )

This is therefore the space left in the vessel for the centre of a
Gh

V

molecule, when terms of four different orders with respect to

are considered.

Il. Correction of the equation of VAN rr WAALS.

The shortest way to calculate this correction by means of formula
11 is that which I followed 1. ec. § 61. If we substitute the expression
D,, which has now been found for the expression D, which has been
used 1. ec. § 61 and has been represented by equation 173 there,
we obtain

17 v2 ml? 2357 y? m3 bs
i [o—2 mb dn Sel —2 3) el
16 )

v ra

Sera
vy? ml

ly

2vmh 15 vp? ml? (an

2s = Ep)
v 16 v> 6720 | Ô

Did

instead of the first formula on p. 174, and so instead of the formula
which is found for S six lines lower

stef nere tE DE

The formula for

ZE NE Ce tia
ot

v | wv 8 x3 8960 | 2

( 404 )

so that the corrected equation of VAN DER WAALS would have the
following form

2

a ri see Bees ae be
dae ary ed bare 3 \5000 2 =|

v

ia ae EE)
db: 957 3 2 U?
v_—b A ( 8 >|
8 v 8960 2 / v
In this formula is according to Mr. vaN LAAR
4 MLA
73/24 81.17 ( aretg /2 — 7)
— se EE — ES r
B ie 32.35 x = 0.0958 .
Physics. — “The galvano-magnetic and thermo-magnetic phenomena

in bismuth”. (Second Communication.) By Dr. E. van Ever-
DINGEN JR. (Communication N°. 48 from the Physical Labo-
ratory at Leiden, by Prof. H. KAMERLINGH ONNES.)

1. In the Proceedings of the meeting of June 25th 1898 we
have communicated the resuits of the observations of the four trans-
verse galvano-magnetic and thermo-magnetic phenomena, all of
them made in one and the same magnetic field with one and the
same electrolytically prepared plate of bismuth. By means of the
same plate of bismuth we have now observed the decrease of con-
ductivity for electricity and heat and also the longitudinal thermo-
magnetic phenomenon. It has given us much trouble to measure the
two last phenomena with sufficient accuracy, and the variation of
the conductivity for heat can only approximately be deduced from
the measurements. Yet I communicate the results for two reasons:
in the first place, for a preliminary theory it is sufficient that the
order of magnitude of the phenomena is known, and secondly in
consequence of the small dimensions of the plate it is not probable
that further measurements with the same plate would yield a much
more exact result for the absolute value. Moreover the plate during
one of the last experiments has developed a crack and this has
put an end to all further observations under the same circumstances,
even if we had wished to continue them.

These measurements having been finished we have obtained for

( 405 )

the first time results in one and the same plate, in the same
magnetie field and at the same temperature, for all the phenomena
relating to the theory of the conduction of electricity and heat in
metals. For a complete theory it would also be necessary to investigate
the variation with temperature of the different phenomena; at the
same time a question would arise about a possible change of the
THomson-effect in the magnetic field. But at this stage I wished to
leave variation with temperature out of consideration. It is true, in
measurements for which a current of heat is required, different tem-
peratures occur, but we will suppose this variation with temperature
small enough to be neglected in a preliminary theory of the phe-
nomena. So far as we can judge from the results obtained, they are
not contradictory to this supposition.

2. I have sueceeded in representing variation of resistance and
longitudinal-effect by means of an empirical formula of the form

C, M2

= 1
ete Orr ee )
in which Z represents the phenomenon observed and M the magnetic
force (in these calculations expressed in the unit 1000 C. G. 5).
Together with the quanties observed we also give the values ob-
tained by means of this empirical formula. It will be shown that
it represents the observations very satisfactorilv; applied to those
made by others, it offers an easy way of comparing their results
with mine. Moreover the formula is of great use in deciding that
variation of resistance and longitudinal-effect are proportional for all
magnetisations, a result which is very important for the theory of
the phenomenon. If for instance, we consider the longitudinal-effect
as a variation of the thermo-electric power, it follows that we might
deduce the change of the Tromsor-effect in the magnetic field from
the variation of the increase of resistance with change of temperature,

3. Variation of the electric resistance.

a. Measurements. The observations of this variation are made

1) In the denominator 1/ M2, where the root has to be taken with a positive value,
was written in view of GOLDHAMMER’s remark (Wied. Ann. 36, p. 824, 1889) that
the phenomena which do not change sign on reversing the field should be functions
of A.

( 406 )
foliowing the method, deseribed in the “Verslag der Vergad.” of April
2lst 189%, p. 493 2).

As resistance electrodes we used the same thermo-elements which
were used in the measurements of the transverse phenomena, the
copper wires of which were again connected with one of the coils
of a differential-galvanometer. Fig. 1 shows the principle of this
method of observation.

7 = Element.
P= Plate oF
bismuth.
R = Rheotan-

wires.

Th = Thermo-ele-

ments.

W, and W, = Resistance-

boxes.
Fig. 1
C, = 0,258 C, = 1,000
Marnetie field | Percentage increase niee
eaigneuc chest | Observed l Calculated | ;
| |
4650 | 9,7 | 9,8 | + 0,1
| | |
6100 | 14,5 14,5 0.0
|
9200 | 25,1 | 25,1 0,0
|

From these observations we could also deduce an approximate
value for the specific resistance of this bismuth at about 20°, for
which 182,000 C.G.S. was found.

We need not be astonished at this number being much larger than
that of FLEMING and Dewar, 116,000, which we used in the cal-
culations of the previous communication. For, our method, although

1) Comm. Phys. Lab; Leiden, N°. 37, p. 5. Compare also my thesis for the
doctorate.

( 407 )

it shows us very precisely the proportion of the resistances in the
different magnetic fields, was neither devised nor fit for precise mea-
surements of the specifie resistance.

First, the distance of the resistance-electrodes cannot be accurately
determined, and second, it is not certain that the current-lines are
entirely parallel with the sides of the plate, a supposition which
must be made in the calculation. In order to convince myself that
these circumstances did not influence the measuring of the increase
of resistance I have moreover repeated that measurement with another
plate of a very regular shape, electrolytically prepared in the same
way. The specific resistance being found to be here 121,000, the
percentage increase of resistance was almost the same as in the
case of the other plate.

b. Results of other observers.

HENDERSON !)

Temp. 18°, C, = 0,2847 C, = 1,798
Magnetic Geld,| _ Tereentage increase | Difference,

960 1,5 1,3 — 0,2
1740 3,4 | 3, + 0.2
2860 8,2 8,1 = Ou
4160 | 14,8 14,2 i of6
6200 | 25,9 25,3 — 0,6
7190 | 30,7 30,5 |) te
8740 | 39,7 39,4 US
9650 | 45,2 | 44,7 = 05
10950 53,0 52,4 E06
12750 62,3 63,1 + 0,8

In order to investigate how far the empirical formula retains its
meaning outside the range of the observations which were used in
calculating the constants, I substituted the value M = 38,900, with
which HeNDERSON found 233,40/,; this gave 245,70/, which is in suffi-
cient agreement considering the extent of the extrapolation.

") Wied. Ann. 53 p. 912, 1894. The numbers here mentioned concern the measu-
rements with the large spiral of bismuth, which are graphically represented in fig. 4
of Table X of that Volume.

( 408 )

VON ErTINGSHAUSEN and Nernst !)

C, = 0,1841 Cy = 0,8882
Ei] i |
AS Percentage increase. Per.
Magnetic field. | observed. | calculated. Dierenees
1600 2,58 1,87 — 0,7
3160 | 7,87 | 6,24 ALG
5880 19,7 | 17,2 — 2,5
8410 | 30,8 | 29,6 = 2
11200 | 43,6 14,6 41,0
FLEMING and DEWAR ”)
Temp. 19°. C,=— 0,03084 CG. =0,1805
= sl Percentage increase ee
Magnetic field. | observed | calculated. ee
= |
2450 | 6,3 | 1,2 55a
5500 | 13,6 | 6,6 Ero
14200 60,9 64,9 ED

As appears from the negative sign of C; and the large deviations,
the observations in the last table cannot be represented by our for-
mula. But from this discussion it would appear that the accurate
representation of my three results by a formula with two constants
signifies more than would at first be expected.

4, Variation of conductivity for heat.

a. Measurements. It being our object to observe all the pheno-
mena as far as possible under the same circumstances, we in this
‘ase had to determine the variation of temperature at different distances
from the source of heat, in order to calculate from it the variation
of the conductivity.

We therefore first observed the temperature in the stationary con-
dition without magnetic field, then that temperature in the new
stationary condition in the magnetic field. It appeared however after

1) Wied. Ann. 33 p. 474, 1888,
*) Proc, Roy. Soc, 60, p. 425, 1896.

* (409)

some time that if the plate were moanted between the poles as had
been done until then, the condition was never steady enough to make
the measurement in this way; the irregular variations of temperature
as compared with the fall of temperature to be measured were too
large. This difficulty was almost entirely removed by using a U-
shaped water-jacket placed between the poles of the electromagnet,
through which water was streaming under a constant difference of
pressure, so that the temperature remained constant for several hours
within a few tenths of a degree.
The new mounting of the plate may be seen from fig. 2.

P.= Plate of bismuth.

Th. = Thermo-element.

W. = Water-jacket.

K.= Copper tube through which
the steam is driven.

A. B. C.= Grooves for intro-

ducing the thermo-ele-
ments.
H. = Piece of wood for clamping

the plate.

Fig. 2.

The plate having been put into this jacket, the remaining space
was filled with cotton-wool. A test-experiment in which the jacket
was closed on all sides with paper did not yield any different results,
so that we may assume that no errors arise from currents of air.

In inserting the thermo-elements in their places we had to secure
proper contact on the one hand, and on the other, we had to make

28
Proceedings Royal Acad, Amsterdam, Vol. I.

( 410)°

sure that the copper or the German-silver wires did not separately
touch the bismuth.
The observations were made in the following way:

1. Observe for five minutes the deflection by the thermo-element
without magnetic field.
2. Observe for five minutes with the magnetic field in one direction.
3 a on a » without 5 Ps
4, 5 nn „ With the 5 we on OUNCE ae
5 5 eu 4 » without 5 5
And so on.

During the five minutes after interrupting the magnetising current
the temperature returns slowly to its original value.

Mainly by help of the deflections just before applying the mag-
netic field, the remaining variation of the deflection without magnetic
field was represented graphically and from this was interpolated the
value of that deflection at a moment five minutes after the closing
of the current. ‘The difference of this value and the deflection
observed just before interrupting the current gives the fall of tem-
perature we require.

By taking the mean for the two directions of magnetisation the
error is avoided, which would otherwise be caused by the rotation
of the isothermals.

Here follow some of the results obtained. A, B and C again
indicate the three fixed places on the plate; the temperatures above
each column give approximately the values as they occurred during
the observations.

Magnetic A | B Cc
field. +240 |+ 36° | + 19°
| |
2800 | — | 0°,38| 0°,07
i]
4800 | 0548) 0°,83 | 09,18
6100 09,67 | 1°,25 | 09,28

The temperature of the water-jacket in all these observations
was about 8°,

The following are the results from which the number 0°,28 for
GC. was deduced, given in order that we may judge of the accuracy
of the separate determinations.

( 411 )

Deflection Deflection Deflection
without magn. with with
(interpolated). magn. A. magn. B. Variation. Mean.
37,90 36,80 1,10
0,90
38,06 37,35 0,71
0,95
38,14. 36,95 1,19
0,90
38,12 37,52 0,60
0,86
38,33 37,22 nat
0,89
38,86 38,20 0,66
0,90
39,42 38,28 1,14
0,90
39,80 39,13 0,67 ter
0,90

With several of the observations mentioned above the agreement
of the separate values was still greater.

c. Calculation of the variation of conductivity for heat.

Let ¢ be the difference between the temperature in the plate and
that of the surrounding atmosphere, and let « be the distance from
the heated end, then we can assume when using certain simplifying
suppositions that

d*t ,
de? — at = 0
re)
A 5 os
in which a
dg

d= section of the plate.
o = circumference of the plate.
s = coefficient of the exterior conduction of heat.

JS ” » » interior » » »”

We assume that s is independent of the magnetic force.
For t we find

t=pe—42+ getaz,

The great difficulty in the measurements with our plate of bismuth,
is that, as would be the case for a longer plate, we cannot neglect
the second term for moderate values of # and take the coefficient
p constant (this could only be the case if the plate were soldered
immediately to the heated tube). In the magnetic field p, g and a

28*

(412 )

vary; it is probable that the temperature at both ends does also not
remain the same, and only with the aid of three observed tempera-
tures we can calculate a. It is evident that in this way errors of
observation should acquire a great influence, especially as the deter-
mination of the falls of temperature could not possibly be made at
the three places at the same time; the stationary temperatures were
about the same in each experiment, but small differences could not
be avoided.

For the calculation, the temperatures, observed at the heated
end and in the places A, Band C were united in a graphical repre-
sentation with « as abscissa. From this the temperatures in the
places «= 0, 0,6, 1,2, 1,8, and 2,4 were deduced. These must
satisfy the relation.

tn =e tn +2
tat1

= e—0,6a — e+ 06a,

Putting e—°%6¢ =k, we find & from the equation

tnttn+e2
tn+1

kh? — k-- 1= 0.

Supposing the mean value of k to be correct, I then calculated
from the set of 5 temperatures the coefficients p and g, and from
these again the temperatures themselves. ‘he result being:

k = 0,626 p= 43,16 9 == 0,39
a t | tn + tn+2 , t .
7 (interpolated) Sham. 5 (calculated) Differenge,
|
0 43,5 43,5 0,0
0,6 | 28,0 PVs 0,666 27,6 —0,4
|

1,2 17,5 2,29 0,584 17,9 0,4
1,8 12,1 2,22 0,629 12,2 0,1
2,4 9,4 9,2 —0,2

Fig. 3 shows the calculated curve. The signs show the tem-
peratures and the places which where used in the calculation, the
signs + show the really observed temperature in the places A, B
and C.

SOx

40.

rH

Q QS {0 1s 20 25

au

Fig. 3.

Next, we have read the falls of temperature also from a graphical
representation; with a view to the small accuracy of the results I
have confined myself to the observations in the strongest field and
have omitted the value for = 0 as being unreliable. I then found

M= + 6000
| t th +. tn+2 7
Z we (calculated) Tl bnl
0,6 19,25 270,6 26°,35
1,2 0,90 17,9 17 ,00 2,935 0,6185
1,8 0,55 12,2 11 ,65 2,227 0,6237
2,4 0,26 9,2 8,04

As the distance from C to the heated place was only 2,37 the
value for 2,4 has been extrapolated already. Let us therefore take
the value of & 0,6185 as a basis. From the value 0,626 follows a
value of a= 0,778; 0,6185 gives a’ = 0,801.

( 414 )

For an investigation of the variation in different magnetic fields
the observations are not accurate enough; yet they already show
that the increase is more rapid than proportional to the first power
of the magnetic force, but not so rapid as proportional to the second
power |).

b. Results of other observers,

As far as I know it is only Lepuc®), the discoverer, and von
ETTINGSHAUSEN *), who have observed this phenomenon.

From the former’s observations follows for = 7800 dl — Joie
g

VON ETTINGSHAUSEN finds numbers varying from 1,052 to 1,021
in a field of about 9000.

In both these cases the bismuth was directly soldered to the
source of heat, and for the calculation use was made of the term
pet” only. As my value, 1,058 in the field 6000 is rather too
large than too small, we can deduce with certainty from the obser-
vations that this change is considerably smaller than of the elec-
trical conductivity.

5. Longitudinal thermo-magnetic phenomenon.

a. Measurements. This phenomenon may be considered as an
increase of the thermo-electric power of bismuth in the magnetic
field. I therefore wished to measure the variation of the deflection,
observed with the galvanometer, when the copper wires of the thermo-
electric couples were connected to it, in percentage values for diffe-
rent magnetic fields, always with both directions of the magnetic
field, in order to avoid the disturbances caused by tranverse pheno-
mena; afterwards it would only be necessary to determine the thermo-
electric power ouiside the magnetic field once for all, in order to
be able to express the longitudinal effect also in absolute measure.
Now it was also desirable to make these measurements with the
thermo-elements at the places B and C; but as the temperatures of
these places vary on applying the magnetic field, a disturbance arises
which reduces the change in the deflection, because the fall of tem-

1) A variation of g with temperature, outside or in the magnetic field, ought to
appear from a similar change in /, It is evident that the accuracy of the observa-
tions is not sufficient to draw from them conclusions as to such a variation; how-
ever the variation cannot be very large.

*) C. RR. 104, p. 1788, 1887.

* Wied, Ann. 83, p. 129, 1888,

(415 )

perature is greatest at the highest temperature. At first I intended
to calculate this disturbance from the measurements of the fall of
temperature mentioned in the preceding part. But I have changed
my mind because it appeared that in spite of accurate placing of
the thermo-elements, deviating falls of temperature occurred with
different measurements. For the most part, these deviations must be
ascribed to the existence of an other slope of temperature. There-
fore of late I have determined the fall of temperature on both these
places before and after the measurement of the longitudinal effect.
If we knew exactly the difference of temperature between the two
places of contact we might have expressed the correction in percen-
tages. Although the temperature of the places of contact between
German-silver and copper is exactly known, there is however no
sufficient certainty that this is at the same time the temperature of
the place of contact of bismuth and copper. The same uncertainty
is the reason that the thermo-electric power of bismuth can also
not be exactly deduced from these measurements; the values of the
difference bismuth-copper, calculated from the results of different
experiments, range from 8400 to 10500 per 1° for temperatures
ranging from 20° to 50°. It should be remembered that in the
place B we find a slope of temperature from 2,5° to 5° per mm.,
while the whole difference of temperature was 20° to 30°. For
these reasons I have for the time being given up a calculation
of the longitudinal effect in absolute measure and have calcu-
lated the correction by taking for the thermo-electric difference
bismuth-copper 10000 per 1°; for the thermo-element German-silver
and copper was found 1590. In the correction there remains an
uncertainty of probably not more than 10°,; the correction itself
amounted at most to 25% of the total effect, so that for this there
remains an uncertainty of 2,5°/); as moreover the fall of temperature,
as afterwards appeared, shows almost the same variation with the
magnetic force as the longitudinal-effect, the proportion of the phe-
nomenon in different magnetic fields will not be changed by the
error.

A great number of measurements had been made already before
the method of observation described here was applied. In order to
use these in the calculation, I interpolated from all the sets of
observations the percentage variation for the fields 2000 to 6000;
then I always assumed 10 as the value for the field 6000 which
was the result according to the last method, and changed the other
figures proportionally. The following results were obtained.

(416 )

Magnet. field. 21 July. | 9 Sept. | 16 Sept. 18 Febr. (6-9March, Mean.

2000 yi 1,60 1,94 2,27 1,60 1,84
3000 3,66 3,21 3,69 3,86 3,35 8,55
4000 5,79 5,02 5,60 5,70 5,50 5,52
5000 7,83 7,21 7,69 7,67 7,75 7,63

6000 10.0 10,0 10,0 10,0 10,0 10,0

The empirical formula was applied to these mean results.

C, = 0,2341 C, = 0,6663
Magnet. field. Berden Oe Difference.
observed. calculated.
2000 1,84 1,81 | —0,03
3000 3,55 3,52 —0,03
4000 5,52 5,51 —0,01
5000 7,63 IL 7,67 +0,04
6000 10,00 9,98 —0,02

As we see, the agreement is very satisfactory. The coefficient C
is almost the same as for the increase of the resistance, whence we
conclude: — the two phenomena differ in different magnetic fields only
by an almost constant factor ').

b. Results of other observers.

It appears that the observations of von ETTINGSHAUSEN and
Nernst cannot be represented by our formula. Therefore I shall
only recalculate their results for the longitudinal effect and compare
them with the increase of resistance in their bismuth.

1) In my thesis for the doctorate (p.111—114) I pointed out that the phenomena
mentioned might have a common cause in a variation of the number of free charged
particles due to the magnetic field. The found proportionality renders a common
cause very probable.

( 417 )

| Percentage | Percentage
Magnet. field. value of long.) increase Ratio.
effect. of resistance.
2800 1,01 7,0 0,14
4720 2,57 14,7 0,18
9480 11,00 | 3,55 0,31

That nothing can be seen here of the proportionality found by
me, may probably be ascribed to some extent to errors of obser-
vation; the more so, as the object of the measurements was not to
determine the relation between the strength of the magnetic field
and the two phenomena, but to compare the behaviour of bismuth
with that of bismuth-tin alloys.

Moreover their bismuth was cast. Therefore disturbances, caused
by irregular crystallisation were probably present.

Chemistry. — Professor BAKHUIs ROOZEBOOM presents a commu-
cation by Dr. Ernst Conen, “On the velocity of electrical
Reaction. II.”

The velocity of the reaction Zn + Hge SO, 2 Hg, + Zn SO.

I, An open galvanic element is not a system in equilibrium;
this is obvious from the fact that if the circuit of such an element
is closed by means of a wire, the reaction which can take place in
the cell at once occurs.

We must assume, that, owing to the resistance of an open cell
being very (infinitely) great, the velocity of the reaction is practically
reduced to zero !),

2. If, on the other hand, it is, for example, desired to study
the course of a chemical reaction at different temperatures as a
function of the temperature, a galvanic element may be constructed
in which the reaction will take place as soon as the circuit is
closed.

In what follows I shall describe briefly the results obtained in

the study of the reaction

1) Compare Nernst, Theor. Chemie. 2e Aufl. 1898, 658.

( 418 )
Zn + Hg, SO, = Hey + Zn SO,

at different temperatures.

The reaction represented by the above equation takes place in a
CrARK-cell when its circuit is closed.

When the cell is short-circuited by a short, thick wire (whose
resistance is practically zero) the constant of the electrical velocity
of reaction (see my first communication) at ¢° is

Ky ==

QO ’

where ZE is the electromotive force of the cell at ¢° and Q the
specific resistance of the saturated solution of zine sulphate in the
cell at the same temperature.

According as the solid substance present is Zn S Oy. 7 Ha O or
ZnS O,. 6 H, O, we shall find at one and the same temperature, two
values for K, since both Z and © depend on the nature of the
solid phase.

3. JAEGER!) has found that for an element in which the stable
solid phase is ZnS Oy . 7H, O, the electromotive force at the tem-
perature 4° may be represented by:

E,= 1. 400—0, 00152 (t—39) — 0, 000007 (t—39)? Volts.
If, however, the solid phase is ZnSO,y. 6 H,O, we have
B, = 1. 400 — 0, 00102 (£—39) — 0, 000004 (t—39)? Volts.

I have determined the resistance of the different solutions by
means of a KOHLRAUSCH dipping-electrode *) ( Tauchelectrode) the
resistance capacity of which, at 18°, was determined by a 0.5 N. KCl
solution, and controlled by a 0.5 N. NaCl solution at the same
temperature.

Table I contains the values of 2, 2, and 4, for the case that
Zn SO. 7 H,0 is present in the element and Table II, the same
quantities for Zn SO,. 6 HO.

1) Wriep. Ann. Bd. 63 (1897) 354,

2) Korrrauscu a. HorLBoRN, Das Leitvermögen der Electrolyte. (Leipzig 1898).
p. 18 u. 19.

( 419 )

MARBLE

Temperature. _ Z (Millivolts). Q Kk, X 10-2
— 5°.0 1453.3 0.0491 296.0
0°.0 1448.6 0.0423 342.0
Se 1443.6 0.0371 388.5
9°.0 1439.3 0.0337 426.6
15°.0 1432.5 0.0299 478.3
25°.0 1419.9 0.0260 544.6
30°.0 1413.1 0.0248 574.2
35°.0 1406.0 0.0241 583.6
39°.0 1400.0 0.0237 590.9

1 AB: TE SIE

Temperature. E (Millivolts). L2 kX 10-2
— 5°.0 1437.1 0.0577 248.7
0°.0 1433.7 0.0498 287.8
5°.0 1430.1 0.0437 326.8
9°.0 1427.0 0.0397 359.5
Pre 1422.2 0.0348 408.5
250.0 1413.5 0.0302 467.5
30°.0 1408.9 0.0274 513.8
35°.0 1404.0 0.0252 557.3
39°.0 1400.0 0.0237 590.9
45°.0 1393.7 0.0220 631.8
50°.0 1388.3 0.0211 659.0

4. Representing the electrical velocity of reaction graphically as
a function of the temperature, the two curves shown in the follo-

( 420 )

wing figure are obtained according as we are dealing with the
modification which is stable, or with that which is metastable
below 39°.

=
iS]
-5 d Fe 15 20 25 Ja JS 40 45 ST
Temperature.
As _ to be foreseen, the velocity of reaction at 39° is the

same in both cases; below this temperature the reaction in the
element containing the stable phase is always the faster (at the
same temperature).

Phys. © — ‘Diffraction of Réxtorn Rays”. By Prof. H. Haga
and Dr. C. H. Winp.

Investigations!) formerly undertaken in the Groningen Laboratory
rendered it already clear that, if X rays are due to vibrations of the
ether, their wavelength can be but a few ANGSTRÖM units. In the course
of the further enquiry a phenomenon was observed, indicating traces
of real diffraction and tending to give a wavelength of one or two
ANGSTRÖM units. Now it became possible to perform a new series
of exnc iments under circumstances more qualified to exhibit diffrac-
tion. A simple consideration makes it clear that in order to obtain
great intensity it is better to use narrow slits than to make the
distances great.

DC. H. Winp, “On the influence of the dimensions of the source of light in
diffraction phenomena of FrrsNeL and on the diffraction of X rays”. Kon. Akad. van
Wetenschappen. Proceedings, June 1898.

( 421 )

All the apparatus could now be mounted on one plate of free-
stone, whereby moreover greater steadiness was secured.

The first slit (X slit), the second (diffraction slit) and the photo-
graphic plate were mounted on heavy metallic stands, resting on
a free-stone plate (200 X 40 x 30 em.) This plate was supported
by three columns of the same material, resting on the great pillar
of the edifice; stands, plate, column and pillar were united by
plaster of Paris.

Behind the first slit was the RÖNTGEN tube, one of the excellent
tubes made by Mürrer (Hamburg) with automatic vacuum regu-
lator.

The induction coil was an excellent piece of apparatus made by
Siemens and Haske, with a maximum spark-length of 30 cm. and
a Deprez interruptor with two contacts.

The current for the induction coil was given by 6 accumula-
tors. The tube and the first slit were surrounded at all sides —
except at the backside, where space was kept for the connecting
wires between the coil and the tube — with thick leaden plates;
in the direction of the diffraction slit a small aperture was spared
in order to enable the X rays to reach the photographic plate.
Much pain has been taken to obtain the slits as excellent as possible;
the small platinum plates, thick 1/, mm., which formed the edges
of the slit, had been very carefully flattened and ground and were
screwed on flattened plates of brass. The width of the X slit was
14, 18 or 25 microns; by means of a leaden plate the height was
limited to 1 cm.

The diffraction slit (height 3 cm.) was 14 microns at the upper
end and gradually narrowing to a width of a few microns.

On one of the sides of the diffraction slit and very near to it
there had been drilled small round holes in the platinum, near to
the upper and lower end and to the centre o the slit, in order to
enable us, in a way afterwards to be mentic ned, to know the effec-
tive width of cach part of the diffraction slit. The diffraction slit
ended at the top and at the bottom in a slit of considerable width
(3 m.m), the axis of which was the prolongation of the axis of the
diffraction slit; the RÖNTGEN tube was placed behind the first slit
in such a position that these wider slits cut from the pencil of
X rays the most intensive, middle part, as could easily be controiled,
from time to time, by means of a fluorescent screen; of course the
rays then passed also in the desired manner by the diffraction slit.

With this arrangement were taken the experiments of which the
results are given in the following table, where signifies

( 422 )

o : width of the first slit in microns.

» .» »„ diffraction slit

a : distance between first and diffraction slit in cm.

” ”

diffraction slit and photografic plate in em.

5 5
a= 15 em. s: 24a 14 z.
0 bot exposition zn
25 1 29 5
25 20 57 3
25 45 66 4
14 75 60 1
14 75 100 2
25 105,5 150 6
18 1 30 8
18 75 130 7
18 75 200 9

In the experiment Nr. 1 a plate sensitive on both sides was used —
mark B II of the Actien-Gesellschaft für Anilin-Fabrikation. The
image on the second side of the plate however was many times
fainter than that on the first side; moreover on account of the
rather strong fog it seemed very desirable to destroy the image on
the second side and to remove the gelatine film; in the other expe-
riments LOMBERG-plates were used. The plates were developed a
very long time (at least half an hour) using rodinal (1 at 35), po-
tassium bromide being added.

In experiments 5 and 8, the photographic plate was pressed against
the brass plate, on which the diffraction slit was mounted. Measu-
rements, in order to give the width of the slit, were made on the
images obtained by these experiments, greater accuracy being attainable
in this manner than by direct measurement of the slit; on account
of the small distance between the plate and the slit, the image could
not be sensibly broadened nor by diffraction nor by the X slit being

EEN and Cr ho WIND.

THe DIFFRACTION OF THE RONTGEN=RAYS:

I.

FIG.

yi sates

eet
$3

ase

feng fs.

a

wadden.

Proceedings Royal Acad, Amsterdam Vol. 1,

ee

Hedi

sebas

5.08.

( 423 )

not infinitely narrow. The measurements were made by means of
a microscope made by Zeiss, object-glass D, compensation eye-piece
6 with micrometer; also low powers were used.

The above mentioned small holes in one of the slit sides gave
on 9 and 8 circular and on the other plates — on account of the
height of the X ray source — elongated dark images (cf. fig. 1 and 2).
On all plates the distances between the centres of these images
were divided with the dividing engine in the same number of equal
parts. Whenever for a definite division in one of the diffraction
images the corresponding width of the diffraction slit was wanted,
we could by this way immediately take it from the measurements
of 5 and 8.

If, using small power — object-glass a*, index at 10, compen-
sation eye-glass 6 — plate N°. 2 is gradually displaced, one sees
that the image of the slit appears in the broader part as a black
line, dark in the centre and with hazy edges, that however in the
narrower part the darker part — nucleus — ceases and the image
of the slit broadens out somewhat like a plume, showing but little
difference of intensity in a direction perpendicular to the length
of the image. In accordance with the gradual narrowing of the dif-
fraction slit, the image becomes of course weaker, but narrower
alone at a few places, in such a manner that from the point, where
the nucleus seams to disappear, maxima and minima begin to appear
in the width of the image.

The same thing occurs also in the other negatives, most clearly
in N°. 2, 6 and 9.

In order to give some idea of the character of these faint broadenings,
which are observed at their best with the microscope, we have made
of the narrowest part of 5 and 2 enlarged photographs by means of
a so called mikroplanar N°. I, made by Zeiss. Figures 1 and 2
are reproductions of these enlargements by means of heliography.

Fig. 1 is enlarged 16 times, fig. 2 14 times.

Identical numbers at the divisions indicate corresponding places.
In fig. 1 is given also the width of the diffraction slit.

In order to be sure that the real cause of the described pheno-
mena is to be attributed to diffraction, we have carefully consi-
dered other different causes which might cause a broadening of the
image of the slit. It appeared however, that though photographic
irradiation, local differences in the sensibility of the photographic
film, secondary rays (SAGNAC), small motions of the stands during
the experiments, often extending over more then 10 days, may have
changed in different degrees the image of the slit, these causes

( 424 )

cannot explain the broadenings of the image, which as we observed
oceur with the narrowing of the diffraction slit.

It might however be argued that if the influence of the width of
the first slit is taken into account, also with linear propagation of
the rays, the image of the slit might make upon us the impression
of a broadening with the gradually narrowing of the second slit.
In this case however the apparent limits of the image should at
the utmost diverge at the same rate as the edges of the second
slit approach each other. In our experiments however the diffrac-
tion slit narrows in so slow a manner that a broadening from this
cause would be totally imperceptible.

Hence we can only draw the conclusion, that the broadenings
of the slit image we have observed must be attributed to a Diffrac-
tion of the Röntgen rays. With this hypothesis the different
broadenings of the slit image, which are to be interpreted as mani-
fold formations of plumes, are easily explained, because it is only
necessary to suppose that there are rays of considerably different
wavelengths, rays of some definite wavelengths possessing greater
energy than others; the rays with great energy cause the separate
broadenings resembling plumes, the height of the ray source favou-
ring haziness.

The small intensity of the broadenings resembling plumes, the
haziness of their edges make accurate measurements and hence a
precise determination of the wavelength impossible. We were obli-
ged to make only an estimation of the wavelength of the more
prominent rays.

In FRESNEL’s diffraction theory is introduced the quantity 7; in
conformity therewith we now introduce the quantity vs, as given
by the relation

2 (a + bd)
ab

I=

This quantity determines, s, a, b and A being given, the kind of
the primary diffraction image to be expected, so that by means of
CorNu's spiral the intensity curve of the diffraction image can be
constructed. We have done so for the values 2, 1.5 and 1 of the
quantity vs. The width of the first slit, ¢, must however be taken
into account, or which comes to the same thing, from the primary
the secondary diffraction images must be deduced. !)

1) ©. H. Winp, „Over den invloed van de afmetingen der lichtbron bij FresNrL’sche
buigingsverschijnselen”. Verslag der vergad. April 1897,

( 425 )

In order to obtain a somewhat general survey of the different
possible cases, which were for us of importance, we have made

concerning the ratio

the significance of which will be clear, three hypotheses, viz.
d=3, d=1 and 0— 0,6.

The first slit is with the first hypothesis rather wide, with the
third rather narrow as compared with the second slit. The intensity
curves for the diffraction images in the 9 cases are plotted down
in fig. 3 at.

In the same plate are represented also by dotted lines the intensity
curves with the seme slits and with rectilinear propagation, using
the circumstance that the areas enclosed between the intensity
curves and the axis must be the same with and without diffraction.

From these figures it appears that already with great values of
es broadening will be visible, provided that the least perceptible
intensity, is very small as compared with the greatest intensity,

o
to)

which with given width occurs in the image of the slit.

However in our case of the broadenings resembling plumes the
last condition is certainly not fulfilled; in the centre of the slit
image the intensity is already small, and a high ratio at the edges
would be necessary in order to be perceptible.

In this case we see at once from the curves, that with a value
v; = 1 there must be in all eases a distinct broadening, with 7,=2
probably never, with v,=1.5 only under favourable circumstances
as to the width of the first slit, and then only in a small degree.

It is also clear that, though the influence of the value of 0 on
the visibility of a broadening exists in general, yet this influence
is not great for values of rv, between 1 and 1.5. Taking this into
account we think to be justified to take »,= 1,3 in every case the
slit image is sensibly broadened, that is in the case of every plume.

Hence we find by means of the relation

CA nd 3
a 93 sy
1.3? ab

Proceedings Royal Acad. Amsterdam, Vol. I.

( 426 )

where sj is the width of the diffraction slit corresponding with a
broadening, the values in the following table :

N°. of | 2 = | À in Ancsrrém
é sj, in micra. enn
experiment. | | units.
| 7 185
| 6 1,1
2
| | 5 0,8
| 4 0,5
| gr) 2,7
| (6) | (1,0)
4 |
3 0,4
| 2,9 0,25
8 7
| 7 ie)
6
4,5 0,5
| 3 0,25
4 0,5
9 |
2 0,12

If, and this is not impossible, these values of sj, are enlarged by
photographie irradiation, the wave lengths would still become smaller.
Though very desirous to be enabled to give the limits of the Ronr-
GEN rays with more certainty, we think this an impossibility with
the means at our disposal. Not till RénrGEN tubes are produced,
remaining in good working condition as long as those we have
made use of, but giving out rays of much greater energy, one may
succeed to make measurements instead of estimations.

Physical Laboratory

University Groningen.

Physics. — “Simplified Theory of Electrical and Optical Pheno-
mena in Moving Systems”. By Prof. H. A. LOREN?TZ.

S 1. In former investigations I have assumed that, in all elec-
trical and optical phenomena, taking place in ponderable matter, we
have to do with small charged particles or ions, having determinate
positions of equilibrium in dielectrics, but free to move in conductors
except in so far as there is a resistance, depending on their velo-
cities. According to these views an electric current in a conductor
is to be considered as a progressive motion of the ions, and a
dielectric polarization in a non-conducter as a displacement of the
ions from their positions of equilibrium. The ions were supposed to
be perfectly permeable to the aether, so that they can move while
the aether remains at rest. I applied to the aether the ordinary
electromagnetic equations, and to the ions certain other equations
which seemed to present themselves rather naturally. In this way
I arrived at a system of formulae which were found sufficient to
account for a number of phenomena.

In the course of the investigation some artifices served to shorien
the mathematical treatment. I shall now show that the theory may
be still further simplified if the fundamental equations are imme-
diately transformed in an appropriate manner.

§ 2. I shall start from the same hypotheses and introduce the
same notations as in my , Versuch einer Theorie der electrischen und
optischen Erscheinungen in bewegten Korpern”. Thus, > and 9 will
represent the dielectric displacement and the magnetic force, g the
density to which the ponderable matter is charged, » the velocity
of this matter, and € the force acting on it per unit charge (electric
force). It is only in the interior of the ions that the density o differs
from 0; for simplicity’s sake I shall take it to be a continuous
funetion of the coordinates, even at the surface of the ions. Finally,
I suppose that each element of an ion retains its charge while it
moves.

If, now, V be the velocity of light in the aether, the fundamental
equations will be

DONNE Ne wo Oo a o £ (L.)
Pig 0%. 92-4) EN

Rot Hh=Angvt4ind, ... . . (UI)
Br VERO diz Da Gane es wes ea
E=—4nV2d+[0.H].. (Va)

( 428 )

§ 3. We shall apply these equations to a system of bodies,
having a common velocity of translation », of constant direction
and magnitude, the aether remaining at rest, and we shall hence-
forth denote by », not the whole velocity of a material clement,
but the velocity it may have in addition to p.

Now it is natural to use a system of axes of coordinates, which
partakes of the translation p. If we give to the axis of « the direc-
tion of the translation, so that », and p- are 0, the equations
(La)—(Va) will have to be replaced by

DD on A NEE (Ip)

Dir «Jos ute Ee ee (11)

0D: df: d d
Ae — DE == 455 vv, 4- 4 7 IE —- Py a) dy» (LI)
d Dy d De / d d
== _ Ed { TOY — 4; ee Sir Ò-
da dy 1 bal ae } a) Der
2 C Zz 0 dy d d \
ta v2 (SP) = (open) De
: 7 Ye vd dare SON |
„(Ode ddz /d d
4 a J ‘ce en 5) (LV)
/0 d, C Vz C C |
EE
\d 4 dy / \0 t Ou }

Cain V2ot[p. Al Eloi

In these formulae the sign Div, applied to a vector A, has still
the meaning defined by

OA- OU AA
Dio l=S ae gE

As has already been said, v is the relative velocity with regard
to the moving axes of coordinates. If p==0, we shall speak of a
system at rest; this expression therefore means relative rest with
regard to the moving axes.

( 429 )

In most applications p would be the velocity of the earth in its
yearly motion.

S 4. Now, in order to simplify the equations, the following
quantities mav be taken as independent variables

là pr

== ath
9 le
2

V re? ne

The last of these is the time, reckoned from an instant that is
not the same for all points of space, but depends on the place we
wish to consider. We may call it the local time, to distinguish it
from the universal time t.

Tf we put

y
SSS = Is
V Va per
we shall have
d F d EE: d d d 0 d 0 0
de =a" Ve Ot dy ady dz de dt dae’

will be denoted by
Di U.

We shall also introduce, as new dependent variables instead of
the components of > and $, those of two other vectors 3' and 5,
which we define as follows
Vel aV%de, Fy AakV2 by kpn Fe wk VID + kyr Hy:

A AEN Dy = RH +4 ak ped. Dek be Ark pe dy.

In this way I find by transformation and mutual combination of
the equations (Ih)—(V) :

( 430 )

4;
Dio! § = — V29—Amkpee ws, : ¢ 2 ne

DIHH=0, Pore Lee

Ae wy F 28's
arene se Q 2 -+ Pot \
00's 9D * O8'y

yr == En == 4 7 k ? Dy a p2 ae : (LIL)
0D", 09'r ie 08’:
ick REE yes ee

oe" 3, 7 v Dz + V2 at!

08": Oy am 0D'» )

EN De! = Ot!
03 r OF z ON,
—— — ee ee (U
dz) | oF ue Ole
8, We ADE
de’ 0y/' Pe dt’
Er =de +k FE, (ty By + 0-8 2) + (vy De — v2 Dy)
an 1 1 5 '
=D =) ae oy (a ve Da — Ye 5) ee (Ve)
3 1 pe vase ;
c= TE i ere k — De Sz 4- (oe J gp TE vy A) +)

Putting »=0 in the three last equations we see that

are the components of the electric foree that would act on a particle
at rest.

§ 5. We shall begin with an application of the equations to

( 431 )

electrostatic phenomena. In these we have » = 0 and §' independent
of the time. Hence, by (II.) and (III)

th} ==)
and by (IV) and (L)
aS: AF, 28 A8, IB 98
dy ET ’ a de 1 dz! Oy ’
Div’ §! == V2

These equations show that §' depends on a potential w, so that

AN mede Sy il OO) oe
‘ jak a ae du” dz
and
26 2 a 26 47
re dd
dend Sas ke

Let S be the system of ions with the translation pz, to which
the above formulae are applied. We can conceive a second system
S, with no translation and consequently no motion at all; we shall
suppose that S is changed into S, by a dilatation in which the
dimensions parallel to OX are changed in ratio of 1 to &, the
dimensions perpendicular to OX remaining what they were. Moreover
we shall attribute equal charges to corresponding volume-elements
in S and Sj; if then ¢@ be the density in a point P of S, the
density in the corresponding point P, of S, will be

1
Co == TE Q.

If x,y,2 are the coordinates of P, the quantities 2’, y',2', deter-
mined by (1), may be considered as the coordinates of P,.

In the system Sp, the electric force, which we shall call €,
may evidently be derived from a potential @, by means of the
equations

dee

y' j de

and the function @, itself will satisfy the condition

Comparing this with (2), we see that in corresponding points
Oi
and consequently
Br Cir, D= Cn Oe — Ce

In virtue of what has been remarked at the end of § 4, the
components of the electric force in the system S will therefore be

Parallel to OX we have the same electric foree in S and S but
0)

in a direction perpendicular to OX the electric force in S will be
le En
=F times the electric force in Sp.

By means of this result every electrostatic problem for a moving
system may be reduced to a similar problem for a system at rest;
only the dimensions in the direction of translation must be slightly
different in the two systems. If, e.g., we wish to determine in
what way innumerable ions will distribute themselves over a moving
conductor C, we have to solve the same problem for a conductor
Co, having no translation. It is easy to show that if the dimensions
of C, and C differ from each other in the way that has been indi-
cated, the electric force in one case will be perpendicular to the
surface of C, as soon as, in the other case, the force €, is normal
to the surface of C).

Since
he (1 we ie
V2
exceeds unity only by a quantity of the second order — if we call
Dr 7 : 5 :
PE of the first order — the influence of the earth’s yearly motion

7
on eleetrostatie phenomena will likewise be of the second order.

_ ——

nn

(433 )

S6. We shall now shew how our general equations (L)—(V)
may be applied to optical phenomena. For this purpose we consider
a system of ponderable bodies, the ions in which are capable of
vibrating about determinate positions of equilibrium. If the system
be traversed by waves of light, there will be oscillations of the
ions, accompanied by electric vibrations in the aether. For con-
venience of treatment we shall suppose that, in the absence of light-
waves, there is no motion at all; this amounts to ignoring all
molecular motion.

Our first step will be to omit all terms of the second order.
Thus, we shall put #= 1, and the electric force acting on ions at
rest will become 8’ itself.

We shall further introduce certain restrictions, by means of which
we get rid of the last term in (le) and of the terms containing
Yr, Oy, De m (Ve).

The first of these restrictions relates to the magnitude of the
displacements a from the positions of equilibrium. We shall suppose
them to be exceedingly small, even relatively to the dimensions of
the ions and we shall on this ground neglect all quantities which
are of the second order with respect to a.

It is easily seen that, in consequence of the displacements, the
electric density in a fixed point will no longer have its original
value g,, but will have become

a ca

d 0
DSE (Op A) — = (Vo ay) —_— — (Q a-).
ow oy dz

Here, the last terms, which evidently must be taken into account,

co
: 0 fp e
have the order of magnitude —, if ce denotes the amplitude of
a
the vibrations; consequently, the first term of the right-hand member

of (I.) will contain quantities of the order

72 pp
V CU

a

On the other hand, if 7 is the time of vibration, the last term
in ([.) will be of the order

( 434 )

Dividing this by (3), we get

an extremely small quantity, because the diameter of the ions is a
very smail fraction of the wave-length. This is the reason why
we may omit the last term in (I,).

As to the equations (V.), it must be remarked that, if the displa-
cements are infinitely small, the same will be true of the velocities
and, in general, of all quantities which do not exist as long as the
system is at rest and are entirely produced by the motion. Such
are Do, Dy $' We may therefore omit the last terms in (Vo),
as being of the second order.

The same reasoning would apply to the terms containing = if
we could be sure that in the state of equilibrium there are no
electric forces at all. If, however, in the absence of any vibrations,
the vector %' has already a certain value §,', it will only be the
difference §'—6,', that may be called infinitely small; it will then
be permitted to replace §'y and Sz by Soy and Foz.

Another restriction consists in supposing that an ion is incapable
of any motion but a translation as a whole, and that, in the posi-
tion of equilibrium, though its parts may be acted on by electric
forces, as has just been said, yet the whole ion does not experience
a resultant eleetrie force. Then, if dr is an element of volume,
and the integrations are extended all over the ion,

7 la)

| 0 dy dT = Jo, Fred =O EE

«

Again, in the case of vibrations, the equations (V,) will only
serve to ealeulate the resultant force acting on an ion. In the
direction of the axis of y e.g. this foree will be

fesvar.

Its value may be found, if we begin by applving the second of
the three equations to each point of the ion, always for the same
universal time ¢, and then integrate. From the second term on the
right-hand side we find

( 435 )

Pz cz!
EN KAN dr,

or, since we may replace §', by &', and @ by oo,

Dz low
== 5 Oz fe, 8 oy dias

which vanishes on account of (5).

Hence, as far as regards the resultant force, we may put € = 3’,
that is to say, we may take % as the electric force, acting not
only on ions at rest, but also on moving ions.

The equations will be somewhat simplified, if, instead of §', we
introduce the already mentioned difference §’/—¥',. In order to do
this, we have only twice to write down the equations (I.)—(LV.),
once for the vibrating system and a second time for the same system
in a state of rest; and then to subtract the equations of the second
system from those of the first. In the resulting equations, | shall, for the
sake of brevity, write 3’ instead of §’—4',, so that henceforth §' wilt
denote not the total electric force, but only the part of it that is
due to the vibrations. At the same time we shall replace the value
of g, given above, by

We may do so, because we have supposed ar, a,, az to have the
same values all over an ion, and because g, is independent of the
time, so that

de 0 vo
Ov dz
Finally we have
4 0 Op 3 Qo dg
Diy §' = — 470 Ve ( = Ene - LO ci
io! CUA nt (0

1D DS Oe BS ed 6 oo (LL)

( 436 )

Since these equations do no longer explicitly contain the velocity
p,, they will hold, without any change of form, for a system that
has no translation, in which ease, of course, £ would be the same
thing as the universal time t.

Yet, strictly speaking, there would be a slight difference in the
formulae, when applied to the two cases. In the system without a
translation @,, a7, a would be, in all points of an ion, the same
functions off, i.e. of the universal time, whereas, in the moving
system, these components would not depend in the same way on £
in different parts of the ion, just because they must everywhere
be the same functions of f.

However, we may ignore this difference, of the ions are so small,
that we may assign to each of them a single local time, applicable
to all its parts.

The equality of form of the electromagnetic equations for the two
eases of which we have spoken will serve to simplify to a large
extent our investigation. However, it should be kept in mind, that,
to the equations (Ia)—(1Va), we must add the equations of motion
for the ions themselves. In establishing these, we have to take into
account, not only the electric forces, but also all other forces acting
on the ions. We shall call these latter the molecular forces and we
shall begin by supposing them to be sensible only at such small
distances, that two particles of matter, acting on each other, may
be said to have the same local time.

§ 7. Let us now imagine two systems of porderable bodies, the
one S with a translation, and the other one S, without such a
motion, but equal to each other in all other respects. Since we
neglect quantities of the order p2?/V?, the electric force will, by §5
be the same in both systems, as long as there are no vibrations.

After these have been excited, we shall have for both systems
the equations (la) —(IVa).

Further we shall imagine motions of such a kind, that, if in a
point (a',y',2') of S, we find a certain quantity of matter or a
certain electric charge at the universal time #, an equal quantity
of matter or an equal charge will be found in the corresponding
point of S at the local time f. Of course, this involves that at
these corresponding times we shall have, in the point (2', y', 2’) of
both systems, the same electric density, the same displacement a,
and equal velocities and accelerations.

Thus, some of the dependent variables in our equations (Ia)—(1Va)
will be represented in S, and S by the saine functions of a’, 4’, 2, ¢,

2.

( 437 )

whence we corclude that the equations will be satisfied by values
of 6',, Dy, 9'., Fr, By, 82, Which are likewise in both cases the same
functions of 2’, y', 2', £. By what has been said at the beginning
of this §, not only %', but also the total electric force will be the
same in S, and S, always provided that corresponding ions at cor-
responding times (i.e. for equal values of #) be considered.

As to the molecular forces, acting on an ion, they are confined
to a certain small space surrounding it, and by what has been said
in § 6, the difference of local times within this space may be
neglected. Moreover, if equal spaces of this kind are considered in
S, and S, there will be, at corresponding times, in both the same
distribution of matter. This is a consequence of what has been sup-
posed concerning the two motions.

Now, the simplest assumption we can make on the molecular
forces is this, that they are not changed by the translation of the
system. If this be admitted, it appears from the above considerations
that corresponding ions in 5, and S will be acted on by the same
molecular forces, as well as by the same electric forces. Therefore,
since the masses and accelerations are the same, the supposed motion
in S will be possible as soon as the corresponding motion in S, can
really exist. In this way we are led to the following theorem.

If, in a body or a system of bodies, without a translation, a system
of vibrations be given, in which the displacements of the ions and the
components of §' and 9’ are certain functions of the coordinates and
the time, then, if a translation be given to the system, there can
exist vibrations, in which the displacements and the components of
N' and $' are the same functions of the coordinates and the local
time. This is the theorem, to which I have been led in a much
more troublesome way in my „Versuch einer Theorie, ctc.”, and by
which most of the phenomena, belonging to the theory of aberration
may be explained.

§ 8. In what precedes, the molecular forces have been supposed
to be confined to excessively small distances. If two particles of
matter were to act upon each other at such a distance that the
difference of their local times might not be neglected, the theorem
would no longer be true in the case of molecular forces that are
not altered at all by the translation. However, one soon perceives
that the theorem would again hold good, if these forces were changed
by the translation in a definite way, in such a way namely that
the action between two quantities of matter were determined, not
by the simultaneous values of their coordinates, but by their values

( 438 )

at equal local times. If therefore, we should meet with phenomena,
in which the difference of the local times for mutually acting par-
ticles might have a sensible influence, and in which yet observation
showed the above theorem to be true, this would indicate a modifi-
eation, like the one we have just specified, of the molecular forces
by the influence of a translation. Of course, such a modification
would only be possible, if the molecular forces were no direct actions
at a distance, but were propagated by the aether in a similar way
as the electromagnetic actions. Perhaps the rotation of the plane of
polarization in the so-called active bodies will be found to be a
phenomenon of the kind, just mentioned.

§ 9. Hitherto all quantities of the order p*z/V? have been ne-
glected. As is well known, these must be taken into account in
the discussion of MicHELsoN’s experiment, in which two rays of
light interfered after having traversed rather long paths, the one
parallel to the direction of the earth’s motion, and the other
perpendicular to it. In order to explain the negative result of this
experiment FITZGERALD and myself have supposed that, in consequence
of the translation, the dimensions of the solid bodies serving to
support the optical apparatus, are altered in a certain ratio.

Some time ago, M. Liftnarp!) has emitted the opinion that, ac-
cording to my theory, the experiment should have a positive result,
if it were modified in so far, that the rays had to pass through a
solid or a liquid dielectric.

It is impossible to say with certainty what would be observed in
such a case, for, if the explication of Micurison’s result which I
have proposed is accepted, we must also assume that the mutual
distances of the molecules of transparent media are altered by the
translation.

Besides, we must keep in view the possibility of an influence, be
it of the second order, of the translation on the molecular forces.

In what follows I shall shew, not that the result of the experi-
ment must necessarily be negative, but that this might very well
be the case. At the same time it will appear what would be the
theoretical meaning of such a result.

Let us return again to the equations (I-)—(V,}. This time we
shall not put in them #== 1, but the other simplifications of which
we have spoken in § 6 will again be introduced. We shall now
have to distinguish between the vectors € and §', the former alone

1) L’Kelairage Electrique, 20 et 27 août 1898,

( 439 )

being the electric force. By both signs I shall now denote, not the
whole vector, but the part that is due to the vibrations.

The equations may again be written in a form in which the
velocity of translation does not explicitly appear. For this purpose,
it is necessary to replace the variables 2’, y', 2', Uv, 5, 0’, a ando,
by new ones, differing from the original quantities by certain con-
stant factors.

For the sake of uniformity of notation all these new variables
will be distinguished by double accents. Let € be an indeterminate
coefficient, differmg from unity by a quantity of the order y»,2/V2,
and let us put

€
Ee RE Shaye poe sil et we (GD)
k
’ Le J
i Qa, dy SFU yy, SSE OT aot. chy (7)
: 5
k " 2
Co = 5 Yo Ne REAR Ee eren val (©)
1 1
a a) eo " len mt
WL = Sivan y ia DR) jo — "2,
ES Gee En
B ks A" epen 6! Ki eel!
Le Divs D= cy) fog Sa ry hye)
€ & 2

eee eh es Pic,” wer (9)

0 (5 1 d F fl. d qr i d Br
nd sen aes 6 wl
Oy" de’ Oo Oe | V2 d t!! g ue ( )
BR A8 do
A See CNS)
by 2" dt
oa or 1 Cn - 1 eal
C= 2 WS xy €, == he Ö ys ¢, = ke wz ot, fe (Ve)

( 440 )

These formulae will also hold for a system without translation ;
only, in this case we must take #= 1, and we shall likewise take
e= 1, though this is not necessary. Thus, 2”, y", 2" will then be
the coordinates, ¢” the same thing as ¢, 1. e. the universal time, a”
the displacement, g," the electric density, 9” and 6" the magnetic
and electric forces, the last in so far as it is due to the vibrations.

Our next object will be to ascertain under what conditions, now
that we retain the terms with »p.?/V2, two systems S and S,, the
first having a translation, and the second haying none, may be in
vibratory states that are related to each other in some definite way.
This investigation resembles much the one that has been given in
§7; it may therefore be expressed in somewhat shorter terms.

To begin with, we shall agree upon the degree of similarity there
shall be between the two systems in their states of equilibrium. In
this respect we define S by saying that the system S) may be
changed into it by means of the dilatations indicated by (6); we
shall suppose that, in undergoing these dilatations, each element of
volume retains ils ponderable matter, as well as its charge. It is
easily seen that this agrees with the relation (8).

We shall not only suppose that the system Sy may be changed in
this way into an imaginary system S, but that, as soon as the trans-
lation is given to it, the transformation really takes place, of itself,
i. e. by the action of the forces acting between the particles of the
system, and the aether. Thus, after all, S will be the same material
system as 8.

The transformation of which [ have now spoken, is precisely such
a one as is required in my explication of MICHELSON’s experiment.
In this explication the factor « may be left indeterminate. We need
hardly remark that for the real transformation produced by a trans-
latory motion, the factor should have a definite value. I see, howe-
ver, no means to determine it.

Before we proceed further, a word on the electric forces in S and
S, in their states of equilibrium. If ¢=1, the relation between
these forces will be given by the equations of $5. Now « indicates
an alteration of all dimensions in the same ratio, and it is very
easy to see what influence this will have on the electrie forces.
Thus, it will be found that, in passing from 5, to S, the electric
force in the direction of OX will be changed in the ratio of 1 to
ee and that the corresponding ratio for the other components will

1
be as 1 to —.

KES

a

( 441 )

As to the corresponding vibratory motions, we shall require that
at corresponding times, i.e. for equal values of ¢”, the configuration
of S may always be got from that of S, by the above mentioned
dilatations. Then, it appears from (7) that az, a",, a". will be,
in both systems, the same functions of 2", y",2",t', whence we con-
clude that the equations (I.)—(IV-) can be satisfied by values of
Fr, "2, ete, which are likewise, in S) and in S, the same functions
DOED

Always provided that we start from a vibratory motion in S, that
can really exist, we have now arrived at a motion in S, that is
possible in so far as it satisfies the electromagnetic equations. The
last stage of our reasoning will be to attend to the molecular forces.
In S, we imagine again, around one of the ions, the same small
space, we have considered in §7 and to which the molecular forces
acting on the ion are confined; in the other system we shall now
conceive the corresponding small space, i.e. the space that may be
derived from the first one by applying to it the dilatations (6). As
before, we shall suppose these spaces to be so small that in the
second of them there is no necessity to distinguish the local times
in its different parts; then we may say that in the two spaces
there will be, at corresponding times, corresponding distributions of
matter.

We have already seen that, in the states of equilibrium, the
electric forces parallel to OX, OY, OZ, existing in S differ from
the corresponding forces in Sy by the factors

From (V,) it appears that the same factors come into play when
we consider the part of the electric forces that is due to the vibra-
tions. If, now, we suppose that the molecular forces are modified
in quite the same way in consequence of the translation, we may
apply the just mentioned factors to the components of the total force
acting on an ion. Then, the imagined motion in S will be a pos-
sible one, provided that these same factors to which we have been
led in examining the forces present themselves again, when we
treat of the product cf the masses and the accelerations.

According to our suppositions, the accelerations in the directions

En re é 1 1 lie ee
of OX, OY, OZ in S are resp. — , —- and —— times what they

Kerem Kae hie ;
30

Proceedings Royal Acad. Amsterdam. Vol. I.

( 442 )

are in S). If therefore the required agreement is to exist with
regard to the vibrations parallel to OX, the ratio of the masses of
ko

é

the ions in S and S, should be

; on the contrary we find for

NE: eee
this ratio — , if we consider in the same way the forces and the
€

accelerations in the directions of OY and OZ,

Since & is different from unity, these values cannot both be 1;
consequently, states of motion, related to each other in the way we
have indicated, will only be possible, if in the transformation of S,
into S the masses of the ions change; even, this must take place
in such a way that the same ion will have different masses for
vibrations parallel and perpendicular to the velocity of translation.

Such a hypothesis seems very startling at first sight. Nevertheless
we need not wholly reject it. Indeed, as is well known, the effec-
tive mass of an ion depends on what goes on in the aether; it
may therefore very well be altered by a translation and even to
different degrees for vibrations of different directions.

If the hypothesis might be taken for granted, MICHELSON’s expe-
riment should always give a negative result, whatever transparent
media were placed on the path of the rays of light, and even if
one of these went through air, and the other, say through glass.
This is seen by remarking that the correspondence between the two
motions we have examined is such that, if in S, we had a certain
distribution of light and dark (interference-bands) we should have
in S a similar distribution, which might be got from that in S, by
the dilatations (6), provided however that in S the time of vibration
be ke times as great as in S,. The necessity of this last difference
follows from (9). Now the number ke would be the same in all
positions we can give to the apparatus; therefore, if we continue
to use the same sort of light, while rotating the instruments, the
interference-bands will never leave the parts of the ponderable
system, e.g. the lines of a micrometer, with which they coincided
at first.

We shall conclude by remarking that the alteration of the mole-
cular forces that has been spoken of in this § would be one of the
second order, so that we have not come into contradiction with
what has been said in § 7.

( 443 )

Physics. — Sroxes’s Theory of Aberration in the Supposition of
a Variable Density of the Aether. By Prof. H. A. Lorentz.

In the theory of aberration that has been proposed by Prof. Srokes
it must be assumed that the aether has an irrotational motion and
that, all over the earth’s surface, its velocity is equal to that of the
planet itself, in its yearly motion. These two conditions are easily
shown to contradict each other, if the aether is understood to have
everywhere the same invariable density.

Prof. PraNcK of Berlin had the kindness to cali my attention to
the fact that both conditions might be satisfied at the same time,
if the aether were compressible and subject to gravity, so that it
could be condensed around the earth like a gas. It is true, a certain
amount of sliding is not to be avoided, but the relative velocity of
the aether with regard to the earth may be made as small as we
like by supposing the condensation sufficiently large.

At my request Prof. PLANCK permitted me to communicate his
treatment of the case; it is as follows.

Instead of considering the earth moving through the aether we
shall suppose the planet to be at rest and the aether to flow along
it; this comes to the same thing. Let this motion be steady and
irrotational and let the velocity at infinite distance be ¢, constant
in direction and magnitude. Let the aether obey Boyre's law and
be attracted by the earth according to the law of Newron.

We shall piace the origin of coordinates in the centre of the planet
and give to the axis of z the direction of the velocity c. Finally we
shall call the distance to the centre r, the radius of the earth ro,
the velocity-potential ~, the pressure p, the density k,and the poten-
tial of gravity per unit mass V. We shall denote by w the constant

ak
ratio —, and by g the value
P

e= ro)

of the acceleration at the surface of the earth.
The motion will be determined by the equations

(9 Op
EEE

Pave l)+ En le, RECOM TANN (2)

and

( 444 )

The problem becomes much simpler if, in the second equation, we
suppose the variations of the square of the velocity to be much
smaller than those of either of the first terms. We may then write

“ah
ee + V = const. ,
k
or, since
3
re
0
V=—9 —,
=
ao
log k — ug —- = const.
r

If %, be the density at the surface, and
ON == (5

the last equation becomes

1 1
log & — log ky al) =0. ree so a ©)
r

To

As we see, our simplification consists in this, that the distribution
of the aether is independent of its motion, that is to say that it is
condensed to the same degree as if it were at rest.

Substituting the value of & from (3) in (1), we find a differential
equation for the determination of p. It can be satisfied by

omelet). @

the form of the solution being chosen with a view to the remaining
conditions of the problem. These are
Vo: stor aco

pW, WL,

oz dy dz
20. for > =,

op

es),

dr

They give us the following relations between the constants of
integration a and b:

u a ae
= \Gape Ie CEN co. ENG)

The velocity with which the aether slides along the earth is
found to be

a

rupert Peg ae foam)

ae

ZE 3°
Ar,

where 9 is the angle between the radius of the point considered
and the direction of the velocity c. Now, Prof. PLANCK remarks

that, by (6), if only ~ be large enough, a will be very small rela-
7 :

tively to 5, so that, as (5) shows, b is nearly equal to c. But then,
the value of » given by (7) will be a very small fraction of itself.
If the quotient of the pressure and the density had the same
value for aether as for air of 0°, and if the force of gravity acted
with the same intensity on the aether as on ponderable matter, we
should have
== Oi ‚ approximately.
"9
The sliding would then be absolutely imperceptible, but it should
be noticed that this would be due to an enormous condensation,
the ratio x between the densities for r= 7) and r= oo being by (3)

iS
e To,
In order that the aether may follow the earth in its motion in
so far as is necessary for the explication of the phenomena, we
need not require that the condensation should have such a high

3 ela: k
value. Of course, it would be less, if either — or g were smaller
P
than for air.

We can easily determine what degree of condensation must
necessarily be admitted. Indeed, the constant of aberration may be
reckoned to correspond to within !/, pCt. to the value given by
the elementary theory of the phenomenon; consequently, in the theory
of Srokes, the velocity of sliding should be no more than about
ls pCt. of the earth’s velocity. Now, putting ae 10, I find for

0

the maximum value of the velocity of sliding 0,011 c. i a :
"9

( 446 )
this value would be 0,0055c. Thus we are led to the conclusion

that = cannot be much different from 11, so that the least admis-
0
sible value of the condensation is nearly » =el!,

Calculations which we shall omit here may serve to estimate the
error that has been committed in simplifying the equation (2). It
is found that far away from the earth the error may become rather
large, but that nearer the surface, precisely on account of the small-
ness of the velocity in these parts, we need not trouble ourselves
about it. Thus, what has been said about the condensation may
be true, even though the state of motion in the rarefied aether, at
great distances, depart widely from the equation (4).

Strictly speaking, the condensation must be still more considerable
than the value we have found to be necessary. If the aether be
attracted by the earth, it is natural to suppose that it is acted on
likewise by the sun; thus, the earth will describe its orbit in a
space in which the aether is already condensed. In this dense aether
the earth must produce a new condensation.

Of course it is not necessary that the attraction follow precisely
the law of inverse squares; any law which leads to a sufficient
condensation will suffice for our purpose. To understand the con-
nexion between the condensation and the velocity of sliding, we
may consider a simple case. Let the aether have a constant small
density & outside a certain sphere, concentric with the earth, and
within this sphere a constant density k' > h.

If now the earth were at rest, and the aether flowed along it,
a diametral plane of the sphere, perpendicular to the mean direction
of flow, would be traversed by a quantity of aether, equal to that
which enters the sphere on one side and leaves it on the other
side. If this shall be the case, the velocities inside the sphere must

kk ee ;
be of the order zo if outside the surface they are of the order c.

If we wish to maintain the theory of Prof. Srokes by the sup-
position of a condensation in the neighbourhood of the earth, it
will be necessary to add a second hypothesis, namely that the velo-
city of light be the same in the highly condensed and in the not
condensed aether. This is the theory that may be opposed to that
of FRESNEL, according to which the aether has no motion at all.
In comparing the two we should, I believe, pay attention to the
following points.

1. The latter theory can only serve its purpose if we introduce
the well known coefficient of FRESNEL, concerning the propagation

( 447 )

of light in moving media. Now, this coefficient has been found to
be true by direct measurements and may be calculated by means
of well founded theoretical considerations. It might be deemed strange,
if in these ways we arrived precisely at the value that is required
by a wrong theory.

2. Jf we hope some time to account for the force of gravitation
by means of actions going on in the aether, it is natural to suppose
that the aether itself is not subject to this force,

On these and other grounds, I consider FRESNEL’s theory as the
more satisfactory of the two. Prof. PLANCK is of the same opinion.
Nevertheless it will be of importance to consider the question from
all sides, and it is for this reason that the following remarks may
here be allowed.

1. If the large condensation that has been spoken of and the
constancy of the velocity of propagation, whatever be the density,
be taken for granted, one can indeed explain all observed pheno-
mena. At least, I for one have been unable to find a contradiction.
It is true, as has already been stated, that, far away from the
earth, the equation (4) will no longer hold. In considering the motion
in those distant regions, the square of the velocity in the equation
(2) has to be taken into account, and the sun’s attraction will have
to be considered. But, after all, I find that there may always exist
an irrotational motion, and this, in addition to a sufficient conden-
sation near the earth, is all that is required.

2. If we apply to the moving aether the equations which
Hertz has proposed for moving dielectrics *) the propagation of light
will obey very simple laws. Suppose the earth to be at rest, and
the aether to flow, and let the axes of coordinates be fixed in space.
Then, if > be the dielectric displacement, 5 the magnetic force, »
the velocity of the aether and V that of light, and if the electro-
magnetic properties of the aether be supposed to be wholly inde-
pendent of its density, the equation may be put in the form

Th y= On
0D: 09, dr d 9
“Oy En = == UU lear + ay (Wy De — Ve Dy) — as (vx De — We de) | ‚ etc.
Dis = 0;
dd. dd, de. 9 : 4
Dee ea ak Ee Te (0, Bede ~(p2f-—v2H2), ete.
4 En 2/ at mre ö Pu) + a(t Dz vz) ete

1) Wied. Ann. Bd. 41, p. 369.

( 448 )

We shall apply these equations to a steady motion with velocity-
potential q, without supposing that Div» vanishes. We shall how-
ever neglect quantities of the order v?.

Now if, instead of f, we introduce as a new independent variable

Pies gp
t=t+ 7.

and instead of d and the vectors *' and &', defined by

Cl. = 47 V2 de + (pe Dy hy Hz), etc.,

and
D'r = Dx — At (vz dy — Hy De), etc.,

the equations become

DES = -
dps adn See
—— —- = = = —., ete.
oy z V2 ot i
Din
Os Oy 0D'x
SS SSS = SS) BL
dy dz ot

These formulae have the same form as those that would hold for
an aether without motion, and this is sufficient to obtain ina moment
the well known theorems concerning the rotation of the wave-fronts
and the rectilinearity of the rays of light. At the same time we
see that at the boundary of the different layers of the aether, which
slide one over the other, there is never a reflection of light.

It is curious that in the two rival theories somewhat the same
mathematical artifices may be used.

3. There seems to be nothing against the assumption that, while
the aether may be condensed by gravitation, molecular forces are
incapable of producing this effect. In this way it might be explained
that small masses, e. g. the flowing water in Fizeau’s experiments,
cannot drag the aether along with it. In these cases the coefficient
of FRESNEL would remain of use.

4, <A decision between the two theories would be soon obtained,
if the phenomena of the daily aberration were sufficiently known.
Unfortunately, this is by no means the case; even, as Prof. VAN DE
SANDE BAKHUYZEN assures me, one has never purposely examined
what the existing observations teach us concerning this aberration.

Mathematics. — “On reducible hyperelliptic Integrals.” By Prof,
J. C. KLUYVER.
(Will be published in the Proceedings of the next meeting.)

(April 22th 1899.)

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING

of Saturday April 22th 1899,

Ce

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

Afdeeling van Zaterdag 25 Maart 1899 Dl. VII).

Contents: “On reducible hyperelliptie Integrals.” By Prof. J. C. Krurver, p. 449. — „Melting
points in systems of optic isomers.” By Prof. H. W. Baxuvis RoozeBoom, p. 466. —
„On the deduction of the characteristic equation.” By Prof. J. D. van Der Waars —
discussion with Prof. Borrzmayn. p. 468. — „The galvano-magnetie and thermo-mag-
netic phenomena in bismuth (2nd Communication continued)” By Dr. E. van Ever-
DINGEN Jr. (Communicated by Prof. H. KAMERLINGH ONNES). p. 473.

The following papers were read:

Mathematics. — “On reducible hyperelliptic Integrals’. By
Prof. J. C. KLUYVER.

(Read in the Meeting of March 25t 1899).

In some cases an Abelian integral of the first kind and of defi-
ciency p can be reduced to an elliptic integral. According to a
theorem of WererstRAss!) when such a reducible integral presents
itself, it is possible to transform by a substitution of order 7 the
J-function of the first order into an other one of order r, so
that the p—l constituents 7’j2, 7'j3,....7'1, in the first row of the
period matrix all assume the value zero. If, conversely, it is
possible by a substitution of order r to find a %-function whose
period matrix shows this peculiarity, at least one of the integrals

1) KowaArevskr, dcta Math. IV, p. 395.

Proceedings Royal Acad. Amsterdam. Vol. I.

( 450 )

of the first kind is reducible, and it is possible to construct rational
functions on the Riemann surface 7, which are doubly periodic
functions of this integral.

Let us suppose that in the #-function of p variables 9 (u; 7),
where « denotes the p normal integrals and 7 denotes the given
period matrix, we make a substitution of order r associated with
the Abelian matrix })

Gh
«(7

of 2p rows and 2p columns of integers, in such a way that the
separate matrices @, /?, «'‚ 2’ satisfy the equations

e'=0 , af'=Pae=af'=fae=r, PR —pp=0.

According to this substitution the integrals « are replaced by
other integrals w determined by the equation

u= dw,
and 9 (u;sr) of the first order becomes a function &(w; 7') of
order # with a period matrix +’ which can be derived from the
equation
ar =p af.
From the above relations we can immediately calculate the inere-
ments 2, taken by the integrals w, when by describing some closed
curve on 7 the normal integrals « are increased by

oa=k+tk',

where & and # denote two columnletters.
In the first place we find

22 Sok sack,
and also by multiplying by the matrix /

Ba =S rQ = pik +- pick.

1) For the notation compare: BAKER, dbel’s theorem and the allied theory. Cam-
bridge 1897,

( 451 )
From
at =d fi

we have

rset a“ — p,
so that we get for the system of the increments {2 of the integrals w
rQ = lk — fk +c'ak.

By supposing that in the first row of the matrix 7’ the constituents
Tio, T13---+T ip are all equal to zero we shall find that every
increment £2, of the integral wj is expressed by

r $2, = Bik = Py k! re Tu ark,

where the first columns of the matrices (3, 7, @ are denoted by
Pr, Py, 1.

Hence the moduli of periodicity of the integral rw, corresponding
to any closed circuit are always multiples of 1 and 7’); and therefore
this integral must be an elliptic integral.

It may be noticed that in the case p= 2, the same conclusion
holds for the integral rw, so that for p= 2 there exist two redu-
cible integrals or there is none.

Assuming rw, to be an elliptic integral we can easily find how
many zeros the function O(rw,; rij), of the single variable rw,
and the period 7'y;, possesses on the surface 7. We have only to
calculate the value of the integral

1
—— f dlogO (rw, 3 Tij),
211
7!

taken round the boundary of the simply connected surface 7’, into
which 7 is resolved by the customary p pairs of eross-cuts A, and
Bj. On opposite edges of a cross-cut Aj the variable zw, has values
the difference of which amounts to /’%, so that on both edges
dlog O(rw,;%,) has the same value and the integrals taken in op-
posite directions round these edges, destroy one another.

oh

(452)

On the contrary by crossing B, the integral rw; increases by

> '
— Pm + Tu Can
and as

d log 6 (rwy— + Tm ms Ti) = A log O (rw, 3 ty) — 2mian drwj,

we finally get

to.

1 = i Me
— | dlog 0 (rw; ; Tij) = — > dn | dn 2, ms
271. h a 7
Ti Bh

Consequently the function @(rw,; 7'jj) admits r zeros on 7", so
that any quotient of the squares of two thetas must be a uniform
function’ of position on the undissected surface 7 with r double
zeros and * double poles. Hence as soon as one of the integrals
of the first kind W is reducible, there exist four adjoint curves
Ry, Ry, Rk; and fy, belonging to a pencil, which each separately,
letting alone any possible common points of intersection with the
fundamental curve f, touch — or at least intersect in two coinci-
dent points — the latter 7 times. The three quotients Zj: Ry,
Ry: Ky, Bz: Ry being quotients of the squares of two thetas save
as to some constant factor, may be taken equal to pW—é&, p We,
pW—e,, whence

be Bis gut. en
Pp w= Re VA hy Ls Ls Ls

The function p/W being however likewise uniform on 7 it must be
possible to replace the product of the four functions 2 by the square of
a rational function /, otherwise said: through the 4r points of contact
of the curves & there can be made to pass an adjoint curve #,
the order of which is the double of the order of the curves &,
which touches the fundamental curve f in the common points of
intersection with the curves R and which for the rest intersects f
only in the double points. The elliptic integral itself is now given
by the equation

Ml = les

VAR, Rp Bs i a

where J (x, y, 2) denotes the Jacobian of f and of the pencil of the
curves 2,

Meanwhile it is clear that when a reducible integral W presents
itself the curves R are not yet uniquely determined. The lower
limit of the integral W is still arbitrary and what is said of the
squares of thetas with the argument W is also applicable to the
squares of thetas with the argument W +. Hence the functions &
‘an be replaced by

S ae | i
We), SWE) =U en,
4 Dy 4

which functions can be expressed rationally in Ry, Ry, Rs, R, and
I’, Evidently the constant @ may be regulated in such a way that
one of the curves S, e.g. Sj, touches f in a given point 2’, 7/,
and by the preseription of this point the remaining »—1 points of
contact of Sj are completely determined. Thus we infer that the
existence of an elliptic integral W implies an involutory grouping of
the points of the curve / in such a way, that the r points of any
group may be regarded as the points of contact of some curve 4.
The fact that the system of the curves A depends on an arbitrary
parameter is important when we consider hyperelliptic curves. For
)
occurs only in the second power and the rational functions contain
no power of y higher than the first. So it is always possible to
choose the constant @ in such a manner that in the ratio Sj : Sy,
and then also in the two others Sy: S, and S;:S,, the term con-
taining y is wanting. In other words: im the case of an hyperelliptie

then in the equation of the curve f one of the coordinates, say y

curve admitting a reducible integral we can suppose beforehand that
each of the curves /, by means of which the reduction has been
effected, breaks up into a group of r right lines, drawn through
the multiple point of the curve.

In the preceding the existence of the funtions ” proved to be a
necessary consequence of the reducibility of one of the integrals of
the first kind; conversely, if the existence of the functions Zl is esta-
blished at least one of the integrals is reducible.

( 454 )

For in this supposition the elliptic integral

is an integral of the first kind belonging to the curve, because it

J(e ye) de
i, EO avail

dy

can assume the form

As for reducible non-hyperelliptic integrals the case p=3, r=?2
has been treated by SoPmie Kowateyski. The curve f is here the
general quartic upon which, 7 being equal to 2, an involutory
correspondence one to one exists. It can be shown that in this case
the curve can be transformed into itself by a reciprocal projective
transformation of the plane. Consequently four double tangents of
the curve pass through the centre of the transformation, so that its
equation can always be thrown into the form

f= ay (ax + by) (ex + dy) — K° = 0.

Evidently the four double tangents passing through the origin
can be identified with the curves ZR. For each of these tangents
touches f in two points, together they belong to a pencil and the
eight points of contact lie on the conic K.

Accordingly we get for the elliptic integral

DSE LDA LE 1
. Zz E y ~~ ar + by a, + dy 4
d c ca + dy

and the integral itself is

( 455

The simplest case of the reducible hyperelliptie integral, p = 2,
r= 2, was already known to LEGENDRE. Again the curve f is of
the fourth order, but it has now a node from which six tangents
can be drawn to the curve. If there is a reducible integral each of
the first three functions R is made up by a pair of these tangents,
as fourth function Ry we must take one of the two double elements,
counted twice, of the involution which is now necessarily formed
by the three pairs of tangents.

The equation of the curve being

f= ry — (a — 1) (ee — bl) (a — Ki) (a@#—-) = 0
we get in this way
R, =x, Ry = (x —1)(e — kl), kg = (# — kh) (er —)), Ry = (we = YAP

and the reducible integral is
wv (= $Y kl) de
: vy

In accordance with what resulted from the theorem of WEIERSTRASS
for the case p= 2 two independent reducible integrals are obtained.

Also the case p= 2, r= 8 has been considered from various sides.
As before the integral is relative to a nodal quartic f the equation
of which we take in the form

(w — ape — ey) y? = (w — ag)(x — ay)(a — Co) — eg).

Burkwarpr!) has pointed out the invariant relation existing between
the binary eubies (w—a,)(*—ag) (eas) and (w—e,) (weg) (w—es) when
one of the integrals is reducible. Previously Goursar ®) had treated
a more or less particular case of the reducibility and finally Burn-
SIDE?) indicated in connection with his more general researches a
remarkable form which the reducible integral can always assume.

After the deduction of some of their results a few remarks will
be added.

The curves 2, each of which breaks up into three right lines, must

1) Math. Annal., Vol. 36, 1890, p. 410
2) Compt. Rendus, 100, 1885, p. 622.
3) Proc. Lond. Math, Soc., 23, 1892, p. 113.

(456)

be required to touch — or at least to intersect in two coincident
points — the curve f three times. From the node six tangents, the

inflexional tangents included, can be drawn to the curve, three of
which (* — @,), (+ — ag), (vw — 43) make up together the curve R,; by
joming to each of the remaining tangents (#—e;), (e—eg), (e—es) a
line through the node (# — bi), (& — by), (« — bs), counted twice, the
four functions thus obtained

Ry = (er —cy)(« —b.)?, Ry = (a — ¢9)(« — by)?,

Rs = (w — ¢3)(w — b3)?, Ry = (w — aj)(e — ag)(x — as)

indeed satisfy all the demands, if only we take care to choose the
quantities b in such a way that the four functions are in involution.
With the aid of this condition we can eliminate the J’s, after which
still one relation remains between the a’s and the es. Hence of a
reducible integral five branch-points out of six may be chosen arbitrarily.

Reducible integrals of the kind considered here are easy to con-
struct if we observe that the four binary cubies belong to the
system of first polars of a binary biquadratic «‚*. Among these polars
there are four of the form («— o)(r — b)?, having a double point, so
besides Pe, Ro, Ry also (# — ey) (w— b4)° belongs to the system
and the four quantities 6 are at once recognised as the roots
of the Hessian A%. Also ej, ea, ¢3, c4 are the roots of a covariant,
found by the following consideration. The four points y, whose
first polars a,ar contain a double point 4, are the roots of the
covariant 1) 37 A* — 2jar!, where ¢ and j denote the two invariants
of «zt. The result of the elimination of 4 between this covariant
and @z@,°, which result is of the 12% order in @ and of the Sth
order in the coefficients @, must be a covariant having the quan-
tities b for double roots and the quantities e for single roots. After
division by the square of A* a covariant of the 4th order in the
coefficients @ will remain, necessarily of the form A7A‘ + wjaz',
the roots of which are ej, ca, Ca, ca. To determine the coefficients À
and «, we consider the special case

21 9 9 2
ar = — «x? (2? — 1), At =— — (2 at 1).
37 sl 3

In this case «2! has a double point, the four values of e are
)

1) Ciensen-LINDEMANN. Vorlesungen, J, p. 231,

(451)

evidently 0 and co, each taken twice, and, as
At D4 ch)
thi + 274° = OTE

we must take à=1l and w=?2. So in general the quantities ¢ are
determined by the equation

tAt+2jaA=0.

As soon as we regard as known one root cy of this equation we
ean construct a reducible integral. For then we can put

Gy Az? = (x — ay)(w — ag)(w@ — as) ,

(At $25 art) = (we — ee — re — 09)

2 — C4

whence it follows that

Ds A" sh Gp pial
VE Ry Ry ky = — ae Ga 1 Ae de)

v— by © — Cy

so that
(a — bj) de

1
age ce — (i At + 2j er!)

U == Cy

is an integral of the first kind relative to the quartie /, which is
transformed by the substitution

pW—e, pw —é, rn
er — er — bj)? ge (@ — eo)(r — bi) id

pW — és A 1

geer U)? err a) ag) — a)

into an elliptic integral with the variable pW.
It is now clear that in this way it is possible to construct the integral
out of five assigned branch-points. If the five branch- points aj, ag, 43) ¢1) Ca,

( 458 )

are given, a binary biquadratie «‚* must be sought which has a given
eubie A,” with the roots aj, a, a4; among its first polars. So there
is an identical equation of the form

2
a: a3 = ¢ A,3,
from which we deduce

zode 24+, 20,+ a, 2a,+ ay

A, A, = Ao A3

a

In the first place these equations determine z, moreover for the

coefficients of «‚* two relations remain, expressed by any two of

the four following equations

6 As Ao — 12 Aj Aj + 6 Ap Ag = Ay i,

2 A, A, — 6 Aj Az +44, Az = Aji,

6 As Ay — 12 Ay Az + 6 A, Ag = Api.
There are still two other conditions for «‚*, namely that the fourth and
the fifth of the given quantities are roots of the covariant ¢ At + 27 aa.
By the four conditions together the quantie «xt is entirely deter-

mined, and thereby the sixth branch-point c, of the integral.
We obtain the example treated by Goursat by putting

A =O @4,=0, a0
Then we have
= me 2
Ao == 0, Aj — aay As, Ag == 3 Ko Car 3 == 0, Aa — TT 2 ks ’
ir as; te) = Cees

the coefficients @ satisfying the equation
A3 Gy @3 — Ag do hy — Ay a3” = 0.
Lastly,
EAL +25 cat = da, (Bare Had — ao og 2 + a ya? — ba)
therefore ej, ca, c3 are the roots of the cubic

Coat + 3 Ca? + Cy = — @ ag a8 + ag ay a? — 4 a3?,

and c‚, associated with the root b‚—= of the Hessian A‘, is deter-
mined by 3 ar + a, = 0.
Hence the integral

dx
ie i a ee eee
V (A, 8 + 8 Aye + AglGy a? + BC; a + Gy)

proves to be reducible under the condition that the coefficients
A and © obey the relation

Ay Cz = 4 A3 C, +12 A, C,.

The formulae of transformation will be found to be

p W—e, Dp W—e, p —_— €3

gi (ee) (ebi)? ge (een) (rbe)? — ga (eea) (bi) 2
es 1
As 8 Age + Ay’

from which we can also deduce

Cy A Ci
AGS +3 A,2¢+ A,

Ap W 4 4 =

We obtain the second reducible integral by regarding
Coat 4-3 Cr H Cz as first polar of the biquadratic @.*. In this
supposition the Hessian Af will admit the root 4, =0, the polar
(ee)(e—bi)® takes the form 2?(4ge—As) and the required inteeral
itself is

ede

W == — === eis EEE 2 =
ic (A, #® + 3 Age + As) (Cat + 3 Ce? + Cs)

The reduction of the integral is obtained by putting

x? (Ag z— A3)
Cy x3 + 3 C, 2? HC

ApW+e=

Another means of constructing reducible integrals is founded on
a peculiar form which can always be given to the invariant relation
between the six branch-points.

( 460 )
From the identical equation
(ray) (rag) (@—a3) = Ay (rey) (ry)? + Ag (@ eg) (eb)

we derive by the successive substitutions # = aj, 42, as

(a, —¢)) (ay —b) * aot (a2—¢)) (a —bj) * = (age) (az) *
(area) (arbo) * (ager) (ag—bo) 2 (Agee) (aglio) *

or

a EE = = EN

Ag—Cg

a i— be dg—bg = a3—by

After multiplying numerator and denominator of these three frac-
tions successively by (a2—as), (¢,—a,) and (a;—¢9), addition gives

0 = ‘ag— ag) (ay-—b) a= — -++ (a3—ay) (ag—})) LS ote

+ (ay—ag) (ag—b

ds En

Similarly by interchanging e and es we obtain

0 = (ag—as) (a; —))) VA, ++ (ag—aj) (dg—b)) Vis

EE
aes pe

++ (ay —a3) (ag —)) Vs

a3 38
and having moreover the identity
9 = (ag—a3) (4; —b)) + (43--@)) (ag—b)) + (a, —ag) (a3—b)),
the quantities (a4;—2,), (az—hj) and (a3—b,) can be eliminated and

the invariant relation between the branch-points of a reducible inte-
gral takes the form

1 1 1
| Va—a Vage Wagt
Fel of 1
Al Vat Vage Wasa |?
1 1 1
| Var—e3 Was-es V as—e3

the arguments of the nine surds being determined save as to a

multiple of z. The symmetry between the a’s and the e’s shows,

that, as soon as there exists the involution we started with, a

similar involution can be found by interchanging the ¢’s and the

a’s, so that reducible integrals always present themselves in pairs.
BURNSIDE stated incidentally that the curve

2K 2K
ry? = (al) (u—sn? u) (ee (u + en (ee (u— 3)

admits reducible integrals. The form given here to the invariant
relation between the six branch-points readily provides a proof for
this assertion.

In order to obtain this proof we introduce elliptic arguments in-
stead of the a’s and the e's by putting

En =S ns ¢) = pu =p(u+»),
Ag = eg, Cy = pug =p (U + v9),
a3 = €3, cz = pug = p (u + 23).

So the invariant relation becomes

Ou Cuy Obs

—_—- te En,

| Ot Ots Os

| . |

0 = | ory Olly COS

Ooy Ogg Ogug

|
Ou) Ou, OUs

: Osj Ozu 033

As a function of « the determinant is doubly periodic ; manifestly

( 462 )

it has several zeros, e. g. w — — vj, hence the equation is identically
satisfied, if we choose vj, vz, v3 in such a way that the function has
no poles. There might be nine poles, since cach of the denominators
can be made to vanish. Consequently we have to find out whether
it is possible to make the corresponding residues equal to zero. If
we take e.g. the pole corresponding to o,u, =0, that is if we take
u = — vj + az, the residue is proportional to

Oy Ug Og ug == Op Ug Oy Us

Oy Uy Op Uy Oy Uz Op Us
The above expression however can be written
Ug + U3 Ug — Ug Ug + Us Ug — Us
5 5
€

2 DEE UG OR ee ENE

Oy Ug Og Ug Oy Us Op Us

2 (es — es) G

and this is zero, if only for «= — vj +, we have at the same
time 3 (ug + Uw) == 0,
This takes place if we have

tol

(va + v3 — 2) =0,

and the residues of all nine poles will vanish if moreover we have
simultaneously

$ (vg + vj — 209) =0,
4 (ui + v — 2v3) == 0.
As solution of these equations can be taken

A0, 40: A0;
2 SO eae

Se 8

PI

==

7 Vg =

where 2.2), 202, 202; denote periods connected by the relation
OQ, + 25 -l- Qs == (I);
So we find the reducible integral

(ebi) de

Ws
jk WA Clear) epe ze ==) (ep =) (epe )

( 463 )

Every reducible imtegral, with five assigned branch-points
Ay Az, Az, Cy, Cg, can be brought into this form by a linear substi-
tution. For by means of the equations

40,
3 ) 6

plu +

dy—0g Cj—43

. ; - ’
a\— ag Cj — a3 e1— e3

40,
putes

as
u —/
ay— ag Cg dg Ee ey —es Pp ( ar 3) €9
a\y— ag 3 Cg —U3 Ee Ey ez ì a
pet Se,

we can determine the ratios ej :es:e5 and the argument w.

A somewhat laborious calculation gives the values of the quanti-
ties 6 and the formulae of substitution.

Putting

p (ug—us) =p (Wz) = p (uur) = pr,
the following results are obtained

Pulg—pus

uz pu
Seem AGEL Metta delat ae pina hoa
bs = — 2pv tpv. ed ;
ply + pug
by + 2pmy dy + Apug bs + pu, pu, pig pus|
b‚=| bipu bapus bspus nn Ga boren
1 1 1 1 1 1

Furthermore the formulae of substitution are

(rp) (e—b;)?

4x3 — gar — 3

DW = (pus + pus + pe)

(e= pus) (e —bo)?

p Weg = (pus + pe + pr) 3
42° — gov —qz

’

ep) et)?
Jp t—Ys

pW = (pu, + pug + pv) ————

( 464 )
so that the roots of the p-function are determined by
&— &3 = Pug—pug 9 Ezi = PUg—ptl y &)—Eég — pul — pug e

By interchanging the a's and the e's we can obtain the second
reducible integral.

Proceeding to consider reducible hyperelliptic integrals of deficiency
p=s, it is clear that by the same methods also these can be con-
structed without great difficulty. If the curve f is given by the
equation

(wa) (w—ag) (w—as) y? = (e—ay) (u—as) .... (L—ag) ,

hat is: if the curve f is a quintic with a triple point, from which
eight tangents can be drawn, each of the curves Zò, Zl, Rs, Ry in
the case r=2 is to be made up by a couple of these tangents.
The twofold condition for the reducibility expresses that these four
pairs of tangents are in involution and it is easily verified that
when Aw?-+ Be + C defines the double elements of the involution,
the reducible integral will have the form

Aa? + Be + C
f- ( dam.

v — a)(¥ — ag)(w — ag )y

The investigation of the next case p= 38, r= 3, is closely allied
to that of the case p= 2, r=3 treated before.
Suppose the equation of the curve to be

(w—ay)(w—ag)(e—as) y® = (w—a'))(e—4'g)(«—a's)(ux— €))(@— Cy).

We regard the product of three tangents (w—aj)(w—ag)(w—a3)
as the curve Zj, in the same way we join the second three
(vw—a', (x—a'y)(w—a's) to a curve Les; the third curve 2s will be the
product of the next tangent (w—c,) and of a line through the node
(w—bg), counted twice, similarly the curve B, is furnished by the
tangent (e—cz) and the double line (w—b»). 3

The twofold condition for the reducibility is that the four binary

cubies
Ry = (& —aj)(w—ag)(w—a3) , Ry = (e—a’})(w—a'g)(u—a's) ,

Rl (x—c))(w—b,) , Ry = (w#—cy)(w—bg)”

( 465 )
are in involution. This will evidently take place when ec, and
cy are two roots of the covariant # Af + 2ja@s4, where @,* is the

biquadratic which has 2; and Zy as first polars. The quantities
bj and by are two roots of Ae; if we call the other two bz and 54,

(a—bs) (r—by) dx

ee
1
| gee a. 1 bx? lt Av +2 jax)

(w—e;) (e—ey)

is a reducible integral,
As an example we may point to the following case

ve re ak)
t == 2 (hy ky — 1) (hy ky — 3), j= — 6 (hy ho — 1),
At = 2 (hy ky — 1) (2 by a? + (hy hy + 3) 2? + 2 ky a),
ep = ke 8k 282k, wa = heh -3 Sh ek®,
At + 2jaxt =e (3a + ky) (why + 3) (ha? + (3 — hy hy) & + hy).

The Hessian Af has two special roots bz =0, 6, = oo, the cor-
responding quantities ce; and ec, are given by 32+4,=0, rk, + 3=0,
ej and cz are the roots of Aja? + (8—,h,)e+hk,=0 and the
resulting reducible integral is

a dz
w= See See Ee eee
|, VO Blah See Be Bar Bk kyo ha)

where under the radical sign we may replace each of the two cubic
factors by any one of their linear combinations. The reduction of
the integral will be effected by the substitution

AWB . ®h +32
EED oi TEE

The case p= 4, r= 3 evidently allows quite a similar treatment.
Seven branch-points of the integral can be assigned arbitrarily; the
triple eondition determining the three remaining branch-points is
again readily obtained by the consideration of the cubic involution.

32
Proceedings Royal Acad. Amsterdam. Vol. I.

( 466 )

Chemistry. — “On melting points in systems of optic isomers.”
By Prof. H. W. Baxuurs Roozesoom.

In order to test the views on melting points of mixtures of optic
isomers, as communicated in the Proceedings of the Meeting of Feb. 25th
1899, page 312, Mr. Aprrani has now in the first place examined
two examples in which the certainty existed of the inactive substance
being a racemic compound.

The first example is the dimethylic ethereal salt of tartaric acid.
Here the d- and /-form have a lower melting point than the racemic
compound.

The second example is the dimethylic ethereal salt of diacetyl
tartaric acid, where the d- and /-form have a higher melting point
than the racemic compound.

For the present only the melting points of mixtures of d- and
r-forms have been examined in all their proportions. Consequently
we could. only get the right half of fig. 3 and 4 (vide page 312).

We found:

I. Dimethylic ethereal salt of tartaric acid.

Mol. percent racemic compound Final melting point.

in the mixture.

0 45°3
1.96 41.7
3.02 41.6
4.78 45.0
6.59 50.6
On 57.0
20 66.8
40 18.7
50 81.8
60 84,2
70 85.9
80 87.3
90 88.5

100 89.4

( 467 )

II. Dimethylic ethereal salt of diacetyltartaric acid.

Mol. percent of racemic compound Final melting point.
in the mixture.

0 104°3
20 99.8
40 95.8
60 90.5
70 87.4
30 84.6
90 83.4
100 83.8

If we represent the numbers graphically, we get the following
figures.

100°/, 80 60 40 20 0
Mol. °/, racemic compound.

1002/5, 180 60 40 20 0
Mol. °/, racemic compound.

In their general form they correspond entirely with the right
halves of fig. 3 aud 4, page 312. In fig. I we remark however
that the melting line for the racemic compound extends very consi-.

32°

( 468 )

derably so as to run as far as the concentration 3°/, before meeting
the melting line of the d-substance. This is connected with the
flat course of the meltingline near the melting point of the racemic
compound, which points to a great measure of dissociation in the
two active components in the liquid state.

In fig. IL it is the melting line of the racemic compound that,
owing to the lower melting point, has the smallest extension (final
point near 86°/,) but this too has a very flat form near the melting
point.

Physics. — “On the deduction of the characteristic equation.” By
Prof. J. D. vAN DER WAALS — discussion with Prof.
BOLTZMANN.

In the proceedings of the former meeting Prof. BOLTZMANN has
inserted a communication, accompanied by a letter. In this letter
Prof. BOLTZMANN has expressed the wish that his communication
would give rise to a discussion. As the result for Prof. BOLTZMANN's

2

bie
values of the coefficients of — , — ete, which appear in the cha-
v u“

racteristic equation, differs from that which I have obtained, I con-
sider the invitation to discussion as also addressed to me. And
though as a rule I prefer to leave the discussion between different
results, obtained in two different ways, to the gradual development
and extension of our views, which is brought about in course of
time, I will not abstain from complying with his request, in the
hope that this discussion may be „useful to science.”

I am perfectly aware of the difficulties attending this discussion.
Prof. BoLTZMANN’s „ Vorlesungen” form a logical coherent whole,
and the different results agree so well, that we may be sure that
they contain a perfectly correct solution of the problem, as Prof,
BOLTZMANN conceives it. On the other hand I am convinced, that
also my solution, leaving same unsolved questions and some minor
points out of account, gives a true explanation of the problem, as
I see it. So I pass by the question whether in equation (11) p. 403

4 sd b?
the factor of 2 Gb is to be put as 1 Ne + — or whether 7
hd U, v

: ieee 2357 ee : 2
must possibly be diminished by emme this is of minor interest.

As our results differ so much, we cannot but have considered
two different problems, and to get some certainty on this point, I

( 469 )

have looked more closely into one of Prof. BOLtZMANN’s Se sy,
viz. the equation Le. pag. 169

‚Db rity 17 B2\ 4hma 7 7 bex 4 Joma {
8 = 2 as 4 = (» — 2 — v
th Des b+ GRK 8 Dy vf ET a) € vp |

which equation is to be applied, when two phases are in equilibrium.

It is well known from thermodynamics that when two phases of
a simple substance coexist, besides p and 7, the thermodynamic
potential must also be equal. The preceding equation of Prof.
BOLTZMANN must therefore be the kinetic interpretation of the ther-
modynamic relation

Hg = Uf

or 3 ;
mee — 6) ST )
“9 ee, If pt pe,

In a paper (Verslag der Vergadering 26 Januari ’95, also published
Arch. Neerl., T. XXX), entitled “de kinetische beteekenis van de
thermodynamische potentiaal’ I have given the kinetic interpre-
tation of this thermodynamic relation. For a fuller discussion I
refer to this paper, and when I compare this result with the equa-
tion of Prof. BoLTZMANN for that equilibrium, it is evident that we
have a different conception of the problem. I do not mean to say,
that our results do not agree at a first approximation. But they
are not identical. a

In the first place there is the following difference. According to
Prof. BourzMann the energy required to remove one molecule’ from
the liquid phasis is simply the work required to overcome the cohe-
sion; according to me that work must be diminished by the quantity
sie I have called the work of the thermic pressure. In the second
place Prof. BOLTZMANN subtracts from the, specifie volume a quantity
twice as large as the quantity which I think must be subtracted
from it .

_ In my opinion there is no doubt that also the work of the ther-
mie pressure must be taken into account, if we ascribe real dimen-
sions to the molecules. If a molecule heae a phasis, not only the
increase of its potential energy is to be taken into account, but we
must also pay attention to the fact that the quantity fom which
the molecule has escaped, has diminished, that the surface of that
quantity has contracted, and that therefore a quantity of work has

( 470 )

been performed, equal to the product of the thermic pressure and
the volume which the molecule occupied in the phasis.
And if a priori we should not be convinced of this, it would
appear as soon as the significance of u —=«— Tr} pv is examined.
The quantity, which must be equal for the two phases, we may
denote

é-+ pv
Seed ant ps

or according to the notation of Mr. GrBBs:
al ta a ’

in which X is the function which Mr. GiBBs has called „heat
function for constant pressure” (Equilibrium of heterogeneous sub-
stances, p. 148).

To compare it with the equation of Prof, BOLTZMANN we put

pv —€ 2e

tT kee Be eeN

ie

a
The quantity p + —-, the sum of the external and molecular
v

a a
If «=——, po—e=o(p + 5
v vw”
pressure we call “thermic pressure”
a
If we put p+ ion TF, not inquiring for the present into the
form of F, the above formula becomes

2 FuvT+2
—ntrFot oe en en i
Even in this form we see that the quantity r F Tv, which may
be considered as work of the thermic pressure, is of the same nature
as the quantity 2e.

This is still more evident, if we put F= and substitute
es

rTtrT

v
for r — meee

oa Vs

( 471 )

We may namely diminish the quantity which is to be the same
for both phases, by an arbitrary constant or function of the tempe-
rature, and we put then

If

and

a db)
nr ge — 6) + fo

and the quantity which is to be equal for the two phases, may be
given under this form:

2
rT {Fb — | Fa) =
Oe

log (v — b) — 7

In my communication to which I have referred before, I have
deduced this formula, starting from the idea that there exists a
thermic pressure, which expels the molecule and is counteracted by
the molecular attraction.

We may write the quantity which must be the same in the two
phases in this way:

By comparing it with the formula of Prof. BOLTZMANN, we find
that he substitutes rlog{v— 2b ete.}-+ C for

If the formula under the symbol log. was perfectly accurate,
Prof. BOLTZMANN should be able to prove, that the entropy could

( 472 )

be calculated perfectly accurately from

d
n—v oN log (v — 2 b ete.)

Ov

Approximatively there is equality, but I have not succeeded in
proving that the entropy of Prof. BOLTZMANN is really identical
with the quantity 7 of this relation.

These considerations have suggested the question to me, whether
the problem, the accurate solution of which Prof. BOLTZMANN gives,
might be the following: In what way do a great number of moving
material points arrange themselves, when they are subjected to an

. . . a
attractive force, which leads to a surface pressure — , when they
\ i KZ)

2)

cannot come nearer’ to each other than at a certain distance (dia-
meter of a molecule). If they are really material points, the work
of the thermic pressure does not exist — and Prof. BOLTZMANN’s
equation for coexisting phases might he defended. But then the
real problem, how do molecules with dimensions arrange themselves,
remains unsolved.

But then there would be no reason to be astonished, that there
is no perfect agreement in the results. I am sooner astonished that
the agreement is as great as it is.

For a full discussion it would of course be necessary to compare
also other equations of Prof. BottzMann with those I have deduced.
Only if this were done it would be possible to make clear the
difference in the nature of our views. This would be specially
desirable for the calculation in first approximation of the influence
of the molecular dimensions on the value of the pressure. Le. p. 7
ete. Here too, the result at which we arrive is only equal at a
first approximation, without the results being identical.

And the question presents itself, whether the problem which is
treated in BOLTZMANN’s „Vorlesungen’’, might be formulated still
more accurately than has been done above, by saying: A great
number of moving material points move in spaces which are dimi-
nished by eight times the molecular volume: — a conception, accor-
ding to which the material points would move in a space, which
would lie outside the distance spheres, which they themselves form.

It is indeed remarkable that Prof. BOLTZMANN succeeds in pre-
venting that in this way he would find an influence on the pressure
which. is .twice too large. » By assuming a perfectly flat wall, and
by... using this. wall as a, means, to, eliminate the; distance „plee

ed

enne

OO en ade ea

( 473 )

on one side, he gets in first approximation the same result as I had
obtained from the beginning. But only in first approximation.

All this is the cause that I still prefer the simple direct deduc-
tion of the pressure, as I have given it. (Proc. of the meeting Nov.
1898) —- even though there remain questions whose solution I have
tried to find already for some time, but in which I have not yet
succeeded.

Physics. — „The galvano-magnetie and thermo-magnetic phenomena
in bismuth.” (Second communication continued). By Dr. E.
VAN EVERDINGEN JR. (Communication N°. 48 (continued)
from the Physical Laboratory at Leiden, by Prof. H. KAMER-
LINGH ONNES).

6. In § 6 of my first communication on this subject) I men-
tioned that in my opinion RrecKE wrongly ascribes the entire con-
duction of heat to the motion of charged particles, and that for the
theory we might perhaps derive some profit from such suppositions
as I have introduced in the theory of the Harr-effect in electro-
lytes. 2) It certainly is remarkable, that, starting from the supposition,
that the current of heat in metals is a pure current of energy, not
accompanied by a current of ponderable substance, we for all trans-
verse galvano-magnetic and thermo-magnetic phenomena can offer
at least a qualitative explanation. For, we have only to represent
the matter in the following way:

In the electric current the positive and negative charged particles,
which for the sake of brevity we shall call ions, move with different
velocities, while also their numbers may differ.

In the magnetic field the electro-magnetic force causes transverse
displacements and consequently charges which increase until the
currents of positive and negative electricity have reached the sane
value. This equalisation may be due to the arising difference of
potential (this is the Harr-effect) as well as to currents of diffusion
of the ions. (If the latter are accompanied by a perceptible difference in
the number of ions per unit of volume in different places, the diffe-
rence of potential to be observed at the Harr-electrodes might be

1) Proceedings Royal Acad. Amsterdam June 25th 1898 p. 72. Comm. Phys. Lab.
Leiden N° 42 p. 18.

?) Proceedings Royal Acad. Amsterdam May 2Sth 1898 p. 27, Comm. Phys. Lab,
Leiden N°. 41.

modified by an electromotive contact force). After the condition
has become stationary, there will still exist a transverse current of
ions, and so on one side free ions must be captivated, a process
by which heat is generated, and on the other side new ions must
be freed, which is accompanied by loss of heat; in this way a transverse
difference of temperature (galvano-magnetie difference of temperature)
arises; together with this a displacement of unelectrified particles
must be brought about.

So far as the free ions are concerned, we must imagine the cur-
rent of heat (now that no displacement of substance may be assumed)
to be such, that although across a surface perpendicular to the direc-
tion of the current of heat an equal number of ions goes in both
directions per unit of time, yet the ions have on an average a
greater velocity during a displacement in the direction of the current
of heat than they have during a displacement in the reverse direction.
The electromagnetic force may then cause transverse displacements,
which have opposite directions for positive and for negative ions. In
the same way as with the electric current there will arise in general
a difference of potential (transverse thermo-magnetic effect) and a
difference of temperature (rotation of isothermals). The answer to
the question in how far these suppositions might lead to a quanti-
tative explanation must be left to further investigations.

7. It is important to inquire whether molecular theories of
thermo-electricity enable us to determine the sign of the variation in
the magnetic field of the thermo-electric difference, for instance between
bismuth and copper, only by means of the hypothesis mentioned in
the previous communication '): viz. that the longitudinal phenomena
would be explained by a variation of the number of free ions, due
to the magnetic field. This however appears not to be the case, as
new suppositions must still be introduced.

As an instance | choose the formula for the electromotive contact
force, lately published by Ricks), which can be put down in
the form:

Ie JE
Vig Var (voo EE a log =)
N 4? J

where the quantities with A relate say to copper, and those with

1) Proceedings Royal Acad. Amsterdam. March 25th. 1899, p. 416 Comm. Phys.
Lab. Leiden No. 48 p. 20. 5
*) Wied. Ann. 66, p. 554, 1898.

(475 )

B to bismuth, and in which V represents the potential, Ca positive
function of temperature, P and N numbers of positive and negative
ions per unit of volume.

The electric conductivity for bismuth has been represented by
RreckE by a formula of the form

y= Pape + Np en

in which ce, and ¢, are again functions of temperature. In the
magnetic field the conductivity decreases. The simplest supposition
is pow that Pg and Nz, decrease proportionally; a thing which
would be self-evident if Pg were equal to “gz, as in electrolytes.

Let us further suppose, which is also very probable, that only
the quantities relating to bismuth vary in the magnetic field, then
a proportional decrease of Pz and Ng appears to lead toa variation
of the difference Vg—V, with a negative amount, and so to an
increase of the thermo-electric difference between bismuth and copper,
which is negative outside the magnetic field. If on the contrary
we should suppose that the variation of Ng is small as compared
with that of Pg, then the variation of V4— V4 would become positive
and the thermo-electrie difference between bismuth and copper would
decrease.

The observations show that the variation of this thermo-electric
difference in the magnetic field corresponds to an increase, and so,
in consequence of the proportionality of increase of resistance and
longitudinal effect found by me, we should have to prefer the former
of the two suppositions.

(May 12th, 1899.)

OON BANS:

ABERRATION (STOKEs’theory of) in the supposition of a variable density of the aether.
323. 443.
AETHER. See Ether.
ANAËROBICS (On the relation of the obligatous) to free oxygen. 14.
ANIMALCELLS (On the influence of salt-solutions on the volume of). 26. 103, 371,
ANOMALIES (On some) in the system of MeNpeLpJerr. 148.
ANoMALY (An) in the course of the plaitpointcurve in a mixture of anomalous sub-
stances, 385.
eNTIMONIAL Alloys for axle boxes (On chemical and microscopical examination for), 35.
stronomy. E. F. van pr SANDE BAKHUYZEN: „On the motion of the Pole of the
Earth according to the observations of the years 1890—1896”. 42.
-— E. F. van pe Sanne BAKHUYZEN: /Some remarks upon the 14-monthly motion
of the Pole of the Earth and upon the length of its period.” 157. 201.
ASYMMETRY (On an} in the change of the spectral lines of iron, radiating in a mags
uetic field. 27. 98.
atoms (On synthetically prepared neutral glyceryl-ethereal salts — triacylins — of
saturated monobasic acids with an even number of C-). 338.
ATTENTION and Respiration. 121.
AXLE BOXES (On chemical and microscopical examination of antimonial alloys
for). 35.
Bacteriology. M. W. Bryrrinck: »On the relation of the obligatous anaërobics to
free oxygen.” 14.
BAKHUIS ROOZEBOOM (HL. W.). Congealing points and points of transition in
mixed crystals of two substances. 101.
— On eongealing- and melting-phenomena in substances showing tautomerism. 176,
— presents the dissertation of Dr. C. van Erk: „On mixed crystals of nitrate of
kalium and nitrate of thallium.” 229.
— On solubility and meltingpoint as criteria for distinguishing racemic combinations,
pseudoracemic mixed erystals and inactive conglomerates. 310.
— presents a paper of Dr. Ernst Courn: „On the velocity of electrical reaction,”
534. 417.
— On meltingpoints in systems of optic isomers. 466.
BAKHUYZEN (E. F. VAN DE SANDE). See SANDE BAKHUYZEN (E. F. van DE).
BALL (The representation of the screws of) passing through a point or lying in a
plane, according to the method of CaroraLt. 258.

33
Proceedings Royal Acad. Amsterdam. Vol. I.

II ClO INSTREGN Das?

BAUCKE (H.) and Tu. H. Beurens. On chemical and microscopical examination
of antimonial alloys for axle boxes, 35.
BEHRENS (TH. H.) and H. Bavekp. On chemical and microscopical examination
of antimonial alloys for axle boxes. 35.
— On some anomalies in the system of MENDELEJEFF. 148,
BEMMELEN (J. M. VAN) presents a paper of Dr. F, A. H. SCHREINEMAKERS :
„Equilibriums in systems of three components. Change of the mixing-temperature
of binary mixtures by the addition of a third component.” 191.
— On Hydrogel of oxide of iron (ferric-oxide). 249.
— presents a paper of Mr. B. pn Bruyn: /The equilibrium of systems of three
» substances, in which two liquids occur.” 253. 7
BEYERINCK (M. w). On the relation of the obligatous anaërobies .to free
oxygen. 14.
— On a Contagium vivum fluidum causing the Spotdisease of the Tobacco-
leaves. 170.
BIBASIC ACIDS (On the action of methylic alcohol on the imides of). 151.

BINARY FORM a?" of even degree (A geometrical interpretation of the invariant

n (ab)? of a). 313.
n+l

— mixtures (Change of the mixing-temperature of) by the addition of a third
component. 191.

BISMUTH (The galvanomagnetic and thermomagnetic phenomena in). 72. 404. 473.

BLOODCORPUSCLES (Cup-shaped red) (Chromoeraters). 154.

BOLTZMANN (L.). On the characteristic equation of v. D. Waats. 398.

BORNEO (On Brackish-water deposits of the Mélawi in the interior of). 245.

Botany. M. W. Bryerinck: /On a Contagium vivum fluidum causing the Spotdisease

of the Tobacco-leaves”. 170.
BRACKISH-WATER deposits (On) of the Mélawi in the interior of Borneo, 245.
BRUYN (B. DE). The equilibrium of systems of three substances, in which two
liquids occur. 253.
BRUYN (C. A. LOBRY DE). See Losry DE Bruyn (C. A.). :
CAPORALI (The representation of the screws of Baur passing through a point or
lying in a plane, according to the method of). 258.

CARBONIC ACID (The composition and the volume of the coexisting vapour- and liquid-

. phases of mixtures of methylchloride and). 83.

— and Hydrogen (Measurements on the system of isothermal lines near the
plaitpoint and especially on the process of the retrograde condensation of a
mixture of), 243. 288. 323.

— (Measurements on the change of pressure by substitution of one component by
the other in mixtures of). 328. :

CARDINAAL (J.). The representation of the screws of Barr passing through a

point or lying in a plane, according to the method of Carorarr. 258.

CATALOGUE Conference (Report on the 2nd International). 117. .

CHEMICAL CONSTITUTION (On the physiological action of methylnitramine in connection

with its). 321.

Or OENE REEN LS, II

Chemistry. Tu. H.- BeureNs and H. Baucke: „On chemical and microscopical
examination of antimonial alloys for axle boxes.” 35.

— ©; A.-Losry pe Bruyn: „The condition of substances insoluble in water for-
med in gelatine.” 39.

— H. W. Baxeurs Roozesoom: /Congealing points and points of transition in
mixed crystals of two substances”. 101.

— CG. A. Losey DE Bruyn: The rate of substitution of a nitrogroup by an oxalkyl”. 144.

— Tu. H. Barrens: „On some anomalies in the system of MenpELEserr.” 148.

— 8. Hoocewerrr and W. A. van Dore: On the action of methylic alcohol on
the imides of bibasie acids”, 151.

— H. W. Bakuuis RoozrBoom: „On congealing- and melting-phenomena in sub-
stances showing tautomerism”. 176.

— F. A. H. ScHREINEMAKPRS: /Equilibriums in systems of three components.
Change of the mixing-temperature of binary mixtures by the addition of a third
component”. 191. é

_— C. van Erk: /On mixed erystals of nitrate of kalium and nitrate of thallium”. 229.

— J. M. van BEMMELEN : „On Hydrogel of oxide of iron (ferric-oxide)”. 249.

— B. ve Bruyn: The equilibrium of systems of three substances, in which two
liquids occur”. 253.

— H. W. Baxuurs Roozrsoom: „On solubility and meltingpoint as criteria for
distinguishing racemic combinations, pseudoracemic mixed crystals and inactive
conglomerates”. 310.

— Ernst CoueN: „On the velocity of electrical reaction”. 334. 417.

— A. P. N. Francurmont presents the dissertation of Mr. L. T. C. Scnty : „On
synthetically prepared neutral glyceryl-ethereal salts — triacylins — of saturated
monobasic acids with an even number of C-atoms”. 338.

_— H.W. Baxaurs Roozesoom: „On meltingpoints in systems of optic isomers.” 466.

CEROMOCRATERS (Cup-shaped red bloodeorpuscles). 154.
crrcLEs (On the eyclographie space representation of JOACHIMSTHAL’s). 1.
COHEN (ERNST). On the velocity of electrical reaction. 334. 417.
COMPONENT (Measurements on the change of pressure by substitution of one) by the
other in mixtures of carbonic acid and hydrogen. 328.
COMPONENTS (Equilibriums in systems of three). Change of the mixing-temperature
of binary mixtures by the addition of a third component. 191.
CONGEALING Points and points of transition in mixed crystals of two substances. 101,
* — and melting phenomena (On) in substances showing tautomerism. 176.
CONGLOMERATES (On solubility and meltingpoint as criteria for distinguishing racemic
combinations, pseudoracemic mixed erystals and inactive). 310.
conics (On the orthoptical circles belonging to linear systems of). 305.
CONTAGIUM vivum fluidum (On a) causing the Spotdisease of the Tobacco-leaves. 170.
continuity (On the deviation of pr HeEn’s experiments from vaN DER Waals’ law of). 82.
CRITICAL Temperature (The influence of pressure on the) of complete mixture. 158.
CRYSTALS of two substances (Congealingpoints and points of transition in mixed). LOL.
— (On solubility and meltingpoint as criteria for distinguishing racemie combi-
‚ nations, pseudoracemic mixed) and inactive conglomerates. 310.

33*

Iv COLNE DR EON TS.

CRYSTALS (On mixed) of nitrate of kalium and nitrate of thallium. 229.
CYCLOGRAPHIC SPACE representation (On the) of JoacHIMsTHAL’s circles. 1.
DEKHUYZEN (Mm, C.). Cup-shaped red bloodcorpuscles (chromocraters). 154.
DENSITY (On the accurate determination of the molecular weight of gases from
their). 198.
— (Srokrs’ theory of aberration in the supposition of a variable) of the ether.
323. 443.

DIFFRACTION Phenomena of FrrsNeL (On the influence of the dimensions of the source
of light in) and on the diffraction of X-rays, 65,

— of X-rays (On the). 321. 420,

DISPERSION of gases (Measurements on the magnetic rotatory). 243. 296.

DORP (W. A. VAN) and S. Hoocewerrr. On the action of methylic alcohol on the
imides of bibasie acids. 151.

ELECrRIC Currents (On a 5-cellar quadrant-electrometer and on the measurement of
the intensity of) made with it. 56.

ELECTRICAL Reaction (On the velocity of). 334, 417.

— and optical phenomena (On a simplified theory of the) in moving systems’

323. 427.

ELECTRIFIED SYSTEMS (On the vibrations of), placed in a magnetic field. A contribution
to the theory of the Zenman-eflect. 263. 340,

ELECTROLYTES (The Harr-eflect in). 27.

ELECTROMETER (On a 5-cellar quadrant-) and on the measurement of the intensity of
electric currents made with it. 56.

EQUATION (Simple deduction of the characteristic) for substances with extended and
composite molecules. 138.

— (On the deduction of the characteristic). 468.

— of condition of van DER Waats’ (Calculation of the second correction to the

quantity 4 of the). 273.

— of v. p. Waars’ (On the characteristic). 398.

EQUILIBRIUM (The) of systems of three substances, in which two liquids occur. 253.

EQUILIBRIUMS in systems of three components. Change of the mixing-temperature
of binary mixtures by the addition of a third component. 191.

ETHER (StoKeEs’ theory of aberration in the supposition of a variable density of the).
323. 443.

EVERDINGEN JR, (B. VAN). The Hatt-effect in electrolytes. 27.

— The galvanomagnetic and thermomagnetic phenomena in bismuth. 72. 404. 473.
EYK (C. VAN). On mixed crystals of nitrate of kalium and nitrate of thallium. 229.
FARADIC Excitation (The effect produced upon respiration by) of some nerve-tracts. 361.
FERRIC-OXIDE (On Hydrogel of oxide of iron). 249.

FRANCHIMONT (A. P. N.) presents the dissertation of Mr. L. T. C. Scuey: „On
synthetically prepared neutral glyceryl-ethereal salts — triacylins — of saturated
monobasic acids with an even number of C-atoms’’. 338.

FRESNEL (On the influence of the dimensions of the source of light in diffraction
phenomena of) and on the diffraction of X-rays. 65.

GALVANOMAGNETIC and thermomagnetic phenomena (The) in bismuth. 72. 404. 473.

— =, le ee

ee ee ee ee a

COUNT EN TS, NV;

Gas (A standard open manometer of reduced height with transference of pressure
by means of compressed). 154. 213.

GASES (Measurements on the magnetic rotatory dispersion of). 243. 296.

— (On the accurate determination of the molecular weight of) from their den-

sity. 198.

GELATINE (The condition of substances insoluble in water formed in). 39.

Geology. K. Marrin: „On Brackish-water deposits of the Mélawi in the interior of
Borneo”. 245.

GLYCERYL-ethereal Salts (On synthetically prepared neutral) —triacylins — of saturated
monobasic acids with an even number of C-atoms. 338.

HAEMATOPOIESIS in the placenta of Tarsius and other mammals. 167.

HAGA (H.) presents a paper of Dr. ©. H. Wino: vOn maxima end minima of
apparent brightness resulting from optical illusion.” 7.

— On a 5-cellar quadrant-electrometer and on the measurement of the intensity
of electric currents made with it. 56.

— presents a paper of Dr. C. H. Winp: „On the influence of the dimensions of
the source of light in diffraction phenomena of FRESNEL and on the diffraction
of X-rays”. 65.

— and C. H. Winn. On the diffraction of X-(RöNtrGen)rays. 321. 420.

HALL-eftect (The) in electrolytes. 27.

HAMBURGER (H. J.). On the influence of solutions of salts on the volume of
animaleells. 26. 103. 371.

HARTMAN (CH. M. A.). The composition and the volume of the coexisting vapour-
and liquid-phases of mixtures of methylchloride and carbonic acid. 83.

HEEN’s (DE) Experiments (On the deviation of) from van DER Waars’ law of con-
tinuity. 82.

HOEK (P. P. C.) presents a paper of Dr. M. C. Dexuuyzen: /Cup-shaped red blood-
corpuscles (chromocraters).” 154,

HOOGEWERFF (s.) and W. A. van Dorp. On the action of methylic alcohol on
the imides of bibasic acids. 151.

HUBRECHT (A. A. W.). Haematopoiesis in the placenta of Tarsius and other
mammals, 167.

HYDROGEL of oxide of iron (ferric-oxide). 249.

HYDROGEN (Measurements on the system of isothermal lines near the plaitpoint and
especially on the process of the retrograde condensation of a mixture of carbonic
acid and). 243. 288. 323.

— (Measurements on the change of pressure by substitution of one component by
the other in mixtures of carbonic acid and). 328.

HYPERELLIPTIC Integrals (On reducible). 448. 449.

IMIDES of bibasie acids (On the action of methylie alcohol on the). 151.

INTEGRALS (On reducible hyperelliptic). 448. 449.

INTENSITY of electric currents (On a 5-cellar quadrant-electrometer and on ‘the meas
surement of the) made with it. 56.
INTERNATIONAL Catalogue Conference (Report on the second). 117.

VI CONTENTS.

INVARIANT fT (ab)? (A geometrical interpretation of the) of a binary form a of even
n+1
degree. 313.

IRON (On an asymmetry in the change of the spectral lines of), radiating in a mag-
netic field. 27. 98.

ISOMERS (On melting points in systems of optic). 466.

ISOTHERMAL LINES (Measurements on the system of) near the plaitpoint and especially
on the process of the retrograde condensation of a mixture of carbonic acid and
hydrogen. 243. 258. 323.

JOACHIMSTHA Ls Circles (On the cyclographie space representation of). 1.

KALIUM (On mixed crystals of nitrate of) and nitrate of thallium. 229.

KAMERLINGH ONNES (H.) presents a paper of Dr. E. van EveRrDINGEN Jr. : The
Harr-effect in electrolytes”. 27.

— presents a paper of Dr. E. van EvERDINGEN Jr: „The galvanomagnetic and
thermomagnetic phenomena in bismuth’. 72. 404. 473.

— presents a paper of Dr. J. VerscHaFFELT: /On the deviation of pp HEEN's
experiments from vaN DER Waats’ law of continuity.” 82.

— presents a paper of Mr. Cu. M. A. HARTMAN: vThe composition and the
volume of the coexisting vapour- and liquid-phases of mixtures of methylchloride
and carbonic acid”. 83.

— Description of a standard open manometer of reduced height with transference
of pressure by means of compressed gas. 154. 213.

— presents a paper of Dr. J. VersCHarreLT: „Measurements on the system of
isothermal lines near the plaitpoint and especially on the-process of the retro-
grade condensation of a mixture of carbonic acid and hydrogen”. 243. 288. 323.

— presents a paper of Dr. L. H. Srextsema: „Measurements on the magnetic
rotatory dispersion of gases)’. 243. 296.

— presents a paper of Dr. J. Vurscuarrenr: „Measurements on the change of
pressure by substitution of one component by the other in mixtures of carbonic
acid and hydrogen”. 328.

KLUYVER (J. c.). On reducible hyperelliptie integrals. 448. 449.

KORTEWEG (p. J.). Report on the 2d International Catalogue Conference. 117.

LAAR (J. J. VAN). Calculation of the second correction to tle quantity 4 of the
equation of condition of vaN DER’ WAALS. 273.

LEE (N. J. VAN DER). The influence of pressure on the critical temperature of
complete mixture. 158. ;

LIGHT (Considerations concerning the influence of a magnetic field on the radiation of). 90,

LIQUID-PHASES (‘The composition and the volume of the coexisting vapour- and) of
mixtures of methylchloride and carbonic acid. 83.

tiguips (‘The equilibrium of systems of three substances, in which two) occur. 253.

LOBRY DE BRUYN (c. a.). The condition of substances insoluble in water
formed in gelatine. 39.

— The rate of substitution of a nitrogroup by an oxalkyl. 144.

LORENTZ (u. A). Considerations concerning the influence of a magnetic field
on the radiation of light. 90.

CO GUN TEE Ni TES: vil

LORENTZ (#. A.). On the vibrations of electrified systems, placed in a magnetic
field. A contribution to the theory of the ZEEMmaN-effect. 263. 340.
— On a simplified theory of the electrical and optical phenomena in moving
systems. 323. 427.
— Sroxes’ theory of aberration in the supposition of a variable density of the
ether. 323. 443.
MAGNETIC FIELD (On an asymmetry in the change of the spectral lines of iron, radia-
ting in a). 27. 98.
— (Considerations concerning the influence of a) on the radiation of light. 90.
— (On the vibrations of electrified systems, placed in a). A contribution to the
theory of the ZEEMAN-eflect. 263. 340.
MAGNETIC rotatory dispersion (Measurements on the) of gases. 243, 296.
MANOMETER of reduced height (Description of a standard open) with transference
of pressure by means of compressed gas. 154, 213.
MARTIN (K.). On Brackish-water deposits of the Mé!awi in the interior of Borneo. 245.
Mathematics. P. H. Scnoure: „On the eyclographie space representation of JoACHIMS-
THAL’s circles”. 1.
— J. CARDINAAL: The representation of the screws of Barr passing through a
point or lying in a plane, according to the method of CaroraLt.” 235.
— Jan DE Vries: /On Trinodal Quartics”. 263.
— Jan pr Vrirs: „On the orthoptical circles belonging to linear systems of
conics”. 305.

2

— P. H. Scnourz: vA geometrical interpretation of the invariant (ab) of a
binary form a? of even degree”. 313. En
— J. C, Kuvyver: „On reducible hyperelliptic Integrals”. 448. 449.

MAXIMA (On) and minima of apparent brightness resulting from optical illusion. 7.

MEASUREMENT of the intensity (On a 5-cellar quadrant-electrometer and on the) of
electric currents made with it. 56.

MEASUREMENTS on the system of isothermal lines near the plaitpoint and especially
on the process of the retrograde condensation of a mixture of carbonic acid
and hydrogen. 243. 288. 323.

— on the magnetic rotatory dispersion of gases. 243. 296.
— on the change of pressure by substitution of one component by the other in
mixtures of carbonic acid and hydrogen. 328.

Merawr (On Brackish-water deposits of the) in the interior of Borneo. 245.

MELTING-PHENOMENA (On congealing- and) in substances showing tautomerism. 176.

MELTINGPOINT (On solubility and) as criteria for distinguishing racemic combinations,
pseudoracemie mixed crystals and inactive conglomerates. 310.

MELTINGPOINTS (On) in systems of optic isomers. 466.

MENDELEJEFF (On some anomalies in the system of). 148.

METHOD of Caporatr (The representation of the screws of BALL passing through a
point or lying in a plane, according to the method of Carorarr. 258.

METHYLCHLORIDE and carbonic acid (The composition and the volume of the coexisting
vapour- and liquid-phases of mixtures of). 83.

METHYLIC ALCOHOL (On the action of) on the imides of bibasic acids, 151,

VIII CONTENTS.

METHYLNITRAMINE (On the physiological action of) in connection with its chemical
constitution, 321.
MICROSCOPICAL EXAMINATION (On chemical and) for antimonial alloys for axle
boxes. 35.
MINIMA (On maxima and) of apparent brightness resulting from optical illusion. 7.
MIXING (Variation of volume and of pressure in). (I) 179. (LL) 232. (III) 390.
— TEMPERATURE of binary mixtures (Change in the) by the addition of a third
component. 191,
MIXTURE (The influence of pressure on the critical temperature of complete). 158.
— of anomalous substances (An anomaly in the course of the plaitpointeurve in a). 385,
MIXTURES of carbonic acid and hydrogen (Measurements on the change of pressure by
substitution of one component by the other in). 328.
— of methylchloride and carbonic acid (Tbe composition and the volume of the
coexisting vapour- and liquid-phases of). 83.
MOLECULAR WEIGHT (On the accurate determination of the) of gases from their
density. 198.
MOLECULES (Simple deduction of the characteristic equation for substances with extended
and composite). 138.
MONOBASIC AcIDs (On synthetically prepared neutral glyceryl-ethereal salts — triacylins —
of) with an even number of C-atoms. 238.
MONTHLY MOTION (Some remarks upon the 14-) of the Pole of the Earth and upon
the length of its period. 157. 201.
motion of the Pole of the Earth (On the) according to the observations of the years
1890—1896. 42.
NERVE-TRACTS (The effect produced upon respiration by faradie excitation of some). 361.
NITRATE of kalium (On mixed crystals of) and nitrate of thallium. 229,
NITROGROUP by an oxalkyl (The rate of substitution of a). 144.
OBLIGATOUS ANAËROBICS (On the relation of the) to free oxygen. 14.
ONNES (H. KAMERLINGH). See KAMERLINGH Onnes (H.).
OPTICAL ILLUSION (On maxima and minima of apparent brightness resulting from). 7,
— PHENOMENA (On a simplified theory of the electrical and) in moving systems,
323. 427.
ORTHOPTICAL CIRCLES (On the) belonging to linear systems of conics. 305.
OXALKYL (The rate of substitution of a nitrogroup by an). 144.
OXIDE of iron (ferric-oxide) (On Hydrogel of). 249.
oxYGEN (On the relation of the obligatous anaërobies to free). 14,
Physics. C. H. Wixp: /On maxima and minima of apparent brightness resulting from
optical illusion.” 7.
_— P. ZEEMAN: /On an asymmetry in the change of the spectral lines of iron,
radiating in a magnetic field.” 27. 98.
— BE. van EVERDINGEN Jn.: The Harr-effect in electrolytes.” 27.
— H. Haca: „On a 5-cellar quadrant-electrometer and on the measurement of the
intensity of electric currents made with it.” 56,
— C. H. Warp: „On the influence of the dimensions of the source of light in
diffraction phenomena of FRESNEL and on the diffraction of X-rays”. 65.

CONTENTS. IX

Physics. B. van BvERDINGEN Jr.: „The galvanomagnetic and thermomagnetic phenomena

in bismuth.” 72. 404. 473.

— J. VERSCHAFFELT : /On the deviation of DE HEEN's experiments from VAN DER
Waats’ law of continuity.” 82.

— Cu. M. A. Hartman: The composition and the volume of the coexisting vapour_
and liquid-phases of mixtures of methylchloride and carbonic acid.” 83.

— H. A. Lorentz: Considerations concerning the influence of a magnetic field
on the radiation of light.” 90.

— J. D. van per Waats: „Simple deduction of the characteristic equation for
substances with extended and composite molecules.” 138.

— H. KAMERLINGH ONNES: „Description of a standard open manometer of reduced
height with transference of pressure by means of compressed gas.” 154, 213.

— N. J. van DER LEE: „The influence of pressure on the critical temperature of
complete mixture”. 158.

— J. D. van per Waats: „Variation of volume and of pressure in mixing”,
(I) 179. (II) 232. (III) 390.

— J. D. van per Waats: „On the accurate determination of the molecular weight
of gases from their density”. 198.

— J. VERSCHAFFELT: „Measurements on the system of isothermal lines near the
plaitpoint and especially on the process of the retrograde condensation of a mixture
of carbonic acid and hydrogen.” 243. 288. 323.

— L.H.Srertsema: „Measurements on the magnetic rotatory dispersion of gases.”
243, 296.

— H. A. Lorentz: „On the vibrations of electrified systems, placed in a magnetic-
field. A contribution to the theory of the Zeeman-effect”. 263. 340.

— J. J. vax Laar: /Caleulation of the second correction to the quantity 4 of the
equation of condition of vAN DER Waals.” 273.

— H. Haca and C. H. Winn: „On the diffraction of X-(RÖNTGEN)rays”. 321. 420.

— H. A. Lorentz: „On a simplified theory of the electrical and optical pheno-
mena in moving systems.” 323. 427.

— H. A. Lorentz: /Stoxes’ theory of aberration in the supposition of a variable
density of the ether’’, 323. 443.

— J. VeRSCHAFFELT : /Measurements on the change of pressure by substitution of
one component by the other in mixtures of carbonic acid and hydrogen”, 328.
— J. D. van DER Waals: /An anomaly in the course of the plaitpointeurve in a

mixture of anomalous substances”. 385.
— L. BOLTZMANN : „On the characteristic equation of v. p. Waars”, 398,
— J. D. van per Waats: „On the deduction of the characteristic equation”. 468.
Physiology. H. J. HAMBURGER: „On the influence of solutions of salts on the volume
of animalcells.” 26. 103. 371.

— C. WINKLER. Attention and Respiration.” 121.

— B. J. Srokvis presents the dissertation of Dr. G. BELLAAR Spruyt: On the
physiological action of methylnitramine in connection with its chemical consti-
tution”. 321.

Xl CONTEN Ts.

Physiology. ©. Winkrer and J. Wrarpr Boekman: „The effect produced upon respiration
by faradic excitation of some nerve-tracts”. 361.

PLACENTA of Tarsius (Ilaematopoiesis in the) and other mammals, 167.

PLAITPOINT (Measurements on the system of isothermal lines near the) and especially
on the process of the retrograde condensation in a mixture of carbonic acid and
hydrogen. 243, 288. 323.

PLAITPOINTCURVE (An anomaly in the course of the) in a mixture of anomalous sub-
stances. 385.

POINTS OF TRANSITION (Congealing points and) in mixed crystals of two substances. 101.

POLE OF THE EARTH (On the motion of the) according to the observations of the
years 1890—1896. 42.

— (Some remarks upon the 14-monthly motion of the) and upon the length of its
period. 157. 201.

PRESSURE (Measurements on the change of) by substitution of one component by the
other in mixtures of carbonic acid and hydrogen. 328.

— (The influence of) on the critical temperature of complete mixture. 158.

— (A standard open manometer of reduced height with transference of) by means
of compressed gas. 154. 213.
— (Variation-of volume and of) in mixing. (I) 179. (II) 232. (ULI) 390.
QUADRANT-ELECTROMETER (On a 5-cellar) and on the measurement of the intensity of
electric currents made with it. 56. !
QUANTITY 4 (Calculation of the second correction to the) of the equation of condition
of VAN DER Waats. 273.
QuarTICS (On Trinodal). 263.
RACEMIC COMBINATIONS (On solubility and meltingpoint as criteria for distinguishing),
pseudoracemic mixed crystals and inactive conglomerates. 310. ;
RADIATION of light (Considerations concerning the influence of a magnetic field on
the). 90.
RESPIRATION (Attention and). i21.
— (The effect produced upon) by faradic excitation of some nerve tracts. 361.
RETROGRADE CONDENSATION (Measurements on the system of isothermallines newr the
plaitpoint and especially on the process of the) of a mixture of carbonic acid
and hydrogen. 243. 288. 323.
RONTGEN-RAYS (Diffraction of). 420.
ROOZEBOOM (H. W. BAKHUTIS). See BaKHurs Roozesoom (H. W.).
SANDE BAKHUYZEN (E. F. VAN DE). On the motion of the Pole of the Earth
according to the observations of the years 1890—1896. 42. :
— Some remarks upon the 14-monthly motion of the Pole of the Earth and upon
the length of its period. 157. 201.
saLts (On synthetically prepared neutral glyceryl-ethereal) — triacylins — of saturated
monobasic acids with an even number of C-atoms. 338.
— (On the influerice of solutions of) on the volume of animalcells. 26. 103. 371.
scurY (L. m. G.). On synthetically prepared neutral glyceryl-ethereal salts —
triacylins — of saturated monobasic acids with an even number of C-atoms. 338.

CWO Nit BNA SL a

SCHOUTE (P. H.). On the evelographie space representation of JoacHIMsTHS1’s circles, 1.

2

— A geometrical interpretation of the invariant TI (a)? of a binary form a? ot
n+1
even degree. 313.

SCHREINEMAKERS (Ff. A. H.). Equilibriums in systems of three components. Change
of the mixing-temperature of binary-mixtures by the addition of a third com-
ponent, 191.

screws of Batt (The representation of the) passing through a point or lying in a
plane, according to the method of Caporarr. 258.

SIERTSEMA (tL. H.). Measurements on the magnetic rotatory dispersion of gases.
243. 296.

SOLUBILITY (On) and meltingpoint as criteria for distinguishing racemic combinations,
pseudoracemic mixed ery-tals and inuctive conglomerates. 310.

SOLUTIONS OF SALTS (On the influence of) in the volume of amimalcells. 26, 103. 371.

SOURCE OF LIGHT (On the influence of the dimensions of the) in diffraction phenomena
of FrESNEL and on the diffraction of X-rays. 65.

SPECTRAL LINES of iron (On an asymmetry in the change of the) radiating in a mag-
netic field. 27. 98.

SPOTDISEASE of the Tobacco-leaves (On a Contagium vivum fluidum causing the). 179.

SPRUYT (c. BELLAAR). On the physiological action of methylnitramine in con~
nection with its chemical constitution. 321.

STANDARD OPEN MANOMETER (A) of reduced height with transference of pressure by
means of compressed gas. 154. 213.

STEGER (a.). The rate of substitution of a nitrogroup by an oxalkyl. 144.

STOKES Theory of aberration in the supposition of a variable density of the
ether. 323. 443.

sTOKVIs (B. J.) presents the dissertation of Dr. C. Bervaar Spruyt: „On the
physiological action of methylnitramine in connection with its chemical consti-
tution.” 321.

SUBSTANCES (The condition of) insoluble in water formed in gelatine. 39.

— (On congealing- and melting-phenomena in) showing tautomerism. 176.

— (The: equilibrium of systems of three), in which two liquids occur. 253.

— (Simple deduction of the characteristic equation for) with extended and com-
posite molecules. 138.

SUBSTITUTION (The rate of) of a nitrogroup by an oxalkyl. 144,

SYSTEMS (On a simplified theory of the electrical and optical phenomena in moving).
323. 427.

— or conics (On the orthoptical circles belonging to linear). 305.
— OF OPTIC IsoMERS (On melting points in). 466.

TARSIUS (Haematopoiesis in the placenta of) and other mammals. 167:

TAUTOMERISM (On congealing- and melting-phenomena in substances showing). 176.

THALLIUM (On mixed crystals of nitrate of kalium and nitrate of). 229.

THEORY (On a simplified) of the electrical and optical phenomena in moving systems.
323. 427.

— (Stokes) of aberration in the supposition of a variable density of the ether.
323, 443.

XII CONTENTS.

THERMOMAGNETIC PHENOMENA (The galvanomagnetic and) in bismuth. 72. 404. 473.

TOBACCO-LEAVES (On a Contagium vivum fluidum causing the Spot-disease of the). 170.

TRIACYLINS (On synthetically prepared neutral glyceryl-ethereal salts) of saturated
monobasic acids with an even number of C-atoms. 338.

TRINODAL QUARTICS (On). 263.

VAPOUR- and liquid-phases (The composition and the volume of the coexisting) of
mixtures of methylchloride and carbonic acid. 83,

veLocity (On the) of electrical reaction. 334. 417.

VERSCHAFFELT (J.). On the deviation of pe HEEN’s experiments from VAN DER
Waars’ law of continuity. 82.

— Measurements on the system of isothermallines near the plaitpoint and especially
on the progress of the retrograde condensation of a mixture of carbonic acid
and hydrogen. 243. 288. 323.

— Measurements on the change of pressure by substitution of one component by
the other in mixtures of carbonic acid and hydrogen. 328.

VIBRATIONS (On the) of electrified systems, placed in a magnetic field. A contribution
to the theory of the ZeeMAN-eftect. 263. 340.

VOLUME (Variation of) and of pressure in mixing. ([) 179. (LL) 232. (III) 350.

VRIES (JAN DE). On Trinodal Quarties. 263.

— On the orthoptical circles belonging to linear systems of conics. 305,

WAALS (J. D. VAN DER). Simple deduction of the characteristic equation for sub-
stances with extended and composite molecules. 138.

— presents a paper of Mr. N, J. van per Lee: „The influence of pressure on
the critical temperature of complete mixture.” 158.

— Variation of volume and of pressure in mixing. (I) 179. (II) 232. (ILD) 390.

— On the accurate determination of the molecular weight of gases from their
density. 198.

— An anomaly in the course of the plaitpointeurve in a mixture of anomalous
substances. 385.

— On the deduction of the characteristic equation. 468.

— law of continuity (On the deviation of pp HeeN’s experiments from). 82.

— (Calculation of the second correction to the quantity 4 of the equation of con-
dition of). 273.

— (On the characteristic equation of). 398.

WATER formed in gelatine (The condition of substances insoluble in). 39.

WIARDI BECKMAN (J.) and C. Winkter. The effect produced upon respi-
ration by faradic excitation of some nerve-tracts. 361.

WIND (c. H.). On maxima and minima of apparent brightness resulting from optical
illusion. 7.

— On the influence of the dimensions of the source of light in diffraction pheno-
mena of FresNEL and on the diffraction of X-rays. 65.

— and H. Haga. On the diffraction of X-(RÖNTGEN)rays. 321. 420.

WINKLER (c.). Attention and Respiration. 121.
— and J. Wrarpr Beckman. The effect produced upon respiration by faradic

excitation of some nerve-tracts. 361.

CONTENTS. XIII

x-rays (On the influence of the dimensions of the source of light in diffraction pheno-
mena of FRrESNEL and on the diffraction of). 65.
— (On the diffraction of). 321. 420.
ZEEMAN (P.). On an asymmetry in the change of the spectral lines of iron, radia-
ting in a magnetic field. 27. 95.
— Effect (On the vibrations of electrified systems, placed in a magnetic field. A
contribution to the theory of the). 263. 340.
Zoology. M.C. Dekuuyzen: /Cup-shaped red bloodcorpuscles (Chromoeraters).” 154.
— A. A. W. Husrecar: /Haematopoiesis in the placenta of Tarsius and other
mammals.” 167.

Koninklijke Akademie van Wetenschappen
te Amsterdam.

PROCEEDINGS

OF THE

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AMSTERDAM,
JOHANNES MULLER.
May 1899.

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(Translated from: Verslagen van de Gewone vergaderingen der Wis- en_

Afdeeling van 28 Mei 1898 tot 22 April 1899. Dl. VIL.) |

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