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KONINKLIJKE AKADEMIE
VAN _WETENSCHAPPEN
-- TE AMSTERDAM -:-
PROCEEDINGS: OL Erp
SECTION OF SCIENGES
VOLUME XII
( — 28> PART — )
JOHANNES MULLER :—: AMSTERDAM
JULY 1910
CeO UN SEE NESS:
—
Page
Proceedings of the Meeting of December 24 NO0ON Hemant) a 00S
> yes » » January 29 and February 26 1910. . . . 547
> >» » > » Mareh 26 1OV0) SSeS ee ee eee ee OD
> >» » » » April 29 Seo Pe ets, os Le LO
Hoey ve
KONINKLUKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.
PROCEEDINGS OF THE MEETING
of Friday December 24, 1909.
Doce —
(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Vrijdag 24 December 1909, Dl. XVID.
(SS) ANP AL AT ANE sa Se
M. J. van Uven: “On the orbits of a function obtained by infinitesimal iteration in its complex
plane”. (Communicated by Prof. W. Kavrryn), p. 503.
J. W. Givray and M. pe Haas: “On the motion of the bridge of the violin”. (Communicated
by Prof. H. Kamerninen Onnes), p. 513.
L. Borx: “On the slope of the Foramen n.agnum in Primates. 2nd Paper. On the comparative
Craniology of Primates’, p. 525.
* Pu, Konnstamm: “A short reply to Mr. van Laar remarks”. (Communicated by Prof. J. D.
VAN DER WAALS), p. 534.
H. R. Kruyr: “The equilibrium solid-liquid-gas in binary systems of mixed crystals”. (Com-
municated by Prof. P. vay Rompuren). p. 537.
Errata, p. 545.
Mathematics. — “On the orbits of a function obtained by injini-
tesimal iteration in its complex plane.’ By M. J. van UVEN.
(Communicated by Prof. W. Kaprryy).
(Communicated in the meeting of November 27, 1909).
When a function y= gy (x) is iterated, each iteration y, = ¢, (x)
will give rise to a conform representation of the complex planes of
& and y,.
If we suppose y= w(z) to be built up by means of infinitesimal
iteration of the function Lim y, = Limp, (wv), so that y, has also
nui— @ m m—@ m
a meaning for broken and unmeasurable values of 7, then the con-
form representation of y= (x) will gradually appear out of the
identity belonging to y, = g, (w) =e.
o+
Proceedings Royal Acad. Amsterdam. Vol. XII.
( 504 )
We now regard a plane V,
» as complex plane of the quantity 2
and we place the complex plane J’, of the quantity y = ¢ () parallel
TON
the- imaginary axes are each other's orthogonal projection. Then to
» at a distance / and in such a way, that the real axes and
each point « of V7, are conjugated by means of the function y = @ ()
one or more points y of J’,. By connecting corresponding points «
and y by rays a congruence of rays is formed which can serve as
the image of the function 7 = @ ().
For the case y= (#)=a we should obtain in this way the
congruence of rays formed by all the normals on the planes V,
and J)’, as representative of the identity.
If now we let the function y= gy (v) gradually arise from the
identity, then to each stage of the generating process a definite con-
eruence of rays will belong. All these congruences form together a
complex of rays. It is clear, that the formation of the funetion
y¥ = v(x) will now be represented by this complex of rays.
Let us first examine the complex cones of the points of V,. Each
point w—=wu- 7 of this plane is the vertex of a cone counting in
any case the normal in w on V, among its generatrices; this edge
namely intersects the plane V, in y=u+mv=w.
The section of this complex cone with J’, will pass through the
point zw and all points representing the values taken by y, = @,(«)
when 7 increases from 0 to 1. So this section also gives us a
representation of the generating process of 7 (v). It goes without
saying that we can continue the iteration also past y = @ (w) and
likewise that we can also regard negative values of 7. The whole
of the complex cone embraces in fact al! funetions 7, = ~, (7), where
n varies from — oa to +. Also the section regarded as a whole
will contain ali the values of the function y, = @, (7), where w is
constant and 2 varies from — g to + ow. Hach value of « possesses
its own complex cone and therefore also its Own section. We shall
indicate this section by the orbit «— y,.
We might also have indicated the increase of g (uv) by allowing
the plane J”
, to grow gradually out of Vy and that by allowing
the distance of the planes to increase regularly from O to 4, so that
~, (wv) is represented in the plane V, at a height nh above J’,. Let
us then suppose in each plane I7, the image , = @» (iv) belonging
to some initial-point 2—=w-+ i to be constructed, then all these
points will form in their regular succession a twisted curve. Hach
of the o* points « of 17, gives rise to a suchlike fivisted curve and
0
the function 7—=g(r) with its different stages of development is
thus represented by a congruence of tvisted curves,
It is clear that the orthogonal projection of the twisted curve of
w on the plane J’, coincides with the orbit 7 — y,,.
We shall for the present occupy ourselves only with the study
of such an orbit «> y,.
To find the orbit «—+y, we have but to solve the functional
equation of ApbrL. We have namely to find that function f(x) of «
increasing with # when for « is substituted y,—=g, (x); this function
increases for the process of iteration with real contributions, i.e. the
quantity §¢= f(“) = V+ cV describes in its complex plane the right
line V=c parallel to the real axis. If once we know the form
of the function ¢=/ (wv), then we also know the orbit of the
quantity «= f_1 (6).
The value of V and the initial value (7 =O) of the real part U
of § represent together two arbitrary constants, of which we do not
dispose until we choose the initial value of 2.
We shall indicate the current point (y,) of the orbit «— y, by 2,
whilst we shall point out w by z,; we then have
F (z)=F (2) +7
or
U iV = U, YUV, + 2,
so that
OSG omn 3 Vi= V,.
The choice of the initial point z, now determines the values U,
and V,.
When working out some examples we shall not always follow
the systematic way sketched above, as it is unnecessarily lengthy in
simple cases.
4 ; : : az +p f
In reference to the broken linear function 7 = Fag we notice
Ly +O
that this has been thoroughly investigated already by Porncaré’) and
KLEIN’), the latter having also included complex values of «, 3, y, and din
. : ; ax +p é
the study. Ktrim too allows the function y= —— - fo arise gradu-
yet
ally out of w and regards the orbit described thereby. For the non-
parabolic cases he builds up the function by infinitesimal iteration
in the sense indicated by us. For the parabolic case, on the other
hand, he takes as parameter of the function in its orbit not the
iteration-index 7, but a complex multiple of it. In consequence of
1) Poincaré. Acta Mathematica I (1882), p. 1.
2) Kiein—Fricke. Vorl. ti. d. Theorie der ell. Modulfunktionen (Trupner, 1890),
p. 165,
34%
( 506 )
this the orbit of 2 found by Kun differs a little from ours. Although
after stating and annulling this difference we might suffice with a
reference to the results of Kivi, we will dwell a little longer on
az +p
the function y = , the more so as, differmg from Kiri, who
ye+d
treats first simple cases and then applies the principle of transformation
of the circle correspondence, we shall immediately investigate the
most general case.
Examples :
I y=a+p, yous np or z= 2, + np.
The point z describes the right line connecting the points z = 2, and
o—=2z,+ 8, in such a way that the distance from z to z, is pro-
~— ~“o
portional to 7.
IT. yaa, yr= eau or = a%Z,.
Let us put z= oe",z, — 0,0, @— oe" then
51) —-_- |N pine. my)
oe! — ore 0,¢ 0,
from which ensues
C=O, OSC) ae ae 5 (1)
or
= Uh
o = Oy oO = cel!
s ‘
Point 2 describes a logarithmic spiral round the origin. The polar
angle @ increases uniformly with 7, 1.o.w. the polar angle @ increases
arithinetically uniformly; it is clear that the radius vector g increases
geometrically wuformly.
If « is real, then t=O. The second equation (1) tells us that the
polar angle remains constant, so that point 2 moves along the line
connecting QO and z, and that with a geometrically uniform increase
of o.
If moda—=1, then o=1. The first equation (1) then indicates,
that the radius vector remains constant, so that point 2 describes the
circle round QO as centre, passing through point 2,. The polar angle
6 increases arithmetically uniformly.
If x is commensurable with a, i.e. if @ is a root out of unity,
then y= ar leads back to v after a whole number of iterations.
| | B
og | & +
a ea)
log a
4 00 5 a. 3 . 5 log go Ke
f(e?) = for « == /g stheretore: \(2)) ( 9) :
log a a—l log a
im a
0n )
If we displace the origin to y and if accordingly we call z — ¢ = o'v’”,
we find for the orbit of 2 the logarithmic spiral y' = ce” vound the
point g. If, however, @ is real, then z describes the line from z, to
ae B
az, +, containing also point g = — Sar Is on the contrary
(0 —
mod @=1, then the orbit of z is a circle round g as centre.
: au+B =S
LVe 4) = ———_,, where (a—o)? — 48 0.
y ye+d (@ 0) = oe
i! petl
ie) = 5 log wee where
EOE (ed)? 4 487
Pla V (a—d) +487
Cay ACs +487
| Mee EV (ed + AB
4(ad— By)
(2—0)— V(a—dy? +48; dy + eg
; aa ek —
23 23
We shall take as general case, that 8, y, and d are all complex;
then 4, p, and q will also be complex.
1 (oa AES ral ae mae one lk i!
Ae) = iyo =- log? + —log aul —_— = STi + —log ae. +n
2 Qea|- UA re Gig tA: Zoo, ee Aa) ae! Zo Ta.
From
ztp-l 2, 4p-l
log aL: == P= l Lo) = au. — An . . . . . . (2)
2g 217
ensues that for an infinite value of ” the point z takes either the
value -—p—' or the value —q~'. We shall call the points z = — p—!
and z=—g! the fimiting pomts and we shall put —p = q/,
9
Thus our equation (2) becomes
z—q' 27
log ——— = log —— = a (ti ep) ey eS 2 (3)
a) nina J
where we have replaced 2 by w+. ;
Let us choose g' and g" as auxiliary origins and let us call
2— G2 oe 5 gag == 2 = ole
we then find out of (3)
4
log ~— + i(6'—6")— log ~* — i (6',—O",) = un + inn,
o Q
s 0
where by separating the real part from the imaginary we find
' !
0 0 1 Wa 7! "
log — — log si = un (—O") — (4'".—6"".) =r, . . (4)
of Yo
or
( 508 )
Oo gv a un A! g" 0.5, A! A! x ia
— == 6 5 —O = 6 —G7, ne se OD)
@ Or
Elimination of m leads, when mw and p are neither of them equal
to zero, to
ue U. u. D
~ is, By ery Ba my
! y ) ! y " y a
ge yi = Ue Uae =C. . (6)
Se
By putting
. A
(iff = Gie
' ! y i = taf y °
(os (1 1, Ol sexe A 5 (7)
we find
C SSyOule i. Gees coke no ee
The equations (7) and (8) determine together a so-called logarithmic
double spiral‘), with the points g' and g" as poles.
From the second equation (5) ensues that the angle 6’ — 6"=@
between the two auxiliary radii vectores y'2 and gz increases arith-
metically uniformly, whilst the first equation (5) shows us that the
quotient of the auxiliary radii vectores increases geometrically uni-
formly.
For the case «, 8, y, and Jd real, some simplifications appear.
We shall distinguish three cases.
A. (a—d)? + 4py > 0, ad — By <0.
The quantities p and g are real, so the points g' and g" lie on the
real axis. Farthermore we have ¢< 0, so that »= <a.
Hence the orbit of 2 is a logarithmic double spiral, whose two
poles lie on the real axis.
A special case is furnished by the condition «+ d=0, or w= 9.
From the first equation (5) now ensues that the quotient of the
auxiliary radii vectores is constant, so that the point < describes a
circle of Apo.Lonius of the triangle g'g'z,, whilst the angle g'zgq" in-
creases uniformly with x. An example of the latter case is furnished
1
by y=-; here qi =-- lg =
B. (a —d + 4By > 0, ad — By > 0.
The points g' and g" lie on the real axis, whilst e > 0, thus »p=0.
Now the second equation (5) shows us, that 6'— 6"=~® is
constant, so that the point z describes the circle passing through
g,g and z
0°
') or the logarithmic double spirals the reader may consult: Horzmiitter, Ueber
die logarithm, Abbildung ete Zeitsehr. f, Math. u. Physik., Vol. £6. (1871), p. 281.
(509 )
All o* initial points 2, furnish thus together all circles of the
pencil of which g' and 7" are the base points.
Let us suppose point 2 determined on its orbit as point of inter-
section of this orbit with an element of the conjugatedJpencil of
circles, intersecting the real axis a.o. in a point s, then evidently
g2:g'2=gs:y's holds, so. that the equation (5) expresses that the
quotient g's: y's increases geometrically uniformly. (This property
enables us to construct easily the points 2 belonging to given values
of n). Farthermore holds g'=z_. and g' =21..
CC (a= by 448, < 0:
The points g' and g" lie symmetrically with respect to the real
axis, p and gq being conjugate complex. As mod. e’=1 we have
u=0. The ratio 9’: 9" is now constant, so that the point describes
a cirele of ApoLLonius of Ag' yg" z,, i.e. a cirele of the pencil with
yg and g" as point circles. We can again regard the point ¢ as if
originated by intersection of the orbit with a circle of the conjugated
pencil of circles. As the angle g'zy" increases uniformly with we
can easily construct with the aid of the conjugated pencil of circles
the points z belonging to definite values of n. It is clear that the
orbit of z when 7» increases * indefinitely is described innumerable
times, so that the function g,(v) has as a function of 7a real period.
If » is commensurable with a, then this period is a mensurable
number.
If particularly ¢+d—0 holds, then »=az. This case is a. 0.
realized in the function y —=—; here g'=1, g' =>—.
aL
i a where (@ xe Dae — Oe
e
ee
{x
Here we are in the parabolic case.
‘ ac + Bp
}(«) = ——————__
a Jd
“e+ 6
2
f p —-28 a—d
OF if we put —- =a — = a
: a cre) 24 I>
2a z—a
7 (a) SSS ee '§
a—dé t— Od
sO
(2) 2a 2z—a 2a zZ,—a Su
Ay 2 =— = ny
a—S 2—g a—d z,—¢
so that
( 510 )
Zu 2 a a—o¢ 2,—a :
= | nm =—— + (utivyn . . . (9)
7] ime, =a Zod
The difference between our method and that of Kiery arises from
é p a—d :
the fact that Kivi allows the quantity >-—. to inerease really.
aa =
If we take a and g as auxiliary origins and if we put
hh vie, Z—q= — (Oita
then the equation (9) takes the form of
'
oO io—6") Oo i(P,—0",) t
et es, + (e+ a)n
g Yo
or
! !
v ; ! Q 7 ' pis F
— cos (G'-4")+ isin (4'-6") | = v } cos (G',-G",) +isin (4',-4",)i +(u+iv)n,
g 0
from which ensues
' !
Oo v |
SS ! LON ee ! QI
— cos (G'— 0") = —— cos (9,—@ ,) + pn,
gv gv 0
Vor fo oe. ((10)
¢ a ay 4! a vy oe 4' 4" ,
— sin (0 —@") = ~~ sin (6,—€ «) —- vn.
Y Y 0 /
, ; ; a—d ’ (
If we put @ = ocost, py =Osint { 1.0. Ww. 5 — = oe )we find out
aa
of (10) when eliminating 7:
' !
st sin (6'—6'—1) = sao) stni(G;,—- 6), 1) == ¢: eee) ee a)
(2)
¢ Go
It is clear, that the orbit as found by Kur follows from ours
by putting r=0. The orbit of Krem ean thus serve as iteration-
a—Jd S
orbit for real values of the quantity ———, thus of —.
~ 220 a
To investigate the curve determined by the equation (11) we
imagine the circle passing through g and @ and of which the are
ga amounts to 27, so that from each point of the supplementary are
the line ga is seen under the angle rt. (See fig. p. 511).
If we connect g with z, and z, the connecting lines will meet
the circle in) m, and m.
Now “/ yma= 4 qm,a=t
Farthermore / zam = 6'— 6" —1, £ z,am,=6',— 6", —t.
If we let fall the normals 2,2, and zz on am, and am, then
zy, = 9, sur (4', — 0", —t) and zn = @' sin (O' — 6" — 72).
0 0 s 0 0 0
The equation (11) now demands
on a) 0] En =m
: or = =
oy 240) mag 2,7 ehiy
(Potala hab)
It is therefore evident that we arrive from points m to points 2
by diminishing or enlarging the chords gm in a definite ratio.
So the orbit of 2 is a circle touching the auxiliary circle (m) ing,
whose tangent in g forms in that way the angle t with the line ya.
If the quantities «, @, y, and d are real, then a and g are real,
whilst »=O, therefore also r=0O. The points a and g therefore
lie on the real axis and the orbit of 2 touches the real axis in the
point gy. If on the other hand «= 0, then the centre of the orbit
lies on the line qu.
The way in which < changes with » we can read from the
equations (10).
If we suppose the point 2 to be furnished by the circle, which passes
through gy and z and whose centre lies on ga, then the first equation
(10) tells us that the reciprocal value of the radius of that cirele
increases arithmetically uniformly that 1.0. w. the radii of the circles
through gy whose centres lie on ga and which pass through z,, 2, ete.,
form an harmonic series. If on the other hand we suppose that the
point z is constructed as point of intersection of ifs orbit with the
circle through z touching the line ga in g, it then follows easily out
of the second equation that also the reciprocal value of the radius
of this circle increases, arithmetically uniformly, that i.o.w. the radii
of the circles touching ga in y and passing through the points
2,, 2, ete. form an harmonic series.
It is clear that for the case «a, B, y, and Jd real, thus » =O and
t=O, only the first determination of the course of 2 can serve,
-( 512 )
whilst in the ease «=O only the second determination retains its
validity 3
n x log log Le
Vk 1 SE OR, = a (a) ==
: ; ; log a
loy log Zz mre log log Zo
j{(z)=— =
‘ log a log ia
Let us put /Joy@=m +m, we then have
log log a loy log zy fe (ut -f i) nN,
6)
log 2 = log z, . 2 (cos yn 4- 7 sin vn),
or
log 9 + 14 = (log 9, + 14,) e?” (cos pn +- BUDD s oo” ((l2))
from which ensues
(log 0)? + @? = j(log 0,)? +- O74 4" ,
vO
log 9 log @, cos yn — A, sin vn | ener icn ) ((82))
6 log a, sin yn + G, cos vn
Out of these equations follows by elimination of 7 the orbit of <.
For the ease @ positive, so r=, the second equation passes into
log YU ete log Q, re
qa GA,
or
ofl)
Oe.
The orbit of 2 is in this case a logarithmic spiral around the
origin, whieh is ‘dependent of a.
If mod a=1, then w =O, so that the first equation (18) tells
us that
(log 9)? + 4 = (log 9)? + O)* =
or .
TEV 25
QO — a .
This curve is likewise independent of the argument of «.
The function y=.2~-', which we have regarded on one hand
under IV A, w= 0, and which then furnished for the orbit of z a
circle, we can also range under the case treated last. If namely
we take y= .2—' as a special case of y = a* (mod. a=1, arg.c=2);
we then find for the orbit of z quite a different curve.
To this remarkable property of y= a! we hope to refer more
explicitly later on.
Physics. — “On the motion of the bridge of the violin’. By J.W.
Ginray and Prof. M. pe Haas. (Communicated by Prof. H.
KAMERLINGH QONNES).
(Communicated in the meeting of November 27, 1909).
1. In the following lines an account is given of an experimental
research the object of which was to make a contribution to ow:
knowledge of the manner in which the vibrations of the strings are
transmitted to the roof of a violin by the bridge.
As far as we know the literature on the physics of bow instru-
ments is very limited and leaves the true nature of the motion of
the bridge undecided.
HrtMHontz') says: “Der eime Fuss des Steges ruht auf einer
relativ festen Unterlage, namlich auf dem sogenannten Stimmstocke,
einem festen Stabehen, welches zwischen der oberen und unteren
Platte des Korpers eingebaut ist. Der andere Fuss des Steges allein
ist es, welcher die elastischen Holzplatten und mittels deren Hilfe
die innere Luftmasse des Koérpers erschiittert.”
From-this description cannot be inferred whether the bridge vibra-
tes principally in its own plane i.e. at right angles to the longitu-
dinal direction of the strings, or at right angles to its own plane i. e.
in the direction of the strings.
Van Scmatk *) remarks: “By the vibrations of the bowed string a
motion of the bridge is set up which consists in an oscillation about
a line parallel to the length of the violin: in this manner the
movable foot of the bridge communicates vibration to the roof of
the violin and thus to the air.” His opinion therefore is that the
bridge vibrates in its own plane perpendicularly to the direction of
the strings.
APIAN-BENNEWITZ *) Observes: “dass namlich der rechte Fuss eine viel
geringere Bebung als der linke zu machen hat und dass die Thiatig-
keit des linken Fusses als eine hammernde zu bezeichnen ist.’ His
view is thus the same as VAN SCHAIK’s, as appears ‘further from
page 133 of his book.
Barton *) in conjunction with Garret and afterwards with PEntzer has
1) Tonempfindungen, 3e Ausg. p. 146.
2) Dr. J. Bosscua, Leerboek der Natuurkunde, III, bewerkt door Dr. W. CG. L.
VAN Scuaik, Sth Ed., p. 170.
5) Die Geige, der Geigenbau und die Bogenverfertigung. Wemar, Bernuarpt
Friepricu Vorer, 1892, p. 125.
4) Philosophical Magazine, 6th Series, Vol X, XIL and XIII.
( 514 )
investigated the nature of the vibrations of the string, bridge, and root of
a sonometer as also of the air inside the sonometer. He examines both
motions of the bridge and finds that for the same point of the bridge
the displacement by the horizontal motion, i.e. in the direction of
the string, is about 17 times the amplitude of the vertical motion ').
As the bridge of the sonometer is entirely different in shape from the
bridge of the violin and the sonometer is moreover not fitted with
a sound bar, the results of the investigation are not immediately
applicable to the motion of the bridge of the violin.
Savart*) in his very important memoir on string instruments does
not refer to the motion of the bridge.
2. It seemed to us a priori somewhat improbable that as VAN
Scnaik and others suppose a comparatively massive object like the
bridge by vibrating as a whole in its own plane about one of its
corners should be able to follow completely the intricate motions of
the strings and communicate them to the roof of the violin. It seemed
to us more probable that, as Barron found for the sonometer, both
motions should be taken into account.
In order to investigate this experimentally we proceeded as follows.
Hig. 1 represents a violin-bridge manufactured by the well
known makers Carrssa & Francats of Paris. Fig. 2 shows a small
ANU
metal clamp which can be attached to the bridge at different points.
In order not to damage the bridge the screw s does not press
1) Phil. Mag. Ser. 6, Vol. XIII, p. 451.
*) “Mémoire sur la construction des instruments a cordes et A archet.’ A
reprint of this paper is to be found in: “Nouveau Manuel complet du !uthier’’, by
Mavain and Matane. Paris, librairie eneyclopédique de Rorer, 1894, p. 333—398.
——“‘S;
(515 )
directly against the bridge but against a moveable piece of steel p
The weight of the clamp is rather more than 7 grammes.
If the bridge swings in its own plane about its right foot 7, then
when we attach the clamp to the bridge at a, the moment of inertia
of the bridge about the axis of rotation at / perpendicular to the
plane of the bridge will be much increased.
On the other hand when we fix the clamp at /, the effect onthe
moment of inertia will be much smaller.
We found however that there was very little difference in the
sound of the violin in the two cases. By fixing the clamp at @ some
damping influence was noticeable in the g string; at 4 the e¢ string
nl
was somewhat damped.
In view of the effect of the clamp being about the same in both
cases it is difficult to conclude that the bridge swings principally
in its own plane about one of its feet. Moreover the influence of
the damper was in both cases very small.
The following experiment speaks even more clearly.
The distance between the middle of the right foot and the middle
of the upper edge of the bridge fc is in our case 38 mms. The
distance fa is 37 mms.
When the clamp is placed at ev a strongly damped sound is
obtained: this is the well known mute-effect, but even stronger in
our case than with the ordmary mute which weighs only about 4
grammes as against ours which weighs over 7 grammes. At a the
effect is as we saw, extremely small.
As fe and fa are approximately equal, the mcrease of the moment
of inertia of the bridge is about equal in both cases. If the sound
were transmitted by the bridge chiefly by its vibrations about an
axis at f, the damping effect of our clamp should be about equal in
both positions.
As this appears not to be the case we cannot but infer from these
experiments that the motion of the bridge in its own plane is not
of primary importance for the transmission of the vibrations of the
strings to the roof of the violin.
We subjoin as an instance some results obtained by two indepen-
dent observers each playing his own violin.
Violin with strong sound, about Old violin by a pupil of Srainrr’s,
50 years old, maker unknown, small strongly arched model,
model Mageini, very large. fine mellow sound, but not
strong in tone, d string least
fine, @ string by far the best,
e also very good.
( 016 )
Metal damper at a. (Fig. 1).
Some damping effect, especially
on the g string. Rather strong
hasal sound.
y string much less fine than with-
out damper.
d harder and inferior.
a inferior.
e improved.
none of the strings damped, respond
as promptly as without.
Metal damper at (.
Some damping effect, especially
on the ¢ string. ¢ better than
usual.
y string better than usual.
d ST AVOLSCHMEEE
a 9 » » >
€ > ” ” ”
y, d@ and a respond more promptly
than otherwise. The e string is
slightly damped.
Metal damper at c.
Damping much stronger than at @.
Effect the same as with a mute,
than with an
only less good
ordinary mute.
It will be seen that the two
main effect:
and +
the damper at
effect
find
the is absent or
observers
as at Ob.
The
due to individual differences but also to the great
the two instruments.
The following observations prove also, that the
gives the ordinary
at least only very
the effect of placing the clamp at
small differences in the results of the two
Mute effect on all strings, but
much more strongly damped
than with the ordinary mute.
observers agree entirely as regards the
mute effect. At @
small; again both
a about the same
observers may be
difference between
parallel motion of
the bridge has little influence in the transmission of the string motion
to the roof of the violin.
The observers and violins were the same as in the previous ex-
periments and the same damper of 7 grammes was. used,
C5L7) )
Metal damper at d. (Fig. 1.)
Mute effect, strongest on the g side. yg string strongly damped.
d string less, bad in tone.
a string still less, bad.
e 3° be) ”> 33)
Metal damper at .
Damping, diminishing towards e¢ damped, but much less than
the g side. The g string has the y in the d position of the
retained its original tone better damper.
than the ¢ string in the d/ posi- a less damped.
tion of the damper. d damped. gives the mute-sound
more than the w string, but is
still comparatively strong in
tone.
gy less damped than d, very ugly.
Both observers thus found, that in the position / the damping
effect diminished towards ¢ and vice versa.
Thus e.g. in the ¢ position of the damper the y string was but
little damped, although in this case assuming the bridge to vibrate
chiefly in its own plane, the g string would act on a
bridge with much increased moment of inertia which
rit would involve strong damping.
We think therefore that we may infer from these
i
experiments that the motion of the bridge does not prin-
cipally take piace in its own plane about one of its feet,
but that it vibrates chiefly transversely, as shown dia-
| grammatically in Fig. 8 where a/ represents the bridge
in section. On this assumption the results of all the above
? experiments are completely explained :
Fig. 3. : ; : :
iE I. A damper placed at @ has much less damping
influence than a damper at c, as the moment of inertia about gh is
much less increased in the former case.
II. The effect is about the same whether tie damper is attached
at a or at 4. It is clear that the moment of inertia of the bridge,
with the clamp attached, about gh has about the same value in
the two cases.
II. Again the results of the second set of experiments become
(518 )
intelligible when a transverse vibration of the bridge is admitted :
we found in that case that the damping effect diminished towards
the right when the clamp is fixed at d and vice versa. By weighting
the bridge at the top corners the vibration is no longer symmetrical;
the part which is loaded at the top will vibrate less strongly than
tue unloaded part.
3. An additional question with regard to the
two motions of the bridge suggested itself in
the investigation. In fig. 4 de represents the
string at rest, be the bridge: when the string
is deflected to the right (da,/), the tension
KY of the string has a component J/ at right
angles to the plane of the bridge and a com-
K
ah ponent .V in the plane of the bridge. When
a ‘ the string has its greatest deviation to the left,
Q;! the component J/ has the same direction as
! before, the component V the opposite. It follows
By
Nes
=
that the bridge completes two vibrations in the
direction of the string to one vibration of the
string itself, whereas the motion parallel to the
bridge has the same period as the string.
Fig. 4.
The sound of the violin is produced almost exclusively by the
vibration of the roof; the string by itself imparts but a very small
amount of energy to the air directly. If we suppose that the sound
given by the string directly may be neglected in comparison to the
much stronger sound which is due to the roof, and that the effect
of the parallel motion of the bridge may also be neglected as against
the much greater effect of the transverse motion, all the notes of
the violin should be an octave higher than the pitch of the string,
assuming that the strings deviate on both sides of the position of
equilibrium.
The correctness of this conclusion however did not seem to us
very probable: presumably if real, this striking faet would have been
observed and communicated by previous observers.
We have therefore investigated the question experimentally by
putting a steel string on a violin and making it vibrate electro-
magnetically.
We took a steel guitar string and put it in the position of the
/ string. Close to it a small electromagnet of the RommrsHavsen type
was fixed in a stand about vertically above the string, near the place
Where it is usually bowed, The coil of the electromagnet was in
9
(519 )
circuit with three accumulators and a Konic electromagnetic tuning
fork (Fa, = 682 v.s.). The fork was placed in a distant room. The
tension of the string was regulated until the violin when the string
was bowed gave a note slightly lower than the fork. The fork was
then started and the note of the siring raised by pressing it with
the finger until no beats were heard.
The note given out by the violin was now unmistakably Fa,.
Now if there really were a difference of an octave between
the note of the violin (/a,) and the note of the string itself, the
string ought under the influence of the electromagnet to have given
the note Fa,. This is however impossible: an electromagnet mag-
netised by a fork /a, can produce in a string the notes Fa, Fa,,
Fa, ete. but never the note Fa,. The experiment was thus by itself
sufficient to show that the note given by the violin has the same
pitch as the note of the string itself, even when the excursions of
the string on the two sides of its position of equilibrium are about
equal.
Thinking that the octave might perhaps appear, if the parallel
motion of the bridge were damped down, we loaded the left foot
of the bridge with our metal clamp, but even then the octave could
not be heard.
As the question seemed to us of great importance we tried to
solve it in a different more direct manner by an experiment in
which the sound of the string was heard by itself.
On a heavy zince-block of 80 by 40 ems and 37/, ems thick
(Fig. 5), two metal bridges are fitted (Fig. 6) at a distance from
each other of 32'/, ems. An a-string 0,7 to 0,75 mm thick was tied
Fig. 5.
to a pin s, the other end being attached to a cord going over a
pulley and a pan weighted with 6 kilogrammes. When bowed the
string sounded a note near U7¢,. The friction of the string on the
bridges and of the cord on the pulley enabled us to slightly alter
a4
39
Proceedings Royal Acad. Amsterdam. Vol. XII.
Fig. 6.
the pitch by turning the wheel of the pulley. In this manner the
string was accurately tuned to Ut, (1023,9 v.s), so that it produced
no beats in a resonator Ué,.
Next an a@ string of the same thickness was put ona violin (fig. 7).
The distance of a to was again 32,5ems. The violin was clamped
Fig. 7.
on the table with some wooden blocks; in the neck of the violin a
hole O was bored, through which the string was made to pass. As
the friction of the string on the usual ebony peg would have been
too great, a metal peg was substituted which is represented in fig. 8.
The string passes over the small metal
wheel a. At p a cord was tied to the
string which ran over a pulley and had
a pan attached to it. The a string was
now stretched by placing weights in the
pan until the violin on bowing sounded
Ut, accurately. It was found that a weight
of 6 kilograms was required to do this,
i.e. the same as with the zine block.
That the violin and the string on the zine block gave the same note,
i.e. without a difference of an octave, was confirmed not merely by
the ear but also by the aid of resonators: the resonator Ut, responded
to both notes, the resonator Uz, did not. If the note given by the
violin had been an octave higher than that of the string on the zine
plate (i.e. Us) the resonator Ut, would not have responded to the
violin note.
( 521 )
We have also determined the note which the string gave at the
above tension by calculation.
For tbat purpose the string was cut at a and 6 (fig. 7) whereby
its length shrunk to 30 ems. The weight of this piece was found
to be 0,15 grams.
pl
By substituting in the formula — ee where ¢ is half the
gs
period, p=0,15 gr, /= 32,5 ems, g = 981,2 cms sec—?, s = 6000 gr,
1
it follows ¢=—— sec.
1099
According to this calculation the string would have a frequency of
1099
= 549,5 complete vibrations whereas in reality the frequency
was 511,9 (Ui,).
These numbers agree sufficiently to show with certainty that in
both cases the fundamental note of the string was heard. The com-
paratively small difference can be explained by assuming that the
tension of the string was not exactly 6000 grams in consequence of
the friction of the string on the bridges and of the cord on the
pulleys.
From these experiments it appears that in the mixed sound which
the violin produces the fundamental note produced by the parallel
motion of the bridge and by the motion imparted to the air directly
by the string is still present in sufficient intensity to give the
sound the character of the fundamental as far as the pitch is
concerned. *)
It is indeed well known that the fundamental which determines
the pitch of a composite note may be of smaller intensity than the
overtones of the mixture, as HELMHOLTZ showed to be the case with
the piano. *)
We thus know that the sound given by a violin must be ascribed
to three distinct causes:
a. a vibration imparted to the air by the string.
6. a vibration which the roof of the violin acquires from the
parallel swing of the bridge.
c. a vibration communicated to the roof by the transverse vibration
of the bridge.
The vibration mentioned under @ will be left out of account as
- being of little importance.
1) Compare Rayteicu, “Theory of Sound”. second ed. Vol.I p. 208 and Barton
and Penzer, Phil. Mag (6) XIII p. 452.
2) Tonempfindungen, p. 134—135.
35*
(522)
If a string is bowed the fundamental of which has a period 7,
the note will be accompanied by harmonies of periods '/,7, */,7,
1/,T ete. respectively.
The parallel motion of the bridge will cause a periodical change
of pressure of its left foot on the roof of the violin. When the
bridge moves to the left the pressure increases and vice versa. The
change of pressure may be represented by the following series:
a, sin 2a + a, sin 20 =e + a, sin 2m - = + a, sin 22 s S00 6
tI: el fed gil
The transverse motion of the bridge will also cause a change in
the pressure between the left foot and the roof. When the bridge
is pulled forward the front of the left foot will exert a greater
pressure on the roof; when the bridge moves back the pressure
diminishes. This change of pressure may be represented by a series
of the form
sin 27 - l ), sin 29 “eg -- 5. sin 23 = =- 6. sin 23 dail ome
b, sin conga D "aT i "Tp 3 Sun "TT
As the foot of the bridge has only a small area compared to the
large surface of the violin which is set in motion, we may assume
that the pressure changes which are due to the parallel and the
transverse motions of the bridge respectively, occur at the same point
of the roof. In order to find the total change of pressure produced
by both motions together we must therefore add the two above
series. If we assume that the excursion of the roof at the point
where the left foot is attached to it is proportional to the change
of pressure, the sum of the two series multiplied by a constant will
give us the type of motion of the roof at that point.
It is well known that in general a sound becomes mellower according
as the partial overtones become weaker and that the intensification
of the even overtones especially renders the sound sharper. Many
instances of this are to be found in HeLMHo.rz’s work already repeat-
edly quoted (p. 129—133 and p. 151—152). As an_ illustration
of the influence of the overtones on a mixed sound we may also
mention the sound of a piano when octaves are played. When an
octave is struck on the piano the two notes cannot easily be heard
separate, as they can be e.g. with thirds. But only very slight
musical training is required to hear in a musical recital that running
octaves are played: the sound is then sharper and rougher. The same
holds for running octaves on the violin.
When in the above series we diminish the coefficient8 a,, a,, a,—
ete. while leaving the 6,, 6,, 6, unchanged as far as possible, the
(523 )
fundamental and odd harmonics are weakened more than the even
harmonies. In accordance with the above results of Hetmno.tz the
sound will thereby be made sharper. We have proved this in the
following manner by experiment :
To the bridge of a violin at the lowest possible point a metal
clamp, represented half size in Figs. 9a and 94, was attached. On
the left side (i.e. on the side of the g string) a copper rod 3 mms
thick and 10 ems long was screwed into this clamp. At the end of
this rod two ordinary binding screws were fixed, weighing about
18 grammes each.
The moment of inertia of the bridge about the axis through the
right foot, perpendicular to the bridge was naturally very much
enlarged by these weights. The violin now gave a characteristic
nasal sound, especially in the gy and ¢ strings ; the timbre resembling
most the note of a hautboy. Still notwithstanding the great weakening
of the fundamental it continued to impart to the sound the character
by which the pitch of a note is distinguished, in other words no
change of an octave was perceptible.
When in addition to the clamp shown in Fig. 94 the bridge was
loaded with two mutes fixed on top of each other and placed on
the upper edge of the bridge, the original sound was approximately
recovered, as now the transverse as well as the parallel motion of
the bridge was damped. Of course the response of the violin at this
load was difficult. The two mutes were an ordinary ebony mute
with a metal mute, as often used, placed on top.
When a,, a, ete. and b,, 6, ete. are all diminished in the same
proportion the form of the curve of motion will not change, only
the amplitude diminishes: the intensity is weakened, but the timbre
remains the same.
If we could diminish the 6’s and leave the a’s unchanged, the
sound would become mellower, as in that case only the even upper
partials would become weaker, including the first overtone which
has the greatest intensity of all.
(524 )
A mute placed on the bridge damps both motions. But from the
fact that it renders the sound mellower we think we may infer
that the #’s are reduced by it by a higher fraction than the a’s.
This would mean that the transverse motion of the bridge is
damped to a higher degree by putting on the mute than the paral-
lel motion.
5. We have also tried to show experimentally that the bridge
in its parallel motion turns principally about its right foot.
For this purpose we screwed two metal rings into the clamp of
fig. 9, which were placed in a horizontal position. The violin was
fitted with a steel string, as before moved electromagnetically. While
the string was moving a small leaden ball was placed alternately in
the two rings; the two balls weighed 34 grms each. They were
attached to a thin cord; as nearly as possible at the same moment
that one ball was lifted out, the second ball was carefully placed
in the other ring. We expected that the sound of the violin would
be perceptibly weakened as the ball on the right was removed and
the left ball simultaneously put in. But we did not sueceed in
arriving at a trustworthy result in this manner; in the first place a
rattling noise was sometimes apparent while the balls were being
exchanged and in the second place the tone of the steel string was
not always of the same intensity.
6. The conclusion therefore to be derived from our experiments
is that the bridge of a violin performs a parallel as well asa trans-
verse motion and that the timbre of the tone, given by the violin,
is modified greatly when the intensity of one of the motions is
altered while leaving the other motion unchanged as nearly as possible.
Herewith we have at the same time given the physical explanation
of the action of the mute and also of the influence which the use
of too thick or too thin a bridge has on the sound of a violin.
The action of the mute is commonly described by calling it “dam-
ping” or “deadening” *). But if the mute caused nothing but a general
damping or reducing of the bridge motion, the mute would only weaken
the sound, and the same effect would be obtained by bowing softly on
a violin without as by bowing hard on a violin with a mute. That
however is by no means the case as every one knows.
Delft, November 1909.
1) Barron. “Textbook on sound”, p. 419: “The mute is a small apparatus
of wood or metal which fits on the bridge, and thus deadens the sound considerably”
(525 )
Anatomy. — “On the slope of the Foramen magnum in Primates”.
By Prof L. Boix.
(2n¢ Paper on the Comparative Craniology of Primates).
In the first paper on the anatomy of the Primate-skull, the
position and shifting of the occipital Foramen in Primates was treated,
This paper will be devoted more especially to the consideration of
the inclination of this plane.
All the writers who have dealt with this subject have pointed out
that these two features: position and inclination, stand in a certain
relationship to each other, in so far as the closer the Foramen lies
to the occipital pole the more vertical a position does it assume,
while as it gradually approaches the middle of the cranial base the
tendency is towards a horizontal position. This variation in the slope,
like the shifting, has been connected with the erect gait of the human
body. In the typical quadruped, where the skull more or less hangs
from the spinal column, the Foramen lies at the occipital pole of
the skull, and the plane is vertical; in human beings, where the
longitudinal axis of the body runs vertically, the occipital Foramen
lies in the middle of the cranial base, while the plane is almost
horizontal. Thus it is seen that this plane is disposed to take up a
position perpendicular to the longitudinal axis of the body. Another
point of view, first fully developed by Huxiey, concerns the connection
which is said to exist between the slope of the plane of the Foramen
magnum and the degree of prognathism ‘). The more pronounced
the prognathism — i.e. the longer the face-skull — the more per-
pendicular would the Foramen magnum stand. If now a rough
comparison be made of an animal’s skull with a human skull, the
parallelism between these two features is at once noticeable. Huxiey,
however, believed he could show it even in the skulls of different
races of men. From the superposition of the mediagrams of the
highly prognathous skulls of an Australian and a Negro on the
skull of a Tartar, it was seen that “the plane of the occipital
Foramen forms a somewhat smaller angle with the basiscranial axis
in those particular prognathous skulls than in the orthognathous”’.
Wetcker') holds a somewhat similar opinion, though he does not
express it as being a connection between prognathism and the slope
of the Foramen magnum, but between prognathism and the position
1) T. Huxtey, On some fossil remains of man. Collected Essays. VII, p. 198.
2) H. Wexcxer, Untersuchungen iiber Wachsthum und Bau des menschlichen
Schadels. Leipzig 1862.
( 526 )
of this opening, which, however, comes practically to the same
thing, if a connection between position and slope be assumed.
“Biegt am Vorderschiidel’, he says (l.c. p. 50), ‘der Oberkiefer
des Menschen mehr nach vorn (Prognathismus) so riickt zugleich
am Hinterschidel das Foramen medullare mehr nach riickwarts’.
Arsy') does not agree with Huxtny: ‘“Huxiny glaubte die Neigung
mit dem Prognathismus in Verbindung bringen zu kénnen. Die Steil-
heit der Stellung sollte in gleichem Masse wie die letztere wachsen.
In unseren Tabellen findet sich keine Bestitigung dieser Ansicht”
(l.c. p. 17). Anpy himself sees a connection between the degree of
development of the occiput and the slope of the Foramen magnum:
“Die Abflichung des Hinterhauptes fiihrt eine Erhdhung des Foramen
magnum im Gefolge.” This opinion does not really differ in prin-
ciple from Wetcxer’s, for if the occiput be markedly flattened the
Foramen magnum will lie further back, and thus the opinions of
Wercker and Axpy coincide after all with the opinion already
expressed by Daupenton, that the For. magn. is the more perpen-
dicular in proportion as it is pushed further backwards. The con-
nection which Huxiry believed he had shown was, however, of
another kind, and Axpy is therefore not correct in representing his
opinion as being in contradiction to Huxtny’s. For it is not impos-
sible that the slope is proportional on the one hand to the degree
of proguathism, and on the other to the position. Is then the relation
between position and slope of such a constancy as TopinarD made
it appear originally when he said*): ‘qu il suffit de mesurer lun
des deux termes par exemple Vinclinaison du trou occipital pour
connaitre l'autre, c'est & dire la quantité du déplacement du trou’ ?
This seems a priori improbable, since Toprnarp’s method of deter-
mining each of the two phenomena possesses merely a very relative
degree of accuracy. Indeed Toprarp himself saw this later *), and
then expressed himself more cautiously: ‘“Toutefois il ny a pas un
parallélisme rigoureux entre les deux phénomenes.”
In general the above writers determined the slope of the Foramen
magnum by determining the angle which was formed between the
base-line adopted by them, and the line which connects basion and
opisthion. The base-line in these researches connected the basion
with the nasion or typhlon, and therefore ran through the skull-
base. This method has been contested by Broca, and quite justly,
for the size of the angle which is formed by these two lines is
) G. Awsy, Die schiidelformen der Menschen und Affen. Liipzig 1867.
2) P. Toprarp. L’Anthropologie, Ame Edition.
) P. ‘Torinanp, Eléments d’Anthropologie générale.
not dependent merely on the direction of the Foramen magnum
because the direction of the base-line, i.e. one of the legs of the
angle, depends on several factors, e.g. the angles of the basis cranii,
the length of the skull, the length of the clivus, the position of the
nasion, ete. To avoid this difficulty Broca determined the slope of
the For. magn. by an angle made by the plane of this opening with
a plane which is entirely independent of the cranial base, viz. that
which connects the axes of the two orbitae. He constructed his
“angle orbito-occipital” '). Broca here was proceeding from the postu-
late that the orbital-plane, in Primates at least, is the natural hori-
zontal plane of the skull, as, in the case of normal sight, these
animals look straight before them and the orbitae in this cireum-
stance therefore will have the same direction. The correctness of
this opinion will be discussed in a following paper.
Ravper*) in a recently published treatise, returns to the old,
disused method, takes as base-line again the nasion-basion, and even
says that: “eine Beziehung der Neigung des Foramen occipitale auf
eine andere Linie als auf die Basallinie fiihrt sehr leicht zu Unver-
standlichkeiten und entbehrt zugleich der morphologischen Bedeutung’.
ScHwaALse, also, lately expressed as his opinion regarding the value
of Axsy’s base-line as follows: ‘So rationell auch die von AxEBy
gezogene Grundlinie ist, ist sie doch nicht geeignet iiber die Aus-
bildung der verschiedenen Teile des Schadelraumes Auskunft zu geben.’’*)
There is a certain contradictoriness in this criticism. A rational
base-line of a craniometrical system must be able to serve as basis
for at least a primary division of the skull. I have already briefly
stated my objections to base-lines which are drawn through the
skull-base, and will come back to this subject in a following paper.
Such a line may have a certain value as boundary line between the
cerebral- and facial-skull, but as basis of a craniometrical system
it is absolutely useless.
Huser‘) finally has determined the slope of the For. magn. in
Hylobates with regard to the so-called German horizontal, a method
which when the skulls to be examined cannot be halved medially
is preferable to those of other investigators. The probable error will
here be less than by the use of the basal line and certainly likewise
less than by employing the horizontal auxiliary line made use of by
1) P. Broca. Sur l’angle orbito-ocvipital. Revue d’Anthropologie 1897.
2) A. Rauper. Der Schidel von Kegel. Int. Monatsch. f. Anat. und Phys. 1906.
8) G. Scuwatee. Kritik zu Koutpruaee’s: Morpliologische Abstammung des Men-
schen. Globus 11 Juni 1908.
4) L. Huser. Vergleichung des Hylobates und Menschenschiidels. Miinchen 1902,
( 528 )
LissavgerR '), running from the protuberantia occipitalis externa to the
point” where the ala of the vomer is joined to the rostrum sphenoidalis.
By the method I have adopted in determining the slope of the
For. magn. I have proceeded from the base-line which was described
in the first paper, and in so-doing have answered the question as
to what angle is made by the plane of the occipital foramen with
this line. To express this angle in all Primates always as a positive
value it is not possible to measure the angle directly. For in the
Primates 3 conditions occur: a. the opisthion lies higher than the
basion, the For. magn. looks backwards, and the angle is therefore
an acute one closed at the back; 6. basion and opisthion lie at equal
distances from the base-line, the For. magn. looks downward, is
parallel to the base-line, and the angle = 0; c. the basion lies higher
than the opisthion, the For. magn. looks forward and the angle is
an acute one closed in front. To prevent confusion between angles
of equal size in cases a and c, a + or — sign could be used. |
think, however, the variations in the inclination might be represented
more simply in determining the angle made by the plane of the
For. magn. with a perpendicular drawn from the basion to the
base-line. In case a this angle is always acute, in case / it is a
right angle, and in case ¢ it is an obtuse angle.
Nae
Fig. 1.
Mediagram of an Ateles skull, illustrating the method of determining
the slope of the For. magn. (8/, natural size).
In Fig. 1 this method is clearly seen on the mediagram of an
Ateles skull. The following table gives the results of the researches
on the skulls of full-grown monkeys.
1) Lissaver. Untersuchungen iiber die sagittale Kriimmung des Schiidels, Arch.
f. Anthrop. XV Bnd. Suppl.
(529 )
Lemur. 40. Propithecus 42.
Myeetes. (18), 33. 45. 53. 59. Average 47.5.
Pithecia. 54. 56. 60. 64. Av. 58.5.
Hapale. 61. 61. 68. 64. 69. 72. Av. 65.
Chrysothrix. 60. 61. 68. 65. 66. 69. 70. 70. 71. 71. Av. 66.6.
Cebus. 63. 64. 64. 65. 67. 67. 68. 72. 73. 75. Av. 67.8.
AieleseOG. OF. 1OSq tla dha (9) Ola Ava tant
Cynocephalus. 68. 64. 66. Av. 64.2.
Inuus. 66. 68. 70. 76. 76. Av. 71.2.
Macacus &. 68. 70. 70. 74. 79. Av. 72.2.
Macacuseo 67. (oe te 1S. 84. Ave 75.4:
Cercopithecus. 74. 80. 81. 82. Av. 79.2.
Colobus. 64. 72. Av. 68.
Semnopithecus. 60. 61. 61. 64. 68. Av. 62.8.
Siamanga. 55. 56. 56. 56. 58. 61. 63. 63. 67. 68. Av. 60.2.
Hylobates. 52. 60. 66. 73. 75. Av. 65.1.
Chimpanzee. 64. 79. 80. Av. 74.8.
Gorilla. 68. 63. 66. 70. 76. 77. 80. 80. Av. 71.8.
Orang. 58: 62: 68. 70. 72. 75. 79. 80. Av. 70:3.
These figures show in the first place that the slope of the Foramen
magnum varies greatly in individual cases, a fact which is apparent
by merely looking at the skulls. This individual variability is espe-
cially noticeable in the large skulls such as those of the Anthropoids.
And yet the general configuration of the skull is but little intluenced
by these great variations in the slope of the Foramen. As a proof
Se
of this, I have given in Figs. 2 and 3 the mediagrams of two
Mycetes skulls, with slope-angles of 18° and 59° respectively.
From the figures it can also be seen that a slight shortening of
the Clivus is of great influence on the angle of the slope. Now
7
Fig. 2.
| Mycetes. (3/,) Angle of inclination of the For. magn. 18°.
( 530 )
OOS a
Fig. 3.
Mycetes. (°/,) Angle of inclination of the For. magn. 59°.
Mycetes occupies a foremost place in the variability of the inclination
as in that of the position of the Foramen magnum for reasons
fully given in the previous paper. For the other skulls, however,
the same holds good. Another cause of the individual variations is
the striking difference in sagittal measurement of the For. magnum
especially in Anthropoids. In the Orang-outang skulls, for instance,
which I used, this measurement varied from 25 to 41 mm.
Nevertheless, in spite of these individual variations some remarkable
features are to be detected between the different primate-genera,
especially if the series be compared as a whole with one another.
It is noticeable that Chrysothrix does not seem to occupy the place
attributed to this family in the literature on this subject. Among the
Plathyrhines, Cebus, and more especially Ateles, have greater angles,
that is to say, in these genera the For. magn. lies more horizontally.
In this respect the Chrysothrix is inferior even to most of the families
of the Catarrhines. On an external observation, however, the For.
magn. seems in this monkey's skull to lie horizontally in consequence
of the enormous development of the occiput, and the large share
that the squama occipitalis occupies in the formation of the cranial
base. (See Fig. 4).
ae
Fig. 4.
Mediagram of the skull of Chrysothrix. (1/;).
( 531 )
Among the Catarrhine monkeys, the greatest angles, 80° and more,
occur among the Anthropoids and the genus Cercopithecus. This
genus thus, also as regards the slope of the Foramen magnum, takes
the high place which we have already awarded to it in the previous
paper on account of the position. And similarly the genus Siamanga
takes again the lowest place among this group of Primates. In this
otherwise so highly developed monkey the Foramen magnum is
inclined more vertically than in any other family of monkeys of
the Old World, although it is closely followed by the genus Sem-
nopithecus. A study of the skull base will afford us the opportunity
of pointing out more particularly what a quite distinct place the
Siamanga takes in the group of Primates, as regards the general
form of the cranium. In the first paper I have already mentioned
that it is difficult to believe that original conditions have been here
persistent.
In the foregoing paper it was also pointed out that during the
infantile and juvenile period the For. magn. shifts towards the
occiput. It appears now that also the slope of the Foramen changes
during growth. For in the skull of a young ape the Foramen
magnum lies more horizontally than in that of a full-grown one.
The following may serve as a proof of this. Whereas ina full-grown
Siamanga the angle varied between 55° and 68°, I found ma juvenile
skull (mixed dentition) an angle of 70°, and in an infantile skull
(complete lactal dentition) an angle of 81°. In a Chimpanzee, with
a complete set of milk teeth, the For. magn. lay almost horizontally
with a angle of 88°. In three infantile Orang-outang skulls I found
angles of 78°, 85°, and 86°, while finally a juvenile Gorilla skull
had a angle of 87° and an infantile one even of 95°. In the case
of this last skull, thus, the For. magn. looked forwards as in that
of man. We shall soon see that as regards human beings also the
plane of the For. magn. turns during infantile and juvenile periods
in the same manner as with the Anthropoids, though I must here
point out that this turning is much more pronounced in Anthropoids
and Siamanga than in human beings.
Thus both in the position and the slope of the For. Magn. the
young Anthropoid agrees more with the human conditions than the
full-grown one.
In respect to the slope of the For. magn., man occupies a distinct
place among all Primates, as in him the opening is not turned
towards the back but towards the front. This fact, which has already
been alluded to by Dasupenron, and after him by all the writers on
this subject, is illustrated by the figures below. I call to mind that
( 532 )
an angle of 90° obtained by my method agrees with a position of
the For. magn. parallel to the base-line, i.e. a horizontal position.
Angle of the For. magn. in full-grown human skulls.
Papuans: 96°,99,99, 99, 100, 101, 103, 107, 107,108, Av. 101,9°.
Negroes: 92°, 96,07, 98, 99,100,100, 101,108,106, ,, 99,2°.
Frisians: 86°, 89,90, 94, 95, 99,100,103, 103,103, ,, 96,2°.
Zeelandians: 93°, 97, 99, 100, 101, 103, 104, 105,109,112, ,, 102,3°.
Javanese: 92°,92,97, 99,100, 100, 103, 103,103,105, ,, 99,4°.
The averages of three of the groups lie comparatively near each
other, and the existence of a difference between dolichocephalic
skulls (the first three groups) and brachycephalic cannot be assumed
on the ground of these figures, although the difference between the
long dolichocephalic Frisian skulls and the short strongly brachy-
cephalic Zeelandian skulls is very remarkable. It is also peculiar that
among the Frisian skulls there were two in which the For. magn.
looked slightly backwards (angles of 86° and 89°) and one where
it lay exactly horizontal. This was caused by the particularly long
clivus in these objects. That the degree of development of this part
of the cranial base in human beings has a great influence on the
slope of the For. magn. is proved by infant skulls. On an average
the For. magn. in young human skulls has without exception a more
considerable inclination towards the front than in full-grown ones,
as will be seen from the following figures.
Angle of the For. magn. in children’s skulls.
O—1i year. 110, 110, 109, 105, 104, 1038, 102, 101, 100, 100, 92.
1—2 years. 100, 110, 110, 108, 106.
2 years. 107, 107, 106, 106, 103, 101, 95.
3 years. 110, 110, 108, 107.
4 years. 114, 109, 106, 105, 100.
5—6 years. 114, 113, 109, 107, 105, 103, 96, 96.
7 years. 108, 100, 100, 99, 98.
8—9 years. 104, 103, 101, 97.
10—11 years. 110, 104, 104, 101, 100 92.
Or
The average angle of the human full-grown skulls can from the
g : g
preceding table be set at 100°. And now it is seen that of the 31
( 533 )
skulls of children under 5 years of age only 2 have a smaller
angle while of the 23 skulls of children between 5 and 12 years
of age this is so in 6 cases. From this it may be inferred that
during infancy when, as has been shown in the 1%* paper, a
shifting of the position of the occipital foramen takes place in man,
also the plane of the For. magn. turns, and in the same direction
as with the Anthropoids. Yet, as has been said, this turning, like
the accompanying shifting of position is more marked in Anthropoids
than in human beings.
We have now seen twice over that a shifting of the For. magn.
and a change in the angle go hand in hand during the individual
development. For in human beings as well as in Anthropoids the
shifting backwards diminishes the angle of inclination. To what
degree this relation between these two features exists in comparative
anatomy will be apparent from the following table. The 2"4¢ column
gives the average of the angle, while the first column shows the
average basal-index as determined in the 1st paper. I may here call
to mind that the greater this index is, the further backwards does
the For. magn. lie.
Index basalis. Angle of inclination of the
For. magn.
Lemur albifrions 87 (4) 40° (1)
Propithecus diadema 80 (2) 42° (2)
Mycetes 86 (3) A7.5° (8)
Pithecia 74+ (6) 58.5° (4)
Hapale lan(S) 65° (8)
Cebus 67 (0 67.8° (41)
Ateles - 64 (13 G2 a)
Chrysothrix 59 (18 66.6° (40)
Inuus 65 (42) 71.2° (44)
Cynocephalus 65 (12 64.2° (7)
Macacus 64 (4) TS") CLT)
Cercopithecus ae (Gls) 79.2; +(29)
Semnopithecus 74 (7) 62.8° (6)
Colobus 75 (5) 68" (12)
Siamanga 76 (4) 60.2° (5)
Hylohates tA (9) 65155 1)
Chimpanzee 64 (15) 74.3° (418)
Gorilla 61. (16) 71.8° (45)
Orang 61 (17) 70.3° (12)
( 534 )
In brackets after the figures of both series is given the place
number which each of the genera would take in a regular classifi-
cation. A comparison of these place numbers shows at a glance in
how far the position and the slope of the For. magn. go hand in
hand. In general there appears to be a decided parallelism between
these features in monkeys, and only in a few cases there is a fairly
marked difference between position and slope. This is, for instance,
the case in Chrysothrix where the angle is small in comparison to
the position, and in Colobus. where the reverse is the case.
At the beginning of this paper mention was made of the opinion
held by Huxuey, viz. that the slope of the For. magn. is in proportion
to the degree of prognathism. In a following communication, which
will deal with the prognathism of the primate skull, this view will
be discussed at greater length.
Physics. — “A short reply to Mr. van Laar’s remarks.” By Prof.
Pu. Kosnstamm. (Communicated by Prof. J. D. vAN Dir WAALS).
In the proceedings of the preceding meeting of this Academy Mr.
vAN LAAR made some remarks suggested by a paper by Mr. Timmer-
MANS and me. Though these remarks do not call in question in any
point the validity of our results, but exclusively deal with the
question whether we have done sufficient justice to the share Mr.
VAN Laar has had in the construction of the theory, | think that
both politeness to Mr. van Laar and deference to the communicator
of these remarks forbid me to leave them unanswered. So I shall
try to state as shortly as possible the reasons why I still think I
have done full justice to that share.
1. Mr. van Laar writes in poimt @ of his remarks:') ‘Here I must
remark that I have never'*) represented the special case a,,=V a, a,
as the general case.”
In writing this Mr. van Laar had certainly forgotten that he
wrote in These Proc. Sept. 1906 p. 227: “In the third paper in
These Proceedings (June 24, 1905) the equation:
a ass 1 1 IED
d=7(G) =9V s4v ale lV =] —1}. 3)
was derived... for the quite general*) case a, $a, ), Sb,”, ete.
And on the same page: “Now the restricting supposition p= 0
!) These Proc. XIL p. 455.
®) Mr. van Laar’s italics.
( 535 )
was relinquished for the determination of the double point of the
plaitpoint line, and the quite general case*) A, 2 a, b,$4, was
considered.
And on p. 228: “We can, namely, characterize all possible pairs)
of substances by the values of 6 and a, and finally it will only’)
depend on these values,') which of the three main types will appear.”
And on p. 230: “The calculations get, however, so exceedingly
intricate that they proved practically unfeasible for the general case’)
dy Za, b, SS
And on p. 231: “This appears already from the fact that the
substitution of the quite general assumption’) 6, $4, for the simpli-
fied assumption 6,=06, has made no change in the existence of a
double point ..., and that also the calculations for the limits of
type III... may be carried out for the quite general case’) b,20,.”
And on p. 232: “The calculation proves that in the quite general
case *) b, S Ox ete:
For, everywhere where the general case is spoken of here, it is
the case a?,,—a,a, that is meant, and also the quotation from
p. 228 is possible only, by an identification of the general case and
this special one.
2. In point 6 of his remarks Mr. van Laar says in connection
with our sentence that his investigations: “very onesidedly, lay
the stress on the existence of open plaits, a circumstance which
by no means can be considered as a result*), as it immediately
follows from the arbitrary, if not erroneous supposition*) of the
linear dependence of 6 and w”’: “Now I have never asserted that
d*h
da?
have simply asswmed*) this in order to make the calculations *)
possible.”
Yet I read on p. 231 of the cited paper: “We shall once more
emphatically point out that the nwmeric*) results of our investigation
will naturally be modified, when 6 is not assumed to be independent
of v and 7... but that qualtatively*) everything will remain
unchanged.”
And on p. 233: “Then further increase of pressure makes the
phases 1 and 2 again diverge . . . without the longitudinal plait
ever closing again — as was formerly considered possible‘) — {ef,
=0O would always agree with what actually happens; again I
1) The italics are mine.
) T. and K’s italics.
3) Mr. van Laar’s italics.
ob
Proceedings Royal Acad. Amsterdam, Vol. XII.
( 536 )
inter alia vaAN per Waats, Cont. IT p. 190 (1900)]. Only at tempe-
ratures higher than 7’,... there can be question of homogeneity to
the highest pressures.”
It seems to me that every unprejudiced reader of these lines
must acknowledge that Mr. van Laar thought that he gave a new
result here, materially differing from the result of a closed plait as
it was thought possible by van per Waats, and that he cannot
possibly have realized when writing these lines that this divergent
ee RID Oe
result was only founded on his assumption FE =0;
3. As to point c, the sentence mentioned there really refers to a
paper by. Mr. van Laar earlier than April 1905 (viz. of January 1905),
I did not know, however, until the publication of the “Remarks”,
(and now I only know it from these “Remarks’”’) that Mr. van Laar
has abandoned his views of this previous paper. Else we should,
of course, not have mentioned it.
4. With regard to point d we must protect Mr. van Laar against
himself. We had said: ‘His results are of importance particularly
because they showed that under certain circumstances non-miscibility
can occur for perfectly normal substances, a fact which was generally
doubted at the time.” Mr. van Laar remarks in this connection that
it was by no means generally doubted up to now whether miscibility
could occur for normal substances but only whether some special
“abnormal” forms of non-miscibility could occur for perfectly normal
substances. | must maintain in opposition to this that both LusrEipr
and VAN DER WAALS, to whom we referred l.c., had by no means a special
case of non-imiscibility in view, but very decidedly ali non-miscibility.
So Mr. van Laar’s merit is decidedly greater than he will own here.
On the other hand I must confess that in our endeavours to be
perfectly objective to Mr. van Laar, we have really got unjust in
the above cited sentence to Mr. van Laar’s predecessors: VAN DER
Waats and Korrrwne. The above statement might lead one to think
that Mr. van Laar had been the first to demonstrate the possibility
of non-miscibility for normal substances. As Mr. van Laar justly
remarks: this is incorrect, and it would have been better if our
sentence had run like this: His results are of importance particularly
because he adhered to the possibility of non-miscibility for normal
substances in a time in which this was pretty generally doubted,
and showed once more that for certain values of a’s and 0’s, which
could not a priori be considered as improbable, non-miscibility must
really appear”
If I wanted to discuss also Mr. van LaAar’s other remarks, I should
( 537 )
x
have to enter fully into the very heart of the matter, as I cannot
assume the reader to be fully acquainted with the details of these
investigations. But then I should think I abused the hospitality
which this Academy so courteously extends in its publications also
to non-members. So I think that the above will suffice. If Mr. van
Laar should, however, wish to pursue this discussion elsewhere, |
am willing, though not desirous, to continue it.
Chemistry. — “The equilibrium solid-liquid-qas in binary systems
which present mixed crystals.” By Dr. H. R. Kruyr. (Com-
municated by Prof. P. van Rompureu.) First communication.
In the Archives Néerlandaises |2| 5 (Jubilee number in honour of
Prof. Lorentz) p. 360 (1900) Prof. Baknuurs Roozesoom published an
article “Sur l’équilibre de cristaux mixtes avec la phase vapeur’
in which he described and illustrated the pfx surface of a binary
system when exclusively homogeneous mixed crystals occur as a solid
phase. He treats the ease of unlimited miscibility in all phases and
especially for a system in which the melting point line proceeds
without a maximum or a minimum. He lias, moreover, limited himself
to the ease that the three-phase line solid-liquid-gas (SG) also oceurs
without a maximum or a minimum.
These matters have not been further investigated theoretically *) ;
there was in fact no inducement to do so, as there has been an
almost entire absence of experimental research. Only two investi-
gators, SPERANSKI*) and Kisrer*) furnished material as to the equi-
librium of mixed crystals with a gas-phase, whereas the researches
of Hoiiman*) belong to a category of more complicated phenomena.
I intend to carry out a series of investigations in order to extend
our knowledge of the systems showing a miscibility in the solid
condition. First of all, I will accept the facts already known and,
therefore will discuss at present, theoretically, the various possibilities
of the progressive change of the three-phase line indicated by
Roozerzoom (I.c.) and communicate later the results of an imvestigation
1) The results obtained by A. Smirs (Proc, (1908) XI p. 165, and Zeitschr. f,
physikal. Chem. (1909) 67, 464) do not differ from those of Roozesoom. The only
paper | know connected with this subject is a communication of Meyeruorrer :
“Ueber Reifkurven”, Zeitschr. f. pbysikal. Chem. 46, 379 (1903).
2) Zeitschr. f. physikal. Chem. 46, 70 (1903) and 51, 45 (1905).
5) Ibid. 51, 222 (1905).
4) Ibid. 37, 193 (1901),
( 538 )
as to the three-phase equilibria in the system p-dichlorobenzene —
p-dibromobenzene, the same system of which, thanks to KisTER
and Sppranskt (l.c.), we already know a series of solid-gas equilibria.
Fig. 1.
Fig. 1 is a combined P7' and Tvx-projection: O4 and Og are the
iriple points of the components. They are connected by the three-
phase line. In the 7% projection this lme divides into three branches
which indicate, respectively, the composition of the solid (S) liquid
(L) and gas (@) phases.
Since the influence of the pressure on the equilibrium ZS, is
very trifling and as triple-point pressures are comparatively low,
the branches S and £ may, usually, be taken as being equal
respectively to the melting-point curve and the freezing-point curve *)
at 1 atmosphere.
In fig. 1 is assumed 10) ee Po,,') which case we will call chief
type 1. We will now ascertain under what conditions three con-
ceivable cases might occur, namely :
case a@ with a maximum pressure in the three-phase line
im » minimum 3 9) » »
ce without a max. or min. ASE sth 56 a
”?
To get an insight as to the change of the pressure with the tem-
!) A (as is customary) is the name of the component with the lowest melting
point and with a vapour pressure greater than that of B at the same temperature.
*) In what follows we shall speak of these curves ‘as the branches of the
melting diagram.”
( 539 )
perature we must first of all proceed in the direction indicated by
Prof. vAN DER Waars') where he treats of the three-phase equilibria
of a binary compound with liquid and vapour.
To the yva-surface of the liquid and vapour condition another
one has to be added which shows the connection between those
quantities in the homogeneous solid phase. If we consider the case
occurring most frequently that the fusion takes place with an increase
in volume this surface will be found between the liquid-vapour
surface and the wa-plane.
As to the form of this new wve-surface it should be observed
that it will practically be a plane with descriptive lines proceeding
from the we-plane for «= 0, to that for 21. For the mixing of
two solid substances to a homogeneous solid phase takes place either
without a change in volume or with a hardly appreciable one’).
If we now wish to know which are the coexisting phases we must
allow tangent planes to move over these surfaces and thus cause
the appearance of the derived surfaces and connodal lines *).
4 , 3B Let us commence by considering a
surface for a temperature below the triple-
» point temperatures of the components.
, Lhe surface for the solid condition will
then be situated very low, the tangent
plane will rest both on this surface and
on the vapovr part of vapour-liquid sur-
face. The lines a,6, and g,h, in fig. 2
indicate the connodal lines so formed.
The derived surface thus obtained will be
situated lower than the derived surface
which rests on the two parts of the
vapour-liquid surface and which, there-
fore, does not represent stable conditions,
but the vapour equilibria of ‘super-
cooled” liquids. The connodal lines (c,d,
“ and ¢,/,) proceeding therefrom are situated
between the connodal lines of the solid-
Fig. 2. - vapour equilibrium.
If we proceed to a higher temperature the correlated connodal lines
S| é,
4
——
1) Verslagen Kon. Akad. V, p. 482, (1897).
2) Cf. Rereers, Zeitschr. f. physikal. Chem. 3, 497 (1889) and
GOSSNER, % ,, Kristallographie 44, 417 (1908).
3) In what follows, the question whether a minimum or a maximum pressure
is possible for the coexistence of two phases has not been considered. All nodal
lines are therefore supposed to proceed in the same sense,
approach each other ;
and metastable branches on the vapour part
especially at the side of the component
melting at the lowest temperature *). For
if we approach the temperature of the
triple point of this component the points
and g, of tig. 2 will have coincided
to the point e,g, in fig. 3, which is
intended for the temperature of O4 (fig. 1).
The two derived surfaces intersect each
other in the yo-plane of the component
A; that intersecting
the tangent to the w-line for the gas-liquid
condition of A and just the one which
is also tangent to the y-line of solid A
(triple point A).
By consulting fig. 4 it will be easily
seen What happens at a temperature
and also the stable
line is, of course,
( 540 )
situated between that of the two triple Fig. 3.
Fig. 4,
points. The rolling tangent plane coming
from the A side will now rest first on
the liquid- and vapour parts; but if a
certain nodal line pg is thus reached the
tangent plane. will rest also on a point
r of the surface of the solid phase. The
angular points of the three-phase triangle
pq’ give us the composition of the three
possible coexisting G, L, and S phases at
that temperature. By further motion of the
tangent plane a derived surface for GS
equilibria is formed, whilst also a similar
movement over the liquid part of the fluid
surface and over the surface of the solid
phase is possible in the direction of the
small volumina. Hence a new system of
connodal lines for ZS equilibria is formed
starting from 7 and g. Fig. 4, however,
will be plainly understood without further
colument and a discussion of the configurations at higher temperatures
will also be superfluous.
') The non-related connodal lines ab (solid) and cd (liquid) diverge from each
ther because as a rule the coefficient of expansion of a substance is smaller in
the solid than in the liquid state.
( 541 )
Prof. van per Waats (I. c. p. 490) has also taught us how to
deduce an expression showing the relation between p,é and w.
From the three equations
Vsdp — ysdt = diy, -+ asd (Mju, — M,u,)
Vidp — yrdt=dM,n, + a1d(Myu, — M,u,)
V gdp — ngdt =dM,u, + wgd(Mu, — M,u,)
1
follows
US YS 1
onenn Ll
dp v@ 7G 1 | #s(qL—Ne@) + #1 (NG—Xs) + «eG (Ys—yZ)
dt | #8 Vs 1 | «s(Vi—Ve) + #1{ Vg—Vs) +«g(Vs—Vi)
\ weve ea
| ay Vg l
This gives us a quite general expression for the three-phase line
in the systems described. It will, however, not be easy to arrive
through it to the desired elucidations. If, for instance, we wish to
dp
know when = will be equal to 0 the numerator thus becoming nought,
F
the question first arising is what do yz — yq@ ete. really represent.
KounstamM ') has rightly observed that such differences must not
be simply called heat of condensation ete. because 47 and yg do
not relate to the same mixture. And the second question as to the
numerical. value of those quantities in a system to be investigated
is still much more difficult to answer.
In order to get a first insight into these systems, I have taken
another course though of less general applicability. We will see how
the pressure changes in regard to the triple-point pressure of A, when
the liquid phase has the composition «, assuming that wy has a
very small value, in other words that but a very small quantity of B
has been added to A.
The temperature 7’, at which that liquid is in equilibrium with
a solid pbase, the composition of which is xs, is found from Roru-
MUND’s formula’) for very dilute mixtures :
Vand he
Tih,
(ita) EES Sy 3 (GN)
1) Proc. Kon. Akad. IX p. 647 (1907).
2) Zeitschr. f. physikal. Chem. 24, 710 (1897).
( 542 )
in which 7, is the temperature of the triple point O4.
The vapour pressure /, at the temperature 7’, is the sum of the
partial pressures of the components p4 and PB:
P,= pat PB
for which we may write
Ia Ie fainG 6 oo 0 8 (A)
if Py, represents the vapour pressure of liquid A at that temperature.
If now we call Py, the vapour pressure of A at its triple point
and use vAN ppR WaAAts’ well known formula for the saturated
vapour pressure we may write
Pees F yf,
l a 7
Pir de
Py nee T,.—T,
PT Tee
By subtraction we get:
IPP ine
ld toe ths
efi ae
2 Te
If now we substitute the value found in (1) for 7, we obtain
adil
jf — (¢s—21)
eT SE
thus writing (2) in this form:
RD
f— (#s—21)
P-— (=a) pene eee Sayiyeo a 0 (8)
If now case la (maximum pressure) is to occur, the three-phase line must
rise from Oy, to higher values of P and therefore P, > P7,. The
chance of seeing this case realised in a certain system, therefore depends
on P, having as great as possible a value in regard to Py, and relation
(3) shows us when this will be the case. For the first term — and
q
ws— evr will then be characteristic. The value of 2s — «xy is indicated
by the difference in initial direction of the branches of the melting
point lines for solid and liquid and this difference is determined
precisely by —'). When therefore we pay special attention to 7g — ay,
q .
') Compare van Laar, Zeitschr. f. physikal. Chem. 64, 257 (1908).
( 543 )
the first term of (3) will be large if 2s— ey is
large, that is to say when the initial directions
of the branches of the melting diagram line differ
greatly (Fig. 5a).
The second term of (3) the partialpressure of
the component # will as arule be greater *) when
t this component gets more volatile; as in the case
of this chief type I we have assumed that its
triple point pressure is smaller than that of A
we shall have the most advantageous conditions
; when they differ as little as possible.
Fig. 5. For the case Ia is, therefore, required 1. a
type of melting diagram with greatly diverging branches near the
A-axis and 2. about equal triple point pressures.
Case Ib (minimum pressure) makes two demands: from (4 an initial
fall, but followed by a rise; if this second demand is not fulfilled
we are dealing with Ic. This second demand means, of course,
a small difference of the triple point pressures; the first demand, a
small /, is, therefore, in regard to the value of pg in (3), opposed
to the second and is, in consequence, determined altogether by the
first term of (3). In order that this may be as small as possible it
is, of course, required that #s— vy shall approach O as closely as
possible, a demand which is complied with in a melting diagram
with branches almost coinciding in the initial direction. (Fig. 26).
We arrive ‘at an identical result if we start from the triple point
of B and examine the vapour pressure P,' of a liquid containing a
little of A, when that liquid can also coexist with a solid phase.
In this case the relations (1), (2), and (3) become:
IAB
P= = = (a5 — 2) ay ea a, 24 (eae)
q
P= pact on P 7, oo 0 oO oa “on a (eS)
Jeet!
BE (ee 2 ory
Pl sR e q SRW a 5 o (@Ue)
which will be readily understood on considering that the accentuated
signs have the same significance for 6 as the non-accentuated ones
had above for A.
In the case of Id the three-phase line must descend from JS, there-
fore P',< P’7,. Now first of all p4 should be at a minimum
1) Apart, therefore, from special differences in the critical quantities and of
special. influences of the components on each other.
( 544 )
which, on the same supposition as above, again demands about equal
triple-point pressures for A and 6; secondly, the exponent of e
with a negative sign should be as large as possible, which requires
widely diverging branches in the melting diagram at the side of the
component B.
These demands put from two sides are brought into agreement
by a conclusion of van Laar (loc. cit. p. 265) that closely adjacent
branches in the melting diagram at the side of the one component
cannot meet a similar configuration at the side of the other.*) If this
were possible, the occurrence of a maximum and a minimum in
one three-phase line would be quite possible.
In the case of Ib we therefore, require:
1. Melting diagram with branches nearly coinciding at the side
of the A-axis and 2. about equal triple-point pressures.
Case Ic finally occurs as an intermediate case between the two
previous extreme cases. Of course, the line O4 Og may be concave
or convex in regard to the temperature axis; this depends on whether
the conditions for Ia or Ib have been partially fulfilled. Let us eall
these cases Ic, and Ic, respectively. For definite forms of the melting
diagram points of inflection may probably occur, but our mode of
treatment is inadequate for their investigation.
A single remark may be made as to the chance of observing a
fall of the three-phase line starting from O4. As stated, the follow-
ing condition is required :
RT,
dp (e,— #,)
(l—#),) Pp e qd + Pp <P:
If now we imagine the most favourable circumstance, in which pp,
may be neglected (because the components differ, for instance, very
much in their melting temperature) the factor (1 —.«,) will cause a
awn
ij ‘
deerease and the factor e @ an increase in the value of
the first member in regard to that of the second one. For 1—a,
is always <1; the other factor is >>1 and only in the case of
@g =x, it is equal to 1: in that case a fall may be expected, but
as soon as vy and «2, differ in value the enlarging factor appears
and the said difference occurs therein exponentially. The enlarging
influence will, therefore, very soon exceed the other, so that the
chance for realising the case Ic will be diminished and that for Id
(2, —w_)
will be reduced to a minimum.
1) At least when we make the same suppositions as in the footnote on p. 543, .
( 545 )
B
Fig. 6.
Let us now consider a second category of possibilities, namely
Po,< Po, which case we will call chief type II.
We again distinguish three possibilities, viz.
a. maximum pressure in the three-phase line
6. minimum 0) 999 » ”
c. no max. or min. x ess 5 *
It will be superfluous to repeat the previous arguments when we
examine the initial directions in the equations (3) and (87s). The
conclusions arrived at are that we require for:
Case Ila: a melting diagram with closely joined branches at the
side of the component 4, and but slightly differing triple-point
pressures.
Case 11d: a melting diagram with closely joined branches at the
side of the component A, and but slightly differing triple-point
pressures.
Case IIe will be again the intermediate case between the two
previous ones; a concave (IIc,) and a convex (Ile,) course will
again be possible.
In a future paper, I hope to communicate the results of an expe-
rimental investigation of the system p-dichlorobenzene — p-dibromo-
benzene which has been going on already for a considerable time.
November 1909. Utrecht, van ’t Horr-laboratory.
ERRATA.
p. 488 line 16 from the top: for 1000 read 10000,
(January 26, 1910).
18
ry
KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.
PROCEEDINGS OF THE MEETINGS
of Saturday January 29 and February 26, 1910.
—————~oece-— -
(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 29 Januari en 26 Februari 1910, Dl. XVIII).
ClOMNG FE EET ANY Sass
Ii. A. Brouwer: “Pienaarite, a melanocratic fovaite from Transvaal”. (Communicated by Prof.
G. A. F. Moreneraarr), p. 547. (With one plate).
C. J. C. vax Hoocrennvyze: “About the formation of creatine in the muscles at the tonus and
at the development of rigidity”. (Communicated by Prof. C. A. PexkELHarrne), p. 550.
E. Reixpers: “Sap-raising forces in living wood”. (Communicated by Prof. J. W. Morr), p. 563.
K. Zisistra: “Contributions to the knowledge of the movement of water in plants”. (Commu-
nicated by Prof. J. W. Mott), p. 574.
- Zeeman and B. Wixawer: “The magnetic separation of absorption lines in connexion with
sunspot spectra”, p. 584. (With 3 plates).
. E. .). G. pu Bois and Koraro Hoypa: “The thermomagnetic properties of elements”, p. 596,
M. Jarcer: “Studies on Tellurium: I. The mutual behaviour of the elements sulphur and
tellurium”. (Communicated by Prof. P. van RomeurGn), p. 602.
J. J. van Laar: “Some remarks on Prof. Kownstamm’s reply”. (Communicated by Prof.
H. A. Lorentz), p. 618.
H. J. E. Bern: “The oscillations about a position of equilibrium where a simple linear relation
exists between the frequencies of the vibrations” (lst part). (Communicated by Prof. D. J
Korrewee), p. 619. (With one plate).
M. W. Beiserinck: “Viscosaccharase, an enzyme which produces slime from cane-sugar”, p.635.
(With one plate).
M. W. Betsertnck: “Variability in Bacillus prodigiosus’’, p. 640.
Pierre Weiss and H. Kamerticu Onxnes: “Researches on magnetization at very low tempe-
ratures”, p. 649. (With 2 plates).
ae]
rt
Geology. — “Pienaarite, a melanocratic foyaite from Transvaal.”
By H. A. Brouwer. (Communicated by Prof. G. A. F.
MOLENGRAAFP.)
(Communicated in the meeting of November 27, 1909).
Among the nepheline syenites on and to the west of the farm
Leeuwfontein to the north-east of Pretoria, which show a complete
series of varieties in chemical and mineralogical composition, the
“collection MOoLENGraarr’’ contains a variety very rich in titanite,
which occurs 1/, mile to the west of the Pienaarsriver near the
boundary of the farm Zeekoegat.
Macroscopically the rock shows red felpars to 1 em. up in length,
which have a tabular development after (010), and smaller crystals
of red nepheline, with which contrast numerous slender prisms of
aegirine and bright crystals of titanite, which make up over half
of the rock.
37
Proceedings Royal Acad. Amsterdam. Vol. XII.
(548 )
Under the microscope the rock is seen to consist of felspar, nepheline,
less sodalite, much aegirine, (aegirine augite) and titanite and small
quantities of apatite, fluorine, calcite, analcime, and titanic iron ore.
The felspars are orthoclase and microperthite in Carlsbad twins.
Nearly always nepheline and sodalite are transformed, respectively
into pseudomorphoses of mica and zeolites. In the crystals of nepheline,
which are not entirely transformed into mica, the transformation begins
along the fissures, but nearly all the erystals are entirely altered.
The sodalite pseudomorphoses consist of zeolites, in which we find
distributed some small flakes of mica.
The aegirine is strongly pleochroic from olive-green to yellowish
green, some crystals are homogeneous, other ones contain a centre
of aegivine augite, which has for the greater part very low extinction
angles; they are very rich in inclusions of small crystals of titanite
and apatite, and they are strongly impregnated with fluorspar.
The titanite forms the well known twins after (O01), in the
rhombie sections the long diagonal is the twinning plane; both
individuals are polysynthetically twinned. They are pleochroic from
salmon coloured to colourless.
The apatite ‘is the first product of crystallization, it is even formed
as small idiomorphie inclusions in the titanite, for the greater part
the crystallization of the other elements was simultaneous ; the aegirine
is idiomorphic in relation to felspars and felspatoids but in general the
contactlines are irregular and show simultaneous crystallization. The
felspar includes some idiomorpbie crystals of nepheline and sodalite,
mainly it is the latest product of crystallization. Probably in pneuma-
tolytical way, fluorine, calcite, and analcime erystallized in the remaining
cavities.
It is evident how much the mineralogical composition of this rock
differs from that of the normal types of nepheline syenite by its
high content of aegirine and titanite. A. Lacroix’) gave the name
of covite to the mesocratic form of this group and of teralite to the
melanocratic form; as the type of covite he considers the rock of
Magnet Cove in Arkansas, described by Wasnineton and as type
of teralite the alkali felspar-nepheline rocks from the Crazy Moun-
tains in Montana.
The chemical composition of the rock here described is shown
in I of the following table (analysed by F. Pisani); it is compared
with the analyses of some covites and teralites.
1) Matériaux pour la Minéralogie de Madagascar. Extr. nouy. Arch. du Museum,
4e serie, Tome 1, pag. 184.
H. A. BROUWER. “Pienaarite, a melanocratic foyaite from Transvaal.”
Explanation of Figure.
(X< 30).
A part of a large individual of felspar shows poikilitic relation to aegirine,
titanite, nepheline (at the top to the left) and sodalite (at the lower edge, in the
middle and to the right).
The aegirine contains numerous idiomorphic inclusions of titanite, apatite and
fluorspar
i]
- Proceedings Royal Acad. Amsterdam. Vol. XII.
ie. | a m | ow V VI
SiO, | 49.20 49.70) a1 10 | 47.67 | 44.65 | 47.85
TiO, 7.13 1.33 1.38 | Joo |) WEE | =
Al,O, 9.23 48.45 | 21.40 | 418.92 13.87 13.24
Fe,0, ae 3.39 0.90 | 3.65 | 6.06 | 2.74
FeO 3.9% | 4.39 5.58 | 3.85 | 2.94 | 2.65
MnO = Bs Se) Oe oe =
CaO 14 55 7.91 5.35 8.03 9.57 | 44.36
MgO 1.35 2.39 2.81 6.35 5.45 5.68
Na,O 6.20 Beooet| nessa 4.93 5.67 3.72
KO 1.96 4.95 | 4.91 | 3.82 4.49 5.05
P.O, 0.06 O40) Wye | = 2:97 al, sono 2.14
H,0 2.20 N3Ee | V0:87 | 4.50 | 2.49
| | = — es
Som 99.85 | 99.44 | 99.65 | 400.145 | 99.93 | 400.65
| |
—_
Pienaarite. Leeuwfontein (3820) Pretoria. Transvaal.
II. Covite. Magnet Cove. Arkansas cf. H. S. Washington. Journ.
of Geol. IX. 614. 1901.
III. Covite. Nosy Komba. ef. A. Lacroix Mat. Minéral. Madagascar
Extr. Nouv. Arch. du Museum 4e Ser. I. 32.
IV. Teralite. Crazy Mountains Bull. U. S. Geol. Surv. no. 150.
V. Teralite. . ” »” ” »” ”» > ” ”
”
VI. Teralite. (nepheline pyroxene malignite) ef. A.C. Lawson Bull.
Dep. of Geol. Univ. of California I. 337. 1896.
We see how the rock, here described, differs in mineralogical and
chemical composition from the melanoeratic nepheline syenites, which
are hitherto known, its characteristic features are the large amount
of Fe,O0,, TiO,, and CaO (abundance of aegirine, aegirine-augite
and titanite) and its low content of lime (diminuation of the felspars
and felspatoids). Prof. MoLENGrAArr proposed to me the name Pienaarite,
after the Pienaarsriver because the locality, where he collected this
rock, is situated in a region between a tributary of the Pienaarsriver
called Mundtspruit, and the above river itself.
one
( 550 )
Physiology. — Prof. Prkennarine offers a communication, also in
‘
the name of Dr. C. J. C. van Hooernnvuyze: “About the for-
mation of creatine in the muscles at the tenus and at the
development of rigidity.”
(Communicated in the meeting of December 24, 1909).
On a preceding occasion’) in this Academy I have made a com-
munication concerning an investigation by Mr. van Hoocrnnuyze and
Mr. VerreLorcy about the exeretion of creatinine in man, from which
it appeared that the excretion of this substance in a sufficiently nourished
person was not increased by muscular labour. Since that time the
investigation, which promised new results, now that a good method for
the determination of the creatinine had been furnished by Four, has
been continued by Van Hoocrnsuyze and VerpLorcn and by several
others. From these investigations has arisen the opinion that, through
the consumption of protein in the tissues of vertebrate animals,
creatine is formed, and that this matter is partly decomposed under
oxidation, partly, particularly by the liver, changed into the anhy-
dride, creatinine, that further the creatinine thus formed is for the
greater part removed from the body through the kidneys ’*).
If this opinion is correct, one cannot but assume that the creatinine
excreted by the kidneys, originates for the greater part from the
creatine of the muscles, not only because the muscles are richer in
creatine than other organs, but also because it is especially the mus-
cles which contain so considerable a part of the proteis which the
body contains. This supposition did not seem unacceptable, notwith-
standing it has been found that the excretion of creatinine is not
increased by muscular labour. Observations were made which pointed
to a connection between the excretion of creatinine and another
phenomenon, which has to be distinguished from the muscular con-
traction in a narrower sense, the muscular tonus. Van Hoocrnnuyze
and VerrLorcn found the exeretion during the night to be smaller
than in the daytime; likewise did they find remarkably little creati-
nine in the urine of old men and of patients who had a number of
muscles paralyzed, whereas in case of fever the urine appeared to
contain more creatinine than usual.
That really the tonic shortening of the muscle is brought about
in another way than in case of rapid contraction, which has been
examined so much more, and that, when a single stimulus is followed
1) Proceedings of the meeting of 30 Sept. 1905.
) See: Zentrallbl. f£. d. ges. Physiol. und. Pathol. d. Stoffwechsels. 1909. No. 8.
(7554)
by a slow contraction, the two ways collaborate, is rendered very
probable.
Already more than 20 years ago GritzNur') made the supposition
that the long continued contraction was brought about by another
kind of muscular fibres than those which cause a more rapid con-
traction. In the first case fibres of the type of the red, in the second
fibres of the type of the white muscles, were supposed to be brought
into play. Afterwards others, more particularly Borrazz1?), have
defended the theory that the double contraction is caused by two
different component parts of the same muscular fibre, the rapid by
the double-refracting fibrils, the slow ones by the sarcoplasmia.
Mosso*) had objections against this theory and drew attention to the
double innervation of the muscular fibres, not long ago once more
made clear in this Academy by Bowker‘).
Meanwhile, .whatever the opinion may be, at any rate there is
some reason to assume that the contractions of two kinds must be
accompanied by a chemical action of two kinds. Now that in the
usual muscular labour, which is principally based on rapid and
tetanie contractions, no increase in the consumption of protein and
in the excretion of creatinine was found, it might be asked, whether
perhaps in the tonic contraction formation of creatine in the muscles
could be proved.
That under certain definite circumstances the muscles at their
contraction yield more creatine to the blood than otherwise, has
already been found by Weber’), with respect to the heart treated
after Lancenporrr’s method and beating in Rrnaur’s solution. He
also found a considerable increase in the excretion of creatine with
a dog, after violent cramps had been caused in the animal with
cinchonine. Not only in the last case, in which the animal for’
an hour “was in violent tonic and clonic cramps’, but also “with
respect to the heart taken from the body, it may be assumed that
tonus has played a part.
However, in order to draw more certain inferences, we have
examined the quantity of creatine in muscles, under circumstances
which, as much as possible, allowed to judge about the influence,
either of tonic, or of rapid contractions.
1) Prricer’s Archiv. Bd. XLI, S. 280.
2) Journ. of Physiol. Vol. XXI, p. 1, Arch. f. Physiol. 1901, 3. 377, Arch. Ital.
de Biol. T. XLII, p. 169.
3) Arch. Ital. de Biol. T. XLI, p. 183.
4) Proceedings of the Meeting of 23 April 1909.
5) Arch. f. exp. Path. und Pharm. Bd. LVIII, 8. 93.
( 552 )
The determinations always took place in the same way. The minced
muscles were for some hours at a stretch boiled in 0.1°/, HCl, im
consequence of which the tissue breaks altogether and all the creatine
passes into the liquid. By evaporation the extract after being freed from
protein, was concentrated and then with then double volume of normal
HCl heated to 115° C. in the autoclave for half an hour, by which
the creatine is completely changed into creatinine. Then the determi-
nation took place, according to the method of Fortin, with the colori-
meter formerly shown in the meeting of this Academy.
First of all we have some observations to mention about decrease
of the quantity of creatine in muscles, of which the tonus, in conse-
quence of section of the nerve, was eliminated. In the outset we
came to very irregular results when examining the muscles of the
hindlegs of rabbits and of a young dog, after a one-sided cutting of
the nervus ischiadicus. Now less creatine was found in the muscles
of the paralyzed leg, now more creatine in those of the paralyzed
side. The cause of this irregularity appeared to be that we did not
compare exactly corresponding muscies. Especially in the rabbit the
difference in quantity of creaine in white and red muscles is rather
considerable. With 10 rabbits we found in the gastrocnemius or an
average 4.463, in red muscles (soleus, semitendinosus and semimem-
branosus examined together) 2.925 mgr. creatinine in | grm. of the
muscle.
When this source of error was avoided, the influence of section
of the ischiadicus became clear. With 3 rabbits we have, taking
into consideration what has been said above, repeated the experiment
and three days after the section of the nervus ischiadicus, we have
examined the gastrocnemius of the paralyzed and of the not paralyzed
leg. We found:
Not paralyzed. Paralyzed. Loss after paralyzing.
I 4.708 4.232 0.471 mer. cr. p. gr. of the muscle
Il + 4.448 4.289 0159 i Fests oa" -35 a
UI 4.983 4.013 O91 ee eee nc s
Although the differences found lie without any doubt beyond the
limits of the errors of observation, yet we have not continued these
experiments, because too little can with certainty be concluded from
them concerning the influence of the tonus. It is true, the muscles of
the leg the ischiadicus of which has been cut through, are distin-
guished from those of the other side by the loss of tonus, but there
are also other differences, which are perhaps of importance, as WrBer
has already observed, who also found the quantity of creatine in
the muscles of the paralyzed leg smaller than in those of the normal
leg in a dog after section of the ischiadicus. That the normal
lee continues performing voluntary movements, is no objection, there
being no ground to assume that then creatine is formed. But the
muscles of the paralyzed leg degenerate. Although we killed the
animals already three days after the section of the nerve, yet every
time the paralyzed gastrocnemius appeared to be of asmaller weight
than the normal one. Nothing is known about the formation and the
destruction of creatine in degenerating muscles. Of no less importance
seems to be the change in the circulation of the blood after section
of the nerve, in consequence of which the removal of creatine from
the muscles may be altered in a quite incalculable degree.
On account of these objections we thought of entirely giving up
the attempt to inquire into the influence of the muscletonus in warm-
blooded animals, and of being obliged to occupy ourselves only with
cold-blooded vertebrates, in which without any trouble the blood-
circulation can be shut out (in muscles of invertebrates no creatine
has been found; they were not fit for our purpose accordingly) when
my colleague Prof. R. Magnus drew our attention to a means of
bringing muscles of one half of the body of a cat into strong tonus,
whilst the corresponding muscles on the other side, without any
disturbance in the action of the centrifugal nerves and in the cireu-
lation of the blood, remain slack.
SHERRINGTON ') has found that, when in deeply narcotised dogs,
monkeys, cats, rabbits or ecavias, the action of the cerebral hemi-
spheres is excluded by a section in the region of the hindmost
corpora quadrigemina, after a short time the so-called ‘“decerebrate
rigidity” develops itself, a long continuing tonic contraction of definite
muscle-groups, among which especially the extensors of the extre-
mities and the retractors of the head and the neck are the chief.
This state of things is dependent on impulses which arise in the
periphery, and by centripetal nerves are led to the spinal cord. That
1s why ‘the stiffness does not arise in those parts of which the
corresponding dorsal roots are severed.
Now Prof. Maenus had the kindness to operate upon five cats in
such a way that one foreleg was brought in tonus two, three hours
at a stretch, whilst the other leg remained slack. The perfectly nar-
eotised animal, the narcosis being brought about first by means of
ether, then by means of chloroform, after section on the left side
of the hindmost roots of the four or five lowest cervical nerves and
of the two highest thoracic nerves was decerebrated. Soon, the right
1) Journ. of Physiol. Vol, XXII, p. 319.
( 554 )
leg got into tonus, the left one remaining slack. Sometimes, in order to
strengthen the tonus in the foreleg, also the’ spinal cord, at about
the eleventh breast-vertebra, was cut through. When the tonus had
lasted a few hours, the animal was killed by suffocation. Directly
after the triceps brachii on both sides was prepared, minced and put
into hydrochloric acid.
In all experiments we found the muscle that had been in tonus,
richer in creatine than the one that had remained slack, and that,
expressed in mgr. creatinine on 1 grm. muscle, as follows :
Tonus Slack Difference
I 3.690 3.090 0.600
II 4.840 3.848 0.492
II] 4.291 3.902 0.317
IV 3.806 3.185 0.621
Ve 398 2.963 0.235
It is remarkable that this difference pretty well keeps pace with
the difference that in the experiment of the contraction of the muscles,
right and left, was observed. In experiment I and still more in IV,
the stiffness on the right was very beautifully developed, in II the
tonus was strong, but of a shorter duration, in III the tonus on the
right was good, but also the left foreleg occasionally showed some
stiffmess, which also occurred in V, though in a smaller degree,
whilst the stiffness developed here slowly and to not so high a
degree as otherwise. .
We think we are entitled to derive from these experiments that
by the muscles in tonus more creatine is formed than by those
which are slackened. For the supposition that the difference may be
attributed to an increased decomposition of creatine in the slackened
muscles, it seems that there is not a single ground to be adduced.
Besides this we have made a number of experiments with frogs
(Rana esculenta).
In the first place the influence of irritation with induction-currents
on the quantity of creatine in muscles was examined. About this
communications have been made by Mer.uansy') and by Granam
Brown and Carucart*). By direct irritation MrLLansy brought the
muscles in tetanus and then he found so slight an increase of the
quantity of creatine that he came to the result: ‘that the perfor-
1) Journ. of Physiol. Vol. XXXVI, p. 447.
*; Bio-Chemical Journ. Vol. LY, p. 420.
mance of muscular work leaves creatine unaffected”. Brown and
Carucart stimulated the muscles by means of the nerve and found
a somewhat more considerable increase, of 7°/, a 13°/,, in four
experiments, at which the circulation of the blood had been excluded.
If the circulation was intact, they found a little diminution, not only
with frogs, but also with rabbits, where it ought, however, to be
taken into consideration that, in consequence of the stimulus, the
muscle was more amply provided with blood, so that an exact
comparison with resting muscles is scarcely possible.
We have made experiments with frogs, in three different ways,
always excluding the current of blood. First, after destroying brain
and spinai cord and after section of the heart, the nervus ischiadicus
on one side, laid bare high in the thigh, was cut through and stimu-
lated with a series of rapidly succeeding induction-strokes. Each stimu-
lation lasted */, minute, after which */, minute of rest was afforded,
during about one hour. In the second place the experiment was for
the rest. made in the same way, but the nerve was, for about half
an honr, with the help of ENGrLMany’s rhythmic polyrheotome, stimu-
lated 24 times per minute, alternately with a closing and an opening
induction-stroke. At last two more experiments were made thus: the
frog was cut through transversely in the lumbar region, after which
the skin of the hind part was taken away. Now this was put astride
on the partition of two basins of celluloid, standing against each other
and filled with RineGer’s solution, so that each leg was immersed into
the liquid to about half way up the thigh. Then the ischiadieus was
on one side, from the pelvis, stimulated for half an hour, 24 times
a minute, with single closing and opening induction-strokes.
The quantity of creatine, expressed in mgr. creatinine per 1 grm.
of muscle, was found as follows :
Stimulated Rest Difference Stimulated Rest Difference
I 3.490 3.418 + 0.072 | I 3.5668 oo 5001020
Il 3.5387 3457 + 0.080 A Ti 3.616 3.683 — 0.067
eB Ill 3.629 3.550 + 0.079 | Ill 3.796 3.856 — 0.060
IV 3.567 3.560 -+ 0.007
C I 3.203 3.230 — 0.027
ilies boy atotooS ——O008
The differences are slight and do not fall, or fall scarcely, beyond
the boundaries of the inevitable errors of observation. Moreover the
difference is now in favour of the stimulated, now of the not-stimulated
muscles. Even if one wishes to attach some importance to the greatest
( 556 )
differences found in these experiments, one need not yet derive from
them that the muscle during the rapid contraction forms or loses
creatine. For on the one hand the decomposition of creatine in the
muscle is no doubt subject to quite unknown, but certainly varying
influences, whilst on the other hand long continued irritating can also
give rise to some lasting contraction, tonus.
That in the frog during the muscle-tonus in contradistinction to
the rapid contractions, the quantity of creatine in the muscles increases,
whilst, in default of tonus, it decreases, appears from the following
experiments.
In the first place the influence of the elimination of the tonus, by
excluding the innervation, was examined, first while the current of
blood was stopped, then with undisturbed circulation of the blood. In
the former case the ischiadicus was on one side cut through and
then an both sides the root of the thigh was so well tied up with
an elastic ligature that the blood in the vessels of the webs stood
still, in such a way that the ligature ran below the ischiadicus not
eut through. In the latter case the ischiadicus was simply cut through.
Three days after the section of the nerve the animals were killed
and the muscles of the hindlegs examined.
intact cut difference Intact cut difference
I ES aelaye OOS" I 3.784 3.342 0.442
II 2.678 2.282 0.1396 Il ~ 4.000 ~ 3:653)—) 0134%
LI 29901 22790) 103200 Ill 4446 3.688 0.458
(IV 92:98%) 22887, = O00 3.490) S592 Ons
Vi 226 Re ool) ee Onli(5 V 34384 3.131 0.303
VI 2.833 22688 9 Of-f5 VI 3.685 3.3834 01351
Vil esha 32:900 OOM
peddojs poojq jo yuating
paginjsipun pooyq jo Juating
=
Without any exception, therefore, there was found in the muscles
that had lost the tonus for three days, less creatine than in the
unhurt leg. If the current of blood was stopped, the difference was
smaller than when it went on undisturbed. Yet in the tied up legs
the quantity of creatine was, also on the side of the unhurt nerve,
smaller than it is usually found in the frog. It is therefore probable
that on both sides, after the current of blood had been stopped,
creatine was decomposed. With respect to the experiments with
undisturbed circulation of the blood the same_ objection may be
raised which has been made mention of concerning similar experi-
ments with the rabbit, viz. that it is unknown how far; perhaps
(aN)
by a change of the current of blood, the removal of creatine from
the muscles is altered. It is, however, not to be assumed that the
differences observed should be attributed to this.
With much more certainty, however, the connection between tonic
contraction and formation of creatine in the frog may, in our
opinion, be derived from another series of experiments in which,
with exclusion of the current of blood, muscle-tonus was caused.
We have exposed the muscles to the action of substances of quite
different nature, which, however, resemble each other in the fact
that they cause tonus, viz.: veratrine, nicotine, calciumchloride
rhodan-natrium and coffeine.
Tt is especially Borrazz1 who has pointed out the tonicizing action
of veratrine’). If the gastrocnemius of a frog is immersed in Rincrr’s
solution containing 1; 20000, or even less, veratrine, stimulation
of the ischiadicus with a single induction-stroke causes a contraction
which lasts much longer than with a muscle immersed in pure
Rincer’s solution. To the rapid a slow contraction is added.
In order to examine the influence on the formation of creatine
the hindlegs of a frog were brought into the above mentioned cellu-
loid basins, of which one was filled with Rriegr’s solution, the other
with the same solution, in which a definite quantity of veratrine
had been dissolved. Now the two ischiadici were, from the pelvis,
during half an hour, stimulated 24 times per minute alternately with
a closing and an opening induction-stroke. After that the muscles were
prepared off, and with the liquid in which they had been immersed,
treated in the usual way for the determination of creatine. The
result was:
RinGeEr’s solution Veratrine. Difference.
(1 : 40000)
I 3.442 3.561 0.119
(1 : 20000)
ee slS9 3.389 0.200
(1 : 5000)
III 3.056 3.430 0.374
IV 3.250 3.670 ; 0.420
(1 : 1000)
Ve 32029 3.429 0.400
In III, IV and V the legs immersed in veratrine ceased to con-
tract before the half hour had elapsed. besides these legs showed in
the end some stiffness in these experiments.
1) loe. cit.
( 558 )
The faculty of nicotine to cause tonic contraction of muscles, has
been amply studied by Laneiny in his experiments on receptive
substances’). The forelegs of the frog, the flexors of which are so
easy to bring in tonus, also by dripping with nicotine, would have
been very fit for our purpose, if not the mass of the available
muscles was so small that for a single determination of creatine a
large number of frogs would be necessary. The experiments of
Lanetny, however, made us surmise that also the hindlegs would
be fit for our purpose, which surmise was corroborated by the result.
First an experiment was made as follows:
After destroying brain and spinal cord 1 CC of a 1 °/,-solution of
nicotine in RineEr’s solution was injected into the abdomen, after
which the tonie contraction of the forelegs soon made itself manifest.
Half an bour after the injection the current of blood, by section of
the heart, was brought to a standstill. Now the left ischiadicus was
laid bare in the upper part of the thigh, ent through and for
half an hour stimulated 24 times per minute with induction-strokes.
Till the end the muscles reacted upon the stimulation of the nerve
and at last a slight rigour was to be observed.
The stimulated muscles produced 3.491 mgr. of creatinine per
erm. of muscle, the non-stimulated 3.090 mgr. Difference 0.401.
Then the experiments were made in the same way as with vera-
trine, with the following result :
Rryeger’s sol. Nicotine. Difference.
(1: : 100)
I 3.286 3.766 0.480
Il 3.090 3.492 0.402
(1 : : 200)
Il 3.276 3.538 0.262
(1 : 100)
IV 3.037 3.401 0.364
At the end of the experiment the leg immersed in nicotine did
not visibly contract any more and each time this leg was some-
what. stiff.
Through an examination of the action of kalium- and caleium-salts
also Gurntuer®) has come to the result that the muscular fibre
possesses contractile substances of two kinds, one of which is made
more susceptible to stimulation by K, the other by Ca.
1) Journ. of Physiol. Vol. XXXII, p. 374, Vol. XXXVI, p. 347, Vol. XXXVI,
p. 165, p. 285, Vol. XXXIX, p. 235. Proc. Royal Soc. B. Vol. LXAXVIL, p. 170
2) Amer. Journ. of Physiol. Vol. XIV, p. 73.
559 )
“The first contractile substance of the sartorius”, he says, “responds
quickly with a contraction when subjected to a 1 percent solution
of potassium chloride. Caleium chloride in a 1 percent solution
produces no contraction of the first contractile element of the sar-
torius, gives rise to a slow contraction of the second contractile
element, and produces quite a vigorous contraction of heart muscle.”
We had, therefore, to expect that excitation of muscles immersed
in calciumehloride would make the quantity of creatine increase.
Indeed this appeared to be the case. One basin was now filled with
Rinekr’s solution, the other with a solution of CaCl, isotonic with
it. For the rest the experiments were made in quite the same way
as the preceding one. The results are the following :
Rincer’s sol. CaCl, 0.72 °/, Difference
I 3.177 3.820 0.643
Il 3.193 3.703 0.510
III 3.340 3.894 0.554
IV 3.040 3.647 0.607
V 3.156 3.501 0.345
In the first four experiments the contraction of the muscles immersed
in CaCl, left off before the half hour was past and these muscles
showed distinct stiffness. In V the contractions of the muscles immersed
in CaCl, were at the end of the experiment clearly to be observed
and stiffness was not to be perceived.
To the examination of the action of rhodane and coffeine we were
led by a communication of von Fiérra and Scuwarz’), from which
it appeared that these substances, like e.g. veratrine, are able to con-
siderably increase the labouring faculty of the muscles. The supposition
that also here the tonus, the ‘innere Unterstiitzung’, of which
GritzNer spoke, was playing a part, we found corroborated. The two
gastrocnemii of the same frog were hung, one in a vessel with
Rinerr’s solution, the other in a vessel with the same liquid in which
some citras coffeini was dissolved, or of which the sodium chloride
had been replaced by rhodan-natrium. After both muscles, under
the same tension, had been fastened to registrating levers, they were
now and then, by means of the nervi ischiadici laid upon a single
couple of electrodes, excited with an induction-stroke. Now while
the muscle immersed in RuineGur’s solution after each contraction
returned to its former length, or was even somewhat lengthened,
1) Pruiiger’s Archiv, CXXIX, S, 525.
( 560 )
the muscle brought in contact with coffeine or with rhodane, whilst
it continued reacting well upon the excitation, became gradually not
inconsiderably shorter.
The influence upon the quantity of creatine was examined in the
usual way. The following figures were found :
Ringers’ sol. NaCNS 0.614°/, Difference
I 2.822 3.098 0.276
II 3.106 3.304 0.248
il 3.051 3.937 0.486
IV 3.129 3.459 0.330
Vi 222916 3.146 0.230
Towards the end of the experiment the muscles did not contract
any more. Stiffening was not to be perceived.
Ringer’s liq. Citr. Coff. Difference
1 3.017 3.432 dl) 0.415
I] 3.055 3.623 1: 200 0.568
Ill 3.090 3.422 — 1: 400 0.332
IV 3.194 3.551 1 : 400 0.357
Vv 3.316 3.519 1: 800 0.203
The leg brought in contact with coffeine was in I quite stiff after
10 minutes, in II after a quarter of an hour, the contractions leaving
off. In Il, IV and V the contractions remained visible till the end
of the experiment. Also in those cases the rigour was clear, though
in V not so strongly as in III and IV.
In all cases, without any exception, therefore, the quantity of
creatine was found to be increased in the muscles that had been in
tonus. The difference, except with coffeine, may even be estimated
somewhat higher than the figures given, because, leaving the men-
tioned exception out of consideration, the tonus appeared to be
accompanied by a slight increase of the quantity of water. This
difference is, however, so insignificant that it need not be taken into
consideration.
Increase of the quantity of creatine was found only then when
the muscles had been brought inte tonus by excitation. Immersion
of the legs, during half an hour, in the solutions, without excitation,
had no influence upon the quantity of creatine. ‘The following expe-
riments were made in the usual way, only with this difference, that
the nerves were not excited.
( 561 )
RinGEr’s sol. Veratr. 1 : 5000 Difference
3.954 3.954. 0
Nicotine 1 : 100
3.544 3.910 0.034
CaCl, 0.72°/,
3.399 3.394 0.005
NaNCS
3.340 3:00 0.004
Coffeine 1 : 100
3.295 aah 0.032
In none of these cases was anything to be perceived of stiffness
of the muscles.
Therefore our results are perfectly in keeping with the opinion
that the muscular fibre, when reacting upon a stimulus with a rapid
contraction, works in quite another way than when it is brought in
tonic contraction. In the first case it consumes non-nitrogenous matter,
in the second it forms creatine, consequently consumes protein.
Against the supposition of GritzNer that each of these actions should
belong to a special kind of muscular fibres, tells among others our
experience, that, with the rabbit, it is just the red muscles, which
are distinguished for slowness in contraction, that contain less creatine
than the white ones. Though the opinion of Borrazzt that muscular
fibres show the phenomenon of tonus the more, as they are richer
in sarcoplasma, as has already been pointed out by Mosso, is not
quite in keeping with the observations, it may, however, especially
after ENGELMANN’s imporiant researches, be assumed that the rapid
contraction is performed by the anisotrope elements, accordingly by
the muscular fibrils. The seat of the tonus must therefore be sought
in the sarcoplasma or perhaps in the parts of the fibrils between
which the anisotrope elements find a place. In a further investigation
into the two different kinds of contraction of the muscular fibres it
will certainly be of importance to keep the attention also directed
to the double innervation again demonstrated by Borkr.
As to the starting-point of our investigation we think we are
entitled to give an affirmative answer to the question whether the
formation of creatine, and consequently the consumption of protein
in the body, is largely influenced by the tonus of the muscles.
Already many years ago it was proved by Pritcer') of how great
an importance the muscular tonus is for the production of heat. If
our opinion is correct, it also follows from this that limitation in the
supply of protein with the food, which is at the present day aimed
1) Pritieer’s Archiv., Bd. XVIII, S$. 247.
( 562 )
at by many, has its dangerous side. Mechanical labour the muscles
can perform at the cost of food free from nitrogen; however to be
of service to the organism, also in other respects, by means of the
tonus, they want protein.
The opinion has offen been pronounced that the stiffening of the
muscles after death should be considered as a Jast contraction of the
muscles. Especially Hermaxn has indicated the agreement between
the changes the muscle undergoes at coagulation and those which
are observed in the contraction. In the above mentioned paper of
Von Férta and Scuwarz it is proved that it is such substances espe-
cially, which are capable of promoting the coagulation of the muscle-
plasma, that raise the labouring-faculty of the muscles.
It seems that the agreement does not refer to the rapid contraction
but to the tonus. We have found an increase of the quantity of
creatine in frog-muscles which were stiffened by immersion in water
of 42° or 45° C. In four experiments the increase amounted on an
average to 0.305 mer. creatinine on 1 grm. of the muscle (min.
0.204, max. 0.460 mer.).
For the rabbit the investigation offered some difficulties, because
here the decomposition of creatine, proved by GortLims and STANGASSINGER
plays an important part and the so much thicker rabbit-musele is
not so rapidly coagulated as the thin muscles of the frog. When,
however, the errors arising from this are avoided as much as possible,
also in the majority of cases, both with the red and the white
muscles of the rabbit, a distinct increase of the quantity of creatine
was observed in the stiffened muscles.
Also in the investigation into the spontaneous stiffening of muscles
after death, the postmortem disappearance of creatine has to be taken
into consideration. When, however, the muscles of one side of the
body were, directly after death, put in hydrochloric acid and the
corresponding muscles of the other side after three or four hours
when the stiffening had been well developed, each time there was
found more creatine in the coagulated muscles than in those examined
in a fresh condition. In the four cases dealt with in this way, we
found an uncommonly great difference in one, and in the three others
on an average 0.260 mer. of creatinine more (min. 0.124, max. 0.336
mer.). The description in details of these and the other observations
mentioned we intend to give somewhere else.
From our investigation we think we are entitled to derive that in
the muscles of vertebrate animals, at the heat-coagulation and the
postmortem rigour as well as the tonus, a chemical process takes place
which causes the origination of creatine.
(563 )
Botany. — “Sap-raising forces in living wood.” By HK. Reinvers.
(Communicated by Prof. J. W. Mott).
Of the many theories, which have been advanced in explanation of the
transpiration-current of trees, most are at present only of historical impor-
tance in the literature. The imbibition theory of Sacus*); BOuM’s atmos-
pheric pressure theory *); the gas pressure theory of Harrie *); the views
of WesTeRMAIER ‘), who regarded the xylem parenchyma as the water
conduit and considered the vessels to be reservoirs; Ewart’s °) hypo-
thesis that the living elements help te overcome the resistance, the
cohesion theory of AskrNnasy *). which neglected to adopt the conti-
nuity of water as a conditio sine qua non all these have been
given up. On the other hand opinion is still divided with regard to
two hypotheses, the advocates of which combat the views of their
respective opponents with remarkable asperity. GopLEwsk1') and his
supporters defend the view that the transpiration-current cannot be
explained without postulating the cooperation of the living elements
of the wood; Dixon and Jory‘) on tie other hand advance the
proposition that the living elements have not, and cannot have,
anything to do with the process. They explain the phenomenon that
water ascends up to the summits of the highest trees by assuming
that in these trees the water, enclosed in the narrow water conduits,
hangs like a thread from the surface of the leaf cells, where it is
held by capillary or other physical forces. The thread does not break,
because, as is supposed, it is nowhere in contact with air, and in
these circumstances water can support a tension of 150 atmospheres.
When the water evaporates in the leaves at the summit, this thread
is drawn up through the tissues.
The keenness with which the two parties oppose each other is
best illustrated by a couple of quotations.
ScHWENDENER ’), an advocate of the more physiological theory,
Says :
«An der Vorstellung, dass die Lebenstiitigkeit der Zellen irgendwie
in die Saftbewegung eingreift ist . . . . unbedingt festzuhalten. Ohne
dieses Eingreifen ist die Hebung des Wassers auf Héhen van 150-200
Fuss und dariiber einfach unméglich und alle Bemiihungen, die vor-
handenen Schranken mit unklaren physischen Annahmen zu durch-
brechen, sind nicht viel mehr als ein Suchen nach dem Stein der
Weisen ’.
In the same year 1909 Dixon *°) writes:
“The adhesion of writers to the vital hypothesis .... is so
38
Proceedings Royal Acad. Amsterdam. Vol. Xil.
( 564 )
remarkable that we must devote some space to examine fully the
grounds for their contention”.
When we attempt to trace why opinions diverge so widely, the
cause seems to lie principally in a different appreciation of certain
experiments and in the somewhat adventurous aspect which the
Dixonian explanation presents at first sight. It is necessary to become
accustomed to the idea that the life of our trees hangs upon a water-
thread, before we can become reconciled to it. GopLEWskI '') indeed
required a much more adventurous hypothesis in order to reconcile
the anatomical structure of the wood with its power of pumping up
water. This part of his theory has in consequence received adhesion
from no one and so I will leave it out of discussion. In what follows
below, ‘GopLEwskr’s theory” will therefore mean the view that the
living wood must be regarded as the cause of the transpiration current.
In order to facilitate a judgment of the state of affairs I will
tabulate the most important arguments of the two parties side by
side and will then, discuss them in pairs. From this table I omit
everything relating to the question whether the cohesion of water
is sufficiently great to account for the work which Dixon and Jony
attribute to it. I will assume, if I may put it thus, that there is no
technical objection to their theory and I think this assumption may
be made with safety.
(JODLEWSKI ©¢. Ss. Drxon and Jony.
da. There is not sufficient con- l6. There is no reason for
tinuity in the water columns of doubting the continuity of the
the wood to admit cohesion as an water columns ‘’).
explanation **).
2a. The remaining available 2b. STRASRURGER’S experiments
physical forces are insufficient to in which the water ascended in
raise the water more than 14 poisoned trees, prove the con-
metres **). trary):
The cohesion theory has at its
disposal forces which would be
able to provide a tree of 200
metres and more with water **).
3a. URSPRUNG’s experiments, with 36. In Ursprune’s experiments
branches which had been killed for the conduits become blocked and
part of their length, after which the the leaves were poisoned because
(565 )
leaves faded, prove that dead wood they got a decoction of wood for
cannot transport enough water to their drink **).
balance the transpiration ‘’).
4a. The structure of the wood is 4/. “The very structure of the
in favour of GopLEWwskt’s theory **). wood offers the strongest evidence
against GopLEWSKI’s theory” **).
Living wood offers the same
resistance in either direction to the
forcing through of water *°).
da. Arguments from analogy **). 5). Arguments from analogy *’).
6a. The distribution of pressure 6). The measurements of pres-
in living transpiring trunks isop- sure are considered unreliable or
posed to the cohesion theory **). are left out of account.
Point 1. The question of the ‘continuity of the water-threads”’
in the wood amounts to the following. The cohesion theory requires
the assumption that the water in the tree forms one connected mass
from the root to the leaves. Every xylem vessel in which there is
an air-bubble has according to this theory become useless for the
conduction of water, for in such a vessel the water cannot be under
negative pressure; if is at once sucked empty by the adjoining vessels.
Every bubble of air therefore puts one vessel out of action.
Now if it could be shown that by far the largest proportion of
vessels contain air bubbles, only a small percentage would remain
available for the conduction of water, and perhaps here and there
the required connection of the water would be entirely interrupted,
so that there could be no question of the cooperation of cohesion.
It is of course difficult to prove the absence of air, for in the
necessary manipulations preparatory to the examination there is always
the chance that air bubbles in some way or other get into the
vessels **). If air is found in the majority of the vessels this does
not prove that it was already present in the living plant, for it may
have penetrated during manipulation.
For the further course of my argument it matters little, however,
whether Dixon and Jory or whether their opponents are right on
this point. I will not therefore discuss it any further.
Point 2. The proposition, that physical forees alone are insuf-
ficient**) to raise water higher than 13—14 metres is a very weak
point in the defence of GopLewski’s theory, for STRASBURGER’s intoxi-
38*
(566 )
cation experiments have proved in the most striking manner, that
this proposition is untenable. He found that water still ascended to
the highest tops of the poisoned trees, up toa height of 22 metres.
The attempts of GopLrwskI’s supporters to maintain their proposition
in spite of this fact give a very unsatisfactory impression. STRASBURGER
is attacked in vague terms*’); he is accused of a want of critical
insight, he is reproached for not making any attempt at explanation :
the fact itself remains.
The following argument appears to be somewhat more weighty.
It is said *’): “with the help of a Jamm chain atmospheric pressure
may be imagined to force water up to 13—14 metres”; but four-
teen is not twenty-two and moreover a Jamin chain can by no
way explain anything in this case. It might perhaps be applied to
this purpose with some chance of success, if the vessels ran through
continuously from the root to the leaf, but certainly not in a system
of vesicles like the wood, where the bubbles cannot pass the par-
titions, dividing up the conducting tracts, to say nothing of the
multitude of other clinching objections.
It is further adduced against SrRAsBuRGER, that continuous liquid
threads are formed when the trunk, having been sawn off, is placed
in water ?’), but in the first place it is not clear what objection is
really meant by this and in the second place it is difficult to imagine
how these threads are supposed to originate. The water which is
sucked up cannot remove the air present, for the air is enclosed ;
it is moreover saturated with air, and is more likely to give off
bubbles than to absorb them, as soon as it is exposed to a lower
pressure at a certain height. Sawing off the tree will hardly affect
its air-content except to increase it; the air which enters does not,
however, endanger the cohesion, as it cannot ascend.
Point 3. Urspruna’s experiments ‘%) with branches, which had
been killed by steam over part of their length, in consequence of
which the leaves faded, do not prove much for GopLEwsk1 either.
The steam not only kills the living elements, but also induces other
changes.
For some time the vessels must conduct a decoction of wood
instead of water and a blocking of the membranes or even of the
lumina of the vessels may be the consequence, so that the resistance
increases. The cells of the leaves are further more or less poisoned
by this liquid, so that it is very doubtful whether the death of the
leaves may be attributed to a want of water **).
These experiments are therefore not of much importance in decid-
ing the question under consideration.
( 567 )
Point 4. The anatomical structure of the wood is a better argu-
ment for Dixon '’)*°) than for GopiEwski, for as yet it is quite
impossible to imagine in what way the living elements could really
exert any successful pumping action. The unidirectional resistance
without which such an action can hardly be conceived, has never
been observed, in spite of a careful search for it.
This argument is therefore no longer always adduced in support
of GopLEWSsKI.
Point 5. In eritical cases the arguments from analogy are hardly
more valuable than illustrations. I will therefore not discuss them here.
We see therefore that the arguments which have been advanced
so far give little support to GopLuwski’s theory. On the other hand
the striking and conclusive result of SrraspurGER’s intoxication expe-
riments is in favour of Dixon and Jony. If to this be added the
great convincing power which proofs from analogy exert, when well
presented (and here Dixon and Jony are much more fortunate than
their Opponents), we may readily understand, that the cohesion theory
has many supporters.
There are, however, two facts which are adduced against this
theory with more success.
In the first place a second series of experiments by Ursprune ?%)
in which he used ice instead of steam, in order to render part of a
branch inactive. This series of experiments does not of course suffer
from the objections which deprived the other series of its argumen-
tative value. The fact, however, that fading only occurs after several
days, makes the result less convincing.
Another objection is more important:
Point 6. The distribution of pressure in living trees is opposed
to the theory **).
In a hanging water-thread the pressure decreases gradually as one
ascends and the decrease is at least one atmosphere for an ascent
of 10 metres. In living transpiring trees it has been impossible to
demonstrate this; it was found on the contrary that manometers
placed at different heights up the trunk, behave quite independently
of one another. Sometimes one shows a lower pressure, sometimes
the other.
It is true that objections can be raised against many of these
measurements of pressure, but some of them in SCHWENDENER’s opinion
proved positively and undeniably that there can be no question of
a regular decrease of pressure. For in this case it would be incon-
ceivable, “dass ein Baumstamm der nach 2—3 Regentagen durch
Nachschub von unten etwas wasserreicher geworden, in mittlerer
(568 )
Héhe (wo vorher Saugen stattfand) Luft in das hier angebrachte
Manometer hineinpreszt, wahrend oben in der Krone und insbesondere
23)
unten am Stamm weder Saugung noch Pressung stattfindet”
It is remarkable that Drixoy, in his review of the state of the
problem in the ‘“Progressus’’, does not at all refer to the ice experiments
of Ursprunc, nor to measurements of pressure, although he there
considers at length and refutes much less important objections.
Thus we have traced the causes of the remarkable phenomenon
mentioned in the introduction. The partisans of GoDLEWskI point to
the measurements of pressure and maintain that SprasBuRGER’s expe-
riments are invalid, whereas Dixon points to STRASBURGER and is
not concerned with pressure measurements.
As will be seen the position is somewhat confused. In my opinion
no advance can here be made aiong a theoretical road. Experiments
alone can lead us out of the confusion.
I think I am able to supply conclusive, experimental proof that
the normal living wood is able to pump water actively.
In order to give this proof I started from the following preliminary
conception. If the irregularity of the results of pressure measurements
is really caused by a pumping action of the living wood, this
irregularity must at once disappear as soon as the experimental trees
are killed or paralyzed. This was indeed found to be the case.
Moreover, as soon as the trunk was dead the differences of pressure.
followed the same rule as would be expected to apply to a glass.
tube. When the conditions became unfavourable to evaporation, as
in the evening and when rain supervened, the indications of the
manometers approached each other more and more. At midday, in
sunshine, on the other hand they differed more. This becomes
intelligible, when we consider that a more rapid evaporation requires
a stronger current; for a stronger current larger differences of pressure
are however necessary, in order to overcome the greater resistances.
First I will describe the experiments somewhat more in detail.
Later I hope to publish the curves of the positions of the manometers,
together with the result of a more extensive investigation of this
subject.
Of a + 24 metres high specimen of Sorbus latifalia, which divided,
a little above the ground into two almost equal, strong branches,
one branch was left intact as a control; to the other I fixed above
one another some U-shaped open mercury manometers, in the following
manner. Some lateral branches were cut off from the main branch
in such a way that a stump of 5 cm. length remained. A tube was
slid over this stump, and to it the manometer was afterwards fixed
(569 )
this tube was blown out in the middle to a small bulb, and was
hermetically fixed to the stump with a piece of india rubber tubing.
It was then half filled with water, and momentarily pumped empty
that we may inject the cut vessels. I then left it open for half an
hour and finally closed it with the perforated rubber stopper, through
which the manometer was stuck. Once a day the bulb-tubes had to
be replenished, for the wood always leaks a little from the inter-
cellular spaces. The bark leaks still more and for this reason I always
removed it at the place where the rubber tube was to come.
As long as the tree was alive, no regularity could be perceived
in the indications of the manometers: they all showed a pressure,
smaller than that of the atmosphere, but sometimes one ‘“sucked”’
more, sometimes another. After a few days I killed the portion of
the branch bearing the manometers over its whole length by means
of steam. At once the manometers followed the rule indicated above,
and did not depart from it. The differences of pressure became very
considerable towards midday, showing that the dead portion offered
a great resistance to the strong current.
The crown and the base of the branch remained intact during
this treatment. The leaves showed only after 3 weeks, that they had
suffered from the operation; up to that time they remained perfectly
fresh. When at last they began to change, they gave the impression
that they were diseased, rather than that they suffered from want
of water.
Two manometers were attached to the small trunk of a Cornus
and fixed to almost equal stumps of branches, the one 66 em. above
the other. The whole tree was 2 metres high. Before I cut off the
branches, which were to yield the stumps, I killed the trunk at
these two places with steam over a length of 10—12 em. The
manometers were thus attached to dead branch stumps on dead
pieces of the trunk, separated by a living portion.
I wished to investigate whether the living intermediate portion did
pump or not. If so, it would always be occupied in diminishing the
difference of pressure between the two dead pieces of the trunk. If
it was then suddenly cooled with ice, the manometers would have
to diverge suddenly and would once more approach each other if
the tree was left to itself. Finally if it was killed, the well-known
regularity would be bound to appear.
The result was different, however. The intermediate portion evi-
dently did not pump, for the manometers behaved exactly as in a
dead tree. At midday they sometimes differed by 24 cm. of mer-
cury. However — on the fifth day their behaviour changed fairly
( 570 )
suddenly and on the sixth day it was as irregular as in living trees!
Avidently the intermediate portion had suffered too much by this
treatment, to function immediately, but on the sixth day it had so
far recovered, that it could work again. It lived on until the end
of December, as could be seen by the perfectly fresh bark. Now, at
the end of January, it is dead. The crown, however, still looks
healthy, as also do the buds.
Although those facts, as far as I can see, do not permit of an
explanation other than the one given here, a proof may still be
adduced that such phenomena cannot be attributed to a change in
the resistances. Such, a change would moreover have to be of a
very remarkable nature to be of any use as an explanation.
Four manometers were attached to the trunk of a lilac tree
(Syringa vulgaris) 2 metres in height, and they were numbered in
ascending order 1, 2, 3, and 4. After a short time they all showed
an approximately equal “suction”, whieh oscillated with diurnal
periods between 48 and 28 cm. of mercury. Although the differences
were small, some times one was the highest, some times another.
After 15 days, when I knew the course of the pressure curves
sufficiently, stump 2 was killed, together with the piece of the stem
to which it was attached. This was done by passing through it for
an hour the discharges of an induction coil capable of giving a
spark of 10 cm. long, without sparking in the secondary circuit.
The stump and the portion of the trunk became heated to nearly
60° ©.: a few pieces of glass cement of that melting point, which
I had fastened to it, just began to melt.
While the induction current was being passed, the suction of stump
2 first diminished greatly, as a result of the heating, the other
manometers remained constant. Soon the fall of the mercury
in no 2 stopped and the suction increased again. After the interruption
of the current the mercury rose higher than usual; this abnormally
high suction subsequently persisted; no 2 afterwards followed the
periods of the other manometers, which went on without hindrance,
but sucked always strikingly more. How we can deduce from this
the proof that this phenomenon is not caused by changes in the
resistances, will be explained presently.
Thus far the description of the experiments. I will now consider
what may be deduced from the results.
The course of the manometers in Sorbus proves that the water
current in a living tree is caused by quite different forces from those
of a dead one. The result cannot be attributed to the imperfectness
of measurements. Most of these are the same before and after death
( 574 )
and we cannot suppose that the circumstances which are changed
in the operation, are altered exactly in such a way as to bring to
light the observed regularity. Thus the distribution of pressure before
death can only be explained on the assumption that there are pressor
factors, i.e. pumping actions in the wood.
This view receives important support from quite a different side,
through the experiments of Zurstra*’). He allowed a solution of
Sdureviolett to ascend living and dead branches and then examined
them microscopically. In the living ones only the tori of the bordered
pits were stained, together with a thin layer of the walls of the
vessels; in the dead ones, however, the whole of the wood was
coloured uniformly. It follows from this that the water current
takes quite a different course in dead wood from that taken in
living wood.
That in the lilac only the one manometer was affected, which was
attached to the portion killed by induction shocks, cannot in my
opinion, be explained in any other way than by the aid of Gop-
LEWskr’s theory. If one imagines, with Dixon and Jory, that the
whole trunk behaves like a dead tube, the phenomenon cannot be
explained. An increase of resistance cannot be the cause, for then
the other manometers would have undergone this influence. If on
the other hand, we imagine a tree-trunk to be a system of tubes in
which everywhere small pumps occur, the phenomenon becomes
intelligible. The death of the piece of trunk puts the pumps out of
action locally and the suction must there be somewhat greater to
get the water through the piece of dead wood. This would not
necessarily be observed at the following manometers, since the inter-
mediate elements bring the pressure back to normal.
I regard all the above as proof positive that the living wood has
a hydromotory power. The experiment with Cornus already proves
this very clearly: one could almost see the recovering intermediate
portion suddenly begin pumping, as it were before one’s eyes.
After thus having given the positive proof that the living wood
assists in the ascent of the water | will again take up the theoretical
considerations with which I started, and see to what extent this
proof can modify the condition of affairs.
We encounter the difficulty that SrrasBuRGER’s intoxication experi-
ments prove that help of living elements is not necessary, whereas
the only theory which is not adversely affected by these experiments
becomes untenable on account of the pressure measurements. The
solution is clear from the preceding.
The adherents of GopLuwskt are wrong in asserting that water
cannot ascend more than 14 metres without the help of life, for
STRASBURGER’S experiments show that this is indeed possible. But that
is not the question. The position is simply this, that in a living
tree the water is pumped up by living elements, where-
as in a dead one it also ascends, but through other
causes e.g., with the help of cohesion.
Let us test this view by the data in the table:
Point 1. The question of continuity is only of importance for the
cohesion theory. As soon as this has been refuted in another way,
the question of the continuity of water, may be left untill if may
perhaps arise again in connection with new questions.
Point 2. The intoxication experiments of SrRAsBuRGER have been
included in my thesis.
Point 3. Although the experiments of Ursprune do not prove
anything certain in favour of GopLuwskrs theory, they certainly
prove nothing against it.
Point 4. The anatomical structure of the wood can never be
adduced as an actual objection to the view here put forward. As
soon as it has been proved that the living wood pumps, this fact
cannot of course be weakened because we cannot at once imagine
from its structure how this action may take place. The investigation
of this point must simply be left for further research.
Point 6. The distribution of pressure is quite in agreement with
GopLEWwsk's view. When pressor factors are everywhere present in
the trunk, the distribution of pressure cannot be predicted as long
as these factors themselves are not fully known.
We see therefore that the questions discussed here do not produce
an objection t¢ my view. In this preliminary communication I have
of course limited myself to the most important matter; afterwards
I hope to treat the same subject more completely.
I might have omitted the literature entirely, but it seemed desirable
briefly to justify my quotations and references. The small figures in
the text refer to the bibliography which is appended below.
I wish to conelude this preliminary communication by pointing
out that the method which is here introduced, may also be of service
in the solution of other questions. By its aid we might, for instance,
ascertain whether the living elements cooperate, when a branch is
made to transport water in the inverse direction; the influence of
all sorts of stimuli (heat, cold, electricity, stimulant substances) on
the activity of these elements can be examined. Should the intoxi-
cation experiments of SrraspurGErR be repeated with manometers
fixed to the experimental trees, they would at once constitute a
( 573 )
definite proof in favour of Gopimwski. A small tree would, however,
be sufficient for this.
The method in which a living piece of wood is isolated between
two dead portions is especially to be recommended. The portions
to be killed should not, however, be heated above about 60°, in
order to spare the intermediate position (compare the experiment with
the induction current). If possible a leafy branch should be left attached
to the intermediate portion, for otherwise it must soon die of hunger.
Groningen, January 28 1910.
BIBLIOGRAPHY.
1) Sacus, Ein Beitrag zur Kenntniss d. aufsteig. Saftstromes in transpirirenden
Pflanzen. Arb. des Bot. Inst. in Wiirzburg, Bd. II. 1882; F. Etrvine, Ueber die
Wasserleitung im Holz. Bot. Ztg. 1882 p. 706; J. Vesgue, Ann. d. Scienc. Nat.
Bot. Sér. VI, 19, 1884, p. 188; J. Bots, Publications before 1884. 2) J. Boum, Ueber
die Ursache der Wasserbewegung, etc. Bot. Ztg. 1881. EB. Goptewsk1, Zur Theorie
der Wasserbewegung in den Pflanzen. Pringsh. Jahrb. Bd. XV, Heft 4 1884.
3) R. Hartic, Die Gasdrucktheorie Berlin 1883. E. Goptewskt. |. e. sub. 2), 4) Wes-
TERMAIER, Zur Kenntn. d. osmot. Saug. d. lebenden Parenchyms. B. d. Deutsch.
Bot. Ges. 1883; idem, Ueber die Wanderung d. Wassers im leb. Parench. Sitzber.
d. Berliner Akad. d. Wiss. 1884; Drxon, Transpiration and the Ascent of Sap.
Progressus Rei Botanicae, Bd. Ill, Heft 1. 1909. *). A. J. Ewart, The Ascent of
Water in Trees, Phil. Trans. Roy. Soc. Londen, Ser. B, Vol. 198, 1905 and Ser.
B, Vol. 199, 1908. ©) AsxEnAsy, Ueber das Saftstelgen Verh. d. Nat. Med.
Ver. zu Heidelberg. N. F. Bd. V. 1895; Drxoy, 1. ¢. sub. 4), p. 65. 7) GopLEwskt,
l. c. sub 2). %j Dixon and Jony, On the Ascent of Sap. Proc. Roy. Soc. Lond.
Vol. 57 (1894) B. p. 3, Dixon 1. c. sub. 4). p. 31 and followmg. 9) HoLteRMANN,
ScHWENDENER’S, Vorles. 26 Mech. Probleme d. Botanik. Leipz. 1909, p. 80.
10) Dixon, |. c. sub. 4). p. 16. |) GopLEwskt, |. c. sub 3), 32) HoLTERMANN,
l. ec. sub 9. p. 79. 18) Dixon, |. c. sub 4), p. 43—46. 44) HonrerMany, |. c. sub 9),
p. 80. 1%) Dixon, 1. ¢. sub. 4) p. 15. 1) idem, p. 60 and elsewhere. 17) HoLTERMANN,
1. c. sub 9), p. 80. UrspruneG, Die Beteiligung lebender Zellen am Saftsteigen,
Pringsh. Jahrb. 1906. Jansn, Die Mitwirk. der Markstrahlen bei d. Wasserbew. im
Holze, Pringsh. Jahrb. 1887. 15) Drxoy, 1. c. sub 4), p. 19. 19) idem, p. 16. 2°)
JANSE, 1. c. sub 17); Dixon, |. c. s. 4) p. 16. 7!) idem p. 46, 47, 49, 50, 51,
56, and elsewhere. 22) GopLEWwsKI, |.c. sub 3, p. 605 and 598. *3) Hotrermann,I. ec.
sub 9), p. 66 and 67. 74) Dixon, |. c. sub 4), p. 45. *®) HoLTERMANN, l.c sub 9.
p. 80. 26) PrerreR, quoted in idem, p. 78. *7) idem, p. 79. *%) UrspRUNG, die
Beteiligung lebender Zellen am Saftsteigen. Pringsh. Jahrb. 1906. *°) Drxon. |. c.
sub 4). 3°) Zrsustra, Contributions to the knowledge of the movement of water
in plants. Kon. Ak. v. Wetensch. Nat. Afd. Proceedings, this volume p. 574.
( 574) ;
Botany. — “Contributions to the knowledge of the movement of
water in. plants.” By Dr. K. Ztstra. (Communicated by
Prof. J. W. Motr1).
(Communicated in the meeting of January 29, 1910).
For some time I have been occupied in the botanical laboratory
at Groningen with the problem of the movement of water in plants
and have carried out experiments of a somewhat diverse nature.
Various circumstances have prevented me from continuing my ex-
periments in this direction, so that the investigation has not been
rounded off. I did not intend publishing it, but as I shall presumably
have for some time no further opportunity of continuing my studies,
I think I may be justified in publishing the data I have collected ;
possibly they may be of service to other investigators who have chosen
for their researches the subject of the movement of water in plants.
The experiments referred to may be arranged under three heads, viz.:
1st. The trunk or stem of intact plants cooled to about 0° C.
2d. The ascent of a dye solution in eut branches.
3", Interference with the movement of water in a tree-trunk by
means of deep incisions.
First I propose to discuss the considerations which led to these
experiments and the results obtained, and then I will give a more
detailed account of the execution of the experiments.
1. Trunk or stem of intact plants cooled to about O° C.
As is well known, GopLewski (Zur Theorie der Wasserbewegung
in den Pflanzen. Jahrb. f. Wiss. Bot. Bd. 15) attempts to find the
cause of the movement of water in the activity of the living cells
of the medullary rays and of the wood parenchyma; these cells
would therefore have to act as it were as suction-pressure pumps.
Gopiuwski did not, however, adduce any direct experimental evidence
in support of this theory. His theory is only made plausible with
the aid of various data obtained by others, and it is urged that the
theory does not conflict with the facts adduced by other investigators.
Various botanists (JANsn, StraspuRGER, Weber, Urspruna) have after-
wards attempted to test the theory experimentally.
The most obvious method for such a test would be the following:
to cut out the action of the living cells of medullary rays and wood
parenchyma, and then to see whether the movement of water had
become impossible.
(575 )
This elimination of the action of living cells was most easily
obtained by simply killing these cells by poisons or by a high
temperature.
This method is, however, open to objection; such interference not
only attains the elements which it is desired to put out of action;
others also, especially the water-couducting vessels and tracheids
will undoubtedly be affected, so that it is questionable whetier the
results of the experiments can only be attributed to the elimination
of the activity of the living cells.
A method already used by Ursprune but with a result opposite
to mine — which meets this objection, is the cooling of the trunk
or stem of the plant to about 0°. By this means it is possible to
reduce the activity of the living cells to a minimum, while neither
dead nor living elements undergo a permanent change. Moreover
the advantage of being able to establish the original conditions after
the conclusion of the experiment and therefore bring the plant back
to normal conditions, should not be underrated. The experiment and
its control can both be carried out on the same intact plant.
If by this means the plant could be made to fade, and to assume
its original fresh appearance after the cooling had been stopped,
GopLEwski's theory would receive considerable support.
According to this method I have myself carried out 3 experiments.
The trunk of a small apple-tree, 2 stems of Polygonum cuspidatum
and 2 stems of Helianthus tuberosus were cooled to about 0° C.
over a length of 50 em. The experiments lasted 6, 7, and 8 days,
under conditions which were very favourable for a possible fading.
Nevertheless | have in no case been able to observe even incipient
fading, although the transpiration from the leaves was strung, as
shown by the cobalt test. Cut leafy branches, hung up near the
plant, withered very rapidly.
We may not, however, conclude from the negative result of these
experiments that the living cells do not play a part in the movement
of water. It is quite possible, even probable, that cooling a length
of 50 em. is not enough. This slight obstacle was perhaps easily
overcome by differences of pressure present in the trunks. Had the
results been positive it would have supported Gopinwskt's theory.
My negative results are, however, not able to oppose this theory.
The nature of the results notwithstanding, I think it may be useful
to bring them to the notice of others.
Description of the experiments.
The cooling of the trunk or stem was brought about by melting
ice, which was placed in an apparatus indicated by the -figure.
(576 )
The apparatus consisted of two equal parts, i.e. of two semicircular
tin-plate reservoirs with fixed bottom and loose lid. The two half-
cylinders had on the middle: of the flat side a portion which was
bent like a half cylinder, so that the two reservoirs when joined to
form one cylinder, left in the centre a space for the passage of the
trunk, which was to be cooled. The height of the apparatus was
50 em., its diameter 30 cm.; the space left free for the trunk had
a diameter of 10 em. Each reservoir was provided at the bottom
with a tap, through which superfluous water could run off. The
cylindrical surface of each reservoir and also the bottom and the lid,
were covered on the outside with a laver of felt, 15 mm. thick and
over this there was a covering of asbestos paper, 2 mm. thick. In an
experiment the two reservoirs were placed round the stem and
screwed together, after a piece of felt had been placed between the
two flat surfaces in apposition.
The reservoirs were filled with ice. The space through which
the trunk passed, was closed off above and below round the stem
by a solid plug of cotton wool through which a thermometer passed.
The temperature in the annular air space surrounding the trunk
varied between 0° and + 8° C.
The apparatus was sufficiently protected by the felt and the asbestos
against the heat of the surrounding atmosphere. Even on hot days
it was only necessary to renew the ice twice in 24 hours.
( 577-)
During the experiment the apparatus rested on some bricks, so
that it was about 20 em. from the ground.
EXPERIMENT I.
Apple tree.
The ice apparatus was fixed round the trunk having a diameter
of 3'/, cm., of a small apple tree, about 2'/, metres high, on July
21st 1904, at noon, the weather being hot and sunny. The apparatus
was filled with ice and in the course of the afternoon the temperature
in the space round the trunk fell to about 1° C.; not the slightest
fading of the leaves could be detected, although such fading would
have at once been noticeable by comparison with two other apple
trees which stood next to the tree experimented on.
Nor could any change be observed on the following days. The
temperature of the air space round the stem remained continuously
between 0° and 3°.
The maximum temperature of the atmosphere on the days of the
experiment oscillated between 23° and 29°.
On the sixth day, when the temperaiure of the atmosphere was
20° and that round the trunk 9°, an strong transpiration of the
leaves was demonstrated by means of the cobalt test. On the seventh
day the trunk was sawn through immediately above the ice apparatus ;
a hole was drilled in the portion of the trunk still inside the apparatus,
and a thermometer was placed in it.
In this way I was able to show that the temperature imside the
trunk was the same as that of the annular air space round the trunk,
i.e. in the course of three hours it oscillated between 2° and 3°,
while the temperature of the atmosphere was 24° to 25°.
Exprrm™Ment II.
Polygonum cuspidatum.
The ice apparatus was fixed round two immediately adjoining
stems, 2 metres in height, on July 6 1905, at noon, and it was
filled with ice. In the course of the afternoon the temperature in
the air space round the stems fell to 0°, without withering taking
place. The numerous stems surrounding the apparatus served as
controls. Nor was any change noticeable during the following days.
The temperature round the stems remained continuously between
0° and 3°. The maximum temperature of the surrounding atmosphere
C578)
on the various days during the experiment oscillated between 19°
and 30°. The experiment was stopped on the seventh day.
Exprerment III.
Helianthus tuberosus.
The ice apparatus was fixed round two immediately adjoining
stems of plants, 1'/, M. in height, on July 14% 1905 at noon, and
was filled with ice. In the course of the afternoon the temperature
of the air space round the stems fell to 0°. No fading could be
observed; several specimens of the same species, standing next to
the plants experimented upon, served for comparison. Cut leaves,
hung up on the plants were completely withered in a few hours.
Nor was withering observable on the experimental plants on fol-
lowing days.
The temperature in the air space round the stems remained about
0°. The maximum temperature of the atmosphere in the days of
the experiment oscillated between 17° and 26'/,°. The experiment
was stopped on the eighth day.
2. Ascent of a dye solution in living and dead cut branches.
When cut branches, with a freshly cut surface, are placed with
this surface in a dye solution, the liquid will in general ascend inte
the branches for some distance, and thus may be easily traced by
cutting them across at different levels. Various elements of the wood
are then found to have been stained. It matters litthe whether one
takes for this experiment living or dead branches, with or without
leaves; the fluid always ascends in the branches, even when these
are upside down, i.e. are placed in the solution with their cut
apex. I generally carried out such experiments with twigs 30-—
40 em. Jong; sometimes with pieces of a branch, which had also
been cut at its upper end. After some days the stain shewed itself
on the surface of the upper section of these latter branches.
Although the dye ascends in all branches, the way in which the
various elements are stained is not the same in living and dead
branches. A sharp difference is observable.
In comparing living branches with dead ones, it was of course
necessary to use a harmless stain; the experiments of STRACKE’:
investigation of the immunity of the higher plants towards their own
poison (Dissertation), led me to choose Sdureviolett of Grisier. I
used this stain in a '/,,°/, aqueous solution. The twigs were placed
(579 )
separately in a small bottle with the solution of the stain, the neck
of the bottle being closed with a plug of cotton wool to prevent
evaporation.
After the experiment the twigs were examined at different levels
by microscopic sections. Transverse, radial and tangential sections
were examined in oi/ of cloves, a medium in which Saureviolett is
insoluble, so that the stain remained properly localized. The sections
were cut without the use of any liquid and were at once placed in
the oil of cloves. The slight water content of these preparations did
not interfere. After a very short time the oil had thoroughly permeated.
This method had moreover the advantage, that after most of the
clove-oil had been wiped away, the preparations could be very well
enclosed in Canada balsam, without further treatment.
A comparison of the behaviour of the xylem elements of living
and dead branches brought out the following differences :
living branch dead branch
a. torus of the closing membrane of «a. torus not stained, or only very
the bordered pits deeply stained. slightly.
b. adjoining the lumen, a thin #. the walls of the vessels, fibres
layer of the wall inthe border | and parenchymatous cells are
of the pits is stained. The walls stained uniformly.
of vessels and fibres are only
stained in a very thin layer,
which is immediately adjacent
to the lumen.
c. contents and wall of the cells | c. contents of the cells are coloured.
of medullary rays and wood
parenchyma are unstained.
The deep staining of the tori in living branches was especially
noticeable, also in transverse sections, the more so because the
staining of the layer next to the lumen in the walls of vessels and
fibres was often difficuit to see and because the living cells of the
medullary rays and parenchyma were quite colourless.
In the wood of Saltz and of Fagus, in which the tori cannot
otherwise be seen at all, they were made very obvious by this
staining of living branches.
The staining of the tori by eosine in a living branch of Ginkgo
was already mentioned by Jaysr in “Die Mitwirkung der Markstrahlen
bei der Wasserbewegung im Holze” (Jahrb. f. Wiss. Bot. 1887
Bd. XVIII. In’ this case also the stain had aseended the branch :
39
Proceedings Royal Acad. Amsterdam. Vol. XIL.
( 580 )
the “primare Wandlamelle” of the medullary ray cells was according
to Jansp all that had been stained.
In my experiments with living branches the staining extended not
only to the tori of the vessels and fibres, but also to those of the
half bordered pits between the medullary ray cells on the one side
and the vessels and fibres on the other side; the contents of the
medullary ray cells however remained colourless, as stated above.
The results of other experiments carried out by me, agree well
with these facts. Instead of taking dead branches, | caused to ascend
in living branches a ‘/,, °/, solution of Saureviolett in strong alcohol,
and also a ‘/,,°/, solution in water containmg 4°/, formaldehyde.
As controls I employed living branches in a */,,°/, solution of
Séiureviolett in water.
I now found that the living branches in the poisonous solutions
were stained practically in the same way as the dead branches in
innocnous ones, only not so completely. It was clear that the aleohol
and the formaldehyde only gradually exercised their fatal action on
the plant. The tori were always unstained; only a few were
stained very faintly. The walls generally showed a uniform staining ;
the medullary ray and parenchyma cells with contents were coloured
dark blue.
Finally I may add that microscopical transverse sections throngh
living branches, which sections were afterwards placed for 20 hours
in an aqueous Séureviolett solution of */,, "/,, were stained quite
uniformly dark blue, exactly in the same way as those sections
made after the stain had ascended in dead branches; the colour was
only somewhat more intense. The transverse sections through control
branches, which bad previously stood in the same solution for 4
days, on the other hand showed, as was to be expected, a staining
quite similar to that which was described above for living branches,
Description ef the experiments.
Expurient TV.
Fagus silvatica.
A living leafy twig, about + mm. thick at its base, stood for 9
days in a solution of Saureviolett. The stain ascended to the top
and into the leaves. The bark, the cambium and the pith remained
quite unstained; the staining was limited to the. wood and here the
stain was only in the inner layer (adjoining the ‘Iumen) of the walls
of vessels and fibres; the tori of the bordered pits were stained a very
( 581 )
deep blue-violet, and this was also the case with the half bordered
pits between medullary ray cells and fibres. The medullary rays and
the xylem parenchyma were quite unstained, both as regards wall
and contents.
EXPERIMENT V.
Larix decidua.
A living leafy twig, 6 mm. thick at its base, stood for 5 days
in the solution, after which the stain had penetrated to the apex.
Staining completely limited to the wood, but no stain in the oldest
of the 6 annual rings.
The stain only taken up by a very thin layer of the wall,
adjoinng the lumen of the tracheids and the cavities of the pits.
Torus of the pits deep blue-violet, also in the half bordered pits
between medullary rays and tracheids. For the rest everything
unstained.
ExprrImMENt VI.
Salix spec.
Two living leafless branches, provided at either end with a cut
surface, both 80 em. long and more than */, em. thick, stood for
2 days in the aqueous solution of Saureviolett; one of the branches
had its lower end in the solution, the other its upper end.
The stain ascended readily, and in the two branches simultaneously.
The stain only present in a thin layer of the wall adjoining the
lumen of the vessels and fibres and the cavities of the pits. Tori
deep blue-violet.
ExprrmeEnt VII.
Lagus silvatica. Taxus baccata.
Of each of these plants two similar 3
5 year old leatless branches
were placed with the cut surface in the aqueous Siureviolett solution
for 3 days. One of the branches of each species was alive, the other
had been treated as follows. It had stood for L*'/, hours in boiling
water. Then water was sucked through the boiled branch by means
of a filter pump in order to remove possible obstructions, finally a
fresh surface was cut.
39%
( 582 )
After 3 days the stain had almost reached the top in all the four
branches.
In the living branches staining was scarcely visible against the
walls of the vessels and tracheids. The tori, including those of the
half bordered pits were deeply stained. Medullary ray- und parenchyma
cells quite colourless.
In the boiied branch of Fagus the walls of the libriform fibres
and of the vessels were a uniform pale blue. Against the walls of
the vessels in the spring wood a darker layer. Nowhere however
coloured tori. The medullary rays also proved to be colourless.
In the boiled branch of Zaxus the walls of many tracheids were
stained a uniform pale blue; towards the inside against the walls a
darker layer. The tori unstained. The medullary rays dark blue.
Exprrtmrnt VIII.
Taxus baccata.
Two living branches were taken. One was placed with its cut
surface in a solution of 0.1 gram of Saureviolett in 100 c.c. of water ;
the other in a solution of 0.1 gram of Sdureviolett in 100 ¢.c. of alcohol.
Both branches remained standing in the solution for 48 hours,
after which time sections were made through both at a height of
7 em. The staining was as follows:
Branch in aqueous solution: staining only in the secondary xylem.
A very thin blue layer against the walls of the tracheids, and of
the cavities of the bordered pits. Tori dark blue, including those of
the half bordered pits. Medullary rays unstained.
Braneh in alcoholic solution: the stain had also penetrated into
the cambium and the innermost layers of the cortex parenchyma,
where both walls and contents were dark blue. In the secondary
xylem the tracheid walls light blue; against the walls also clearly
a blue layer, further in the cavities of the pits. Tori unstained.
Medullary rays dark blue, both as regards walls and contents.
The walls also coloured in the primary xylem.
Exrpnrimpnt IX.
Taxus baccata.
A living branch was placed with the cut surface in a solution of
O.1. gram of Séureviolett in 100°-c.c. of a 4°/, formaldehyde solution
diluted formalin).
After 5 days the branch was examined; the stain had already
reached the apex.
Staining only in the secondary xylem. Against the walls of the
tracheids there was a thin blue layer, also in the cavities of the
bordered pits. Tori colourless. Of the medullary rays both the walls
and the protoplasm dark blue.
‘
EXPERIMENT X.
Salix spec.
A living twig was placed with its cut surface in a solution of
0.1 gram of Saureviolett in 100 ¢.c. of a 4°/, formaldehyde solution.
After 3 days the stain had penetrated to the apex and the twig
was examined.
Staining only in the secondary xylem. The walls of the vessels
coloured light blue with an indication of a somewhat darker layer
adjoining the lumen. Tori practically colourless. The medullary ray
cells, which adjomed the vessels, are coloured blue.
3. Interference with the movement of water in a tree-trunk
by means of deep incisions.
Exprrment XI.
An experiment with a small willow tree in the Botanic Gardens
at Groningen showed, that in a trunk in which the transpiration
current had been largely prevented or perhaps completely cut off
as a result of transverse incisions on both sides at various heights,
measures were taken in course of time which ultimately led to a
complete recovery of this current.
The experiment was carried out as follows.
The trunk of the tree, 11*/, em. thick, was sawn into transversely
to slightly beyond the centre at four places, alternately on either
side of the trunk. The incisions were 22 cm. apart, and the lowest
was 1.25 Metres from the ground. They were prevented from closing
up again by the insertion of tin plates, which in future remained =~
in position. At these four places the water current was therefore 4?
irreparably interrupted. ae
As the trunk had of course been greatly weakened by this operation
the tree was supported by four iron wires, which were attached
high up to the trunk and also to four pegs driven into the ground
at some distance round the tree.
( 584 )
This expeeiment was started on July 14% 1908; the incisions were
ready and the plates were pushed in at 9.30 a.m. At 10 a.m. the
leaves were already drooping and they remained so througheut
the day. ;
In the course of the five following days, in cool dry weather, the
leaves gradually recovered. ~On the 7'' day of the experiment the
foliage began to wither from the top downwards; mary yellow leaves
also appeared in the crown. In all these days the temperature had
not risen above 18° in the neighbourhood of the tree. On the 9% day,
the temperature rose in the afternoon to more than 26°, and probably
as a result of this the number of yellow leaves now increased
rapidly. Those leaves which had remained green also began to droop
again. The tops of the branches in the upper part of the crown
withered completely.
The 3 following days were warm and sunny with temperature
maxima of 27° and 28°. Most of the leaves now fell off, while in
the upper half of the crown the foliage withered completely.
After this time cooler weather supervened and the few remaining
green leaves recovered and remained in good condition until the
autumn.
That the tree had not suffered greatly however from the incisions,
was shown in the following summer, for then the foliage developed
as well as before the experiment, and remained fresh throughout
the entire season.
Wageningen, Dec. 13 1909.
Physics. — “Vhe magnetic separation of absorption lines in connexion
with Sun-spot spectra.” (1). By Prof. P. Zreman and Dr. B.
WINAWER.
1. As a consequence of the intimate connexion between emission
and absorption, there exists closely corresponding to the magnetic
separation of emission lines, a magnetic division of absorption lines.
The dark lines which appear in a continuous spectrum, if a beam
of white light traverses an absorbing flame, are divided and _pola-
rized under the influence of magnetic forces in exactly the same way
as the emission lines. This correspondence between emission and
absorption was shown to exist already in some of the first experi-
ments on the subject by one of the present authors. Our knowledge
of emission spectra under magnetic influence has’ since been extended
considerably. The experimental study however of the inverse effect
i.e. the magnetic division of absorption lines has less advanced.
( 585 )
After the first experiments of the first named of the authors of
this paper, the change of absorption lines in a magnetic field was
studied by K6éxig*') and Coron *); Rieut*) gave an elaborate study
of the subject, to which we have to return later on. It contains the
only investigation of the magnetic effect in a direction inclined to
the lines of force. Closely connected with our subject are finally
some observations by Lopen and Davins*) on the influence of a
magnetic field on flames, emitting “reversed” lines.
The consideration of the inverse effect forms the basis of Voter's
magneto-optical theories *); and it is considered also by Lorentz *)
in his investigation of the magnetic separation in a direction inclined
to the line of force.
Theory indicates different points, which may be tested by expe-
riment. The inverse effect has become of supreme interest in solar
physies, since Hate’s*) discovery that the dark lines of the sun-spot
spectrum exhibit the characteristic phenomena of magnetic separation.
The experiments we intend to describe in the present communi-
cation. relate to the division of the sodium lines D, and D,. Some
of our results may already be found in the work of the cited authors.
In order to present the subject in a connected form it seemed
necessary not to exclude these.
The facts now ascertained in combination with former results
appear to be of some value in explaining peculiarities observed in
sun-spot spectra. Some instances will be given later on.
2. Type and relative amount of the magnetic division of the
sodium emission lines, D, and D,, are
Q
given in Fig. 1.
Gali | [. De a vepresents the observations when the
line of sight is at right angles to the
eh, | a peeaa magnetic field, 4 when it is parallel to
| | pe the field.
In a weak magnetic field D, exhibits
the triplet type, at right angles to the
1) Konia. Ann. d. Phys. Bd. 62. 240. 1897.
2) Corron. Eclairage Electrique. 5 et 26 mars. 1898.
5) RigHt. Sul fenomeno di ZeeMAN nel caso generale dun raggio luminosa
comunqne inclinato sulla direzione della forza magnetica. Mem. di. Bologna,
17 Dicembre 1899.
) Lope and Daviess. Proc. R. Soc. 61 413. 1897.
5) W. Voter. Magneto- und Elektrooptik. Chapter IV and the papers there cited.
6) H. A. Lorentz. These Proceedings, Vol. XII, p. 321, 1909.
7) G. E. Hate. On the probable existence of a magnetic field in sun-spots.
Contributions from the Mount Wilson Solar Observatory Nr. 30. 1908.
( 586 )
field; the doublet type if the light is examined parallel to the lines
of force. D, seems to exhibit a doublet in both principal directions.
The Fravnnorer lines in the spectra of sun-spots investigated by
Harn are either broadened, or changed to doublets (often incom-
pletely resolved quartets), or to triplets. The resolutions exhibited
by sodium vapour are therefore the very types of special importance
to astrophysics; this and also the facility of producing sodium
vapour in the magnetic field induced us to commence our experiments
with this substance.
3. The explanation of the inverse effect is easily understood by
means of the well known law of resonance. If there are in a
flame under the influence of a magnetic field three periods of free
Vibrations, then we may expect that from incident white light vibra-
tions of these very three periods will be taken away. The absorption
is a selective one, with this peculiarity that the selection refers not
only to the period but also to the direction of vibration. Consider
for example the central component of a triplet which in the emission
spectrum is due to vibrations parallel to the field. From incident
white light only vibrations, corresponding as to period as well as to
direction of vibration with the middle component, are absorbed.
Vibrations, perpendiculer to the field, though of the period of the
unmodified line, pass unimpeded.
On the contrary white light of periods coinciding with those of
the outer components is only deprived of its vertical constituents.
It will be clear from these very simple considerations what we
may expect to observe with white light under the conditions of the
experiment. The arrangement was the following: White light of the
incandescent positive pole of an are-lamp traverses a sodium flame,
placed between the poles of a pu Bots-clectromagnet. This light is
analysed by means of a stigmatic spectroscope with large Row1Lanp
grating. The observations are made in the first order.
If the observation is made at right angles to the lines of force,
we see in the continuous spectrum 4 dark components in the case
of D,, 6 dark components in the case of ,, as represented for both
lines under @ in the diagrammatical Figure 1.
In order to observe all these components the field must be strong
and the vapour density adapted to the field.
The groups of lines indicated by 4 are seen, if the light is examined
axially.
All these components, if narrow, are seen only diffuse and not black.
From the considerations above given the reason will be clear at once ;
each of the components absorbs only half the incident natural light.
( 587 )
With very diluted vapour no absorption at all or only very weak
traces of absorption are seen.
4. The introduction of a Nicol in the beam before or after the
field entirely changes the phenomenon. The absorption lines can then
be seen very narrow and black.
Let the observation be made at right angles to the horizontal
field, then, if the Nicol is placed with its plane of vibration vertical
D, exhibits its two, D, its four outer components.
After a rotation of the Nicol over 90° both D, and D, give only
the two horizontally vibrating components.
Let a beam of natural white light traverse axially the magnetized
vapour placed between the perforated poles of an electromagnet.
Then by means of a quarter-wave plate and a Nicol we may quench
either the right-handed or the left-handed circularly polarized
component.
A combination of a quarter-wave plate and a Nicol, converting
incident light into right-handed circularly polarized light may be
called a right-handed circular analyser. The absorption line corre-
sponding to a right-handed circularly polarized component is seen
with both increased clearness and darkiess by examining it with a
right-handed circular analyser.
We introduce here this simple matter because there has been
occasionally some confusion on this subject.
5. The behaviour of horizontal and vertical vibrations may be
studied simultaneously by using according to the suggestion of
Cornu and Konic a calespar rhomb. By means of it we can
obtain two oppositely polarized images of a horizontal slit of suitable
width, placed near the magnetic field.
tight-handed and left-handed circular vibrations can be separated
on the same plan by the introduction of a Frrsnen rhomb between
the calespar and the slit of the spectroscope.
It is, however, of considerable interest to examine also the behaviour
of the lines in natural light. A separate examination after the removal
of the polarizers might be made. The vapour density ought to be
the same in both experiments. It seems difficult to realise this.
The desired end is secured more simply and surely, and with
only half the labour, by adopting the width of the borizontal slit and
the thickness of the calespar in such a manner that the two images
given by the calespar partially overlap. We now obtain tliree stripes ;
the central one exhibits the phenomena as seen without polarizing
apparatus. (See fig. 2).
( 588 )
The upper and lowest stripes show the influence
of polarized light on the phenomenon.
The observations given in this communication
have been made by the described method. By
Fig. 2. its use all particulars of the phenomenon are
simultaneously exhibited; we also succeeded in photographing the
essential points. Examples of our photographs are given on the plates
annexed to our paper.
6. If the absorption lines are not narrow or if the magnetic field
is weak, the components of a magnetically divided line will partially
overlap. This partial superposition is the cause of some particularities,
especially manifest in the inverse effect and probably also apparent
in sun-spot spectra.
The nature of these particularities may be illustrated by a few
examples. We will consider the case of the magnetic triplet and
the magnetic doublet.
In Fig. 3 the curves show the distribution
ite fl of intensity of the three components of a
Yh triplet, if the light is examined at right angles
to the lines of force. If natural light traverses
a source of light placed in a magnetic field,
two black bands are seen, corresponding to
the wavelength, for which vertical as well as
horizontal vibrations are absorbed.
These black bands are surrounded by less
dark parts, which absorb only one of the
principal vibrations, the other proceeding
unimpeded. (ef. §§ 3 and 4).
If now a Nicol with its plane of vibration vertical, is introduced
two black bands are again seen. The darkest part of these compo-
nents corresponds to the maximum of the
OKO curves relating to vertical vibrations.
As a general rule the distance of the com-
ponents exceeds that of the lines first considered.
7. Parallel to the lines of force a partial,
not too small, overlapping of the components
produces a black line limited by two less dark
parts. This case is illustrated diagrammatically
in Fie. 4.
The two components may be separated by
Vio A s x
Wig. 4. a circular analyser.
These considerations may be applied to the magnetic division in
(589 )
sun-spot spectra; as a general rule we may expect that the separation
of lines in spot specira becomes more distinct and of larger amount
by the use of analysers.
The introduction of a Nicol in the beam may also reveal lines
invisible without analyser.
Several peculiarities observed in the distribution of intensity in
spot lines, remind one of the now_ specified superposition pheno-
mena'); cf. § 19 below.
8. Superposition effects of nearly, though not exactly, the same
nature occur if lines with the same direction of vibration are superposed
and if the continuous source of light emits unpolarised light. In the
more complicated divisions the now specified superposition occurs also.
It is just possible that the superposition of the outer components of
the sextet, type D,, produces only dark, that of the inner and the
next outer components, black lines in the continuous spectrum.
It is easily seen that also in the case of the quartet, type D,,
black lines may be produced. The darkest parts may be seen some-
what nearer to the middle of the complete figure, than the outer
components of the quartet.
It seems unnecessary to illustrate this by figures. Examples of the
specified actions will be given presently.
9. Our observations and spectrograms relate besides to the two
principal directions (parallel and at right angles to the lines of force),
also to directions inclined to the field.
In the present, first, communication, observations are discussed,
relating to 5 different angles between the field and the direction of
propagation of the beam (Vorer’s yw, LORENTz’s 9).
These values are: 90°, 0°, 60°, 45°, 36°—39°.
The results of the work relating to these angles have been recorded
on nearly 100 spectograms.
10. Observations perpendicular to the jield.
In the upper of the three stripes which are present in the field of
view (see § 5), the light vibrates vertically ; in the lowest one hori-
zontally, whereas the middle part relates to natural light.
Under the influence of the magnetic field we therefore see the
vertically vibrating components as narrow black lines. The quartet
of the D, line, the sextet of the DY, line, may be seen very clearly
1) A figure equivalent to the one now given concerning the influence of super-
position of magnetically divided components was already drawn for emission lines
in Zeeman. Doublets and Triplets in the Spectrum produced by external magnetic
forces. Phil. Mag. July 1897 § 7.
( 590 3
by this method. A small disturbance is produced by the narrow
reversed lines due to the electric are light. The intensity of these lines
depends upon somewhat variable circumstances of the are itself. In
some cases these lines are almost invisible, in other ones more prominent.
They are to be seen on some of our reproduetions ; with our present
subject they have nothing to do.
As regards the central stripe we refer to the remark previously
made, that the image of the separation must become, on account of
the only partial absorption, rather indefinite and weak. (§ 3).
The partial superposition of components gives, at least in the case
of diluted vapour, the most conspicuous lines. (§§ 6 and 7).
In the case of the quartet, for example, one sometimes sees instead
of four, only two components, situated between the inner and outer ones.
We made experiments with different vapour densities. The observed
phenomena may be classified under three phases :
1. The vapour is very dilute. The components are clearly: visible
in the upmost and lowest stripe. In the central stripe the absorption is
either hardly perceptible (Plate I, Fig. 1) or the components of the
quartet and the sextet are seen as separate, but weak lines. (Plate I,
Fie. 2).
In this phase of the phenomenon the great difference of detiniteness
of the central and outer regions is very remarkable. This contrast
is sull more marked with eye observation.
In order to obtain good photographs, it was necessary to increase
the density of the vapour above the one required for the observation
of the very first trace of absorption.
2. Vapour of dtermediate density.
The components in the upmost and lowest stripes are now no more
separately visible or only in the ease of the quartet. In the central
stripe a superposition of the kind mentioned in § 6 takes place. In
place of the quartet an apparent doublet is seen, the components of
which are situated between the outer and inner components of the
quartet. This case is very clearly represented in Plate I, Fig. 3.
The phenomena exhibited by the sextet (D, line) become rather
complicated.
The superposition phenomenon is often very distinct. The D, line
on Plate I, Fig. 8 shows sufficiently the appearance.
3. With still denser vapour, the components become very broad
and the magnetic change hardly visible. The polarisation of the edges
of the broad line may be recognized. This phase is represented in
Plate I, Fig. 4 It corresponds to the emission effect as it was first
discovered: a slight change of broad lines in a weak field.
( 591 )
With still greater absorption the influence of the field becomes
imperceptible.
All these phases appear with great regularity. If the intensity of
the field is known, it seems possible, the resolving power of the
spectroscope being given, to deduce the density of the vapour from
the nature of the observed phenomena.
The magnetic division phenomena hitherto observed in sun-spots
appear to fall under the second and third phases above mentioned.
Hate from measurements of spot lines, compared with laboratory
experiments, deduces a maximum intensity of the spot field of 4500
Gauss. Hence, one would be inclined to think that the density in
the layers, which bring about the absorption in the sun-spot spectrum
can only be small. Moreover, the non-uniformity of the field of
sun-spots produces by itself a widening of the components. Light from
a limited portion of the spot would give perhaps very narrow spectral
lines. In the light, however, of the critical remarks of Kayser *)
concerning our knowledge of the influence of pressure and of tem-
perature on spectra all such considerations most be put forward
with great diffidence.
11. Observations parallel to the lines of force.
In the present experiments the absorbing vapour subjected to mag-
netic forces is placed between perforated poles.
After putting on the current, one sees in the continuous spectrum,
2 dark bands in the case of D,, 4 in the case of D,, according to
the diagrammatical figure 1. The absorption is incomplete also now,
because of some wave-lengths only right-handed circularly polarized
light, but not left-handed is absorbed and the reverse. In order to
observe the separation and the polarization a Fresnen rhomb is placed
with its principal plane at an azimuth of 45° with the horizon, a
horizontal slit being placed in one of the perforated poles. The
Fresyet rhomb converts circularly polarized into plane polarized
light. By means of a calespar rhomb also now three stripes are
obtained. The first phase (very dilute vapour) is represented in Plate
I, 1g “oy
Vapour of infermediate density (second phase) exhibits the super-
position phenomena mentioned in §) 7 and 8, and diagrammatically
illustrated by Fig. 2. In the central strip one line, at the position
of the unmodified one, surrounded by feebly absorbing regions, is
1) Kayser. Handbuch. Kapitel V. Bd. I,
(592 )
seen. Plate I, Fig. 6 shows these lines for the doublet and the quartet ;
especially with D, the effect is very marked.
12. Observations in directions inclined to the field.
According to Lormntz’s elementary theory of magnetic division one
generally observes in a direction, which is oblique under an angle
% with the lines of force, a triplet with elliptically polarized outer
components *).
The ellipse, which characterizes the state of polarization of the
components with period 7’, -+ v, is the projection on the wave-front
of the cirele perpendicular to the field, in which the electron with
period 7)-+v is moving. v is a small quantity. The direction of
the motion of the moving electron also determines the motion in
the ellipse. The ratio of the axes is as | tocos #. For the other
outer Component with period 7,—v holds mutatis mutandis the same
reasoning.
The central line with the unmodified period 7’, always remains
linearly polarized. The vibrations of the middle component are in
the plane determined by the ray and the line of foree and the
amplitude of the vibrations is proportional to sino.
If we put ®—0, i.e. in the case of the longitudinal effect, only
circular motions remain.
All’ this applies to very narrow spectral lines in a strong field,
the distance of the components being much greater than their width.
According to Voier and Lorentz we must expect some interesting
particularities if this restriction be discarded. We return to this point
later on.
As a general rule the deductions from the elementary theory are
verified. Also in the case of the quartet and the sextet the outer
components become elliptically polarized, as has been observed already
by Riau *).
In contradiction with the elementary theory, though not strictly
applicable to the case, is the very shght diminution of intensity of
the middle components of the quartet even for = 45°.
13. Observations at 9% = 60°.
A .
If the observation is made with a caicspar rhomb, the image
1) cf. Rieu 1. c.
*) Ricui’s observations |.c. all refer to an angle of nearly 55°, the angle at
which according to the elementary theory the three components of the triplet are
of equal intensity.
( 593 )
remains as with the -transversal effect. Yet the presence of elliptic
polarization ought to manifest itself by the appearance in the lowest
stripe of lines, corresponding to the outer components.
With very dilute vapour and with that of intermediate density as
good as no trace of it is seen.
Fig. 7, Plate Il shows the first phase with dilute vapour, Fig. 8
the second phase with denser vapour. Only traces of absorption,
indicative of elliptic polarization can be seen near D,, Fig. 8.
The ellipticity is, however, undoubtedly proved by means of the
FresneL rhomb, placed with its principal plane at an azimuth of 45°
with the horizon. Fig. 9 shows the appearance.
The outer components of the quartet towards the red or towards
the violet, dependent upon the stripe and the direction of the field,
are now considerably weakened; in the case of the sextet they have
vanished altogether. All this proves the elliptical polarization of the
outer components. For, if the polarisation were linear, as might be
inferred from observations with the calespar alone, then the obser-
vation with calespar and rhomb combined, ought to show no difference
between the upmost and lowest stripe. The light of all plane polarized
components would issue circularly polarized from the rhomb and,
the calespar making no selection between right-handed and_ left-
handed polarizations, the components towards red and towards violet
would all be alike. Such a condition is disproved by photographs
such as Fig. 9.
14. One point must be considered somewhat more in detail. What
is the reason that the ellipticity is not shown by the calespar
rhomb alone, whereas its existence is most clearly demonstrated by
means of the Frrsnen rhomb
Let an elliptic vibration with vertical axis 6, horizontal axis a,
be incident upon the rhomb, the principal plane of which is at an
azimuth of 45°.
It is easily proved that the elliptic vibration issuing from the
FresneL rhomb has its axes in the same direction as the original
' A : ay b—a phe ; he xa:
motion and a ratio of the axes = , the original ratio being
b, ba i mao
If « be small in relation to 6 (an elongated ellipse), then, the light
issues from the FresneL as a more circular vibration, which is more
easily analysed.
It depends upon the magnitude of 7, whether : is greater or less than
)
b — (0?
b+a ;
(594 )
We distinguish the following cases :
b—a a
1. a very small, then :
2 pta h
b—=a a
Dae EO atinen —
» +a b
‘ ~ == (és a
3. a >> 0,414 6, then :
a b
|
We shall apply these results to the interpretation of our observations.
Two eases dependent upon the magnitude of @ are of principal -
importance.
In the first case we can observe the effect of both the axes of the ellipse
by means of the combination of the FresxeL rhomb and the calespar
(this is the case of the quartet) (D, Fig. 9), whereas without Fresner
rhomb no effect of the small axis is visible. In the second case the
effect of the small axis becomes apparent by the use of the cale-
spar, whereas its existence cannot be demonstrated with the Prusnnn,
b—a . .
the value of ee being too small. This case is represented by the
sextet, (D, Fig. 9).
If the observation is made by means of the calespar rhomb, we
indeed see with dense vapour new components in the lowest stripe
(see Fig. 8, D,). The theoretical import of this result will be discussed
on another occasion.
Afier introduction of the Fresxai rhomb the component to the
left of the central line (small axis of the ellipse) remains invisible.
(Fig 9; D,, inferior stripe).
Hence we may conclude that at the angle now investigated the
au
ellipticity of the outer components of the sectet (the ratio 5) exceeds
that of the quartet (and is also larger than 0,414).
15. Observations at’ 3 = 45°.
The photographs taken with the calespar alone, show very clearly
the ellipticity of the outer components.
With vapour of intermediate density the phenomenon is already
very marked, especially in the case of D, (Plate I, Fig. 10). Very
remarkable is the slight diminution of intensity of the inner com-
ponents of the quartet. According to the elementary theory the inten-
sity of the central component of a triplet ought to have diminished
already to less than /ad/ the original value.
Prof. P. Zeeman and Dr. B. Winawer. The magnetic separation
of absorption lines in connexion with sun-spot spectra
1. 3.
D,
1
Proceedings Royal Acad. Amsterdam. Vol.
XII
PLA
Prof. P. Zeeman and Dr. B. Winawer. The magnetic separation
of absorption lines in connexion with sun-spot spectra
(60 °) 10 {5 °)
8. (60 °) 11 (45 °)
9. (60 °)
_
bo
D, D, D, Dy
Proceedings Royal Acad. Amsterdam. Vol. XII
Prof. P. Zeeman and Dr. B. Winawer. The magnetic separation
of absorption lines in connexion with sun-spot spectra
13. (39 °)
Types of sun-spot lines. (Mitchell)
5, 6. Widened lines with centres reserved bright.
7. Widened and weakened line. 10. Winged line.
1). O bd i* 10!
5’, 6’, 7. Types of magnetic resolutions in non-uniform fields.
10’. Superposition of magnetic components.
Proceedings Royal Acad. Amsterdam. Vol. XII
a
~
(595 )
16. If a Fresxet rhomb combined with a calespar rhomb is intro-
duced in the beam, one of the components of the quartet also entirely
disappears. At an angle of 60° this was only the case with the
sextet. (Plate li, Fig. 11)
17. Observations at = 39°.
The elliptic polarisation tested by means of the calespar rhomb is
very marked, even with dilute vapour (Plate II, Fig.12, Plate HI, Fig.13).
The inner components of the quartet are now decidedly less intense
than the outer ones.
Plate Ill, Fig. 13 especially shows the smaller intensity of the
components of D, in the lowest stripe. Indeed, they are unmistakably
thinner than those in the upmost stripe.
18. According as the angle between the ray and the lines of force
is diminished, the intensity of the field must diminish at the same
time. In order to make it possible for the rays to traverse the field
under smaller angles the vertex semiangle of the cones must deviate
more and more from the theoretical optimum of nearly 55°.
The decrease of the magnetic separation is clearly shown in our
photographs.
We intend ‘o communicate on another occasion experiments under
smaller angles ® and to enter upon some details concerning the case
in which the components of the triplet are not neatly separated.
Some measurements of the ellipticity of the components will also be
given. On the present occasion we only intended to give a general
survey of the inverse effect, illustrating it by some purticular cases.
19. Types of separation in spot and laboratory.
In one direction we shall now enter upon some more details. The
magnetic separation of lines in a non-uniform tield has been treated
on a former occasion.*) The results then obtained and our present
observations may be of some interest in connection with certain
phenomena observed by Hate. We intend to return to this subject.
Presently it seems interesting to allude to Mircueny’s descriptions of
the various types of spot lines as indicated in the diagram published
in the Transactions of the International Solar Union”).
Our Fig. 14, Plate Hil has been copied from this source. The
types 5, 6, 7, and 10 of the Figure are very characteristic. Type 9
perhaps falls under the type of lines invisible without Nicol mentioned
1) Zeeman. These Proceedings, April 1906, November 1907.
2) Transactions Intern. Union Solar Research, p. 199 ete. 1908.
40
Proceedings Royal Acad Amsterdam. Vol. XII.
(596 )
§ 7 above. In Fig. 15 are represented some separations observed in
/ 77
the laboratory without Nicol or other analyzer, 5’, 6’, 7’ have been
7,
taken in non-uniform fields. 5’ is the quartet of D, observed across
the field; 6’ the sextet of D, observed axially in a non-uniform,
in the central part very strong, field; 7’ also refers to D, in a
weaker field, the observation being made across the lines of force.
The type 10’ refers to the D, line, when observed in a direction
parallel to the field. The field is uniform. The separation gives an
example of the superposition phenomenon mentioned in § 7.
The analogy of the type 10’, Fig. 15 and the type of the “winged
line” seems very remarkable. Of course observation of the state of
polarization would be necessary in order to prove the analogy.
EXPLANATION OF PLATES I—Il.
The figures 1—13 are about thirteenfold enlargements of the images given by
the grating of the absorption lmes D, and D, in a magnetic field.
The upmost and lowest of the three stripes of these figures relate to (oppositely)
polarized light; in the central part the phenomenon is represented as it is seen
in natural light.
Pirate lL. 1, 2, 3, 4, okservations 1 lines of force with different vapour density.
5, 6, observation // lines of force with different vapour density.
Pate Il. 7, 8, observation al S$ = 60° calespar rhomb alone.
9, S = 60°, calespar combined with FREsNEL rhomb.
10, 11, $= 45°.
OTS
Poare 3 Si — 239%
14, Types of sun-spet lmes (adopted from MircHe.).
15, 5’, 6' 7', separations in non-uniform laboratory fields. 10! super-
position phenomenon § 7.
Physics. — “The thermomagnetic properties of elements.” By Prof.
H. E. J. G. pu Bots and Prof. Koraro Honpa. (Communication
from the Bosscha-Laboratory ).
(Communicated in the meeting of January 29, 1910.)
In 1895 Curtin’), though he had investigated relatively few substances,
believed that he coald formulate his results in the following rules:
1. For paramagnetic substances the specific susceptibility is in-
versely proportional to the absolute temperature.
2. Kor diamagnetic substances, on the contrary, the susceptibility
is almost independent of temperature.
3. For the latter class of substances, changes of physical state
generally have hardly any influence.
1). P, Curie, Ann de Chim. et de Phys. (7) 5 p. 289. 1895, Oeuvres p. 252
Paris 1908,
( 597 )
4. The same holds for variations of chemical state (allotropy).
One of us in 1900 proposed to eall the first of these thermomag-
netic rules Curin’s law and to introduce a Curie’s constant such that:
4 (6 —- 273) = €.
It was also expressly stated that very probably this was only a
kind of “limit-law’ in the sense of the analogous law for ideal
gases. In addition it was very soon shown that the usual theory
of directed magnecules leads to such a law, when generalised from
a more magnetokinetic point of view; this was theoretically proved
and experimentally confirmed in the Lorwxrz- and BosscHa-volumes
of the “Archives” '). With all due regard for Curtn’s important re-
searches and for his first rule, the second can and could have no
general signification, for it at once contradicted the results of other
observers, e.g as in the special case of water.
With regard to the third and fourth rules even their author pointed
out several exceptions. As the values of the susceptibilities of the dia-
magnetic substances tested proved much less than those of the paramag-
netic bodies, Curr came to the conclusion that these two Opposite
forms of magnetic induction were due to completely different causes.
Starting from these experimental conclusions, LAaNGrvin ?) in the
year 1905 elaborated an electronic theory of magnetism; he also
gave a kinetic representation of Curie’s first law, completely analogous
to the one mentioned above, without, however, mentioning it, and which
is in addition perfectly independent of the introduction of electrons.
It appeared, therefore, desirable to investigate the ihermomagnetic
properties of more substances: in the first place those of elements,
in order to judge whether Curiv’s conclusions admit of such an
extensive generalisation. If may be at once remarked that such is
not at all the case.
Experimental Arrangement. The method, previously used by Curtand
other investigators, of the torsion-balance combined with a non-uniform
field was applied, employing the semicircular electromagnet recentiy
described in these Proceedings. The axes of the two cores formed an
angle of 10° to 20°; the maximum gradient of the field then lies at
a certain distance to one side of their point of intersection. The field
1) H. vu Bois, Rapp. Congr. d. Phys. 2 p. 486, Paris 1900. — Arch. Neét).
(2) 5 p. 246, 1900, also 6. p. 581, 1901. — Verh. nat. en gen. Congr. 8 p. 60,
Rotterdam 1901. Notations:
a, Atomic weight. 6, Temperature.
C, Cupte’s constant. %, Specific susceptibility.
*) P. Langevin, Ann. de Chim, et de Phys. (8) 5 p. 70, 1905. Journ. de Phys.
(4) 4 p. 678, 190,
40*
(598 )
itself at this particular point amounted to 25 kilogausses; it was
measured from point to point by means of a small standardised
spherical test-coil. The sensitiveness of the torsion-balance could be
varied; it was determined in the usual way by means of applied
additional moments of inertia.
The furnace consisted of a porcelain tube wound with platinum
wire and insulated with kaolin powder and asbestos. With a con-
sumption of 1.2. kilowatts a temperature of 1250° was attained,
which was measured by means of a thermo-element, previously checked
by observations on the melting-points of tin, tellurium, antimony,
and gold.
Tvst-samples. The great difficulty with all experiments in this
sphere of work is and always will be the prevalence of iron,
with its overwhelming ferromagnetic properties, though it hardly
ever seems to act quite freely. In the case of fifteen elements, their
binary alloys with iron were examined in TAamMany’s laboratory, not
in the very diluted state, however, which generally corresponds to
ferrugineous impurities. Of 81 elements, 48 were tested; many of
them were supplied as pure as possible by Kantpaum; Prof. Conn
and Dr. Horrsema of Utrecht kindly placed several elements at our
disposal; as yet the LO gaseous elements have not been tested ; Li,
Rb, Cs, Ca, Sr, Ba could not be obtained sufficiently free of iron;
while Be, Se, Ga, Ge, Y, Rd, ana the rare metals could not be
procured. Fe, Co, Ni, of course, form a class by themselves. Dr. M.
Hanpa kindly determined the percentage of iron colorimetrically by
the Berlin blue-reaction.
The experimental results, moreover, furnish certain physical criteria of
their own reliability, for in so far as the susceptibility proves indepen-
dent of the field there can hardly be question of a ferromagnetic ingre-
dient. With about one third of the samples this was not the case, for the
susceptibility diminished (in the algebraic sense) with an increasing field
according to a hyperbolic law. From this Mr. Morris Owen caleulated
the value x, which would hold asymptotically for an infinite field ;
and, in addition, the influence of the ferromagnetic ingredient, which
at most amounted to only one sixth — and generally much less even —
of what could be imputed to the iron in the free state. The thermo-
magnetic properties also afford a test of purity up toa certain point ;
a few stronely ferrugineous substances show a great diminution
of susceptibility between 500° and 600°, whilst above 700° the
influence of iron hardly need be feared. In no: case is there reason
to doubt that the value of the suseeptibility of absolutely non-ferru-
eineous Clements would remain constant, at least within the usual
(599 )
field-range. The full communication of the results obtained would
require many tables and curves; we therefore draw attention to the
principal points only.
Specific susceptibility *) at 18°. The values found lie between 2
and + 5 (amorphous carbon and palladium respectively). ft cannot
be maintained that the positive paramagnetic values are onthe whole
larger tian the negative diamagnetic ones. Oxygen alone forms an
exception with a value of about 100: the value for manganese was
approximately 10; this contained, however, ‘/,°/, of iron.
Ccerie had already pointed out the influence of allotropy in the
case of phosphorus and antimony, and also that there is no such
influence with sulphur, though it is so well-known for its polymor-
phous properties. A difference was shown to exist between diamond
(— 0,49) and amorphous carbon (— 2,02); silicium crystalline (0,12
and amorphous ‘— 0,14); and especially between common tetragonal
tin (+ 0,03) and grey tin (— 0,29). In the case of tin, the first —
the tetragonal — was KaAuLBAUM’s very pure electrolytic material;
it was afterwards inoculated with a small quantity of grey tinpest,
kindly sent by Prof. Coney from the stores of the vax ‘t Horr Laboratory.
For weak fields indium seemed to be paramagnetic; in a field of
7 Kgs. the value of the susceptibility passed through zero and became
negative, doubtless in consequence of 0,018°/, iron : this phenomenon
0
is of no consequence because it is also discovered in complicated
substances such as certain kinds of porcelain, glass, etc.
Notwithstanding many omissions, it was still possible to follow the
general course of the curve 4 = funet. (a); the curve appears to be
rather intricate, but still shows a distinct relation to the periodic
system. According to the arrangement of MenpELesErr-Bravner’s table,
the rows (1, 2, 3, 4), ‘5, 6, 7, 8), and (9, 10, 11, 12) each form a division
I, HI, HW in which the shape of the curve repeats itself in a peculiar
way. At the junction of I and II Cr, Mn, Fe, Co, Ni lie on a
positive maximum; between II and III, in the same way, the ‘‘rare”
metals: within I, If and Ill the diamagnetic negative peaks are
occupied by the similar pentavalent elements P, Sb and Bi of the
fifth group (8¢, 7, 11% row). In more than one respect further
magnetic analogies of secondary importance exist, which, however,
must be left unmentioned in this communication.
Susceptibility at high temperatures. As a rule the path of the curve
7 = funet. (A) for any substance proved to be the same when the
temperature was increased or afterwards decreased ; certain deviations
probably depend on a change of condition of the iron present afte;
1) Everywhere below expressed in millionths
( 600 )
PeAP REAM AGN Eat IG DIAMAGNETIC
=
C I | D G I D
| |
! ] |
Na (0°—97°) Ti {O] B, cryst (400°—1200°)| B cryst (0°—400°) C, amorphous
Al (657°—1100)? V (500° —1200°) Mg (0°—657°) Si, crystalline | Diamond Cu
|
K (0°—150°) Cr (5002°—1100°) [Fe] (800°—1350°) | P, white | Ag Zn (300°—700°)
V (02—500°) Mn | Coy ISTP =) 2 S, rhombic | 1 @°—114°) Zr (5002—12009)
Cr (0°—500°) Mo [Ni] (350°—800°) Zn (0°—300°) Cd (300°—700°)
Nb (0’—400°) Ru (550?—1200°) As, Sublim | In (0’— 150°)
Pd
W Rh Se, Metallic Sb (0°—631°)
Rare metals?
Os Ir Zr, cryst (0°—500°) Te
Ta
Th (0°—400°) Cd (0°— 300°) | I (1149—200°)
Pt
Au Tl
U - es
Hg (0°-—350°) Pb (0°- 3279)
Pb (327°—600°) Bi (0°—268°)
( GOL )
heating. Me and Ru shewed the above mentioned diminution in a
marked manner between 500° and 600°. The results are collected
in the table p. 600. The elements in square brackets have pre-
viously been examined by others; the atomic weights in each
column increase from top to bottom; the elements under column
C show a constant susceptibility, under / a numeric increase on
heating and under ) a numeric decrease. The fewest number (4)
of elements appears in the fifth column, in the case of which the
susceptibility increases on heating, the increase being, however, very
small in each instance.
From a thermomagnetic point of view a certain relation also exists
in connection with the periodic curve 7 = funet. (a): the paramagnetic
elements under / all lie at the principal maxima or at the secondary
peaks; on the contrary, those under / lie on the ascending branches
of the curve. Therefore the sharpness of the bends would be flattened
more and more at higher temperatures; probably at lower tempe-
ratures they would become more accentuated, and it may be that
only then do they attain their most characteristic shape; of course
the temperature of + 18° is quite arbitrary. Concerning Curtr’s
rules the following statements may be made:
1. Only palladium foil from Kaurnpaum, with 0,70°/, of iron and
%Z= + 6,12, on heating followed, more or less, Curin’s law, but on
cooling it shewed complications. With much purer palladium from
Dr. Herarvus, with 0,038°/, iron and ~,—=-+ 5,79, the susceptibility
fell less rapidly than would follow from Curir’s rule; temperature-
hysteresis was not observed on cooling’).
2. There are only 6 diamagnetic elements which do not vary
within the whole temperature-range. Of these P, 5 and Se had already
been experimented upon by Curtin.
3. On melting or solidifying, sometimes — not always — a dis-
continuity appears, which can be classified under one or other of the
two following divisions: I, a large or small leap in the curve of
zx itself, as with P (44°), Ag (961°, Sn (233), Sb (631°), Te (450°),
Au (1064°), T1 (290°), Pb (827°), Bi (268°); IT, a rather sudden change
of dy/d@ as with Mg (633°), Cu (1065°), Cd (322°), 1(114°); with
regard to sulphur, the curve at the melting-point departs slightly from
its otherwise avdsolutely vectilineal character, which variation was
probably overseen by Curin.
1) By chance palladium is the only paramagnetic element examined by Curie ;
perhaps it was not pure enough. The important resuits for oxygen, for ferromag-
netic metals at very high temperatures and also for their salts crystallised or in
solution, of course continue to hold.
( 602 )
4. As regards the thermomagnetic examination of polymorphous
transformations, a discontinuous diminution of 15°/, of the specific
susceptibility was found at the transition-point of ¢-thatlinm and
B-thalliam at 234°. But the most remarkable properties are shewn
by tin: If diamagnetic grey tin is slowly heated, at 32° the specific
susceptibility (— 0,29) changes almost suddenly (like the density)
and at 35° passes through zero. Possibly this change would wholly
take place at the point of transformation (18°) but then at a
much slower rate. Further heating continuously increased the sus-
ceptibility so that at about 50° the value (+ 0,03) for paramag-
netic tetragonal tin was reached, which afterwards remained practically
constant; according to Draenxs the point of transformation tetragonal
= rhombie tin lies at 161° at which temperature nothing particular
was noticed; at the melting point (233°) a discontinuity from
y= +0,03 to ,=— 0,04 once more appeared; the diamagnetic
liquid metal remained nearly unchanged.
An extension of these thermomagnetic investigations towards low
temperatures is in preparation
From the above, especially from the conclusions arrived at under
1 to 4, it seems to follow that Curie’s four corresponding rules are
certainly devoid of the general meaning, which has rather rashly
been ascribed to them. At the same time the experimental starting-
points of Lancrvin’s theory are evidently undermined; more solid
and broad foundations for future theories can only be laid with the
aid of more extensive research.
Chemistry. — “Studies on Tellurium: 1. The mutual behaviour
of the elements sulphur and tellurium’”’. By Prof. F. M. Jawerr.
(Communicated by Prof. Van Rompurcn).
(Communicated in the meeting of January 29, 1910).
§ 1. Whilst we are in the main thoroughly informed as to the
relation of selenium and sulphur, the views as to the mutual behaviour
of the elements tellurium and sulphur still differ somewhat. KTAPRorH ")
has already investigated this subject. He states that on melting
together tellurium and sulphur leaden coloured masses are formed
crystallising in vays, which, on heating, give off sulphur and yield
a porous metallic looking mass, which he takes to be telluriumsulphide,
Berzenivs®), thirty years later again broached the subject ; he found
that no compounds were formed on melting, but thought that the
1) KLApRorH, Crelle’s Ann, (1798). 191.
2) Berzeiius, Gilb-Pogg. Ann. 8. (1826). 413.
{ 603 )
compounds TeS, and TeS, are present in the brownish-black preci-
pitates, formed when passing HS through solutions of tellurites and
tellurates. He arrived at that conclusion on account of the solubility
of these precipitates in aqueous potassium or sodium hydroxide, which
is also the case with TeO, and TeQO,.
BECKER") was the first to analyze these precipitates and he finally
arrived at the conclusion that their composition actually corresponds
with TeS, and TeS,. He proved however, that nearly all the sulphur
may be removed from these substances by treatment with carbon
disulphide: TeS, yielded a residue containing 6.14°/, of sulphur
instead of 42.85 °/,,
33.4 °/
whose composition agrees nearly with those of the supposed com-
TeS, a residue contaming 3.69 °/, instead of
,. He coneludes that the black precipitates are only mixtures
pounds According to him they are formed primarily as ephemeral
compounds, which are at once decomposed by the solvent. Burznrivs *)
and Opprnneim*) obtained double sulphides to which they assigned
the formulae 3k,5+ Tes,, etc. In more recent times, Brauner‘) and
GuTBier *) again inclined to the opinion that we are dealing here
with mixtures of the elements.
§ 2. Since Dumas placed tellurium in the sulphurgroup, as the
first homologue of selenium, and thus the well-known difficulty as to
the position of tellurium, in regard to iodine, in the periodic system
introduced later, was created, — the question as to the relation of
tellurium on the one side and sulphur and selenium on the other
has again become of actual importance. For now it is undoubtedly
certain that the atomic weight of tellurium is 127.6 and therefore
greater than that of iodine. On the other hand the differences between
tellurium and the other two elements are so strongly pronounced
that Rereers on account of the isomorphism between tellurates and
osmiates, thought it would be better to include tellurium in the group
of the platinum metals. Tellurates to wit, are not isomorphous with
sulphates, selenates, manganates, ferrates etc. On the contrary, PELLINI
showed an isodimorphism in the case of (C,H,),SeBr, and (C,H,),TeBr, ,
whilst Norris and Mommers noticed a direct isomorphism between
the selenium- and tellurium double chlorides and bromides of dimethy|-
1) Becker, Lieb. Ann. d. Chem. 180. (1876). 257.
2) BERZELIUS, Traité de Chimie. (1830).
3) OPPENHEIM, Journ. f. prakt. Chem. 71. (1857). 270
4) BrRAuNER, Journ. Chem. Soc. 67. (1895). 527.
5) GuTsigER, Berl. Ber. 34, 2114. (1901).
( 604 )
amine. But on the other hand many objections have been raised to
the position assigned to tellurium: for instance, the different consti-
tution of tellurie acid) whieh, probably, must be looked upon as
H,TeO, and the totally different hydration of tellurates in comparison
with sulphates and selenates. However this may be, it is highly
desirable to obtain more dafa as to the position of tellurium among
the other elements and for this reason, the relation to sulphur had
io be ascertained in the first place.
§ 3. The tellurium was obtained from 1'/, kilo of erude tellurium
probably derived from American ore. It appeared to contain the
following elements: tellurium, selenium, sulphur, lead, copper,
bismuth, iron, silicon and traces of antimony, zine and a few other
metals.
The first puritication was carried out by oxidation with aqua regia,
evaporation of the filtrate to dryness, and repeated extraction of the
residue with strong hydrochloric acid. The boiling filtrate was then
precipitated by sulphur-dioxide; the first portions of the precipitate
being rich in selenium were each time rejected. This operation was
repeated three times. The amorphous telluwrium was divided into two
parts; one portion was converted, by the process given by Norris,
Fay and Eperriry'), into basic tellurium nitrate Te,O,(OH)(NO,)
and by repeating the process five times, which operation lasted
many weeks, it was finally obtained quite pure in the form of the
said salt: from this, pure TeO, was then obtained by gentle ignition
and this, dissolved in pure hydrochloric acid was precipitated by
SO,. The other portion was converted into tellurie acid by means of
CrO,, according to STAUDENMAYER’s process as modified by GursiEr *);
this was purified by precipitating twelve times with nitric acid and
then erystallising from water. It is necessary to reduce the adhering
CrO, with aleohol, otherwise the telluric acid crystals retain a yellow
colour whieh is caused by oecluded solid CrO,; this: matter I hope
to refer to shortly.
The pure telluric acid was then reduced completely by hydrazine
hydrate.
The crystalline form of the basic nitrate has not been described
up to the present. The following data have been obtained from the
substance crystallised from nitrie acid.
1) Norris, Fay and Epareriey, Americ. Chem. Journ. 23. 105.
2) Gurpier, Z. f. anorg. Chem. 29. 22. (1901); 32. 96. (1902).
( 605 )
Colourless, very lustrous needles up to
5 man. in length and usually flattened
along {O10}. They exhibit many vicinal
planes particularly in the vertical zone, and
greater angular differences occur also in
different individual erystals. The measure-
ments must, therefore, be regarded only as
approximations.
Rhombic-bipyramidal.
Ob 601590 Ak O16 OF.
Forms : m= {110}, 65= {010} and p=}{120},
very lustrous; particulary 6, which is also
a cleavage plane and possesses a high lustre.
On the other hand g = {011} and s=§021}
Fig. 1. are dull, the form {021} is mostly absent.
Crystalline form of basic The erystals exhibit a pronounced inclination
tellucium nitrate. to tetragonal symmetry.
Angular values : Measured : Calculated :
m:m = (110) : (110) =* 61° 5’ _
O:q == (010): (O11)=* 58 444 —
Ts = (AO) = 420) == Ol 2 19eS 1S
p20. — (120) (010) ==) 39) 59 40 24
Gig) == (Old) O11) = OF a) 62 «31
Teg —* (AO) Oli) ie ot 74 438
tO — 1 ALON ONO) Oi 2 a9 274
Des = Old). C2) = 38 26 S929
SEO) — O28) (O11) 9 Oo LF AG
Completely cleavable towards {O10}.
The optical axial plane is {OO1{ with the a-axis as first diagonal.
Strong rhombie dispersion with @ << v; the apparent axial angle in
cedar oil (1.51) was about 68°.
It may be observed here that the tellurium precipitated from
tellurie acid by hydrazinehydrate is distinguished from that preci-
pitated from a hydrochloric acid solution by sulphurdioxide which
is also amorphous, by a perceptible darker colour. It is, as yet,
undecided whether this is merely due to another degree of division
or to a real allotropism of the amorphous modification.
( 606.)
§ 4. Both masses of tellurinm: mixed with 5—6 times the amount
of powdered, freshly prepared potassium cyanide were fused for
some hours in large Rost crucibles in an atmosphere of coal gas,
with the aid of a large Purrror-furnace. In the course of a few
months, about 5 kilos of these melts were obtained. When carefully
powdered, the dark coloured masses dissolve in recently boiled, hot
water to beautiful purple coloured solutions, which on cold oxidation
by purified air deposit from the K,Te all the telluriam in’ brilliant
needles. Ou melting the masses, the poisonous influence of the hy-
drogen telluride, which is formed in small quantities, was experienced
only too plainly, also the disagreeable consequences of breathing the
very small quantities of TeCl, formed during the treatment with
aqua regia. For weeks afterwards the breath has a powerful odour
of (CH,), Te, which resembles phosphine and is exceedingly sensitive
to the olfactory nerve of bystanders. ')
The crystalline and already very pure tellurium thus obtained is
free from selenium as proved by the exceedingly delicate Norrts’
potassiumiodide-reaction and by the non-reduction of the TeO, by
hydroxylamine in strong hydrochloric acid solution. All the selenium
has been removed as KCNSe, whilst the tellurium has passed into
k,Te and then has again been liberated by the action of air free
from H,s.
The purified element was now distilled in vacuo at about 600—-
700° in lone tubes made of hard glass and containing plugs of
asbestos; a Tcru furnace was used. This operation was repeated
about seven times, each time about LO grams were used. The pure
tellurium thus obtained was silvery white and coarsely crystalline,
much resembling crystallised antimony.
The determinations carried out have been made with the produet
obtained from tellurie acid. The sulphur was recrystallised twice from
boiling toluene and heated in a drying oven at 90° for some hours.
1) The opinions as to the physiological actions of tellurium are shill very much
divided. Although seleninm is an element hardly less poisonous than arsenic, tellu-
rium is considered by CzAprK and Weritt (Chem N (1893), 1098 2) to be com-
paratively harmless, owing to the much more rapid reduction of the telluriam
compounds and the consequent localisation in the organism. The experience gained
in my laboratory proves this view to be incorrect.
Tellurium is undoubledly poisonous, but the individual sensitiveness to small
traces varies widely with different persons. TeH., in particular, is a poison causing
severe headache and vomiting; other telluriumecompounds such as TeCly, for
instance are supposed to cause much inconvenience only, owing to their conversion
into. malodorous substances, but still. there can be no doubt whatever as to their
poisonous nature.
( 607 )
§ 5. The construction of the melting apparatus will be readily
seen from fig. 2. The hard glass tubes always filled with 10 grams
of the weighed and well mixed complex of the two elements were
placed in iron cylinders filled with fine sand. Tube and cylinder
were covered with asbestos; the requisite atmosphere of nitrogen
was supplied by way of a hard glass gas-inlet-tube. The nitrogen
was prepared from NH,Cl and KNO,, freed from oxygen by means
of alkaline pyrogallol and sodiumhydrosulphite and dried by sul-
phurie acid. The furnace was constructed of chamotte stone furnished
with an asbestos filling and a central cylinder of unglazed earthen-
ware; it was covered with an asbestos board resting on three little
chamotte blocks, which were either removable or not so, for the
regulation of the velocity of cooling. The icekettle for the cold
solderplace of the platinum-platinumrhodium thermoelement (38> mm,
is double walled and allows of working for some six hours with
the single supply of ice; all the conducting wires were isolated by
elass tubes.
The galyanometer of Stemens and Haske was verified by deter-
mining the meltingpoints of tin, lead, bismuth, cadmium, zine, anti-
mony and silver and by making use of the values found by Day
and Horsorn and by Day and Cement, which were compared with
the gasthermometer. The reading was taken with the aid of a lens,
the counting of the time by means of a clockwork, which gave a
signal every 10 seconds.
to} ©
( 608 )
§ 6. Great difficulties were experienced in the determination ;
when we dealt with mixtures containing much tellurium every pre-
caution had to be taken to prevent the boiling off of the sulphur,
and in the case of complexes contaiming much sulphur trouble arose
from the great viscosity of the fusions and the very slow crystallisation
of the masses. If the percentage of sulphur exceeds 80, the deter-
MELTING POINT DIAGRAM OF SULPHUR-TELLURIUM COMPLEXES.
; : Initial ~ End Period of
Mol. 0/9 by Weight solidifying solidifying
Sulphur Sulphur | point In
(Ce | seconds
( 609 )
minations often become very uncertain; some of these mixtures only
exhibited a sharp end-solidifvingpoint. Still it was generally possible
to get concordant results on repeating the experiments.
The subjoined table shows the results of the experiments.
Liquid in presence
of the mixed crystals T. H kee
"| ite fs
ike he
~ fh S
H Es Is
= ' o
H = a
or} ; s
oe) t- 106° ' y
ae Sar ——a =
alee ese e
sae sau : re \
i Mixed erystalsS + \ yer
" Mixed erystals T ‘ "
wet — Bae a a
Gamo 7) Sy) Fe 37 0) 0) Ae Wt We Wie Wipes ps as
Fig. 3.
§ 7. These data represented graphically in Fig. 3 in the usual
manner show, therefore, that the elements sulphur and tellurium
when melted together yield, when solidifying, two series of mixed
crystals of a different crystalline form. The condition diagram is
that which has been noticed frequently with isodimorphous substances ;
there is a very extended hiatus starting from almost pure sulphur to
perhaps 27°/, of sulphur at the side of the trigonal mixed crystals.
The temperature of the eutectic point / is 106°; the time required
for solidification, as far as could be ascertained, increases continuously
with the percentage of sulphur until the pure sulphur is reached.
The mixed erystals rich im sulphur have a slight ruddy colour; as
very small amounts of tellurium impart to sulphur an intensely red
colour, their tellurium content must be small indeed. They exhibit
the thin needle shaped form of monoclinic sulphur. The transformation
at 106° may be seen beautifully with the eye in the various melts
on cooling as well as on warming. The monoclinic mixed crystals
( 610 )
rich in sulphur appear to change into the rhombie form at a lower
temperature. In these circumstances nothing is noticed as to compounds
between tellurium and sulphur; even at lower temperatures no heat
effects are observed. The melts of the mixtures rich in tellurium
are dark brownish black and in thin layers yellowish brown; unlike
the melts rich in sulphur they are thin fluid up to their solidifying
pots.
§ 8. Considering all that is known up to the present as to the
behaviour of the elements sulphur, selenium, and tellurium on being
melted together, we may say that in this respect, tellurium certainly
deserves the place assigned to it by Dumas. Sulphur and selenium
form, according to Rrcer?), a trimorphous series of mixed crystals,
selenium and telluvium. according to Prniost and Vio *) an uninter-
rupted series of trigonal mixed erystals; but no compounds are formed,
as may be expected, looking at the experience gained, apart
from the exceptions in such triads of homologous elements, — at
any rate in the central groups of the periodic system. With sulphur
and selenium the matter is even somewhat still more complicated,
as three instead of two heteromorphous kinds of mixed erystals
occur in this ease. If we accept Rwraurs’ view according to whom
a less stable form, mostly unknown in the free state, of each of
the components should correspond to each of these forms, the isotri-
morphism in the case of selenium and sulphur is certainly more
difficult to explain than the dimorphism of sulphur and tellurium.
For of the two monoclinic series in the system: sulphur-selenium
one, according to MuTnMann, is analogous to the form of y-sulphur,
whereas the trigonal series would already possess the form of metallic
selenium. But neither of the two known monoclinic modifications of
selenium is isomorphous with any monoclinic modification of sulphur *),
whilst the trigonal so-called ¢-form of this element differs from the
trigonal form of selenium. Looking from Reraers’ standpoint both
these elements should be eredited, in addition to their well known
allotropie forms, with at least another two unknown, less stable
moditieations. In the trigonal series of the system: sulphur-tellurium
we are dealing obviously with the same less stadle trigonal form
of sulphur as in Rincer’s investigation, whilst the assumption of an
unstable monoclinic form of tellarium cannot have anything artificial
about it, in view of the fact that this symmetry occurs frequently
1) Ringer, Z. f. anorg, Chem 32. 183. (1902).
2) PeLLint and Vio, Gazz. Chim. It. (1906). II. 476.
*) Grovu, Ghemische Krystallographie, Bd. 1. (1906). p. 28—3o,
( 611 )
both with selenium and sulphur. The research of PeLiimi and Vio
also does not introduce any further complications; the two elements
are united there in all proportions to one trigonal series, so that
only the sulphur-containing complexes of selenium and_ tellurium
exhibit the hiati on mixing in the solid condition.
All this admits ‘of the conclusion that the elements sulphur, selenium
and tellurium form indeed a natural triad of perfectly homologous
elements which are more adjacent to each other than their group-
fellow oxygen is to any one of them. There can be only question
of true “compounds” when one of the elements combines with oxygen’).
§ 9. Now there is still the question: what must be thought of
the tellurium-sulphur complexes which are formed, at the temperature
of the room, by means of H,S from solutions of tellurites and
tellurates, and in what sense must the so-called double sulphides
obtained by Oppennem and Berzetius be regarded.
First of all, I soon succeeded in showing that the element tellurium
and particularly its amorphous modification dissolves, without leaving
any residue, when heated with a solution of alkali- or ammonium-
sulphide, also that the solubility increases with the concentration of
the sulphide; and further that the solubility also increases when
potassium hydroxide is added to the sulphide solution, thus retarding
the hydrolysis. Clear yellow solutions are so formed turning some-
what ruddy on boiling, and oxidising rapidly in contact with the air
with formation of a black precipitate. They are strongly alkaline and
give with hydrochloric acid a heavy, black precipitate with evolution
of H,S; the precipitate appears to contain tellurium as well as sulphur
and is soluble in alkalihydroxyde.
The analysis of these black precipitates did not give constant
values; the tellurium content is much dependent on the modus operandi
and oscillated between 46.9 °/, and 80.9 °/,.
Thereupon, the action of H,S on different tellurium compounds
‘was investigated: on the basic nitrate, on the finely divided dioxide
suspended in absolute alcohol, on dioxide in hydrochloric acid solution,
on telluric acid in water and on the tellurite- and tellurate-solutions
obtained from TeO, or telluric acid. A beautiful, somewhat crystalline
looking product was obtained from the alcoholic suspension of TeQ,;
the analysis of the blue-black substance gave 80.1 °/,—80.9 °/, of
tellurium whereas theory requires 79.9°/, for TeS, 66.6°/, for TeS,
1) It is, moreover, also known that O and §, for instance, never give isomorphous
substitutions in organic compounds. S, Se and Te, however, behave differently as
shown by the research of Petiryt, Norris, Turron, and others.
41
Proceedings Royal Acad. Amsterdam. Vol. XII.
( 612 )
and 57°/, for TeS, so that the composition came very near to that
of TeS, but with an excess of tellurium.
The telluric acid was not reduced in the cold; the TeO, dissolved
in hydrochloric acid yielded a black precipitate with 71.2°/, of
tellurium and therefore situated between TeS and TeS,.
The basic nitrate is rapidly attacked by H,S, but only at the
surface; on the other hand it dissolved completely in boiling ammo-
niumsulpbide, which solution, after being concentrated in vacuo at
40°, and allowed to erystallise in a vacuum desiccator over CaO,
yields hard, pale yellow needles of a compound which may be
recrystallised in vacuo without decomposition. The colour of the
needles is greenish-yellow: they dissolve in water to aclear, yellow,
strongly alkaline solution, which rapidly oxidises when exposed to
the air; the erystals also soon turn black on exposure. The analysis
gave a varying tellurium-content according to the method of prepa-
ration; in one instance were found 20.1°/,(NH,), 42°/, Te and
37.9°/, 5, which leads to the formula (NH,),Te,5, *).
In an analogous way the potassium compounds were prepared from
the tellurite and tellurate with H,S, by solution of the precipitate in
the solution saturated with H,S, or by solution in KOH, and by
conduction of H,S through it; the solutions were evaporated in vacuo,
and were then left to crystallize over calcium oxide. Apparently the
same yellow compounds are formed in all these cases, which crystal-
lize in rosette-shaped aggregates of hard, fine needles, which in a
humid condition smell strongly of H,S, and yield clear, readily
oxidisable solutions. Also the solid salts themselves oxidise rapidly,
in which they become greenish yellow, and finally perfectly black.
On close investigation the colour appears to assume different shades,
even if to all appearances the same mode of preparation is used.
Attempts to find a constant composition for these salts, have been
unsuccessful; successively it was found to be: 35.4°/, Te (calculated
1) The analysis of these complexes is a very tedious operation. If tellurium only
has to be estimated and no sulphur, the reduction process with SO, or NaHSO;
is still to be preferred. In our case, the tellurium had to be precipitated from a
boiling, strongly ammoniacal solution with hydrazine hydrate, which reduction
proceeds very slowly and also incompletely, and had often to be repeated half a dozen
limes. The last traces of still dissolved tellurium betray themselves on heating by
the fine steel blue colour of the colloidal tellurium present; this is generally
completely precipitated on rendering the liquid acid, and by way of control the
solution may then be heated once more with ammonia and hydrazine hydrate.
The tellurium was collected on a weighed filter dried at 100° and weighed as
such. The SO; was weighed as BaSO,, the K as KCl or KCIO, the NH; as NH,Cl.
For obvious reasons the analysis of the barium salt is a very tedious affair.
( G6f3>)
for K,Te,S, 35.7°/,); 33.5°/, Te, 33.4°/,S and 33.1°/, K, which
answers to a formula K,,Te,S,,; another time (for a product prepared
from K,TeO,): 44.7°/, Te, 31.477/,S, and 23.7°/,K, which would
correspond to K,,S,,Te,; again another time at somewhat higher
temperature: 37.5°/,Te, 34.3°/,S and 28.1°/,K, which leads to a
formula K,,Te,S,,.
The behaviour is practically analogous to that found in the poly-
sulphides of the alkalies towards sulphur, where, according to
Kisrer’s researches*), very complicated equilibria between different
polysulphides and their dissociation products occur in the solution;
and to that of selenium towards sulphides where, according to
MgssINGER*), a portion of the sulphur of the complex sulphohydrogen
sulphides may be replaced by selenium, forming such compounds
as Na, SSe, which, therefore, belong to the type of a ¢risulphide.
The behaviour of amorphous tellurium towards sulphide solutions as
described previously also agrees with the notion that we are dealing
here with salts of complex tellurohydrogen sulphides which in such
solutions are in dissociation-equilibria with each other and are
moreover split hydrolytically.
The type of the ¢rzsulphides becomes then of particular importance
next to that of the disulphides: K,,5,,Te, may be derived from
K,5, by isomorphous substitution of '/, of the S by Te; K,Te,S, and
(NH,), Te,S, similarly from K,S,, or (NH,),5,; on the other hand
K,,Te,S,, has again the character of the type K,S, ete.
§ 10. Although these compounds do not as a rule occur in measur-
able forms (the K-salt was obtained a few times as beautiful rhombic
parallelopipeds with faint double refraction and without perceptible
dichroism) I finally succeeded in obtaining very large, yellow crystals,
with many planes, of a barium salt prepared by dissolving the black
precipitate formed by the action of H,S on potassium tellurite in
BaS-solution. The analysis indeed, did not always yield precisely the
same results, but still the composition agreed closely with the formula
Ba,5,Te,; in one instance the normal composition; 45,8°/, Ba; 25°/, S
and 29,1°/, Te was actually found. These crystals were accurately
investigated and proved to be so well constructed that, in their habit,
they did not remind us of mixed crystals but, on the contrary,
made a vivid impression of belonging to a true chemical compound.
The following data were found:
Large yellow transparent crystals fairly stable in the air but, after
some time, assuming a greyish colour. They are well constructed,
1) Kiser, Z. f. anorg. Chem. 44. 431.
2) MESSINGER, Berl. Ber. 30 805 (1897).
41*
( 614 )
yield constant angular values and have, crystallonomically, quite the
appearance of a well defined compound of constant composition.
Or
es
Sy
Fig. 4.
The compound has, in moist air, a strong odour of hydrogen-
sulphide and is decomposed by water with separation of a black
substance which contains tellurium and sulphur.
Triclinic-pinacoidal.
a@:6¢=1.6835:1:1.5515
A= A095 43" e413" Tay
B= 122° 10} B = 124° 13’
C= 790732¢ Vs ea 39,
Forms observed: c= {001}, strongly predominating‘ a = {100}
and 6 = {010} equally well developed and lustrous; g = {011} and
y= {101} quite as much developed as a and #, and yielding sharp
reflexes; o = {112}, lustrous and fairly large; m = {012} small but
lustrous; «== {111}, small and subordinate, generally with but one
plane ; m = {110}, well developed and lustrous, also without the
parallel opposite plane.
The habit is flattened towards {001} with slight stretching in the
direction of the b-axis. A complete or distinct plane of cleavage
is not found.
The following angular values were measured :
( 615 )
Measured : Calculated :
100) : (010) =*89° 281 —
(OOD =F 70% Az. -
(00) —* 57 492). —
: (101) =*53 467/, =
: (011) =*65 45 —
>
|
=)
S
a
lon)
i
5
~
S
S
Tar
a
~
NaN ee an
S
S
pee
e:¢= (001
o:b6 = (412): (010) = 67 32 67° 36’
r:b6= (101): (010) = 68 47 68 471/,
a:q = (100): (011) = 67 29 67 26
c:0 = (001): (172) = 50 5 49 49
a:r=(100):(101)— 68 24 68 24
c:n = (001) : (012) = 38 17 380 On
n:q = (012):(011) = 27 24 a7 8
q: 6 = (011): (010) = 43 56 43 58
—
S
SiS
: (112) = 52 35 528 47
: (011) = 32 24 32 49
ia)
|
SS
Se
_—
i)
wm
=
=)
SR
T10): (010) = 33 51 33. 37
m:a = (110): (100) = 56 44 56 55
m: r= (110): 401) = 59 37 59 322/,
ey
b>
S
SES
(O14) 335) 10 35 21'/,
: (010) = 40 55 40 47
:(001)= 85 46'/, 85 481/,
oO: @— Git) = 400) 74.28 74 30'/,
wo g= (111) 711) = 38 5 SBraoe
The agreement between the observation and the calculation is an
excellent one.
Etching figures were not obtained. It may be, — looking at the
acentrie habit and plane-development of some of the forms, — that
the symmetry is triclino-pedial. The situation of the optical axial
angle could not be determined. That of the optical main directions
was such that the angle of extinction on {001} with the side (001):
KS
I
|
©
>
|
FEN GES GER GER
—_—
—
&
ey
|
—_
=
las |
(101), was about 15°, but on {101} with the same side it amounted
to about 12°, and that with an inclination which on {101} proceeds
from the left in front to the right at the back, and on {001} from
the right above to the left below.
Here we are, consequently, also dealing with a polysulphide of
the type BaS, in which */, of the sulphur has been replaced by
tellurium.
( 616 )
Efforts to obtain this compound, prepared from BaS and S, in a
measurable form, and thus to obtain an argument in favour of the
said view, in the event of an isomorphism between the two sub-
stances, have been found so far unsuccessful.
§ 11. In the electrolysis of a dilute solution of the potassium
salt, in which the platinum-dish acted as the cathode and a dise-
shaped platinum-electrode as anode, it looked as if tellurium was
precipitated at both electrodes. ‘lhe liberation of the black substance
at the anode is nothing else than an oxidationphenomenon.
The tension at the electrodes was 2.6 Volt, the current 0.05 Am-
pere; the oxygen formed at the anode oxidises the liquid, so sensitive
to oxygen, with separation of tellurium-sulphur complexes which
partly stick to the anode and partly collect above the same on the
liquid; if the current passes for some time the precipitate redissolves
and the anode again turns bright. I have ascertained that the adhering
precipitate contains tellurium as well as sulphur.
On the other hand, the precipitation of a black substance at the
cathode takes place continuously but very slowly; after twelve hours
only a small portion of the salt, about one gram and a half in 50 ce
of distilled water, had been decomposed by the current. This black
precipitate has now proved to be pure tellurium and this observation
would, therefore, go against the assumption that tellurium forms a
constituent of the anion. This experiment, however, cannot be used
as evidence against that view, since we know an analogous case in
the electrolysis of sodium-sulphantimonate'), where the antimony
also proceeds, apparently, to the cathode, although it acts, in the
salt, as a constituent of the anion.
It has also transpired in these experiments that the metal does
not wholly take part in the electric conductivity, but that in the
electrolysis of the solution, the sodium sulphide is decomposed, and either
the sodium liberated at the cathode, or the bydrogen which it causes
to be evolved, precipitates the antimony by a secondary reaction.
Only when a very little alkalisulphide is present, the anion ''SbS,
also moves towards the anode. Obviously, the explanation in our
case is the same; the tellurium is formed secondarily at the cathode,
whilst at the anode, as in the experiments cited, fairly complicated
and somewhat obscure oxidationphenomena occur. In each case,
this apparent contradiction does by no means prove the incorrectness
of the view, that the said salts may be considered as derivatives of
9
‘.
1) Osr und KLAppRotH, Zeitschr. f. angew. Chemie (1900). p. 82
( G17 )
complex tellurohydrogen sulphides. The investigation of this exceedingly
complicated subject is being continued in the direction indicated.
§ 12. Summarizing the results of these investigations, I believe I
may say :
1. That the elements tellurium and sulphur do not form compounds,
but mixed crystals.
2. That the elements tellurium, selenium and sulphur behave in
quite an analogous manner towards the sulphides of the alkali and
alkali-earth metals, and cause the formation of complex sulpho-,
seleno- or teilurohydrogen sulphides of a different type, and that it
is quite unnecessary to presuppose the intermediate formation of
selenium-sulphur or tellurium-sulphur compounds.
3. That the position, given by Dumas, to tellurium in the sulpbur
group as the first homologue of selenium is quite justified so far as
the mutual behaviour of these elements is concerned, and that sulphur,
selenium, and tellurium form a natura! triad of elements, which are
more adjacent to each other than any one of them is to oxygen.
Groningen, Inorg. Chem. Lab. of the University.
Physics. — “Some remarks on Prof. Kounstamm’s reply.” By Dr.
J. J. van Laar. Communicated by Prof. Lorentz.
In these Proceedings of Jan. 6% 1910 Prof. Kounstamm has inserted
a reply to my remarks suggested by a paper by Messrs. TrmMERMANS
and KounstamM. Though I, too, very reluctantly continue the discus-
sion, I feel obliged to briefly revert to this matter for the last time,
in order to prevent further misunderstanding.
So I will just point out that Mr. Konnstamm is quite silent about
the cardinal point of my remarks, given in point @ second part,
point e and point /; viz. that Messrs. T. and K. in consequence of
their disregard of the last five of my seven papers on the subject
in question have wrongly asserted that the ‘‘abnormal” type II could
not occur for normal substances, and that this would be due to my
restricting supposition a,,—=WVa,a,. Only to remove this misunder-
standing — as I had asserted the very opposite of this — I wrote
my preceding paper.
( 618 )
On the other hand a few minor questions are extensively discussed
: . fic /—— d*b
in the answer, viz. the question a,,—=Va,a, and aa | I must
a
remark here that when I repeatedly spoke of the ‘quite general”
case a, Sy b, S b,, this expression “quite general” was obviously
meant in contrast to the special case a, S$ a,, 6,= 6,, treated by
me before in the first two Papers, as would be clear to everybody,
and that the ‘generality’ meant by me according to the whole tenour
of my papers, of course, only holds within the area of the once
assumed supposition a,,—=V a,a, (BerTuEtor’s). For this supposition
I explicitly premised in all my papers, and I repeated it more than
once (loc. cit.).
Now with regard to the question itself of the supposition a,, =Va,a,
(which, however, is not the point at issue), I may be allowed to
remind Mr. K. of a paper of his in the Zeitschr. f. physik. Ch. 36
p. 41 (1901), where it, inter alia, says at the end (p. 62): “So weit
ich aus dem mir bekannten Material zu schlieszen vermag, scheinen
mir jedoch die Tatsachen sehr zu Gunsten der (BrRTHELoT’sche)
Annahme zu sprechen....” [ will add that I, too, consider the
supposition @,, =WVa,a, as very probable, and that seeming deviations
from this supposition are attributed by me to the formation of com-
pounds. But I hope to treat this more fully on a later occasion.
I now demonstrated that even on this simple supposition the ab-
normal type HI can occur for perfectly normal substances. And this
Mr, K. denied — as my later papers on this subject in which this
was proved by me, had evidently escaped his notice.
[3
With regard to the supposition ae Mr. K. refers to my state-
av
ment that “qualitatively everything will remain the same if 6 is not
assumed independent of » and 7’”. This, however, is quite beside
Peas ends0 f Pe
the question whether the supposition a = 0 is of influence on my
results or not; for v and 7’ are not the same thing as z. I fully
maintain my contention, and Mr. K. will, no doubt, understand,
that this dependence on v and 7’ was only mentioned by me, because
VAN per WaAats’ later investigations have shown that 0 still depends
on this quantity. But this is not the point in question.
I, however, readily acknowledge that when writing the lines
about the longitudinal plait closing again, quoted by Mr. K., I did
( 619 )
not sufficiently clearly state that the divergent result was only
d*b
founded on the assumption Ae I knew, however, that VAN DER
ve
Waats in his Continuitat I] p. 24 has already treated this question.
Yet on theoretical considerations I abide by my opinion that in the
neighbourhood of the limiting volume, so at very high pressures,
‘2
must be = 0.
dz
And now I think that I for my part, have sufficiently elucidated
Mr. Kounstamm’s Reply, so that further misunderstanding seems
almost precluded.
Baarn, Febr. 21, 1910.
Mathematics. — “The oscillations about a position of equilibrium
where a simple linear relation exists between the frequencies
of the principal vibrations.” (1st part). By Mr. H. J. E. Bera.
(Communicated by Prof. Korrrwne).
Introduction.
§ 1. In his paper'): “On certain vibrations of higher order of
abnormal intensity (vibrations of relation) for mechanisms with more
degrees of freedom” (Verhandelingen der Koninklijke Akademie van
Wetenschappen, Vol. V. N°.8, 1897; Archives Néerlandaises Vol. I,
series II, pages 229—260) Prof. Korrewne has written down the
expansions in series for the principal coordinates of an arbitrary
mechanism with more degrees of freedom, performing small oscilla-
tions about a position of stable equilibrium. From these expansions
in series could be deduced that in a certain case it was possible for
some vibrations of higher order, having in general a small intensity
with respect to the principal vibrations, to obtain an abnormally
great intensity; this is the case when between the frequencies
n,n, ete. of the principal vibrations a relation exists of the form
(is => Ujby sooo S08
where p,q etc. are positive or negative integers and 9 is with respect
tO x,y etc. a small quantity, called residue of relation.
Furthermore however it became evident that, when S< 4 (Sis the
sum of the absolute values of p,q etc.) and at the same time ge = 0,
1) “Over zekere trillingen van hooger orde van abnormale intensiteit (relatie-
trillingen) bij mechanismen met meerdere graden van vrijheid”.
( 620 )
the above-mentioned expansions in series lost their validity; we must
therefore investigate in a different way what becomes of the movement
in the case mentioned. In what follows we shall investigate this
for a mechanism with two degrees of freedom. As a base for this
investigation a very simple mechanism is selected, namely a material
point which moves without friction yet under the influence of gravi-
tation on a given surface in the vicinity of its lowest point. Every
time one of the cases S<-4 is discussed we shall pass to an arbitrary
mechanism with two degrees of freedom.
Movement on the bottom of a surface.
§ 2. We shall accordingly first pass on to the treatment of the
simple mechanism we have chosen as a base for our investigation.
When the surface has positive curvature in the vicinity of its lowest
point O, when plane XY is the tangential plane in O, and the YZ-
and YZ-planes are the principal sections of the surface in that point,
whilst the Z-axis is supposed positive upwards, then the equation of
the surface in the vicinity of O takes the form of:
1
= = (c,a? + ey? + da* + diay + day? + dy +...); . (1)
€
where c, and ¢c, are positive.
The equations of motion of the material point become:
Cpe : |
a + an (g + 2<)=9, ]
Seen: E (
y+>W+23 =0.|
y
Availing ourselves of (1) to eliminate z we find:
. Oz 07z yeas 072 _ Oz .. Oz ~ Sete
#& + aa Si On? ea Ody wy + Oy? Yai ay at dy y)= |
2
ce OY Pennies One, O72 - z z @)
ye a USE ree Se | ay 4 aoe aa) 0.
Let / be the small quantity (small e.g. with respect to the principal
radii of curvature R, and F, of the surface in OQ) which determines
the order of greatness of # and y, then the equations (2) become,
omitting the terms of order /° and higher:
a+ 20a Oe
ot ae EB)
y + 2c.47=0.
(621%)
These equations are in general sufficient to arrive at the solution
at first approximation. This then becomes:
av = Ah cos (n,t + 4),
y = Bh cos (n,t + uw);
=V2¢,, ny =V 2c,.
Here Ah, Bh,2 and w are constants of integration; we suppose
A and B to be of moderate greatness.
At first approximation therefore the horizontal projection of the
moving point describes a Lissajous curve, which is closed when
pn, = qn,, Where p and q are integers. If pn, =qn,+e, the curve
described is not closed, but it consists of a succession of parts each
of which differs but little from a closed curve. These last closed
curves have however various shapes which answer to different values
of the difference in phase. They are all described in the rectangle
with 2A and 24h as sides.
54)
where 7,
§ 3. If we wish to take into consideration the terms of a higher
order appearing in (2) we generally have but to apply small modi-
fications to the first approximation.
These modifications are, however, not small in case a relation
exists of the form:
pr, = qn, + 9;
Vv
where S=p-—+q<4 and — is very small (what is meant here by
ny
“very small’ will be evident later on).
When by applying the method of consecutive approximations,
starting from (4) as first approximation, we try to find expansions
in series for wv and y, we shall find, when substituting the expres-
sions (4) into the terms of higher order of (2) and developing
the products and powers of the cosines, in case 2 is very small,
1
periodical terms which have about the same period as the principal
vibration, to which the equation in which the indicated term appears
relates more especially. Such terms in the equations of motion give
rise in the expansions in series for 2 and y to terms with abnor-
mally great amplitude. These amplitudes may reach the order / and
even seem to be greater still.
This proves that in the case supposed our first approximation was
not correct. It is evident that in the equations of motion there are
terms of higher order, which are of influence even on the first
( 622 )
approximation. So we shall have to find in the equations (2) which
terms give rise to the failure of the application of the method of
consecutive approximations. These terms we shall have to include in
the abridged equations, serving to determine the first approximation.
We shall consecutively discuss the cases :
S=3)(2n,— 1,0), eS tn =e) ot — een)
S= 3.1) Strict relation.
§ 4. We suppose 9 — 0; therefore
Dp PVOR
In the equations of motion appear for the first time among the
terms of order 4? terms which, according to what was said in § 3,
must be ineluded in the abridged equations. They are: in the first
equation 2d,zy, in the second d,x*. These are the most important
among the terms referred to. Omitting the remaining terms of higher
order we therefore have to consider :
x +n a+ 2d,ay=0,
a
y + 4n,? ytd,a* —0.
We may also write this system as follows:
OR a |
- n,* x ane ae |
OR
y + 4n?2y— — = 0;
Oy |
in which:
IR — Oh oy
To this we apply the method of the variation of the canonical
constants. This means, as is known, that the equations, arising
OR oR
when the terms ae and iy are omitted, first are solved; in which
solution 4 arbitrary constants appear; we then investigate what
functions of the time must be the quantities just now regarded as
constants, so that the expressions for « and v, taken in this way, repre-
: Sn Lene OR
sent the solution of the complete equations containing -and at The
uy
Pas: OR OR
equations in which an and a are lacking, are solved according to
x y
1) In a following paper we shall discuss the cases S=2 and S= 4.
( 623 )
the method of Haminron-Jacozi in order that the constants we obtain
may form a canonical system.
If @,, @,, 8, and 8, are the canonical constants then by substitution
of the expressions found for # and y in F# this R will become a
‘function of @,, a@,, 8,, 8, and ¢. The variability of the @’s and #’s
with the time is then given by:
da, OR da, OR dp, oR dg, OR ss
en ata One Peds Ogee us da.
In case R is a function of the @’s and the #’s alone, and conse-
quently does not contain ¢ explicitly, the system has as an integral:
I= (WET 9 6 6 9 oo 6 6 (Ch
§ 5. If now we solve the equations
x +rfae= i
y + 4ny=0,
oR R
arising from (5) by omission of the terms ae and ante according to
FE Zi
the method Hamitron-JAcosi we may arrive at:
Vas :
oo cos (n,t + 2n,8,), |
an (8)
Va,
y = > 008 (2n,¢ + 4n,8,);
an,
where a,, @,, ?,, 8, form a canonical system of constants. We must
suppose «, and a, to be of order /? as the amplitudes of the z- and
y-Vibrations must be of order /.
Substitution of (8) in & = — d,u*y furnishes 3 terms:
at, ae aVa,
“tS cos (2,t + 4n,8,), ~*~? cos nyt + 4n, (B, + B,)} and
a Va,
ae COs An, (8, at Bs);
each term multiplied by — d,.
The first two terms contain ¢ explicitly ; setting aside the variability
of the @’s and p’s we can say that those terms are periodical, whilst
the period is comparable to that of the principal vibrations. The
last term, however, does not contain ¢ explicitly. Only this last term
is of importance for the first approximation; the two others we omit
(we shall revert to this in § 6).
We therefore take:
( 624 )
d
R= — —_a, Ya, cos 4n, (8,—8,).
8n,°
Consequently system (6) takes this form:
dit, ;
—_— — 2 Nm, a, a,* sin gy
dt
da, “ ;
— = — 2 Nn, a, a,} sin g,
dt
(9)
dp, she
sa mM, Uy? COS PP,
dp,
— =} m, a, Cet COS P3
dt
where JN is written for n, = 2n,; further:
d,
Nes
— 2 N(8,—8,).
As ¢ does not appear explicitly in R we get according to what
has been said at the close of § 4 as an integral:
my, —
a, Va, cos p = constant. . . LO)
Furthermore it appears at once from (9) that:
Ce aa,
dt dt
Therefore :
Ca Unum So 9 Go ao o 0 (iil)
1
is another integral.
The latter gives us reason to introduce a new variable §, in such
a way that:
a
1
= ai R,*? N? lh? (1—S);
$ is then always situated between 0 and 1, 2, is of moderate greatness.
By this (10) obtains the form:
SVT EG 008) j= Kgs bs at ce
in which A represents a constant.
The first equation of (9) becomes:
1
— i RENE RAG ; a
a
d dR ——
+ Sb V IRE sin gh ieee eS
By elimination of g between (12) and (18) we arrive at:
ig 1,R
- ASE a eae Teds
VF) — Kk? N
( 625 )
Now put:
Fi (5) LG PBS
then for the initial value of ¢ we find /(S)>0. For =O and
S=1 we find /(5)< 9. Thus the equation /($)—=0 has two roots
between O and 1.
So AK? cannot have all values; the possible values of A? lie between
two limits; in § 9 we shall revert to this and to the special cases,
corresponding to the limiting values of K?.
The roots between 0 and 1 which the equation
EG) Ne Op ete, ah (LAS
has in the general case will be called ¢, and ¢,, where we suppose
¢,>$,. The third root is negative, we call it — 4.
The differential relation between § and ¢ may now be written:
dg PHENOLS
VE—9) 6-8) 6 +2)
So with the aid of elliptic functions ¢ may be expressed in ¢.
It changes periodically between the limits ¢, and 6¢,.
Now with the aid of (12) we can also calculate g as function of
t. And £§, and 8, likewise, it being possible to write the last two
equations of (9):
[dee ot kee (A)
bh
d8, _d,R,K h
cde, SOD NA WG
dg, d,R,K h
di 4N? 1-8
So now «x and y are also known as functions of ¢’).
In fig. 1 the relation (12) between § and @ is represented in
’
polar coordinates, g is taken as polar angle, V41— as radius vector.
The circle drawn has unity as radius. The curves change with the
value of K. For K > 0 the curves lie to the right of the straight line
, for A <0 to the left of it; A —O furnishes degeneration
r|yQ
Q
into the straight line g =~ and the circle ¢[=0. By the maximal
cep eee 2
positive and negative value of A (AK = == Gl) the curve has
contracted into an isolated point. The special cases of the motion
9)
belonging to A —O and to A= + 5 V3 will be discussed in § 9.
1) These calculations will be found in my dissertation, which will appear before
long.
( 626 )
§ 6. When astronomers try to obtain in the Theory of the distur-
bances of the movements of the planets by the application of the
method of LAGRANGE expansions in series for the coordinates of the
planets or the elements of their orbits, then terms may appear with
abnormally large coefficients in consequence of small divisors, ori-
ginating from the integration. This takes place when between the
inverse values of the periods of revolution of some planets a linear
relation with integer coefficients is almost fulfilled. Besides some
other properties the terms are also distinguished according to their
class, by which is meant:
mem
a————;
2 2
where « represents the exponent of mw (a small quantity indicating
the order of greatness of the disturbing function), m the exponent
of ¢, m’ the exponent of the small divisor, as they appear in the
coefficient of the term indicated. Now it is the terms of the lowest
class which we have to take into consideration if we wish to make the
expansions in series to hold for a long space of time. By DrLaunay
a method is indicated to determine the terms of the lowest class. It
consists principally in omitting all terms of short period (period
comparable to the periods of the revolution of the planets) in
the disturbing function and retaining the most important of the
others. (Comp. e.g. H. Porncaré, Lecons de mécanique celeste, vol. I,
page 341).
The problem under discussion has much resemblance with the one
mentioned from the theory of disturbances. In the preceding § in
omitting some terms in & we have imitated what is done in the
theory of disturbances.
It is easy to see that the terms omitted have really no influence
on the first approximation, when we consider the terms which appear
e.g. in a, by introduction of such a term.
Osculating curves.
§ 7. In § 5 we have found that the movement of the horizontal
projection of the material point might be represented by:
Ve,
cos (n,t + 2n,8,),
ny
Va
a =— cos (2n,t + 4n,B,);
an,
aa du
. . 1 2
1> @, 8, and £, are slowly variable; for ; and =: are
; at (
where «
dp, dp,
of order /*?, —— and —— of order h. (Comp. (9)).
dt dt
For every arbitrary moment the @’s and the ’s have a definite value.
These values determine a certain Lissajous curve. This curve we
shall call the osculating curve for the moment indicated, which
name is in use in the theory of disturbances. (See among others
H. Poincaré, Lecons de mécanique céleste, vol. I, page 90). Thus
in our problem the osculating curves are the wellkuown Lissajous
figures for 2 octaves.
By the change of the origin of time we may write the equations
of an osculating curve :
— RAVE cos nyt,
FS MR IINZ Laz cos (2n,t—¢) ;
where as in §5 we have introduced § instead of «, and a,; here
too g means 4n,(3,—?~,).
We now see that g is the value of the difference in phase, to
which the oseculating curve corresponds when the phase is calculated
from the moment of the greatest deviation to the right.
The amplitudes of the 2 and y-vibrations being respectively
Rvs and 4k, V1—S, the vertices of the rectangles, in which the
oseulating curves are described lie on the circumference of an ellipse
with its great axis along the z-axis and having a length of
2 Lh, and its small axis along the y-axis and having a length
of Roh.
Now 6 changes its value between §, and &,, so the rectangles in
which the osculating curves are described also lie between two
extremes.
Moreover as according to (12) to each value of § a value of cos
belongs all osculating curves may now be constructed.
It follows from (13) that for the extreme values of § we find
sin =O; so in the extreme rectangles parabolae are described.
The distance from ON of the node of an arbitrary osculating
curve is — —_—, from which it is evident that the nodes and
also the vertices of the parabolae lie all on the same side of O
lying below O for positive values of A’ (see fig. 2).
Envelope of the osculating curves.
§ 8. If we perform the elimination of ¢ and g from:
Proceedmgs Royal Acad. Amsterdam. Vol. XIL.
( 628 )
1
i — Kyh V ¢ cos Din = 5 Rh V 1—6 cos (27, t—-g) and
SV1— cos Cin Nike
we find for the equation of the osculating curves with Sas parameter :
: y : f 1
gk + ¥?) + O( KY — X* — X*) + ( Kk? —2hKX* Y+ x) (ie
where for the sake of a simplified notation is put :
- v are yf,
X for —, Y for —.,
R,h Rh
Thus the envelope has as equation
1 \
AN (Xe =) G ke—2KX*Y + ey) (Kk ¥ — X? NO == 0),
After reduction and division by X* (the Y-axis is the locus of the
nodes) it may be written:
(K—4Y°§—3 XY + VP = (XX? 5 4 Y? — 1)? (X? + F*),
or if we solve Ky:
i= = (YVR) See
Putting
K
Vee VX. = :
U
if passes into
ie k IKE
ae tae
iP d=) = Ko
Now this eubie equation has the same coefficients as (14), so it
also las the same roots. So the envelope is degenerated into the
3 parabolae having as equations:
= 5, 5 fe : T=— ks
which after reduction and reintroduction of w and y take the form of:
5 a -
TT] S Lv K mn we
Cyne eee ee = —— -f- —= Q S parabola,
Rie Ko URS
y Ge x Kk e
Oe — + —— 0 iS, parabola,
Roh K tepals S,
y 2 a? K
= = : =~ — () 4 parabola.
Roh K Eines 2 :
The parabolae are confoeal and have O as focus. When J’ is
positive the & and the &, parabolae have their openings turned upwards,
( 629 )
the 2 parabola has its opening turned downwards (this case is repre-
sented in fig. 2, where besides some osculating curves the enveloping
parabolae are also given).
Special CASES.
§ 9. At the close of § 5 we saw that two special cases may
a)
occur, viz. when K=O and when K=+ V3
A. K=O. We deduce from the relation
G7 Gicosig — Ke
three possibilities :
1. $=0. The movement remains confined to the Y/-plane.
2. $1. The movement remains confined to the V/#plane. This
form of motion however proves to be impossible when «== 0 and
y = 0 is substituted in (5).
ku 3
3. cosg=O0, therefore g = or g=-,
invariably. The os-
2 2
culating curves have their nodes at VU. The form of movement
approaches asymptotically to a motion in the }’Z-plane. What becomes
of the enveloping parabolae has been represented in fig. 3, in which
some osculating curves have been drawn too.
“143. Then ¢ = re as Now cos gy =+1
9 SA -2 < 3 . =
bo
Se —— +
invariably, thus g=0O or g=a. The same parabola is continuously
described, in which also the §, and §&, parabolae have coincided.
(Fig. 4). When A’ undergoes a slight change, $, and §, fall close
together. So this form of movement is stable.
je RO ake oar h
=o) 5 — BW Of order Pe
ny yy
§ 10. The expansions in series written down by Prof. Korrewne
’ . h .
lose for S=3 their convergency as soon as — passes into order
,
o Spare . ; QO. , ; h
— (page 18 of his paper) or i. 0. w. as soon as — sinks into order
n n R
1 1 1
We shall now discuss this case.
We again take as first approximation :
Va
2 = —— cos (n, t -- an, B.),
ny
Va, e
u = 5 cos (2n, t + 4n, p,);
ol,
42*
( 630 )
and we must investigate what form the function A now assumes.
As we have supposed that
9 een !
20 — et Oy
the terms of the order / in the equations of motion would become
a +n,* 2
and
y + (2n, — 9)? y-
; 0 f h 5 5
Because — is of order —- and we take no terms of higher order
a Lu
1 1
than /? in the equations, we may write for the latter:
y + 4n,* y — 4n, oy.
If we thus take the above expression for « and y as first approxi-
mation, then we must admit in the function R besides the term
—d,a*y also a term 2n, oy’.
In the expression
— d,a?y + 2n, oy?
we substitute the above expressions for and y and omit the terms
containing ¢ explicitly. In this way we arrive at:
d @
es, 2 Va yoy
k= — va a, Va, cos p +
1
aN?
where again V is put for n, + 9 = 2n,.
The equations which serve to determine the «s and ~’s become:
da, +
= QIN mh 0 ee SING
ee 1 Gy &y SIN Fy
dt
da, a ne
—— —2Nm, @, 4, sn,
dt
dp, i
— = M, ft, COS &f,
1 2
dt
dp, —
a t Ly ry A
-=—oh + 4m, a, a, cosy;
lt
where
d, bere oO
i 4 a
N* 2Nh
We again see that
da, dit,
Pen
if —_
dt dt
so
at, \- a, = constant;
for which reason we put;
( 651 )
1 : , [ere Poe, to x
—— i TiN ie 5 = R,? N? i? (lL — 6).
Furtber we have according to § 4 as an integral of the system :
d, — Oo
—— 4, V a, cos + ae at, = constant.
l 2
Introducing ¢, it becomes
SV 1—S cos p — eo! (5) = «;
where A is a constant and
" oN
oo .
an GRA
In the same way as this was done for the case 9 =O we may
write down the differential relation between § and ¢ and find w and
in the way indicated there as functions of the time; they get quite
the same form as for 6 = 0°).
In general 5 keeps changing periodically between two limits €,
and 2,; 5, and £, being the positive roots of
5 —2) —{K + o" (1-H P= 0.
Yet there is a considerable difference between the cases 6 =O and
e of order h.
§ 11. We notice this difference most distinctly when we represent
the relation established between © and gy in polar coordinates.
If we put
then we find :
K—o9"+o0"F
eis
We take » as polarangle,/1—f as radius vector and we inves-
tigate the site and shape of the curves for positive values of 9" and
for all possible values of KX.
For A = 9" there is degeneration into the circle £ =0 and a straight
line normal to the origin of the angles at a distance 9” from pole O,.
We have two cases now: 9" <1 and 9 >1
oe” <1. Let us now investigate the shape of the curves for different
values of A. For A > o"" they lie to the left of the straight line just
mentioned, for increasing value of A’ they contract more and more
until for the maximal value of A, belonging to a certain value of
COs —p ==
1, Vide Chapter V of my dissertation.
fe YR \
\ IIS
7m)
eo” we get an isolated point. If 0< A <0” the curves surround
point O,; if A=O we have a curve through O,, for K < 0 they
lie to the left of O,; for the minimal value of A’ we again get an
isolated point (fig. 5).
For increasing values of 9'” the straight line separating the domains
kK>o" and K<e" moves to the right. The domain A> 9" becomes
smaller and vanishes for 0!”’=1. For 0” 21 we therefore have
curves surrounding QO, and curves to the left of O, only. When 9”
increases still more the remaining isolated point approaches to O, and
the curves farther from ©, approach to circles.
For e=0 we had (with the exception of the special case A = 0)
only eurves to the right of O,, and curves to the left of O,. For @
ot order / we have moreover curves around Q,, which are even
more frequent for great values of
L
The curves around 9, point to a form of motion, where » takes
all values, the nodes of the osculating curves lie then above as well
as below the point 0 of fig. 2; the oscuiating parabolae have their
openings turned to opposite sides.
That for increasing valnes of @'” the curves in general begin to
resemble circles more and more, indicates that § is about constant ;
it changes between narrow limits.
This also appears in this way. From (16) we deduce:
Gs (Le ee ne
mea Yi)
ka 6) hla) re aie
2
By subtraction we find:
For greater values of 0’ we find £, — <2, becoming very small.
In this way we approach the general case where there is no
question about relation.
§ 12. How the transition to this general case takes place is also
clearly evident from the limitation of the domain of motion, which
limitation we find by determining the envelope of the osculating
curves. In the same way as this was done for the case @ = 0, we
find that the envelope degenerates into three parabolae, of which the
equations are:
( 633 )
y Ik— go" o ie wv :
0 . all. : + oO = - whe sss oS) parabola,
Rh & K—o Tots
Se San Z -
yf K—o ur be ve c
2— ai : Oe — be parabola,
Rh & K—o ahd
y K—o" st 2 a” :
2 - OS Sse 51° == parabola
Roh 7} K—o Rh
The pomts of intersection of the 4 parabola with the ¢, and ¢,
parabolae lie again on the ellipse having Rj and 22h as axes. The
parabolae are confocal; the focus lies on the y-axis at the height
of —3R,h.o". In fig. 64, 6%, 6° we find those paraholae (and
also the osculating parabolae) corresponding to the cases 0!” << 1 and
oe
K a QO.
In fig. 7 we see how the limitation approaches more and more
to a rectangle for increasing 9”
The £, and ¢£, parabolae coincide for maximal and minimal A.
Arbitrary mechanism with 2 degrees of freedom
for which S=3.
§ 15. Let g, and q, be the principal coordinates of the mechanism ;
they remain during the movement of order 4 and are zero in the
position of equilibrium.
The kinetic energy 7’ and the potential energy U7 may be written:
a cal eps se oe i 1
P= 2 Uiaele 2 q2 Ds i TS) (2. qa ar n,* 42°) aR U,,
where 7’, and U, are expressions in whose terms /: appears at least
to the 3" degree.
Let us write down the terms of order /* in 7):
i 3 ror (29,9,° + bad,” 2 (12 + 2 d9.9,9> + e919." sda) a Obit
As far as and inclusive of the terms of order /* the equations
of LAGRANGE now become:
ht = — 9 — 99,9, — 59,91 — 5919. — 29192 — 19292 +
it 1 Nee
é—a lq, — 7
2 : 09,
iG be) WS hh dq. 4192 = &9,92 —JsV_ +
=
2
te
=
we
we
a
ey AG 5E
= res 0g, Y
In ease the relation n, = 2n, is strictly satisfied or nearly so, the
disturbing terms are:
in the first equation those with 9, , Gide. 92> Ua
= SeCOnd) ss, » ae 5 RC hen Rec
”
If at first approximation we try to satisfy the equations by :
gq, = Ah cos (nyt + 4) 5 9. = Bheos(n,t + w)
where A, 6,2and « are functions of ¢, however in such a manner that
A, B, 2, w are of order 4 or smaller, we may replace in the
second member of the equations :
Up Oh Wak (APE SGP 5) gq. Dyan? (Bh? 9.7);
Gy by — 1 Qi» 2 by —— Is Jo:
If we take this into account for the disturbing terms and if we
omit the non-disturbing terms, the equations become:
th a nq, = (bn,° We cn? a5 2p) N72 a b0;4:
: 1 f
do + 22°Fs = (2 Dy oe bn,* r) re \
The terms 2pq,g, in the first equation and pq*, in the second
originate from a term — pq’,g,, appearing in:
To get rid of the term with q,q, we use the new variable q’
so that:
; 1
Gar Waste qed:
Then:
# * ees 1 H ae
4 = hi + = bq, lp -+|- = ba, I -+ bq, —
ie ae il v ik
== Gette eo Usa 5 b (n,* 4 22”) 1 Yo
Therefore :
a SOG Gi pant Os ete Da) Oa Che
The equations now pass into:
oh zy! 2 2 1 2 9 '
\ Ore fetes (Ora En ames bn,” + 2p) Mes
1
q+ M2” Ja = (2 ¢n,* — 9 On Pp) qi:
For we may replace in the second members qg, by q,’, as
difference is of order 1°.
their
{ 635)
Let us now suppose n, to be = 2n,; then we get:
q se ea q; S(t oS ne ae Sy) q: as
So we find:
where
The equations determining the first approximation have exactly
the same form as those found in § 4. What was fornierly deduced
for the simple mechanism holds consequently, if #7, = 2n,, for an
arbitrary mechanism with two degrees of freedom in such a sense
that the horizontal projection of the point moving over the surface
may be regarded as the representative point for the arbitrary mechanism.
We finally observe that any mechanism for which
— 2en,* + thn? —-p=0
is not sensitive for the relation 7, = 2n,. So this is the condition
requisite to make the mechanism for n,—=2n, a mechanism of
exception in the sense indicated by Prof. Korrmwne (§ 26 of his paper).
Mechanisms of exception therefore are among others the symme-
trical mechanisms (§ 31 of that paper); for here c, 4, and p are all
equal to zero.
Microbiology. — “ Viscosaccharase, an enzyme which produces slime
from cane-sugar’. By Prof. Dr. M. W. Brtrrinck.
The emulsion reaction.
Many spore-producing and a few non spore-producing bacilli, cause,
when growing in presence of cane-sugar or raftinose on neutral or
feebly alkaline agarplates, a very peculiar “colloidreaction”’, which is
also valuable for the diagnosis of these bacteria. This reaction consists
in the formation, in and also on the surface of the agar around the
colonies or streaks, of a liquid “precipitate”, 1. e. an emulsion, which
can best be recognised in transmitted light, and at the same time in
a swelling of the agar caused by the increase of volume produced
by the emulsion.
The emulsion consists of drops (see plate) of different size, mostly
very small, but sometimes growing to 0,2 mm. so that they may
( 636 )
be distinguished with a magnifying glass. At feeble magnification
they might be taken for droplets of oil suspended in the agar, but
as strong sulphuric acid dissolves these drops immediately, and a
feebler acid more slowly, there can be no question of oil or fat.
Characteristic for the reaction is that it can only be distinetly
observed in agar but imperfectly in gelatin. In the agar the
process is impeded when acid is produced by the microbes. Thus
bouillon-agar, yeastwater-agar, and wort-agar with cane-sugar can
well be used, but the emulsion is more distinctly formed in
agar with mixtures of substances that prevent the acidification,
to which cane-sugar is so very apt. For that reason nitrates as
nitrogen-food are especially favourable, as the withdrawing of nitrogen
then necessarily must produce an alkali, while for example ammonium-
salts, used as source of nitrogen, must promote the acid reaction.
A good experiment to produce the emulsion is the following: A plate
is prepared of the composition: tapwater, 2°/, of agar, 2 °/, of cane-
sugar, 0,02°/, KNO, and 0,02 °/, K,HPO,. Nitrogen food may also
be quite left out, so agar-plates with 10 °/, of cane-sugar and bikalium-
phosphate only, are very well fit to demonstrate the emulsion with
Azotobacter and the hereafter mentioned Bacillus emulsionis. The
quantity of cane-sugar can vary between 0.1 °/, and 50°), without
much difference in the result.
After the solidifying of the agar-plate and the removal of the
adhering water, soil-bacilli are dispersed, obtained by shaking some
garden-soil with water, and heating it a few minutes at 70° to 380°C.
in order to kill the not sporulating microbes, Then the water is
poured over the plate and allowed to flow off. The adhering germs,
for so far they live, are nothing but spores of bacilli, which can
germinate at 30° C.
After one or two days the colonies become visible and simulta-
neously the emulsion around some of them; the majority does not
produce the emulsion.
Cane-sugar may be replaced by raftinose, which acts in the same
way; but glucose, levulose, mannose, galactose, lactose, maltose,
trehalose, melibiose, mannite, inulin, dextrin and xylose, do not give
the emulsion.
The emulsion is distinct round the colonies of Bacillus mesentericus
vulgatus (see plate Fig. 1), B. megatherium and a not yet described
soil-bacillus, commonly also found in cane-sugar itself, recognisable
by its small terminal spores, which may be called Bacillus emut-
sionis and whose transparent colony is likewise given on the plate
(Fig. 2). The emulsion is wanting in B. subtilis, B. mycoides, b.
( 637 )
pelymyaa, B. nitrous, B. sphaerosporus, B. luteus, besides in the
anaérobes Granulobacter butylicum, Gr. saccharobutyricum and Gr.
pectinovorum.
The moulds, the various yeast species, even those which invert
cane-sugar, besides all species of Streptothriv, and most of the non-
spore producing bacteria, do not produce the emulsion either.
An exception to the last rule makes the non-spore producing Azoto-
bacter chroococcum, which ou piates of 2°/, of agar, 2 to 10 °/, cane-
sugar, and 0,02°/, K,HPO,, in water, gives a strong emulsion,
which extends to a large distance round the colonies; later, in their
vicinity, perhaps by the influence of a specific enzyme or an acid
it vanishes, while near the colonies of the soil-bacilli the emuision
is permanent. With the exception of 5. chroococcum the other
forms of Azotobacter do not produce the emulsion. From = cul-
tures of Azotobacter, prepared with garden soil and destined for
the absorption of free nitrogen, a species related to b. radiobacter
can be obtained, which produces no spores, but does also give a
strong emulsion.
Ane mulsion, from a physical view analogous but quite different by
the manner in which it takes rise, was described by me on another ocea-
sion’). It appears when a 10"/, solution of gelatin in water is boiled with
a 10°/, solution of soluble starch, or with a 2°
agar-solution. Even
by boiling the two watery solutions do not mix, which, of course,
is also the case after solidifying. This reposes evidently on the fact
that here two colloidal solutions are brought together, which cannot
diffuse and whose emulsionated droplets constantly have a positive
surface-tension with regard to each other. The same explanation
must hold good for the emulsion formed by the viscosaccharase
0
with regard to the agar, and as I may add, to culture-liquids
Wherein Bacillus emulsionis produces the emulsion also.
The emulsion is produced by an enzyme.
If from the emulsion field round a colony a small piece of agar
is cut out, without touching the colony, and placed on an other cane-
sugar-agar-plate, the emulsion itself does not diffuse out of it, but
into the plate, a substance goes over, whicli produces the emulsion
again and with regard to the quantities used rather strongly. This
points with certainty to the presence of an enzyme as the cause of
the emuision, an enzyme which must have the property of moving
through the agar by diffusion. This agrees perfectly well with the
1) Centralbl. f. Bacteriologie 2te Abt, Bd. 2, p. 627, 1896.
( 655 )
ovigin of the emulsion round the colonies, for a substance which is
evidently insoluble in the agarplate, can only be found at the place
Where it is produced. This substance having in our case the nature
of a plant slime, the enzyme may be called viscosaccharase.
The enzyme is prepared by filtering a culture of B. mesentericus
vulgatus and precipitating the filtrate with alcohol, whereby, of course,
other enzymes formed by this bacterium such as diastase, and
also. the slime substance itself, are precipitated. Whether to the enzymes,
present in this mixture invertase must be reckoned, which is usually
considered as a secretion-product of B. mesentericus, has become
doubtful by the discovery of the viscosaccharase, at whose action,
as will be seen below, together with the slime, the production of a
reducing sugar is stated.
Even in presence of chloroform the emulsion reaction takes rise
on cane-sugar agar-plates through the enzyme produced from the
mesentericus cultures, without anything being perceived of the develop-
ment of the germs of L. mesentericus itself, which may be still
present after filtering and precipitating.
It is not difficult to prepare plates of any size containing the
emulsion everywhere, and fit for experiments to demonstrate by
what influences it may disappear.
To this end the required culture-agar is mixed before solidifying
with a not too large number of germs, for example of B. emalsionis,
and then placed one or two days in the thermostat ; when the plate
becomes quite turbid by the emulsion, the sugar is washed out
and it is ready for the experiment. A drop of dilute acid thereon
rapidly produces a clear space.
At the action of viscosaccharase, besides the slime a
reducing sugar ws found.
When small pieces of agar containing the emulsion are introduced
intO an experiment-tube and cautiously warmed with a little FEHLiNG’s
copper solution, a strong reduction is seen, which does not take rise
with the same sugar-agar if the emulsion is wanting.
The question arose whether this reaction should be ascribed to
the slime itself, or if at the same time, through the viscosaecharase,
or in another way, some other reducing substance is formed. There-
fore small pieces of the agar containing the emulsion were washed out
with water, whereby the slime, which cannot diffuse from the agar
into the water, remains behind, but the reducing power of the agar
is lost, whilst the water used for the washing becomes itself strongly
M. W. BEIJERINCK. Viscosaccharase, an enzyme, which produces slime
from cane-sugar.
Fig. 1. Bacillus mesentericus
Fig. 2. Bacillus emulsionis.
LO rae,
}
Alaa
wn BA f
The emulsion-reaction.
Proceedings Royal Acad. Amsterdam. Vol. XII.
( 639 )
reducing. Hence it is sure that at the “emulsion reaction’, together
with the non-reducing slime, an easily diffusing and reducing substance
(probably a sugar) is formed. The chemical composition of this
substance is still unknown, just like that of the slime itself.
The possibility exists that the reducing substance is invert-sugar
produced by invertase, which latter enzyme then should always
accompany the viscosaccharase. Decisive experiments on this subject
in progress.
Viscosaccharase is a synthetically acting enzyme.
As to the nature of the slime it must be accepted that its molecules
are much larger than those of cane-sugar, else it would not be clear
why the slime cannot diffuse through the agar, which cane-sugar does
very easily. Viscosaccharase must therefore be a synthetically acting
enzyme. This circumstance suggests a relation between the slime and
“dextran” *). This is, however, a substance forming the cell-wall of
the concerned microbes, which substance may spread in water, and even
to some exient diffuse into agarplates, bat is not the product of an
exo-enzyme, i.e. of an enzyme able to leave the bacterial body and act
outside of it like the viscosaccharase. In relation to this it is not
astonishing that “dextran” can very well originate from glucose and
some other sugars, which do not produce the emulsion.
Very remarkable is the fact that all the hitherto examined bacteria
which show the emutsion-phenomenon, are able, at detinite culture-
conditions, for example on cane-sugar gelatin, when no emulsion is
produced, to form non-diffusing “dextran”, by which their colonies then
become visible on the plates as large transparent drops. This also
points to a narrow relation between the two phenomena and leads
to the conelusion that the drops of the emulsion must be identic
with, or related to dextran.
Perhaps by further research modifications of viscosaccharase will
prove to exist, which also act on glucose and other sugars and from
these may form “dextran”, but which cannot leave the body, or rather
the cell-wali of the microbes, and must be considered as endo-enzymes
whose product, which itself does not diffuse, cannot be found beyond
the limits of the colony.
If in accordance with my expectation, the emulsion is really brought
about by ‘dextran’, then light will be thrown on the formation of
the wall-substances of plant cells in general; for there is no doubt
1574. L. Maquenne. Les sucres et leurs principaux dévivés. p. 745, 1900,
( 640 )
that ‘dextran’ is a modification of cellulose, and the till now not
explained secondary changes, observed in so many cell-walls, may
then freely be ascribed to the action of specific enzymes, related to
the viscosaccharase.
Why the emulsion is distinctly observed in agar, and less easily
in gelatin-plates, must probably be explained by the dimension of
the molecules of viscosaccharase, which are small enough to enter
without much trouble the relatively wide canals of the agar, but
too large to pass through the much narrower ones of the gelatin.
Many of the experiments here related I owe to Mr. D. C. J.-
MINKMAN, assistant in my Laboratory.
EXPLANATION OF THE PLATE.
Fig. 1. Colony of Bacillus mesentericus culgatus on: canal water, 2°/o of agar,
19) of cane-sugar, 0.029/, KNO, and 0.027/, K,HPO,. with emulsion around
colony. Magnified 8 times.
Fig 2. Colony of Bacillus emulsionis n. sp., on canal water, 2°/, of agar, 0.1"/5
of cane-sugar, 0.02°/’ CINH,, 0.02'/, K,HPO,, with emulsion around colony,
Magnified 9 times.
Microbiology. — “Variability in Bacillus prodigiosus.” By Prof.
M. W. Briserinck.
In a former paper’) I showed how easily new constant variants
of Bacillus prodigiosus and other microbes may be obtained. Here
follow some further observations, made with the aid of Mr. H. C.
JACOBSEN, assistant in my Laboratory.
The keeping constant of the cultures.
The principle on which the keeping constant of B. prodigiosus
seems to repose is preventing the cultures from becoming alkaline by
their own action. Thus, by re-inoculating in quick suecession, for
instance every 24 hours, into bouillon or on bouillon-agar at 30° C.,
each form of Bacillus prodigiosus, whether the natural or normal
form, or a variant obtained from it, remains unchanged probably
for an indefinite time.
For the transplantations only very little material must be used
and an abundance of food.
If some lactic acid is added, for instance 0,5 to 1.5 em* normal
per 100 cm* of bouillon, the culture likewise remains unchanged
1) Royal Acad. of Sciences 21 Nov, 1900,
( G41 )
after a prolonged series of transports, if these are always carried
out before the acid is neutralised by the alkali produced from the
bouillon by the bacteria themseives ').
Addition of 1 to 2 pCt. of glucose acts in the same manner as
free acid, 6. prodigiosus therefrom producing acid which may rise,
if sufficient glucose is added, to 3 to 4 em* normal per 100 em*
of bouillon. As the titre of alkali, originating in the bouillon alone,
can amount to 2.5 em* N= per 100 em*® of bouillon, and as from
1 pCt. of glucose there results no more than 1.5 to 2 em* N of
acid, addition of 1 pCt. of glucose is sufficient to prevent variation,
if the re-inoculations take place quickly; but not if effected with
long intervals, for in the latter case more alkali may result from
the bouillon than acid from the glucose.
If to the bouillon so much ammoniumearbonate or natriumcarbonate
is added that the titre of alkali amounts to about 3¢m* N per LOO
em’ of the medium, 4. prodigiosus likewise remains constant after
repeated inoculations at 380° C., whilst the control culture, without
carbonate but for the rest under the same conditions, strongly varies.
The same result may be obtained with magnesiumhydrophosphate
(Mg HPO,.2H,0) to excess; this, however, quickly precipitates,
and in order to be active should be used in a bouillon-agarplate or
in a thin layer of liquid. In ordinary bouillon-agarplates 1 pCt. of
this salt changes entirely into crystals of ammoniummagnesiumphos-
phate (Mg NH, PO,.6H,O) the plate becoming quite transparent; a
plate with 3 to 4pCt. on the other hand, remains white and turbid.
Although it may be admitted that by these various means the
formation of secretion products by the bacteria is prevented, on
whose stimulating action the variability probably reposes, yet it, is
not clear how this preventing takes place. Evidently substances
should be thought of here which, once produced, cannot or only
with difficulty leave the bacterial body.
Of the said means quick transplantation is the simplest for always
disposing of constant stocks for the experiments.
The origin of the variants in general.
When cultures, placed under favourable nutritive conditions, but
for the rest prepared without special precautions, are growing older
between 10° and 30°C., they exhibit a certain variability at which,
as formerly described (I. ¢.), variants are thrown off, while beside
1) At 4cm> of acid per 100 cm® of culture liquid the growth of B. prodiciosus
is slackened, at 9 cm® it is quite stopped,
( 642 )
these the original form is found unchanged. As by transplantations
in rapid succession (and under constant and favourable conditions)
no change oceurs during thousands of cell-partitions, this variability
cannot repose on some law governed by internal causes only, but
a particular agency is wanted, which may have its seat within the
cells, but which must yet be enacted on by external circumstances.
Although the variability can reveal itself already in an ordinary
same well arranged culture, e.g. in bouillon or in maltwort, allowed
to stand for a few weeks, yet this process may considerably be
accelerated by repeated transplantations, no after a very short time, but
with longer intervals, for example two days, with cultures kept at
30° C., a not too small quantity of the material for the inoculation
being used, e.g. two loops of the platinum thread. After three
or four repetitions, so after about a week, the variation can then
be in full course, the first culture, left to itself, not yet showing
any perceptible change.
This evidently reposes on the following circumstance. The influence
which causes the variability in the culture when it gets older, acts
in the chosen conditions already after two days. If now a re-inoculation
is performed, the germs affected by that influence can increase as
well as those that remained normal, whilst by not re-inoculating,
thus in the first culture, the non-affected germs are by far more
numerous and remain so as the cell-division slackens after the
second day, because of want of food. At inoculation after two days
there result at each time new modified germs, and those which
are modified already, are enabled to augment without losing their
modification.
In this explanation it must further be accepted, that a transplan-
tation after two days gives no cause for atavism; for if this were
the case, the reverse ought to take place of what is observed:
after a week’s growth the first culture should be more varied than
that which has repeatedly been transplanted, but this is not so. This
shows how earefully the variation experiments must be carried out
in order not to become obscure.
Particularly the cultures on solid media must very accurately be
observed. If these are allowed to stand for some days or weeks
without further precautions, then in many cases, even with magni-
fying glass or microscope no variation at all ean be detected, although
it is actually going on, commonly to “rose” or ‘white”.
Colony culture then shows that here and there varied germs or
groups of such germs must be present, for from the seemingly
homogeneous matter large numbers of white and rose variants are
( 645 )
obtained, which prove as constant as the normal form itself. However
unchanged colonies, representing the pure stock and producing a
material as fit for further experiments as the original culture, lie
among the variants.
Experiences afforded by other bacteria seem to prove that the
frequent repetition of the thus possible process of selection, produces
a form which varies less than the original material. But it is not
here the place to enter upon this important fact.
All colony cultures of . prodigiosus are best made on bouillon.
agar-plates, which after solidifying have been cautiously dried on a
thermostat at cirea 40° C. The water which then condenses on the
glass cover can easily be removed; if this is neglected, B. prodigiosus,
which is strongly motile, spreads over the surface of the agar and
the colonies coalesce.
I shall now enter into a short discussion of the most important
variants.
The obtained variants.
The variants derived from 5. prodigiosus may be considered as
plus- or gain-variants, minus- or loss-variants, and qualitative variants.
This is exposed below in the table of descent, which shows the
origin of the obtained forms; the qualitative variants (auratus and
hyalinus) ave placed on the same line with the normal form, the
plus-variants above it, the minus-variants beneath. Hence, the arrows
not only denote the descent but also whether the variability reposes
on gain or loss of characters, or if it is qualitative. Dotted arrows
indicate that atavism has with certainty been observed. The names
indicate the chief qualities characterising the variants.
A survey of the variants without regard to their descent precedes ;
then follows their pedigree, which does not repose on hypothesis,
but simply gives the result of the experiments.
The obtained variants are :
1. Bacillus prodigiosus. Normal form, isolated from nature *).
2. a a roseus 1.
oe a . Rupe. 2
4. ” 55 albus.
D. i . 2 hyalinus.
6. 3 a DISCOSUS.
te 5 . - albus.
8. 35 50 AuUralus.
1) About 1890 from mouldering bones of a gelatinfactory near Delft.
. 45
Proceedings Royal Acad. Amsterdam. Vol. XII.
( 644 )
9. Bacillus prodigiosus. auratus viscosus.
AO) # x, - * mMiiias (= 7 ?)
Ale 5 5 is albus (= 4°).
i| De a 5 hyalinus.
ils. ~. 3; re VISCOSUS.
14. 0 55 Ae 3 albus.
1. eres - re albus (= 5?)
The relation and origin of these variants is given in the following table.
aur. ViSCOSUS ViISCOSUS hyal. viscosus
ve aL x
iz i \ ; hyal.viscosus
aur. ViSC. albus : viscosus albus albus
¢ :
v a
auratus <————_ prodigiosus normal ——___ hyalinus
peel x <
oe =
roseus? roseus 2
'
i
. R is
aur. albus: albus albus hyalinus hyaLalbus
The upward arrows denote “gain-variation’”’, the horizontal ‘qualitative
variation”, the downward arrows “loss-varialion’’. Dotted
arrows signify that atavism has been observed.
The two qualitative colour-variants, auratus which is orange-
coloured and hyalimus of a deep vine-red, vary in a way quite corres-
ponding to the normal form and like this throw off, under the
same circumstances, slime-variants and white variants. Besides, the
normal form may return by atavism as well from auratus and
hyalinus themselves as from the variants derived from them. In the
pedigree table atavism is indicated by dotted arrows for a few of the
cases where it has been stated with certainty. But there is no doubt
that also the other variants are disposed to atavism.
It should moreover be noted that the auratus-variant approaches,
at least in colour, the natural variety Bacillus Kieliensis, but that
the latter possesses a stronger power of fermentation, and produces
much gas (CO, -+ H,) from maltwort with dextrose or cane-sugar,
the former fermenting only dextrose.
For the rest, B. Nielensis itself, which varies in a way quite
analogous to that of the normal form of prodigiosus here considered,
has not yet been obtained as a variant from the latter,
\
( 645.)
A new character which may rise in addition to the already existing
ones, is the production of a large quantity of slime substance by excessive
growth of the cell-wall, which slime may spread through the liquids,
and makes the individuals of the colonies on agarplates colere into
one tough mass. From £B. Aveliensis was even a variant obtained
whose colonies appear on the agar plates as a very consistent, almost
dry zoogloea, but the analogous variant did not till now arise from
the common prodigiosus. The viscosus (6), derived from the latter, is
an ordinary red slime bacterium.
This red-coloured, tough-slimy form, which may be called B. pro-
digiosus viscosus, is no doubt a plus-variant. Its production has been
observed under the most different nutritive conditions, between the
temperatures 10° (in a cellar) and 30° C., but always and exclusively
in liquid media, never on a solid one. The latter circumstance is
apparently the reason why the numerous experimenters, who have
studied 6. prodigiosus, have not seen this variant. It is true that
SCHEUERLEN *) observed that old prodigiosus-cultures sometimes turn
slimy, but he aseribed it to their becoming alkaline and overlooked
that a new constant form was produced.
The only distinet condition which seems different in the liquid
cultures compared with the solid, is the access of oxygen. In the
depth of the liquid this access must, of course, be very deficient for
a long time, or even be entirely lacking, as the upper layers of the
culture, which are rich in bacteria, take up all the oxygen. Conse-
quently anaérobiose becomes possible in the depth, which is not the
case in cultures lying free on a solid medium, and this partial
anaérobiose is apparently the stimulus which induces the formation
of the slime variant. That here a rather complex influence and not
a direct action must be aseribed to the partial withdrawing of tie
oxygen, follows from the fact that the culture of L. prodigiosus at
complete exclusion of air, as in a closed bottle, does not, even with
repeated transports, give rise to the slimy variant. At temperatures
of about 35° C. this variant is no more formed, although the growth
of prodigiosus is then still very strong; at 87° the growth slackens
or ceases entirely, according to the food.
In the following liquid media the production of the slime variant
has with certainty been observed, as well after repeated re-inoculations
as after prolonged keeping of one and the same culture at 25° to
30° C.: in broth, in broth with 1 pCt of glucose, in malt-wort, in
tap-water with 5 pCt of pure gelatin. and 0,02 pCt K,HPO,, and in
1) Archiv. fir Hygiene. Bd. 26 p. 1.
43%
( 646 )
tap-water with 2 pCt of glucose, 0.5 pCt of asparagine, 0,02 pCt
K,HPO,, always cultivated at 30° C. and with repeated transports after
two days or longer. From this we also recognise that there is no
question of a direct influence of the food on the production of the variant.
The awratus- and hyalinus-variants, also, have only taken rise in liquid
cultures, namely in broth and in the glucose-asparagine solution.
Moreover, hyalinus, which is of a deep vine red, is easily obtained
from a solution of pure gelatin in tap-water with 0.02 pCt. K,HPO,,
after repeated re-inoculations, at 30° C., whereby also /yalinus
viscosus results.
The colourless or white variants, which only differ from the original
form in producing no pigment, should certainly be considered as
minus-variants. They are obtained with more ease than the slime
variants and, at least as to N° 4, have also been detected by other
authors *).
Except under the said conditions, apt to keep them constant, all
the cultures as well in liquid as on solid media, vary sooner or
later towards white. The original form does remain preserved, but
a colourless variant is thrown off, which is still more constant than
the stock itself.
Not always does one and the same variant result in this case:
two uncoloured constant forms, N° 4 and 5 can easily be distinguished
if they originate at the same time, and their colonies are on the same
agarplate so that they may be compared somewhat magnified.
One, albus hyalinus, then looks more blueish transparent, the other,
albus, is more of a cloudy and opake white; under the microscope
the former proves to consist of smaller cells than the latter.
The cause of the production of white variants cannot be a more
or less abundant access of oxygen, but must probably be sought in
a stimulus, exerted by secretion products which remain enclosed in
the interior of the cells.
Although the presence of ammoniumearbonate in the medium
(broth-agar), as also cultivation at temperatures higher than 80° C.
e.g. at 338° C., prevent pigment production, no hereditary variation
at all is caused by these influences. [f the thus treated colourless
cultures are transported at 20° to 25°, no white variants are obtained
from them, but the normal form is found back unchanged, if at
least’ the above mentioned precautions to preserve the constancy of
the stock are not neglected.
') In Leamann and Neumann's Atlas, 41) Ed.'1907, Table 30, Fig. 3, shows
a coloured image of a “pure culture” of prodigiosus, consisting of red and white
colonies,
( 647 )
When the white variants of the normal form are cultivated at
30’ C. in bouillon or in malt-wort, the cultures will, after a few
re-inoculations, turn slimy like those of the red normal form itself.
Colony culture on bouillonagar proves that white slime variants are
thrown off, in the same way as the normal form throws off the red
ones. The white slime variants (N°. 7 ? and 14) correspond by the
nature of their colonies to the two white forms, a/bus (4) and albus
hyalinus (5), considered above.
There is still another method to obtain the colourless slime variant
from the red one. If this latter is cultivated at 307 in malt-wort
or in bouillon, we find after one or two transferrings, each time
after two days, and when sown on bouillon-agar, many white slime
colonies together with the unchanged red, moreover a considerable
number of quite normal, not slimy red colonies, N°. 1, which
is to be considered as atavism, but an atavism reposing on the loss
of a character. The white slime variant, thus obtained by minus-
variation, and found in the table as N°. 7, seems identie with the
one produced by plus-variation from the not slimy white variant,
which latter for that reason has not been specially mentioned.
Already in my earlier paper I spoke of rose variants, which so
to say, keep the middle between the normal form and the white variant.
They may be produced in various ways, for instance, by cultivating
the normal form on plates of pure gelatin dissolved in distilled water
(H,O0, 10°/, of gelatin) at room temperature, at which rapid growth
and vigorous melting occur. By daily streaking off on a bouillon
agarplate the same colony obtained on such pure gelatin, and provided
the temperature be kept between 14° and 17° C., we find, on the
fifth or sixth day, the first rose variants, either or not with the
white, which under these conditions appear later. Two rose variants
(table N°. 2 and 3) are easily distinguished, but it is possible that
there are many more whose perception is beyond the reach of our
observation. In any case, it is a fact that the character: “the
faculty of producing pigment’, is divisible in many ways. The here-
ditary constancy of at least one of these rose variants proved not
to differ from that of the normal form.
Another method to obtain rose variants is cultivation of the
normal form in bouillon, which by evaporation has been reduced
to a threefold concentration. After a. single transport already, a
large number of rose variants (3) had appeared by the side of
normal forms; by a much lighter colour they showed a disposition
to lose their colour entirely. The variability of the different rose
vanants is not the same; the form, obtained by the concentration
( 648 )
)
experiment (3) produces, more readily than the rose variant (2), as
well red normal forms (1) as white ones (4). For the rest, this
more variable variant has also proved to remain constant when
quickly transplanted.
Cases of atavism are frequently observed in these experiments.
Thus, for example, the production of the normal form from viscoswus
(G) may easily be seen if the latter grows for a fortnight without
transport on a bouillonagarplate; along the margin of the streaks
some few normal colonies (1) will then become perceptible.
The albus-variants, also have a disposition to throw off a few
red normal forms, but they do so only after growing for weeks or
months on bouillon-agar; at first they are very constant.
The to a certain extent completely regular production of the same
variants of Bacillus prodigiosus, suggests the existence of variability
in a special and determined direction, of orthogenesis, as Eimer
expressed it.
As under different nutritive conditions the same variant may
appear, the food itself cannot be the stimulus; there must be, as
said above, another cause in the interior of the cells, which, for Bb.
prodigiosus, seems only active in an alkaline environment.
On the other hand, the food, in a wider sense, has certainly a
decisive influence on the variability, albeit indirectly. So we considered
already the influence of the alkaline reaction of the medium if
this alkali is produced by the microbes themselves. Another example
is the following. As well in malt-wort as in bouillon the viscosts
variant is regularly produced; but from malt-wort the auratus
variant, whieh so readily takes rise in bouillon, is not obtained
at all. Indeed, every culture condition gives a peculiar but con-
stantly returning mixture of variants, differing both quantitatively
and qualitatively from that found under any other conditions. But
the real factors here active could not as yet be detected.
From the foregoing the following results may be derived.
1. Bacillus prodigiosus produces as well qualitative, as gain- and
loss-variants, all obtained with certainty by determined experiments ;
the stock-form is always found unchanged in the same culture with
the variants.
All the variants are from their origin as constant as their stock.
The true factors which govern the variability in these experiments
are still unknown.
2. By rapidly repeated re-inoculations and by other methods, nor-
( 649 )
mal form and variants may be kept constant, as it seems for an
unlimited length of time.
3. All the variants vary in a way analogous to that of the normal
form, thus, the auwratus-variant produces an qauratus-slimevariant,
which must be considered as a gain-variant, and an a/bus-variant, which
must be taken for a loss-variant.
The natural variety B. Nieliensis, which approaches the auratus-
variant, also varies in an analogous way. The variation thus seems
to be directed or orthogenetic.
4+. Gain-atavism in loss-variants and loss-atavism in gain-variants,
can be obtained with certainty by determined experiments. Qualita-
tive variants, too, may give rise to atavism.
d. The experimental variants of L. prodigiosus have not yet been
found in nature. From another bacterium, Bacillus herbicola, a variant,
took rise which I had before repeatedly isolated from nature and
which I had taken for quite another species.
6. The variants of prodigiosus, and this holds good for many
other microbes also, differ from each other and from their stock
forms in the same way as closely related natural species or varieties do
among each other. But their disposition to atavism is much more
pronounced,
7. The sub-variants, e. g. the rose variants of different colour-
intensity, arise in the same way as the chief variants and _ possess
the same degree of constancy.
Physics. — “fesearches on magnetization at very low temperatures.”
By Pinrre Weiss and H. KameriincH Onnes. Communication
N°. 114 from the Physical Laboratory at Leiden.
§ 1. Object of the research; results.
a. Introduction. The extension of LanGrvin’s') kinetic theory of
magnetism to all ferromagnetic phenomena by means of the hypothesis
of the molecular field *) rendered the testing of deductions from this
hypothesis by experimental data of great importance. The first results
of this comparison were very encouraging; in some respects a
remarkable correspondence was found. For instance the curves
1) Langevin. Ann. Chim. et Phys. 8 Sér. t. 5, p. 70; 1905.
*) P. Werss. Journ. de Physique 4e Sér. t. VI, p. 661; 1907.
( 650 )
calculated for the intensity of the magnetization at saturation as
a function of the temperature corresponded very well with those
which had been found experimentally for magnetite at temperatures
above the ordinary. Moreover, the law determining the susceptibility
above the Curim-pornt*) developed from the hypothesis of the molecular
field was found in Corts experiments, and in others which will
soon be published, to be accurate over a temperature range of some
hundreds of degrees. Finally the sudden changes in the specific heat
at the Curtm-point were in correspondence with the values calculated
from magnetic data. But other observations do not correspond so
well with the theory. Fig 1, Pl. I in which the theoretical curve for
the change of saturation-magnetization with temperature is shown by
the full curve a, also shows the experimental results for magnetite,
and the corresponding curve, 4, for nickel *). The last curve is drawn
to such a seale that the best possible correspondence with the theore-
tical is obtained at the Curtn-point. In contrast with what was found
for magnetite, nickel shows a deviation from the theoretical gradually
increasing over the whole curve. Iron and cobalt behave practically
the same as nickel. When all this is taken into consideration it is
seen that the hypothesis of the molecular field is of the nature of a
working hypothesis; the partial confirmation shows that the hypothesis
contains a kernel of truth, and from the experimental deviations one
will have to see how it should be modified or extended while still
retaining its essential features.
It is not probable that these modifications will attack the property
of reacting against the orientation by the magnetic field that has been
ascribed to the kinetic energy, or that they will come into conflict with
the manner in which the Maxweti-BoLtzMann partition law has been
employed. Not only are these hypotheses of fundamental import, but
they are still further forced upon our consideration by the ease with
which they account for the fact that for paramagnetic substances the
susceptibility varies inversely as the absolute temperature — an
experimental law that is one of the most firmly established for a
number of substances. In their important investigations upon the mag-
netization of the elements, of which an account was given at the last
1) In this Gommuniecation we shall give the name Curte-point to the temperature
al which spontaneous ferromagnetism ceases. This is by no means inconsistent
with Curie’s idea that the transformation temperature is a function of the strength
of the field, since the temperature at which spontaneous ferromagnetism ceases is
the temperature obtained by reducing the field to zero.
2) According to preliminary measurements. Accurate experiments upon the three
melals and magnelile are in* progress.
( 651 )
meeting '), H. pu Bots and Honba have, it is true, shown that this
law of the dependence of susceptibility upon temperature is not
generally valid, and that paramagnetism also occurs which is inde-
pendent of the temperature or increases with increasing temperature,
But it is by no means the case that the foregoing hypotheses should
be discarded on that account; what we learn from experiment in
this case is only that these suppositions are not sufficient to explain
magnetism as a whole. In particular it will be necessary to revise
LaNGEVIN’s hypothesis that the magnetic moment of a molecule is
constant, or at least quasi-constant, and also that concerning the
nature of the mutual action of the molecules, which until now has
been represented by the introduction of the molecular field. For an
at low estimation of the value of both of these hypotheses, experi-
ments temperatures are especially valuable.
For it is only at the absolute zero that the magnetization gives
the sum of the molecular magnetic moments, as it is only then that
heat-motion can no longer prevent the magnetization from attaining
its full value; and at low temperatures, too, is the strongest demon-
stration of the mutual action of the molecules to be expected, since
they are then at the smailest possible distance from each other.
h. Ferromagnetic substances. We have, therefore, aimed at the
continuation of the curves connecting magnetization and temperature
in the three ferromagnetic substances and in magnetite down to the
neighbourhood of the absolute zero. By utilising the methods and
appliances’) suitable for long-continued accurate measurements at such
constant temperatures as are obtainable with liquid hydrogen, we have
been able in our measurements to reach a temperature of 20°,3 Kk. with
hydrogen boiling under atmosphere pressure, and of 14°,0 Kk. with
hydrogen near its melting point. The number of degrees on the absolute
scale which separate these experimental temperatures from the absolute
zero is but such a small fraction of the number between the absolute
zero and the Curig-point (even in the case of nickel this number is
still so much as 648 Kelvin degrees) that, considering the nature of
the curves, we may regard the saturation-magnetization at the absolute
zero as being determined by our experiments. All this, of course,
with the proviso that the phenomenon in the region to which extra-
polation is carried should give no occasion for adopting another point
of view. Since the object of the measurements was a determination
of the saturation-magnetization, it seemed suitable to direct the expe-
1) These Proceedings Jan. 1910.
*) H. Kameruincu Onnes, these Proceedings Sept. 06, Comm. Leyden N°. 94f.
( 652 )
riments towards obtaining data for magnetization in strong fields,
and from these the deduction of the law according to which the mag-
netization approaches its limiting value. But the method chosen for
the: magnetic measurements, viz: the determination of the maximum
value of the couple exerted by a magnetic field of varying direction
upon an ellipsoid of the experimental substance, was, as we shall
presently show, less suitable for this determination of the law of
approach than for comparisons of the magnetizations of the substance
in the same field at different temperatures. The data to determine
the law of approach were therefore made the subject of a separate
investigation’) This gave the following values for the difference
betweei the magnetization in a field of 10000 gauss and that in the
limiting case :
Iron 0.08 °/,
Nickel Osea
Cobalt (soft) ITU od es
Magnetite Oxo
For these substances, the cobalt excepted, the approach of magneti-
zation as a function of the strength of the field is hyperbolic, so that
in a field of 20000 gauss, which we reached in our present experiments,
the above differences were reduced to half thei values. Observations
by the ellipsoid method in different fields and at both low and
ordinary temperatures have not, indeed, enabled us to test the law of
approach, but they show sufficiently well that there is no essential
difference between the behaviour in this respect at the two temperatures ;
and that at low temperatures, as could have been supposed the
magnetic hardness does not assume an excessive valué, the molecules
hindering each other in assuming a new direction.
Further, by means of comparative measurements, magnetizations
at ordinary and at low temperatures in fields of great strength were
compared, and it was found that the ratio between the two is pretly
well independent of the strength of the field. Thus, leaving the
result. uncorrected for the dilatation between the two temperatures
(see note 2 on p. 11.) we found for the ratio of the intensity of
magnetization at 20°,2 K. and at ordinary temperature the following:
Nickel (itsea (C3) 1.0548
lron (20) as) 1.0210
Magnetite (15°.5 C.) 1.0569
The exact value of the ordinary temperature is given between
brackets. In § 5 it will be explained why the experiments with
1) P. Wetss, Areh. des Se. phys. et nat. février 1910 and Journ. de Phys. 4e Sér.
t IX. avril 1910.
(( 1333.)
cobalt have not been brought to a conclusion. It is difficult to know
exactly the degree of accuracy of these results. Experimental work
in every branch was carried out so that an accuracy of 1 in 1000
or even higher could be expected. But when one considers the
disturbing influences which made themselves felt in the experiments
upon cobalt, it seems rather incautious — and this is particularly
the case with the magnetite measurements — to ascribe to the
results an accuracy greater than 0.5°/,, even though the occurrences
which have thrown suspicion upon the cobalt measurements were
nearly absent in the case of the other substances, and though in all
its properties and particularly im its extraordinarily large magnetic
hardness cobalt stands evidently alone. Since our experiments indicate
these causes of uncertainty, they show how a higher degree of
accuracy may be reached if so desired. The present accuracy is quite
sufficient for the treatment of various problems.
The experiments with iron and magnetite were carried to 14°,0 kK.
The change of magnetization between 20° K. and 14° Kk. is too small
to be expressed in figures. These experiments, therefore, only extend
down to 14 Kk. the temperature region within which the diminution
of the kinetic euergy and the approach of the molecules to each
other do not occasion the appearance of a single new phenomenon.
The portions of the curves for nickel and magnetite which have
been newly obtained are given by broken lines in fig. 1, Plate I.
Magnetite is of particular importance on account of the pertect
correspondence between observation and theory over the greatest
portion of the region between the Curtg-point and the absolute zero,
and on account of the occurrence of a deviation of observation from
theory only at low temperatures. Here, theory gives for the ratio
between the magnetizations the value 1.139 instead of the value
given above, 1.057. The result that theory aud experiment clearly
differ at these temperatures is corroborated by earlier experiments
upon four samples of different kinds of magnetite, two obtained from
natural crystals, the third from a fused natural crystal, and the
fourth from artificial magnetite. These gave the following. values for
the ratio between the magnetizations at the temperature of solid
carbon dioxide (—79°C.) and ordinary temperature :
1.083 ordinary temperature 16° C.
1.042 23°.2
1.043 24°
1.037 21°.5
mean 1.039 PA ore Op
while theory gives 1.053 for the same temperature.
( 654 )
An analogy thus seems to exist between this and compression and
expansion by heat, for which VAN ber Waats’s theory and law of
corresponding states are supported better as a rule in the neighbour-
hood of the critical point than at low reduced temperatures where
the ideal representations of ihe molecule and of molecular attraction
no longer cover the phenomena sufficiently well and the differences
between the specitic properties of the real molecules appear.
The hypothesis that molecular magnets are essentially invariable
would be established conclusively if there existed simple relations
between the magnetic moments as calculated per atom, which one
might be led to suspect from the increase by regular steps of the
saturation-magnetization of the three metals.
The following table in which the numbers in the first column are
taken from the paper’) referred to above and in which the relative
increase for cobalt is estimated from comparison with iron and nickel
shows that this is not the case. The data are not corrected for the
dilation (see note 2 on p. 11 ).
Specific \Increase by | Specific Atomic | Moment
saturation at reduction tosaturation at weight or of |
temp. (_ ). | low temp. low temp. | !/, mol. wt. | gram-atom. |
Ni 54.6 (17° C.) 1.0548 57.6 58 7 3381
Co AG2E (eNEs) 1.01 163.6 i) 9650 |
| | |
Fe 217 (20° C.) 10201 | 921.6 56 1410 |
FeO 4/,. | 90.75 (15°.8' C.) | 1.057 95.9 Tihs |) TAT
In connection with this we must not lose sight of the fact that
although the proof ihat the above magnitude is of great significance
may have eseaped us, still there is nothing whatever to justify an
Opposite conclusion.
When we look upon our measurements as a whole we remain
inclined to retain the hypothesis that in ferromagnetic substances the
magnetic atom does not in itself change much with temperature.
There were indeed reasons for questioning if this approximate inva-
viability, granting that if was proved in other circumstances, still
existed at extremely low temperatures. Electrical resistance of
metals, phosphorescence of sulphur compounds, absorption of light
by the salts of the rare earths with or without magnetic field,
all, at very low temperatures, exhibit characteristics that one may
1) P. Weiss. Arch. des Se. phys. et nat. and Journ. de Phys. 1910.
(SE)
try to explain by ascribing them to forces exerted by ponderable
matter upon electrons; these forces in that explanation become of
primary importance when the temperature sinks to that of liquid
hydrogen, and it is aseribed to them in particular, that they make
the current-carrying electrons in metals suffer an important diminution
in number at very low temperatures by their being, as it were,
frozen to the atom by the low temperature ').
It would also be possible that the motions of the electrons which
cause magnetism while remaining constant or changing not much at
other temperatures, begin to show considerable changes at very low
temperatures.
The negative result that nothing happens even at the lowest tem-
peratures, which should throw doubt upon the relative smallness of
the variability of the magnetic atom itself, is not perhaps without
importance when regarded as a means of weighing the value of the
above assumptions regarding the phenomena mentioned, or as means
of separating the group of electrons which occasion magnetism from
groups which form the prime factors of other phenomena.
c. Vanadium, chromium, manganese. The question has often’ been
asked if a gap which cannot be bridged over exists between the
ferromagnetic metals of the iron group on the one hand and the
paramagnetic metals of the same group on the other, or that the
latter metals should also exbibit a very low Curir-point if the
temperature were sufficiently lowered.
Cu. Ep. Guiniavme*) says with reference to the Hevsiur alloys
of Mn, Al, Cu and Mn, Sn, Cu which are ferromagnetic : “The reason for
this can be found in the faet that aluminium or tin when compounded
with manganese, a metal from the magnetic group, raises its trans-
formation temperatures, which, following an hypothesis already sug-
gested by Farapay, ought to lie very low.” It can indeed be seen
that aluminium and tin raise the melting points of various alloys
which they form with other metals (the series Al—Au, Al—Sb,
Na—Sn) and seem to possess the general property of raising tem-
peratures of transformation.
We might, therefore, expect that vanadium, chromium, and man-
ganese should at very low temperatures exhibit either the characteristics
of ferromagnetism (magnetization not proportional to strength of field,
1) Cf. H. Kameruincu Oxnes, Comm. fr. the Leyden labor. Suppl. n°. 9, p. 27
1904 and P. Lenarp, H. Kamertinen Onnes and W. E. Pauw, These Proceedines
June 1909, Comm. fr. the Leyden Laborat. n°. 111, p. 3, nole 2 1909.
*) Ch. Ep, Guittaume, Actes de la Soe. helv, der Sc. nat. Vol. 1 p. 88, 1907,
( 656 )
saturation, hysteresis) or, in conformity with Curin’s law, a strongly
increased paramagnetism. The susceptibility at the temperature of
solid hydrogen should be about twenty times as great as at ordinary
temperature‘). At this time we were not yet aware of the results
published last month by H. bu Bots and Honpa *), from which it
appears that the inverse proportionality of paramagnetism to the
absolute temperature is but one of the possible cases. To get an
idea of the order of magnitude of the expected phenomena we may
suppose that the paramagnetic y iron still exists at 14° K. with the
same Curim constant (product of absolute temperature by susceptibility ).
In that case a value of about 400 is found for the magnetization
of this substance in a. field of 20000 Gauss.
Some time ago GersBHarpr*) determined the susceptibility of man-
ganese at ordinary temperature and found A = 322.10—° (density
6.4). The above calculation gives a value 134 for the magnetization
of this substance in the same circumstances. And as the deflection
in our apparatus is proportional to the square of the magnetization,
one would obtain a deflection smaller in the proportion of 18 in the
case of y iron or 160 in the case of manganese than that which
was found for iron at the ordinary temperature; as this was 100 em.
the manganese deflection should still be quite easily readable.
When we now introduced into our apparatus roughly formed
ellipsoids of MotssAn vanadium and Go.pscumipr chromium and
manganese in succession, the’ awaited change did not appear. In
every case the deflection at the temperature of solid hydrogen as
well as at that of hydrogen boiling under atmospheric pressure
remained the same as it was at ordinary temperature, that is, to a
few tenths of a millimetre, and these must be ascribed to the
magnetism of the suspending apparatus. There was therefore no
ferromagnetism and we were obliged to choose between the following
two hypotheses for these substances. We were either dealing with
pavamagnetism of a new kind or with diamagnetism, which is also
') A similar supposition formed the starting point of a research by H. Kamer-
LiInGH Onnes and A. Perrier, which will shortly be published, and is closely
connected with the present research. This investigation has been taken to hand
al the same lime with the present subject. Using the method of the maximum
couple and the hydrostatic rise the magnelizations of liquid oxygen at various
temperatures and of solid oxygen at the temperatures of boiling and solidifying
hydrogen were measured. The increase of the magnetization at low temperatures
was found to be very great, though not so much as was expected, and a distinct
deviation from Curie’s law and a characterislic curve were found.
*) H. pu Bors and Honpa |. cit.
5) Gepnarvr. Inaug. Dissert. Marburg 1909.
| 657 )
found in copper while most of the salts of this metal are paramagnetic
pu bois and Honpba’s paper in which these three metals are classified
under those whose paramaguetism is invariable or increases with
the temperature shows that the first assumption is the correct one.
The behaviour of copper with the present research made us consider
the other hypothesis a reasonable one.
One could always assume that the paramagnetism, which, as a
general rule is ascribed to the metallic manganese, results from the
presence of its oxides, which are strongly magnetic, or of a small
quantity of iron. To put this assumption to the proof we prepared very
pure manganese from Merck’s pure chloride, which had been proved to
be free from iron. The preparation was accomplished by electrolysing
the salt between a cathode of distilled mercury and an anode of
iridium alloyed with 40°/, of rhodium which is not attacked by the
chloridion. The almagaim obtained in this way was separated in a
stream of pure, dry hydrogen. In this way a grey powder was
obtained which when compressed in a glass tube as a mould took
the shape of a solid rod. A rod prepared in this manner exhibited
paramagnetism. A glass tube with the powdered manganese was also
paramagnetic. The same manganese contained in a magnesia boat
was thereupon fused in an electric resistance furnace and in an
atmosphere of hydrogen. In this way an ingot was obtained which
was covered with a light oxidised crust. It was found impossible to
grind away this crust with quartzpowder, since the metal was of
the same hardness as quartz. Emery could not be used as it is
magnetic. The impure crust was therefore turned off with a diamond
tool, and a small cylinder of pure substance was obtained.
This cylinder was found to be ferromagnetic. Fig. 2 Pl. 1 gives
the hysteresis curve for this substance. The maximum value of the
specific magnetization is 100 times weaker than that of iron, and
the coercive field is 670 gauss, that is to say, 10 times as strong
as the coercive field of steel which is used for the preparation of
good permanent magnets. This peculiar substance seems moreover to
have striking magneto-crystalline properties. The rod was strongly
attracted between the poles of a magnet and placed itself perpendi-
cular to the field.
Manganese of the same degree of purity can therefore occur in
two states: paramagnetic and ferromagnetic. GEBHARDT’s experiments
give a susceptibility five times greater than that observed by pu Bots.
If Grsnarpt’s powder was not impnre or oxidised, it is thus possible
that there are two paramagnetic states.
1) Secxerson, Wied. Ann. LXVII, p. 37, 1899.
( 658 )
As regards the ferromagnetism of manganese, this had already
been observed by SeckeLson*) with electrolytic manganese which was
liberated at 100° C. from the chloride upon a platinum wire, and
with a regulus prepared by Bunsen from manganese fluoride. The
very indefinite observations concerning the magnetization which he
published do not contradict our measurements.
By a more direct method we have proved the absence of strong
magnetism in vanadium, chromium and manganese at low temperatures.
For this purpose we introduced ellipsoids of the three substances
into. a narrow unsilvered vacuum tube whose walls were separated
by the smallest possible distance; this was placed in a second similar
tube also as narrow as possible and filled with liquid air. We then
determined the distance from the poles such that the ellipsoids were
attracted from the bottom of the tube to the poles of the magnet.
This experiment was made first with the inner tube empty, and then
with the inner tube filled with liquid hydrogen. The following results
were obtained :
Ordinary temperature In liquid hydrogen
Vanadium Not attracted |}
: erty Bes | The same as at
Manganese Attracted from distance of 6 to 8 mm.
‘ . : ordinary
Chromium @ a5 3 7 ahead 1 ee
t emperature
Chromium / x rs i en () p Per
>
The results for Chromium 4 which probably contained a small
splinter of iron must be rejected. We also found further that a
crystal of iron sulphate at ordinary temperature was attracted from
a distance of 25 mm. while in liquid hydrogen it was attracted
almost from the base of the magnet. Thus the weak magnetization
of the three metals was found to be practically invariable, while the
iron sulphate exhibited a very great increase in magnetic properties.
This experiment is well adapted for displaying the characteristic
difference between the two groups of substances and is a typical
example of the significance which even the simplest experiments
acquire within the fallow region of very low temperatures.
§ 2. Methods and apparatus.
a. Discussion of the method of the maximum couple. We measured
the intensity of magnetization by measuring the couple exerted ona
prolate ellipsoid of revolution of the experimental substance arranged
so that the angle of the field with the major axis of the. ellipsoid
might be varied. The expression for the couple is
( 659 )
M = (N,—N,) Lv sin cos p
where NV, and N, are the coefficients of demagnetization of the
ellipsoid, /, the intensity of magnetization of the substance, v the
volume, and gy the angle between / and the major axis of the
ellipsoid. The maximum value of this couple is
Niels
a BD)
9
a
M =
for y = 45°. Hence to measure / it is not necessary to know either
the strength or azimuth of the field which yields the maximum
couple. To make use of these methods the ellipsoid is suspended
from a torsion-spring whose displacement is determined by a mirror-
method, and an electromagnet turning round a vertical axis is used.
The method has already been described’). Its advantages consist of
the small range over which strong fields are necessary and the extreme
simplicity of the relative measurements.) We shall now discuss two
sources of error which affect it and which, although they may be
made as small as one wishes in theory, render it less suitable for
the search after the law of approach to saturation, although they
do not take away from its value as a method of comparing in the
same field two successive and slightly differing states of the same
substance.
Influence of inhomogeneity of the field.
The ellipsoid is placed in the centre of a magnetic field possessing
the symmetry of a body of revolution. The strength of the field at
this centre is a maximum for a displacement in the plane of the
equator, y, and a minimum for a displacement in the direction of
the # axis. It it given by the series
em OREM ye 0 OPEL
ers :
ot a(a)+ SG(gs) te
which, remembering the equation AV =O for the magnetic potential
V, and converting to polar coordinates 7 and 6, transforms into
1) P. Weiss, Journ. de Phys. 4 sér. t. VI, p. 655, 1907.
*) For comparing the intensities of magnetization J and J' at two temperatures
we have to take into account that v = m/d, m being the mass of ellipsoid and
JE M i
a= M. a ve and = ar we The dilatation at the low
temperatures and therefore the proportion of d@ and d! being unknown, we have
emitted the correction for the difference of this proportion and unity, the value of
which may be estimated at 0,004. [Added in Translatiou].
d its density, so
dt
Proceedings Royal Acad. Amsterdam. Vol. XII.
( 660 )
” (CH 1
slit sae cos” @ — 5 sin* (ep \\
ZEN Oba) 2
Now, the energy of a volume-element dv of the ellipsoid which
we consider to be very long and magnetized with equal intensity /
in the direction of the field, is
W — — JHdv
and therefore the moment of the couple exerted by the field on this
element is
ow 3 ERY
eae: dv. ee) sin @ cos 6.
Ou?
The couple exerted by the field //, on the ellipsoid is
M = (N, — N,) Lv sin & 08 gy.
In very strong fields the condition is fulfilled that the magnetization
is parallel to the external field nothwithstanding the demagnetizing
forces of the ellipsoid, and therefore 6 = g.
Hence the disturbing moment dJl’ varies with azimuth of the
substance in exactly the same manner as the chief couple M7. The
maximum value of the couple dJ/’ is
3 ORIEN, &
dM = =dv £ . | — | 7?,
2 On? F
which for the whole ellipsoid gives
3 oH
i — | nn ena
10 Ou? ‘
where w is the semi-major-axis of the ellipsoid.
Let us now make the assumption that the field changes confor-
mally, and let us call the field 1em. from the axis in the direction
of the y-axis (1 — «) H,, then
ey AOR EL
eH, = — ~-
4 \ dx?
6
Te Hv . a?
5
and therefore
i
and the ratio between the maximum values of the couples is
Mi 6 ae léls
— = —— £ a ———__—_...
Wha (N,—N,) I
With constant magnetization, therefore, the second last equation
shows that the disturbing couple increases proportionally to the
strength of the field. In the /H diagram, a sloping instead of a
( 661 )
horizontal asymptote will be found. This was shown clearly in some
of the foregoing experiments. If the field is constant the disturbing
couple increases with /. Therefore, if in the measurements with the
greatest values of / for which the experiments are carried out, made
with a certain apparatus the disturbing couple does not make its
presence felt, then a@ fortiord is it negligible for the smaller values
of /. The last equation shows that the re/ative value of the couple
for non-uniformity of the field increases as the intensity diminishes.
Hence it is to be feared particularly when one works with small
magnetizations, and when, to increase the sensitivity of the apparatus,
the torsion spring is replaced by a weaker one.
For the purposes of our measurements if is sufficient to get an
idea of the order of magnitude of the error. For this purpose the
non-uniformity of the field was measured for three different values
of y; it was found to be proportional to y° with ¢= 0.0087 as factor.
With a= 0.15 it follows that & = 0.000238 eet . For the
M (MNja
ellipsoids used NV, =1.90 and NV, —5.59, and (V,—N,) J is almost
6600 gauss for iron and 1800 gauss for nickel. Hence, for iron the
correction is scarcely 1 in 1000, while for nickel it increases to
some thousandths.
Reaction of the ellipsoid on the pole-pieces.
When the ends of the ellipsoid come into the immediate neigh-
bourhood of the end surfaces of the poles, they exert a noticeable
influence upon the distribution of magnetism in the pole-pieces, and
the couple becomes increased thereby. This fact was established by
previous experiments with a larger electromagnet with flat pole-pieces
of 15 cm. diameter. In these experiments was measured the couple
exerted upon an ellipsoid with various distances between the poles
by a field of the constant value of 9770 gauss regulated each time
by passing the required current. In this way the following values
were obtained for an iron ellipsoid 9 mm. long and 4 mm. thick.
Distance between poles Maximum couple
9 mm. 335.6
1S Ee 320.45
0B 319.32
oo, 319.18
Bb. 2s 319.08
44*
( 662 )
The law according to which this magnitude changes shows that
the change is not a consequence of the non-uniformity of the field ;
for just when the disturbance reaches its greatest value, the field is
most regular owing to the closer approach of the flat pole-pieces. For
distances of 23 mm. and greater the influence is insignificant, and
the couple is constant.
bh. Electromagnet. From what has been said about the influence
of the ellipsoid and the pole-surfaces it follows that the distance
between the poles should be about three times the length of the
ellipsoid. The total thickness of the four walls of the Dewar tubes
and of the holder (§ 2c) could not be made smaller than 5 mm.
Hence, keeping account of the difficulty on the one hand of obtaining
strong fields of wide extension and on the other hand of reducing
very small ellipsoids to the correct form, we decided upon an inter-
pole distance of 9 mm. and a length of 3 mm. for the ellipsoids.
With this distance comparatively strong fields (up to 25000 gauss)
may be excited with a magnet whose cores are 9 cm. in diameter.
The electromagnet of this power which was used in these experiments
has already served for magnetic experiments at high temperatures.
It bas already been described ') and is represented diagrammatically
in fig. 1 Pl. I. Comparatively light (132 KG.) and, taking its power
into account, easily transported, it was possible to study it in Zurich
and to use it in Leyden. Hand-wheels, whose position is read from
divided circles, communicate a horizontal micrometric movement to
the pole-pieces.
The magnet turns upon a vertical axis and for that purpose is
mounted upon a ball-bearing support. The azimuth is determined by
means of a fixed mark on a eylindrical scale /, attached to the
movable portion of the supporting base. Each of the coils has 1500
turns of 2.5 mm. wire and has a resistance of about 2 ohms. As
the coils are arranged for a current of 10 amp. under ordinary
circumstances, and as the current can for a short time be increased
to 25 amp. the number of ampere-turns at one’s disposal may reach
as high as 75.000. The water circulation 7; between the double
walls of the coils has this immediate advantage that the duration of
an experiment may be doubled, but it is chiefly of importance in
protecting the pole-pieces from heat. Such a beating would lead to
various difficulties, of which one of the worst would be that the strength
of the field would noticeably change, for the expansion of the com-
1) G.. Zinver. Revue électrique 20 Juin 1909 and Elektrot. Zeitschr. XXX,
p. 446, 1909,
( 663 )
paratively long core by heat could distinctly alter the comparatively
short distance between the poles.
c. Cryogenic apparatus. As it was necessary to shut off from the
air the space in which the ellipsoid was freely suspended since it
contained liquid hydrogen and its vapour, a fairly complicated eryo-
genic apparatus had to be employed. This is shown diagrammatically
in Pl. I fig. 1 and in section in fig. 3. The apparatus consists
chiefly of three tube-shaped portions which, naming from outside
inwards, we call the cover, the adjusting tube f, and the holder b.
The cover consists of a silvered vacuum tube A, a brass tube 4,
a glass tube C, and a cap D which shuts off the apparatus from
the air.
Holder. The ellipsoid a (figs. 3 and 5) can turn round a vertical
axis with the holder 6 in which it is fixed. For the greater part
of its length the holder is made from a tube 6, of german
silver a substance that is rigid, little magnetic, and a bad heat-
conductor. The lower end is joined to a copper rod 6,, which has
only a very weak inherent magnetism. The holder is connected to
the rod & by the spiral spring y, (y, was used for iron and cobalt;
the weaker spring g,, which was used for nickel and magnetite is
shown at the side). To make the equilibrium stable ard to prevent
the ellipsoid from being attracted to the poles of the magnet the
holder is held fast underneath by a wire of platinum-iridium of
0.1 mm. diameter, for the torsion of which a correction need hardly
be applied (§ 4).
The tube 6, and the rod 4, are carefully adjusted on the lathe,
and the ellipsoid a@ (fig. 4) is fixed carefully in a cylindrical opening,
the diameter of which is equal to the minor axis of the ellipsoid.
If the ellipsoid is nickel or magnetite it can be fixed in position
with a little wax. With iron and cobalt, however, the ellipsoid is
subject to such strong forces that it is necessary to clamp it fast by
covering it with a thin piece of sheet copper and then driving it
forcibly into the opening. The tnrning of the ellipsoid is transmitted
through the rod 6,, and the thin-walled german-silver tube *) 4, to
the mirror 4. From the mirror through the opening /,, and the
window C, (figs. 1 and 3) the torsion of the spring g, is read. A
1) A slight twisting of this tube is of no account. Only that portion of the
apparatus between the mirror and the cap acts as a spring. Twisting of the
portion of the apparatus below the mirror only transmits the couple to that
spring, its sole effect is to slightly, but not noticeably, alier the azimuth of the
magnet.
( 664 )
glass scale 1.5 meters long, and subdivided into half millimeters is
used; it is placed at a distance of 4.525 m. and is illuminated by
spherical mirror strips'). The tension of the spring is regulated by
the rod & (fig. 3), which passes through a stuffing box D, in the
cap D. Vertical motion is communicated to & by turning the nut
), and at the same time preventing the motion of D,;. The tension
is read through the opening /,, from the pointer / on the scale ,,.
Before mounting the apparatus, that division of the scale ,, is
determined which corresponds with the tension that is to be used,
by suspending known weights from the stretching wire.
The apparatus is, like a stretched string, very liable to start vi-
brating under the influence of small impulses. This tendency is
counteracted by immersing the vanes of a vane-damper #, (fig. 6
and fig. 8) in oil contained in a circular vessel divided into different
chambers by the partitions 6,,. These partitions are attached to a
cylinder which turns with slight friction in the adjusting tube and
is therefore carried round by the vanes 6,, whenever the holder
must experience a somewhat greater torsion (§4)*). The vanes must
be wholly immersed in the oil so as to ensure that capillary reactions
do not bring forees into play (see §4), whose torsional effect could
not be neglected. In strong fields the torsion oscillations are damped
extremely well by the FoucaunrT currents.
The whole holder and spring hang in the adjusting tube 7 the
upper end of which is screwed to the cap D; this cap also carries
the rod /:, and is itself supported by the glass tube C. The adjusting
tube, consisting of the portions /,, /;,/,,/;, is three times diminished
in cross-section. The lowest portion /; is narrow and surrounds the
rod 6, of the holder as closely as possible. Against the bottom /,
(fig. 5) rests the cone c, which is soldered to the wire d and serves
to keep it taught. A slit in the bottom allows the conical portion to
be placed in position (fig. 5). When the apparatus is put together
the adjusting tnbe sinks into the Drwar vessel A so that the thin
tube f, is centred in the narrow portion of the vacuum tube. The
adjusting tube as well as the tube 6, of the holder is made of
german-silver.
To mount the adjusting tube already containing the holder in the
cover, the cap D is screwed to a bronze ring cemented to the glass
tube C' of the cover; the screws D, are tightened, and the junction
1) H.Kamertincu Onnes, Comm. fr. the phys. Lab. Leiden, n°. 25. (1896).
2) It is essential to free the oil beforehand from volatile substances, and also
to prevent the accumulation of air bubbles under the oil, since the apparatus has
to be completely evacuated after it is put together.
( 665 )
is made air-tight by means of the rubber sleeve D, which is smeared
with rubber solution and bound with copper wire. The lower end
of the glass tube C is cemented to a second bronze ring, which is
soldered to the brass tube £ of the cover. To the centre of this
brass tube is attached a ring 4, carrying the bolts of the supporting
rods 6, which hold the vacuum glass in position.
The Dewar tube itself consists of a narrow lower portion A, com-
pletely silvered and a wider upper portion that is silvered up to
A, (the upper portion is left transparent so that we might be sure
that we were not allowing too much liquid hydrogen to enter the
glass). It fits into the brass tube 4, and is protected by a wooden
ring. The supporting rods 4, keep the vacuum tube in position and
at such a height that it is just clear of the wooden safety ring.
Fig. 7 shows how, by means of the screw 4,,, the vacuum glass
protected by a layer of paper is clamped to the thin brass ring 4,, to
which are attached ithe ends of the supporting rods £,. The lower
portion of the vacuum tube has an external diameter of 8mm. and
an internal diameter of 5 mm. The glass walls are 0,5 mm. thick,
which leaves only 0,5 mm. as the distance between the two silvered
walls.
The apparatus is centred by placing it on an auxiliary support by
means of the ring 4,. Before the vacuum tube it yet in position, the
narrow portion 7, of the adjusting tube is adjusted by a central ring
in an adjustable centring-plate. The loose ring is then removed from
the plate and a second is fitted such that it just fits the narrow
portion of the lower end of the vacuum tube. The nuts 4,, serve
to bring the vacuum glass to its proper position, and, as before, it
is made aii-tight by a rubber sleeve £,, which is smeared with
rubber solution and bound with copper wire. By adopting this method
of attaching the vacuum tube one need not fear alteration of the
cover when the apparatus is evacuated, and only small further
adjustments are necessary for recentring the apparatus after evacuation.
In the tube B is soldered the steel capillary 6, (figs. 1 and 3) ofa
helium thermometer *) with german silver reservoir 0, (figs. 3 and 7) and
glass stem 6,, which is permanently attached to this portion of the
cover. The quantity of helium is so chosen that at the boiling point
of oxygen the mercury stands at a mark in the lower portion of the
stem, and at the melting point of hydrogen at one in the upper
portion. If, as is the case with hydrogen boiling under ordinary
atmospheric pressure, the temperature is sufficiently well known
) Compare the apparatus for the liquefaction of helium. H. Kameruincu Onyes
These Prove May/June 1908, Comm. Leid. N®. 108.
( 666 )
without reading the thermometer, the thermometer is still necessary,
however, to indicate the position of the upper surface of the liquid
gas which is no longer visible beneath A,. As soon as the level
sinks below the upper end of the reservoir 6, of the thermometer,
the mercury in the stem 6, sinks.
d. First the electromagnet is adjusted which operation is independent
of the centring of the adjusting tube, the holder and the vacuum
tube. The axis round which it turns is made vertical, and then the
pole distance is centred round this axis. Next the centre of the truncated
spherical socket G,, (fig. 1, 2 and 3) is made to coincide with the axis
round which the magnet turns. It is supported by a plate which is
attached by two beams to the freestone pillar ©. The cryogenic
apparatus is then brought from its auxiliary support and arranged
in ils proper position by placing the ball-shaped portion of the surface
of the ring B, in the concentric socket G,,; the centring of the
narrow portion of the vacuum tube on the turning-axis of the inagnet
is completed by means of wing nuts on the ring b,. This centring
must be done with great accuracy, for the magnet must turn freely
and the distance between the vacuum tube and either pole is not
more than half a millimetre. It ean, however, easily be accomplished
to 0.25 mm.
e. Liquid hydrogen is introduced into the apparatus by a german
silver tube B, (ef. Comm. N’. 94/). The gas formed by evaporation
escapes through B, (figs. 3 and 1) and through the valves X,, A, (tig. 1)
to a gasometer or to a vacuum pump. By means of the valves the
vapour pressure is regulated, and its value is read on a manometer
HT which at the same time acts as a safety valve. In experiments
made in the neighbourhood of the melting point of hydrogen the
pressure was kept slightly above that of the triple point.
Before introducing liquid hydrogen through the tube 4,, which is
closed by a rubber tube with a glass stopper, the air is pumped out
of the apparatus through the valve A,. It is absolutely essential that
the apparatus should be air tight, for traces of air would solidity
in the liquid hydrogen and, owing to magnetic attraction, would
eolleet in the neighbourhood of the ellipsoid.
To prevent the cooling of the upper portion of the apparatus
containing the torsion spring by the boiling hydrogen, a number of
large openings are made in the tube /, (fig. 3) arranged in such a
way that no injury is done to its resistance to torsion. In addition to
this copper screens surrounding /, and soldered to 4,, are arranged
( 667 )
so that the tube moves with slight torsion in them. A little cotton-
wool placed on the bottom of the vacuumglass and attached to the
holder lessens the sudden bubbling’) up of the hydrogen’),
Further additions of liquid hydrogen are made in the same way
as the first. As a rule various series of measurements could be made
with a single filling with hydrogen. The point of the vacuuimglass
which could not be silvered was protected by a small silvered
vacuum beaker / containing liquid air. When the portion of the
apparatus above the diaphragms 4,, is again at ordinary temperature
after a filling with liquid hydrogen, one can hardly notice that there
is liquid hydrogen in the apparatus at all, if it is not above A,.
In the course of time a little mist is precipitated on the vacuum tube.
By surrounding the tube at A, with blotting paper, the moisture
is prevented from trickling down between the pole-pieces. Further-
more a stream of air is directed against the tube between the pole-
pieces. Hence the pole-pieces are in no way affected by the cryogenic
operations.
J. The springs are phosphorbronze. This substance is non-magnetic
and acquires very little permanent set. Springs of the same constant
can be made by winding a spiral either of a thin short wire
or of a much longer thicker one. Of the two, the one which
has the greater mass will experience the smaller specific changes,
and consequently will be the more perfectly elastic in working. This
circumstance has been duly taken into account. The springs are provided
with straight extensions in the direction of their axis and are connected
with the holder and the rod / (fig. 3) by serews. The turns of the
spirals do not touch each other. The temperature of the spring is
measured by a mercury thermometer that is clamped against the
cap D and with it is insulated with wool. The constants of the two
springs used are 261000 and 22300 dyne-centimetres per radian.
The corrections for the influence of the stretching wire and for the
temperature change of the spring will be discussed in § 4.
The ellipsoids of iron, nickel and cobalt are 3 mm. long and
1,333 mm. thick. They have been made with great accuracy by the
Société Geéneévoise pour la Construction d’Instruments de Physique.
They were turned under a microscope giving a 30-fold magnification
and provided with a camera lucida so that the image of the object
and an enlarged drawing could be superposed. Measurements with
1) Should this occur one must ensure that the oil of the damper is not cooled
by the drops that are thrown up.
( 668 )
the dividing-engine have shown that the ellipsoids are very accurately
shaped.
The iron was obtained by melting pure electrolytic Merck iron
contained in a magnesia boat in en electrical resistance furnace and
in an atmosphere of nitrogen. The nickel and cobalt were prepared
in the same way, starting with the purest possible nickel and cobalt
powder specially prepared by Merck for these experiments. The
magnetite was obtained by constructing an approximate ellipsoid
from a drop of very pure magnetite obtained by melting very pure
Merck sesquioxide in an oxy-hydrogen flame. Since experiment showed
that it was only at very high temperatures that the last trace of
oxygen was driven out and real magnetite’) obtained an iridium
cupola was used for this operation.
Ellipsoids of approximate shape were also constructed from GoLp-
SCHMIDT chromium and manganese and Moissan vanadium. As can
easily be seen it is not necessary for comparative experiments that
the ellipsoids should be constructed with particular accuracy. This
was, moreover, experimentally demonstrated for magnetite, of which
various samples roughly worked to various ellipsoidal shapes were
used for obtaining curves for the thermal change at high tempe-
ratures, and these curves were in agreement with the theoretical
curve, and consequently with each other.
§ 3. Experimental method. As mentioned in the introduction our
aim was not to obtain absolute values for magnetization in strong
fields at ordinary temperature and at the temperature of liquid
hydrogen, but to compare the values at these temperatures; for we
might expect that the change would be only a small fraction of the
quantity to be measured. Hence it was an obvious procedure to
make observations at these temperatures alternately in the same field.
The change, however, from the one temperature to the other neces-
sitated operations of such duration as to prohibit the use of this
method. Hence we usually began with a series of measurements at
ordinary temperature, in which the field was made the required
series of strengths. Then an analogous series of measurements was
made at a low temperature, and after the apparatus had returned to
ordinary temperature, some individual measurements were repeated
so as to make sure that the apparatus had not in the meantime
undergone any change.
1) See also P. Weiss. Arch des Sc. whys. et nat. fevr. 1910 and Journ. de physique,
4e Sér. t. IX mars 1910.
( 669 )
Each series of measurements consists in turn of two branches.
First by tentative approximation from both sides for all values of
the field those values of the azimuth of the electromagnet are found
for which the couple is a maximum. In this way two azimuths are
found which are symmetrical with respect to the major axis of the
ellipsoid and which exert couples of opposite sign. This determination
‘an be made accurately to within 0,5° to 1°, which is quite sufficient.
Then follows the true measurement in which the magnet without
current is placed in one of these positions, the circuit is closed and
immediately afterwards the deflection is read. As soon as this is
done, the circuit is broken, the magnet is placed in the symmetrical
position; once more the current is allowed to flow and the new
deflection is obtained. Since these operations occupy only a short
time, the after effects in the spring are of no account. The difference
between the seale readings gives twice the value of the couple to
be measured, independent of the residual magnetism remaining after
the current was broken, which however occasioned only an extremely
small couple. The field was given as a function of the current indi-
cated by the ammeter. For these observations the same ammeter
(Stemens and Hatskn instrument, no temperature coefficient) was used
which was employed in the study of the field. This method of
evaluating the field was quite sufficient for our purpose. The distance
between the pole-pieces was read off the divided cylinders of the
magnet and was verified by passing between them callipers which
had been previously adjusted to the desired distance. The fields given
above are corrected for the demagnetizing fields of the ellipsoids.
§ 4. Corrections and controls; auxiliary measurements. The inherent
magnetism of the holder is not so weak that the corrections neces-
sary for it may be neglected. On that account a series of measurements
was made with no ellipsoid in the holder at ordinary and liquid
hydrogen temperatures. With the weaker spring we found:
TAG By Eve
Correction for the magnetism of the holder.
ordinary temperature ¢—= 20°.2 K.
4000 gauss 0.18 em. 0.26 em.
8000 0.29 0.48
12000 0.36 0.61
16000 0.43 0.73
20000 0.50 0.86
24000 0.57 0.98
( 670 )
22300
261000
they are very small. Direct measurements have shown that the values
calculated in this way are correct, which indicates that the inherent
magnetism of the carrier is not changed by the various operations
of mounting.
For the stronger spring these corrections are multiplied by
There is still a correction to be applied to the couple-ratio for the
change in elasticity of the steadying wire under the carrier when
its temperature changes from ordinary to that of liquid hydrogen.
To obtain that correction the ratio of the torsion modulus of the
platinium iridium wire and that of the weaker of the phosphorbronze
springs was measured’ at the two temperatures. This was done in an
apparatus similar to the one we have described with the exception
that the cap D could turn relatively to the cover. By a mirror
method the: position of the cap was read on a scale at a distance
of 175.9 em. The cap was turned through an angle of about 360°,
and the exact measurement of the angle was obtained from the same
scale. This angle is the sum of the torsions of the spring and the
wire caused by the same couple. The torsion of the wire was read
from the mirror of the holder. In this way the ratio of the modulus
of the wire to that of the spring was found to be
0.0125 at ordinary temperature
0.0144 in liquid hydrogen.
The fourth decimal is uncertain; hence the correction is two
thousanths for the weak spring and two ten-thousandths for the
stronger. The temperature coefficient of the phosphorbronze spring
was obtained from determinations of the period of oscillation of the
same oscillating system while the spring was first at the ordinary
temperature and then surrounded with steam. By means of the
temperature coefficient thus determined viz. :
k = — 0,00053
the observations are reduced to the same temperature.
The temperature of the liquid bath in the vacuum tube was proved
to be constant to 0,1 degree, by carrying out temperature measure-
ments with a platinum resistance thermometer placed at different
heights in a similar vessel. When placed alongside the thermometer
@ it indicated temperatures corresponding with those deduced from
the vapour pressures.
Capillary action in the oil damper.
Care was taken to fill the oil vessel to such a height that the
cylindrical ring carrying the vanes of the damper was partly immersed
in the oil so that the vanes were completely immersed and should
experience no capillary action. But still we wished to know the order
of magnitude of the forces brought into play by capillary disturbances ;
for this purpose we greatly magnified them. A damper as like ours as
possible was filled only to such a height that the vanes and partitions
intersected the surface of the liquid. The movable portion was suspended
by a platinum-iridium wire 20 cm. long and 0,1 mm. thick ; detlec-
tions were read from a mirror on a scale 2 metres away. The oil
vessel was placed successively in two different azimuths such that
the approach of the vanes towards the partitions would bring into
play ‘couples of opposite moments. The scale deflection was 5 em.
The moment of the couple is therefore of the order of two thousandths
of that of the couple exerted on the nickel ellipsoid.
§ 5. Details of the observations.
Nic kel :
The first series of measurements was made at 17°.2 C.
TASB SWB sail:
HT (gauss) I* (em. of the scale)
2230 89.42
6250 89.97
10270 90.12
13280 90.3
17760 90.50
20300 90.66
21540 90.79
22760 90.81
The scale reading was always corrected for the ratio of the tangent
of the double angle to the double angle of the deflection. The zero
as determined by the mean of readings to left and right remained
constant to a few tenths of a millimeter.
_ After this series the apparatus was accidentally damaged; it had
therefore to be taken to pieces and remounted. That occasioned a
small change in the magnitude of the deflections. Since the change
of 7’ with H is determined by the foregoing series, only two points
were subsequently determined at ordinary temperature before and
after determinations in liquid hydrogen.
TABLE IIL
as Le ea nN OF Hydrogen at atm. pressure (20°.2 Kk.)
H (gauss) 7° (em. of Hl (gauss) 2 fem. sof
| the scale) the scale)
before 1780 93.57
16100 91.74 5410 100.49
20540 92.09 5050 101.54
after 11830 101.84
16100 91.79 16100 102.13
20540 92.20 19050 102.34
20540 102.51
22020 402.48
22840 102.49
The zero determined from the mean of readings to right and left
changed by about 2 mm.
. T30.2K
For H= 16100 gauss —— = 1.0549
199.50
» H= 20540 _,, m 1.0547
mean 1.0548 not connected for dilation.
Cobalt.
The measurements with cobalt did not lead to the desired result.
It was the extreme difficulty of bringing the magnetization of cobalt
{6 saturation encountered in preliminary experiments that had led
to the choice of an apparatus of such small dimensions. For the
other substances a weaker field would have sufficed, and hence a
ereater distance between the poles would have served.
In the observations at ordinary temperature something unexpected
already happened. Although the mean of the readings to right and
left ought to have given the zero-point of the apparatus, the point
was actually observed to vary with the field. This change was after-
wards seen to be about twice as great at low temperatures. The
following figures bring this out clearly. (In the cobalt measurements
the external field is given uncorrected for the demagnetizing field of
the ellipsoid. When saturation is reached this is 5000 gauss).
TASB It Be TVe
Cobalt [ at ordinary temperature.
H, (gauss) /* (em. ofthe scale) calculated zero
4025 AAG 76.73
8050 38.14 WAT the observed
12075 50.48 78.96 zero Was
19560 ye! 78.37 not
23340 53.29 78.18 recorded
25650 53.30 78.63
Cobalt [ at temperature of solidifying hydrogen (14°.3 K.).
4025 113395) 77.62
8050 32.59 78.84
15820 53.23 81.93 observed zero
19560 54.33 81.40 78.26
21800 54.43 81.16
23340 54.45 81.02
24760 54.46 80.08
From this it appears that asymmetric disturbing forces affect the
main phenomenon. It is probable that we are here dealing with
phenomena of crystal magnetism arising from the fact that in the
small ellipsoid the crystalline elements of the cobalt are not suffi-
ciently numerous to realize isotropy by compensation. The magnitude
and sign of these subsidiary actions are independent of the main
phenomenon, and they can even be of opposite effect for both azimuths
of the electromagnet; they can become of very great importance if
the substance possesses a more or less pronounced magnetic plane,
and the example of pyrrhotine shows us that their influence becomes
greater at lower temperatures. Further, the law of approach to
saturation in cobalt which differs from that which holds for the
other substances is consistent with the existence of strongly developed
magneto-crystalline phenomena °*).
These experiments were repeated with a second cobalt ellipsoid,
and the same asymmetric action, but somewhat weaker, was observed.
But in this case a disturbance of another nature was encountered,
which shows how concomitant disturbing phenomena may affect the
measurement of magnetization: the magnetization at low temperature
was now found to be apparently smaller than at ordinary temperature.
The following table contains an extract from the results obtained
with this ellipsoid.
1) P. Weiss, Arch, des Se. phys. et nat. février 1910, Journ. de phys. mars 1910.
( 674 )
TAB ty By ave
Cobalt IE anh pS ibs (0:
H, (gauss* I? (cm. of scale) Cale. zero Obs. zero
4025 20.33 77.56
12075 54.16 76.49 en
23340 59.76 76.86
25560 59.94 76.90
Cobalt IT in H, at atm. pressure (20°.2 K.).
15080 53.53 76.61
23340 58.09 77.07 78.90
25650 58.46 77.24
The same ellipsoid was removed from the carrier and replaced
with Khotinsky cement; one could easily understand that very strong
strain-magnetic phenomena might be occasioned by forcibly driving
it into its mount. At the same time it was for the new experiment
displaced through a different angle of rotation with respect to its
major axis; by this operation the sign of the change of zero point
as a function of the field was reversed.
TABLE VI.
Cobalt I] t= 16°.5 C.
Hi, (gauss) I? (em. of scale) Cale. zero Obs. zero
8050 40.99 1942
19560 56.48 78.80 79.45
23340 57.07 78.89
25650 57.34 78.90
Cobalt Il in H, at atm. pressure (20°.2 K.).
8050 34.07 78.88 79.20
19560 oemA 78.24
23340 54.26 78.33
25650 54.63 78.42
The only conclusion one seems to be able to draw from these
experiments with cobalt seems to be that the increase in magnetization
of cobalt between ordinary and liquid hydrogen temperatures is very
much smaller than that undergone by magnetite and nickel, for, if
this were not the case, the increase could not have been obseured
by the disturbing influences.
PIERRE WEISS and H. KAMERLINGH ONNES. ‘Researches on magnetization
at very low temperatures.”
Plate I.
j|__ 3,5] Le 1 ——
Fig. 2.
Proceedings Royal Acad. Amsterdam. Vol. XII.
PIERRE WEISS and H. KAMERLINGH ONNES. “Researches on magnetization at very
low temperatures.” Plate II.
WITH TOOTS
to
te
620
30
ei \v=
WD) Sg. 4.
Sy) me
Proceedings Royal Acad. Amsterdam. Vol. XII.
( 675
AB B= NL:
Tron.
H (gauss) I? (cm of scale)
== AUP (Oh i—*), Veesnie I= NEOUS
(H, atm. press.) (H, solidifying)
1700 95.23 101.98 101.95
5675 98.47 102.58
8680 98.65 103.01
13160 98.91 103.31
15700 99.04 103.31 103.23
16940 99.08 103.27
18360 99.06 103.27
19250 99.07 103.25 103.25
. 2 20 Rok ;
for == 19250 Tae = 1.0209
18360 1.0210
16940 1.0209
15700 1.0213
mean not corrected for dilatation 1.0210
In all the iron experiments the zero as deduced by taking the
mean of readings to right and left remained remarkably constant.
As a rule its displacement was only a few tenths of a millimetre in
any one series, and 6 mm. in proceeding from one series to another.
The few measurements at the temperature of solidifying hydrogen
are sufficient to show that nothing particular happens between
20° K. and 14° K.
Magnetite.
We have already mentioned that the preparation of magnetite by
heating the sesquioxide needs an extremely high temperature if one
wishes to make sure that the last traces of oxygen are removed. A
first ellipsoid obtained from iron oxide that had been insufficiently
heated exhibited only little more that one half of the magnetization
that was expected; it showed, too, a very distinct hysteresis, which
was about three times as great at liquid hydrogen temperature as
at ordinary temperature, while in all the experiments with the other
substances hysteresis phenomena were insignificant. Moreover, the
magnetization of this substance was the same at ordinary and liquid
hydrogen temperatures, while between them it reached a maximum.
These peculiarities were not displayed by a second ellipsoid cut
45
Proceedings Royal Acad. Amsterdam. Vol. XII.
( 676 )
out of well heated magnetite, but with this second ellipsoid further
phenomena were observed which have not yet been explained but
which seem to be of secondary importance. The zero point deduced
from. the mean of the two seale readings differed noticeably from
tle observed zero, while in any one series of measurements at the
same temperature it remained practically constant. Further and
this is more worthy of notice — the deviations differ according to
the direction of the field. It would clearly be very rash to attempt
to ascribe to magnetite a hemimorphous symmetry lke that of
tourmaline from this sole observation. It seems more probable that
some experimental error has here escaped our notice, and this can
the more readily be accepted seeing that magnetite gives results much
less regular than those of the metals. The following table contains
an extract from the observations; the observations for the positive
and negative directions of the field are given separately.
fA Bee Vili:
Magnetite.
f= ily i ©.
Observed zero — calculated zero + 0.9 em.
H (gauss) + Field — Field
I? (em. of scale) I? (em. of scale)
8600 71.40 TA72
18100 71.83 72.00
21800 EG) 12.57
233800 ES) 72.57
24200 ale 72.45
H, under atm. pressure (207.5 K.)
8600 79.78 79.88
18100 80.69 80.79
21800 80.73 $0.96
23300 80.34 $51.10
24200 80.08 . 81.37
H, solidifying (14°.0 K.)
18100 80.90 $1.10
21800 81.12 81.64
24200 80.96 81.84
From these numbers follow these ratios of the intensities at 20°.3 Kk.
and 15-8:
( 677 )
TABLE IX:
Field +L. - Field —
Ta0° 3k. L99°.ak.
H gauss z
115°.8 Cc. 115°. ©.
8600 1.0559 1.0553
18100 1.0591 41.0601
21500 1.0593 1.0567
23300 1.0564 1.0572
24200 1.0563 1.0628
mean 1.057 1.0564
20°.3KK. ean : ; :
Hence “"™ — 1.0569 not corrected for dilatation.
UHASKGS
Similarly for the ratio of the magnetization at 14°.0 K. to that at
15°.8 C. we find
1.0609 1.0622
hence
11 4°.0x. ia : A . ; ee:
———~ — 1.0616 not corrected for dilatation
ESP ISIC.
a ratio which deviates from the foregoing in the expected direction.
Collecting the foregoing results we find in this branch of the
research for the ferromagnetic substances omitting the correction for
dilatation (see note 2 pg. 11)
190° 3.
Nickel —wIeEObAS
1)72.3¢.
190° 3k.
Tron SS SS AIUD)
L299 (
. £20. 3K. Ls
Masnetite ——— — 1.0569.
l5e-e Cs
(March 24, 1910).
KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.
PROCEEDINGS OF THE MEETING
of Saturday March 26, 1910.
(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van 26 Maart 1910, Dl. XVII).
GIS) ANP AL aD ANY SE Se
A. IX. M. Norexs: “Communications about the electrogram of the atrium cordis”. (Communi-
cated by Prof. IT. ZwaarpemMAKER), p. 680. (With one plate).
C. van Wissetincn: “On the tcsis for tanning in the living plant and on the physiological
significance of tannin’. (Communicated by Prof. J. W. Mot), p. 685.
H. Zwaarpemaker: “The camera silenta of the Physiological Laboratory at Utrecht”, p. 706.
Jan DE Vries: “Qn pairs of points which are associated with respect to a plane cubie”, p. 711.
L. E. J. Brouwer: “On continuous yeetor distributions on surfaces” (2nd communication,
(Communicated by Prof. D. J. Korrewee), p. 716.
H. J. E. Bern: “The oscillations about a position of equilibrium where a simple linear relation
exists between the frequencies of the principal vibrations” (2nd part). (Communicated by
Prof. D. J. Korrewee), p. 735. (With one plate).
W. van DER Wovpr: “The cubic involution of the first rank in the plane’. (Communicated
by Prof. P. H. Scuoure), p. 751.
J. Bruin: “On the surfaces the asymptotic lines of which can be determined by quadratures”’.
(Communicated by Prof Hk. pe Vrrgs), p. 759.
A. Sirs: “A new theory of the phenomenon allotropy”. (Communicated by Prof, A. F.
HoLieman), p. 763. (With one plate).
Erratum, p. 774.
46
Proceedings Royal Acad. Amsterdam, Vol. XII.
( 680 )
Physiology. — “Communications about the electrogram of the atrium
cordis.” By Dr. A. K. M. Noyoys. (Communicated by Prof
H. ZWAARDPMAKER).
(Communicated in the meeting of November 27, 1909).
Involuntarily the ventricle-image, the tops R and 7 of which are
prevailing, has, in the study of the electric phenomena of the heart,
up till now been the principal subject. The top P by its smaller
size drew less attention and at the outset was not even observed.
At present, however, there are in the literature already some
data to be found here and there concerning the top P. Thus
EInTHOVEN ') has pointed out how with increased action of the heart
after great physical exertion ? may gain in size, how under certain
definite circumstances P may more or less be split up into a dim
double-topped image, and besides how under pathological relations
top P may be altered, which is demonstrated by cases of mitral
stenosis. In this case of disease /? would appear longer and enlarged,
which Ernrnoyen thinks may be attributed to a stronger activity of
the atrium for the sake of its compensative function. Division of the
top may also appear. Kraus and Niconai?) have corroborated this
find, just as Samosnorr®) and Sresuinsky *), who have also been
able to prove that the phenomenon is not pathognomonic, but de-
pends on the relative welfare of the heart in case of mitral stenosis.
According to VAANDRAGER®), top 2 in absolute measure would be
higher with the dog than in man. With N. vagi cut through
Vaanpracer found in the dog that P gréw three times its height
and conversely could he make P smaller by stimulating the N. vagi.
Besides this diminution he got at the same time an alteration in the
form of top P.
With moderate bleeding of a sample-animal P increased in size,
o
whilst after strong bleeding ? grew smaller in the dog.
Top P was from the outset attributed by EiyrHoven to the ven-
{ricles.
1!) Eryrnoven: See: Onderzoekingen van het Physiol. Lab. te Leyden. Second
Series VII and the literature pointed out there.
‘) Kraus F. and Niconai G. FP. Ueber das Electrocardiogramm unter normalen und |
nathologischen Verhiiltniszen. Berl. klin. Wochenschr. 1907 No. 25 and 26.
" 8) Samostorr A. Electrocardiogramme. Jena 1909. Sammlung anat. und physiol.
Vorlriige. .
‘) Samostorr A. und Sresnrysky. Ueber die Vorhoferhebung des Elektrokardio-
gramms bei Milralstenose. Miinch. mediz. Wochenschr. No. 38, 1909.
5) Vaanpracer B, Dissertatie Leiden 1908.
( 681 )
The following grounds may be adduced for this, partially borrowed
from my experiments :
1. P always appears with a definite interval of time before the
mechanical change of the atria.
2. P continues existing at the registration of an isolated atrium
(Rana, Emys).
3. P is absent when the electrogram is written of the isolated
heart-ventricle of Anguilla vulgaris.
4. P continues existing when a certain detraction of the ventricle
does not show itself. This may be observed both in the patho-
logical heartblock and in the heartbloek called into existence
by experimental causes, &mong others:
a. by stimulating the N. vagus in the dog or the tortoise.
b. by administering toxical materials like chloroform.
c. by forming, resp. removing a ligature on the boundary of
auricles and ventricles in Rana.
5. P may be made to disappear temporarily, when in appropriate
sample-objects a heartblock is brought about by ‘stimulating
the N. vagus at the transition of the sinus to the atria, with
which, it is true, the sinus-contractions are preserved, but the
atrium-contractions with top P in the electrogram disappear.
6. P does not arise from the sinus, witness the fact that a small
top may be registrated before the appearance of top P, which
may be attributed to the sinus.
~
Size and form of P depend upon the way in which the
atrium is derived.
If we consider the electrocardiogram of man and animal super-
ticially, we get the impression that P has a very simple form. Under
quite peculiar circumstances this shape has been seen to alter. On
closer investigation, however, it has appeared to me that the electric
phenomenon of auricles is practically a whole complex. This becomes
clear at the registration of an isolated pulsating atrium. Very fit for
this purpose is one of the auricles of the heart of Emys.
Thus the adjoined figure 1 renders the electrogram obtained by
derivation of apex and basis of an isolated right atrium of Emys
with the appertaining myogram registered by simple suspension °).
This image, in many respects, makes us think of an electrogram
1) The registration of the electrograms was brought about by means of EtnrHoven’s
string-galvanometer (Epgtann’s small model) according to the method pointed
out before; see: Proceedings of the Kon. Akad. vy. Wetensch. 31 Oct. 1908.
46%
( 682 )
of the ventriculus cordis, as it is to be registered with numbers of
animals and with man.
The tops that are found in this atrioelectrogram are, as it were,
analogous to the tops &, #& and P of the ventricle phenomenon
and may respectively be called here P,, Pz, Ps. The tops P,and Pz,
like Q@ and &, which are analogous to them, fall in the ventricle-
image wholly before the commencement of the muscle-contraction.
In the electrocardiogram of man and animals derived indirectly,
we find, evidently on the ground of the P-elevation, only P; expressed.
Again by derivation of a heart of Rana derobed from ventriculus,
accordingly consisting only of sinus and atria, we get, a propor-
tionately less large, but yet also a complicated electrogram of the
atrium, as also by registration of the isolated atrium of the carp,
where for example the first half of the atrioelectrogram shows a
pronounced diphasie nature.
It is also possible with a sample-object to derive both the atria
at the same time The same thing I did also with the cut-out heart
of Emys deprived of ventriculus, where one electrode invariably
found a place on the backside of the sinus, whilst two other electrodes
respectively caused the derivation of the atriatops. By means of a
swing-apparatus the galvanometer was connected with the sinus and
respectively with one of the atria or with both. The electrograin of
the one atrium obtained in this way differs at such a derivation
somewhat from the image got with the other atrium. The electrogram
of the left atrium has a strong diphasic character; at derivation
from the place of separation between the two atria with the back
wall of the sinus, we get a less pronounced diphasic image, whilst
the electrogram of the right atrium is only very feebly diphasiec.
The action-current of the heart is considered as a summary utterance
of the electric negativities, which show themselves in the tissue
successively in different places and at different times. This negativity,
as Hermann formulated it, arises by the circumstance that every
point of an irritable tissue at the moment of the stimulation stands
in a negative relation to the parts that are in rest. At the derivation
of such a tissue in different succeeding points we shall, therefore,
every time get a deviating electrogram, but at the same time we
shall be able to get an impression of the way which the proceeding
stimulus has taken through the tissue. For this last purpose I
have effected derivations of one atrium in different places, lying in
regular order. In this experiment I made use of the heart of Emys
deprived of its ventricle and then derived with an electrode constantly
from the sinus, whilst the other electrode (store-electrodes with
( 683 )
movable pith) was placed: 1. at the apex; 2. '/, em. lower than the
apex and 3. 1 em. lower than the apex of the afrium. This took
place both for the right and the left atrium, and also for the two
atria combined.
Fig. 2 (a, 6, and ec) shows how the amplitude of top 3: from the
atrio-electrogram diminishes in size as we descend with the electrode
from the apex along the lateral side of the right atrium. The greatest
potential difference, therefore, is manifest between basis and point,
whilst each point of the atrium, lying lower than the apex, at deri-
vation offers a smaller potential difference with the sinus. This is
quite in accordance with the usual representation, at which it is
supposed that, taking into consideration the fact that the contraction-
stimulus arises from the sinus, the stimulus regularly goes on in
the atrium tissue from the basis to the point of the atrium.
In the same figure 2c may also be demonstrated the appearance
of a small elevation, with following slight fall in the electrogram,
mauifesting itself a full second before the commencement of the myo-
eram of the atria.
This elevation may be attributed to the sinus, amone others for
this reason that this elevation in size increases according as we draw
nearer to the sinus.
Already in a former communication | have alleged grounds to
prove the independence of the electrical phenomena of the heart with
respect to the changes of form. In the atria of Emys this quality
can be demonstrated very clearly.
A part of the heart of Emys consisting of only atria and sinus is,
isolated, brought into a gas-chamber, and derived in one place
from the sinus, in another place from one of the (wo atrium-tops
or from boti tops at the same time. In this way different combina-
tions of derivation may be brought about. The movements of the
two atria are, by means of a simple suspension, registered by the
silhouette of the little levers. If 2 em?’ of chloroform are administered
which are evaporating in the gas-chamber, the mechanic movements
ave gradually growing smaller, so that at last they stop entirely,
11 minutes after the administration the chloroform. Also at an examina-
tion of the atria no trace of motion is to be observed, whilst however,
the electric phenomena continue showing themselves periodically very
clearly, through in shape they are a little more complicated than
before the poisoning. In fig. 3a and fig. 34 the electrograms have
been denoted as they are obtained by derivation of the sinus with
the one electrode and derivation of the two atria-tops with a double
other electrode. After evaporation of the chloroform by opening
( 684 )
the gas-chamber the atria begin to recover and after 39 minutes
the electrical phenomena reach their original size again with their
mechanical changes. Such poisoning-experiments can be repeated a few
times without any great harm for the sample-object.
It is striking how the right atrium every time recovers first
from the poisoning, and only later the left atrium begins to show
mechanical changes. If the electrogram is examined during and,after
the poisoning, it is remarkable that the general form is not really
altered here, but that the amplitude of the tops is greater than after
the recovery of tie poisoning, whilst the mechanical changes are
altered in exactly the other way.
The form of the atrio-electrogram is evidently also dependent on
nervous influences. Etnrnoven and VAANpRAGER have already directed
attention to this for the cardio-electrogram of a dog derived indirectly.
For the atria of Emys this may be proved very distinctly at direct
derivation under the influence of vagus-stimulation. 1
A heart of Emys derobed of ventriculus, so consisting only of
the sinus and the two atria, is derived to the string-galvanometer.
Derivation of one of the two atria separately or combined makes
no particular difference. Therefore the derivation in the experiment
takes place from sinus and right atrium-top. The right n. vagus in
the neck is prepared free. The electrogram shows a fine double-
topped image, accompanied by regular mechanical changes. At
stimulation of the right n. vagus with induction-currents the mechanical
utterance undergoes alterations. After a last contraction of the sinus,
showing itself in a slight elevation in the myogram of the atria
there begins for the object a vagus-standstill, which, as soon as the
stimulus is put a stop to, is broken off and causes a new series of
atrium-contractions with a strong sinus-contraction. During the vagus-
standstill the object has produced no electrical phenomena that are
to be registered. Directly after the vagus-standstill the atrio-
electrograms show themselves again, but now altered in form. The
double-topped image has been replaced by a phenomenon with a
strongly pronounced diphasic character, which however, the stimulation
being stopped, passes into the original double-topped image by a
gradual alteration. In this experiment the n. vagus was stimulated by
means of the sledge-inductorium of pu Bors Reymonp, without a
kernel, at a secondary coil-distance of 5.5 em. and a Lussinc-element
in the primary chain.
When weaker currents are used for stimulation, a state of things
may be obtained in which the vagus-standstill does not appear, but
in which the peculiar alterations in the form of the electrogram of
( 685 )
the atrium show themselves, as they have been described above.
These alterations in the form of the electrogram, apart from tonic
changes, are not accompanied by changes in the motoric utterances.
Fig. 4.
The tonic alteration cannot be considered as the cause of the
changes in form of the electrogram, because, in using still weaker
currents as stimuli for the n. vagus, the same tonic change may
appear, without having any effect on the electric utterances of the
atrium.
Botany. — “On the tests for tannin in the living plant and on the
physiological significance of tannin.” By Mr. C. van Wissbincit.
(Communicated by Prof. J. W. Mom...)
(Communicated in the meeting of February 26, 19°0).
In this paper a method will be described for demonstrating the
presence of tannin in the living plant, a method which enables us
moreover to obtain an idea of the amount of this substance in the
Jiving cells, and to ascertain whether after a given period of time
the amount has increased or diminished; the method does not
noticeably affect the living funtions of the plant or damage the
latter to an appreciable extent.
In addition a few results of experiments on tbe physiological sig-
nificance of tannin will be communicated; these results are in my
Opinion a real contribution to our knowledge of this subject.
Before proceeding to a discussion of the method which I bave
worked out, I think it desirable to make some observations on the
meaning of the word “tannin” and to give an account of the present
state of the physiological tannin-problem.
As regards the meaning attached to the word tannin there is no
uniformity. Botanists formerly meant by tannin every thing in the
cell which was coloured blue or green by ferric salts'). This has
led to confusion with other substances and to the view that tannin
is a generally occurring constituent of plants. Rwitrzer’) especially
has drawn attention to this. As a result of his investigations he came
to the conclusion that the word tannin is a misnomer, introduced
into science from the leather industry. According to him it should
1) J. Dexker, De looistoffen, Bot.chem. monographie der tanniden, 1908, V. I,
p- 197 and 210.
F. Czarex, Biochemie der Pflanzen, II. Bd. p. 576.
2) F. Rettrzer, Bemerkungen zur Physiologie des Gerbstoffs, Ber. d. d. bot.
Gesellsch. Bd. VII, 1889, p. 187.
( 686 )
again disappear from scientific terminology, but his suggestion did
not receive any support. WaaGr') especially has objected to it.
With reference to this question Drkker*) rightly remarks in his
botanico-chemical monograph of the tannins, that there certainly
exist plant substances, which are sharply marked off from other
‘rarbon compounds by common characteristic properties, such as the
property of transforming animal skins into leather, which depends
on the property of forming with protein compounds insoluble in
water, the adstringent taste, the presence of several phenolic hydroxyl-
groups in the molecule, the power of precipitating alkaloids from
aqueous solution and other properties; these substances must there-
fore be collected in a separate group. Until the chemical constitution
of these substances is completely known, the group in which they
are united, should not be split up.
Some authors, e.g. Remirzer*) and Bragmer*) consider that a
group of plant substances cannot be studied physiologically so long
as our chemical knowledge of it is incomplete. WaAacn’), in my
Opinion, is quite right in not agreeing with this. Of course it will
be necessary in the physiological investigation of tannins to ascertain
in each case with the means at our disposal, whether the plant
under investigation actually contains a substance belonging to the
tannin class, so that confusion with other bodies may be excluded.
The opinion of botanists concerning the physiological significance
of tannins has always been much divided. Tu. Harrie") supposed
that tannins contribute to the building up of the vegetable organism.
SCHLEIDEN’) on the other hand considered that tannin is only a
decomposition product of the cell wall.
In agreement with Hartia’s view tannin is, according to WIGAND‘),
a real factor in the chemical process of plant life and belongs phy-
siologically to the group of carbohydrates, on the formation and
iransformation of which the life process of the plant is especially
based. In contradistinction to starch, which appears as reserve ma-
1) Th. Waage, Die Beziehungen des Gerbstoffs zur Pflanzenchemie, Pharm.
Centralh. f. Deutsch]. N°. 18, 1891, XII. Jahrg. N. I. p. 247.
2) 1. c. 1908, Vol. I. p. V; Vol. IL. p. 66; Vol. I. pp. 211 and 212.
S)aline:
4) L. Braremer, Les tannoides, 1890—91. Ref. Bot. Centralbl. Jahrg, XII, 1891,
Bd. 47, p. 275.
KG
6) Tu. Harria, Entwickelungsgeschichte des Pflanzenkeims, 1858, p. 103.
7) M. J. Scutemwen, Grundziige der wissenschaftlichen Botanik, 1861, p. 141.
8) A. Wiaanp, Einige Siitze tiber die physiologische Bedeutung des Gerbstoffes
und der Pflanzenfarbe, Bot. Zeitung, 20. Jahrg. 1862, N°. 16, p. 121 and 129.
( 687 )
terial in the resting periods of vegetation, tannin generally belongs,
according to WicGanp, to the fluid active substances necessary for
growth. In some cases it appears, according to the same author, to
act as reserve material. It thas follows that in Wieanp’s opinion
tannin is an extremely important product of vegetable metabolism.
No other investigator has declared this so clearly and so emphatically.
Wicanpb’s view has been attacked, especially by Sacus, and has
not received much support from botanists in general; this is evident,
for instance, from the chapter ‘Die physiologische Bedeutung der
Gerbsaéuren” in Czarek’s Biochemie der Pflanzen’), where WiGanp’s
view and that of TH Harria*) concerning ‘““Gerbmehl” as carrier of
tannin and organized reserve material is reckoned among the “irrigen
Auffassungen iiber die physiologische Rolle der Gerbsauren”. WiGanp
has not published the details of the observations on which his con-
clusions are based and this has probably contributed to the ready
rejection of his results by other authors °).
The conception of the role of tannins arrived at by Sacus*) in
his investigations on the germination of seeds, has received more
support than that of Wicanp. Sacus considered the tannins formed
in germination, to be merely excretory products, by-products or
decomposition products. He thought it very improbable that tannins
could serve in some way or other as material for the building up
of cell-walls.
The results of some other observers agree with those of Sacus.
Thus for instance Kravs*), who was particularly interested in the
physiological significance of tannins, arrived at the conclusion that
tannin, once formed, in no case takes any further part in metabolism.
According to GerrBer*) the tannins disappear by oxidation, without
the formation of carbohydrates from them. Ar Kiercker*) regards
Y Le. p. 588.
*) Tu. Harrie, Das Gerbmehl, Bot. Zeitung 23. Jahrg. N°. 7, 1865, p. 53. Weitere
Mitteilungen das Gerbmehl! betreffend, Bot. Zeitung 23. Jahrg. N®. 30, 1865, p. 235.
3) Compare Emm Kurscuer, Ueber die Verwendung der Gerbsiure im Stoff-
wechsel der Pflanze, Flora, 66. Jahrg. N°. 3, 4 and 5, 1883, -p. 37.
4) J. Sacus, Physiologische Untersuchungen iiber die- Keimung der Schmink-
bohne (Phaseolus miulltiflorus), Sitzungsber.. d. kais. Akad. der Wiss. Wien, 37.
Bd., 1859, No. 17, p. 57. Zur Keimungsgeschichte der Dattel, Bot. Zeitung, 20.
Jahrg., 1862, No. 31, p. 241 and 249. Handbuch der Experimental-Physiologie
der Pflanzen, 1865, p. 360.
5) G. Kraus, Grundlinien einer Physiologie des Gerbstoffs, 1889, p. 88 and 44.
6) C. Gerser, Role des tannins dans les plantes et plus parliculiérement dans
les fruits. Compt. rend. 124, p. 1106.
7) J. E. F. Ar KLeRcKER, Studien tiber die Gerbstoffvacuolen. Bihang till k. Svenska
Vit.-Akad. Handlingar, Bd. 13. Afd. Ill, No. 8, 1888. Ref. Bot. Zeitung, 47. Jahrg.
1889, p. 210. .
( 688 )
tannins as exeretion products. Waace') calls them by-products of
metabolism. BiscEN *) insists, that the observations which have been
made, afford no justification for the assumption that tannin acts asa
plastic material. On the other hand Scnutz*) considers the tannin
of evergreen leaves to play the part of reserve-material.
According to a few investigators tannins must, in some cases, be
regarded as excretory products or as by-products of metabolism,
whereas in other cases they take part in metabolism and serve as
plastic material. Such was the conclusion of ScHe.. *), of Kurscuer *)
and of WEsTERMAIER ‘).
According to ScurogpEeR’) the tannin of the birch and the maple
is not a reserve material, but it is not an excretory product either.
In the author’s opinion it possibly in these cases constitutes a final
product of metabolism. He does not, however, attempt to answer the
question as to the physiological significance of tannin.
Many investigators have adopted the view, that tannins serve to
protect plants against harmful external influences. These might be
of very different kinds. SrauL*) assumes that on account of its
unpleasant taste tannin serves to protect the plants from the attacks
of animals, especially slugs. Kraus") also considers tannin to be a
protective agent not exclusively against animals, but serving in
addition to counteract the putrefaction of the plant.
In plants with evergreen leaves WarminG '") regards the tannin
content of the epidermis as protecting the plant from desiccation,
while exposed to dangerous dry winds in winter, and as being at
Ly leiceepss2b0:
2) M. Biisaen, Beobachtungen tiber das Verhalten des Gerbstoffes in den Pflan-
zen, Jenaische Zeitschrift fiir Naturwissenschaft, 24. Bd., N. F. 17. Bd., 1890, p.
59, Erlauterung zu dem Referat tiber Beobachtungen etc., Bot. Zeitung, 1890, p. 381.
3) EK. Scuunz, Ueber Reservestoffe in immergrtinen Blittern unter besonderer
Beriicksichtigung des Gerbstoffes, Flora, 1888, p. 256.
4) J. Scuett, Physiologische Rolle der Gerbsiéure, Kazan, 1874 (Russian), Botan.
Jahresber. Ill. Jahrg., 1875, p. 876
GC 0 7a
6) M. WesterMAIER, Zur physiol. Bedeutung des Gerbstoffes in den Pflanzen.
Sitzungsber. d. kénig!. preuss. Akad. der Wissensch. zu Berlin, Jahrg. 1885, 2.
Halbb. p. 1124 and 1125.
7) J. ScHroepEeR, Die Friibjahrperiode der Birke (Betula alba L.) und der Ahorn
(Acer platanoides L.), Die landwirthsch. Versuchs-Stationen, Bd. XIV, 1871, p. 146.
8) Ernst Sranu, Pflanzen und Schnecken, Jenaische Zeitschrift fiir Naturwissen-
schaft, XXII Bd., N. F. XV. Bd., p. 590 and 594.
®) Grundlinien zu einer Physiologie des Gerbstoffs, 1889, p. 21.
10) §. WarminG, Beobachtungen tiber Pflanzen mit tiberwinternden Laubblattern,
Botan, Centralblatt, Jahrg. IV. Bd. 16, 1883, p. 350
( 689 )
the same time a means of rapidly restoring lost turgor. Scnet *)
considers that tannin in seeds is probably a protection against harmful
influences from without. Biseun*) also supposes that tannin affords
protection to the plant.
Other authors again have attributed different functions to tannins.
According to Grrper*) they prevent the transformation and fermen-
tation of sugar in fruits and Prnrrer*) thinks it very likely, that
their role also consists in fixing sugars and other substances in the
cell. Kurscuer *) considers it most plausible that tannin serves as a
respiratory agent and is oxidized in respiration.
Various other functions have further been attributed to tannins in
connexion with the metabolism of the plant. Thus Wicanp °) supposed
that the red colouring matters are formed, from tannins, a view
shared by Pick 7), Mieiky*), and Tscuircu *) amongst others.
Some authors connect tannins with the formation of resin. WiEsnEr *°)
thinks that starch and cell-wall may be transformed to tannin, and
subsequently to resin. Scueni.'*) and Misikr **) also regard tannin as
an intermediate stage between starch and resin and between cellulose
and resin. Both authors, however, also suppose, that tannin can be
converted into starch. Bastry and Trimsin*’) in their investigation
of the resin-passages of conifers, have also received the impression,
that tannin is connected with resin formation.
oc
ih) 1h Gs fos (Sie
3) Ibs {ob let
3) ne.
4) W. Prerrer, Uber Anfnahme von Anilinfarben in lebende Zellen, Unter-
suchungen aus dem botan. Institut zu Tiibingen, 2. Bd., 1886—1888, p. 310.
Delemcraps dios
Sy e:
7) H. Pick, Ueber die Bedeutung des rothen Farbstoffes bei den Phanerogamen
und die Beziehungen desselben zur Stirkewanderung, Botan. Centralblatt, Jahrg. LV,
1883, p. 284.
8) G. MieLKe, Ueber die Stellune der Gerbsiuren im Stoffwechse] der Pflanzen,
Programm der Realschule vor dem Holstenthore in Hamburg, 1893. Ref. Botan.
Centralbiatt, Jahrg. XV, 1894, Bd. 59, p. 281.
9) A. Tscurrcu. Schweiz. Wochenschr. f. Pharm. N’. 7. Pharm. Centralbl. N°. 10,
1891, p. 141.
10) J. Wiesner, Uber die Entstehung des Harzes im Inneren der Pflanzenzellen,
Sitzungsber. d. Wiener Akad., 1865, 52. Bd. IL. Abt. p. 126 and 129. Ref. Jahres-
ber. iiber die Fortschritte der Chemie etc., 1865, p. 627.
11) |. ¢.
12) ], ¢.
18) E. Bastin and H. Trimsie, A contribution to the knowledge of some North
Amerikan Coniferae, Amer. Journ. Pharm. 68, 1896,
( 690 )
According io BureNer') tannin in fruits contributes to the formation
of sugar and according to STADLER *) it supplies in the nectaries of
Oenothera and Saxifraga the material for the formation of honey.
In connexion with the physiological significance of tannins in plant
metabolism, I think it desirable to point out, what results botanists
have arrived at with regard to the translocation and origin of tannins.
Some investigators suppose that tannin can be transported in the
plant, namely Kraus, Morir, and Westrrmaipr. According to Krats*)
tannin travels as such, Mogiirr*) thinks it probable, that carbo-
hydrates are transported in the form of tannin compounds. WesTER-
MAIER *) leaves it an open question whether tannin travels as such,
and whether starch travels in the form of a soluble carbohydrate or
in that of tannin.
The opinions of botanists are divided as to the origin of tannins
in the plant. As was stated above, tannin is according to SCHLELDEN °)
a decomposition product of the cell wall. According to Ta. Hartoe ‘)
it arises from starch during the germination of Quercus pedunculata.
Similarly according to ScHen. *) tannin is formed from starch in the
germination of the seeds of Fuba vulgaris and Pisum sativum.
Mim.ke*) supposes that tannin is formed from carbohydrates, from
tannin glucosides, and also from starch and from cellulose. WerstEr-
MAIER ?") regards it as an assimilation product but supposes that it is
also formed by the decomposition of proteins. According to SCHROEDER **)
it is formed by oxidation from organic material present in the plant.
Kraus ™) thinks that it isa decomposition product of amido-compounds
formed during the synthesis of proteins. The observations of MorLier *’)
1!) H. Bouranet, Recherches sur la matiére sucrée contenue dans les fruits
acides, son origine, sa nature et ses transformations, Compl. rend. 51, p. 894.
2) S. Srapier, Beitriige zur Kenniniss der Nectarien und der Biologie der
Bliithen, Berlin 1886.
3) G. Kraus, Grundlinien zu einer Physiologie des Gerbstoffs, 1889, p. 20.
4) Herman Moretier, Anatom. Untersuchungen tiber das Vorkommen der Gerb-
siiure, Ber. d. deutschen bot. Gesellsch. Bd. VI, p. LX XX.
. 5) M. Wesrermaier, Neue Beitrige zur Kenntniss der physiologischen Bedeutung
des Gerbstoffes in den Pflanzengeweben. Sitzungsber. d. kénigl. preuss. Akad. d.
Wiss. zu Berlin, Jahrg. 1887. 1. Halbb. p. 134.
6) lie. p. 141.
7) Le. p. 102.
8) ‘le.
lic:
10) Zur physiol. Bedeutung des Gerbstoffes in den Pflanzen, lc. p. 1124.
11) le. p. 146.
12) Grundlinien, p. 47.
13) MorLupr, Mitt. des naturw. Vereins f. Neu-Vorpommern und Riigen in Greifs-
wald, 1887.
( 691 )
on the leaves of Ampelopsis hederacea and those of Biscrn ') on
germinating seeds of Vicia Faba and on wounded leaves which were
floated on a 10 percent grape sugar solution, have proved that tannin
is formed from sugar.
Kravs”) and Westrermarer *) have pointed out that in some cases
the formation of tannin depends on the influence of light.
It is evident from the above, that botanical opinion is much divided
on the subject of the physiological significance of tannins. It may be
summarized as follows. According to some botanists tannins are of no
value to the plant; they are merely excretory products. Others regard
tannins as protective agents against various harmful external influences.
A few believe that tannins contribute to the building up of the
vegetable organism. A small number think that tannins can fulfil
different functions.
Various authors e.g. Czapek*) in his Biochemie der Pflanzen and
Dekker *) in his Botanisch-chemische Monographie der Tanniden,
have pointed out that the numerous investigations on the physiology
of tannins have as yet produced but few results of any importance.
DekkKeER arrives at the conclusion, that if this group of substances is
of significance to the plant, which he thinks probable, it is quite
uncertain what function they fulfil, Noti*) in Srraspurcer’s Lehr-
buch der Botanik expresses himself in the same way. The fact that
the significance of the tannins is still so obscure, is attributed to
various causes. Thus according to Czapkk’) a few observations of
microscopical or chemical facts led to generalisations and to the
construction of untenable theories. Drkkrr*) further points to the
imperfection of the methods of investigation and the one-sided use
of these methods, which sometimes causes tannins to be confused
with other plant substances.
In my opinion the chief cause must be sought in the want of
criticism, which often impairs the drawing of conclusions. The physio-
logical tannin problem is most certainly a very difficult problem, the
answer to which will have to take into account a large number of
factors. These factors are known to us to a smaller or larger extent,
1) Le. p. 34 and 35.
2) Grundlinien, p. 20 and 44.
8) Zur physiolog. Bedeutung des Gerbstoffes in den Pflanzen, l.c. p. 1117. Neue
Beitrage etc. lc. p. 128 and 133.
4) l. c. p. 588.
5) lc. V. I, p. 220.
6) 1. c. 8. Aufl. 1906, p. 190.
7) 1. c. p. 588.
8) 1. c. V. I, p. 210 and 211.
( 692 )
but unknown factors may also come into play. Hence it is necessary
to exercise the greatest caution in drawing conclusions. In advancing
an explanation of an observed phenomenon, we must consider care-
fully whether it is the only one possible and we must attempt to
prove it in various ways by means of comparative experiments.
The extent to which these precautions have been observed by no
means corresponds to the complexity of the problem. As a result of
a few experiments many observers have put forward certain expla-
nations, when other explanations were equally plausible, or they have
combated the opinions of other investigators, who perhaps had a
more correct insight, although they were unable to adduce sufficient
proof for it. Even serious investigators have made this mistake. I
will illustrate this very briefly, by showing the insufficiency of the
reasoning which led to the rejection of the possibility that the tannins
might serve as plastic material.
As was said above Sacus does not believe that tannins can act in
any way as plastic material in the formation of the tissues. This
opinion he has partly supported by observation and partly by drawing
what is in my opinion an erroneous conclusion. Sacus*) found that
in the germination of seeds which do not contain tannins in the
endosperm or in the embryo, tannins are formed in metabolism and
primarily there, where the formation of tissue has just started. He
never saw the tannins diminish or disappear during germination. In
other cases, namely in that of the acorn and of the chestnut, where
the embryo contains tannin, he did not observe a diminution either,
but rather an increase. He made similar observations on the development
of buds. Sacns concludes from the above-mentioned facts, that tannins
remain in plants in the places where they have been formed, and
that therefore they do not take part in the formation of tissues, for
if this were the case, a diminution would have been observed. I
consider this conclusion to be incorrect. Quite a different conclusion
might equally well be based on Sacus’ observations, namely that the
frequent appearance or presence of tannins in tissue-formation shows
that these substances have probably a function to perform in this
process. Nevertheless I do not at all consider that Sacus has proved, that
tannins remain in the places where they are formed and that they
do not serve as plastie material in tissue formation. For if in the
germination of seeds more tannin is formed than is decomposed, a
diminution of the tannin content need not occur, and an increase
yy Physiolog. Untersuchungen iiber die Keimung der Schminkbohne, 1. c. jo, Lali.
Zur Keimungsgeschichte der Dattel, 1. c. p, 246. Handbuch der Experimental-
Physiologie der Pflanzen, 1865, p. 361.
( 693 )
may even take place. Reserve-materials like starch and fatty oils
may not be assumed to participate directly in the building of the
cell wall. They must first be converted into soluble substances. Now
suppose that tannins also belong to this category, i.e. to such a
plastic material as is present in the plant in a dissolved state, then
it is not at all surprising that for the maintenance of growth plenty
of this material should always be present, and that occasionally,
when more of it is being produced from the reserves than is used
up in the growth of the cell-walls, the tannin content increases.
Anyhow it has not been proved that, because the tannin does not
diminish, it remains unused at the place, where it has been formed,
and that it does not serve for the building up of cell walls.
Like Sacus, Kraus') also assumes that an increase in the tannin
content in germination proves, that this substance is not used up
and does not serve as building material. Thus with regard to the
germination of the acorn Kraus states, as a result of quantitative
tannin determinations, that not only is tannin not used up, but that
its quantity even increases, so that it cannot be of service in growth.
Whereas Sacus only observed an increase of the tannin content
of germinating seeds, Scueti*) found in some plants an inerease
and in others a decrease or disappearance. In the first case ScHELL
supposes, in agreement with Sacus, that the tannins are by-products
of metabolism, but in the latter case he regards them as plastic
material. With reference to what has already been said, it is a matter
of course that I cannot either agree with ScHEn1’s conclusions. In
my opinion it is not necessary to conclude. on the ground of an
observed increase in the tannin content in some cases and a decrease
in others, that tannins behave so differently in different plants.
Supposing the tannin to be a plastic material in both cases, then
the occurrence of an increase or decrease will depend on the quan-
tities produced and used up. I also think it very plausible that in
one and the same plant sometimes an increase, and sometimes a
decrease takes place, according to circumstances.
Several botanists suppose that tannins can undergo translocation
in the plant. How this might happen is still a moot point, but there
can be no doubt that the possibility of translocation greatly compli-
cates the question of the use of tannins as plastic material. The
increase or decrease of the tannin content ofa particular organ would -
then not depend wholly on production and consumption, but transport
1) Grundlinien, p. 38.
*) lic. p. 876.
( 694 )
to and from the organ would also have to be reckoned with. The
mere increase or decrease of tannin in a seedling or a vegetable
organ will not supply data of any value for the solution of the
problem of the significance of tannin as a plastic material.
Hitherto botanists have chosen the higher plants for the study
of the physiological significance of tannins. For the study of
complicated vital processes and of the physiological significance of
chemical constituents certain lower plants appear to me to offer
advantages above those of the higher ones, the structure of which
is so much more complicated. For such an investigation the thicker
species of the genus Spirogyra seem particularly suitable. It is true
that the tannin of Spirogyra has not yet been examined chemically,
but numerous microchemical reactions allow us to conclude with a
fair degree of certainty that Spirogyra contains in its cell sap a
considerable quantity of tannin. Dw Vries’) has proved this, after
abnormal plasmoiysis, with various tannin reagents e.g. ferric salts,
potassium bichromate, osmiec acid. In addition to these reagents many
others also give in the cell sap precipitates which agree completely
with those caused in tannin solutions.
The advantages which the thicker species of Spirogyra have over
the higher plants are the following. Pieces of the filaments may be
examined microscopically without killing them or damaging them,
and the changes in the cells can be studied in the living plant. They
are particularly suited to all sorts of experiments. They are not too
small to be handled and not too thick for microscopic examination.
The various constituents of the cell can readily be observed under
the microscope. As in the case of unicellular Algae a transport of
foodmaterial from one cell to another is very probably excluded
in Spirogyra. This important factor, which must be taken into account
when dealing with the higher plants, need generally not be considered
in the case of Spirogyra. By means of the centrifuge all sorts of
abnormalities may be obtained, such as polynuclear cells, cells without
nucleus, cells with a large and with a small chromatophores-mass,
and even cells without chromatophores. In this way we can eliminate
the assimilation process, i.e. the intake by the chromatophores of
earbon from atmospheric carbon dioxide under the influence of light.
With Spirogyra a number of comparative experiments may be made
which are impossible in the case of the higher plants, and because
1) Hugo pe Vries, Plasmelytische Studien iiber die Wand der Vakuolen, Pringsh.
Jahrb. f. wissensch. Botanik, Bd. 16, 1885, Heft 4, p. 575. Over looistofreactién
van Spirogyra nitida, Maandblad voor Natuurwetenschappen, 1885, N°. 7, Reprint
p: 7s
( 695 )
certain factors are excluded or eliminated, others may be studied
with a greater chance of success.
Because the investigation of the higher plants has yielded such
unsatisfactory results for the knowledge of the physiological signifi-
cance of tannins I have attempted to obtain more definite results for
the solution of this problem in the case of the lower plants, parti-
cularly of Spirogyra; to this I was led by the above considerations.
The first question to present itself was, which method would be
most satisfactory. In the case of the higher plants investigators have
followed various methods. Of the many reagents which give precipitates
or colour reactions with tannins, ferric salts and potassium bichromate
have mostly been preferred. Potassium bichromate especially, which
yields with tannins a reddish brown or orange precipitate, has often
been used, e. g. by ScuRoeDER'), ScHELL*), KurscHer*), Ruur *),
Scuuiz *), Mornier*) and Biscen’). KurscHer made a dish with 8
sections, the colour of which agreed with that of the precipitate, but
shaded in such a way that the intensity of the colour in two sue-
cessive sections always differed by the same amount. This dish was
used for the determination of the strength of the precipitates.
Kravus*) determined the amount of tannin by means of titration
with potassium permanganate or precipitated the tannin with cupric
acetate and weighed the precipitated copper as copper oxide. The
titration with potassium permanganate was also employed by Rute‘).
These titrimetric and gravimetric methods cannot, of course, be
applied to a small object like Spcrogyra; moreover no method satis-
fied the demand which I had imposed upon myself. I desired a
methcd which would enable me to determine the tannin content of
one and the same cell at different periods, with sufficient accuracy
to allow me to decide whether an increase or decrease had taken
place, and this without killing the cell or harming it appreciably.
The want of such a method had made itself felt in the investigation
of various abnormal cells such as polynuclear and anuclear ones,
1) Le. p. 140.
ilveaps Oo:
3) lic. p 38 and 39.
4) P. Ruxr, Ueber das Verhalten der Gerbsiiure bei der Keimung der Pflanzen,
Zeitschrift fiir Naturwiss. in Halle, LVIL Bd. Vierte Folge Bd. III, 1884, p. 42.
Sy lies 227.
5) Hermann MOELLER, Anatomische Untersuchungen iiber das Vorkommen der
Gerbsdure, Ber. d. deutschen botan. Gesellsch., Bd. VI, 1888, p. LXVI.
f) Nesp y ds:
8) Grundlinien, p. 61.
9) lc. p. 42.
417
Proceedings Royal Acad. Amsterdam. Vol. XII.
( 696 )
and cells containing many, few or no chromatophores. While I
could determine the growth of such cells by measurement and could
deduce from the size of the starch foci whether the starch content
had increased or decreased, | wag unable to obtain for one and the
same cell an idea of the tannin content during the various periods
of its existence. The usual reagents only permit of a single examina-
tion being made, because during it the cells are killed. I had
therefore to look for another method.
I wondered whether methylene blue might perhaps satisfy the
above requirements. According to Prrrrer') this substance forms a
compound with tannin in the living ceil, and this compound separates
as a fine blue precipitate. For various physiological investigations
Prerrer strongly recommends aniline dyes particularly methylene
blue. Of this he says i.a. the following’): ‘In alien Fallen werden
also Methylenblau und andere Farbstoffe wertvolle Reagentien sein,
mit deren Hiilfe, ohne Schadigung Aufschliisse iiber Vorkommen und
Verteilung gewisser K6rper in der Zelle zu erhalten sind. Mit soleher
vielseitig ausnutzbaren Methode lasst sich unter richtiger Erwagung
nach vielen Richtungen hin eine Kontrole des jeweiligen Zustandes
des Zellsaftes und der Verénderungen dieses im Laufe der Ent-
wicklung erreichen.” When dilute solutions are used, the penetration
of methylene blue into the body of the plant and its accumulation
in the cellsap continue, according to Prrrrer*), without any harm
to life and even when complete saturation has taken place, it is
still innocuous. Spirogyra was one of the objects with which Prerrar
experimented.
Prrrrer’s experiments were repeated by me a few times with
Spirogyra maxima, but with very unsatisfactory results. Even after
several days only a slight granular precipitate was obtained in the
cells, and at least the greater part of the tannin remained in solution;
inoreover, even very dilute solutions were found to be harmful.
I cannot therefore agree with Prrrrer in praising his method of
investigation, and after this disappointment a better method was
sought.
Preliminary experiments were carried out on Spirogyra maxima
with various tannin precipitants, such as alkaloids, antipyrine, am-
monium vanadate and many others. Of all the substances examined,
caffeine and antipyrine were found to be the least harmful, and
therefore the action of these two substances was investigated more
)ecamp eau:
IEG) Dy EM
]. c. p. 195, 196 and 197,
( 697 )
closely, in order to ascertain their value for the study of the phy-
siological tannin problem. In doing this, special attention was directed
to the following points: whether the substances penetrated rapidly
into the cell and the cell sap, whether the tannin was completely
precipitated, and what concentration of solutions was required for
this; the nature of the precipitate and whether it redissolved on
removal of the precipitant, whether the strength of the precipitate
corresponded to the quantity of tannin in the cells and whether the
method was sufficiently innocuous. After a number of experiments
with antipyrine and caffeine solutions of various concentrations,
which were allowed to act for a longer or shorter time, I came to
the following conclusion:
The antipyrine and caffeine solutions penetrate rapidly into the
cells and in sufficient concentration produce in the cell sap a_preci-
pitate, consisting of minute grains or globules, which are in constant
motion to and fro. In order to precipitate the tannin as completely
as possible, it is desirable to have the antipyrine solutions not more
dilute than 1°/, and caffeine solutions not weaker than '/,,°/,. The
greater the tannin content, the heavier the precipitate. Not infrequently
the precipitate is so heavy, that the nucleus, which ordinarily can
be readily discerned in Spirogyra maxima, cannot be distinguished
_at all and sometimes the precipitate is even heavier. If the Spirogyra
filaments are placed in ditch water or in distilled water, the preci-
pitate disappears in a short time, say in 10 minutes, and the Spiro-
gyra threads are as before the experiment. No change whatsoever
can be detected. If the Spzrogyra filaments remain in the solution,
the precipitate settles down and the small globules or spheres, of
which it consists, gradually coalesce to larger globules, which appear
perfectly colourless and may sometimes be very large closely resem-
bling fat globules. This was generally the appearance of the preci-
pitate after a few days. The settling down of the precipitate in the
cells and the fusion of the globules to larger, purely spherical masses,
proves that it is heavier than water and that it is liquid. From several
data I deduce that it is not thinly liquid but viscid. The fusion to
larger globules proceeds slowly and cannot, for instance, be brought
about by a few minutes centrifuging. When the Spirogyra-cells with
the globular precipitate are placed in water, the globules dissolve.
Solution takes place more slowly, however, than in the case of a
recently formed and still finely divided precipitate. If the preparations
are placed in ferric chloride solution, instead of in water, the globules
are coloured blue, while the cell sap is not coloured. It is rational to
use caffeine as precipitant for this experiment, since antipyrine gives
47*
( 698 )
a reddish-violet coloration with ferric chloride. Since the coloured
compound is soluble and easily diffuses through the preparation, the
ferric chloride-tannin reaction of the globules may also be detected
when antipyrine is used, and the non-appearance of the reaction in
the cell-sap may be observed, at least when the ferric chloride acts
sufficiently rapidly. If the preparations are transferred from the anti-
pyrine- or caffeine solution to a one percent solution of osmic acid,
the globules are first coloured blue and soon afterwards black, whereas
the cell sap remains colourless.
It is evident from the experiments with ferric chloride and with
osmic acid, that the tannin is completely or almost compietely preci-
pitated by a one percent antipyrine solution and by a 0.1 percent
caffeine solution, for otherwise the cell sap should have shown a
blue or black coloration. If the antipyrine or caffeine precipitate,
whether it be a finely divided recent precipitate or one which has
fused to globules, is dissolved by placing the Sprrogyra-tilaments in
water, and if ferric chloride- or osmie acid solution is then added,
the cell-sap is coloured blue or black, just as is the case with cells
which have not been treated with antipyrine- or caffeine solutions. Wien
the cells finally die off in antipyrine- or caffeine solution, the globules
are stained brown; their solubility in water has then decreased, but they
still give with ferric chloride and osmic acid the reactions referred to.
By means of comparative experiments with antipyrine- and caffeine
sojutions, and various other tannin reagents, such as potasssium bichro-
mate, osmic acid and ferric salts, with Sperogyra cells containing
a varying amount of tannin, | was able to show that the strength of
the antipyrine- and caffeine precipitates agreed with the strength of
the precipitates and colorations, given by the above-mentioned reagents.
For these experiments I used Spirogyra filaments, which had been
centrifuged afew weeks before, and in which there were also all sorts of
abnormal cells, such as cells without a nucleus, without chromato-
phores, with several nuclei etc. The tannin content of the cells of
these filaments varied very much. First the filaments were treated
with antipyrine- or caffeine solution and the strength of the precipitate
in the various cells was noted ; afterwards the filaments were placed
in water, and when the precipitates had dissolved, they were placed
in a solution of potassinm bichromate, osmic acid or ferric chloride,
and the intensity of the reaction in the various cells was noted. On
comparing the various notes it was found that the strength of the
antipyrine- and caffeine precipitates agreed with the intensity of
reaction obtained with the other reagents, and therefore corresponded
to the quantities of fannin present in the various cells,
( 699 )
The strength of the precipitates with antipyrine and caffeine was
judged in various ways. Thus it was noted, whether the nucleus,
which in normal circumstances is very clearly visible in Spirogyra
maxima, could still be distinguished after precipitation of the tannin.
Furthermore it was noted whether the suspensory threads, the chroma-
tophores and the starch foci above and below in the cell could still
be discerned. In order to judge in which cells the precipitates were
strongest, the various cells were not only compared after precipitation,
but it was also noted in which cells the precipitate first appeared
and remained visible for the longest time after the filament had been
transferred to water. I had previously found that the precipitate first
appeared in the cells with the largest tannin content and that after
the filaments had been placed in water, it could be observed in these
ceils for the longest time.
In connexion with the use which I wished to make of antipyrine-
and caffeine solutions, it was very important to know to what extent
these solutions are harmful to life and whether a short stay in these
solutions, sufficiently long to obtain an idea of the tannin content,
might be regarded as harmless or practically harmless to the Spzrogyra
filaments. [ found that, if a one percent solution of antipyrine, or
a ‘/,, percent solution of caffeine were used, made up with ditch
water or with distilled water (a solution of such concentration
therefore that all or nearly all the tannin was precipitated in the
cells) and tnat if the Spcrogyra filaments remained in this solution,
“no further divisions took place and growth was soon arrested or
was stopped at once. If, on the other hand, solutions were used
which were ten times as dilute, and which did not cause a precipi-
tate in the cells, it was found by comparative experiments with
Spiroayra filaments in ditch water or in distilled water, that growth
was retarded by antipyrine and by caffeine, and that fewer nuclear
and cell divisions occurred.
I made some experiments with a one percent antipyrine solution
and with a */,, percent and a one percent solution of caffeine, in
order to see whether a daily sojourn of 10 minutes in these solutions
was harmful to Spirogyra, grown in ditch water. A period of 10
minutes was selected because it is sufficient for an examination of
the tannin content. The result of these experiments was, that it could
not be ascertained with certainty whether the procedure employed
was harmful to the Spirogyra. Sometimes the growth of the controls
in ditch water was the stronger, sometimes that of the filaments
which had been periodically treated with antipyrine and caffeine
solutions. It is not improbable that the differences observed depended
( 700 )
largely on the nature of the cells under investigation. 1 surmise this
because the growth of cells in normal and equal nutrient solutions
also showed differences. We may deduce from the results that in
general a short daily stay in the various solutions has at most a
slight influence on the growth and the vital processes of Spirogyra.
The above method of investigation of the tannin content may there-
fore be strongly recommended, especially when it is desired to examine
the same cells repeatedly at intervals, without harming them.
As far as I have been able to ascertain, antipyrine- and caffeine
solutions have not yet been employed as microchemical tannin
reagents. For the sake of completeness | point out, however, that
such solutions have already been used by botanists in microchemi-
cal investigation, namely by Lorw and Boxorny*), to demonstrate
the presence of non-organized active protein in the living cell. The
above-mentioned reagents are supposed to separate this in the shape
of small globules, called by these authors proteosomes. This is
therefore an explanation of the phenomenon produced by antipyrine
or caffeine in the living cell, which is totally different from that
given by myself. As a result of my investigations described above,
I adhere to my opinion that antipyrine- and caffeine solutions are
valuable tannin reagents, and suppose that Lorw and Bokorny have
given an inaccurate explanation of the phenomenon which they observed.
In the historical survey I poimted out, that, as regards the physio-
logical significance of the tannins, there is a great difference of
opinion among investigators, and that in the opinion of various
botanists, there is but little, which may be regarded as sufficiently
proved, so that we are here face to face with a problem, which has
in no way been solved. As was stated above the view that tannins
might serve in the formation of cell walls has received little support
and met with much opposition. With the aid of the method I have
worked out, I have now been able to bring to light facts concerning
Spirogyra, which indicate that tannin plays an important part in the
formation of cell walls, and that during this process tannin is used
up, so that it very probably serves as building material. Below |
will mention some observations which relate to this. They refer in
the first place to the conjugation.
Cells which showed a tendency to conjugate, 1 found to be richly
provided with tannin. I could make out, that the tannin content
diminished during conjugation and in the adult zygospores which
were filled with reserve material, I could only occasionally observe
1) 0. Lorw and Tu. Boxorny, Versuche tiber aktives Eiweiss fiir Vorlesung
und Praktikum, Biologisches Centralblati, 1891, X1, p. 5.
(701 )
a feeble tannin reaction with ferric chloride. It does not result from
this observation what is the fate of the tannin, but when the conju-
gation is followed in greater detail, it is found that there is good
ground for supposing, that at least a portion of the tannin serves as
plastic material for the cell wall. Conjugation is a process which
proceeds in such a way as to allow us to expect that its study
in connexion with the point of investigation referred to will furnish
us with important data, for conjugation does not start simultane-
ously in all cells. Some cells are in advance of others; in a smaller
or larger number of cells there is evidently a tendency to conjugate,
but the conjugation does not succeed, and other cells again do not
show a trace of the conjugation process. Whereas the conjugating
cells form much reserve material as starch and fat, those which do
not conjugate are apparently very poor in contents and they finally
perish. The above mentioned differences seem to be determined by
accidental circumstances. such as the coming into touch with ceils
of other filaments, the proximity of such cells and the position of
the cells with regard to each other. They may even be observed
with material which before conjugation consists cxclusively of
healthy normal cells.
The point of interest in connexion with the tannin problem is
the possibility of comparing, in conjugating Sprrogyra filaments, cells
which a short time before were quite equal and afterwards show
more or less important differences, induced by accidental and rather
superficial circumstances. It is of interest to trace in these various
cells what happens to the tannin content. This was investigated with
the caffeie- and antipyrine solutions I have recommended, and it
was striking to note, how differences in the development of the cell
wall corresponded to the quantity of tannin present in the cells.
Thus I could ascertain, that in cells where the lateral protrusion
and mutual fusion had taken place, the tannin content was always
appreciably smaller than in cells which only showed the first
beginnings of the lateral protrusion. These two kinds of cells only
differed as regards cell wall and tannin content; for the rest they
still agreed perfectly. They were distributed promiscuously over the
filaments, as is usual in conjugation. These facts seem to me to prove
that there is a connexion between formation of the cell wall and
the tannin content, and the supposition, that tannin serves as plastic
material for the cell wall is very plausible.
Furthermore there is a remarkable increase in the tannin content
of those cells which have not had an opportunity of conjugating or
in which the process was interrupted at an early stage; these cells
( 702 )
degenerate and are generally described as having a poor cell content.
These cells continue to produce tannin for some time and since the
tannin in them is not used up in the formation of cell walls or
reserve material, the tannin content increases and on the death of
these cells a considerable quantity of plastic material in the form of
tannin is lost.
The loss of tannin in nature, e. g. in the fall of leaves in autumn,
has repeatedly been used as an argument for the view that tannin
cannot be a plastic material and does not take part in metabolism. I
cannot share this view and do not think the waste of quantities
of a substance, which certain plants require for their development,
to be at all strange, and certainly not a proof that it cannot serve
as plastic material in the development of the plant. How often do
things in nature fail to attain their end and how many are not
wasted without being able to fulfil their purpose! Moreover, it
seems to me desirable that the plant should have an excess of plastic
material at its disposal, in order that development may never at
any time be hindered for want of it. The fact that in the autumn
the stem is unable to take up all the tannin from the leaves, or all
that remains in the leaves from former abundance, hardly proves
that tannin cannot serve to build up the tissnes. Still less need we
wouder at the waste of tannin in Sprrogyra, for evidently it is here
not the-intention of nature that it should be wasted. Nature ensures
a sufficient supply of tannin in Spirogyra, because this substance is
required in development, as for instance in conjugation and spore-
formation. The occasional failure to conjugate, as a result of which
then much tannin is lost, does not prove that it is a waste product
and not a plastic material.
A second series of observations, which show that tannin plays
a part in the formation of the ceil wall, relate to the formation of
transverse walls. On investigating Spirogyra filaments containing cells
undergoing division, it at once struck me that the tannin content
of these cells is somewhat smaller than that of other cells, not
undergoing division. The difference was not large and perhaps, even
escapes detection by some of the tannin reagents which have been
used hitherto, such as ferric salts and potassium bichromate, but with
antipyrine- and caffeine solutions the existence of a difference in the
tannin content could be established with certainty. Not only was it
clear that the precipitate with antipyrine- or with caffeine solution
was somewhat less in the cells undergoing division than in the
others, but on treatment of the filaments with these solutions, it was
also found, that the precipitate appeared somewhat later in the cells
(2g)
in process of division and that on transferring them to distilled water
or to ditch water the precipitate also disappeared somewhat sooner.
For the sake of completeness | further mention, that no difference
could be traced between the tannin content of cells in which the
nuclear and cell division had just started, and the tannin content of
cells not undergoing division, but the tannin content was found to
have diminished, when the process of nuclear and cellular division
was at its height or could be considered at an end.
These results show, that a connexion must be looked for between
the diminution of tannin content and the process of nuclear and
cellular division. This process really consists of two processes, going
on simultaneously, and therefore the question arose, which of the
two exerted its influence on the tannin content. With reference to
this question I carried out some experiments.
As has already been stated, the growth of the cells and the
division of cell and nucleus is stopped in a one percent antipyrine
solution or in a 0.1 percent caffeine solution. I therefore studied the
effect of these solutions on the. formation of transverse walls and on
karyokinesis, when the dividing cells and those showing the very
earliest signs of the process of nuclear and of cell division, were
placed in these solutions for some time. Filaments, in which such
cells occurred, were left for 14 hours in the above mentioned solutions,
and were then examined next day with regard to the division of
cell and nucleus. The transverse walls; in process of formation, had
been disturbed in their development, and therefore in these cases
the cell was incompletely divided. The result in the ceils which were
on the point of dividing, when placed in the antipyrine- or caffeine
solution, was more interesting; often in these cells no trace of a
transverse wall could be found next day. The process of cell division
had been completely suppressed.
The process of nuclear division was however quite different. In
all the cells where it was,going on, or where it was about to begin,
it had continued to the end and two normal daughter nuclei always
resulted, which were generally situated a little apart in the axis of
the cell.
It follows from these experiments, that a temporary fixation of
the tannin by antipyrine or caffeine prevents the formation of trans-
verse walls, but does not directly affect nuclear division. On the
Strength of this result I feel justified in assuming that there must
be a connexion between the diminution of the tannin content, referred
to above, and the formation of transverse walls. Both abolition of
transverse wall formation through fixation of tannin and the dimi-
( 704 j
nution of the tannin content during the formation of transverse walls,
point to the tannin being necessary for, and used up in the formation
of transverse walls.
In order to obtain still greater certainty with regard to this con-
clusion, the influence of antipyrine and caffeine on the formation of
transverse walls in Cladophora was investigated. With ferric chloride,
osmic acid, and antipyrine I did not obiain tannin reactions in Cla-
dophora and I therefore was interested in knowing how, for instance,
the formation of transverse walls would be affected by transferring
to a one percent antipyrine solution. I found that transverse walls,
which were just beginning to be formed, continued to grow until
they were completed. This was even the case if the specimens were
left in antipyrine solution during the whole of the process of cell
division. This result still further strengthens my view that in Spirogyra
the interruption or prevention of transverse wall formation is wholly
due to the fixation of the tannin. For in Cladophora, where no
tannin can be used in the formation of transverse walls, a one percent
solution of antipyrine does not bring about this disturbance. The
only ready explanation which, in my opinion, can be given of the
results obtained in the conjugation and transverse wall formation, is
this, that the tannin serves as plastic material in the building up of
the cell wall.
I wish to add a few results to those already mentioned, which
point to a connexion between the tannin content and growth of cell
wall. In Spuogyra filaments cells are sometimes observed, which,
judging from the position of the transverse walls, are distinguished
from the others by increased turgor. These cells are generally also
distinguished by a larger starch content. On closer examination it
is found that the growth of these cells is less than that of the others,
or that growth has completely come to a standstill. These symptoms
indicate a pathological condition, for generally 1 was able to ascertain
that the above-mentioned cells did not divide further and died off.
I cannot give the reason for this condition, but it is remarkable that
the tannin content of these cells as revealed by antipyrine or caffeine
solution, is larger, and often much larger, than that of the other
cells. Once more it is found, as in the case of cells in which conju-
vation failed, that a cessation of growth is accompanied by an
increase in the tannin content.
As was shown by the investigations of Grrassimorr') and of
1) J. J. Gerassimow, Ueber den Einfluss des Kerns auf das Wachstum der Zelle,
Separat-Abdruck aus Bull. d. 1. Soc. Imp. des Nat. de Moskou, 1901, No.1 en 2,
p. 193. Zur Physiologie der Zelle, Separat-Abdruck aus Bull. d. 1. Soe. Imp. des
Nat. de Moscou, 1904, No. 1, p. 7.
( 705 )
myself‘), the growth of cells without nuclei is very slight and
gradually stops completely. In anuclear cells with chromatophores
and in those without chromatophores, the two kinds being obtained
by centrifuging the cells before or during karyokinesis, the tannin
content after a time becomes very considerable, as shown by exami-
nation with caffeine- and antipyrine solutions. In the absence of a
nucleus growth stops, and as a result the consumption of tannin
must have fallen off or has stopped altogether. Its production is
however continued for some time; hence the increase of the tannin
content in cells without nucleus. In this case also there is cessation
of growth and an increase in the tannin content.
The results obtained with non-growing nucleated and with non-
nucleated cells, agree with those which I obtained with cells con-
jugating and undergoing division, out are of less importance for the
explanation of the physiological significance of tannin, because non-
growing nucleated cells. must be considered diseased, and those
without nuclei are very abnormal. The results obtained with con-
jugating cells and with cells undergoing division, I consider on the
other hand of great importance for the explanation of the physio-
logical meaning of tannin, which in my opinion must be regarded
in Spirogyra as a substance which serves in the formation of the
cell walls. The tannin is here not a reserve-material, however ; it
belongs to the soluble substances which the plant continually requires
for its development. It disappears and gives way to reserve-materials,
when the plant forms zygospores and passes into the resting condition.
Hence I have arrived at a result, which agrees with the conclusions
published by Wicanp nearly half a century ago, but which militates
against the view of later investigators, such as Sacus, Kraus and
others. For the sake of clearness I must add, that I do not at all
claim that tannin is the only substance, which is used in the formation
of the cell wall of Spirogyra, nor do 1 wish to argue that the only
physiological significance of tannin is its use as a plastic material.
This paper is a preliminary one. It is my intention to report at
some future time more fully on the physiological significance of
tannin in Spirogyra, and to illustrate with tables the conclusions
relating to the comparative experiments on the growth of Sperogyra
filaments under various conditions, 1.e. in antipyrine- and caffeine
solutions, in ditch water ete. At the same time various points of
investigation, relating to the tannin problem, and not mentioned in
this paper, will be dealt with.
1) C. van WISSELINGH, Over wandvorming bi kernlooze cellen. Reprint from
Bot. Jaarb. Dodonaea, Vol. 13, 1904, p. 5 and 6. Zur Physiologie der Spiro-
gyrazelle, Beihefte zum Botan, Centralblatt, Bd. XXIV, Abt. I, p. 170.
( 706 )
Physiology. — “The Camera silent’) of the Physiological Labo-
ratory at Utrecht’. By Prof. H. ZwaarDEMAKER.
(Communicated in the meeting of February 26, 1910.)
‘
The extension of the means of communication calls forth nearly
everywhere to a higher or lower degree the disadvantages connected
with the continual presence of noise. Therefore we want in many
instances apartments free from sound, and that at first in those cases
in which the continuous existence of disturbing sounds forms an
insuperable impediment. Such cases present themselves :
a. in acoustic experiments when the observations have to take
place in the proximity of the minimum perceptibile ;
}. in public consulting rooms for diseases in the ear where through
the coming and going of patients the required silence never reigns,
and more frequent visits render every minute investigation well nigh
impossible, consequently cause also uncertainty of diagnosis, of advice
and of decision in ease of examination ;
c. in modernly built hospitals, which with their smooth walls, naked
floors, construction of stone and iron, ete. show a kind of strong reson-
ance, and which, through their many technical ‘institutions’ can never
be quiet; the consequence is the impracticableness of a really efficient
percussive and auscultatory examination.
Since 1904 a camera silenta (2.28 x 2.28 « 2.20M.) has been
used for the purpose mentioned under @ in the Physiological Labo-
ratory at Utrecht*) and also since that time my advice has repeatedly
been asked in the building of new laboratories, polyclinies and
hospitals in this country and elsewhere. In connection with this I
venture here to pronounce the conviction that an apartment free from
sound, intended for one of the three above mentioned purposes,
will have to satisfy three conditions in order to preclude disappoint-
ment. These conditions are:
1. The inner surface of the apartment has to be covered with
1) Silentus, adj. occurring in Getuus, in a fragment from Lagvius used by “loca”,
is, on account of its shortness, preferable to silentiosus.
2) Ned. Tijdschr. v. Geneesk. 1905, Part 1, p. 571. Zeitschr. f. Ohrenheilk.
Bd. 54, p. 247.
( 707 )
a material that does not reverberate sound; for if this is neglected,
not only the involuntary sounds that are made by us, will have a
disturbing influence, but we shall also be hindered by the small
remainder of sound that might still be left on account of incom-
pleteness in the construction; the resonance of the space that is shut
off will itself seize definite parts of the small quantity of noise that
arises or penetrates into it and make them audible in a_ higher
degree.
2. The isolation must be brought about by a double wall, with
interstices of air of such a trifling thickness that resonance of audible
jones is quite out of the question and moreover no other contact is
left between the two walls than of a few narrow lead-contaets.
3. The isolation of the outer wall of the building and of its
bottom has to be as complete as possible: the first isolation has to
take place through a purposely constructed secondary apartment.
The first condition is fulfilled in our laboratory by means of a
covering of horsehair some centimeters thick (trichopiése), as it is
used in telephone-cells. Thanks are due to Dr. biurris of Gent for
making me acquainted with this material, which, moreover, procures
an excellent isolation of sound.
The second condition is satisfied at Utrecht by making use, in
fastening the trichopiese, of a wall of porous stone and by con-
structing outside it a second wall, consisting of corkstone of German
manufacture. Plates of peatmoss from Klazienaveen in the province
of Drente would have answered the purpose even better.
The third condition requires the exclusive use of lead-contacts. Espe-
cially the bottom has to be well provided for. At Utrecht faults have
been made in this respect, which could only partly be made up for
by the subsequent addition of an extra-covering.
Taking the above-named chief conditions for granted, we shall
have to answer the question, whether an apartment free from sound
will have to be constructed underground, on a level with the ground
or on a higher floor. My answer is decidedly on a higher floor, for
the conduction of the sound coming from the bottom is the obstacle
which it is most difficult to overcome. An efficient isolation of the
bottom can much more easily be brought about on a higher floor
than on a foundation. In the first case the only thing one has to do
is to provide lead-contacts with the stone beams, which in their turn
are not directly connected with the bottom, whilst in the second
case, under the most favourable circumstances, short columns con-
( 708 )
sisting of many strata can be made use of, which, however, have a
constant direct communication with the ground.
As to the different tones, the most difficult thing appears to be to
keep away the low tones. Inaudible vibrations of very slow perio-
dicity are even not at all excluded in our camera silenta, so that a
sensitive microphone, conducted to a gold-thread string-galvanometer
does not appear to subside, not even when at a complete adaptation
of the organ of hearing not a trace of sound is to be observed.
(This does not disturb acoustically, but a somewhat faster periodicity
would have been a hindrance).
Besides an apartment’ free from sound ought to have porous walls,
for if perfectly impermeable walls are chosen, it will appear that in
case of long experiments a ventilation is necessary, which in its turn
would require the supply of ventilation-channels, consequently of
sound-leaks. For double-door and double-window (the latter in my
opinion hygienically indispensable) as a matter of course apparatus
are wanted which require much care and a lasting control. When
acoustic experiments are made, the supply of sound should come
from sound-sources. placed outside the apartment, right through a
leaden stopper, that the principle that the two walls of the double
wall should have none but a lead-contact, is not discounted *). Electric
light, telephone, supply of air for organ-pipes and sirens through a
narrow leaden tube and the necessary conducting-wire to the galvano-
meter offer no technical difficulties.
An accidental additional advantage of an acoustic apartment with
a double wall, double door and double window, duly separated from
the outer-walls of the building by means of by-apartments, is this,
that it forms a calorimeter. The camera silenta at Utrecht remains
without an inhabitant of a constant temperature to within 2 deci-
grades. By covering the trichopiese-walls with some meters of extre-
inely fine brasswire (0,1 mm.), a bolometer may be made with a
Wheatstone bridge and galvanometer placed in a by-apartment, by
which bolometer the rise of temperature that the space undergoes
through an inhabitant, may be measured. The production of heat which
this causes is determined empirically (bD’ARsoNVAL). As a respiration-
calorimeter, however, the sound-free apartment is not to be used.
This is impossible because the walls are porous, and if this is given
up, it is no longer free from sound for longer experiments.
A number of investigations may take place in the camera silenta.
1) The leaden stoppers are 5 cm. thick and possess a central bore, at its narrowest
point being 0.4 em, wide; comp. Onderz. Physiol. Lab, Utrecht (5) VI. p. 188,
( 709 )
Those which have been made in the last six years, are, it is true,
not so numerous and extensive as I should wish, but an enumeration
with a list of the publications may follow here in order to serve as
an example of what is to be reached in a sound-free apartment.
1. The sensation of stillness may be experimented on; unless a
perforation of the tympanum exists, a kind of buzzing may be
observed, in which at a closer analysis a soft rustling as of the wind
in the tops of the trees, accompanied by a high-toned whistling (+g’)
may be distinguished; persons in whom this physiological ear-buzzing
is indistinct, perceive a feeling of oppression *).
2. The influence of the adaptation may be traced; then appears
among others a gradual diminution of the physiological tinnitus
aurium, which after a 3 hours’ stay in the sound-free apartment has
entirely disappeared (Borronorti), whilst at the same time the feeling
of oppression, if existing, gradually increases (Minkema); from this
one might be inclined to derive that the physiological ear-buzzing,
entirely or partly, possesses the character of an after-image ”).
3. The phenomenon of accommodation, discovered by Hensgn,
may be more closely studied, by conveying to a person standing
outside the camera silenta through bone-conduction the tone of a
tuning-fork, which then from the person’s ear is conducted into the
apartment through an auditory tube; whenever a metronome placed
outside the apartment is ticking, the sample-person accommodates and
the observer bears a strengthened sound (Qurx).
4. From the shortest exposition-time the smallest observable
number of sound-vibrations may be derived in the tone of a tuning-
fork or that of an organ, conducted to it from the outside; according
to Bopr this number seems to vary in the scale in atypical manner
(pe Groot *) and van Mens).
1) For my ear the physiological ear-buzzing can be suppressed: «. by the ticking
of a watch; 6. by the sound of a tuning-fork of the c’-pitch and a sound-force of
68.10-3 Erg. per cm.? and per sec. (Erg. d. Physiol. 1905 p. 452).
*) According to Borro.orrr the buzzing returns directly, afler one has left the
camera for a moment and then returns.
*®) H. pe Groor, Ztschr. f, Sinnesphysiol. Bd. 44 p. 18 and Onderz. Physiol, Lab,
(5) X p. 137,
( 710 )
Dd. The minimum perceptibiie during the unity of time may be
fixed by the scale (MINKEMA *)).
6. The limit of distinction may be traced and the typical variation
it undergoes in the scale (DEENIK *)).
7. The sensation of a report, observed by Hensrexy at a sudden
intonation or interruption of siren-tones, may be demonstrated in
tones of different origin and piteh, with the aid of a sudden opening
or closing of a telephone-contact or a sudden opening or closing of
a particularly constructed lead cock.
8. The spreading of the sound round a tuning-fork with the
situation of the well-known interference-planes may be accurately
traced, without making the mistakes that must necessarily arise in
apartments with echoing walls.
9. The action of the winding molluse-shells as to their resonance
for buzzes may be proved directly.
10. The sound-extinguishing action of different means of isolation
may be traced with perfect security; for reports by dropping steel
balls on a steel plate*) (fall-phonometer of Zorn), for tones by eléctri-
cally touching purely tuned bells; in both cases the instrument put
in a small non-resonant space; the walls of this space are covered
with the materials that are to be examined, and, on the one side
the energy with which the bells are touched, and on the other the
distance at which the sound is heard, is defined; the completest
isolation with an equal thickness of the walls is got in the case of
trichopiese, then, follows the peatmoss-plate from Klazienaveen, then
the corkstone; other materials that we examined had a considerably
smaller sound-extinction.
1) H. F. Minkema, Onderz. Physiol. Lab, (0) VI. p. 134.
2) Meeting of this Academy 3 Noy. 1905.
5) In order to prevent resonance the stale plate has to be soldered upon a
heavy piece of lead.
211.)
Mathematics. — “On pairs of points which are associated with
respect to a plane cubic.” By Prof. JAN DE Vries.
(Communicated in the meeting of February 26, 1910).
J. By the symbolical equation
a} = 0
3
a plane cubic c* is represented. If the points X, Y, and Z are
connected by the relation
ay dy dz = 0,
each of them lies on the (mixed) polar line of the other two, and
every two of those points are harmonically separated by the polar-
conic of the third point; they form a polar triangle of c’.
Let us look more closely at the case that the three points lie in
one line /; then Z is the point of intersection of 7 with the polar
line of X and Y.
It is evident that the triplets Y, Y,Z lying on / form a eubic
involution ds of order two having the points of intersection P,Q,R
of c® with / as threefold elements.
According to a well known property of the 13 we find that P, Q
and R form at the same time a group of the 73. This is indeed
directly to be seen; for, the polar conic of P intersects 7 in P and
in the point H, which is harmonically separated by Q and R from
P; the polar line of Q with respect to that conic therefore passes
through R.
To J: belongs a neutral pair, U, V forming with each point of
/ a triplet and therefore having / as polar line. The polar conics
of the points lying on / form a pencil; two of those conics wu? and
v? touch / in the points V and U.
We shall call U and V associated points.
Evidently each point U is associated with two points V, viz.
with the points which have the polar line and the polar conic of
U in common. The associated pairs are thus arranged in an involutory
correspondence (2, 2).
If 7 becomes tangent to c’, then in the point of contact L two
threefold elements of the 73 unite themselves with the two neutral
points U, V. For, all polar conics whose poles lie on / pass through
ZL and one of those curves touches / in LZ. So c* is curve of coin-
cidence of the (2, 2) correspondence.
48
Proceedings Royal Acad. Armsterdam. Vol. XI.
2. We shall see whether there are points U, for which the
corresponding points / form again an associated pair, so that there
is a triplet of points which are two by two associated. If we take
the three points as vertices of a triangle of reference, their polar conics
will be represented by :
ay == Oy 6s Gy ==, a, a, SS Une oh ly a; a |b, %, t, 0
for, each of those points has the connecting line of the other two
as tangential chord with respect to its polar conic.
If w=O0O is the equation of c*, the three polar conics are also
represented by
du : du du
oes —Ssn SSS ee
aE. bs] 9
dz, dx, dx,
From this ensues in the first place that the coefficients },, },, ,
must be equal. Farther on it is directly evident that the equation
Ot Conse
3 3 3
a,@, ta, +a,03+3b2,2,07,=—0.
The triangle of coordinates is therefore a triangle of inflection, 1. e.
a triangle of which each side contains three points of inflection of
c*. There being four triangles of inflection, the (2,2)-correspondence
of the associated points contains fowr involutory triplets.
3. We shall now determine the locus of the associated pairs,
collinear with a given point D.
In the first place D is a node of the locus; the points D' and
D' associated with D are the points of intersection of the polar conic
d? of D with the polar line d of D. The locus is therefore a nodal
biquadratic curve d'.
The tangents out of D to c*® are at the same time tangents to d‘,
for in their tangential points two associated points continually coincide.
So d? is the conic of Bertini of d*. For an arbitrary nodal c* this
conic contains besides the six points of contact of the tangents out of
the node, the points of intersection of c* with the line connecting the
two tangential points of the node, and the tangents in those ‘“funda-
mental points” to the conic concur in the node ‘).
The curve d‘ is a special curve, because its fundamental points
coincide with the tangential points D' and D", so that these are at
ihe same time the points of contact of a double tangent.
1) See my paper “La quartique nodale” (Archives Teyler, t. IX, p. 263).
(713 )
4. It is easy to find the equation of d*.
: 7 uae 3 5 ve
The polar conic of Z with respect to a; == 0 is represented by
2 2 ‘ r
ad; = 0, the polar line by a:a,—=0. For the tangents out of Z to
that conic we have thus
2,3 2 2
a2d,b, = a2dzb-by.
If these contain the given point Y, then 7 is a point of the curve
d* belonging to Y. So it has, as equation (in current coordinates 2):
2 3 2,2
4,azb~ = ayb,azb-.
From this it is again evident, that the polar line of D is double
tangent, and that it touches d* in the tangential points D’ and D".
rene : 2 , 2 2 2
For, by combination with a,a, =O we find a,az . byb: = 0. The
° : - : . 3 ate Ne
same is obtained by combination with 6: =O; by this is confirmed
that d* is touched in its points of intersection with the polar conic
of D by c* and the polar line d.
Out of
8) LH 2 Bs OF 22
dyt=b, — aybyazb, = byb.az — byaybza,
‘follows that the equation of d* can be transformed into
1 (ayazb: = by b-a:) (a,b. — azby) = 0,
so also into
(aybz — azby)? azb. = 0.
Now
ab. — azby = (aib2) (yiz2) + (a2bs) (y2z3) + (4361) (yse1)-
If thus we represent the coordinates of the line YZ by &, the
above equation passes into
é (abs)? ab. = 0.
This equation expresses that the polar conic of Z is touched by
the line YZ’).
5. At the same time is evident from this that the line (&) cuts its
poloconica in two points, This is more closely confirmed by the
observation that the poloconica of (§) is the locus of the points whose
polar conics touch (§), from which ensues that it intersects (§) in two
associated points.
The curve d* can therefore be generated by determining the points
of intersection of each of the lines s through D with the conjugate
poloconica 6. The poloconica describes there a system with index 2.
For, when o passes through any point Y the polar conie of X is
touched by s. And as two lines s satisfy that condition, XY lies on
two curves 6. This generation of d* with the aid of a system of
1) Crepscu, Lecons sur la géométrie, t. Il, p. 278.
48%
(714)
conics with index 2 and a pencil projective to it is characteristic
for the nodal biquadratie curve‘).
6. Each nodal biquadratie curve d* of which the nodal tangents
pass through the points of contact D' and D" of a double tangent
d is related in the way mentioned above to a c’.
The polar curve d? of D has in JD the tangents / and ¢’ in common
with d* and it intersects it in the points of contact RA of the six
tangents concurring in D. Of the 16 points which d* has in common
with the system of d* and d six lie in D, four in D! and D", six
in the points &. The tangents ¢ and ¢’ contain eight of those points ;
so the remaining eight lie in a conic (curve of Bertini).
This conie d? unites the six points R to the points D' and D".
Let us now regard the pencil determined by d* and the conic d?
counted twice; one consisting of the double tangent d and a
cubic c’ belongs to it. From this ensues that d* is touched by c*
in the points of contact & of the tangents drawn out of D to d'*.
As d® passes through the points &, it is the polar conic of D with
respect to c*; because D! and D" are the fundamental points, so
that DD' and DD" are touched by d* in D' and D", d is the polar
line of D with respect to d* and of c*. So d* is the locus of the
points asseciated with respect to c* and collinear with D.
7. If d* is represented by
wa? + xxx? — 3x3 = 0
rate a een — o8.tg >
where
o= (cei +- ¢2@9)()
x“
then ¢, ¢', and d are indicated by z,=0, «,=0, and z, = 0, and
@ by 2a,2,2, —c? = 0. From
12 2 SP RS TOY Wi cen rere Trt ny ti Og | trys
(w' ae +. age? cars) x3 (2x xov3 oe) =——()
then follows for d? the equation
2\vo — a = (1),
and from
Ty Oa (oe nap oe
(12 — a*) (w+ we $ aagare cars) =)
we find for c*
08 — 8a\xa3 + as == (0);
For the polar conic 4? of Y with respect to c* follows from this
Cy0? -— Y1@2%3 — Yreyvs + Ys (ws — v\e2) = 0,
ees
for the polar line of D with respect to 7?
2y 3%, — Yi, — Yot, = 9;
1) Bosex, Denkschriften der Akad. in Wien, Bd. 53, S. 119.
( 715: )
thus for the tangents out of D to the polar conic 7?
Ay tee? — ¥,@2%3 — youia3 + 93 Ce — v 02)} = (2433 — yiv2 — you).
When one of these tangents passes through Y we have
4ys (ch — 3yiyeys + Ys) = (245 — 2yiy2)"s
or
2,2 Py) a Oe ETI)
Up UX —— a
Ys Yiyey, — Cs
From this is again evident that the curve indicated by this equation
is the locus of the points associated with respect to ¢* and collinear
with D.
This special nodal d* is characterized by the property according
to which it is touched by a cubic in the six points whose tangents
concur in the node. For, when considering the pencil which
is determined by d* with the conic of Bertini counted twice it is
immediately evident that the remaining points of d* lying on this conic
are points of contact of a double tangent, which must then also lie
on the nodal tangents.
8. We shall now see into what a line (3) is transformed by the
correspondence of the associated points. To that end we eliminate
ye out of the three equations
§, = 0, a, a = 0 and a (i == (0)
Out of the first two we find
yi ty2ty3 = (a2 §s) a> 3 (a3 §1) a? 2 (a &2) a,
Substitution in the third then produces
(ab§) (ae§) ax a= 0.
A line & is thus transformed into a curve & of order five. This
could be foreseen, for the two associated points lying on § pass
in the transformation into each other, whilst the three points of
intersection of § and c* correspond to themselves,
When the point U describes the line §, its polar line w envelops
the poloconica §*, whilst its polar conic uw? describes a pencil. From
this ensues that §° is generated by a pencil of conies and a pencil
of rays of index 2 projectively related to it. Consequently &* has
nodes in the four basepoints of that pencil and the points associated
with U form the pairs of the fundamental involution of pairs ap-
pearing on §°'). In connection with this §* is touched by the polo-
conica §° in five points (l.c. p. 48).
1) See my paper: “Ueber Curven fiinfter Ordnung mit vier Doppelpunkten” (Sitz.
Akad. Wien, Bd. 104, 5. 47).
( 716 y
Mathematics. — “On continuous vector distributions on surfaces”.
(2°4 communication)'). By Dr. L. E. J. Brouwer. (Commu-
nicated by Prof. D. J. Korrrwse).
(Communicated in the meeting of february 26, 1910).
§ 1:
The tangent curves to a finite, uniformly continuous vector distri-
bution with a finite*) number of singular points in a singly connected
inner domain of a closed curve.
Let y be the domain under consideration, then we can represent it on
a sphere, so we can immediately formulate on account of the property
deduced in the first communication (see there page 855) :
TurorEM 1. A tangent curve, which does not indefinitely approach
a point zero, is either a simple closed curve, or its pursuing as well
as its recurring branch shows one of the following characters: 1%.
stopping at a point of the boundary of y; 2°4. spirally converging
to a simple closed tangent curve; 3°. entering into a simple closed
tangent Curve.
We now shall farther investigate the form (in the sense of analysis
situs) of a tangent curve 7, of which we assume, that at least one of
the two branches (e.g. the pursuing branch) approaches indefinitely
one or more poinis zero, i.e. singular points of the vector distribution.
We start the tangent curve in a point A, (nota point zero) and we
pursue that curve in the following way: By ¢: we understand a
distance with the property that in two points lying inside the same
geodetic circle described with a radius #:, and possessing both
a distance >e from the points zero, the vectors certainly make an
1 ; ,
angle < a with each other. We farther choose a fundamental series
of decreasing quantities €,, €,€,,.... converging to 0, and of corre-
sponding decreasing distances (3, , 82, ,.+.+; which all we suppose,
if a is the distance of A, from the points zero, to be smaller
than a—é,.
We then prove in the manner indicated in the first communication
p. 852, that, when pursuing r from A,, a point A, is reached,
possessing a distance @., from A,; we call the are A,4, a B,-are.
According to our supposition there now exists a finite number », in
1) Mor the first communication see these Proceedings Vol. XI 2, p. 850.
2) This restriction we shall drop in a following communication.
¢ 117 )
such a way, that after having completed n, £.,-ares, but not yet
n,+1 £.,-ares, we reach a point A,, where for the first time we have
approached the points zero as far as a distance ¢,. Then again there
is a finite number mn, in such a way that, having completed from
A, n,, but not yet m, +1 .,-ares, we reach a point A,, where for
the first time we have approached the points zero as far as a distance
é,. From there we pursue 7 with @.-arcs and continue this process
indefinitely.
If we understand by m(e,) the maximum distance from the points
zero, which 7 reaches when being pursued after having for the first
time approached the points zero as far as a distance &,, then a first
possibility is, that m(«,) converges with &, to zero.
In that case the pursuing branch converges to one single point
zero and it is an arc of simple curve, stopping at that point zero.
We now suppose the second possibility, that m/(¢,,) surpasses for each
é, a certain finite quantity e. Then we can effect (by eventually
omitting a finite number of terms of the series of «,'s), that each
1 1
fu << 5 ¢ and each B < 9 &
On the pursuing branch then certainly two points P, and Q, can
be indicated both at a distance e from the points zero, and separated
on 7 by at least one point at a distance «, from the points zero,
1 :
whilst the distance between P, and Q, is < ; 8.,, Let P,S and Q, U
be pursuing @,-ares, and P,R and Q,7' recurring ?.,-ares.
Fig. 1.
Let H, be a point of TU, having from P, the smallest possible
distance, then H, cannot coincide with 7’ or U, so that the
geodetic arc P,H, is in H, normal to the vector direction, and the
vector directions in all points of that geodetic arc, forming with
( 7418 )
1
each other an angle Sa are directed to the same side of the
geodetic are P,H,.
Let A, be the last point of intersection of the are P,H, of 7 with
the geodetic are P,H,. Then the are K,H, of r and the geodetic are
K,H, form a simple closed curve, and we prove in the manner
indicated on page 853 of our first communication, that either the
pursuing branch of r from #/, lies in the inner domain, and the
recurring branch from A, in the outer domain, or the pursuing
branch from H, in the outer domain, and the recurring branch
from /Y, in the inner domain.
Let us first assume that the pursuing branch lies in the immer
domain, then certainly two points P, and Q, can be chosen on it,
both at a distance e from the points zero and separated on 7 by at
least one point at a distance ¢, from the points zero, whilst the distance
1
between P, and Q, is << ia B.,. With the aid of those two points we
construct in the same way as above now a simple closed curve,
consisting of an are K, H, of r and a geodetic are A, H,, in whose
inner domain lies the pursuing branch of 7 from H,.
Going on in this way we construct a fundamental series opened
CULVES U;, Uy, Us,+... lying inside each other. If there is a domain
or set of domains G, common to all the inner domains of these
curves (which, as we shall presently show, is really the case) then
the boundary of G can only be -formed by points belonging to none
of the curves w,,2%,,U,,... but being limit points of fundamental
series of points lying on those curves.
We assume q > >p, and B to be a point of wu, having a distance
> 3 & and > 3 Bs, from the points zero. Let C be the first point
when recurring from 8, and PD the first point when pursuing from
B, which reaches a dist om £, then we shall assume for
a moment that there exists on w,, but not on the are CD, a point
: 1
S lying at a distance — from 4, and we shall show that
this assumption leads to an absurdity.
e
: ; iE
Let SV be a_ recurring “5 B.,-are and SW a pursuing Be -are
2
on uy, then the ares CD and VIV can have no point in common,
(719 )
and the geodetic are A, H,, belonging to w,, has either no point
in common with VW, or none with CD.
In the first case we determine on IV a point M/, having from
B a distance as small as possible. The geodetic are LM is then in
M normal to VW, and has a last point of intersection N with CD,
so that the geodetic are NM forms with one of the ares NM of
Ug, not containing e.g. the point C, a closed curve; w,, taken with
a certain sense of circuit, would at JZ enter one of the two domains
determined by this closed curve, to leave it no more; further C’
would lie outside that domain; thus w, would never be able to
reach C, with which the absurdity of our assumption has been proved.
In the second case we determine on CD a point M having from
SS a distance as small as possible, and on tlie geodetic are SM the
last point of intersection NV with VW. The further reasoning remains
analogous to the one just followed: the parts of the ares VW and
CD are only interchanged.
Let now £&, be the only limit point of a certain fundamental
series of points B,, B,, B,,..., lying respectively on w,, w,, U;,..-
We assume that 4, is not a point zero; it has then for a suitably
selected p a distance >4e, and > +B. from the points zero.
Let further each m;, be >p and let B,,, Bn,» Bn,,... be a fun-
damental series contained in the series just mentioned, whose points
1 1
have all from ., a distance <a é, and < = a.
If then further on the different vw, Bn,Dn,, are pursuing, BrCn,
{ 1
recurring > (Ge ares, we prove by the reasoning followed in the
first communication p. 854, that there exists a series Car,
Ci, Pin, Cr, Digs»... Converging uniformly to an arc CD, of a
tangent curve w in such a way, that all ares C, lie on the
nN} Dn,
same side of C. Du.
Mh: : Sith
lf we describe round 4, a geodetic circle with radius ae :
Pe
then it cuts from C, D, an are FJ containing B.; this are divides
its inner domain into two regions, into one of which, to be called gq:
neither the ares C,, D
"he
ny» MOL any other parts of the curves Un, can
ny”
As further the region g cannot lie outside all curves w,,, it must
1
penetrate, as they would get there a distance < Oess: from B
lie inside all curves Un»
( 720 )
So there is certainly a domain or a set of domains G', common
to all the inner domains of the curves w,, and to the boundary of G
belong all points of the limit set 2 of the w,’s, which are not points
zero, thus also all points of 2, which are points zero, as the latter are
limit points of the former ones. So the boundary of G is identical
to the limit set of the w,’s, is therefore coherent and identical to
its outer circumference, whilst abroad from the points zero it consists
of tangent curves to the vector distribution, which on account of the
existence of the domain g can show nowhere in a non-singular point
the character mentioned in theorem 1 sub 3.
We shall now show that a tangent curve 7’ belonging to the boun-
dary of G cannot have the property of 7, that its pursuing or
recurring branch converges spirally to the boundary of a domain or
set of domains (’.
We should then namely be able to form, in the same way as was
done above and in the first communication for 7, also for r’ a closed
aye 1
curve w'; consisting of a geodetic are <7 32, and an are p. Ol Te
joining the same two points A’ and H’. And there would exist ares
of r which would converge uniformly to g’ from the same side, e.g.
from the inner side of w). But when pursuing such an are w of r
situated in sufficient vicinity of ~’, we should never be able to return
between w and q’.
As farthermore in the case considered here, that the pursuing branch
of 7 lies in the inner domain of w,, it is also excluded, that 7’
reaches the boundary of y, only one form remains possible for 7’,
namely that of an are of simple curve, starting from a point zero,
and stopping at a point zero. (For the rest these two end points can
very well be identical).
Of such tangent curves there can be in the boundary of @ at
most two, which possess the same end points, when these end points
are different: but there can be an infinite number, which are closed
in the same point zero. Of these however there are only a finite
number, of which the extent surpasses an arbitrarily assumed finite
limit. For, each of these contributes to G a domain with an area,
which surpasses a certain finite value.
The curves 7’ whose extent surpasses a certain finite limit are run
along by a wu; of sufficient high index in the same order, as they
succeed each other on the outer circumference of G. From this
ensues that for all curves r' the pursuing sense belongs to the same
sense of circuit of the outer circumference of G.
Cc 21)
If the pursuing branch of 7 lies in the owter domain of w,, the
preceding holds with slight modifications. A point of the limit set
of the w;,’s now necessarily bounds a region belonging to y, and
lying outside all w,’s, only then when it is not a point of the
boundary of y. The inner circumference, to which r now converges
spirally on the inner side, consists here again of ares of simple curve,
which are tangent curves to the vector distribution, but these tangent
curves can lie entirely or partially in the boundary of y.
However they have all again a pursuing sense belonging to the
same sense of circuit of the circumference.
We now agree about the following: When a pursuing branch ofa
tangent curve reaches a point zero, we continue it, if possible, along
a pursuing branch, starting from that point zero, and not meeting
the former within a certain finite distance; but if such a continuation
is impossible, we stop the branch at that point zero, and so we do
likewise when the branch has entered into a closed curve or has
approximated spirally a circumference. Then we can resume the
preceding reasonings as follows:
TuroreM 2. A tangent curve is either a simple closed curve, or
save its ends it is an are of simple curve, of which the pursuing as
well as the recurring branch shows one of the following characters:
1st. stopping at a point of the boundary of ¥; 2°. stopping at a
point zero; 3°. entering into a siniple closed tangent curve; 4". spirally
converging to a circumference, consisting of one or more simple
closed tangent curves.
From this ensues in particular:
TunorrM 3. A tangent curve cannot return into indefinite vicinity
of one of its points, after having reached a finite distance from it,
unless it be to close itself in that point.
That the last theorem is not a matter of course, is evident from
the fact that it does not hold for an annular surface. On this it is
easy to construct tangent curves of the form pointed out by Lorrnrz
(Enz. der Math. Wiss. V 2, p. 120, 121).
We finally notice that the vector distribution considered in this §,
does not possess of necessity a singular point (as is the case on the
sphere). This is proved directly, by considering in the inner domain
of a circle, situated in a Euclidean plane, a vector every where constant.
§ 2.
The structure of the field in the vicinity of a non-singular point.
To classify the singular points we shall surround each of them
(7224
with a domain which we shall cover entirely with tangent curves
not crossing each other and we shall investigate the different ways in
which that covering takes place in different cases. For the sake of
more completeness and as an introduction we first do the same for
a non-singular point.
Let P be the point under consideration, RS an are of tangent
curve 7 containing P, UV an are containing P of an orthogonal
curve of the vector distribution. We draw through U and V
tangent curves «, and «,, and through F and S orthogonal curves
y and gd, and we let the four points R, S, U, and V converge
together to P. Before they have reached P, a moment comes when
a, «@, y, and dé form a curvilinear rectangle, inside which lies P,
and inside which lies no point zero of the vector distribution, thus
inside which on account of the first communication no closed
tangent curve can be drawn.
We shall cover this curvilinear rectangle with tangent curves
not erossing each other.
We number e@, with 0, 7 with = at,
inside or on the rectangle A, B, SR (tig. 2) having from @, and r
with 1. Let Qi be a point
4
Fig. 2. Non-singular point.
a distance as large as possible. We draw through Qi a tangent curve
4
«1, about which we agree, that, if it meets «, or7, we shall continue
4
it, by pursuing or recurring a, or 7, until we come upon y or J,
Then ai is a tangent curve joining two points Ai and Bb: of
- 5 5 —
4 4 4
y and Jd between «, and y. In the same way we construct inside
(723 )
the rectangle 4, b,S Rk a tangent curve, a@3, joining two points
4
As and Bs of y and d between rand a,. The rectangle A, 5, B, A,
4+
4
is then divided into four regions. In these we choose in the way
described above successively the points Qi, Qs, Q5, Q7, draw
8 8 8 8
through Q: a tangent curve a! joining two points Ai and Bi of y
8 8 8 8
and d, and we deal analogously with the other three points.
e . - a
Going on in this manner we construct for each fraction a 1a
tangent curve @a@ joining two points of y and J; two of these curves
gn
chosen arbitrarily can coincide partially, but they cannot cross each
other.
All these tangent curves must now cover everywhere densely the
inner domain of the rectangle A, 6, B, A,. For, if they left there
open a domain G, then a domain G",, bounded by two tangent curves
a a = :
with indices =~ and —>— would converge to (. For n sufticiently
an an
great however the point Q2a41 would then lie inside G, thus in
on+l1
contradiction to the supposition also a tangent curve @a+i would
gt +l
pass through G.
From this ensues, that, if we add the limit elements of the tangent
curves @a, Which are likewise tangent curves, the inner domain of
Dn
the rectangle A, 6, 6, A, is entirely covered, and further there is
for each real number between 0 and 1 one and not more than one
of these tangent curves having that number as its index.
§. 3.
The structure of the field in the vicinity of an isolated
singular point. First principal case.
We surround the point zero P, supposed isolated, with a7simple
closed curve c, inside which lies no further point zero. And we
assume as a first principal case that c can be chosen in such a way
that inside c no simple closed tangent curve exists, inside which P
lies. On account of the first communication there can exist inside c
neither a simple closed tangent curve, outside which P lies. We now
distinguish 2 cases:
( 724 )
a. There exists inside c a simple closed tangent curve 9 through
P. We ean then choose ¢ smaller, so that it meets 0, thus containing
in its inner domain a tangent curve @, which (in its pursuing
direction) runs from P to c, and another ge, running from ¢ to P,
and we further look for such tangent curves inside ¢ which cross
neither @
Sal
nor 9,. Of the possible kinds of tangent curves mentioned
at the conclusion of §1 we shall agree about those, which enter into a
closed tangent curve, to continue them along that tangent curve until
they reach either P or c, and to stop there. Spirally converging to
an inner circumference cannot appear, as the other end of such a
tangent curve would be separated from P as well as from c, and so
would determine a closed tangent curve, outside which P would be
lying, which is impossible. Neither can appear spirally converging to
an outer circumference, as P would have to le in that outer cireum-
ference and the spiral would necessarily have to cross @, and Q,.
b. There exists inside ¢ no simple closed tangent curve through
P. Then inside ¢ there exists no simple closed tangent curve at all,
so that again spirally converging is excluded.
In any case, if we agree not to continue a tangent curve, when
it reaches P or c, we can distinguish the tangent curves inside ¢, and
not crossing g, and 9, if the latter exist, into three categories:
1st. Closed curves, containing P but not reaching c.
204, Ares of curve, joining two points of c, but not containing P.
3°, Arcs of curve which run from P to a point of © (positive
curves of the third kind) or from a point of ¢ to P (negative curves
of the third kind).
Of this third kind there must certainly exist tangent curves. For
otherwise the closed sets determined by the curves of the first, and
by those of the second kind would cover the whole inner domain of
c, thus would certainly possess a point in common ; through this point
however a curve of the third kind would pass.
So we ean commence by constructing one curve of the third
kind and we choose eventually @, for it. Lf possible, we then draw
a second curve of the third kind not crossing the first and we choose
eventually 0, for it. Into each of the two sectors, determined in this
way inside c, we introduce if possible again a curve of the third
kind, not crossing the already existing ones, and chosen in such a
way that it reaches a distance as great as possible from the two
curves of the third kind, which bound the sector, whilst, if the new
curve terminates somewhere on one of the curves bounding the sector,
we further follow the latter curve. In each of the sectors, deter-
mined after that in the inner domain of c, we repeat if possible this
( 725 )
insertion, and we continue this process as often as possible, even-
tually to an indefinite number of insertions.
If in this manner we have obtained an infinite number of tangent
curves of the third kind, they determine limit elements which each
are either again a tangent curve of the third kind, or contain such
a curve as a part. And in particular a fundamental series of positive
respectively negative curves of the third kind determines in its limit
elements again positive respectively negative curves of the third kind.
After addition of these limit curves of the third kind we are,
however, quite sure that no new curves of the third kind not crossing
the existing ones can be inserted. This is evident from a reasoning
analogous to that followed in § 2. The whole of the curves of the
third kind, obtained now, we shall call a system of base curves of
the vicinity of P.
An arbitrary positive base curve and an arbitrary negative one
enclose inside ¢ a sector, of which the area cannot fall below a
certain finite limit. For otherwise we should have a fundamental series
of positive base curves, and a fundamental series of negative ones,
possessing the same base curve as a limit element, which is impossible,
as that limit base curve would have to be positive as well as negative.
So the inner domain of ¢ is divided into a finite number of sectors
which can be brought under the two following categories:
First category. Sectors bounded by a positive and a negative base
curve, between which lie no further base curves. The areas of these
sectors surpass a certain finite limit.
Second category. Sectors bounded by two positive (respectively two
negative) base curves and containing only positive (respectively negative)
base curves. A sector of this category can reduce itself in special
cases to a single base curve.
We shall first treat a sector of the jirst category and to that end
we first notice that outside a curve of the second kind lying in it
(i.e. between that curve and c¢) lie only curves of the second kind,
and inside a curve of the first kind lying in it only curves of the
first. kind.
If we draw in the sector a well-ordered series, continued as far
as possible, of curves of the second kind enclosing each other, then
it converges either to a curve of the second kind, or to two curves
of the third kind and between them a finite or denumerable set
of curves of the first kind, not enclosing each other, and not
approaching c indefinitely.
lf we can construct an infinite number of such series not enclosing
(726 )
each other, then there are among them which cut from the sector
an area as small as one likes, and at the same time the maximum
distance, which such a series reaches from c, decreases under each
finite limit.
And analogously, if we draw in the sector a well-ordered series,
continued as far as possible, of curves of the first kind enclosing
each other, it converges either to a curve of the first kind, or to two
curves of the third kind and between them a finite or denumerable
set of curves of the second kind, not enclosing each other, and not
approaching P indefinitely.
If we can construct an infinite number of such series not enclosing
each other, then there are among them which enclose an area as
small as one likes, and at the same time the maximum distance,
which such a series reaches from P, decreases under each tinite limit.
From this ensues that for the sectors of the first category we have
to distinguish two cases:
First case. There are curves of the second kind in indefinite
vicinity of P. Then the domain of the curves of the second kind is
bounded by the two base curves which bound the sector, and a
finite or denumerable number of curves of the first kind, not enclosing
each other, and not approaching c indefinitely, in whose inner domains,
which we call the /eaves of the sector, can lie only curves of the
first kind.
The region outside the leaves can be covered as follows with curves
of the second kind not crossing each other: we first construct one
which reaches a distance as great as possible from ¢ and the boundary
of the leaves; in this way two new regions are determined, in each
of which we repeat this insertion. This process we continue indefini-
ely, and finally we add the limit curves. That then the region
outside the leaves is entirely covered,
; is evident from the reasoning fol-
lowed in § 2.
And in the same way we fill each
of the leaves with curves of the first
kind not crossing each other. The
whole of the tangent curves filling
the sector finally gets the’ form in-
dicated in fig. 3. The sectors being
ip in the discussed first case we shall
Fig. 3. Hyperbolic sector. eall hyperbolic sectors.
Second case. There are no curves of the second kind in indefinite
vicinity of P. Then the domains covered by these curves are cut off from
(7279)
the sector by a finite or denumerable number of curves of the second
kind, not enclosing each other, and not
approaching / indefinitely. These do-
mains we take from the sector (conse-
quently modify an are of c), and there
remains a new sector, bounded by the
same base curves as the old one, but
consisting of one leaf inside which lie
only curves of the first kind. This leaf
we can fill with curves of the first kind
not crossing each other (see fig. 4).
These sectors of the second case, P
which are reduced to a single leaf, Fig. 4. Elliptic sector.
we shall call elliptic sectors.
We now pass to the discussion of a sector of the second category,
of which, to fix our ideas, we assume, that it is bounded by two
positive base curves.
Let us consider the set of points lying in the sector or on its
boundary, through which curves of the second kind not crossing
the base curves can be drawn. This set of points cannot approach
P indefinitely, as otherwise it would give rise to a negative curve
of the third kind not crossing the base curves, which is excluded.
In the same way as for the elliptic sectors we destroy the regions
covered by this set of points, and there remains a sector of the
second category bounded by a modified are of c, inside which no
curves of the second kind not crossing the base curves can be drawn.
In the modified sector we now consider the set of points, through
which curves of the first kind not crossing the base curves can be
drawn, and it is clear that this set of points cannot indefinitely
approach the just now modified curve c. The regions covered by it
are therefore bounded by a finite or denumerable number of curves
of the first kind, nof enclosing each other,
not indefinitely approaching c, and each
enclosing a domain which forms a lea/,
not differmg from those appearing in
the hyperbolic sectors.
By the method applied above already
several times the region outside the
leaves can be filled with curves of the
Je third kind (for instance we can choose
Fig. 5. Parabolic sector. for them the system of base curves
49
Proceedings Royal Acad. Amsterdam. Vol. XII.
( 728 )
present already in the sector), and finally each of the leaves with
curves of the first kind (see fig. 5).
The sectors of the second category we shall call positive (resp.
negative) parabolic sectors.
In special cases the whole inner domain of ¢ can reduce itself to
a single positive (resp. negative) parabolic sector. A point zero where
this occurs we shall call a source pomt resp. vanishing pot.
§ 4.
The structure of the field in the vicinity of an isolated
singular point. Second principal case.
In this case any vicinity of P contains a simple closed tangent
curve inside which P lies. We can then construct a fundamental
series c¢, c', c",.... of simple closed tangent curves converging to P,
of which each following one lies inside each preceding one, and we
ean fill in the following way the inner domain of ¢ with tangent
curves not crossing each other.
In each annular domain between two curves c” and c+) we
choose a point having from the boundary of that domain a distance
as great as possible and we lay through it a tangent curve situated
in the annular domain. According to § 1 it is either closed or
it gives rise to two closed curves, situated in the annular domain
with its boundary, into which it terminates or to which it converges
spirally, and which we draw likewise. (These closed tangent curves can
entirely or partially coineide
with c”) or ct)). So the
annular domain is either made
singly connected or it is divided
into two or three (annular or
singly connected) new domains.
In each of these we again
choose a point having from the
boundary a distance as great
as possible and we lay through
it again a tangent curve. A
singly connected domain is
certainly divided by it into
two singly connected domains;
on an annular domain it has
ihe effect just now mentioned.
We repeat this process inde-
Fig, 6. Rotation point, finitely. For each domain it ean
( 729 )
happen only onee that it undergoes no division; after that namely
it becomes singly connected, so is divided at each new insertion of
a tangent curve (see fig. 6).
We finally add the limit curves, and we prove in the same way
as in § 2 that then through each point of the inner domain of ¢
passes a tangent curve.
A point zero being in the second principal case we shall call a
rotation point.
So we can say:
Turorrm 4. An isolated singular point is either a rotation point,
or a vicinity of it can be divided into a jinite number of hyperbolic,
elliptic, and parabolic sectors.
The filling of a vicinity of a non-singular point in § 2 furnishes
in this terminology two hyperbolic and two parabolic sectors.
We must add the observation that in the most general case, where
neither in a singular, nor in a non-singular point the tangent curve
is determined, sometimes by a modified method of construction, the
structure of the first principal case can be given to a vicinity of a
point zero being in the second principal case.
Even the form of the sector division of the first principal case is then
not necessarily unequivocally determined. Out of the reasonings of the
following § we can, however, deduce that, if modifications are
possible in the form of the sector division, the difference of the number
of elliptic sectors and the number of hyperbolic sectors always
remains the same.
§ 5.
The reduction of an isolated singular point.
For what follows it is desirable to represent the domain y on a
Kuclidean plane, and farther to substitute for the curve c a simple
closed curve c emerging nowhere from c, containing likewise P in
its inner domain, and consisting of ares of tangent curves and of
orthogonal curves. In the second principal case this is already
attained, and in the first principal case we have to modify in a
suitable way only those ares of ¢ which bound the hyperbolic and
the parabolic sectors.
In a hyperbolic sector we effect this by choosing a point on each
of the two bounding base curves, and by drawing from those points
H and XK inside into the sector orthogonal arcs not intersecting one
another, Then there is certainly an are of a curve of the second kind
49%
( 730 )
joining a pot 4 of one of these orthogonal ares with a point C of the
other, and we bound the modified sector by the orthogonal ares HB
and CK and the tangent are BC.
If a parabolic sector is bounded by the base curves / and £’, it is
always possible to choose between them a finite number of base
eurves k,,k,,....kn, in such a way, that each kp» and #,11 can
be connected, inside the sector but outside the leaves lying in it,
by an orthogonal arc. By those orthogonal ares and the ares of base
curves joining their endpoints we bound the modified sector. The
simple closed curve c obtained in this way has a direction of tangents
varying everywhere continuously, with the exception of a finite number
of rectangular bends. To a definite sense of circuit of c’, which we
shall call the positive one, corresponds in each point of c' a definite
tangent vector, and for a full circuit of c’ that tangent vector
describes a positive angle 22.
We shall now consider two successive parabolic sectors, a, and
a,, Of which (for the positive sense of circuit) the first is positive,
therefore the second negative, and we suppose them to be separated
by a hyperbolic sector +. On the orthogonal arcs belonging to the
boundary of a, the given vector then forms with the tangent vector
5)
a
1
an angle (2 — — |= (measured in the positive sense), on the orthogonal
é 1
arcs belonging to the boundary of a, an angle (2n + = |ioe
The transition takes place along the tangent are belonging to the
boundary of fF, by a negative rotation over an angle a of the given
vector with respect to the tangent vector.
The same remains the case if we suppose a, to be negative, 2,
to be positive.
But if we suppose - to be an elliptic sector, then the transition
under discussion takes place along the tangent are bounding Ff, by a
positive rotation over an angle a of the given vector with respect to
the tangent vector.
As now the total angle, which the given vector describes for a
full cireuit of c’, is equal to the total angle which the tangent vector
describes plus the total angle which the given vector describes with
respect to the tangent vector, the former angle is equal to 2 (2 + n,—n,),
where n, represents the number of elliptic sectors, 2, the number of
hyperbolic ones.
Let further j be an arbitrary simple closed curve enveloping P,
but enveloping no other singular point, then we can transform c’ into
J by continnous modification in such a way, that at every moment
( 731 )
P, but no other singular point, is enveloped by the modified eurve.
If we consider for each of the intermediary curves the total angle
which the given vector describes by a positive circuit, then on one
hand it can only have continuous modifications and on the other
hand it must remain a multiple of 2%. Thus it remains unchanged,
and we can formulate :
TurorrM 5. The total angle which, by a cirewt of a simple closed
curve enveloping only one point zero, the vector describes in the sense
of that circwt, is equal to «(2+ n,—n,), where n, represents
the number of elliptic sectors, n,
the number of hyperbolic ones, which
appear when a vicinity of the point zero is covered with tangent curves
not crossing each other.
In particular for source points, vanishing points and rotation points
this angle is equal to + 22.
We now surround P with a simple closed curve x which can be
supposed as small as one likes, and we leave the vector distribution
outside x and on x unchanged, but inside x we construct a modified
distribution in the following way :
Let us first suppose that for a positive cireuit of x the vector
describes a positive angle 2na. From an arbitrary point Q inside
* we draw to x n arcs of simple curve (,,8,, ..-@n, not cutting
each other and determining in this order a positive sense of cireuit.
Let us call ,x the arc of x lying between 8, and 8,4;, and G', the
domain bounded by 8,, ,x and 3,4). Along 8, we bring an arbitrary
continuous vector distribution becoming nowhere zero and passing on *
into the original one. Then along @, such a one passing on x and
in Q into the already existing vectors, that along the boundary of
G, positively deseribed the vector turns a positive angle 2a. Then
along 8, such a one passing on # and in Q into the existing vectors,
that along the boundary of G, positively described the vector turns
a positive angle 27, etc.
As the angle described by the vector in a positive circuit of x is
equal to the sum of the angles described in positive circuits of
the boundaries of the domains G,, G,,....G,, it is finally evident,
that also for a positive circuit of (, the vector describes a positive
angle 22.
In each of the domains G, with boundary x, we choose a simple
closed curve c, not meeting #,, of which in a suitable system of
coordinates the equation can be written in the form a y=.
Inside and on c, We introduce a finite continuous vector distribution
vanishing only in the point (0,0),, which is directed along the lines
( 732 )
=e and from the point (0,0),. This vector describes along ¢, a
Ly
positive angle 22, just as the existing one along x,. If then according
io Scnorneiims we fill the annular domain between z, and e, with
simple closed curves enveloping each other and as functions of a
cyclic parameter passing continuously into each other, then we ean
thereby at the same time make the vector distribution along x, pass
continuously into that along c,, and in this way give to the annular
domain between z, and c¢, a finite continuous vector distribution
vanishing nowhere. Inside x, we have now obtained a finite con-
tinuous vector distribution, having but one point zero, namely the
point (0,0),, and that a source point of very simple structure, which
we shall call a radiating point
And the inner domain of * is covered with a finite continuous
vector distribution passing on * into the original one and possessing
inside x, instead of the original point zero P, m radiating points.
Let us furthermore suppose that for a positive circuit of # the
vector describes a negative angle 22. In an analogous way as
above we then divide the inner domain of # into 7 regions G, with
boundaries «,, and we bring along each of these boundaries such a
vector distribution, that for a positive circuit of x, the vector describes
a negative angle 27. ;
The curves c, are introduced again as above, but inside and on
c, we introduce a finite continuous vector distribution vanishing only
in the point (0,0),, which is directed along the ines 2,7) —@ sllor
a positive circuit this vector describes along c, a negative angle 22,
just as the existing vector along %,.
So the annular domain between %, and c, can be filled up in an
analogous way as just now with a finite continuous vector distribu-
tion vanishing nowhere, and the whole distribution inside %, possesses
then only one point zero, namely the point (0,0\,, having four
hyperbolic sectors of very simple form (the four separating parabolic
sectors are each reduced to a single line), which structure we cha-
racterize by the name of reflexion point.
After this the inner domain of x% is covered with a finite continuous
vector distribution passing on x into the original one and possessing
inside *, instead of the original point zero P, m reflexion points.
Let us finally suppose that for a circuit of % the total angle
described by the vector is zero. We can then choose inside z# such
a simple closed curve c, that in a suitable system of coordinates its
equation can be written in the form a* -+ y*? = 7r?. Inside and on ¢
we introduce a finite continuous vector distribution vanishing nowhere,
( 733 )
which is directed along the lines y= «. The total angle described by
this vector along ¢ is zero, just as the one described by the existing
vector along x. The annular domain between # and c can thus be
filled up as in the two preceding cases with such a finite continuous
vector distribution, that the whole distribution inside x is now free
of points zero.
So we can formulate:
TueorEM 6. A jinite continuous vector distribution with a finite
number of points zero can be transformed, by modifications as small
as one likes inside vicinities of the points zero which can be chosen
as small as one likes, mto a new finite continuous vector distribution
which has as points zero only a jinite number of radiating points,
and a finite number of reflection points.
In particular those points zero about which the angle, described
by the vector for a positive circuit, is positive, are broken up into
radiating pourts; those about which this angle is negative, are broken
up into reflexion points; whilst those for which it is zero, vanish.
In a following communication we shall extend this theorem to
distributions with an infinite (denumerable or continuous) number of
points zero.
§ 6.
Remarks on the tangent curves and singular points on a sphere.
If we have on a sphere a finite continuous vector distribution
with a finite number of singular points, then the reasonings of § 1
lead with small modifications to :
TuxoreM 7. A tangent curve to a finite continuous vector distribution
with a jinite number of singular points on a sphere is either a
simple closed curve, or save its ends it is an are of simple curve, of
which the pursuing as well as the recurring branch either stops at a
point zero, or enters into a simple closed tangent curve, or converges
spwally to a circumference consisting of one or more simple closed
tangent curves.
From this ensues that also on a sphere a tangent curve cannot
return into indefinite vicinity of one of its points, after having reached
a finite distance from it, unless it be, to close itself in that point.
Out of the reasoning of § 1 we can deduce farthermore without
difficulty that a fundamental series of closed tangent curves with
the property that of the two domains determined by one of them,
( 734 )
one contains no points of the preceding, the other no points of the
following curves, converges either to a single singular point, or to
the outer circumference, consisting of simple closed tangent curves,
of a domain or set of domains.
Let now an arbitrary finite continuous vector distributionon a sphere
be given. On account of § 5 we reduce it by means of in-
definitely small modifications to a “reduced distribution’, possessing
as singular points only radiating points and reflexion points, and we
investigate the tangent curves of that reduced distribution.
A closed tangent curve can possess no radiating points, but reflexion
points it can possess (its tangent direction shows there a rectangular
bend).
On the other hand a tangent curve ean only stop at a radiating point.
We now consider an arbitrary tangent curve: according to theorem
7 it is either an are of simple curve joining two radiating points,
or it gives rise to a simple closed tangent curve j,, which divides
the sphere into two domains G and G’.
Then on 7, no radiating point can lie, but we shall prove, that in
G as well as in G’ there must lie one.
If namely there were no radiating point in G, we could consider
within G a new tangent curve, and as this would not be able to
stop in G, it would on account of theorem 2 give rise to a new
simple closed tangent curve j, enclosing a domain G, being a part
of G. Within G, we could again consider an arbitrary tangent curve,
and in this way we should arrive at a simple closed tangent curve
j, enclosing a domain G, being a part of G,.
Continuing this process indefinitely we construct a fundamental
series of closed tangent curves j,,),,J.5J3,-.-»» Which cannot con-
verge to a single singular point, as neither a radiating point nor a
reflexion point contains closed tangent curves in an indefinitely small
vicinity. On account of the remark made at the beginning of this §
there must thus be at least one domain G,,, bounded by a simple
closed tangent curve j,, and contained in each of the domains
GGG
Within G. we could again construct a closed tangent curve 7,41
bounding a domain G4; being a part of G,, and we could continue
this process to any index of the second class of numbers, which
on the other hand is impossible, as the set of domains G— G,,
G,—G,,... Go—Go4i,... G.—Gr4i,... must remain denumerable.
So we finally formulate :
Tunorem 8. A reduced distribution on a sphere possesses at least
two radiating points.
( 735 )
Mathematics, — “The oscillations about a position of equilibrium
where a simple linear relation exists between the frequencies of
the principal vibrations.” (Second part). By H. J. E. Brrn.
(Communicated by Prof. D. J. Korrnwne.)
(Communicated in the meeting of February 26, 1910).
iS — 4. 1)
§ 14. In this case the ordinary expansions in series hold as
(Ceres ; hen? 4
long as ~ is great with respect to ee) (see page 7 of the paper by
n f =
1 1
i)
Prof. Kortrwre, mentioned above). The difficulty arises as soon as ~
ny
has fallen to the order ie The calculations not getting simpler
YW
with the absence of a residue of relation, we shall immediately
assume a residue of relation of order h’.
When the relation
n, +o = 3n,
exists and we proceed to investigate with a view to this which
terms in (2) (page 620 of these Proceedings) become disturbing in
the sense indicated in § 3, we easily see that no terms of order /”
appear among the disturbing ones. So when determining the first
approximation we may omit the terms of order h* in the equation
of the surface, which terms agree with the just mentioned terms
of order /?. It then becomes
1 :
a aA (c,a* + cy” + e,a* + e,a*y + e,07y? -+ e,xy*® + e,y*);
for we need not take for the first approximation in the equations
of movement any terms of higher order than h’,
The abridged equations of motion, containing only terms of order
h, still run as follows:
a+ 2c,2=0,
y + 2¢,y = 0.
Now
la eS (VO Gy SS (VO
are the frequencies of the principal vibrations.
1) For the case S=3 see 1% part, pages 619—635 of these Proceedings.
( 736 )
So
2c, = (8n, — 0)’.
We change the abridged equations into:
x =e 05
y = Oey 10)
but then we must admit into the function RR a term:
3n, OY’.
The canonical solution of the abridged equations is:
Va
— 1 cos (n,t + 2n,8,),
n,
Va
y = —— cos (8n,t + 6n,8,).
Bn 5
To find which functions the «s and ;’s are of ¢, we must in-
vestigate which form the function AR now assumes.
§ 15. As the disturbing terms in the equations of motion are of
order h® we shall find that «,, a,,8,, and B, can never exceed
order h. Of this we may make use to simplify the terms of order /*
containing v,7,7?, and y?. We may namely replace in those terms:
2 DY ec ear
Te Sin Oe = SOR a
a a == (Ne bh
and
Wr xe — 9n,* y.
Then the equations become :
a+ n> a + de, a® + 8¢e, ay + 2e, wy? +e, y*® + ;
4 c 6
n,
'
ite
u 2
ey 1
(a, + 9a,) e — —-(2?+ 81y7)e#=0
v
yy + 9n,* y — 6n, oy + e, w* + 2e, wy + de, wy? + 4e, y*? +
oa 18n,°
al
on yan Q
+ (a, + 94,)y — > (w* + 81 yy = 0.
Now the terms of order /* are all disturbing except e,y* in the
first and 3e, vy® in the second equation; so these may be omitted.
The terms 38e,27y in the first and e,7* in the second equation
owe their disturbing property to the supposed relation.
The remaining terms are always disturbing, also when no relation
exists.
(737 )
To transform the equations to such a form that the disturbing
terms may be regarded as derivatives of one and the same function
resp. to 2 and y, let us consider the term with wy* in the first and
that with 277 in the second equation. If we substitute the expressions
found above as first approximation for w and y in these terms, after
the development of the products and powers of the cosines among
others terms will appear, differing only in coefficient from the
expressions indicated for « and y; the remaining terms which appear
are not disturbing. From this ensues that we may replace :
: ‘ n IL Gz.
in the first equation: «w° by ign
57,
. ; a
in the second equation: wy by > —, y.
A Dao
Accordingly the equations may be written :
2n,° , re 5 e; ibe
wate =|, 4e) — ta a® + de, x* y + On? Of, == a: OF 4) 4) == Ue
d ER ‘
3 . 1458n,°\ |
Oe oI, aT ees) — a jr 4p ath Se
g
‘ oth 8ln,* ,
S| Wii @ == ei a, + 62, \\j =e
/
2
1 g
We thus see that they take the form of :
‘ ee net as
a+ Dal ar eas |
a“
\ OR
y + 9n,? y—— = 0;
Oy
where:
§ 16. We must now write / as function of the «@’s and p's by
substituting for 2 and y, in the expressions obtained, the expressions
by which they are represented at first approximation, and by retaining
only those terms in which ¢ does not appear explicitly. Thus we
arrive at:
1 1 BS kale
—k= 3 aa,* + ba, a, + ‘i ca,” + yo h? a, + m, a,? a,? cosg,
where :
8's, is now:
dp,
dt
where iV is
From this
therefore
*-
i. ==
P=
3
Py
2Nm, a,? a
2
— 2Nm, a,
aa, + ba, +
O08 n,'
rt)
80°
6x, (8, —B,)-
The system of equations giving the time-variability of the «’s and
1
2 2 GOs Do
3
ba, + ca, + o' hk? + 5 mM COs,
put instead of 3n,.
system it appears at once that :
So we put:
da,
dt
da,
+——=(Q,
dt
a, + a, = constant.
ba 7D) She ea thal
Celanese 10m
’
Furthermore according to § 4:
= aa,’? + ba, a, +
a
a
is an integral of the system.
By introduction of
SI (=)
c Gl ==6) cos p = p>? 4 gs +,
2 cos & ;
1
$ this integral takes the form of:
(17)
yt Oy Fe Ti Duy So
5 CH,” + © h? a, + m, a,? a,? cos p = constant
(18)
( 739 )
where :
where C represents a constant, dependent on the initial state.
The first equation of (17) becomes by the introduction of &:
d 2 ees
=o =—m, RY? N*h? 5 Vals GOs 0 6 5 ee (()
dt 9
By eliminating g between (18) and (19) we arrive at:
dG 2 ga,
———— = + —m, R,? N* kh’. dt.
SoS) (95 96-7)" 4
Let
pHe) = 6) (U2) (= 95 22s
then f(<) >9 for the initial value of 2, but f(2) < O for ¢ =O and
£=1; so f(c) becomes zero for two values C, and ¢, lying between
0 and 1.
So 5 will generally vary periodically between two limits. It may
be expressed in the time with the aid of elliptic functions, after
which 3,, @,, “, and y are also known as functions of the time.
For the extreme values zero and one of the modulus x of the
MeN) do: ts 2c re
elliptic functions (= oT cuthe cquanion (=) 0
(8—C,) (4—S,)
has two real roots « and 2 besides £, and ¢,) we get special cases.
Osculating curves.
§ 17. At first approximation we have found :
Va
o— * cos (n,t + 2n, B,),
n,
Va ae
y = —— cos (8n, t + 6n, 83),
n
1
where the e«’s and 3's slowly vary with the time.
By introduction of © and g and by change of the origin of time
we find that we may determine the equation of an osculating curve
by eliminating ¢ between
{ 740 )
— R, hy Cc cosn,t
and
1
y= 3 R,hV1—E cos (3n, t — ¢).
For ¢ and g we must substitute the values, which these quantities
have at the moment for which we wish to know the osculating
curve.
The osculating curves are Lissajous curves answering to the value
for the ratio of the periods of the vibrations. They are described
3
9, a
in the rectangles having as sides 2 R,hVCE and — R,hAV1—C.
fo) c 0 = 3 0
As € varies between two limits the rectangles in which the curves
are described lie between two extremes. The vertices lie on the
DD)
circumference of an ellipse having 2 Rk, / and = R,h as lengths of
2)
axes.
The shape of the curve described in a definite rectangle is stil
dependent on the value of g, i.e. on the value of the difference in
phase at the moment of the greatest deviation to the right.
To an arbitrary value of g the wellknown Lissajous curve with
it ON :
two nodes of fig. 8 answers. For gy = OL ihe curve is sym-
_ ~
metrical in respect to the axes; the nodes lie in the Y-axis on
1
either side of O at distances — #, h (fig. 9). For » —0 or 2 we get
a curve, which is described in both directions alternately and which
passes through @Q (fig. 10).
In fig. 11 we find some of those osculating curves represented
for a definite case of motion: fro belonging to gm =a; theo for
gy = 5, and one for an arbitrary value of #(> ie
i}
a a
de ;
Out of (19) follows that — =O for sin g—=O. In the extreme
at
rectangles the curves are described which we have for g—=0 or a.
Now a number of different cases are possible, of wlich we get a
clear representation by representing equation (18) in polar coordinates.
In fig. 12 some of the curves obtained in this way are represented,
where g is taken as polar angle, } 1—< as radius vector. The different
shapes of the curves correspond to the roots of the equation:
OL — fy) — (pgs + HO + ss + (20)
( 741 )
The cases are:
1. The curve indicated in the figure by --- keeps to the right or
to the left of O,; g changes between two limits; the limits are
: ont : T
equal and opposite; the positive is smaller than >. For the extreme
<
values of ¢ we find g either both times O or both times 2.
. . . a .
2. The curve — —- — intersects the straight line g = 5 at two points
above ©, and at 2 points below 0,. For the extreme values of ¢
we again find » either both times O or both times a.
3. The curve consists of two closed parts (a continuous line in the
figure), which surround 0,. Now g assumes all values. For the
extreme values of ¢€ p= 0 one time y=O and g==2 the other.
The transition case between 2 and 3 is represented by —.__. _.
Fig. 11 relates to the 2" case; for the two extreme values of £
we find p=.
Special CASCS.
§ 18. These occur for the extreme values of the modulus ~ of the
elliptic functions; two roots of equation (20) have coincided.
1. x=1. The elliptic functions pass into hyperbolic ones. The
geometrical representation just now discussed of the relation between
¢ and mg and already mentioned as transition case between the
second and third cases bas a node situated on the axis of the angles.
The form of motion approaches asymptotically to a form of motion
belonging to y= 0 or p=7z.
2. x=O. The elliptic functions pass into goniometrical ones. The
curve of fig. 12 becomes an isolated point C’ (special case belonging
to the 1st case of §17 as limiting case) or it consists of an isolated
point and a closed curve (special case belonging to the 3° case of
§ 17 as limiting case). If the initial value of © coincides with the
twofold root of (20) we find that © remains constant: @ is conti-
nually 0 or a. Thus the same curve is continually described.
Arbitrary mechanism with 2 degrees of freedom for which S= 4.
§ 19. In the case that »,=3n,+ 0 the terms of order /? can
give no disturbing terms in the equations of motion.
So we may write:
U
|
ng + ana + Uy
( 742 )
where Ll/, represents a homogeneous function of degree 4 in q, and
q.. Furthermore we find:
T=49,4+44, 4 $7.4? Pigg +4 Pog.
where :
P= 4,95 4+ 44% +d»
Py = 6, 9)? + 52 91 2 + 9s M's
Py = 6, gq," + 63 91 Ga + 3 Gas
the a’s, 6’s, and c’s being constants.
The equations of LAGRANGE become :
i i ra soe 1 OP, ue ORe :
Wtny i= JES Uf Peds = 9 On, VQ 00; Oh Oe
1 OP, OP, cing OU,
iF 9 0 = 0 G38 a Ry, by
2 vi VE vir
Qs site De Cy == Je h a Ise Qs ==
Hae CIM ON toe IR 10, een
Sicalieae 4A nS q, ¢ UP .
209, Og) Soa, 1 eg ame
In the same way as was done in §15 we may replace q,, q,,
q,’, and q,” in the terms of order /* by others.
Now in the first equation a term — a@,q,q,q. appears which
we must consider separately (in the second equation also there are
terms containing q, y,, but these are not disturbing).
We introduce for this a new variable q', in such a way that:
' 1 °
mat tk Cr the Ghp
Then we find:
a, Jo (1 h ts 9°) + 4,91 1 qos
bo}
Reef ae te
q1 = 6h ar Ze COR >=
where q, and q, in the terms of order 4° may again be simplified.
Of the terms now appearing in the equations of motion the following
are disturbing: in the first equation those with /7q,, q.°, q,’°q2 and q,q,°,
in the second those with /*q,, g,*°, g.° and q,’q,. Now just as in § 15
the terms with q,g,* in the first equation, those with q,*q, in the
second equation may still be simplified.
If we perform these calculations the result proves that the terms
of order h* to be inserted in the equations may be put in this form ;
Ph?q, + eq,7G, + ¢g,° in the first equation.
Qh?q, + fq? + 4q,° ., , second is
( 743 )
Here P and Q are homogeneous quadratic functions of a, and
Va, ; and
1
Coy (82,7 — n,*) a, + b,n,? — 3),
1
a 2 fo} 2
ee a Ot ate
2
(The terms —3/ in e and —/ in / originate from the term
lq,°d, appearing in U/,).
In the terms of higher order we may substitute 8n, for n, in the
coefficients. We then find:
1
3 (-pa tae Jara,
1
i — (- Un ae 30, n,? — I.
So we find that
C= 37
We may now write the equations of motion:
; . oR
ht Mn = ay," |
vB
Ee Foe ca
VE) St PT Fe Hee
Ys
where
1 1 1 1
R= = Pig? + > QW'as? + fara + Zon‘ +z 4s".
So they get the same form as for the simple mechanism so that
in case S=4 also the horizontal projection of the point moving
over the surface may be regarded as representative point for an
arbitrary mechanism with 2 degrees of freedom.
S ==.2.
§ 20. So we suppose that the relation exists:
7; =, | 0;
o a Ne
where = is of order (=) However, as we have already seen in
1 1
the cases S—3 and S=4 in which way such a residue of relation
may be taken into account by inserting in the function R a term
with oa,, we restrict ourselves here to the case that the residue of
relation is zero, therefore:
50
Proceedings Royal Acad. Amsterdam. Vol. XII.
( 744 )
For the surface the lowest point is an umbilical point. To this
belongs as special case the surface of revolution with the Z-axis as
axis of revolution, which case is treated by Prof. Korrewne at the
close of his treatise quoted before.
Omitting the terms of higher order than /‘, because in the equations
of motion we admit no terms of higher order than /°, and omitting
the terms of order h*, because in the equations of motion no terms
of order h? can be disturbing, we may write the equation of the
surface :
1 2 2 4 3 24,2 3 4
— - (c,v? +- c,y? + e,x* 4-e,a°y + e,n°y? + e, ay® + e,y*),
€
where we avail ourselves of the fact, that by means of a rotation
of the system of coordinates round the Z-axis the coefficients of
vy and a*y may be rendered equal.
The solution at first approximation is:
J
c— Vas cos (nt +- 2np,),
n
a
Ve cos (nt + 2nf,);
n
Y=
where 2 =V 2¢, =V 2c,.
§ 21. Let us now pass to the simplification of the equations of
motion. Corresponding to what was said in §15 for the case S=4
we may here replace in the terms of order h*? of the equations of
motion :
2? by a, —n’x’,
y na, — n'y’,
x 3 — n'a,
nas — ny.
The equations become :
2 n‘ an*
wtniut 4e,0*+ 8¢,x7y + 2e,vy?+e,y* + ? (a, +a,)¢— ? (v?+y?) e=0.
Dy 8
F n‘ <
Wnty beet + Peary + Seyey? + Aes" + | (a tag)y—— (ety) y=0.
Here we may omit no terms, for all the terms of order /° are
disturbing. The equations may be written as follows:
25 OR
z+ nae ——= 0,
ie
4 : OR _ or
¥ AF n 7] Oy cai aa?
( 745 )
where we must take
— Ree" + e,0*y -| ea7y? + egy? + egy* +
n‘ n®
stare (Ca ts) (Etat oo i Ye)
29° 29
§ 22. If we substitute in the function F for z and y the expressions
assumed at first approximation and if we retain only those terms
not containing ¢ explicitly, we arrive at
+
1 i
i —— a aa,” + ba,a, + — ca,” + faa, sin? p + f, (a, + @,) V-a,4, 008 g,
where
de, +5 n
o— ——> —
4n‘
3e n°
j= 3
Sn‘ + ea 8q? 2
Oe, n*
a —<— ==9
89° F
f= es ee n°
7 ant 4g? ;
: de,
Is = =— b)
Sn
y = 2n (8, — B,).
The system of differential equations indicating the time-variability
of the a’s and §’s becomes:
= = — 4nfa,a, sin 7 cos p + nf, (a, + a,) V aa, . sin ~ \
da, : Seman f3:
7a = + 4Anfa,a, sin ~ cos p — 2nf, (a, + a,) Vaa, - SIN YP,
(21)
d 1 — ;
aes =aa, + ba, + fa, sin? +—f,| 3V ae, +4, + \ cos Y,
dt 2 a,
dB,
a = = ba, + ca, + fa, sin? yg + at 3 Viaje, cosep.
It appears at once from the Ls ae
50
a, + a, = constant.
50*
( 746 )
Another integral is according to § 4:
1 1 ——
Pete ig ba,a, + oe ca,” + faa, sin’? p + f, (a, + @,) Vaa, cos (p—const.
~~
a
§ 25. ‘The results become very intricate for the general case. This
is evidently a consequence of the circumstance, that in the function R
appear cosg and sin? g or in other words cos g and cos 2y. The
problem is considerably simplified if we suppose /, = 0, thus e, = 0,
which means, that we suppose the planes XZ and YZ to be planes
of symmetry for the surface.
Let us again introduce ¢, so that
RAG, On hh? (i —");
then the last integral may be written in the form:
VEA—Ljcosp=pl>+qt+r,
so that we can perform again all integrations in finite form, and «
and y may then be found as functions of the time.
Osculating curves.
§ 24. We return to the general case and shall proceed to investigate
what becomes of the osculating curves. They are ellipses whose
equations are found by eliminating ¢ between
cos (nt + 2nf,)
Va
c—
n
and
= Yb cos (nt + 2nf,).
n
By changing the origin of time we see that for a definite osculating
curve we can also find the equation by elimination of ¢ between
Va,
x“ == —— cos nt
n
and
a
= ee cos (nt — @p),
so represents the difference in phase.
When g has an arbitrary value, the ellipse has an arbitrary shape
and position.
If gy =O or a a straight line is described passing through OQ.
x : ‘
If ~ = > the axes of the ellipse lie along the axes of coordinates.
a
( 747 )
The ellipses are deseribed in rectangles having their sides parallel
to the axes and whose vertices, as is evident from
a, + a, = constant,
lie on the circumference of a circle.
To investigate the change in shape and position we may write
down the well-known relations which may serve for the calculation
of the axes of the ellipse and the angle of inclination of the long
axis with the X-axis. If Ad and Bh are half the larger and half
the smaller axis and if 6 is the angle in view, then these relations
become :
] 1 a A
p= ee (1)
PAE Je ROR GID:
1 n'‘ 2
ABS aya, sin? gy’ ©)
2 V aa,
tg 260 = — =. COS &. Se te ON. oo en Ai)
a, — a,
From (1) and (2) we now deduce at once: The sum of the
squares of the axes of the ellipse is constant.
§ 25. From what we have just found we can easily prove that
in case the surface is a surface of revolution the osculating ellipse
has an invariable shape.
Then namely we find:
—R=ha(a,+a,)’ + fa, a, sin’ g,
where:
8e, n®
= By 5
ea Op n?
J=— ou
As
4 a(a,t+a,)? + fa, a, sin? p = constant,
and also
a, + a, = constant,
we find
a, &, sin® ~ = constant.
From (2) it then follows that
ABh? = constan',
from which in connection, with the close of § 24 we may con-
clude that
( 748 )
Ah = const. , Bh = const.,
and so our proposition is proved.
If in further consideration of the case of the surface of revolution
we wish to see in what way 6 varies, we have to write down the
differential equations giving the variability of the @’s and #’s. They
now become:
da, A .
—= --4nfa,a, sng cop ,
dt
da, ; ,
—_= 4 nfa, a, sin pcos®@ ,
dt ;
dB, a
ao (a, +a,) + fa, sin® gy ,
dp, rN anes
oe a(a,ta,) + fa, sin? .
. 4B, dp, :
We see that in ; and - 3 on equal constant term a (a, +-@,)= a R,? h?
a €
appears. This means that the frequency 2 is modified by an amount
of 2na R,?* h*. :
When we now differentiate according to ¢ the relation
a 2V aa,
a, — a,
tq 26 cos ~p
we may arrive after some reduction at:
oY a AB er.
dt c
from which it is evident, that the ellipse revolves with a constant
angular velocity.
These results agree quantitatively with those found by Prof.
KORTEWEG.
§ 26. The change in shape and position of the osculating curve
does not seem to become simple for the general case n, = 7,.
Let us therefore restrict ourselves to jthe case e, == 0; then the
XZ-plane and the YZ-plane are planes of symmetry for the surface.
The first equation of (21) now becomes
de, : ,
— = — 4nfa, a, sing cos @.
dt
Or by introduction of C:
at
a ae 4nf R,? h? ¢ (1—f) sin @ . cos &.
¢
( 749 )
The relation between £ and g becomes:
Pat pee Saint Means ty ns oe (22)
c(1—¢)
Here 5 again varies periodically between a greater and a smaller
dz hate
value. Now however — may become. equal to 0 for sing =0
at
and for cosy =O. Thus barring special cases there are 3 general
Cases :
1st. For the extreme values of ¢ cosy =O. Then in the extreme
rectangles ellipses are described with the axes along the Y-axis
and Y-axis (fig. 18).
2.4. For the extreme values of £ sin =O. In the extreme
rectangles straight lines are described (fig. 14).
3', For one of the extreme values of € sin 7 =O, for the other
cos ~ = 0. (fig. 15).
Special Cases.
§ 27. These we have again for the extreme values of the modulus
x (* has the same form as in § 16) of the elliptic functions; which
occurs when 2 roots of the equation:
f(\=(p? +45 +E —D — (pS + oF 4+} =0
have coincided.
The special case corresponding to £B of § 9 and the second of
§18 occurs here in two ways. We refer to the cases in which
the same straight line is continually described (continually sin g = 0;
when the surface is surface of veyoiution, this form of motion
is possible in every meridian) and that continually the same ellipse
is described (cos p =O; this becomes for the surface of revolution
the uniform motion in a parallel circle).
The special case corresponding to A of §9 and to the first of
§18 exists here too. The form of motion approaches asymptotically
the motion in a definite ellipse.
Envelope of the osculating curves.
§ 28. Two cases may be indicated, in which the envelope assumes
a simple shape.
1. For p=—1, q=1 in (22) (the case of a surface of revolution),
the envelope has degenerated into two concentric circles.
2. For p=0O andq=O in (22) the envelope has degenerated into
two pairs of parallel lines, enclosing a rectangle.
Arbitrary mechanism with 2 degrees of freedom for which S=2.
§ 29. The equations of LaGrancE get quite the same form here
(750 )
us for S=4. In the terms of order 4* we may in the same
way substitute other terms for the terms dis as q,?, and es
: ‘Nee OP.
Then we have to reduce the terms — —— q,q, and — 4, Gs -
VE 07,
To this end we introduce q', and q', in such a way, that
! 1 9 1 °
CES Rea Sor Tie Ob Spe CH ti CSc
1 1
Dis 9s ote eq CHChs se ry iin ee
4
After these reductions it is evident that the terms of order /* in
the first equation assume the form:
v a, 1 a,
— a, ae + (a,—b,+¢,) a ents 9 eames n? EB
1 me 1
+ 2a, 9,° + (F +h) Q1” Iz — (@,—26,+¢,) 9, 92° — G Oy 3,
4
We now substitute a q,, for B*h?q,. This is allowed, because
Oe 4
substituting g, = Bh cos (nt + 4) in = q,', We obtain besides a term
Bh*q, terms which are non-disturbing.
We wish to investigate whether the disturbing terms in the two
equations are again derivatives of the same function. For this we
need not consider the terms with qg, and q,’, in the first equation
and those with qg, and q,* in the second. The remaining terms become
in the first equation :
1 2 9 2 1 1
rr a,+6, "1 I (a, 26, ‘F Cy) 1 92 a= 3 b, =F ry C3 ds
In the second :
gil 1
ay G th) 1° a (a, —26, +¢,) re qs aa (?. = 2 “) ver qa"
qe
So finally we find that the disturbing terms are derivatives of the
same function ; so the equations become:
ce
Qh ts eda a asi 0,
|
“ a. OR
qs + n Vs a 07, — 0 cy
where R= Pi? g,* + Qh? qy? + (Oh, :
when P and Q are homogeneous quadratic functions of Ve, and
Ve, and when U, is a homogeneous function of order four of q, and
q,. The results found for the simple mechanism hold therefore for
an arbitrary mechanism with two degrees of freedom.
( 754 )
Mathematics. — “The cubic involution of the first rank in the
plane.” By Dr. W. van per Wovupr. (Communicated by Prof.
P. H. Scwovre.)
1. If V is a plane it is in different ways possible to arrange
the points of V in groups of three in such a way, that an arbi-
trary point forms a part of only one group. If P, is a point of V
there must exist between the coordinates of P, and those of the
other points of the group, to which P, belongs, some relations by
which those other points are entirely determined. It is however
possible that P, can be chosen is such a way that one of these
relations is identically satisfied; in that case P, forms part of an
infinite number of groups.
We now start from the following definition :
The points of a plane V form a cubic involution of the first
rank, when they are conjugate to each other in groups of three in
such a way that (with the exception of some definite points) cach
point forms a part of only one group.
A triangle of which the vertices belong to a selfsame group we
eall an involution triangle; each point which is a veriex of more
than one, therefore of an infinite number of involution triangles, we
call a singular point of the involution; each point coinciding with
one of its conjugate points is called a double point. If one of the
sides of aa involution triangle rotates around a fixed point, then the
third vertex of this triangle will describe a right line or a curve;
we shall restrict ourselves in this investigation to the case, that one
vertex of an wvolution triangle describes a right line, when the opposite
side rotates around a fixed point.
2. When the points of a plane V’ form a eubie involution of the
first rank which satisfies the just mentioned condition and which we
shall furtheron indicate by (7;,), we can conjugate projectively to
each point of V the connecting line of its conjugate points. Each
vertex of an involution triangle and its opposite side are pole and
polar line with respect to a same conic, which in future we shall
always call y,; each involution triangle is a polar triangle of y,.
It is clear that reversely not every polar triangle of y, is an involu-
tion triangle of (¢,); for each point of V is a vertex of an infinite
number of polar triangles of y,, but of only one involution triangle.
If however S is a singular point of the involution, then S must
be a vertex of an infinite number of involution triangles, thus each
polar triangle of y, having S as vertex is at the same time an
( 752 )
involution triangle. If we assume a point G of the conic y, as a
vertex of an involution triangle, then one of the other vertices must
coincide with G, so G is a double point of the involution; y,, the
locus of these double points, is the double curve of the involution.
Each line 7 whose pole with respect to y, is no singular point of
the involution is a side of only one involution triangle, namely of
that triangle having the pole of / as vertex. On the other hand
each line whose pole is a singular point is a side of an infinite
number of involution triangles all having that point as vertex. From
this ensues that also the lines of V’ form a cubic involution (?’,) of
the first rank; the polar lines of the singular points of (¢,) are the
singular lines of (v';), the tangents of y, are its double lines and y,
is its double curve. Both involutions are with respect to y, polarly
related.
The involution triangles of y, are all polar triangles of a selfsame
conic y,, which is at the same time the double curve of (i,). The lines
of V form an involution (iy) which ts with respect to y, the polar
jigure of (i). Each polar triangle of y, having a singular point of
the involution as vertex is at the same time an involution trian yle.
3. We make a point describe a line a, and we ask after the locus
of its conjugate points. If we draw through A,, the pole of a, with
respect to y,, an arbitrary line p,, then P,, the pole of p,, lies on
a,, whilst the two points conjugate to P, lie on p,; these two points
lie also on the locus under discussion. Moreover A, itself is conjugated
to two points of a,, so that A, is a double point of this curve and
, ¢uts this curve in a double point and two
points more. Hence we find:
Lf one of the vertices of an involution triangle describes a line a,,
then the two others describe a curve a‘ of order four with a node
in A,, the pole of a, with respect to y,. As a, cuts all singular
lines, all singular points le on a*.
A tew properties of this curve @* may still be given here:
1. Let A, and A, be the points conjugated to A,, then the polar
line of A, with respect to y, — that is the line A,A, — must
cut @ in A, and in the points forming with A, an involution triangle.
These two points are A, and A,. So will «* be touched im A, by
the lines A,A, and A,A,; A, and A, are points of intersection of
a
each line through A
and a’.
2. Besides in A, and A, the curve a‘ will be intersected in two
points more by a,; these points are at the same time the points of
1
intersection of a, and y,.
( 753 )
3. Besides in these last points @* will still be cut by y, in 6 points
more, the tangents in these 6 points to a@* must pass through
A,. From this ensues that a‘ is of the tenth class, by which the
PLickrrR numbers of a* are entirely determined (n= 4, m= 10,
d=1). This holds, for it is easy to investigate that a@* cannot
possess a double point differing from A,.
4. If a vertex of an involution triangle describes a line, on which
lies a singular point, the curve described by the two other vertices
degenerates into the polar line of that singular point and a curve
which must be of order three. If a vertex of an involution triangle
describes a singular line s, then one of the other two vertices will
be a fixed point,’ namely the pole of s and the other point will
describe s itself and as many other lines as there are singular points
on s. As both points together must describe a curve of order four,
three singular points will lie on s. In like manner each singular
point is point of intersection of three singular lines.
If now again a, is an arbitrary line and if «* has the same signi-
fication as above, then the curve «* will cut a line 6, four times;
from this ensues that four times a point of @, and a point of 6, are
vertices of a selfsame involution triangle. Thes2 vertices we call
P,,Q,, R.,S, and P,, Q,, R,,S,, whilst the third vertices of these
triangles may be represented by 7,, Q,, R,,.S,; farthermore 7’, is
the point of intersection of a, and 6, and 7, and 7, are the two
points forming with 7’, an involution triangle.
If now a point describes the line 6,, then its conjugate points
describe a curve $* of order four; @* and #* have 16 points of inter-
section. These are:
1. the two points 7’, and 7,;
2ethe: tour points: P,Q; , F.0s,;
3. ten points more having the property that to each of them two,
so an infinite number of pairs of points, are conjugated and which
are thus the singular points. Therefore:
The involution (i,) has 10 singular points; their polar lines are
the 10 singular lines of (v’,).
These singular elements have such a position that on each of these
lines three of these points lie and that in each of the points three of
the lines intersect each other; so they form a configuration (10,, 10,).
If s,, is a singular line and 4,, its pole with respect to y,, then
there are besides S,, still 6 singular points not lying on s,,. If S,,
is one of these points and s,, the polar line of \S,,, then the point
of intersection of s,, and s,, is at the same time the pole of S,,S\y
( 754 )
This point forms an involution triangle with S,, and with another
point of s,, and an other one with S,, and with a point of s,, (an
“other one’, as S,, and S,, which do not lie on each other’s polar
line cannot be vertices of a selfsame involution triangle) ; so the point
of intersection of s,, and s,, is also a singular point and S,,S,, a
singular line.
Yach line connecting two singular points not lying on each other's
polar line is a singular line; each point which is the point of inter-
section of two singular lines not passing through each other’s pole is a
singular point.
On s,,, the polar line of S,,, lie 3 singular points; the remaining
6 are connected with S,, by 3 singular lines. So each line connecting
S,, with one of the singular points on s,, is not a singular line,
as only 3 of these lines pass through S,,.
We can indicate the position of the singular points by the following
diagram, where the indices have been chosen in such a way that
always the points Sz, Sz: and S, lie on a selfsame line, that the
lines sy, sg¢ and sy intersect each other in a selfsame point, and
that the point Sj, and the line s; are each other’s pole and polar
line with respect to y,.
5. We make a point describe a conie @, and an other point
a line 6, the two points which are conjugated to the former describe
a curve a”, those which are conjugated to the latter a curve (*.
As B* and «@, intersect each other in 8 points, 6, and «@ must have
8 points in common, so @” is a curve of order eight; we shall call
it in future a’. As a, intersects all singular lines twice, @* will have
in each of the 10 singular points a node.
If a, is described around an involution triangle, then «* has also
double points in the vertices of this triangle. As all involution
(755 )
wiangles are at the same time polar triangles of a selfsame conic y,,
we can describe a conic around each pair of involution triangles ;
if a conic 8, is described around two of these triangles, then the
curve 6° conjugate to it will have 6 nodes in its circumference.
Also the remaining points of intersection of 3, and ~* are easily
indicated; they are the four points of intersection of 8, and y,.
We know moreover that a conic described around an involucon
triangle and through two of the vertices of an other involution
triangle must also contain the third vertex of the latter.
6. It is also clear, that we can easily construct conics described
around three involution triangles; to that end we make a conic,
pass through the vertices of an arbitrary involution triangle and
through two singular points not lying on each other’s polar line; for
this we choose S,, and S,,. As @, is described around a polar
triangle of y,, it is described around an infinite number of these
triangles; further each polar triangle of y, having one of the
singular points as vertex is at the same time an involution triangle,
so that @, is described around three involution triangles.
Now the curve a@® will have in the circumference of «, nine nodes ;
so it must degenerate and a, must be one of the parts into which
it breaks up. If P, is an arbitrary point of @, then always one of
the two points P, and P, forming with P, an involution triangle
will also lie on a@,, so also the third vertex lies on a, (5). If now
we let P, describe the conic «,, then P, and P, will describe the
same curve; every time however that P, coincides with one of the
singular points on a,, P, and P, will be bound to no other
condition, than that they must lie on the polar line of that point and
must form with P, a polar triangle of y,. So the parts into which
a® degenerates are:
1. the conic a, to be counted double;
2. as many lines as there are singular points lying on «,.
From this ensues that besides S,, and S,, 2 more singular points
lie on 4,.
This last we can prove still in another way; we construct a
second conic ,, described around an involution triangle Q, Q, Q,
and through S,, and S,,; it will cut @, in two points more, which
being both the vertices of two, i.e. of an infinite number of involution
triangles, are therefore singular points. If we construct another conic
J, described around a triangle of involution R, Rk, R, and through
S,, and §,,, then this must still cut @, in two singular points; these
(756 )
must be the same as the points of intersection of @, and ~,, because
on a, no more than four singular points can lie.
So all conies passing through |S,, and S,, and farthermore described
around one, hence around an infinite number of involution triangles
will form a pencil; the two other base points of this pencil are also
singular points. We determine these first: if we choose as p, the
pair of lines S,, and S,, and as J, the pair S,, and S,,, it is evident
that S,, and S,, are the discussed base points. Therefore: [/ the
10 singular points, hence also the double curve y,, of the involution
are known, we can generate the involution triangles in this way:
We can construct five different pencils of conics of which each
conic is described around an injinite number of polartriangles of ¥,,
which are then at the same time the involution triangles in view ;
the base points of these pencils consist of the sets of points (S,,, Sys,
Strep Shak (Se Sa Sar S50); (Sis; Saa7 Sho Sib (Si, Sin Shr Si) and
(Stes SaG3 Sie S ADE
These pencils we shall call in future respectively (B,), (6), (B,),
(B,) and (B,).
If a, and «, are two conics, the first taken arbitrarily out of (B,),
the second arbitrarily out of (B,), these two will have four points
of intersection, viz. .S,, and the vertices of an involution triangle.
Now it can happen in two different ways that 2 of these points of
intersection coincide: 1. S,, ean be at the same time a vertex of the
involution triangle 2. one of these vertices can lie on the double
curve y,. In each of these two cases @, and a, will have only three
different points in common, but they will touch each other moreover
in one of these points.
7. Out of these 5 pencils we choose one — e.g. (B,) — arbitra-
rily; an arbitrary conic d, out of (4,) is described around an infinite
number of involution triangles whose vertices form in its cireum-
ference an involution of order three. The latter has four double points
in the points of intersection of d, with y,, the double curve of the
involution (7,). Inversely the conics of the pencil (6,) determine an
involution of order four on y,; the latter has 6 double points in
the points in which y, is touched by a conic out of (5,). In each
of these points three points have thus coincided, forming together a
group of (7,).
The involution (¢,) has 6 triple points; in each of the points y, is
touched by a conic out of each of the pencils (B,), (b,), (B,), (By),
and (b;).
( 757 )
8. A point whose conjngate points coincide we call a branch point,
the locus of these points the branch curve. If we let a point G describe
the conic y,, then the curve of order eight, generated by the points
conjugate to G, must degenerate into 2 parts, of which one is y, itself
and the other the branch curve. From this ensues that the latter is
of order six and possesses nodes in the 10 singular points; so it is
rational as it should be, as it corresponds point for point to a conie.
Also in an other way we can easily deduce the order of the
branch curve; if a point describes a line a,, then the conjugate points
describe a curve a‘ having with y, eight points of intersection, of
which two coincide with the points of intersection of a, and y,,
whilst the others point to 6 points of intersection of a, with the
branch curve.
If G,, is a point of the double curve y, and g the tangent in that
point to y,, then g will intersect the branch curve in 6 points of
which one G', forms with the double point G,, a group of conjugate
points; so in the triple points of the involution y, and the branch
curve will have to touch each other.
The branch curve is a rational curve of order six, having double
points in the singular points and touching the double curve in the
triple points of the involution.
Observation. A rational curve of order six has 10 double points;
of which however only 8 can be taken arbitrarily’); from the pre-
cediny follows however that 10 points determining a Cf (10,, 10)
can always be double points of a rational curve of order six.
In an other form C. F. Geiser (see his paper quoted in the fol-
lowing number) makes the same observation.
9. We shall now apply the preceding to some problems out of
Threedimensional Geometry. To that end we regard the pencil
(B) of twisted cubies which can be brought through 5 fixed points
P,, P,, P;, P,, and P,. These determine on an arbitrary plane V
a cubic involution of rank one; the lines P; Ls eut V in the sin-
gular points Sj, the planes P, P; Pn cut V in the singular lines
sj of the involution. Through an arbitrary point of V passes only
one curve out of this pencil, through a singular point Sj; however
pass an infinite number of curves, which have all degenerated into
the fixed line P;P; and a variable conic; these conics form a pencil
with Pr, P, P» and the point of intersection of P; P; with the
plane P; P; Pn as base points. Each double point of the involution in
V is now a point, in which a twisted curve out of the pencil (2)
1) Satwon-Frepter : Héhere ebene Kurven, Zweite Auflage, p. 42.
( 758 )
touches the plane V; the third point of intersection of this curve
with V is a point of the branch curve forming with the point of
contact a group of mutually conjugate points of the involution. A
triple point of the involution is a point, in which a twisted curve
out of (4) is osculated by V. From this ensues :
1. All twisted cubies passing through 5 given points and touching
a gwen plane V form a surface F*° of order ten, which touches
V in a cone and cuts V moreover according to a rational curve
of order six.
2. There are 6 twisted cubics passing through jive given points
and having a given plane as osculating plane.
As a special case of this last theorem we have still: through jive
given points pass six twisted parabolae.
Through the pencil (5) of twisted cubics with P,, P,, P,, P, and
P, as base points a plane V is cut according to a cubic involution
of the first rank. If @ is a curve out of this pencil cutting Vin
A,, A, and A,, then e@ is projected out of A, by a cone cutting V
according to the lines A, A, and A, A,. If however a curve y out
of (5) touches a plane V in a point G,, and if moreover it cuts
V in a point G,, then y is projected out of G,, by a cone cutting
V according to G,, G, and the tangent in G,, to y; y is projected
out of G, by a cone touching V according to G', G,,. We have
seen that G,, must lie on the double curve and G, on the branch
curve of the involution, whilst G, G,, touches the former; if there-
fore a quadratic cone is to pass through the base points of the pencil
(B) and to touch V moreover, then its vertex must lie on the branch
curve and the tangent with V must touch the double curve.
The number of quadratic cones passing through jive gwen points
and touching a given plane is singly injinite; the tangents envelope
a conic. The vertices of the cones form a rational curve of order six.*)
The tangential planes of all these cones whose number is a?
envelope a surface of which we wish to determine the class and
which for the present we will call ®,. If A, is one of these cones
and G, its vertex, then through a line 7 drawn in V through G,
one more tangential plane to A, will pass; as 7 has with the branch
curve 6 points of intersection, it lies still in 6 tangential planes
of ®, except in V. Farthermore V is a trope of ®, (that is a
tangential plane touching (y,) in the points of a conic) to be counted
double; the surface ®, is therefore of class eight.
The tangential planes of these cones envelope a surface of class
eight *)
1) G. F. Geiser: “Uber Systeme von Kegeln zweiten Grades”.
( 759 )
We finally put the question how many twisted circles can be
brought through five points where we understand by a twisted circle
a iwisted cubic cutting the isotropic circle in two points. All twisted
eubies through these five points describe on the plane at infinity an
involution; if now a point describes the isotropic circle, its conjugate
points will describe a curve of order eight having with this circle
sixteen points in common; four of these points are at the same time
double points of the involution, whilst the other lie two by two on
a same twisted circle.
So through jive yiven pots pass ten twisted circles, of which four
touch the plane at infinity.
Mathematics. — “On the surfaces the asymptotic lines of which
can be determined by quadratures’. By J. Bruix. (Com-
municated by Prof. Hk. pre Vrirs).
In a paper entitled as above A. Bunn (Nowy. Ann. de Math.,
4° série, vol. 8, page 483, vol. 9, page 337, Rev. sem. XVII 2, page 62,
XVIII 1, page 58) discusses the surfaces given by the parameter
representation
z=rcos 6,
y=rsin8,
9 (24) =a64 F(r),
in which w,y,2 refer to a rectangular system of coordinates, so that z,
6, and r are the so-called cylindric coordinates; these are the only
ones which are used in the course of the investigation.
Bunt now gives the differential equation of the asymptotic lines
of ¢(2) =a6+ F(r) with 6 and ¢r as independent variables as well
as with z and 6. It is then evident that this equation embraces
many special cases, where the determination of the asymptotic lines
comes to quadratures.
We can put the question more in general: which are the surfaces
of one of the forms z= ¢(r,4), or 0=/(r,z), or r=/(z, 4), whose
asymptotic lines can be determined by quadratures ?
Starting from the differential equation of the asymptotic lines
D du? + 2 D' du dv + D" dv? =
(Brancut-Luxat, “Vorlesungen iiber Differentialgeometrie’, page 109),
where D, D' and D" have the values, to be found on page 87 of
the quoted work, we find for the differential equation in r and 6
of the asymptotic lines of z= ¢& (r, 4):
51
Proceedings Royal Acad. Amsterdam. Vol. X{l.
( 760 )
d°e a2 dz 0*2
Bee eo (pee Ir dO =| ao? = 0.
aaa ere va) + (+55 agi =) ()
This equation gives rise to quadratures in the following cases:
a. c=a6-+ f(r), Bunt, |.e¢., vol. 8, p. 439, comp. also TisseraNnD,
“Rec. compl. d’exercices”, p. 426.
b. U(z)=a6+ f(r), Bunn, l.c. p. 440.
« 2¢=Arsin(O+a)4 46 + F(r),
d. (2 — 17, () Ja (A);
e zarksin(A@YVk+e,
f. g=r-* eh k-Fe,
= — #*? + 21 (r).
¢
co)
2. The differential equation of the asymptotic lines of 6 = f (r,<)
in r and z we find by eliminating @ between (1) and 6= f(r, 2).
We find:
yr SO: of Wier zh oF 4 of \* of es ie
1 Or? ae ee dr } \ as “Gear is or) Oz | Oz an ioe
077 of (0
» ot i rd
" (02? dr dz) |
This equation gives rise to quadratures in the following cases:
a O0=1() +f),
k
b. 06 =arecos — + f(z), Buhl, |.c., vol. 9, p. 343,
r
besides a few others mentioned above.
3. In an analogous way we find the differential equation of the
asymptotic lines in z and 6 of r= f(z, 4).
It runs:
of of 1 of of | Of yD O\e
J Ghee ale we —— — —} dzd6 + I : y | 19" =0.
dz? |" (0200 f 06 dz (OG? saan mnnnyaNag
Besides in the above mentioned cases this equation gives rise to
quadratures for =f, (2) /, (4), surfaces of Jamnr (Ann. de lécole
norm. sup., 1887, Suppl., page 50 etc.; further: Prcarp, ‘“Traité
d’analyse” I, 24 ed., page 433).
The classes of surfaces found above are not strictly separated ;
some even are to be regarded as subclasses of others. They can be
ranked according to the most general types to be found among them,
whilst others fall under these types, namely as follows:
( 761 )
2 = Arsin(O + a) + a6 4+ F(r) 2=a84+ F(r)
2 = f,(9) + f: (9)
r=f(2) 19) Ur) = 6 + 7(2)
z=rk sin (Yk + co)
= r—k ot k+e
= — & + 2(r)
wQ
co)
U2) = a8 + f(r)
k
6 =are cos a + 7 (2).
Il. Let us discuss one of the above mentioned classes more
closely, viz.
en (ONG) x ea ees (2)
It is the general equation of the scrolls with the z-axis as directrix.
Of these scrolls we can find the striction line in the following way.
: z 1 ‘
Brancut (Lc. p. 223) deduces that the curvature AK =—., for which
Tl,
: ‘ tC DD Ds , é
in another place was found A = ee larger in the central point
Cp! =
than in all other points of a generatrix. If we make up A for (2)
we find
2 ais)?
K=— — - » oo
AES Ch)? st Gage erry feet (7a) I
Along a generatrix @ is constant; there only the denominator of
the expression for A changes. If we determine the value of 7 for
which A becomes maximal we find
— - Jods so Go (8)
DiS (Fa) tse)
So this is the (7,4) projection of the striction-line.
This equation can be found in an other way, too. We bave the
property that the tangential plane in the central point of a generatrix
is normal to the tangential plane in the point at infinity of that
generatrix. We now determine for f/=—z+7rf,(6)+//,(4) the
of of of
da’ Oy’ Oz
infinity on the same generatrix. If then p is to be central point the
values of in an arbitrary point p and in the point at
Ow
Of of
sum of the products (z) () must be equal to 0. This gives
Ak p a
again the equation (3).
1) In future we shall write f,; and f, for f,($) and 7,8).
o1*
( 762 )
Let us now consider in how far we can find the surface (2) for
a given striction line.
a Let r=y(4) be the given projection of the striction line.
This furnishes, regarding (8), the relation between /, and /,:
Fifa
+ (Ay + (AY
sy EL ARCA ARs
Jat ae i .
Ji
pl Gee
Pr oe (A) =F (f.) ‘d6, where
= |p
Thus: The surface z=r/,(@)-+ =
Ji
7, is an arbitrary function of 4, has as (7, 6)-projection of the striction
line the curve r= +p (@).
6. Let now be given that the striction line must be a plane curve
lying in the plane z= Av + By+C or z=r(AcosO+B sin) + C.
By substituting this value for z in (2) we must get (3). This
furnishes between f, and /, the relation
te OS Fea gt. Sih
Ee), US EIGAE SE GAP
or
a ae eee ects a
ve YO Ces DS a).
fp Se
So the surface z= 7/, (@) +e jl Aces "8 sind) 2 Caainerianen
7, is an arbitrary function of @, has a plane striction line lying in
sega
. The most general problem here is: what is the surface (2) for
mee = (9), z= w(9) is striction line?
To solve this we substitute these values for 7 and z in (2) and (3)
and we obtain then two equations with /, and /, as unknown
quantities. If we eliminate between these two /,, we retain f, as
only unknown quantity in the equation :
p+ qHAyY +Aw — off’ =.
If f, is solved out of this we can find /, out of:
w= oh +h
We can find the solution in explicit form for the special case
y = const., for which constant we take 0. We then find:
el+(AI—-G@AL = 0,
from which ensues
Va veo
7 7
SS e —1,
( 763 )
whilst further
f,=— GPC
The result is therefore:
The surface
eb (7 a) e a
has the plane striction line r= gy, z= 0.
The formulae deduced above hold for the surfaces (2). As was
noticed the general types mentioned at the conclusion of I are not
strictly separated, however, so that there are still amongst them
scrolls with a right directrix, to which then the above formulae are
applicable.
Examples of this are:
Of the type z= Arsin(@+ a) + a6+ F(r)
the surface z= Ar sin (6 + a) + a6 + dr.
Of the type Az) =a6@ + f(r)
the surface (2) = a6 + l(r + p);
these have the z-axis as directrix.
Of the type r= f,@) f,(@) the scrolls
gn Yn—1
wi(z > 1) 274, or r= (tg @)' 1—T see A (Sel
1 n
vt = (y—ca)z” or r= sec 6 (tg9—c)—! 2—!
and
have still the y-axis as directrix.
Physics. — “A new theory of the phenomenon allotropy.” By Prof.
A. Smits. (Communicated by Prof. A. F. Houtmman.)
Introduction.
In two short communications inserted in the “Chemisch Weckblad”
7, 79 and 155 (1910) I have already sketched the main lines of the
theory, an extension and experimental confirmation of which follow
here.
Before passing on to this I may, however, be allowed to give the
gist of this theory in a few words.
In the investigation of the phenomenon tautomerism it has been
possible to show by means of the process of solidification that the
liquid phases of tautomeric substances are composed of two kinds
of molecules.
( 764 )
Besides, however, by deposition of different solid substances the
complexity of a liquid phase can also be shown in another way,
and investigations in this direction have led to the result that it
may be considered as the rule that the liquid phase of a substance
is built up of different kinds of molecules (ions included).
Bancrort') and Bakavis Roozesoom’) bave pointed out that when
a substance behaves as a unary substance, this is accounted for by
the fact that the setting in of inner equilibrium takes place so
rapidly in the homogeneous phase that the inner equilibrium if
disturbed, is immediately restored by the appearance or disappearance
of a new phase; the melting-poit, boiling-point, critical-point ete.
of a substance which behaves as a unary one, does not relate then
to a single kind of molecules, but to an equilibrium between d/erent
kinds of molecules.
Bancrort’s pupils, viz. Carvers, Soc, and Campron*) have inves-
tigated different tautomeric substances; it then appeared that it may
be pretty easily shown in some cases that under certain circumstances
the existence of two kinds of molecules in the liquid phase may
lead to a binary behaviour, for when the liqnid cooled rapidly, the
inner equilibrium conld not follow the temperature, and the mass
solidified at a temperature which differed from the unary stable
melting-point, for then a point was realized of one of the melting-
point lines of the pseudo-binary system A + 6, which for the
examined substances always showed a eutectic point.
As is evident we find the unary stable melting-point where the
curve for the inner liquid-equilibrium meets one of the melting-point
curves of the pseudo-binary system.
Now it is remarkable, as 1 already wrote, that nobody has observed
what surprising results are arrived at when it is assumed, what is
undoubtedly true, that not only mixed erystals are always formed
in a greater or less degree, but that moreover the ner equilibrium,
which exists in the liquid phase, continues to exist in the solid
phase.
Starting from this supposition we get the relation between /efero-
geneous and homogeneous allotropy, indicated in Fig. 1, from whieh
it appears that the phenomenon of enantiotropy means wamiving
in the solid state, which phenomenon appears when the curves for
1) Journ. Phys. Chem. 2, 143 (1892).
2) Zeitschr. f. phys. Chem. 28, 289, (1899).
3) Journ. Phys. Chem. 2, 159 (1818).
ibid. 2, 364 (1898).
ibid. 2, 409,
( 765 )
the stable and metastable solid equilibria s,g and s,n meet the mixed
erystal lines ep and dm of the pseudo-binary system.
In case of monotropy these meetings between the unary and the
pseudo-binary system do not take place wrder but above the unary
melting-point temperature, and this is the reason that in this case
the second line for the solid inner equilibria everywhere indicates
metastable states.
I started from Grpps’ principle of equilibrium, which states that
with constant temperature and pressure a number of substances
arranges itself in such a way that the thermodynamic potential is
a minimum; and then I showed how sharply the relation between
the pseudo-binary and the unary system can be defined also in this
way, when we bear in mind that a state of inner equilibrium must
always lie in the minimum of a potential line.
Further the case was considered that the three-phase temperature
hes between the melting points of the substances A and 4. After
having discussed the phenomena of enantiotropy and monotropy also
for this case, I finally pointed out that when A and £/ are miscible
in all proportions in the solid state, heterogeneous allotropy is excluded,
and only homogeneous allotropy can occur, wrless unmixing occurs
in the pseudo-binary system at lower temperature.
Discussion of the curves of wner equilibrium.
After this introduction which seemed indispensable to me to make
the reader acquainted with the main facts, I will consider fig. 1 a
little more closely and discuss the curves of inner equilibrium.
It follows from the course of the curve jS’,,S’, that it is assumed
here that over the corresponding range of temperature the equilibrium
shifts towards / with increase of temperature, and so that
Az B—acal
or in words that the transformation froin the left to the right is
endothermic.
With application of the equation:
dink Q
eae ee
we know therefore that Q is positive in the assumed case.
Neglecting the external work we can split up @ into two differen-
tial heats of mixing, one of which has the negative sign, because
it is a case of unmixing, and further into a heat of transforma-
Yon, so:
( 766 )
Q = — (Qn) A ++ Q, =F (Qn)B
Q,,)A = differential heat of mixing of A
(Qn)B= » » » » ee
Q,—= mol. heat of transformation.
It is of importance to point out here that as (Q,,).4 and (Q,,)z have
a different sign, the possibility exists that Q has another sign than
Q,; this might e.g. oecur when Q, was very small, and then we
should have the special case that e.g. when Q was negative and
Q positive, the equilibrium shifted from B to A with rise of tem-
perature, whereas the transformation of <A into 6 is endothermic
in itself; this, however, will only rarely occur.
If we drop this question for the present, it is noteworthy that in
the point 0S’, unmixing occurs, another solid phase |S’, appearing
by the side of S',. Two cases may be distinguished here.
Generally the newly-formed solid phase .S’, will possess another
form of crystal than S’,, but it is possible that the two solid phases
are isomorphous, for as is known, also isomorphous substances can
show partial miscibility; if this latter, the simplest case occurs,
the heat of transformation will be the sum of a heat of unmixing,
a beat of transformation, and a heat of mixing’), another thermal
quantity being added to this, viz. that which accompanies the change
of crystalline form, when |S’, and JS’, are not isomorphous.
If we now follow the inner equilibria above the transition-point,
it is to be expected that the curves S', q for the solid-, and /, & for
the liquid inner equilibria will have the same direction as \S’, S’, ,
as is also assumed in fig. 1.
Socu, however, has found in his investigation of benzile-orthocarbonic
acid that the curve of the inner liquid equilibrium meets the melting-
point curve of the modification with the highest melting-point viz.
4, and runs to the A-side for higher temperatures. Further he found
that at 65° A passes into B, and combining these two facts, he
arrives at the conclusion that the thermal sign of the transformation
A> B
must have been reversed between the point of transition and the
unary melting-point (137°).
When the pseudo-binary 7v-figure for this substance agrees with
fig. 1, which is still an open question, we must of course come to
the same result also going by this theory, but I will point out here
that this conclusion is not yet imperative at this moment, because
though it is not probable, the possibility exists that the mixed erystal
1) | shall discuss this and the before-mentioned splitting up more fully later on,
( 767 )
curve dm of the pseudo-binary system has the same direction as
ep; in this case the three curves of equilibrium S’, S', , S', S, and 1,4
might still have the same direction, and so the sign of Q need not
be reversed.
If we look upon the question of the reversal of the thermal sign
from a general point of view, the following may already be remarked.
When A and B&B are isomers, as for benzile-orthocarbonie acid, a
reversal of the sign of Q seems possible, because Q, is probably
small in this case’). If, however, we have to do with the pheno-
menon polymerism, we may expect with great probability that Q,
will always predominate, and that the curves for the inner solid
and liquid equilibria will always run in such a way that the
equilibrium shifts towards the side of the less complex substance
with rise of temperature.
This leads us at the same time to the question what the 7'2-
figure will be for the case that ihe substance 6 is a polymer of A,
and that a transition point exists.
Fig. 2 shows that when the pseudo-binary system possesses a
eutectic point, the curve for the inner liquid equilibria must meet
the melting-point curve of the less complex substance, because only
jin these circumstances all the curves for the inner equilibria can
run to the A-side with rise of temperature.
Yet this figure will not appear to be quite correct either, in
my opinion, as a supposition is implied in it, which is highly
improbable.
When & is a polymer of A, and the pseudo-binary system pos-
sesses a eutectic point, this means that there are liquids (ac) which
contain more polymer than the coexisting solid phases (ad), and
this is very improbable, so much so that we may disregard this
figure altogether, in spite of HoLLMANN’s*) assertion that he has found
a eutectic point for the system acetaldehyde-paraldehyde. Probably
this assertion of HoLLMANN’s rests on not quite reliable observations,
for my assistant, Mr. pe Leeuw, who tested the said assertion at
my request, has not found it confirmed.
So for the case that 5 is a polymer of A and the two substances
are not miscible in all proportions in the solid state, we must conclude
to the existence of a Y%v-figure as indicated by fig. 3, in which the
1) In consequence of the considerable displacement of the inner equilibrium at
the transition temperature it is possible, that while Q, predominates below thic
temperature, above it the reverse takes place.
Q,, too, can reverse its sign, but this seems less probable to me.
*) Zeitschr. f. phys, Chem. 48, 129 (1903).
( 768 )
three-phase-temperature lies between the melting-points of the pseudo-
components.
Now on this assumption, the solid phase possesses every where more
of the polymer B than the coexisting liquid phase, and if in the
unary system a transition point occurs, the course of the curves of
inner equilibrium must be as indicated by £/,, S,S', and S,'S‘,.
If the curve A/, met the melting-point line of 6, monotropy alone
would be possible, as for enantiotropy reversal of the thermal sign
would have to take place in this case, which is very improbable here.
Experimental conjirmation.
It is clear that this theory requires that every substances which
shows a transition point, must consist of two different kinds of mole-
cules, which are in equilibrium at every temperature.
So if we consider the substance HgJ,, the ved modification ot
which passes into the yellow one at 127°, we must assume two
different kinds of molecules, the former of which gives rise to the
formation of red, and the other to that of yellow HeJ,.
The investigation of this substance, whieh was carried out in
collaboration with Mr. S$. C. Boknorst chem. cand. has led to a
very remarkable result.
That it would appear that working quickly, the substance would
betray its binary character, was expected, but that we should find
here that case which I already mentioned, but considered as an
exception, was highly surprising.
For the sake of clearness the observed phenomena will be dis-
cussed here in connection with the schematic fig. 4, in which «
means yellow and ’ red HeJ,.
At 127° the red phase passes into the yellow one, which new
phase remains intensely yellow up to about 180°; on further heating
we observed that this phase assumed a red colour, at first hardly
perceptibly, but then more and more pronounced, and that it becomes
a dark red liquid at the melting-point temperature 255°,4.
This phenomenon, which also appeared with very siow rise of
the temperature, was studied in different ways with the naked eye
and by means of the microscope, when it appeared that this change
of colour takes place continuously, and is not owing to a second
transition-point.
This continuous change of colour between comparatively narrow
limits of temperature made it therefore probable that above the
point of transition the curve for the solid inner equilibria at first
( 769 )
runs vertically upwards, after which it bends sharply to the red
side, and meets the mixed-crystal curve of the pseudo-binary system
near the axis of the red modification.
As therefore, this inner equilibrium curve appears to traverse the
T-«-figure over a large concentration range, this pointed already to
a region of partial-miscibility in the pseudo-binary figure, which was
closed at the top, and so also toa continuous mixed crystal curve ach.
In order io test this supposition more closely, the following ex-
periments were made with HgJ,, either in thin-walled narrow capil-
laries or in so-called alcaloid tubes; it was, namely, quite immaterial
which of these were taken, for in cither case the experiment yielded
the same result.
In these tubes the HgJ, was heated in a melting-apparatus up to
a certain temperature above the transition-point, and then all at once
transferred to an oil-bath of lower temperature, but always above
the transition point.
The considerations which led us to these experiments, were the
following.
If it is possible to make the cooling take place so rapidly that
the inner equilibrium cannot keep pace with the temperature, the
pseudo-binary character must appear, and entering the region of
partial-miscibility the substance must split up into two phases.
Suppose that we start from the inner equilibrium p and that we
cool this suddenly, in which not the curve of equilibrium, but the
curve pS, is followed; then the red phase S, will appear by the
side of the yellow phase S, and will have to be clearly visible.
This three-phase system will be strongly metastable, so that it is
not to be expected that it will be very permanent; on the contrary,
we may confidently predict that this state will very soon change
into the only stable equilibrium which must lie on the curve SS,.
If we now start from the inner equilibrium g, which lies on the
right of the critical mixing-point A, the mixing-curve can be reached
in S,, and by the side of phase S,, the phase S, must be found,
which has a lighter colour. .
As appears from the subjoined table (p. 770) not only these phenomena
could be observed with great clearness, but moreover it was ascer-
tained by these preliminary experiments that the mixing-point AC
must lie above 147° *).
Though it follows from these experiments that above the transition
temperature the 7’2-figure of the system HgJ, would be as indicated
1) This investigation is continued in different directions,
(770 )
Temp. HgJ, peucden hee Remarks
200° 130° | No unmixing as yet.
205° * _Unmixing, red phase appears, but has
disappeared again after a few seconds and
the whole mass is again yellow.
207° Fs 5
210° ” ”
2128 | : | :
215° | ” | ”
2950 - | Unmixing, but now yellow phase ap-
pears and after a few seconds everything
| is yellow.
930° Fs The same phenomenon, and still more
| pronounced.
919° 140? | Unmixing red phase appears etc.
912° 145° | =
249° | 447° | No unmixing is to be observed.
here, the question what the rest of the figure, i.e. under the transi-
tion point, would look like, remained unanswered. The answer to
this question cannot yet be given in this communication, because
the equilibrium sets in exceedingly slowly at temperatures under 100°.*)
So the dotted curves under the transition temperature do not re-
present anything but a supposition. For the end in view here,
however, the want of certainty below the transition temperature is
of minor importance, as the phenomena observed at higher tempe-
ratures furnish a convineing proof for the validity of the theory.
Before I leave the substance HgJ, and proceed to another subject,
I will only point out, that if the equilibria are considered not at
constant pressure, but at the variable vapour-pressure, also the vapour-
curves should be inserted in the 7’v-figure, which lie on the side
1) If a tube with red HeJ, is immerged in liquid air, the colour becomes indeed
much lighter viz. orange, but this change of colour has nothing to do with a
displacement of the equilibrium.
If a mixture of yellow and red HgJ, is taken, and this is cooled down to
—190°, the yellow colour changes into white, and the red inlo orange-yellow.
When heated to the temperature of the room the heterogeneous mass is found to
be entirely unchanged compared with the initial state.
(ria)
of yellow HegJ,, because the yellow phase is always deposited from
the vapour.
If we now consider the question whether the literature mentions
results in support of this theory, the answer is affirmative. These
are chiefly the results obtained in the investigation of sw/phur’) and
that of phosphorus’).
In the system sulphur we have two different crystalline modifica-
tions, and besides them a third modification Su, which has not yet
been obtained in crystalline form.
Considered in the light of this theory we must therefore assume
three different kinds of molecules, and su/phur being known as a
substance which is very slow, we can assume with great probability
that sw/phur is not pseudo-binary, but pseudo-ternary, i.e. will behave
as a ternary system.
This, however, be only remarked in passing, as these considera-
tions are of no further importance for what follows.
If we now direct our attention to the 7.z-figure of the system Su
and rhombic sulphur Sp (Fig. 5), it is noteworthy that by extra-
polation 110°,6 has been found for the unary melting-point, and
112°,8 for the melting-point of pure rhombic sulphur.
It further appeared, however, that when from rhombic S was started
from, where the equilibrium had set in at 90°, a melting-point was
found at 110°.9, the melting-point amounting to 111°.4 when the inner
equilibrium had set in at + 65°.
These are results which support the theory given here, for they
point to the fact that we have to do here with a curve SS, for the
solid inner equilibrium, which runs to the left with rise of tempe-
rature. For this curve shows that as we, working quickly, start from
an inner equilibrium established at ower temperature, this phase
will begin to melt at a /Azgher temperature, which was also observed
here.
The curve for the inner liquid equilibrium, too, runs to the left,
so that the two curves of equilibrium have the same direction.
Though the sulphur can furnish further proofs, we now proceed
to the phosphorus.
As Couren and One already mentioned, investigations of Troost
and Havurereui.te, Lemormer, Hirrorr, and themselves point to the
1) Kroyt, Z. f. phys. Chem. 64, 513 (1908).
2) Conen and Ore, Chem. weekblad 6, 821 (1909).
fact that for phosphorus we have to do with solid inner equilibria
between white and violet phosphorus.
lf we consider the following results of the determinations of the
specific gravity :
spec. grav. of red P obtained at 550° = 2,25
» so se ats * edo Oe
” y sires, _ 5 BO = DD
0 3 Gee * 5, 255° = 2,20
at .
x A Fae es 5 sf 2d 29
we should, in view of the fact that the spec. grav. of white ?— 1,82,
and that of violet ? may be put at about 2,34, come to the con-
clusion that the curve for the inner solid equilibria runs to the
violet side with rise of temperature to 450°.
As it, however. followed from the experiments of CouENn and Onix,
that when red P was reduced from a higher to a lower temperature,
the spec. grav. in general was not lowered, it is clear that they
have not investigated states of equilibrium, and that we, therefore,
cannot draw conclusions about the course of the curve of the inner
equilibria from the above results. As to the existence of the inner
equilibria, however, this is no longer doubtful.
So if we start from this, and if we then think of the phenomenon
observed by CHAPMAN ') that red P when melting, gives a colourless
liquid i.e. a liquid which perfectly resembles melted yellow P, a
7, «figure may be constructed in main lines for the pseudo-binary
and the unary system, in which, however, the existence of a eutectic
point is still an open question.
It has been assumed in fig.6 that red P(8P, is a polymer of
white P(eP), and therefore no eutectic point is drawn. In this
figure the phenomenon observed by CHapman has been illustrated,
for heated to the melting-point, the red solid phase will pass into a
liquid /,, which lies entirely on the side of the white P. We see
further from this diagram that melted yellow P has about the same
composition as melted red P, and that melted yellow P means
undercooled liquid red P.
Applications.
Besides the phenomena mentioned here there are others which
seen in the light of this theory find a plausible explanation. I allude
1) Journ. Chem. Soc. '75, 743 (1899).
(773 )
here to the phenomena of retardation for so far they only appear
when we work rapidly’).
If we consider first of all the phenomenon of wndercooling and
superheating of the solid, for so far as they are only observed with
quick change of temperature, fig. 7 gives a satisfactory explanation.
Starting from the inner liquid equilibrium p, not the curve of
equilibrium p/,, but another curve e.g. p/, will be followed with
rapid cooling, and when we get beyond /, the state is not only
unarily, but also pseudo-binarily metastable.
Let us assume for simplicity that in the pseudo-binary system no
retardation worth mentioning appears, then the substance will solidify
at 7; and the solid substance S, is deposited.
Now this two-phase equilibrium is metastable to a high degree
in the pseudo-binary system.
In the unary system equilibrium between liquid and solid sub-
stance can only exist under constant pressure at one temperature,
and now it is the rule that a metastable state like that of the system
i, S, is at once destroyed. Thus we see e.g. that a supersaturate
solution in contact with the substance which this solution must
deposit to pass to the stable condition, generally immediately deposits
this substance.
So the metastable two-phase equilibrium /, +S, is changed into
the stable state /,-+ S,, and this being a process which generates
heat, the temperature rises to the unary melting-point.
Starting from the solid inner equilibrium g we get just the reverse,
because then the substance melts at too high a temperature if
quickly heated, as has already been observed for rhombic sulphur.
If now the curves of inner equilibrium run as in fig. 8, the
liquid can solidify too early if cooled two rapidly, the solid sub-
stance can melt too early if heated too rapidly, and then the result
is that for a perfectly pure substance there is a range of temperature
over which the solidification and the melting extends, which probably
often occurs for organic substances, in which the equilibrium sets
in so slowly.
With regard to the phenomena of retardation at the transition
point I need only refer to fig. 9, which will now be clear without
further elucidation.
It is further hardly necessary to remark that when a substance
is not di-, but tri-, or polymolecular, the phenomena discussed here
remain essentially the same.
1) The peculiar phenomena, which will also appear for more complicated
systems, as e.g. #e + C when we work quickly, will have to be accounted for in
the same way.
(774)
In conelusion I want to point out that this theory gives the first
plausible explanation of the metastability of the metals.
In this it is viz. noteworthy that the cooling of the solidified
masses proceeds in such a way that the inner solid equilibrium can
certainly not follow the temperature, and this is one of the reasons
why the metals, as we generally have them, are nearly always in
metastable state. We must further bear in mind that if we have a
metal which is in inner equilibrium, and it is subjected to some
mechanical operation, a necessary consequence of this will be that
the metal becomes metastable, because in stable state a change of
pressure is generally attended with a shifting of the inner equilibrium,
which, however, in consequence of the inner resistance does not
appear at all, or on account of the slight velocity of transformation
will take place only after a very long time.
The above mentioned circumstances account at the same time for
the fact that it hardly ever occurs that two pieces of the same metal
are perfectly identical, for this could only oceur when the inner
state, stable or metastable, was perfectly the same.
Just as so many others the metastable states discussed here can
be changed into the stable state by different influences, as increase
of temperature, vibration, contact with the stable state ete., in
which the transformation which takes place, manifests itself in a
recrystallisation.’)
Amsterdam, March 1910. Anorg. Chem. Lab. of the University.
ERRATA;
In the Proceedings of the Meetings of Jan. and Febr. 1910.
p- 652 line 9 and p. 677 line 5 from the bottom, p. 654 line 17
from the top: for 11 read 659.
p. 669, 672, 674 for 20.2 read 20.3.
p. 670 ete. for carrier read holder.
line 9 and 19 from the top: for modulus read constant.
line 5 from the bottom: for corresponding read in agree-
ment with.
p. 672 line 16 from the bottom: for dilation read dilatation.
p. 673: for 14.3 read 14.0.
1) It is to be expected that this metastability will not be met with only for
metals and metal-alloys, but also for other substances, which have been obtained
by rapid cooling and solidification of melted masses.
(April 28, 1910). i
—_——_
KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.
PROCEEDINGS OF THE MEETING
of Friday April 29, 1910.
(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van 29 April 1910, Dl. XVIII).
GO) any Aaa any 2a (Sy.
Jan pe Vries: “On polar figures with respect to a plane cubie curve”, p. 776.
J. G. Sreeswisk: “Contributions to the study of serum-anaphylaxis” (4th Communication).
(Communicated by Prof. C. H. H. Spronck), p. 781.
L. E. J. Brouwer: “On the structure of perfect sets of points”. (Communicated by Prof. D. J.
Korrewera), p. 785.
M. W. Beierincx: “Emulsion laevulan, the product of the action of viscosaccharase on cane
sugar”, p. 795.
H. Kamertincn Onnes and A. Perrier: “Researches on the magnetization of liquid and solid
oxygen”, p. 799. (With one plate).
Sr. Loria: “The magneto-optic Kmrr-Effect in ferro magnetic compounds and alloys”. (Com-
municated by Prof. H. E. J. G. pu Bors), p. 835. (With one plate).
Erratum, p. 845.
52
Proceedings Royal Acad. Amsterdam. Vol. XIL
(776 )
Mathematics. — “On polar figures with respect to a plane cubic
curve. By Prof. JAN DE VRiEs.
(Communicated in the meeting of March 26, 1910).
1. If a plane cubic curve y* is represented symbolically by ae=0
then a, a, a, =O represents the polar line p,, of the points X and
Y, ie. the polar line of Y with respect to the polar conic 2, of Y
and at the same time the polar line of )” with respect to the polar
conic a, of _X.
The three polar lines p,,, pr:, and p,. will concur in one point
W when the three conditions are satisfied
AzAyty = 0, Ons 035 —OR AyAzty —0. . . . (iL)
by elimination of the coordinates w, we find out of it
(abe) agtybrb-cyez = 0 a Creda ey ate Bo (4)
So to two given points X, Y belongs a conic y?, as locus of
the point 7; it passes also through Y and Y, for when Z and
YX coincide, we find
(abe) dy Drly lr = (cha) x0 yay z = — (abc) ,ybatyer = (i),
As we can substitute (adc) Ay Ay Cx Cz 6,6. = 0 for (2), thus also
(abc) az Ay bz Cz (bz Cy — by Cr) = 0, we can also represent Te by
(abc) a,a,b-c: (bc) = 0, where §;, are the coordinates of the line XY.
Consequently (2) can be replaced by
(Oc) Gen) (6262510 ears wea 6 (I)
From this ensues that the conic ey is the poloconica mz, of the
lines § and 7.
So the poloconica of two lines is the locus of the points Z which
with relation to the points of intersection X,Y of this conic with
one of the given lines are in such a position that the polar lines
Pez and Pyz coucur on the other one of the given lines, which is
then at the same time polar line of Y and Y.
2. If Z and W are the points of intersection of a: with 7, it
follows out of the symmetry of (8) in connection with the equations
(1), that the four points X, Y, 7, W form a closed group, so that
each side of the quadrangle determined by them is the polar line
of the vertices not lying on it, therefore a polar quadrangle (Reve).
Out of our considerations ensues that a polar quadrangle is deter-
mined by two of its vertices, but also by two of its opposite sides.
In the last case the vertices are determined by the poloconica of
the given lines; in the former case we can use the poloconica be-
longing to the polar line of the given points and their connecting
line,
((777.)
Out of a,4,4, = 0 and a,a,a: = 0 follows
Ay (Ady + paz) = 0.
Here 4 and w can be determined in such a way that hay+ua-=a,
relates to the point of intersection U of XY with WZ.
As Aye, = 0 indicates the polar conic a, of U we find that
and Y according to the relation a@,a,a,—=0 lie harmonically with
respect to a,. In an analogous way ensues from a,,a@,a, =O and
Awt-dz =O the relation a,a-a,—=0, according to which W and Z
are also separated harmonically by 2.
But then also the points T=(XZ,YW) and V=(XW,YZ) are
conjugated with respect to a,, i.e. we have a,a,a,—=0. Now U,V,T
are the diagonal points of the complete quadrangle X YZW, so that it
is proved that the diagonal triangle of a polar quadrangle is always
a polar triangle’).
3. When the conic ee degenerates we can take for Z each point
on the line XY. To trace for this the condition, we put 2,=20.+-byz;
from (2) follows
(abe) ayaybrey (Aby + jby) (Aca + cy) = 9,
so
22(abe) axdybrcxcy + Au (abe) dxtybre, +
+ Au (abe) aza,brbyexey + uw? (abo)araybbycy, = (1),
By exchanging two of the symbolic factors a,b,c, we see that
three of these terms are identically zero; so we have
Au (abe) Ay cy =i (0s
For an arbitrary choice of X and Y this equation furnishes only
= 0 and «0, thus the points XY and J’. It furnishes each point
of XY Y, as soon as
(Gho\lawe bac OM ae ity re na se n(4)
When X, Y, and Z are collinear, the polar line p, of X and the
polar lines pr,, pr: concur in one point; for these three lines are
the polar lines of Y, Y,Z with respect to the polar conic z,. If
now (4) is satisfied, then also p,. passes through that point, hence,
the six polar lines p,, py, Pz, Poy» Pyz> Pxx concur in a point W. But
when pr, p, and p. are concurrent, the poloconica of §= XYZ,
degenerates and § is tangent of the Cayleyana.
From this ensues that for given Y the equation (4) will represent
1) Mentioned without proof by Caporat: (Transunti d. R. A. dei Lincei 1877,
p. 236).
52*
(778 )
three right lines, namely the three tangents which we can draw
out of Y to the Cayleyana.
This can be confirmed as follows. Let 7 be a point of the locus
of YX, which is determined by 4) and YX a second point of that
locus lying on YZ, so that we have adz=aa,+ua:. Out of (4)
then follows
(abe) Cy (Aa, + faz) (Ab, + wb:)? = 0.
By exchanging a and c we see at once that
22
(abe) aye, (Ab, 4- wb-)?
vanishes identically. Analogously we: find that (abc) ly Cy(tedy and
2 : : ° > » 2 2
(abc) ayc,azb,b. vanish identically. As finally the form (abc) (hy Cy(tzb-
is zero because Z lies on the locus indicated by (4) the above
relation is satisfied by all points of YZ, so the locus consists of
three lines through Y.
4. That the line §— NX)’ is tangent to the Cayleyana as soon as
(4) is satisfied, can be confirmed by reducing (4) to the tangential
equation of that curve. In the first place we find out of
(abc) dyaybxcy =0 and (acd) iy yezby ——a()
the relation
(abc) Ay My (bx, + byCx) (baty — bycy) = 0.
The last factor can be replaced by (dc§) where &; indicate the
coordinates of YY. After that the equation can be broken up into
two terms, which pass into each other when 6 and c are exchanged.
So we can replace it by
(abc) agaybrcy{be§) =O - «. . «~~ - + (8)
farthermore it is evident from
(abc) avaybiey =0 and (cba) catybiay ==A0}
that at the same time is satisfied
(abc) braycy (ac) = 0,
so also
(bac) azbycy (BoB) = 0. - . . . - s - (6)
By combining (5) and (6) we find
(abe) aycy (be) (abs) = 0.
So
(abe) exay (eS) (ab§) = 0.
Out of the last two relations follows finally
(779)
(abc); (ceb)\ (Ges) (abs) = Oa ae ee ee
This tangential equation really represents the Cayleyana‘).
So we have found that the six polar lines pr, Py Pz Pays Pyz> Pz
concur in one point when the points X, Y, Z lie on a tangent of
the Cayleyana.
5. When p,, p,, ps are concurrent we have
2
(Go) a= buena Sn pe eee (8)
This equation gives thus the relation between the coordinates of
three points lying on one and the same polar conic.
For an arbitrary choice of X and Y this equation is satisfied
except by X and } by no point of the line YY. If it is to be
satisfied by <= Ac, + wy, Wwe must have
(abe) an by (Ac; + uc,)° = 0,
therefore
2,2
Au (abe) ay by ex ey = 0.
This is satisfied for each value of 4:u° when the relation (4) is
satisfied, so when X, ), Z lie on a tangent of the Cayleyana.
Now in general the polar lines p,,, px-, py: form a triangle inscribed
in the triangle pr p, pz (see § 3). If (4) is satisfied then pry, Pez, Py:
are concurrent; but then their point of intersection must be at the
same time point of intersection of p,, Py, pz.
If X, Y,Z are three collinear points of the cubic, then p,-, per
and p,, pass successively through X, )’, and Z.
For, : from a = (0); tly = Oand (da, + ua,). =() follows that the
point Z is indicated by aay (Aay + way) = 0. So we have a,a,a. = 0,
so Z lies on the polar line pz,.
If moreover Y, Y,Z lie on a tangent of the Cayleyana, then
Pyz> Pze» Pxy Must coincide with the tangents p,, py, p: in X, Y, Z.
6. For pr, py, and pr, to be concurrent, there must be a point W
for which we have Ady = 0, Dib = (0, and HEY Mie 0.
But then (abc) abilaly == 0!
For arbitrarily chosen Y the locus of XY becomes a figure of the
third order, passing through Y, because we have (abc) ee O:
But by taking notice: of (4) we see that this figure consists of three
tangents of the Cayleyana. Out of
andy = ()); aya = 0 and aza,jay = 0
1) See e.g. Crepscu, Legons sur la géométrie, Il, p. 284.
( 780 )
follows indeed
(Adz + ay)? aw = 9;
ie. if Z lies on XY’, then p. will pass through the point of inter-
section W of py, p, and pr,, which bears then at the same time
Pyz and Ppzz-
So the three lines p,, p,, and p,, coneur only then in one point
when XY and Y are united by a tangent of the Cayleyana. Their
point of intersection bears then also all the polar lines and mixed
polar lines belonging to the points of those lines.
The lines p., Pry, and p,- will be concurring, when
2
(abe) a,b, bye,cz = 0
is satisfied, thus also
2
(abe) Ay CyCyby 0s
hence also
5
(abe) a,b,c, (byez _ b.cy) = (0),
If we put
YkEl — YLEk = Sn ;
we have the condition
9 vd ,
(abc) a,bzc, (beS) = 0.
As this can also be written in the forms
(abe) Ax bree (acs) == (0) <einel (abc) Pans (abS) ——a)
and as out of
te Gia ||
ya tie) by
follows the relation
(abe) § == ay (be§) -+ bx (caS) + ex (ab5)
the above condition can be replaced by
(abe)? a,b,¢r52 = 0.
With arbitrary position of X this is satisfied by ¢,=0, i.e. when
X, Y, and Z are collinear (see § 3).
If however
(abc)? azbzc, = 0,
so that Y lies on the Hessian, then X, Y, and Z are quite arbitrary.
This was to be foreseen, now namely a, is a pair of lines, so that
the lines pr, Py, and pz: concur in the node of ay.
( 781 )
Physiology. — “Contributions to the study of serum-anaphylaais.”
(From the “Institut fiir Infektionskrankheiten” at Berlin). By
Dr. J. G. Sierswiuk. (Communicated by Prof. C. H. H. Sproncr).
(4 communication.)
(Communicated in the meeting of March 26, 1910).
During the first months of last year I had an opportunity, in three
communications’), to make the results of my investigations about
serumanaphylaxis known to the Academy. Since that time the lite-
rature about this subject has not inconsiderably increased. It is not
my intention at all here to go in for a discussion of this. Only let
it be allowed to me (and I even consider myself obliged to do this
before the Academy) to treat here in a few words of these publica-
tions, in which my own investigations either directly or indirectly
were discussed, and to add the results of a number of further ex-
periments. May it be presupposed that in general the facts commu-
nicated by me must be acknowledged as correct.
Principally we have to pay attention to three points:
dst. the part of the red corpuscles of the guinea-pig with respect
to horse-serum in the phenomenon of Tu. Smrra, 2°¢. the problem
of the alexine-fixation and of the haemolysis in the anaphylactic
shock, and 38" the application of the specitic hypersensibility for
proteins in medicina forensis.
Last year I explained why I was of opinion that the sensitizing
principle of the first injection and the toxic substance of the second
administering of serum must be considered identical and that only
quantitative differences are met with here. In the meantime BrsreDKa *)
has changed his mind and taken’ this standpoint. Now the logical
consequence of my observation that horse-serum by treatment with
the blood of a guinea-pig can be deprived of its poisonousness for
animals made sensitive, was therefore that with this at the same
time the sensitizing substance is fixed. Levapitr and RaycHMan, who
could also really prove what I mentioned last, do not refrain, therefore,
in this connection, from referring to my communication.*) Also
Satus corroborated my observation concerning the depoisoning action
of the red corpuscles on horse-serum. *)
The problem of the complement fixation has of late attracted
attention to a high degree. I remind of my first communication in
which I said already, “that a sensitized guinea-pig, which reacts
1) These Proceedings: January, February, and March 1909.
2) Ann. de I’Inst. Pasteur, Oct. 1909.
3) C. R. Soc. de Biol. T. 67, 1909, p. 1078.
4) Wiener Klin. Woch. 1909, no. 48.
( 782 )
upon the second serumadministration with symptoms of intoxication
some time after that injection produces a serum that is exceedingly
poor in haemolytic alexine.” By the side of this I have proved that
the serum of hypersensitive animals in not 2 single combination with
horse-serum gives a precipitate, nor is it able to fix complement.
A remarkable incongruity therefore, and by which the anaphylactic
state is distinguished from the phase of immunity, at which prae-
cipitines are formed, and at which in vivo as well as in the test-
tube alexine is fixed. I point out that here I came in conflict with
Niconze and Apr’), who had found that the serum of sensitized
guinea-pigs does fix complement with horse-serum in vitro. For
Fripppercer, who considers anaphylaxis as a peculiar form of the
immunity for proteins, at which the praecipitines only for a trifling
part have passed into circulation, but principally have remained
fixed (sessile) to the cells, the fixation of complement was a welcome
phenomenon. He took for granted (evidently without any further
control) that the communication of Nicotie and Apr was correct,
whilst, on the other hand, he could confirm by his own investigation
my observation about the loss of alexine during the anaphylactic
shock.?) Yet even here such quantitative differences came to light
that at first sight my observations seemed to show a shade of in-
correctness. I had said for example, that the maximum of complement-
loss is reached after about half an hour, whereas FriepperGer found
this to be* the case already within five minutes. Therefore I am
compelled to enter into this somewhat more closeiy.
Frieppercer has evidently not asked himself where the cause
may lie of our diverging results, quantitative as they may only be.
He speaks only in passing of “Differenzen in der angewandten
Anaphylaxie-technik.” But here lies the cardo quaestionis, and what
I presumed already, appeared to me on closer investigation to be
reality. I had namely administered to my animals the toxie serum-
injection in not too great a dose in their abdomen; the reaction is
then less violent and has a slower course, so that — through the
investigation of blood-samples taken from the animals consecutively
at different times of the anaphylactic shock — I could in general
fix the course of the complement-curve. Frirppercer, however, injected.
his hypersensitive animals intravenously: the reaction then goes so
quickly and is so violent, that the guinea-pigs usually die within
few minutes. And at the same time also the complement-loss has
soon reached its maximum. Now in Wassrrmann’s laboratory I have
By) “Ann. de I'Inst. Pasteur 1908.
2) Zeitschr. f. Imm. forsch. Bd. IIL, H. 6,
(783 )
been able to fix these differences in a series of exact quantitative
complement-titrations. From these it appeared among others that a
few minutes after intravenous injection of 0.2 em* of horse-serum
the complement-quantity of the testanimal-serum may have decreased
nearly as strongly as at intraperitoneal injection of 3 cm* after
half an hour.
My investigations and those of Frreppercer, accordingly, do not
contradict each other; they complete each other. Therefore I cannot
see in FriepBerGer’s results anything but an essential corroboration
of my observations. The same thing holds good for the haemolysis,
which in the anaphylactic shock shows itself in the test-animals.
FRIEDBERGER corroborates also this fact, just as Ports’) does. My
contention, therefore, that Brsrepka with his exclusivistie opinion
that it is only the elements of the central nervous system which
are to be brought to hypersensibility, is wrong, finds satisfactory
support in this haemolysis which has been proved in more than
one hand. :
Now as to the alexine-fixation of the anaphylactic serum with its
antigen in vitro, I think I can maintain my negative results over-
against Nicottke and Apr. In many series with mixtures of falling
quantities of horse-serum with rising quantities of anaphylactic
guineapig-serum I could not observe anywhere a specific retardment
of the haemolysis. Not even though I stuck accurately to the quan-
titative proportions, as Niconie and Apr have mentioned. In the
meantime, thanks to the necessary controlling experiments, I came
to the following conclusions. Even normal guinea-pig serum (inactivated)
often retard the haemolysis, quite independent of the presence of
horse-serum; nay, Wwe sometimes meet a normal serum which has
a stronger fixing power than an anaphylactic serum which has also
been examined*). Therefore I abide by my former contention that
there is bere no question of a specific complement-fixation in the
test-tube. This incongruity of the alexine-fixation in vitro and in
vivo, to which I drew attention already a year ago, was the other
‘J
day corroborated with certainty by MicHaéLis in the meeting of the
““Physiologische Gesellschaft” at Berlin (21 January 1910). Also
F'RIEDBERGER seems after all to share this opinion (Zeitschr. f. Imm,
forsch. Bd. IV, H.5). It now seems to me that the labile state of
physiological equilibrium, in which the hypersensitive organism finds
itself, is biologically characterized by the incongruity referred to
just now.
1) Handelingen v. h. Nederl. Natuur- en Geneesk. Congr. te Utrecht, April 1909,
2) Ampler details I hope to publish e/sewhere.
( 784 )
Not long ago Tsurvn*) tried to reduce the signification of the
alexine fixation in vivo in anaphylaxis. Thus already in normal
guinea-pigs normal serum from dog or rabbit would cause loss of
complement. This certainly does not hold good for horse serum, as
had already appeared from my former controlling experiments ; indeed,
about this Tsurun does not speak. But moreover this investigator
has worked with corpuscles sensitized not strongly enough and with
insufficient dilutions of complement, so that his results do not deserve
a very great confidence. Leaving this out of consideration, he found,
just as I did before, that the intoxication-phenomena and the loss of
complement need not run parallel, from which I drew the conclusion
that these two are not directly dependent upon each other, but have
a common cause.
I now come to the third point that 1 wish to treat of here, viz,
the application of anaphylaxis in the practice of medicina forensis.
Evidently this application was so clear that about at the same time
and independent of my communication, similar results were made
known by THomsen, Untenautu, and H. Prrirrer. The last lays stress
upon the strong fall in the temperature of the body during the
anaphylactic shock as a resource for the diagnosis.
Concerning the technique of this investigation the following may
still be mentioned. If a blood spot has to be identified, and if guinea-
pigs are treated intraperitoneally, several cm* of serum are necessary
for each animal that is to be examined. If the animals are treated
intravenously (in the jugularis), much smaller quantities of serum are
wanted, but then an operation in the neck has to take place, which,
however, after some practice for this purpose offers no objection. It
has now appeared to me that also with young rabbits of about
1 K.G. the experiment can be very well made, because here both
the sensitizing and the trying injection can be easily made in the
earvena. A small dried up blood-spot is dissolved in 1 em’. of
physiological salt-solution and injected in such an animal; after a
fortnight 1 em*® of the suspected kinds of blood is injected also
intravenously. To rabbits, which had thus been previously treated
with extracts from haman blood-spots, I have administered on conse-
cutive days serum from goat, horse, cow, and guinea-pig, without
the animals reacting in the least. Lastly 1 em* of human serum
caused them within a few minutes to answer with spasms and
paralyses, with respiratory disturbances, incontinentia urinae et alvi,
ete. The anaphylactic reaction will, in my opiion, in the practice
1) Zeitschr. f. Imm. forsch Bd. IV, H. 5.
( 785 )
of medicina forensis henceforth maintain its position by the side of
the precipitation in vitro as a valuable method.
Among the many questions that show themselves in the study of
our subject, there was also the following: what happens to the
injected horse-serum during the anaphylactic shock? If there were
only a minimal quantity free and unchanged in the circulation of
the intoxicated animal, it ought to be possible that with its blood a
normal animal could be sensitized. Now it has appeared to me that
this is.never crowned with success. From this it may be inferred that
all the antigen taken up in the blood-circulation is at once fixed by
the cells of the hypersensitive organism, resp. deprived of its specific
character at the same time.
Mathematics. — “On the structure of perfect sets of points’. By
Dr. L. E. J. Brouwer. (Communicated by Prof. Korrewne).
(Communicated in the meeting of March 26, 1909).
§ 1.
Sets of points and sets of pieces.
The sets of points discussed in the following lines are supposed
to be lying within a finite domain of a Sp,.
By a piece of a closed set of points « we understand a single
point or closed coherent set of points, belonging toru, and not con-
tained in an other closed coherent set of points belonging to «.
We can regard as elements of uw its pieces as well as its points,
in other words we can consider « on one hand as a set of points,
on the other hand as a set of pieces.
Let us choose among the pieces of w a fundamental series /S,, S,,
S,,.-., then to w belong one or more pieces ,S,, ,S,,... with the
property that 4S, lies entirely within a for indefinitely increasing n
indefinitely decreasing distance ¢, from one of the pieces S,. These
parts .S, we shall call the limiting pieces of the fundamental series
OSS Soke:
As thus the set « possesses to each of its fundamental series of
pieces at least one limiting piece, a closed set of points is likewise closed
as set of pieces.
By an vsolated piece of w we understand a piece having from its
rest set in w a finite distance, in other words a piece, the rest set of
which is closed.
( 786 )-
Tunorem 1. Lach piece of wu is either a limiting piece, or an isolated
plece.
Let namely S be a non-isolated piece, then there exists in uw a
fundamental series of points 4, ¢,,¢,,.... not belonging to JS, con-
verging to a single point ¢ of S. If ¢, lies on S,, then S, has a
certain distance ¢, from S. There is then certainly a point ¢, of the
fundamental series possessing a distance < s, from S, lying therefore
not on SS, but on an other piece »S,. Let ¢, be the distance of S,
from S, then there is certainly a point ¢, of the fundamental series
possessing a distance <¢, from JS, lying thus neither on JS,, nor
on §,, but on a third piece S,. Continuing in this manner we
determine a fundamental series of pieces S,,.S,,.S,,..., containing
consecutively the points ¢,,¢,,¢,,... converging to ¢. So the pieces
S,,S,, S,;-.. converge to a single limiting piece which can be no
other than JS.
By a perfect set of pieces we understand a closed set, of which
each piece is a limiting piece.
A perfect set of pieces is also perfect as set of points ; but the
inverse does not hold. For, a perfect set of points can very well
contain isolated pieces.
We shall say that two sets of pieces possess the same gecmetric
type of order, when they can be brought piece by piece into such
a one-one correspondence, that to a limiting piece of a fundamental
series in one set corresponds a limiting piece of the corresponding
fandamental series in the other set. So in general a closed set
considered asa set of pieces possesses not the same geometric type
of order as when considered as a set of points.
A closed set we shall call punctual, when it does not contain a
coherent part, in other words when all its pieces are points.
§ 2.
Cantor's fundamental theorem and its extensions.
The fundamental theorem of the theory of sets of points runs as
follows: :
If we destroy in a closed set an isolated point, in the rest set
again an isolated point, and so on transjinitely, this process leads
after a denumerable number of steps to an end.
The discoverers of: this theorem, Cantor ') and Brenprxson *) proved
1) Mathem. Annalen 23, p. 459—471.
2) Acta Mathematica 2, p. 419—427.
(75m)
it with the aid of the notion of the second transsinite cardinal 2, which
is however not recognised by all mathematicians. LINDELOF ‘) gave a
proof independent of this notion, where, however, the process of
destruction itself remaining non-considered, the result is more or less
obtained by surprise.
Only for linear sets there have been given proofs of the fundamental
theorem, which at the same time follow the process of destruction
and are independent of 2°).
The rest set which remains after completion of the process of
destruction and which we may call the Cuntor residue, is after
Cantor *) a perfect set of points, however of the most general kind,
thus in general not a perfect set of pieces.
An extension of the fundamental theorem, enunciated by ScHOENFLIES*)
and proved by me*), can be formulated as follows:
If we destroy in a closed set an isolated piece, in the rest set again
an isolated piece, and so on transfinitely, this process leads after a
denumerable number of steps to an end.
My proof given formerly for this theorem was a generalisation of
Linpenor’s method, but at the same time I announced a proof
which follows the process of destruction, and which I give now here;
in it is contained a proof of the fundamental theorem, which in
simplicity surpasses by far the existing ones, is independent of 2, and
follows the process of destruction :
By means of Sp,—i’s belonging to an orthogonal system of directions
we divide the Sp, into n-dimensional cubes with edge a, each of
y 1
these cubes into 2” cubes with edge 5h each of the latter into 2
1
cubes with edge i & etc.
'
All cubes constructed in this way form together a denumerable
set of cubes K.
Let now «w be the given closed set, then A’ possesses as a part a
likewise denumerable set A, consisting of those cubes which contain
in their interior or on their boundary points of uw.
1) Acta Mathematica 29, p. 183—190.
2) Scuoenruies, Bericht tiber die Mengenlehre I, p. 80, 81; Gétt. Nachr. 1903,
p. 21—31; Harpy, Mess. of Mathematics 33, p. 67—69; Youne, Proceedings of
the London Math. Soe. (2) 1, p. 2830—246.
3) 1. c. p. 465.
4) Mathem. Annalen 59; the proof given there p. 141—145, and Bericht iiber
die Mengenlehre II, p. 181—135 does not hold.
5) Mathem. Annalen 68, p. 429.
( 788.)
To each destruction of an isolated point or isolated piece in up now
answers a destruction of at least one *) cube in A,; but of the latter
destructions only a denumerable number is possible, thus also of the
former, with which Cantor’s theorem and ScHoENFLIEs’s theorem are
proved both together.
Let us call the rest set, which remains after destruction of all
isolable pieces, the Schoenjlies residue, then on the ground of theorem
1 we can formulate:
Turorem 2. A Schoenjlies residue is a perfect set of pieces.
§ 3.
The structure of perfect sets of pieces.
Let S, and S, be two pieces of a perfect set of pieces wu. Let it
be possible to place a finite number of pieces of fe into a row having
S, as its first element and S, as its last element in such a way, that
the distance between two consecutive pieces of that row vs smaller
than a. Then we say, that S, belongs to the a-qroup of S,.
If S§, and S, both belong to the a-group of S,, then S, belongs
also to the a-group of S,, so that « breaks up into a certain number
of “a-groups’. This number is finite, because the distance of two
different a-groups cannot be smaller than a.
a,<a,, and if an a,-group and an a,-group of mu are given,
then these are either entirely separated or the a,-group is contained
in the a@,-group.
If two pieces S, and S, of u are given, then there is a certain
maximum value of a, for which .S, and S, lie in different a-groups
of w. That value we shall call the separating bound of S, and S, in
u, and we shall represent it by o, (S, ,,).
If fartheron we represent the distance of S, and S, by a(S, ,S,),
then «, (S, ,S,) converges with a(S, ,S,) to zero, ae also inversely
a(S,,8,) with o, (S,,S,). For otherwise convergency of 6, (S, ,S,) to
zero would involve the existence of a coherent part of gf, in which
two different pieces of « were contained, which is impossible.
The maximum value of a@ for which « breaks up into different
a-groups we shall call the awzdth of dispersion of w, and shall represent
it by S(u). This width of dispersion of uw is at the same time the
greatest value which o, (S,,S,) ean reach for two pieces S, and S,
of u.
‘) Even of an infinite number.
( 789 )
The maximum value of a, for which uw breaks up into at least n
different a-groups we shall eall the n-partite width of dispersion of pw,
and shall represent it by dn(u). Clearly J, (uw) is <d(u).
For « exists furthermore a series of increasing positive integers
n,(u), 7,(4), n,(w),....-in such a way that d,(u) for nm between
nye—1 (4) and n;(u) is equal to Dn (u)(U): This quantity 4), ,)(a) we call
the At width of dispersion of mw and as such we represent it by
J(u).
We now assert that it is always possible to break up « into m,
perfect sets of pieces m,,.... fn, So as to have d(u;) < d,,,(u) and
(U1, » Uhy) 2 In, (4)-
Let namely be d;,,(#) = d(u); we can then obtain the required
number m, by composing each mu, of a certain number of dM (a)-
groups belonging to a same d“—!)(u)-eroup. We are then also sure
of having satisfied the condition e((y, , 4; ) 2 Jn,(u).
Fartheron we can place the d\(u)-groups of a same d@—)(u)-group
into such a row that the distance between two consecutive ones is
equal to d(u). If we take care that each uw, consists of a non-
interrupted segment of such a row, then the condition d(u,) < dn, (qu)
is also satisfied.
Let us now break up in the same way each mu, into im, perfect
sets of pieces f4y1,-... im, mM such a way that (quai) < dn,(u,) and
A(uyi, » Lhi,) 2 Gp,(un), and let us continue this process indefinitely.
If then we represent by Ff, an arbitrary row of v indices, then
we shall always find
On,(up, )S Sim, + my... +m, + 1—» (W) . as is (A)
As mw is a perfect set of pieces, the width of dispersion d(u,. )
can converge to zero only for indefinite increase of »; out of the
formula (A) follows, however, that for indefinite increase of » that
convergency to zero always takes place and, indeed, uniformly for
all vt elements of decomposition together.
At the same time the separating bound of every two pieces lying in
one and the same vt element of decomposition converges uniformly
to zero; so these elements of decomposition converge themselves
uniformly each to a single piece.
If finally a variable pair of pieces of ge is given, then their distance
can converge to zero only when the order of the smallest element
of decomposition, in which both are contained, increases indefinitely.
The simplest mode in which this process of decomposition can be
( 790 )
executed is by taking all im,’s equal to 2. If then we represent the
two elements of decomposition of the first order by uw, and «,, those
of the second order by yo; Moss Moor f422, and so on, then in this way
the different pieces of w are brought into a one-one correspondence
with the different fundamental series consisting of figures O and 2.
And two pieces converge to each other then, and only then, when
the commencing segment which is common to their fundamental
series, increases indefinitely.
Let us consider on the other hand, in the linear continuum of
real numbers between O and 1, the perfect punctual set a of those
numbers which can be represented in the triadic system by an infi-
nite number of figures O and 2. The geometric type of order of
a we shall represent by $.
Two numbers of a converge to each other then and only then,
when the commencing segment which is common to their series of
figures, increases indefinitely.
So, if we realize such a one-one correspondence between the pieces
of mw and the numbers of 2, that for each piece of uw the series of
indices is equal to the series of figures of the’ corresponding number
of a, then to a limiting piece of a fundamental series of pieces of
« corresponds a limiting number of the corresponding series of
numbers in a, so that we can formulate:
Turorem 3. Each perfect set of pieces possesses the geometric type
of order §.
For the case that the set under discussion 7s punctual and lies in
a plane, this theorem ensues immediately from the following well-
known property:
Through each plane closed punctual set we can bring an arc of
simple curve.
Combining ScHornriizs’s theorem mentioned in § 2 with theorem
3 we can say:
Tunorem 4. Each closed set consists of two sets of pieces; one of
them possesses, if it does not vanish, the geometric type of order &,
and the other is denumerable.
§ 4.
The groups which transform the geometric type of order § in itself.
Just as spaces admit of groups of continuous one-one transforma-
tions, whose geometric types of order’) are again spaces, namely
1) In this special case formerly called by me *Parametermannigfaltigkeiten”
Comp. Mathem. Annalen 67, p. 247.
( 791 )
the finite continuous groups of Liz, the geometric type of order ¢
admits of groups of continuous one-one transformations, which possess
likewise the geometric type of order ¢.
In order to construct such groups we start from a decomposition
according to § 3 of the set uw into m, “parts of the first order”
Hy >a y+++ Un, of each of these parts of the first order into m, ‘parts
of the second order” wri, ttr2, fia, -- +--+ Wim, ete.
The parts of the first order we submit to an arbitrary transitive
substitution group of m, elements, of which we represent the order
by p:, and which we represent itself by g,.
After this we submit the parts of the second order to a transitive
substitution group g, of m,m, elements which possesses the parts of
the first order as systems of imprimitivity and g, as substitution
group of those systems into each other. We can then represent the
order of g, by p, po-
The simplest way to construct such a group g,, is to choose it
as the direct product of g, and a substitution group y,, which of
the parts of the second order leaves the first index unchanged and
transforms the second index according to a single transitive substi-
tution group of m, elements.
We then submit the parts of the third order to a transitive sub-
stitution group g, of m,m,m, elements which possesses the parts of
the second order as systems of imprimitivity and g, as substitution
group of those systems into each other. We can represent the order
of g, by P. Ds Ps-
In this way we construct a fundamental series of substitution
STOUPS 91> 92> Is -- >
Let t, be an arbitrary substitution of g,; rt, a substitution of g,
having on the first index of the parts of the second order the same
influence as t,; t, a substitution of g, having on the first two indices
of the parts of the third order the same influence as t,; and so on.
The whole of the substitutions r, then determines a substitution
of the different fundamental series of indices into each other, in other
words a transformation t of the pieces of w into each other.
This transformation is in the first place a one-one transformation ;
for, two different pieces of uw lie in two different parts of a certain,
e.g. of the rt order, and these are transformed by +t into again two
different parts of the rt order.
If fartheron S,,.S,,.S,,... is a fundamental series of pieces, pos-
sessing S,, as its only limiting piece, then, if 4(n) is the lowest possible
order with the property that S, and S, lie in different parts of that
order, 4(m) must increase indefinitely with 7.
Proceedings Royal Acad. Amsterdam. Vol. XII.
¢ 792 )
So by the transformation r+ the fundamental series passes into a
new fundamental series having as its only limiting piece the piece into
which JS, passes by t.
As a set of pieces ft is thus continuously transformed by t.
be a series of substitutions satisfying the same
a
Ibe Pastor
conditions /as: the) series’ 7) 7,,.7,,)..- Wt then, = 23) er
etc., then the series t”,, t’,, t’,,... likewise satisfies the same conditions.
If farthermore +t’ and t” are defined analogously to t, then 17’ is
equal to t”.
So the transformations satisfying the conditions put for t form a
group, which we shall represent by gq.
To investigate the geometric type of order of this group, we
decompose in the way indicated in § 3 a perfect set of pieces 9 into
p, parts of the first order @,,0,,--++,,; each of these into p,
parts of the second order @j1, @i2,- +++, Qhp,; and so on.
The p, substitutions of g, we bring into a one-one correspondence
to the parts of the first order of 9. Then the p,p, substitutions of
g, into such a one-one correspondence to the parts of the second
order of vy, that, if a substitution of g, and a substitution of g, have
the same influence on the first index of the parts of the second order
of uw, the part of the second order of @ corresponding to the former
lies in the part of the first order of @ corresponding to the latter.
In like manner we bring the p, p, p, substitutions of g, into such
a one-one correspondence to the parts of the third order of @, that,
if a substitution of g, and a substitution of g, have the same influence
on the first two indices of the parts of the third order of uw, the
part of the third order of @ corresponding to the former lies in the
part of the second order of @ corresponding to the latter; and so on.
The parts of @ corresponding to a series t,,7,, 7, ,--. then converge
to a single piece of @, which we let answer to the transformation
t deduced from the series. Then also inversely to each piece of 0
answers a transformation 1, and the correspondenceattained in this
goer
manner is a one-one correspondence.
Farthermore two transformations t and t’ converge to each other
then and only then, when their generating series t,,7,,7,,--..and
r,,t',,t,,.+.-- have an indefinitely increasing commencing segment
in common, in other words when the corresponding pieces of @
converge to each other. So the correspondence between the trans-
formations t and the pieces of y is continuous.
The transformations zt, in other words the transformations of the
group g, have thus been brought info a continuous one-one correspon-
dence to the pieces of 9, so that g possesses the geometric type of order S.
( 793 )
If now we adjoin to each substitution group g, a finite group
gin of continuous one-one transformations of fas a set of pieces in
itself, tranforming of the pieces of mw the first m indices according to
gn, but leaving unchanged all their other indices, then the funda-
mental series of the groups 4’,, 9's» Y/x5++» converges uniformly to
the group g.
The set whose elements are the groups g of the geometric type of
order € constructable in the indicated manner possesses the cardinal
number of the continuum. For, already the set of those series
m,, M,, M,,-.., Which consist of prime numbers, possesses this
cardinal number, and any two different series of this set give rise
to different groups g.
We can sum up the preceding as follows:
Turorem 5. The geometric type of order § allows of an infinite
number of groups consisting of a geometric type of order 5 of con-
tinuous one-one transformations and being uniformly approximated
by a fundamental series of groups consisting each of a finite number
of continuous one-one transformations.
If in particular we consider those groups g for which each g, is
chosen in the way described at the commencement of this § as the
direct product of g,—; and a group y,;, we can formulate in par-
ticular :
Tueorem 6. The geometric of order § allows of an infinite number
of groups consisting of a geometric type of order § of continuous
one-one transformations and being uniformly convergent direct pro-
ducts each of a fundamental series of finite groups of continuous
one-one transformations.
§ 5.
The sham-addition in the geometric type of order §.
Let us choose the factor groups indicated in theorem 6 as simply
as possible, namely g, as the group of cyclic displacements corre-
sponding to a certain cyclic arrangement of the first indices, and
likewise each y, as the group of cyclic displacements corresponding
to a certain cyclic arrangement of the n> indices; g is then com-
mutative, and transitive in such a way that a transformation of g
is determined uniformly by the position which it gives to one of
the elements of u.
Let us further choose an arbitrary piece of u as piece zero. Let
us represent this piece by S,, and the transformation, which trans-
fers S, into S, and is thereby determined, by “{S,’. That the
: 53*
( 794 )
piece JS; is transferred by this transformation into .S,, we shall
express by the formula
Sef S.= 8,
which operation is associative and commutative.
Let us finally choose, in order to make the resemblance to ordinary
ciphering as complete as possible, all m,’s equal to 10, let us take
for each system of nt" indices the digits 0,1, 2,3,4,5,6,7,8,9 in
this order, and let us give to the piece zero only indices 0.
The different pieces of gu we can then represent biuniformly by
the different infinite decimal fractions lying between O and 1, in
such a way, however, that finite decimal fractions do not appear
and that -80 is not equal to -29, whilst each group y, consists of
the different ways in which one can add the same number to all
nth decimals, modulo 10.
Now according to the above we understand by ‘5473... 4 -9566...
the decimal fraction, into which ‘5473... is transferred by the
transformation which transfers -0 into -9566..., or, what comes
to the same, the decimal fraction, into which °9566.. . is transferred
by the transformation which transfers ‘0 into -5473...
We shall call the operation furnishing this result, on the ground
of its associativity and commutativity, the “sham-addition” of -9566 . . .
to ‘d473....; it takes place just as ordinary addition, with
this difference that in each decimal position the surplus beyond 10
is neglected, thus that different decimal positions do not influence
each other. So we have:
PSAT Bl. 21, OOOO km. 6 sao ne
Let us understand analogously by °5473....—-9566.... the
decimal fraction, into which -5473.... is transferred by the trans-
formation which transfers -9566.... into -O, and let us call the
operation furnishing this decimal fraction the ‘“sham-subtraction” of
-9566.... from °5473....; then this sham-subtraction is performed
in the same way as ordinary subtraction with this difference,
that “borrowing” does not take place at the cost of the preceding
decimal positions, so that here again different decimal positions do
not influence each other. So we have:
“DATS weit 95660) HOO era
By operating only with a finite number, great enough, of conse-
cutive figures directly behind the decimal sign, sham-addition and
with the exact one up to any desired degree of accuracy. In this
too they behave like ordinary addition and subtraction of real numbers.
sham-subtraction furnish in the type of order 5 a result agreeing
( 795 )
Microbiology. — “Emulsion laevulan, the product of the action
of viscosaccharase on cane sugar’. By Prof. M. W. BEeErINck.
In the proceedings of the Academy of 9 February 1910 an enzyme
was described which produces from cane sugar and raffinose a
viscous matter incapable of diffusion. My further investigations, made
conjointly with Mr. D. C. J. Minkman, proved that this substance is
closely related to the laevulan of Lippmann’) but not identie with it.
Our emulsion laevulan originates in watery nutrient solutions in
quite the same way as in the agarplates, so that these solutions
change into a milkwhite emulsion; the liquid between the suspending
Jaevulan droplets opalises very strongly. In hot water the substance
is fairly soluble and the specific rotation of the polarised light, which,
on account of the opalisation can only approximately be determined,
is about
@,= — 80
whilst Lippmann gives for his laevulan
Qa ile.
D
On account of this considerable difference in its rotating power,
anew name, e.g. “sinistran”, might seem desirable. But the word
laevulan having a collective meaning to which also the more and
the less soluble forms of our substance may be brought, we shall
here use the general denomination, the more so as it is sure that
the laevulan of the literature, like ours, consists of the cell-wall
substance of bacteria. ‘
Besides by Lippmann the formation of laevulan by bacteria has
also been observed by Maassen*), who does not, however, describe
the appearance of the emulsion, so that in this case, too, a modifica-
tion of our emulsion laevulan seems to be produced. The here
concerned microbe is a sporulating fermentation organism, called by
Maassen Semiclostridium commune, but not yet found by us.
Preparation and properties of emulsion laevulan.
We were first of opinion that emulsion laevulan might be best
prepared by using Bacillus emulsions, for we had stated that this
species does not decompose the once formed laevulan, whilst B.
megatherium and 6. mesentericus, which likewise produce emulsion
1) Chemie der Zuckerarten 3'¢ Aufl. 1904. Pag. 906, 1312.
*) Arbeiten aus dem Kaiserl. Gesundheitsamte. Biol. Abt. Bd. 5, p. 2, 1905,
( 796 )
laevulan, attack this substance and use it as food as soon as the
cane sugar fails. We have, however, found that with some precaution
it is much easier, especially with B. mesentericus, to produce large
quantities of laevulan, than with B. emu/sionis; this reposes on the
circumstance that the former species, particularly at high temperatures,
about 40°, possesses a very strong vegetative power, whilst the latter
always grows slowly and has a relatively low temperature optimum,
below or near 30° C.
Hence we used for the preparation of laevulan the common hay
bacterium, which is the form of B. mesentericus obtained by accu-
mulation methods, such as the method of potato slices and that of
malt solutions. But this form is so common in our surroundings and
so well adapted to the life in cane sugar solutions of for the rest
different composition, that these, after pasteurisation or short boiling
and when kept warm, of themselves produce laevulan by the devel-
opment of the spontaneous spores of the hay bacillus. Such solutions
then turn milky and slimy by the formation of the microscopic
laevulan emulsion.
For the experiments were used large ErLenmeyer-flasks with 500
em’ of a medium of the composition: tapwater, 20°/, canesugar,
0:05,°/, KNO;, and 0:05°/, K{-HPO,, cultivated at) ==27°3C:
This liquid inoculated with 6. mesentericus very soon obtains the
said milky appearance. The same emulsion which to the colonies
of B. mesentericus and B. emulsionis on cane sugar agarplates gives
so peculiar a character, is now in large quantity produced in the
culture liquid, saturated besides with laevulan in true solution, which
causes the strong and characteristic opalisation, not known to us to
such a degree in any other substance. Besides, at the bottom of the flasks
a thick transparent slime layer is slowly formed, which also proved to
consist of laevulan, wherein, however, the bacterial bodies themselves
are accumulated, whilst the liquid above it is poor in bacteria but
abounds in viscosaccharase and laevulanemulsion. The acid formation
in this solufion is sight but not absent.
The Jaevulan may be precipitated with alcohol for which 50 °/,
in the solution is sufficient. Only at a much greater alcohol concentration
other substances of the liquid also precipitate. by dissolving in boiling
water and again precipitating the further purification is easy. After
drying and pulverising a snowwhite nearly tasteless powder results.
From a flask as the above which at first contained 100 G. of
cane sugar, 8 G. of pure dry laevulan were obtained after 7 days
cultivation, there still being in the liquid 20 G. of invert- and 70 G,.
of cane sugar; the slime at the bottom not being collected.
(797 )
From another flask quite alike to the preceding, which also con-
tained 100 G. of cane sugar, were gained 15 G. of laevulan after
17 days, 45 G. of cane sugar and 35 G. of invert sugar still being
present.
The slime adhering to the bottom, consisting of B. mesentericus
with thick cell-walls of laevulan, was used for a new culture for
which a solution of 2°/, of cane sugar, 0.05 °/, K NO, and 0.05 °/,
K, HPO, was used. After 18 days were obtained 2.25 G. from the
10 G. of original cane sugar, accordingly 22,5 °/, of laevulan was earned.
Pure laevulan is somewhat soluble in cold water, much better in
boiling; all solutions opalise very strongly. It does not reduce FEHLING’s
coppersolution; only after prolonged boiling a feeble reduction is
observed. It is incapable of alcoholic and lactic acid fermentation,
but by butyric acid ferments, in absence of air, it gets into as strong
a fermentation as cane sugar, whereby hydrogen, carbonic and volatile
acid result.
A number of bacteria can feed on it when growing with access of
air. Azotobacter chroococcum can use it under fixation of free nitro-
gen and formation of some acid.
By a treatment with acids, especially when warm, it changes
readily into laevulose and so becomes fit for alcoholic and lactic-
acid fermentation. After the inversion, by heating with resorcine and
strong hydrochloric acid, the red colour appears, characteristic of
laevulose, whilst with orcine and hydrochloric acid the violet colour,
indicating pentose, is completely absent. When distillated and
treated with sulphuric acid no perceptible quantity of furfurol can
be detected.
As said, the specific rotation, which cannot be exactly determined
on account of the strong opalisation is
«n= 80°,
and after hydrolysis
tp = AO
After prolonged heating with acid in the autoclave at 120° the
rotation lowered even to
= AO
t= 64°.
That of pure laevulose is
— oF
e)= 9
There is some probability that this diminution is due to destruction
of part of the laevulose.
( 798 )
As we had found that the slime at the bottom of the flask is less
soluble than that obtained by alcohol from the emulsionated liquid
above it, we prepared laevulan from this slime also by separate
experiments, for we supposed that dextran might occur therein, which
is much less soluble in water than laevulan. However, it was found
that the laevulan obtained in this way gives no other rotation after
inversion than the emulsion laevulan, from which it does not differ.
Hence it is sure that hay bacteria produce no dextran at all, but
that their cell-wall consists of various modifications of laevulan of
different solubility.
Not only in media of the above composition B. mesentericus pro-
duces laevulan, this happens quite as easily in a yeast decoction
with 2 to 20°/, of cane sugar, addition of chalk proving favourable.
The temperature of cultivation may also vary and even rise to 40° C.,
but then care should be taken that the laevulan itself be not attacked
by the producer.
From the preceding it may be concluded that the large lumps of slime
so easily formed on cane sugar agar-plates by Bb. mesentericus and
the other emulsionating species consist as well of laevulan as the
emulsion which occurs round the colonies of this species in the agar.
Hence, it can neither be doubted that the slime of these colonies,
which does not diffuse in the agar, is produced by viscosaccharase
from cane sugar, and that this enzyme only partly gets out of the
bacterial body proper, the cell-wall included. Evidently in the cell-
wall itself the enzyme forms new laevulan by converting the cane
sugar, with which both cell-wall and agar-plate are imbibed.
The production of cell-wall substance in consequence of the action
of an enzyme, which in my former communication was called pro-
bable, must now, as regards laevulan, be considered as proved.
Dextran and the dextran bacteria, which we have likewise studied,
shall later be treated more thoroughly. For the moment it may be
observed that by this substance the polarised light is strongly rotated
to the right; we found
en= = 1322.
whilst in the literature by various authors is given for dextran
&p) = + 199° to 230°.
Quite like laevulan it results exclusively from cane sugar. So lae-
vulan as well as dextran are produced by microbes, neither from
laevulose, glucose, or any other sugar, but solely from cane sugar
and rvaffinose. The slimy cell-wall substances formed by other microbes
from glucose, laevulose and maltose, are of a different nature.
( 799 )
Physics. — “Researches on the magnetization of liquid and solid
oxygen.” By H. Kamertinch Onnes and ALBERT PERRIER.
Communication N°.116 from the Physical Laboratory, Leiden.
§ 1. Introduction. It is scarcely necessary to remark that the
investigation of the magnetic properties of oxygen at low tempera-
tures has long occupied a position on the programme of the cryogenic
laboratory, or that this has been considered one of the most important
items on the programme since the investigation of both liquid and
solid oxygen has been made possible by the perfecting of the methods *)
of obtaining detailed series of measurements at constant temperatures
in the region of liquid hydrogen. Indeed, while the strongly magnetic
properties of oxygen of themselves select it from all other substances
as especially suitable for the study of para-magnetism, we can in the
meantime for no other substance obtain the magnetic equation of
state*), which gives a representation of the magnetic properties of a
substance in the three states of aggregation at as many successive
temperatures and pressures as possible.
The investigation of oxygen at very low temperatures and at
pressures that can easily be realised was expected to give at once
results of much importance.
Curiz") found for gaseous oxygen between 20° C. and 450° C.
that the specific susceptibility (magnetization per gram for H = 1)
was inversely proportional to the absolute temperature, and FLEMING
and Dewar‘) concluded from their latest measurement of the suscepti-
bility of liquid oxygen at its boiling point that Curtn’s law was obeyed
down to —188° C.
Does the specific susceptibility continue to increase so strongly at low
temperatures or does it approach a limiting value? Is oxygen in the
solid state ferro-magnetic? Does the magnetization finally at extremely
low temperatures perhaps begin to decrease and disappear completely
at the absolute zero? *)
Ee KAMERLINGH OnnEs, These Proc. Sept. 1906, Comm, from the Leyden labor.
no. 94f (1906i.
2) H. KamertincH Onnes, Commun. from the Leyden labor. Suppl. no. 9 p. 28.
3) P. Curte. Ann. chim. phys. (7) 5 (1895) p. 289.
4) Firemine and Dewar Proc. Royal Soc. London 63, p. 311, 1898.
5) It has since appeared that the magnetization of ferro-magnetic substances
does not yet give any justification when the temperature is lowered to the
melting point of hydrogen for the assumption that the electrons whose motion
causes magnetization are frozen fast to the atoms and that therefore this disap-
pearance at the absolute zero may be expected. (P. Weiss and H. KameruneH
Onnes, These Proc. Jan./Febr. 1910, Comm. from the Leyden Labor no. 114 p. 9).
( 800 )
These are questions which, considering the possibility of obtaining
important contributions to the knowledge of the influence of density
upon susceptibility by high pressures in the region where the gaseous
state of aggregation changes continuously into the liquid make it a
very attractive work to realise, even from a purely experimental
point of view, the representation to which we have just referred.
The work was commenced though only when Prof. Wuiss ex-
tended his magnetical researches to very low temperatures and the
measurements on the magnetization of ferro-magnetic and cognate
substances at very low temperatures, which were communicated to
the February Meeting’), were undertaken. With that investigation
which was carried out at the same time, the present one is very
closely related, and for part of them we made use of the same
appliances. In our present investigation we haye also in various
ways made use of Prof. Wuiss’s method’) of determining the magne-
tization by means of the maximum couple exerted by a magnetic
field of variable direction upon an ellipsoid of the experimental
substanee, a method which had been entirely successful in the other
research. We must also express the great advantage we derived
from the continued support given us by Prof. Wuiss, and we take
this opportunity of gratefully acknowledging our indebtedness to him.
The change with temperature of the specitic susceptibility of oxygen,
the investigation of which was our first object, is of particular
importance seeing that Cvurin’s law follows from Lanegvin’s kinetic
theory of magnetism’). It was soon apparent to us that this law
was not valid for oxygen, as was thought, down to — 183° C., but
that it would have to be replaced by another. According to the
important paper of pu Bots and Honpa communicated to the January
Meeting — our experiments had already been completed at that
time — various elements were found for which Curtr’s law did not
hold at temperatures above 0° C. This at once increases the impor-
tance of the further investigation of oxygen, for which over a definite
region of temperature Curm’s law is valid, while over another region
it obeys a second law, viz.: that of inverse proportionality to the
square root of the absolute temperature. The results concerning this
law and also concerning the probability of a sudden change m the
value of the specific susceptibility on solidification will be discussed
in § 5.
1) P. Weiss and H. Kamertinan Onnes. These Proc. Jan./Febr. 1910. Comm. fr.
the Leyden labor. no. 114 (1910).
2) P. Weiss. Journ, de phys. 4e série t. VI, p. 661; 1907.
8) Langevin. Ann. chim. phys. (8) 5, p. 70; 1900.
( 801 )
We have been occupied with another question besides the change
of specific susceptibility with temperature, which was suggested
both by the experimental results obtained by Frewne and Dewar
and by the theories of Langevin and Wuiss.
In the experiments of the first-named there appears sufficient
evidence for the conclusion that there is a decided diminution of the
susceptibility as the strength of the field increases (the diminution is
of the order of 10°/, in a field of 2500 gauss). Now, according to
the theory of LaneGrvin para-magnetic substances must, it is true,
exhibit this phenomenon, but calculation from his formulae limits
the magnitude of this change to less than 0.1°/, in the case of liquid
oxygen at its boiling point. Should a higher value than this be
obtained, then one would be led to assume the existence of a WrIss
molecular field’). We arranged our experiments so that the liquid
and the solid oxygen could be subjected to a field of 16000 gauss,
a field very much stronger (about six times) than that used by
Freminc and Drwar, so that we might expect the phenomenon which
appeared in the course of their experiments to be exhibited to a
much greater degree in ours even at the same temperatures as were
used by them. If what was observed by FLeminc and Dewar could
really be ascribed to the beginning of saturation then the theory
would further lead us to expect that as the temperature sank the
change would strongly increase (becoming infinite at 7’= 0), and
that in our experiments with liquid hydrogen it would become very
striking. We have, however, observed only small deviations, which
we shall discuss further in § 5.
As regards the experimental methods employed by us in our in-
vestigation, two completely different schemes were adopted: on the
one hand was measured the magnetic attraction exerted upon a
column of the liquid, and on the other the maximum couple
exerted by a homogeneous field upon an ellipsoid. The second method
is more especially suitable for comparative measurements and can also
be used for frozen oxygen; the first can be used only for the liquid
phase, but on the other hand it makes very trustworthy absolute
measurements possible; we have therefore adopted it as the basis of
our other measurements. In the carrying-out of each method further
precautions are still desirable, so that while we are busy pushing
on the investigation, we propose at the same time to repeat it in
part in order to increase the accuracy of the results obtained by
taking such further precautions as have appeared possible in the
course of the work.
1) Weiss, L’nyp. du champ moléc. loc. cit.
( 802 )
Liquid oxygen I.
§ 2. Method of the magnetic rise. As mentioned above, we have
rendered the method of the magnetic rise employed by Qurckg,
pu Bors and other observers suitable for use at low temperatures.
One limb of a vertical O-shaped tube, the upper portion of which
contains the gaseous, and the lower the liquid phase of the experi-
mental liquefied gas was placed between the poles of a magnet
whose field was horizontal.
Let // be the field, (//’ the field in the other limb is supposed to be
so small that (/7’//)* is negligible), g the acceleration due to gravity,
z the difference in height of the levels of the liquid under the in-
fluence of 7, @ and o, the densities of the liquid and of the gaseous
phases respectively, A and A, their respective volume susceptibili-
ties, then
(KK, A? =2z(o=os)\g) «hae me
or, by introducing the absolute specific susceptibility x
(HO NeOn) 2 e021 (O— 05) 9)
If y=y, then the equation becomes simply
ey 9
— ya) a (2)
which is the formula we have used for our calculations. *)
So there are striking advantages offered by this method parti-
cularly for an absolute measurement, on account of its applicability
to the case of a liquid in equilibrium with its own vapour. There
are only two magnitudes to be determined, the distance z, which
can be measured very accurately with a cathetometer, and the field
H; nor have we to know the density of the liquid in order to be
able to find the specific susceptibility.
Magnetic rise apparatus. lt is a very easy matter to cause an
ordinary liquid to ascend under the influence of magnetic attraction,
but the experiment is attended by serious difficulties when one has
to deal with a liquefied gas. Boiling must be completely avoided,
and care must be taken that the vaporization is unnoticeable. The
first precaution is necessary because the motion of the liquid or of
its surface would render adjustment quite impossible, and the second
1) In § 5 we shall give the reasons why we think that x = xo, and should it be
possible that this is not the case there is still the greatest probability that
xo <1.5 %; in the most unfavourable case at the boiling-point the correction remains
below 0.002 in value, while at lower temperatures it is quite inegligible on account
of the small value of <.
( 803 )
is necessary that the total quantity of liquid may not appreciably
alter during the measurement of one rise. Moreover magnetic
action itself increases the difficulties; it is easy to see that it can
oceasion the formation of gas-bubbles which divide the column of
liquid into two parts, so that the one portion remains suspended
between the poles, while the other falls back again. In that case
measurement of the ascent is out of the question.
Starting from the thermodynamic potential it appears that in every
case the relation
29y 9 > K (H* — H,’)
must hold, where # is the field at the surface of the liquid, and
H, the field at a distance y below the surface of ‘the liquid. These
conditions shew that there is a limit to the intensity of the fields in
which measurements may be made, for they necessitate a range of
extended fields (in this case in a vertical direction). Conical pole-
pieces are thus as a matter of fact barred.
After several preliminary experiments an apparatus was constructed,
the most important part of which consisted of two concentric double-
walled vacuum tubes, with which we already succeeded in obtaining
rather successful measurements. The walls of the double vacuum
tube were not silvered, so that we were able to watch how the
liquid behaved during the experiments. From the experience thus
acquired the improved apparatus which we shall now proceed to
describe was designed and constructed.
It will be seen that the construction of the apparatus lays a very
heavy tax upon the art of the glass-blower’). As before, the chief
part consisted of two independent U-shaped vacuum tubes, the one
fitting inside the other. The double walls of each tube are completely
silvered on the vacuum side, except in the case of the inner tube,
where the distance which the liquid ascends is left free, and in the
outer where a sufficient length is left unsilvered to leave a strip of
a few millimeters breadth through which the level of the liquid can
be read. One of the tubes completely surrounds that portion of the
other which contains liquid; this we call the protecting tube. The
narrowest portion J/, (fig. 2) is placed between the poles of the
electro-magnet. The narrow limb of the inner tube must of course
be perfectly cylindrical. The cther limb is enlarged and serves as a
reservoir. In order to be able to apply equation (2) all care was
taken that the temperature of the liquid and vapour up to a height
1) The double vacuum tube was prepared by Mr. Kessetrine, Laboratory glass-
blower, and the remainder by Mr. Fim, technical assistant at the Laboratory.
( 804 )
somewhat greater than that reached by the column of liquid was
everywhere the same both in the wide and in the narrow tube;
and further care was taken that where the temperature of the vapour
above the liquid in the upper parts of the apparatus changes to
ordinary temperature it was as far as possible the same at the same
height in the two limbs of the O-shaped space. With this end in
view the liquid in the inner tube was, by means of the magnetic
field, repeatedly moved up and down under constant vapour pres-
sure, until we might assume that in this tube equilibrium was suffi-
ciently well attained. To make this equilibrium possible the inner
tube is surrounded with liquid at the same temperature as that
which the liquid in it must attain. In the outer or protecting
tube the liquid is kept constantly in motion by means of a stirrer
consisting of a brass ring |S, that can be moved up and down; it is
possible to do this and still keep the space closed by utilising the
flexible rubber tube S,. The vaporization in the inner tube is thus
very small (between 0.5 and 1 litre of gas measured under normal
atmospheric pressure escapes per hour).
Notwithstanding all these precautions temperature differences
must stili be encountered. In the liquid, in which the convection
currents maintaining heat-equilibrium can be followed by the
small particles which they carry along with them, these tempe-
rature differences must have been very small. In the gas layer
in the upper portion of the O-shaped space there must indeed have
been considerable differences; but on account of the small density
of the gas, these have but small influence upon the difference of
level in the two limbs, and, moreover, that influence may be almost
entirely neglected seeing that the observations are simply comparative
measurements with and without the magnetic field. Now, care has
been taken that the temperature over the distance that the liquid
rises can vary but slightly, while in the upper portions of the tube
practically the same state of affairs is maintained during both obser-
vations. We have therefore omitted the correction that should still
have to be applied for possible temperature differences.
Comparing the positions of the liquid in the narrow cylindrical
tube with and without the magnetic field also reduces the correction
for capillarity to the insignificant differences in form of the menisci,
and this correction, too, we have omitted.
The inner and the outer tubes are closed independently of each
other by means of the German-silver caps P,; P,, Q,, Q, (fig. 1);
the junction is made air-tight by the rubber sleeves J/,, V,, which
at the same time unite the two tubes firmly together. Liquid oxygen
( 805 )
is introduced into the protecting tube through the small tube P,,
and into the inner tube through Q,. The two tubes P, and Q, lead
the vaporized oxygen through the valves P, and Q, (fig. 2) to two
gasometers. Two manometers 7, and Q,, the latter of which is
provided with an indicator Q, so that small vaponr pressures may
be read off aecurately, serve at the same time as safety valves. It
is not necessary that the oxygen in the protecting tube should be as
pure as that in the inner tube; for the latter, with which the obser-
vations were made, very pure oxygen was used.
A double sliding movement F allowed an easy adjustment of the
apparatus each time, so that the meniscus in the measuring tube
just reached the desired point in the field between the poles, usually
in the axis of the pole pieces.
Course of a series of measurements. The field is brought to the
desired strength and by means of / the meniscus is made to rise to the
desired point, which is read off on asmall scale. Then the meniscus is
moved up and down several times while care is taken that the field slowly
increases. In this way the temperature is made everywhere the same
and the walls of the tube are wetted. While the field has the desired
value the position of the meniscus is read off; then a reading is
made while the field is off; after the meniscus has been three times
allowed to rise somewhat higher than the desired position, another
reading is made while the field is on; once more a reading is made
with the field off and so on several times. In this manner the error
arising from vaporization of the liquid during the adjustment of the
cathetometer is eliminated’). It is not essential to know the position
of the level in the cther limb of the tube; so as to be able to take
account of this, we ascertained the ratio of the cross-sections of the
two limbs of the tube.
We have further made sure that the residual magnetism exerted
no appreciable influence upon the position of the meniscus after the
current was cut off. For this purpose a feeble current was sent
through the coils in the direction opposite to that which had just
been broken. Had the residual field exerted any appreciable influence
we should have seen first a further sinking of the level, and
then a rise as the current was slowly increased. This has not been
observed.
We used the same electro-magnet as was used for the cryogenic
investigation of the ferro-magnetic metals”), to which we must refer
-1) To control the position of the meniscus without the magnetic field, we
measured the quantity of gas vaporized (cf. preceding page).
2) P. Weiss and H. Kamertinca Onnzs, l. c.
( 806 )
for details regarding its construction. It was only necessary to replace
the conical pole-pieces by cylinders with flat ends. Their distance
apart was micrometrically adjusted to 25 mm. and controlled with
an accurate callipers. We may here remark that between the measu-
rement of the ascent and that of the field, the pole-pieces remained
clamped tight to the cores, so the adjustment of the distance could
give rise to no error.
Since in the subsequent calculation the strength of the field is
involved to the second power, and since we are concerned with an
absolute measurement, we endeavoured to make our measurement
of the field strength as trustworthy as possible with our present
appliances. With this end in view we measured the strength of
an arbitrarily chosen standard field by two different processes, and
we compared the strengths of the fields used in our experiments
with this standard by successively withdrawing the same coil
attached to a ballistic galvanometer from the standard field and from
the various fields which we desired to measure.
The standard field was set up with the same flat pole-pieces at
a distance of 9 mm. apart, and with a current of 5 amp. All pre-
cautions were taken to ensure the demagnetization of the magnetic
cycle beforehand. This field was first measured by means of
Corton’s magnetic balance’). As is well known this method consists
of equilibrating weights of a total mass m against the ponde-
romotive power of the field H on a straight portion of length /
of a conductor through which a current flows of intensity 7; then
we get
m g
al
For the degree of accuracy, however, which we wish to reach,
several corrections must be taken into account. In the first place
the various parts of the balance were accurately calibrated. The
length 7 of the current element was determined micrometrically and
on the dividing engine, and so also was the distance between the ares
of the balance which distance ought to be the same throughout
seeing that the arcs must be accurately concentric. The very small
deviations from this were allowed for by means of a_ ballistic
investigation of the topography of the field. The balance arms of
the weights and of the current element were measured with the
cathetometer. The topographical study of the field also gave us the
5) ID).
1) For this method of measuring the field and for the magnetic balance see:
P. Weiss and A. Corron, Le phénoméne de Zeeman pour les trois raies bleues
du zinc, Bull. Séances Soc. frang. de phys. 1907, p. 140, also J. de phys. 1907.
( 807 )
correction necessary for the force exerted upon the second straight
element of the balance (i.e. that outside the pole-gap). The sum
total of these positive and negative corrections came to some units
per thousand.
The greatest care had to be devoted to the absolute value of 7,
which was measured by means of an accurate ammeter by SreMENS
and Hatsks. This was calibrated in absolute amperes by comparing
on the potentiometer the potential difference between the terminals
of an international ohm (or for the stronger currents of 0,1 2) with
the electromotive force of a Weston cadmium cell. For the requisite
accuracy of the measurements the influence of neighbouring instruments
or currents upon the ammeter, or of its position in the earth’s field
were by no means negligible; we got rid of almost all these irregularities
by a suitable adjustment of the distances and of the positions of the
rheostats, and we eliminated further possible remaining errors by so
connecting a/l the conductors that the currents in all except the am-
meters could be reversed wt the same time. Finally we always used
the ammeters in the same position with respect to the earth’s field
as that in which they had been calibrated.
When all calculations and corrections had been completed it was
found that the strength of the standard field was 9857 gauss according
to this method.
The second method by which the value of the same field was
found consisted .of the sudden withdrawal from between the poles
of the magnet of a coil of wire of which the area encircled
by the current was known. The change thus caused in the number
of induction lines embraced by the coil was compared by means of
a ballistic galvanometer with the number of induction lines embraced
by a solenoid the dimensions of which were accurately known.
The coil consisted of 19 turns of silk-insulated wire, 0.25 mm.
thick, wound round a cylinder of ebonite, 20 mm. in diameter.
The dimensions were obtained by various measurements with the
micrometer screw and the dividing engine, and were repeatedly
controlled. At the same time a control coil was constructed by
winding bare copper wire in a helical groove cut in the curved
surface of a cylinder of ebonite; the area encircled by the current
was then measured for this control coil by the same methods and
with the same precautions as were adopted in the case of the first.
The ratio of the two was in agreement with the ratio of the deflec-
tions of the ballistic galvanometer which were obtained by connecting
the two coils in series with the galvanometer and then withdrawing
them successively from an unchanged magnetic field. We may further
54
Proceedings Royal Acad. Amsterdam. Vol. XII.
( 808 )
say that we had previously verified the absence of magnetie pro-
perties from the ebonite by means of an apparatus after Curm in
which we utilised the attraction in a non-uniform field.
For the measurement of the field there were placed in eireuit
with the galvanometer the coil on the ebonite cylinder, a manganin
resistance to regulate the sensitivity, a secondary coil of 500 turns
fitting round the standard solenoid. and tinally, an electromagnetic
arrangement which could be used as a damper if desired. We
also allowed for the very small deviations from the law of pro-
portionality between the deflections of the galvanometer and _ the
quantities of electricity, which had been determined for the galvano-
meter (one of the Drprez-p’ArsoNnvaL type) by a previous investigation.
The solenoid was constructed with the greatest accuracy by winding
bare copper wire on a core of white marble ’).
The standardisation of the galvanometer was made by reversing
the current in the solenoid; the observations made by withdrawing
the coil from the field always took place between two standardisations
of the galvanometer; there was, however, no change in the galvano-
meter constant to be observed. The corrections and precautions
necessary in obtaining the strengths of the current are the same as
in the case of the balance, and have already been described. The
final result of this ballistic method is
9845 gauss.
The relative difference between this and the value given hy Corron’s
balance is therefore 0.0012; and this can be neglected especially
when one remembers that almost every one of the numerous meas-
urements necessitated by the one method as much as by the
other, beginning with the adjustment of the field by means of the
ammeter, is accurate only to 0.0005. It may be useful to comment
here upon a particular point that increases the difficulty of obtaining
this agreement and therefore enables us to rely more upon the
correctness of the numbers which we have obtained. The equation
for Corron’s balance involves the strength of the current in the
denominator, while this magnitude in calculating according to the
ballistie method occurs in the nwmerator; a systematic error there-
1) For the dimensions and the description of the solenoid and galvanometer
see: P. Weiss, Mesure de Vintensité d’aimantation & saturation en valeur absolue,
Arch, Se. phys. et nat. February 1910, J. de phys. May 1910,
( 809 )
fore in the absolute number of amperes would, of necessity, occasion
a relative difference twice as great between the values of the field
obtained by the two methods (the same ammeter was used with the
balance and with the solenoid).
We have given the ballistic method a somewhat greater weight
than the other on account of the smaller number of corrections it
involved, and thus we have finally taken as the value of the
standard field
9850 gauss.
Once this standard field was definitely fixed all other measurements
could be rapidly made by the ballistic method described above.
For the conical pole-pieces which are employed in experiments
according to the maximum couple method, and which give much
more powerful but much less uniform fields, we used a_ coil
of 7 to 8 mm. diameter accurately centred on the axis of the
pole-pieces. In this case direct comparison with the standard
field just mentioned was not possible since the flat polepieces
had to be screwed off to make room for the conical poles.
To meet this case the area of the small coil encireled by the
current was determined once and for all by withdrawing it from
the standard field before the flat pole-pieces were removed, and
comparing the change thus brought about in the number of the
induction lines with those of the solenoid by means of the ballistic
galvanometer.
All the measurements that we have given up to the present refer
to the field in the centre of the space between the poles. For the
few exceptional values of the field, and, consequently, of the ascent
of the liquid oxygen for which it was necessary to cause it to rise
pretty far above the axis of the pole-pieces, the field was determined
at those points by simple ballistic comparison with the fields on the
axis, and we made use of the cathetometer to adjust the position of
the small coil.
( 810 )
Results of observations and calculations.
Series of observations with the apparatus with unsilvered walls.
Ay Beles ala: t= — 183°.0 C. ') |
Position of Obs. rise hetwnt he H in ae
meniscus. | s'in cm. | ESevalE gauss, | 4?
Level of axis 1.032 1.064 | 2980 1.194
. 1.646 4.690 | 3727 1.246
‘ 1.656 4.701 | 3727 1.224
axis + 2.44cm.) 3.024 3.410 5182 1.458
axis 3.198 3.289 | ~ 5205 1.214
: 4.16 4.978 5848 1.251
axis + 2.44 4.90 5.050 6570 1.168
axis 5.124 5.270 6600 | 4.240
axis + 244 7.87 8.094 8075 1.249
axis + 2.44 9.20 9.462 9043 1 .158*
The difference in height z was obtained from the observed ascent
from z= 2’ (1 + 0.0285). The observation * was very difficult and
is little rehable.
The deviation in the case of the observation in a field of 5182
gauss is probably due to a mistake of 1 in the number of whole
millimeters which were read off, but of this we are not certain.
Deviations from proportionality with //? are considerable but by
no means systematic. If we take the mean of all the measurements
with the exception of the last in which special difficulties were
encountered we reach the value
=== 120915 Osi,
Jat
and for the specific susceptibility with g = 981.3 for Leiden
F90°.1 ——— Doleo. . 10S,
') The boiling point of oxygen according to H. Kamertinga Onnes and C, BRaak
These Proc. Oct 08. Comm. fr. th. Leyden labor. N°. 107a § 6,
TA BL Ee: #=— 2019-75 C.
re : diff. in ; |
Position of Obs. rise height with Hin Ca
: . reservoir H Ens
meniscus. | g'in cm. aa Gait gauss. H
Level of axis 1.192 1.229 2980 1.376
. 41.893 1 944 3727 4.399
| : 1.881 1.935 3727 4.393 |
s 3.643 3.7417 | 5905 ie Se3 ee
é 4.623 4.752 5848 4.389
5 5.01 6.078 6600 4.395
| axis-+-2.5 cm. | 7.376 7.586 T421 1.378
axis +2.5em.| 8.715 | 8.963 | 8069 | 1.372
mean. aE = IES GrelOm4
whence it follows that y-,095 x,= 272,0.10-°.
Finally, at — 209°,2 C. a single observation was made. The rise’
was 6.115 cm. in a field of 6600 gauss, which with the correction
for the sinking in the reservoir gives
— — 1.444 10-7 and yos2.0 x. = 283.4 . 10—6.
We shall now give the series of observations made with the
silver-walled apparatus which we have already described.
TABLE Ila: t= — 183°.0C.
Position of Obs. rise leeere in | H in eae |
meniscus. | ¢ in cm. | pescwols ' gauss. | ey
axis [ied 0602-7) “4090 \I" 20gjer |) e2o7
x 1.669 | 1.716 | 3727 | 4.935
3 3.169 3.958 | 5183 | 4.913
A | 3.220 | 3.310 | 5198 1.295
i 4.035 | 4.448 | 5807 4 230
4.093 4.208 5848 1.230
4101 4.216 5848 4.233
5.119 5.262 6578 1.216
axis -+ 2.5 cm. 7.750 | 7.967 8075 | | 1.994
; | 8.950 9.201 8659 1 297
axis + 3.5 cm.| 9 296 9.484 8808 1.299
_ | 9.266 9.525 8808 1.298
For this apparatus z= z' (1 + 0,0280).
The mean value of = is 1,226.10—°, whence it follows that
¥90°.1K, = 240.6.10—6,
Position of
meniscus
axis + 2.5
axis
axis + 3.5
| axis + 2.5
axis + 3.5
axis + 2.5
axis + 3.5
axis
axis + 3.5 cm.
cm.
cm.
(Sle)
t= — 2019.75
Obs. rise oe Be H in BA p
2' in cm. en ee gauss Has
AP ADS 4.228 | 2980 1.383
1.879 1.932 3727 1.291
3.625 3.726 5205 4.375
4.567 4.0695 5848 AeSio
5 461 5.614 6399 ‘avn
5 832 5.995 6567 1.390
5.852 6 O16 6600 41.381
6.463 6.644 | 6086 | 1.365
6.899 7.092 | 7169 | 4.380
8.207 | 8.437 | 7863 | 1.365
8.654 8.892 8069 1.366
8.988 | 9,240 8212 | 1.370
8.913 | 9.162 8212 1.358
Mean of all observations is 1.375 whence it follows that
4719.35 K, == 269.9 . 10—6.
TPAGB Ese lic: t= — 208°.2 C.
| Position of Obs. rise [height with | H in ae
meniscus g! in cm. | Deoant | gauss He
|
axis 1277 Peot3 2980 | 1.478
‘ 1.996 2.052 3727 1.477
3 3.813 3.920 5005 | | 1.447 |
Fs 4.841 4.977 | S48 1.461
| axis +2.5 cm. 6.012 Git20... |) e567) | 4.433% a
axis 6.094 6.264 6600..,|. 4-488he]
6.113 6.284 6600 1.4453
axis + 2.5 cm. 7.146 7.346 | 7169 | 4.429
axis + 3.5 em. 8.579 8.819 7863 1.426
\— = as
| (813 )
Mean of all obServations 1.448, whence it follows that
4612.9. = 284.2. 10-6.
Finally for finding the specific susceptibility the density of
oxygen was found from the formula’)
o = 1.2489 — 0.00481 (7 — 68).
From table II we obtain
Keoo°, K. = 27552 . 10—6
K71° 35K. = 332,8 . 10-6
Ker°s K = 359,0. 10-6.
Table Ill gives yV 7 for each of the temperatures and for each
of the series.
Series with the first apparatus Series with the improved apparatus
lof. eee Pee A ee) Ae
if 105 WT.A103 T | x.4108 WV T.A0
= Ee hes Se ee |
90.1 PRY (5a) 9.95 | 90.4 240.6 DF OBS |
71 35 272 0 9.99 | * 2.85 269.9 2.979
39 983.4 2.96 || 64.9 ISA 2 2.989 |
| re r| eo ea
| mean 2.27 | 2.284
There is no systematic change to be noticed in the product yy 7’;
the greatest deviation from the mean is 1°/, with the first apparatus,
and only */,°/, with the second; moreover the deviations in the two
series at corresponding temperatures are in opposite directions. Hence
within the limits of accuracy of the observations the specific suscep-
tibility can be represented by the formula
2284 =e
j= VT :
In the comparative measurements which we shall describe in the
sequel we shall find the same law, at least as far as its form is
regarded. For the discussion of this point we refer to § 5.
The differences between the various values of the ratio EE are
greater than we should be led to expect from the accuracy obtained
1) Baty and Donnan. J. Chem. Soc. 81 (1902) p. 907.
( 814 )
(0,05°/,) in the measurements with the cathetometer of the displace-
ments of the level, and from the accuracy of the measurements of
the field-strengths, of which a discussion is given above. It is certain
that the cause of these deviations must arise from a source other
than the measurement or these two data, though we cannot with
certainty indicate what this may be.
We may in the meantime remark that, at least in the case of the
first series, the unsteadiness of the apparatus in the vertical direction
in the not quite homogeneous field, and the slight inconstancy of
the temperature have certainly been contributory causes of these
deviations, since the second apparatus which was improved exclusively
in these directions gave much more regular results. This remark,
however, does not seem to account sufficiently for certain appreciable
changes that occurred without any noticeable corresponding irregularity
in the pressure or in the convection current of the liquid, while
there was also no noticeable change in the shape of the meniscus.
Liquid oxygen TI.
§ 3. Measurements by the method of the maximum couple exerted
upon an ellipsoid. Further comparative measurements for liquid
oxygen at various temperatures were obtained by means of the
method of the maximum couple exerted by a uniform field upon an
ellipsoid. This method has already been described and discussed in
connection with the research on ferro-magnetic substances *); it will
be sufficient to discuss the modifications which were found to be
necessary owing to the particular circumstances under which the
method had to be applied to the present research.
In the first place on account of the small value of the susceptibility
it was necessary to make the couple to be measured as large as
possible; with this end in view we chose an oblate ellipsoid of
revolution, instead of a prolate; its axis of revolution was placed
horizontal in a field which could turn round a vertical axis.
The ratio that is taken between the axes is not a matter of in-
difference; for a given major axis the couple, which is proportional
to (V,—N,)v, is a maximum for a ratio of the major to the minor
axis that is only slightly smaller than 3; we have therefore taken
this value of the ratio for the construction of the ellipsoids.
We used the same electromagnet as served for the measurements
made by Weiss and KamertincH Onngs (loc. cit.). Two pairs of pole-
1) P. Weiss, J. de phys. (4) 6 (1907) p. 655. P. Wetss and H. Kameruincu Onnes,
Comm. N°. 114 These Proc. Jan /Febr 1910.
~
ae
( 815 )
pieces were used; first the cylindrical pole-pieces with quite flat end
surfaces that had been used for the measurement of the magnetic
rise, and then truncated conical pole-pieces the end surfaces of which
(slightly concave, see in this connection p. 818) were 4 em. in dia-
meter, and the side surfaces of which were connected by convex
surfaces of revolution to the cylinders that formed the cores; these
were 9 cm. in diameter. These pole-pieces were constructed to give
the strongest possible field when the distance between the poles was
taken to be 20 in.m. By this means a field of about 16000 gauss
was obtained.
Our observations were made with an ellipsoid that was diamagnetic
with respect to the surrounding medium — a solid silver ellipsoid
immersed in a bath of liquid oxygen. The ellipsoid was turned by
the “Société genevoise pour la construction d’instruments de physique”
from a block of very pure Merck silver. A preliminary experiment
showed that it was very slightly diamagnetic with respect to air, and
that this was quite negligible with respect to the liquid oxygen. The
axes were measured microscopically on the dividing engine; this gave
major axis = 1.0973 em. and axis of revolution = 0.3654 em.
Furthermore, two intermediate ordinates parallel to the axis of
revolution were measured on the dividing engine, and they were
found to be 2°/, greater than the corresponding ordinates of a perfect
ellipse with the same axes. This deviation from ellipsoidal shape was
confirmed by a direct determination of the volume from the weight
and the density, which gave
0.2329 c.c,
while calculation from the dimensions of the axes gave
0.2308 c.c.
In the calculations we made use of the value 0.2329.
The cryogenic apparatus, essentially the same as that used by
Weiss and Kamer“incGH Onnes is shown in PI. I fig. 3. Once more
we see the cover B, the adjusting tube f’, and the holder b’. The
cover with its various parts: the cap with the stuffing-box D, glass
tube C, window with plane parallel glass plate C,, the system BG
for adjusting the whole apparatus, the tension rods 4, for supporting
the Dewar tube, the helium thermometer 6, the little screens to
protect the upper portions of the apparatus from cooling, ete. is just
the same as before. The Dewar tube is of the same shape, but the
lower portion is of greater diameter. The only difference between
the adjusting tube 7’ and that which was used in the other investi-
gations is that the lower portion /,' is of greater diameter.
( 816 )
The holder and the torsion spring ave, on the other hand, completely
altered. On account of the smallness of the couple to be measured
all foreign magnetic actions had to be eliminated as carefully as possible.
Preliminary experiments showed us that a metallic holder could not
be used, not only on account of the traces of para- or ferro-magnetic
impurities that are never absent from workable metals but also on
account of the difficulty of keeping the surface sufficiently clean ;
this difficulty was encountered repeatedly in the silver ellipsoid
that we used in our experiments, and it is probable that the
constant contact of the hands with iron tools plays a part in causing
it. Glass seemed to be by far the most suitable material both oa
account of the absence of inherent magnetization and of the fact that
the surface on account of its smoothness can be kept quite clean.
The holder which we finally adopted was made completely of
elass: it consists of a tube 6’ 5 mm. in diameter that at 0’, is drawn
out to a narrow but thickwalled stem, 0.7 mm. in diameter. To this
stem the silver ellipsoid was attached; for this purpose a hole of
sufficient width to fit was bored along one of its greater diameters
and the ellipsoid was then fixed at the desired height by means of a
little wax that completely filled the narrow space between the glass
and the metal. The tube was then pumped free from ir and sealed
off, so that the liquefaction of the air that it would otherwise contain
would be prevented. The flat mirror for measuring the angle of
torsion and the oil-damper were also attached to the holder.
The torsion springs. On account of the smallness of the couples
to be measured (the constants of the springs were of the order of
1200 e.g.s. while those used for the investigation of the ferro-
inagnetic substances were ‘some tens of thousands) it was found more
suitable to use a straight instead of a helical spring. We took a
strip of phosphor bronze about 5.5 em. long (/’) and 0.2 >< 0.01 sq. em.
in cross-section. The upper end was soldered to a spiral spring of
three turns made from a much thicker strip than the other; the
greatest dimension of this strip was horizontal so that in this way it
fulfilled its purpose of being elastic to tension while taking no part
in torsion; its presence is essential to prevent the breaking of the
thin glass stem or of the platinum-iridium stretching wire that is
soldered to the stem. This stretching wire is made from. a platinum-
iridium wire of O.1 mm. diameter, which was rolled very thin so
as to make its torsion constant extremely small without diminishing
to any great degree its resistance to breakage.’ The stretching wire
is fused at 6’, to the lower end of the glass stem, and at its other
extremity it carries a knob c’ which is held fast in a-ring 7’,.
EE —
( Bi7 )
The mounting of the apparatus took place with the same pre-
cautions regarding the centring of the whole, the tension of the
springs, ete. and by a method similar to that which has been described
in the research upon the ferro-magnetic metals.
The course of the observations is very simple once everything has
been set up in position. First, those azimuths of the electromagnet
are tentatively determined for which the couple in both directions is
a maximum. It was sufficient to do these experiments two or three
times with suitably chosen fields, since the azimuth changes but very
little with the field, and for other values of the field one ean without
danger have recourse to interpolation. After that the series of obser.
vations took place in the following manner: Before making a measure-
ment with any particular current this was reversed a certain number
of times so as to obtain a well-defined field; we had not here to
deal with a value of the saturation-magnetization, which changes but
slowly with the field, but in our case the couple was proportional
to the square of the field, so that inaccurate values of the field that
might be obtained notwithstanding the fact that the iron of the
electromagnet was extremely soft would make their influence very
strongly felt in our results. Then the electromagnet was adjusted to
one of the determined azimuths, the torsion angle was read off for
the two directions of the field, the current broken, the electromagnet
turned to the opposite azimuth, and so on several times. At the end
of a series a measurement with one of the first fields was repeated
as a control.
Sources of error, difficulties, corrections, and controls.
1. Inhomogeneity of the magnetic jield. As will be seen from the
following discussion this source of error is by far the most important
in our case and is indeed the only one that need be taken into
aceount. If we assume that the field near the centre’ of the pole-gap
may be represented by an expression of the form
Pe osel :
H=H,-+=—= ( "| (cost ——= i strt= |) es ye eee (e))
where H, is the field in the centre, and 7 and 6 polar coordinates
of a point in the pole-gap with respect to the centre as origin *).
Let us now replace the ellipsoid by a vertical dise whose diameter
is equal to the major axis of the ellipsoid; by taking the expression
for the energy of the magnetized disc in the field and differentiating
it with respect to the angle between the disc and the lines of force,
we obtain for the couple caused by the inhomogeneity of the field:
1) Cf. P. Weiss and H. Kamertinen Onnes L.c.
( 818 )
ma 3 a (CEI
at eG vl (az) (GXCOSIGio naa ete tn)
(7 = radius of the disc).
The ratio ay of this couple for an angle of 45° to the fundamental
0?
Mir a8 Oy? J,
M6 (N= Na
If then we suppose that the relative change of the field in the
couple is
space occupied by the ellipsoid is of the order of 1 in 1000, the
formula given above shews us that although the disturbing couple is
a little smaller than the chief couple, the two are of the same order
of magnitude. Hence we see the great influence that this source of
error can have in the investigation of weakly magnetic substances.
(With ferro-magnetic bodies it is quite negligible : see the previous paper).
We have accordingly devoted the greatest attention to this source
of error. The conical pole-pieces were made slightly concave, during
which process we every time determined the inhomogeneity of the field
by means of a ballistic galvanometer and a small coil that was slightly
displaced. We ascertained that the change in the field in a space of
about 1 ¢.e. was certainly less than 1 in 2000. We have not had
time to pursue this investigation further, and, besides, we should
have to obtain a much more sensitive ballistic galvanometer. But it
will be seen that the homogeneity of the field was sufficient for the
comparative measurements we proposed to make. We may further
remark that all these precautions refer exclusively to the conical
pole-pieees; the experiments with the cylindrical pole-pieces were
nearly free from these sources of error.
We allow for these disturbing couples in the following way :
2
oT
Assuming that ees 2H the expression for the couple due to
0
ao
inhomogeneity given above becomes (y = 45°):
3
— vr? 41H
3
or
or? AK H*,
which we shall represent by
BKH?.
If « is the angle of torsion of the holder and C' the constant
of the spring, then
( 819 )
éa=—> (N= N,) K2H* A BK? on 7. (8)
Thus just as if there were no correction for inhomogeneity the
second side of the equation remains always proportional to the
square of the field. -Even without knowing that correction, if 3 is
itself a constant we should be able to deduce from the observations
whether A’ is a function of the field or not. We see, however, that
the constancy of p requires that of 2, i.e. that the field must remain
homothetic no matter how great it should be. Now this is not the
9
case as can be seen from the quotients = in tables V, VII, and
VIII. Table V_ shows first an increase, then the quotient reaches a
maximum and diminishes considerably; tables VII and VIII shew a
change in exactly the opposite direction; this is just what one would
expect if $8 were variable and A constant, for the tables refer to
two practically identical bodies, of which the one is dia- and the
other para-magnetic. Now in either case the fundamental couple
(uniform field) is in the same direction while the couple due to
inhomogeneity changes sign with the susceptibility ; should, therefore,
the correction in the one case first increase and then decrease, it
must in the other case first decrease and then increase. We shall
return to this point in § 4.
Since this determination aims only at relative measurements, we
have once and for ali taken as the value of the susceptibility of
oxygen at —183°C. the value that was given by the improved
apparatus for measuring the magnetic rise. With the help of this
value we have calculated the values of p for each field from equation
5): (see tables V and VI). These values fall pretty well on a curve of
means. Finally the susceptibility at the lower temperatures is caleu-
lated by means of the value of P as a function of the field given
by this curve. We shall take the opportunity of the corresponding
series of observations to make some remarks upon the influence of
the inhomogeneity for each of the three pole-gaps that were used.
2. The inconstancy of the magnetization as a function of the
azimuth. The general expression for the couple in a uniform field
(N,—N,) I? v sin —p cos @
only reaches its maximum value just at g = 45°, and consequently
sin p cos p="), since 1 remains constant during the torsion. Here
again we see a fundamental difference between the application of
this method to the investigation of saturation magnetization and to
that of a body of constant susceptibility. It is clear that in the first
case the condition / constant is, as it were, fulfilled by definition.
( 820 )
In our case the deviation from this is by no means @ priori negligible:
the two limiting values of /?(@=O° and g= 90°) differ in our
case by 0.3°/,, and since /* always changes between these two
limits in the same direction the error caused thereby when
sin ¢ cos p ="), is less than 0.1 °/,.
In contrast with the two foregoing sources of error, the reaction
of the magnetized ellipsoid upon the distribution of magnetism over
the surface of the pole-pieces can clearly have no effect in the case
of a body of small susceptibility while on the other hand, it had to
be taken into account in the case of the ferromagnetic bodies. Indeed,
with oxygen we have to deal with a magnetization that in the
strongest fields of the electromagnet reaches a value of only a few
units (in the case of iron it was 1700!).
3. Influence of the holder. In this connection we may notice two
actions that may go together. In the first place there is the inherent
magnetism of the stem, and then there is also an action analogous
to that which we wish to measure, for if the stem is not a perfect
body of revolution, it is acted upon in the liquid oxygen just as if
it were a supplementary ellipsoid. We investigated these two sources
of error in a blank experiment in liquid oxygen in which the silver
ellipsoid was removed, and the surface of the glass was carefully
freed from all traces of wax. From this we obtained a maximum
of only 1 to 2°/,, which need not be taken into account
+. The concentration of the oxygen. The oxygen in the bath contained
a little nitrogen, the concentration of which constantly decreased during
the experiment Owing to its faster vaporization. So as to be able to
allow for this we analysed the gas at the beginning and at the end
of each series of observations. The mean concentration was 1.25°/,
at the beginning and 0.35°/, at the end (at the moment that the Dewar
vessel was almost empty). We allowed for this concentration as far as
possible; in this respect there remains an uncertainty of about 0.3°/,.
5. Calibration of the suspension springs. The main torsion spring
described above was calibrated outside the apparatus by observing
the time of oscillation of a system suspended from it with and
without the addition of a known moment of inertia. For the latter
we used a bronze ring of rectangular meridian cross section, the
diameters and height of which were measured with the cathetometer.
Calculation gave the moment of inertia as
582.09 c.g.s.
Care was taken that the spring was subjected to the same tension
during the calibration as it experienced while in the apparatus (by
attaching suitable weights to it by a torsion-less wire).
( 821 )
For the constant of the spring we found 1184,5 ¢.g.s.
The platinum-iridium = stretching wire gives a torsion couple as
well as the spring; the correction for this was determined by the
same method as was used in the analogous case by Weiss and
KAMERLINGH ONNeEs (loc. cit.) and it was found to be 0.0152 times
the constant of the spring. The difference between the values of the
constant at 18°C. and at —190°C. is smaller than the errors of
observation. The calculations were therefore carried out with the
constant 1184.5 (dd + 0.0152) — 1202.5.
6. Oscillations. The silver ellipsoid should be protected sufficiently
from the influence of oscillations arising from external causes by the
occurrence of intensive FoucauLr currents, but the occurrence of
these currents, which were unusually strong gave rise to great difficulties
in the observations. In the first place the holder was extremely slow to
reach its position of equilibrium. Further, the smallest change in the
current flowing through the electromagnet occasioned a sudden kick
in the whole moveable apparatus, an immediate result of the oblique
position of the ellipsoid with respect to the lines of force. Hence the
regulation of the current had to be done with the greatest care.
We retained the oil-damper but removed the fixed partitions, for
the capillary action of these gave rise to couples that, although
small, were still not negligible.
Results of the observations.
TABLE IVa.
Cylindrical pole-pieces 21 mm. apart.
t= — 183°.0C.
ets |e oe een
gauss ern of he H2° :
|
9950 | - 0.37 0.731 217
4537 1.44 0.685 268.8
6676 3.21 0.7200 275.3 |
8339 5.10 0.7335 278A ||
9387 6.44 | 0.7307 277.5
| 40120 7.45 | 0.7974 277.0
| 410685 8.26 | 0.7234 276.4
11120 | 98.99 | 0.7258 971.6
11440 9.38 | 9 7167 974.8
11765 | 9.90 | 0.7155 | 274.6
\ |
Mean Kooi. = 275.6
( 822 )
| TABLE IV6é.
Cylindrical pole-pieces 21 mm. apart.
| t= — 201°.1 C.
Pe eee alec a ae
| gauss | cm gre H2° a
9950 0.50 | 0.988 324
4537 2.10 1.020 328.0
6676 4.66 1.041 331.4
8339 7.36 1.058 | 334.0 |
9387 9.47 1.012 | 331.4 |
10120 10.63 | 1.038 330.8
10685 11.81 1.034 | 330.2
11130 12.70 1.025 | 328.6
11440 13.44 1.02% | 328.4
11765 1414 1.022 | 328.0
Mean K72°.0x. = 3500)
Without being corrected for lack of uniformity in the field the
means give the following values:
das 10—6 = 241.1. 10-6
A902. WK. = 1.143 . = Neeeleeare 6
330.0 ap nde eee >
Ki2°.0 KK. = 1.230 10 ==/2,6820)-01 Use
The corresponding results obtained by the method of the magnetic
rise were
240.6 .10-§ and 269.3 .10—§.
The differences between the results as obtained by the two methods
are scarcely 0.4°/,. This gives us great confidence in the ellipsoid
method even for this particularly difficult determination, and it shews
that the method is also suitable for absolute measurements if only
the necessary care is taken to ensure the uniformity of the field and
the correctness of the shape of the ellipsoid.
We must remember that there was a great number of absolute
os
(78339)
measurements whose results had to be used (axes and volume of the
ellipsoid, constants of the springs, magnetic field, density of the liquid
oxygen) and also that the shape of the ellipsoid was not perfect. On
the other hand we must remark that the application of the correction
for the non-uniformity of the field might conceivably have diminished
the correspondence between the results obtained by the two methods,
We have, however, both theoretical and experimental grounds for
the assumption that this correction remains within the limits of
accuracy of not more than 0.5°/, in the case of cylindrical pole-pieces
with flat end surfaces 90 mm, in diameter and at a distance of
21 mm. apart.
PAV B EV EnaVia:
Conical pole-pieces 20 mm. apart.
| t= — 1830.0 C. fh, hate |
(To determine # we assumed %99°.4 = 240,610 ~),
a ee are
3685 1.27 0.935 58.5
4615 1.96 0.920 54.7
6944 4.55 0.9437 60.8
9205 7.96 0.9400 59.7
11280 41.90 | 0.9348 | 58.5
12835 | 15.44 0.9374 5M
14015} 18.26 0.9295 57.0
14900 20.19 0.9098 51.9
15585 24.73 0.8945 48.1
16120 | 22.87 0.8802 44.5
A graph of # as function of H was made, which was used for
the following table.
55
Proceedings Royal Acad. Amsterdam. Vol. XII.
( 824 )
| TABLE Vo.
Conical pole-pieces 20 mm. apart.
t= — 208°.2 C.
| A | fection vs | 22 107 3,108 K.168
| gauss. cin, of tie HH? ie ae
0996 | 0.79 | 4.498 | 56.0 [357]
4615 0.75 | 1.991 57.8 [328]
6044 | — 6.82 Nea NO eee 344.2
9205 | 4u.45 4.435 59.8 346.3
14280 18.25 1.434 59.7 346.2
| 19835 23.67 4.437 59.2 346.9
14015 27.89 4.420 56.5 346.4
14900 30.84 1.389 52.4 345.1
15585 33.24 1.368 48.0 345.0
16120 35.44 1.363 43.8 347.3
The mean with the exception of the two values placed between
brackets is 345.9 and it gives
464°.9K, = 275,0. 10-6 q
while the method of the magnetic rise gave
{64.9 K. = 288,5 . 10-8
The difference is 3°/,; but in this connection we must remember
that the correction for non-uniformity is about 16°/,, and that the
temperature of the liquid becomes very uncertain at the pressure of
11 mm. under which the liquid boils at this temperature.
Finally, we now give two series of measurements which were
made with other pole-gaps so as to obtain other deviations in
the uniformity of the field. They were hastily made and under un-
favourable circumstances, since oscillations and disturbances caused
by the running of machines in the neighbourhood interfered with
the observations. We give them more as examples of how the method
of calculation followed still leads to good results even when the
couples due to non-uniformity of the field are extremely large (28°/,
of the chief couple).
—————<«—— rc Sr tt—<‘CSCS
( 825 )
eA Bale Ee Via
Conical pole-pieces 18.2 mm, apart.
6—— 4183900
(To determine 6 we assumed Zgyo 4 = 240.6. (Om)!
H | double de-
| | flection 26) 22 4, 3. 106
| | cm. of the | H2° ue
SareS | scale
|
|. 5013 3.34 1.328 159.2
TD47 ead 1.283 147 4
9993 12 64 1.246 137.9
12165 18.33 1.238 136.2
13760 92.39 4.183 194) .7
| 44900 26.26 1.182 191.5
45750 28.83 4.162 116.6
17005 35.58 | 1.230 133.9
6B was again graphed as a function of H, which led to the cor-
rection for A in the following table.
TABLE VIo.
Conical pole-pieces 18.2 mm. apart
t—— 2080.2 C.
2 a eae as
gauss | om of the | H2” Bole K. 106
scale |
5013 46.8 1.861 152 SH |
7547 10.71 1.880 146.5 348
9993 18.88 1.862 437.5 351
12165 27.92 4.885 130.7 357
13760 35.35 4.868 | 195.5 a
44900 A.36 1.861 123.0 360
15750 45.67 1.840 122.5 357
17005 51.81 1.794 197.5 347
( 826 )
,
The mean 3538 gives % == Sa a value that is not
much smaller than 283.5.10-6 which was obtained by the method
of the magnetic rise.
Solid oxygen.
§ 4. Ellipsoid of solid oavygen. In this case observations had to
be made directly upon an ellipsoid of oxygen. The oxygen therefore
had to be frozen in a mould of approximately the same form and
dimensions as the solid silver ellipsoid described above. This new
condition necessitated the following experimental arrangement.
The cover and the Drwar tube are the same as for liquid oxygen,
with the exception of the cap D. The adjusting tube is also the same,
but it is so arranged that it can be moved as a whole up or down,
while the whole apparatus remains closed and in its place. With
this end in view it is attached to the tube m, which moves through
the stuffing-box D",; this corresponds to D, of the liquid oxygen
apparatus, but in this case the wide glass tube C, is lengthened by
a rigid brass tube MM that serves to give sufficient play to the
vertical movement of the whole adjusting tube. The former stem &
had to be lengthened by the same amount (L", L",), and is contained
in the tube m.
The holder is also a glass tube 6"; it is not however closed, but
at 6", it changes into a very much narrower tube (0.5 mm.) that
ends at 6", in a glass ellipsoid a". To this ellipsoid there is fused a
solid stem 6", that connects it with the stretching wire. The oxygen
vets to the ellipsoid through the holding tube which it enters at 6",.
A rubber tube » (¢d=83 mm.) admits the gas from outside; it is
attached to the inlet tube m, that passes through the cover and is
soldered to it. With this arrangement it is easy to cause the oxygen
to solidify inside the ellipsoid. When the apparatus is ready for use
the adjusting tube is pulled upwards by the cap A till the glass
ellipsoid reaches the unsilvered part of the vacuum glass. The vacuum
elass is then filled with liquid hydrogen. While the ellipsoid is still
connected with a reservoir of oxygen, the adjusting tube with the
ellipsoid is slowly pushed downwards until it does not quite touch
the liquid hydrogen but is in its vapour. The oxygen is then seen
to condense slowly, and, if the operation is carefully performed, the
whole ellipsoid and supply tube are seen to fill with liquid oxygen.
The tube being lowered still further, vapour is reached that is suffi-
ciently cold to cause the oxygen to solidify. On account of the large
( 827 )
contraction of the oxygen on solidification it is seldom that one does
not see some empty space in the ellipsoid; the operation must then
be repeated several times, since the oxygen that is still liquid at this
temperature has a pretty great viscosity and flows with difficulty
from the tube; we shall return to this point later. When the ellipsoid
is completely filled with solid oxygen the adjusting tube may be
lowered right down. A mark is made beforehand, so that the ellipsoid
may be accurately adjusted to the centre of the gap when the
silvered tube is again in its place.
Errors, corrections, auxiliary measurements.
2. Couples due to inhomogeneity. As will presently appear, we made
measurements not only in liquid hydrogen (solid oxygen), but also
keeping everything else the same, at two temperatures in a bath of
liquid oxygen (i.e with the same ellipsoid of liquid oxygen). Since
the susceptibility of the liquid oxygen was known, we had therefore
two measurements of the couples due to inhomogeneity as a function
of the field; they are given in Table VII. As a result of the some-
what smaller dimensions of the ellipsoid, these corrections are com-
paratively much less important.
2. Purity of the oxygen. The oxygen was freed from nitrogen by
vaporizing a large quantity of impure liquid oxygen under reduced
pressure.
3. Density of the solid oxygen. We have already mentioned the
difficulty of completely filling the ellipsoid with solid oxygen. On
account of the opaqueness of the oxygen that has already solidified
one cannot with certainty assert that this condition has been fulfilled *).
Since the specific susceptibility is determined from a known
volume this error would have immediate effect upon the result.
We tried to eliminate this error as well as possible by deter-
mining the density with the same ellipsoid by filling it with solid
oxygen under the same circumstances as those obtaining in the
experiments and then measuring the quantity of gas formed from
it on vaporization. We may assume that the small cavities that may
form are pretty much the same in the various cases. Indeed, from
two similar measurements the density measured in this way was
found to vary by only about 1°/,. By taking as the mean density
that determined by these experiments, the eventual presence of
cavities is allowed for. In this way we obtained
ova" 1.41,.
The absolute values of the couples due to inhomogeneity of the
1) When there is an empty space af a few mm%, however, it can be seen quite
well. ;
( 828 )
field are not modified by a cavity formed in the vertical axis, as
was usually the case, for it is clearly those portions towards the
surface of the ellipsoid that are the chief contributors to them. On
the other hand, they might obtain a greater relative influence, but
as the observations shew, the sum of the corrections arising from
this cause is so small that they may be regarded as independent of
ihe susceptibility within the limits of accuracy of the experiments.
In that ease this difficulty completely disappears.
4. Dimensions of the ellipsoid. The internal volume was obtained
by filling the ellipsoid with mereury and weighing it. [t was 0.1812 e.e.
The change of volume under atmospheric pressure was found to be of
no account by pumping the space above the mercury free from air
and observing the position of the mercury in the capillary.
The external axes were measured directly. Then the thickness of
the glass at ten different points was determined by focussing a
microscope on the image of the outer surface formed on the mercury
with which the ellipsoid was filled. It changed but slightly from
place to place. The mean was taken and twice that value was sub-
tracted from the external measurements. The results were:
1.044 em.
and
0.335 em.
Caleulating the volume from these figures we get 0.1925 c.c. which
is about 6°/, greater than the true volume as directly determined.
This is accounted for by the special shape of the meridian section
which curves somewhat too strongly at the outer ends. For caleu-
lating the coefficients of demagnetization we took a mean ellipsoid
with the same major axis and the minor axis small enough to give
the real volume’). The data for the calculation were therefore :
1.044 em.
and
0.3173 em.
5. Opposing couple. The suspension spring and the stretching
wire were the same as were used for the liquid oxygen. We must,
however, allow for the rubber supply tube for the oxygen. This
(which was chosen as thin as possible) modified both the zero and
the constants of the total opposing couple, as soon as the pressure
1) It is clearly not quite right to do this; there are, however, experimental data
to support this method of correcting: V. QuirTNER (Diss. Ziirich 1908, also Arch.
sc. phys. et nat Geneve, Sept.—Noy. 1908) found that this method of treatment
was sufficiently accurate even for discs, bodies that deviate far more from an
ellipsoid than those we used.
( 829 )
difference between the inside and the outside of the tube appreciably
altered (on account of the change in shape of the tube). In all ow
experiments, therefore, we took care that there was a constant
pressure difference of 70 mm. between the pressure inside the cover
and that inside the holder (the latter was the smaller of the two).
We got a very sensitive indication of the constancy of this difference
not only from the manometers but also from the zero position of
the holder. Experiments carried out outside the apparatus shewed
that the constant of the total couple changed about 10°/, between
the complete flattening of the rubber tube by the atmospheric pres-
sure and equality between the pressures on both sides. This cor-
responds to a deflection on the reading scale of more than a metre.
If we assume rough proportionality we tind that a displacement
of 1 em. would indicate a change in the opposing couple of only
0.1 °/,. The zero was kept constant to a few millimetres.
The calibration was made under circumstances exactly the same
as in the experiments (pressure difference, etc.).
The total constant with the addition of that of the stretching
wire was
1503 + 18 = 1521 -cgs.
Results.
TABLE VII.
Calculation of the corrections for non-uniformity from observations made in
a bath of liquid nitrogen.
Conical pole-pieces 20 mm. apart.
t= — 195°.6 C. t=—210°0¢. || Fae
ae? | 93 om. | Fe 1or | 2.108 || 22cm. | 2% 107 | 2.108 Eat
4615 || 1.48 | 0.554 | —0.137 1.59 | 0.746 9.199 ii 158
6944 || 2.69 | 5577 427 || 3.53 |" 0.7322 232 162
9205 || 4.73 | 5580 | 126 6.21 | E80) 231 160
/41980 || 7.08 | sco | 132 | 9.23 0/4 7251 250 171
49835 | 0.417 | see | 131 | 12.10 7341 | 998 163
(44015 jf 41.14 | 5670 100 14.49 | 7378 219 140
| 44c00 || 42.90 | se12 | 060 | 16.94 7613 162 09%
| 15585 |1 14.99 | 5884 039 | —-~ | = —- —
“16120 | 15.67 | 6034 | 003 | 20 21 ! 7781 | 124 | 040
| |
( 830 )
[t can be seen that the values obtained for 2 are not the same at
the two temperatures. Meanwhile it has to be applied here only asa
correction for the susceptibility of solid oxygen which at the most is
0°/,. A difference of temperature of 1° C. in the bath under reduced
pressure gives more than half the difference betwéen the two values,
whence we have given the determination under reduced pressure
only half the weight accorded the measurement at ordinary pressure.
The uncertainty of the mean has less than 1°/, influence upon the
value of the susceptibility of solid oxygen. The curve for 8 as well
as its sign correspond with what were found for the silver ellipsoid.
TABLE VIII.
SEscep Hey, po sone oxygen.
(bath of liquid hydrogen boiling under atmospheric pressure). |
H Otani | os Pe el creed
gauss the scale H* uncorrected prea
2296 0.89 1.69 519 533
4615 3. 57 1.676 518.3 532.9
6244 7.92 1.642 512.3 Sy 53}
9205 14.07 1.660 515.0 530 4
11280 21.14 1.661 515.2 530.4
12835 27.92 1.684 518.7 532.8
14015 | 39.96 1.678 517.6 529.0
14900 37.38 1.683 518.4 SPA) G3)
15585 40.77 1.678 517.6 52307
16120 44.05 1.696 520.0 | 523.6
Mean 529.0
529.0
10-6 == 375.2). 1058.
1.41
Whence it follows that y20°.3K, =
ual
( 831 )
iy Te ene |
UOTE) Oh. sole oxygen. |
(bath of liquid vdibcen ender 70 mm. vapour pressure).
BU raibahesicm. of)|: 28 seme Rees Rekes ||
| gauss the scale H2° | uncorrected} corrected
9996 4.149 | 9.957 | 600.5 614.5
4615 | 4.80 | 9.953 | 600.4 614.6
6944 10.86 | 2.959 600.0 615.0
9203 19.2% | 9.970 | 602.2 617.4
11280 98.13 2.210 | 594.3 609.2
12835 37.09 9.950 | 599.6 613.7
14015 15.05 2.993 | 604.7 616.7
14900 51.24 | 2.306 | 606.8 615.9
15585 5.73 2.2993 | 605.3 611.4
16120 60.20 2.317 | 608.5 | 6194
614.0
From the mean 614.0 follows y.o).14°.2x, = TE = 435.6 .10-8 The
products into 1“ 7’ are
— 252.°8 375.2. 10-6 V 20.3 = 1690. 10-6
— 258.°9 435.6 . 10-6 V14.2 — 1641. 10-6,
Hence we can represent the two observations pretty well by
1690
which is adjusted to the measurement at the higher temperature.
The deviation from this ratio for the lower temperature, however,
is somewhat greater than the errors of observation.
§ 5. Summary and conclusion. As regards the dependence of specific
susceptibility upon temperature our most reliable determination gives
Alig. 90°.1 K. = 240.6 . 10-6.
33700
Curt found 7 = Saar 10-© between 20°C. and 450° C. whence it
( 832 )
would follow that for 7’= 90°41 K. ,=374.10—° a number that
differs essentially from ours *).
There is therefore no possibility of extrapolating Curie’s law to
the liquid phase of oxygen. This was also the conclusion reached by
Fieminc and Dewar in their first treatment of the question, but
after more careful experiments they rejected their former result’).
The results obtained from the two magnetic rise apparatus at lower
temperatures can, within the limits of experimental ervor, be expressed
by a very simple law: the specific susceptibility is inversely propor-
tional to the square root of the absolute temperature. From the
observations obtained with the more reliable apparatns we deduce
the formula
2284 7
hig. T = WT lOm5
which holds to within 5°/,. None of the results obtained by the method
of the maximum couple are in conflict with those deduced from the
formula.
The results with solid oxygen approximately follow the relation
Ysol:1 = — > - 10-6.
At the lowest temperatures there is a small deviation indicating
a smaller increase at lower temperatures; it is, however, so small
that we may still accept the formula given as approximately correct
for the solid state of aggregation below the melting point of oxygen
and down to 14°.2 Kk.
Further experiments at more numerous temperatures must show
exactly how far these deductions hold for the liquid and solid states.
They shew (see fig. 5) that there is a jump in the value of x at the
melting point, since
Alig. 7, = 158 Aso.
1) R. Hennia’s (1893) result should give
27600
— ro 10—6 and y99°1 x, = 307. 10—®.
2) Lemina and Dewar’s results: 1st paper (1896) %90°.1K.=200.10—*; 2nd paper
(1898) 287.10-8, mean 243.5.10—® pretty much the same as our result. Accord-
ing to the mean of the result of Farapay and Brcqueret the specific suscep-
tibility for oxygen at 0? is 91.10~°; this gives by extrapolation from CuRIE’s
law %902.1K. = 299.10-® The English savants used this number in their second
research for the comparison of tbe susceptibility of liquid oxygen with that of
the gas.
( 833 )
We hope to answer the question if this jump really exists by
special experiments arranged for the purpose; we may, in the mean-
time, consider that it does probably exist. What Curie found in the
transformation of y iron to Jd iron is analogous to the sudden change
which we here assume to exist while the form of the law remains
unaltered, and which can occur at the melting point or at a point
of transformation to an allotropic modification. Weiss’) has shown
that this can be accounted for on the assumption that at this particular
point di-atomie iron changes into tri-atomic.
On the other hand we consider it probable that the law according
to which the specific susceptibility increases with the temperature,
viz: inverse proportionality to the square root of the absolute tem-
perature at lower temperatures, gradually transforms into that of
inverse proportionality (Curim’s law) at higher temperatures, and that
each of these laws, therefore, may be but approximative to the
same function over different ranges of values of the independent
variable 7’.
The supposition that the change of specific susceptibility with
density is of no importance lies at the bottom of the assumption of
the gradual transformation of Curir’s law into that of 7’-?. If, on
the other hand, we assume that this change is of importance, that
e.g. when the internal pressure is considerable the molecules under
its influence undergo not only a compression but also a lessening of
their magnetic moments, then a region of great molecular compres-
sibility in which the specific susceptibility should change both with
the temperature and with the density should exist between the gaseous
phase in which the specific susceptibility would be pretty well in-
dependent of the pressure, and the liquid phase at lower temperatures,
in which the molecules would not be appreciably affected by an
additional external pressure on account of their already great internal
pressure, and in which, therefore, the specific susceptibility would
also be pretty well independent of the pressure. As regards the
difference between the magnetic moment of the elementary magnets
in the condition of saturated liquid and vapour and that at normal
or smaller density at the same temperatures, it is to be expected
according to that representation, that this difference will change with
temperature in consequence of the change of density with temperature.
The assumption can also be made that complex molecules are
formed in the liquid state, and that these diminish the intensity of
the elementary magnets; in that case changes in susceptibility of
1) P. Wess, loc. cit.
( 834 )
mixtures of liquid oxygen with non-magnetic gases should obey the
thermodynamic laws that govern the number of such complexes.
But all this must he established by further experiments which we
hope to complete; in the meantime the most probable assumption is
the old one that the specific susceptibility is independent of the
pressure.
As regards the question as to whether the specific susceptibility
at lower temperatures still follows the law of inverse proportionality
to the root of the absolute temperature, if the ferro-magnetism with
a very low-lying Curm point according to Weriss’s theory of corre-
sponding magnetic states does not exist, then the change to a still
slower increase with decreasing temperature and the approximation
to a limiting value is, perhaps, more probable.
The law of 7} at once gives rise to the question if instead of
the Lanervin elementary magnets whose intensity is independent of
the temperature, we should assume that their intensity varies directly
as V7’; that is, that we should assume the existence of elementary
currents or electrons moving in their paths with speeds proportional
to (and, therefore, determined by) the speeds of molecular heat
motions. In other words, while Lanenyin’s theory already supposes
that the planes in which the electrons move follow the motions of
the molecules, but that the areas described in those planes are still
independent of heat motion, we should now assume that the electrons
undergo the influence of heat motion at their motion zm their paths,
and, if the radius of their path has also become invariable, revolve
while remaining in the same position with respect to the atom; they
would be electrons that are frozen fast to the atom, an assumption
that has already been made to explain other phenomena.
This addition to Laneervin’s theory, however, does not lead to a
specific susceptibility proportional to 7’~*as one at first sight would
be inclined to think, but to a constant specific susceptibility.
To substantiate that addition it will probably be necessary to proceed
to still lower temperatures than those of our experiments. It seems
at present that it is not impossible that then the law x proportional
to 7—* changes to y= const.: our observations on solid oxygen seem
to indicate a change in this direction. The assumption to which this
is equivalent: viz, that the magnetic motions of the electrons cease
at the absolute zero, and to which our experiments seem to lead,
much more satisfactory than that the magnetic motions of the ees
trons still persevere even at the absolute zero.
The second question to which we devoted attention — the depen-
dence of susceptibility upon field strength requires no detailed treat-
S22 eS *
pet Po Re
( 835 )
ment. The method of the magnetic rise seemed in some instances to
give a decrease of the order of 1°/, in a field of 8000 gauss, while
the method of the maximum couple gave with the cylindrical poie-
pieces up to 12000 gauss only a very small systematic deviation and
with the conical pole-pieces (16000 gauss) the deviation was scarcely
appreciable.
The solid oxygen ellipsoid with which a much lower temperature
was reached seemed to give a small decrease at 16000 gauss; it is
possible, however, that a greater deviation is obscured by the cor-
rection for the non-uniformity of the field. We consider, however,
that, assuming that the experiments were accurate to within 1°/, the
change of the susceptibility with the field up to 16000 gauss remains
within the limits of experimental error. This is in agreement with
the theory of Lancrvry, if this, notwithstanding the deviation from
Curtz’s law, is still applied.
Physics. — “The imagneto-optic Kerr-Ejject in ferromagnetic com-
pounds and alloys’. By Stanistaw Lorta. (Communication
from the Bosscha-Laboratory).
It has been shewn by Kaz’), Ricui*), Kunpr*), Sissryen ‘), ZEEMAN ®)
and also by Kerr*) himself that the phenomenon discovered by the
last named in 1876 depends not only on the orientation of the
reflecting surface with respect to the magnetic vectors, but also (in
a somewhat complicated manner) on the angle of incidence and the
position of the plane of polarization of the incident beam. In the
simplest and by far the most important case of almost normal incidence
of light polarized perpendicularly or parallel to the plane of incidence,
the reflected light in general is elliptically polarized according to
Rieni’); the rotation of the major axis of the ellipse depends on the
magnetisation and the wave-length.
According to the measurements made by bu Bots‘) it is in every
case proportional to the former; as regards the variation with the
) P. CG. Kaz, Diss., Amsterdam 1884.
) A. Riest, Ann. de Chim. et Phys. (6) 4 p. 433, 1885.
) A. Kunpt, Wied. Ann. 23 p. 228, 1884; 27 p. 199, 1886.
4) R. Sissincu, Arch. Néerl. (1) 27 p. 173, 1894.
) P. Zeeman, Leiden Comm. no. 15, 1895; no. 29, 1896. Arch. Néerl. 27 p.
1894.
8) J. Kerr, Phil. Mag. (5) 3 p. 339, 1877. Phil. Mag. (5) 5 p. 161, 1878.
) A. Riem, Ann. de Chim. et Phys. (1) 9 p. 120, 1886.
8) H. pu Bors, Wied. Ann. 39 p. 25, 1890.
( 836 )
latter, the rotatory dispersion, according to the same author, shews
certain regularities. For iron, cobalt, and nickel the rotations visually
observed were always negative; for iron the dispersion-curve seems
to indicate a numerical minimum in the ultraviolet and thence ascends
from violet towards red; in the ease of cobalt the minimum occurs
between blue and green, and for nickel in the yellow. These
numerical minima of negative rotation may be considered algebraic
maxima, their wave-length increasing as the metal’s position in the
periodic system advances. For magnetite the observed rotations were
in every case positive, though the curve appeared directed towards
negative values beyond the blue; a distinct maximum occurred in
the yellow, corresponding to the above algebraic maxima.
More recently INGeRsoLL') has contributed important papers relative
io this subject; he was able to supplement bu Bois’ curves in the
infra-red up to about 3y. According to this author the complete
rotatory dispersion-curves thus obtained shew a marked resemblance
to a typical dispersion-curve in the region of an exceedingly broad
band of resonance-absorption. The particular cases of nickel and
magnetite are notable, for the rotation appears to vanish between
1 and 1,54 and then to change in sign.
Further progress in this subject was difficult in view of the fact,
that as yet the only ferromagnetic substances suitable for a study of
the Kurr-Effect were the four above-mentioned bodies. Several attempts
to study with reflected and transmitted light the magneto-optic pheno-
mena connected with the Kurr-Effect were made with partially
transparent tilms of metals prepared electrolytically, after the manner
of Kunpt, or by cathodic discharge. Although the latest investigations *)
on the optical properties of these films of magnetic metals brought
to light further interesting but confusing results, yet the conditions
in the films can obviously depend on their structure and on their
mode of preparation in a very complex way. As a reflecting surface
such a film is certainly inferior from a physical point of view to a
mirror polished on a compact and massive block of metal.
An attempt to add to the number of substances which exhibit the
Kurr-Effect was thus of some interest. I entertamed some hopes in
this respect, since several chemists of late have synthetically prepared
new ferromagnetic substances. In the first place, a number of com-
binations of different oxides with iron oxide, so called metaferrites,
1 L. R. [narrsout, Phil. Mag. (6) 11 p. 41, 1906 & 18 p. 74, 1909.
2) CG. A. Skinner & A. Q. Toot, Phil. Mag. (6) 16 p. 833, 1908. H. BeHrens
Inaug. Diss. Miinster i. W. 1908. L. R. Inaursott, loc. cit.
( 837 )
prepared by Hinprerr’), presented an interesting field of research. In
all these cases, the chemical structure resembles that of ferroferrite
(ferroso-ferric oxide), in that the iron sesquioxide plays the acidic
part, thus imparting ferromagnetic properties to the compound. Of
this class of substances however, only cupriferrite and calciumferrite
could be obtained in a state suitable for my experiments. Secondly,
certain alloys of more or less ferromagnetic metals, and in particular
those of nickel-iron *), together with the well-known ternary HEusLer
alloy, and Wepekinp’s*) binary manganese-antimony alloy present
considerable interest. So far as I am aware, the magneto-optic pro-
perties of these alloys have been only partially investigated, the only
account of similar experiments, which I have come across, being
INGERSOLL’s Communication previously referred to and a Russian paper
by TokmatscHew *), who described experiments with Hrvsixr’s alloy.
I have studied the magneto-optic properties of the above mentioned
bodies and also those of the well-known magnetic chromic oxide.
Below an account of the preliminary results of my research is given.
Experimental Arrangement. Solar rays were exclusi-
vely used; they passed through a direct-vision monochromatic illumi-
nator*), with divergence 1:4, thus furnishing light of great intensity.
The rays passed (Fig. 1) through a lens (L), a total reflecting prism
(P), a Lappicn’s arrangement of two halfshade Nicols (N,, N,) and
falling nearly normal on a mirror between the two poles of an
electromagnet, were reflected, finally passing through an analyser
(N,) and a telescope of fourfold magnifying power. The dimensions
of the lenses, of the diaphragms, of the width and angle of the
conical bores in the cores and poles were all calculated beforehand,
particular care being taken to maintain maximum brightness, a
uniform field of view, and also the avoidance of all unnecessary
reflections °).
The observations were carried out with nearly normal incidence.
Rieu’) found, that up to an angle of incidence of 15° there was
1) S. Hiwrerr. Ber. deutsch. Chem. Ges. 42 p. 2248, 1909. Verh. deutsch. Phys.
Ges. 11 p. 293, 1909.
2) Cu. Ep. Guittaume, Les aciers au nickel, Paris 1898.
8) E. Wepexinp, Ztschr. f. phys. Chem. 66 p. 614, 1909. K. Honpa, Ann. d.
Phys. 32, 1910.
4) S. Toxstatscuew, Journ. d. russ. phys.-chem. Ges., 42 (phys. T.) p. 15, 1910.
3) H. pu Bots, Verh. d. D. Phys. Ges. 11 p. 708, 1909.
6) A description of the analyser and polariser mentioned is given by H. pu Bais,
Wied. Ann. 46, p. 545, 1892.
7) A. Rieu, Ann. de chim. et de phys. (1) 9 pp. 120, 132, 1886.
( 838 )
searcely any variation of the effect. However, in my experiments
the angle between the incident and reflected beams was only 2° or 3°.
The incident light was polarized horizontally in the plane of incidence.
From Rica's observations it is known that even a normal incident
beam of linearly polarized light when reflected from a magnetized
mirror becomes elliptically polarized, the ellipticity however being
only slight; Zeeman *) later measured this ellipticity in the case of
iron and cobalt. Up to the present the evaluation of the ellipticity
in my experiments has not been attempted; 1 considered that the
slight reflecting power of some of my mirrors would not warrant
such an attempt, and in addition it must be borne in mind, that the
rotations themselves are small. Moreover the ellipticity, if any, must
be nearly inappreciable, for by employing the best of my mirrors
and by carefully avoiding diffused light, | have never been confronted
with any difficulties, while the extinction of light in each half of
the field of view was satisfactory. Even when the rotations are
very small it is possible by means of the half-shade arrangement to
observe and to measure them with sufficient accuracy. Hence it was
thought unnecessary to use the method of multiple reflections, there-
by avoiding new complications and further sources of error. The
azimuth of the analyser was determined by means of a vertical
scale seen through a combination of mirrors.
For the production of the magnetic field a small pu Bots semicir-
cular electromagnet of resistance 9 £2 was employed. To avoid the
danger of sparking with reversal of current about 60 2 were shunted
across its terminals. The field was determined by means of a standar-
dised thin glass-plate silvered at the back, which could be placed
immediately in front of the mirror. The light (4 = 589 uu), being
reflected by the mirror as described above, suffers a double magnetic
rotation in the glass. The ensuing very slight double rotation of the
light in its passage to and fro through the magnetized air could be
computed from the data of Stertsema *), but proved quite negligible.
Indeed, by using a silver-mirror, it was found that the rotation lies
within the limits of experimental error. All the measurements were
made with “polar” magnetization and at ordinary temperature.
Test-Specimens. The following substances were experimen-
ted upon: Cupriferrite (CuO. Fe, O,), Caleiumferrite (Ca O . Fe, O,),
Magnetite (Ferroferrite) (FeO. Fe,O,), Llmenite (Ti, O,.Fe,O,), ferro-
magnetic chromic oxide (Cr, O,), “Invar’ (86 Ni, 64 Fe), the HeusLEr
1) P. Zeeman, Leiden-Comm. No 15, 1895.
2) L. H. Sterrsema, Versl. Kon. Akad. Wet. Amsterdam 7 p. 289, 1899.
( 839 )
alloy (26 Mn, 13 Al, 61 Cu). The first two were kindly prepared by
Dr. Hitprrr in the metallurgical Laboratory of the ‘Technische
Hochschule” in Charlottenburg; the natural magnetite is from the
collection of the Bosscha-Laboratory, and is the same specimen,
possessing a polished octahedral surface, which was formerly examined
by pu Bors'). A very fine-formed crystal of ilmenite was kindly
lent by Prof. Lirpiscn. The Herusier alloy was supplied by the pr
Hain chemical factory in Seelze; its interior was full of bubbles,
but its surface was capable of polish and supplied a very good
mirror. The “invar’ contained about 36°/, Nickel and came from
France (Société de Commentry-Fourchambault). For the chromic
oxide | am indebted to Dr. Kopprn. I desire to express my obli-
gations to all the above mentioned gentlemen.
Throughout this paper I shall denote as usual by: f, the field
intensity in kilogausses, ¥ the magnetization, 3,, its saturation
value, « single rotation of the plane of polarization in minutes,
K, Kerr’s constant. In the tables, the column under N shows
the number of readings in each series of measurements, which depend-
ed upon the polish of the mirror and the variable brightness, 2
denotes the wave-length in uu, A the direct scale-reading in mm. of
the double rotation produced by reversal of the current. The average
values of the single rotations are given in the fourth column and
in the fifth and sixth the average errors in minutes and in percentages.
The sense of the rotation is referred as usual to that of the
magnetizing current; e.g. in the case of iron the “polar” Kerr
rotation is negative.
Results. The results obtained with the various substances were
as follows:
1. Cupriferrite. Measurements were made on two mirrors’ of this
material with similar results. The relation between the rotation and
the wave-length in a field of 10,2 kgs. is shown numerically
in Table 1 and graphically in Fig. 2. The dispersion-curve exhibits
a type which has not been observed hitherto in the visible spectrum.
In the violet the rotation is positive, a maximum occurring in the
blue; with increasing wave-length the rotation gradually decreases
and in the neighbourhood of 587 wu goes through zero, becoming
negative for longer wave-lengths. Between 640 and 670 uu a rather
flat minimum is exhibited, the curve then gradually proceeding upwards.
The rotations are small throughout, the maximum value not being
1) H. vu Bois, Wied. Ann. 39, p. 25, 1890.
56
Proceedings Royal Acad. Amsterdam. Vol. XII.
( 840 )
4h 153 Ibi 13}, “Al
= = funct (A) Cupriferrite ©) = 10.25 Kes:
N 2(42) A (mm) | = (Minutes) oz
19 136) 29 3aess St) al spl 0a=3 50
48 Ca eee eee er eh.
43 530) | eLes tly eto es |eeenae == Sune
AO), |. e574) etre ieee tonaan Meio loom acnme
52. le 509) >| eeoNg Ie =orag anl| sO rGsu =e ae
45 637: || 2.5620) |= 310,950 ee Oro
54 B88. b= 4911) == ONS EO. 030 ares
ereater than + 1,75’, but they still admitted of exact measurement.
The above-mentioned change of sign is analogous to that found by
InGprsoLt in the infra-red and presents a characteristic and theoretic-
ally important phenomenon.
The relation between the rotation and the field was also investigated,
and the results are shewn in Table 2 and Fig. 3. For low values
of the field the two are proportional to each other, the rotation
DPA Buri 2
== funct (9) Cupriferrite 2= 477 ve
i
N (kgs) a(mm) | «(Minutes)
|
£0 | 0.98 | + 5.3 ) 4270.85!" 2 0109" — 907;
92 | 9.95 | 18.4 | +434 | + 0.04 — 3,
59. | 4AM 0.7" || 4 458! | Seor0s0— 2m
34 7.49 | +40.2 | 4 41.63' | + 0.03'=2,
20 | 9.32 | +40.4 | 4+4.66 | + 0.037 —2,
4g | 10.45 | 444.4 | 44.75" | + 0.0'= 3,
afterwards assuming a maximum value, which remained nearly
constant for further increase of the field. Considering the form of
the curve «—funet (9) and accepting the results previously found
ean
( S41 )
by pu Bors in the case of iron, nickel, and cobalt, we may assert
the proportionality between « and ¥ with great probability. Bearing
in mind this fact we are able to determine from purely magneto-
optic measurements the order of magnitude or at least an inferior
limit of maximum magnetization. As pu Bots ') has shewn in the
ease of an unlimited homogeneous plane disc, the magnetization of
which is uniform and normal, the abscissa of the point of intersection
of the straight line «== K 3= K)/4a and of the asymptote ¢ = const.
has the value 47 %,,.
Accordingly 32140 c.g.s. in the case of cupriferrite. The small
inclination of the upper part of the curve in Fig. 3 may be explained
by the fact that for irregularly formed specimens the real conditions
do not correspond to those in the ideal case mentioned above. How-
ever this inevitable difference can only produce a decrease in the
apparent value of J, so that an inferior limiting value is really
determined ; small fissures, cavities, and impurities in the reflecting
surface are particularly capable of exerting such an influence.
2. Magnetite. The dispersion of the Krrr-Effect is shown in Table 3
and Fig. 4 (continuous line). If we compare this curve with the
DEAS Belin ios
z= funct () Magnetite = 11.56 Kgs
N (4%) | ¢ (mm) | = (Minutes) de
| |
30 ||| 436 7) — 24.0 | — 3.81" | + 0.03'= 0.99),
25 442 — 19.9 | — 3.15! {| st Q205,— sip be
15 453 | — 9.6 Nee Aaa?) 02030 2ae
30 M4 0 0 ae
4 417 + 6.7 + 1.06! =1-0503!— 2s
26 510 + 19.4 + 3.07! + 0.02'— 0.6,
25 539 + 24.3 + 3.84’ + 0.02'= 0.5,
30 574 + 28.2 + 4.45! + 0.02)= 0.4,
30 599 + 24.9 + 3.94! + 0.02'= 0.5,
3l 637 + 21.0 + 3.32! ap OA al |.
30 688 + 16.0 + 2.50! = ORO TE same
1) H. pu Bois, Wied. Ann. 31 p. 965, 1887; Phil. Mag. (5) 29 p. 301, 1890,
( 842 )
previous one given by pu Bors (dotted line), which he obtained with
the same specimen (a holoédrie regular crystal, possessing a natural
octahedral surface) we see, that with the exception of a displacement
throughout the whole range of wave-lengths amounting to about
10 to 380 uu — which is explained by the fact that 20 years ago
only an imperfect method of spectral decomposition was available —
the curves are in agreement in the region between 486 and 671 uu.
The rotation attains a maximum value of 4,45’ in the yellow and
decreases rapidly with decreasing wave-length. Du Bots’), who was
unable to proceed further than the blue on account of insufficient
intensity of light, observed that the rotation probably vanished in
the blue; he also considered that a change of sign possibly might
oceur in the ultraviolet. I have located this zero-point in the visible
part of the violet at 464 yu. For smaller wave-lengths the rotation
has rather a large negative value, which seems to approach a mini-
mum. Unfortunately it was impossible to carry the investigation
beyond 436 yu since the light at that point becomes too feeble.
At all events, the existing observations establish satisfactorily the
fact that the dispersion-curve obtained with natural crystalline
magnetite (FeO .F,O,) is of the same type as that obtained above
with cupriferrite. Without entering into theoretical considerations it
may be seen at once that in both cases the curve passes through
a maximum, yoes through zero and probably also through a mini-
mum. Experiments are being carried out to see whether the course
of these curves depends on the optical constants. of the substances
investigated, viz. their ordinary absorption- and dispersion-curves.
In the same way as in the case of cupriferrite the relation between
the rotation and the field was also investigated. The results are
shown in Table + and Fig. 5. They give ¥, 2 358C.G.S., which
agrees with that obtained by pv Bots *) (850).
The magnetic properties of magnetite crystals have been recently
investigated by Qurrrner*), adopting Wetss’ methods. From his
measurements it follows that the component magnetization parallel
to the field, which in this case is alone of interest, reaches a
saturation value of about 475 C. G.S. ; this subject and the cause of the
discrepancy ought to be investigated in greater detail. One remark,
however, may be made at once. In many cases the natural magnetite
slightly departs from the simple structural formula (Fe 0, Fe, 0;);
1) H. pu Bors 1. c. p. 38.
2) H. pu Bots, Phil. Mag. (5. 29, p. 301, 1890.
3) P. Wess, Journ. de Phys. (8) 5 p. 485, 1896 and (4) 9, p. 373, 1910,
V. Quirrner, Dissertation, Ziirich, 1905.
( 843.)
TAC Be iyi 74:
- = funct () Magnetite d = 574 pp
N | 4) (Kgs) | 4 (mm) | = (Minutes) Oz
15 DAO) P= 1089) | <b 2.07" |) = 0.04" = 19) oy,
15 3740). [ 24.8) = 3:37) | + 0.05f= 1.5),
45 | 5.87 -| 498.7] +454 |4+007=1.5 |
15 | 8.87 4+ 98.0| + 4.439 |4+0.0/=1 ,
15 40.82 | 4- 98.9) + 4.577 | + 0.06'=1 ,
30 | 44.56 | + 28.2] + 4.4 | + 0.0704,
also QuirTNER has established the great diversity of samples by
measuring their variable densities. It is difficult to foretell the influence
of all this on the magneto-optic properties.
3. Other ferromagnetic compounds. The distinct analogy in the
dispersion for substances of similar chemical structure as e.g. cupri-
and ferroferrite in contradistinction to iron, nickel, and cobalt
suggests whether the properties of other ferromagnetic ferrites and
oxides are not similar. The investigation of calciumferrite was in
this respect of importance. This substance is very feebly magnetic
and brittle. A small piece was surrounded by the easily fusible
Woop alloy and then thoroughly polished. No Kerr-Effect however
was observed although the mirror was sufficiently good. The effect,
if it exists, must be smaller than 0,35’. A similar result was
obtained with 7¢/menite'). The light was reflected from the base of
the crystal as well as from a plane parallel to the principal axis,
but in no case could a rotation be detected. (<< 0,3'). It was also
impossible to detect any rotation with chromic ovide Cr,O,, which
without doubt is ferromagnetic. The following alloys were tested:
4. Nickel-tron with 36°/, nickel, so called “Invar’, known to
possess a very small coefficient of expansion, is strongly magnetic and
distinctly shows the Krrr-Effect. The rotation is exclusively negative
in the region of the spectrum investigated, and there is only a slight
variation with wave-length. (Table 5, Fig. 6). The dispersion-curve
lies considerably below the zero-line; with increasing wave-length
1) See B. Bavinx, Magn. Influenz in Krystallen, Géttinger Dissertation 1904.
( 844 )
IX, 183 Wb 1B) 8},
= = funct () “Invar” § = 13.30 Kgs.
N 2 (4) A (mm) : (Minutes) dz
151 |) ASG. |b Tae) dae!) S05! 10 wA0/t
15 | 477.| — 78:8 |.— 42.48 | +0.0¢0—0.5,
15 | 539 | — 83.5 | —43.99 | + 0.06'= 0.4,
co | 574-1 — 86:3" |) — 43.66! + 0/03" = 0.9),
[By le 599M 8628) 1374! Bie 0205) ==) Ono).
Abel G37) a= 86 7 lle Se 72" A= AOF ON lor
15- | GSBen| = 8620" |= — ASIAN NOOR )0.0-
it proceeds slowly
downwards, passes through a flat numerical
maximum in the orange, after which the rotation decreases very
slowly. The relation between rotation and magnetization, as in the
cases above, exhibits distinct proportionality and we have 3,, 2 530
(Table 6, Fig. 7).
QP UN WI 18)
« = funct (4) “Invar” 2 = 574 pp
N (kgs) | a (mm) | < (Minutes) dz
31 0.54. | 6.5 | == 41.00" | 4210:02" — oy vor
|
15 1.80 | —23.2 — 3.67! = 0.02! =10°5.
15 3.90 | \=23950|) == B.A Ono 1005 2
15 6.32 | —69.7 | —14.03" | + 0.05'= 0.4,
15 40.37 | —84.5 | —413.36 | + 0.03'= 0.2,
15 42.60 | —86.6 | —13.74' | + 0.02 —0.4,
20 43.30 | —86.3 —13.66! + 0.03' = 0.2 ,
15 14.51 | —86.2 | —13.65' | + 0.03'= 0.2 ,
|
It would be interesting to study the magneto-optic behaviour of
g y g |
the nearly non-magnetic nickel-iron alloy, which contains 25 percent
nickel,
5. The Hevsiur alloy, supposed to contain 61"/, Cu, 26°/, Mn and
13°/, Al is rather strongly magnetisable. Different portions of two
well-polished mirrors were carefuly examined in various parts of the
spectrum but proved to be magneto-optically ineffective. It is of
course possible that the Kurr-Effect might be less than 0,3’ in this
case. Quite recently there appeared a communication by TokmaTscHEW
recording similar experiments on the Hnuster alloy No. 32 (58,9 Cu,
26,5 Mn, 14,6 Al). From theoretical considerations the author arrives
at the conclusion of the probability of an effect capable of measurement
occurring in the neighbourhood of 450 uu. i have carried out a series
of readings at this wave-length but no rotation could be observed.
InGersoLi also failed to notice any measurable effect either in the
visible spectrum or in the infra-red.
The discussion of the theoretical signification of the above partially
positive and partially negative results I reserve for a future occasion;
further experiments are in preparation, and the determination of the
purely optical properties of the investigated substances is already in
progress.
ERRATA.
In the Proceedings of the Meetings of Jan. and Febr. 1910:
p. 672 Table III for 5050 read 8050.
p. 675 Table VII for 102.58 read 102.85.
p. 676 Table VIII for 71.75 read 71.95.
(May 26, 1910).
r . ete ry
ye Wy ae Ie ae Py See
Ei CNG ET ake yen
;
’
i
it
it
|
CONTENDS:
ABDUCENS NUCLEUS (On the motor facialis and) of Lophius piseatorius. 44.
ABEL (Contribution to the solution of the functional equation of). 208.
ABSORPTION LIN®s (The magnetic separation of) in connexion with sun-spot spectra, 584.
ALDEHYDES (On a synthesis of) and indole. 42.
ALKALINE EARTHS (The behaviour of the phosphorescent sulfides of the) at various
temperatures, and particularly at very low temperatures. 157.
ALLOTROPIC modifications (The atomic volume of) at very low temperatures, 437.
ALLoTRopy (A new theory of the phenomenon). 763.
amMonta and Water (On the compounds of). 185.
Anatomy. A. B. Droogierver Fortuyn: “On the motor facialis and abducens-nucleus
of Lophius piscatorius”. 44.
— C. T. vay VatkensurG: “Surface and structure of the cortex of a microcephalic
idiot”. 202.
— L. Boux: “On the position and displacement of the Foramen magnum in the
primates”. 362,
— L. Boux: “ On the slope of the Foramen magnum in primates”. 525.
ANTHRAQUINONE (The P-T-X- spacial representation of the system Ether-). 231.
APOROSA CAMPANULATA J. J. S. (On Distylium stellare O. K. and). 341.
ASYMPTOTIC LINEs (On the surfaces the) of which can be determined by quadratures. 759.
ATOMIC VOLUME (The) of allotropic modifications at very low temperatures. 437,
ATRIUM CORDIS (Communications about the electrogram of the). 680.
BACILLUS PRODIGIOsUS (Variability in). 640.
BACTERIA (The decomposition of uric acid by), 54.
BASALT (On micaleucite) from Eastern-Borneo. 148.
BASILICUM OIL (Javanese) and Methylchavicol. 15.
BECQUEREL (HENRI AND JEAN) and H. KamMeRLINGH OnneEs. On phosphor-
escence at very low temperatures. 76.
BETH (H. J. BE.) The oscillations about a position of equilibrium where a simple
linear relation exists between the frequencies of the principal vibrations, 1st part.
619. 2nd part. 735.
BEYERINCK (Mm. w.) presents a paper of Mr. F, Lixpert: “The decomposition of
uric acid by bacteria”. 54.
58
Proceedings Royal Acad, Amsterdam. Vol. XII.
II CONTENTS.
BEYERINCK (M. WwW.) Viscosaccharase, an enzym which produces slime from
cane-sugar. 635,
— Variability in Bacillus prodigiosus, 640.
— Emulsion laevulan, the product of the action of viscosaccharase cn cane sugar, 795.
BINARY MIXTURES (Isotherms of monatomic gases and their). LIL. Data concerning
neon and helium. 175.
BINARY sysTEMs (The equilibrium solid-liquid- gas in) which present mixed crystals. 537.
Birps (A brief contribution to the knowledge of endozoic seed distribution by) in
Java, based on a collection made by Mr. Bartnets on the Pangerango and near
Batavia. 108.
BLOOD SERUM (On the ehanges in the) of sharks after bleeding. 377.
BOESEKEN (J.). Contribution to the knowledge of catalytic phenomena. 417.
BOIS (i. E.J.G. DU) presents a paper of Mr, Sr. Loria: ”The magneto-optic kurr-eflect
in ferromagnetic compounds and alloys”. 835.
BOIS (H. FE. J. G. DU) and Koraro Honpa. ‘lhe thermomagnetic properties of ele-
ments. 596.
BOLK (L.) presents a paper of Mr. A. B. Droogursver Fortuyn: “On the motor
facialis- and abducens-nucleus of Lophius piscatorius”. 44.
— presents a paper of Dr. C. T. van Vaukensure: “Surface and strueture of
the cortex of a microcephalic idiot’. 202.
— On the position and displacement of the Foramen magnum in the primates. 362.
— On the slope of the Foramen magnum in primates. 525,
BORNEO (On oceanic deep-sea deposits of Central-). 141.
— (On micaleucite basalt from Esstern-). 148.
Botany. Miss C. J. PexeLiarine: “Investigations on the relation between the
presentation time and intensity of stimulus in geotropic curvatures”. 65.
— S. H. Koorpers: “Some brief remarks relating to the communication of Prof.
Cc. &. A. Wicumann: “On fen formations in the Kast-Indian arenipelago”. 74.
— $ H. Koorpers: “A brief contribution to the knowledge of endozoie seed dis-
tribution by birds in Java, based on a collection made by Mr. Bartuets, on the
Pangerango and near Batavia” (Contribution to the knowledge of the Flora of
Java. V). 108.
— 8. H. Koorprrs: “Some remarks on the nomenclature and synonymy of Xylosma
leprosipes Clos., X fragrans Decne and Flueggea serrata Miq”. (Contribution to
the knowledge of the Flora of Java. VI). il6.
— Tu. Wervers: ‘The physiological significance of certain glucosides”. 193.
— J. Kuyrrer: “The influence of temperature on the respiration of the higher
> ¢
plants”. 219.
— W. Burcx: “Contribution to the knowledge of water-secretion in plants”. 306. 400.
— J. J. Smiru; “Qn Distylium stellare O. K. and Aporosa campanulata J. J.S.” 341.
— bb. A. F.C, West: “The inadmissibility of the statolith theory of geotropism
as proved by experiments of Miss. C. J. PEKELHARING”. 343.
— Kk. Reinpers: “Sap raising forces in living wood”. 563.
a
CUOlN DEES Ls: 15 8
Botany. K. Zisusrra: Contributions to the knowledge of the movement of water
in plants”. 574.
— C. van Wisseuincu: “On the tests for tannin in the living plant and on the
physiological significance of tannin”. 685.
BRANDSEN (P.). On the stable positions of equilibrium of floating parallelepipeda. 383-
BRIDGE of the violin (On the motion of the). 513.
BROUWER (H. A.). On micaleucite basalt from Eastern Borneo. 148.
— Pienaarite, a melanocratic foyaite from Transvaal. 547.
BROUWER (L. E. J.). Continuous one-one transformations of surfaces in themselves.
2nd Communication. 286,
— On continuous vector distributions on surfaces. 2nd Communication. 716.
— On the structure of perfect sets of points. 785.
BRUIN (J,) On the surfaces the asymptotic lines of which can be determined by
quadratures. 759.
BUCHNER (E. H.). On the radioactivity of Rubidium compounds. 154.
BURCK (w.). Contribution to the knowledge of watersecretion in plants. 306. 400
BUYTENDYK (Ff. J. J.). On the consumption of oxygen by cold blooded animals
in connection with their size. 48.
— On the changes in the blood serum of sharks after bleeding. 377.
— On the constitution of the urine of sharks with normal and increased diuresis. 380.
CAMERA SILENTA (The) of the Physiological Laboratory at Utrecht. 706.
CANE SUGAR (Viscosaccharase, an enzym which produces slime from). 635.
— (Emulsion laevulan, the product of the action of viscosaccharase on). 795.
CARDINAAL (J.). The constructive determination of the velocities of a spacial
system. 12.
CATALYTIC PHENOMENA (Contribution to the knowledge of). 417.
Chemistry. P. van Rompurcu: “Javanese Basilicuin oil and Methylchavicol.” 15.
— P. van RompureGu; “The essential oil from the fruits of Morinda citrifolia L.” 17,
— R. A. Weerman: “On a synthesis of aldehydes and indols”. 42.
— Ernst Cowen and W. Tomsrock: “The electromotice force of zinc amalgams”. 98.
— C. J. Enxtaar: “On the action of active copper on Jinalool”. 104.
— E. H. Bicuner: “On the radioactivity of Rubidium compounds”. 154.
— A. Smits and S. Postma: “On the compounds of ammonia and water”. 186.
-— J. Bo&srKEN: “Contribution to the knowledge of catalytic phenomena”. 417.
— A. Sirs: “On retrogressive meltingpoint lines”. 227.
— A.Smrits: “TheP-T-X-spacial representation of the system ether-anthraquinone”. 231.
— A. Smits and J. P. Wurrs: “On the system water-natrium sulphate”. 244.
— F. E. C. Scuerrer: “On heterogeneous equilibria of dissociating compounds”. 257.
— P. van Rompureu: “The nitration of diethylaniline”. 297.
— A. P. N. Francurmont: “On sodium alkyl-carbonates”. 303.
— Orro pve Vries: “On the abnormal reduction of an aromatic nitrocompound
with tin and hydrochloric acid and an interesting case of dimorphism”. 305.
— H. Dutita: “On partial racemism”. 393.
— A, P. N. Francuimonr and E, Kramer: “On derivatives of piperazine”. 452.
58*
lv ClO NeTeEe NS Tes:
Chemistry. H. R. Kruyr: “The equilibrium solid-liquid-gas in binary systems which
present mixed crystals”. 1st Communication. 537.
— F. M. Jarerr: “Studies on Tellurium. 1. The mutual behaviour of the
elements: sulphur and Tellurium”. 602.
CHROMOSPHERIC LIGHT (On the origin of the). 446.
COHEN (ERNST) and J. Oxte Jr. The atomic volume of allotropic modifications
at very low temperatures. 437.
COHEN (ERNST) and W. Tomsrock: The electromotive force of zinc amalgams. 98.
compounbs (On the) of ammonia and water. 186.
— (On heterogeneous equilibria of dissociating). 257.
copPer (On the action of active) on linalool. 104.
corTEX (Surface and structure of the) of a microcephalic idiot. 202.
CREATINE (About the formation of) in the muscles at the tonus and the development
of rigidity. 550.
crystaLs (The equilibrium solid-liquid-gas in binary systems which present mixed). 537.
cusic (On pairs of points which are associated with respect to a plane). 711.
cuBic CURVE (On polar figures with respect to a plane). 776.
cuBIC INVOLUTION (The) of the first rank in the plane. 751.
DEEPSEA DEPOSITS (On oceanic) of Central-Borneo. 141.
DIETHYLANILINE (On the nitration of). 297.
pimorPHisM (The abnormal reduction of an aromatic nitrocompound with tin and
hydrochloric acid and an interesting case of). 305.
DISTYLIUM STELLARE O. Kk, (On) and Aporosa campanulata J. J. 8. 341.
PORP (W. A. VAN) presents a paper of Dr. R. A. Weerman: “On a synthesis of
aldehydes and indols”. 42.
DROOGLEEVER FORTUYN (a. B.). On the motor facialis- and abducens-nucleus of
Lophius piscatorius. 44,
DUTILH (H.) On partial racemism. 393.
ELECPRIC DISCHARGE in gases (Remarks on the experiments of Witson and Manryn
on the velocity of rotation of the) in a radial magnetic field. 428.
ELECTROGRAM (Communications about the) of the atrium cordis. 680.
ELECTROMAGNET (An improved semicircular). 189.
ELECTROMOTIVE FORCE (The) of zinc amalgams. 98.
ELEMENTS (‘The thermomagnetic properties of). 596.
BLEMENTS sulphur and tellurium (The mutual behaviour of the). 602.
EMULSION LAEVULAN, the product of the action of viscosaccharase on cane sugar. 795.
ENKLAAR (Cc. J.). On the action of active copper on linalool. 104.
Equation of aBeL (Contribution to the solution of the functional), 208.
EQUILIBRIA (On heterogeneous) of dissociating compounds. 257.
— (The photo-and electrochemical). 356.
FQUILIBRIUM (On the stable positions of) of floating parallelepipeda. 383.
— (The) solid-liquid-gas in binary systems which present mixed crystals. (1st Com-
munication). 537.
CONTENTS. v
FQUILIBRIUM (The oscillations about a position of) where a simple linear relation exists
between the frequencies of the principal vibrations. 1st part. 619. 2nd. part. 735.
ERRATUM. 88. 179. 545. 774. 845.
ETHER-ANTHRAQUINONE (The P-T-X-spacial representation of the system). 231.
FEN FORMATIONS (On) in the East-Indian Archipelago. 74.
Fens (The) of the Indian Archipelago. 70.
FERROMAGNETIC compounds and alloys (Lhe magneto-optic Kerr-eflect in). 835.
FLora of Java (Contribution to the knowledge of the). V. 108. VI. 116.
FLUEGGEA SERRATA MIQ. (Some remarks on the nomenclature and synonymy of
Xylasma leprosipes Clos., X. fragrans Deene and). 116.
FORAMEN MAGNUM (On the position and displacement of the) in the primates. 862.
— (On the slope of the) in primates, 525.
FOSSILS (On jurassic) as rounded pebbles in North Brabant and Limburg. 422.
FOYAITE (Pienaarite, a melanocratic) from Tranavaal. 547.
FRANCHIMONT (aA. P. N.). Gn sodium-alkyl carbonates. 303.
— presents a paper of Dr. Orro pe Vries: “The abnormal reduction of an aromatic
nitrocompound with tin and hydrochloric acid and an interesting case of
dimorphism”. 305.
FRANCHIMONT (a. P. N.) and E, Kramer. On derivatives of piperazine. 452.
Functions (Investigation of the) which can be built up by means of infinitesimal
iteration. 208. 427.
Gases (Isotherms of monatomic) and their binary mixtures. III. Date concerning neon
and helium. 179.
— (Remarks on the experiments of Wr1tson and Marvyn on the velocity of rotation
of the electric discharge in) in a radial magnetic field. 428.
Geology. A. Wicumann: “The fens of the Indian Archipelago”. 70. |
— G. A. F. Mo.eneraarr: “On oceanic deep-sea deposits of Central-Borneo”. 141.
— P. Tescu: “On jurassic fossils as rounded pebbles in North Brabantand Limburg”.422.
— H. A. Brouwer: ‘“Pienaarite, a melanocratic foyaite from Transvaal”, 547.
GEOMETRY (On pentaspheric). 19.
Geophysics. J. P. van per Srox: “On the determination of tidal constants from
observations performed with horizontal pendulums”. 2.
GEOTROPIC CURVATURES (Investigations on the relation between the presentation time
and intensity of stimulus in). 65.
GEOTROPISM (The inadmissibility of the Statolith theory of). 343.
GILTAY (J. w.) and M. pe Haas. On the motion of the bridge of the violin. 513.
GLucosipEs (The physiological significance. of certain). 193.
HAAS (M. DE) and J, W. Gixray. On the motion of the bridge of the violin. 513.
HELIUM (Data concerning neon and). 175.
HERMANIDEs (J.) About odour-aflinity, based on experiments of (-). 90.
HOLLEMAN (a. F.) presents a paper of Dr. EK. H. Bicuner: “On the radioactivity
of rubidium compounds”. 154.
— presents a paper of Prof. A. Smits and S. Postma: “On the compounds of
ammonia and water”. 186,
vi CHOEN ET EaNE TESS
HOLLEMAN (a. F.) presents a paper of Prof. A. Smits and Dr. J. P. Wurre: “On
the system water-natrium sulphate”. 244,
— presents a paper of Dr. F. BF. C. Scnerrer: “On heterogeneous equilibria of
dissociating compounds”, 257.
— presents a paper of Prof. J. Boésrxen: “Contribution to the knowledge of
catalytic phenomena”. 417.
— presents a paper of Prof. A. Smits: “A new theory of the phenomenon allotropy”. 763.
HOOGENHUYZE (G J. c. vAN). About the formation of creatine in the muscles at
the tonus and at the development of rigidity. 550.
INDIAN ARCHIPELAGO (The fens of the). 70.
— (On fen formations in the East-). 74.
INDOLE (On a synthesis of aldehydes and). 42.
INTENSITY of stimuius (Investigations on the relation between the presentation time
and) in yeotropic curvatures, 65.
ISOLHERMS of monatomic gases and their binary mixtures. III. Data concerning neon
and helium. 175.
IPERATION (Investigation of the functions which can be built up by means of infini-
tesimal). 20S. 427.
— (On the orbits of a function obtained by infinitesimal) in its complex plane. 503.
JAEGHR (F. M.). Studies on Tellurium. I. The mutual behaviour of the elements:
sulphur and tellurium. 602.
gava (Contribution to the knowledge of the flora of), V. 108. VI. 116.
JuLIuUsS (w. H.). Regular consequences of irregular refraction in the sun. 266,
— On the origin of the chromospheric light”. 446.
KAMERLINGH ONNES (H.). Isotherms of monatomic gases and their binary mix-
tures. IIL. Data concerning neon and helium. 175.
— presents a paper of Prof. Exnst Conen and J. Ouir Jew “The atomic volume
of allotropic modifications at very low temperatures”. 437.
— presents a paper of Mr. J. W. Grvray and Prof. M. pe Haas: On the motion of
the bridge of the violin”. 513.
KAMERLINGH ONNES (u.) and Henri and Jnan Becqueret. On phosphorescence
at very low temperatures, 76.
KAMBERLINGH ONNES (u.), P. Lexanp and W. E. Paurt. The behaviour of the
phosphorescent sulfides of the alkaline earths at various low temperatures. 157.
KAMERLINGH ONNES (H). and ALBert Perrier. Researches on the magneti-
zation of liquid and solid oxygen. 799.
KAMBERLINGH ONNES (uH,) and Prerre Wertss. Researches on magnetization at
very low temperatures. 649.
kK APTEYN (W.). presents a paper of Dr. M. J. van UvVEn: “Investigation of the functions
which can be built up by means of infinitesimal iteration, Contribution to the
solution of the functional equation of ABEL”. 208.
— presents a paper of Dr. M. J, van Uven: “Investigation of the functions which
can be built up by means of infinitesimal iteration”. 427,
CONTENTS vit
KAPTEYN (W.) presents a paper of Dr. M. J. van Uven: “On the orbits of a function
obtained by infinitesimal iteration in its complex plane’. 503.
KER R-EFFECT (The magneto-optic) in ferromagnetic compounds and alloys. $35.
KOHNSTAMM (PH.). A short reply to Mr. van Laar’s remarks. 534.
— (Some remarks on Prof.) reply. 617.
KOHNSTAMM (PH.) and J. Timmermans. On the influence of the pressure on the
miscibility of two liquids. 235.
— (Some remarks suggested by a paper by). 454.
KOORDERs (s. w.). Some brief remarks relating to the communication of Prof. C.
E. A. Wicumann: “On fen formations in the East-Indian Archipelago’. 74.
— A brief contribution to the knowledge of endozoic seed distribution by birds in
Java, based on a collection made by Mr. BartHEets on the Pangerango and near
Batavia’. (Contribution to the knowledge of the Flora of Java. V). 108.
— Some remarks on the nomenclature and synonymy of Xylosma Jeprosipes Clos.
X fragrans Decne and Flueggea serrata Miq.” (Contribution to the knowledge
of the flora of Java. V1). 116.
KORTE WEG (D. J.) presents a paper of Dr. L. E. J. Brouwer : “Continuous one-one
transformations of surfaces in themselves” 2nd Communication. 286.
— presents a paper of Dr. P. BRanpsen: “On the stable positions of equilibrium
of floating parallelepipeda’’. 383.
— presents a paper of Mr. H. J. E. Bern: “The oscillations about « position of
equilibrium where a simple linear relation exists between the frequencies of the
principal vibrations” Ist part. 619. 2nd part. 735.
— presents a paper of Dr. L. E. J. Brouwer: “On continuous vector distributions
on surfaces” 2nd Communication. 716.
— presents a paper of Dr. L. E. J. Brouwer: “ On the structure of perfect sets
of points”. 785.
KOTARO HONDA and H. E. J. G. vu Bors. The thermomagnetic properties of
elements. 596.
KRAMER (£.) and A. P. N. Francuimonr. On derivatives of Piperazine. 452.
KRUYT (H. R.). The equilibrium solid-lquid-gas in binary systems which present
mixed crystals. lst Communication. 537.
KUYPER (J.). The influence of temperature on the respiration of the higher plants. 219.
LAAR (J. J. VAN). On the solid state. II, 26. ILL. 120. IV. 133.
— Some remarks suggested by a paper by Messrs TIMMERMANS and KonnstaMm. 454.
— Some remarks on Prof. Konnstamm’s reply. 617.
LAAR’s (vAN) remarks (A short reply to Mr.). 534.
LENARD (P.), H. Kameruince Onnes and W. E. Pauut. The behaviour of the
phosphorescent sulfides of the alkaline earths at various temperatures, and parti-
cularly at very low temperatures. 157.
LIEBERT (£.). The decomposition of uric acid by bacteria. 54.
LINaLoon (On the action of active copper on). 104.
LINEAR RELATION (The oscillations about a position of equilibrium where a simple)
exists between the frequencies of the principal vibrations. lst part. 619. 2nd part. 735
VIII cON TENTS
tines (The degree of completeness of the circular polarization of magnetically
divided). 345.
LINES OF FORCE (On the theory of the Zeem,n-ettect in a direction inclined to the). 321.
Liaurps (On the influence of the pressure on the miscibility of two). 235.
LOPHIUS PIscaToRIUSs (On the motor facialis and abducens nucleus of). 44.
LORENTZ (H. A.) presents a paper of Mr. J. J. van Laar: ‘* On the solid state’.
D265 UE 205 Ve 333
— On the theory of the Zerman-effect in a direction inclined to the lines of force. 321.
— presents a paper of Dr, J. A. VouiGrarr:” Remarks on the experiments of
Witson and Martyn on the velocity of rotation of the electric discharge in gases
in a radial magnetic field”. 428.
— presents a paper of Mr. J. J. van Laan: “Some remarks suggested by a paper
by Messrs. TimMerMaNs and KouNnsramM”. 454.
— presents a paper of Mr. J. J. van Laar: “Some remarks on Prof. KouNSTAMM’S
reply”. 617.
LORIA (sv). The magneto optic Krrr-eflect in ferromagnetic compounds and alloys. 835.
MAGNETIC FIELD (Remarks on fhe experiments of WiLson and Martyn on the velocity
of rotation of the electric discharge in gases in a radial). 428,
MAGNETIZATION (Researches on) at very low temperatures, 649,
— (Researshes on the) of liquid and solid oxygen. 799.
MARTYN (Remarks on the experiments of Wiison and) on the velocity of rotation
of the electric discharge in gases in a radial magnetic field. 428.
Mathematics. J. Carpinaax: ‘The constructive determination of the velocities of a
spacial system”. 12.
— S. L. van Oss: “On pentaspheric geometry”. 19.
— M. J. van Uven: “Investigation of the functions which can be built up by
means of infinitesimal iteration, Contribution to the solution of the functional
equation of ABEL”, 208.
— L. E.J. Brouwer: ‘Continuous one-one transformations of surfaces in themselves.”
2nd Communication. 286,
— P. Branpsen: “On the stable positions of equilibrium of floating parallel-
epipeda”’. 383.
— M. J. van Uven: “Investigation of the functions which can be built up by
means of infinitesimal iteration.” 427.
— M. J. van Uven: “On the orbits of a function obtained by infinitesimal iteration
in its complex plane”. 503.
—H. J. BE. Bern: “The oscillations about a position of equilibrium where.a simple
linear relation exists between the frequencies of the principal vibrations’’. Ist part.
619. 2nd part. 735.
— Jan pve Vries: “On pairs of points which are associated with respect to a
plane cubic.” 711,
— L. E. J. Brouwer: “On continuous vector distributions on surfaces” 2nd
Communication. 716.
— W. van per Woupe: “The cubic involution of the first rank in the plane.” 751.
CONTENTS IX
Mathematics. J. Brurx: “On the surfaces the asymptotic lines of which can be
, determined by quadratures.” 759.
— Jan ve Vrirs: “On polar figures with respect to a plane cubic curve.” 776.
— L. E. J. Brouwer: “On the structure of perfect sets of points.” 735.
MELTING-POINT LINES (On retrogressive). 227.
METHYLCHAVICOL (Javanese Basilicum oil and). 15.
Microbiology. F. Lizserr: “The decomposition of uric acid by bacteria.” 54.
— M. W. Berertnck: “Viscosaccharase, au enzym which produces slime from
cane-sugar.” 635,
— M. W. Beyertnek: “Variability in Bacillus prodigiosus.” 640.
— M. W. Beisertnck: “ Emulsion laevulan, the product of the action of visco-
saccharase on cane sugar.” 795.
MICROCEPHALIC IDIOT (Surface and structure of the cortex of a). 202.
MISCIBILITY (On the influence of the pressure on the) of two liquids. 235,
MOLENGRAAFF (6. a. F.). On oceanic deepsea deposits of Central-Borneo. 141.
— presents a paper of Mr. H. A. Brouwer: “On micaleucite basalt from Eastern-
Borneo”. 14.
— presents a paper of Dr. P. Tescn: “On jurassic fossils as rounded pebbles in
North Brabant and Limburg.” 422.
— presents a paper of Mr. H. A. Brouwer: “Pienaarite, a melanocratic foyaite
from Transvaal.” 547.
MOLL (J.w.) presents a paper of Mr. E. Rernpers: “Sap raising forces in living wood.” 563.
— presents a paper of Mr. K. Zistsrra: “Contributions to the knowledge of the
movement of water in plants.” 574.
— presents a paper of Prof. C. vAN WissELINcH: “On the tests for tannin in the
living plant and on the physiological significatice of tannin.’ 685,
MORINDA CITRIFOLIA L. (The essential oil! from the fruits of). 17.
MOTOR FactaLIs (On the) and abducens nucleus of Lophius piscatorius. 44.
MuscLes (About the formation of creatine in the) at the tonus and the development
of rigidity. 550.
NATRIUM-SULPHATE (On the system water-). 244.
NEON and helium (Data concerning). 175.
NITRATION (On the) of diethylaniline. 297.
NITROCOMPOUND. (The abnormal reduction of an aromatic) with tin and hydrochloric
acid and an interesting case of dimorphism. 305.
NOYONS (a. K. M.). Communications about the electrogram of the atrium cordis. 680.
ODOUR-AFFINITY (About), based on experiments of Mr. J. LieRMANIDEs. 90.
or (The essential) from the fruits of Morindw citrifolia L. 17.
OLIE jr. (J.) and Ernst Couey. The atomic volume of allotropic modifications at
very low temperatures. 437.
orBIis of a function (On the) obtained by infinitesimal iteration in its complex
plane, 503.
osciLLations (The) about a position of equilibrium where a simple linear relation
exists between the frequencies of the principal vibrations, 1st part. 619. 2nd. part. 735.
x Oto ON fe NaS
Oss (Ss. L. VAN). On pentaspheric geometry. 19.
OXYGEN (On the consumption of) by cold blooded animals in connection with their
size. 48.
— (Researches on the magnetization of liquid and solid). 799.
PARALLELEPIPEDA (On the stable positions of equilibrium of floating). 383.
PAULI (Ww. £), P. Lenarp and H. Kamertincu Onnes. The behaviour of the
phosphorescent sulfides of the alkaline earths at various temperatures and _parti-
cularly at very low temperatures. 157.
PEBBLES (On jurassic fossils as rounded) in North Brabant and Limburg. 422.
PEKELHARING (Cc. A.) presents a paper cf Dr. C. J. C. van Hoocrnauyze:
“About the formation of creatine in the muscles at the tonus and the develop-
ment of rigidity’. 550.
PEKELUARING (Miss C, J.). Investigations on the relation between the presentation
time and intensity of stimulus in geotropie curvatures. 65.
— The inadmissibility of the statolith theory of geotropism, as proved by experi-
ments of (—). 343.
PENDULUMS (On the determination of tidal constants from observations performed
with horizontal). 2.
PENTASPHERIC Geometry (On). 19.
PERRIER (ALBERT) and H. Kamertincn Onnes. Researches on the magnetization
of liquid and solid oxygen. 799.
Petrography. H. A. Brouwer: “Ou micaleucite basalt from Eastern [orneo.” 148.
PHOSPHORESCENCE (On) at very low temperatures. 76.
Physics. J. J. van Laar: “On the solid state.” If 26. IIL 120. IV 133.
— Henri and Jean Becqueret and H. Kamerutncu Onnes: ‘On phosphorescence
at very low temperatures.” 76.
— P. Lenarp, H. KamerirncH Onnes and W. E. Pau: “The behaviour of the
phosphorescent sulfides of the alkaline earths at various temperatures, and parti-
cularly at very low temperatures.” 157.
-— H. KamertineH Onnes: ‘“Lsotherms of monatomic gases and their binary mixtures.
ILI. Data concerning neon and helium.” 175.
— A. Sirs and E, C. Witsensure: ‘On the phenomena which occur when
in a ternary system the plaitpoint surface meet the two sheet three-phase surface.” 182,
— H. E. J. G. pu Bois : “An improved semicircular electromagnet.” 189.
— J. Timmermans and Pu. Kounstamm: “On the influence of the pressure on the
miscibility of two liquids.” 234.
—. W.H. Junius: “Regular consequences of regular refraction in the sun.” 266.
— H. A. Lorentz: “On the theory of the Zenman-eflect in a direction inclined
to the lines of force.” 321.
— P. Zerman: “The degree of completeness of the circular polarization of magne-
tically divided lines,” 345.
— A. Smrrs: “ The photo- and electro-chemical equilibria”. 356.
— J. A. Vor.erarr: “Remarks on the experiments of Wiitson and Marryn on
the velocity of rotation of the electric discharge in gases in a radial magnetic
field.” 428.
con TEN DS Al
Physics. Erxsv Conen and J. Ouie jr.: ‘lhe atomic volume of allotropic modifications
at very low temperatures.” 437.
— W. H. Junius: “On the origin of the chromospheric light.” 446.
—- J. J, van Laar: “Some remarks suggested by a paper by Messrs. TIMMERMANS
and KounstamM.” 454.
| — J. W. Giuray and M. pe Haas: “On the motion of the bridge of the violin.” 513.
— Pu. Kounstamm: “A short reply to Mr. Van Laar’s remarks.” 534.
/ — P. Zerman and B. Winawer: ‘The magnetic separation of absorption lines
in connexion with sun-spot spectra”. 584.
— H. E. J. G. pu Bots and Koraro Honpa: “The thermomagnetie properties
of elements.” 596.
— J. J. van Laar: “Some remarks on Prof. Kounstamm’s reply.” 617.
— Pierre Welss and H. Kamertincu Onnes: “Researches on magnetization at
very low temperatures,” 649.
— A. Sirs: “A new theory of the phenomenon allotropy”. 763.
— H. KamertincH Onnes and Apert Perrier: “Researches on the magneti-
zation of liquid and solid oxygen.” 799.
— Sr. Loria: “The magneto-optic Kerr-effect in ferromagnetic compounds and
alloys.” 835.
Physiology. F. J. J. Buyrenpiyx: “On the consumption of oxygen by cold-blooded
animals in connection with their size.” 48
— ll. ZwaarpemMaker: ‘About odour-aflinity, based on experiments of
Mr. J. HeERMANIDES. 90.
— F. J. J. Buyrenpix: “On the changes in the blood serum of sharks after
bleeding.” 377.
— F. J. J. Buyrexpux: “On tke constitution of the urine of sharks with normal
and increased diuresis.”’ 380.
— C. J. C. van Hoocenuuyze: “About the formation of creatine in the muscles
at the tonus and the development of rigidity.” 550.
— A.K.M. Noyons: “Communications about the electrogram of the atrium cordis.”680,.
— H. Zwaarpemaker: “The Camera silenta of the Physiological Laboratory at
Utrecht.” 706.
— J. G. Sueeswik: “Contributions to the study of serum-anaphylaxis’ 4th Com-
munication. 781.
PIENAARITE, a melanocratic foyaite from Transvaal. 547.
PIPERAZINE (On derivatives of). 452.
PLACE (f.) presents a paper of Mr, F. J. J. Buyrenpiyx: “On the consumption
of oxygen by cold-blooded animals in connection with their size.” 48.
PLANE (The cubic involution of the first rank in the). 751.
PLANT (On the tests for tannin in the living) and on the physiological significance
of tannin. 685.
pLaNts (Lhe influence of temperature on the respiration of the higher). 219.
— (Contribution to the knowledge of watersecretion in). 506. 400.
— (Contribution to the knowledge of the movement of water in). 514,
XII CONTENTS
points (On piirs of) which are associated with respect to a plane cubic. 711.
— (On the structure of perfect sets of). 785.
POLAR FIGURES (On) with respect to a plane cubic curve. 776.
POLARIZATION (The degree of completeness of the circular) of magnetically divided
lines, 345.
postMa (s.) and A, Smits. On the compounds of ammonia and water. 186.
PRESENTATION TIME (Investigations on the relation between the) and intensity of
stimulus in geotropic curvatures. 65.
PRESSURE (On the influence of the) on the miscibility of two liquids. 235.
primates (On the position and displacement of the Foramen magnum in the). 362.
— On the slope of the Foramen magnum in), 525.
QquapratureEs (On the surfaces the asymptotic lines of which can be determined by). 759.
RACEMISM (On partial). 393.
Raproactivity (On the) of Rubidium compounds, 154.
REFRACTION in the sun (Regular consequences of irregular) 266.
REINDERS (€.). Sap raising forces in living wood. 563.
RESPIRATION (The influence of temperature on the) of the higher plants. 219.
riGipity (About the formation of creatine in the muscles at the tonus and the deve-
lopment of). 550.
ROMBURGH (P, VAN). Javanese Basilicum oil and Methylehavicol. 15.
— The essential oil from the fruits of Morinda citrifolia L. 17.
— presents a paper of Prof. Ernst Conen and W. Tomprock. “The electromotive
force of zinc amalgams”. 98.
— presents a paper of: Dr, C. J. Enkuaar: “On the action of active copper on
Linalool”’. 104.
— On the nitration of diethylaniline. 297.
— presents a paper of Dr. H. Durriu: “On partial racemism’’. 393.
— presents a paper of Dr. H. R. Kruyr: “The equilibrium solid-liquid-gas in
binary systems which present mixed crystals”. 537.
— presents a paper of Prof. F. M. Jagger: “Studies on Tellurium. I. The mutual
behaviour of the elements sulphur and tellurium”, €02.
ROTATION (Remarks on the experiments of Wilson and Martyn on the velocity of) of
the electric discharge in gases in a radial magnetic field. 428,
RUBIDIUM COMPOUNDS (On the radioactivity of). 154.
SAP-RAISING forces in living wood. 563.
SCHEFFER (r. B. C.). On heterogeneous equilibria of dissociating compounds. 257,
sCHOUTE (ve. H.) presents a paper of Dr. 8S. L. van Oss: “On pentaspheric geome-
try”. 19.
— presents a paper of Dr. W. van per Woupe: “The cubic involution of the
first rank in the plane”. 751.
SEED DrsTRIBUTION (A. brief contribution to the knowledge of endozoic) by birds in
Java, based on a collection made by Mr. BarvHE.s on the Rangerango and near
Batavia. 108.
SERUM-ANAPHYLAXIS: (Contributions to the study of), 4% Communication. 731, 9 __
EE a
Ss
CONTENTS XIII
sHarks (On the changes in the blood serum of) after bleeding. 377.
— (On the constitution of the urine of) with normal and increased diuresis. 380.
SLEESWYK (J. G.). Contributions to the study of Serum-anaphylaxis, 4th Commu-
nication. 781.
SMITH (J. J.). On Distylium stellare O. kK. and Aporosa campanulata J.J. S. 341.
SMITS (a.). On retrogressive melting-point lines. 227.
— The P-T-X-spacial representation of the system ether-authraquinone”. 231.
— The photo-and electrochemical equilibria. 356.
— A new theory of the phenomenon allotropy. 763.
— and S. Posrma, On the compounds of ammonia and water. 186.
—and E. C, Wrtsensurc. On the phenomena which occur when in a ternary
system the plaitpoint surface meets the two sheet three-phase surface. 182.
— and J. P. Wuire. On the system water-natrium suiphate. 244.
SODIUM ALKYL CARBONATES (On.), 303.
SOLID sTATE (On the), IT. 26. ILL. 120. IV. 183.
SPACIAL REPRESENTATION (The P-T-X-) of the system ether-anthraquinone. 231.
SPACIAL SysTEM (The constructive determination of the velocities of a). 12.
SPRONCK (C. H. H.) presents a paper of Dr. J. G. Sierswisk: “Contributions to the
study of serumanaphylaxis” 4th Communication. 781.
STABLE PosiTIoNs (On the) of equilibrium of floating parallelepipeda. 383.
STATOLITH THEORY (The inadmissibility of the) of geotropism. 343.
sTOK (5. P. VAN DER). On the determination of tidal constants from observa-
tions performed with horizontal pendulums. 2.
suLriEs (The behaviour of phosphorescent) of the alkaline earths at various tempe-
ratures, and particularly at very low temperatures. 157.
suLPHUR and Tellurium (The mutual behaviour of the elements). 602.
suN (Regular consequences of irregular refraction in the). 266.
suN-spor spEcTRA (The magnetic separation of absorption lines in connexion with). 584.
surrace (On the phenomena which occur when in a ternary system the plaitpoint
surface meets the two-sheet three-phase). 182.
suRFacEs (Continuous one-one transformations of ) in themselves, 2°¢ Communication, 286.
— (On continuous vector distributions on). 294 Communication. 716.
system ether-anthraquinone (The P-T-X-spacial representation of the). 231.
— water-natrium sulphate (On the). 244,
TANNIN (On the tests for) in the living plant and on the physiological significance
of tannin. 689.
reLLuriuM (Studies on). I. The mutual behaviour of the elements: sulphur and
tellurium. 602.
TEMPERATURE (The influence of) on the respiration of the higher plants. 219.
TEMPERATURES (On phosphorescence at very low). 76.
— (The atomic volume of allotropic modifications at very low). 437.
— (Researches on magnetization at very low). 649.
— (The behaviour of the phosphorescent sulfides of the alkaline earths at various)
and particularly at very low temperatures, 157.
XIV CONTENTS.
TERNARY SYSTEM (On the phenomena which occur when in a) the plaitpoint surface
meets the two sheet three-phase surface. 182.
TESCH (P.). On jurassic fossils as rounded pebbles in North Brabant and Limburg. 422.
THEORY (The) of the ZeemaN-effect in a direction inclined to the lines of force. 321.
— (A new) of the phenomenon allotropy. 763.
THERMOMAGNETIC PROPERTIES (The) of elements. 596,
TIDAL CONsTaNTs (On the determination of) from observations performed with horizontal
pendulums. 2.
TIMMERMANS (J.) and Px. Konnstamm. On the influence of the pressure on the
miscibility of two liquids. 235.
— (Some remarks suggested by a paper by). 454.
TOMBROCK (w.) and Ernst Coury. The electromotive force of zine amalgams. 98.
ronus (About the formation of creatine in the muscles at the) and the development
of rigidity. 550.
TRANSFORMATIONS (Continuous oue-one) of surfaces in themselves. 24 Communication 286.
TRANSVAAL (Pienaarite, a melanocratic foyaite from). 547,
uric acrp (The decomposition of} by bacteria. 54.
urtNE (On the constitution of the) of sharks with normal and increased diuresis. 380.
UVEN (M. J. VAN). Investigation of the functions which can be built up by means
of infinitesimal iteration. Contribution to the solution of the functional equation
of ABEL. 208. 427.
— On the orbits of a function obtained by infinitesimal iteration in its complex
plane. 603.
VALKENB8URG (Cc. T. VAN) Surface and structure of the cortex of a microcephalic
idiot, 202. ‘
VARIABILITY in Bacillus prodigiosus. 640.
VECTOR DISTRIBUTTONS (On continuous) on surfaces. 2.4 Communication. 716.
vetociries (The constructive determination of the) of a spacial system. 12.
visrations (The oscillations about a position of equilibrium where a simple linear
relation exists between the frequencies of the principal). lst part. 619. 2¢ part. 735.
viotIn (On the motion of the bridge of the). 513.
VISCOSACCHARASE, an enzym which produces slime from cane-sugar. 635.
— (Emulsion laevulan, the product of the action of) on cane-sugar, 795.
VOLLGRAFR (g. a.). Remarks on the experiments of Wiuson and Maxrin on the
velocity of rotation of the electric discharge in gases in a radial magnetic
field. 428.
VRIES (HK. DE) presents a paper of Mr. J. Brun: “On the surfaces the asymptotic
lines of which can be determined by quadratures.” 759.
VRIES (JAN DE). On pairs of points which are associated with respect to a plane
cubic. 711.
— On polar figures with respect to a plane cubic curve. 776.
vrirs (orto pe). The abnormal reduction of an aromatic nitrocompound with
tin and hydrochloric acid and an interesting case of dismorphism, 305.
CONTENTS. XV
WAALS (J. D#V AN DER) presents a paper of Prof. A. Smrrs and E. C. Witsenbure:
“On the phenomena which occur when in a ternary system the plaitpoint surface meets
the two sheet three-phase surface’’. 182.
— presents a paper of Prof. A. Smits: “On retrogressive melting-points lines.” 227,
— presents a paper of Prof. A. Smirs: “The P-T-X+spacial representation of the
system ether-authraquinone.” 231.
— presents a paper of Dr. J. TimMERMaNs and Prof. Pa. Konstam: “On the
influence of the pressure on the miscibility of two liquids.” 235.
— presents a paper of Prof. A. Saits: “The photo- and electrochemical
equilibria.” 355.
— presents a paper of Prof. PH. KouNstamm: ‘‘A short reply to Mr. van Laar’s
remarks.” 534.
water (On the compounds of ammonia and). 186.
— (Contribution to the knowledge of the movement of) in plants, 574.
— natrium sulphate (Cn the system). 244.
WATERSECRETION in plants (Contribution to the knowledge of). 306, 400.
WEERMAN (R. A.). On a synthesis of aldehydes and indols. 42.
WEEVERS (TH.). The physiological significance of certain glucosides. 193.
WEISS (PIERRE) and H. KamerRLIncH Onnes. Researches on magnetization at
very low temperatures. 649.
WENT (F. A, F. ©.) presents a paper of Miss C. J. PEKELHARING: “Investigations on
the relation between the presentation time and intensity of stimulus in geotropiec
curvatures’, 65,
— presents a paper of Dr. Tu. Wrevers: “The physiological significance of certain
glucosides,” 193.
— presents a paper of Mr. J. Kuyrer: “The influence of temperature on the respi-
ration of the higher plants’. 219.
— presents a paper of Mr. J. J. Smiru: ‘On Distylium stetlare O. K. and Aporosa
campanulata J. J. S$.” 341.
— The inadmissibility of the statolith theory of geotropism as proved by experiments
of Miss C. J. PEKELHARING.” 343.
WICHMANN (a.). The fens of the Indian Archipelago. 7v.
— (Some brief remarks relating to the communication of Prof.). On fen formations
in the Hast-Indian Archipelago.” 74.
witson and Marvyn (Remarks on the experiments of) on the velocity of rotation of
the electric discharge in gases in a radial magnetic field. 428.
WINAWER (B.) and P. Zeewax. The magnetic separation of absorption lines in
connexion with sun-spot spectra. 584.
WISSELINGH (c. yan). On the tests for tannin in the living plant and on the
physiological significance of tannin. 685.
WITSENBURG (ek. c.) and A. Smits. On the phenomena which occur when in a
ternary system the plaitpoint surface meets the two sheet three-phase surface. 182
woop (Sap raising forces in living). 563.
WOUDE (Ww. VAN DER). The cubic involution of the first rank in the plane. 751
XVI CON TEN Zs
Wwurrer (J. Pp.) and A. Smirs. On the system water-natrium sulphate, 244.
XYLOSMA LEPROSIPES CLOS. (Some remarks on the nomenclature and synonymy of),
X. fragans Decne and Flueggea serrata Miq. 116.
ZEEMAN (P.). The degree of completeness of the circular polarization of magneti-
eally divided lines. 345.
— and Bb. Winawer. The magnetic separation of absorption lines in connexion
with sun-spot spectra. 584,
— eErrrcr (On the theory of the) in a direction inclined to the lines of force. 321.
ZINC aMALGAMS (The electromotive force of). 98.
ZWAARDEMAKER(H.). About odour-affinity based on experiments of J. HErMANIDEs. 90.
— presents a paper of Mr. F. J. J. Buyrenpisk: “On the changes in the blood
serum of sharks after bleeding.” 377.
— presents a paper of Mr. F. J. J. Buyrpnpisk: ‘On the constitution of the urine
of sharks with normal and increased diuresis.’’ 381.
— presents a paper of Dr. A. K. M. Noyons: “Communications about the electro-
gram of the atrium cordis.” 680.
— The Camera silenta of the Physiological Laboratory at Utrecht. 706.
ZIJLSTRA (K.). Contributions to the knowledge of the movement of water in plants. 574.
i ht Adi ; vi
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