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KONINKLIJKE AKADEMIE
VAN WETENSCHAPPEN
-:- TE AMSTERDAM -:-

PReocee DINGS: OF- THE
SEC TION-OF SCIENCES

VOLUME XIv
(= 2 PART —2)

JOHANNES MULLER :—: AMSTERDAM
JULY 1912

\ af ]'|i\ ) Oe
‘

(Translated rota’ Verslagen van de Gewone Vergederingen der Se en. a Ne u

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ClO NTE Ne TS:

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5),
KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING
of Saturday December 30, 1911.

= DOC

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 30 December 1911, DI. XX).

SS) INT BL Aa aANp eS

P. Zepman and C. M. HooGrsoom: “Electric double refraction ia some artificial clouds and
vapours”, Ist part, p. 558.

J. J. van Laar: “On the variability of the quantity ) in vAN peR Waats’ equation of state
also in connection with the critical quantities” 11I. (Communicated by Prof. H. A. Lorentz).
p. 563.

A. Pannexork: “A photographical method of research into the structure of the galaxy”.
(Communicated by Prof. E. F. van prE Sanne Bakuuyzen), p. 579.

M. J. vay Uvyen: “Homogeneous linear differential equations of order two with given relation
between two particular integrals’. (Communicated by Prof. W. Kaprryn), p. 584.

L H. Siertsems and M. pre Haas: “Determinations of refractive indices of gases under high
pressures”. First paper: “The dispersion of hydrogen”. (Communicated by Prof. UW. Kamer-
LINGH ONNES), p. 592.

J. BOrseKEN and H. Waterman: “On a biochemical method for the determination of. small
quantities of salicylic acid in the presence of an excess of p-oxybenzoic acid”. (Commu-
nieated by Prof. M. W. BrisErincn), p. 604.

J. Borsexen and H. Warrrman: “On the action of some benzene derivatives on the develop-
ment of penicillium glancum”. (Communicated by Prof. M. W. Brierixen), p. 608.

J. Borsexen, A. Scnweizer and G. F. van per Want: “Op the velocity of hydration of
some cyclic acid anhydrides”. (Communicated by Prof. A. F. Horiewan), p. 622.

H. R. Doornxwoscu: “On the iodides of the elements of the nitrogen group”. (Communicated
by Prof. P. vay Rompuren), p. 625.

Morris Owen: ‘The thermomagnetic properties of elements”. (Communicated by Prof.
H. E. J. G. pu Bors). p. 637.

J. P. Kurnen : “Investigations concerning the miscibility of liquids”, p. 644.

P. Zeeman: “Note on the insulating power of liquid air for hizh potentials and on the Kerr
electro-optic effect of liquid air”, p. 650.

J. D. van ber Waats: “Contribution to the theory of binary mixtures”, XVII, p. 655.

H. Kameriincm Onnes and Ars. Perrier: “Researches on magnetism”. IV. “On paramagne-
tism at very low temperatures”, p. 674.

H. Kamertinen Ones: “Further experiments with liquid helium”, p. 678. (With one plate).

A. F. Horreman: “On the chloration of benzoic acid, according to experiments of the late
Mr. J. Tu. Bornwarer”, p. 684.

T. van per Linpen: “On the magnetism of the benzolsubstitution and on the opposition
of the formation of para-, ortho- against meta-substitution products”. (Communicated by
Prof. A. F. Horiemay), p. 684.

H. Vermevren : “On some trinitroanizoles”. Communicated by Prof. A. F. HottEemay). p. 684.

38
Proceedings Royal Acad. Amsterdam. Vol. XIV.

Physics. — “Electric double refraction in some artificial clouds and
vapours.” (First Part). By Prof. P. Zeeman and C. M. HooGensoom.

(Communicated in the meeting of November 25, 1911).

1. Some time ago one of us') suggested a method of attacking
the problem to discover an influence of electric fields on radiation
frequency, as predicted by Vorer’) from theoretical considerations.
The experiments installed according to the mentioned method have
not yet come to a definite close.

We intend to give here a short account of a parallel series of
observations relating to a closely connected subject, which were
begun already a considerable time ago.

They relate to the Kerr electro-optic effect, the double refraction
induced by powerful electrostatic fields, Till now the effect has been
specially studied in solids and liquids; we intend to investigate the
behaviour of some clouds and vapours.

If it is once proved that under the influence of electric forces
double refraction is induced in clouds of suspended particles, then
the phenomena may be pursued further, when the size of the
particles is taken smaller and smaller. By increasing the sensitiveness
of the optical method clouds of smaller and smaller values of double
refraction and ultimately gases can be investigated.

Corron and Movuron*) in the course of their remarkable investi-
gation of magnetic double refraction induced in liquids have formulated
the hypothesis, already proposed by Sir Josepn Larmor for the Kerr
electro-optic effect, that in both cases the double refraction is due
to a directive action of the external field on the molecules of the
liquid. The only cause interfering with a parallel arrangement of the
molecules is their thermal motion. LanG@nyin *) has shown in how simple
a manner this hypothesis of the molecular orientation explains
quantitatively the phenomena mentioned and also others.

It seems still somewhat questionable in how far the hypothesis of
molecular orientation may be applied without modification to gases,
at least if exhibiting narrow absorption bands.

The study of artificial clouds seems interesting for the reason that
the suspended particles play the rdle of the molecules in the

') Zevman. These Proceedings, January 1911.

*) Voiar. Magneto- und Electro-optik. 1908. Kapitel 9. u. 10.

*) Corrvon et Mouton. Ann. de Chim. et de Phys. T. 19. 1910, cf. also the
interesting paper of Corpro. Physik. Zeitschr. 11. S. 756. 1910.

') LANGEVIN. Le Radium T. 7. Sept. 1910.

(559 )

hypothesis of molecular orientation. It is now possible to examine
separately also the constituent particles; they can be shown to possess
(or not to possess), before their exposition to the field, magnetically,
electrically, and optically the symmetry of a solid of revolution.

Especially interesting are those vapours which exhibit narrow
absorption lines. In this case the opinion expressed by Vorer') that
in the neighbourhood of absorption lines the amount of the double
refraction will assunie considerable values, can be tested. Indepen-
dently of a special form of theory there is much to be said in
favour of this opinion.

2. There is only one investigation known to us, which seems to
give evidence that electric forces induce double refraction in some
clouds. E. Biocn’) while investigating the influence of dust particles on
the electric conductivity of gases, made the following two observations.

In the first place he found that a cloud of sal-ammonia, if present
between the plates of a condenser and if seen against a dark back-
ground in diffuse light, becomes white and more manifest as soon
as the plates are charged.

The other observation made by Brocn is this. A parallelepipedical
box is closed at two opposite sides by glass windows, two other
sides consist of metal plates at a distance of a few centimetres and
can be connected to an electric machine. If a cloud of sal-ammonia
is mtroduced and the box is placed between crossed Nicols, then
the light of a source behind the polariser is seen at once with the
making of the field. The rest is perhaps given best in the original:
“La modification de la lumiere diffusée (ou diffractée) par les parti-
cules est done accompagnée dune anisotropie du milieu constitue
par lair et les particules. [Il reste done a savoir s'il y a birefrin-
gence ou dichroisme et a faire l’étnde quantitative du phénomene’’.

It is indeed easily seen that by induced dichroism alone, the light
would reappear. Let the electric force be horizontal, and suppose
the light issuing from the polariser being polarised under azimuth
of 45°. Let the vibrations be resolved into vertical and horizontal
components. If we suppose that the horizontal vibrations are absorbed
powerfully by the vapour, but the vertical ones not, and that there
oceur no differences of phase, then on emerging the resulting vibra-
tions will have an azimuth larger than 45° and there will be there-
fore revival of light.

*) Votat. lc. p. 381.
ER BLOCH. Cs, Reale 465.1908:
38*

( 560 )

3. Our experiments prove that in a cloud of sal-ammonia there
isyonly double refraction but no dichroism. (see § 4).

The light from a Nernst filament is made parallel by means of
a lens and polarised in a plane inclined to the horizontal at 45°.
The vapour or the cloud is introduced into a horizontal tube, which
contains in many experiments interior plates connected with the
source of electricity. The tube is closed by plates of thin coverglass ;
two side tubes served resp. for the introduction and for the egress
of the vapours. The analysing Nicol, of course, follows after the tube.

The double refraction to be observed is so small that special means
are necessary for observing and measuring it. Between the polariser
and the tube we introduce a horizontal bar of glass, perpendicular
to the beam of light*). Near the middle of its length the strip is
supported by two small glass cylinders and subjected to a small
flexure. It is therefore in a condition of strain and double refraction.
Between crossed nicols there is revival of light, especially near the
edges of the bar, while near the middle a horizontal band remains
dark. It seams superfluous to comment upon the optical theory of
the strained glass bar, which is rather simple and moreover given
in many text-books. The most refined investigation made with the
strained bar, is probably Lord Rayinicn’s, when discussing the question
whether motion through the aether causes double refraction. *)

The position of the band is determined by two horizontal wires
inclosing it, and disposed close to the bar. If a double refracting
substance, with horizontal and vertical principal directions, is intro-
duced into the beam a motion of the band occurs, upwards or
downwards, depending upon the sign of the double refraction.

The sensitiveness of the method can be changed within rather
wide limits. It is increased, 1. by diminishing the loads at the ends
of the bar, 2. by increasing the distance of the supporting cylinders.
We are thus enabled to choose the sensibility according to cireum-
stances.

The absolute value of the amount of double refraction was deter-
mined, at, least for higher values, by means of a carefully constructed
compensator of Sonuu.— Bapiner. By its means the displaced band
can be moved until it is again in its original position. The compen-
sator is so mounted that it can be easily introduced into or removed
out of the beam. For very small values of the double retraction
if seems appropriate to use a second strip instead of the compensator,
and to restore the original conditions of the field of view by a

1) RayereH. Phil. Mag. (6) 4. p. 678. 1902:

( 561 )

flexure of this second bar in a suitable direction. We have not yet
had occasion to try this method systematically.

In order to determine the sensitiveness of the metiod a thin vertical
glass plate was introduced in the course of the light and the weight
determined necessary to cause a marked shifting of the band. During
this operation the compensator of So.rm—Bapiner is removed. The
constant determining the influence of one sided pressure on double
refraction is measured in a separate experiment. The glass bar and
the compensator are then used simultaneously. The difference of phase
just perceptible was in our case 6.10~° 2.

4. The cloud of sal-ammonia was made in an anteroom, preceding
the observation tube. The two gases, hydrochloric acid and ammonia,
were introduced under slight pressure after being partially dried.
After passing the observation tube the cloud escaped in the free
atmosphere. The density of the cloud and the magnitude of its
constituting particles could be chosen by regulating the ratio of the
two gases.

The source of electricity was either an electrostatic machine or a
transformer, allowing potentials between 1000 and 10000 Volts
being used.

The question whether there is dichroism or double refraction (see
§ 2) could now be settled immediately. By dichroism a rotation of
the plane of polarisation will occur, and therefore a fading of the
dark-band and not a displacement must take place. Double refraction
shows itself by a displacement alone. Our first experiments with the
sal-ammonia cloud at once made it clear that only double refraction
is operative. The effect was nearly proportional to the square of the
electric intensity.

If a transformer is used then a displacement of the dark band
must take place as well; it can be easily calculated. The direction
of the displacement of course depends upon the nature of the substance
under consideration.

5. The results of our measurements will be given later on. The
sign of the Kerr-effect in the sal-ammonia cloud is opposite to that
of ordinary glass.

6. We also tried to determine the relation of the specific values
of the effects in the sal-ammonia cloud [and in large crystals of
salammonia. The latter were never faultless. Perhaps this cir-
cumstance accounts for the very small specific action found for a

( 562 )

separate crystal. The result seems too striking to be accepted without
further evidence. Or would it be possible that the mobility of the
particles in the large crystal is considerably reduced ?

7. The experiment of § 4 proves very clearly that in the ease of
the Kurr-effect there is a direct action of the field and not one due
io a mechanical pressure from the condenser plates.

8. Besides clouds of sal-ammonia in different degrees of dilution,
we have made observations with some other clouds; details will be
given later. They were obtained by heating of substances in some
eases, in others by chemical processes, among which we count also
the process generating TynpaLi’s actinic clouds. In some of our
experiments we made use of dust clouds, the substance under review
being first reduced to very fine powder and then blown by a cur-
rent of air between the condenser plates. It is easy to obtain clouds
in this manner with glass powder and with different salts of tartaric
acid. The effect of a glass cloud is, as is to be expected, in the
same sense as that of the original glass.

9. The method, resumed in § 8, and especially the combined use
of a glass bar and a compensator of SoLuim-Bapiner (or of a second
bar previously gauged), can be used to ascertain sign and magnitude
of the Kerrr-effect of very small quantities of fluids. With condenser
plates of only a few square millimeters’ area and with voltages of a
few hundreds Volts the Kwrr-effeet in nitrobenzene is easily observed.

In order to obtain quantitative results a condenser of some exten-
sion in the direction of the beam is necessary. The greatest difficulty
in all experiments on electric double refraction give the optical per-
turbations caused by heating effects from the part of the electric field,
Which interfere very seriously with observation. The time of obser-
vation must therefore be reduced as much as posible. The following
mode of Operation is advisable. Let the shift of the band be com- -
pensated as accurately as possible with the field on. Then put the
field off. The band then is shifted again. It is now easily controlled
Whether the compensation was exact, by puiting on the field for one
moment. The time necessary to ascertain whether or not the dark
band jumps back just. inside the two horizontal wires is very short.

( 563 )

Physics. “On the variability of the quantity 6 in VAX peR WaAa.s’
equation of state, also in connection with the critical quantities.”
I. By J.J. van Laar. (Communicated by Prof. H. A. Lorentz.)

(Communicated in the meeting of November 25, 1911).

The coefficients found in the preceding paper can be found by
another way still. I will call this method the symmetrical method,
because it is based on fvo logarithmic ecuations which are symme-
trically constructed. We mean the relations

8 d' ad 3—a 1 ;
—m —— log| — - == = d'—d
3 3(d—a') * \d' 3—d 3—d
8 d da 3—d 1

qe | ree log =e = = > | d—d
3 3(d— d') d 3—d 3—d }

which have been formed by the combination of the two original
equations (a). (see Il p 482).
If again we put:

d=1+ 2e¢+ 2y=1+42p ; d@=1 — 2x + 2y =1 — 29,
in which #=ar+cr'+..., y=br? + dr*+..., the two above

equations become:

2 ae 1 fess =) | is we
= m| ———* bog FF) _ | ty)
3 3(p + q) 1—2¢q 1—p 1—p |

2 1+ 2p l+2p 1+q Ly
—m | ——— — log | — = —|=ptq
3 o(p+q) l—2q 1—p l4+q

because 3 —d=2(1l—p), 3 —d' =2(1+q) and d—d=2(p-4 4).
Now the logarithm gives (see Il p. 440), after p+q has been
placed outside the parentheses :

5

f 1 2 2 3 3
3(p+4) | ete a ite Ol 9, ons (BE — 9") =

Wil : il : 45
stares? —..+ Via) as (pp—.-—g*) + cee B Sic +9)

After division of the log by 3(p+q), multiplication by 1— 2q, and
subtraction of 1:(1—p)=1+p+p?+... the former of the two
above equations passes into
Crt ae Se 1 1 ee ee
eu Tae i meTo .9 (Bp? +p*g—pa? +q*) +

1 oe ee l a cee :
Page te IP oP — 9) aOR ado eae le a

Pl)

1 \ 78 5 2 S38 2
Se a MS aw bal 2 i ter —0) |= +4),

in which the coefficients 8, 0, 9, 6, 27, 36, ete. in general are
represented by 7, AA—3), O(6* —49 + 6), AG—5#+109—10),
O(6*—60* + 159? — 200 + 15), 0 (65 — 704 + 216°—356* + 359 —21),
etc., where 0 = 3.

The corresponding second equation is now evidently obtained by
substituting —q for p, and — p for q, as is immediately seen by
comparison of the above equations (4). If then the first equation is
divided by —(p-+gq), the second by p+q, we get:

ea I
m E +: 5 8p’ 209 9 )\— = (Apt Op ag si Bye) te

eRe oe Geena. apy +q' ars (6p*- Spline are pn) | =!

my] 1 als 9 (p? 2p4q ae 39°) a (p*- 2p"q Spq- 7) -
5

# (P20 Any 0 (WB Php p99) ia
Subtraction yields:

) 2 1 2,3 2 2 DYAt}
229) lige MORE Pate piled ly

3 |

Det SOUR Dyan) 4 Jertee 4 32 2.3 ALP Tes p
ge APO? 91 2a eae) = cl Rie ae hea -38pq' +59") = 9,
or after division by p+ q:

1 2 Q,3
(PSY) a oen OP eed arid eae

Y ‘ » 2 . 2 3 4 6 03 2 p
4 = (4p*—6p*q+-6pq?-4q") - 7 (5p*-8p*g +- 9p*q?-8pq* +591) = 0 . (a)

Addition, and division by 2m yields:
i : Laan r

(2 pa): PP GPa ite
9g

= (p' —p'q | Py —pq° +¢q°) => 2 (p>— an, —q’) = Ta 44 ° ’ (7),

because m= 1— 2? and soi:m=1+774+ 77-4...
Re-substitution of wy for p, of «—y tor q¢ (see above) transforms
«) and (8) into

( 565 )

1 3 4
2Qy—— (2a? + 10y*)+ — .2y(Ua*4-10y?)- — (824+ 422774? 4 35y') = 9
py) 3) ‘

1 = 9
(w°+38y")-—.2y(2a°+2y/° A (0441007 y?4-5y*)-2 2y (82449274? +3y1)=1? 413 |
Z i)

?

which is easily obtained when we consider that 4p*—6p*q +
= Spq'—4g°=(p—)IA(p*+9°)—2pq] 5 Sp*—8p*g+ ete. = 3(p*+9*)—
—8pq(p*+-q")+- 90°" ; ete.
And if finally we substitute the values at+er® and br?+-dt* for
w and y, we get:
9

2 12 + \
2(br* drt) —=( wie 41200 -ab%p ++ — br*(3a?t?)— = (Bat?) = oH
o 3) (

>

9 ,
(wr 4: (2oe bane! 2h er) + — (a*v*)=1° +14 \

»
in which the development need not go any further than +t‘, whereas

in the asymmetrical method (see the preceding paper) we had to go

as far as t°. In consequence of this amongst others the whole last

term of the first member of the second equation in w and v vanishes.
Summarizing this, we get finally:

2 . 4 30, 12 ,
2b— = a® |x*?-- | 2d—— ac—2b?-+ — a*b— — af | t* = 5
5 5 5 f

9
at (20 +36? —2a°b + — «) tit? + 1 |
oO

from which follows :
9
Gilt 2act+ 3b°?— 2a°b+ —ai=1
o
a eae 4 io eee
i eG) |
5 5 5 7

and from this by successive substitution and solution :

1 13 64
ao = b= . —— s d =—_,
5 50 875

as in the first method. But here the coefficient ¢ is not required to
determine (, because they are not found in pairs together, — always
from two equations with two unknown quantities — but szcces-
sively, always from but one equation. It is again self-evident that
if we only desire to know a and 4, the above calculation is again
considerably shortened, and the result is obtained almost immediately.
For then only the terms with <* are necessary.

Lastly we will also mention a third method, .that of the dz/fe-
rential quotient; the shortest method of all, but yet possibly slightly

( 566 )

longer than the two discussed methods, because first the differential
quotient must be derived. Let us start from the two equations
(12) and (2) [See II, p. 432 —433], viz.

1 3—d' 3 d—d
(8—d)(3—d')\(d+d') = 8m 3; log é i pie (« - aay) ,
d 3—d 8

m

Now we differentiate with respect to 7 (m = 1 — 1°, sor = V1—m),

. : : ; ; dd
and obtain in this way from the first equation, putting auras
at

dd'
and ree
a“ y aty PX a
3 oq) 2a gaa a ere
from which:
3—2d—d' 3—d —2d ar ‘
ae =e 4 one i = (dod) re a (@)
The second equation yields:
Fy y y x 3 d—d' ay) (Gea!
GG a) | 2 , 585i Cay) 8 a eu)
3 2r Wn ‘
ag al a) (6 — (d+-d)) ;
i.e.
E ate Meee lo — +2) a+
d 3—d Sm Sm
a [ : us + Y (d — d') + FAG _— ua))| 7
d' 3a! Sm 8m
3 2r hs. ;
= a (d—d') (6 —(d + d)),
or
| Z a ae (2d — | a 4 | — z — + z (62a) | ——
d(3—d) Sm d' (3—d’) Sm .
3 2t Ral .
= 7-7 4—4)(6 = (d+d)).

If in this (8 — d) (8 —d’)(d +d’) is substituted for 8m, we get:

1 2 Tl 2 ,
E (3—d) (3—d') (a4 F | et E —d) (8-d(d =a IS

Qt
= —, d—d)(6—(d+ 2),

Sm?
or also

(567 )

(d—d) (8—2d--d’) : (d—d') ( 3—d—2d')
d (3—d) (3 — d') (d+d') d' (3—4d) (8 —d’) (d+ ai

. a
= (d—d)(6—(d+4)),
hence finally, writing again 8m for (8—d)(8— d’)\(d+d’):
Soda) Bd = 2a ae ae
So a (6 —(d td)). - (8)

We must now combine (@) and (3) to solve w and y. Elimination
of y gives:

ee ea eee lL (gia ay (3 ana
(8 —2d ) ae gee REE ( —( +d!) )\—( —d)(d4+d) |,

Feet ty 5 Qt ' .
rene) = gars ( = 9)
so that we get:
ld 2 1(3—d
Se SS elle Se Si fol o hae ee (OS)
dt 1— 7? 3—2d—d'

ie dd’ ae
and a similar expression for 7 = ae which differs from the above
at

only in this that ¢@ and d’ are interchanged. It is this comparatively
simple result, which makes us find the coefficients «, 4, c, ete. pretty
3 aes ,_- (a =
soon. Substitution, namely of = ] + Zar + 2bx? s+ Qcr® + Jd
id
immediately gives:
2 (lar 26r?+ . je (l—av — br? —..)

l= — Sax —6br? Ser? 6dr4 —

2a4 Abt ber?-+8de? = —

lL. €.
(a+-2br 4 der® + 4dr’) (a+ 3br-+- cr? + 8dr") =
Bee Zar + 2br° “se 2er*) ( (L—ar—br? —¢t' )
= =i 2 —= :
or
a> + d5abr -+ (dace -+ 667) ce? 4 (Tad -+- pe) —
2

on Laetesel ee G mele ay i baa") o8 (a edad)’.

And from this follows :
a — 1; ab — a; 4a6¢—— 66" — 1 + 6— 2a’; Tad + 1lbe=a-+ ¢ — 4abd,
i €:

For the knowledge of a and 6 only we should have to go no
further than terms with 7, and so the calculation would then be
very simple indeed.

8. After the above digressions, which have made us acquainted
to a certain extent with the nature of the problem, and the results
of which may later on be used for a comparison, we proceed: in
the first place to derive the reduced equations for the case of association
of the molecules, and in the second place to determine from this the
coefficients @ and 6 of the expansion into series:

d=1-+ar+ br?

in the neighbourhood of the critical point.
From the equation of state

1+.2p
Beales RT
eich a
Sater gs oy

in which all the quantities are made to refer to single molecular

quantities, and in which RT is therefore multiplied by (1--a@) : (I--a)

instead of by 1 + a3, the equation
1l+ap 8 1a

m

1 eee! ela v4 by. a
ov 9 7 &=—- Se pe = —- ae
a2 b)? Del bp. re by y (20)? bin? ’
or
1+2xp
: ——_—— 5
Js 1l+e 27

fl Bin=y © Gye
follows by substitution of
pe, Lm vn OO Wers
in which (see I, p. .296—297)
] a 8 a

— lan LSS ee LILA
er CHIR 7 pee ae

> aa : : SD ;
Hence, by equalisation of the expressions for « for the two co-
Ji
existing phases :

ete a . 10
2,1—yd 2,1—y'd' 8 m ee

When we again introduce the densities d=1:n and d’=1:n’. For

( 569 )

x=1(v=2) (association to double molecules) we have viz. (see I
p. 297):

27 iy] QF

6,042
— = - = ==/6, 016;
(2,1) ip — (2,114)? < 1,004 4,469 « 1,004 1,0043

for which we have written 6 for brevity’s sake. So in later calcu-
lations in (10) 2,1 must always be replaced by 2,114 and 6 by
6,016 at least for c=1. At constant + this value 6 becomes
OT _ ni?

al

a Wered,
—== 3, while tee y ete. become all = 1, so that then the original

aie Zi

relation (1) is found back (see II, p. 482).

The former logarithmic relation, formed from | pdv must now be
obtained in a somewhat different way, because the direct integration
would become too intricate in consequence of the variability of 3
and 4. The same result is, however, obtained by equalisation of the
thermodynamic potentials of the two coexisting phases’), and the
formula

pth: 3 Tee eilaal me ale 1 \ ital
14-2) lox ay = || 0 eae el ee }
( +a) tog] Lafeltxe p RT ie = Nha 3 v2)

is then found, as we derived before [see among others Solid State V
p. 456 (These Proc. Nov. 1910) and VII p. 89 (June 1911). But as
here everything refers to double molecular quantities, and in future
everything will refer to single quantities, we must substitute a : (1 +, 2)"
for a, b, for (1 + 2) 6,, v:(4-+.2) for v, and we get:

v—b' Bp a il IL (adi Nw
log {| —— =} = —] 2( —-— “al ei). ( — —— 2) A a (1H)
t—O p y Higa v vo z as ve y
1+ #8

when p+ “%/,2 is replaced by ; RT: (v—b) and p+ ¢/,2 by the
> v

corresponding expression.
In this connection we will just show that equation (11) is identical
with that which would follow from p= | pte. Let us for this
U—v

y

purpose write (11) in the form

RT log (7 =i) p =(<—5) L € _ 4 are a oe '
Lv—b 3! v oh v v vy vi

in which the expression between | | can be written:

1) Cf. also Chemisch Weekblad 1909, N?. 51.

(707)

. oP ep | = i

a a + av 2 |

~ (v—b,)— = (2! —b,)= i /(G=0) —\ —— -—p } (v-b,),
aS i

\ v—b ; Ds /
or

eee aR
rr zs 2 2 trap [tre ==);

2 v—b le vib!

Hence after substitution and solution of p:

‘1+ ap v6, : Lap v —, 5 (okies)
1+2 y' —6' lte v—b

Teele v a b Bp ct RL
p= ; log ( =F ;
v uv

v—b fp te aan

1 ——

And now it is immediately seen that in (11°), for 6 constant —

in which 6= 6’ =¢,, while +): (d+) and (1+ 7’): (1+) both

become = 1 the last term disappears and the following equation
remains :
Viel v—b' a
P —— ; log —— AK)
i =v 9 = 6 ve

as before. So the second member of equation (11°) can be considered

1 .
as the value of the integral —— | pee, but obtained by an indirect
(i — Ve
F
course by equalisation of the thermodynamic potentials.
Now, after this short digression, we return to (11). In consequence
of the substitutions 7 = nv,, ete. — to which 6, = shz can be added,
this equation reduces to

P iC lbpn'-bpy' B a ee ] 1 sbhp ral 1
ne DO lben=bpy py) eo 2 Tae n' (2 1)?b,? ace ;

Si 4/ teeape
21 bp

; ‘d 2,1-y'd' El 6 d—d' 5 rok jee 12
lox Seer || Se a Cd (((e/ + (le
9 ie 2d 8} 8 om : a sil Ce

or to

because 1:2—d, ete. and (for « —14) 6 has been substituted for
27 : (2,1)° 7, = 6,016. Here too our former relation (2) for 6 constant
(II, p. 483) is found back when we put @ and 8, y and y' =—1,
replace 6 by 35 (see above), 2,1 too by 3, while also s becomes = 1.

Now if is the equations (10) and (12) that quite determine d and
das functions of m. But the presence of 8 and y now makes the
problem much more intricate. We shall see that in the expression
for the coefficient @ of the expansion d= 1-—+ ar bdr’ even the
third differential quotient with respect to v of the quantity b of van

Gomley =:

per Waats’s equation of state occurs, whereas in the expression for
d*b

the coefficient 4 even the fifth differential quotient mi plays a part.
an?

9. Of the different ways by which we can arrive at the know-
ledge of the coefficient a, the following one seems the simplest to
me. As (see I p. 283)

b =b, —(1— 8) Ad,

be is also = b, — (1 — pe) 4b, and we find by subtraction:
b — b = (6 — By) Ab;
i.e. after division by by:
bi:
A be = Ap Gal

because 4 = yh,. Now we put (see I, p. 283).

(1 + #3)—— =¢
a—b
hence we have also:
: Ab
(1 + wpz) == Pk»
vji-—D-
; vj — bp
and so we can substitute —— Sa Pk for Ah, so that we eet:
={r Uk
by. 1+ exp,
B - B= —— — -(y — 1),

and hence, putting (1 + 273): +2)=a:

a auye ee -(y ye erase aceeceee (13)

1,1 pe
because: vy: 5, = 2,1, so (vp — b,) : 6 = 2,1 —1=1,1. (This value
1,1 is subjected to a slight modification, just as the other numeri-
eal values, when x is taken successively —1, 2, etc.). Now we

have always:

1 l
b = bp + BE (v -= vy) + = by.” (v — vz)? 4- = bg” (v — v,)* 4 ete.,

4 b

db
in which n=(F , ete. Hence division by /, gives:
k

av

—— eri p (n—1) 4. Del p" (n—1) 4 arnt p(n - Dy 1 ete., (14)

v— vj: w—N)or (v—v;)? (1) sa
because = a = 2.1 (a1)
Ye by. by. by.

(v—»,)* (n—1)? vy) 3

== el (2—l) os — 5 = =i : == (n—1)* . v4? 5
h Vk
while
era F Le iver i
by. — P 7 5 by Uh == P > 6 by). vj." — Pp

has been put.
In consequence of (14), (18) now reduces to

Dal: (1 = B)ay all (1 a Bk, Z A
B=pet+ p (n—1) + AO yeaa oo 9, (Id)
all Like fel Like
and so also, because « = (1+): (1-++.c) (see above) :
1 7 ae 2,1 a4 = 1° 2 a (i:
« ap + 1d oe (n—1) + il ge (n—1)? 4-...] 2% 5a)

By the aid of ithe found expressions for 7 and « we shall now
calculate the fraction
1 + #B d
lta ad Sr O!
Daya) oe dm oy
in (10). We find for it:

a Pani? 1) 4 Bly ta oa
ae Vana Meee Wile ey
2,1n—y a oe ea = 2,1 p! '(n—1) - —— 2. Lys i aaah eae a
But as evidently 2,4 .—1 = 1,1 + 2,1 (n—1), this becomes:

Aik ee 2,1 2 \
1 pot = let
« Me = Lk: lyk

Sil jgeene me Tae ae a

| ae pyr) — p (n—1)? —

heal
If now the second member is represented by

Cl. Paes Ail | 1) 4 2,1 B “he
7 ' — Ld y (7 — -}- 1 >: (9 — So eo |)(5
(Ge

’

the coefficients A, B, etc. may be determined from

iF 2,1 2,1 '
= aa A(n—1) +... at + ri ee (n—1) — .. '

In this we find by equalisation of the coefficients of the different
powers of n—1:

' & 2,1 ' " v
A=1—p ee, ; 1b ee) ai eae

2,1 ) 2,1 " ir aH
ernie ft qth oP (: te =)

elle PS ON eer lias , i ) . (16)
a ri. (aia Se +e7(a44)
= git ID Faye au Cp" — 2s? Bp ae aS AplV_—p r( +=)

Is)! ial iL a Ch

Now equation (10) passes into
| A lo 1) — (' | + B jy - 1p =
6 (n'—n) (n'+n)

8 n?n'? 2m

2.lap
(1,1 Nie

= | yay — (n'— | +.. | =

(10a)

i 6
In this the coefficient i may be replaced by another expression.

We saw, namely (see above), that 6 is properly = 27: (2,1)*f,, in
which (see I, p. 297)
lta nz? (8mz?— 2nk)
Lu 1+ xp, mye :

In this m, and ng (given by (5) on p. 288 loc. cit.) have of course
another meaning than the above m and n, so that we have marked
them with the index / to distinguish them. Now we can also write

POM /at:
; 1 9 fvp—by N? by
haz. J 8 me,
a, 4 Vie VE
UE— by Qn 6b. = 38m? —2nz P
because —_ aan wl ee ee (coe) 1, p. 288). In
3m’; Vk; 3 me

consequence of this we obtain

27 (1,1)? mi

CREE
because vp: b, = 2, and (7%—b,): 6, = 1,1. What we have represented
by the figure 6 is therefore, properly speaking:

a (CREE aR
(2,1)? x 27(1,1)? mg (1,1)? mp
= eee 2,laz
So we get, dividing both members of (10a) by (ty? (n’'—n):
» ee

Proceedings Royal Acad. Amsterdam. Vol. XIV.

ASB (p= yee (—1)| de ¢ Jim—y + (n—1) ('—1) + (r'— 1)? +... =

eee ea) Ieee een aR (108)

2,,/2
Mp nn>.m

in which m, has been given by (see p. 288 loc. cit.) :
mp=1 + eal Bp (1—Bp) (e@+-¢ x)’.

For «= 1 mz, is.e.g. = 1,107 (see p. 297 loc. cit.). If we now
put again, just as in the expansion of d=1:n (the further develop-
ments confirm again that 1—n and n’—1 are really of the order
of magnitude t= V1—m):

n ==" aie HE be 30 a) 3)
n==1 + at s- bc? . :
we may write for the second member of (108) :
1 14b'z? I i 1402?
mp [(1-3't?)?—a?x? |? (= ~ mp [1—(2a"* —40/r?](1—2?)’
as m= 1—r’, and because we shall for the present content ourselves

with terms of the degree 1’.
Now (10%) passes into

1
A — B (26't*) + C (a*x?—at? 4 a2?) = — (: + (1-+2a'?—30') >) (10c)

Mp

and it is only left to calculate A, Band C. For A we find

from (16):
Avail (1 + =).
Lk

; 1
But we can easily show that this = —. For we found in T,
MI:

p. 292:

—— B(1—8s uc
db eres B) gy (@+~¢@) ae es

~ 1
i aE B (1—§) (e7+¢)?

I ame (a)

db a cto om

because m has been written for the denominator of the expression for

b j ;
ini? =F (see above). Hence also, because 6', =p’ has been put:
av

1) See for the equality of the numerical values of the coefficients a’, b', ete. for
n and n' the observations in II, p. 488—439.

so that the equality of the terms with r° identically has been fulfilled.
So there remains:

1
— B (20'c?) + C (a2?) = — (14-2a"?—30') r?. . . (10d)

Mp

1
After substitution of A—=— we find for B from (16):
Mi

2,1 1—p' a
B= + p"| 1 + - ;
Le ri. Pk

x ?
In this p" (1 + =) can be expressed in p’ by the aid ofa relation,
Pk

holding between p’ and p" at the critical point. We have viz. (see
I p. 285):

dp 2a Tul AG

dv vi Db (v—b) m’

and hence:
dp 6a RT(1—b/)¢ RT d(@
dv? —— vt Ab(v—b)?m_ ~=Adb(v—b) dv :

m

a. 5 ee d?p
At the critical point Pies and BISOF esta hence we have there:
Lv Vv

m wv Ld (v—b) " o—bm dv

fp 2a Tagg 1—b'¢ d (4 6a, RT
v4 Ab (v—b)

m

And from this follows:

1—b' ¢ UG SG.
v—b m dv 4) a mn?

d (¢ 1—b, 3\ Fk
—({(-—-|Jj= —-— J—, 2. ws « s @- (a)
dv \m /. vE— bE vey mM,

in which we must bear in mind that this relation only holds for 7%,
dp Oe
a and = being =O only there.

or

m

x“ 1
Now we saw above that 1 — 0’ (: + =) =-—, so also:
Pp

g
g—U(et—=—,

and hence
39*

(576 )

1 , d (4g
(1—d’) — — b' («e+g)=—|-],. -- - - (8)
dv dv

which relation holds everywhere, and not only for 7. But only there

Ch 1 bes
(2) may be replaced by its value from (@), and we get:

dv \m
ys ENC
(1—}/) ue, =i (e+¢ ) = : Ve = = Lr :
dv /p k & vp—bp vp] my,

Ih ie hes : f
~— for — (see loc. cit. p. 285):
v—bm dv

3 al =a Li.

or after substitution of

Vk vie— bE | me ,
IG.
MO Cites AYE Luli Vie
— bru —— == = (1—d';) -
9 &k Lk my. | 2 vp—by.

or (see above)

“fy a 1 83 2,1 1 , 5
P Sle Py ee 5} 1° j2)) \\ 2 5 3 (Gla)

This is the required relation between p" and p’ at 7), and in
consequence of this the value of 6 (see above) passes into

ee ae le exit 3 1

B= Sa =(L==/) | =o.

Fa aliigerae my. | 2 ell my

Now our last equation (10d) becomes :

3b aad Tt ae 3b!
Se ts se (Cot SS == (1 } 2a Ns : T.
My Mi Mi

’

so that also the terms with the coefficient 6’ are cancelled, and only

Coa ee : (em St Woe co, (ILC
Me
is left, from which immediately
jee
C_—— Cie . . . . . . . . (18)

is found.

And now the coefficient a’ is found, because C’ can easily be
calculated. Also from the second equation, viz. (12), we might have
calculated the value of a’, but then the calculation would have been
more lengthy, and the result quite the same, of which we have
convinced ourselves for the greater security. For the calculation of
the following coefficient 6’, however, we shall have to use the equation
(12) by the side of (10).

(577 )

By way of control the following remarks may serve. It follows
from (16) for the case } constant, in which p’, p",p", ete. are all

2, ye) Pe Zell
—0, that C= — B, i.e. Cn, = —- — . But then — passes into
ie Leas Ba tic
2 :
eS (since v,: bg is*not =2,1 then, but = 3), so that Cm, becomes
9 ; 1 .
=x Henee a? = Hs —— As anidensOl du 2) asiett) should) ibe:

14
(Before we put (see II, p. 438) d=1-4 2ar, whereas we now put
w= 1:d=1—a't, so that a’ = 2a).
In the general case we find for C from (16):

al 2,1 3 7) 2 1 p" mr v
C= — ~— — + — — — p"(14—],
112 mp, 1,1 mz Lk

]
Aa ow ee EEE Eee re 184
i Ze 3 I 1 n mr 1 v (9) ,
Tiler) | 2 mele aa)

I will just call attention to this, that the value of a’ has been
derived by me in at least four different ways, and that always
identical results were obtained. Moreover I have convinced myself
that the coefficients in the development of » and n’ have really the
same numerical values; only with difference of sign for the odd
powers of t=V 1—rm (see also II, p. 488).

It also follows from the expression derived by us just now for
the coefficient a’ in the expansion into series n = 1—a’t+-0’r’, that
— for the determination of the relations at the critical point — it

; ae se ; db
is not sufficient to know the differential quotients 6), = (3) and
av k

dh
—— (=) , but that also the knowledge of the third differential
5

3
quotient of 6 with respect to v, viz. 6",—= (3) at the critical point,
In* )

is indispensable. And for the coefficient 6’ in the above expansion
into series, which coefficient determines the direction of the “straight”
diameter in 7%, the knowledge even of the fourth and jifth diffe-
rential quotient will appear to be required.

Let us now proceed, therefore, to the calculation of the third
differential quotient.

( 578 )
10. The third differential quotient. We start from the

db :
formula (11) for 6’ a (see 1, p. 292), viz.
v

1
~ BIL—B)¢(2+¢)
uv 1 &_-@

i earl = Oh eve -—— + dae? 21)

) 1 2
BI —p)(w+y) Aa BIL —B)p(@+¢4)

I
“a+

| / . 1
From this follows ( representing r
Cs ad

N
that 3'= ~):
ral a7 DE es ih R (1 3) ; ae ) 1 gf is
oho ae a+ 1 Pi ole) tha v—b m

1 (1+.28 x WG
—— y t- ¢ 2 == co -
+7 e+ 90 — 2). we | al =a

taking the values found in I, p. 255 (formulae (J) and (e)) for
Oh tee amas
dv

; B( —8)g(#+ ¢g) by N, so

anc into consideration, viz.
av
df lo ¢ dB eee,
diene ee a v-—b gp’

l
bearing in mind that 1 Trae ao — 8) (e+ g)* =m has been put,

sia
!

l
and the second member of (d) is evidently == Eas Hence:
Pp

1
———— — Pyrola £2-
yg | eyo Bele $29)
pa N?(v—b)|_ = ; mo

5 (@ + @) (1 + #8) (1 — 28) | ——__—.

<

a fad 1 ;
Now WN is evidently = d'm (see above), and SiS] BAU—Bf)¢(@ +27) :m=
+

aG
= map b', so that we get:

(v—) 6" — ie a Paney aS TG
m? ety a+1

(1 + #8) (28 — 1) oe

qm

i. €.

(579 )

Vfetey wty mi
2. bo” = — = + is 1 23 DY eee | chia :
dl | min + #3) (2 )+ta 7

|

1
Replacing in this inh’ by Saeed — p)g(« + ¢@) (see above), we
ae -

Tes

get:

b) b" 2 | acl aaah eres yor eae eee y |
(v—b) b mec sia el r + xB) (23 — 1) 4-23 1 = fs
1. €.

bf a+2 x
(ob)! == E an To oe 428-0]. He)
m*|-utg atl

identical with (12) in I, p. 293, paying attention to the above
expression (1) for 6’. This derivation seems somewhat shorter to me
than that in I, p. 292—293, and besides confirms the validity of the
result, so that we can ecaleulate 4” from it with full assurance.

Clarens, Nov. 13, 1911.
(To be concluded).

Astronomy. — “A _ photographical method of research into the
structure of the galary.” By Dr. A. PaANNrkork. (Communicated
by E. F. van DE SanDE BakHUYZEN).

(Communicated in the meeting of November 25, 1911).

In my paper: “Researches into the structure of the galaxy”,
published in the Proceedings of the Meeting of June 25, 1910, I
have pointed out that the chief difficulty in this kind of researches
consists in the lack of completeness and homogeneity in the material
of star-countings that is at our disposal. Herscarn’s and Epsrern’s
gauges and the countings on photographic and other stellar charts
have relation to small, generally non-coincident parts of the examined
galactic region. Owing to this the fluctuations of density, which may
be considerable even in smaller regions (comp. Max Wo r’s and
Barnarb’s photographs of the Milky Way), appear with their full
amount as errors of the function N(m) (number of stars per square
degree as function of the limiting magnitude m). At best we may
only hope that in the mean of a great amount of countings these
irregularities lose their influence. Still there always remains uncertainty
and doubt justifying the question whether these drawbacks may not
be avoided by another method.

( 580 )

This may be done by having recourse to photography. In this
manner the chief condition may be fulfilled at once : for all magnitudes
m exactly the same part of the heavens is taken and counted.
Hence the local differences in star-density become altogether harmless ;
as the irregularities shown by the function M(m) itself are probably
much smaller, this function may now be more easily deduced. If
all numbers 4 for different m can be determined on one and the
same exposure then the influence of the transparency of the air, of
the different sensitiveness of the plates, of the development ete.,
disappears at the same time.

Another condition which is of the greatest importance for the
practicability of the method, consists in the fact that for the deter-
mination of WN only countings are wanted without estimates or
measurement of the brightness of the stars.

One can e.g. make two photographs on one plate with the same
time of exposure, one without and one with a screen interposed,
the absorption of which is known to be @ magnitudes. This absorp-
tion may be determined by photometrical measurements, most
precisely by measuring the diminution of surface-brightness by the
screen, This is equal to half of the stellar absorption in magnitudes
and it is independent of the wave-length of the light. By counting
the stars appearng only on the photograph taken without the screen
and the stars showing both images we get two numbers JV (m) and
N(m—a), for which we accurately know the difference @ of the
limiting magnitudes, which is specially important for determining

' ‘ d log N
the, value of the gradient ——
, dm

found by measuring a few individual stars. We might also in order
to find a third value, count the number of stars, for which moreover
the first diffraction-image is visible. But only when the gauze is so
coarse that the first spectrum is contracted practically into a star-
shaped image, its visibility depends on the entire quantity of light.
Otherwise the limiting visibility depends also on the colour of the
stars and the difference in visibility between the diffracted and the
principal image is theoretically unknown.

Another method will be more practical. We take a number of
photographs on the same plate with geometrically progressing times
of exposure. Of each star we then obtain a series of images, each _
time differing in brightness a constant number of magnitudes. Now
we simply have to count the number of stars with one visible
image, with two images, with three, with four, with five images.
These give the numbers N corresponding with the limiting magni-

. The absolute value of m may be

( 5814 )

tudes m, which increase each time with a constant amount. ‘lo remove
the uncertainty owing to the confusion of the faintest star-images
with spots in the plate it is advisable to take the photograph of
longest exposure twice. The faintest stars are then all double and
undoubtedly recognisable, while there can be no doubt about the
visibility of the faintest image of the brighter stars, because the place
where we have to look for it is accurately known.

In this method, however, the difference in brightness between
the several images is not known beforehand and must therefore
be determined by special measurements. We know approximately
how many magnitudes are gained by a certain lengthening of the
time of exposure, ') but this increase differs for different plates and must
therefore be determined for each plate by itself. Therefore a scale
of photographic magnitudes must be fixed on the plate. These
magnitudes cannot be derived from a scale of visual brightness since
the spectra of the faint stars are unknown. It must be performed
independently by photographic methods.

Up till now there does not exist a scale of photographic stellar
magnitudes (defined by m= 2.5 logy L), which is independent of
visual brightness. Generally it is determined in such a manner that
they correspond for the stars ofa certain spectral class (HarvARD A.) to
the visual photometric scale. Also in Picknatne’s “Report on stellar
magnitudes in Kapreyn’s selected areas’ *) the necessity for fixing
the scale of magnitudes for the fainter stars by means of prismatic
companions, of exposures of different length or with wire-gauzes,
is only mentioned in general terms. It is plain, however, that the
first two methods cannot give an independent scale-value. This ean
be done only by a wire-gauze the absorption of which has been
determined by physical experiments. Another independent method
has heen proposed recently by Huertzsprunc, viz. to use the first
diffracted image obtained with a coarse screen in front of the ob-
jective, the strips of which are of the same width as the spaces
between them.

_ So a “seale-plate’ must be taken of the same part of the heavens
of which a ‘“counting-plate’” has been made, in order to determine
the magnitudes; on the first one two exposures of the same

1) According to Scuwarzscuitp (Beitriaige zur photographischen Photometrie der
Gestirne) is Jog 1+ plogt=const.; the values found for p were generally lying
between 0,7 and 0,9. Accepting 0,8 as mean, then with a tenfold time of exposure
jog I=0,8, and the gain is exactly two magnitudes.

2) J. CG. Kapreyy, First and second Report on the progress of the plan of
selected areas 1911. p. 31.

(582

duration have to be made, one with a free objective, and one with
a wire-gauze, or according to Hrrtzspruneas’s method, the second
one with the coarse screen. We thus obtain two images of each star
on the plate, differing a known number of magnitudes and from this
there may be deduced a scale of photographic magnitudes on the
plate, which is altogether independent of visual magnitudes.

This method, however, has this drawback that the two exposures
are taken one after the other, so that, owing to changes in the
transparency of the atmosphere the real difference in brightness does
not correspond to the difference found on the plate. Hence the basis
of the method becomes doubtful. In order to escape this objection
another photograph should be taken at the same time with a second
apparatus to control the first. Another means is the application of
SCHWARZSCHILD’s method in which a fine wire gauze is interposed in
the cone of rays a litthe way before the focus. This produces the
same kind of images as a gauze before the objective and the dimi-
nution of brightness of the principal image is the same. If for the
first exposure the gauze is placed before one half of the plate, leaving
the rest uncovered, and if for the second the gauze is placed before
the other half of the plate, we obtain two images of every star on
the plate, one undiminished, the other weakened, except in the central
zone which is no use because the rays partially passed through the
gauze. If @ stands for the absorption-coefficient, @ for the difference
in brightness owing to the change of the atmospherical transparency,
then the difference of the images on the one half of the plate is
a@+td, on the other half @—d, and in the mean the influence of
d disappears.

As soon as an accurate, independent and reliable scale of photo-
graphic magnitudes has been fixed for a definite region of the
heavens (e.g. for the zone near the norih-pole), then we can determine
the stellar magnitudes of any other part simply by taking it together
with the polar region on one and the same plate. As long as this
ideal has not been attained the scale must be fixed for each region
individually, for which purpose ScHwarzscHiLp’s method with a half
gauze in the cone of rays seems the most practicable.

For a practical determination of the stellar magnitudes we can
measure the diameters of both the undiminished and the weakened
images of a number of stars forming a series of decreasing bright-
ness. For the faintest images a scale of blackness gives a continuation
of the scale of diameters. From this the stellar magnitude as function
of the diameter may easily be computed. The same end, however,
may be attained just about as accurately by estimates without the

( 583 )

need of measurements. To this end a scale of star-images must he
construed, regularly progressing through properly chosen times of
exposure with */, or ‘/, magnitude. If a group of stars is photo-
graphed for instance with exposures of 9, 12, 16, 21, 28, 38, 51,
67, 90, 120, 160 213, 285, 379, 506, 675 and 900 seconds, we
obtain a scale covering 4 magnitudes with intervals of 0,25, between
which each stellar image on a plate may be interpolated. It does
not matter whether the difference between the extremes deviates
more or less from 4 magnitudes. This scale is only a makeshift
and fulfils as it were the part of a scale of millimeters in which
each star is classed by measuring its diameter. With the help of a
few of such overlapping scales, covering together a still greater range
of stellar images it is possible to determine by estimate both the
images of each star on the scale plate. The known difference between
the two images enables us to reduce the brightness expressed on this
provisory scale (just as the millimeter-scale of the diameters) into
real magnitudes. Thanks to this the photographic brightness of a
number of stars, from the brightest to the faintest, is known. The
absolute value, the zero-point, may be deduced from a few bright stars
of from the 6" to 8" magnitude, and need only be roughly known.

When in this manner the magnitudes of a number of stars have
been determined on the scale-plate, which has to be exposed a little
longer than the longest exposure of the counting plate, there only
rests to be seen which of these stars show 1, 2, 3,4, 5 images on the
counting-plate. In this way the limiting brightness of each of these
classes is immediately given.

With this method we therefore only want — besides the seale for
estimating the magnitudes — 2 plates for each region of the Milky

Way: a counting plate and a scale-plate. Practically without any
measurements, hence without any other instrument than a magnifying-
glass, only by countings and estimates we can thus obtain all the
data which must otherwise be compiled with a great deal of trouble
and far more incompletely from the different sources of catalogues,
stellar charts and gauges. As Professor SCHWARZSCHILD, Director of the
Astrophysical Observatory at Potsdam graciously offered to have a few
plates made for this purpose with the exceedingly appropriate Zeiss-
triplet of 1500 mm. focal-distance and 150 mm. aperture, and as
Mr. HertzsprunG astronomer at the same observatory, kindly made
the photographs for me, I take these as a standard of what may be
attained in this direction.

On a photograph of the polar region with this instrument on an
exceedingly sensitive Lumiere Sigma-plate a 10 minutes’ exposure

( 584 )

showed stars up to magnitude 13,0 according to Pickxrine’s scale.
Consequently when we use on the counting-plates exposures of 1900,
600, 190, 60, 19, 6 seconds, the limiting magnitudes of the different
classes of stars are 14,0 13,0 12,0 11,0 10,0 9,0. So they penetrate
just as far into the region of the faintest stars as Herscuet’s gauges
do. The field within the limits of which the stars retain their perfectly
round and well-defined shape has a diameter of 6°; so one plate can be
used to cover a part of the heavens of more than 25 square degrees.

Here lies before us a field for research on which with little trouble
and simple implements very important data ean be gathered for the
structure of the galactic system. The necessary photographs take but
little time; the deduction of the results wants more, but on the other
hand asks very little instrumental help; hence this is a very suitable
field for the cooperation of observatories with persons who cannot
command large instruments. Formerly it often happened that amateurs
gathered valuable data by the observation of the heavens. This will
gradually have to cede its place in future to the discussion of stellar
photographs as an opportunity to cooperate succesfully to the promotion
of science.

Mathematics. — “Homogeneous linear differential equations of order
two with given relation between two particular integrals”.
gy Dr. M. J. van Uven. (Communicated by Prof. W. Kapruyn).

(2°¢ communication).
(Communicated in the meeting of November 25, 1911).

In the preceding communication we made the two rectangular
coordinates v, y of a point satisfy the same homogeneous linear diffe-
rential equation of order two:

144

av da
ig eg CU te = Ui Ate re ated)

and showed a given relation between « and y makes also a
functional relation between p,qand ¢. This was evident particularly
when we brought the equation (A) in a standard form, either in the
form

dia alc) wae

= 4 ree ah Sew Ge ay Geo (Ue

or in the canonical form:

(585 )

ax

Chie

S ROA Gh) iat —n) eee as er (CO)

The form of / as a function of 7, or of g, as a function of 4,
was then governed by the relation existing between wv and 7:

iD) Se 5 oe ee ace mea)
or
TAGAS ea Go shee ((P))
or in homogeneous form,
Jon Oe) a oc) one acne wee (a!)

If we regard x,y, and z as homogeneous coordinates the triangle
of coordinates of which is formed by the two axes and the line at
infinity, we can define the line coordinates w, v, and w belonging to this
same triangle by the relation

Aue + Bry + Cwz = 0,
or passing to the non-homogeneous form by putting z=1 and w=—1
JN to ad OS al Sl Ces) Te] Re a a RSE)

This equation determines, as is known, either the line (2, v) in
point coordinates (7, y), or the point (v, y) in line coordinates (w, v).

If now a relation (11) or (12) is given we can determine the
tangential equation (in w,v) of the curve represented by them. The
line coordinates uw and v will then satisfy a certain differential
equation. If we note the autodual character of the homogeneous
linear transformation, against which the differential equation (A) — resp.
(B) and (C) — is proof, we can expect the differential equations for
w and v to show a close relationship with those of w and y.

It is our aim here to investigate the differential equations for
wu aud v.

The tangent in point (vy) of curve (11) or (12) drawn to this
curve has as equation

dy ks
Y—y =— (X—2)
Ak
or
— Xdy + Ydwu + (#dy—ydz) = 0.

If we call «w and v the line coordinates of this tangent, it is

determined by
AuX + BouY + C=0.

From this ensues (see (14) and (15) dst communication p. 395).

C dy C dy _ C dy oy

aii aeAds 7 OA di A’

C du C dx C da Ce
coz ep ai ueaa OBS <i cnan ay at Bae
50
CG. C

Pe il ‘ v= +52 auiice Ge See a(S)

By differentiation according to ¢, we find with the aid of (C),

Cee CG
Vie a! = em

" C ' C ! OR !
== a pad Thy — gat ae

so that w satisfies the differential equation
” Canny oh
“u——uw+gqu=0.. .% « « = (36)

It is easy to see that v satisfies this same equation.

If we wish to put (86) in the canonical form
au :
—4- gs(¢:) aS 0. a ee ee ee
iss

2

we have to put (see (5) and (6), 18t communication p. 392)

+f Sah
dae "dt SH odtt oe n ee
2f—“a, 4
Ga =e : —t ce ae co. bo (ae)
qh

where we have discarded an irrelevant constant.
To obtain the standard form (B)

au I(r.) du
a SENSE

dt,? 2 dt

=u == 0

2

we must put (see (9) and (10) 1s communication p. 394)

OG, == En dt == 1G at ee (EO)
3 3
We2ndg. me 2ndg:

= See 6 LO)
ies ee (40)

By a proper choice of the algebraical sign and of the constant of
integration we can attain that the standard form (#4) has for the line
coordinates the same independent variable as the form (B) for the
point coordinates, whilst in this case the function I(x) reverses its sign.

The standard form (2) for w (and v) runs therefore

Sead ee a Ti = aa ee oe Ron (B')

This last result satisfies, with respect to the connection of the
differential equations for 2 and w, in high degree the expectations
expressed by us. z

Let the tangential equation of the curve (11) or (12) be

DSO; o 6 0 oo oo o fo 6 (CRD)
or
IWG@O)=WUn 0 6 6 co 6 6 8 o oF KC)
or, made homogeneous,
Ii) Us oc om 2 oo oo oa (Cs)

The equatiens can also be easily interpreted as equations between
the point coordinates §= wu, 47 —=v ($= w). We obtain them namely
by polarising the given curve (11) or (12) and that with respect
to the conic

Aine byae tO 0N es 8 ees 4. (44)

having its centre in UV.

The pole (§ 9) has then after all as polar line

Agz« + Bny + C=0,

so that § and 4 are really coupled by the same equation to wand y
as uw and v.

The result obtained by us can therefore also be given as follows:

If we transform the curve (11) or (12) by polarisation with respect
to the conic (44) then there is generated a new curve dualistically
conjugate to the original one, whose function / is the opposite of
the function / belonging to the given curve.

If we had applied for the polarisation instead of the conic (44)
the conic

Pax Ory ys Si, 25. . « = (40)
which has its centre likewise in (©, we should have attained the
same result. The curve 7, =—,(§,) or L,(§,,7,) = 9, obtained by
means of polarisation with respect to (45) out of (11) or (12) is then
generated, as can easily be shown, out of the curve 1 = w(§) or
L(§,4) = 9, generated by polarisation with respect to (44), by appli-
cation of the transformation
§=a8,-+ Bn, » n=75. + On,

irrelevant for the differential equation.

So we have but to polarise the given curve with respect to a
conic having its centre in O.

( 588 )

We shall in future call those curves generated by homogeneous
linear substitution out of the given curve, equivalent to that given
curve. On the other hand we shall call the curves deduced out of
the given curve by polarisation with respect to a conic having Oas
centre, semi-equivalent to the given curve. Our result can now be
formulated as follows: ;

Equivalent curves have the same functions I, semi-equivalent curves
have opposite functions I.

Whilst the equivalent curves form a group, mutually connected
as they are by the group of the homogeneous linear substitutions,
the semi-equivalent curves form together a so-called eatended group
(Gruppe 2** Art). The semi-equivalent curves can be deduced from the
equivalent curves by extending the group of the homogeneous Jinear
substitutions with one so-called pseudo-substitution (Substitution 2ter
Art), for which we can choose the polarisation with respect to a
definite conic with O as centre, e.g. with respect to ay = 1.

We can compare this state of affairs with the group of congruent
plane figures (mutually connected by the transformations of the group
of the movements in the plane) which is extended by reflections to
the extended group of the congruent and symmetric plane figures.
The extension to symmetric figures demands but one reflection.

From (87) follows. still

CaCO O 4 bmn oo oo (a)

The increment dz of the independent variable of the standard form
(4) is therefore mean proportional between the increments of the
canonical independent variables conjugate to the given curve and to
the curve semi-equivalent to it.

When a curve A is semi-equivalent to itself, it means that
there is a homogeneous linear transformation +, which transforms the
curve AK’ generated by polarisation out of A into A again.

In this case, although (§,7) (apart from +) satisfies the same
equation as (wv, y), it is not necessary for dt, to be equal to dt, . For
this is moreover necessary that point P’ of A’, generated by polarisation
out of point P of KX, is likewise brought back by transformation =
to point P. If however this last condition is satisfied, then we have
dt, =dt,, also g,=1 (or equal to a constant). The coordinates of
a point of such a curve XX satisfy the equation

ge =i == 0;

The general relation between two particular integrals of this

equation runs as follows

Pa? + 2Qey + Ry? + S= 0.

(589 )

The only curves, satisfying the above mentioned condition, are
therefore the conics with centre in QO, just those curves with respect
to which the polarisation takes place.

We can in the first place regard the canonical variable of the
line coordinates as the area described by the radius vector out of
O of a point of the curve generated by polarisation. It can however
be interpreted in the second place as follows.

Let us call g the perpendicular let down out of O on the
tangent of point (a, y) of the given curve A, and 6 the angle made
by this perpendicular with the X-axis, then @ and @ are evidently
the polar coordinates of a point of the pedal curve of KA.

Let us now compare the normal form of the equation of the tangent

XcosO + Y sind —o=0
with
AuX + BY +C=0;
we then find

as C cos@ C sind
Pee 4k C 9 Ue Bee i
from which ensues
C26

2dt, = udv — vdu = —. —.
A 2

b&
2

If we now submit the pedal curve to an inversion with respect
to a circle, with centre O and radius R, then

C7 — a OO
Q

holds for the point conjugate to (@, 4), so that

C? dé C? 2
; ae ge > ape 8

If we now choose
i= 4 a
AB’

we find
2dt, = 0, 40, = 2d, .

So the canonical variable ¢, is the area described by the radius
vector out of O of a point of the curve generated by inverting the
pedal curve of the given curve K with respect to the circle with
C?

AB
We now return to standard form (5).

O as centre and radius R = i

40
Proceedings Royal Acad. Amsterdam, Vol. XIY.

(590 )

If we replace here r by t, = —r, we find
aa LI (—t,) da
sil Nilay ee HN) —+e=0.
dt,? 2 dt,

With respect to function / we have different cases to distinguish :

1. J is a univalent even function of t.

Then /(—1,)=J(r,), so that the equation (47) belongs to the
semi-equivalent curves. As however the change of t into —r has
no influence on the connection between x and y, the curve y = ¢(«)
or F(x, y) =O. must be semi-equivalent to itself. In other words
there must be a homogeneous linear transformation = which trans-
forms the curve A’ obtained by polarisation again into A. An example
is furnished by / = const. We shall look at this example more closely.

Let us put

i=2(k+ ke);

then the integrals of the equation

z + (k + kl) x +w#=0

Ss —hkt
are we and y=e_, so that the relation existing between x and
y runs as follows:

yp aka.
The curve A’ is therefore a (higher) parabola for 4? >0O whose
singular point les in O and a (higher) hyperbola for 4? < 0, of
which the (multiple) asymptotes meet in O.

1 :
The parabola of 2"¢ order demands 4? = 2 (or ih oy Jf = 32 1 2,

A]

The hyperbola of 2°¢ order requires &? ——41, therefore /=0.

1 8
For the cubic parabola holds 4? = 3 (o a sso JS se 5 V3.

For the semi-cubic parabola we have 4? = = (er5) so

f=>+ 6.

3!

The cubic hyperbola furnishes 4? = — 2 (or :) so f=22y72

2. / is a univalent odd function of r.

Now /(—rt,)=—AZ(t,) so that the equation (47) is identical
to (DB).

The given curve is now not semi-equivalent to itself,

If we now put

( 591 )

a(t) —a(—2) w(t) + «(—z)

a I ata =J/Z(G) = 2 ==) P(r);

then P, is an odd function of 1, P, an even one.
We then find

sue I(t)

jae «+ z={P() + P+ — Po) + P.(r)} + {P,(1)+P,(x)'=0(48)
and
Oe I(—r) de e
‘=o. \ peices
ns [@ Pi(—t) @&P(—t) " I(—t)(dP,(—t) _ dP,(—)
mal a(aan)e Mi daa \iad mboeea cae) d(—r)

Siptea at) ts a(t)

as P, and P, are even functions and P, and P, odd, we find

SQ) CAE dG hie =
ee eer enema z= yp
dP,(—t) Ly : im dP,(—rt) a .
TS) ten) 2 d(—r) — P,(t),
hence :
Ur

— Pon) + Po} — "O12. —P,}+\—P.) +P.) = 0, (49)

so that we find the following equations:
Ic x ho
LE are te a i ae ; Pete Ea by — 0.

From this follow three possibilities :
a) all integrals are even functions of rt,
8) all integrals are odd functions of rt,
y) one of the integrals is an even function of r, a second integral
is an odd function of t.
As an example of case (a) we choose
SCX

1
Here is pe, Gr =, Prz = C*, CPr—Y = (« — le; y= Ee ;

r= [V0 de = 2st, e=145

w,—2ap? 2e+1 +6

i = — ———
ye Vie-1

=an odd function of rt.

40*

red

2 1+
t “ .
The integrals «= 1 + i and y =e * are both even functions

Of,
By polarisation with respect to the conic

a? — Oe —="C

the curve y =e passes into the curve:
541

+ g
Hee :

which is, as could be expected, not equivalent to y = e”.
Here holds;

ete ee es Sis Be hice
see Ee §+1 E 1 es E
fp = se 5 a Y RI a Ey SS —— EG :
5 S
i 2 = 4
ears oe MWA: Ss 7 gs ;
o Yr -— 2S y” 3§--2 v7 +6
~ rapt Vs v
ae
. 4 a. (2 4
Hence too the integrals §—=— andy = —e are both even
T T

functions of t.
As an example of case (y) we give
a + y=1.
The calculation shows us

7 eae 87 Gar) 8 3t
= sim— , y= cos—— , 1 =— cot” 9
Vai) Vas) 5) V5

I is odd, w is odd, y is even.

Physics. —— “Determinations of refractive indices of gases under
high pressures’. First paper. The dispersion of hydrogen. By
L. H. Srertsema and M. pe Haas. (Communicated by Prof.
H. KAMERLINGH ONNEs).

(Communicated in the meeting of November 25, 1911).

1. The modern theories of ight which have been developed from
the theory of electrons lead to many relations that can be tested
experimentally in various ways. One of us’), for instance, has
endeavoured to obtain from his experiments upon the magnetic

1) These Proc. V. 1902/03 p. 413. Comm. phys. lab. Leiden N® 82.

( 593 )

rotational dispersion of gases values of e/m for the electrons which
participate in the light vibration. For this deduction values of dn/da
(n= refractive index, 2 wave length) for those gases at high
pressure were needed, while only determinations made at atmospheric
or, at least, at low pressure were available. It is doubtful whether
it is justifiable to apply to high pressure the values thus obtained.

The few measurements which have hitherto been made upon the
refractive indices of gases at high pressures have all had the object
to obtain the relationship between the index of refraction and the
density of the gas. The question as to whether the dispersion varies
with the pressure or not has not yet been made the subject of an
experimental investigation. We have therefore undertaken a more
complete investigation, which includes a determination of refractive
indices at high pressures for various wave-lengths.

The high degree of accuracy attainable by the use of an inter-
ference method renders it highly advantageous to use such a method
for the determination of the refractive indices of gases. Many expe-
rimenters have used interference methods for obtaining such measure-
ments. In our experiments we used a JAMIN interferential refracto-
meter. In the path of one of the interfering rays a tube containing the
experimental gas is placed, and, by using monochromatic light, the
number of bands passing the cross-wire of a telescope can be counted
when the quantity of gas contained in the tube is varied. The
dispersion is evaluated by counting the bands crossing the field
when different wave-lengths are successively employed. For if /, and
k, represent the number of bands crossing the field for light of
wave-lengths 2, and 2, respectively when the density of the gas
varies from O to a given value, then

k, a= ,—l)fe ; k, A, = (nm,—l)e

where n, and », are the refractive indices at that particular density

for the two colours, and e is the length of the tube. Furthermore
in the ratio
n,—l Ak

inal

n,—l aye “13

2°°2

we obtain a quantity which expresses the dispersion of the gas, and
which we shall call a dispersion constant.

We may remark that the values of these dispersion constants may
be obtained without knowing the length of the tube, e; this is
necessary only for evaluating the refractive indices n, and n,. A
high degree of accuracy can be reached in determining the numbers
k,,ky-... for the whole numbers involved can be obtained by direct

(594 )

counting, and fractional portions can be determined from the position
of the telescope cross-wire between two successive bands. When the
number of bands crossing the field reaches some hundreds, it is
obvious that the numbers / can be evaluated to a degree of accuracy
far in excess of that possible in the measurement of e. It follows,
too, that in measuring refractive indices the temperature and the
pressure of the gas must also be known to a corresponding degree
of accuracy, while the dispersion constants will vary but little with
the density of the gas.

This led us to divide our research into two portions, one involving ,
a determination of dispersion constants, the second a determination of
refractive indices. The measurements described in the present paper
relate to the first branch of the investigation.

2. A diagram is here given of the tube containing the experi-
mental gas which was placed in the path of one of the interfering
light rays.

A B, steel tube, with cylindrical boring, externally hexagonal.

C, nut tightening D, E, and F.

D and £, glass plates 8 mm. thick,

FP’, steel cylinder about 2 em. long with projecting rims surrounding the glass
plates.

Between J and the glass plates are washers of klingerit, a packing which is

( 595 )

used for steam joints and which suited the present purpose admirably. Brass rings
prevented the squeezing of the packing into the tube. Outside the glass plates and
the metal on either side are a brass ring and some paper washers. /’ is coupled
to the ligh pressure system by the screw connection G.

This coupling leads to a manometer and fo a reservoir filled with the
experimental gas under high pressure, while through it connection can
also be made with an airpump, Garpe’s rotatory pump (‘‘Kapselpumpe’’).

The circular scale of the metallic manometer has a diameter of
16 em., and on it pressures up to about 150 atmospheres can be
read to '/,, of an atmosphere.

Mr. Kounstamm kindly afforded us an opportunity of comparing
this manometer before and after the measurements with the SrTick-
RATH manometer which he has fitted in the Amsterdam Physical
Laboratory. We found that the manometer readings remained prac-
tically the same, the difference being, at the most, not more than
‘/,, of an atmosphere.

Beside the tube traversed by one of the interfering rays and in the
path of the other ray are placed two glass plates identical with those
in the experimental tube. by means of three adjusting screws these
plates can be moved a little, and the breadth and the direction
of the interference bands so regulated that they are in the best
position for observation. For this purpose the adjusting screws of
one of the glass plates of the interferometer can, of course, also be
used. A wide slit in front of the first glass plate of the interfero-
meter was found necessary in order to obtain clearly defined
bands. The whole apparatus was enclosed in asheet-iron case, which
in the later experiments was filled with cotton wool leaving free
only the paths of the light rays. The openings in this case were
closed by glass plates. The high pressure connection and the mano-
meter were also wrapped in cotton wool as far as the first regulating
tap. Beside the experimental tube was placed the reservoir of a
thermometer whose scale projected outside the case.

3. The measurements discussed in the present paper were made
with pure hydrogen which we obtained through the kindness of
Prof. KamertincH Onnes from the Leiden laboratory, where it had
been prepared from impure hydrogen by freezing out the impurities
at a very low temperature’). i

In the first series of measurements the source of light was a

1) KameRLINGH Onnes, These Proc. XI. 1908/09, p. 883. Gomm. phys. lab.
Leiden, No. 1U9b.

(596 )

Herarvs quartz mereury lamp, and the light was concentrated through
a lens upon the slit already mentioned in front of the interfero-
meter. By means of light-filters the three wave-lengths (yellow, green
and blue) of which the light emitted by this lamp chiefly consists,
were isolated ').

The interference bands were observed through a telescope provided
with cross-wires, and the number of bands was determined that
passed the point of intersection of the eross fibres as the density of
the gas in the experimental tube was altered; to evaluate fractions
a JAMIN compensator was used.

The accuracy attained in these measurements was not so great as
that of later experiments; we shall not, therefore, describe them in
detail but shall content ourselves with communicating the results.

In the accompanying table are given the numbers /,, #, and 4,
of the bands crossing the field while the density of the gas
changed from that determined by the pressures and temperatures
given below to zero, for each of the three colours 2, = 0,578 nu,
., = 0,546 and 2, = 0,436 4. The table also includes the dispersion
constants

n, — 1 Hee ke n, — l bd,
Ca fa ea) oS ee Se
n,—1 eae n, —1 k, a,
: | | Press. | ;
hy | ky | hs | C2 €32 atm. | Temp.
| } |
LN ee. SE
190.28 201.98 | 256.98 | 0.99713 | 1.01546 | 81.7 | 18.0°C
182.45 193.69 246.31 | 0.99701 1.01495 76.8 | 14.0,
172.48 183.08 232.81 0.99716 1.01492 13:5, |, 1600
164.86 174.99 222.62 | 0.99716 1.01537 69.6 | 14.2,
|
152.17 161.51 | 205.38 0.99723 1.01492 64.2 | 14.1,
= 114.20 145.20 = 1.01478 44.9 | 11.0,
90.07 | 95.64 121.62 0.99679 1.01493 Si-4 alalilncne
Mean..... "0.99708 1.01505
+ 0.00007 |+0.00010

1) We used a solution of eosin which transmits only yellow, and a concentrated
solution of didymium nitrate, which absorbs the yellow. In the latter case the
other two colours were isolated by using grcen or blue glass. For the blue one
of the newer glasses of Scuorr and Grn. No. 3(86, was used with excellent
results. These glasses are described in detail by Zstamonvy, Z, f. Instrumentenk. 21 p. 97,

( 597 )

In the more recent experiments a Heravcus quartz amalgam lamp
(220 volt, 5 to 6 amp.) was used as a source of light. The spectrum
of this light consists of a number of lines among which those of Hg,
Zn and Cd are particularly bright. Owing to a copious formation
of ozone it was found necessary to put the lamp in a fume cupboard.

A collimator with a rather wide slit was placed close to the
lamp, but outside the fume cupboard. The light beam emerging
from the collimator passed through the interferometer from which
the JAMIN compensator had been removed and then fell upon the
prism of a Hincer constant deviation spectroscope. In the field
of the telescope we thus obtained a series of images of the slit,
each corresponding to one of the wave-lengths emitted by the
amalgam lamp. The collimator slit was made so wide that some
of its images partially overlapped. Each image of the slit was
crossed by a system of interference bands, horizontal in the
green, but slightly sloping in the blue and violet. About 3 bands
were visible in the red, and about 5 in the violet. It appeared that
the bands in any one slit image did not all lie in the same plane,
so that they were not all quite in focus at the same time in the tele-
scope. Even their apparent position in the field altered slightly when
the density of the gas in the experimental tube varied. The telescope
was so adjusted that for all the densities of the gas, occurring during the
experiments, one of the bands not far from the central band could
be brought into sharp focus.

In these experiments measurements were made upon six different
images of the slit; these were:

a. The image of the red cadmium line 4, = 0.644 ». This image was partially
covered by that of the zine line 0.636 4. The uncovered part, however, was of
sufficient width to allow the interference bands in it to be brought under proper
observation.

b. The image of the green mercury line 2) =0.546,. This image was very
bright. The interference bands were also easily observed, but still they were not
so clearly defined as one would expect from their great intensity. Possibly satel-
lites exert here a disturbing influence.

c. The image of the green cadmium line ?¢=0.509. The bands in this
case were perfectly dark throughout.

d. The image of the blue zinc line Ad =0.472 4. This image was situated
amongst a number of others in such a way that only a portion of it was free,
in which the bands, which were very well defined, could be examined,

e. The image of the blue mercury line +e = 0.436 4%. This image was very
bright with well defined bands.

f. The image of the violet mercury line -f=0.405 4. The brightness of this
band was much less.

( 598 )

These images of the slit, or rather their uncovered portions,
were brought in succession into the centre of the field of vision
by a rotation of the spectroscope prism. The spectroscope telescope
had a micrometer eye piece with a vertical screw. The movable
wire could be made to coincide with the bands. In our measurements the
difference of phase between the interfering rays was determined in
each case for a fixed point in each image of the slit. We tried to do
this first by measuring the distances between the fixed point and each
of the two bands immediately above and below it. This was done
for the six images a, 6, ce, d, e and f/f in succession, and then
again in the reverse order f, e, d, c, 6 and a. Some time elapsed
before this could be completed and it was found that during
that period the bands did not remain sufficiently stationary to
obtain accurate resulis. Another method was therefore adopted
in which we were more independent of this disturbance.
In this method the distance of only one band from the fixed
point was determined, and from that measurement the phase diffe-
rence at the fixed point was obtained. From separate measurements
the variation of the required phase difference with the distance of
the bands from the fixed point was determined. ’') By now focussing
with the movable wire several times alternately a band in the image
a, and then a band in the image 6, the difference-(a)) between the
phase differences at the fixed points in the images a and 5 was
obtained, and then in the same way, the differences (cb), (db), (eb)
and (fb). The measurements from which these data were obtained
could follow each other in rapid succession, so that sufficient accu-
racy could be reached even though the bands did not remain abso-
lutely stationary.

Properly speaking only the fractional parts of the differences (),
(cb) ete. could be evaluated in this way; the whole numbers were
obtained afterwards, by the method indicated below.

These measurements were first made at the highest pressure available;
a small quantity of the gas was then allowed to escape while the
number of bands was counted which crossed the fixed point in the
green image 6; another series of measurements of differences of
phase-difference was then made, and so on until the last series which

1) From these measurements it was found that the distance between the bands
in any one image was not constant, and consequently the desired phase difference
could not be represented by a linear function of the distance z of the point under
examination from the fixed point. For this difference, therefore, we assumed a
quadratic law of variation 9 =az-+ bz, the coefficients of which we calculated
by the method of least squares from several measurements made upon various
bands in the same image.

( 599 )

was made with the tube completely evacuated. The reverse order
of operations with rising pressure was not so successful, as during
the admission of the gas, the bands became confused and disappeared,
which probably resulted from the difference of temperature between
the gas in the tube and that in the reservoir.

By a separate investigation we ascertained that the admission
of gas at a high pressure occasioned no change of shape in the ex-
perimental tube sufficient to influence the values of the dispersion
constants.

For the 65 image, the integral part of the phase differences
at the fixed point can be evaluated by the direct counting of
the number of bands crossing the field; for this purpose one ean
give the value zero to the phase-difference at one of the bands
in the final state (vacuum). Similarly in the other images the value
zero can be assigned to one of the bands in the final state (vacuum),
and we then obtain for that state the integral parts of the
differences (a4),... It is then ascertained from a separate experiment
how much these values change if one band is allowed to eross
the field in 6, and as these changes will be less than one band it
is easy to determine them completely. From this follows how many
units (ab), (cb) ete. will change when a larger number of bands,
e.g. 10, is allowed to cross the field, and in this way we can soon
find how great these changes will be for 50 or 100 bands, which
were the numbers allowed to cross the field in our series of obser-
vations. Finally, if these differences (ab) ete. are completely known
for all densities, one can easily find the number of bands that
cross the field in each image in passing from any one density to
vacuum. We shall represent these numbers by ha, hy, hk.» ka, ke and
kr. The ratios

are then calculated.
As an example we give a series of results for the density deter-
mined by a pressure of 71.8 atm. and a temperature of 19,49° C.

ky = 367.067 kq = 309.073 | hq | ko = 0.84201
ky = 367.050 ke = 395.687 ko | kp = 1.07802
ky = 367.023 kq — 428.186 | ka | ky = 1.16665
hy = 366.986 ke = 466.758 | ke | kp = 1.27181

hy = 366.942 | kg = 506.037 bp | ko = 1.37907

( 600 )

In this way the following results were obtained:

a | | | :
Je = 0509 4g =O04T2 | tp =0.436 | 2p = 0.405

2 g }2 7, — 0.644
zal ft cate a Re ies
= | & |(mean).| ha he ka | he | Af
2) | kb kb kp | kb kb
eA | ee
11.8 19.49 907.014 0.84201 | 1.07802 | 1. 16665 1.27187 | 1.37907
62.0/19.77317.160, 0.84199 1.07798 1.16667 1.27179 | 1.37902
52.1/19.95267.315| 0.84203 1.07799 | 1.16667 1.27183 1.37897
42.3 19.95 217.264 0.84202 | 1.07807 | 1.16666 1.27178 1.37897
32,220.01 167.118 0.84206 | 1.07796 | 1.16659 1.27170 | 1.37883
|
68.5 19.15345.631, 0.84201 1.07803 | 1.16673 | 1.27207 1.37925
68.1 19.33 343.616 0.84200 1.07806 | 1.16680 1.27205 1.37927
58.0 19.49 203.244 0.84202 | 1.07805 | 1.16672 | 1.27208 1.37930
47.8 19.65 243.198 0.84205 1.07807 | 1.16669 1.27205 1.37923
38.0'19.75/193.451| 0.84206 | 1.07809 | 1.16668 1.27201 1.37921
27.9) 19.85, 143.354 0.84212 | 1.07805 1.16670 | 1.27192 1.37899
| | |
65.4 20.35 336.393, 0.84203 1.07799 1.16662 | 1.27176 1.37882
65.2/20.52 335.013 0.84203 1.07798 1.16669 | 1.27177 1.37886
63.9 20.67 327.868 0.84203, 1.07800 1.16659 1.27181 1.37892
58.8/20.85 302.103, 0.84207 | 1.07798 1. 16662 1.27218 1.37891
39.0 20.94 202.607 0.84210 | 1.07796 | 1.16667 1.27179 1.37902
| | | }

The values obtained for the various densities are fairly constant,
and the deviations are in no definite direction. AS means we obtain
0.84204 1,07802 1,16667 1.27190 1,37904

+ 0,9 =t=eilleh a= 1183} Seoul =t=24()
If these ratios are constant, so also are the dispersion constants
Na —1 hada Ne—1 hede
Oh — — <6 —= ——_- = ete.

inl yay : =k oe kody
in which the refractive index for all wave-lengths in the final state
is taken as unity.

We thus find as the result of our experiments that the dispersion
constant of hydrogen is the same at all densities used, and we
obtain for it the following values:

| n—1
| > (vac.) | c pl
Juul be Se
a | 0.64403 0.99280 + 0.000011
6 | 0.54623 1
¢ | 0.50873 | 1.00401 + 0.000010
d 0.47234 ‘1.00885 + 0.000011
e 0.43597 1.01516 + 0.000030
f 0.40478 1.02193 + 0.000030

We can compare our results with those obtained by other experi-
menters, especially with those of Mascarr’), Perreau ?), SCHEEL °),
Hermann‘), Kocn®) and Curnperson*'). To make comparison possible,
the values of the dispersion constant for the wave-lengths we used are
deduced from their results by graphical interpolation (Mascart,
Perreav, Kocn, Curuperson) or from the dispersion formula given
(ScHEEL), while from HprMann’s observations they were calculated
directly. In this way we obtain

A MASCAaRT.| PERREAU.) SCHEEL. eR MAtNt Kocu. eee SIERISEMA
le | | | | DE Haas.
0.644 | 0.9962 | 0.9927 | 0.9939 | 0.9924 | 0.9934 0.9930 | 0.9928
0.546 1 la 1 1 1 lier \aateh
0.509 | 1.0030 | 1.0041 1.0034 1.0038 1.0037 | 1.0040
0.472 1.0090 | 1.0074 | | 1.0085 | 1.0088
0.436 | | | 1.0125 1.0114 1.0152 1.0152
0.405 | | 1.0219

An interpolation formula can be obtained from our values of the
dispersion constant. We will take the ordinary form

b, b,
n—1l=a({(1l+—44—
72 a

in which 4 is the wave length in air; we then get

1) Mascart, Ann. de l’éc. norm. (2) 6 p. 61 (1877).

2) PERREAU, Ann. de ch. et de phys. (7) 7 p. 335 (1896).

5) ScHeet, Verh. d. D. phys. Ges. 9 p. 28 (1907).

+) alpeghO Nis se LONp 47, (1908):

®) Kocu, Nova acta regiae soc. scient. Upsaliensis (4) 2 No. 5 (1909).
8) CUTHBERSON, Proc. R. S. (A) 83 p. 151, 1910.

b, Es b,

n—1 + 3s ZH
i a b :
; 1 a cliea i ae

ae Cie

The coefficients 4, and 6, were calculated by least squares valuing

each observation according to the mean error. We thus obtained
b, =" 00073375 Nb; <— 10.0.00089
and hence,
n-—1 peti 0.007337 - 0.000089
— ai = 0,97504 (: +- ia -+- —)

The following table shows the accuracy with which this formula

represents the dispersion constants:

| A (air) C(cal.) | C(obs.) ik weight | = [p A?]

a ee
a | 0.64385 » | 0.99281 | 0.99280 |-105x1) 8 | 8

6 | 0.54608, | 1 Ws |

e | -0:50850,, | 1.00309 | 1.ondon eee sail fe) Wl) eee
d | 0.47221 ,, | 1.00886 | 1.0085 |— 1] 8 | 8
a ihores » | 1.01510 | 1.01516 |+ 6) 1 | 36
f | 0.40467 ,, || 1.02196 | 1102193 |=" 3.) iveuwmg
97

Good agreement is also obtained between experimental and
calculated values by using the dispersion formula ?)
ni —] Ne,? Ne,?
n? 42 as m, (ee) as m, (v,? — vy?) os
of the theory of electrons, in which », », and », are frequencies
and e, N, m,, m

»+-+ are the known constants in that theory.
Even with one term on the right-hand side we obtain agood agreement.
We then get the formula

il 1

n=l omg tl nie See
a ny—1 = n+ 1 “ny +2 ori 1
eo 7B

in which 4, 2,, and 2) now represent wave-lengths in vacuo. An
examination of the factor

n+1 ; ny +9

1) See e.g. Lorentz, The theory of electrons, p. 144.

( 603 )

shows that its value may be taken as unity without appreciable error.
We then get

1 1

ica ie
nee

1 I

ae /

An evaluation of 4, by the method of least squares valuing the
observations on the plan already mentioned gives
}, (vac.) = 0.08703 ue
while the following table shows the agreement obtained.

2 (vac) Ccal) | C(obs.) A weight | = (pc?)
| |
a | 0.64403 » | 0.99274 | 0.99280 soe 8 | 288
b | 0.54623 ,, 1 | 1 |
c | 0.50873, | 1,00400 1.00401 — 1 9 | 9
d | 0.47234,, | 1.00886 1.00885 1 8 | 8
e | 0.43597,, | 1.01506 1.01516. | — 10 1 100
f | 0.40478 ,,| 1.02185 1.02193 | — 8 1 64
469

We thus find that the natural vibration of hydrogen corresponds
to a wave-length of 0,08703 u, a value that agrees quite well with
that determined by Kocu, 0,0880u, from dispersion measurements
extending to the ultra-red, and still better with the value 0,087 «
deduced by NataXson’) from Prrrvav’s experiments. It differs some-
what from CuTHBERSON’s value, 0.08516 wu. :

A ealculation of the absolute values of the refractive indices is
postponed until the completion, in a subsequent part of this research, of
the investigation of the refractive index for the wave-length 4 = 0,546
with special reference to its dependence upon the pressure. We also
intend if possible to extend these measurements to higher pressures,
and to other gases. In the meantime we may remark that, assum-
ing n—1 to be proportional to the density of the gas, and that
n = 0,000139 at 0° C. and 1 atm., the calculation of e/m by the
method given by one of us in a previous paper *) leads to the value
OES<10%

Delft. Physical: laboratory of the Technical University.

1) Naranson. Bulletin de l’Ac. des sc. de Cracovie 1907, p. 336.

2) StertsemA, These Proc. V. 1902,03 p. 413. Comm. phys. lab. Leiden
N°. 82.

( 604)

Chemistry. — “On a biochemical method for the determination of
small quantities of salicylic acid in the presence of an excess of
p-oxybenzoie acid.” By Prof. J. Borseken and Mr. H. Waterman.
(Communicated by Prof. M. W. Brtsurincr).

(Communicated in the meeting of November 25, 1911).

On the oceasion of an investigation as to the proportion in which
o. and p. oxybenzoic acid are formed in the Kose reaction, the
details of which will be described fully in the dissertation of Mr.
WaterMAN, we had found that the para-acid (also the meta-) could
be used as a carbon nutriment by the penicillium glaucum.

As salicylic acid exerts a retarding influence on the growth of the
organism, we have tried to base a quantitative method of determination
on the different behaviour of these isomers.

With small quantities of salicylic acid we have been successful,
so that the method has been of service to us in the quantitative
determination of the acid mixture formed in the Kone reaction,
when one starts from potassium phenolate.

If an aqueous 0.5°/, solution of p-oxybenzoie acid in which are
also present 0.05 °/, of potassium dihydrogen phosphate, 0.05 °/, of
ammonium chloride and 0.02 °/, of magnesium sulfate (the solution
of the inorganic salts must have a faintly acid reaction) is sterilised,
cooled to the temperature of the laboratory and inoculated carefully
with a culture of penicillium, a perfectly constant development
phenomenon is always noticed under the same conditions, the same
differences being observed from day to day.

By adding definite quantities of salicylic acid this development
phenomenon is changed in a constant manner. Very small quantities
cause, at first, a small increase of the growth; with quantities over
1°/, a decided retardation sets in.

To carry out the experiment we introduce into small ErRLENMEYER
flasks of the same size, exactly similarly and freshly prepared solutions
of p-oxybenzoic acid with inorganic salts to which are added increasing
quantities of salicylic acid, the liquids are sterilised by boiling and,
when cold, inoculated with a very small quantity of the same
penicillium culture. Simultaneously, a 0.3°/, solution of the mixture
to be analysed, which otherwise is treated in the same manner, is
offered to the penicillium and compared with the seale of the standard
solutions.

The method is, therefore, somewhat like a colourimetric one. It
looks very subjective but this, however, is only apparent, for the

9

( 605 )

experiment extends over several days, so that onemay at any time
repeat and control the observations.

Moreover, the first development phenomena are usually very plainly
visible and the period thereof is constantly delayed further by
increasing quantities of salicylic acid.

Another drawback to the method might be its too great sensitiveness ;
small quantities of other substances, which may form in the Kose
reaction, might possibly interfere.

We have been able, however, to demonstrate that of all oxy-
compounds which may form, salicylic acid is the only one which
exerts a retarding influence.

Care, however, should be taken to start from pure phenol, because
the methyl group does act injuriously.

The solution of the inorganic salts must not be kept too long; we
have noticed that a solution which had stood in a glass bottle for
some months had taken up a retarding constituent the exact nature
of which is unknown to us.

We give here in the first place a survey of some standard solutions,

Inoculated on 17 January.

N°. 1 2 3 | 4 5

Quantity of (p-- 0.1507gr. 0.1502 0.1502 | 0.1499 | 0.1507
acid Koa! Wasdaec 0.0004 0.0019 0.0074 0.0178

— = = SS 7, == SSS SS == —_ alae = _ = =

20 January | ae | afk | Jt a | = | =

23» $e | Ste =] + =

25a eee | | op -

| | |

Inoculated on 24 January.

N°. eae ty 8 | 9 10 1h |
| |
| Quantity of ¢p-| 0.1501 | 0. 1404 | 0.1494 | 0.1492 | 0.1493 | 0.1499
emtacidies te: 0... 0.0023 0.0046 0.0068 0.0082 | 0.0132
—_ Ho — = = = ——
26 January | + + -- | — | _ |
27 > tps Meta | | Gee =P |
28 > ce eae exe <8| + —
|

30 ae seer! 4 <0). +

| abe Ae | z t

41

Verslagen der Afdeeling Natuurk. DI. XX. A’, 1911/12

( 606 )

The flasks which had a capacity of about 200 ce all contained
50 ce of solution. The experiments were carried out in the laboratory
‘are being taken however, that the flasks were put in a moderately
warm place and in the dark. The observations were made with the
naked eye or with the aid of a small lens.

According to this method we can determine, with an accuracy
of a trifle over 1°/,, quantities of salicylic acid varying from 1 to
10 °/, in an excess of p-oxybenzoic acid. This accuracy is not great
but still much inferior to that attained in most of the investi-
gations on the simultaneous formation of isomers (HoLLeMan “Die
direkte Hinfiihrung”’).

Afterwards we have subjected the acid mixture, prepared according

not

io Kore, to the biological investigation ; a preliminary test had shown
us that the mould developed on it after some days, so that, in any
case, the amount of salicylic acid was but small.

Inoculated on 27/9 1911.

= — tS
; , Mixture of unknown
No. I 2 2 | “ | composition
oe Dall ae eee ee ae = ——
| |
Quantity (P- | 0.1503 | 0.1507 0.1505 0.1506 | Oates antares
erac en | 0 0.0020 | 0.0043 | 0.0062
—a i SS = —_ l = = = = =a = =
2Oct *11 | ++ + py) jl 8} Developed as
~ between | and 2
Stee ane All more firmly developed but becoming >
| less from 1—4
| cee >
From this experiment it follows that in any case the mixture

contained less than 1'/,°/, of salicylic acid.

This we have again confirmed by a second series, in which we
added increasing quantities of salicylic acid to the flasks containing
the mixed “Korner” acids; in this manner each sueceeding flask
controlled its predecessor.

Indeed we notice that al/ flasks with Konpr’s mixture behaved
like the artificial mixtures which contained about 2 mg. more;

hence we may conclude that this was really the case, so that we
can now say with certainty that this quantity is about, but not fully,
7) Vuayeds (oye ALAS aie

By way of a check, we have confirmed this result by applying
one of the methods described by Horniman (“Die direkte Einfiihrung’’)
namely the extraction process (1. ¢. p. 17—26) to the Kobe mixture,

( 607 )

Inoculated on 24/10 711

Pee comalesie | ae fg |g

sl | s
| | |
} |= | rn) =a | |
Quantity 4P> | 91505 | 0.1503 | 0.1507 | 0.1505 | 0.1500 | 0.1500 |
of acid (4. | 9 0.0021 | 0.0045 | 0.0056 | 0.0082 | 0.0102 | |
|
wh |e ed st eae eae |
27 Oct’) | ++ | + |+<2| +<3 2 - |
=== — SS = a a a ———— = = = >|
No. a b | c Gh |G | if)
ne —— ——- = - = u —=+ -= = — La — —
3 | |
Kolbe’s | 0.1497 | 0.1503} 0.1504 | 0.1495 | 0.1501 | 0.1495
Quan- | mixture | |
tifyaon | UOTE (0 0.0024 0.0047 0.0060 0.0082 | 0.0101 |
| | | | ae | | ede he |
> a : | 5 le a Ih ri 7 | -
| Development } fl SS 6 ARSON =
on 27 Oct. | between 4 | Sani:
| | | and 5 but |
| | Winith al iwuat 7]
| | distinct |
| growth
| =

For this purpose the mixture was shaken out with dry benzene
in which salicylic acid is readily soluble, the acids were determined
by titration and from this result was deducted the amount of dis-
solved p-oxybenzoic acid. As the solubility of para-acid is modified
by the ortho-acid, this influence was determined experimentally and
the quantity of dissolved para-oxyacid could be corrected graphi-
cally. In this way we found 1.1 and 1.2 °/,.

It is well nigh certain that this method is capable of extension,
particularly because we have at our disposel a large variety of orga-
nisms and, if necessary, we can also modify the quality of the inor-
ganic nutriment in many directions.

In this case we could restrict ourselves to the macroscopic obser-
vation of the growth phenomenon in the solution. It is evident,
however, that the “technic” of the method can be refined in many
directions.

Delft, 1 Nov. Org. Chem. Lab. 0. th. Technical
University.

41*

( 608 )

Chemistry. — “On the action of some benzene derivatives on the
development of penicillium glaucum.” By Prof. J. BorseKen and

Mr. H. Waterman. (Communicated by Prof. M. W. Briserincr).

‘ (Communicated in the meeting of November 25, 1911).

1. The investigation mentioned in the previous communication
as to the action of penicillium glaucum on the oxybenzoic acids has
been extended by us in different directions.

In the first place this was necessary because we wanted more
data as to the reliability of the quantitative salicylic acid estimation.
In Korpe’s reaction some other compounds can be formed which
may have a disturbing influence on the development of the organism.

In the second place we had been struck by the contrast between
an orthobenzene derivate on one side and the para- and meta-
derivatives on the other side, because in other cases the ortho- and
para-derivatives are mostly found opposite the metaderivatives.

As this last contrast is caused by the nature of the benzene ring?)
this natural contrast must, in this case, be surpassed by another one.

It would be obvious to connect this different behaviour with the
ereat dissociation constant of salicylic acid; but this is undoubtedly
not the cause, as the more strongly dissociated compounds: 2.4- ;
2,3-; 2.6-dioxybenzoic acid and even 2.3.4- and 2,4,6-trioxybenzoie
acid did not appear to have any particular retarding action, whereas
the much weaker benzoic acid and the toluic acids appeared to
retard the development of the organism in a still higher degree.

We have, therefore, ascertained whether the theory of H. Mryrr’)
and E. Overton*) could give us a satisfactory explanation of the
phenomenon. This theory starts from the idea that the modifications
which oceur in the fatty or lecithin part of the organism will in
the first place exert an influence on the change of the different
functions. If, therefore, a substance is more soluble in fat than in
water it will for that reason exert a narcotic action, because it will
accumulate in the fatty portion.

By determining the division coefficient of a great number of sub-
stances between water and olive oil and comparing this with the
narcotic action the above investigators were able to test the value

1) HotteEMAN and BéESEKEN, These Proc. 24 Dec. 1909.

2) He Meyer. Zur Theorie der Alkoholnarkose. Arch. f. exp. Pathol. u. Pharma-
kol. 42 p. 109 (1899) and 46 p. 838 (1901) s. a. CG. ARCHANGELSKY 46 p, 347.

') E. Overvon. Studién tiber die Narkose. Zugl. ein Beitrag zur allgem. Physiologie
Fischer. Jena (1901).

( 609 )

of the theory by means of an extensive number of facts, and Mryerk
could even demonstrate that if the division coefficient was modified
by a change in temperature the narcotic action was influenced in
the sense expected from the theory.

It appeared to us indeed that, whereas the division coefficient of
salicylic acid between olive oil and water at 25° was 11.8, the
same quantity for p-oxybenzoic acid amounted to 0,6 and for i-
oxybenzoie acid to 0,4.

Further, we have investigated a number of other benzene ‘deri-
vatives as to their action on the development of the penicilliam and
have also determined, in many cases the division factor between
olive oil and water.

In all cases we have noticed a distinct parallelism between the
retarding action and the value of the division factor.

The investigation also brought to light some facts as to the maxi-
mum of development of the penicillium in solutions of different
carbon derivatives, which to us do not seem unimportant. They also
support the Mryrr-Overton theory.

The Method.

2. As the biochemical method employed by us varies somewhat
from the usual process and excels by a great simplicity, a short
description may be given.

The experiments were always carried out in steamed Erlenmeyer
flasks of about 200 ec. capacity in which were placed 50 ce. of
water containing */,,°/, of potassium phosphate, '/,,°/, of ammonium
chloride and ‘/,,°/, of magnesium sulphate and which was, if
necessary, acidified with a trace of phosphoric acid. In this was
dissolved the substance either alone in varying quantities, or this
was added in increasing quantities to a standard of p-oxybenzoic acid
of generally 150 mg. and otherwise provided with the same inorganic
nutriment. The solutions were sterilised in the usual manner and
inoculated with a pure culture of penicillium glaucum, which was
generally cultivated on p-oxybenzoic acid or protocatechuic acid as
carbon source. After that they were placed in an incubator at
28°--29° and observed from day to day. The inoculation always
took place in the same manner, so that only a very little of the
material was introduced.

The solution of the inorganic salts should not have been kept too
long, as it has appeared to us that one which had stood for half a
year exerted a retarding action on the development of the mould
(see previous communication).

( 610 )

The flasks were well aerated and the incubator was closed, so
that the experiments took place in the dark.

As stated in our previous communication the progress of the
development was always quite normal; in the many series of experi-
ments it very rarely occurred that a single flask exhibited an abnormal
phenomenon; in the ease of such an exception several abnormalities
occurred simultaneously, such as darkening ete.

3. In the experiments on the retarding action a number of these
solutions, but now provided with increasing quantities of the substance
to be investigated, was presented to the penicillium, besides one
(sometimes more) standard solution with pure p-oxybenzoie acid;
they were observed during a series of days and compared with each
other. The moment at which the development of the organism
commenced was noticed very sharply in the clear solution.

In this manner it could be observed whether a same quantity of
different substances retarded more or less the development, or what
quantity of a substance was required to prevent the development
within a definite time 3—10 days, for instance.

When the development set in, the retarding action was still very
well perceptible and comparable for a period of several days, so
that the observations could, continually, be repeated and controlled.

All this shows that the penicillium is a material eminently fitted
for these experiments owing fo the quiet growth of the organism
and its remarkable power of taking to all kinds of carbon containing
material, yet coupled with a satisfactory sensitiveness.

4. Besides these experiments which concern the action of different
substances on the growth of the organism in an excess of one very
definite carbon source it was ascertained whether the said substances
(which were selected in such a manner that their chemical construction
exhibited a fairly great similarity to each other and to the carbon
source) could act themselves as a source of carbon and, such being
the case, in how far the development was dependent on the quantity
of these substances.

For this purpose increasing quantities of the said substances, mixed
with the above named inorganic nutriment, were offered to the
penicillium and the growth of the organism was observed for a series
of days. Generally, different series were placed together into the
incubator so that the results could be directly compared with
each other,

( 611)

5. We have already pointed out (in 3) some of the advantages
of this method; the most important is that all carbon sources,
except the one which is to be studied, are carefully avoided so that
one may be certain that any development is due to the presence
of the substance to be investigated and not to the carbon of the
nutrient base.

We had also convinced ourselves tbat the carbon dioxide from the
atmosphere was in itself not sufficient to cause any development and
the amount of inoculating material was always so small that this
could not in itself be regarded as a source of carbon.

Hence, we could suffice with the very simple observations of the
development, and there was no need to trouble about determinations
as to the fate of the organic matter.

Owing to this, we were not bound to use considerable quantities
of the substance, and often a few mg were found to be sufficient.

It appears to us that the results obtained with those very small
quantities of the substance are not the /east important ones

6. The substances which we have submitted to this biochemical
research are as follows:

a. phenol, pyrocatechol, resorcinol, hydroquinone, pyrogallol, phlo-
rooglucinol.

b. o-, m- and p-oxybenzoie acid; 2,3-; 2,4-; 2,5-; 2,6-; 3,4-dioxy-
benzoic acid, anisic- acid, guaiacolearboxy lic acid ; 2,3,4- ; 2,4,6-; 3,4,-5
trioxybenzoic acid.

c. benzoic acid and the three toluic acids.

d. A few more distant compounds such as quinie acid.

The phenols were carefully purified, o- and p-oxybenzoic acid
were prepared according to Ko.se from phenol absolutely free from
cresol, and used after repeated crystallisation; m-oxybenzoic acid
by fusing the sulphonation product of benzoic acid with potassium
hydroxide.

2,3-dioxybenzoic acid was obtained from guaiacolearboxylic acid
by heating with aluminium chloride; 2,5-dioxybenzoic acid (gentisic
acid) by oxidation of salicylic acid with potassium persulphate.

2,6-dioxybenzoic acid has been forwarded to us for this purpose by
Prof. Brunner to whom we again tender our sincere thanks.

Protocatechuie acid was among the collection and was purified by
recrystallisation, the same was the case with anisie acid, guaiacol-
carboxylic acid, benzoic acid, and the toluic acids, whilst 2,4,6- and
2,3,4-trioxybenzoic acid were prepared from pyrogallol and phloro-
glucinol with KHCQ,.

( 612 )

Experimental.

It is not our intention to give here a “detailed account of all the

experiments ;

it will suffice

review the results.

to

mention some of the series and to

TABLE I. Action of larger quantities of different carbon compounds on the deve-
lopment of the penicillium.
Period of | ne ee eee
: Name (Quan- | Beginning |
a of the compound | tity | 9 Jan. 19 Jan. of March | Remarks
| athe
24 Dec.’10| salicylic acid 0.050 | — | — |
p-oxybenzoic acid|0.14 | \
m-oxybenzoicacid |0.20 |
strong development
3.4.5-trioxybenz. ac. 0.50
3.4-dioxybenz.acid/0.50 | |
|
| |, development
2.3.4-trioxybenz. ac. 0.15 —- | — i and
a | | | darkening
| 27 Jan. 30 Jan. 16 Febr.
25 Jan.’11} quinic acid 0.1015 + strong development
2.4.6-trioxy benz. ac.|0.0807, — ? |strong develop-
Z ment
16 Febr. 20 Febr 1 March
13 Febr.| 2.4-dioxybenz. acid|0.1004) ? 4 ++ Darkening
oe —aP a ke
3 Febr. | 5 Febr. 8 Febr.
1 Febr. | p-oxybenzoic acid \0.1500) 9 -- +--+ ++-+ Controldeter-
{mination
p-oxybenz.methyl 0.1500) — == —
anisic acid 0.1500) — —_ + Increases regu-
| |
4 , ; = —— ae {larly
piperonylic acid (0.1000
7 Febr. | benzoic acid 0.1500
aspirine 0.1500 \ after two months no deve-
lopment
| guaiacolcarbox.ac.|0.0994
Opianic acid 0.1002
anisol 0.0235

( 613 )

TABLE | (continued). Action of larger quantities of different carbon compounds

on the development of the penicillium.

- : —===— -
Perioa | |
= Name Quan- lo, | | |
er inva of the compound | ‘tity aed 24 6 28/6 | | Remarks
|
] jl
19 June 11) 2.3-dioxybenzoic 0.0814 — | al ale
acid \ |
» 2.5-dioxybenzoic 0.2376, — | — = = |
acid | |
p-oxybenzoic acid}0.1 | —) +) ++ /+4-+ | Control
31|57| 67 | 7/7 | 17/7!
1 July | 2.4-dioxybenzoic {o.10277 —|— | + | + |+4+! Darkening
acid |
10/7|13/7| 17/7
eS
5 » resorcinol 0.100 | + |++) +++
8 » pyrocatechol 0509925 f= 13/7 Yellowish green
| solution
> hydroquinone 0.1005, — | — |+ slight | Reddish brown
| solution
> pyrogallol 0.0973) — | — 2 | Solution very
Pe dark
|37|5;7| 7,7
1 July tannic acid 0.1021) + +--+) +++
> mELaphenolsulignie 0.10 | | | ‘| As mono-
| :
> paraphenol » |0.10 ia development functasciusiesalt
> > » 10.10 |) As dipotassium
7 salt
288
~~
20 July phenol 0.035 | ff |
> > 0.070 | | a
g9 | 3/10 |
1 Sept. phloroglucinol 0.15 a | +--+ |
> > 0.15 | + +++
26/9289) 2/10 |
| Pies SS eee |
21 Sept. 2.6 dioxybenzoic |0.0476, — | — |-+slight! |
acid oe fl sli IS Sr
lagj10 24/10 26/10 | 27/10 |
- - Sa)
20 Oct. o-phtalic acid 0.124 | — | 2?) + +

( 614 )

If we look over the result of these experiments, we notice that
the property to serve as a nutriment is not connected with the
degree of dissociation of the acids but depends on the nature, the
number, and the position of the groups.

A. The nature. Favourable in the first place is the OH group:

This is shown from the behaviour of phenol which, in small
concentrations promotes the growth. Why, in larger quantities, it
begins to exert a retarding action we will state presently.

All polyoxyecompounds may be assimilated to a greater or lesser
degree.

In the second place the carboxyl group:

That this is much less favourable than the OH group is shown
from the comparison of benzoic acid with phenol; o-phtalic acid on
the other hand is taken up in fairly large concentrations.

Unfavourable is a methyl or methylene group, and the sulphonic
acid group.

This is shown from the comparison of anisic acid and p.oxybenzoie
methyl ester with p-oxybenzoic acid; of piperonylic acid with proto-
eatechuic acid; of guaiacolearboxylic acid with 2.3 dioxybenzoie acid ;
of p- and m-oxybenzenesulphonic acid with p- and m-oxybenzoie acid.

B. The number. A combination of several OH-; COOH-groups, or
of both generally increases the liability to attack. Compare the polyoxy-
compounds with the mono- ete.

C. The position. The ortho-position diminishes as a rule the favourable
action’) so that this may even become an unfavourable one; the
meta-position promotes it most.

The most striking example is the behaviour of salicylic acid
towards its isomers; compare also hydroquinone, pyrocatechol, and
pyrogallol with resorcinol and phloroglucinol.

In the case of the polyoxyearboxylic acids we must take account
of a resolution into CO, and polyphenol, which takes place even
at the ordinary temperature so that the assimilation does not concern
the acid itself but the polyoxy-compound.

This is certainly the case with phloroglucinolearboxylic acid, so
that the favourable action on the growth of the organism must be
largely contributed to the phloroglucinol.

That these decompositions may play a role in the other oay-acids
~2) This seems, however, to depend also on the nature of the groups; thus we
have found that o.toluic acid acts in a less retarding manner then p.toluic acid
and it was known that o.cresol acts less narcotic than the para. The “positive”
methyl group, therefore, behaves differently from the “negative” hydroxyl group
to be more correct, a combination of two opposed groups behaves differently

or,

from one of two analogous oues.

( 615 )

TABLE II. Retarding action of different compounds on the development of peni-
cillium in a nutrient base with 0,15 gram of p-oxybenzoic acid per
50 cc. as a source of carbon.

Salicylic acid. T= 28° a 29°, Exclusion of light.

|
Quantity inmg. 1.3

| agen oe |) Ha Ihe

Development | |. za | ;
Bedaysmaiter | \-te t-te begin

inoculation.

o-Cresotinic acid

Quantity inmg. | 1.3 Pel! a0), |) Meek

“Development |
5 days after +--+ a

inoculation

Salicylic acid

Quantity inmg. | 2.3 | 4.6 6.8 8.2 10.5 1322

Development |

after 3 days: || ---- |) ---- ||) = ? = =
after 4 days |++4+-+) ++ ++ ab
afterio days |e) mn ?

Gentisic acid . 5- dioxybenzoic acid).
iF | >.

late | ees, |) 092 ithout
Quantity inmg. | 90.3 to 18.2 mg poxybenzoic acid | p oxybenzoie ane

Development With this experiment it was
after 3 days -+ | proved that gentisic acid has
no perceptible action on the
after 8 days | + + | growth of the organism, al-
though it hardly acts itself as
after 19 days | +++) a source of carbon. (See
Table I and below).

Resorcinic acid (quantity 2.6-dioxybenzoic acid
p-oxybenzoic acid = 0.1014 gr.) (0.1 gr. poxybenz.).
| ; a ] ; |
| Quantity in mg. 31.1 | Quantity in mg. | 20.5
Development After 4 days | + +

| after 5 days | +++ |

| 2% ane eC

leuheretoce: this fama does ws arrest
‘the growth any more than the2. |
dioxybenzoic acid

| after 17 days | very
| strong |
|

( 616 )

is already evident from the fact that phenol, in smaller concentrations
is an excellent carbon nutriment.
Retarding action of different compounds on the growth of penicillium
with OAS gram of p-oxybenzoie acid as source of carbon.
In order to be able to compare the influence of different substances
small but increasing quantities thereof were added to 0,150 gram
of p-oxybenzoic acid treated, and observed simultaneously in exactly

the same manner.
Table IIIA gives a survey of the quantities with the Nos of the

TABLE Ill A.
1 2 3 4 —s | _o.
2.5 mg); 2 mg |2.4 mg| 2 mg 2 mg 2 mg
p-oxy- o- m- p- benzoic | salicylic
benzoic | toluic toluic | toluic acid acid
naciel Sil sacia plese Ce eect ae ee
Nos of experiments) 7 8 9 108 |) St
blank |
Salicylic ac.(in mg). control | 1.0 Wack || Plate} 13.6
12 13 14 15

Benzoic acid ,,

o-Toluic acid ,,

m-Toluic acid ,,

24 pay || 720) 27
p-Toluic acid ,, |

120° *|) 3220 8508 30

TABLE III B. TABLE Ill C.
5 days after inoculation 7 days after inoculation
1 2 3 4 | 5 6
Salinen 8 9 10 | 11
Salic. | vigorous R |
acid |sowh | < Ti < gsl<ol 4 strong |] = 7] < 8} <9] +
12 13 | mire | Pl
Benzoicacid | — |. |< 9 ee | iS
= eal <= OGL beginning
( Le
o-Toluic acid ‘
—— pli,
‘ : 20 21
m-Toluic acid
|= 16| = 20
| 24 25

p-Toluic acid) ~

( 617 )

experiments, IIIB and I'IC a survey of the development after 5 and
6 days respectively. Nos. 1—6 relate to very small quantities of
p-oxybenzoic acid and the retarding substances investigated, Nos. 7—27
to mixtures of the latter with 0,15 gram of p-oxybenzoic acid:

After nine days the phenomenon had practically remained the
same and owing to the vigorous growth, the differences in the low-
percentage solutions were no longer plainly perceptible.

An always distinctly perceptible criterium is the commencement
of development.

From this investigation it follows with positive certainty that
benzoic acid and the toluic acids exert a stronger retarding action
than salicylic acid, and that of the four first the m- and _ p-toluic
acids exert a somewhat greater influence than the other two (see
note p. GLO).

From tables | and 2 it isshown that we may divide the substances
into three groups although of course no sharp lines can be drawn.

A. Substanees which can serve as a source of carbon, for instance

p-oxybenzoic acid.

b. Substances which do not act as a nutriment and do not exert

a retarding influence such as genitisic acid.

C. Substances which exert a distinct retarding influence such as

salicylic acid.

As it appeared to us that after 17 days a distinct growth could
be observed in the flasks 2—6 (Table III) in which nothing was
present but a retarding substance as a source of carbon, we have
also investigated that phenomenon systematically.

It may be observed that we had kept these flasks, because we
did expect the growth to take place.

For when we found that quantities of more than 10°/, salicylic
acid in excess of para acid could not prevent a growth in the long
run we asked ourselves what happened to this salicylic acid.

Some flasks with increasing quantities of salicylic acid in 150 mg.
of p-oxybenzoic acid were treated in the usual manner and after the
growth had set in thoroughly the solution was filtered. ‘fhe filtrate
was sterilised and again inoculated; a fresh growth took place which
could not be distinguished from that formed in a flask with pure
p-oxybenzoie acid; the salicylic acid is, therefore, consumed *).

1) We were able to demonstrate by means of the very characteristic iron reaction
that gentisic acid had, formed; under the influence of the organism an H-atom,
which has a para position in regard to the OH-group already present, is substituted
and the retarding salicylic acid is simultaneously converted into the harmless
gentisic acid.

( 618 )

From this it follows that the retarding substances must possess
nutrient powers. This indeed appeared from the behaviour of the
flasks 2—6 which all exhibited a slight development after some time.

[t seems remarkable that the least development took place in
flask 4 albeit a good carbon nutriment was present in the form of
p-oxybenzoie acid.

That this was not merely accidental will be shown later.

TABLE IV A. Action of increasing quantities of carbon containing material on the

development of penicillium.

p-oxybenzoic acid; T= 28°— 29° light excluded, except during the observations.

Nex, [ok | 2 | | def sie qi tee elleceal ie
Seay | 2.9 | 5.2 | 10.5 | 38.9 | 58.0 | 89.7 | 119.7] 173.5 Begs
‘After 2days =, fee | + +24) to8l3 26) =a) =e ss
> 4>/—|—] + }44) 4 >5 |B(<6) <7 |—8 |=9
5 so) =| 4 | + | et Bos] os |e jaune] <o |=
> 6 >» | ? lace at | 5 Pre ieee =
Noe | eect 2 air ease L <Bmuch<1] <8 | =9

In this first series, there is therefore a distinct maximum between
89,7 and 119,7 mg. A second series gave a maximum between 94,4

and 124,7.

TABLE IV B.

m-oxybenzoic acid; as with para,

in l
Nos | 1 | ue| Sem Aamo Nia!
Quantity | , ee | |
in mg. | 4.3 | 12.8 | 41.7 | 93.3 | 172.8 | . 300 | 553.6
SS SSS SS — — = a = = Ne == === dt
‘After 3 days | , | small | + | =3 mmuch< 44 =2 | 2
35 i eetoen alt lis 12 3 > 3;much<4 very small < 6
|
saat Ig 2
Here, the maximum lies also a little beyond 93,3; the harmful

action of a large concentration is
With protocatechuic acid the

very evident.
maximum was only attained at

+ 600 mg.; with o-phtalic acid at 71,2—124,0.

( 619 )

TABLE IV C.
phenol; as with oxybenzoic acid.
Noe escesr eae | 5s ll) 6. | 7

Quantity | ;

in me. | 2.6 | 8.5 | 10.4 | 12.9 | 42.6 | 60.9 | 141.7
| After 4 days |beginning) = 1 | ete || eet — — _
+6 eels ieSa h—w|es)e—- |
eset se PIS | S|) 2) 3.) = | =. [p=

The maximum is, therefore, situated between 8,5 and 10,4 mgs.,
in this concentration it is an excellent source of carbon.

From these experiments it is shown that the substances investi-
gated must be looked upon from a common point of view. They
act as a source of carbon as well as in the capacity of a retarder.

If they were exclusively a source of carbon the development
would increase continuously with the concentration ; if exclusively
retarding they could not, of course, allow any development to take place.

Owing to these experiments we have also got acquainted with a
method to ascertain the suitability of a definite substance as a carbon
nutrient; the higher the maximum lies, the more suitable is the
substance. Protocatechuic acid appears to have more favourable
properties than m- and p-oxybenzoie acid and these substances are
better than phenol.

Finally, it struck us that phenol in small concentrations caused a
more rapid development than p-oxybenzoic acid, a phenomenon
already observed with the other retarding substances such as benzoic
acid and the toluic acids. If this were a general phenomenon, the
substances which act still more favourably, such as pyrocatechuic
acid in small concentrations ought again to cause a less rapid growth
than p-oxybenzoic acid.

In fact, 4,5 and 8,2 mgs. of pyrocatechuic acid, respectively, when
observed a few days after each other, showed a very much smaller
growth than 3,7 and 9,2 mgs. of p-oxybenzoic acid, respectively.

Now it has been decided that there is no essential but a gradual
difference between these benzene derivates, the main cause can only
lie in a gradual difference of properties, for instance, in a difference
of oxidability or even of solubility.

Although it is rather probable that we shall have to search in
many directions we have, provisionally, restricted ourselves to the
solubility and determined the division factor between olive oil and
water of the most important compounds.

( 620 )

On the division factor of several compounds, between
olive oil and water at 25°.

For this purpose the solubility of the substances in water as well
as in olive oil was determined by shaking them for a long time
with the solvents in a thermostat and then estimating the amount
taken up. The measurements were always made in duplicate, one of
the flasks being shaken for a longer time than the other.

The acids were determined by titration after first ascertaining the
accuracy of the process; when dealing with solutions in olive oil
this had to be first thoroughly extracted ; for this purpose it was
shaken repeatedly with fresh portions of water (or boiled) until it
yielded practically no more acid; 10 extractions were generally sufficient.

Division factor in connection with retardation and growth.
TABLE V. Factor calculated for 100 grams of solvent.

| | Dive | Retarding | Growth at | Maximum
| N f ound | No. Tp | tities
a ae ae ratte ek |dactonat call ecice Z| O50 ie development
[to - PT bes 1/0 oan eee ee — | :
donee eee
| o-toluic acid he | 40.5 | ) No. 2and 3 |
p-toluic acid | 2 | 29.5 ++tH | —
| m-toluic acid 3 2160 ee
benzoic acid 4 12.6 ++ | — |
| anisic acid 5 12.5 | -
| salicylic acid 6 11.8 +-+ = No.4 — < 2mg
_ phenol 1 | >9<10.3 + + | 9 a 10 mg |
| terephtalic acid 8 9.25 af pore
guaiacolcarboxylicacid) 9 3.7 + — |
| 2.4..dioxybenzoic acid 10 | 1.0 + <No.6 | +>No.7 |
-di i i | Ni etd ue — | |
2.6-dioxybenzoic acid | 11 ot yet ee | We tert
| ' a e| want of | |
2.3-dioxybenzoic acid 12 material. | = \+
| p-oxybenzoic acid 13 0.6 | _ | ++ | + 100mg.
| m-oxybenzoic acid 14 0.4 a i es. + 100 mg |
2.5-dioxybenzoic acid 15 0.3 — —_ |
| |
3.4-dioxybenzoic acid 16 0.05 -- 4 + 60) m
g |
| resorcinol 17 0.04 — +++
| 3.4.5-trioxybenzoicacid 18 0.025 — +++ |
| o-phtalic acid 19 0.01 a= stats + 125 mg

The solubility of the non-acids was determined by gradually adding
the substance to the solvent until no more was dissolved.

In this way were found the following division numbers, which
we at once compare with the growth-phenomena caused by them
and the retardation thereof.

The parallelism between the division factor and the retarding
action is undeniable.

As regards the promotion of the growth, this is also the case in
the reverse sense.

From these experiments we may draw the conclusion that the retard-
ing action increases when the solubility is greater in oil than in
water, from which it follows that this action is connected with a
fatty constituent of the organism.

There are still two points which are now also elucidated.

1. Small quantities of retarding substances can promote the growth ;

2. in very small concentrations they promote the development
better than the substances with a small division factor, under the
same conditions.

When small quantities are present of substances readily soluble in
oil, these will for the greater part accumulate in the fatty part of
the organism; from the fact that they are being assimilated it fol-
lows at once that the assimilation is also connected with the fatty
part of the organism.

The fact that they are assimilated more rapidly than the favour-
able carbon sources is due to this difference in solubility; the latter
which are much less soluble in oil than in water will, at the small
absolute concentration of a few mg. per 50 cc., practically not enter
the fatty part of the organism and, therefore, be assimilated very
much more slowly.

An absolute parallelism does not, of course exist. First of all,
olive oil is something else than ‘‘a fatty constituent of the penicil-
lium” and secondly the division coefficient is only one particular
factor (though plainly an important one) among the many factors
which may be of importance here.

Among these, the more or less ready oxidability will Eavoubiedlp
play a role. In order to eliminate this influence we have used i
our research, as much as possible, analogous substances. Yet, we
attribute the ready assimilation of phenol as compared with that of
guaiacolcarboxylic acid to the ready way it may be attacked.

This perhaps also explains why gentisic acid (N°. 15 Table 5)
although harmless on account of its low division coefficient yet can-
not serve as a carbon-containing nutriment, and why ortho-phtalie

42

Proceedings Royal Acad, Amsterdam, Vol, XIY.

( 622 )

acid (No. 19) notwithstanding its very low division factor yet
promotes the development not so well as, for instance, 3,4 dioxy-
benzoic acid. (Notice the amount required for a maximum develop-
ment, last column Table 5).

Presumably, this is also the reason why o-toluie acid with its
large division factor acts somewhat less retarding than p-toluic acid ;
we have shown that o-toluic acid is oxidised to a substance which
is also formed during the assimilation of o-phthalic acid; it is, there-
fore, very probable that o-toluic acid is first oxidised to the favour-
able o-phthalic acid.

The research will be continued by us in various directions.

It is our pleasant duty to thank Prof. Dr. Beyermnck and Mr.
Jacopsen for their kind support in the biological part of the research.

Org. Chem. Lab. Techn.

November 8, 1911. University Delft.

Chemistry. — “On the velocity of hydration of some cyclic acid
anhydrides.” By Prof. J. Borsexen, A. Scuweizer and G. F.
vAN prrR Want. (Communicated by Prof. A. F. HonLLeman.)

(Communicated in the meeting of November 25, 1911).

In connection with the research of A. Scawerizer and myself, of
which a communication is inserted in these Proceedings (November
26, 1910, p. 534), we have measured the velocity of hydration of
some saturated cyclic acid anhydrides in order to collect more data
as to the value of the figures thus obtained as a measure of the
ring tension.

In the said communication we already pointed out that it is not
excluded that the velocity of hydration of those anhydrides will be
affected by their affinity for water and their ring tension so that in
the figure found both these causes will find their expression.

It is, of course, not feasible to ascertain what part is due to the
affinity, yet, we may expect that this affinity will be connected with
the dissociation constant of the acids obtained from the anhydrides.

The dissociation constant is up to a certain degree a measure for
the velocity with which the acid is further divided into its ions;
we may expect that the quicker this takes place the more rapidly
will the disappeared acid molecules be replenished from the anhydride.

If we compare the figures for the hydration- constant, obtained by
ourselves and other investigators, with those of the electrolytic disso-
ciation, a parallelism cannot be denied, particularly when we choose
analogous substances for comparison.

( 623 )

The number of substances investigated is, as yet, far too small
to enable us to draw general conclusions; still in the succinic acid

Hydration constant of some acid anhydrides calculated for a monomolecular

reaction with the minute as time unit; and the dissociation constant K.

| a | . - | Dissociation
| 9 Anhydride of oa coy | Investigators constant
st |
s) Qe | S | K of the acids
a — — —~ So, — = | —_ — = =
succinic acid (0.0736 | Voerman |
| ; 0.0693, Rivett and Sidgwick || 0.00652 (V.) |
> | 0.0088 Béeseken and Schweizer | |
|
I methyl succinic acid 0.0965 Riv. and Sidg. | 0.0086 (O.)

s.dimethyl > |
Mpa S12 0.110 | | 0.0132 (V.d.W,) |
| | Bo. and V. d. Want | |

s.dimethyl > }
m.p. = 429 (0.153 | / 0.0194 >
| | 2 -== |
| | | |
maleinic acid 0.690 Riv. and Sidg.
| | 1.17 (Schw.)
> 0.125 B6. and Schw.
Il itaconic acid 0.0776. 0.012 (0) |
citraconic acid 0.459 | | >Riv. and Sidg. | 0.34 » |
|
o.phtalic acid (0.2766) | Os121 ys
| | |
SS | ae |
glutaric acid [peo Voerman | 0.0047 (V.) |
III | acetyl oxyglutaric 0.096}, |
acid) Bé. and Schw. | 0.0157 (Schw.)
| > | 0.0117 |

group the increase of the velocity of hydration with that of the
dissociation constant is so striking that it cannot be quite accidental.

The same is true for the maleic acid group to which even
o-phthalic acid is connected.

The slight increase of the velocity of hydration, noticed by Vorrman,
when one passes from succinic anhydride to glutaric anhydride now
finds a very simple explanation in the slight dissociation constant of
glutaric acid, as compared with that of the succinic acid.

From this point of view the difference in tension between this
6-ring and the 5-ring of suecinie anhydride would be considerably

42%*

( 624 )

greater than might be surmised from a comparison of VorrMan’s
figures.

In both the symmetric dimethylsuecinie anhydrides"), we notice
that the two constant-couples are almost proportionate, so that the
relation of the dissociation constant with the hydration is particularly
striking; the influence of the ring tension (to be expected on account
of the difference in configuration) appears to become quite incon-
spicuous.

In other cases, this affinity is less pronounced, so that we can
say, as a rule, that the hydration changes in the same sense as the
dissociation constant, but that the changes do not keep equal pace.
Whether this bears a relation to the ring tension remains to be seen
when a much greater number of experiments have been made.

At present we can, however, state with great probability that in
the hydration of acid anhydrides the affinity of water for anhydride
plays a very important role.

The description of the experimental part of this research carried
out with the assistance of Messrs. A. Scuwerizer and G. F. vAN DER
Want will shortly appear in the Recueil des travaux Chimiques.

Org. Chem. Lab. Techn. University.
Delft, Nov. 20, 19114.

1) [| call attention to the fact that some confusion exists in the denomination of
the two symmetric acids. They are indicated by the names cis and trans, fumar-
oide and maleinoid, para and anti, racemic and meso (anti).

The last is undoubtedly the most rational one, but it cannot be applied, because
it is not known, as yet, to which of the sterec-isomers the racemic configuration
appertains.

One is accustomed to give to the acid with the highest melting point the name
of para- or trans-dimethylsuccinic acid in the idea that this is the racemic acid;
but this is only hased on some speculative ideas of BiscHorr (B 24 p. 1086) and
y. Banyrer (Ann. 258 p. 180) as to the privileged position of the groups, which
in this case have now little value.

So long as not one of these acids has been resolved into its oplical components,
there is no certainty; it is even more probable that the acid with the lowest
melting point (128°) will prove to be the racemic acid because the anhydride of
this acid, which melts at 87°, is stable and because we may expect that the
methyl-groups on both sides of the ring will render the same more stable than
when they are siluated at the same side. The trans-anhydride belongs to the
racemic acid (Compare also MicHArt Journ, f. pr. Ch. [2] 46 p. 422).

Provisionally, | have indicated the anhydrides with their melting points. (J. B.).

( 625 )

Chemistry. — “On the TIodides of the Elements of the Nitrogen
Group’. By H. R. Doornposcn. (Communicated by Prof. P.
van RomBuRGH).

(Communicated in the meeting of November 25, 1911),

§ 1. Frequent investigations have been carried out in regard to
the iodides of the elements nitrogen, phosphorus, arsenic, and antimony,
but these chiefly concerned the two first elements of this group.

So far as nitrogen-iodide is concerned, the question as to the
existence of a free compound of the formula ./, may now be
answered in a negative sense.

As the result of the latest investigations as to this question, such
as those of Cuattaway?), Rurr*) and Hucor’), it is well nigh certain
that .V./J, can exist only in complex molecules with 12, 3, 2 and 1
mols. of NH,, respectively, and then only at low temperatures.

Of phosphorus, two iodides are known ; according to the literature
on the subject, the «d-iodide P,/, m.p. 110° (according to this
research 124°), whose vapour under reduced pressure is said to deposit
mainly PJ, with formation of red phosphorus :

3
8 P= OIait ais

‘i=
further the ¢r-iodide PJ, m.p. 55°—60° which is said to yield a
dissociated vapour, but only at a higher temperature.

With arsenic on the other hand, it is only the compound As./,,
which is accepted with absolute certainty, as the statements*) as to
As,J,
considered to be of a doubtful nature, particularly so because ArzRuni’s

(analogous to the phosphorus compound) must in any case be

crystal-measurements of these products do not admit of safe conclu-
sions as to the individuality of the supposed compound. Whilst with
the phosphorus, no derivative of the pentavalent element is described,
some statement as to As/, are found in SLoAN’s paper’).

Of antimony we find in the first place a compound \Sd./, de-
scribed supposed to be isomorphous with 52/,. Van per Espr’) and
afterwards PenpLETON’) have noticed a compound Sé./, with a melting
point of 78°—79°; the existence thereof has, however, been denied

1) Coarraway, Norton, and others, Amer. Chemic. Journ 23, 363, 369 (1900);
24, 138, 159, 318, 331 (1900).

2) Rurr, Ber. d.d. Chem. Ges. 338, 2025 (1300).

3) Huaor, Ann. de Chim. et Phys. (7), 21, 5 (1900).

4) Bampercer ond Putpp, Ber. dd. Chem. Ges. 14, 2644 (1881).

5) Stoan, Chem. News, 46, 194 (1882).

6) Van per Hspr, Arch. Pharm. (2), 117, 115 (1864).

7) Penpteron, Chem. News. 48, 97. (1884),

(°626'')

by Mac Ivor’), in whose opinion only one compound, namely Sé/,
can exist.

This incompleteness of the statements in the literature coupled
with the experiences gained by Eaaink*) with the chlorine-derivatives
of the analogous bismuth, and the suspicion that a two-layer formation
might occur also here as a confusing complication, caused Prof. JAEGER
to suggest to me to investigate some of the disputable questions. We
may, therefore, state briefly in this paper the results obtained in the
study of the binary systems: As + / and S++ J, also of those of
AsJ, + PJ,, SbJ, + PJ, and of AsJ; + SbJ,. Further details will

be communicated later in a dissertation now in hand.

§ 2. Antimony and Todine. The binary molten mixtures investigated,
were prepared from .Sb/J, sublimed in a CO,-current, with the aid of
S) or J,. The fusion, in order to avoid loss of iodine by volatilisation,
took place in the case of mixtures rich in Sd, in evacuated and
afterwards sealed glass tubes. With the mixtures very rich in jSd
the cooling- and heating-curves were also recorded in closed apparatus.
In the tables are found, besides the actual temperaturereadings, also
tie corrected ones; the thermometers were compared with a certi-
ficated normal thermometer. By way of comparison, the solidifying-
and the melting-points are given side by side, so as to point out
the difference between the results of cooling- and heating-experiments.
Gn account of the rapid setting in of the equilibrium, and the want
of an appreciable undercooling, these differences are not large in
this system.

From these determinations it is shown, that when the binary molten
mixtures solidify, Sd and J form only one compound, namely Sé/, .
This compound has a sharp melting-point of 170°.8.C. It does not
mix perceptibly with. antimony; if more antimony is added than
corresponds with the composition )S)./,, the melt separates into two
liquid layers of which the upper one differs but exceedingly little
in composition from .S/,, whilst the lower one has the composition
71.6 at °/, Sd and 28.4 at °/, J, as proved by repeated analysis of
suddenly cooled mixtures. The transition-temperature is 169° C.; at
that temperature the liquid with 28.4°/, of J, will, with deposition
of Sb, form the layer whose composition practically does not differ
from S)/,. As the eutecticum then following between that resulting

75 9/

/, of J, the inter-

0

layer and pure S0./, practically coincides with
1) Mac lyor, Journ. Chem. Soc. 29, 328 (1876); Chem. News. 86, 2
*) Eeaink, Zeits. f. phys. Chem. 64, 449 (1908).

( 627 )

Binary melting-point-line of Sb + J.

Qyby weight byatoms|) ;,O8enred |) ,Comedied || Duration
| |e __| of the effect
Sb A Sb df | a mp. a mp. in seconds.
| point, || point.
10. | 0. |[100. | 0. |! 630. = || 632° 3 ae
g9.5| 10.5|| 90. | 10. || 1634| 165.8 || 1665| 168.9 130 |
79.1} 20.9) 80. | 20. || 164.15 = 167.25 = 230 |
15. | 25. | 16. |-24. || 1658| 167.2 169.05 170.45 330
70.9{ 29.1)| 72. | 28. || 165.9 167.2 169.0 170.3 380 |
58.7 | 41.3 || 60. | 49. || 165.5] 167. | 168.5 170.15 500 |
48.6) 51.4|| 50 | 50. || 165.45 167.1 || 168.6) 170.28 580 |
38.7| 61.3|| 40. | 60. || 165.5) 166. || 168.45, 168.95 630
28.9 11.1|| 30. | 70. || 1652| 166.8 168.1 169.7 780 |
24.0| 76.0|| 25. | 75. || 1671| 167.6 || 1703| 170.8 |
End solidi- | End solidi-
| fying point. fying point.
23.4| 76.6|| 24.4) 75.6 160.8 77.9 || 164.4 78.7 300
22.7| 11.3|) 23.6) 76.4|| 154.95 79.2 || 158.35, 79.75 420
20.5| 79.5|| 21.5| 78.5|| 1448| 79.4 || 147. 79.7 740
18.8| 81.2|| 19.6] 80.4|| 1328 79.8 || 134.25] 80.2 1040 |
16.5| 83.2|| 17.3] 82.7]| 116. 79.25 } 117.7 80.15 1220 |
14.2) 85.8 14.9, 85.1|| 95.3| 79.3 || 96.55] 80.2 1500
12.4] 87.6]| 13.0] 87.0] 8355 79.35 || 84.45 80.25 1520
11-3 88.7]| 11.8] 88.2]| 79. 79.25 TOES) OSE) 1700
10.7) 89.3 11.2. g8.8|| si.1| 79.25 || 820| 80.15 1480
7.9| 92.1)) 8.3| 91.7|) 91.85 79.45 || 92851 80.2 7 1080n |
4.3| 95.7|| 4.5] 95.5|| 1024| 78.3 103.75, 79.15 W200 |
0.9] 99.1] 1.0) 99.0|| 1108) 76.85 111.8 71 210 |
0. ;100. |} 0. | 100. || 1121 = fi3os| —= |

vals superpose each other. Hence, the abnormal course of the time line.

The melting point of iodine (113°.3 C.) is lowered by addition of
SbJ, and the eutectic point appears to lie at 80°C. and a content
of 88.2 at. °/, of iodine. From the fact that the eutectic separation
is found quite close to the vicinity of the pure iodine, it follows,
that a notable formation of solid solutions does not occur; the same
is true for the mixtures in the immediate vicinity of the Sb/,. The

( 628 )

composition of the mixtures S/./,+-./, was each time determined
by direct analysis, after recording the cooling-curve.
The value for the heat of fusion of pure iodine is, according to

140°

130°

She 9 29 30 bo So bo yo a2 ge ‘oore

an old statement of Person (Jahresberichte 1847) 11.7 calories. From
this we find for the molecular freezing-point-constant: 253°.2 C.
TimmerMANS (Journ. de Chim. phys. 4 (1906) 171) found a value of
252°.13 C. When this value is accepted we find, for the depression
of the melting-point of the iodine by added .Sé./,, amounts which
agree well with the temperature on the branch of the melting-point-
line at the -J/-side.

( 629 )

Binary melting-point-line of As + J.

| | | Duration of the |
%/o, by | 9 | Observed Temp. | Corr. Tem oe el
weight | by atoms : P- | Saeaasaeaneete
| I of atoms)
Initial so-| End soli- | Initial so-| End soli- Of Of
J || As | J | lidifying | difying | lidifying| difying lowest) highest
| point | point | point | point | temp. | temp.
he er SIS si eal rae ahh ee |
0 | 100 0 = - | -- el
15.8|90 10 = = = 117.3 |! 150 =|
2780/20 \\"120.2 | — 122.5 | 120.5 | 200 | 90
32.0 || 78.2 Pipe)|int25s00 |» Wie.7) || 127.8) | 118-9 | 300 | 60 |
42.1||70 |30 || 128.9 | 116.8 || 131.5 | 119.1 |) 200 | 90 |
53.0|/60 |40 || 130.8 | 117.4 || 133.5 | 119.7 || 380 | 200
62.9|50 |50 I) 132.2) | 117.4 || 134.0%| 119.7 380 | 200 |
71.8||40 |60 || 132.0 | 117.7 134.7 | 120.0 || 480 | 370
71.2 | 33.33,66.67/ 130.2 | 117.8 | 132.9 | 120.1 540 | 310
71.5)|33.0|67.0|| 131.6 | 117.3 || 124.6 | 119.8 || 530 | 400 |
78.2||32.0|68.0)| 134.0 | 117.3 || 136.8 ; 119.6 | 485 | 490 |
79.0||31.0/69.0)] 133.7 | 117.0 || 136.5 | 119.3 || 480 =
79.8||30.0|70.0|| 128.4 | 118.4 || 131.1 | 120.7 || 600 =
81.0 28.5 W.5|| 119.5 | 119.2 || 121.8 | 121.5 |) 1100} —
81.7||27.5|72.5|| 126.4 | 118.8 || 128.9 | 121.2 || 640 | —
82.8||26.0/74.0|| 134.8 | 112.2 || 137.6 | 114.3 || 160 | —
83.55||25 (75 || 138.1 | — 140. 7eM | == | = =
83.7|/ 24.8] 75.2|| 137.2 70.4 || 139.9 | 71.1 | 70 =
84.1||24.2|75.8)| 132.5 72.2 || 134.9 | 72.9 || 250 | —
86.8||20.5/79.5|| 109.7 | 71.8 || 111.4 | 72.4 || 40) —
90.6||14.9|85.1|| 79.5 | 72.2 || 80.3 | 72.9 |) 1380) —
91.2||14.1|85.9|| 73 73 13.15 | 73.75 || 1500 — |
92.2||12.5|87.5|| 75.8 | 72 16.6 | 72.75 || 1420; — |
93.8|/10 joo || 86.3 | 71.8 || 87.2 | 72.5 | 1220) — |
[97.0], 5 |95 || 101.3 i.3 || 1026 | 72.0 || 80 | —
|99.7)| 0.5/99.5 | 110.0 68.0 || 111.75 = 110 2
= 0 | 100 | 112.1 | al MSs Sed le” | ll) —

( 6380 )

Reversely, as S27, is not or bnt little dissociated in the molten mass,
and assuming that iodine dissolves therein as molecules of /,, we can
calculate for the molecular heat of fusion of .Sé.7,: 11 calories; it is,
therefore about equal to that of iodine itself and A’ becomes here 357° C.

The melting temperature of 79°C. found by Prnpieron for .Sb./,
answers to the eutectic temperature and a composition of about
88.2 at. °/, of iodine. In this way nothing is noticed of a compound
SbJ, or a compound Sd,./,.

I have also carried out experiments to ascertain, whether any of
these compounds might perhaps form at a lower temperature, for
instance in strong /7/./-solutions, or as a double-iodide such as are
known of Sé/, and (VH/,)/, BaJ, and b./*). Up till the present
we have not succeeded in obtaining such compounds which would
confirm the existence of the supposed iodides.

§ 3. Arsenic and Jodine. In a manner analogous to that given

}
bso 152°
ho} 140°
i
130° 130°
110° 120°
{1324
(ffal | {10°
loo lo0°
go°| go
= 80°

jo fe
bo bo°
5 oO
Souja eer) ee Agss $0
Oo 10 320 $09 4 50 bo 7° 8o go lo
As J

1) WHEELER. Zeits. f. anorg. Chem. 5, 253. (1894),

( 631 )

for the binary liquids of S$) + -/, the system As-+ J has also been
investigated. The results are found in the subjoined table.

From these figures which are represented graphically in fig. 2, it
follows that there is first of all a compound As ./, stable at its melting
point, and that this system exhibits in the main the peculiarities of
the system Sb+/. The compound As./, melts at 140°,7 and is
apparently but little dissociated in the liquid. Secondly, on closer
examination of the eventual possibilities, there is no other possible
interpretation of the data obtained but this one: from one of the
two liquid layers a compound As, ./, is deposited which, therefore,
has no rea/ melting-point, but melts at 135°—136° to a complex of
two non-miscible liquids. The one layer has a composition which
corresponds nearly to that of As, /,, but contains a little more iodine.
As the mean of various analyses (the /-determinations as Ag J and
the As-deierminations according to the method of Goocu and Morris ')
the composition of the upper layer was found to be: 79,4°/, of ~
and 21,6°/, of As, or in at. °/,: 69.5 J and 30.5 As; the lower
layer has a more varying composition so that the arsenic-content
(70.8°/, by weight) is certainly a little too high. The temperature of
the eutecticum at the arsenic-side hard/y differs from that of the first
eutecticum, so that it looks as if the eutectic temperature proceeds
from 125° further towards the arsenic-side.

Although the whole construction of the diagram already points
to the occurrence of a binary compound in compositions which are
situated within the sphere of the two liquid layers, there are still
more arguments in favour of the existence of As,-/,. First of all
the plainly perceptible heat-effects which occur in mixtures in the
vicinity of 66—68 at. °/, of J and which appear in the figure as
an apparent increase of the two-layer temperature: 135°,5. The
course of the time-lines also confirms distinctly the above two
explanations and makes the impression that we are dealing here
again with a superposition of two time-effects.

It admits, moreover, of no doubt that the compound looked upon
till now as As,-/, has really been nothing else but the upper layer
“present at 135°,5. According to BamBercer and Parupp a compound
AsJ, is formed on melting 1 part of arsenic and 2 parts of iodine
at 230° in sealed tubes for 7 or 58 hours. They state that ‘‘super-
fluous arsenic” is deposited in the tubes. On repeating their experi-
ments, it appeared to us, that the product of fusion contained
79,73 °/, of J and in a second experiment 79,52°/,. As AsJ,

+) GoocH and Morris, Zeits. f. anorg. Chem. 25, 227 (1900).

( 632 )

requires 77,20°/, and As.J/, 83,55 °/, of iodine, the composition of
the product lies between that of As,/, and As./,.

Afterwards we have tried, like B. and P. to obtain from the fused
mass a compound As,/, by means of carbon-disulphide.

Working in an atmosphere of C'O,, arsenic seemed to deposit ;
the solution exhibited definite colour-differences with these of pure
AsJ,, which compound on boiling with CS, always communicates
a violet colour to the condensed liquid (owing to iodine split off.)
The liquid was filtered, cooled in a C'O,-atmosphere with ice and
salt and the crystals deposited were carefully dried at 50° in a
C'O,-atmosphere. The analysis gave: 80,11 and 80,63 °/, of iodine.
These analyses prove that those otherwise homogeneous crystals
contain more As than As./, itself. These experiments were now
repeated with fusions which contained more As to start with, in the
hope to obtain perhaps in this way, by extraction with C'S,, crystals
which contain still more As than the above named. I succeeded
indeed in finding an arsenic-content of 19,28 °/, and 19,58 °/,. The
solution was cherry-red, the crystals were dark red, and therefore,
of a different colour from those of As-/,.

A mixture of As/, with much finely powdered As was now
boiled a long time with xylene (138°) in a current of CO,. The
filtered liquid was cooled rapidly, the mother-liquor evaporated in
vacuo and the residue analysed. Found : 81.86 °/

» therefore again
more As than corresponds with As-/,. This experiment proves plainly
that a solution of As./, may take up a certain amount of As (other-
wise insoluble in the solvent) to form a product containing more
As than <As./,.

Previously, when recrystallising AsJ/, from toluene, it had been
found that the product obtained always contained more As than
corresponds with the normal composition.

In diverse experiments were found: 83.16 °/,, 83.33 °/,, 83.05 °/,
of J; after a single recrystallisation was found: 83.02 °/,, after a
double recrystallisation 83.2°/,, after a third time 82.77°;, of J.
Pure As/, can only be obtained, when the substance is recrystallised

0?

from toluene, containing iodine. When subliming As-/, in a current
of COV, we also noticed an elimination of iodine, so that As-/, belongs
to those compounds which very readily dissociate, when in the state
of vapour. From the melting diagram it would just appear that, at
any rate in the fused AsJ,, but comparatively little dissociation occurs.

Consequently we may well assume that a dissociation-equilibrium
is present, expressed for instance by 2 AsJ/, 2 As,/, + J,; and also
that in the liquids, in which As./, has been brought together with

( 633 )

As, according to: 8 AsJ, + As, = 6 As,/J,,—6 As,/, may be formed
from 8 AsJ, and As, which latter reaction would then dominate the
situation in the upper layer of the melt when heat is being abstracted.
Up to the present I have not sueceeded in obtaining the compound
in a pure condition; but that it does exist can, in my opinion, no
longer be doubted.

§ 4. Finally, we have collected data to ascertain the behaviour
of AsJ, and SbJ,, of AsJ, and P.J,, also that of SdJ, and PJ,

Ir"

St i a 2)

Binary melting-point-line of AsJ, + SbS, (tig. 3).

iG 10 yo 60 Jo PO com, y
: As),

| End Solidi- |

a | Initial Solidi- | be
Composition. | fying point. End mp. fying point. Initial mp.
| |
les ee. eae ll ks a a
/0(, by weight} mol. %) |
|| (corrected). (corrected).
AsJz3 AsJ3 ||
| ‘at |
Ao ——
| 2 | |
| 0 0 170.3 | 170.8 = | =
2353) |= (25 | 154975 156.5 || 149 | =
47.6 | 50 139.6 140.5 136 | 135
60.3 62.5 || 135.9 138.6 135.5 | 135
66.9 | 69 135.85 138.4 135.5 135
3.2 | 136.35 139.1 135 | 134
Sordi ee eS. ¥. ||) pel B22 140.1 137 135.5
; |
ine |) 100:=.> | 140.75 | = | — —
| | |

( 634 )

Binary melting-point-line of AsJ, + PJ, (fig. 4).

Composition ae = ID. aon
in 9% by pee ae Observed Temp. Observed Temp. Duration :
_ weight eke ‘calculated on

| End solidi. | Same nuinber

} ital | : End solidi- i . |
AsJ3 || Initial | Effect Aree Initial | Effect iving paint (Ok molecules

PJs AsJ3 PJ3

0 | 100 ||0 | 100 4) 138.4) = | 2. ll ais

| | o || ae

9.0| 91.0] 9.9} 90.1] 134.3] — ea ig0cl] 137.1) — |eats2.5]) =

12.8| 87.2|| 14.0 96.0l| 132.1 | — |ca. 125°] 194.9| — eata7 || =
16.8| 83.2\| 18.3| 81.7| 129.5| 68.5| — || 192.2| 69.1] — 20
18.5| 71.5|| 20.1| 79.91 1281| 69.8/ — || 130.8] 70.5] — 20
34.6| 65.4|| 36.9| 63.1] 116.7] 71.0) — || 119.0) wi.) — 110
45.6| 54.4|| 48.1) 51.9] 108.0] 71.6| — || 109.9] 72.3| — 140
63.5| 36.5|| 65.8) 34.2i| 92.1) 73.0) — o3/4\| astral aeeso
76.4| 23.6] 78.2) 21.8) 77.4| 72.3 \ca. 70 || 78.2| 73.0 |ca. 70.7) 240
g0.7/ 19.3|| 82.2} 17.8) 72.7/ — |ca. 66|| 73.4; — |ca, 66.5) ——
84.6| 15.4) 8.8 14.2) 70.2, — (ca 65 70.9) — (ca. 65.5| —
81.0} 13.0) 88.1} 11.9] 68.1.| — ca 64 || 68.75] — ca. 64.5) —
99.9| qes|| 92-9] 7-1l| 64.0| — ca, 62/| ‘65:5. =Seelicn moors] ieee
fo02| Mslmooe © || on) = | — Oo p= =

( 635 )

in regard to each other. The results of the determination of the
binary melting-point-lines are represented in the subjoimed tables
and in the fig. 3, 4, and 5.

Binary melting-point-line of SbJ, + PJ, (fig. 5).

Composition in Composition in Observed Observed Puree of
%/, by weight Mol. %J/ Temperature. | Temperature. Bficetineee:
——= = a — : (calculated
Initial End Initial End on a same
P Jz Sb J3 P J3 Sb Jz _| solidifying | solidifying | solidifying | solidifying Number of
| point point | point point | mols).
0 100 0 100 167.1 -- 170.3 — | --
P26 Dike 3.2 |) 9628) | 164.3 _ 168.0 --
8.6 | 91.4 10.3 89.7 159.1 | 52.8 | 162.55 | 53.25 100
(O17 || 890 |) oes 87.9 | 157.7 | 52.5 | 161.5 | 52.95 | —
Spel 64.9 39.7 60.3 | 135.4 | 55.85 | 138.05 | 56.3 360
60.4 | 39.6 65.0 35.0 | 108.2 | 55.85 | 110.15] 56.3 740
83.3 16.7 85.9 14.1 ee) |! Bio 7) 58.35 | 56.15 900
al : |
92.2 | 128) | 93-5 6.5 — 57.2 57.65 920
100 0 100 0 | 60.4 _ 61.0 - -

Fig. 4 needs no further comment: P./, and As./, form an isodi-
morphous niaing series, with a transition-point at 73°.5 C.

The liquid coexisting with both mixed erystals, contains about
82 mol. ° , P./,, whereas the two mixed crystals have at that tempe-

( 636 )

rature a composition of about 75 mol. °/, of PJ, and 18 mol. °/, of
PJ,, respectively ; the solidus-line .at the side of the AsJ, is so
steep, that only a few points could be indicated with some degree
of accuracy.

The crystallographic measurements of P/, and As.J/, left, up to
the present, some doubt as to the isomorphism of the two compounds.
According to NorprnskséLp') PJ, is hexagonal (or trigonal ?) with
a:¢=1:1, 1009 with {0001} and {1010}, when recrystallised from
S,, or with {1010}, {0001} and {10123 from the melt ; twins accord-
ing to {1122}.

On the other hand, As./,, according to FrimpLANDrER ’), is trigonal
with a@:¢ =1,2998 with base {211}, {110}, 411} and complete cleavage
parallel {111}.

These data indeed do not lead without further confirmation to
the assumption of an isomorphism. The melting-experiments now
prove, that As/, and P./, do possess indeed a different symmetry ;
it is not improbable that each of the compounds still exhibits a meta-
stable modification, which corresponds with the more stable form of
the other substance.

The case represented in fig. 3 (A./, + S4/,) also leaves but little
doubt. We have here an isomorphous mixing series with a minimal
temperature.

SbJ,*) is trimorphous; the rhombic (yellowish-green) as well as the
monochnie (greenish-yellow) modification, are however metastable,
monotropous forms are only obtamable under very particular con-
ditions. On the other hand, the mixed crystals are trigonal and coloured
red, just like the more stable, trigonal, red modification of .SdJ/,.

The trigonal S0./, shows {111}, {100} and {110}; the angles found
by Cookr, are, however, not correct as shown by Negeri (Rivista di
Min. Crist. Ital. Padua 9. 48. (1891)). For the angle « he finds 50°40’
whilst that for As-/, was determined as 51°20’.

All this, in connection with the melting-point-line found, points
sufficiently to an actually existing isomorphism between the two
compounds.

The case of fig. 5 (Sb/,+ P/,) points to an ordinary mixing
series with an eutectic temperature at 56°.

Whereas in the case of //, and As./,, there was already present
an uninterupted mixing series with a large hiatus, the miscibility in

1) NORDENSKJOLD, Z. f. Krist. 8, 214 (1897).
®) FRIEDLANDER, Bihang K. Svenska Vet. Acad. Stockholm (1874).
3) Cooke, Proc. Amer. Acad. 18. 74. (1877); Abstract Z. f. Krist. 2, 634.

( 637 )

the case of PJ, and S4/, has completely disappeared, or at least
been limited to concentrations in immediate proximity to the axes.
All this is systematically connected with the steadily increasing
distance between the elements phosphorus, arsenic, and antimony,
in regard to each other.

November, 1911. Inorg. Chem. Lab. University.
(rroningen.
Physics. — “The Thermomagnetic Properties of Elements.’ By

Mr. Morris Owen. (Communicated by Prof. H. E. J. G. pu Bots).

A short account was given in a recent communication ') of expe-
riments upon 43 elements at ordinary and high temperatures. The
present investigation was undertaken with the idea of increasing the
number of elements to be experimented upon, and also of finding
the effects of low temperatures upon the magnetic susceptibility.

I. Keperimental Arrangement.

This has already been deseribed in detail. It is only necessary
here to mention that the method of Curm and previous investigators
was employed with one exception, viz. that the investigated substance
was not placed at that point of the magnetic field where ,. 05,/dy
is a maximum.*) This was due to the fact that about this point the
field-variation can be quite considerable, especially in the case of a
substance of comparatively somewhat large dimensions. In fixing on
a point at which to work at more stress was laid upon the
attainment of a maximum field, because the iron impurities then exert
a proportionally smaller detrimental influence.

Three different adjustments of the apparatus were employed differing
only in the length and thickness of the suspending silver wire of
the torsion balance, and the inclination of the axes and the distance
apart of the two cores of the electromagnet. The latest large type
model of the pv bors electromagnet, recently described in these
Proceedings, was placed at my disposal. The whole arrangement
for ordinary temperature work was much more sensitive than any
used previously.

The sensitiveness of the torsion balance could be varied: the
directive force per unit degree torsion was measured in the ordinary
way by means of applied additional moments of inertia.

1, H. pu Bots and K. Honpa, These Proc. XIl p. 596.
3) K. Honpa, Ann. d. Physik 32, p. 1027, 1910, Fig. 1.

45
Proceedings Royal Acad. Amsterdam. Vol. XIV.

( 638 )

Silvered Dewar-vessel. This had an inner diameter of 15 mm.
and was 170 mm. long. It contained a copper tube, closed at its lower
end, of 10 mm. diameter, in order to protect the investigated sub-
stance from the direct effects of the liqnid aid. This was poured
into the interspace between the two tubes. It was found advisable
to work in nitrogen at low and ordinary temperatures, and in carbon
dioxide at high temperatures: this has the further advantage of no
correction being necessary for the magnetisation of the surrounding
atmosphere. To determine the low temperatures, the thermo-element
was standardised by means of a platinum-resistance thermometer.

Electric oven. This consisted of a porcelain tube wound with
platinum wire and insulated with kaolin powder. A temperature of
1250° could be attained, measured by the above-mentioned thermo-
element connected to a pyrometer: this had previously been stand-
ardised by observations on well-known melting-points.

Notation.

a, Atomic weight. 6, Temperature.
§,, Field intensity. Yb Specific susceptibility.
0.5,/dy, Field-gradient. yx, Iamit value of the same.

le Test-Samples.

The same difficulties were encountered as those enumerated by
Honpa. Of the 83 (70 + 13 “rare”) elements, 58 were tested; many
samples of the same element were supplied by different firms, and
gave in the majority of cases different results, not always explainable
by the influence of iron-impurities. Many of the elements were supplied
as pure as possible by Kani_paum and Merck. For particularly pure
specimens | am indebted to several chemists. It is important here
to mention that the iron-impurity is not homogeneously distributed.
This made it necessary for the same piece to be chemically analysed
as that magnetically tested. Apparatus containing iron in any shape
or form were carefully removed from the chemical room of the
laboratory, where the analysis was carried out.

If the susceptibility proves independent of the field, there can be
no question of a ferromagnetic impurity. It is imteresting here to
note that the magnetic method can be made more sensitive than the
chemical one in testing for iron. With the majority of the tested
samples however the curve showing the relation between the specific
susceptibility and the field took the form of a hyperbola; I calculated
the most probable value of y,, which would hold asymptotically
for an infinite field, by the method of least squares; and, in addition,

( 639 )

the influence of the ferromagnetic ingredient, which in the great
majority of cases was less than 10°/, of that which could be imputed
to iron in the specimen. As Honpa has already shown, the thermo-
magnetic properties also afford a test of purity up to a certain point.

As the insertion of my full tables and curves would require too
much space, a somewhat short discussion of my principal results is
given, no mention being made in most cases of those elements which
are independent either of the field or of the temperature.

Ill. Specific susceptibility*) at 18°.

Second Series. Contrary to expectations Mrck’s Li (4, =+3,11)
gave a higher value than KaHLBaum’s specimen (z,, = + 0,25), which
contained the lesser percentage of iron. Be, although containing 4°/,
iron, was still diamagnetic (— 1,03). It is noteworthy that the three
allotropic forms of carbon, viz. diamond, graphite, and amorphous
snow widely divergent results. The highest diamagnetic value (—0,71)
for amorphous carbon was obtained with that prepared from ordinary
sugar in this laboratory. Gas carbon, taken out of the ordinary iron
retoris of a gasworks, gave a still higher numerical value (— 1,81).
Ordinary are-carbon gave a value of — 1,82. Ceylon graphite gave
very interesting results, for in addition to showing a decided directional
effect, incapable of quantitative measurement with the apparatus
used, it also gave in one direction the highest diamagnetic value,
as yet achieved (— 15,0). The powdered specimen gave a constant
mean value (— 4,0).

Third Series. Two Me specimens extracted from the same lump
of material, and containing different amounts of iron, gave different
values (+ 0,31 and + 0,26). The iron-impurities in three Al specimens
tested were somewhat considerable. The NruHauseN specimen gave
ultimately the lowest value (+ 0,58). A difference was shown to
exist between Si crystalline (— 0,13) and amorphous (— 0,15). This
is not the case with regard to S crystalline and amorphous, a fact
previously pointed out by Currie.

Fourth Series. In eontradiction to Honpa’s result, K gave a
constant value (+ 0,58). Both the KanriBaum- and Merck-specimens
of Ca contained much iron: whereas the first was constant (+ 1,1),
the second varied considerably with (+ 3,7). It is noteworthy that
in the case of Ti the specimen which contained the lesser percentage
of iron was more paramagnetic than the other. The best Cr specimen
came from KawiBaum (+ 2,87); Merck’s specimen (+ 3,90), on the

1) Everywhere expressed in millionths.

43*

( 640 )
other hand, proved independent of .6. The results obtained by various
experimenters with Mn show that different specimens of this element
behave quite differently. This series is throughout paramagnetic, the
susceptibility increasing with the atomic weight.

Fifth Series. Two Ga specimens from the same flask gave
different results. One of them proved independent of the field (—0,12);
the other specimen, however, gave the higher numerical value
(— 0,24). Ge varied only slightly with (— 0,12). All the other
elements of this series are in sufficient agreement with previous
experimenters and it is throughout diamagnetic.

Sixth Series. Rb gave a small constant paramagnetic value
(+ 0,08). The two Sr specimens tested varied considerably with .5,
and although paramagnetic within the field-range applied, gave ulti-
mately diamagnetic values for x,. Merck’s Zr (— 0,44), although
dependent upon 9, agrees well with the value found by Honpa for
the pe Hain specimen (— 0,45). Although PoGeunporrr found his
Nb diamagnetic, bis result is stil questionable on account of the
paramagnetic values found by Honpa (+ 1,29) and myself (+ 1,65)
for specimens of quite different origins. Different results were obtained
with four Mo preparations, all of different origins: the lowest,
numerical value was given by Mprcn’s specimen (+ 0,56). Honpa’s
value for this element is much smaller (+ 0,039). Ru (+ 0,48)
decreased rapidly with the field. Rh (+ 1,05) and Pd (+ 5,2) agree
sufficiently with previous values.

Seventh Series. With the exception of ordinary tetragonal
tin the elements of this series are diamagnetic. Several Ag specimens
were investigated, that from Heranus giving a value (— 0,20) iden-
tical with that of Honpa’s. I obtained a higher diamagnetic value for
Cd than any previously found (— 0,18). My In specimen, in contra-
diction to the former value, was throughout diamagnetic (— 0,11).
The results for tin and greytin must form the subject of a special
paper. All my Sb > preparations showed a magnetocrystallic action.
On account of the fact that the values obtained differed by about
50 °/,
of the crystal in the magnetic field, it is a matter of difficulty to
fix upon the value of ¥. The powdered material gave a value
(— 0,82) approximately half way between the two extreme values.

with the same specimen, depending on the position of the axis

Te and I agree well with previous values.

Kighth Series. Six elements of this series stood at my disposal.
It is noteworthy that Cs (—- 0,10) is the only member of the alkali
metals which is diamagnetic, Ba (+ 0,93), containing 15 °/, Hg, was
non-homogeneous. La (+ 1,04) conjecturally contains admixtures of

es ( 641 )

other cerite earth metals. Two Ce specimens of different origins
showed a satisfactory agreement (+ 15,4). Pr (+ 25,2) and Nd (+ 36,2),
in spite of the high numerical value, exceeded only by that of
oxygen, were independent of -9.

Ninth Series. Both the Mrrck (+ 22,3) and the pr Hatin
(+ 28,3) Er specimens were rich in iron, and varied rapidly with 9
and are certainly to be considered only as very impure powdered
mixtures of several elements.

Tenth Series. This series was completely represented and
throughout paramagnetic. Ta (+ 0,81) and W (+ 0,22) gave smaller
values than those previously found. Two Os specimens from the
same flask gave identical values (+ 0,048). Two small pieces of Pt
from the Hrrarvs supply were tested, and both varied with . The
calculated x, in each case is smaller than the value of y% found by
Honpa, who, in additiou, found his specimen independent of the field.

Eleventh Series. This series again was completely repre-
sented and proved throughout diamagnetic. The calculated y,, for the
Heragus Aw(—0,15) agrees well with Honpa’s final value. This is
not the case with the specimen from the same source of supply. A
colloidal specimen gave a constant diamagnetic value (— 0,24).
Although only a trace of iron was detected in Hg, this was sufficient
to cause the specimen to vary slightly with 5. This is one of the
eases in which magnetic testing for iron is superior to chemical
analysis. The calculated y, was —0,18. The colloidal preparation gave
a somewhat higher numerical constant value (—0,23). Powdered
electrolytic Bi gave a susceptibility of — 1,40. Two specimens from
the same flask of the colloidal preparation were investigated: one
gave a constant value (— 0,45), the other, although containing
exactly the same percentage of iron impurity varied with the field
—— == (0) 5i1)), :

Twelfth Series. Th(+ 0,081 and + 0,164) contained 15°/,
thorium oxide: this is not of itself sufficient to explain the observed
discrepancy in the two above results: in all probability this arises
from the non-homogeneity of the iron-impurity. Three different
specimens of U/ were tested: they were all very rich in iron. The
smallest calculated value tor ~, was + 2,60.

The curve 4= funct. (a) appears to be rather intricate. According
to the above remarks, a more or less great uncertainty still exists
with regard to many of the solid elements, which at present cannot
be overcome. Mn is a good example of this. We can only advance
conjectural hypotheses to explain such phenomena. The omissions in
the curve are not so great as formerly: if anything, however, the

( 642 )

curve is more intricate than before, although a general relation to
the periodic system is still observable. The influence of polymorphy
is very pronounced, and the choice of the allotropic modification to
be considered offers some difficulties. The general shape of the curve
has been deseribed in the previous communication. Beryllium has added
a new negative peak to the curve, which divides itself into three
analogous parts. Magnetic analogies of secondary importance also
exist: elements which belong to the same group and exhibit analogous
chemical properties are, in many instances, situated on corresponding
parts of the curve.

IV. Susceptibility at low and high temperatures.

At low temperatures only readings by increasing temperatures were
possible. At high temperatures the path of the curve y = funet. (4)
was, with the apparent exception of gallium, the same for increasing
and decreasing temperatures.

Second Series (hi, Be, b, C). The susceptibility of Be increased
numerically with the temperature remaining constant above +- 700°.
One may conclude that this is partly due to.the iron impurity present.
Diamond, are carbon, and the amorphous modification exhibited a
constant diamagnetic value. The mean susceptibility of powdered
Ceylon giaphite decreased rapidly with the temperature, and particularly
so between — 170° and + 18°.

Third Series (Na, Meg, Al, Si, P, S). The susceptibility of
Me decreased somewhat rapidly from — 170° upwards. This result,
as Honpa has already shown, is due to iron-impurity. The diamagnetism
of crystallised Si was only a little greater at — 170° than at + 180;
% was constant with amorphous Si.

Fourth Series (K, Ca, Ti, V, Cr, Mn). The paramagnetic
susceptibility of Ti decreased appreciably between 170° and — 80°.
In contradiction to Honpa’s results for the same element, my specimen
of Mn remained constant between — 170° and about + 500°, after-
wards suffering a slight decrease; at about + 1015° a rather large
sudden increase of ~% was noticed, which was reversible.

Fifth Series (Cu, Zn, Ga, Ge, As, Se, Br). On increasing the
temperature from 170°, Ge showed a small numerical decrease ;
y% remained constant above + 200°, increasing suddenly at the melting-
point (+890°); above +900° y numerically mereased. At the melting-
point of Ga (+30 ) a sudden numerical decrease of y was observed. The
molten element was very weakly diamagnetic, and its suseeptibility
afterwards increased very slowly with the temperature. On cooling,
this weak diamagnetism was still observed until a temperature of

( 643)

+ 16° was reached, at which point the element was still liquid ;
this very characteristic undercooling is known to be possible down
to 0°. As and Se scarcely varied with the temperature. No sudden
discontinuity in the value of % was exhibited by Br at its melting-
point (— 7°).

Sixth Series. (Rb, Sr, Y, Zr, Nb, Mo, Ru, Rh, Pd). The value
for Y decreased rapidly as the temperature increased: this substance,
however, in all probability, contains admixtures with the other highly
paramagnetic ytter-earth metals. From — 170° to + 15°, x for Zr
showed a slight numerical increase. The influence of temperature on
paramagnetic Nb was very small. With Mo, x decreased very slightly
as the temperature rose. A decrease was also noticed in the case
of Ru. Rh exhibited a practically linear increase of zy with the tem-
perature: x for Pd suffered a somewhat large decrease from —170°
upwards.

Seventh Series. (Ag, Cd, In, Sn, Sb, Te, I). The diamagnetic
susceptibility of Ag between — 170° and + 18° increased slightly
numerically, while that of In and Te numerically considerably de-
creased. I exhibited a numerical increase in the value of .

Highth Series. (Cs, Ba, La, Ce, Pr, Nd). Almost all these
elements were investigated at low and high temperatures. Cs showed
no deviation from the linear character of the (y, 6) curve at its
melting-point: the same remark applies to all the alkali metals.

The value for Ba increased between — 170° and + 18°.

Only a small decrease was noticed in the case of La on raising
the temperature from — 100°; the decrease was somewhat larger
between —170° and — 100°. Ce (Merck) showed a decrease of
susceptibility as the temperature increased: but another specimen
exhibited a sudden large increase at about — 110°, which is rather

difficult to explain. In the case of the latter specimen, ~ remained
constant between — 170° and —140°. Above — 80° the value was
only slightly greater than that of the Merck specimen, and the courses
of the two curves are nearly similar. Pr and Nd decreased as the
temperature rose.

Ninth Series (Er). A decrease of x with increasing temperature
was also observed in the case of this element.

It was found that the four highly paramagnetic elements Ce, Pr,
Nd, Er only very approximately obeyed Curin’s law for para-
magnetic bodies.

Tenth Series. (Ta, W, Os, Ir, Pt). The susceptibility of Ta
decreased slightly as the temperature increased. y in the case of Ir
increased with 7. The reverse is true in the case of Pt.

( 644 )

Eleventh Series (Au, Hg, Tl, Pb, Bi). x for Hg between —170°
and — 150° was approximately constant, and afterwards underwent
a gradual numerical increase: at the melting point (— 39°) it suffered
a sudden change. The susceptibility of Tl numerically decreased

between — 170° and + 18°. The same was true for Pb, the change
in this case being very slight. For Bi, ,=—1,58 at —175°, a

value which agrees well with that found by FLemine and Dewar
(— 1,61 at —182°)'). With regard to some colloidal specimens of
this series, 7 for He was throughout constant: that of Au was
constant between — 170° and + 50°, afterwards decreasing slightly
numerically. The character of the (4,7) curve for colloidal Bi was
very peculiar.

Twelfth Series. (Th, U). The susceptibility of Th increased
with the temperature. The value for U on the other hand decreased.

On the whole, we may say that the curves 7 = funet. (4) show
most varied aspects. Roughly, the elements are more or less distributed
over the six possible classes, viz. para- or diamagnetic, each constant,
increasing or decreasing as the temperature rises. Only seven dia-
magnetic elements do not vary within the whole temperature range,
amongst them the three that Curim happened to investigate. The
thermomagnetic properties also show a certain correlation with the
periodic system.

Physics. “Investiaations concerning the miscibility of liquids.”
By Prof. J. P. Kumnen.

Several years ago | began a systematic experimental investigation
of the miscibility of liquids, in particular as regards the influence of
temperature and pressure, or to express it differently an investigation
into the shape and the change of shape of the projected liquid plait
of the y surface and its position relatively to the vapour-liquid plait *).

A fertile combination and one which turned out interesting in many
respects was found in the saturated hydrocarbons with the lower
alcohols. The investigation of these and other mixtures which was
discontinued from various causes was recently taken up again and I

') J. A. Fremine and J. Dewan, Proc. Roy. Soc., 68, p. 311, 1898.

*) I take this opportunity to say that in my communication of October 28 on
the geometrical properties of these plails 1 did not wish to imply anything but
what I thought I had distinctly expressed and that the implications which are
attributed to me by Prof. van Der Waazs in his paper of November 25 are
entirely outside my meaning.

( 645 )

propose to communicate the results to the Society from time to time.

A decided gap in the research was the absence in the series of
hydrocarbons of a term with four carbon atoms and in one of my
last papers on the subject ') I stated, that the preparation of normal
butane had been tried and that it had not met with the desired
suecess. The method was by electrolysis of sodium propionate, which
yields a very impure gas, the chief products being carbon dioxide
and ethylene. The treatment with bromine for the absorption of
‘ethylene showed that bromine acts on butane anda repeated attempt
to procure pure butane by this method did not succeed.

Better methods were not then available. In the mean time two
new methods of preparing hydrocarbons from bromides or iodides
have been published: one by the action of sodium dissolved in liquid
ammonia (Leseav) and the other (GriGNarD) with magnesium. Butane
has been prepared by the first method by Lrerau himself *) and by
the second method by Ovépinorr *).

The results obtained by them do not agree accurately. I have applied
both methods and again obtained results which do not quite agree
either with each other or with those of the other investigators. [|
subjoin a table of the critical constants and boiling points.

Normal Butane.

Method of

Observer preparation Crit. Temp. Crit. press. Boiling point
Lebeau Lebeau 151— 152 0.5
Ouédinoff Grignard 146.5 0.6
Kuenen Electrolysis 158.5

» b 145.5 —17
(3) Lebeau 148 7 + 39
(OD) 5 Grignard 150.8 37.5 — 0.1

The experiments communicated below were made with the two
samples of butane indicated as (a) and (4)‘*).
In the mean time some observations have been made by TimMeRMANS

1) J. P. Kuenen. Phil. Mag. (6) 6 p. 647. 1903.

*) P. LeBeau. Bull. Ac. R. de Belg. 1908 p. 300—304.

) OUEDINOFF. Bull. Soc. Chim. de Belg. (23) Juin 1909.

) Later on I hope to communicate a set of physical constants of butane obtained
with sample (b), mainly determined by S. H. Visser, science student at Leiden.

( 646 )

and KouNstaAmMM') on mixtures of butane with a few other substances,
butane having been given to them by Ov&éornorr.
I begin by communicating a few critical endpoints?) which | have
determined.
Critical endpoints.

methylalcohol +- isopentane 10.5

D + n. pentane 19.4 *)

: + n. butane (6) 17.0(7. and KX. 16.6%)
aethylalcohol -+ isopentane 30

2 + n. butane (a) + 37.5.

The critical end-point for methylaleohol and normal butane agrees
well with the result of the other observers.

Very unexpectedly an entirely different result was obtained when
use was made of butane (a), although in its constants but little
differing from butane (4). This difference must be due to some
impurity and although I cannot throw any light on the nature or
action of this impurity, I will describe the observations, as they
have brought to light a new phenomenon, which appears to be
of interest.

When a mixture of butane (@) and methylalcohol was heated in
a compression tube (Cailletet) in the fpresence of the vapour, the
surface between the liquid layers disappeared about 22°, a somewhat
higher temperature than for a mixture of butane (4) (17°.0). When
however the temperature was further raised the meniscus soon
reappeared and the definite critical end-point was not reached till
38°. Beyond 388° no separation of two liquids took place. The
appheation of pressure revealed a similar abnormality: at tempe-
ratures above 22° a gradual increase of the pressure always had
the effect of making the meniscus grow faint and disappear and
afterwards permanently reappear.

It is not difficult to see what shape has to be attributed to the
liquid) plait in the v-v diagram in order to represent the above
phenomena. The fact that pressure ultimately produces separation

6) J, TimmMerMANS and PH. KoHnstamM. Proc. XIL 1909—10, p. 234 table on
page 239.

2, By critical end-pomt is meant the critical pomt of the liquid layers in the
presence of vapour, i.e. the point where the liquid plait touches the vapour-liquid
plait. In former papers | have usually called this point the critical mixing-point.

%) Determined by me on a previous occasion (|. ¢. p. 647) and erroneously.
attributed hy TimMERMANs and Konnsranm (lI. c.) to isopentane instead of norma

pentane.
4) 1. c. p. 239,

( 647 )

of the two liquids shows that the plait is open towards the «axis.
This is in aecordance with the result obtained by Timmermans’),
that the critical temperature of the liquids is in this case raised by
pressure, which means that beyond the critical end-point the liquid
plait lies outside the vapour-liquid plait with its plaitpoint turned
towards the latter. But the abnormal phenomenon was not noticed
by him, nor have I been able to reproduce it with mixtures of
butane (0).

If the liquid surface temporarily disappears as described, the plait
would have to consist of two parts as shown in fig. 1 where the

we

Fig 1.

relative position with respect to the liquid branch of the vapeur-
liquid plait is also indicated. It seems unnecessary to show in detail,
that the behaviour of the mixture under changes of pressure or
temperature agrees with the assumed diagram. In itself a diagram
of this nature is by no means improbable. In this connection it is
important to consider the behaviour of a mixture of methylaleohol
with isobutane as observed by Timmermans. The critical end-point is
in that case very near a point where the liquid plait divides and it
would be quite possible for the plait in the case of the nearly allied
normal butane to be divided in the manner assumed in fig. 4.
Further investigation of the phenomenon showed however that the
assumption was incorrect. It may be remarked that the observations
were extremely difficult owing to the great indistinctness of the liquid
surface compared to other mixtures (TimMErRMANS notes the same
peculiarity for mixtures of methylaleohol and isobutane). When I
repeated the observation under the most favourable conditions with
regard to illumination I found that the meniseus did not really

1) J. Tumermans. These Bruxelles 1911, p. 82.

( 648 )

disappear when it seemed to do so temporarily before, but as a rule
remained just visible in the form of a dark and sometimes slightly
coloured horizontai line near the axis of the tube.

The moment of minimum distinctness could be observed with fair
accuracy; in the table are given the observed pressures as also some
- three-phase pressures. The readings were not more accurate than to
about */, atmosphere.

Temp. Least distinctness at Three phase pressure :
14.0 — atm. 1*/, atm.
22.5 2 2

22.8 31/, =

24.2 Dts 2a
25.0 131/, -

25.5 16 —

26.3 2d fs 2"/,

27.2 25'/, —

28.5 33 —

29.3 36'/, _—

31.0 43 --

32.4 53?/, 3

33.7 62'/, 3)
36.8 75

37.0 78 —

38.1 = 40 /,

38.2 — Cr. end-point
38.6 84 —

The plait cannot therefore be divided as in fig. 1 and our suppo-
sition has to be modified in the sense that the plait is only strongly
contracted as in fig. 2.

Xe

|
| va 5

(——2
2 AB aaa

lig. 2:

But the facts speak against this supposition too; for with fig. 2

( 649 )

one would expect phenomena which also occur near a eritical point
e.g. a distinct change in the relative volumes of the two phases (at
38° this phenomenon was very marked) and a slow settling down
of the liquids after having been stirred up. This was not what
happened at the points of indistinctness: in so far as the meniscus
was visible at all, it reappeared (after stirring) comparatively quickly
as if there was a difference in density between the liquids of the
same order as at other points of the plait.

The only explanation which remains is that the refractive indices
of the liquids become equal: the plait need not have any abnormal
shape, but at some distance from the plaitpoint there is a point where
the two coexisting liquids have the same index, which point, if
outside the vapour liquid plait i.e. above 22°, may be reached by
change of pressure. Though this phenomenon cannot but be very
rare, it is not by any means impossible even with two pure substances.
When the indices of the components differ little, there is a chance
that the phenomenon may occur: there will be a maximum or
minimum in the indices in that case for one particular proportion,
Probably the index of butane is not much higher than that of methyl-
alcohol (this question is being investigated): the indistinetness of the
surface between the liquids even at a distance from the critical
region makes this probable.

The question remains what impurity may have occasioned the dif-
ference in the behaviour of the two samples of butane in this respect ').
I am inclined to think, that butane (4) was purer than butane (7),
especially as the experiments were made with the last remaining
fraction of the butane (a) available, in whieh an admixture of higher
boiling point may have been concentrated and during the operation
of introducing the substances into the compression tube some mois-
ture may also have got into the tube. However that may be it is
very remarkable that an impurity which cannot have been large, as
appears from the constants of the substance, can have had such a strong
effect on the mixing phenomena, shifted the critical end-point from 17°
to 38° and moreover produced the abnormality in the refractive index,

Finally it may be remarked, that the probable conclusion with
respect to the impurity of the butane (~), raises some doubt as to
the accuracy of the critical end-point for mixtures of ethylalcohol
and butane. I hope shortly to be able to throw more light on the
questions raised by these observations.

1) If the mixture contains a third substance it is properly speaking no longer
possible to represent the phenomena with the aid of a v.c-diagram, unless the
admixture is so slight that it may be disregarded for the purpose of the graphical
representation.

( 650 )

Physics. — “Note on the insulating power of liquid ar for high
potentials and on the Kerr electro-optic effect of liquid air.” By

Prof. ZEMAN.

1. Im a series of experiments undertaken in order to look
for an influence of an electric field on radiation frequency, an
account of which [ intend to publish rather soon, a small condenser
consisting of metal plates immersed in liquid air was made use of.
A selectively absorbing erystal the optical behaviour of which was
to be studied, when under electric influence, was introduced
between the plates of the condenser. A first question to be answered
relates to the value of the electric forces which can be sustained
by liquid au. The fact that the dielectric constants of various liquid
gases could be measured by Linpr'), Dewar and Friemine’), and in
the Leyden laboratory by HasknOuri*), proves that the gases in-
vestigated, among which figure also oxygen and liquid air, are good
insulators. The methods of measurement used only involve, however,
low voltages. HasrenOurL gives for the sparklength at the terminals
of his secondary wire 0.05 m.m. The small condenser in FLEMING
and Drwar’s experiments is charged with 100 volts. The excellent
insulating power of liquid air under still much higher potentials,
is illustrated in a separate experiment due to the last named
physicists, but which only came under my notice while writing
the present paper‘).

The high potentials in my experiments were obtained by means
of a motor-driven influence machine. In order to keep the potentials
as constant as possible, the arrangement given in the subjoined figure
was used; it is the one often employed in analogous investigations. The
condenser plates are connected to the inside and outside surfaces of
a Leyden jar; between the machine and the jar a very high resis-

1) Linpe. Wiedeman Ann. 56. p. 546. 1895.

*) Furmine and Dewar. Proe. R. 8. London. p. 358. Vol. 69, 1896.

5) Hasenoure. Leiden, Communications n°. 52. These Proc. I, p. 211.

*) “As a further instance of the very high insulating power of liquid air, we
may mention that we charged the small condenser when immersed in liquid air
with a Wimshurst electrical machine, and, after insulating the condenser and
wailing a few moments, closed the terminals of the condenser by a wire, A small
spark was seen at the contacts. We have constructed a little Leyden jar, the
dielectric of which was liquid air, and the coatings the aluminium plates. This
liquid Leyden jar held its charge perfectly.” 1. c. p. 361.

It would have been possible in the light of this experiment to shorten some-
what our §§ 1—4.

( 651 )

tance is introduced. Two fine points or two bundles of fine needles
shunt the machine. By varying the distance between the points or
the needles the potential can be regulated to a given value.

2. The small condenser was placed inside an unsilvered Dewar

©

Fig. 1.

vacuum vessel of 5,5 em. internal diameter. The plates were of
4.5 em. length, 1 em. width, their distance being 3 mm. They were
soldered to copper wires, covered by glass over their entire length.
The wires passed through the ebonite cover of the vacuum vessel,
their distance being 2,5 cm. It was immediately clear that liquid
air was a very perfect insulator. Loud, brilliant sparks could be taken
by means of a discharging rod from the wires in the neighbourhood
of the ebonite cover. The potential could be estimated by means of
a spark micrometer. Potentials of 30.000 Volts were obtained; this
gives, the distance of the condenser plates being ‘/, em., an electric
force of 90.000 Voli/em. This value, however, does not indicate the
maximum electric intensity in liquid air, nor the one always obtainable.

3. After continuing the observations for a short time the intensity
of the sparks in the micrometer rapidly diminished. Even after
removing the micrometer none or only poor little sparks could be
got from the wires entering the vacuum vessel. It seemed probable that
the moisture of the atmosphere after condensing on the ebonite cover
produced a conducting layer which prevented any considerable dif-
ference of potential between the wires. A small box of glass and ebonite
was placed on the ebomte cover and the air of the box dried by
means of some chloride of calcium. The result was extremely satis-
factory. There was now no difficulty of maintaining very high poten-
tials for hours.

4. Next to the external perturbations resulting from a deposit on
the ebonite cover, two other causes of irregularities, originating in
the liquid air may be mentioned. One is due to small erystals of
i¢e and solid carbon dioxide present in the liquid air. These small
crystals are attracted by the electrically charged plates, the liquid
air becoming at the same time very transparent. A discharge between
the plates is much favoured by the crystals. As soon as the plates
are uncharged the crystals disperse into the liquid. If the air is
freed from these crystals by filtration’), then there is still another
cause of disturbance, viz. the generation of gas in the liquid ai.
The small bubbles take their origin from one or two points of the
inner surface of the vessel, and the succeeding bubbles form a file
moving irregularly through the liquid. As long as the small bubbles
remain outside the space between the condenser plates they do not
interfere with the voltage attainable between the plates. If, by some
hydrodynamical accident, a gas bubble arrives between the plates
their difference of potential immediately goes down, the discharge
taking place under intense ebullition of the liquid.

The general conclusion to be drawn from these considerations is,
that for attaining high potentials the liquid air must be carefully
freed from impurities and that the visible generation of gas must
be reduced as far as possible; the Dewar vacuum vessel must be in
excellent condition.

5. After being satisfied that it was possible to maintain high
potentials for a considerable time, I tried to prove still more con-
vineinely that large electric forces exist in the interior of the
liquid air. For it were possible, though rather improbable, that a
surface layer existed at the surface of the condenser plates so
that there is a large potential gradient in the neighbourhood of the
plates, but only a small one in the liquid air. If we succeed, however,
to discover the Kerr electro-optic effect in liquid air, we have
proved at the same time the existence of large electric forces in the
interior of the liquid.

6. It was to be expected that the electric double refraction of
liquid) air shall be small. Recently R. Leiser?) succeeded in measu-
ring the Kerr electro-optic constant of several vapours and gases.

Notwithstanding his method was very sensitive he did not succeed
in establishing an effect, even if the gases were under a pressure of 2
atmospheres, for nitrogen, oxygen, carbon monoxyde and nitric oxid.

1) The liquid air, which I had the pleasure to receive many times from the
Leyden cryogenic laboratory, was remarkably transparent.

*) R. Letser. Physikalische Zeitschr. p. 955. XU. 1911.

( 653 )
The same vaccuum vessel with immersed condenser referred to
above (§§ 1—+4) was also made use of for experiments concerning
electric double refraction of liquid air. The optical arrangement is

partially identical with the one recently described *) and figured below.

w~
C

te)
V

SK:

Fig. 2.

The light of an are lamp J, traverses the nicol V,, then the
compensator, the vacuum vessel with condenser, the nicol V, and
is finally analysed by means of a low dispersion spectroscope. An
image of the black band exhibited by the compensator between
crossed nicols is projected upon the slit of the spectroscope. In the
former experiments referred to the spectroscope was absent.

ihe prismatic analysis had the following meaning. As is well-known
the absorption spectrum of oxygen exhibits conspicuous bands. They
are strongly developed by the 5.5 em. of liquid air. As the vacuum
vessel is not closed, and as the boiling-point of nitrogen is lower
than that of oxygen, the former gas evaporates more quickly and
the percentage of oxygen of the residual gas becomes gradually
high. The wavelengths of the oxygen bands have been measured *)
by Ouszewski, Liveine and Drwar, and Bacorr. The most conspicuous
bands, in the most luminous part of the spectrum, are at 581—573
and at 481—478. It seemed possible that the electric double refrac-
tion could have a considerable value in the neighbourhood of the
absorption lines, being insensible in the other parts of the spectrum.
In that case an effect would become apparent only by spectral
analysis. In the cases of magnetic double refraction and of magnetic
rotation of the plane of polarisation in sodium vapour the absorption
lines indeed are lines of exception.

7. Before communicating the results of the investigation for double
refraction, a difficulty in the observation must be mentioned. It is
due to the strained condition of the imperfectly annealed walls of
the vessel, causing irregular double refraction. As the four glass
walls to be traversed by the light are all strained, it is not a matter

1!) P. Zeeman and C. M. Hoogexsoom. These Proceedings November 1911.
*) Kayser. Handbuch. Band III. S. 357,

44
Proceedings Royal Acad. Amsterdam. Vol. XIV.

( 654 )

of surprise that it is only after some trials that a part of the glass
wall is found remaining dark between crossed nicols. But even then
the dark band, which is so extremely sensitive to small traces of
double refraction, may be invisible. It is rather easy to project on
the slit the black band of an ordinary BaBinet-compensator. These
compensators however proved to be not sensitive enough. At last
we found a small part of the walls of the vacuum vessel which
was in a state of ease, and admitted an observation to be made
with a bar only slightly loaded. Probably some compensating device
might be used with advantage (see § 9).

In the field of view of the spectroscope now appears the con-
tinuous spectrum with the vertical absorption lines due to oxygen
and with an approximately horizontal band, which must change its
position by eventual double refraction.

8. With this optical arrangement it was observed that by the
eradual charging of the Leyden jar the horizontal band was displaced
downwards; at a discharge of the liquid air condenser the band
jumped back in its original position.

The double refraction is clearly visible along the whole spec-
trum. In the neighbourhood of the absorption bands no singular
behaviour of the refraction was observed. The changes in the
neighbourhood of the absorption bands certainly were not very
large in comparison with the whole amount of double refraction.
It is interesting to compare this result with observations of ELtas *)
concerning magnetic double refraction in a concentrated solution of
erbium nitrate. Also in that case only very small anomalies were
observed in the neighbourhood of the absorption lines.

Probably the absence of any large anomaly is in both cases due
to the want of steepness of the curve representing the index of
absorption as a funetion of the frequency.

9. In order to fix the sense of the electric double refraction in
liquid air and to attempt at a rough approximation of its order of
magnitude the following experiment was made. After the removal
of the vacuum vessel (see fig. 2.) a thin strip of glass was intro-
duced in the beam of light.

By compressing the strip in a vertical direction the dark band in
the spectroscope moves downwards. Comparison of this result with
§ 8 shows that the electro-optic effect of liquid air is positive, like
carbon disulfide.

The magnitude of the displacement in the case of the experiment

1) Exias. Verhandl. deutsch physik. Gesellschaft. S. 958. 1919.

( G55 )

with an electric field of 50.000 Volt/em. is comparable with that
caused by the application of 1000 gms. on a strip of 15 mm. width.

According to Wertuem (Mascart. Traité d'Optique T. 2, p. 232)
a load of 7 to 15 kilograms, say 10 kilograms per millimetre of
width produces a relative difference of phase of '/, 2, so that with
the strip under consideration a load of 140 kilogrammes would be
required. ’) The estimated phase difference is therefore of the order
of */,4/140, the electric force being 50.000 Volt/em. From these
data would follow a value for the Kerr electro-optic constant of
liquid air (oxygen) about 20 times smaller than that of carbon
bisultide.

Hence it need not astonish us that nobody has as yet succeeded in
measuring the mentioned constant for oxygen under atmospheric
pressure. Our numerical determination for liquid air has to be
repeated with a better vacuum vessel. It must not be overlooked
that the preceding observations (§§ 6

9), though satisfactory so far
as they go, intend nothing more than establishing the existence of
an effect and its order of magnitude; we see in its existence a very
direct proof that liquid air is a substance, which represents extremely
closely an ideal liquid insulator.

Physics. — “Contribution to the theory of binary mixtures.” XVII.
By Prof. J. D. vaAN DER Waals.

The concentration of the gas phase between that of two
coexisting liquid phases.

In the preceding contributions I discussed some forms of the
curve for the course of 7, 2-figures of the plaitpoints. Leaving the
cases in which closed figures occur, or those in which these curves
do not extend to =O and «x=—1, on one side, I have only to deal
with the cases beginning in the point c=Oand 7—7;,, and termi-
nating at e=1 and T= 7;,. As such a curve must have a gra-
dual and continuous course, and as no double points and cusps can
oceur in it, the course is always comparatively simple. Thus in the
case treated in Contribution XIII, and drawn already in 1905 (These
Proce. VIL p. 184) only a highest and a lowest value occur in fig. 3.
Some particularities are, however, not perfectly accurate in this

1

figure. So both in the highest and in the lowest point must be

v

1) c.f. RaYveies. Phil. Mag. (6) 4. p. 678° 1902.

44*

( 656 )

equal to 0, because these points are heterogeneous double plaitpoints,
; aT dp . :
and in such points both os and 7, 8 2er0. In fig. 40 of contribu-
tion XIII, however, this has already been paid attention to. Besides
in the figures mentioned the course has been indicated for the 7',7-
curve of the coexisting phases. As there can be three coexisting
phases for given 7’, this curve too must possess a maximum and a
minimum value of 7. At such a value of 7’ the x-values of two of
the three coexisting phases coincide, and they indicate the two tem-
peratures between which three-phase pressure can exist. The three-
phase pressure exists then between two temperatures, the higher of
which is below 7,4, and the lower above 7',;,. This same simple
form of the 7'v-ligure comprises a number of eases which differ
from a physical point of view.

Thus Tnax and 7’,;, can both be higher than 7. For this case
the curve was drawn attention to for the first time in consequence
of the observations of Kurnen on mixtures of ethane with higher
alcohols. Then 7%, is of course higher than 7%. But as second case
Tin can be lower, even much lower than 7},; then Ty, need not
be greater than 7%, and 7%, can even lie far below 7);,. Whether
retaining the existence of three-phase pressure also the intermediate
case (7), equal to or almost equal to 7%) can occur, we have not
yet succeeded in deciding. At first sight it seems unlikely. but not
impossible. It should be borne in mind that for the possibibity or
non-possibility of the existence of this three-phase-pressure not only the
value of 7, and 7, will be decisive, but also that of pg, and pa, ,
and these latter values can differ greatly with equality of the criti-
cal temperatures if the size of the molecules differs much.

If we keep to the raie to place the components always in such
a way that first a maximum, and afterwards a minimum value
oceurs, there are only two cases viz.: 1. 7; > T;, and 2 Ty, < 7;,.
Of course with reversal of the two components first a minimum,
and then a maximum value for 7’ would occur, but this would of
course not be a new case.

But it is not my purpose just now to discuss the particularities
which refer to this, any further. I will only point out that if we
may assume, as has been tacitly supposed up to now, that for given
T’ the saturation pressure of the substance with the greatest value
of 7% is smaller than that pressure for the other component, we
always find ihe value of « for the gas-phase in case of three-phase
pressure outside the values for the two liquids, at least if no new
circumstance is taken into consideration. And this circumstance con-

( 657 )

cerning the concentration of the vapour phase has led me to put
the question: “What must be the shape of the 7\7-line for the
course of the plaitpoints that the concentration of the vapour phase
be between that of the two coexisting liquid phases?”

For that this will frequentiy occur, is certain. And without
examining for the moment whether retaining the discussed shape
with a maximum and a minimum unchanged, this can be brought
about through a deviation from the supposition about the value of
the saturation pressures, which was stated above, I will show by a
modification in the course of the Zyxz curve, which I had considered
possible for a long time, that the case that the concentration of the
gas-phase lies between that of the liquid phases, can be accounted
for. At the conclusion of this communication it will however have
appeared that strictly speaking the modification which will be applied,
is not necessary.

To render plausible the modification which I want to apply to
the course of the Zx-curve, and which I have already drawn
(Fig. 43 of this Contributions), I consider the case that for a binary
mixture for which three-phase pressure occurs, the value of the
critical temperature for phases taken as homogeneous, would possess
a minimum. If for such a mixture no three-phase pressure occurs,
the phenomena are known.

The 7T\x-curve for the plaitpoints slopes down on both sides to a
certain minimum value, which is not very far from the value of «
at which the critical temperature of the mixture taken as homoge-
neous has the minimum value. Also the p,z-curve for the plaitpoints
is known, and this has a still simpler shape, for it has neither
minimum nor maximum value. If we assume the size of the molecules
of the first component to be greater than that of the second, the
p.t-line is ascending throughout, just as is the case with the p,a-
line for the critical pressures for homogeneous phases. The latter is

a
a=
; a ia dp ee: a db _@
namely proportional to — or — —, and — =— — ———. If -
lb? b b da b dx Lb? dx b
: are db : dp. o : ;
is minimum and A negative, then — is positive even in the point
ax Av

where 7’ is minimum.

The principal features of the spinodal curve are also known. It
consists of a liquid branch and a vapour branch, which intersect at
an acute angle at the minimum plaitpoint temperature, and move
further apart on the left and on the right of that point of intersection.

( 658 )

| suppose that this point of intersection lies very near the first com-
ponent, so at very small value of a. As 6 decreases with «, the
point in which at the same value of w a value of p on the liquid
branch and on the vapour branch of the binodal line are equal, lies
on the righthand side of the point of intersection of the two branches.
As we know the value of wv, for which this equal value of p occurs,
is variable with the temperature, and that in such a way that the
distance between the two points mentioned increases with the tem-
perature. At 7’=O they would coincide. Also the course of the
binodal lines is mainly known. These too consist of a liquid branch
and a vapour branch, which intersect at 7?,;, in the same point as

; ; 5 A : dp
the spinodal curves, and which have both points in which a N()
av

for given 7. At 7 above 7),;, the spinodal and binodal curves have
got detached, and there is question of a lefthand and a righthand curve.

A first question which now presents itself, is this. To what is it
owing that there was no question of three-phase pressure in the
mixtures discussed up to new, for which 7’, occurs? The reason
will most likely be found in the circumstance that for these mixtures
the critical temperatures of the components differ little, so that the
ratio between these temperatures differs little from unity. But also
in the circumstance that the size of the molecules of the components
differs little, and that accordingly the ratio of the critical pressures
of the components was not a high value either. What is most likely
also in connection with this is the circumstance that the value of z
for which 7); has a minimum value, was not found very small. In
this investigation we assume a high ratio between the 7’,’s of the
components, asafor ether and water, which may be put at about 1,4.
But most of all a high ratio between the size of the molecules e.g.
as 5 to 1, and accordingly a very great value for the ratio of the
pes, Which would rise to 1 to 7 for the values given, if we viz.
disregard the fact that for the critical point the value of 6 is no
longer equal to 6,. And now it is easy to show that the said ratios
can be so great that at the given temperature three-phase pressure
would occur to all probability. To show this we shall examine the
course of the branch of the spinodal curve with small volume,
assuming the course of the isobars on the side of the component
with small size of the molecules to be known. We need not know
this course further than just past the mixture with minimum 7%.
To facilitate a survey I shall first suppose that the temperature
chosen is exactly this minimum 7). At this temperature the spinodal
line has the double point. Moving from this point to the side of the

( 659 )

component with small value of 4, it first cuts isobars with increasing
value of p, till it touches a line of constant p in the double point
of the isobars, so it reaches a maximum value for p; hence it further
moves to lower p. The decrease of the value of p takes place at
an accelerated rate, and if this decrease of p continued to the side
which is now supposed far distant, the spinodal curve would at last
terminate at an isobar of very low value of p. For ether and water
the saturation pressure at 7% is for ether 385 and about 14 atms.
These are pressures in which one is not only a very small fraction
of the other. And now it is indeed true that the spinodal cnrve must
not coincide with the volume of the saturation pressure at «= 0,

dp
but witb that of the volume for which aaa and then p is smaller.
av

But at this temperature the influence of this is not great enough to
deprive our reasoning quite of its validity. Besides the conclusion I
want to draw, can also be derived by means of the binodal curve,
and in this the values 35 and 14 would still be of use. From the

equation :
as
v2, dp = («,—2,) (=) dx,
dt?) pT

if z,—«, had always to keep the same sign, a difference in pressure
for water and the minimum pressure would have to be expected,
many times smaller than agrees with the values 14 and 35. The
difficulty is entirely removed if we assume that the spinodal curve
does not proceed continuously in its course to the component with
small value of 4 towards isobars of lower p, but that it will
touch an isobar again, and then proceed again to isobars of
higher value of p, after which it again touches an isobar, and
finally descends to the value of the isobar at w=. All this
may be considered as an attempt to derive the existence of 2 double
plaitpoints, and so of three-phase pressure from the course of the
isobars and the ratio of the values of 4, and to demonstrate that
for the existence of three-phase pressure we need not have recourse
to the practically meaningless statement that the cause must be found
in the abnormality of one of the components. More and more | tend
to the opinion that calling a substance abnormal only means that
some numerical data have a somewhat different value from what
we should expect. But in the main features of the course of the
phenomena no differences occur, nor in the behaviour with regard
to other substances — unless there should be real chemical interaction.

The spinodal curve touches an isobar three times, the first time
on the side of the great volumes. But the point of contact is no

( 660 )

plaitpoint then. As ( ) is always equal to 0 when we follow
rye be

dx*

the spinodal line, always

as ‘da? v dp
eas. +- ( : — = (0).
aa?) pr dx? },7 da

2 . dp : - .
In this point = is =O for the spinodal curve, and so we have
AX

ANS Soe :
( ) = 0, but not because two phases coincide in this point, but
7
/

de®

because the spinodal curve has a maximum yalue for the value of

dad
p. Also in the point of intersection of the spinodal curve Ae:
dx" ])T

Qei~ Av

dv dp. nf
because ( ) —0. There “ is not equal to 0. So not only the
pr

ae =. BS
plaitpoints are included in the common solution for | =="0
pl

dx?
at Sse Te aap ia
and a =0 for given 7. Nor does the spinodal curve always
da’ te
touch an isobar in a plaitpoint.

At the second contact the spinodal curve touches a line of equal
p on the side of the small volumes. Then we have again a plaitpoint,
but a hidden plaitpoint. Or rather a plaitpoint of the second kind.
For we saw before (see among others These Proc. VIII p. J84) that
both kinds of plaitpoints can be Aidden. And at the third contact the
contact of the spinodal curve with a line of equal p takes place on
the side of the great volumes, and we have a plaitpoint of the
first kind.

The liquid branch, of whose course we have examined here the
particularities which might lead us to expect an intricate shape, has
after all a pretty simple form. Starting from the double point [- 3)

Ak” J spin
is positive, and at the end at «= 1 this quantity must have the
same sign. The question which we have had to solve, comes to the
same thing as the question whether this quantity has retained the
same sign over its whole breadth, or whether it has perhaps been
negative between. If the latter is the case, and at this conclusion
we have arrived, two points of inflection must occur in the spinodal
curve. And when the figure of the p-lines for the case of the small
value of 6 for the second component has been drawn well, we
conclude naturally to the existence of these two points of inflection.

(661 )

dv

But then this is the only complication. The sign of ) need not
AX J spin

vary. We may, indeed, assert that it is always negative as would
be the case when the two points of inflection did not exist.

If for the course of the 7,v-curve of the plaitpoints, I refer to
fig. 48, some details must be modified. This figure is, indeed, entirely
schematic and has not been designed with a view to the special
case that we will examine.

Thus in fig. 43 the branch of the plaitpoints of the second kind
lies at very low temperatures very near the side of the first com-
ponent, and the possibility is even to be foreseen that the order of the to
two first points of contact is reversed, and so that the plaitpoint of
“the second kind lies at smaller values of w than the first point of
contact. I have made a close inquiry into the possibility or non-
possibility of such a particularity, and this has taught me that this
is not impossible, but on the other hand improbable; whereas the
complication that occurs in the shape of the spinodal line, is very
great. For the case under consideration it is certainly not necessary,
and so it is better to have the descending branch of these plaitpoints
run regularly to greater values of z. Also in fig. 45 the course of
the three-phase curve has been drawn quite schematically without
descending to particulars. There are, namely, different cases possible,
in which fig. 43 might be of use. We might ascribe either smaller
or greater values of / to the second component. We might make
the three-phase pressure terminate on the branch AQ, or on the
branch Q,P.a. In fig. 48 [ have drawn a middle case, in which the
three-phase pressure would just terminate at the minimum plaitpoint
temperature, because then I had not yet carried out all the investi-
gations about the meaning of these particular suppositions. But the
special investigations about the points mentioned and other not men-
tioned points I have now quite or partly completed, because I wanted
for myself to arrive at a conclusion about what would have to
be assumed specially for the case ether-water and it has become
clear to me that we should have to assume for it: 1 possibly
the existence of a minimum 7), on the ether side. 2. the termina-
tion of the three-phase pressure on the branch Q,P.a, so on the
again ascending branch of the plaitpoint curve, which runs to the
point where it joins the branch of the plaitpoints of the 2"¢ kind.
This ascending branch, however, must rise higher than in fig. 43.
Compare the adjoined fig. 52.

( 662 )

I have arrived at this conclusion by drawing the p7-figure for
the course of the plaitpoints.

This p7-curve is known for a binary mixture with minimum 77,,,
if there exists no three-phase pressure. It runs vertically at the mini-
mum temperature, and then turns to higher temperature with a
branch with inereasing value of p. The upper branch runs to the
component with smaller value of pz, the lower branch to the other
component with decreasing value of p. As we suppose the minimum
T,i1 very near the side, the lower branch does not exist, or exists
only for a very small part. As is known, on the upper branch is
found the remarkable point for which the plaitpoint temperature is
the same as the critical temperature of the mixture taken as homo-
geneous. In it two phases of equal concentration coincide to one.

In the cases examined before with minimum fy the upper branch
soon terminated at a second component, and therefore three-phase
pressure did not occur. But for ether and water this branch must
be prolonged to mneh higher temperatures, and this branch must
run to exceedingly great pressures. In what precedes I have demon-
strated that this branch does not ascend so far beyond the said
remarkable point that this would account at 7%, for this very high
pe, At least this is the interpretation of the former reasoning for
the course of the p,7-curve. So three-phase pressure may be expected,
and this means for the p,7-curve that there must occur a cusp of
the 14st kind past the above mentioned remarkable point on much
further prolongation. But already before this cusp, which always
lies in the covered region, the point occurs in which the three-
phase pressure ends. That part of the ascending branch under
discussion which lies between 7%,;, and the point in which the
three-phase pressure ends, can be observed. And now it happened
that just when I had come to this conclusion, Dr. Scarrrrr showed
me a drawing in which a part of the p,7-curve according to the
observations on the side of ether was represented which had entirely
the shape that has always been observed, when the course is normad.
The publication of his observations would be very desirable. Accord-
ing to the said drawing it is not perfectly certain that the minimum
plaitpoint temperature really occurs for ether and water; but as we
shall see presently, this is a point,of minor importance. The obser-
vations with such a small quantity of water, or such an exceedingly
small value of «are after ali not to be carried out with perfect certainty,
beeause it is not certain then whether this insignificant quantity of
water really mixes homogeneously with the quantity of ether, or
perhaps adheres to the glass wall. But he himself had also drawn

( 663 )

the curve in such a way that there was question of retrogression
of the temperature. So this means that the point Q, of the fig. 43
(I do not speak here of the point of the three-phase pressure that
by accident has been drawn coinciding with Q, in the figure) is
really present. If this retrogression was not found, the curve would
have to begin vertically, or it would immediately have to rise
abruptly to higher temperatures. And whether the said remarkable
point had already been observed by him also with absolute certainty,
I shall leave for him to decide when he communicates his observa-
tions. But in the following consideration I shall assume it to be
present. At any rate we may consider as perfectly certain the rapid
rise stretching over an appreciable
range of temperature. And _ this

ae

must account for the circumstance
that the three-phase pressure for
ether and water at given temperature
is greater than the saturation pres-
sures of each of the components,
and so for the circumstance that the
gas phase, as far as its concentra-
tion is concerned, lies between that
of the two coexisting liquid phases.

We then draw again (fig. 48) the
pT-line with two cusps repeatedly
drawn before, taking care that the

io.)

Fig. 4

three-phase curve passes at 7}, through a point that lies higher than
pe,» and this can casily be done without straining the p,7-curve in
consequence of the rapid rise in the beginning at 7;,. If we then
examine the special points of this line, I mention 1. the point where
7 has a minimum value, differing little from 7%, so the point
dp

: : : iP.
where the tangent is vertical. 2. the remarkable point where ae
c

te ce 3. th fit, a t] ti fever
equa oO 5 ». 1e YO1U where le nega lve value oO aaa
I" dv), aT?

passes into a positive value. 4. the 1s* cusp, where the retrogres-
.; ’ d’p

sive line has the same tangent, but ae suddenly changes from
positive to negative. 5. probably two points of inflection on this
retrogressive line. 6. the second cusp, where the retrogressive line
changes again intO a progressive one, and thus represents the course
of the plaitpoints of the 1st kind. This second cusp need not exist

( 664 )

really, and at such low temperatures as we have to do with here
it is of no practical importance, because the circumstances will be
quite modified in consequence of the formation of solid states. About
the last branch we observe that it must terminate at 7%, and at a
pressure equal to pz. This branch need not cut the first rapidly
ascending branch, and if it does, there would have to be two points
of intersection. If the first and the third branch intersect, there is
a temperature at which there lie two plaits above the three-phase
line, which lie at the same height. As will appear further the plait
on the ether side will be preseut only for a short time, and it will
not be able to reach a height which can be compared with the
height of the plait on the side of the other component. If all these
particularities have been represented well in the drawing, the course
of the three-phase pressure can be traced between a point of the
first branch and a point of the second branch. It must, moreover,
cut the first branch in order to lie above pg, at 7%, and now it
also lies above the vapour tension line of the first component at all
temperatures below 7, and a fortiori at all temperatures above
the vapour tension line of the 2"¢ component.

It might be surmised that in some cases this line does not cut the
first branch, and lies somewhat below pg, at T= 7), or would lie
at a level with jp,,, and I myself did not consider this impossible
at first. But in any ease there must be intersection, either above or
below 7, but then with the vapour tension line of the first com-
ponent. We shall see further on where this intersection is to be
found. According to the results obtained in what follows the inter-
section must take place in the so-called remarkable point.

What is the meaning of this situation of the three-phase line bzlow
the first branch and of the necessary intersection either with the
branch itself or with the vapour tension line? When at given 7
the three-phase line lies below the plaitpoint line, the p,t-figure has
two tops or plaitpoints above the three-phase pressure, that which
lies nearest to the first component has a plaitpoint pressure of whieb
we are speaking, and the other top is the plaitpoint of the last
branch of the p,7-line, which runs to the critical point of the second
component. Then the p,v-curve has the shape drawn already several
times before (see among others These Proc. VIII p. 184), whieh I
might almost call the usual one when there is three-phase pressure.
At the highest three-phase temperature the width of the first elevation
above the three-phase pressure has become equal to 0, and the figure
which exists then, is also known: it also being known what must
then still happen in the hidden region above this temperature.

( 665 )

In the cases treated before the width of the first elevation above
the three-phase pressure continually increases with decrease of tem-
perature, and that of the second elevation continually decreases. This
is changed in the case that we are treating now, and of which ether
and water is an example.

It is true that the width of the first elevation begins at first to
increase with decrease of temperature — but it reaches a maximum.
Then it decreases again and becomes again equal to 0 at the tem-
perature of the point of intersection of the three-phase line and
plaitpoint line. I shall at least suppose here that the plaitpoint line
itself is intersected. And at still further lowering of the temperature
the plaitpoint lies on the other hand below the three-phase line. Then
there is no longer an elevation above the three-phase line, but there
is a plait which hangs at the lower side. The other plait which has
remained above the three-phase line, has increased in width at the
expense of the first, and extends over the full width, because there
is now but one plait above the three-phase pressure. At still further
lowering of 7’ to 7%, the plaitpoint of the plait hanging on the lower
side has got on the side of the first component, and has become the
critical point of this component. So the p,r-line for this temperature
consists first of two lines ascending from the critical point of the
first component, ascending because the three-phase pressure is larger
than pz, They cut the straight line which contains the three coexist-
ing phases in two points which are not very far distant as yet,
and of which the point that lies most to the left is a liquid phase,
and the point lying most to the right a vapour phase. besides these
two lines‘there are also two starting from the righthand component
beginning in the pressure of saturation, and they also cut the said
Straight line in two points. Of course of the two last-mentioned
points the lefthand point must coincide with the righthand point of
the first pair. We then have a vapour phase with a concentration
between that of the two coexisting liquids. Above the straight line
on which these three points lie we have then finally the curve for
the equilibrium of the two liquids at pressures greater than the three-
phase pressure with a highest point, which is then again a plaitpoint.
At lower 7’ the two ascending pairs of lines begin of course in the
saturation points of the components. At temperatures which lie only
little above 7%, the elevation above the pressure of coexistence will
only slowly ascend on the side of the component with greater value of 0.

If we now direct our attention to the curve of the concentrations
of the coexisting phases, fig. 43 may again be of use, of course with

( 666 )

the modifications necessary for the case ether-water’). First of all,
but this I already observed before, the highest point must be chosen
on the branch Q,P.a, and then the point where the conversion
occurs in the concentration of the two lefthand phases must lie at
much higher temperature, and even when the three-phase pressure
at 7%, lies above pg,, this point must lie above 7% . In the other
case below 7);. What the shape is of the branch of the vapour
concentrations at very low temperatures, is theoretically of impor-
tance, but not practically. I have not yet seriously taken the inves-
tigation of this point in hand.

If we imagine the p7v-surface, and the course of the vapour
phase plotted on it for coexistence with two liquid phases, it lies
according to our results at the highest temperature on the upper
sheet, but goes to the lower sheet on decrease of the temperature.
So there must be a temperature for which it may be asserted that
it lies both on the upper sheet and on the lower sheet. I mentioned
the possibility of such a transition already long ago. but U always
imagined it in such a way that this had to take place in a point
where a section of the p, Ta-surface would have a vertical tangent
at constant temperature. For in such a point a curve which first
lies on the upper sheet, may go to the lower sheet. If I still held
this view, this transition would certainly have to take place above
7T,,, and the possibility that this would happen below 7%, was
excluded. As the result of the investigation of the preceding pages
I must now say that my opinion about the properties of the pTa-
surface in the point where the vapour-phase is transferred from the
upper sheet to the lower sheet, has changed. If the section is drawn
at the moment of transition, we arrive at the result that this section
has not a vertical tangent in the point of transition, but that it has
a horizontal tangent there. Or rather two horizontal tangents which
have coincided — for there is a cusp. At any rate a configuration
where two branches ending in one point, have one and the same
tangent. And this follows immediately from our previous considera-
tions. If yet on decrease of temperature this 7’ is reached, in which
the lefthand plait on the upper sheet disappears, there is a horizontal
tangent and a point of inflection in that point of the upper sheet
(see among others fig. 9 These Proce. VIII p. 184). And in the same
way there is at least one horizontal tangent on the lower sheet, when
with rise of the temperature this same 7’ has been reached, and the
plait that hangs down, disappears. But if the point of transition is a

1) In fig. 52 I have drawn the course of the curve of the concentrations anew,
as it is according to these results.

( 667 )

cusp, the possibility that the transition takes place below 7%, seems
not to be entirely excluded; but this will be treated presently.

To make it easier for ourselves to form an idea of the p, 7’, 2-
surface above 7%,, we imagine the p, z-lines at certain 7’ of a mix-
ture with maximum tension. Then there are two branches which run
upwards from the first component and touch cach other ata certain
distance from the axis. If the line was here broken off, we might
speak of a rhamphoid cusp. If the line is prolonged, the two lines
descend to the other component, which in our case has the smaller
value of 4. It has appeared from what precedes that on the side of
the first component the existence of three-phase pressure brings about
hardly any change; on the other hand a very great change takes
place if we draw near the side of the second component. If we
think the three-phase pressure entirely confined to beyond the maxi-
mum value of p, then contact of vapour- and liquid line has conti-
nied to exist; but then the Mguid line is specially subjected to a very
great change and the vapour line is comparatively Jess changed.
Instead of descending the liquid line has been foreed to ascend
rapidly before it slopes down again. Let us examine after these
preliminary considerations what must be the case when we descend
from the highest three-phase temperature to lower temperatures, but
always remaining above 7%,. The highest three-phase temperature is
so high above 7,,, that the entire first part of the p, z-line has dis-
appeared including the point of contact of liquid and vapour line.
On decrease of temperature the lefthand top gets slightly above the
three-phase pressure, on further decrease it approaches again the
three-phase tension and it finally coincides with it. Then the tempe-
rature has been reached of the transition of that plaitpoint to the
lower sheet. The point in which this takes place, is the point in
which two phases of equal concentration have coincided. The dis-
appearance of the first part of the p,.z-line is now more restricted,
and only that part that must have been present before the contact
of liquid and vapour, has disappeared. If this first part was made
to disappear for a mixture without three-phase pressure, there would
again be question of a rhamphoid cusp. But as in consequence of the
three-phase pressure the remaining liquid line ascends steeply, it has
become the cusp to which I concluded above. I do not discuss the
hidden equilibria here, which would deserve a separate investigation.
The point of transition in the order of the two first phases of the
three-phase pressure lies 1. of course again on the branch of the
plaitpoint curve Q,7ca of fig. 43; 2. at such a high temperature
above 7;, that the ascending part of the p, w-line has just disappeared

( 668 )

at that temperature; 3. closer to the side of the first component than
the point in which the three-phase pressure first originated. So the
liquid branch of the concentrations has had to change its course to
the side of the second component to a rapid retrogression. So
at the temperature of transition of the vapour phase from upper
sheet to lower sheet, there is properly speaking no three-phase
pressure, and the p, «-curve proceeds continuously upwards *)
on the side of the second component, reaches a maximum in the
plaitpoint of the remaining plait, rans downwards on the side of
the first component, and continues to represent liquid concentrations
to the cusp. Descending further from there with negative curvature,
it again reaches the second component. We could only still speak
in so far of three-phase pressure, if in the case of equilibrium of
three phases as special case that is included in which two phases
Ip

Gi la al . ap u
have the same concentration. That then the value of —— for the
‘

dp
three-phase equilibrium is equal to = for the equilibrium of the
€

two phases which have the same concentration, is known. So all
this takes place when the three-phase tension and the p7-line of the
plaitpoints intersect. At lower 7’ the three-phase tension lies above
the line of the plaitpoints. According as the temperature falls and
approaches 7%, a larger portion of the pwz-curve, which serves us
for illustration of these phenomena, is left, though it is greatly modi-
fied by the existence of the three coexisting phases. Now the re-
maining part has extended to beyond the maximum tension, and so
contains also a part of the branch which runs down again towards
the first component. For so far as it can be realized the p7w-sur-
face has now the following shape: Under the line of the three phases
there hangs a ‘still closed plait on the side of the first component,

1) Continuously, just as this is always the case for a two-phase equilibrium
above the critical temperature of the first component. Now too there is nowhere
three-phase equilibrium throughout the course of the p,v-curve. Nor js this the
case in the cusp, fer the two phases rich in ether, which are otherwise present,
and which differ then, have now united to one single phase. The discussed transition
takes place in a plaitpoint. Neither is there anywhere an abrupt change in the
character of the phases. That a cusp may be found on the other side is owing

as

to the circumstance that in that point ( ; is eqyal to 0. | am, however,
pr

dx,
not perfectly convinced of the existence of this cusp — and the surest proof of
this is certainly that I so often return to this subject. Repeatedly the thought
has occurred to me, that after all the p,v-curve might be rounded in this point. I
have only reluctantly asstimed the existence of this point.

( 669 )

and from the point of intersection lying on the side of the second
component another vapour branch goes further to the second
component with abrupt change of direction as has already been
described. And above the three phase line. we have the liquid-liquid
plait extended to the side of the first component. The plaitpoint of
the hanging plait soon begins to approach rapidly to the side of the
first component, and coincides at 7 — 7%, with the critical point.
How the liquid and the vapour line of the hanging plaits run then-
in the hidden equilibria, and whether they proceed there still in
unmodified form, and reach the point in which vapour and liquid
have the same concentration, cannot be ascertained without a close
investigation of the hidden equilibria, but so far as my investigation
of these equilibria is advanced at the moment this seems pretty
certain.

But if we had only purposed to arrive at a result, we might
have obtained this in an easier way. The point of transition for the
two first phases is such a point that for points on the side of the
component with the lower value of 4 the line of the pressures is
curved in such a way that the top les above, and that on the other
hand it lies lower on the side of the component with greater value
of 6. If we now have such a temperature that the three-phase tension
just passes through the highest point of the p,v-line, the tensions lie
really below the three-phase line on the side of the component with
the greater value of 6. On the other hand the vapour tension, indeed,
goes down on the other side, but on account of the modification
caused by the existence of the two plaitpoints which has been indi-
eated as the cause of the three-phase pressure, this liquid pressure
runs upward. But though our deseription will be right in the main,
there remain enough questions about further particulars, which ren-
der it very desirable that such 7’v-lines above the critical tempera-
ture of ether should be investigated experimentally.

If this cusp is to occur in the order of the two first phases, the
said remarkable point will have to occur on the ascending p,.-line
on the ether-side, and that at lower value of 7’ than the highest
three-phase temperature. In this remarkable point under considera-
tion the three-phase pressure line cuts the curve of the plaitpoints,
and so if there is really minimum 7), this point of intersection lies
appreciably above (7),))min. For this intersection to exist it is not
absolutely indispensable that the minimum 7; really exists. So the
minimum Q, need not really exist in the 7v-line of the plaitpoints.
For 7;., we might also have a point a little past Q,, but always in
such a way that the rapid rise of the p, 7-line continues to exist.

45

Proccedings Royal Acad. Amsterdam. Vol. XIV.

( 670 )

We must, however, not make it rise to that point of the line Q, P.a
where the transition of the two first phases takes place, or above it.

If it coincided with it, the coinciding concentration would be equal
to zero and then a perfectly pure substance could coexist witha
mixture at 7),. In connection with this remark we conciude that
the three-phase tension at 7%,, wili always have to lie above pj,.

But though I may have to put off the treatment also of the hidden
equilibria to a later occasion — yet I will not conclude without
pointing out that there are more possibilities than the case I have
treated here. For instance in the p, 7-figure of the plaitpoints the two
points which the line of the three-phase equilibrium has in common with
ihe first branch of the plaitpoints, may coincide, or become one single
point (fig. 49). In this case the two concentrations need not reverse their
signs any more, because then the gasphase lies between the two others
starting from the highest point. Then the highest three-phase pressure
begins at a temperature which lies nearer the minimum value of 77,,.
We might continue in this direction’and make the end of the line of

Fig. 49. Fig. 50.

coexistence approach to that minimum value (Fig. 50) or if there
is room for it through the choice of the substances even below
that minimum. (Fig. 51). In this latter case the highest three-
phase equilibrium in fig. 43 would have to be drawn on _ the
branch AQ,. The elaboration of this latter case has been carried
furthest, also as far as the hidden equilibria are concerned; but
this requires so many figures that I have not yet decided
to publish it. Moreover it is the question whether such mixtures

really occur. I made some reservation with regard to this possibility
when treating tigure 43, but now I must confess that | have met

with no contradictions. I did, however, meet with great complications.
For the present it seems to me that in the above example a sufficient
number of indications are to be found for the treatment of all these
eases. The realisable first branch of the plaitpoint line can at once
show which case occurs.

For the case that the minimum 7, is found in the figure of the
p.,T-line, and we want to find the distance from the plaitpoint of
the top hanging under the three-phase line to the three-phase line,
there would seem to exist two distances at the same temperature.
The greater distance then belongs of course to the plaitpoint which
has got detached, and which at last retreats into the first axis at 7’, .

Postcript. I have since examined the course of the line which
represents the concentrations of the three coexisting phases also at
lower temperatures, or would represent them if the solid state or
states did not prevent their formation.

First of all the possibility exists that the point P., of fig. 48,
does not exist at 7 =O. Then there need not be a heterogeneous
double plaitpoint at a certain low temperature. In this ease the line
of the concentrations, which begins at the highest three-phase pressure
with the vapour phase first, and which possesses a point of inter-
section in the remarkable point of the plaitpoint line Q,P.q at the
somewhat lower temperature, need not possess a point of intersection
again at much lower temperature. Then the three points of this line
will have approached a certain limiting position at 7’= 0, the first

45*

( 672 )

liquid phase at =O, the second liquid phase at «= 1, and the
vapour phase at a certain value corresponding to:
lim —— = lim!
Teh, Pe
when p, and p, represent the saturation pressures of the two com-
ponents. Water and mereury, e.g., may be in this position.

But also with retention of the heterogeneous double plaitpoint P,,,,
which then would again have to be thought at higher value of x than
would follow from fig. 48, as I said above, the course of the line
mentioned can be accounted for. (See fig. 52). We must premise
that the point Q, of fig. 52 will have to represent a coinciding of
two liquid phases. If this is to be possible, there must exist a second
point of intersection in the line of the concentrations at much lower

Tk,

K

Fig. 52.

temperature. This second point of intersection does jot lie on a
plaitpoint line. And so there is no need to accept the retrogression
of the branch of the plaitpoints of the 2°¢ kind to render the
existence of this second point of intersection possible. So it is, indeed,
advisable to let this branch keep its usual course.,

How is the second point of intersection which lies so much lower,
then to be accounted for? Let us again consider the p,t-line of a
mixture with minimum 7), in our case on the ether side. Then
we have a maximum tension there. First two ascending lines, a
liquid and vapour line, which touch each other somewhat higher.
Then two descending lines with the vapour line in front. Let us
then draw the three-phase line, which must then, of course, have
been chosen lower than the maximum tension. The third phase of
the three-phase equilibrium lies at much greater 2, and is of no

( 673 )

importance for the explanation. If now the three-phase curve has
a width such that also the two first-mentioned branches, so the
ascending ones, belong to the three-phase equilibrium, the vapour
phase lies between the two liquid phases. The intersected descending
branches then lie in the hidden region, and the maximum pressure
cannot be observed then. If on the other hand the width of the
three-phase line is less, so that only the two descending branches
are cut by the three-phase line, the vapour phase lies again outside
the two coexisting liquids. The transition takes place when the
three-phase line just passes through the highest point of the p,7-line.
We have then again two phases of equal concentration of the
three-phase equilibrium. If only the two descending branches are
cut, the maximum of the p,z-line must, accordingly, be able to be
realized.

So between ihe temperatures of the two points of intersection the
maximum on the p,v-figure lies in the hidden region. And in
the two points of intersection the maximum lies just on the boundary
of this region. The value of x for such maxima of pressure
approaching to the value of « of the mixture with minimum 7),
at fall of temperature, the two points of intersection in fig. 52, will
have to he at greater distance from the first axis than the minimum,
but the lower point of intersection nearer the value of « for that
point. Only at temperatures below that of the lower point of inter-
section this maximum is possibly observable; for at temperatures
above that of the upper point of intersection the critical state prevents
the appearance of the maximum. If my supposition is correct that
for this mixture the point P,, exists, a temperature at which ether
may possess a minimum of solubility to water lies between the
temperatures of the points of intersection; nevertheless the contrary
remains possible. If the solid state does not prevent it, it must be possible
to realize experimentally both the points of intersection of vapour
branch and liquid branch, which have been discussed. The upper
point lying above (7,))nin by the investigation of the then prevailing
system of equilibrium, in our case water in which ether has been
dissolved — and particularly by ascertaining the temperature, at
which the existing three-phase equilibrium behaves as a two-phase
system, or if one likes as a pseudo two-phase system. The lower
point by the determination of the temperature at which the maximum
pressure in the p,v-line will just present itself. Then, however, there
is a real three-phase system, for then the two phases of equal
concentration are different, viz. one is a vapour phase, the other a
liquid phase.

( 674 )

Physics. — “Researches on Magnetism. IV. On Paramagnetism at
very low temperatures”. By H. Kamurtrcn Onnes and ALB.
Perrier. Communication N°. 124a from the Physical Laboratory
at Leiden.

(Communicated in the meeting of November 25, 1911).

§ 1. Sold Oxygen. In a former Communication (May 1911) we
inentioned our suspicion that the susceptibility of oxygen follows a
law at liquid hydrogen temperatures quite different from Curtr’s
law, which is obeyed at ordinary temperatures. A continuation of
our attraction experiments has amply confirmed this suspicion. The
susceptibility, indeed, remains practically unchanged as the tempe-
rature sinks from the boiling point to the freezing point of hydrogen,
and we have even fqund clear indications that after becoming
constant the susceptibility begins to decrease when the temperature
is lowered still further.

In our experiments the oxygen was contained in a closed thick-
walled glass tube, narrowed at the lower end. The gas enclosed in
the tube was at a pressure of about 55 atmospheres at ordinary
temperature. The tube was suspended in the apparatus and was
kept in an equilibrium position in exactly the same way as the
tubes containing powdered substances in our former experiments
and, as with those tubes, it was completely surrounded by the
vessel which held the bath of liquefied gas. In the present experi-
ments the lower portion of the tube was slowly cooled by pouring
liquid hydrogen drop by drop into the vacuum vessel which served
to hold the bath of liquid gas. In this way the oxygen was caused
to freeze to a solid piece practically cylindrical in shape, filling the
lower part of the tube. To make measurements possible, this cylinder
was placed in that part of the magnetic field where the attraction
was a maximum. The correction to be applied on account of the
influence of the glass, which was pretty considerable at very low.
temperatures, was obtained by control experiments with an evacuated
tube. For the specific susceptibility we found the values, given in table I.

The corrections which are still to be applied to these values are
insignificant about 1°/,). In the Table, A and B refer to two
different experiments (different freezings of the oxygen). The difference
between the absolute values in Columns A and B can be explained
by the fact that the practically cylindrical piece of solid oxygen
11 mm. long and 4 mm. thick) was not of exactly the same length
n the two cases. But even so, what we are immediately concerned

( 675 )

with is not so much absolute values as the ratios between the
values for the same cylinder at different temperatures.

TAL BPESE, I

Solid oxygen.

A B
La lta | ae “7.10!
20.3K 54.3 20.3K 52.3
8.5 | 55.8
17.0 54.6
15.5 54.7
13.9 50.8 13.9 49.1

Our formula from Communication N°. 116 gives for oxygen Jiquid
at — 210° C. the much greater value

Nes 2 10% 288

In the course of our present experiments we have actually been
able by direct observation of the magnetic attraction during the melt-
ing of the oxygen cylinder to establish as a fact the existence of
a considerabie sudden change in the susceptibility of oxygen on melting
and freezing. In Communication N°. 116 we concluded that such a
sudden change must exist, but it now appears that the magnitude
of this change is actually much greater (four times) than the value
which we then estimated for it.

We cannot yet with certainty say how we are to explain the
considerable difference between the values of the susceptibility of solid
oxygen which we have now obtained by the attraction method and
those which we got before by the method of the couple. We were just
on the point of investigating this question more closely when we
were obliged for particular reasons to postpone further experiments
for a considerable time, so that we shall now content ourselves with
giving the explanation which we consider the most probable. This
tentative explanation is that solid oxygen possesses magneto-crystalline
properties, which was not previously known and which we had no
reason to suspect. If the magneto-crystalline anisotropy of oxygen
on the track of which our experiments should bring us if our expla-
nation is correct — is somewhat considerable the values of the suscep-
tibility given by the method of the couple can depend to a considerable

( 676 )

extent upon the positions taken up by the crystals on solidi-
fication. In this way chance could play a considerable part in the
results. We have already obtained an indication that this is the
correct direction in which we must look for the proper explanation, for,
on repeating our measurements by the method of the couple we obtained
ereat differences in the values of the susceptibility according to the
manner in which the freezing of the oxygen took place. While we
were at first of the opinion that the manner in which we carried out the
freezing for our measurements by the method of the couple was the most
suitable for our purpose, and that for correct results we need only attend
to the necessity of filling the ellipsoid completely with solid oxygen,
we now think, in view of our later knowledge, that it had rather
the disadvantage of enforcing a definite distribution of crystals along
the walls of the ellipsoidand thus giving rise to a magneto-crystalline
couple which was greater than the demagnetizing couple.

It is easily seen that the forces exerted in our recent experiments
in a non-homogeneous field (always with small values of the suscep-
tibility) depend to a mueh smaller extent upon the positions
of the erystals than the couples exerted in our former experiments
in a homogeneous field. And, on the other hand, both our observa-
tions during the process of melting and the correspondence between
the values of the susceptibility given by the attraction method for
three successive freezings lead us to the conclusion that, as regards
the absolute values obtained, our later results should be taken in
preference to the others.

The results obtained with the ellipsoid for the change of suscep-
tibility between 20° K. and 14° K. do not conflict with those given
by the attraction method if a suitable correction is applied for the
glass of the ellipsoid. To get an idea of the influence of the glass
we give values for its susceptibility and its specific susceptibility in
the following table.

TiA BASE
09) BGiasse anna
T Vaio eo
290 K < 0 0
78 2.8 1.2

(67 )

The absolute values are only rough approximations as the shape
of the tube was very irregular, but as the correction for the glass was
determined independently as a whole in the application of the attrac-
tion method to oxygen, uncertainty in the absolute values does

not affect the correction in this case.

§ 2. Anhydrous Ferrous Sulphate. With ferrous sulphate practi-
cally anhydrous we found that the susceptibility at higher tempera-
tures increased, and at lower temperatures decreased as the tempe-
rature was diminished. Much to our regret we were compelled for
the same reasons as before to posipone for some time a continuation
of these experiments. In particular we should have liked to have
carried out experiments in a bath of liquid nitrogen to settle defi-
nitely at what temperature occurs the maximum susceptibility which
is clearly indicated by our other results. This is evident from Table II
in which we collect our data. The measurements at 143°.1 K and
i70°.6 K were made in a bath of liquid ethylene.

TAC BEE Il:

} 293K 65.0

170.6 102.6

| 143.1 ies
| 20.3 251
18.0 240
| 15.9 231

Indeed, these results show without doubt that cases of maximum
susceptibility can and do occur. We communicated this result to the
Swiss Physical Congress in August, and at the same meeting DrByE
gave an explanation of this maximum which was based on the
theory of finite elements of action. This supports the hypothesis
communicated last May to which we had been led by our experi-
mental results, that deviations from Curin’s law are intimately related
to the energetic properties of the PLANck vibrators.

§ 3. Conclusions. If we supplement the reasoning developed in
‘§ 3 of Communication N°’. 122a by the present results for oxygen and
4 I ys

( 678 )

anhydrous ferrous sulphate, we are led to the conclusion that for
all paramagnetic substances there exists a region of higher tempe-
ratures within which deviations from Curin’s law are but insignifi-
cant, while as the temperature sinks deviations slowly increase so
much that a maximum is eventually reached, and then, with further
lowering of the temperature, the susceptibility, instead of increasing be-
gins to decrease, disappearing finally at the absolute zero of temperature.
This generalisation renders probable the assumption that, with respect
to paramagnetism, there exist corresponding (absolute) temperatures
(temperatures at which deviations from Curim’s law are the same) which,
for every substance, must be considered proportional to a certain (absolute)
temperature characteristic of the particular substance, the temperature
of the maximum specific susceptibility of the substance. This tempe-
rature, then, would be very low for crystallized gadolinium sulphate,
for oxygen it would lie not far below the boiling point of hydrogen,
and for anhydrous ferrous sulphate it would lie well above the
latter temperature. Were this generalisation confirmed for definite
classes of substances, it would lead to a general law of which could
be taken profit in the evaluation of the number of magnetons in
the molecules of solid substances belonging to those classes.

Physics. “Further Experiments with Liquid Helium. F. [sotherms of
Monatomic Gases ete. LX. Thermal Properties of Helium”. By
Prof. H. Kamertincoh Onnes. Communication N°. 124° from
the Physical Laboratory at Leiden.

(Communicated in the meeting of November 25, 1911).

§ 1. Vapour pressures of helium above the boiling point. Critical
pressure and critical temperature for helium. The helium-eryostat
described in Comm. N°. 1238 (Proce June 1911) made it possible for
me to undertake an experimental determination of the critical con-
stants for helium. A determination of these constants was particularly
desirable with a view to investigating the deviation of heliam from
the law of corresponding states. With that end in view I had
endeavoured as far back as 1909 (see Comm. N°. 112, Proc. June 1909)
to measure the critical pressure to at least a first approximation ; I
then obtained from expansion experiments the value pz = 2,75 atm.
while in 1908 I had estimated that p, should not be much greater
than 2,3 atm. and that 7’. should be 5° Kk.

From the experiments described in the present paper it will be clearly
seen that these expansion experiments led to too large a value; but

( 679 )

it must be remembered that in communicating those results (Comm.
N°. 112, 1909) it was definitely stated that the measurements made could
only be regarded as a preliminary approximation. Those experiments
were made under variable temperature, while it is very desirable
for determinations of critical constants that one should have available
a cryostat giving a range of constant temperatures in the neigbour-
hood of the critical temperature. Moreover, there was no stirrer
inside the tube into which the helium was brought to its critical
state. During the experiments the temperature within the experimental
tube seems to have been so different at different levels, that
the impression of the presence of a meniscus could have been
obtained while the pressure was higher than that which we now
find to be the eritical. Besides, on expansion to 2,5 atm. this would
have oceasioned the appearance of a local mist such as is seen
ordinarily in the critical state. It must be left for further experiment to
clear up the exact circumstances obtaining during those expansion
experiments, and to explain why they are apparently able to afford
only an upper limit to the value of the critical pressure. Under the
much more favourable circumstances of temperature constancy and
effective stirring under which the present experiments were conducted,
vapour pressures could be measured close up to the critical point,
and joint with them the critical pressure could be obtained. For
this constant, the value 2,26 atm. was obtained, which must, from
the nature of the method adopted, be regarded as a lower limit.
We must regard it as fortuitous that this value differs so slightly
from the estimate of 1908.

In the present experiments the critical temperature was determined
directly for the first time. I found 7; —=5°K. In 1908 7; was
estimated as slightly in excess of 5° kK. With regard to the value
7; = 5.°8 K, which was deduced in Comm. N°. 119 (Proc. March 1911)
from the vapour pressures below the boiling point, using the expe-
rimental value of pe of 1909 (Comm. N°. 112), it was even then
suspected that the value should prove too high, so that in §5 of the
same communication the value 7% = 5.°5 K was taken. (The reason
for its excessive value is now seen to be that the value of px
used for the deduction was too high).

The present experiments were carried out in the following manner.
(See accompanying Plate fig. 1). In the helium glass S, of the helium
eryostat described in Comm. N°. 123 (These Proc. XIV p. 204), parts of
the apparatus are represented on the accompanying Plate by the letters
which were used for the same parts in the diagram given with that
Communication) is placed another glass reservoir of which the lower

( 680 )

part consists of a double walled vacuum glass a, provided with an
outlet spiral a,, the upper part a, is single-walled, and terminates
in two narrow tubes, a, and a,. One of these tubes, a,, is, at its
upper extremity, provided with a side tube which is closed by a
tap. The ends of both a, and a, are cemented to the tubes 7, and
b, (b,,, 6.,), whose functions will presently be described, by means
of which the reservoir a is completely closed from above. If liquid
helium is present in the helium glass S,, by opening the valve a,
it can be forced through @, into the inner chamber which is itself
protected by the vacuum vessel a,. If the tap a, is now closed,
ordinary communication of heat by conduction and radiation, supple-
mented, if necessary by development of JouLE heat in the small coil
of constantin wire d, will drive the liquid back along a, leaving the
inner chamber filled with heliam vapour. The lower portion of this
chamber thus becomes a cryostat chamber, protected by a transparent
vacuum glass and immersed in liquid helium, an inner cryostat whose
temperature can be brought to a Uttle above that of the surrounding
liquid helhum in the outer cryostat. In this cryostat for temperatures
just above the boiling point of helium is now placed the experimental
reservoir $, which is used for the determination of the critical constants
of helium. This reservoir is concave underneath, 6,; itis also provided
with two narrow tubes one of which 6,, contains the thermo-
meter capillary, being fused to it at 6,,, while the other 6,, admits
the stirrer string, and at the same time allows helium to be admitted
or removed through 6,, or, if necessary, to be blown off through d,,.

The temperature is maintained constant and uniform by means of
the stirrer 6, which is operated by the string 6, by ineans of an
electromagnet acting upon the soft iron cylinder 6,.

The temperature of the helium inside 6 was measured by a helium
thermometer whose reservoir 6, was placed within the experimental
reservoir >. In a note at the end of this section we shall return to
this thermometer, which is, for the rest, the same in principle as
that deseribed in Communication N°’. 119 (see accompanying Plate
fig. 3). The thermometer capillary goes by 6, and then a, to the
outside.

To fill the experimental reservoir 6 with liquid helium, pure
compressed helium: is admitted along 6,, through the tap A (fig. 2),
while the inner cryostat is kept full of liquid helium by drawing
off through a, the vapour that is formed. Part of the tube whieh
supplies pure helium to the reservoir 6 consists of a spiral immersed
in liquid air, through which the gas must first pass. The necessary
connection with the mercury vacuum pump can be obtained through

( 681 )

the tap / (fig. 2). The pressure of the gas in the supply tube is read
on the spring manometer g, and the pressure of the helium in the
experimental reservoir is read on the open mercury manometer J/.
(Fig. 2).

At temperatures a little above the boiling point a constant tempe-
rature is obtained within the experimental reservoir by leaving the
valve / a little open, so that a small amount of gas flows off uni-
formly through it. By the resulting vaporization the liquid in & is
cooled, and the rate at which the gas escapes is so regulated that
while stirring is kept up the temperature remains constant. The
pressure difference due to the escape of the gas is neglected. On
stirring, the liquid forms an emulsion as if of oily liquid drops. In
the neighbourhood of the critical temperature this emulsion of liquid
in vapour assumes the appearance of a milky cloud. During the
measurements, the stirrer was repeatedly stopped for a moment so
as to see at what level in the reservoir the meniscus of the non-
emulsified liquid stood.

In this way determinations of vapour pressures were made with
perfect regularity up to 5°15 K., but from that point onwards it
was found difficult to complete a temperature measurement in the
short time elapsing before the liquid meniscus reached the bottom
of the reservoir on account of the rapid escape of vapour. On that
account the tap was then closed and the temperature was regulated
by passing a current through the warming coil d and at the same
time allowing gas to escape through a,, so that the experimental
reservoir was cooled by the passing over its walls of the colder
vapours arising from the helium vaporising within the inner cryostat.
In this way measurements were made of vapour pressures to a point
very close to the critical temperature. Just a little higher than the
highest temperature thus attained, but higher by an amount which
could not be measured, there was still a slight trace of milky cloud
to be seen following the motion of the stirrer, while at a temperature
just a little higher still, but with a temperature difference no more
measurable than before, the experimental tube remained quite clear. The
indications of the pressure were much more accurate than those of the
temperature. I could tell accurately to within a centimetre the pressure
of transition of the one state to the other within the reservoir. The tem-
perature change corresponding to this small change of pressure is still a
good deal smaller than that which has just been mentioned as too small
for measurement. The pressure at which the transition was observed
was taken to be the critical pressure. As we have already mentioned,
the manner in which this value has been obtained makes us regard

€ 682 )

it as a lower limit; but still, the actual value can only be very
slightly greater. We may therefore assume Ty, = 5°,25K, pe= 2,26 atm.
(see Table p. 683).

The thermometric measurements with the constant volume’) helium
thermometer, for whieh, as well as for other assistance, I gladly
acknowledge my indebtedness to Dr. C. Dorsman, were made with
a zero pressure of 300 mm. This is about double the zero pressure
used in the determinations of Comm, N°. 119. For other measure-
menis the zero pressure was 667 mm. and for the measurements
made in 1908 it was practically 15 atm.

From the agreement between the values of the boiling point of
helium obtained under various conditions I think I may safely put

Zz
>

the boiling point at 4°.26 K, or better in round numbers 4°.25 K
with an accuracy greater than 0°.1. The same degree of accuracy
can be ascribed to the value found for the critical temperature of
helium.

The thermometry of these low temperatures, however, must still
be made the subject of a special investigation. In particular, an
investigation must be made of the correction which is to be applied
on account of the influence which, as appears from KNupDsEN’s
researches, the mean free path of the gas molecules in the upper
part of the thermometer capillary can exert upon the value of the

1) Plate I, fig. 3 shows the helium thermometer modified for very low temperatures.
The figure should be compared with fig. 1 of Pl. 1 Comm. N°. 119; in the two
figures identical parts are indicated by the same letters, while those parts which
have undergone modification are indicated in the new figure by accented letters.
To avoid development of vapours at cemented joints and to avoid metal capil-
Jaries at places where a constant high vacuum is necessary tor control expe-
riments, the steel blocks f’ and fa with their reading points have been brought
inside the glass tubes and fastened to the walls with a minimum of seafing wax.
To reduce the dead space, e' has been rounded off above. The connections of the
adjusting tubes with the reservoir d; and with the thermometer capillary as far
as the tap K9, are now made completely cf glass d,', dj’ with a ground joint at
d,!. The connections at g'g la'g lo! Js la’, are also all ground joints (when these
joints were being greased, care was taken that the grease did not come in contact
with the mercury). A‘jq has been introduced for the filling of the thermometer for
which the ground joint Koz is also used. /,' has been taken of such a size that
in filling the thermometer the mercury from g,' can be brought over into /'3. An
internal air-trap is introduced at d;,. The copper thermometer capillary Th'g is
joined to the capillary dj) by the coupling piece @'jg and the capillary @q) is
in turn cemented on with the sleeve dy’) above the lap Ke, .

A correction of —0,°07 has lo be applied to the figures given in col. IT ofthe
Table in § 4 of Comm. No 119 on account of an error ascribed to development
of vapour and not introduced into the calculation. The supposed development of
vapour has since been ascertained to be due to a small leak.

( 683 )

pressure. It might, for instance, be, that the mean free path could
no longer be neglected in comparison with the width of the capillary.
Expressing p in atmospheres, the following results were obtained :

TABLE I.

Vapour pressures of helium.

Ife 160 Pooér
4.28 K 167
4.97 1329
5.10 1520
BslS 1569
5.22 1668
5.25 critical 1718 critical

§ 2. Values of certain thermal constants of helium.

In Comm. N°. 119 a value for the constant fy in the vAN DER
Waals vapour pressure formula (with common logarithms) was found
which was strikingly low, viz. 1.2. This value was obtained from
the slope at the boiling point of the tangent to the curve giving

; 1 ;
log p as a function of we and from the value which was _ then

assumed for the critical pressure, viz. 2.75 atm.

If we use the value of p, now given, we find from the tangent
to the curve at the boiling point the value 7, = 1.3 for common
logarithms, so there is still a large deviation from the ordinary
value of /.. But the figures which we now give have brought to
light the important property that above the boiling point fw increases
very rapidly. If the tangent is drawn at the critical point the
common logarithm constant is found to be f.;—= 1.95 (round numbers
from 1.94). This value of f,; is still smaller than that for any other
substance, but still, considering the gradual transformation of the
equation of state as one goes from substances of high to substances
of low critical temperature, it agrees pretty well with that for other
substances (lowest 2,2).

vy, is thus the only one of the critical constants which has not
yet been determined from direct observation; it can, however, be
assumed in the meantime that it can with sufficient accuracy be
deduced by the method adopted in Comm. No. 119 from the obser

( 684 )

ved densities of co-existing liquid and saturated vapour. This method
gives O¢¢ = 9.066 and vq = 0.00271.

In contradiction to what I have before deduced, our new knowledge
of Ave and the improved data for p, and 7; confirm, at least appro-
ximately, vAN DER WAALS’ expectation that the relation he deduced

between the critical constants should be found to hold for helium also.
ais te tT), :
The critical virial quotient —— = K, thus becomes 3.13 (for argon
PRI
it is 3.288, see Comm No. 120); hence using van per WAALS’ relation

T dpeoee. - ; ;
sure coefficient ( -— ae) = K,; this leads to the common logarithm
ip @ k

constant fwe= 2,2, whereas 1,95 is the value actually found. The
difference remaining is not great, and, in connection with it, it
must be remembered that the value now found for pg is a lower
limit, and that the relation would hold better for a higher value of
pr We may therefore conclude that the apparent association at the
critical temperature is, in the case of helium, still subject to prae-
tically the same laws as hold for ordinary normal substances.

The great difference between helium and normal substances makes
itself apparent at lower reduced temperatures, as shown by the
marked diminution in the value cf fy at lower reduced temperatures
at which also the liquid density attains a maximum. This difference
can well be the result of an influence of proximity to the absolute
zero at very low temperatures quite different from thatwhich obtains
ordinarily for the same values of the reduced temperature, due to
the fact that the liquid state lies much closer to the absolute zero
with helium than with any other substance.

Chemistry. — ‘On the chloration of benzoic acid, according to
experiments of the late Mr. J. Tu. Bornwarrr.” By Prof.
A. F. HoLieman.

(This communication will not be published in these Proceedings).

Chemistry. — “On the magnetism of the benzolsubstitution and on
the opposition of the formation of para-, ortho- against meta-
substitution products.” By Dr. T. vax per Linpen. (Communi-
cated by Prof. A. F. HoLieman).

(This communication will not be published in these Proceedings).

Chemistry. — ‘On some trinitroanizoles.” By Dr. H. VERMEULEN.
(Communicated by Prof. A. F. Houteman).

This communication will not be published in these Proceedings).

(January 24, 1912).

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING
of Saturday January 27, 1912.

—- = DOC

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 27 Januari 1912, Dl. XX).

ClO; Se BENG ES:

Ei. F. van pe SanpE Bakuvuyzen: “Investigations into the empirical terms in the mean
longitude of the moon and into Hansey’s constant term in the latitude’, p. 686.

C. B. A. Wicumann: “On the so-called atolls of the East-Indian Archipelago”, p. 698.

J. J. van Laar: “On the variability of the quantity b in vAN DER WAALS’ equation of state,
also in connection with the critical quantities’ 1V. (Conclusion). (Communicated by Prof.
H. A. Lorentz). p. 711.

F. M. Jarcer and J. B. Menke: “Studies on Tellurium II. On compounds of Tellurium and
Iodine”. (Communicated by Prof. P. van Rompurcn), p. 724.

¥. M. Jarcer and J. R. N. van Kreoren: “The question as to the miscibility in the solid
condition between aromatic Nitro- and Nitroso-compounds”. ILI. (Communicated by Prof.
P. van RomepurGn), p. 729.

J. Ovm Jr. and H. R. Kruyr: “Photo-electric phenomena with Antimony sulphide (Antimonite)”
Preliminary communication. (Communicated by Prof. P. van Romeurcm’, p. 740.

F. E. C. Scuerrer: “On gas equilibria”. (Communicated by Prof. J. D. van per Waats),
p- 743.

H. Zwaarpemaker: “The effusion of acoustic energy from the head, according to experiments
of Dr. P. Nrkirorowsky”, p. 758.

W. Kapreyn: “On partial differential equations of the first order”, p. 763.

J. J. yan Laar: “On some relations holding for the critical point’. (Communicated by Prof.
H. A. Lorentz, p. 771.

A. J. P. vay DEN Broek: “On the relation between the symphysis and the acetabulum in
the mammalian pelvis and the signification of the cotyloid bone”. (Communicated by
Prof. T.. Bork), p. 781.

P. Zerman and C. M. Hoocrnsoom: “Electric double refraction ia some artificial clouds and
vapours”. (2nd part), p. 786.

A. Swits: “Das Gesetz der Umwandlungsstulen in the light of the theory of allotropy”. (Com-
municated by Prof. A. F. Hotteman), p. 788.

Pu. Kounsiamm and L. S. Ornsrri: “Nernst’s theorem of heat and chemical facts”. (Com-
munieated by Prof. J. D. van per Waats), p. 802.

If. Kamertixcu Onnes: “Further experiments with liquid helium”, p. 818. (With one plate).

J. D. van peR Waats Jr.: “Energy and mass”. IT. (Communicated by Prof. J. D. van DER
Waatrs), p. 822.

M. Lave: “On the conception of the current of energy”. (Communicated by Prof. J. D. yan
pER Waats), p. 825.

J. D. vAN DER Waars Jr.: “On the conception of the current of energy”. (Communicated
by Prof. J. D. van DER Waats), p. 828. ;

M. J. van Uven: “Homogeneous linear differential equations of order two with given relation
between two particular integrals’. (3d communication). (Communicated by Prof. W.
Karteyn), p. 832. :

A. F. Hotreman and J. Vermevren: “The nitration of benzenc”, p. 837.

T. van DER Linden: “On the addition and the additionproduets of chlorine to the chlor-
benzenes”. (Communicated by Prof. A. F. Hotteman). p. 837.

Errata, p. 837.

46
Proceedings Royal Acad. Amsterdam. Vol. XIV.

( 686 )

Astronomy. — “J/nvestigations into the empirical terms in_ the
mean longitude of the moon and into Hansen’s constant term
in the latitude.’ By Prof. E. F. van bE Sanpr BakHuyzen,

(Communicated in the meeting of December 30, 1911).

lt is generally known that the mathematical theory of the motion
of the moon has been brought a great deal further these last years
by Hint’s, Rapav’s and Newcomp’s and especially E. Brown’s researches.
But it is equally well known that the thus acquired accurate knowledge
of — we may perhaps say — all appreciable inequalities due to
eravitational forees has not yet been able to make theory and
observation agree.

For the difference between the theoretical and the observed value
of the secular acceleration a plausible explanation may be found in
the tidal friction, although the numerical amount of this influence
cannot be computed theoretically. The terms of long period in the
mean longitude, shown by observation, however, offer absolutely
unsolved problems.

The last mentioned deviations were first found by Newcoms in his
Investigation (1876) and were subsequently thoroughly investigated
in his Researches (1878). After a long time in between he has again
taken the problem in hand in the last years of his life and has
studied it more closely by means of all occultations observed up to
the present time. He succeeded in completing his research before his
death and gave a short account of the acquired results in Monthly
Notices 69, while we may expect a detailed communication about them.

With the help of the observations of the moon made at Greenwich,
P. H. Cowen had in the meantime accomplished an ‘Analysis of
the errors of the moon” in a series of papers published in the
Monthly Notices and BarrrrMaxn bad obtained important results by
discussing 83 great series of occultations (Beob. Ergebn. Berlin 5,
11 and 13). Finally I had also found occasion for a partial investi-
eation into the errors of the tables of the moon (Proc. Acad. Amst.
6, 1908, p. 870 and 412) in the observations of lunar altitudes
accomplished by Mr. Sanpgrs on the west coast of Africa.

Lately I returned to some points of this problem owing to oecult-
ations observed these last few years by Mr. Sanpers and to the solar
eclipse of 1912, the particular circumstances of which will be dependent
to a high degree on the errors of the tables of the moon. With
a view to its instant importance for the prediction of this eclipse
I shall here communicate the results of this — be it fragmentary —

Investigation,

( 687 )

I shall treat :

1st. the empirical terms of long period in the longitude of the
moon.

2nd. the constant term in the latitude introduced by Hansen and
explained by him by the non-coineidence of the centre of gravity and
the centre of figure.

I. The empirical terms of long period in the mean longitude.

In my first paper of 1903 (Proc. Acad. Amst. 6, p. 3870) I said that
for the determination of the mean errors left in the longitude of
Hansen-Newcomp (i. e. according to Hansen with Newcomp’s Correc-
tions) | had computed annual means of the errors in longitude or
in R.A. according to the meridian observations of the period 1847—
1902. 1 shall now say something more about the method for deducing
these means. Besides the Greenwich observations I had also used
the Washington ones according to Newcomp’s /nvestigation, for 1862 —
1874; and for 1880— 1892 the Oxford ones according to the mean
values given by Stonn in Month/. Not. 44—54. As it afterwards seemed
better to me, however, to confine myself to the Greenwich obser-
vations, I shall say a few words of these only.

As far as regards annual means we may consider those of the
errors in longitude and those in R. A. as equal; so I have employed
indiscriminately the former as well as the latter. In JMonth/. Not. 50
we find an accurate comparison between the observations of the
moon at Greenwich from 1847 up to 1861 and Hansen's tables.
From this Stons has computed annual means of A 2% which he com-
municates in Monthl. Not. 51. He has also deduced annual means of
the errors in 4 for the years 1862—1882, the Greenwich observ-
ations of which had been directly compared Hansen (Month/. Not.
51—54). I have simply adopted these means, the only alteration
being that I took into account the different fundamental systems in
R.A. which have come into use at Greenwich in the course of years.
I reduced all to the mean system of the 7 Year Catal., with which
the 2nd 10 Y. Cat. agrees almost entirely. From these errors of
Hansen’s longitudes those of HaNnsen-NEwcomsB had now to be com-
puted and I effected this by adding to the former the differences
between Table XLI in the Corrections and the original Table XLI
in the Tables de la lune. ;

For the years 1883—1894 I derived the mean errors of HaNsEN-
Newcoms from the Greenwich Annual Reports in the Month/. Not.,
assuming the means of the 4e to be the error of the mean longitude.

46*

( 688 )

Finally, for the period 1895—1902 I used the results of my own
investigation of the Greenwich observations. Here too attention was
paid to the employed fundamental system. As an instance of the
accuracy of these different means we may take that the greatest
difference between my means and those derived by Newcoms in his
Investigation from Greenwich and Washington together, amounts to
0.83. Further, the differences between the Greenwich annual means
and the Oxford ones increase up to 1.18, while for the years
1895—1902 the greatest difference between my results from the
Greenwich observations and those according to the Reports amounts
to O".36.

I had not communicated these annual means, as I had not sueceeded
in finding anything with certainty about the law followed by the
deviations. I did remark, however, that the assumption of a term of
a period of about 50 years with maxima about 1862 and 1887 and
a coefticient of 3” would improve the agreement, but not yet sufficiently.

Not till 1909 did I find oceasion to return to the problem and,
after having added to my means those of 1904— 1908 according to
the Reports to the board of visitors, 1 tound that the differences
Observ.— Hansen-Newcoms for the 62 years from 1847 upwards might
he represented tolerably satisfactorily by a formula with 2 terms
of a 48-years’ and a 24-years’ period, viz.

+ 1".29 + 2".36 sin 7°.5 (t 1848.0) + 1".41 sin 15° (1852.8)

Of the 62 residuals there were 13 greater than 1.0 and 2
among these exceeded 1”.5'). Especially because in these last years
the results according to the observations and those according to the
formula had a clearly different gradient, I fully realised that the value
of this formula for extrapolation was still doubtful.

Meanwhile about the same time there appeared Nrwcoms’s import-
ant provisory communication about his last researches. In this paper
he gave a new derivation of the secular acceleration and deduced
anew empirical “great fluctuation” which again clearly left unaccounted
for “minor residuals’. For the secular acceleration 7.96 was found,
i.e. O'.46 less than the value of 1878 and the period of the great
inequality remained practically unaltered: 275 years against the
former 273 years, while the coefficient was diminished from 15'.5
to 12”.95.

The further discussion of the results from the meridian observ-
ations had to be preceded by a comparison with Nrwcoms’s new

1) Here, however, the mistake had been made of not taking into consideration
that since 1903 the Greenwich R. A. had been reduced to Newcoms’s system, which
is Os.054 greater than that of the 2nd. 10 Y. C.,

( 689 )

empirical theory, which I shall call Newe. 1909 or Newe. II. In
the very short article in Month/. Not. Newcomes, Ay oe does not
mention the accepted values for the mean motion and for the longitude
of the epoch. I now assumed with Barrermann (beob. Ergeb. Berlin
13, p. 44) that the former would be equal to the value of Newe. iheilbe
(or Newc.1) and that the correction + 1°14 4 1".4—= + 2"5

Corr. Hansen + 1.4) would have been added to the longitude 2S
1800.0. Therefore the difference between Newc. II and Newc. I consists
in 1st the constant term, 2”'y the term with the square of the time,
3dly the difference between the new “great fluctuation” and the old
long-period-inequality.

I intended to take the means of the differences between the meri-
dian observ. and Newe. Il and of the corresponding deviations deduced
from the occultations (Newcoms’s Minor residuals) and then to try
and represent these mean deviations by a periodic formula. In the
meantime, however, there appeared in Month/. Not. of last November
an article by Frank E. Ross in which Newcoms’s minor residuals
are first corrected for a more accurate value of the principal term
of the perturbations by the ellipticity of the earth and are then very
satisfactorily represented by two periodic terms. I therefore resolved
also to compare my mean values with Ross’ computation.

Now I first reduced the Greenwich R. A. to Nuwcoms’s system
and here follow the corrections added for this purpose:

1847—48 = Catal. 1842— 45 + 0:076
1849—55 12 Year Cat. 24. Part + 0. O76
1856—6l 6 Year Cat. 1850. +0. 044
1862—69 7 Year Cat. + 0. 054
1870—77 New 7 Year Cat. + 0. 064
1878—87 Clock St. 9 Year Cat. + 0. 049
1888—92 Clock St. 10 Year Cat. + 0. 049
1893—98 5 Year Cat. + 0. 054

1899—02 Clock St. 24 10 Year Cat. + 0. 054
19038 Clock St. 2°¢10Y.C.+0°054 — 0. 000
1906—10 = Stand. R. A. 2° 9 Year Cat. 0. 000

Leaving my former annual means up to 1902 for the rest unaltered,
I tried to deduce more accurate values for the years 1908
the Greenwich-Observations using exclusively the results obtained with
the transit-cirele. Keeping the results from Limb I and Limb II separated
to the last, I computed annual means in three ways: 1*' directly
from all observations of each limb, 2°’ by first forming monthly

O9 from

( 690 )

means and taking the mean of these with equal weights, 3"¢ly by
taking the mean of the mean values for the different observers, which
| could take from the Gireenw. Obs. up to 1908, computing them
myself for 1909. Besides, since 1905 also observations have been
made of the crater Mésting A, from which I derived mean values
in the first and second way. In the following table all these mean
values have been collected ; those from the observations of the limbs are
the means for the two. Finally mean values have been computed, for
the observations of the limbs from those after the three methods,
and for the erater-observations from those after the 1s* and 204,

The differences have always been taken in the sense Obs.—Comp.
3 (Limb I + Limb II) Mosting A
1 2 | 3 | Mean 1 | 2 Mean

| s s s | Ss
1903 | -+0 174) +0 179 +0 204 | +0 186

1904 | 238 . 246 244 243,

1905 | 344 | 340 340 341 +0 339 | +0 337 +0 338
1906 .3TT | .375 376 | 376 346 324 335
1907 374 386 371 377 425 417 421
1908 | 397 | 401 .397 | 398 454 | 448 451
1909 452 426 444 | 441 462 | 463

For the year 1910 the only result I employed was the one men-
tioned in that year’s report derived from 98 observations of the limbs
with the transit-circle, viz. Qa — + 05.5438. Besides this there is also
mentioned in the /eport as results from 69 observations of the
limbs and 36 of the crater with the Altazimuth A@ = + 05.59 and
+ 08.55 respectively.

Now in the foliowing table there are given first of all (col. 2)
the mean values representing the differences between Mer. Obs. and
Newe. 1 and from these have been derived (col. 3) the differences
between Mer. Obs. and Newe. Il. My computation of the great
fluctuation according to Nwwcome’s formula gave values, however,
which were in the mean — O”.18 ereater than those mentioned in
the Monthl. Not. Whatever may be the cause of this small difference,
it seemed advisable to me to keep to the formula and in accordance
with this correct also the minor residuals with + 0".2) In Ross’
formula if is exactly the constant term — 0".18 which has to dis-

( 691 )

M-NI M-NII Occ.-M. & Ross M-NI | M-NII Occ.-M.\ 4 os

5 | +0717 +006 | +-1"64 | —0"14] 1882.5 | + 0”81 | —1"21 | +-0"01 | +-0"08
5|+-1.38|+1.24) +0.86 | +0.66] 83.5 | +-0.26 | —1.81 | —0.19 | —0.52
49.5 | --2.09|-+1.91| —1.61]+-0.19] 84.5) +0.45|—1.68|—0.22| —0.30
5|+2.16|+1.95| —0.75'4+0.56| 85.5 +0.36|—1.84 —0.46 | —0.28
51.5 +3.32| +3.05 —2.05)+0.91] 86.5/-+0.28|—1.98|—0.62;| —0.40
52.5) +3.18| +2.87) —1.77|+0.67] 87.5|—0.16| —2.49|+0.09 —0.26
5 +4.01| 43.64 —2.74| 40.66] 88.5|—0.63|—3.02|—0.28| —0.78
54.5|+4.40/+3.98/—2.38/+40.78] 89.5/+0.57/—1.88|—1.42| 0.00

55.5| 13.71) +3.23/—0.93,+0.35] 90.5/+0.42|— 2.08 —1.12/ +0.04

56.5|13.59/+3.06|—0.96|—0.24] 91.5|—0.46|—3.03/+0.13| — 0.28

51.5|+4.76| +4.18|—1.88}—0.08| 92.5|—0.52|—3.16|+.0.76| —0.20
5 4 44. |

42/44.
85 +6.
.50| 5.
.86| +6.
98) $5.
.60| +3.
3.82] +2.
42.5
ae Oe
+0.
i).
emi.
a0)

a)
5
a)
oO
a)
a)
BL)

on oo

or

ou

appear and his ‘outstanding residuals” remain unaltered. For the
years 1905-1909 a second line of the table contains the results
according to the observations of Mésting A.

Further, column 4 contains the differences between the mean
longitude according to the occultations and according to the mer.
obs., which have been arrived at by subtracting col. 3 from the
min. res. corrected with + 0.2. Finally in the last column I have
taken down the comparison of Ross’ formula with the mean results
of occultations and mer. obs. The latter had first been corrected,
however, for the mean of their differences with the former, since
these may be regarded as more free from constant errors. Although
these differences are distinctly fluctuating, the results of all observations
of the limbs were corrected with — 0.63 '), those of the crater observ-
auons with —O".43. Equal weights were given to the results from
both sources; for 1905—1908 I formed '*/, (occult. ++ obs. limb + obs.
crater). For 1909—10 only the results from the merid. observations
could be used, and I formed for 1909 */, (limb + crater).

From the comparison in the last column it appears, just as had
been shown by Ross’ comparisons themselves, that his formula cor-
responds fairly well with the observations; and we may say that
the errors of the mean longitude are known pretty accurately up
to 1909. If we mean, however, to obtain the most reliable value
for this error for the epoch of the solar eclipse of 1912.3, we must
pay special attention to the last difference for 1910.5 (which is
altogether confirmed by the results of the altazimuth-observations)
and on the course of the deviations in the last few years and we must
take it as probable that also in 1912 there will exist a positive

deviation of about + 1". Assuming this we find:
4 Ross. A Newe. II. A Newe. I.
1911.5 + 10 + 3"9 + 75
12.5 + 1.0 + 4.0 + 7.7
Although we must not forget that extrapolation by means of an
empirical formula is always dangerous, and that also before 1850 the
agreement with Ross’ formula was less close, I think that we may
assume as the most probable correction of the mean longitude for
1912.3, a value between + 7".5 and + 8.0.

2. HANsEN’s constant term in the latitude of the moon.
It is generally known that Hansen believed he had rendered
probable that the centre of gravity of the moon does not coincide

1) The correct mean deviation is — 060; the difference is immaterial.

( 693 )

with its centre of figure. He showed that two of the three relative
co-ordinates, the one in the direction of the radius vector and the one
perpendicular to the radius vector and on the ecliptic’), might be
determined by the observations. The first he derived from the values
for the great perturbations which he thought were found greater
from observation than from theory. The second he derived from a
constant difference between the declinations observed at Greenwich
and those computed with the assumption that the centre of the
moon in the mean describes a great circle.

Now as regards the first point, Newcoms has clearly shown in
18687) that Hansen’s grounds were fallacious and since that time
it has been assumed — I believe without closer investigation —
that there was no ground either for the assumption of a deviation
in the direction of the latitude. Hansen himself had already pointed
out that the last mamed deviation might be explained by constant
errors in the observed declinations, and this is at any rate a point
of great importance for the question.

When I commenced my first investigations in 1903, 1 supposed
the constant term in the latitude of —1".0 to have been omitted
in the ephemerides already for a long time. I was strengtliened in
that belief by finding only small amounts for the mean difference
4d between observation and computation: as mean value for the 5
years 1895—1899 exactly 0.00 (Proceedings Amsterdam 6 p. 384).

Mr. Cowk.u’s remarks, however, in his first paper on the analysis
of the errors of the moon in The Observatory (September 1903)
made plain to me my iaistake. HaANnsen’s term appeared to be still
taken into consideration in the computation of the ephemerides.
Yet I could come to no other conclusion than that notwithstanding
this the mean differences between observed and computed declinations
were small (Proceedings 6 p. 4138 footnote 3 and p. 421).

As, however, the error in latitude is of special importance for
predicting the circumstances of the approaching eclipse, and as the
problem of a possible asymmetry of the moon is also worth our
attention by itself, I was desirous to elucidate this point if possible.
I tried to do this by investigating the mean deviations in d for the
years 1895—1909 according to the Greenwich observations.

To this end there was wanted first the formation of the mean
annual deviations 4d (= Obs. —Comp.), secondly an investigation into
the systematic corrections still to be applied to these Ad.

The first work had already been accomplished for the years
1) Monthl. Not. 15 p- 13 et seq. Memoirs R. Astr. Soc. 24.

2) Proceedings of the American Association for the advancement of science 1868.

( 694 )

1895—1902 (Proceedings 6 pp. 384 and 421) and it seems to be better
to use the values @ of p. 421, which, moreover, differ only slightly
for the first 5 years from the */, (N +5) of p. 384. We must only
pay attention to the fact that following Newcoms’s Investigation,
those differences had been taken in the sense Comp.— Obs., so that
we have to reverse all the signs.

For the years 1903—09 | formed annual means of the 4d in
the Greenw. Obs. (A N.P.D. C—O = Ad O—C) after the same three
methods 1, 2 and 3 which I had followed for the Ae (see above).
Naturally instead of the observations of Limbs I and II we had
now to take apart those of the North and South limbs. Besides, for
the last 5 years [I could also use the observations of Mésting A for
which I formed mean values in the same two ways 1 and 2 as |
had done for the Aa. Finally I took again the means of the mean
values 1, 2, and 3 for the limbs and 1 and 2 for the crater as these
seemed to be for the present moment the most reliable results.
These different results have been collected in the following table.

3 (North Limb + South Limb) Mésting A
1 2 3 Mean 1 | 2 Mean
Leeman |
1903 — 0"26 | — 0"16 | — 0"26 023
1904 | — 0.11 | — 0.26 | — 0.21 io 0.19
1905 0.36 0.28 0.49 | — 0.38 |} — 0”15 | — 0"24 | — 0"20
1906 | — 0.07 | ~ 0.28 | — 0.28 — 0.21 | — 0.05 | + 0.05 0.00
1907 | — 0.53 | — 0.28 | — 0.51 | — 0.44] — 0.79 — 0.66 — 0.72
1908 | — 0.09 | — 0.12 | + 0.25 | + 0.01 | — 0.04 | — 0.13 | — 0.08

1909 | — 0.19 | — 0.05 | — 0.24 | — 0.16 | — 0.23 | — 0.18 | — 0.20

We must now consider the systematic corrections which have to
be applied to these results. They are of two kinds; Ist those which
proceed from the declinationsystem used at Greenwich in the different
years, 2ndly those which have special reference to the observations
of the moon.

As regards the first mentioned corrections, I thought it best to
reduce all 4d to Newcome’s fundamental system, which offers, at
least for low declinations, the best guarantees for freedom from system-
atic errors. There appears in the introduction to the 2nd 9 Year

( 695 )

Cat. p. 381 a comparison of the declinations of this catalogue with
Newcomsp and taking the mean of the results in this table between
65° and 115° N.P. D. we obtain

Jd Nuwc. —d 2°99 Y.C. = + 0".14.

So the only thing left to do is to reduce the results of the different
years to the 2nd 9 Y. Cat., paying attention Ist to the employed
flexure, 2ndly to the employed colatitude and refraction. The varia-
tions in the constant corrections of the zenithpoint are of little
importance.

For the flexure used which was always deduced from the differ-
ence between direct and reflexion-observations, we can consult p. 18
of the introduction mentioned above. There it also says why it is
believed at Greenwich that the 7vea/ flexure has remained unaltered,
while the cause of the discordance in the different years must lie in
the reflexion-observations. As long as nothing has been proved to the
contrary this has to be accepted as probable. So we must add cor-
rections to the declinations of the moon, just as has been done to
those of the stars in constructing the 2nd 9 Y. Cat., in order to
reduce them to the flexure + O"60 sin Z. From 1906 upwards this
value has been used directly for the formation of the annual results. We
thus obtain (see for 1895 and 1896 the introductions to the Ods.; for
1897—1905 the introduction to the 2nd 9 Y. Cat.), assuming 0.75
as mean value of sin Z for the moon:

A Flex.-coeff. 4 Jd Moon
1895 + 0719 — O"'14
1896 + 0.23 =— (0) suf
1897 + 0.50 —— 0:38
1898 = 0.50 — ().38
1899 + 0.38 — 0.28
1900 + 0.28 — 0.21
1901 + 0.16 — 0.12
1902 + (0.34 —— () 26.
1908 + 0.34 — 0.26
1904 SEA D5) =019
1905 47029 == 1092

As regards the colatitude and the refraction, up to 1905 21'90 and
the refractions of the Zab. Regiom. have been invariably used, and these
values have served also for the construction of the 2nd 9 Y. Cat. Then
in 1906 the “Pulkowa-refractions” have begun to be employed and in
connection with these the colatitude 2180 was adopted. In the intro-

( 696 )

duction to the 2nd 9 Y. Cat. p. 20, a comparison is given between
the declinations according to the two systems. There we find as mean
difference between N. P. D. 65° and 115°:

Jd Cat — Jd New syst. = — 0" 36.

Finally a correction has to be applied in particular to the deeli-
nations of the moon, which results from the facet that the parallax-
values used at Greenwich are not the most accurate. We must dis-
tinguish between the correction of the general parallax-constant dp,
and that of the local constant for Greenwich dp,’. Their difference
depends on the ellipticity of the earth and they are connected by

do. ;
the equation dp’, = dp, + p, = in which @ is the earth’s radius

for Greenwich. At Greenwich HAnsrn’s p, has been employed and
further the ellipticity 1: 300.

So we must first see what correction is needed for Hansen’s p,
and for this we must also use the most probable value of the ellip-
ticity. | adopted as its reciprocal value 297.5, the mean of the results
of Hetmert and Hayrorp.

The value of p, is first of all determined by a comparison between
the foree of gravity on the moon and on the surface of the earth.
We find as the most probable correction of HANsEN’s constant assuming
ellipt. = 1: 297.5, according to Barrermann 13 p. 12,d p, = + 0".38,
according to Monthl. Not. 71 p. 539, dp, = + 0".40. I adopt

dp, = + 0".39.

In the second place a determination of this value is possible from
the corresponding observations of Mésting A made at Greenwich and
at the Cape in 1906—1910. Their discussion is to be found in
Monthl. Not. 71 526—540, from which we obtain with ellipt.
== Blea) 2

d i + 0'.26. :

These results agree very satisfactorily, but as the weight of the
first is probably considerably greater I adopt this unaltered.

Further, with ellipt. = 1: 297.5 we find for Greenwich, taking into
account the height of 47 m. above the sea-level, log 9 = 9.999111,
while at Greenwich 9.99911386 is employed.

In this way we find

)
pP,—- =r 0".02
and
dp,’ = + 0".37.
Thus the mean correction of the moon’s declination for Greenwich

becomes:

( 697 )

dé = + 0.75 & O".37 = + 0".28.

So we finally find as resulting corrections for the declinations of
the moon first of all always + 0.14 + 0'.28 = + 0".42, and in the
second place for 1895—1905 the corrections derived for each year
resulting from flexure and for 1906—O9 the correction — 0".36
resulling from refraction and colatitude. Our results from the Green-
wich observations, the sums total of the corrections and the corrected
results are

Ad Correction A d corr. Mean.
S95 O6 + 0"28 + 0'12
See I ENS, St 05s
9% O27 2 0.04 + 0.31

93) —=0:08 + 0.04 — 0.04
99 — 0.35 + 0.14 — 0.21 + O"14
1900 —0"55 + 0'21 — (aye
Oil = OB 10.30 = 0:24
02 —0.438 + 0.16 =) DY
C303 + 0.16 = 0%
04. — 0.19 + 0.23 + 0.04 — ("17
0555 —= 038 + 0.20
ee () Es — 0.09
OG — OA + 0.06
OO " —— ().04
07 —0.44 + 0.06
— .72 a — (0752
08 + 0.01 + 0.06
— 08 5; + 0.02
1909 —OAG + 0.06
— 20 ie — (0.12 — (0.15

Mean — 0'06

For the years 1905—O09 in’ the second column there are given
first the results from the observations of the limbs, then those from
Mosting A; in the fourth column they have been taken together.
The results from the separate years often show rather considerable
fluctuations, but in the mean values from 5 years which are given
in the last column, these have already diminished greatly and the
final result from the whole of this 15 years’ period amounts to — 0°06.
The mean result from Mésting A is in good accordance with that from
the limbs. In Proc. Acid. Amst. 6 p. 422 1 observed that from inequalities
in longitude with a period of about a month, there proceed terms of

( 698 )

long period in latitude; and that with the greatest inequality of this
kind which is neglected in the ephemerides, — the Jovian-eveetion —
corresponds a term of 17 years’ period in latitude with a coefficient
of about 02. The influence of this term, however, must have almost
disappeared in the result of the 15 years’ work.

Thus the result of our investigation is that HANsen’s constant term
in the latitude — 1.0 is necessary to make theory agree with the
observations of the limbs and of Mésting 4, even when these have been
freed as well as possible from systematic errors. We now find dp*=
—1".06 while Haxsen found —1".01"). Can this result point to the
existence of an inequality in the latitude of very long period or must we
accept Hansen’s hypothesis of asymmetry in the moon? In the latter
case the centres of figure and of gravity, according to this computation
would be 2.0 kilom. apart, which distance is much less than what
Hanspn believed he had found in the direction of the radius vector
(59 kilom.) and which perhaps we need not consider too abnormal.

Geology. — “On the so-called atolls of the Kast-Indian Archipelago”.
By Prof. A. WicHMANN.

(Communicated in the meeting of December 30, 1911).

The geographer J. F. Nimrmnyrr pretended a short time ago that
hitherto it was generally held that barrier-reefs and atolls “were
entirely or almost entirely denied to the coasts of the Archipelago”,
that “this view was an error’ and that the structure of these barrier-
reefs “was a new evidence against the theory of Darwin”. *)

This ‘generally’? supposed absence of barrier-reefs and atolls had
hitherto not been evidenced at all, though a great number of natura-
lists will have been convinced, that they are wanting, because the
reports lacked sufficient conclusive force, and moreover the Archipelago
in general bears the character of an extensive upheaval territory in
which there is no place for such like coral-formations. In order to
remove as much as possible every uncertainty, I intend to investigate
in how far these reports are well founded.

When about SO years ago Crartes Darwin first published *) his

1) Monthl. Not 16 p. 14.

®) Barriére-riffen en atollen in de Oost-Indiese Archipel. Tijdschr. K. Nederl.
Aardr. Genootschap. (2) XXVIII. 1911, p. 877, 898. — Barriére-riffen in den
Oost-Indischen Archipel. Handelingen van het 13de Nederl. Natuur- en Geneesk.
Congres te Grouingen. Haarlem 1911, p. 368.

3) The Structure and Distribution of Coral Reefs. London 1842,, 24 ed, 1873,
3' ed. by T. G. Bonney, 1889., new. ed. by Jonny W. Jupp, 1900.

( 699 )

work, the evidence he disposed of was still very incomplete and
not in every respect to be relied upon, so that he was not always
able to decide into which category the mentioned reefs were to be
placed. He came to the result that, with sufficient certainty, only
fringing-reefs could be pointed out in the East Indian Archipelago,
yet he was inclined to think the existence of other forms of reefs
possible and even probable. We shall first submit the latter to a
further investigation.

According to the then existing charts he thought if possible, as
regards the Aru, Vanimbar and Timor Laut Islands, that they
were surrounded by barrier-reefs, but on account of the prevailing
uncertainty he desisted from colouring them as such on his map’).
From the reports of F. A. A. Grecory it appears already that there
ean only be question of fringing reefs’), extending, according to the
most recent reports, generally 1—6 sea miles, S. W. from the island
of Trangany even as far as 13 from the shore. *)

Sumba or Sandal-wood Island. On account of a statement of JAMES
Horspurcn regarding a reef, extending at the southern shore of this
island as far as 4 miles, and of the great depth of the sea in the
neighbourhood *) Darwin thought the existence of a barrier-reef
there likewise probable (p. 174). From recent information it appears
however that only a fringing-reef exists.

Luang. According to a statement) that the extensive reef of this
island is steep outside and there within has a depth of 12 feet, Darwin
supposed that it might be a barrier-reef. The most recent statements
however prove it to be a fringing-reef. ")

Ceram Laut, Goram and Kefying. In his supposition that the reefs
extending from these islands into deep water belong to the barrier-
reefs, Darwin refers to G. W. Eart.*). According to the most recent
evidence however the Ceram Laut /slands are situated, on a large
“very steep coral-reef, extending eastward to the North of Suruahz.
“In this coral-reef some deep gullies are found among which the

1) The Structure and Distribution &e. 1842, p. 172.

2) Zeemansgids voor de Vaarwaters naar en door den Molukschen Archipel.
Amsterdam, 1853, p. 263, 277, 284.

3) Zeemansgids yoor den Oost-Indischen Archipel V, ‘s-Gravenhage 1908, p.
13, 17, 29, 55.

4) India Directory. 4t® ed. 11. London 1836, p. 607.

5) D. H. Kotrr Jr. Reizen door den weinig bekenden zuidelijken Molukschen
Archipel. Amsterdam 1828, p. 130, were it is said 9—12 feet.

8) Zeemansgids voor den OostIndischen Archipel V. 1908, p. 9.

‘) Sailing Directions for the Arafura Sea. London 1837, p. 9.

( 700 ) :

“straits of Kefying and Kilvaroe are navigable for large ships. *)

Further Darwin writes (p. 176): “in the space of the sea, north
“of the great voleanic chain, from Timor to Java, we have also
“other islands, such as the Postillions, Nalatoa, Tokan-Bessees, &ce.,
“which are chiefly low, and are surrounded by very irregular and
“distant reefs. From the imperfect charts I have seen, I have not
“been able to decide whether they belong to the atoll or barrier-
“classes, or whether they merely fringe submarine banks, and gently
“sloping land.

“In the Bay of Bonin, between the two southern arms of Celebes,
“there are numerous coral-reefs; but none of them seem to have an
“atoll-like structure. IT have, therefore, not coloured any of the islands
“in this part of the sea: I think it, however, exceedingly probable
“that some of them ought to be blue. I may add that there is a
“harbour on the 5. E. coast of Bouton, which, according to an old
“chart, is formed by a reef parallel to the shore, with deep water
“within, and in the voyage of the Coquille, some neighbouring is-
“lands are represented with reefs a good way distant, but I do not
“know whether with deep water within. I have not thought the
“evidence sufficient to permit me to colour them”. As to the Sabalana
| Postillon| Islands it is known that they form a group of low and
overgrown islands, rising above a submarine plateau *). The 528 m,
high Kalao Tua slopes steeply down towards the sea and is only
provided with a fringing-reef*). Binongka, the principal island of the
Tukany Besi-group, consists of terraces of coral-limestone and is
surrounded by a narrow fringing reef‘). What regards the reef on
the south-east coast of Budo *), there reefs of any signification are
in reality unknown‘). Darwin’s expectation that atolls would be
discovered in the bay of Boni was not realised. Only low coral-

1) Zeemansgids ete. V. 1908, p. 141.

*) F. A. A. Greaory. Zeemansgids 1853, p. 18. — Zeemansgids voor den
Oost-Indischen Archipel V. 1996, p 380-382. — Max Weser. Introduction et des-
cription de l’expédition. Siboga-Expeditie 1. Leiden 1902, p. 23.

8) G. I. Typeman. Hydrographic Results of the Siboga Expedition. Siboga-
Expeditie III. Leiden 1903, p. 18.

4) Max Weser. Introduction et description, blz. 95—97. — G. F. Typeman.
Hydrographic Results, p. 41—42. — Zeemansgids voor den Oost Indischen Archi-

pel IV. 1906, p. 208 — 209.

°) L. I. Duperrey. Voyage autour du Monde sur la corvette La Coquille. Hydro-
graphie. Atlas. Paris 1827, Pl. 37. Carte du détroit de Wangi-Wangi.

‘) Zeemansgids voor den Oost-Indischen Archipel IV. 1906, p. 214, — Aanvullings-
blad 2. 1909, p. 28.

( 701 )

islands of the common character’) are found there. Two spherical-
shaped reefs indicated on the chart, with deep water within, in the
Straits of Makassar (4°55’S.), showing a more atoll-like character
than any other in the Archipelago, were left uncoloured, because
Capt. R. Moressy doubted this fact.

Karakelang (Talaut-Islands) was said by J. Horssuren to be lined
by a dangerous reef, projecting several miles from the northern shore,*)
Darwin had left the whole group uncoloured, because he could not
find any other account. According to recent, more reliable, statements
only fringing-reefs are found near Karakelang *).

The Aju and Mapia-Islands belong indeed to the Duteh possessions,
but are situated already in the Pacifie Ocean, so that they should not
be treated of here. Occasionally we may remark that it was Darwin,
who indicated the atoll-character of the Mapia-Islands according to
the chart published by Pain. Carteret‘). Darwin was less well-
informed with regard to the Aju-/slands ‘). These possess no atoll-forms.

Not until the year 1875 new atolls were supposed to have been
discovered in the Indian Archipelago. On May 11, 1875 the
corvette “Gazelle” commanded by G. E. G. von Scaieritz anchored
near the island of Dana { Hoki| situated between Sawu and Sumba
10°49’ S., 121°19’27" E.*). According to TH. SrupxEr it consists of a
ring-shaped wall of coral-limestone about 120 m. high’), and has an
opening in the N.E.*). There is a cup-shaped valley within containing
a saltwater-lagoon. According to other statements the island is low
and only along the north-east coast a ridge of hills reaching a level
of 170 feet extends, whilst on the westside a separate hill rises
having the shape of a short horn’). There can be no doubt that

1) Ibid., p. 265 et seq.

2) India Directory. 4th ed. If. London 1836, p. 504.

3) F, A. A. Grecory. Zeemansgids 1853, p. 320. — Zeemansgids voor den
Oost-Indischen Archipel IV. 1906, p. 68.

4) Journ HAwkeEswortH. An Account of the Voyages ete. I. London 1773, p. 608

5) Tus. Forrest. A. Voyage to New Guinea and the Moluccas. London 1779,

p. 82. — J. Dumont pD’URvILLE. Voyage de la Corvette 1’Astrolabe. Atlas, Pl. 38.
6) Die Forschungsreise S. M. S. “Gazelle” 1874—1876. I. Reisebericht. Berlin
1889, p. 146.

7) Elsewhere (Travaux de l'assoe des Soc. Suisses de Géogr. II. 1882 Genéve.
p. 180), Sruper says, that that level amounts to 60 m,

5) Die Forschungsreise S. M. S. “Gazelle”. III. Zoologie und Geologie. 1889,
p. 197—199. According to von ScHLeErnitz however the opening of that ridge is
towards the W.

9) A. G. Fryptay. A Directory for the Navigation of the Indian Archipelago.

3d ed. London 1889, p. 747—748. -- Zeemansgids voor den Oost-Indischen
Archipel IV. 1906, p. 457—458. According to the most recent report there are in
47

Proceedings Royal Acad. Amsterdam. Vol. XIV.

( 702 )

the upperpart of the mentioned ridge consists of coral-limestone, but
whether — as StTupER supposes — it is an upheaved atoll may be
doubted. For he says himself that there is found in it “streifenartig
eingelagert ein réthliches Conglomerat von Kalk und dichtem Thon”
which does not correspond with it. At any rate the island in its
present condition is entirely normal, as it is surrounded by a fringing-
reef of 0.2—O.3 miles.

Lucipara Islands | Nusa Pari|. This group situated in the Banda
Sea, consists of 5 smal! islands of coral-limestone’),- united by a

«no

484

(101

153

1:3000C9
Fig. 1.

connecting reef about 9.38 km. long from N.W.—S.E, (Fig. 1). When
in 1875 the above-mentioned “Gazelle” approached that group von
ScHLEINITZ supposed he ought to regard it as an atoll, but the boat
that happened to come in the neighbourhood of the western island
was not able to find the entrance to the “wie es schien, flache
Lagune’”’ ’).

Since that time the Lucipara Islands were regarded as an atoll,
though it was difficult to find a satisfactory explanation*) for it, and

Dana 2 lakes with saltwater, and on the north coast rises a recognisable barren
rock almost as high as the 120 feet high plateau in the eastern part of the island.
(Zeemangids LV, Aanvullingsblad 3, 1910, p. 68).

1) R. D. M. Verpeex. Molukken-Verslag. Jaarboek van het Minwezen in Ned.
Oost-Indié. XXXVIL Wet.ged. Batavia 1908, p. 568—570, fig. 487. — Voor-
loopig verslag over een geologische reis naar het oostelik gedeelte van den Indi-
schen Archipel. Batayia 1900, p. 35.

2) Frhr. von Scuurtntrz. Die Expedition S. M, 8. “Gazelle”. Ann. d. Hydrogra-
phie. IV. Berlin 1876, p. 53. — Die Forschungsreise 8S. M.S. “Gazelle”. I. Reise-
bericht, p. 157.

3) R. LAnGpNBECK. Die Theorieen tiber die Entstehung der Koralleninsela und
Korallenriffe. Leipzig 1890, p. 141.

( 703 )

though from older descriptions and charts it was obvious that there
was no sufficient foundation for this view'). It was undeniably
refuted by the researches of the “Siboga’” by which, at the same
time, the southern island was determined at 5°30'40" S., 127°33'22”" E.
(Fig. 1)*). According to the recent investigations of VerBerk there
is no longer any foundation for the supposition that a voleano was
hidden under these islands.*)

Gisser | Gesir] (8°52’29" S., 130°52'26" E.). Since the time of
F. Vatentiwn we have known about Gisser, belonging to the Ceram
Laut Islands that there was “een fraai bogtje vlak in *t midden” *
{a beautiful little bay exactly in the middle]. J. A.C. Ouprmans too
makes mention of a ‘“‘schoone 4 a 5 voet diepe baai’’ °).

H. von Rosrensere called the island a ring-shaped upheaved sand-
shoal"), whereas Henry O. Forprs was the first to take it for “a
mere horseshoe-shaped, cocoanut-fringed atoll’) and most of the later
visitors concurred with him in this view‘). As I remarked before
et W. H. Romspour van Loon. Mededeeling aangaande de Lucipara- en Schild-
padseilanden. Verhandel. en Berigten betrekkelijk-het Zeewezen. IV. Amsterdam
1844, p. 752—757 — F. A. A. Gregory. Zeemans Gids. 1853, p. 153—154.
— Gevaren in de Jndische wateren. Tijdschr. teegew. aan het Zeewezen. (2) LV.
Medemblik 1844, p. 317.

2) Siboga-Expeditie I. Max Weber. Introduction et description, p. 97—100,
Ill. G. F. Typeman. Hydrographic Results, p. 42, Pl. XIl. — Maatschappij tot
Bevordering van het Natuurk. Onderzoek der Nederl. Kolonién, No. 10, p. 14.,

No. 11, p. 8. — Zeemansgids yoor den Oost-Indischen Archipel. V. 1908, p. 83.
3) R. D. M. VerBEEK and R, Fennema. Geologische beschrijving van Java en
Madoera. I. 1896, p. 8. — R, LAnGENnBecK |]. c. — MAx WEBER l. ec.

4) Oud en Nieuw Oost Indien. I. Dordrecht—Amsterdam 1724, p. 60. For the
- rest VaLentiyN was not thoroughly acquainted with the island, for he called it
“high, narrow and mountainous”.

5) Verslag van de bepaling der geographiscke ligging van eenige punten in de
Molukken. Natuurk. Tydschr. Ned. Ind. XXX. Batavia 1868, pp. 184—185.

6) Beschriving van eenige gedeelten van Ceram. Tydschr. voor Ind. T. L.
en Volkenk. XVI, Batavia 1867, p. 1382. — Der Malayische Archipel. Leipzig
1878, p. 295. :

7) A Naturalist’s Wanderings in the Eastern Archipelago... trom 1878 to 1883.
London 1885, p. 299. — Wanderungen eines Naturforschers im Malayischen
Archipel. Il. Jena 1886, p. 21. The cocoa-nut trees existed only in his imagination.
These trees are not found in the island.

8) Siboga-Expeditie I. Max Weser |, c. p. 79, Ill. G. F. Typeman |. c. p.
39—36 — Maatschappi tot Bevordering van het Natuurk. Onderz, Bull. No. 31.
1899, p. 12. — [N. M. van pen Ham]. Mededeeling betreffende de reede yan
Gisser. Meded. op Zeevaartkundig Gebied, No. 17/46. ’s-Gravenhage 1900. p.8 —
Zeemausgids voor den Oost-Indischen Archipel V. 1908, pp. 142—143. — H. Hirscut.
Reisen in Nord-West Neu-Guinea. Jahresbericht der Geogr. Ethnogr. Ges. 1907 —8,
Ziivich 1908, pp. 142—148.

47*

( 704 )

this view was erroneous’). The whole
island is only the part ofa shoal rising
above high-water mark and chiefly
consisting of coral detritus and fora-
minifera, and may be regarded as the
upper part of a coral reef. The lagoon,
ostensibly an excavation into this debris,
drains itself entirely at ebb-tide, so that
one can walk through it dry-shod. Its
formation may be compared to that
of Kuropa Island in the Canal of
Mozambique, with this difference how-
ever that its bed remains below the
level of low water’).

Pasigi (2°21' N., 125°18' O). From

Pig.2. olden times the island of Pasig, situated
W. of Vaglandang (Sangi Islands) was only known as a low, flat
little island *).

A. J. van Deniprn added to this that it was lying on the top ofa
reef rising above the level of the water. *) J. Sipnny Hickson, who
saw Pasigi in 1885 from the top of the voleano in the island of
Ruang supposed that it might “serve as a diagram of an atoll” *).
Afterwards he expressed himself thus: “The part above water
covered with trees is only a small are of the rim of a large almost
ringshaped atoll’ "). He considered this to be a fact not agreeing
with the theory of Darwix. M. Korrrserg who had seen Pasig? from
the same standpoint expresses a more reserved opinion. Moreover
the commander of the Govern. S.S. “Raaf’ J. Kaan had declared
the island to be a coral bank’). None of them has ever observed

1) Maatschappij tot Bevordering van het Natuurk. Onderzoek der Nederl. Kolo-
nién. Bulletin, No. 43, 1903, p. 22, vide likewise R. D. M. VerpeeK. Molukken-
Verslag. Jaarboek v. h. Mijnw. XXXVI. Wet. ged. 1908, p. 642.

2) Aurrep VorLrzKow. Bericht tiber eine Reise nach Ost-Afrika. Zeitschr. Ge-
sellsch. f. Erdkunde. Berlin 1904, p. 428.

3) F. VaLentisn. Oud en Nieuw Oost Indien. I. 1724, p. 61.

4) De Sangir-eilanden in 1825. Indisch Magazijn. lste.Twaalftal, No. 4, 5 en 6.
Batavia 1844, p. 356.

5) Omzwervingen in Noord-Celebes. Translated by P. P. CG. Horx. Tijdschr.
Aardr. Genootsch. (2) IV. 1887, M. U. A., p. 141.

6) A Naturatist in North Celebes. London 1889, p. 44.

7) Verslag van een onderzoek naar de uitbarstingen in 1904 op het vulkaan-
eiland Roeang. Jaarboek van het Mijnw. N. O.-Indié, XX XVIII. Wet. ged. 1909,
Batavia 1910, p. 210.

( 705 )

any thing of a lagoon, and the somewhat bent shape does not
authorise us to regard it as an atoll.

According to the most recent statements Pasigi has a diameter
of about 0,5 mile, is a low coral island surrounded by a reef extend-
ed on the south side as far as 0,2, on the north-side as far as
2,5 miles ').

The statement of Hickson that Tagulandung was surrounded by a
barrier-reef has neither proved to be correct. Besides a reef in the
fairway of Ruang and Tagulandang there is only a fringing-reef?).

Agnieten Islands | Pulu Pangang\, Hoorn Islands { Pulu Ajer|
and Groot-Kombuis | Pulu Lantjang\. C. Pu. Siurrer was of opi-
nion that he had discovered atolls in the Java Sea, namely in the
Bay of Batavia. “Auch die grésseren Gruppen, die Agnieten-
“Inseln und die Hoorn-Inseln, sowie die Inseln ‘‘Groote Kombuis”’
“oder “Pulu Lantjang”’ sind betrachtlich altere Riffe, welche schon
“deutliche Atolle bilden. Es ist allerdings bei den Agnieten- und
“Hoorn-Inseln nicht unméglich, dass dort ein anderer Zustand besteht,
“wegen der ziemlich plétzlichen Senkung des Meeresbodens bis zu
“50 Faden. Vielleicht kommt hier ein unterseeischer Kraterrand vor,
“auf welchem die Korallen sich angesiedelt haben’ *). Siurrer had
previously asserted that in the Emma Harbour | Brandewyns Bay),
near Padang, in the neighbourhood of the islands of Arakataw in
straits Sunda, and Barwean in the Java Sea, barrier-reefs were found.
Contrary to this assertion R. Lancenpeck had already remarked that
in the above-mentioned regions all those reef-forms are wanting, and
that they are to be regarded as coral-formations of the shallow seas
(patch reefs), the rims of which are some times higher than the other
parts ‘). With regard to the Agnieten Islands we are further informed
that they consist of 5 low islands, lying on a common reef 4
miles long and 1,3 miles wide*). On these reefs one finds basins of
which the western one is rather extensive, they can however no
more than the others be compared to lagoons of atolls, but are to
be regarded as depressions part!y formed by sejunction, such as are

1) Zeemansgids voor den Oost-Indischen Archipel 1V. 1906, p. 53-54.

*) Ibid. p, 52.

3) Eimiges iiber die Entstehung der Korallenriffe in der Java-See und Brannt-
weinsbal und tiber die neue Korallenbildung bei Krakatau. Natuurk. Tijdschr. Neder].
Indié. XLIX. Batavia, 1890 p. 378. — Ueber die Entstehung der Korallenriffe
in der Java-See... Biologisches Centralblatt. IX. Erlangen 1889-90, p. 751.

4) Die neueren Forschungen tiber Korallenriffe. Geogr. Zeitschr. III. Leipzig 1897,
p. 570.

*) Zeemansgids voor den Oost-Indischen Archipel I. ’s-Gravenhage 1899, p. 139,

( 708 )

fre jnently found on coral-reefs*). In the Hoorn Islands, the western
ones of whieh -— Great and Little Tidung — rest on a narrow
and low reef, whilst the eastern one — Pajung — is surrounded by a
separate reef I have not been able to detect any lagoons, no more
could | do so in Groot-Kombuis, consisting of 2 low islands ’).

Muaras {wmaras-|\reef (4°50' N., 112°55' O). This reef situated N. E.
of Borneo has become known by the British war-ship “Samarang”
which almost stranded on it‘). It has in NW.—-SE. a length of 30
km. and a breadth of 8.8 km. Whilst some parts fall dry at ebb-
tide as shoals, a few rise as little islands above the level of high
water. Inside the rim of the reef lies a deep basin which is however
not navigable on aceount of the great quantity of stones *). Whilst
Max Weber writes: “Ce récif rappelle, jusqu’au certain point, un
atoll’ °), J. F. Niermeyer considers it an undubitable fact that we
have here a real atoll-reef*). Thougb the reef shows indeed some
resemblance with an atoll, the north-western part proves already
that it is a coral-bank, which on account of the more rapid growth
of the rims gave oecasion to the formation of a basin.

Maratua (2°15’ N., 118°35’ E.). Until a short time ago very little
was known about the group of the Maratwa-[slands situated N.E. of
Borneo. In the 18 !century attention was first fixed on it by ALEXANDER
DaLRYMPLE*), and it was Maratua itself that was repeatedly touched
at by the Sulu pirates on account of its fresh-water springs. It served
likewise as temporal settlements of Badjos. Whilst the general very
particular shape of the island had been known for a long time, a
more careful survey was only undertaken in the beginning of this
century by the Royal Duteh Navy (fig. 3). From this survey and

1, The above-mentioned Zeemansgids (LI. 1900, p. 542) says about the Thousand
Islands: With some of these reefs one finds on the outer side dikes of coral stones
lying dry, within them more or less deep basins occur. In some of the large reefs
there are basins, in which a depth of 3 fathoms and more is sounded, and where
proas entering at high-tide can find a safe anchorage.

2) Zeemansgids voor den Oost-Indischen Archipel I. 1899, pp. 182, 138. —
Westelijke Vaarwaters naar Reede van Batavia. ‘s-Gravenhage. 1899. Dep. van
Marine, No. 86.

3) Str Epwarp Bexcuer. Narrative of H. M. S. Samarang during the years
1843—46. I. London 1848, p. 247—248, chart at p. 223.

) Zeemansgids voor den Oost-Indischen Archipel Ill. 1908, p. 843.

®) Introduction et description de l’expédition, Siboga-Expeditie I. Leiden 1902,

6) Barriére-riffen en atollen enz. Tijdschr. K. Nederl. Aardr. Genootsch (2)
XXVIII. 1911, p. 890, kaart XIII, No. 13.
7) Oriental Repertory. I. London 1793, p. 580.

(707 )

the additional description it appears that Maratua has the shape of
a V, the opening of which is towards the S. E. It was represented

aus
180

42400090
Fig. 3.

there in such a way, as if the V-shaped hill-ridge, the highest point
of which is 400 feet high, represents the upheaved northern rim of
an atoll, extending NW.—SW. over a length of 16 miles‘). In
this form this assertion is decidedly incorrect. The island is a ruin
of an older date, the reef on the contrary a real fringing-reef — a
recent formation. Whether in earlier times Maratwa has been an
atoll can only be decided by further investigation.

Kakaban. This island situated 4 miles S.W. of Maratua consists
of a rock-wall 300 feet high, which in some parts is no more than
150 m. broad and encloses a large salt-water lake. According to the
statement of natives this lake must be in connection with the sea,
as it is influenced by ebb and tide. If another statement that only
small fishes are found in it, should be true, there can be no question
of an open connection. In most places the help of ladders is required
to land on the island, because the rocks fretted by the sea, beetle.
Only by careful investigation it can be decided whether AKakhaban
has in former times been an atoll. In its present state it cannot be
regarded — as it is pretended as an atoll ’).

The fact that it is surrounded by a fringing-reef, which however is

1) Zeemansgids “voor den Oost-Indischen Archipel III. 1903, p. 849—851., vide
likewise J. Ff. NrerMeyer. Barrieré-riffen en atollen, p. 890.

*) Zeemansgids voor den Oost-Indischen Archipel III. 1903, p, 851—852, —
J. F. Nrermeyer. Barriére-riffen en atollen, p. 890.

( 708 )

nowhere broader than 100 m., proves that, for the rest, it is in a
normal condition.

The Bril | Taka Rewataya] (6°4' S., 118°55’ E.). This very dangerous
reef, situated in the middle of the fairway has been known long
since '). Not before 1792 however a local survey took place, when
a boat of the ‘Pitt’ found in some spots 2 feet of water and a
sandy nature of the bottom’). Whereas in former times the Bril
was always regarded as a bank*), the latest author calls it a coral-
overgrown atoll-shaped bank, which is a contradictio in terminis.
It runs dry for the greater part at ebb-tide, with the exception of
the rather deep basin in the middle, and the southern part where
from 3'/, to 5 fathoms of water stands ‘*).

Brisbane-reef. On the 15. Januari 1880 the steamship “Brisbane”
stranded on a hithertho unknown reef, which was called after this
ship’). In 1902 a light-house was erected in the island JMeati
Miarang (4° 22' ,' S., 128° 29'/,' E.) situated near the southern
point*). Between this island and the two Ukenao Islands (Meati
Rialam and Amortaun) situated in the N., extends the very large
reef 221!/, km. long and 9'/, km. broad, enclosing on the East-side
along basin, nearly for the whole length; the southern part only
was explored. On the east-side there is an opening’’. According
to the researches of R. D. M. Verpevk the three islands mentioned
consist of coral-limestone and are consequently older than the reef
that is their common fringing reef*). There can be no question of
the existence of an atoll, though Nimrmeiver calls it so °).

Angelica-reef | Pasir Layaran| (7°46,5' S. 122°15' E.) This reef
was discovered on 3" of July 1801 by the ship “Angelica” and described

') The Bril was apparently called after a ship of that name that was reported
in 1694 (l’. Vatentin. Oud en Nieuw Oost-Indien. I. 2. 1724, p. 29). The reef
has been known by its present name since the beginning of the 18th century.

*) The Oriental Navigator. 2d ed, London 1801, p. 516. — J. HorspurcH
India Directory. 4th ed. IL. 1836, p. 532.

®) J. Scoréper. Over de Bank de Bril. Verhandel. en Berigten betr. het Zeewe-
zen. IV. Amsterdam 1844, p. 651—652.

*) Zeemansgids yoor den Oostind. Archipel III. 1903, p. 608 2nd edit. 1909,
p. 511. — J. F. Nuekmeyer. Barriére-riffen en atollen, p. 890, map XIV, fig. 18.

®) Rif en eiland (‘‘Brisbane’’) ontdekt. Bericht aan Zeevarenden. ’s-Gravenhage
1880, N°. 15/397.

®) Licht wordt ontstoken. Bericht aan Zeevarenden. 1903, N’, 229/1713,
248/1870.

7) Zeemansgids voor den Oost-Indischen Archipel. V. 1908, p. 8—9.

*) Molukken-Verslag. Jaarboek van het Mijnwezen. XXXVII Wet. ged. 1908,
p. 445.

°) Barriére-riffen en atollen, p. 890, map XIV, fig. 17.

( 709 )

as of a circular shape, 4 miles in diameter and at the north- and
south-end nearly dry’). Repeatedly ships were wrecked on it. When
in 1846 the brig “Haai” ran aground on it, if was discovered that
the reef was divided into three parts by two small gullies, on the
middle-part rocks rose just above the level of the sea*) Not before
1908 an exact survey was made by the exploring vessel “Soembawa’”’,
which gave the very remarkable result, that the Angelica-reef was
io be considered as an atoll, 6.95 km, in WNW.—ESE. long and
417 km. broad?). It is the first of all reefs that has a real atoll-
shape, though it differs from the normal form, and two basins are
found in it.

GosongBoni (8°23' S,, 122°14' E.). This reef was discovered in
1851 by P. Konine*) and represented by him as a small island
(Pulu Boni)*) with which a semi-circular reef was united that ran
dry. According to the surveyings of the “Soembawa” this reef has
likewise the shape of an atoll*). It has a diameter of 2'/, km.,
whilst the depth of the basin amounts to 40—50 fathoms’).

Lalanga-reef (1°2' S$. 120°40' E.): This reef situated in the bay of
Tomi is described as a large coral reef running for the greater
part dry and steeply sloping down everywhere except on the east-
side*), From the fact that there are on the east-side two diverging oft-
shoots NreRMEYER supposed he might conclude that the reef had the
character of an atoll’). This conclusion has no foundation whatever,
not even the shape reminds of an atoll.

Somewhat more than | km. to th south of the Lalanga-reef, a
ring-shaped reef is found. A regular fishing is going on in the basin.

1) James Horspurau. India Directory. 4th ed. Il. London 1836, p. 610.

*) CG. F. Sravenisse DE Brauw. Het vastzeilen van Zr. Ms. brik De Haai op de
Argelika’s Droogte. Verhandelingen en Berigten betr. het Zeewezen. VIIL. 1848, p. 704.
H. D. A. Sirs. Zeemansgids voor de Kilanden en Vaarwaters beoosten Java.
2nd ed. Amsterdam 1859, pp. 39—40.

8) Bericht aan Zeevarenden. ’s-Gravenhage 1908, No. 154/232. — Zeemansgids
voor den Qost-Indischen Archipel 1V. Aanvullingsblad 2, p. 91. — J. F. Nipr-

MEYER. Barriére-riffen en atollen, p. 891. map XIII, fig. 16.

4) Chart of part of the North-coast of Flores, Novbr. 1851 (J. G. F. Brumunp.
Indiana. I. Amsterdam 1853, at p. 131).

*) Boni is the name of the Malay navigators, the inhabitants of the neighbouring
north-coast of Flores call it Taping.

6) Zeemansgids voor den Oost-Irdischen Archipel. IV. Aanyullingsbl. 2. 1909,
p. 90. It is remarkable, that the bottom of the basin consists of white clay.

7) NIERMEYER reports I. c. p. 891 1.5 f. t. a depth of 885 m., 1.9 f. b. of
105 m.and according to map XIV. fig. 19. of 85 m.

5) Zeemansgids voor den Oost-Indischen Archipel 1V. 1906, p. 138.

*) Barriére-riffen en atollen blz. 891, chart XIV, fig. 21.

( 710 )

This reef is however no atoll. Nrermeyer still supposes that he must
regard another reef, likewise in the bay of Tomini SW. of the town
of Tomini about 0°24' N., 120°32', as belonging to the atoll- formations.
It is impossible for me to recognise an atoll-formation in it’).

At last two more reefs in the Java-Sea remain, situated NNE. of
Boompjes Island | Pulu-Rakit|, which Nimrmuyer considers as two
remarkable curiosities, beautiful atoll-shaped bars. “One would certainly
“call them atolls, if the notion deep-sea upheaval were not insepar-
“ately connected with this name” ’).

The result of the above considerations is, that among the islands
of the East Indian Archipelago, that are supposed to be atolls,
Dana, the Luciparas, Maratua, Kakaban and Meat Miarang
are formations of no recent date and provided with fringing-reefs,
whilst Gisser, Pasigt, the Agnieten Islands ete. represent coral form-
ations of the shallow sea. Consequently J. F. van BrMMELEN’s words
are still valid: ‘However rich the Indian Archipelago may be in
“such coral reefs, yet the two most known types of coral formations
“are wanting: Barrier-reefs and Atolls’ *), As to the reefs, that rise
only partly above the level of the sea, among these we meet no
more atoll-form with the exception of the Angelica-reef and the
Boni-reef,

Inseparately connected with this question about atoils is that about
barrier-reefs. As stated above those reported in former times do in
reality not exist. J. F. NigrmeEr supposes he has discovered them
now on a much larger scale, and adds the following explanation
to his report: “They are always built up along the rims of the

“sub-marine plateaus.... It is easily seen that, as a rule, they
“begin as isolated small reefs...., which can afterwards arrange

“themselves and form longer bars and islands. This structure is a
“new proof against Darwin’s theory, according to his theory the
“barrier-reefs would have originated in fringing-reefs. For in that
“case they would as a rule appear in more serried rows” *). It is
not very well possible to contest a theory when choosing as point
of issue another notion than the author’s. Darwin considered as barrier-
reefs “those, which like a wall with a deep moat within” surround
the islands, and held that “the lagoon-channels may be compared
“in every respect with true lagoons” *). The further explanations

1) Ibid. p. 891, map XIV, fig. 20.

®) Ibid. p. 892, map XIV, fig. 22.

5) Eneyclopaedie van Nederlandsch-Indié. II. ’s-“Gravenhage—Leiden, [1899], p. 290.
4) Barriére riffen en atollen, p. 879, 893.

5) The Structure and Distribution of Coral Reefs. 1842, p. 41, 48.

( Fit j

which he gives of these formations do not leave the least doubt
that his barrier-reefs are different from those described by NrermMewer.
These are formations of the shallow seas, patch reefs, or pelagic
reefs and no other reefs could be expected in an area of upheaval.

Physics. — “On the variability of the quantity b in VAN DER Waatls’s
equation of state, also in connection with the critical quantities.”
IV. (Conelusion). By J. J. van Laar. (Communicated by Prof.

H. A. Lorentz).

(Communicated in the meeting of December 30, 1911).

Let us write therefore:

2 (i) —— i( F ‘ Y \ a, 92 5) ,
g? (v—b) b"=— b (4) E + eg Saar (7p? + 22—1)], . (a)

then we get:

Go — 0) 8" + 47 (1 — 8)" — 290" T=

‘p\* dA -f1—v' 3 C(pNe
eas S) ae ee Oe ee ee ir
mj) dv me v—b v m

representing the form between [ | by A, and bearing in mind that

ap ee OA Von (LO 3 ¢
dv” v— bm’ dv (ale v—b ) m’
That last relation (see III, p. 575, formula (a@)) holds only for the

critical point, and is not general; so that we cannot derive /V ete.
from the formula for 6'", which we shall presently obtain. Now in

"

eV’ :
virtue of (a) (2) A may be replaced by —¢? Pas?) 0 and so we get:
m !

ee Dien ep (ll — Bly e?— om =

m
gp dA v—b (Giz
ee LH | eM a OWA
({) dv eee ey oss eo a>) Bie
1. e.
. . (py aa t=). & b"
g? (v—b) b"= — b 4) ae + b"q? r 1—d') — 6 pare +-— + (v —d) = | ;
m/) dv v m b
1 } ata

or as = 1 — 6’ 3 = which follows immediately from (1) (see III,

: 1 x
p. 578), hence also — = (1—d’) — 0’ al , we obtain :
m ¢

m?* dv

aA Fie een b
(00) = joe) ay peas : eae : D5 |.

J : : CA
So we still have to determine a From
av

gf r+¢
Az=1 + — + ap? 20>— 1
ziy e+1 Gee )

dA ip MG :
dv («+¢)? 2 =m) >i

ie Il a
+— | (- 34) oF 28-4 HM pe 4-2). 204 aie
etl v—b m

follows :

y (v—b)
; di dp -
when we substitute for < and — their values (see III, p. 578).
av av

Hence we find :
dA 1 a g
ales eis ——(wB*+-2p- 427 F page
dv v—b —m(e+tg)? ” v | | =

ea! : Lt
Now for ——-b’ we may write 1—W— (see above), so we have:
Y m

dA os Lh a p a er ap" +28—1 i 2 (1 +23)’m—1
dv v—b m ((«+-y) a+l1 w+l m

In consequence of this we get finally :
(v—b) 6” = - Bg ad at a peal = ae eee) ee! i
mo) e-g? | afl etl g

v—)b

2
-h'—— 2

a 35! jan) =
oO f v

GO| bk
(my
S
oa
a
S| Sy
~

or also

ily v Ae wv | ep? + 28-—1 2 (1 +28)’ m—1
is han r= 8: m* | (e@+q)? gon v+l f vite

v aD v—b 1 v—b b"v
ae 3b" v ; (1 = b') —_ 3 O_o + —- —
poe c

(3)

TT v sO)

So from this the value of 6” v? can be ealeulated at different
values of w, however (see above) only at the critical temperature,
because for the derivation from 6” we have made use of a relation
that only holds at the critical temperature.

The values of 6’v for different values of « will be calculated
further from the relation which also only holds at 7% (see III, p. 576

formula (17))
"(a a it |S} ;
9 —)/=——}] -— — — —p
é =| m | 2 v—b re y

( 713 )

In this p’ ='/,6'v. With regard to 6’ (or p’) we shall make use of
l /a 5 l

the relation (see above)
i ff
) <= — —-—,
m x«-+@

For e=1 and «=2 we have already the values of 8,y,m and
v:b. (See I, p. 295—296; II,.p. 429—430); for e=3 and «=4
we will first calculate them now.

For «=83 we find:

B= O9600) 3% = 054732

For then we get (see I, p. 295):

4
n= 0,947 < —— = 0,947 X 1,0309 = 0,9763
1+3p

~%

m = — nm = 151158,

“1| ©

Whereas we also have:

1
m=1 +7 B(L—B)(34+9)? = 14 0,0096X 12,063 = 1,1158

9 1
n=l $= A -B)B+9) + 55 BAL + 48-983 4 9)"
0,0012 35,4544 & 41,897
== 0597063;
3m?
——— ($5 15 jo, ZED) e
n

3m? —2

= 1 + 0,04323,473
lel O 150000175

9
eh
if

7 UR a ~ Uk
For — we find from —=
Df bp

Dee 3 (ll6)3| 73
Fee iO IETS

Ab : : A
As ¢~ = (1-+-28) —_, 0,122 is found for the value of —-— at
v—-b vp— bp

Co.
At x=4 we calculate (again in order that « may get the value

0,265, and f the value 7 (see I, p. 295)):
B= 096123) @—— 00408.

For then we have:

5
n= 6,947 < noe= = 0,947 1,0320 = 0,9773

(0 == Illia)

x1) ~o

m —

and also:

( 714 )

m—=1-+ - B(1 — 8) (44+ gy =1 4 0,007458 15.615) 169

0

6 |e A -
rl ane Bd ——) (4+ 9%)+ 50 B(t —)(1 + 68 — 1287) (4 + ¢)?
= 1+ 0,04475 < 38,9592 — 0,0007459 x 4,3197 x 62,061
= 1 + 0,1772 — 0,1999 = 0,9778.
So we find further :
18 XK a
bp id. —1,955 1,788. ——

Ab
For carrie find — 0,00842, so already negative.
vp— 0k

Now we are able to calculate the values of 6,', bg", and b,”.

m= 4
11. With regard to 6;/, we find successively from 6'= L
ep
(see above):
«1 |b, =0,05335 (see also H, p. 428)
UP —— 2 by. = 0,03187 ( ” ” ” ” 431)
z= 3|b,=0,01414
x=4| 0, = — 0,001079.
And for bg ve we get from (see above)
2,1
1 eee
Td (Ua)
| ie a a ade NC
&
m (: +- =
fp
successively :
2 = 15) pp" = — Oo, Ope 02990
w= 2 | p" = — 0,09788 | be'vg = — 0,1957
(See also II, p. 428 and 431)
v= 3 |p" = — 0,04720 | bp've = — 0,09441

«= 4 | p'=—0,003844 | by"ve = 0,007688. *
And now we ean also ealeculate the values of },'"v,?, namely from
the formula (3) mentioned above.
Writing in (8) for the last part with 6"v:

aa v Bre 28d 5 Oe
3b"v (1—b') -- — b'— | — b'v | 6 — — ],
v—b Bh) (a b

we find for 7z=1:

bpl'og? = 1,9953.

This value is very high. We have, however, taken the trouble to

( 715 )

derive a formula for 6'"v? in two more ways; the calculation yielded
in both cases 2,00, i.e. an identical result.
For «=2, however, this value already becomes lower. We
find then:
ays eye Sa cateetsy
For «=3 a still lower value is found. Then we have namely :
be'vz? = 0,6830.
For «=4, just as for b, and d,g'vg reversal of sign takes place.
We find:
bp vj? = — 0,05655.
From the available material of numerical values we may draw
up the following survey. It gives the values of 8 and ¢ ( and so

b Vie 4
also of 57M n, be bx, Ox'v~ and b'';2)2 } necessary that we may
v— D ke

get #=0,265 and f=7 in the critical point on our condition of
partial association to (7-+-1)-fold| molecule-complexes (see I, p. 295).
From this follow, indeed, certain values of 8 and gy, and from these
the other quantities are calculated.

== SS eT =

| ab | _ |
[We Pe

| |e + - i N in
z| B | ¢ n verbe | b', | bglvg | byl"0,2 (18a)

1 O2955) | 122711), 0.63 | 1.107 | 0.969 || 2.114 | 0.053 |—0.295 | 2.00 || —0.25
0.958 | 0.916 oa 1.113 | 0.974 || 2.102 | 0.032 |—0.196 | 1.38 || —0.23
| |

0.960 | 0.473 0.12 7 1.116 0.976 | 2.095 0.014 0.094 | 0.68 || —0.19
2.093 -0.0011 +0.0077—0.057, —0.14

—& WO ~

0.961 -0.041 . aU 1.117 | | 0.977 |
||

It is certainly striking in this that the values of @ and vg: b,
remain almost constant. When @ remains = 0,96, we always find

mr

, 0',6"",and

the value 2,1 for vg:bg. Only gy and with it also

E10)
Ab
Up— Op
be about 0,43 to bring the limiting volume at v=4 for constant x
to about 4-times the critical volume. So aceording to the above
table this would correspond to about 21,5 (association to double
or triple molecules). But if we assume w to be variable, it is very
Ab

v—

change greatly. We saw in I, p. 296 that the value of must

well possible that for 7% is e.g. only =0,12, and _ increases

( 716 )

when the formation of complexes progresses with decreasing liquid-
volume.
This is not inconsistent with the fact that in our above table

Ab P
ae becomes smaller and smaller when w increases. For the values
Up—OR
given in the table are those which would have to be assigned to

the different quantities at the critical temperature in order that ube

= 0,265 and f=7 — not those which can hold below or above

; Be Lb

it. If wee.g. take xv = 38 at 7p, then there ae = 0,12 Gn order that f
VUk—9R

may be = 7; ete.), and we may very well suppose that this quantity

assumes greater values below the critical point, when x becomes > 3,
because we may of course assume arbitrary values of 4b for the
different complexes; e.g. corresponding to the then holding vaiues of
the coexisting liquid volumes. Ete. ete.

However, no greater complexity may certainly be assumed at 7%
than at the utmost on an average quadruple molecules (v= 3),
because else A would become negative, i.e. b would decrease with
increasing volume at 7%, which is contrary to reality.

Let us now examine what the value becomes of the coefficient a’

of b', 6", and +" at 7 for different values of x in the formula (187)
derived by us, viz.:

' 2,1 \ 3 ' at " Ser
Co ale — (l—p') + pp") = pms | 1 + —2].. (182)
: | LR
For the denominator we get the following values.
FOL 2 ——ale
N = — 0,25387.

So we find a negative value for a’, viz. 1: (—0,2537) = — 3,942.
We shall see presently what the meaning is of this result.

For «= 2 we get:

N = — 032309:
For «= 8 we find:

N = — 0,1924,
And finally for «= 4:

N = — 0,1390.

We see from this that the denominator .V of the second member
of (18"), indeed, becomes smaller and smaller negative as a becomes
greater at Zk, but so slowly that it is the question at what value
of @ this negative value will pass into a positive one. At any rate

at a value of « for whieh (see the above table) Ad bas long become
negative, and so at an impossible value (for 7).

So we have to deal with the fact that @” isnegative, and the question
of the meaning: of this result.

12. This now is nothing but that the value of @ ie. of 4d,
caleulated with constant x, and hence also the values of 6, , bev: ,

by'"v.? are found too large. If we take w as variable — as agrees
with reality’) — also the differential quotients of « (with respect

to v) will occur in the expressions which we have derived for
bb", 6", and it will quite depend on the (as yet unknown) law of
the variability of « with v, what value the differential quotients of
6 will then have. j

As we said, nothing is known about the law concerning the in-
crease of the complexity with the diminution of the volume. For it
would be required for this that we knew a little more of the con-
stants of entropy *). The question: how many molecules will be asso-
ciated in a given volume to double, how many to triple, quadruple
ones etc. — this question will have to find its solution in statistical
thermodynamics.

At the same time.the question will then have to be answered,
what will be the variations of volume &b — real and apparent ones —
accompanying this; the apparent variation of volume of the asso-
ciating molecules in connection with the influence on the pressure.

But until these fundamental questions have been solved, we can-
not advance in this theory, and we shall have to content ourselves
with the obtained results.

If a* became really negative, this would imply that in the imme-
diate neighbourhood of the critical point not n= 1— a’V 1—m,
but m= 1 — a’Vm—1 would hold, in other words that when the
phases diverge, the temperature did not get below the critical tem-
perature, but above it, and that the saturation curve near 7% would
present a concave shape turned upwards (viz. in the v,7-diagram),.

This now would be impossible, even though it should be proved
mathematically that the saturation curve liquid-vapour then formed
a closed S-shaped region, which would be. entirely enclosed within
the more extensive region of the saturation curve solid-vapour. Then

1) I drew attention to this already in I p. 281 (ef. also Solid State VII p. 98
at the bottom) -
2) See among others KonnstammM and Ornstein, These Proc, of Dec. 1910,
p. 704 et seq.; OrnstEIN, Thesis for the Doctorate.
48
Proceedings Royal Acad. Amsterdam. Vol. XIV.

(748)

the isotherm in the point A’ would have the usual shape of the
isotherms below 7%, but with a point of injlection in the unstable
part. But this has no physical importance, so that as has been said,
we shall have to find the solution in a diminution of the values of
be, be’, and bg" in consequence of the increase of «(»=2+1 is
the number of molecules united to one complex).

Now it is noteworthy that the relation between the said values
changes little with increase of w.

From the above table (p. 715) we calculate e.g. :

RL——l | = bp've : bg =5,6 | dgvp? : — dp'vp = 6,8
2 6,1 | 7,0
3 Ox 4 7,2
4 | Un 7,4

If now, retaining$ the values of vg: bz, me, and gz), we take the
values of 6’, etc. found above all e.g. 0,68 times larger, we have :

p= De=0,68 ><10,05335 == 0103628) pt = top op —

— 0,68 X 0,1475 = 0,1003; pl” =7/, bye, — 0,68 X 0,33255 — 0,2261,

and further :
2,114
1,114

Hence we find for a? according to (19) 1: 0,0985 = 10,15, so

v

3 é 4
5 (l—p’') + P"| — p'' mr (: aa \- 2 = 0,0985.

Lk

that a becomes = 3,19.

If on the other hand we take the values mentioned 0,70 times

larger, the above expression becomes :
0,0763
with
p =10,03789 45 po 010330 ay pe Oe aes

For a? we find 1 :0,0763 =13,11, so for a the value 3,627’).

We see from this how sensitive the value of a’ is to even slight
changes in the values of 6, etc.; so that we need not wonder that
a more thorough modification in consequence of neglect of the varia-
bility of @ with v, can bring about a reversal of the sign of a.

1) Really the values va: be and mz will only suffer a slight modification when
x yaries, as appears from the table on p. 715. The value of g& will probably
change much more; but this we leave out of consideration, because the above is
only intended for a rough estimation and orientation. ;

2) We saw in II, p. 437 that for CjH;F and SO) a’ has probably a value be-
tween 3,2 and 3,6, so that the values of bg’, ete. (for 2 = 1) will be about 0,7

of the values calculated in § 11.

( 719 )

So our result about «a? becoming negative, found in § 11, need by
no means be inconsistent with the theory developed by us, but only

points to its mcompleteness.

18. As matters stand now, it is of course useless in connection
with what precedes to carry the analysis any further, and to derive
an expression for the coefficient 4’, for which the knowledge of the
fourth and fifth differential quotients of 4 with respect to v would
be required.

But by the determination of the values of ~ (or d) for some coex-
isting phases near the critical point we can find out something
hy approximation concerning the direction of the so-called straight
diameter. For though the concavity of the saturation curve is
turned upwards instead of downwards, the direction of the locus
‘(d+ d')—=/(m) determined in this way will not differ much from
the real direction. And this is so, because we have seen (see the
table) that the place of the critical point given by the relation
ve: b, hardly changes at all with change of the value of a, and
always remains in the neighbourhood of 2,1, so that also close to
the critical point, where the values for ¢ and d’ in consequence of
the varying value of the coefficient a’ are augmented, resp. dimi-
nished by an equally large amount, */, (d+-d’) continues to keep
about the same value.

In order to find the values of d and d’ for coevisting phases in
the case considered, we proceed as follows.

As we have seen, the equations (10) and (12) hold for coexisting

ae i il oS up 4
phases (see III, p. 568 and 570; « has been put for a Viz.

+a
ad ad’ 6ea2——de |
au ees
y i i (10) and (12)
| d 2,1—y'd' B 6 d—d ol dtd
06 = — a,1—s
ING 2,1—yd 8 om we (
; } ; ae ad
If we now put again, as in II, p. 433, ———— = A and = = All
2, yd 2,1—y'd
then we get on division of these two equations :
ad B ald’ B
log —: — ;
2,l—yd1+af8 2,1—y'd' 1+ Salk
ice Se aa

=e ~~ Ga

taking the above value of @ into consideration. Hence:
48*

( 720 )

B B'
log A ar log —— — od A ff log a ;
; Sere : “ 1+ap Anil

A= er Uce™ ie. A )

or also:
log A + log B — log(1+28) =P 3; log A’ + log B' — log (1+28') = P’
putting
P—F' 21
(Le Mea ©

(4°)

quite analogous to (3% in II, p. 433. With 8 = 1, in consequence
of which 2,1 becomes 3 and s = b, : bg becomes 1, (47) passes namely
immediately into

log A -—log A' , 6
AE aaa:

We will now sketch the course of the calculation, e.g. in the
case «=1. From the equation of dissociation (see I, p. 283, equation
(12)

AB alsin

1—* ff
we calculate first the value of 6 from the values of 3 and ¢ holding
for the eritieal point. This quantity @ is properly speaking a function
of the temperature, but we saw in I, p. 291, that as with association
under the influence of the molecular forces g, and y may be put
equal to 0, 6 may be considered as a constant. Now (see the table,
and also I, p. 295) for 21 (in order that f may become = 7
and == 0265. at. 7;)

ey UY a RG th

and from this we find 6 = 43,079; log’ 6 = 1,6345.

If now for gy we take successively values from 1,227 — going to
lower values for the vapour phase, to higher values for the liquid
phase (as y= (1 + 8) Ab: @’— b)) — we find the corresponding
values of 6 from

2
log?® ee — 1,6348 — 0,43848y7 —log’ y ... . . (@)
ak
From
Ab Ab: bp
f= 0 See
up—bp ill
follows :
b ge) lade Se 207
Abi Ge ae = ~= 6.6999"

bp 1 + [ik rae 1.9547

( TE)

in consequence of which
Ab Abe
gp = (1 + B) ae (1 + 8) aes
passes into
__ 0,6992 (14-8)
See
and hence we find for
ad a (1+8):2_

= ea Pie 2 de nay 2,ln—y 4

p

A — == h
1,3984 (°)
Further from
; 0,6992 (14-8)
2,12—-—y = ————__,
fp
: : : : Ab
in connection with 6=/, —(1—f) Ab, so y=s—(1—8) F ==
Ik
= s — 0,6992 (1—B), follows :
0,6992(1+-8
2,1n = s — 0,6992 (1—p) + — ( ar)!
1/2)
and so we find for d=1:n:
2,114
d= ; . . . 5 (c)

112
1,0317+0,6992 ( al (a)
Pp

because sb, : bg=1,0317. It follows namely from b,=6,— (1—,) Ah
that b, : bg = 1 + (4—#x) (AO: bg) = 1 + 0,0453 & 0,6992 — 1,0317.
Then we calculate P from (see above)
= 2,3026 (log? A + log**8—tlog'*(1+8)). . . . (ad)
In this way we calculate e.g. the following table (p. 722).
For the determination of the coexisting phases we have now only
to seek according to (4%), viz.:
P—F' 2,114
AEA Hira)
for an arbitrary set of corresponding values of P', A’ and @& the
set of values of P, A and d belonging to them in order that (e) be
satisfied. :
Then m can be determined from (10), namely
6 @—d"

iS} m

TROBE, , . . . . . (e)

A—A' —

b)

(7229)

could

4 \ toes oe | B 2 — (ie ) [2 a Le
Wa oe
0.95 | 1.2440 | 17.54 0.973 | 2.049 | 2.465 | 0.8578 | 0.6794 1.0936
3 1.05 | 1.1571 14.36 0.967) 1.840 | 2.318 | 0.9119 | 0.7509 | —0.9966
s 1.15 | 1.0741 111.86 0.960 1.665 2.196 | 0.9627 | 0°8223 | —0.9092
1.20 | 1.0339 10.81 0.957 | 1.587 2.142 | 0.9871 | 0.8581 | —0.8685

| |

1.25 | 0.9955 |o.874 0.953 | 1.515 | 2.091 | 1.0110 | 0.8939 | —0.8297

|—0.7927

| 0.7285

1.50 | 0.8067 6.408 0.930. Wea by) 1.883 | 1.1230 | 1.0726 | — 0.6599
|

1.30 | 0.9559 9.035 | 0.949 | ie

a

48 | 2.044 | 1.0341 | 0.9296
0.8801 | 7.588 0.940 | 1.326 | 1.959 | 1.0793 | 1.0011

Liquid
>
o

1.60 | 0.7353 |5.436/0.919) 1.118 | 1.814 | 1.1656 | 1.1442 | 0.6015
| |

from which follows:
6,016 d?—d”

m = Andee oh hoe ee (7)
as we saw (see III, p. 569) that for brevity’s sake 6 is written
for 6,016

Thus we find e. g. that d = 1,1280 about corresponds with
d’ = 0,8578. For then the first member of (e) becomes 1,1030 and
the second 1,1028.

But we draw attention to the fact that the determination of the
coexisting phases near the critical point is exceedingly difficult on

account of this that — in consequence of the almost horizontal
course of the saturation curve — also neighbouring values of d give

an almost equally good agreement.
Now we find further for mm:

nr 004M
As '/, (d+ d') = 0,9904, we have:
N(d+d')—1

l—m

— 20.

ah)

If however we take an only slightly higher value for d, e. g.
d = 1,1387, to which A = 1,0905 corresponds — in which case (e)
is almost as well satisfied as by the above value of d@ — we find

m = 1,0050.

But '/,(d+d’) is now = 0,9957, so that

C7250)

SA == 059.
]—m
in agreement with what experiment has taught us.

Though it appears in this way that the value of the coefficient 4
cannot be derived with certainty from the calculated values in the
neighbourhood of the critical point: this is certain that it is now
greater than with the ideal equation of state without association, in
which case we found the value */, = 0,4.

The value 0,9 is also in accordance with the well known fact
that the limiting density at low temperatures would amount to
about 3,8 times the critical density. So for m=O we have
/, (d+ da’) =*/, (38,8 + 0)=1,9, so that the straight line which
connects this point with the critical point has as coefficient of direction :

/,(d+da') — 1
sls sa) a)

If for a definite temperature (e.g. the critical) we wish to calculate
the isotherm, we have:
fa Sam 6,016

———— -
Ji 2,l2—-y n

2

(see III § 8, p. 568), or as (e.g. for z= 1) f, : f, = 1,007 : 1,004 — 1,003,
a
and’ ———— = A is put (See above):

2

2,l2—y
1.0036 8Am— 6:016d* ~~ = «= =. 3 2 (5)

Now we can derive for successive values of y the corresponding
values of A and d from the table calculated above (which we can
extend to g=0O and ¢ =o), and in this way easily calculate the
successive values of 1,003 « for a definite value of zn.

If in this way we have once calculated an entire isotherm for a
definite value of m, e.g. m=1, we find exceedingly easily all the
other isotherms by adding 84 (m’—m) to the found values of 1,008 ¢,
when a’ is the new reduced temperature.

But we will not enter any further into this subject now, which
we think we have now studied from all sides, in the expectation
that further theoretical investigations will give us a better insight
into this subject.

Clarens, December 12, 1911.

( 724 )

Chemistry. — ‘Studies on Tellurium I. On compounds of Tellurium
and Iodine”. By Prof. F. M. Javenr and J. B. Menke. (Com-
municated by Prof. P. vax Rompuren).

(Communicated in the meeting of December 30, 1911).

§ 1. The object of this investigation was to ascertain what com-
pounds of tellurium and iodine can form from the binary fusions of
the two elements and such in connection with the experience
gained thus far in the study of the mutual behaviour of iodine and
one of the other elements of the oxygen-group.

When we provisionally, disregard the oxygen itself, because in
any case well defined compounds with iodine such as O,/, are
positively known, the chance of forming iodides of these elements is,
evidently, not particularly great.

Of iodides of su/phur a great many were supposed to exist, such
GS Seeley een S ie) obs) aiSc/ k=) wel ana Sed eae

After a long controversy it now seems well understood that these
are merely murtures, and the recent work of Smita and Carson °*)
and a little later that of Kruraim') have proved conclusively that
from binary fusions of S and / no compounds are deposited. Iodine
can take up 7 to 8°/, of 5 in solid solutions; but further there is
only a eutecticum at 65,° and 81,3 mol. °/, of sulphur. The melting-
point 66° attributed by Grosourpy to the so-called S, /, is, therefore,
evidently the eutectic temperature. Sulphur in the liquid state has
here probably the formula S, and the previously accepted double
compounds of sulphur-iodides with As,S, and Sv./, have also proved
to be only mixtures.

In an analogous manner we find described iodides of selenium
SeJ, and SeJ/,"). Trommsporrr, however, states that these products
obtained by melting together the components, allow all their iodine

1) GRosourpy, Journ. de Chim. Médic. 9 429; Lamers, Journ. f. prakt. Chem.
84. 349. (1861); Emerson, Mac Ivor, Chem. News 86. 5. (1902).

2) LineBpARGER, Amer. Ghem. Journ. 17. 33. (1895); BouLoucH, Compt. rend.
136 577. (1903); Prunier, Journ. Pharm Chem. (6). 9. 421. (1899).

8) Gay-Lussac, Ann. de Chim. et Phys. 88. 319. (1813) ; Gururiz, Journ. Chem.
Soc. 14. 57, (1862); Mrnkr, Chem. News 39. 19; (1879); Mac Lrop, Chem,
News. 66. 111. (1892). ;

‘) Besides the mentioned investigators, aiso: Raru, Pogg. Ann, 110. (116. 1860);
Henry, Journ. Pharm, Chem. 18, 403. (1848).

5) SmirH and Carson, Zeits. f. phys. Chem. 61. 200, (1908).

‘) Eparaim, Zeits. f. anorg. Chem. 58. 338, (1908).

7) Trommsporer, N. Journ. Pharm. (2). 12. 45. (1826); ScunerperR, Pogg. Ann.
129. 627. (1866); Guyor, Compt. rend. 72. 685. (1871).

( 725 )

to be extracted by aleohol and Guyor observed that on heating, the
iodine volatilises. The Se/, of Scunerper was prepared in different
ways; from C,H,/ +SeBr,; from SeO, + H/; by melting Se with
J. In all cases the character was doubtful and the little stability of
these so-called compounds créated suspicion. It is very probable that,
as in the case of the sulphur, there is here also only a question
of mixtures with a eutecticum, which is situated in the vicinity of
70°. A short time ago this has been finally confirmed by PELLiN1 and
Preprina ‘), who demonstrated that from binary fusions only mixed
crystals are deposited.

§ 2. The analogous problem in the case of the element ¢edlurium
is of importance from more than one point of view. On a previous
occasion one of us?) was able to conclude, from the behaviour of
Te to S, to the complete analogy in this respect, between .S,Se and
Te. The behaviour of Ze and / might therefore be expected to be
also analogous to that of the elements S and Se.

Such a behaviour would then be in conflict with the statements
as to the tellurium-oxides which are found in literature. On the
other hand if we could meet with some compound which is per-
manent and, therefore, but little dissociated in the melt and which
possesses a sharp melting-point, if might be possible to decide
whether the atomic weight of tellurium is greater or smaller than
that of iodine.

As regards the first fact we find indeed a description of several
tellurim-iudides: Te.J,, Te/,, TeJ,, by Burzetivs and other investi-
gators °)

; the latter compound, however, has never been isolated
and was only suspected by BurzeLius to exist in the brown liquid
obtained from telluric acid and H./. Te.J/, is said to be a substance
readily fusible at about 80° and prepared by subliming 1 at. of Te
with a little over 1 at. of J/; it readily loses iodine and finally
leaves iodine-containing tellurium.

‘TeJ,‘) can be obtained as a hydrate Te/,. H/.8H,O from Te0,
and strong #./-solution; the hydrate melts according to Metzner
at 55°, and solidifies on cooling —- at least in a closed tube, —
again unchanged.

1) Pettin1 and Peprina, Atti dei Lincei (5). 17. Il. 78; Chem. Centr. Bl. (1908).
II, 1010.

2) F. M. Jancer, Proc. (1910).

3) BerzeLIus, Ann. de Chim. et Phys. 58, 113. 150, 225, 282, (1835); Merz-
NER, ibid. (7). 15. 203. (1898). WHEELER, Z. f. anorg. Chem. 8. 428. (1893);
GuTBIER and Fiury, Z. f. anorg. Chem. 32. 31, 108. (1902); Hamer, J. Chem.
Soc. 54. 887. (1888).

( 726 )

Further, there are double salts of Ze J, with NH, J, KJ ete.
ceseribed by WHereLer. Gurpier and Fiury prepared the compound
from a very concentrated solution of telluric acid with strong HL/ ;
it is totally resolved by //,O with formation of ZeQO,; alcohol also
decomposes the compound. According to their opinion however, the
substance 72/, cannot be considered as a compound and no trace of
this was observed neither in the case of 7'e./,. It is, therefore, evidently
of importance to obtain a better insight in the matter.

§ 3. For our purpose we have made use of the tellurium
obtained and purified‘) by one of us (J.) in the manner described pre-
viously. The investigation on tellurium was quietly continued not-
withstanding the alarming statements of Browninc and FLint*) on the
complicated nature of tellurium, because their method employed —
after experiences gained in the hydrolysis of tellurium-chloride —
appeared to us very much open to criticism. A short time ago the
incorreetness of their conclusions was proved elsewhere *), and
after the exact determinations of MarckwaLp and Foizrk, BAkrer and
Bennerr, Lenner and Harcourt and Baker *), the elementary nature
of tellurium may be accepted as being undisputable. As atomic
weight has been accepted here the most probable value of 127.6
and 126.9 for iodine. The latter was purified and distilled in the
usual manner.

In order to prevent any loss of iodine, the binary fusions were
prepared in sealed tubes; with mixtures containing 80°/, of Te or
more, this is unavoidable. Weighted quantities of the two elements
were thus melted together at 500°. After solidifying, the mass was
powdered and the cooling curve repeatedly recorded in another tube
made of hard glass which possessed an ege-like form and to which
was sealed a hard-glass screening tube for the thermo-element.
With mixtures containing O—10°/, of Ve the heating-curves were
determined in an oil-bath; for higher temperatures a small gas-furnace
as previously described in the case of the tellurium-sulphur-mixtures
was always employed. After the behaviour of the melt was thus
sufiiciently known, an analysis was made there-of by placing about
0.15 gram in a distilling flask and adding 20 ce. of sulphuric acid

1) Loco citato.

2) BRowNING and Fuinr, Amer. Jour. of Science (4). 28. 347. (1909); (4). 30.

209. (1910).

3) Harcourt and Baker ‘Trans. Chem. Soc. 99. (1911); Chem News 104.
260. (1911).

4) MARCKWALD and Forzrk, Ber. d. chem. Ges. 48. 1710, (1910); BAKER and
Benner, Trans. Chem. Soc. 91. 1849. (1897); Lanner, Jour. Amer. Chem. Soc
31. 1. (1899); Harcourt and Baker, loco cit.

( 727 )

(1,4). After passing a slow current of CO, through the ground-joint
apparatus, the liquid was carefully distilled into a receiver filled with
Na, SO,-solution, while through the funnel-tube a solution of sodium-
nitrite ran continuously into the reaction-mixture. In this manner
all the iodine could be carried over. To the distillate was now added
an excess of AyNO, and Na,SO,, then nitric acid (D.1.4) and the
liquid boiled foursome time. The Ag-/ was then determined by
weighing.

For the measurement of the higher temperatures was used a
platinum-platinumrhodium thermoelement, which was standardised on
the melting points of ice, tin, /ead and zinc ; for the lower tempera-
tures also an element standardised on ice and lead and made of
silver and constantan. Evidently a stirring of the mass was excluded ;
consequently, undereooling often took place, which rendered the

Binary Melting point line from tellurium and iodine.

Composition of the melt First Under- | ~ Second — Under- pure |
in mol. % eet effect cooling effect cooling ee |
Te J HOG sel! _ — = — — |
100 0 100 0 452°.5 - — - — |
92.2 T.8 {|| 92.3 Tat 405 29° 1522501552)" 1225 (62)i) 120!
84.7) 15.3) |) 85.3 | 14.7 385 (386) 5 (10), 159 (161) 6 (5) 180
80.7 | 19.3 |) 81.3 | 18.7 362 (360) 10 (10) 161 (161) 37 (3) —
71.4 | 28.6 || 71.6 | 28.4 306 _ 165 = } —
41.66 58.34 41.8 58.2 169 — 165 10 (12) 840
35:0 | 65.0 |) 35.2} 64.8 196 (195) 0 (0) 151 (152) | 10 (10)} 330
25.6 | 74.4 || 25.7 | 74.3 250 (250) 00) | 141 (140) 0 (0) | —
24.8 | 75.2 || 24.9 | 75.1 25an(25Si On (2)a\i39) (3a) \= k. 2.) —
22.4 | 71.6 || 22:5 | 77.5 259 (258)| 2 (2) || 130 (129), | — 120
20.5 | 719.5 || 20:6 | 79.4 255 — 109 (109) = —
20-4 | 79-6 || 20.5) 79.5 258 (259) — 110 (110) = —
17.5 | 82.5 || 17.5 | 82.5 256 (256) 3 (5) | 106 (107) | 0 (0) 540
10.0 90.0 | 10.0 | 90.0 217 — , 106 0 840
3.0 | 97.0 3.0 | 97.0 = — 106 = 900
0 100 0 100.0 113.4 _ _ _ | —

(728m)

measurement of the fme-dntervals, if not quite illusory, still rather
uncertain. These must, therefore, be only taken as approximations.
The data obtained are collected below and represented graphically
in Fig. 1 in the usual manner.
In previous determinations the eutecticum was always found at
170° up to 60°/, of Te.

300°

oO ‘o 10 30 40 50 60 0 80 go 100

iain: A con proemlin.

§ 4. From -these data and from the diagram of Fig. 1, it may be
concluded that from binary fusions a single compound is only formed,
namely 7e/,, which in the melted condition is fairly strongly disso-
ciated. The formerly accepted 7e/, is a product which lies in the
neighbourhood of the eutecticum, situated between tellurium and this
compound ; this eutecticum has a content of about 41 '/, of Te and
corresponds with a temperature of 165°. The eutecticum at the
iodine-side lies in the immediate vicinity of the pure iodine and
corresponds with a temperature of about 108°. Solid solutions are
evidently not formed to any extent. No trace can be found either
of a compound Te/,.

( (29 )

§ 5. The compound Te/, was once more recrystallised by us
from strong /// with addition of some V/H/,. Instead of the ammo-
nium-compound, we obtained erystals with a metallic lustre, which
on analysis contained 1 °/, more of ./ than corresponded with Te/,.
A little too much iodine was also found in the hydrate obtained
from tellurie acid.

An investigation by one of us as to the phenomena occurring in
solutions of Ve/, in strong /// with excess of dodine, is already in
progress.

Inorg. Chem. Laboratory

December 1911. University, Groningen.

Chemistry. — “Zhe question as to the miscibility in the solid
condition hetween aromatic Nitro- and Nitroso-compounds’. U1.
By Prof. F. M. Jancer and Dr. J. R. N. van Kreeren.
(Communicated by Prof. P. van RomBuren).

(Communicated in the meeting of December 39, 1911).

§ 1. In consequence of the formation of solid solutions between
0- Nitroso-benzoic acid and o-Nitro-benzaldehyde, also owing to a
treatise of Brunt and Catiecarr') on the formation of solid solutions
between aromatic “nfroso- and nitro-derivates, as a general pheno-
menon, investigations have been carried out by one of us (J.) to
get a better knowledge of the mutual relation of both classes of
nitrogen-derivatives *). This investigation which comprises many
nitro-, and nitroso-derivates of analogous structure could only lead
to the conclusion, that, certainly, in some cases, there was a
question of a morphotropous relation and resulting miscibility, but
that in most cases such a relation did not exist and could not, in
homologous series, even be called a generally occurring phenomenon.

In the following some more data regarding these questions have
been collected, which enable us to supplement the previous state-
ments Im some respects.

§ 2. Nitrobenzene and Nitrosobenzene.
The simplest representatives of the compounds to be discussed are
nitro- and nitroso-benzene.

1) Brunt and Catteeart. Gazz, Chim. Ital. 34. IL 246. (1904).

*) F. M. Jarcer, Proc. 1905. 658, 1908. 436; Zeils. f. Min. und Kryst. 42.
236. (1906). Comparisons have been made between: p-Nitro-, and p-Nitroso-
diethylaniline ; Nitro-, and Nitrosobenzene; p-Nitro-, and p-Nitroso-phenol ;
o-Dinitro-, and o-Nitro-nitrosobenzene ; 0-Nitro-, and o-Nitroso-aceto-anilide.

( 730 )

The nitro-benzene was purified by three times freezing and subse-
quent distillation. The fraction boiling at 211°,6 under 76,7 m.m.
pressure was used for the investigation. The thermometer was com-
pared with a normal thermometer; at 0° it appeared to indicate
0°,2, and at 100°, 0°,1 too low.

The solidifying-point, with different outer-bath-temperatures, appeared
to be always + 4°,9; the same temperature was also found for
the melting-point. In these last experiments the solid substance
was heated slowly in an oil-bath. Pure nitrosobenzene*) therefore
solidifies and melts at + 4,°9.

BINARY MELTING-POINT-LINE OF NITRO-BENZENE
+ NITROSO-BENZENE.

| Composition in mol. °/, | etait i }
NOE ComdlO5 NOcGom:| ae aomee eeemetemiseall mectenas
= | : pound pound :
100.0 0.0 4.9 2 =
| 971.5 | 2.5 3.6 = =
O5.7)0 \iaer4e3 3.1 0.8 = ial
94.1 5.9 Oe = 0-7 240
9253 ai} eal 1.2 we 480
| 88.9 | died = 0 560
86.0 14.0 = 0 1080
82.8 2 1.8 0.1 990
33.390 Qin 5.2 0.2 960
67.0 33.0 18.6 0.5 780
56.5 43.5 27.5 0.2 630
45.3 54.7 36 0.2 480
26.4 13.6 46 eee 240
15.0 85.0 54.8 =e) —
3 92.7 61 —10.0 =
4.0 96.0 60 = = |
2.1 97.9 60.2 | = ss
0.0 | 100.0 68 | — | — |

1) In the literature are given for this temperature-values varying from + 3° and
+ 5°; for the boiling-point is found 208° under 760 m.m. pressure. We, however,
find both values a little higher.

The nitroso-benzene was first repeatedly reerystallised from hot
alcohol and then from benzene. The melting-point was always found
too low. Afterwards the substance was reerystallised from a mixture
of alcohol and ether in an atmosphere of carbon-dioxide to prevent
oxidation. After rapid suction it was dried in vaeuo over sulphuric
acid. The melting-point was then found to be at + 68°. This com-
pound, however, is decomposed a little above its melting-point (at
about 7°) suddenly and with great evolution of heat, with formation
of a brown liquid.

If the decomposition, caused by careless heating, is only partial,
the solidifying-point will be found later to be somewhat lower.

Solidifying-points only could be recorded with sufficient sharpness.

The data given in the table on p. 780 have been recorded by us.

These data are represented in fig. 1 in the usual graphical
way.

§ 3. From this it appears that nitro- and nitroso-benzene — perhaps

road SA
(hee

|

ee,
~~ C HLNO, GP C, H, NO.

(733 )

with exception of concentrations situated in the immediate vicinity
of the axes — do not, or hardly at all, form mixed erystais.

A miscibility at exceedingly small concentrations of both components
occurs, however, more or less distinctly in all systems formed
from carbon-compounds.

Otherwise, the differences in erystal-form are not readily noticed,
because the yitro-benzene is liquid and ean only be obtained from
fusions at a low temperature in a crystallisable form. It is, probably,
rhombic and analogous to the crystal-form of benzene, at least in
one of the two parameter-relations.

Nitroso-benzene is rhombic-bipyramidal ') with a:b:¢ = 41,4770:
1: 0,7006 and the forms: {100}; {110}; {111}; {340}; {221}; {001}.

benzene is rhombic, with a:b:c¢=0,591:1:0,799; these para-
meters are in no case analogous to those of the n7troso-derivative
and probably also not to those of the nzto-compound.

All this seems to indicate that there can be no question either of

| BINARY MELTING-POINT-LINE OF p-NITRO-
| ANILINE + p-NITROSOANILINE
| Composition in mol. 9

| lo | Solidifying | 2nd

0/9 NOy-anil. | °/, NO-anil. temperature | Heat effect |

100.0 0.0 147° =

| oi 4 8.6 144 141
82.9 17.1 137.7 a
74.7 25.3 133 a
66.7 33.3 ay | = |
58.6 | 41.4 120.5 | 119
50.8 | 49.2 119 120
432.0 |) 156.8 = 120
35.6 64.4 = 115
AsO" 79.0 = | 124
13.8 86,2 decomp. | 124
6.9 93.1 decomp. | 124
3.4." il) 49626 decomp. | 122
0:0 | 10020 169° | _

1) F, M. Jaecer, Zeits. f. Min, u. Kryst. 42. 246, (1907).

a pronounced form-analogy, or of a perceptible formation of solid
solutions between nifroso- and nitro-benzene.

§ 4. p-Nitro-Aniline and p-Nitroso- Aniline.

Whereas, on account of the presence of //-atoms in the amino-
group, a tautomeric structure of the nztoso-compound is not excluded,
this system was sufficiently interesting to deserve further investigation.
This investigation, however, was, unfortunately, rather unsatisfactory,
owing to the fact that a decomposition of the p-N¢étroso-Aniline
could not be prevented: whereas the melting point is situated at
168’—169°, the temperature of decomposition is about 170°.

The p-Nitro-Aniline used was recrystallised from benzene and also
trom water; at 100° 2,2 grams of the compound dissolve in 100 ce.
of water. The melting temperature proved, on repetition, to be 147°.

The p-.Nitroso-Aniline was recrystallised from benzene and dried
in a current of carbon-dioxide to prevent oxidation. Immediately
after melting at 163°—169° a sudden decomposition took place with
evolution of heat and a violent evolution of gas.

By working carefully, the approximate data contained in the
table on p. 782 could still be obtained.

In fig. 2 these results are
represented graphically; there
can be no question of an
exact determination of the
diverse points, but only ofa
first orientation. The whole
seems to point to a formation
of mixed crystals at the side
of the Notro-compound to a
considerable concentration (85
to 40°/,) with the Nitroso-
compound, but to only a
slight mixing at the side of
the latter.

As all the fusions were
too dark in colour owing to

the decomposition, a micros-
copical investigation did not
much avail. In no ease,

19 20 34 40 §0 60 70 680 90 ito

Tet.

N0. however, is there any question
of a continuous mixing-series.
49
Proceedings Royal Acad. Aiasterdam. Vol. XLY.

( 734 )

A few remarkable phenomena, which are communicated here, were,
however, noticed microscopically.

From the brownish-red melt of 83°/, NO,- and 17°/, NO-aniline,
there are deposited on cooling, at first fairly rapidly, elongated, orange-
red needles in thick bundles. After waiting for some time, these appa-
rently become covered with an innumerous number of very small
yellow needles; if a primary needle has been placed between two
crossed nicols in such a position that it gets dark, it suddenly
becomes luminous in the process described. There are now present
in the preparation two components: the partly unchanged, original
brownish-red needles and the subsequent yellow ones; both are feebly
dichroic. In convergent polarised light is seen a remarkable, biaxial inter-
ference image can be observed, namely four orange-red, equilateral
hyperboles and a green cross; apparently, the axial planes for the
diverse colours are crossed, and an enormous dispersion is present.

A mixture with 73 °/, of N0O,-compound also behaves, optically,
like the above. The transformation, however, takes place more slowly
than in the first case. With the 51°/, NO,-compound brownish-red
needles are obtained; of a transformation little more is visible; with
the 21 °/, NO,-compound there are present dichroic (red-orange yellow)
aggregates, spherolitically built. In these two latter cases it is difficult
to decide whether we have one or two structural components ; the
fused masses are also almost opaque by decomposition.

In each case, the mixed crystals at the VO,-side, therefore at a
lower temperature, seem to pass into another modification, with
considerable changes in their symmetry and volume.

§ 5. p-Nitromonoethylaniline and p-Nitrosomonoethylaniline.

The p-Nitro-Monoethylaniline was recrystallised repeatedly from
benzene and afterwards the heating- and also the cooling-curves were
several umes recorded.

The melting-point was. situated at 94°, the solidifying-point at
93°.9. The melting point given in the literature (95°—95°.5) is,
evidently, a little too high.

The p-Nitroso-Monoethylaniline was also recrystallised repeatedly
from benzene; it melted, constant, 75°—76° in a capillary tube;
when taking the melting-, and solidifying-points in the more delicate
manner, these were, however, always situated at 74°, undercooling:
was always avoided by inoculation.

The following data were obtained ;

( 735 )

| Soliditying | Eutectic

temperature temperature

%/) NO, (NO |

10 6} 60st =

95 5 92 ca. 40°

90 10 9.2 | 54

80 20 Bae Wh 83

70 30 71.5 54

60 40 73 51

50 | 50 64.7 | 51.4

Ao men an 60 58 | 54.6

30 70 54 =

20 80 59.6 49

10 90 66.9 46
5 95 10.5 Eom ae
0 100 Tey ee |

100° 100
94° ,
90° 90
bo” go°
lg 5
We Je
bo° \ b0°
50 50°
4o 4o°

NO 30° : so” NO,

0 1 10 30 4o so 60 P § 90 (0
Fig. cs

49%

( 736 )

As, notwithstanding the inoculation, a great undercooling was
sometimes perceptible, the deviations especially’ from the eutectic
temperature are considerable here and there.

§ 6. Although the diagram makes the impression as if no mixing
in the solid condition were present here, but that there is only a question
of an ordinary binary melting-point-line with a eutecticum, — in each
case declining at both sides, — the microscopical investigation still
shows that we have no right to look at the matter in this way
without further evidence.

The pure nitroso-compound presents itself under the microscope
in the form of spherolitically-grouped, strongly dichroic platelets ;
the colours are may-green and grass-green.

The nitro-compound forms long, lemon-yellow but faintly dichroic
platelets, which between two crossed nicols do not become dark in
a single position, but exhibit on turning of the table, a vivid display
of colours, green, yellow etc. In convergent light it appears that we
have here nearly parallel to the direction of the “normal” of the
platelet, the bisectrix of a very remarkable interference image of a
biaxial crystal, for we notice a dark horizontal beam which intersects a
bright green field in the centre, while in the vertical plane are
situated two red fields, which are intersected by dark beams, ter-
minating at some distance from the centre. The green field is limited
in four quadrants by a system of bluish-purple equilateral hyperboles.

Evidently we are dealing here with a crystal, whose axial plane
for red and green light is the longitudinal direction of the needles,
but for blue rays their latitudinal direction: such in connexion with
an exceedingly small angle for the diverse colours, while that for
the red is larger than that for the green.

If now we investigate the binary, solidified fusions, it is at once
visible to the naked eye that they congeal to a homogeneous aggre-
gate of erystals. From solutions in ethyl-acetate are also formed
homogeneous green crystals.

With 5°/, VO,-compound were found green fern-like mixed erystals;
with an increasing content of the Q,-substance their colour turns
more and more yellowish-green, but the solidified melt remains exist-
ent as a single crystal-form. Only at a 40°/, NO,-compound the
remarkable axial image of the pure nztro-compound plainly returns;
at 70°/, the erystals are nearly monaxial for red; at 90°/, and 95°/,
of the .VO,-compound, the mixed crystals obtained from a solution
in ethyl-acetate are beautifully greenish-yellow, very faintly dichroic
and exhibit the characteristic axial image in a remarkably plain

( 737)

manner. These experiments quite confirm the suspicion that a conti-
nuous series of mixed crystals is formed here. If so, there is no
other possibility but to assume that the binary melting-point-line is
also a continuous curve with a minimum temperature at 54° and a
content of about 30°/, of the m7troso-compound; and that owing to
the occurring undercooling, and to the evidently incomplete setting
in of the equilibria, the solid line has declined to such an extent
that it nearly assumes the form of a eutectic horizontal line. Such
has been already observed previously in systems without a minimum
in the liquidus-line; compare for instance the case of Sb + Li inves-
tigated by Htrrner and TAMMANN ’).

True in this particular case the said authors attribute the cause
of the deviations to the fact that the mixed crystals which have
deposited at first, get coated and that it then becomes impossible for
them to get into equilibrium with the melt at any moment; but
they stiJl point out that a similar behaviour may be expected each
time when the said setting in of the equilibrium takes place with
insufficient velocity, and that might be the case here also. The for-
mation of an uninterrupted series of mixed erystals both from solu-
tions and binary fusions, and this without subsequent transformations
or dissociations agrees with this view.

§ 7. p-Nitro-Monopropyl-Aniline and p-Nitroso-Monopropyl-Aniline.

Finally, we have investigated the system of the above compound
in the same way.

The p-Nitro-derivate was first recrystallised from hot benzene from
which splendid, large crystals are deposited. Their melting-point
appeared to be 53°—54°; moreover they were found to turn soon
turbid owing to loss of benzene. The compound was, therefore,
powdered, dried and repeatedly recrystallised from absolute alcohol.
From this are also sometimes deposited splendid erystals which melt
constant, at 64°—65°. They mostly have curved planes and con-
sequently can only be measured with difficulty.

_ The p-Nitrosomonopropylaniline was also purified by recrystallisa-
tion from benzene; it then also contains benzene of crystallisation
and melts at 45°—50?.

After expelling the benzene in vacuo and repeatedly recrystallising
from a mixture of absolute alcohol and ligroin, the melting point, in
a capillary tube, was found to be 58°, which yalue is also given in
the literature.

1) Hiirrner and Tammany, Zeits. f. anorg. Chem. 44, 131. (1905).

( 738 )
BINARY MELTING-POINT-LINE p-NITRO- AND
p-NITROSOPROPYLANILINE

E sition in mol. °/, ee wae
on geu en "Initial solidi- End solidi-

0/, NO» o//, NO fying point | fying point
= ! —_ . “|
a = =
100 0 62.9 | a
95 5 61.2 =
(weak effect
at 580)
90 10 59.3 =
| effect at 49>)
80 20 | 56.5 54.5
710 30 52.9 51
60 40 49.3 47.5
50 50 47.0 44.5
40 60 44.5 43
30 10 42.8 42
20 80 40.5 40.5
10 90 48 =
0 100 56.5 | -

N0.° 10 t© 30 46 50 bo die fo aN VF)

ao

(739 )

First of all, the solidifying points of both derivatives were accurately
determined by recording the cooling lines. In this way was found,
with slight undereooling, 62,°9 C. for the solidifying point of the
nitro-compound and 56°,3—56°,5 C. for the nitrosu-derivative.

Suceessively, the following mixtures were investigated (see table

previous page).

§ 8. These data graphically represented in fig. 4, prove that
there exists here a continuous series of solid solutions between the two
components, with a minimum temperature of 40.°5S C. and a concen-
tration of about 80°/, of the m7tro-compound.

The microscopical investigation also confirms the existence of such
a series of mixed crystals.

The p-Nitro-compound crystallises from its yellow melt with great
rapidity in lemon-yellow, hexa- or octangular plates, which are
immediately followed by a darker coloured modification, generally
occurring in parallelogram-like plates, joined in all directions. They
are strongly dichroic: yellowish-white and dark yellow. Between
crossed nicols they are black and on our turning the table slightly to
the right or to the left, the colour changes to brown or green. In
convergent polarised light one branch of a hyperbola is visible excen-
trically, and coloured red at the inner side and blue at the outer
side. Very strong dispersion.

The nitroso-derivative has an extraordinarily small crystallisation-
velocity ; fern-like aggregates exhibit a splendid steel-blue lustre and
are strongly pleochroic: green and brownish-yellow.

Mixed erystals with 5, 10, 40, 60, 90°/, NO-compound have been
investigated. A yellowish-green melt with 5°/, VO-derivative solidifies
to an aggregate of yellow plates of the NO,-form, which after about
half a minute suddenly burst and pass into another modification of
a more yellowish-green colour and a much stronger double refraction ;
previously dark crystals become luminous ete. The crystallisation-
velocity is still very considerable; whereas the first modification,
between two crossed nicols, is dark in two positions, the second
is not extinguished in any position. After some time the first crystal-
lisation is succeeded by a feather-shaped aggregate of the second one.

With 90°/, of the Nctro-compound there is hardly anything more
to be observed of the polymorphous conversion, notwithstanding the
great velocity of crystallisation. With 60°/, .VO,-derivative we have
homogeneous mixed erystals which are strongly dichroic: green and
bright-yellow. With 40°/, idem; the crystals are: dark-brown and
yellow. With 10°/, NO,-compound the velocity of crystallisation is

( 740 )

already extraordinarily small; mostly spherolitie aggregates which
are strongly dichroic: bright yellow and green.

§ 9. The above proves that the m7tro-compound is here also
dimorphous; with the 90°/, mixed-crystal, the strongly decreased

temperature of conversion of the pure NQO,-substance —- which lies
just below the melting point, — is still determinable by the corre-

sponding heat-effeet.

With a larger content of V.O-compound, that determination is, how-
ever already impossible owing to the enormous retardation of the poly-
morphous conversion through the admixture of the slowly crystallising
nitroso-derivative.

§ 10. From the investigation it has appeared anew, that mixed
erystal formation can occur in binary fusions of corresponding aromatic
Nitro- and Nitreso-derivatives, but that this miscibility must not be
looked upon as a general property of these compounds in regard to
each other. Moreover, the mutual behaviour of these two kinds of
substances becomes often more complicated by the appearance of
polymorphous modifications and by the difference in erystallisation-
velocity in the two components. The most simple representatives of this
class of. substances nitrobenzene and nitrosobenzene do not, or only in
au insignificant degree, form solid solutions with each other.

Inorg. Chem. Lab. University Groningen.
9g 4 4

Chemistry. — “Photo-electric phenomena with Antimony sulphide
(Antimonite)”. By Drs. J. Oui Jr. and H. R. Keroyt). (Commu-
nicated by Prof. vy. RompurGu. (Preliminary communication).

(Communicated in the meeting of December 30, 1911).

Janapr') discovered some years ago a very remarkable property
of native antimonite which, however, seemed to belong exclusively
to the large crystals of this mineral found only in Shikoku (Japan).
The mineral exhibited, as regards sensitiveness of the electrie con-
ductivity power to irradiation, a very great analogy with selenium,
Illumination strongly lessened the resistance of the material. The
fatigue so troublesome with selenium for the practical application
of this property was here but insignificant. Immediately after stop-
ping the irradiation, the resistance regains about its original value
called, briefly, “the darkness resistance’’.

1) Proc. Kon. Acad. y. Wet, Amsterdam 1907, p. 809—814.

(741 )

Jarcrr, however, found that the remarkably strong sensitiveness
to light totally disappeared on remelting; the specific resistance
then also became several thousand times smaller. On powdering the
mineral, the sensitiveness to light also completely disappeared, but
the resistance was only little affected. It was therefore obvious to
connect the sensitiveness to light with the macroerystalline structure
of the material, te which Javerr already called attention’) without,
however, attempting to further explain the phenomenon.

As, however, with none of the other substances which exhibit a
similar sensitiveness to light in a greater or lesser degree, such as
selenium”) tellurium, sulphur, Ag,S, AgJ ete. (although in most of
these substances the causes of the phenomenon are far from being
elucidated) anything like a dependence of the photo-electrie effect
on macrocrystalline structure has up till now been noticed, the
antimonite would then constitute a case by itself. This seemed to
us somewhat improbable and caused us to investigate whether the
explanation of the phenomena observed by JArcrr might not perhaps
be found by working in another direction.

Now, according to Jancrr, his Japanese antimonite is very pure
and has almost exactly the composition Sb, S,; all other specimens
(none of which exhibit a light effect) are less pure. We, therefore
prepared from pure materiats*) an artificial antimonite in order to
test this as to its sensitiveness to light. Already at a first experiment
we succeeded in obtaining a strongly sensitive preparation *) by
rapidly heating, in an open tube, antimony powder mixed with a
small excess of sulphur. The subsequent orientating experiments gave
alternately a positive or negative result, which made us resolve to
investigate systematically a series of mixtures of varying quantities
of S and Sb in order to ascertain whether small modifications in
the composition of the antimony sulphide, which was otherwise quite
free from foreign substances, might be the cause of the greater or
lesser sensitiveness to light.

As on heating in open tubes in an atmosphere of carbon dioxide
a loss of sulphur through volatilisation could not be avoided, we
proceeded to operate in sealed evacuated tubes, which could be

1) Zeitschrift fiir Krystallographie etc. Vol. XLIV, p. 45—48,

2) By one of us, an explanation of the phenomenon in the case of selenium
has been given from a phase-rule point of view H. R. Kruyr, Die dynamische
allotropie des Selens Zeitschr. f. Anorg Chem. 64, p. 305 (1909),

5) Sb from Kautpaum. S recrystallised from CS).

4) The illumination always was done in the same manner with a small Halbertsma
are-lamp at about 30 em. distance from the preparation.

C7)

heated in a specially constructed oven at about 600° and also be
regularly shaken to make sure of a complete homogeneous mixing.
As regards the result of this investigation it may be stated

provisionally that the pure compound — Sb and S in the exact
proportion Sb,5, — appeared to possess the highest photo-electric

effect. This sensitiveness to light amounted in some cases to about
400°/, 7). This sensitiveness relates to Sb,S, in massive little rods of
about 10 mm. in diameter. As the light effect must be a superficial
action and as relatively thick massive rods are therefore a less
advantageous form to promote this effect, the relative sensitiveness
can be very strongly enhanced by choosing a more suitable form of
antimonite-cell in which the relation of the surface to be irradiated
to the section of the conductor is very much larger. In any ease it
has appeared that the observed sensitiveness to light in artificial
antimonite is of the same order as that found by Janenr in the
native mineral?) and which we have verified ourselves with Japanese
Antimonite procured from Kaniepaum. We hope, shortly, to refer
more in detail to the method employed in the investigation of the
dependence of the photoelectric effect on the composition of the
substance. In the main it amounted to this, that by means of a very
sensitive instrument (galvanometer, system Siemens Hanske Deprez-
@’ Arsonval) we determined the relative conductivity power in dark-
ness of small rods of antimonite of different composition and also
the relation of the “conductivity in darkness” to their “conductivity
in the light” (namely the conductivity power on illumination).
From the relative conductivity power in darkness and better still
from the temperature coefficient thereof we were able to deduce the
form of the melting diagram of the system S—Sb in the+sphere
investigated *) that is in the vicinity of the compound Sb, §,; starting
from the compound towards the antimony side we first found a very
small mixed erystal sphere — about 0.3 at °/, and further a sphere
of partial miscibility. All this is greatly in harmony with the inves-
tigations published in these proceedings, by JAuceEr*) on the system S—Sb
where the melting diagram was constructed by means of a thermic
analysis. Jawenr, howeyer, found no mixed crystals. It is, however,
just this mixed erystal series, (notwithstanding its small extent

1) That is to say when the conductivity power in the dark is expressed in an
arbitrary measure, say 100, this rose to 500 by illumination.

2) Prof, Jaraer kindly obliged us with one of his antimonite-cells for comparison,

8) From 57—62 at. 0/9 of sulphur.

#) Verslag Kon. Akad. November 1911 p. 497—510.

( 743 )

and the difficulty to determine thermically such a very small sphere
with certainty) which could be determined very sharply by the
electric process. And this seems to us all the more of importance
because a connection seems to exist between the appearance of solid
solutions on the one side, photoelectric or photochemical effects and
photoelectro- or triboluminosity on the other side.

We further got the impression that certain very small impurities
may be of influence on the sensitiveness to light, and think we have
observed at any rate an influence exerted by the kind of glass of
which the melting tubes were constructed. In a whole series of
experiments which took place, accidentally, with tubes constructed
of a different kind of glass, we obtained not a single sensitive pre-
paration, but when again using tubes of the old kind of glass the
phenomenon reappeared as expected.

In this may be probably found, in our opinion, a partial expla-
nation of the fact that, contrary to JAnGER’s experience, we succeeded
in remelting the native (Japanese) antimonite w/thout this losing its
sensitiveness to light. It is, however, necessary to operate, as we did,
in sealed evacuated tubes. The compound at the melting point is
already somewhat dissociated so that the operation in an open
tube could not take place without loss of sulphur and change in the
composition of the melt. According to our observations this loss of
sulphur need amount to only 0.5 at°/, to obtain a totally inert
preparation.

The conductivity power in darkness remained, on remelting, also
quite of the same order. On the other hand it appeared that on
powdering the mineral, which was then again compressed to a very
solid pastille, the conductivity power very strongly decreased. The
light effect, however, remained unaffected.

Utrecht, van ’t Hoff-laboratory.

Chemistry. — “On gas equilibriv’. By Dr. F. E. C. Scuvrrer. (Com-
municated by Prof. J. D. van per Waats).

(Communicated in the meeting of December 30, 1911).

1. It may be accepted as known that the total energy, the free
energy, the entropy and the thermodynamic potential are quantities
which can only be determined with the exception of an additive
constant. In the purely physical processes, i.e. changes of state, in
which the molecules of the substances do not change, these constants
need not be taken into account, and on the other hand a physical

( 744 )

change can teach us nothing about the values of these constants.
In chemical changes, however, this zs the case, at least partially. If
in a mixture of substances a chemical reaction can take place, a deter-
mination of the energy of transformation under definite circumstances
will make known to us the algebraic sum of the constants of energy
of the reacting substances, at least if we know the energy in its
dependence on the quantities that determine the state. Each of the
constants in itself remains quite indefinite just as for physical changes;
experiment only gives us the algebraic sum of the constants of
energy, in which the constants of the substances of one member of
the equation of reaction are taken positive, those of the other member
negative.

We find something similar for the entropy. The constants of entropy
for the purely physical processes are without any importanee, but a
chemical transformation which is conducted isothermie and reversible
may make the algebraic sum of the constants of entropy known to
us, provided we know how the entropy of each of the substances
depends on the independent variables.

Of late the sum of the constants of energy, resp. entropy, and
especially the latter have been the subject of many a treatise. As
the sum of the constants of entropy occurs in the expression for the
chemical equilibrium as a constant, its knowledge is of the greatest
importance for the calculation of these equilibria. Hence Prof. Haper
in his work on the ‘“Thermodynamik technischer Gasreaktionen”
repeatedly calls attention to the so-called “thermodynamisch unbe-
stimmte Konstante”, which is the aforementioned algebraic sum of
the constants of entropy. And also Prof. Nrrnsr’s theorem of heat
deals with the determination of these constants, for the so-called
“constant of integration” of the chemical equilibrium contains these
constants of entropy.

For a calculation of the constants of entropy from the theory a
priori an idea of the chemical action i.e. the knowledge of the so-
called forces of affinity, will be indispensable — Bo.rzMann carried
out a first attempt to do so in his ‘‘Gastheorie’ — for the present
we shall have to content ourselves with a calculation of these constants
from the observations.

In the first place, however, the knowledge of the energy and the
entropy as function of the quantities which determine the state is
required for such calculations. When, to take the simplest case, we
confine ourselves to rarefied gases, we know that the molecular
energy and the entropy of a simple gas can be represented by:

“1
B= Ero + | aa ; pene Fa)
Og
7 iy i
jase Lees | pat—Ring . . . . . (2)
— le

in which Hy» and H7y—, represent the aforesaid constants of energy

v=]
and entropy, c. the real molecular specific heat, 7’ the absolute tem-
perature, c the concentration (number of gramme molecules per
Liter), and R the molecular gas constant (1,985 eal.).

If at a definite temperature we now measure the algebraic sum
of the energies (Yn/), i.e. the heat of transformation at constant volume,
end the sum of the entropies (27/7), i.e. the latent heat for a
reversible isothermic transformation divided by the absolute temperature,
we can find the values of XnHy=) and YnHz=, by calculation, if

v=l1
we know ec, as function of 7.

The value of 2nE7—= is generally calculated, indeed, according to
equation (1) from the calorimetric data. The sum of the constants of
entropy, on the other hand, is generally not determined directly
from the latent beat, but indirectly from the value of the constant
of equilibrium.

If we suppose a reaction

Nw Are ane Al ates «ee Al tI.
to be possible, the total change of energy, resp. change of entropy
on transformation of n, gramme molecules A, with 2, gramme mole-
ecules A, ete. with formation of m', gramme molecules A’, ete. is
represented by :

ve 2
ZnB = EnBpao + nf cd. oo a0. 6 0° op (led)

Ow
and
= SI if Cy Gal 5 5
nH = SnHyp=\ + Zn po eae inic) Tae aca)
v=1 1

The algebraic sum of the molecular thermodynamic potentials, which
must be equal to zero in case of equilibrium, becomes therefore :

Sn = Snk — TSnH + TnpV*)=

T oi
SnBpao-+Znf ol? Enf , aT + RT Snlne—TSnAy3+ RT Zn.
0 le |

If now in the state of equilibrium we represent nine by Ink,
in which A denotes the “constant of equilibrium’, then:

1) In this V is the molecular volume, p the partial pressure.

=niET=0 1 ie apIETG gal >. 11 wiics 1
= — —_____ — ___ Sn ]feodT+ —= —dT+ — SnH p= — =n (3
InK RT RT nf + R nf 7! +z n r= n (3)

So if we have now ealculated YnHp—o from the calorimetric data
(according to equation 1”), we ean calculate the value of SnH7—

v=1

from an observation of A’ at a definite temperature.

2. For these caleulations c, is generally represented in a series
of terms with ascending powers of 7, which is then continued as
far as is necessary for agreement with the generally insufficiently
known values of the specific heats. For bi-atomic gases the series
can already be broken off after the term with 7’, for tri-atomic
gases after that with 7’.

Hence if we put in general:

ne; =a + bT+ cT?

and thus determine the integrals in equation (3), we get:
=nET=9 a b ¢
hi S>— soa SE ee i == [2 Ci ee
, RT ge Sige ign tal (4)
in which
2a 2
6225 SAH oes (5)
= aR

In the above equation (4) the constant of equilibrium is expressed
in concentrations; to find the value of the constant in partial pres-
sures from this, which is generally used for gas equilibria, we must
bear in mind that

p= RT 2 SS ee)
in which p is the partial pressure of the gas concerned, and that
therefore :
mK =Lnlkne=Lnlnp—LnnR—-— TanlnT.

If we now put 2nunmp=MmK,, in which K, represents the
constant of equilibrium in partial pressures, then after some trans-
formations and transition from Neperian to common logarithms:

eee nH To | Ca r b Tr ty PLC.
9 =—F308RT! R93 .8.908R- '6.a808R, 10?
in which C’= 0.4343:C -— Spilogihaw. 2 ee ee

In this we must bear in mind that the value of R should be
expressed in calories in equation (7), because the energy and the
specific heats are measured in calories, whereas in equation (8) the -
unity in which “# is expressed, depends on the unity of pressure
and volume in equation (6). If we express the concentrations in

( 747 )

gramme molecules per liter, and so if we choose the liter as volume
unity, and the atmosphere as pressure unity, # must be expressed
in liter-atmospheres in equation (8). So in this case we must sub-
stitute A—=1.985 in equation (7), on the other hand R=0.0821 in
equation (8).

From the equations (7), (8), and (5) we see accordingly that

a]
Y 9

the so-called constant of integration of the chemical equilibrium does
not contain only the sum of the constants of entropy, but also =n
and the constants yielded by the integrals occurring in equation (3).
C” owes its name of constant of integration of the chemical equi-

librium to this that equation (7) can also be found by integration
of the well-known law of van ’t Horr:

dnK Q

a RT
in which A’ represents the constant of equilibrium either in con-
centrations or in partial pressures, and Q the heat of transformation,
in the first case for constant volume, in the second case for constant
pressure. If, however, we derive equation (7) in this way, we do not
get equations (5) and (8), because in this way the constant of inte-
gration does not become known in its dependence on the constants
of the reacting substances.

§ 8, We shall now apply the calculation of the constants of

entropy to the equilibrium:
2CO0+ 0,222 C0, .

The value of nF can be found from the calorimetric determi-
nations of ‘Thomsen and Brrruenot, which yielded resp. 67960 and
68200 cal. for the heat of combustion of one gramme molecule CO
under constant pressure and at 18° C. From the mean value Q, = 68080

we calculate Q, = 67790, and so:
Sl SISO Hl; FS Poh se Aa ee (9)

Now we derive from equation 1°:
Shp = Sn — al Ole —— 9 / eR.

So for the further calculation we must first know c, as function of 7.

+. For the dependence of c, on the temperature all kinds of
different expressions have been proposed in course of time. From
this large number of expressions I will only choose some of the
most reliable ones. In the first place I will use the expressions
which follow from the experiments of Hontsorn and_Avstin, which

( 748 )

were carried out in 1905. The real specific heats can be represented
pretty accurately up to 800° C by
¢c, = 4.68 + 0.000536 7 (bi-atomic gas) *) and
Cy = 5.112 + 0.00729 7—22.05 10—? 7? (Carbonic acid) *)
From these values follows:
ney = 3.82—0.01297 T+ 44,1 107 7”.
So in the above equations 7, 8, and 9 must be substituted:
a—=8,82 ; b= —0,01297 and c—44,1 10-7. . . (10)
If we substitute these values in equation 9, we get:
SnHp=o = 134980
and the expressions 7 and 8:

295380
log K, = — —,—+2,92 log T—0,001419 7 + 1,61 10-7 7* + C’. (11)
in which :
nH)
' v=]
(Ci ee D5 Petes) yy). (i
4,571 isis Ce)

The values of Joy K, in the third column of the following table
have been calculated from the most accurate determinations of the
carbonic acid equilibrium, which have been inserted in the first two
columns*); in the fourth, fifth, sixth and seventh columns the values of
the other terms of the second member of equation 11 have heen
given, and the last column gives the value of C’.

TAM BIAE st
T | | log K, = ae 2.92 log 0.001419 7 1.61 10-7 72] Cr
|
1300 |4.14.10-8| 13.48 | —22.72 | 9.09 1.84 0.27 |41.75
1395 |1.42.10-4| —11.84| —21.17 | 9.18 1.98 0.31 1.82
1400 11.5 10-4| —11.77 | —21.09 9.19 1.99 0.32 |41's0
1443 [2.5 10-4| —11.11| —20.46 | 9.28 2.05 0.34 |41.83
1478 |3.2 10—-4| —10.79 | —19.98 | 9.26 210 0.35 |+1.68
1498 |4.71.10-4 | —10.28 | —19.71 9.27 2.13 0.36 |41.93
1500 |4 10—4| —10.50 | —19.69 |. 9.27 213 0.36 |41.69
1565 6.4 10-4) — 9.88) —18.87 | 9.33 2.29 0.39 1.49

So the value of C” appears to oscillate round a mean + 1,75.
If this value is substituted in equation 12, we get:

1) See Aprac, Handb. Ul, 2, 181.

2) Recalculated from the expression of Horporn and Austin. Sitz. Ber. preuss
Akad. 1905. 175.

8) Apece, Handb. IL, 2, 183.

(749 )

Snip = + 18.7.

v=]

5. The equation derived above deviates only little from the
equation given by Prof. Nernst in his ‘Theoretische Chemie” for
the equilibrium of carbonic acid"), which may be written after
recalculation :

29600 es
log K;, = — ripe 2,93 log T—0.001286 7 + 1,61 10—-77?+C’,. (11%)
in which C’ = 1.51 aecording to Prof. Nernst.

The oscillations of C” appear from the following table:

TP NBS Ti Veh ADE
| 2 | |
P|) Voys Ky | —— 2.93 log T | 0.001286 is 1.61 10-7 ee Ge
1300 —13.45 —22:71 9.12 1.67 0.27 +1.60
1395 —11.84 =i 9.21 1.79 0.31 1.65
1400 iil 7 —21.14 9.22 1.80 0.32 +1.63
1443 Silfilaalil - 20.51 9.26 1.86 0.34 +1.66
1478 —10.79 — 20.03 9.29 1.90 0.35 SEE 50
1498 —10.28 —19.76 9.30 1.93, 0.36 = Ts)
1500 —-10.50 = Ows 9.31 1.93 0.36 41.49
1565 — 9.88 —18.91 9.36 2.01 0.39 | +1.29

So C” oscillates round the middle value -—+- 1,57, which differs
but very little from the above mentioned value of 1,51.
For the value of YnH7—, we find for this case + 17,9.

=I

The discrepancies between these values and those of. §4 must be

partly ascribed to another assumption about 2n/, for the greater

part, nowever, to the changed value of } in the expression of the
specific heats.

6. In the second place we can use the more recent determinations
of Horporn and Henninc*). After recalculation these yield for the
real specific heats :

ey = 4,32 + 0,00107 T (bi-atomic gas)
cy = 4,90 + 0,00783 T — 2,38 10-6 T? (earbonie acid),

from which follows:
=e, — 3,16 _0:01245 2 -- 4.76 10-6 73.
So in this case we must substitute in equations 7, 8, and 9:

1) Theor. Chemie (1909) 681. See also Asrag Handb. Ill, 2, 181.
*) Ann. der Physik. (4) 23 809 (1907).

50
Proceedings Rayal Acad. Amsterdam. Vol. XIV.

( 750

—

a=, 16) 6 =] — 0012451 lands oA O08 ee nis)
This substitution yields :
SnEp=o = 135150
log K, = — + 2,59 log T—0.0013627 + 1,74 10-77? + C’, :(14)

in which :

Se
Vas ||
Ca So ke eee
4.571 ce)

The caleulation from the observations will be clear from the sub-
joined table without further elucidation :
TASB EF silk

ie log Ky - a | 2.59 log T+} 0.001362 7 | 1.7410-777| ©
| | | \ (

1300 13.45 22.15 Sx0ds || lean 0.29 Bei
1305 | 11.84 | 21.20 8.14 1.90 0.34 +2.78
Coe nan | maea2 8.15 1.91 0.34 42.77
1443)" =ai9 119 | 290,49 ehie | |) 107 0.36 +2.81
1478 | 10.79 | 220.01 8.21 | 2.01 0.38 | aipied
1498 | 410.28 | 19/74 8.22 2.04 0.39 42.89
1500 <to50. | Stole ses 204 0.39 | 42.63
1565 = 9.88. | Dig'go 8.21 2.13 0.43 ~ | qm

| |
So C" oscillates round the mean value + 2.71.
Now it follows from equation (15) that :

SnAyp~ = + 22.5.
7. In the first. paper on the theorem of heat!) Prof. Nernst pro-
posed the expression :
29600 _ hae
“a + (1475 log T— 0,00066 7 4+ C . . (16)

If we use this expression for the caleulation of C’ from the

log Ky == —

observations, we have :

TAUB LE IW:

29600

T | log Ky |—p— 1.15 log T 0.00066 Tr Cc!

1300192450) 220 5.45 | 0.86 =Av713
CO || sili tse oy Ol 2 500) 0,92 +4.80
1400) Seah Ol An 5 a5 0.92 | +4.78
1443 | —11.11 | —20.51 5153) 0.05 +4.82
1478 10.79 | —20.03 ees) 0.98 +4.67
1498 | —10.28 | —19.76 | 5.56 0.99 | -14.91
1500 | —10.50 | —19.73 | 5.56 0.99 | +4.66
1565 | — 9.88 | —18.91 5.59 | 1.03 +4.47

1) Gott. Nachr. 1906, 1.

(751)

C” oscillates round the mean value + 4.78 in table IV.

If we calculate the sum of the constants of entropy from this
value of CY” we find:

SnHy= = + 30.1
=I :

8. It will be sufficiently clear from what precedes that the results
of the calculations of the constants of entropy depend entirely on
the expressions which are assumed for the specific heats as function
of the temperature. Up to quite recently we had to content our-
selves with the above discussed expansions into series ; not long ago,
however, appeared a paper by Dr. Nits Bserrum, in which two
expressions derived from the theory of indivisible units of energy are
proposed and tested by the latest observations. *) It has appeared there
that with a suitable choice of the oscillation frequencies of the atoms
in the gas-molecules it is possible to account for the observed influence
of the temperature on the specific heat. The most remarkable thing
is now that with regard to the order of magnitude these frequencies
really agree with the vibrations which oceur in the absorption
spectra of the gases concerned, as was predicted by theory. Accord-
ing to Nernst the specific heat of the gases can be divided into
three parts. The translatory energy, which is exclusively determined
by the motion of the gas molecules as such, is represented by */, RT’
independent of the number of atoms in the molecule.

The rotatory energy is found by multiplying the number of
degrees of freedom by */, R7, and amounts to R7’ for bi-atomie
gases, to */, ART’ for tri-atomic and multi-atomic gases. So for
the specific heats these two parts of the energy yield two expres-
sions independent of the temperature (bi-atomic */, R-+ R; tri-or
multi-atomic */, + */, R). The third part, the energy of vibra-
tion of the atoms in the molecule will, however, depend on the
constitution, of the molecule in a much more intricate way. This
energy of vibration, which in its dependence on 7’ furnishes a part
of the specific heats which depends on 7, is now found by means
of the expressious drawn up by Erste, resp. Nernst and LinpeMANN
according to the theory of indivisible units of energy.

The real specific heat of a bi-atomic gas is now found by diffe-
rentiation of the said three parts of the energy with respect to 7’:

: d
o="/,R+R+——(RT~), . . . + » (17)

in which according to Einsrers gy is represented by :
1) Zeitschr. fiir Elektvochemie. 1911. 731.
50*

Bp
Lr
Sipe at
according to Nernst and LinpumMann by
By By
1 oe ] at
aE a a
ool pelt —— ||

The universal contant 8 has here the value. 4.86 10-!', » being
the frequeney of oscillation of the two atoms with respect to each other.

(Juite analogously the specific heat of a tri-atomie gas is repre-
sented by:

d
=", Rh +, B+ RT (Ot 0.4 Pal Be (lis)

in which g,, y, and g, vefer to the three vibrations possible in the
tri-atomic molecule.

9. If we now also apply these equations for the specifie heats
to the carbonic acid equilibrium, we find :

aif
=n | dT = {1,54+294+ gp—2¢,+9.+9,)} RT . - (19)

Oe

=n| = A4L= ai in T a a i 2yp. A a P.tFs) ) aT an

a
+R | Qpat+ ~B—APit+P.+Pa) ~ + > (20)
1
in which the indices A, 6, 1, 2, and 3 resp. refer to carbonic
oxide, oxygen, and carbonic acid.
If now the expressions (19) and (20) are substituted in equation

(3), we find:

ii
nk T= a2 Lop —2(p,-
fn Kas SEE St ral| <2 oe ee
R17 1 il

in which

]
C= —25 — 2ga+gp—2A¢.t+9.4+¥,)37=1 + pots

L |

ag 7d S715) pe ie) ET erin (2

( 753
The integral occurring in equation (21) can, if we use the g-value
according to Eixsreim (see § 8), be found, if we bear in mind that:

e dre if —-
ae — : ee cn | = Ke — In(l—e r); (23)

if we use the value of g of Nernst and LINDEMANN, we get:

4 ee Gee) oe oT) ae al (24)

Finally it appears from equation (17) that:
SnEk = SnEp— + fl, + 244+ ¢e2- 2¢,4¢,41 8, RT . (25)
When using the g-expression of Einstein we must, according to
Bserrem, substitute resp. 3.64, 3.6, 14.7, 6.2 and 6.2 for 2
or 4050, 4050, 992, 2350, and 2350 for prin ga, GB, GF, PY, and g,.
If the g-expression of Nerxst and LinpDEMANN is used, we must
substitute for 2: 2.594, 2.594, 81, 5.0 and 5.0 and for pr:
5630, 5630, 1800, 2920 and 2920.
If now in equation (25) we substitute these values with the values
of nF from equation 9, we get:
SnEy—>o = 134850 (Erstery) resp.
— 134800 (Nernst and LINDEMANN).

Hence the expressions for the carbonic acid equilibrium become :

29500 eset ae
(ih —=—— a + 2,5 log T—8log\1—e VT J+ 2log\1l—e TV f+

_ 2880
+ 4 log \ 1—e JE) ECW a ec) ok Ou a ee CN (A),

2490 _wa)\( we
log i == — + 2.5 log T—*/, log \1—e 1 l—@ 2!

ts

iso) i. es e270
+ log =o l=? dh +2log ie ih 2 27 = On L(27)

In both expressions the constants C’, and Cy; have the values:
Cx = 0,4343 Ce + log 0,0821 and
Cyr = 04843 Cy, + log 0,0821,

( 754 )

in which the constants without aecents are represented by equation
(22), because the lower limit of the integral occurring in equation
21 may be neglected.

If we consider that also the values for y in equation (22) for
T= 1 may be put zero, we get finally:

il
Cag = CN Tp AAS (- 2.9 of R Snir.) -- log 0.0821

vl
or
nH —\
v—]
Cph= CNEL = = Yale 28
ss 4571 2)
TAB aE way)
| 29500 | 29490 ies
| = = im ! !
if | San: | a. 25logT loge 2logn,| C'g C'NL
1300 | —22.69 | —22.68| 7.78 | —0.80 0.78 +2.26| +2.23
1395.| 21.15) | —onet4 |) (ae86" | 0787) —04854)| “wosson| meiBowog
ANP PO =P Oar sce | —Oneui | Ose || ey) je. D7)
1443 | —20,44.|~ 90.44 | ‘790° | —o.91 | 018g | Sora") sfonsy
1478) | =T0 106.) —=TONO5t I a7kO27 nh LLOnOS HOSOI Mee ouTigal ne mtEs
1498 | —19.69 | —19.69| 7.94 0.95 | —0.92 | 12.49 | 49.39
1500 | 19:67 |.=19:66 | 7294 || —0/05 | =0'03'| 4-o.1g |* Mots
15657| 218285) | texea4| oon ==oNoon|! 20807) =a1koTE Seiad

So ihe mean values of C"pg and C'yz, amount to:
+ 2.25 and + 2.22.
From equation 28 follows:

np = + 20.2 and + 20.1.
v=]

10. If we now consider the results of the five tables, it appears
that all five have been caleulated with the aid of the same data
concerning the chemical equilibrium, that the same value 2n/ was
used for tables I, HI, and V, that the values on which tables II
and IV are based, differ at the most some tenths of percentages
from them, which accordingly can only bring about a deviation of
some hundredths in the value of C', and that therefore the greatly
varying values of C" resp. Sn/f7—\ must be attributed to the different

v=]
expressions which are introduced for the specific heats.

The term, produced by the constants of energy, differs at the
most O,1 in the five tables; the great influence, to which the difference
of the obtained C” values is to be ascribed, lies chiefly in the different
factor of log 7, which varies between 2.93 (table IT) and 1,75 (table IV).

( 755 )

This can bring about a difference of more than 3 in the terms
concerned, because /og 7 is of the order 3.

Though accordingly the different assumptions concerning the specific
heats give a maximum deviation in the constants of energy of at
the most some tenths of percentages, they give rise to variations
from 17,9 to 30,1 for the constants of entropy. So the accuracy of
the constants of entropy is far inferior to that of the constants of
entropy.

It will be clear from the above that the extrapolation of the specific
heat from the region of - observation to the lower temperatures is
the cause of the deviations. For where e.g. for bi-atomic gases the
expression Cy=a-6T implies that the specific heat retains its
linear dependence with descending temperature, it becomes constant
at low temperatures on assumption of the expression of Bsrrrum.
The line that represents the specific heat as function of the tempe-
rature, exhibits the same shape (with a point of inflection) in the
latter case as the specific heats for solid substances, which of late
have become known specially by the investigations in the laboratory
of Prof. Nernsv.

We may eall here special attention to this that all the five expres-
sions which have been mentioned for the carbonic acid dissociation
equilibrium, account equally well for the observations, for the oscil-
lations of C’ have the same value in all the tables. And we have
here only to take the absolute, not the relative deviations of C’
into consideration.

That a change in the expression of the specific heats can have a
great influence on the value of (”, is moreover a conclusion which
is not new. Everybody who knows the work of Prof. Haprr already
mentioned in § 1, which appeared already in 1905, and which
treats the gas-equilibria with the facts known at the time in a very
clear way, will find back this conclusion there. As it appeared to
me, however, that this conclusion is not generally known, and the
newer data have hardly modified it, I have thought it necessary
to elucidate it in what precedes by one of the most fully studied
reactions.

If we ask which value of the constants of the entropy must be
taken as the most probable, we come to the conclusion that this is
certainly the value of Table V. In the first place the expression
proposed by Bserrum has a theoretical foundation in the theory of
indivisible units of energy, and besides this formula renders the newest
investigations of HoLsorn and Hennine and those of Pier very well, as
appears with the greatest clearness from the cited paper by Bserrum.

( 756 )

A drawback mentioned by Bsrrrum, exists, however also when we
use this’ expression. It is namely pretty certain that this formula
will not rigorously retain its validity at low temperatures, because
the rotatory energy at low temperatures will deviate from the
value given in the expression. This, however, does-not detract from
the fact that in my opinion this theoretical formula is to be preferred
to the empirical expansions into series.

11. If we apply Bsrrrvm’s’ data to the equilibrium of the water-
dissociation we tind at 7—= 273 for Yn the value 115660, resp.
115260 according to BertueLor and MaticNon, resp. to THOMSEN.

If we take a mean from this, we get according to equation 25:

=n ET=» —— 114650.

If the y-values according to Einstein, resp. Nernst and LINDEMANN

are used, the expressions for the equilibrium become :

4860 4050

= 25080 ie ==3 are
log K, = ——~— + 2.5logT—2 log | 1—e L |)—log J\—e F J+
2650 5610

7
a 2log( te | 4 log € Tr ) LiCl, ) oe pean

and ‘
72° 7290
i 25080 : <E, \ — at ==
log (K@—S— - + PLS) log —_— log l=) 1 l—e 27
7 56380 5630 6075 6075

= "fale 1-¢ FQ oT) 4 sloy( 1 a) ples 27 jr (30)

The most accurate observations, which were carried out in Prof.
Nernst’s') laboratory, now yield :

1A Bo Ea var

| 25080 | . S | > LH ee

T | logK,|———| 2:5 logT | = loge | logy, | Clr | Gi
1300 | —14.01 | ---19.29 7.78 —0.10 —0.09 | —2.40 | —2.41
1397 | - 12.63 | —17.95 7.86 =0812 —0.10 | —2.42 | —2.44
1480 | 11.47 —16.95 7.93 —0.14 —0.12 | —2.31 | —2.33
1500 | —11.42 | —16.72 | 7.94 —0.14 0.12 | —2.50 | —2.52
1561 | —10.71 | —16.07 7.98 =0,15 —0.13 | —2.47 | —2.49
1705 | — 9.28 —14.71 8.08 —0.18 —0.16 | —2.47 | —2.49
2155 | — 6.08 | —11.64 8.33 —0.27 | —0.26 | —2.50 | +2.51
2257) | — 555) | — tent 8.38 —0.29 | —0.28 | —2.53 | —2.54
2300 | — 5.04 | —10.90 | 8.40 0.30 | —0.29 | —2.24 | —2.25

|

1) Theor. Chem. 1909, 680,

(757 )

The mean values of C’y, and C’y;, amountto 2,48 and —2,44.
It appears from equation (28), which holds here unmodified that :
Sein — iL Oeande— Aas

v=)

12. The water gas equilibrium can be found by calculation from
S | 4
the water aud carbonic acid equilibrium.
0c Cena Conc

5
~ 7 Wak 90) = CoO 6. JEG WCLOY, 5
From Ki o= i ay on -——* it appears, that

———— and Ky»=
2 Oe CnC
H,0 C0, co “H,0
log Ky = */, (log Kio — log Kvo, ).

Hence if we subtract equation 26 from 29 resp. 27 from 30, we
find after division by 2:

29 10 ta 4860 r. o82 33 2350
logue — oT log 1—e FT }—loy\1—e T J—2log\1—e T
_ 4150 __ 2600 3610
+ log Ie 1 _- log le ff + 2 log l—e L - CO wr, (3 1)

and

99()5 Ri. eet 2 tel EIN
logK y= = jlog (1-. L ‘ie 27 ) —*/ log Ge if Jt. 27 )
‘ __ 2920 2920 563) 5630
—log\1—e TF je He "l,log\1—e T l—e 22
( - =) ( 4 7)
as */,logy\1—e T l—@ 2ue se Cw yr. 5 mf o wo, 6 6 (GY)

For the calculation of the constants we use the determinations
of Haun 2). :

ASB EEE AVI

1h Ke! log K — log, & log C e

BE NL Wr Wp
959 0.534 0.27 283002030. 0.23 0.24 — 2.26 — 2.27
1059 0.840 0.08 2.09 | 2.08 0.27 0.27 —2.28 —2.27
1159 1.197 ~ 0.08 1.91 | 1.90 0.30 0.30 —2.29 — 2.28
1259 1.571 —0.20 De 6y ela: 0.33 0.33 —2.29 —2.28
1359 1.96 —().29 L263" | 1362 0.36 0.36 —2.28 — 2.27
1478 2.126 —0.33 1.50 1.49 0240) i) 10239 —2.23 —2.21
1678 2.49 —0.40 soe ven baeeyy| 0.45 0.44 —2.17 —2.15
So the mean values amount to — 2.26 and — 2.25.

The constants of entropy can be found from :

1) Aveac. Handb. Ul. 2. 198.

yy

into which for this ease equation (22), in which 27 = 0, passes.
The calculation yields:

SnHy= = — 10.8 and — 10.38.

v=1

If we now compare the values which the direet determinations
of the watergas equilibrium bave yielded, with the values which
are caleulated from the constants of the water and carbonic acid
equilibrium, we find:

TVANBs ES WII:

Watergas
Carbonic acid Water — = aca
Calculated Direct
Cc =nH7_, C! nH, Cc! 2nH7_, C 2nH7_,
v= | v=1 v—1 —
+2.25 + 20.2 —2.43 | —1.19 —2.34 —10.7 | —2.26 = 1053
42.22 + 20.1 —2.44 —1.23 —2.33 | —10.7 —2.25 | —10.3

This agreement proves that the observations on which table VII
is founded, correspond sufficiently well with those of the tables
V and VI. This, however, cannot be advanced as a proof of the
accuracy of the used expressions for the specific heats, as such an
agreement may also be obtained on other assumptions concerning
the specific heats.

Inorganic Chemical Laboratory of
the University ef Amsterdam.

Physiology. “The effusion of acoustic energy from the head,
according to experiments of Dr. P. Nikirorowsky”. By Prof.
ZW AARDEMAKER.

(Communicated in the meeting of December 30, L911).

In the months just past, Dr. P. Nikirorowsky from St. Petersburg
has earried on in the Physiological Laboratory at Utrecht an investi-
eation as to the effusion of acoustic energy from the head whilst
the sound was introduced, either from the head or from the vocal
organs or from the crown of the head along the stem of a vibrating
tunine-fork which had been placed there. The intensity of the sound
produced, was about uniform, which appeared from special measure-

(. 759))
ments (in the case of voice comparatively, by testing the sound at
a microphone placed in a camera silenta and connected with a
small string-galvanometer, in the case of the diapason vertex by
measuring the amplitudes of the oscillations).

The problem which the experimenter has set himself, and which
he has solved is the following: how does the vocal energy amounting
uncorrected to from 1 to 7 megaergs per second according to an
investigation made in collaboration with A. DE Kieyn (see my Leer-
boek der Physiologie, Haarlem 1910 Vol I p. 82) distribute itself
over the natural egresses (mouth, nose and ears) and the hard and
soft parts of skull and face. For obviously not only from the lips
but also from all other parts the head will yield sound to its surroundings.

The sound when issuing forth was received in closely fitting leaden
funnels or by ear-pieces and was led by sound-proof leaden channels
to a microphone, placed in a leaden chamber with very thick walls.
The current-fluctuations, produced in the microphone, manifested
themselves, after having been transformed in the manner usual in
telephony into an induction apparatus, at a string galvanometer with
a gold string 5 thick and about 30 mm. long. The tension of the
string was regulated in such a manner tnat it reverberated distinctly
at all vowels and produced a vibration the double amplitude of
which could be easily read off on the scale of the instrument. Provided
we restrict ourselves to the comparison of sounds of the same pitch,
it may be assumed that in spite of the multiple resonance of the
system (sound-channels, microphone, transformator, string) the intensity
of the sound acting upon the microphone was proportionate with
the squares of the amplitudes measured. Sounds of different pitches,
however, cannot be compared, as the manifold repeated resonatory
strengthening, which the sound undergoes, is very different for different
pitches; this became manifest when the micro-telephonic system after
it had been constructed was tested, in the manner usual in the
Laboratory, by means of a series of uniformly tuned organ-pipes,
ranging from a, to e,. If necessary a comparison of the various
vowels might have been attempted with the aid of this supplementary
investigation, but on account of the numerous sources of mistakes
it gave rise to, the idea was relinquished.

On comparing the values of the same column in the above tables,
we become aware of considerable differences in intensity, the more
so if we remember that the actnal strength of the sounds has been
proportionate with the squares of the deviation of the galvanometer.
The cause of this great difference will probably have to be sought
in the co-operation of two causes :

( 760 )

TABLES I

Intensity of the sound flowing away, calculated per cm’, the chest voice
being the sound-source.

Place whence the Double amplitude whilst the

sounds ie tae vowels were being pronounced Remianke
telephone-apparatus | a to) oe e T

Nose 84 84 = 168 84 16s leaden ear-pieces
Mouth 168 168 | 84 Hes | 84 F :
Ears | 4 4 8 4 | 8 " =)
Zygomatic arch(temp. 0.4 0.4) 0.8 0.4 | 0.8 leaden funnels
Supra meatum ga) POE Ou 04a 10) tO | 0.4 mi a
Proc. mastoid. 0.4 0.4 0.4 0.4 |) 0-4 7 i
Zygomatic arch O-49) 1024 1 038i) 20545) 1088: > +

(middle) |

Forehead (side part) O54) 20542) 1054 10220) 1074: " 5
Forehead (middle) | 0.2! 0.4) 0.8] 0.2] 0.8] one funnel
Os parietale | 0.4/ 0.4] 0:4] 0.2] 0.2) leaden funnels
Crown 0.4) 0.4 0.8) 0.4, 0.8 one funnel

Nape anOkel 0.1 OF25 Ora 0.2. one funnel
Cheek 4 4 8 4 8 leaden ear-pieces
Sides of the nose 4 2 2 2 1 _ ;
Planum submentale 4 4 8 4 8 = “
Chin 4 4 eee 8 P 3

a. the timbre of the various vowels is different, even when
pronounced at the same pitch,

b. the width of the mouth-eavity is different in the pronunciation
of different vowels, for in the case of the wide vowels of Bgtt-
Sweer the effusion of energy through the mouth will be promoted,
in the narrow vowels impeded, in inverse proportion of which the
effusion of energy by other channels takes place (a and e are open
vowels, w and 7 are closed ones).

From the tables it appears that the greater part of the acoustic
energy of the voice leaves the head by the lips, a much smaller
part by the nose, and a still smaller part by the auditory canals.

A totally different result is arrived at, if it is not the voice that
produces the sound, but if the acoustic energy is derived from a
tuning-fork set vibrating by means of electricity, and placed on the

( 761 )

ALB Ey Eee lls
Intensity of the sound flowing away calculated per cm’, the falsetto voice
being the sound-source.

Place whence the | Double amplitude whilst the

SPU Ete. peas vowels were ane pronounced Remarks

telephone-apparatus a ta) oe e l

Ears 2 0 4 0 4 leaden ear-pieces
Zygomatic arch (temp. 0 0 0.3 | 0 0.3 | leaden funnels
Supra meatum ee 0 0 Ne 0 a .

Proc. mastoideus 0 0 te 0 fc -
Zygomatic arch 0.16 | 0.2 | 0.4 | 0.2) | 0.4 7 -
(middle)

Forehead (side part) 0.1 0.16 | 0.4 | 0.16 | 0.4 FA .
Forehead (middle) 0 ? if fe ? one funnel

Os parietale 0 0 0 0) 0 leaden funnel
Crown One| ORS NORA NOR2e |) .0)2 P .
Nape 0 0) ? 0 ? y ”
Cheeks 2 4 8 2 8 leaden ear-pieces

crown of the head. In this case mouth and nose orifice get hardly
any share at all, the rest of the effusion being thus:

=I FUE} VIE NE

Intensity of the sound flowing off calculated per cm’, the sound-source
being a diapason vertex.

Place whence the

sound was trans- eek: Remark
mitted to the micro- canine | pe
telephone-apparatus Pp
Ears 32

Zygomatic a rale} 2 The experiments were made

Forehead 6 with the aid of a tuning-fork of

Supra meatum 4 EDELMANN with running-weights
at the ends. The double amplitude

Nape 4 cea :
amounted there uninterruptedly

Nasal bone 4 to 1 mm., sustained by electro-

Soft parts of the nose \ magnetic motive force.

Cheeks 2

( 762 )

We have not succeeded in any other way than the one described
above, in introducing an amount of sound-energy into the head,
sufficient to import enough intensity to the sound which flowed off,
to measure it by means of the microtelephone apparatus and _ the
string-galvanometer. Only very strong sound-sources such as MARAGE’s
“sirene a voyelles’, when one places oneself before it with open
mouth, or a loud speaking telephone, led directly to a nostril, produce
enough sound to bring about a measurable deviation of the galvano-
meter, and that only when the sound is derived from both ears ie.
in the most favourable condition. If we leave out of consideration
sounds introduced by actual contact, the sound of one’s own voice
is evidently the only one which penetrates the skull in great intensity.
The sound transmitted by the air to which we listen in ordinary
life, acquires only its well-known preponderance by the structure of
the middle-ear, eminently calculated to conduct sounds. In itself a
tone passing through the air and piercing the skull, is always weak.

It also seemed desirable to make an absolute determination of the
sound issuing from the head. For this purpose that which es “apes
from between the lips when we pronounce the vowel “a” was
received into a phonograph (as this was done in the camera silenta,
the sides of which are covered with thick horse-hair, absorbing sound,
better resulis were obtained than before). Then the impressions made
on the wax cylinder were measured according to the method of
BorkeE and analyzed according to the method of Fourrrr. Finally
on the ground of this investigation the vowel was imitated in exactly
the same strength by means of organ-pipes’). The total strength of
the imitating sound appeared as follows:

TABLE IV. Vowel “a”.

o Onn - & 5 w ) Ss
2 PS bem eee tees ices gees ars Log
S |sa —/SOQEe%a| oS | aSOeke| Bo aoe)
2 Seo} Gu lcs E.ns| ES |Meas) ba o>
S|) o-| 2 3 S700! 2S. | SEV 2] abe Sets
S | —22)is |e222 RS |eaXS| ee | wos
= = Sis nS) eal) OE 8) heel) SSE Bae
Se | 26 S els sasst SS c Emme
mM |Add A= 2 as Ss = Ss

2.45

6 jasharp?, 804 | 1.035) 107.5 2 210915 | 0.
2

_ >
P=

7 |b sharp*) 938) 1.71 | 308 16 | 4834368 | wee
|

8 1ic3 1072 | 0.825) 107.5; 2 210915 | 0.014,’ pro see.

1 Megaerg = 10° ergs
Hence it appears that the intensity of Dr. Nikirorowsky’s voice

1) ZWAARDEMAKER and Minkema, Arch. f. Anat u. Physiol., Physiol. Abteilung
1906 p. 433.

( 763 )

issuing from his lips when loudly sounding ‘a

”

amounted to 2.35
megaergs per second. According to this standard the effusion of sound
from the other parts of the head may be determined. This is set
forth in Table V.
Te Seb Eevs
Acoustic energy emitted by the head per second whilst “a” was pronounced
with chest-voice.

Extent of

Fite ne Total energy |

Energy per

Regiones cM® in facenani in megaergs Remarks.
megaergs cM? per sec.
Nose 0.131 1.1 0.144 both nostrils together
Mouth 0.524 4.4 2.306
Ears 0.000297 0.475 0.00014 both ears together
Bony parts 0.0000297 | 2233 0.066
Soft parts 0.000297 559 0.166
2.68

The total effusion of sound amounted therefore in the above
experiment to 2.68 Megaergs per second. Of this the greater part
viz. 2.45 Megaers left the head by the mouth and the ears, an
extremely small part by the auditory passages and about ‘/,, by
the bard and soft parts together. These data we offer uncorrected
i.e. without an estimate of the efficiency of a well-regulated organ-
pipe. Not all the energy imparted to the pipe is transformed into
sound. Some of it is lost in the vortices of air. Hence our values
are greater than the real acoustic values. Though the latter accord-
ing to a recent publication by Zurnov ') may be esteemed of about
the same order, yet it seems to me that the importance of Dr. P.
Nixtrorowsky’s figures lies in the mutual relation of effusions which
differ topographically.

Mathematics. — “On partial differential equations of the first order’.
By Prof. W. Kapreyn.

1. When a partial differential equation of the first order
EBay yp) =e ee ce 8 on ae eal)
is transformed by a tangential transformation, the new equation will
generally show the same form. Sometimes however the transformed
equation will be linear. In this case the complete primitive of the
1) Zernov, Ueber absolute Messungen der Schallintensitiit. Die Rayleighsche
Scheibe. Ann. d. Physik. (4). Bd. 26 p. 79. 1908,

( 764)

non-linear equation and the integralsurface passing through a given
curve (the problem of Cauchy) may be obtained from the transformed
linear equation.

The object of this paper is firstly to determine the necessary and
sufficient conditions which must be fulfilled by the equation (1) when
it may be reduced to the linear form by one of the two known
tangential transformations of Lecenpre and AmprERR; secondly to
show how in these cases the problem of Cavucny may be solved.

2. If the tangential transformation of LeGrenpre
e =P, oy = OS PRY pp
reduces (1) to the linear equation
AAG, Z) PB (XK, 6Z)'O— © (XIE)

where A, B and C are arbitrary functions, the former evidently
must be equivalent with ;
vA (p,q, pe + qy—2) + yB(p, 9. pe + qy — 2) =C (p. 9. pa + ay — ).

Therefore, writing

A(X, 2, 2)2 4 BUS) 0— COC, V2) = wie BO

we have

ow pale. tips Oy FRE ye!
ae Z) . 0Q B(X, Y,Z)

and
at iat 07yp 0
OF? P00 moO er
Inversely, these conditions being fulfilled, yw represents a linear
form with regard to the variables P andQ.
These condiuions may be transformed in the following way
F (a,4,2,p,9) = w (A, Y,Z,P,Q)

therefore
oy oF OF dy OF OF
GPamce De: OOS, 0:
ap 8F OF OF
We ae ee
ope See Oe
0PIQ dad Owe dy0e 02?
op OF UP | OF
0Q2 9 072 Oydz 02?

so the necessary and sufficient conditions, in this case, may be
written

Fr or or

aa? +P aeae TP ast — ”

PY ORF ar | .
CRO areas ory heme te a
or or oF

== Ny 2 __ = (0)
Oy? y Tagged 02?

oe i

In the same way, considering the tangential transformation of
AMPERE

LG yf OZ — AO) pag == Vi
we obtain the necessary and sufficient conditions
oF — ()
Op? ;
ap OPE =—=1() step ene 6 A)
i or Oy

<> 2g —— + 7 =~ =
ago evan agg

3. Assuming now that the equation (1) has been transformed by
the transformation of LeGENDRE in the linear form
A(X, ¥,Z)P + B(X,Y,Z)Q = C(X,Y,Z)
we will proceed to examine how the integralsurface of (1) which
passes through the curve
Y¥=G(x%) » 2 =yYV(2)
may be obtained.
Let the integrals of the system of ordinary differential equations
de ay dZ
AUGIRZ) oe BUX CRAY)

be

UO (SVAZ — an ViURAY 2) 6
where a and @ are arbitrary constants, the difficulty of the problem
consists solely in the determination of the relation or the relations
which must exist between the constants a and 0.

Designing a point v,¥,2 and a plane passing through this point
with angular coefficients p and qg by the name of element, the x?
elements which are related by the three conditions

y= G(r), 2<=—Y(2), dz—pdzx + gdy
are transformed in the o* elements (YX YZPQ) which satisfy the
three conditions
51
Proceedings Royal Acad. Amsterdam. Vol. XIV.

( 766 )

Q=g4(P), PX+QY—Z=4(P), w(P) =X + YP)
or
Q=4(P), XP+Yo(P)—Z=y(P), X + Yy(P)—viP).
These elements are precisely the elements of the developable sur-
face generated by the plane

Xt + VY¢(t)—Z — y(t) = 0.
For this developable is obtained by eliminating ¢ from

Xt + Yg¢()-—yw) = 7

£4. Fol win 20 Oh
and determining

2S em i ee

ox OX

OZ : Ot

=) +1X+ YHO—VOS = 40

it is evident that the angular coetticients of the tangent plane through
the point X, Y’, Z of the developable surface are related by

Q= ¢(P).
Hence the constants @ and 4 must be such that the curve
U(X,Y,Z) =a, V(X,Y,Z)=6b
touches the surface (5).

This condition leads to two or one relation between a and 0,
In the first ease we have

U(X,¥,Z) =m, V(X,Y,Z)=n
where m and nm represent the values found.
If now we transform again X, Y’, Zin w, y, 2. p, q these relations give

U (p,q ep + yg — 2) =m, V( p,q, ep + yg — 2) = 2
and by eliminating p and qg from these and
F(a@,4y,2:p:9) =90
we obtain the required integral surface.
In the second case, which is the general one, let
b = O(a)
be the only relation between the constants a and 6. From these
we deduce
V(X, Y,Z)=6[U(X, Y, Z)].

Differentiating with regard to X and Y, we have

(G9)

OF se Y Oleg. 580
a ae 7)

oe soa
aV gol ey (2 , 00
ane 67 str cane

Transforming now 2, y, 2, p, q and eliminating p and q from
these, we get the integralsurface passing through the given curve.

4. The first case presents itself in the following problem.

Let

a PY

be the given differential equation which satisfies the conditions (3)
and let it be the question to determine the integralsurface passing
through the curve

°

ele
Transforming the differential equation, we get

Pee OF Ixy

and
= ve at ae Nera
XC. 2) —— —"a, Vig 254) = —— = b.
xX Xx
The developable surface (5) being
— X*
L— Ya a
the curve
a Z—XY)
x= aie = li

will touch this surface if
4a —1=0 and bJ—a=—0O.
The solution of the linear equation is therefore
4Y—X=0, 4Z7—4XY—X=0.
which transformed to 2,y,2,p,q gives
4qg—p=0 4(—z2+pe+qy) — 4pg —p =2.
Joining to these
-=pq
and eliminating p and q we obtair the required solution
16z = (4x-+ y—1)?
which satisfies the differential equation and passes through the curve
i —
The second case will be met with by taking the same differential

equation with the condition that the integral passes through the line
51*

( 768 )
y= 2 2 Nan
Here U and JV are the same as before, but now the «? elements
(XY YZPQ) must satisfy the conditions
Q=2P , (X12 r 2) 2= 7 = 0), ro
or
QS OP e200 | OX a 0
Here the developable surface reduces to a line and the a’ ele-
ments consist of all points of this line with all planes passing through
this line. For representing these planes by
Z—k(X +2 ¥ —2)

it is evident that whatever /£ be, we have the relation

C= 2
Expressing now that the curve
Xx Z—XY
Yocuhe ee

meets the line
T=) n OO = E= 0

we find but one relation between a and 0, viz.
2a + b(1 + 2a)=0.

This gives the solution of the linear equation

7 tigen See

ete ae aeRO

and by differentiating with respect to X and )

4Y?

PSY.

(X+42Y)?
2X?

= X= a,

: (X27)

Transforming again and taking p=W— from the differential equa-
q

tion, the first of these equations and the quotient of the second and
third give
2yg* — 4eg* + 2(2e + y + 2) g* — 2279 4+ «2? — 0
2yq* — 22q° + 27¢ — ez? = 0.
Adding and subtracting these equations and writing
Ba=2+y+2
we obtain

( 769°)

4yq° — 62q* -+ Beg —2? =0
2q° — Bq? + 32q — 202 = 0

so finally

| 32—yB 6y—B 2—4tay
| 2(6y—B) B’—16z—8zry 2(122a—B)| = 0.
| z—4ay 1272—B 32—27B
5. Secondly we suppose that the given equation (1) satisfies the

conditions (4). Then the transformation of AmprrE reduces it to the
linear form
Ake A) 1B (Xk YAO C(x, ¥, Z)
whose integrals may be written again
WAG Me Ae or 7 (OGD GVA) 0
The a* elements subjected to the conditions
y = (a). Zn (a) dz =pda + qdy
will now be transformed in the o* elements (Y Y Z P Q) satisfying
the conditions
—Q=,(X), Z—VYQ=y(X), wy! (X)= P+ Yo'(X).
These elements consist evidently of every point of the surface
Tit SY pi (Xi) == Ab (CXS) ett Ds ed 2k? (6)
with the corresponding tangent plane. The curve
U(X, ¥,Z)=a, V(X, ¥,2=b
touching this surface, it is evident that if we eliminate Vand Z, the
resulting equation must have equal roots XY.

This gives sometimes two, but generally one relation between a
and 6. Both cases may be treated in the same way as before, the
only difference being the transformation, which is now

X= 2, 9, | i= 2 — gy, =p, C= — x.

6. As the differential equation
BES /08)
satisfies also the conditions (4), the transformation of AMpirE may also
be applied if we wish to determine the integralsurface passing through
the curve
y=u 2z=(e+1) (42).
This transformation gives
Vypal Vaasa

whose integrals

are easily obtained.
Joining to these the equation (6)
Z4+ XY =(X+41) (X42)
and eliminating } and Z, we get
(a+b—3) X + ab —2—0.
This equation does not admit equal roots unless
a+b—3=0 and a—2=—0.
Hence

and
YX = Il 7 = 2%
The transformation applied to these equations gives
q—@ 1 2—qy = 29
and after elimination of ¢
2 = (#+1) (y+2)
which is the required solution.
If, in the second place, the integralsurface through
2a

Ce
is required, the constants @ and 6 of the integrals
Y—X=a, ==b
Y
must be such that this curve touches the surface (6)
GA OXY = Ox
This condition gives
(6—2a —2)? = 16a
so the solution of the linear equation may be written
7 2 OF (Y =X) ana

from which by differentiation we obtain

Bion,
poly =
VYy—
6Y—-4X
Q—4Y+ DE = Yk a
VAN GN

Hence, after transformation

2— qy — 2q(q—w4+1) = 4¢ Vq—x

p+%aq=>-

4vu—6q
4g + y — 2a + 2 = —__—.
Ea
Introducing z= pq and putting Vqg—x—t the first and the third

equation give :
2¢* + 42° 4+ Be + 4at4+ ay + 22 —2=—0
424 6 + Bt + 2e=0
therefore the discriminant of the first member of the first equation
must be zero.
If we assume
24 (ay—z) = A
this may be written
(A + B)? —{B(3A—B?) + 2162}? = 0
or, after a slight reduction
A(A—3B?)? —- 4822 B (3A—B?) — 466562" = 0.
This solution, though different in form from the former result,
represents the same surface; that it passes through the line
i — Oe

may be easily verified.

Physics. — “On some relations holding for the critical point’. By
J. J. van Laar. (Communicated by Prof. H. A. Lorenz).

1. In this paper we will derive some important relations which
exist between some critical quantities.
If it may be accepted that in the association to multiple molecules
no generation of heat (change of energy) takes place, so that g = 0
may be put, we saw already in I, p. 293 that the relation

T dp a
SN ere cs ne cee» (L')
p al /x PRUE
holds.
If we now put v,:+,=7, and substitute for pz its value, viz.
(see I, p. 289) ;
apa i i @
Pk 37 Jia be 1
we find:
27
(f-1) 7? = — ee (2)

If instead of (1) we write;

—
~I
~I
Nr

—

ple 1 fe? ap RTE

Pk ———sP (ex)
: 1+ «py = ;
in which ef = mere and if we substitute the value (seel, p. 288
=.Ah
and 297)
Rhy = Om ead
et Saige

for R7,, and further the above values for p, and vz, we get:

srl) = 8a" Bake MeO OG C ne)

z

From:
Prk
L=—e
RT;
follows after substitution of the values for pag, v_ and RT):
? if
oe (4)
lu Js
From (3) and (4) follows also the remarkable relation:
ela :
fe ——— een CD)
r

Finally by combination of (2) and (4) we find:
PAC ihe
i 64 7,7 ;

w (f—1) (6)

The relations (2), (4), and (6) have also been derived by Van DER
Waats (see among others These Proc. June 1910, p. 118, and
those of April 1911, p. 1216 et seq.) in the following form:

7 64
Gai oe ae ra a) (all this by approximation).
In this the quantity s is =1:y, while 7’ is not =v,: b;, but

=v: 6,. In consequence of this our relation (5) is VAN DER WAALS’s
relation (he has not taken into account the factor @ by the side of 27’)

by 8
x es (1 —_ =).
b, ‘ J

P r—| eae
According to (5) —— would namely be =— with a, = 1, or r
5 : Q 7

s
(: = ) = 1. In this r=v,;: b:. So if we substitute 7’ = v,;: 6, for
j

s by
r, we get 7 (1 — =\=5 ,
J bg

Geer

It was also already made probable by Vax Der Waats loc. cit.),

that (f-—1)r? < 27 and rs < 8, but s?: (#1) almost exactly = 64: 27°).

The theory developed by us confirms these relations perfectly.

We found namely in I (p. 297) and II (p. 480 and 431) for the

factors 7, and /,:

_ 14a n*(8m?—2n)
ok aaa
3m?—2n)?(4n—3

peer NE an PUT 0hg 7 (or) ind 1, OT (o 9)

5

m

= 1,004 (x1) and 1,010 (c=2)

See equation (5) in I, p. 288 for the signification of the quantities
m and n.
Really (f—1)r? = 27:1,007 is < 27, but only little smaller ;
1,004
1,007
2 =1 (partial association to double molecules), but the same holds
also for = 2 (triple molecules).

rs = 8 also <8, but also only little smaller. This holds for

rs 64 (1,004)? | 64

But we see also that Fai oT aH00T SS Ven WEDS also in

. eS 1,010)* : 1,004)?

the case of «=2, where — = a =1,001, just as ee:
i 1,019 1,007

So the value of s*:(7—-1) is only a thousandth of the value higher

64
than = viz. 2,3727 instead of 2,3703.

=

As w= pave: RT, and f—1 =a: pgrz’, we have also

which equation together with the equation that follows from (1), viz.
a= (f—1) peve’,
can serve for the determination of a (see also van pER Waats, loc. cit.)

1) I may point out here that the different critical quantities were already expressed
by me in experimentally determinable quantities in 1905 in a quite analogous
way (see Arch. Teyler 1£05 p. 46 and 47). The quantity f was there excluded
on account of the possibility that b might be a function of the temperature. For
then the fundamental equation (I) no longer holds, as we have proved (1 p. 291).
And instead of the quantity r=o,:6, the quantity 2 = a : RTyx, was then

introduced by me by the side of uz. So @ is evidently = zs . a

of

(774)

Our relations (3) and (5) may effectually be used to calculate ag,
ie. the state of association at the critical point. Specially (5) is
particularly suitable for this purpose, because /, and /, no longer
occur in it. As @ has been added by us as a factor to 7% in the
equation of state, it can he also decided whether the associated
molecules really behave as one molecule as far as their influence
on the pressure is concerned, i.e. whether there is real association,
as vAN DER WAALS cautiously expresses it — ‘“‘quasi-association.”

Now we saw in I, p. 295 that @, must be = 0,955 for z=1;
and’ in II, p. 429 that @, becomes 0,958 for «= 2 (in order that

or

f may become -=7 and «= 0,265 for 7). So we find the value
1,955 = . 2,916
= — 0,977 for ag if c=1, and if c=2 the value 3 ——=(())49}7/ 2).

oI :
so that fu "—~ would have to be = 0,98 4 0397 and not =17 @naly
: i

a very accurate knowledge of the quantities 7, and r= vg: dp
could decide this.
It follows from (2) and (3) that
201 1
i etree 6
Js rs J: Pal
If we. put 7, and «,f,: 7. both = 1 (or 2—1 7. 00 mand
Giff = OU Xx 1,004 : 1,007 = 0,974), we get by approximation ;

— = 1+ eo 2 (7)

By approximation this is really fulfilled by values of 7 in the
neighbourhood of 3 (for 73, where f,, 7, and a, =4, (7) would
be quite accurately fulfilled). Thus the two members for 7 = 4 become

8 43 4 : _
resp. — = 2,67 and — = 2,69; and for 7== 2) resp. 8 anditefo-
3} 6

If we take the factors 7,, 7, and a, into consideration, the first
member becomes = | + 27: (1,007 4,469) = 7,00 for r= 2,114,
and ihe second member (= 8 < 0,9744: 1,114) equally= 7,00 (= /).

It is owing to this accidental property of the expression

27 5
l Fe es te ‘
” r—1

namely that it differs only very little from zero for values in the
neighbourhood of += 3, that the factors /, and f, differ so little
from 1, and that also in the case vg: 6, = 2 the expressions & 7;

8 a

: ee oe On aa
and px; are again =-——-—, resp. ——~ with close approximation.
5 27 by 27 by

( Win)

With regard to the course of the quantities /, 7, and « for different
values of 8, we may make the following remarks.
a. With regard to f, given by (see I, p. 294)
4n
~ 4n——3m’
in which (for «= 1)
m=1 + 1/,8(1—8) (+9)
n=1+?/,8(1—B) (149) + '/, 8 (1—8) (1—38) (1+)

(see I, p. 288 and 295), we see immediately that — in view of the
fact that m and nm assume the value 1 both for 8— 1 and for ’=O
— this quantity is —4 for B=1 and also for B=0O. But for

intermediate values of 8, if g has only any value (i.e.: if 4é differs
from 0), f will be greater than 4 in the neighbourhood of 8=1,
and smaller than + in the neighbourhood of B=0O. Only if g=0,
i.e. Ab where = 0, / would be permanently <4, which is easy to
prove from the above expressions for m and n'). So it follows
from this — as f is found =7 for normal substances — that Ad
must necessarily be > 0, if f is to reach so high a value. Accord-
ingly we found in I, p. 295, that 8 must be = 0,955 and g = 1,23
for «= 1, i.e. Ab:b, about 0,7, if we are to get at the same time
f=T7 and »«=0,265. For =2 we must have for this 8 = 0,958,
gy = 0,916, ie. Ab: 6, about = 0,35 (see II, p. 429).

1) So the value found by Kameruincu Onnes for Helium, namely f = 2,8, need
not be impossible, as van peR Waats thinks (These Proc. April 1911, p. 1217).
When Ad =O (hence } remains constant), f is, as we saw, always < 4 for values
of B between O and 1, which is owing to the factor @= (1+ ):2 by the side
of RT (which van peR Waats omits; see above). And when Abd has a slight
positive value (which may be the case for Helium), and so when 0 suitably
diminishes with v, f will become >4 only near 8—=1, but all over the further
range between B= almost 1 and B=O f will be again <4. So it is very well

possible that such an association exists for He at the critical point for not too
great value of Abd (it need only be slightly greater than the normal association),

that f becomes < 4.

It remains only to consider whether f can be so much smaller than 4. For
g=9 (Ab=0), f can decrease to about 3,4 for 3=0,5; but for g>0 this
value can become considerably lower, if 3 is only sufficiently lower than 1.

Note added during the correction of the Dutch proof. After the above remarks
had been written, K.O has carried out some new measurements, and found 4,5
for Helium for f at 7; (These Proc. Dec. 1911, p. 684), so f>4 also here. But
at lower temperatures a considerably lower value is still found, namely f= 3 at
the boiling point, so somewhat higher than the former value 2,8 (see above).
Now in normal cases / is always about 4 °/9 lower for m= 0,8 than for m=1
(6,7 instead of 7); for Helium, however, this would amount to as much as 33°,

(6)

If for #=1 and g=1,23 we take the value of 3 only little
less than 0,955, e.g. 0,9, we find for / already the value 17,6 with
m= 1,223, n = 0,973. (for 8 = 0,955 these values were resp. 1,107
and 0,969). [For «= 2 this value, though > 7, would be considerably
lower].

Sut if we take P=O1, we find f= 3/6 -with m=1,223,
n = 1,271, so again < 4.

Now for the so-called anomalous substances f is really found > 7;
for water 7,5 is found, for acetic acid 8, for ethylaleohol 9. So it
would follow from this that at the critical point these substances
have a value of ~, which is < 0,955, resp. < 0,958. But as the
curve f= /(8) does not intersect the straight line f= until in
the neighbourhood of 3='/;, 3 could even be considerably smaller
than 0,96. But on no account can # be near O, because then / would
again become < 4.

So for acetic acid, water, alcohol ete. there does exist a greater
association than for the normal substances at the critical point, but
most probably not a considerably higher association, and certainly
not an almost complete one (3 near 0).

b. The value of r. From (see J, p. 288 and 296)

Up 3m*

— —

bk ~ 3m?—2r

we can easily derive that 7 is always a 5 when 8<1 and >0.
With the above values of m and m we find e.g. that r= 2,114
for 8 = 0,955; assumes the value 1,77 for 8 = 0,90; the value es
for B= 0,1 (all this with «= 1).

So for abnormal substances a value < 2,1 must be found for 7

c. The quantity wp. From (see I, p. 289 and 294)

eugal e

= igtiue ae (4n-—3m)

follows that «= 0,375 for B= 1, but takes the value 0,1875 for
8—0. Further it can be shown that the curve xp = / (8) always
lies above the straight line that joins aie Dewi) — a) enn
y = 0 (4b=0). This is moreover clear from the above formula (5),

from which immediately follows that then ¢ is always Zag ae

ut if g>O (Ab > 0), the curve p= / (8) lies above the said
straight line at 60, but falls pretty far below ite at el

So we find already the value 0,265 for B= 0,955; the value
0,124 for @=0,9; but the value 0,270 for B= 0,1. (again all this
tee lee — done

(UL

Hence we shall find a value < 0,265 for w for abnormal sub-

stances. This is actually found. For acetie acid e.g. uw is 0,20, for
alcohol we find 0,25.

It is noteworthy that / and m again approach closely to the ideal
values 4 and 0,265 for H,; for f we find namely 4,8, and for u
the value 0,84. So this means that then the state of association at
the critical point is less than the normal; i.e. 38 > 0,96. From formula
(5) the value 2,5 would follow for r, which also comes nearer to the
ideal value 3.

2. The formula for the vapour pressure at the critical
point. From the wel) known formula (see among others my Ther-
modynamik in der Chemie p. 59 (1898) )

Pex 1 y dp
see = — | dv
ar —) aay).
dp 1 a
(2)=4633)

for @ independent of 7’(q=0) :

Apex = 1 Pal =| ;
rie as | TENG is pe gi

v

follows, as (see p. 290)

Hence
dpex it ‘ H "a d
y a5 ’
dT v fe cs — zee
v v
or also
r dpex = a
dT Pex + ve’

in which p., denotes the pressure of coexistence. If henceforth we
omit the index cr, we get:
T dp a
sade eee ae Wa SAP TITS. 1, UE), 05(8)
padi pev
For this we may also write:
m dé 1 a dd
é dm PRR E y

or as a: pave’ is evidently = f—1, when / denotes the value of
T dp

par

at the critical point :

= (f—1) Ee ars CS)

dm m m

So this is the most general differential equation, which gives ¢€ as
a function of m. But only when d and d’ should be perfectly
accurately known as functions of m, the integral expression ¢ = /(m)
can be found.

Now the solution is possible for two extreme cases: 1 in the
neighbourhood of the critical temperature, and 2 at low temperatures
when the vapour follows the laws of the ideal gases; and the liquid
density does not change much any more.

Near the critical temperature.

Then d=1 + ar-+ br’, d’ =1—ar- bdr’, hence

dd! = (1-4 br?)? — att? = 1 — (a?— 20) 1?
when t=)1—m. (See I, p. 488). If we now put
a’? — 2b= y,
we get accordingly
dd' = 1 — y (1—m).
If we write further :
é=1— f(l—m) + 7/, f'(1—m)?,

= dé : ie dé
Y TNs) a os dm? );,’

dé m dé
because m=1 at 7;, and (=) = (: =) was denoted by /.
k k

dm e dm

then we have :

In consequence of this (9) passes into
io) 1 1 — y(1—m)
r= Mair (1-—m) ’

=f ln)
or in
|f—J'—m)] — [= (f=1) dm] = (7-1) [1 — @-1) =m),
from which immediately follows:

1) From YounG’s. data in his famous summary in the Proc. R, Dublin S. of

June 1910 it appears however, that this relation is not accurately satisfied. We
m dé dd’

find viz. values for @ =I — — ') : SE which increase from 6 (at T,) to
about 9 (at m+0,5). In the neighbourhood of 7), even very rapidly. Thus for
CyH;F the value of @ is already = 6,23 at m—=0,9985; for m—=0,9942 we find
6,71 etc. etc. VAN ppR WAALS already stated that @ is pretty accurately repre-
sented by @=1-+) 1—m — 1/3 (1—m). We shall, however, his variability, which
is also in that form with V1—m an impossibilily, leave out of consideration in
what follows.

(779)

det Af 1) = yd),
ie:
f =(f-1)7,
or also
a “
SS SS SS SPA op 10
Fg are (10)
i a ORE ds
a very remarkable relation between the quantities —— and -— at the
dm dm*

critical point, and the coefficients a and 4 of the densities of the
coexisting phases d and d’.

We find for Argon according to CromMenin’s data (Comm,
LS) p: 9):

_ 0,4714 3,05
a — d= —— at 1 —-m=—_.,
0,509 150,7
and as a ="/, (d—d’):V1—™m, we get:
0,4714 4 E
‘=S = 49) 4 =-0,463 < 7,03’ = 3,26.
1,018

For 6, the coefficient of the direction of the straight diameter,
has been found
b= 0,9027,
so that y = a? — 26 = 10,63 — 1,81 = 8,8.
The value 5,7 has further been found for /, and by approxima-
tion we may calculate :

dé 5.54 150,7

at — 123°,96 = —— IS 2e x Staion 0

dm 3.05 48,0
d 6,61 150,7
SS, Tae ee See
dm 4,34 48,0
from
T | p
—— =e. a =
— 1229.44 C. | 48,00 (crit.)
— 125 49 | 42,46
— 129 ,83 35,85
0,92 d*s
So we find 150i Son tor

3,70 dm?

( 780 )

This value 38 can of course not lay elaim to a high degree of
accuracy, because the data are too incomplete for this. If we take
around number 40, we get /’:(/—1)=40:4,7=8,5, while we
found above about 8,8 for y. So the agreement is satisfactory.

So for substances where a is about 3,2 (see II p. 487), 6=0,9,
f= 7, we should have to find about // = 8,4 x 6=50.

From the data of Fluorbenzene (see Kurnen, die Zustandsgleichung,

0,322 0,206 d?¢§
— = 6,44, and =~ = 410-50) ae
dm’

: dé
p. 99) follows ay 2eSP-

Ape 0,05 0,05
2.32

proximated = AoE 46, which really gets very near 50’).
Wo

Formula (10), which is quite accurate and of general application,
i.e. in the critical point, can therefore render good services — when
the quantities f and /” are known from vapour-tension. observations
near 7), — to calculate the quantity y=a*— 2b, which renders it
possible to calculate accurately the quantity a@— which in other cir-
cumstances is so difficult to determine experimentally, and which
indicates the divergence of the two phases just below 7; — when
6 -is known, i.e. the direction of the straight diameter. Then,
however, the direction of this locus should be taken very near Ty,
which will probably differ somewhat from the further direction —
at least if it is confirmed that very near 7; the straight diameter
undergoes an abrupt inflection to the vapour side [Carposo; see II,
p. 437 (read p. 480 last line concave instead of convex side)].

I draw here attention to the fact, that the well-known formula of
VAN DER WAALS, viz.

l—m

—lge=/ ;
m

which in this form holds for a large part of the temperature region,

is no longer quite accurate in the neighbourhood of 7%. For though

; ; dé : : ;

this formula then gives the suitable value for Gl , it deviates in
dm),

the second differential quotient. We have namely :

dé ip

— =E€6&
dm m
henee :

1) From Youna’s tables loc cit. we derive from four successive values of m between
0,9347 and 0,9888 resp. f'=80 and 42. For m=1 f' will draw near to 59, But
for a we find at least 3,4, so that y becomes = 10, and hence f' = 60.

(781)

dé iene 2e
dm The m? dm Ts j

which becomes for 7", :

instead of /' = (f—1) (a’?—2b), as we found above. So according
to Van per Waats’s formula f’ would be = 7 * 5 = 35, whereas
really 7’ is about = 6 x 8,5a10 = 50a 60.

So according to VAN per Waaus we should have at 7):

e= 1—f(1—m) + */, f(f—2)1 —m);
and according to our formula :
= 1—f(1—m) + */,(f—1)(a—*28)(1—m).
Clarens, Dec. 15, 1911.

Anatomy. — “On the relation between the symphysis and the aceta-
bulum in the mammalian pelvis and the signification of the
cotyloid bone.” By A. J. P. v. D. Brorx. (Communicated by
Prof. L. Bork).

In the course of investigations on the structure of the pelvis of
Primates I met with some phenomena in the acetabulum, namely
the development of the cotyloid bone os acetabuli, that induced us
to a comparison with the pelvis of otber mammals.

In the Primates the cotyloid bone appears as is pointed out by
me’), in the form of two little triangular bones, an anterior and a
posterior one. The anterior cotyloid bone lies between pubis and
ilium, the posterior between ilium and ischium. The former excludes
the pubis from the acetabulum.

An investigation in the cotyloid bone in other mammals brought
to light a distinct correlation between the development of the sym-
physis and the composition of the acetabulum, which I shall explain
in this note. This correlation is, as I think, of some value for our
knowledge in the morphologic signification of the cotyloid bone.

In the following explanations I shall divide the pelvis of mammalia
after the composition of their symphysis.

I. Symphysis composed by the os pubis and os isehii. In the
Monotremes, as is known, os pubis and os ischii take the same part
in the forming of the symphysis, which is very high. The acetabulum
is formed by the three components of the os coxae, namely the os

52

Proceedings Royal Acad. Amsterdam. Vol. XIV.

( 782 )

ilei, os ischii and fos pubis which take about the same part in it.
An os acetabuli has not yet been found in the monotremes.

Marsupialia. In the marsupials the symphysis is high and is for
the greater part formed by the os pubis, and for a smaller part by
the os ischii.

In the marsupials has been found an os acetabuli as well, but
only as a very small calcified piece of cartilage, against the os pubis.
It does not extend to the border of the acetabulum, as Lecne *)
writes, the pubic bone taking part at that border in the formation
of the articular surface. (Didelphys, Phascolomys.).

Rodentia. Hydrochoerus and Sciurus are two genera by whom
the ischium also; but only partially takes share in the symphysis.
The os acetabuli is developed in the same manner as in the Marsupials
above-mentioned. It is a little bone on the os pubis, excluding this
bone partly from the acetabulum. The os acetabuli exists of calcified
cartilage. ;

Carnivora. Only in Canis familiaris as is pointed out by Lec
the pubic bone takes part in the formation of the acetabulum, in all
the other carnivora it is excluded therefrom by the cotyloid bone.

After Enienprrcrr and Baum’) the symphysis in the dogs pelvis
is a symphysis pubis et isehii.

Ungulata. Except in Tapirus americanus, an os acetabuli fails,in
ungulata so far as we know; the os pubis forming, as is described
by GEGENBAUR *) “einen bedeutenderen Theil der Pfanne” (Le. p. 234).

It is well known that the symphysis in the ungulata is very high
and is formed by the pubie and the ischial bones.

It is necessary to remark that Weser gives a figure of the pelvis
of a Cervus speciosus (l.c. pg. 107 fig. 85) in which we see a very
great cotyloid bone extending over the whole breadth of the aceta-
bulum; yet the os pubis is taking part in the formation of the
articvlar surface.

Il. Symphysis formed exclusively by the os pubis.

Tubulidentata. Although the symphysis is very high, it is formed
exclusively by the pubie bone.

In Oryeteropus [ found a very great triangular shaped os acetabuli
between ilium and pubis. It has quite excluded the pubis from the
acetabulum, and reaches for a part the medial surface of the os
coxae between the bonepieces above-mentioned.

Rodentia. In the majority of Rodentia the symphysis is exclusively
a symphysis pubis. In two of them, namely Cavia and Mus, the os
acetabuli which is situated at the ventral side of the acetabulum,
has nearly quite excluded the pubie bone and the pubic bone reaches

( 783

the acetabulum only at the border; in the others, namely Lepus-
Hesperomys Xerus, the os pubis is quite excluded from the formation
of the articular surface.

As far as | know and could observe (Hystrix, Dasyprocta) in
Rodentia only at the ventral side of the acetabulum between [lium and
Pubis an os acetabuli is found and Ilum and Ischium verge directly
upon each other at the back. It consists of calcified cartilage.

Carnivora. In earnivora fissipedia, where the symphysis is limited
to the os pubis (Viverra, Mustela) *) the os acetabuli is strongly deve-
loped, reaches the medial surface of the pelvis and thus separates
ilium and pubis, quite excluding the latter from the acetabulum.

For earnivora pinnipedia prevails, according to Weber’) that the
os acetabuli is “besonders ausgedehnt’, though, as Lecun describes, the
pubie bone reaches the articular surface and takes part in its formation.

As to the symphysis, Wrper’) says that notwithstanding the length
of the ossa pubis, “die Kiirze der Symphyse auffalt’’.

Prosimiae and Primates. In both these groups and also in homo,
by whom the symphysis is exclusively formed by the pubie bone
the os acetabuli shows a very important and at the same time
remarkable way of development. As has been said already in the be-
ginning, and described some where else more fully we see nearly
always two ossa acetabuli, one between the ilium and pubis, the other
between ilium and ischium, which IJ distinguish as a dorsal and a
ventral os acetabuli. Both are triangular in shape with their top
towards the middle of the acetabulum. They so to say push out
the ilium partly from the acetabulum, it is at the cost of this bone
that the ossa acetabuli develop themselves further in the articular
surface.

They form the transition between the simple os acetabuli and one
as I found in Myrmecophaga that extends over the whole breadth of
the acetabulum and now separates the ilium from the pubis as
well as from the ischium.

UI. Symphysis formed by a small part of the os pubis and for
the greater part by the so called “epiphysenknorpel”.

This form of symphysis only appears as far as known in Galaeo-
pithecus. Here the composition of the acetabulum, which only for
the third part is formed by the ilium, for the rest by the ischium
and the os acetabuli, is important ; while the pubis is quite excluded
from the formation of the articular surface.

IV. Symphysis formed exclusively by the so called “epiphysen-
knorpel.” A connection between the two halves of the pelvis exclusively
formed by the so called “epiphysenknorpel” is found among the Insecti-

02*

(aga)

vora, in Myogale-Erinacaeidae-Centetidae-Chrysochloridae. In some
(Erinacaeus, Centetes) the os acetabuli shows in its extension con-
formity with Galaeopithecus, in others — Myogale (in Chrysochloris
it has not yet been observed) this bone is developed more strongly,
and it excludes the os pubis as well as the os ilei from the formation
of the articular surface.

The acetabulum is thus formed only by the ischium and the os
acetabuli. When we study the medial surface of the os coxae it
appears that the os acetabuli does not quite reach that surface ; there
ilium and ischium, and also ilinm and pubis partly verge directly.

Thus it represents in the main a small piece of bone on the
external surface of the ilium. Save in the named Insectivorae a
formation of the symphysis by the so called “epiphysenknorpel” is
observed in Manidae, after the description of Lecue*) in “Bronn’s
Klassen und Ordnungen des Tierreiches’. I observed in Manis an
os acetabuli excluding as well the os pubis as the os ilei from the
acetabulum. It did not reach the medial surface of the os coxae.
At the ventral border of the acetabulum it is broader than at the
dorsal border.

The composition of the symphysis in Xenarthra is apparently not
yet well known. In the above mentioned study of Lrcue *)- one
finds on page 583 “die kurze, stets nur durch das Schambein ge-
bildete Schamfuge”, and on the same page further ‘das Schambein
ist ventralwiirts ausgezogen in einen langen Process, welcher durch
einen Schamfugenknorpel met den gegenseitigen verbunden ist”. A
figure of Tatusia peba (Plate 92 fig. 10) shows us the presence of
an “epiphysenknorpel’. The os acetabuli is strongly developed, in
Dasypodidae it is still greater than in Bradypodidae. It excludes the
os pubis from the acetabulum and reaches the medial surface of
the os coxae between these two bones. In Choloepus and Myrme-
cophaga the ilium only forms a very little part of the border of
the articular surface.

In the Dasypodidae both the pubis and the ilium are, after the
description of Rurynarpr*) excluded from the acetabulum. I found
this condition in Dasypus duodecimocinctus ; in which the os acetabuli
reached partially the medial surface of the os coxae. At the dorsal
border of the acetabulum it covered only the outer surface of the illum.

V. Symphysis fails.

At last we have to consider the mammals in which a symphysis
is failing in the adult. This condition is, as is well known, only to
be observed in some of the Jnsectivora, viz Soricidae, Talpinae and
Urotrichus. In these three forms the cotyloid bone is very great and

( 785 )

separates the ilium from the pubis and the ischium. The acetabulum
is only composed by the ischium and the os acetabuli. This bone
reaches also the medial surface of the os coxae, so that also there
the ilium is separated from ischium and pubis.

The above given survey leads to the following conclusions.

1st. The os acetabuli shows among the mammals a very different
degree of development. It is greater and forms a more and more
important part of the acetabulum as the symphysis is lower.

2nd. The development of the os acetabuli shows no more than the
symphysis a regularity, in this sense that it shonld be otherwise
in the so called primitive mammals than in the so called higher
mammals.

In more than one order of mammals we meet with very great
differences in the degree of development of the os acetabuli and of
the symphysis (Edentata-Rodentia-Insectivora-Carnivora).

These two conclusions lead to the question by what reasons
would be determined the development of the symphysis and what
would be the morphologic value of the os acetabuli.

The answer to the first question musi be removed to later; here
it can only be said, that, as the result of comparative anatomical
and embryological researches one can say, that a high symphysis
is a secondary condition (Lxcne |. ¢. p. 23).

Applying this to the mammals above deseribed, it follows that
in those mammals which possess, in consequence of their high sym-
physis a primitive form of pelvis, an os acetabuli seems to fail
(Monotremens, Ungulata?). As soon as the symphysis is not so high
we can observe an os acetabuli, growing more developed as the
symphysis becomes lower.

It is not yet permitted to say that the os acetabuli_in mammals
is a constant, so called fourth element of the os coxae, for which
can be shown a homologon in other vertebrates.

If one wishes to compare the os acetabuli in the mammalian
pelvis with the litthke bone known as the “pars acetabulavis” in the
pelvis of crocodiles, as is done by Lecun, one has not yet the right
to speak of an independent bone, because we know that, after the
investigations of WrepgrsHEmM *) this pars acetabularis is a secondary
part, separated in the course of the development from the processus
acetabularis ilei.

If the os acetabuli and the pars acetabularis are homologous bones,
the former can only be regarded as a bone of a secondary signifi-
cation; in his development dependent on development of the pelvis.

( 786 )

LITERATURE.
1), vy. p. Brork (A. J. P.) Uber das Os acetabuli bei Primaten. Archiv. f. Ana-
tomie und Entwicklungsgeschichte 1912.
2), ELLENBERGER (W.) und Baum (H.) Anatomie des Hundes.

3), Geaenpaur (C.) Uber den Ausschluss des Schambeins von der Pfanne des
Hiiftgelenkes. Morph Jahrb. Bd. 1.

4) Lecus (W.) Zur Anatomie der Beckenregion der Insectivora Konig. Sy. vet.
Akad. Handl. Bd. 20. no. 4.

»). Lecue (W.) Mammalia, in Bronn’s Klassen und Ordnungen des Tierreiches.
Bd. 6, Abth 6, pg. 583, ;

6), Rerygarpt Nogle Bemaerk. om Gumlernes, is aer Baeltedyrenes Baekken.

Vidensh. Meddel. fra naturk. Forening, Kjobenhaven 1881.

7). WEBER (M.) Die Saugetiere.

5). WiepERSHEm™ (R.) Vergleichende Anatomie d. Wirbelliere.

Physics. — “Klectric double refraction in some artificial clouds
and vapours’ (second Part). By Prof. P. Zeman and
C. M. Hoocensoom.

10. The condenser mentioned in the experiment of § 3 was
placed in the interior of the horizontal glass tube; the metal plates
were of 1S em. length, their distance being 16 mm. The investigation
of gases and vapours, acting chemically upon the metal of the
condenser plates is better conducted in an apparatus with external
plates and the same apparatus may be serviceable also in other
cases as it is more easily cleaned. An apparatus made of glass and
of parallelipipedic form was therefore constructed, (length 46,5 cm.,
distance between the insides of the vertical walls 5 mm., height
10 em. thickness of glass 3 mm.). At the outside strips of tin foil
40 >< 3 em. were arranged. The tube is closed by plates of thin
coverglass.

11. The experiment with the sal-ammoniae cloud produced in an
anteroom (§ 4), was repeated with the new condenser, bat with the
old optical arrangement (§ 3).

It now appeared that the result obtained in § 4, indicating solely
a double refraction induced in the sal-ammoniac cloud, was a rather
special case.

The sal-eammoniae cloud now exhibited dichroism also. As it is
probably the greater density of the cloud operative in the new
apparatus, which made it easier to observe the new property, the
anteroom (§ 4) was removed altogether. In our further experiments
the gases, hydrochloric acid and ammonia, were introduced directly

( 787 )

into the observation room, the cloud produced being now much
denser than before.

Small differences of potential caused a downward motion, accom-
panied with a slight fading of the black band (§ 3), a potential difference
of 8000 Volts made it disappear completely. It became visible again
by a clock-wise rotation of 10° of the analyser, which had been
erossed with the polariser before establishing the field. The position
of the polariser is defined in § 15.

This experiment proves that in asal-ammoniae cloud double refract-
ion, accompanied by dichroism is induced by electrostatic fields.

12. No effect was exhibited by the unmixed gases, hydrochloric
acid or ammonia.

13. Strong currents of ammonia and of hydrochloric acid were
introduced into the apparatus, a dense cloud being produced. Under
the action of the electric field or by a slight rotation of the analyser,
the transmitted light looks yellow red. If the currents of gases are
interrupted after a while there is only a general diminution of the
light of the Nernst filament. That there is still absorption by a cloud,
is proved by the illumination of the field of view produced when a
current of neutral gas displaces the cloud.

The slow change of colour of the sal-ammonia cloud was observed
in a separate experiment, using a glass tube of 3 or 4 em. width
and of 50 cm. length. This change of colour apparently varies with
the size of the particles in the cloud.

14. It is extremely remarkable that in parallel with this change
of colour there occurs a change of the electric double refraction of
the sal-ammoniac fog.

Producing a fog as in § 13 above and crossing the nicols with
a field zero, the black band became invisible with a_ potential
difference of 9000 Volts. By a clock-wise (§ 11) rotation of the
analyser it reappeared; its displacement was downward.

The supply of the gases being interrupted the effect remained the
same for perhaps a quarter of an hour. Then the effect apparently
had diminished and finally the sign of the double refraction appeared
to be the reverse of the original one. On throwing on the electric
field the black band jumped wpwards. In order to produce complete
blackness of the band, again a clock-wise (§ 11) rotation of the
analyser is uecessary.

Hence we see that the sal-ammoniac cloud undergoes in the course
of time a remarkable change: the induced double refraction is at
first positive, afterwards negative; the dichroism does not change
its direction.

( 788 )

15. The direction of vibration which is more strongly absorbed
is very easily determined.

We know that a clock-wise rotation of the analyser (§ 11)-was
necessary in order to produce complete blackness of the band. The
direction of vibration of the polariser joined the upper left, and the
lower right quadrant. Hence it follows, as is easily seen, that the vibra-
tions parallel to the electric force ave the more strongly absorbed ones.

16. This result may be controlled by the following experiment.
If we turn the polariser through an angle of 90° from its former
position (§ 15) then we shall expect that in repeating the experiment
of § #1, an anti-clock-wise rotation of the analyser will be necessary
in. order to see most clearly the neutral axis. This consideration is
confirmed by experiment.

17. Our observations hitherto given, prove that at least two
different modifications of sal-ammoniac clouds exist, which exhibit
double refractions of opposite sign, at the same time the absorption
of vibrations parallel to the field always exceeds that of vibrations
at right angles to the field.

One of the special intermediate states of the cloud, when under
electric action, exhibits dichroism a/one and no double refraction.

(To be continued ).

Chemistry. — “Das CGesetz der Umivandlungsstufen in the light
of the theory of allotropy’. By Prof. A. Surrs. (Communicated
by Prof. A. F. Honieman).

(Communicated in the meeting of December 30, 1911).
Introduction.

Already in 1886 Frankennem ') pointed out that it cannot be said
that a depositing pure substance will be solid or liquid according
as the temperature at which this takes place lies under or above
the melting-point of this substance. Thus phosphorus and sulphur,
e.g. can deposit from solutions in liquid state, in spite of the tem-
perature lying below the point of solidification. The same phenomenon
has sometimes been observed when vapours were cooled.

Concerning this FRANKENHEIM writes as follows:

“Schwerer als aus Auflésungen kann ein Kérper aus dem Dampfe
fliissig niedergeschlagen werden, wenn die Temperatur unter dem
Schmelzpunkte steht. Jod, welches sehr leicht, auch bei gewohnlicher
Temperatur sublimiert, habe ich nur in Krystallen erlangen kOonen....
Bei dem Phosfor war jedoch das Resultat entscheidend. Ich brachte
ihn auf ein etwas hohl geschliffenes Glas, legte eine diinne Glas-
~ 1) Pogg. Ann, 39, 380 (1836).

( 789 )

platte darauf, und hielt diese durch verdampfenden Aether auf einer
niedrigen Temperatur.

Der Phosfordampf, mochte er sich schon in der Luft oder erst
auf dem Glase niederscblagen, hatte daher nirgends eine héhere
Temperatur als die des Zimmers, etwa 20.°5 erlangt, und dennoch
bildete er zwar kleine, aber deutliche Tropfen auf der Glasplatte.
Der fliissige Agregatzusiand greift daher weit in den festen hinein.
Wahrend diese die Temperatur des Schmelzpunktes nie iiberschreiten
kann’), bleibt der KOrper nicht nur in niedriger Temperatur fliissig,
sondern er wird es auch, wenn er durch Abkiihlung des Dampfes,
oder einer Auflésung, oder durch chemisch wirksame Mittel ausge-
schieden wird”.

A phenomenon which is in close connection with what precedes,
and which has been observed by different investigators, is this that
from a super-saturate solution, from which different substances can
erystallise, the most soluble often deposits first.

Another peculiar phenomenon, which was brought in connection
with what precedes, is the following: If we have a solution of
HgJ, in methyl alcohol, then on addition of water the yellow modi-
fication, which is the metastable and more soluble one, deposits at
the usual temperature as Bancrorr describes, whereas the red modi-
fication represents under these circumstances the stable and less soluble
form. In connection with this Bancrorr*) remarks: “Es scheint, als
wenn man die Verallgemeinerung machen konnte, dass bei plotzlicher
Fallung die weniger bestandige Form die zuerst erscheinende ist’.

Starting from Frankenneim’s observations Ostwanp *) showed that
similar phenomena are also to be observed where the change of a
state of aggregation is attended with a chemical process.

First of all he cites here the example “phosphorus”. Phosphorus
vapour does not at once pass into the stable state, red phosphorus,
but first into liquid, and then into yellow phosphorus *).

He further points out that the vapour of eyanic acid yields the
metasiable cyanic acid on compression, just as the vapour of para-
cyanogen yields the metastable liquid cyanogen.

_ Finally Ostwanp shows that we also meet with such phenomena
in chemical conversions, and he pronounces the opinion that all this
points to the existence of a Jaw which he calls “das Gesetz der
Umwandlungsstufen”, and which he formulates as follows: ‘‘Beim

1) Our opinion has changed in this respect.

2) Journ. Phys. Chem. I, 142 (1896).

3) Zeitschr. f. phys. Chemie 22, 306 (1897).

4) It was not yet known at the time that there exist three crystallized states of
phosphorus.

( 790 )

Verlassen eines unbestandigen Zustandes sucht ein gegebenes che-
misches Gebilde nicht den bestaindiesten Zustand auf, sondern den
nichstliegenden d.h. den (voriibergehend oder dauernd) bestiandigen,
welcher von dem augenblicklichen aus mit dem geringsten Verlust
von freier Energie erreicht werden kann’.

It is now my purpose in the following discussion to demonstrate
that “das Gesetz der Umwandlungsstufen” is by no means so simple
as OsTWALD imagined, and that the order in which the phases appear
can be derived from the theory of allotropy, when also some new
considerations are introduced about the existence and nature of nuclei,
from which a new phase can originate.

I will commence, by pointing out that different cases must be
distinguished, two of which are essentially different.

In the first place a new phase may be formed by sudden cooling
of a vapour or by addition of a liquid to a solution, which causes
the dissolved substance to precipitate suddenly. In this case, which
is the simplest, we can speak of jixing.

In the second place the new
phase may appear by slow
cooling and in general in slowly
proceeding processes, and then
the explanation of the case is
slightly different.

Starting with a discussion of
the phenomena which are to

be observed for the system phos-
phorus, we may make use of
the projection of the three-phase
regions on the 7’X-plane, which
is represented in fig. 1, and will
not require any further elucid-

ation but this that the vapours
are indicated by G, the liquids by
LL, and the solid substanees by S.

Let us now first take a very
simple case, and Jet us think
the violet phosphorus heated to a

temperature of 150° in vacuum,

and the vapour cooled to 60°;
then we see that the line S’Q
indicates the violet phases which
xP x AP coexist with the vapours lying

(791 )

WwW

on the line G"’,G,. So the obtained vapour phase is a vapour
represented by a point on the line G,"G,, and now it appears
experimentally that even on slow cooling to 60° liquid phosphorus
is formed. In my opinion this phenomenon is to be explained in the
following way. As follows from fig. 1 the different phases in which
the phosphorus may occur, are chemically distinguished by the
situation of the chemical equilibrium :

aP = BP.

Phosphorus vapour and liquid phosphorus contain much e«P,
whereas red and violet phosphorus are rich in @P.

I think I must assume that in the vapour phase not only molecule
groups or quasi associations’) occur, which preponderate in the liquid
phosphorus, and are to be considered as nuclei for the formation of
the liquid phosphorus, but that there will also be molecule groups
in it, which preponderate in the solid red resp. violet phosphorus,
and from which these phases may arise. This consideration, on which
the nucleus theory to be discussed later on, is based, I will pass
over in silence. It may only be pointed out here that as the just
discussed vapour phase lies nearest the liquid phosphorus so far
as its concentration is concerned, it will also be richest in nuclei
for the formation of liquid. Moreover the liquid formation has
this advantage over the formation of solid phases that for the
latter a certain orientation of the movement of the molecules is
required.

In consequence of the circumstances mentioned the velocity of
condensation of the vapour may be greater than its velocity of
crystallisation, in which case liquid will be formed. Whether the
liquid remains, will depend on the velocity of crystallisation of the
liquid at the condensation temperature. At 60° the number of
erystallisation nuclei for red and violet phosphorus will be very small,
first because this temperature lies about 500° under the melting-points
of these modifications, secondly because liquid phosphorus differs so
greatly in concentration from red and violet phosphorus. So it is
owing to these circumstances that in the mentioned experiment the
liquid phosphorus may be preserved for an indefinite time in the
dark and in the absence of a catalyser.

") Van per Waats has first introduced the idea of quasi association, but has
not brought this into connection with the formation of new phases,

( 792 )

If we now choose another case, and suppose that white phosphorus
is kept in a vacuum at the usual temperature, and that part of this
vacuum is cooled to a temperature at which the velocity of crys-
tallisation of white phosphorus is still comparatively slight, then
liquid is formed in spite of the slight difference in concentration
between the vapour and the solid white phosphorus, because the
velocity of condensation then still exceeds the velocity of erystallisa-
tion. At a temperature at which the velocity of crystallisation is
greater, no liquid will be formed or it will disappear again imme-
diately. When in this way liquid phosphorus has once been obtained,
experience teaches that this metastable state on further cooling can
suddenly turn to the solid white modification, which latter can be
transformed to red phosphorus by the influence of light or of a
eatalyser. The red modification, which is also still metastable can
finally still further be transformed to the stable. violet phosphorus by
means of a catalyser.

In order to explain these conversions I must enter a little more
deeply into the process of crystallisation than I did just now, in
which at the same time the preceding case will be elucidated
further. Let us consider liquid phosphorus at the unary melting-point
temperature. The mean concentration will correspond with the point
L,, but in aeeordance with what precedes it is now assumed that
in this liquid three molecule groups or quasi-associations are found,
which are to be considered as nuclei for the three come phases, the
white one, the red one, and the violet one.

In general if may be said that the number of quasi-associations
will be smaller as they differ more in concentration from the mean
concentration, and therefore the number of nuclei for the white
phosphorus will be greater than that for the red, and the number
of nuclei for the violet phase will be the smallest.

To all probability the phenomenon of quasi-association is a pro-
cess that increases with fall of the temperature, and therefore it is
to be expected that the number of nuclei will always augment with
decrease of temperature. According to these considerations however,
nucleus formation is attended with a chemical reaction; when e. g.
molecule groups separate to form a nucleus for the white phospho-
rus, the equilibrium

CP SPP

is disturbed in the immediate neighbourhood, and this will be
reestablished by @P being converted to aP. Now it will depend on

( 793 )

the velocity of this reaction, how rapidly the nucleus is formed, and so
too how great the number of nuclei is which can form per time unity.
In consequence of the rapid decrease of the velocity of reaction with
fall of temperature and in consequence of the increase of the viscosity
the setting in of the equilibrium will have decreased so much in
velocity that we get the phenomenon that the number of nuclei that
forms during a certain time in a definite volume of undercooled
liquid of constant temperature increases at first with the degree of
undercooling, reaches a maximum, and then decreases again. If we
now suppose that the liquid phosphorus has got the temperature of
0°, we shall certainly be on the descending branch of the nucleus
curve at this temperature, which lies so far under the melting-points
of red and violet phosphorus, and that so far from the maximum
that the number of red and violet nuclei which has certainly never
been very great, will be exceedingly slight.

This is, however, not the case for the white phosphorus. The num-
ber of white nuclei must comparatively be great here, so that when
we seed the liquid phosphorus with solid white phosphorus, a rapid
crystallisation takes place, during which the nuclei pass into the
crystallized state after the movement has become ‘molecular geord-
net”. The velocity of this crystallisation will increase with the number
of nuclei, but fall of temperature will make the velocity of
crystallisation decrease also in case of a constant number of nuclei,
so that also in the velocity of crystallisation as function of the degree
of undercooling a maximum will occur, which need not coincide in
temperature with the maximum in the nucleus-curve. That the maxi-
mum in the curve for the velocity of crystallisation lies mostly at a
higher temperature than the maximum in the curve for the number
of nuclei proves that the influence of the temperature on the velocity
of crystallisation is very great.

As is known the nuclei may also lead to spontaneous crystal-
lisation, when the number of nuclei is great at not too low
temperature.

An analogous reasoning holds for the conversion of one solid
modification into another.

For it follows immediately from the foregoing remarks that what
holds for liquid phosphorus, must also apply to the white phosphorus,
and this remark might suffice. We might, however, also begin at
the transition points (metastable or stable) for the conversion of the
solid phases, and then starting from these points we might reason
in the-same way as we did just now.

It is to be attributed to the great difference of temperature between

( 794)

the point of transition and the temperature of the white phosphorus,
and to the great difference in concentration of the phases that there
are exceedingly few red nuclei and still fewer violet ones to be found
in the solid white phosphorus.
It appears, however, now immediately from the given consideration
that if* we have recourse to a positive calalyser for the conversion
aP— BP,

the number of nuclei will greatly increase, and with it the velocity
of conversion. Such a catalyser is now furnished by iodine and now
I think that the fact that white phosphorus in contact with a trace
of iodine is comparatively quickly converted to the red modification
and with vise of temperature also to the violet one, must be
attributed to the catalytic acceleration exerted by this substance on
the chemical conversion.

In connection with what precedes | will devote a few moments
to the transition of the nuclei of crystallisation. Before a nucleus of
crystallisation changes into a microcrystalline body the “molecular
ungeordnete” motion must pass into “molecular geordnet”. For most
substances these two processes, the state of motion and the erystal-
lisation getting “ordered”, seem to take place at about the same
temperature, so that they cannot be observed separately. We known,
however, one category of substances, for which this zs the ease,
namely the liquid crystalline substances, which therefore in my
opinion distinguish themselves from the ordinary erystailising sub-
stances only in this that the two processes mentioned now take
place at appreciably different temperatures.

I will further point out here that the given theory of the nuclei
is based on the assumption that before the appearance of a new
phase processes take place which are to be considered as a
preparation for what will happen later on. So when a new phase
is formed it may be concluded from this that the molecule complex
of which this phase consists, was already present beforehand in the
mother phase which seemed to be homogeneous, only with this
difference that then the movement was “molecular ungeordnet”.

If we now proceed to the system HgJ,, we shall make use of
the 7Z-N-projection, which has been schematically represented in fig. 2
in agreement with the data which we have now at our disposal ’).

In this diagram <G.G',, GG, Gy and.G. GaG

0 0?

, are the vapour

1) These Proc. XII, p. 763,

eurves, SS, S’, and S", S,S’,
the lines of the solid substance
and ZL, LL' the liquid curve of
the unary system.

If we start from the equili-
brium at a temperature above
the unary point of transition,
127°, it will most probably not
be difficult, especially in view
of the great difference in con-
centration between the vapour,
and the solid substance to obtain
first of all liquid HgJ, when
the vapour is cooled, and not
before then the solid phase, just
as this was the case for the
phosphorus. I cannot go any
further into this question here,
however, because it has not yet
been investigated, and will be
further examined later on in the

continued investigation.
Therefore we have not referred

to the system HeJ, becanse of Ho. X BHO:
this possible phenomenon, but
in order to account for the
repeatedly stated fact that when the vapour of HgJ, is cooled below
the unary point of transition, not the stable red modification is formed,
but first of all the metastable yellow form. This phenomenon follows
immediately from fig. 2. From this we see namely that the vapour
lines lie very markedly on the side of eHgJ,.

As the equilibrium of the system HgJ, on the whole sets in slowly
it is necessary to point out here two possibilities. It is possible

Fig. 2.

that in the usual sublimation experiments, in which the vapour
saturate at higher temperature is cooled down to the ordinary tem-
perature, a fixation of the internal vapour equilibrium takes place,
so that solid substance is formed of the concentration of the vapour.
In this case it is of course at once clear that this solid substance
must then be light yellow. If, however, we assume as second possi-
bility that the cooling does not give rise to fixation, the appearance
of the yellow phase from the vapour at a temperature under 127°
must be attributed to this that the velocity of crystallisation of the

( 796 )

yellow modification at the temperature to which the vapour has
been cooled is greater than that of the red modification owing to
the much greater number of yellow nuclei in consequence of the
comparatively small difference in concentration between the vapour
and the yellow modification, whereas the difference in concentration
between the vapour and the red modification is certainly many
times greater *).

If we now proceed to the phenomena which have been observed
for solutions of HgJ, in different solvents, it will appear that it is
possible also here to explain the observed facts in a simple way.

One of these facts was already mentioned in the introduction.
We namely referred already there to the phenomenon discussed by
Bancrort that on addition of water to the methyl alcoholic HgJ,-
solutions at the ordinary temperature at first the metastable yellow
modification deposits, which is later converted to the stable red form.
Another fact which was not yet mentioned here and will be discussed
in the second place is this that also on slow cooling of super-saturate
solutions of HgJ, e.g. in nitrobenzene the yellow metastable modi-
fication can be formed first at temperatures under the point of
transition, provided the concentration of the super-saturate solution
lie above a certain limit.

Before I can proceed to the explanations of these phenomena, I
must mention that 1 have found from preliminary experiments at
higher temperatures that at the same temperature HgJ,-solutions
assume an intenser red colour according as more HgJ, has been
dissolved, from which I have provisionally drawn the conelusion
that the equilibrium

a) Hod 228 Hed,

which lies decidedly on the @-side as long as the concentration is
not great, slowly moves to the ?-side with increase of the concen-
tration. Most likely we have not to do here with an electrolytic
phenomenon °*).

If we now make use of this datum, and if in accordance with
the theory of allotropy we suppose the system //y./,-solvent to be
pseudo-ternary, the explanation runs as follows:

1) 1 will avail myself of this opportumity to point out that HgJg is the first
system of which we know that it possesses no metastable melting-point, though
it presents heterogeneous allotropy.

2) The direction of the shifting of equilibrium by change of concentration will
be studied more in detail, though it is of minor importance in this case.

In an equilateral triangle, fig. 3, we trace two solubility-isotherms
ab and cd for a definite solvent and for a definite temperature
under the unary point of transition) and pressure. Further as ¢ Hed,
and pHeJ, partly dissolve into each other we must suppose that
the mixed-crystal phases AU coexist with the liquids on the isotherm
ae, and that the mixed-cerystal phases bV can be in equilibrium

B phy.

with the liquids on the isotherm ce. The point of intersection of
these two curves e then represents the liquid which coexists both
with the yellow mixed-crystal phase (7 and with the red one JV’.
If we now call a liquid unsaturated with respect to a certain substance
when brought into contact with this substance it does not deposit
it, the solutions which are unsaturated with respect to the red 3-mixed
crystals lie under the line cd, and the solutions which are super-
saturate with respect to these mixed crystals. lie above it.

In the same way the solutions which are unsaturated with respect
to the yellow a-mixed crystals lie on the leftside of the isotherm ad,
and the liquids which are supersaturate with respect to these mixed
crystals lie on the righthand side of this line’).

1) In this definition it is feund that a solution which is at first unsaturate with
respect to B and super-saturate with respect to A can become super-saturate
with respect to B by deposition of A. If we call a solution super-saturate with
respect to these substances which must continue to deposit to make the solution

53

Proceedings Royal Acad. Amsterdam. Vol. XLV.

( 798 )

The metastable branches of these isotherms will be required to
find the degree of super-saturation of a solution with respect to @-,
resp. a HeJ,.

If we now assume that the equilibrium between a- and @ HgJ,
always sets in, and so that the system does not behave asa ternary
system, but as a binary one, it is noteworthy that two of the solid
mixed-erystals are in internal equilibrium, a red mixed erystal phase
Sr, which is in stable internal equilibrium, and a yellow mixed crystal
phase Sg, which is in metastable internal equilibrium. When diffe-
rent solvents are used, it appears that the solution which is in equi-
librium with the stable red phase at the ordinary temperature, and
in which the two kinds of molecules @ and pHgJ, will also be in
equilibrium, is coloured yellow. From this we derive that the internal
equilibrium in this liquid lies very much to the side of « HgJ,. It
was stated just now that the colour of an HgJ,-solution becomes clearly
inore intensely red with increase of the concentration, which points
to the fact that the internal equilibrium is shifted to the -side with
increase of the concentration.

Taking these data into account, we shall have to indicate the
internal equilibrium as function of the concentration, as has been
schematically indicated by the curve Cy.

So we see from this that 7 is the solution which coexists with the
red phase Spr, which is in internal equilibrium. This solution must
) cones elicdaaee
have a light yellow colour, because the ratio ———— = 1S WAY

aay cone. BHegJ, i
ereat in this liquid, and it will now be clear why the point of in-
tersection ¢ of the solubility curve has been assumed to lie so
much on one side.

The curve Cy, however, also cuts the metastable branch of the
solubility-isotherm of the yellow mixed-crystals and so the point
i; will be the solution which coexists with the yellow mixed-erystal
phase Sg, whieh is in internal equilibrium.

The difference in solubility between yellow and red HgJ, always
seems to be very small, and this is the reason why the two solu-
pass into the saturate condition, the nodal lines ew and ev with the isotherms
ve and ce indicate the boundaries of the different regions.

The mentioned isotherms cd and ab must not be proionged to the line AB,
because here an equilibrium between red, resp. yellow mixed erystals and a liquid
which contains alone z- and ¢-HgJ, cannot occur below the temperature of the
melting-point diagram, not even in metastable state, because #- and B-HgJ, give
a continuous melting-point-line. The isotherms must continuously merge into each
other, probakly by means of a ridge before the line AB has been reached.

( 799 )

bility isotherms here intersect at an acute angle. Then the difference
in concentration in the points / and / will be slight at every temperature.

sefore proceeding to the explanation of the mentioned phenomena
I will state what are the principal changes to which fig. 3 is sub-
jected with rise of temperature.

All the changes take place here as a rule in the direction of a
greater solubility; thus the points @ and ¢ will move towards A
resp. B. The point C will then be moved further away than a, which
makes the point of intersection e move further into the figure.

The equilibrium

a Hg], 2 8 HaJ,

shifts a little to the right with increase of temperature, in consequence
of which the internal equilibrium curve Cy will move a little upwards.

At the transition temperature 127° the curve Cy passes exactly
through the point e, which implies that the solution coexisting with the
mixed crystal phases Sp and Sg, is exactly in internal equilibrium,
so that the mixed crystal phases which coexist at 127° and which
are in internal equilibrium, are the phases Sp and Sc, which, however,
have then been somewhat displaced. At higher temperature the line
Cy cuts the stable branch of the solubility isotherm a and the
metastable branch of the isotherm cd, from which follows that it
is now a yellow phase that is in stable internal equilibrium, whereas
the red one is metastable.

In the neighbourhood of 150° «@ HgJ, and 8 HgJ, mix in all pro-
portions, and instead of two intersecting solubility isotherms we then

vet a continuous isotherm. ') The curve Cy rises continually and the
saturate solution becomes first light and then dark red just as the

coexisting solid phase.

If we now return to temperatures lying below the transition
point, and for which fig. 3 holds, we see immediately that when the
saturate solution / is poured into cold water, in which HgJ, is
exceedingly little soluble, the deposited HgJ, must be yellow, for
then we get a solid phase in which «- and 8 HgJ, occur in exactly
the same proportion in which they occurred in the saturate solution

If we now draw a straight line through C and / the point where
this line meets the side A / will indicate the phase which separates
under these circumstances. This phase indicated by S;;’ lies markedly

1) The partly metastable, partly unstable branches of the isotherms have then

contracted to a point.
no*

(800 )

on the yellow side, and so it will have to be yellow, as is easy to
ascertain in the experiment with solutions in methyl alcohol and
nitrobenzene.

If we now consider the case that an unsaturated solution is cooled
down so much that a supersaturate solution is formed, we may
make the following observations. If the supersaturate solution lies
between f and / at the temperature to which we have cooled down,
the solution is only super-saturate with respect to red mixed crystals,
so that then of course only the red phase can be deposited, and this
continues to be so for a permanent deposition of red mixed crystals
till the nodal line ev has been reached. If however the supersaturate
solution is situated on the righthand side of this nodal line on the
curve Cg, different cases may present themselves. If e.g. we have
the solution 4, we shall have to examine with respect to what this
solution is most super-saturate. The point Z lies on two nodal lines,

on the nodal line ng and on mp, and as ue is greater than oe the

gh pL
solution Z is super-saturate more with respect to the yellow than
with respect to the red mixed crystal phase.

In consequence of this the number of yellow crystallisation nuclei
will be greater than the number of red ones, and the greater this
differenee is, the more probable it will be that the velocity of erys-
tallisation with respect to the yellow mixed crystal phase is greater
than that with respeet to the red one, in which case we may expect
that the yellow mixed crystal phase will ecrystallise first.

So we have arrived at the conclusion that the red phase is sure
to crystallize when the super-saturate solution lies between / and
the nodal line ev. Now it will be clear, however, that the red phase
may also appear first when the super-saturate solution lies on the
vight of this nodal line ev, but as we take solutions which are
super-saturate to a greater degree, it becomes more and more pro-
bable that the yellow phasé appears tirst, after which then the red
one may make its appearance.

Experiment entirely corroborates the theory. Thus from compara-
lively slightly super-saturate solutions of HgJ, in nitrobenzene the
red .phase deposits, whereas from more super-saturate solutions first
of all the yellow phase appears.

When the stable and the metastable substances are of an entirely
different concentration, e.g. different compounds of the same elements
or when one is an element and the other a compound, we have

apparently to do with another class of phenomena, which, however,

( 801 )

do not essentially differ from the discussed ones, and in most cases
are still easier to explain than the preceding ones.

To mention-an example | will cite the case mentioned in a previous
communication, which referred to the deposition of cementite, either
from a liquid or from a solid solution which was not only unsaturate
With respect to iron-carbide, but also with respect to graphite *). It
is easy to see that on cooling the said solutions we have soon
penetrated relatively further into the region for liquid resp. solid
solution + cementite than into the region for liquid resp. solid
solution + graphite, so that the liquid resp. solid solution has become
super-saturate to a greater degree with respect to cementite than
with respect to graphite. Hence the velocity of crystallisation with
respect to cementite may become greater than that with respect to
graphite, and the metastable phase cementite will first separate.

This communication, in which many more examples mentioned in
the introduction might have been treated, but which have purposely
been left undiseussed for want of space, now enables us to set forth
with great clearness the so-called “Gesetz der Umwandlungsstufen”
of OstwaLp.

OstwaLD was of opinion that the succession in the appearance of
the phases was determined by the free energy, and that this was
therefore a purely thermodynamic question. It follows, however,
from what has been communicated here that this is decidedly not
the case, and that in these phenomena by the side of and in connection
with the concentration, an important part is played by the velocity
with which one phase is converted into another at a given temperature
and pressure, so that it will certainly often happen that the order
in which the phases occur is another than would correspond with
the free energy of the phases’). It has also appeared clearly from
this discussion that the phenomenon is much more intricate than
OstwaLb thought, and that the order in which the new phases will
make their appearance under definite circumstances of temperature
and pressure may be derived in a natural way from the new theory
of allotropy, when it is combined with the theory of nuclei given here.

Anorg. Chem. Laboratory of the University.
Amsterdam, December 27, 1911.
1) These Proc. Nov. 1911 p. 530.

2) Becker’s investigations “Ueber Kondensaltion von Dampfen” (Thesis for the
doctorate Géttingen (1911)) are in perfect harmony with this view.

( 802 )

Chemistry. —— ‘“Nernst’s theorem of heat and chemical facts”. By
Prof. Pa. Kounstamm and Dr. L.S. Ornsterm. (Communicated
by Prof. J. D. van per Waats).

(Communicated in the meeting of December 30 1911),

§ J. We regret that occupied with work of various kinds we have not
been able any sooner to answer the objections advanced by Prof.
Nernst in These Proce. of June 1911 p. 20 to our paper: “On Nrrnst’s
theorem of heat” in These Proce. of Dec. 1910. We are, however,
the more desirous to answer these remarks even now, as it has
appeared to us that also others have misunderstood the real intention
of our remarks. Though we will readily admit that this misunder-
standing may partly be due to a want of clearness on our side,
partly we think that it is also owing to a most important modification
of ideas about the meaning of the theorem of heat, which has
appeared from the publications which have been published after our
first paper had already been printed.

Indeed, to attain a chemical end (the determination of chemical equili-
bria) the original theorem of heat of Nurnst dealt with the chemical
question: what is the value of the difference of entropy in a system
in which a chemical reaction can take place, before and after the
reaction, and it pronounced the thesis that this difference of entropy
would be zero, when the reaction should take place at the absolute
zero. between solid unmixed substances, or in other words it put
under these circumstances the entropy of the system before the
reaction equal to the entropy after it. Now we first briefly demon-
strated in our paper that this thesis cannot be stated in this way
because the difference of entropy under consideration is not perfectly
determined, unless it is also stated how the reaction takes place,
i.e. e.g. under constant or varying pressure. Then proceeding to the
theorem proper we have shown that this theorem contains a state-
ment about “the constants of entropy”, i.e. that part of the entropy
of a detinite quantity of a non-dissociating substance, that remains
unchanged with change of temperature and volume. Following
RoL?tzMANN’s example we have further (p. 704—715) inquired into
the nature of these constants of entropy, in which we came to the
conclusion that they are controlled by some quantities characteristic
of the nature of the substance, which, however, bear a specifically
chemical character: i.e. which only make their influence felt at a
chemical conversion or dissociation of the substance, but which are
not felt in all variations of volume and temperature in which the

( 803 )

molecules remain unchanged, so variations of volume and temperature
as are governed by the equation of state’).

So far from having adduced van per WaAAts’s equation of state
against the theorem of heat, as Prof. Nernst says that we should
have done, we have, on the contrary, called it absurd if one should
try and calculate from this equation of state, or any other equation
of state of a substance with invariable molecules, what happens
during chemical reactions, because in our opinion in these chemical
reactions quite different forces come to the fore as those that are
active between the invariable molecules of a simple substance. So
we think that Prof. Nernst labours under a misunderstanding with
regard to our argumentation; his considerations do not bear on the
main point of the question which we discussed (p. 704—-715).
Prof. Nernst concentrates all his attention to p. 701-7038, where
.for brevity’s sake, and as we thought to elucidate the question,
we had made use of the hypothesis, emphatically called fictitious
by ourselves, that the reagents and reaction products considered
separately should follow vay per Waatrs’s law. This hypothesis,
however, did not constitute an essential part of our reasoning; it
was only intended to set forth, as we thought in the clearest way:
1. that the original theorem required a more precise definition of its
contents, 2. that whatever might be the form of the equation of state
of the substances, the theorem of heat always contained also an
assertion that is independent of the nature of the equation of state,
because it refers to the constants of entropy, which in aceordance
with their chemical nature are independent of the equation of state.

We were under the impression that we had stated this with
perfect clearness on p. 701: ‘We shall, therefore, begin by putting
an imaginary case, chosen as simple as possible, and demonstrate
that at least for this case the “theorem of heat’? cannot apply. And
this} not so much because we consider this case in itself as decisive
against the theorem of beat (for we should first have to show that
such a case really occurs in nature), but because this case leads us
into the very heart of the question, and thus will enable us to get
rid of the restricting suppositions from which we started”. And on
p. 704: “And now it has become clear why we could say above
that our result is independent of the special form of the equation
of state”.

But we will readily admit that this may have been less clear
to a reader who is not familiar with our train of thought than it
') Of course we mean the ideal equation of state of a chemically invariable
substance, not some special approximation of it.

( 804 )

seemed to us, and therefore we give the following, we hope clearer,
exposition of our meaning.

§ 2. The theorem of heat is not one simple thesis, but it contains
different and dissimilar theses. This is most clearly seen by working
out a case of chemical reaction on the assumption of a mathe-
matically perfectly determined equation of state, which can then,
however, be at most an approximation, for we do not know the
real equation of state of any substance.

It appears then first of all that the validity of the theorem of
heat requires that the equation of state fulfils certain conditions
which are in contradiction with the law of the corresponding states.
This result is of course of secondary importance, because the con-
tradiction may be attributed just as well to the inaccuracy of the
theorem of heat as to that of the last mentioned law; and in the
light of the considerations borrowed from the theory of indivisible
units of energy presently to be discussed it will really be ascribed
to ihe latter; yet it is not devoid of importance, because in the
original cecaleulations use has been made of the law of corre-
sponding states to test the theorem of heat, though it be for higher
temperatures.

In the second place, however, and this is what we wanted to set
forth, it appears that besides the just-mentioned purely physical
theses about specific heats and coefficients of expansion, the theorem
also pronounces a thesis about quantities which do not oceur in
the equation of state, the already mentioned “constants of entropy”
and our objections are directed against the thesis about these constants
of entropy.

And though now, let it be once more repeated, we readily admit
the possibility that indistinctness in our way of expression has
contributed to lead Mr. Nernst to believe that it should have been
our intention to derive arguments from the equation of state of
VAN per Waats against the theorem of heat, as appears already
from the title of bis reply, we are also of opinion that the shifting
of the real meaning of the theorem of heat mentioned in the be-
vinning of this paper must also have had a share in this misunder-
standing. Under the influence, namely, of the theory of indivisible
units of energy and the theory of Erysrrin on the specific heats,
which is founded on it, and in connection with PLANck’s expositions
in the fourth edition of his Thermodynamik, which appeared after
the publication of our paper, the purely physical side of the question
has more and more drawn the attention, and by the aid of the

( 805 )

theory of indivisible units of energy this has been formulated in two
purely physical theses, of which there was not yet question in the
original theorem of heat. And the confirmation of these physical
theses by experience has coneentrated attention so much on these
theses that the original chemicai meaning of the theorem of heat
is in danger of being entirely thrown into the background. Now
the contents of these physical theses are incompatible with the
law of van pier WAALS applied to.low temperatures, and so when
the theorem of heat is identified with these theses, one can be led
to expect objections to the theorem of heat on the ground of its
contradiction to VAN DER WaAAts’s law.

We shall first elucidate the meaning of these theses, and then
we shall try to show that the original chemical contents of the
theorem of heat is really in danger of being overlooked, all attention
being concentrated on these new physical theses.

These theses furnish the more precise definition of the meaning
of the theorem of heat required in the beginning of our paper, and
as such we accept them of course gladly, though we could not
suppose in our previous paper that it was Mr. Nernsv’s intention
thus to complete the original theorem of heat, because it might still
be very well possible, as Mr. Puanck and Mr. Nernst themselves
state that these theses should be wrong after all and the original
theorem of heat correct.

Now according to the first of these theses the specific heat at con-
stant pressure approaches to the limit zero for every solid substance
with diminishing temperature in such a way, that c, log 7 =O. It
follows immediately from this that the difference between the entropy
e.g. of a piece of ice at finite temperature and the entropy at 7’= 0°
remains finite, and does not become infinite as would be the ease
if the specific heat remained finite.

According to the second thesis at the absolute zero the entropy of
a solid substance becomes independent of the pressure, so that

On e :
( } =0: or in other words on account of the well-known relation:
r

Op.
=| _ dv
(5, a al

the coefficients of expansion of all solid substances approach the limit
zero. So this thesis supplies, of course, at the same time an answer
to the question raised by us how we must imagine the reaction to
take place for the application of the original theorem of heat. For
if the entropy becomes independent of the pressure it is no longer

( S806 )

of any importance whether the reaction takes place at constant
pressure or not.

These two theses are brought in a mutual relation and find a
strong support in Pranck’s theory of indivisible units of energy,
from which they may be derived. They have proved up to now to
be in very good agreement with the observation, particularly as far
as the first is concerned.

§ 3. So, to get a clear insight into what the theorem of heat implies
in its present form, it should be stated thus. For every chemical
reaction at the absolute zero between solid substances, the diffe-
rence of entropy before and after the reaction is :

1. Not infinitely great, because lim (¢, logy 7) =O for all solid

substances.
2. Independent of eventual modification of the pressure with the
On
reaction, because for these substances lim = =——1()
PST

3. The difference of entropy preserves a finite value if among the
reagents or reaction products mixed crystals or amorphous solid
solutions ocear; it becomes equal to zero for the opposite case.

In the third thesis the original, really chemical contents of the
theorem of heat are expressed ; in our paper we only referred to this,
the two other theses had not even been mentioned in connection
with the theorem of heat then. Now, however, as we said before,
the remarkable case presents itself that this last thesis has been
thrown more and more into the background in recent publications,
and it makes the impression as if the first two theses should decide
about the theorem of heat. In fact this opinion is repeatedly empha-
tically expressed by Mr. Nerysr. himself. Thus we read in the
Sitzungsberichte der Kgl. Pr. Ak. der Wiss. 1911 IV p. 88 “Sehr
einfach gestaltet sich aber nun wiederum die Deutung des neuen
Wiarmesatzes. Nach der Quantentheorie sind auch bei endlichen, wenn
auch bisweilen sehr kleinen Entfernungen vom absoluten Nullpunkt
der Temperatur alle festen Stoffe, seien es Kristalle oder unterkiihite
Fliissigkeiten, nur ungeheuer wenig von ihrem Zustande beim abso-
Inten Nullpunkt selber verschieden; hievaus aber ergibt sich sofort
als weitere Konsequenz, dass in diesem Gebiete, wie es unser Satz
verlanet, die Kurven der gesamten Energie und der freien’ Energie
praktisch zusammenfallen, d.h. sich tangieren miissen. Uud es wiirde
sogar wenn, wie es die Formeln von PLanck und Einstein verlangen,
die untere Kurve in Fig. 2 beim absoluten Nullpunkt wirklich die
Abszisse mit unendlich hoher Ordnung beriihrt, das gleiche von der

( 807 )

gegenseitigen Berithrung der beiden Kurven in Fig. 1 gelten miissen.”
And in the same way in These Proc. of June 1911 p. 204: “Indeed
the new theorem of heat is intended to account for the entirely
different circumstances found here; for the rest it necessarily follows
from the theory of indivisible units of energy.” *)

The same statement was made in the lecture delivered by Prof.
Nernst in May at Amsterdam. Yet it cannot be maintained. The
validity of PrLanck and ErnsTEtn’s theory on the specifie heat says
only that the difference of entropy is not infinite, the question whether
there remains still a finite difference of entropy is not mooted. The
logical connection between the original theorem of heat (thesis 3)
and the Pranck-Erxstrin theory of the specific heat is indeed this
that the theorem of heat may be correct, and the PLANCK-EINsTEIN
theory incorrect (provided only the law of Kopp is rigorously valid),
and that reversely the PLANck-EiNstgin theory can be correct, and
ihe theorem of heat incorrect, because there remains a finite difference
of entropy also when no mixed crystals are present. Moreover that
it does not follow so directly from the PrLanck-Erstuin theory that
the difference of entropy becomes zero as Mr. Nernst asserts, appears
convincingly from this that the difference of entropy remains finite
for mixed crystals also according to the theorem of heat, while we
have no reason at all to assume-that they behave so perfectly
differently from unmixed solid bodies with regard to radiation.

§ 4. In opposition to this view as if the theorem of heat would be a
consequence of the PrLanck-Eistein theory, and so as if experimental
proofs for the latter would be just as well confirmations of the former,
it must be most emphatically pointed out that this theorem being of

1) For this proof Prof. Nernsv refers among others to a paper by Mr. Sackur
(Ann. d. Phys. (4) 34 455 (1911). But Mr. Sackur has not given a proof of
the chemical part cf the theorem of heat either. For so far as they concern a
simple substance his considerations do not offer anything new, and the question
may be raised if the definition of entropy of statistical mechanics may also be
applied to the case considered there. With reference to the entropy of a system
composed of several substances SACKUR has proved nothing. If all configurations
have equal energy and equal probability, the probabiltiy of each of them is — &.
If we put that the probability that everything is in bound state is one, and that
other statés, so e.g. those in which the atoms are free, have a probability zero,
Wwe arrive no more at the theorem of heat than in the preceding case. If we
assume that at the absolute zero the probabilities of the state, completely bound
and of the state that all the atoms are free, are equal, and that the probability
of the other states is 0, we arrive at the theorem of heat, but why this should
now have to be the case is not explained, and the considerations about mixed
erystals make it even improbable.

( 808 )

a chemical nature, can only be confirmed or rejected by means of
considerations which rest on chemical facts, and the knowledge of
chemical forces derived from them. Accordingly we did not adduce
vAN perk Waats’s theory as a proof against the theorem of heat in
our paper, but we alleged chemical facts: the fact of valency, the
fact of the structure of the chemical molecule, which in our opinion
are irreconcilable with the theorem of heat. Now that it appears,
however, that the train of thought on which our considerations were
based, is not perfectly clear from our paper, we may be allowed on
account of the great importance of the question to sketch this train
of thought once more here, now deprived of the mathematical garment
in which it had to be clothed for a strict reasoning. This train of
thought, which is strictly speaking not ours, but BorrzMann’s, comes
to what follows.

Given a complex of chemical substances A, which can be converted
to another complex Bb, e.g. a quantity of oxyhydrogen gas which
can be converted to water. Required the increase of the entropy when
the reaction takes place, of course under perfectly definite circumstances.
When we suppose a complete knowledge of all physical changes
which can take place with A and B, so all changes which take
place for unchanged molecules, we need only know the difference
of entropy for one definite transition from A to B to consider it as
known for all transitions. 7

Where shall we now try to find this one difference of the entropy
of the system A and the entropy of the system B. In our opinion
the answer should be: Under such circumstances that a reversible
conversion A= B is possible. We think that it will not be possible
to solve the question first of all for the absolute zero, hundreds of
degrees below the temperature at which chemical reactions are rever-
sible, or even possible, no more than it would be possible to find
the theory of the solid state by paying exclusive attention to the
properties which gases exhibit far above their critical point. And of
all the reversible reactions those in rarefied gases are no doubt the
most suitable, if not exclusively so, for accurate quantitative calculation.
So it is by no means “remarkable” as Mr. Nerst says that we
worked exclusively with rarefied gases for the determination of this
difference of entropy, but it is owing to the nature of the problem
itself. Nor is it strange that to determine the value of the entropy
in case of mixing the substances are thought to be converted into
the rarefied gas state, to be mixed there, and finally to be condensed *).

1) Cf. e.g. VAN DER WAALS Cont. Il p. 94; Lorentz, Abhandlungen | p. 240
Puanck Thermodynamik § 254.

{ 809 )

In entirely the same way the difference of entropy for a reaction is
perfectly determined in all states, if it has been found for the reaction
in rarefied eas state.

When we now want to examine on what properties of the reacting
substances the difference of entropy that is to be determined, depends,
we must of course make such suppositions about the active forces
that we do not come in collision with the known chemical facts.
Now BoutzMann has shown that the fact of the valency of the atoms
already excludes certain suppositions about these forces, and renders
others probable. Given a substance e.g., iodine, at so large a volume
and so high a temperature that it is quite dissociated into the atoms.
If we now assume that the forees which the atoms exert on each
ather spread uniformly all over the surface of these atoms we find
on decrease of the volume that the atoms will not exclusively asso-
ciate to molecules of two atoms, but to complexes of 3, 4 ete. and
ihat even the number of bi-atomic molecules would be very small
compared with multi-atomic ones, briefly we arrive at something
that is in direct contradiction to the facts. To avoid this we must
assume that the chemical attraction does not spread uniformly over
the atom, but is localized in certain parts. Also the stereo-chemical
facts point to this, in fact properly speaking everything we know
of structure formulae. Every somewhat intricate organic formula
points to the fact that the atoms are not placed arbitrarily with
regard to each other in the molecule, but that a certain organisa-
tion prevails, that the atoms are orientated in a definite way with
regard to each other.

If we now assume chemical forces of this kind, and if we caleu-
late by the aid of the statistical theory of the entropy the difference
of entropy between split and unsplit molecules, or more generally
of the system before and after the reaction, it appears that this
difference of entropy depends on certain specific quantities, volumes,
where these forces are localized and which we have indicated as
the “chemical volumes” of the substances concerned. Accordingly
the constant of entropy of a certain substance, e.g. hydrogen depends
on the “chemical volume” of hydrogen, i.e. that part of the entropy
of a certain quantity of hydrogen that remains unmodified, as long
as the hydrogen molecules themselves do not change, but varies
when e.g. the hydrogen dissociates. What happens further to this
hydrogen, whether we liquefy or solidify it, bring it under a high
pressure or cool it down very much, in all this the chemical forces
are no longer active, the value of the entropy constant is not changed
by it, if only the moleeules:of hydrogen remain intact. But then the

( 810 )

difference of entropy of hydrogen and oxygen before, and water
after the reaction, just as it appears to depend on the specific chemical
volumes of the three reacting substances at high temperatures will
still have to depend on these quantities at the absolute zero, and
so may not be put equal to zero in general,

It might be objected to this that here a too pronounced dis-
tinction was made between physical and chemical processes, and
that it is conceivable after all that in the physical processes of
cooling and freezing the same forces are active as in the process
of chemical combination, so that, notwithstanding,
of the physical processes at low temperatures, the difference of
entropy which is in connection with the specific chemical action

in consequence

would have disappeared finally. But in opposition to this it should
be pointed out that it is exactly the theorem of heat itself that
insists on the most rigid distinction between physical forces and
chemical forces where it states a law which is to hold for all solid
substances in pure state, which, however, ceases to hold as soon as
mixed erystals or alloys appear.

What we said just now, can be expressed also as follows. Accord-
ing to the theorem of heat the heat of formation of a compound
from the composing atoms is the only chemical quantity that is
characteristic of it, ie. when e.g. during a chemical reaction some
isomers appear simultaneously, the heat of formation of every com-
pound will perfectly determine the process apart from purely physical
quantities as specific heat at constant pressure, heat of evaporation
ete. It will depend only on the heat of formation of each of the
isomers (and these physical quantities), which substances are formed
and how much of each. BourzMann’s view of this point, of which
we declared ourselves adherents, is that the wealth of chemical
phenomena is not to be explained in this way. By the side of this
heat of formation it assumes other factors relating to the place of
the atoms in the molecule, the orientation, in short the whole structure of
the moleeule which cause ‘zs compound to be formed here, that there,
and in such quantities. Then as far as the entropy isconcerned the sum
of the influences issuing from this may be combined in the value of
the “chemical volume” on certain suppositions, as calculation teaches
us. If we are not mistaken, few chemists, particularly organic chemists,
will be disposed to accept the theory that by the side of purely
physical quantities only a quantity of energy, the heat of formation,
determines the chemical character of a substance.

It is a matter of course that we do not attach importance to the
details of the coneeption of the chemical forees which BoLrzMann

(Sills)

has used for this problem. On the contrary we have pointed out,
and so bas Bourzmany himself, that this conception is only a_ first
rough approximation, and that it must be supplemented to be in
agreement with experience, specially as far as the specific heats are
concerned. It lies to hand to except this supplement from conside-
rations borrowed from the theory of indivisible units of energy. But
so long as attempts to prove the contrary have not been made, and very
certainly no proofs have been furnished, we think that we may
continue to expect that the fundamental idea from which BorTaMann
started in his considerations on the nature of chemical action, the
localisation of chemical forces, and the organisation of the chemical
molecule in connection with this, will prove to be in accordance
with the facts, and that accordingly a specifically “chemical” diffe-
rence of entropy will have to exist between different molecules built
up from the same atoms.

§ 4. Of this nature were the objections which we advanced in Decem-
ber 1910 against the theorem of heat; we fail to see that they are
less urgent now. But it may be urged that in all questions of science
ihe facts are after all the highest judge, and as the theorem of heat
appears to be in such perfect concordance with the facts, it should
be aecepted.

We should undoubtedly not hesitate for a moment to submit to
experimental results which would contain indubious contirmation of
the theorem, but one of the few points on which we have modified
our opinion since December 1910 is this that we doubt much more
strongly now than we did then whether anything can be derived
from the experimental data about the difference of entropy in a
chemical reaction, which would take place at the absolute z2ro.

It should first of ail be kept in view how great the extrapolations
are which we have to make, when we want to test the theorem
of heat by the facts. The opinion is frequently expressed that we
are already far advanced on the way to the absolute zero in this
test, that particularly the work performed by Nernst and his pupils
of late years has furnished important contributions to this. But it
is then overlooked that this work, however admirable, after all only
furnishes material for the specific heats at low temperatures for a
comparison with the corresponding formulae, which are connected
with theses 1 and 2. But when testing thesis 8, the chemical thesis,
which is here the only point of interest for us, we remain just as
far from the absolute zero for all that, beeause the nature of the
chemical reactions involves that most of them cannot be made rever-

( 812)

sible any more already at rather high temperatures, while there is
hardly one to be found below the freezing-point of water. The most
accurate testings of the chemical part of the theorem of leat require
extrapolations of hundreds and hundreds of degrees. That the acen-
racy of the test is greatly impaired in this way, is self-evident. We
shall show this by two examples. The well-known constant A’ for
the equilibrium of dissociation :
200, 2 2C0 + 0,
may be represented by a formula of the form:
: Q
hg Allg DBC Dae
Now to test the theorem of heat we shall have to determine the
quantity /, the constant of integration of the equation of equilibrium.

According to the calculations by Dr. Scurrrer (Proc. of this meeting

p. 743) we find for this quantity from experimental data the values:

= 1.75 or 1.57 when we make use of the specific heats of Hox-
BoRN and Austin for the determination of the coefficients
A, &, and C, taking 135580 for the heat of combustion
at constant pressure and 7 — 291°, from which Q is to
be calculated.

{/=2.71 when we make use of the same value for the heat of
combustion, and the specific heats of HonBorN and HENNING.

7 = 4.73 when the suppositions about the sp. h. are applied which
Nernst made in his original calculations on the theorem
of heat.

/=2.25 when in the same way as Biserrum we make use of the
formulae of Einstein, resp. of Nernst and LINDEMANN for the
sp.h.

If the supposition about the heat of combustion is changed, all
these values are again modified, as appears from Dr. ScHEEFER’s paper.
The results are not much more favourable in the water reaction.

We find for the constant of equilibrium of this reaction:

/ =— 0.2 if we start from Nernst’s original suppositions.

jh 1.2 if these suppositions are brought into connection with the
measurements of Ho1nBorn.

/=—24 if we use the formula of Ersrnin resp. of NeRNsT and
LINDEMANN.

So it appears very clearly how much the value of /, which is
derived from the experiments, is controlled by our suppositions on
the extrapolation of the sp.h.

But there is more. Let us disregard for a moment the great

(S138)

variations of the results of the value that is to be determined, and
let us assume that this value could be perfectly sharply defined from
the experiments. In what way are we to conduct then the testing
of the theorem of heat by these values ? First of all a vapour-pressure
formula for each of the substances participating in. the equilibrium,
is to be drawn up. Nernst writes it in the form:

2 &

ee eee Tale 8 See eG
ae, 4571 7 ee Ta aes

And now the value of the constant C must be determined. Accord-
ing to the theorem of heat the algebraic sum of the constants deter-
mined thus will have to be equal to the just-mentioned constant of
integration J/ of the equation of equilibrium. Now it is again clear
that the value which we shall obtain for the constant in the vapour-
pressure formula will depend to a high degree on the suppositions
made about the specific heat and the latent heat of evaporation of
the substance, suppositions on which the coefficients of the terms in
which 7’ occurs, depend entirely. In his calculation of the chemical
constants Mr. Nernst has started from the supposition that the sp-h.
of gases may be represented by c = 3.5 + 1.5n + aT, and of liquids
by 1.57 -+ eT, and besides from certain suppositions on the heat of
evaporation. But even then the data leave a wide margin as appears
from the fact that Prof. Nernst has first found 2.2 for the chemical
constant of hydrogen, whereas 1.6 has been substituted for it in the
later tables. Yet this value too will have to be modified, because the
value for the sp.h mentioned just now has still been assumed for
it, whereas according to the theory of E1ysrern it ought to be assumed
that the sp.h. in condensed state does not become 1.57, but 0.

The question might still be raised: Is it possible that the equality
which exists according to the theorem of heat between the constants
of integration from the vapour pressure curves and from the equation
of the equilibrium might possibly be independent of the special sup-
positions about the sp.h.? If this were so, and if the introduction of
other sp.h. sbould give rise to other valnes for the equilibria and
just as greatly changed values for the vapour pressure curves, this
would plead in favour of the theorem. But this is not tlie case either,
as the determination of the constants of the vapour pressure curves,
in opposition to those of the equation of the equilibrium, is not only
based on the suppositions about the sp.h. in the gaseous state, but
also on that in the liquid state. Even a different assumption for the
latter, among others that the difference in sp.h. in liquid and gas
state is not 1.5 at 7’=9, modities the C-values already appreciably.

54

Proceedings Royal Acad. Amsterdam, Vol. XIV,

( 814 )

§ 5. But let us not dwell on this second objection any longer either.
Let us assume for a moment that it would be possible also here to
determine the constant of integration with sufficient certainty from
the experimental data. What further course have we then to pursue
to test the theorem of heat ?

The values of the vapour-pressure constants found by means of
the above mentioned suppositions appeared about to agree with 1.1 7
for some ten substances, in which / is the well-known constant from
the empiric vapour pressure formula of vAN per Waats. In how far
this factor 1.1 is accurate, appears from the table of the C and f
values, which Nernst gives in his original paper *).

C ii C i
No 287 DA. CANO 3.56 3.0
0. 290) Vics erGHer 4.07 2.9
NH) 328° 3.0. Gun $45 | Digs
SO. 9340" = 3104" SHO 3.6 3.3
CS, 326 2.75 ©,H,0OH MEY | Si

On the assumption that this relation C= 1.1/7 will probably hold
generally, the number of constants was raised from ten to about
twenty. The result of these calculations is then finally summarised
in the following list of “chemical constants’, which when the che-
mical side of the theorem of heat is correct, must enable us to cal-
culate the integration constants of the equilibria, in which the sub-
stances under consideration take part.

Chemical constants *)

H, 1.6 HCl 3.0 CS, 3.1
CH, 2.5 NO 3.5 NH, 3.3
N, 2.6 N,0 3.3 H,O 3.6
0, 2.8 H,S 3.0 CCl 3.1
CO 3.5 0) 3.3 CHOC a «82
Cl, 3.1 CO, 3.2 C,H, 3.0

The test of the chemical conclusion must now be carried out in
such a way that the algebraic sum of the chemical constants of a
cerfain reaction is derived with the aid of the list, substituted for J
in the equation of equilibrium, and the obtained expression is com-
pared with the observations.

1) Gott Nachr. 1906, I.
2) J. de Qh. Ph. 8 258 (1910).

( 815 )

So if we want to prove now that the cited constants are really
the true values which are decisive for the equilibrium, we must be
able to draw up between the eighteen chemical constants an equal
number of relations of the shape:

BiCy UG. teats DyCy — VC — 2. ——

in which / represents the constant of integration calculated from the
measurements of equilibrium, C, the chemical constant for one of the sub-
stances that participate in the reaction, and yx, the number of mole-
cules of this substance that takes part in the reaction. Not until
then shall we have a proof that the equilibrium is really determined
by the adduced values.

When the number of relations is one less than the number of
chemical constants, we can choose arbitrarily one of the constants,
and then the others are indubiously determined; to satisfy then the
experiments we have an arbitrary choice of one of the values. And
this arbitrariness becomes of course greater and greater as the num-
ber of chemical constants exceeds the number of relations.

If we now examine what reactions between the eighteen substances
given in the list have been studied sufficiently carefully, this number
proves to be restricted to the following:

BB eINe cP POR NIE Mere. cer om ese (1)
DeLee UEEOli 3)
Hee Cee Clie gie a ae o's (3)
NERO OUN OM | eae aes alsa (4)
COM Om ICON a SB)

So when the equilibria for these five reactions are sufficiently
known, we have here jiwe relations between the tem chemical con-
stants: Cy,, Cn,, Co,, Cco, Cor, Caci, Cxno, Ccoo,, Cxun;, and Cy,0. The
remaining eight chemical constants do not even seem to admit of
testing at all. We will here observe in passing that the water gas
reaction, which is obtained by combination of 2 and 5, and the Deacon-
process, which is obtained by combination of 2 and 3, yield two equations
which are dependent on the mentioned ones, so that these reactions can
be left out of account here.

So if we question what requirements a table of chemical constants
should meet to account for the observations of the equilibria, -we
conclude that we can arbitrarily choose five of the ten constants
which occur in the five equations of equilibrium, and for the
remaining eight substances which besides these occur in Nernst’s list
we are entirely free, beczuse the equilibria of them are not known,
or not sufficiently. So the testing which Nernst can perform for the

54*

( S16 )

chemical side of the theorem of heat with regard to these equilibria
comes to this that he has shown that if we choose the constants of
integration of the vapour-pressure curves for these ten chemical
constants, we get one of the many lists which correspond with the
determinations of the equilibrium.

3ut even under these circumstances there remain still very con-
siderable percentic deviations. To show this we choose the example
that Nernst has worked out in his recent paper in the Journal de
Chimie physique.

From the calorie data about the formation of water from its com-
ponents, and by the aid of his hypothesis on the specifie heats
Nernst finds that the equilibrium of dissociation must be represented by

log K = — een) + 1,75 log T +
i 4,5717
2,2 DDE ona § :
a aa 10-3 T — 46 OST ere — he 10—" 7 + ¢.
Now C is determined to be —1.2 from the list of the chemical

constants; after substitution we then find the following correspondence :
T observed 1300°; 7’ calculated 1340°.

Nernst wishes this correspondence to be considered a proof of the
chemical thesis of the theorem of heat.

If, however, we had not taken — 1.2, but —0.6 for C, we had
found a perfect agreement with the experiment (1300°), and the
constant may even be put O without giving a worse correspond-
ence with the experiment (7’=1260°). By a modification in the
supposition about the sp. h. we can reduce the difference between
the formula and the observation to 20°, retaining C=—1.2(7=1320°)
as Nernst has shown in the latest edition of his “Theoretische Che-
mie’. Then too, however, we can arrive at a perfect agreement

with a value of C—=—0.9, and no greater error is made with a
value of —0O.6 than with a value of C= — 1.2, which follows

from the theorem of heat and the vapour-pressure constants. The
same or greater liberties we find for the other reactions, as Nrrnst
himself remarks.

§6. The foregoing refers exclusively to gas-equilibria. If we also con-
sider the reactions between solid substances, other no less important
questions arise. We will elucidate this by a single example’). The
1) The same circumstance, the occurrence of mixed erystals, which we mention
in the text with reference to the system rhombic sulphur rE monoclinic sulphur,
also plays a part in other reactions, e.g. in the cells:

( 817 )

classical example for the chemical side of the theorem of heat, the
example that is constantly cited as its strongest confirmation, is the
transition of rhombic into monoclinic sulphur. According to the
theorem of heat we find for the transition point of these two modi-
fications 369°.5, while the experiment yields 368°.4.

The latest investigations of Smits‘), however, have shown that
this transition point itself is not immutable, but may vary very con-
siderably according to the method of experimenting. Thus a lowering
of the transition point of 10° was observed. This is owing to the
fact that in the transition of rhombie to monoclinic sulphur we have
not to do with chemical individuals, not with the conversion of a
unary system, but with a conversion taking place in a binary or
ternary system, which behaves in a unary way, provided one
waits long enough. Or in other words rhombie and monoclinic sul-
phur consist both of mixed crystals of two, possibly three kinds of
molecules, so that the theorem of heat cannot be applied to them.
And even an appeal to the fact that the concentrations which play
a role here are possibly and even probably very small, cannot
enervate this objection, because it is exactly the variations in these
small concentrations which give rise to the displacement of the
transition point by more than 10°.

In virtue of what precedes we think that we may conclude that
there is no reason to say that the experimental facts compel us to
accept the chemical side of the theorem of heat. Led by these facts
one can, in our opinion, only conclude to a non liquet. And there
is every appearance that this will continue to be so for a consider-
able time. For the only really direct experimental test: the examination
of chemical reactions close to the absolute zero, is not to be realized.

In these circumstances it seems to us that only the theory can

Pb + 2AgCl = PbCl, + 2Ag

Pb + 2HgCl = PbCl, + 2Hg
in which not pure lead, but lead amalgam is used (see e.g. E. Gonzn Chem.
Weekblad. 1911 N°. 3). At this place, however, we do not wish to enter any
further into the question of these and similar reactions, because Mr. Cowen loc.
cit. announces the publication of a paper which will give a full discussion of this
point, and we refer for the present only to the cited communication and another of
his hand (Z. f. Elektrochemie, 19J1, N°. 4, p. 144), from which in our opinion
also only the conclusion can be drawn that the experimental material of facts
leads to a non liguet with regard to the chemical side of the theorem of heat.

1) These Proc. XIV p. 461. Dusem (Zsch. physik Ch. 23 239 (1897)) and Kruyt
(Zsch. phys Ch. 67, 341 and Chem Weekblad N°. 34 (1911)) had already pointed
out the possibility of a variability of the transition point, but before Smrrs’ experi
ments, mentioned in the text this shifting was generally thought to be very small.

( SIS )

decide, a theory of course which first of all takes account of the
fundamental chemical facts which we mentioned above, but which
further sueceeds in avoiding the drawbacks — particularly with respect
to the specific heats — which adhere to the hypothesis on the
chemical forces sketched more at length in our previous paper. And
then it cannot be doubtful, in our opinion, by what way we shall
have to try to find such a theory. We shall have to extend the
iheory of indivisible units of energy, which has led to such remark-
able results, to the chemical phenomena; it will be necessary to
investigate in what way the properties of the reversible chemical
reactions are connected with the phenomena of radiation. When this
connection has been found, the course is indicated to calculate the
difference of entropy of a chemical reaction by the aid of the statis-
tical theory of entropy at temperatures at which this reaction can
actually take place, and then it will be very simple to calculate by
the aid of the acquired knowledge of the specitic heats the difference
of entropy also for temperatures, at which there can no longer be
question of chemical reactions.

One of us has been oecupied with this question, and hopes to
be able before very long to publish farther communications on this
subject.

Physics. — “Further Experiments with Liquid Helium. G. On the
Electrical Resistance of Pure Metals, ete. VI. On the Sudden
Change in the Rate at which the Resistance of Mercury
Disappears.” By HH. Kamertinen Onnes. Communication
N°’. 124c¢ from the Physical Laboratory at Leiden.

(Communicated in the meeting of November 25, 1911).

§ 1. Introduction. In Comm. N°. 1226 (Proc. May 1911) I mentioned
that just before this resistance disappeared practically altogether, its
rate of diminution with falling temperature became much greater
than that given by the formula of Comm. N°. 119. In the present
paper a closer investigation is made of this phenomenon.

§ 2. Arrangement of the resistance. A description was given in Comm.
N°. 123 (Proce. June 1911) of the cryostat which, by allowing the
contained liquid to be stirred, enabled me to keep resistances at
uniform well-defined temperatures; and in that paper I also mentioned
that measurements of the resistance of mercury at the lowest possible
temperatures had been repeated using a mercury resistance with
mercury leads. The immersion of a resistance with such leads in a
bath of liquid helium was rendered possible only by the successful
construction of that eryostat.

( 819 )

The accompanying Plate, which should be compared with the
Plate of Comm. N°. 123, shows the mercury resistance with a
portion of the leads; it is represented diagrammatically in fig. 1.
Seven glass U-tubes of about 0.005 sq. mm. cross section are joined
together at their upper ends by inverted Y-pieces which are sealed
off above, and are not quite filled with mercury; this gives the
mnercury an Opportunity to contract or expand on freezing or lique-
fying without breaking the glass and without breaking the continuity
of the mercury thread formed in the seven l/-tubes. To the }-pieces
b, and 6, are attached two leading tubes Hg,, Hg, and Hy,, Hg,
(whose lower portions are shown at Hy,,, Hy,,, Hy;,, Hy,,) tilled
with mereury which, on solidification, forms four leads of solid
mercury. To the connector 6, is attached a single tube H/g,, whose
lower part is shown at Hy,,. At 4, and 6, current enters and leaves
through the tubes Hy, and Hg,; the tubes Hy, and Hy, can be
used for the same purpose or also for determining the potential
difference between the ends of the mercury thread. The mercury
filled tube Hg, can be used for measuring the potential at the point
b,. To take up less space in the cryostat and to find room alongside
the stirring pump Sé, the tubes which are shown in one plane in
fig. 1 were closed together in the manner shown in fig. 2. The
position in the cryostat is to be seen from fig. 4 where the other
parts are indicated by the same letters as were used in the Plate
of Comm. N°. 123. The leads project above the cover Sd, in a
manner shown in perspective in fig. 3. They too are provided with
expansion spaces, while in the bent side pieces are fused platinum
wires Hg,', Hg,', Hy,', Hy',, Hg,;) which are connected to the measuring
apparatus. The apparatus was filled with mercury distilled over in
vacuo at a temperature of 60° to 70° C. while the cold portion of
the distilling apparatus was immersed in liquid air.

§ 3. Results of the Measurements. The junctions of the platinum
wires with the copper leads of the measuring apparatus were protected
as effectively as possible from temperature variation. The mercury
resistance itself with the mercury leads, which served for the measure-
ment of the fall of potential seemed, however, on immersion in liquid
helium to be the seat of a considerable thermo-electric force in spite
of the care taken to fill it with perfectly pure mercury. The
magnitude of this thermo-electric effect did not change much when
the resistance was immersed in liquid hydrogen or in liquid air
instead of in liquid helium, and we may therefore conclude that it
is intimately connected with phenomena which occur in the neigh-

( 820 )

bourhood of the transition of solid to liquid mereury. A closer
investigation of the true state of affairs was postponed for the mean-
time, and the thermoelectric force was directly annulled during the
measurements by an opposed electromotive force taken from an
auxiliary circuit. The magnitude of this thermoelectric foree, which
for one pair of the leads came to about half a millivolt, made it
impracticable to reverse the auxiliary current as is usually done in the
compensation method. The resistance of the mercury thread was then
obtained from the differences between the deflections of the galvano-
meter placed in cireuit with //y, and Hy, and the compensating
electromotive force, when the main current passing through the
resistance was reversed. The galvanometer was calibrated for this
purpose.

In the accompanying figure is given a graphical representation of
the resistances observed *).

O45
| |
_°
| ,
AV ON ee if — a ae oe
G14. ie
Pa |
KG
|
L = —
|
ae
v
aoe eee bach: ( |
G79 |— : y |
p |
!
f
' |
— baja =|
O08 '
1
1
i
1
1
-“ 4 |
0025 |— qi + =
\
ae hi
10° QU
rn |!
|
Bin \ |
vO te 4 ob’ ~ a =
499 410 429 Jo 4°51

') For the resistance of the solid mercury at 0° CG. extrapolated from the melting
point nearly 60 Ohm can be aceepted. In the solidifying process differences occur
which make necessary special measurements to be able to give the exact proportion
of the resistance of the wire at helium temperatures to that at 0° C. (solid extra-
polated from the melting point). Therefore the resistances themselves are given here.
[Note added in the translation].

( 82h)

As a former experiment showed that there was a pretty rapid
diminution of the resistance just below the boiling point of helium,
there arose in the first place a question as to whether there exists
between the melting point of hydrogen and the boiling point of helium
a point of inflection in the curve which represents the resistance
as a function of the temperature. The temperature of the bath was
therefore raised above the boiling point by allowing the pressure
under which the liquid evaporated to increase, an operation possible
with this cryostat by closing the tap Lak, leading to the liquetier.
The excess pressure was read on an oil manometer connected to S;.
These measurements showed that from the melting point of hydrogen
to the neighbourhood of the boiling point of helium the curve exhibited
the ordinary gradual lessening of the rate of diminution of resistance,
practically the same as given by the formula of Comm. N°. 119.
A little above and a little below the boiling point, from 4°,29 K.
to 4°21 K. the same gradual change was clearly evident (ef. the
fig.), but between 4°,21 K. and 4°,19 K. the resistance diminished
very rapidly and disappeared at 4°,19 kK. (Temperature measurements
are here given with 4°,25 K. as the boiling point of helium).

During the discussion initiated by the communication of these
results to the Brussels “Conseil Solvay” (2 Nov. 1911) M. Lanexgvin
asked if other properties of the substance displayed similar sudden
changes, as would be the case if mercury underwent a structural
modification at 4°,20 kK. Experiments with the object of settling this
point were, of course, immediately planned when this phenomenon
was observed, but they have not yet been concluded. It can well be,
however, that, should there exist such a new modification, it would
differ from ordinary mercury at higher temperatures chiefly by the
property that the frequency of the vibrators in the new state has
become greater, and therefore the conductivity rises to the extremely
large value exhibited below 4°19 k.

§ +. The motion of electricity through mercury at
temperatures below 4°19 K.

The next step was as in the earlier experiments to try by
sending a comparatively strong current through the resistance, to
obtain an upper limit to the value which must be ascribed to the
resistance when this has practically vanished, as is the case at
3,°5 K. The peculiarities of the phenomena whieh then oceur make
it desirable to experiment first with a modified apparatus before
proceeding further.

( 822 )

Physics. “Energy and mass.” IL"). By J. D. vAN per Waats Jr.
(Communicated by Prof. J. D. vAN DER WAALS.)

Herciorz*) has assumed that we can deduce the equations of
motion of a system after the method of PLanck with the aid of the
principle of least action from a kinetic potential, and he has investi-
gated what conditions are necessary and sufficient in order that that
potential has the property to depend only on the “rest-deformations”’
after a “Lorentz-transformation to rest”. With rest-deformation of a
moving element of volume we mean the deformation which it
shows after being transformed to rest, compared with the shape which
it shows when it rests and is not subjected to any stress. For this
he finds the following conditions: 1s*. the tensor of the ‘absolute
stress” must be symmetrical, i.e. Pry=pyz, ete., 274. the current
of energy must be equal to c? >< the momentum, 3". a set of equa-
tions ((77) p. 508 of his treatise), which in the notation used by
me may be represented as follows:

Sy = Ye F ar Yo Pax + vy Pay a5 Vz Prz
Sy = ty FE 8e Pry ty Pyy + M2 Pyz
SE=vy,F + Dy Pre + Vy Pyz + Mz Pez}e © ()

S
|
|
+
|
to
(9
4-
fe
G
++
w
&
(9)

The fourth equation may be considered as the definition of the
quantity 7’.

When these equations are satisfied, the hypothesis of relativity
is satisfied. For when we use different coordinate systems moving
with different velocities, the equations of motion are always derived
in the same way from the kinetic potential, and this potential depends
in the same way on the rest-deformations and on the velocities of the
elements of mass relative to the coordinate systems. From this it
follows that as well the equations of motion as the conditions found
by HeraLorz are covariant for a Lorentz-transformation, and that

1) In Sept. 1911, when I wrote “Energy and Mass” I, it was not known to
me, that investigations of the same kind and with partly the same resulls had
already been published by /

D. F. Comsrocx Phil. Mag. 15, p. 1. Anno 1908.

G. N. Lewis. Phil. Mag. 16, p. 705. Anno 1908.

G. N. Lewis and R. C. Totman. Proc. Amer. Akad. of Arts and Se. 44)
p. 711, Anno 1909,

2) G. Hercrorz. Ann. d. Phys. 36, p. 493. Anno 1911.

( 823 )

they are therefore satisfied in the same way for the different coor-
dinate systems, i.e. that for moving systems w’, y’, 2’ depend on ?’
according to the same laws, as for a stationary system w, y, 2 depend
on ¢.

So we cannot deduce from the way in which different processes
take place, whether the coordinate system which we are using moves

or is stationary. In particular, — and this consequence, which is not
separately mentioned by HerGiorz seems to me to be of enough
importance to draw attention to it, — it is possible to conclude

that if these conditions are satisfied the Lorenrz-contraction must
take place. For we saw, that if these conditions are satisfied the
rest-tensions (i.e. the quantities p, which we find in a volume-element
after we have transformed it to rest) depend only on the rest-defor-
mations. If therefore for a moving system the relative (elastic) tensions
are zero, then the rest-tensions are zero and also the rest deformations;
and the volume element shows in a coordinate system in which it
rests, its normal shape. In a coordinate system relative to which it
moves, it shows then a shape which is shortened in the direction
of motion in the well known way.

The equations (1), however, deduced by Herciorz from the postu-
late of relativity in the way indicated above, are identical with the
equations

S, (1 + B) =(W + prox)»
Sy — Prx © *)
as we see by choosing in (1) the direction of motion as direction
of X, i.e. by putting »,= v= 0.

Now these equations had been derived by me Le. without making

use of the hypothesis of relativity, but only basing my deductions

ue laa
on the supposition m—=— IV. I therefore conelude that we may

aa
derive the whole theory of relativity from classical mechanics, when
we change the principles of mechanics only in this one. point, that
we assume the mass of the bodies to vary with their energy accord-
ing to this formula; and that therefore by working out the idea
advanced by Porncarf in 1900, that the energy possesses mass, we
could have arrived at a theory from which the negative result of the
experiments of Micnetson, etc. might have been predicted.
SoMMEREELD *) declares the theory of relativity not to be any more

1) *Energy and mass’ I p. 252. The symbol Gry occurring there is evidently
a printer’s error for Gy.
*) A. Sommerretp. Phys. Zeitschr. 12, p. 1057. Anno 1911.

( 824 )

actual. If he means to say that in this theory only details should have
been left for further investigation because the principal ideas
have been sufficiently established, this assertion seems to me to be
inaccurate. In my opinion the present state of the problem could be
more aptly compared with the state of planetar mechanics at the
time, when some laws of the planetar motion were known, —
namely the laws of KeppLer — but when the causal explanation of
these laws with the aid of the principia of mechanics of Newron
had not yet been furnished. Thus in the theory of relativity we have
known up till now some laws, — namely the laws of Lorentz for
the contraction in the direction of motion and for the variation of the
mass with the velocity — but an explanation of this variation of
mass and shape was not known. I think I have shown here that
the principia of Newron together with the supposition m = W are
sufficient to give this explanation.

Yet, and I will state this most emphatically, this is no more
than a first step. Many qnestions are still waiting for a solution.
In what way for instance must the kinetic energy be explained, or
in other words why does the mass of a body vary when its motion
is accelerated ; why is an acceleration accompanied with a flow of
mass towards the body ?

A second question is the following one: how must the equation

oS Re OpPrx OPxy Opr-

c Of (On Oy ie
be interpreted? It has exactly the form of an equation of continuity.
A great (perhaps a too great) importance has of late been attached
to such like analogies in the ways in which some quantities occur
in some equations. But this equation suggests the question whether
it is really an equation of continuity and whether it perhaps signifies
that the momentum moves continuously through space.

Finally, the question has often been raised whether the theory of
electricity must be deduced from mechanics or vice versa. Are we
not to consider also a third possibility, namely that they are both to
be derived from a still more fundamental law which determines the
motion of the energy through space? So we should get a theory
which might rightly be called energetics. Moreover the hidden masses
which formerly played a part in mechanics, would have to be intro-
duced again, but we should have advanced so much that we now
know, that these hidden masses are nothing but the energy residing
in the medium.

( 825 )

Physics. — “On the conception of the current of energy.” By M.
Lavz. (Communicated by Prof. J. D. van per WaAAts).

The law of the inertia of the energy, which with perfect generality
brings the momentum per unit of volume § in connection with the
energy current © according to the formula

has again drawn the attention to the conception of the current of

energy, which at the time was discussed with vivid interest in

relation to Poyntine’s theorem. The author has given a rule for the

transformation of the density of the energy current ©. This rule

states that in every department of physics a tensor of stress p exists,
. u

which with the three components of the vector —© and the density
Cc

of the energy JW taken negatively forms the components of a sym-
metrical ‘world tensor’ 7’; i.e. we shall have ,

Tk Pai if ip sr. Ys 2

i aoe
Li A Sil if 7 =2,y,2 and (/=7el).
Ty = — W

In Electrodynamics the tensor p represents the MAXWELL stresses,
in mechanics it is closely connected with the elastic stresses.

Now the conception of the current of energy has been formed in
analogy to the conception of the current of a fluid. If we denote
the density of the fluid by 9, its velocity by 4, then the density of
the current is of course ¢q. In a recent paper’) VAN DER WaAats Jr.
transfers this relation to the energy current, and so he arrives at
the conception of velocity of the motion of the energy, which is
connected with the energy current © and the energy density JW
according to the relation

hl = ieee A ee Soe ue aD)

This velocity appears to him even to be the more lucid conception,
from which the conception of the energy current must be deduced.
And in the final remark of his paper’) he expresses a doubt whether
the above quoted transformation formula for the density of the energy

!) Van per Waats Jr. Proc. Amsterdam. 1911. 239.

2) Van per Waats Jr. p. 253 last paragraph. The note on this page is undoubtedly
the consequence of an oversight, for in formula XXVIII I have explicitly equated
to zero the divergence of the sum of all the world tensors as van DER WAALS wishes.

( 826 )

current follows from the transformation formula for the density of
the energy JW and for its velocity w. He assumes there, if I under-
stand him rightly, that the addition theorem of EiNstrin applies to
w as well as to the velocity of a material point.

This, however, is not the case. For if we start from the trans-
formation for © and W, we find quite a different law for the
transformation formula for w. It is the question if an objection
to that transformation can be derived from this fact.

To me this seems not to be the case. The claim that the addition
theorem should apply presupposes that for energy as for matter we
can distinguish individually the particles of which it consists. Only
on this supposition can the paths of a particle relative to two
differently moving coordinate systems be possibly compared with one
another, which then leads to the addition theorem of Erstrem. This
assumption, however, does certainly not hold, for the transformation
formula for IW, i.e. the equation

aa
W' + Spee + 2—S',
c

Wi

=,
shows, that energy can also then be present in the accentuated
system, when in the unaccentuated system no energy of the same
kind is to be found.

It is true that in the electromagnetic field in vacuo this case cannot
occur. But it can oecur for the elastic energy of a body subjected
to a tension which is equal in all directions.

If the body rests relatively to the accentuated system, then we have

(== (0, Parr < 9, Wi SS10
and if the body is only litthe compressible :
paz] >> Ww".
We shall then have 1/7 =O if the relative velocity of translation
of the two systems reaches the not very Jarge value

()

PAs "pin

v==cC — Ww
If v inereases to a still higher value, W will even become negative.
In such a ease it is certainly impossible to compare the motion of
a particle of energy when evaluated with the aid of the two systems.
Perhaps the objection may be raised against this consideration that
in the last equation the tensor transformation has been used, whereas
its applicability is just to be proved. Therefore I will adduce an
instance which shows independently of every special theory, that the

velocity of the energy cannot be transformed in the same way as
the velocity of a material point. We consider three coordinate sys-
tems, A°, A+, A-~ moving uniformly relative to one another; the
latter two will have the velocity + » relative to A°. A body sub-
jected to a tension (negative pressure) equal in all directions is in
rest relative to A°. In the system At it has the velocity — ¥, in
‘A— the velocity + v. In the same way the elastic energy which is
imparted to the body by the tension is in rest relative to A°, but
flows in the other systems.

This flow of energy is compounded of the convection current of
the energy carried along by the matter and the conduction current
occasioned by the tensions. Only the first component agrees in direc-
tion with the velocity of the body, the second has on the contrary
the opposite direction. If now, as above, we imagine the body to
be only little compressible then the density of the energy W° in
the system K° is small compared with p. In this case the conduc-
tion current will far exceed the convection current, the velocity of
the energy in the system K+ will therefore have the direction + »,
in the system A~ the direction — v; this direction is therefore
exactly opposite to that of the velocity of a point resting relatively
to K°. Now it is true taat van per Waats Jr. tries to evade these
difficulties, which he himself, no doubt, has also noticed, by splitting
up the energy current for one and the same kind of energy into
some components differing in direction and value. It seems to me
still doubtful for the present whether this is the way to reach the
desired end.

Is the conception of a velocity of the energy, which of course can
always be defined and calculated by means of equation (1), after all
efficient? In some eases it is doubtless so. O. Rrynotps’) e. g. has
calculated the group-velocity for water waves, and the present writer *)
and in a still more general manner M. Apranam*) have done so for
light waves according to the electron theory. In both cases we can
imagine a closed surface moving with the velocity ™ through which
passes no energy. As we can disregard the absorption, this surface
always includes the same quantum of mechanical or electromagnetical
energy. It has, however, always only its signification for one coordi-

Put in the equation 102 of my book ‘das Relativitaétsprincip’ (Braunschweig
1911) G=wW.

1) O. Reynotps: Nature 6 p. 343, 1877; H. Lame : Hydrodynamik, p. 446. Leipzig
u. Berlin 1907.

*) M. Lave: Ann. d. Phys. 18, 523, 1905.
8) M. ApraHam. Rendiconti R. Inst, Lomb. d.x.e. lett. (3) 44, 68. 1911.

( 828 )

nate system. For another system the energy flows in general through
the surface. (We find an instance for this fact in the outer surface
of the body, mentioned in the last paragraph but one, which is in
rest relatively to A°. For A° no energy current passes through the
surface, it does, however, in A+ and A—). But this representation
fails altogether when absorption takes place, because then inside such
a surface the energy would gradually diminish indefinitely. Therefore
it seems to me that no great importance can be attributed to the
conception of the velocity of the energy.

Miinchen. Institute for theoretical physics.

Physics. — “On the conception of the current of energy”. By
J. D. van per Waats Jr. (Communicated by Prof. J. D.
VAN DER WAALS).

In the preceding paper Mr. Lave advances some objections
against the way in which I make use of the conception “cur-
rent of energy” in my considerations '). He was so kind as to
send me his remarks in manuscript, in consequence of which I can
answer them in this same number. Lave is of opinion, that we cannot
conceive the current of energy as a product of two factors: the
density and the velocity of the energy ; and more emphatically that
in case of a Lorentz transformation such a velocity must not be trans-
formed according to the ordinary formula for the transformation of
velocities.

As a proof for this assertion he points out, that the elastic energy
of a moving body ean become zero or negative *), but that the corre-
sponding current of energy does not become zero or change its sign
at the same time. This difficulty, however, is not decisive, if we
accept the decomposition of the energy current in components moving
with different velocities, as 1 have indicated, l.c. § 5. And the cir-
cumstance, that energy is transferred from one point of the body to

1) These proceedings p. 239.

2) At first sight it seems to be paradoxal that the elastic energy should become
negative. Still it is really possible, as can be explained in the following way. We
imagine a stationary body. Now we apply equal and opposite forces at the ends
of it. These forces in stretching out the body, do positive work. Then we set the
body in motion, in consequence of which it contracts. During this contraction the
external forces do a negative amount of work, If this negative amount is in abso-
Jute value equal to, or larger than the positive work for the extension, the elastic
energy of the body can become zero or negative.

( 829 )

another, makes the conception of energy moving with another velocity
than the body very plausible. ;

The main point, however, on which the opinion of Laux is based
seems to me to be the fact, that we have no experimental data for
ascribing a definite velocity to the energy and for. decomposing the
energy current in a definite way in components with different velo-
cities. And it is his conviction, if I understand him rightly, that we
are not justified in introducing such like suppositions, which are
founded only on logical and not on experimental considerations. So
he is of opinion that we are not justified in ascribing a definite
velocity to the energy, because we cannot individualise an amount
of energy, and therefore cannot determine experimentally the velocity
with which the energy moves.

In connection with this I will remark, that in the ease of an
electrical current in a wire we are no more able to individualise
the separate amounts of electricity and we have not the least expe-
rimental datum concerning the velocity of the current. Yet several
physicists have tried to find values for the density and for the velocity
of the electrical charge. And though the values they give are not
very reliable in consequence of our scanty knowledge of the motion
of electrons in metals, yet it seems to me that in principle no objec-
tion against such endeavours can be raised. We choose, of course,
such a value for the velocity as enables us to represent the concep-
tions and the laws of the theory of electricity in the simplest manner
possible, and to ascribe to them the most general applicability. In
the same way the close connection between energy and mass induces
me to apply the considerations which hold for the current of mass,
as far as possible also to the energy current.

If however a person who is so intimately acquainted with the
theory of relatively as Laur, and who has contributed himself so
much to its development, can think that we are not justified in
introducing suppositions which are not capable of being directly
experimentally tested, and which only serve for the simplification
and the more general application of the theory, then it seems to me
not be superfluous to investigate, which part of the theory of rela-
tivity as it is at present pretty generally adopted, has after all an
experimental basis, and which suppositions have been introduced in
consequence of more “logical” considerations. In the first place we
see that the conception of an energy current lacks an experimental
basis, at least the current which is assumed to exist in a moving
body, when it is subjected to elastic stress and of which Laur
makes a so frequent use. The observations only teach us that in one

55

Proceedings Royal Acad. Amsterdam, Vol. XIV,

( 830 )

point of the body a force is applied which does work, in another
point a force which absorbs work. We might assume that in one
point energy is annihilated and that at the other point an equal
amount of energy is created. An energy current existing between
those two points is not shown to us by any experiment. Only in
consequence of our more “logical” tendencies, we want the conception
of a continuous motion of the energy, and this leads us to assume
that the current exists. The analogy with the motion of material mass
in space has here undoubtedly been of influence. This current of
energy once admitted, if seems to me only a small step to carry
this analogy somewhat further and speak of a definite density and
a definite velocity of the energy in that current.

But, and this is a more important question, the whole fundamental
assumption, that the laws of nature will be covariant for a Lorunrz-
transformation, has no experimental basis. The most obvious expla-
nation of the experiments of Micnernson, ete. is certainly to assume
that light propagates with a velocity ¢ relative to its source, but that
the velocity relative to an observer who is in motion relative to the
source would have another value. Then the propagation of light
would take place in the way of emitted particles. There would then
no longer be any question of the ether, nor therefore of the equations
of the field. Not the equations of Maxwe.i, but the expressions for
the electromagnetic potentials would have to be considered as the
basis of the theory of electricity. W. Rirz’) has drawn these con-
clusions with the greatest consistency in two papers, to which too
litthe attention has been paid *).

What can be a sufficient reason to reject this natural and obvious
explanation of the experiments? It appears to me that for this only
one reason can exist, namely that we believe the ether to exist, and
therefore assume that light, being a vibration in this medium, pro-
pagates in vacuo with a constant velocity ¢ relative to this medium.
Then one coordinate system must exist, relative to which light pro-
pagates always with the same velocity (according to the theory of
Rivz this is not the case). But then the experiments of MicuEnson,
ete. postulate that for moving coordinate systems we should use

1) W. Rirz. Ann, de Chim. et de Phys. 8th series 13. p. 145, Anno 1908. W.
Ritz. Arch. des Se Phys. et Nat. (Geneve) 26 p. 209, Anno 1908.

2) | do not mean to pretend that I consider everything that Rrrz asserts in his
papers to be aceurate. The assertion e.g. that the theory of Lorentz should be
in contradiction to the principle action= reaction, is decidedly erroneous, I even
think I have demonstrated that a consistent application of that principle leads to
Lorentz’s theory of relativity, and that this might perhaps be adduced as an argu-
ment to prefer Lorenrz’s theory to that of Rrrz.

( 831.)

such variables as measure of length and time, that we find for the
velocity of light also ¢ when measured with them.

So the only argument to justify a choice between the theory of
relativity of Lorentz (covariance of the laws of nature for the
Lorentz-transformation) and that of Rirz') (covariance for the GALLILFI-
transformation) can for the present in my opinion only be the logical
consideration whether we think the explanation of the electrical
phenomena more plausible with or without the use of the conception

of an ether.

Fortunately this need not always be the case. Though both theories
may be equally adopted to explain the hitherto observed phenomena,
other experiments are possible which may enable us to get a decisive
test which of them is the correct one. A direct measurement of the
velocity of light emitted by sources showing the Doppler effect, can
evidently give such a decision. The two theories give here a diffe-
‘rence of the first order. It is not known to me whether other expe-
riments which can more easily be executed, would according to the
two theories yield different results.

1) It appears to me that only these two theories need be taken into consideration.
In my opinion no reason can be found for assuming that the ether does not exist,
and on the other hand yet to assume that one or more coordinate systems should
exist relative to which the velocity of light is always c. Certainly no fexperimental
reason can be found. Yet this assumption is probably the most widely prevailing.
Wircuert (Phys. Zeitschrift 12, p. 689. Anno 1911) has called it “unbedingtes
Relativitiitsprincip”. This name, however,-seems to me to give rise to misunder-
standing. For one might think that the “bedingte” theory claims that the postulate
of relativity is only partially fulfilled. The danger for such an interpretation is the
greater, because according to the original formulae of Lorenvz in his paper of 1904
the postulate of relativity was in fact not fulfilled with perfect accuracy. This,
howeyer, was only due to an error in the determination of the transformation
formula for the velocity. This error has been corrected by Poincaré and by Etysrew.
It has no connection whatever with the difference of the theories called “bedingte”
and “unbedingte” theory by WiecHert, who both claim the same absolute accuracy,
and which are in fact identical in all equations they make use of. The only difference
consists in the assumption or denial of the existence of the ether and in the
answer they give to the question whether ?' is really the time or an auxiliary quantity.
As the “unbedingte” theory assumes that a difference between a moving and a
stationary system is not to be observed and therefore does not exist, and that it
therefore is based on the thesis ‘esse est percipi’ I should rather call it the
sensualistic theory of relativity.

( 832 )

Mathematics. — “Homogeneous linear differential equations of order
two with given relation between two particular integrals.” (3°¢
communication). By Mr. M. J. van Uven, (Communicated. by
Prof. W. Kapreyy).

(Communicated in the meeting of December 30, 1911).

Before giving an example of case (3) (/ is an odd funetion of r,
all integrals are odd functions of r) we wish to make a few obser-
vations holding in general when / is a univalent odd function. Here
we continually suppose that no roots of even power appear in
the integrals (as, indeed, we have up to now always tacitly done).

As in the case mentioned here we may always suppose the inte-
gral to be either even or odd, a change in the algebraic sign of the
integral is exelusively due to the substitution of — rt for rt.

If an integral x (rz) of (B) is known, a second integral y(t) can be
found in the usual way by putting

—— ele
From this ensues then
ySaeodt 22>, Y= 22 2 za + 2a,

Aue ee E
ytoyty =e +

2
F mn ae! &
==) 20) =| :(28+5 |) =

Q
Ci
—-
bo |
3s
+
a
aN
R:
a
bo|
ae
4
ey
II

so that
Zz Dn ero
a ome
or
tmae al

As wv is either even or odd, 2—? is certainly an even function of tr.
To judge whether ¢ will be even or odd, we have nothing else to do
1

but to investigate @ a
We suppose the odd factor 7 developed according to positive and

negative powers of t. Let the highest positive power be 2n- 1, the

[ia:

lowest negative — (2m -+ 1). If necessary n or m or both can later on
be regarded as infinite. So we write

v m = n Okt)

5 = Saat aC Sheree t

I 0 0

By integration we find

( 833 )

anf Mm Ak —2 " be _2et9
Be dias SE oe a, logt +- S ——_ 1F + c= Q(t) +4, logt,
2 1 2k 0 2k+2

where Q,(t) denotes an even function of rt.
The expression

ie
——|Idz Oe a =a
e 2 | =e “a te eg, OY: R, (t)

is therefore the product of an even function R,(7) of tr and 1—-%.

It will be an even or odd function of t according as a, is
even or odd. If a, is an (irreducible) fraction, we then claim in
connection with the above, that @, has not an even denominator.
We then call a, even or odd according as the numerator is
even or odd.

If a, is odd, then z is also odd, hence z is even. The second inte-
gral has then the same parity as the first; we are then in the case
of (a) or (@).

If a, is even, then z is even, hence 2 odd. The second integral
is of an other parity than the first; we are in the case (y).

The equal or unequal parity of the integrals is then governed by
the nature of the coefficient of r~! in —.

-~
If oi is an odd funetion which does not become infinite in r= 0

and which can therefore be developed according to positive powers
of r, then a,=0, therefore even. We are then in ease (y).

For instance (a) x= sinht
: a
i ute —|—dr ae, i
Here holds in 2tanht, so e 2 Zcosh?r,z=coth?r ,
v
2=1t — cothr, y = sinh t — cosh t. ‘
Here too « and y are of different parity.
(d) @ = cosh =
“ i
+ / ea : —|—d:
Now ae oe COE SOR CI — 2). J 2 ——sinhie w,

z=tanh? t, 21 —-tanht, y=t cosh t — sinh t.

Here too w and y are of different parity.

We shall now regard the case in which a, is odd.

It may be possible to develop the integral x(t) according to
positive and negative powers of r; let the highest positive exponent
be , the lowest negative — ju. We can then write

( 834 )

“
2 Sap = = Bark
1
from which ensues

B
x — & hapgr—*—! + SZ hpyré—,
1 1

bt Sk) age 9 + Sk (k—1) Byrk-2,

so that
= u(u+1) are = yztk

i oO. ote oat

2 at amie vl ar
q = dptk

—p—=l
u ae, Cy + SS yarn tere (ut) ay +S yee

=|! Lets!

DS Woe

—p—l

S=p—1 + = ag

u(u+l) a, + S yeret2+k 1 ;
—-p—l = im
——— : 1 DS dguet' +k =
TO] a Oe 1 —p. i |

u(u+l1) a, Ss egret ith

—w".
—— — 4

TO p—1
or, as we have d_,»z—1 = —uea, ,
eet + © part
2 Si 0
so that
Capea.

If is desired as in ease (8) that 2 be an odd function of r,
and if the latter has a pole of finite order in t=O, then mw is odd,
so a,=u+1 is even. The integral y is in this way of a diffe-
rent parity than 2, therefore even. Hence we have not case (3) but
case (y) under consideration.

If w is an integer odd function of + then holds

aS pevet! , ea S(Qk+1) Reve , B= DS 2h (2k4-1) Be,
P

P ©
so
vi ata
2a Ege

2eet DRA! + et N Get Met Bet + ae

9+ Na +. > (2 +1)Bar*

( 835 )

2o(20-+1)p- + ((2e-+1) (20-+2)B-41 + Bae? +E eg 2242
+H

r{(290+1)3, + > (2h+-1)Ber24—21
of

As 8 is supposed Zz QO we can transfer the form between }} in the
denominator (treated as binomium) to the numerator. In this way
we get in the numerator a series of positive powers of t and we

vi Ste
finally find for = an expression in which the lowest power of 1 is

“

t! and that with the coefficient
20(20+- 1p.

a,= — = — 2o.
(29+18.

Here too a, is even, so that we have again hit upon case (7).

The only manner to obtain with odd « an odd value for a,
reached by assuming that the negative powers of t in the series
for xv continue to infinity, hence by putting w=o. We then
evidently start from the supposition that 2 in t=O has a really-
singular point.

We remark, that we are allowed in as far as it regards parity,
to assume that the series for # and y are built up out of powers
of t with broken exponents if but the denominator of that exponent
is not even. We then find accordingly for a, broken values.

Example :

1 1 4 al iil WA
Here holds « = — —cos|=—}|, «= -+ =cos — — sin , so that
Ge T oe T Te T

ete

1 ee A! 2 1 1
——s——Si7 + + sin
Te G a T T 1 il 2
=|) Ni) | eo
T G T

1S

For a, we find ee ae to the domain of convergence,

So here we are really in case (@).
In the first case 7 was an even function oft. As instance we have
discussed the case where / is constant. We shall imagine that J is

( 836 )

not constant and we give as example :
T
Ci—lee

Now weet , waeee + et ee , so that

I ate fel

Cm a“ Cr

= 1 + 2 cosh t.

So here / is really an even function of +. The substitution — r
instead of + now leaves / (t) unchanged whilst the differential equation
passes into

Was
t= 10),

(y—— d
D)

<

so into the one belonging to the semi-equivalent curve.
In order to find the second integral y(t) we again put y= .7z.
Then the function z is defined by

- ; [ la: i a jen

z—a-2e J — e—2e | et+2sinht — pt—e'—e

Furthermore holds

We thus find

dy dz < 3 7 oT T, —t
= 2 2 — eze , pt—e —e Neate) ee

Co ee
dca de x
The coordinate (§) of the points of the curve obtained by polari-

sation is now (but for a constant factor) :

— pe *

xv dy —y dx
So the coordinate § proves to be really obtained by replacing
rin w by —t.
Out of

dy = *
Da) S74 and 2 e<
dx s

dy
log | «— —y ]=—e and lgr=eé,

dy
log | «— —y |].loga=— 1,
; da ; ;

follows:

so

or

( 837 )

dy log x
oe —y = aa
dx :

or
1
dy ——
+e log x “
da ,
so
1
dy y 1 —
SS == —— 6 log DL
dx UG v
so that
l
ee :
P= O98 || =O Wet, o oie 6 6 & we )
a) Ge

where the constant of integration is put equal to zero, as this does
not harm the generality of the integral.
The curve represented by (50) is evidently semi-equivalent to itself.

Chemistry. — “The nitration of benzene’. By Prof. A. F. Honteman
and J. VBRMEULEN,

This communieation will not be published in these Proceedings
]

Chemistry. — “On the addition and the additionproducts of chlorine
to the chlorbenzenes”. By Dr. T. van per Linpen. (Commu-
nicated by Prof. A. F. Honiemayn).

(This communication will not be published in these Proceedings).

Bo ROA TY A:
In the Proceedings of the meeting of December 30, 1911:

p. 674 1. 17 from the top: for “narrowed at the lower end” read
“having an upper wider and a narrower lower end
connected to the first by a capillary”.

]. 15 from the bottom: for “lower” read ‘‘lowest’’.
p- 676 ‘Table II in the heading of the third column read ¥.10°
p. 678 1. 2. from the top: for “all” read “a class of”.

(February 22, 1912).

Py = 5
= <e$- Tay Hs. ie
| ‘
“Thy Wi
a : Pcs
~ : 4 -
; gon
yy
i
‘
’
:
.
.
.
r
-

Cn oe en oe

a 4 eo none FA

& in

are fe JOU Ue aee

Sie Gane eu
che

ulna \¢ fr) i
‘ j ney ae _ r

. a
iJ ay

inh Shea ease
ie
4 'ce Oe al LU

> 4 “waieueal inal « pall

wr . .
tf Win vay) seis let aS fol
, *

os

- -

sel Avi ‘i Wis) i ae! | ra
gd eS gee :
wal) Cet! fewer Pa
Pee 1s) Gh
{Demmi aolt e Uy ata Whe
“Gh oe onl sire “Bh We ar

ee ey )

KONINKLUKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING
of Saturday February 24, 1912.

—DOCGe—

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 24 Februari 1912, Dl. XX).

CONTENZS.

L. S. Ornstein: “Entropy and probability”. (Communicated by Prof. H. A. Lorentz). p. 840.
L. S. Ornstein: “Remarks on the relation of the method of Gipps for the determination of
the equation of state with that of the virial and the mean free path”. (Communicated by

Prof. H. A. Lorentz), p. 853.

J. P. vAN per Srok and P. H. Gatié: “The relation between changes of the weather and
local phenomena”, p. 856.

J. P. vAN per Stok: “On the angle of deviation between gradient of atmospheric pressure
and air motion”, p. 865.

J. D. van per Waats: “Contribution to the theory of binary mixtures”. XVIII, p. 875.

Cu Freie: “On the comparative nocuousness of concentrated and diluted arsenobenzene solu-
tions. The dilution to be applied in intravenous injections”. (Communicated by Prof.
H. J. HampurGer), p. 893.

B. G. Escurr: “On an essential condition for the formation of overthrust-covers” (Commu-
nieated by Prof. G. A. F. MoLencraarr), p. 902,

J. C. Kapreyn: “Starsystems and the Milky Way’, p. 909.

C. van Wissetincu: “On the cell-wall of Closterium together with a consideration of the
growth of the cell-wall in general”. (Communicated by Prof. J. W. Mott), p. 92.

F. A. H. Scurememakers and J. J. B. Duss: “On the system: water—alcohol—manganous
sulphate”, p. 924.

J. BorseKEN and H. Waterman: “On the action of some carbon derivatives on the develop-
ment of peniciJliumglaucum and their retarding action in connection with solubillity in
water and in oil”. (Communicated by Prof. A. F. Horreman), p. 928.

J. Weeper: “Calculations concerning the central line of the solar eclipse of April the 17th, 1912
in the Netherlands”. (Communicated by Prof. E. F. vaN DE Sanpr Bakuuyzen), p 935.

L. Bork: “On the structure of the dental system of reptiles’, p. 950.

W. Karreyn: “On some relations between Brssex’s functions”, p. 962.

Sr. Lorra: “The magneto-optic Krrr-effect in ferromagnetic compounds and alloys”. IT.
(Communicated by Prof. H. E. J. G. pu Bors), p. 970.

L. S. Ornsters: “On the Solid State. I. Monatomic substances”. (Communicated by Prof.
H. A. Lorentz), p. 983.

BE. F. van pE Sanpe Bakuuyzen: “Further researches into the constant term in the latitude
of the moon according to the meridian observations at Greenwich”, p. 991,

A. Perrier and H. Kameruincu Onnes: “Magnetic researches. V. The initial susceptibility
of nickel at very low temperatures”, p. 1004.

A. Huenper: “On the activity of the halogene-dinitro-pseudo-cumoles and their addition
preductivity with nitric-acid”. (Communicated by Prof. A. F. Hottemay). p. 1007.

56
Proceedings Royal Acad. Amsterdam. Vol. XLV.

( 840 )

Physics. — ‘Entropy and Probability.” By Dr. L. S. Ornstern.

(Communicated by Prof. Lorentz).
(Communicated in the meeting of September 30 1911).

Einstrin ') has defined the probability of state ina way by which he
emancipates himself from special hypotheses concerning the structure of
the systems to which he applies his reasonings. He puts the logarithm
of the probability thus defined proportional to the entropy. If there-
fore de is the difference of energy between two states of the system,
and if dA represents the work done by the system if it passes
in a reversible way from one state into the other we have

R de +- dA
dy —— vi log W — — 5

Ris the gas constant and the number of molecules of the gramme-
molecule. The reasoning, used to deduce the proportionality of 7

I ree aoe
and a log W, is perhaps not quite convincing, for on the one side it

is presumed that a system runs through all states possible with
the given energy, and on the other that /og W like the entropy
tends to a maximum value. It is possible by means of statistical
mechanics (as well with the help of the canonical as with that of
the micro-canonical ensembles) to find the relation of entropy and
probability, however using many less general hypotheses as those
employed by Eixsrers. [ will try to show this in the following
communication.

1. We consider a system of a great number (s) of degrees of
liberty. We suppose that the changes of the state in this system
are governed by the equations of Hamiiron. Observation does not
teach us anything on the s general coordinates (g) and the s moments
of momentum (p) but we obtain knowledge of certain (e. g. geome-
trical) quantities A. Suppose that there are / quantities 4, which
are discernable for observation. The number /: is small in comparison
to 2.5. We shall indicate these quantities by A, ..<Ax.. Ax”).

To the 2s values of the coordinates and the moments in a given

1) Ann. der Phys, Vol. 33, 1910, p. 1276.
*) The quantities A may be geometrical quantities but also densities in given
spaces. The quantities determining deformation must be used in several cases, also
the optical qualities of the system, in other cases we have to do with thermical
quantities relating to parts of the system accessible to observation, ‘and which may
be said to characterise the system for it.

(3H )

state of the system corresponds a perfectly determined set of values
A, on the contrary it must be kept in mind that a great number
of systems with greatly differing values for the p’s and the q’s
corresponds to a given set of values of the 4,’s.

Moreover we must presume that the quantities 4, are observable
with moderate accuracy, so that systems for which 4, has a value
between 4, and 4,-+ dA, are undiscernible for observation. The
quantities AA are once for all fixed (in relation to the given accuracy
of observation); 44, will be small compared with 4,.

A system having its 4,’s between the limits mentioned will be
called the system (4,..4,..d,). For the sake of simplicity we shall
suppose that the quantities 4, depend only on the general coor-
dinates *).

The 2s-dimensional space in which the system can be represented
in the ordinary way can be dissolved into the extension in configuration,
(the coordinates being the variables) and into the extension in moments
or velocity. The part of the extension in configuration where the
systems lie for which the value of the 4, is between 4, and 4,+-d4,
will be represented by

MCL 0 0 thre o AIAG thao oa We
or shortly by
ydA,.. dA,., dAy.

We shall further suppose that the potential energy ¢ of the system
of given 4,’s is totally determined by the values of the quantities
,, This is only approximately true, for ¢, depends on the coordinates,
which can still be greatly different for systems of which the 4,’s
are the same. We shall represent the potential energy by

Ah oo 4 lane ACh soe E
the quantities @ denoting parameters on which the potential energy
may also depend; the same parameters shall appear generally also
in the funetion x.

Finally we’ could suppose that there exist relations between the
quantities A,, suppose for example 6(46< #) of the form

fe=0.

For such a case we can always introduce k—b new quantities
A which are mutually independent, we therefore shall suppose that
this is yet the case for the 4,’s mentioned above’).

1) It is however not difficult to extend the considerations to those cases where
this is not so and where the A, can be thermical quantities.

*) This need not be the case if we take as variables such quantities which are
suggested by the nature of the problem, e.g. there exists a relation between the
456*

( 842 )

2. We shall now consider a microcanonical ensemble between
the energies ¢ and «+ de, consisting of the systems described above.
[ shall represent the part of the extension in configuration for which
the quantities 4, are situated between the limits 4, and A,—d4A, by
2(A,.. 4,.. Ar). The value of £2 may be expressed by the equation.

s

——-l

Q(A, ..4,... Ay) = C {(e—e, (A. . 4, . . Ay}?
Yoda, Ae Ade:

C being a determined numerical constant which is of no importance
to us. The quantities 4, must have such values that &, <«.
We shall first consider the question for which values of A, 2 is
a maximum, i.e. which values of the 4, occur in a maximal region.
We find for the maximum condition, proceeding in the usual way,

s 1 Os, 1°05
—(5-1) Pig is 2 =)
2 &—e, (4,.. A... Ay) 0A, y 0A,

The quantity ¢—e,(4,) being the kinetic energy of the system

occurring maximally, this quantity is, as is proved by Gipss, propor-
tional to the absolute temperature 7’ and it can be expressed by
the formula

§ R yy)
SS if .
2N
s
Neglecting 1 with respect to no being very large, we find asa

condition for the maximum of 2
N dé, Dy dye
RT 0A, yx OAL ie
The further conditions that d* log 2< 0 lead to a number of
relations of the form:

s—2 1 (de,\?7 s—2 d's,
2 &,"\0A, 2e, 0.4,°

1 () 12,
=) = ~< 0,

x 0A, xX OA,

0.

(i

and to a number of relations in which the quantities ————
04,0 Me

densities in fixed elements of volume in a gas. In practice one will not use the
relations to eliminate the j, but will use the Laplacian method of undetermined
coefficients. It is also possible that inequalities appear as relations in every case;
it follows from our first hypothesis that we may assume that the relations are
fulfilled without any approximation.

( 843 )

play a part. The complication offered by the appearance of these
quantities may always be avoided by a linear substitution which
removes those differential coefficients. I shall suppose that such-like
A,s are introduced (further representing them by the same symbol
A,); A,, vepresents the value of 7, in the maximum system.

3. The region 2 where those systems are represented for which
A, is situated between 4, + §, and 4,, + § + d&, can be easily
calculated ; we find for it:

k
4 > PeS*
Nec Agr 1. AS, AGLCE
where
s
Di = CK (Ay, - + Any + + Akq) (€—€q)?
and

pare te N 0&, ie N 0%&5 1 + ox ie : rS oe
j Te, \04; RRO! = 77 \0rn) = one

The expression found above can be used to calculate the total
volume of the extension in phase of the space where the energy
is contained ee the given limits. For this purpose we have -to
take the sum of 2, for all the values of .7,’s which are compatible
with the given energy. However, we can integrate with respect to
the € from —o to +o, the values of ¢, which deviate considerably
from 0, attributing only very small amounts. Proceeding in this
way we find for the extension in question, which we shall represent

: OV
by the notation of Gipps ede or ae
é
aV C2
SS i de,
de (Pp, = + Pz Gs - pr)?

C being again a determined constant, the value of which is without
importance for our conclusions.

With the help of the found expression we can express the value
of the function V(«) which determines the magnitude of the part
of the extension in phase for which the energy of the represented
systems is smaller than ¢. _

We obtain for a the expression

—
7 ,! Y (4,,. fees -Aj,,) 2
a nes g \¢ [.Lhy,- «Lap 3
ere
ve

The value of the Tug can easily be obtained in case that the

( 844 )

value of the 4,, for which 2 is a maximum, is independent of «.
Then we may assume ¢(V=0) = «&,(A,,. 4,,..d;,). Substituting this
value we find

s

2
Abeer ie))

10

RO (a ne 4 bon rs DENY 2
V6 BD inh — NE=— Er (A
Gonna) S
But the same relation holds for other cases. The quantity 7%,
depending on ¢, we have

V
== [lee yoo dy Ape V eo Y( Ave ache. acl OE
¢

e( V='0)

€

Nila
Whe

i) .

a

= | Ea Ao) ) 1A), + (e604)

e (V==0) «( V=0)

at
4 (4)

k
s dg 04, 5
1 04, de
2 SEM ay Od
== (Ge Se
ee ae ae

«(V=0)

Combining the integrals we find

; a : = ne (2 8 OE, OF \ GLa ;
vf eet)? x 2 (5 (2,04. 494, =) 7.

=(V=0)

Every term of the integrals is zero. The kinetic energy being
essentially positive we have at the limit ¢(V = 0)-¢—=&, so that
we obtain

9 s

V=— OC (e—by (Aes)? X (Aro)

A,, having the value relating to the energy «.

In this demonstration Vp, has been neglected, the influence
however of these factors is small, they deviate only very slightly
from 1, if compared with the quantities taken into consideration.

4. Gisss has proved that /oy V is equivalent with the thermo-
dynamic entropy. If two microcanonical ensembles whose energy
differs Ae and whose parameters differ by Aa there exists an equa-
tion of the form

( 845 )
e-¥ V Alog V= Aé + Al Aa?) eae eel)
in this equation A] is the average force in the ensemble exercised with

1) For the case under consideration we can prove without applying the general

: € :
discussions of Grpps_ that Po shows a perfect analogy with the temperature, and

as

the relation (1) can be proved somewhat more simply than it has been done by Gripes.

Let us imagine two systems of the kind described above, which can interchange
energy but which considered as a whole are isolated. Let us suppose that the
first has s,, the second s, degrees of freedom, the energy of the first being ¢,, that
of the second <g. The total energy being constant we haye

&, + €& =.
The quantity g). of the combined system can be expressed (Gress |.c. p. 98

form. 316) by
ee =| Fie: dé,.

If we represent the value of (Av-) when the A, have their maximum value by
x(Az-), and if we distinguish for the first system % parameters Az, and for the
second ” parameters Av, we obtain

Oe =| (Gees)

FACS &,) dé,.
The maximum system will contribute a maximal amount to the integral. We
can find this system asking for what values of ¢, and ¢ the function under the
integral is a maximum ¢, + ¢, being a constant. We then find

3} 1 1 eat 8, 1 1 dete
— — 1 ] —_— de — — | |) —— de
2 €— =n : 2 ee ¢2 :
k 5 , Vie
sy ee yet ao ape alte at
1 2 DAk, hi 0Ar., dé,

s 83 1 JEq, i i WE 02, Js. .
; 2 02, Hoke Or ©

From the above considerations it follows that the summations in this equation
are zero, the Ay being the values for the most frequent forms of the separate
systems. We therefore find for the systems occurring maximally

| al

9
A(Lé,)le, 37)

Sy So
2

s,—2 s 2

2

— =a i)
2(€, —€,,) 2(€,—€4,)
or
pi __ &ps
Si a 8,

1. e. that system is most frequent for which the kinetic energies of the composing
systems are proportionate to the number of degrees of freedom.
If we separate the systems, their contents of kinetic energy will fulfill with

( 846 )

respect to the parameter a. GipBs has shown that e~? V corresponds
with temperature. With the help of the given relations we can c¢al-

great probability the theorem of equipartition. Also two systems the energies of
which are proportionate to their number of degrees of freedom will be, after that
communication of energy has been made possible, in a probable state and it is
therefore almost certain that one system will not give or obtain energy from the
other. If two systems are brought into contact whose energies are in another
proportion, their state is improbable and the total system will probably change in

. Ep .
such a way that the system for which © is too great, loses energy. What has
: 8

oat ; €
been said is sufficient to show that can be used as a measure for the temperature.
s

We have next to consider t#e mean force in a micro-canonical ensemble. I
will give a somewhat simpler deduction than that of Greps.. (Hearz has also given
another treatment).

Consider an ensemble for which the densily ¢ in phase is a function of ¢, the
function p (e) being zero everywhere except between narrow limits in the proximity
of ey; between the limits p(e) shall be supposed everywhere positive. Suppose
that ¢; and ¢, are values of ¢ lying outside this region but so, that 4 < ¢) < co; we
have identically

=2 &
~

fe Op Pore 2 dQ =| oe? de.
=

7
Differentiating with respect to the parameters @ we obtain

=2

“do 0& c OMe “00
7 alan CO ene Ci —— “| a) < e de = 5 ANA D eye AG s ——
1

2

1 g

The transformation on the second line follows directly from the signification of J] ,
€

The last expression is obtained by integration in parts. The density » being
zero for the limits, we may neglect the fact that ¢, and e, can depend on a. We
therefore obtain

- As — =
0& i 0g 0a

The values ¢; and gy can be taken as near to each other as we like, therefore

”

( 847

culate e-? V and find for it

2
—
ee)

It is worth noticing that (comp. GissBs form. (377) p. 119)

Can Ve— —— 95,
s

where ve) vepresents the average kinetic energy in the ensemble.
We therefore have
l= Se
The same relation can be obtained with the help of the given
formulae. Using the definition of an average value, we have

Sep2o =.

le VOR = Or &,2, — fx (4, 6 brah oo Ak) .

roe

(e—e_ (4, .. 4... Ax))

The last integral can be transformed into
k Aa NS
DL. — —
ee Ep’ a)

s
we can always take care that the sign of ¢? does not change in the interval.

QA var Aj UA.

1
pat,
Cee (tn Arg Ard) 2, fe 1

nae! V ; ;
Now e’ being ~—— we can transform the last equation to

de
= JV
Al ? = — 7;
e Oa
C depending only on a. Taking for ¢ the least value consistent with the energy,
Ta
we have to take e* and ai equal to zero and we find the same value for (.
a

To prove (I) we have only to keep in mind that

1 /0V OV
(‘Nig VS (== — :
Be ae ha + 5 Ae)

yr

‘ 9 4
remembering that e7 = Ae ke find
&

e-? VAlog V = Al Aa + Az.

Further e *V = —s,| is equivalent to the temperature; this note shows there-
8 5s

fore that (1) is indeed an expression which is comparable with that of thermo-

dynamics.

2
En, f,

dot Mis 0G. Oe

(Pr ++ Px. pay?
which can easily be seen if one remembers that the terms which enter
besides p, in the exponent are very small in comparison to the p,
terms. Using the given value for ¢* we obtain

a= (€ me Ey (A,, , A, he Ax) ) = Epo

The mean energy in the ensemble and that of the most frequently
occurring systems are equal. The same is true for the force in the
maximum system A, and the mean force A].

The force exercised with respect to a parameter in a system of

0€
the energy «, amounts Laas: We therefore have
a
=e “de
A|= — af 5, Seats «+ dy d Ap
a

0€
The value of — can be expressed for a system for which
a

A, = A,, + §, and for which &, is not too great by

0g de iB Ocemee Oceana a2 Osea
Fpl ie Rego eric rats erence | sie a reer
0a 0a 0 1 0A,0a 0A, 0a xejen0 AO Ay
In the integration those systems for which §, are great have very
small influence, we can therefore adopt the given expansion for all
values of &, Introducing the value of 24 we easily see that the
terms with &§, disappear in the integration. We also find:

al 0g iO VeNOGE oP) Be OPE
7 le Gl ; p.9A,20a ae pe 04,70a ‘

In general p, is large compared with —

01,200’

wh
Se

—~Me=
-Me

we therefore have
Al Ale

Comparing the values of log V and log 2,, we see that we have
if s is very great

k
logV = log &, — 4 & log p, + Const.
l

k
The sum 2 /ogp, may be neglected with respect to log 2, if &
1
is small in comparison with s; this being the case we have

( 849 )

logV = loa 2, + Const.
Comparing therefore /og 2, for two ensembles for which the
energy differs by Ae we find:
RT
N

Milcg Oe Ne wAL NG) ne 5 3. (ED)

The quantity log 2 2, fulfills therefore the same relation as the

thermodynamic aie in the corresponding case. The correspond-
ence however ought no longer to be considered as to be formal, all
quantities relating now to real systems, i.e. to the most frequently
occurring system of an ensemble, that may be identified with the
system in stationary state. The function /og V showing the properties
of entropy, the same will be the case for log 2,

9. I shall define the probability W (A, .. 4,) of a system (A, .. 4; .. Ax)
as the integral of 2 taken for a region whose magnitude is given
by observation and which is characterised by the quantities AA,
(comp. (1)). We therefore have

ema Ak+AAk

W (A, .. 4, -. Ay) =i, hes feu, ee ee

Ay—AA, Ak—AAL
2 2

Substituting in this formula the obtained value of @ we find

ae Sate
k
= 4 Day Sy
Wie (AEy oe, Zab on 22) af. ie 1 | a
== PNIANG — AAk
2 De me

The 4-4, being relatively small quantities compared with the &, we
can put this into the form

k
$ = pS"

Wie (A ete 1 ro ne MN A © Ads Np:

>

R
We shall now prove that = loy W =a shows the properties
4

of the entropy, i.e. that

PS i Se
iN v9 — Nn log 2, + aN ~ PrS x + Const. . | (I1)

answers to the relation.

( 850 )

ds +- dA
TAO aera Bee ot org (GAIA)

; ; = Ske
Putting 1, in stead of a log 2, + Const. we can transform (IIT) to

Rate a8
1a = Ne + oy > PS Span be co (CULM)

The energy being the same for the systems under discussion the
relation (IV) reduces to

R 1A
og Wan
iNet T

or
dA
NA — 7 a
iA lo =F T

R
In order to prove the correspondence of the entropy 9 and x log W,

we have to show that
RT

2
eS es,

represents the work done if the system is brought in a reversible
way from the stationary state to that indicated by A.

We can make this transformation reversible in two ways:

In the first place we can imagine an external field of force,
applied in such a manner that the deviating state in the old
ensemble is the most frequently occurring in the new and change
this field of force in such a way that the most frequently occurring
state passes continually. from the states 7 through the state 4-4 §.
In the second place we can imagine fictitious forces influencing the
parameters 4, in such a way that they allow the non-stationary state
to exist. These forces can be changed in such a way, that the
said states follow each other as a series of states of equilibrium *).

I will follow the second way. In order to find the forces wanted,
we can take the quantities € as parameters and determine the forces
=, working on the stationary system by the relation
OGY wave

mye

é—?

0&,

The region V to be used here is found substituting -4,, + §, for

A, in the value found for V(e,....44-), 4zo + §& being now the
equilibrium value for 7%,

1) If we have for example a gas the density of which deviates from the nor-
mal we can as well by introducing a field of force as by fictitious walls change
the non-stationary state into a slate of equilibrium,

( 851 )

In this way we find for the force working on &,

pe Xe L J log V 0? log V
spa sill On, 4 ee )

Introducing these forees in the expression for the work we obtain

Ses

7

é
1A Rea ks \ 0 log V (= log V slg
me 1) oe aa) S| &
ales eS sh o: log V
=! ls: eM et,

the first term en ZeYO as faltons from the condition of equilibrium.

R
It has been shown also that = log W corresponds with entropy

for a non-stationary state. For two deviating states from different
ensembles the same is trae, because it is always possible to pass
from one to the other, passing through the stationary states of the
ensembles, for which states the formula (II) is true.

I will shortly indicate what is obtained if we apply the above
formulas to a gas (or liquid), the molecules of which answer to the
hypothesis of van Der WaAats. Suppose that we have n perfectly
rigid and elastic spherical (diameter 6) molecules in a volume JV.

Let-us divide the volume in / equal elements V,, which contain
n, molecules. The volume of the extension in configuration can be
represented, as I have shown, by

n! Ny EN Ge
w — | V, :
ny! nef. Va

Nz
w (n) =o (F) being a function of density. For the potential energy
we shall use the expression
2 2
a n
Ses) = :
wy WE

The quantities 7, are joined by the relation

k
So

ad I

1
The function x of (1) has the form

n,m, *n, '*(w (nx) V,)”

the members 7, being chosen for 4,.
The condition for the most frequently occurring system is

( $52 )

1 Ny aN n, | d log «(n,) :
— —- — Log w(t, - Ny - == A
09-7 + aap ag 8 OU cee

The quantities 7, are normal coordinates, the value of p, is
1 2 d log w(n,) n, @ log w(nz) aN 1 ix il
0, = — — - = - — - —— — — —_ —
ny Reyne,

= - ———_— anya.
Nxo V, dn, V, dn,’

The last term is again small in respect to the others, we therefore

find
I Gi ( , d log w (n,) |
LS SS D,—D,’ - - :

Ny, ADy dn, PH Rade!

‘ oe
Ep being > RY.

If we take into consideration that the pressure a of a gas (comp.
my dissertation p. 125) is expressed by
=( _dlogw(n) an? )
= Vy We SS ;

we can put p, in the form

1 N dx (n,)
RE

—

The expression log V can easily be used to calculate the pressure.

7. The mean value of (4, —4,,)* i.e. of 3%, can easily be calculated.
One finds for it

or p,§,=1. We can apply this formula to calculate the mean
work necessary to bring the system from the normal into the deviating
state, we obtain for it

— iiveln
dA = k—.
2N
, f : JR
For each quantity /4, this mean work amounts to Sas ©: the
(“Ps

mean work is equal to the energy pro degree of freedom.

The result has also been obtained by Ernsrmm. Indeed it can be
shown that for our case the definition which Einsrrim has given and
the definition used are identical, if only it may be supposed that
the path of the representing point of the system fills the space «=
const. everywhere dense. Eixstew defines the probability of a state
A,.. A, AM, as the fraction of a very long time 7 for which the

( 853 )

system is in the said state. I have shown") that the probability in
a time ensemble can be expressed by

_ ds

fo
ds being an element of the path of the system and V being the velo-
city of the representing point on its path. The quantity Cis given by

“ds
| = integrated along the whole path.

The probability defined by Eistery now can be expressed by
Leds

a
where the integration covers all those elements for which the values
of 4, have the given magnitude. If the hypothesis of ErsTrm may
be used the value of this integral can be expressed by the part of
the space &£=C which is the limit of de2(4,..4%.. 4) A4 if

(

de approaches zero, and the space has been filled in such a way
with systems, that gde has a finite value if de approaches zero.

For by Eixster’s hypothesis all the points for which .4, is between
4A, and 4,+ A4, are on the path of the representing point, and
the given expression represents the part of the space for which
the -4,’s have the given values. The integral f = taken over the ele-
ments indicated above and 2 (-/) are identical.

Using these conditions limiting, however, the generality, we have
proved that the probability as defined by Ernsrrin is proportional
to the entropy.

Groningen, Sept. 1911.

Physics. — “Remarks on the relation of the method of Gisss for
the determination of the equation of state with that of the
virial and the mean free path. By Dr. L. 8S. Ornstery. (Com-

municated by Prof. H. A. Lorentz).

(Communicated in the meeting of December 30, 1911).

In determining the equation of state by means of statistical
mechanics it is useful to introduce a function w, which for a system
of n molecules of diameter o is given by an integral

few co (By = OF a la ot Bae)

') Comp these Proce, of Jan. 28 1910, p. 804.

( 854 )

The coordinates of the centres 2, ... 2, can be situated in all the
parts of a space V” where
(a, — HY + (Yn— pm)? + (4. — a) >o. . . . (la)

In my dissertation I have shown that with the help of this
function the pressure of the gas can be expressed by the form

_ pT _dlogw Z e *
pT nD — n? — =a HOP N13: he Ee ees os eat)

dn

In this formula n represents the number of molecules pro unity
of volume. The function w depends on n and 6. From a simple
dimensional consideration can be shown that w must be a function
of no*. In my dissertation I have calculated the three first terms of
a serial expansion of this function.

It is worth mentioning that the same function plays a role when
p is ealeulated by the method of virial and that it appears too in
the theory of mean free path. For the total surface of the part of
the spheres free for a collision, the quantity which Ciausius represents
by S can be expressed as a function of w. Prof. Lorentz fixed my
attention on the fact that such a relation exists. The equation of state
calculated by the method of virial takes the form

3 1 shat ie Geel ee CO
pe BG =e Sessa) TMS) eters ((3))")
the virial of attracting forces being neglected. In order that (2),
where @ must be put 0, and (8) be identical it is necessary that

d log »
Vi doy 1 ras

= — 6—n —e

o dn
It is easy to prove this relation.
I shall represent the integral (1) by x (m, 0). In differentiating with
respect to o we find

1?)

A

Oy(n , oO wo

Ox(n » 0) ——i Vn ml ==

00 00
and taking into account that w is a function of no*, we obtain
Ox(n , 0 3 dlogw
ok EE Oe ee a" 5 eet) soem op

00 o dn

The differential coefficient can also be expressed with the help of
the free surface S. We shall determine the change of x(n, 6) if 6
increases with do. In order to determine the variation of (7 , 0),

1) For the deduction of this formula compare the translation of my dissertation
which will shortly appear in the Arch, Neérl.

( 855 )

which is caused by an infinitesimal change do we can presume
that either only the diameter of the first molecule or that of the
second, or the third ete. increases with do.

The variation of ¥(7, 6) then is given by the sum of the variations
of this quantity in those several cases, we therefore find dy(n , ¢)
by multiplying the variation in one of those cases by n. Supposing
that only the nt' molecule undergoes the variation, then the radii of
the spheres described round the centres of the m—41 others must

1 ids.
be increased by = do, and the variation — of y amounts to
1
— — Sdo
3)
and y (n—I ,6) remaining the same, the variation in question comes to

1
a5 x (n—1, 6) Sdo.

Hence
1
Jy (n, 6) = — 5 nx (n—I, 0) Sdo
and
dy, (n, 6) n
aie acing 0) Se ci ceoG) Clee A)

The combination of (4) and (5) gives
x(n, 0) 6 dlogw

——
x (n—1, 0) 6 dn

Taking into account that, as I have shown in my dissertation,

“A dloga
n, O
SL = 9(n) =Vwe a
xy(n—1,6) ~*~
we find
6 i “A d log »
d log a 6 dw i
S==— =n A) =— = a= 5
oO dn ot) 0) dae (9)
which agrees with the formula mentioned above.
Craustus') has shown that the mean free path is given by
4W = 4q(n)
= = (7)

MSV Sie
The quantity JW is the space free for the situation of the centre
1) R. Crausius. Die kinetische Theorie der Gase p. 46—83. This formula can
also be obtained by means of statistical mechanics. =
57
Proceedings Royal Acad. Amsterdam. Vol. XIV.

( 856 )

of a molecule in a system of 2 molecules, i.e. the quantity which
we have represented by g(n).

The mean free path /, for the case that the intersection of the
spheres (of repulsion) is neglected and where g(n) is made equal
to V, amounts to

V ]
"nme /2 nx0*//2

Introducing in (7) the value of g(n) which follows from (6), and

using the abbreviation 7,, one finds

2 1
=—|—- 20 |l OR gts Poy oo.
( 30 \) aes (®)

These expressions can be used to put the equation of state in a
new form. Substituting for / the value following from (8) we find

; 2 l
prin (1 a 3 xo° Nn =) — an".

If we have to do with a gramme-molecule of the gas we have

ae LE Gane
a) a — — 3
ae 2 Vat eral

The quantity 6 is the known constant of van per Waats, «NV?
is equal to his a, NV being the number of molecules for the gramme-
molecule. Prof. KounstaAmm') has deduced a similar relation, however
without indicating rigorously the relation, existing between the free
volume and the free surface. The fact that there exists such an
intimate relation between these quantities shows that each further
approximation ef one of them allows to find the following approxi-
mation for the other. At the same time it is shown that the method
of statistical mechanics gives the most simple calculation, as all is
reduced to the determination of one function @ and to the differen-
tiation of this function.

Groningen, Dec. 1911.

Meteorology. — “Vhe relation between changes of the weather and
local phenomena’. By Dr. J. P. vAN DER Stox and P. H. GALE.

(Communicated in the meeting of Januari 27, 1912).

1. Every one whose daily task it is to formulate expectations
concerning the coming weather, knows that the theory of cyclones,
based upon the conditions for steady motion, is of little use.

What he wants to know is what happens, or at least what may
happen, when the situation alters with the time: whether the centre

1) Kounstama, These Proc. VI, p. 787 and p. 794.

( 857 )

o* the cyclone is filling up or receding, deepening or approaching
or, also, whether the centre moves along the are of a circle, distance
and intensity remaining the same.

Obviously if, in the latter case, the velocity of rotation is of the
same order as that of the earth’s rotation, the effect of the latter
may be lessened so that the angle between gradient of pressure and
winddirection becomes smaller or is reduced to zero, or, also, that
this effect is increased thus causing an angle of deviation greater
than the normal value.

On the other hand a disturbance of the equilibrium between the
three concurring forces: viz. pressure gradient, influence of the earth’s
rotation and friction caused by a decrease of the gradient force
must become perceptible as an apparent increase of the effect of
the earth’s rotation and friction, from which results an angle of
deviation and a proportion between windvelocity and gradient force
greater than in the case of normal adjustment.

When these influences are such that their effect becomes clearly
visible in the comparatively rough observations (estimation of wind-
force according to the Braurort scale and of direction in 16 points)
as inscribed in a weather chart, for rates of variation corresponding
to actually occurring velocities of variation, then these effects would
afford a means of drawing conclusions concerning the coming weather
based on deviations from normal values, i.e. on purely Jocal phe-
nomena; the normal condition being defined as what occurs when the
‘motion is steady.

2. In order to investigate in how far these deviations satisfy
the conditions for practical use, let us consider the simple case of
currents moving in horizontal planes, i.e. when the isobars are
straight lines or, also, curvilinear but then at a considerable distance
from the centre of curvature where the vertical motion is nil.

Choosing the place of observation as origin of polar coordinates,
and assuming that, at that distance from the centre, the terms:

Ov Ou
oleae and » >
may be neglected, the equations of motion become:
a

If now: the problem is restricted to the question what happens at
57*

( 858 )

the point of observation (r= 0), all terms containing the angular
velocity :

00
u—=r—
ot
vanish, except :
Uv 00
— = v—
r Ot
and the equations assume the simple form:
) 19,
= + knv = —-<
; Oi Laces. Wear Leo)

where v indicates the windvelocity,

4 the direction in which the air moves, counting from North to
Kast.

a=2sing , p= geogr. lat. of the place.

n the angular velocity of the earth = 7.29>< 10,

kn = / the frictioncoefficient,

p the atmospheric pressure,

o the density of the air.

If we wish to know the coming variation for a short time only,
we may choose an arbitrary function for the gradient such that the
integration is easily effected.

We assume that the variation in intensity of the gradient can be
represented by the function

eqnt
and that the variation in direction can be represented by a uniform
rotation with an angular velocity sn counting clockwise.

Then, if 8 denotes the angle between the gradient and the North
direction at the time tO, the equations (1) become:

Ov
= + knv = Het cos (9 — 8 — snt)

: v ( an — =) = Hei" sin (6 — B —- snt)

They are satisfied by the values :

a Heat

EE OF Fea
from which follows for the angle of deviation :

v

0 = 06, + snt

so that we

( 859 )

tang (0, — 8B) = tanga =

may also write:
H

~ n (k+4q)

egnt

C3 —

a—s
k+q
HAH ejnt ;
sin & .
n (a—s)

(3)

(4)

The other part of the complete solution, derived from (2) by
equalizing to zero the terms on the right hand side of (2), can be

TABLE I.

Angle of deviation. Departures from normal values.

! Wind backing
ee
—a—0.75a — 0.5a —0.25a
| 59°

40 | 42 | 44 | 46

Wind veering

= eee
0 + 0.25a +-0.5a +0.75a +a
| | |
CAST 225 Oko: | LOLS) 1222
50 55 64 84 | 122
32 32 32 32 | —

14 9 0 20 | 58

0 8 20 37 58
12 zo | 30 | 43 | 58
20 | 27 | 36 47 58

5S

EN |! 5) MN ZO I Ze)

Bon Ws el) SE) | 58

Proportion of windvelocity to normal value.

jth | Sea Se

! 0 4) 3S | 13

| 6 TO) | Ls; | 20

| 12 | 15 | 20 | 25 :

TABLE II.

| Wind backing

|| —a—0.75a —0.5a —0.25a

!

| 9.6) 0.6) 0.7 | 0.8

| COD CaF |) Occ |) wae,

| 0.6 | 0.7 | 0.8} 0.9

|| 0.6 0.7| 0.8] 0.9
0.6| 0.6| 0.7| 0.8
OSs | CH || Oa7/ | Ose}
O=s, | 10.6) 0260), O.7
Oss: Ons) O25 || (0.6

|] 0-4] 0.5 | 0.5] oF

Ih }

Wind veering

SS eS ——
0 +0.25a +0.5a +0.75a +a

2

tee] AES le TTe le. 19
Ht 0.5) |\ 92.0) 2°9:)h3:8
Teoaeteas | aaa. |
Lal 15 2.0, 2.9| 3.8
AEOM alc 2h ode Se!) 64.7) 11.9
0.9 1.0. 11 Le2F ote3
0.7 | 0.8) 0.9 | 0.9 | 1.0
0.6} 0.7 | 0.7 | On| 0r5
0.6| 0.6 | 0.6 | 0.6) 0.6
| |

( 860 )

left out of consideration. Its meaning would be a superposed wind
of arbitrary velocity :
Ce—kt,
gradually waning under the influence of friction and rotating with
an angular velocity an.
If we define as normal values:
a ios a, 7 sitian

tanga = — and Vi = — =
ae k : mele n a nV} Eye

then
v k cose a sina Veta

V5 (k +q4)cosa, (a-s)sina, = V (k+-¢)? + (a—s?

Tables I and If exhibit the quantities a—a, and ’/,, calculated for
different values assigned to q and s, for a latitude of 52° N and
the value 4;=1, corresponding with a normal angle of variation:

(geet 0)

Positive differences and proportions greater than unity are printed
in heavy type, negative differences and proportions smaller than
unity in italie type.

The values given to gq and s in the tables correspond with the
following rates of variation :

Time necessary for Rate of

in- or decrease with rotation

50°/, in hours. per hour.

q=—2 1.32 s=—a = 93%

—- 41.5 1.76 — 0.75a -—17.8

—1 2.64 0. 5a — 11.9

— 0.5 5.28 — 0.25a — 59
0 -— )

0.5 3.09 0.25a 5.9

l 4.55 0.50a 14:9,

1.5 1.03 0.75a 17.8

2 0.77 a 23.7

The results given in the tables lead to the following conclusions :

1. An angle of deviation greater than the normal value mostly
indicates a decrease of the gradient force; too small a deviation an
inerease of this force; when the direction of the gradient is veering
the differences are considerably larger than when it is backing.

2. A windvelocity greater than the normal value generally.
indieates a decreasing gradient and veering wind, and is often
associated with abnormally large angles of deviation.

( 861 )

A deficient windvelocity, together with too great an angle of
deviation is an indication of an abating and backing gradient.

A windvelocity smaller than the normal value combined with too
small an angle of deviation always indicates an increase of the
gradient; when the wind is backing, the negative deviations are
smaller than with a veering wind; the latter case only obtains when
the rate of variation is very great.

In applying these rules two cases can be taken into consideration;
firstly when the isobars are straight lines; then an increase or
weakening of the gradient is not necessarily associated with a rising
or falling barometer at the place of observation and its variation
may merely indicate a crowding or dispersing of the isobars in the
pressure field.

When, secondly, wind and angle of deviation are evidently under
the influence of a distant atmospheric depression, then an increase
of the gradient may denote a deepening of the depression, the distance
remaining the same, as well as an approach of the centre, for accor-
ding to the theory of cyclones, the pressure gradient in the+ outer
part of the cyclonic area varies inversely with the distance from the
centre.

The relation of windvelocity and angle of deviation to their
normal values at places situated around the centre will then enable
us to discriminate which of the two cases obtains.

A decrease of the gradient, i.e. a negative value of gq, therefore,
in a cyclonic field, is an indication of a rising, “an increasing
gradient of a falling barometer.

Too strong a wind, mostly associated with too large an angle of
deviation is an indication of an increasing distance of the centre of
depression accompanied by a change in azimuth in the clockwise
direction, and a rising barometer from right to left when standing
with the back to the wind.

These rules for weather forecasting (or rules otherwise formula-
ted and based on the data of the tables) correspond for the greater
part with the rules advocated in several publications by Mr. GuriLpert.’)

In some respects they are more complete in so far that the case
of rectilinear isobars has been taken into consideration, when a rise
or fall of the barometer need not occur, and also because here the
influence of a rotation has been pointed out. In West-Europe where
the weather depends upon the motion of centra of depression, often

1) G. Guitsert. Nouvelle méthode de prévision du temps, avee une préface par
B. Brunues, Paris, Gauthiers-Villars, 1909.

( 862 )

moving with great velocity in the Norwegian sea or in the Channel,
this factor is certainly of some importance.

The weather rules, as found by GuILBERT in an empirical manner,
may therefore be explained on rational mechanical principles and can
supply valuable insights and indications, provided it is kept in mind
that they are applicable only to places situated at a considerable
distance from the centre of depression and when the rate of varia-
tion is rapid.

Only then the deviations from normal values will be sufficiently
evident, but in such cases they are of considerable value as they
enable us to ascertain and timely signalize rapidly evolving variations
which otherwise would perhaps have remained unnoticed.

In the neighbourhood of the centre the rules fail as well as the
formulae given above because there ascending currents play an
important part, and a slackening of wind and gradient may mean,
not an increasing, but a decreasing distance from the centre, as in
this area the gradient varies directly with the distance.

In practice the use of the simple rules is hampered by many
difficulties; the conditions are rarely so simple as implied in the
premises on which the computations in the tables are based and even
the simple case of two gradients, one of which of constant magnitude
and direction and the second variable (e.g. a constant centre of high
pressure and a centre of depression moving with respect to the first,
which often occurs) would lead to formulae too complicated for
practical use. Moreover it is difficult to estimate at first sight the
direction and magnitude of the gradient, the estimation of wind force
and direction is a source of uncertainty and it is difficult to ascertain
what values are to be considered as normal.

3. Although the fact that GuiBerT has found these indications in
a purely empirical manner is a proof of their usefulness in practice,
only a systematical application extended over a considerable time can
lead to a reliable estimate of their merits, and such experiments will
be valuable only when the prognosties are subjected to a severe and
systematic criticism.

Even then it will be difficult to point out what gain the application
of Gumperrt’s rules has afforded because, in formulating the expectation,
now as before, various factors must be taken into account which
bear no relation to these rules.

In our experiment, some results of which are communicated in
this paper, the prognostics were criticized by dividing the area of
the weather chart into nine compartments by means of two sets of

( 863 )

parallel lines perpendicular to each other and by noticing in each
compartment what change in pressure was expected according to the
observed local symptoms.

This was done by the signs +- and —, with sometimes the addition
of the words “much” or “little”; also the symbols + and - were
used in order to indicate that the expected variations were small
(less than 2 or 3 mm.) in positive or negative direction. By drawing

TABLE III, Frequencies of percentages of success.

May 1910, June | gila|s een 3

12u]24ul120) 6 |S) | 2] ae S|

| 3 |e

Ue Web dbcme ly oll lpia tel i a Ua | ace
BD Mf eee yf yp ef a
es ace cls te ee =a ese en ee
ifi9 |} —| —| —| —]—)—| =} -}-|-}-)-]} -
2024} —-]-—| —]-|-]|/-}-) 1}-)-]-]-] 1
a9 |} —}—]—|—|-|-|-]- Bay --|—|| —
30/34 || — —}| 1/—}/—/—]—}|—] 1) -]=-— —|| 2
Secunia ees ee qh yf) Al 38
aac | SE Th | era a ee re ee (a
Ze |= al — | a =) ] a pe a Se 2
7 a 1| 2] 3 | | Sa) al ae
559 || 3/ 3] 3| 2| 5| 2/—| 2|/—| 1/-| —]) 16
6064 || 6| 4] 1] 1 ft) eas gil tei Sell) 24
G5/EN eye se| Os) Salen 535) 201 3.) 2) a 3)! 1) 3) 24
TOS NW ANT ese) oa) i eT| Seo] 21.3] 1 a1] 30
m9 || 3) 3) 7] 8] 6| 4] 3] 4| 4] 5] 2) 4] 2
goes || 2/ 1) 7] 2] 4] 4] 3] 5] 5| 6] 41] 4]) 41
Seat te than 5 os) al ol als |= 1a) sl 2
onom eo tl aes) SN P| BH ae
Os00e ect | ORI ee etl a |i 2) ¢
Total || 30 | 30 | 30 | 30 | 31 | 29 | 19 | 27| 23 | 23 | 9 | 28 || 249
Mean ||68.469. 1/71.9/77.6 72.8 71.5,71.2,71.3,74.3'73.5178.4|79.1|| 72.4

( 864 )

imaginary diagonals it was often possible to form a clearer image
of the future situation.

The experiments were made during the months of May to June,
October to December 1910, January to April and November 1911.
Besides these weatherforecasts also the desirability of boisting storm-
signals was noted.

With a view of obtaining numerical values for the fulfilment of
the expectation the chart was compared with that of the next day and
the following numbers were given separately for each compartment:

4 for complete success

3 ,, nearly complete success

2 ,, half suecess

1 ,, variation in the right direction, but too small
QO ,, no success.

During the months of May and June a critique was made up as
well for a period of 12 as of 24 hours afterwards. The percentage
of suecess for the total area has been calculated from the frequencies
given in the following table, from which appears also on how many
days in each month a forecast was made up.

It appears from this table that in May and June after 12 hours
the percentage of success was somewhat higher than after 24 hours,
as might have been expected. As the greater part of disturbances
come from the West and no stations are situated on the left side
of the westerly compartments (I a, 6, c¢), it is evident that there and
in the south-eastern compartment (IIIc) the percentage of success
must be smallest; this conclusion is contirmed by the following
summary :

ct,

TABLE IV.

I Il Il
a «65%, 75%, 77%,
b, 2 e707. | 70%). | eer)

CEP Out. | HIGH, | 3 162"),

The results of this experiment, separately for the forecasting of
wind, temperature and rainfall and concerning the relation between
gradient and windforce will be communicated in extenso in the
publications of the R. Meteor. Institute.

In making up these prognosties, founded on the observations in-
scribed in a weather chart, it is, of course, impossible to apply the
GuitBert rules without taking into account also the manifold other
indications suggested by the synoptical image.

( 865 )

A better idea of the profit to be gained by the application of
these symptomatical indications might be gathered by determining
the percentage of success if a forecast were made exclusively on the
base of local wind observations and the knowledge of the gradient
for one given station, without consultation of a weather chart.

This has been done for the station Swinemunde and the years
1909 and 1910.

Magnitude and direction of the gradient were computed from the
barometric heights at the stations Hamburg, Whisby and Breslau,
forming a triangle in the centre of which Swinemunde is nearly
situated.

The method of criticizing the degree of success was about the
same as applied to the area of a weatherchart; the result was an
average success of 65.4°/,, which may be considered as a pretty
fair result of the method without the application of other means.

As to the signalling of storms, the result was favourable as might
have been expected especially for rapidly advancing disturbances, a
number of which could be foreseen considerably earlier than if the
relative windforce and angles of deviation were not taken into account.

Meteorology. — “On the angle of deviation between gradient of
atmospheric pressure and air motion.” By J. P. VAN DER Sto.

(Communicated in the meeting of January 27, 1912).

In a previous communication’) I have shown how the average
friction coefficient, and therefore also the average angle of deviation
between gradient of pressure and windvelocity, can be derived from
the semidiurnal variation of barometric pressure and wind.

As a result of this inquiry for two sets of observations made at
de Bilt and on board the lightvessel Terschellingerbank, it was thus
found that the angle of deviation computed according to the well
known expression for steady motion

2nsngp a
2 SSS SS

Ueabd? MERC
fi» dsmegel = ik
y = geogr. latitude
nm = angular velocity of the earth’s rotation
1 = frictioncoefticient

in winter and autumn was considerably smaller than in spring and
summer.

1) These proceedings : Meeting of May 27, 1911.

( 866 )

If we assume that this result is not due to disturbances in the
expressions for the semidiurnal variation or to shortcomings of the
theoretical reasoning, if further we take into account that (at least
in our country) the angle of deviation strongly depends on the
direction of wind and gradient, then two explanations may be
examined.

Firstly it is possible that the specific deviation (i.e. the deviation
as considered separately for each direction) actually remains the
same during the whole year, but that the variability of the mean
deviation must be ascribed to the distribution of the \inddirections
in the different seasons.

The fact e.g. that in our country during spring northerly winds
prevail and that for this direction the deviation is unusually large,
must cause a greater angle of deviation in spring than for the
whole year.

Secondly it is possible that the friction coefficient varies with the
temperature and possibly also with the turbulence of the air; in this
case the specific deviation would be a variable quantity in different
seasons.

With a view of putting these results of a theoretical treatment
to the test of direct observation, we can make use of the values of
the pressure gradient as computed for the hours 7" and 9'380™ a.m.
of each day from the barometric height at the five Dutch stations
which, since Mareh 1904, are printed in the daily weathercharts.

Its mean direction, holding good for de Bilt situated in the centre,
is expressed in 16 points and therefore has an uncertainty of + 11°.25;
in the original computations these directions are, of course, calculated
to a much higher degree of precision, but a simple consideration of
the weather charts shows clearly that angles of deviation of the
most different values are associated with gradients equal as regards
magnitude and direction; the use of more accurate values would,
therefore, be of little use and it is only from a great number of
observations that reliable average values can be derived.

After some trials it likewise did not appear desirable to consider
those cases only in which the gradient exceeds a given minimum,
as frequently the value of a small gradient is evidently accurate
and, conversely, for large gradients the complicated general situation
and irregular curvatures of the isobars give rise to unreliable results.

Therefore, in the following investigation, all observations of the
angle of deviation computed during the period March 1904 to
December 1910 for the five stations are used, without considering
the magnitude of the gradient, with the exception only of those rare

( 867 )

cases in which the values were greater than 135° or smaller than 0°,

Further it is assumed that the same direction of gradient, holding
good for de Bilt, may also be used for the other stations because
the radius of curvature of the isobars generally is large in com-
parison with the distance between the different stations.

In table I the frequencies of the angular values corresponding
with different directions of the gradient are given for the central
station de Bilt.

TABLE I. Frequencies of angle of deviation, de Bilt, 1904—1910.

1]

De | ® 222-5) 45° O75 90° nt20.5 135 | Totat
N || 20 | 98 la02 | 165 | 67 | 17 | 9 || 578
NNE - || 19 | 60 | 105 | 158 j 101 | 17 | 9 || 469
NE } to | 14 | 47 [103 | 111 | 46) 9 360
ENE || 2| 4 | 2 | 73 | 73 | 38'| 4 || 218
E | — | 6 | 16 46 60 | 23 | 9 | 160
ESEMGe |e 2 |) a2) 34] 25 | 13' 4) -3%|, 101
SE | 1 Th | 4a] 55) 44 o | 1 | 131
Sse) = | fo | os | ee | on | as] a | 161
S | 2 | 13 | 7 | 70 30 | 7 | 6 || 207
SSW | 3 | 17 | 58] 73 | 99 | 16 | 7 || 21s
sw | 4 | 13 | 39 | 62 | st | 14] 3 || 106
wsw || 2 | 10 | 29 | 68 | 30 ) teh nil 1s
w Hee te |, #53 gsm ese = era Ih 206
wNw | 4 22 | 14 | 147 | 23 4 | — || 2
NW EONS GONE ee 1 || 377
NNW 9 | 80 | 246 ne AUST Folie | 579
Total | 87 | 386 227 1563 | 196 | 247 | 68 | 404

It appears from this table that the spreading out of the values is
considerable so that the simple relation between angle of deviation,
earth’s rotation and friction, as expressed in the foregoing formula,
is but rarely realized. In table II the values of the angle of devia-
tion are given as computed from frequency tables of the same kind
as table I for the five stations and 16 gradient directions.

( 868 )

TABLE II. Average angle of deviation for different directions of gradient.

Pipetion | Groningen Helder de Bilt | Flushing | Maestricht
N | 62°.9 68°..6 54°.7 63°.0 50°.8
NNE | 69.4 81 .1 61 .7 64 .9 49 .9*
NE | 82 .4 93 .1 15:23 81 .0 54 .8
ENE | 81 .4 94 5 80 .2 94 .0 10 .3
E | 82.7 93 .7 82 .3 92 .3 70 .9
ESE | 8-9) |) saa 135 86 .4 i
SE e140 84 .0 73.3 85 .0 67 .9
SSE 76 .8 feb oll 710 .6 71 .0 59 .0
S 79 .0 ma’) 641 69 .4 57 .1
SSW 15 .4 70 .5 66 .5 62 .2 52 .8°
SW ase |) We 68 .8 61 .0* 55 .3
wsw || 64.1 | 65.3" 68 .4 65.7 69 1
Ww | 64.0° | 68.5 | 63.1 65.4 | 72.8
WNW || 68 .1 2079: sees) ae Oe | 68 .8
NW | 64.2 | 66 .6 Babe) 1 88270) 25 62 .5
NNW || 60 .7° | 65 9" | 52 .9* 61 use |) 52kee
ae :
Mean 67°.9 71°.3 | 66°.9 | 72°.7 | 61°.6

For the first four stations the principal maximum is situated
between the directions NE and E of the gradient; the principal
minimum is spread out over a larger area but mostly associated
with N and NNW directions; secondary maxima and minima occur
more or less distinctly at all stations. Maestricht shows a consider-
able divergence from the other stations as there two equivalent well
defined maxima oceur for the directions ESE and W, and two
minima for the NNE and SSW directions.

The differences between the extreme values amount to: for
Groningen 22°, Maestricht 28°, Helder and de Bilt 29°, for Flushing 338°.

As has been pointed out in another communication, these large
differences can be ascribed to the fact that in our climate steady
motions are of comparatively rare occurrence and that then the simple
formula is not generally applicable

A westerly gradient often indicates an approaching depression

( 869 )

associated with an increase of gradient; an easterly gradient intimates
an increase of distance from the centre with a filling up and extinction
of the depression.

In the first case the tangent of the angle of deviation will be
larger, in the second case smaller than the normal value owing to
an apparent increase or decrease of the friction coefficient.

When northerly or southerly gradients obtain, the eastward move-
ment of the centre of depression is associated with a rotation of the
gradient with constant magnitude and the effect of this rotation
must be equivalent to an apparent decrease or increase of the earth’s
deviating force; this explains the occurrence of two maxima and
minima. The distribution of the different values for Maestricht finds
a ready explanation in the fact that this station is situated in the
river basin of the Maes where the friction experienced by N and S
winds must be considerably less than for E and W_ winds.

In table III, showing the values of the angle of deviation cor-

TABLE Ill. Average angle of deviation for different wind directions.

RT ES RE CS ey ee ee

Direetion| . | | | | Magnetic 14° West
; Groningen Helder | de Bilt | Flushing Maestricht |
Wind | | | | Helder | Flushing
N | 82°.4 | 93°.8 | 779.4 | 929.5 | 710.2 | 94°.4 93°.6
NNE |) 77.5 | 88.0 i730 | 86.2 | 6.0 || 02.2 90-1
NE | Tee | Slo NoTly 0: | “T6..8 58 .2 eS (0) ES XG
ENE TeG) || ciie 5 6\64 4" | 601-6) || 54.16 99.8 | 0.6
E 169 file 66.6 | 1.9 | 54.3* |) 77.2 | 66 .3
ESE || 73.5 | 70.4 |68.7 | 62.1 | 5927 10/15, || “ell -4
SE || 64 .1* | 65 6") 68 4 | 65.7 || 63 .4 Estee llosiG
SSE || 64.5 | 68 .4 | b2ece Gee | 7200 Ico 6 | fEs.6
S GSO) 70 Gn Sisal Geen | 69.1 || 69.2 «| 67 3
SSW 63.6 | 66.6 | 53 .6*| 70.5 | 58 .6 | 70 .6 | 70.3
Sw Gli cori ee0 62 cir S19 || 66 is 67 .0
wsw || 62.6 | 68.5 |57.7 | 63.3 | 50:1" || 67.0 | 62-5
WwW 68.6 | 76 .2 63.9 | 66 .0 Bopleea| a 12 63 .1
WNW || 76.9 | 84.2 172.4 | 5.4 | 60.0 .|| 79.3 TR
NW 8220) | | 20s mea stg: «| 69.2) ||, 87.12 TI .5
NNW |} 81.9 | 91.2 |81.0 | 92.5 | 70.8 | 93.4 | 87.4

( 870 )

responding to different wind-directions, this effect is more clearly visible
than in table II; it is derived from the latter by linear interpolation.

This proves that the variability of the gradient in direction and
magnitude may be regarded as the principal cause of the spreading
out of the angles of deviation, but that local circumstances also play
an important part and the friction coefficient 4a is certainly not the
same for different directions.

When N and NNW winds obtain the path of the air particles
mostly traverses a sea surface where friction is small; but this is,
to some extent, contradicted by the fact that, if the wind is SW,
when it also blows over the sea (although to a smaller degree), a
minimum rather than a maximum value of the angle of deviation
is observed.

TABLE IV. Values of the angle of deviation, de Bilt.

Frequencies | Angle of deviation
Direction|| 5 tp 2 = | Ss 90 2 =
= = E 2) Se = 3
Gradient} = im a Z | 3 a Pa ,
N | 486 | 323| 439) 378 | | 55°.4 | 61°.7 | 572.8" | 50°.2
NNE || 413| 298| 388 | 308 | 61.9 || a 2) lve? eb somes
NE | 282) 242 | 305) 218 | 65 .3 | 77.5 | 10.6 | 63 .5
ENE 154} 199] 234] 151 | [95 2518.1" ):800ede agibaee
E 50| 147| 175] 107 | | 82.4 | 80.8 | 78 .0 | 78 .6
ESE 35| 128) 131| 98 | |83.25 | T6ct | 744 1 7alee
SE 4o| 145| 119) 80 || | 74.2 | 72.9 | 69 .4 | 74.1
SSE TT, 1718) 133))), wild 68.7 | 70.3 | 66 .3 | 68.7
Ss 121 | 191) 122) 147 || | 63 .2 |70.4 | 67.1 | 64.6
SSW 133 | 189] 96) 188 | | 63 .3 | 70.6 | 66 .8 | 64 .1
sw || 121 | 158| 67] 207 | [50.200 7a.e1 noe |soueme
wsw | 108| 146| 69| 223 | 57.9 | 70.7 |90 24° 166 38
W | 149| 148] 99] 238 | 156.0 | 66 .4 | 67.5 | 62.8
WNW | 225| 205| 163 | 264 159 .9 | 61 .2 | 64.0 | 54.3
NW || 360| 268] 274| 328 | 55.3 | 58.3 | 60 .9 | 53.0
nnw || 450! 323) 396 | 365 ] 54 .2* | 58 .0* | 58 .6 | 48 .6°
| |
Total || 3204 | 3288 | 3210 | 3420 || Mean | 64°.7 | 70°.0 | 67°.8 | 64°.3

(Sit

As might have been expected, the difference between land- and
seastations is clearly visible in the general mean values of table II;
the most inland station, Maestricht, showing the smallest value viz.
68°, Helder, the most maritime station, the greatest value viz. 77°.

When we ealculate the angle of deviation for different gradient
directions and different seasons (Table IV), the frequency of occurrence
becomes often too small, principally for E-—-S directions and in
winter. Therefore, as has been indicated in Table IV, all frequencies
have been taken together for each set of three subsequent directions,
so that the computed average values bear relation to an angular
area of 67,°5 and not of 22,°5 as those of the foregoing tables.

Even then the number of observations in the SE quadrant is
hardly sufficient, but still the average values run in a continuous manner.

TABLE V. Values of the angle of deviation.

Groningen Helder
pire sion | Winter | Spring |Summer) Autumn | Winter | Spring |Summer| Autumn
N OZEES a NOSSe 2) OST I OLOo in| 692.6) ||) 682.9) 169°. 1 78°.2
NNE OSP4an eter OOme SiO) oll 1Onrale se1Oe-0% | 138.4 90 .2
NE oye Aan Soe Ola| IanO) |p ionOn NeSia.8: 86) <1, | 82.2) 1100020
ENE Saw soe SSE Ole) dsai2y ale S0ms0- 1) 94e00) 1 93p.7% ||| 89) 53 98 .9
E OOM noo 4) elon On eiie.8 980.69) 93924" 1, 89 4 96 .4
ESE || 92.9 | 84 .4 | 70.7 | 80.3 |101 .9 | 89.6 | 84.1 | 90.8
SE ORT en GSOme li | OOo lies erie dun 98) On eSSer Ome sila 80 .3
SSE SSMS eal Si les Ole sae | ome 5) || GOmsO) Neeleh 120.8 79 .6
S SOR es om Sre ilk ain polaron | Micaela we 56S G 716 .8
SSW Sie Ol iden NOON. Omni Ome Ole ||" Tits Ome lle 4e ul 65956) 14 .5
SW CORO elmer NOOR Camel Sm Ob mile 45869) -30 590 40% i Ones
WSW | 64 <8 |69'-3 | 68.2) || 66 21 Tie GON 9S) 66N.2 68 .1
W 159.8 | 69 .1°| 74.5 | 64.3 || 64.8 | 69 .4 72 .8 69 .2
WNW || 59 .3*| 69.5 | 74.7 | 61.8 || 62.1 | Warell as 83 65 .1
NW 59-5) || 68) 6)" |(§69Re 5) (9595.1 Goes ete Sia | Saco 64 .4*
NNW _ || 60 .0 | 66 .6 | 66 .6* | 57 .9* || 63 .3 | 69 .0 | 69 .8 GineS
Mean 142025) 15ORGe | 10S.S) le lOPSinI9es3) | s1Os3% || 742.5 79°.4
|

Proceedings Royal Acad. Amsterdam. Vol. XIV.

( 872 )

In the same manner the angles of deviation for the other four
stations have been ealeulated and are given in tables V and VI,
for the sake of brevity without the corresponding frequencies.

TABLE VI. Values of the angle of deviation.

ep A OE NT ED

Flushing Maestricht

Direction | Winter | Spring leineigrien Autumn )) Winter | Spring |Summer; Autumn
N | 582.7 | 660.7 | @5¢.0 | 62.9 || 479.4 | 52°.3° | 579.4 | 45°.2

NNE | 66 .4 l69 .9 | 67.2 |.69 3 || 48.7 | 55.8 | 54 .8°| 46 27

nE ||74.8 |79.4 175.5 |75.2 |[54¢.9 |60.8 |58.4 | 49.1

ENE || 86.5 | 87.6 | 86.5 | 88 .5 | 56.9 |67.7 | 65.0 | 58 .2

E 96.3 | 93.2 | 88.6 | 94.2 |! 66.5 | 73.0 | 67.2 | 75 .4

ESE || 92 .9 | 87.8 | 82 .2.| 96 .6 || 62.7 | 70 .4 | 65 .4 | 77.9

SE | 82 .6 178.1 | 75.286 26) || 58.3). 63. 8) [oles Slama ee

|

SSE | 7.0 | 1.2 | 72.5 | 78.7 | 56.1 | 61.6 | 59.0 | 64.8

S es .2 | 64.6 | 69.2 | 70.7 || 51 .9*| 58.2 |57.9 | 55 .4

SSW 63.0 | 62.1 | 66.0 | 66.5 || 54.0 | 57 .6*|57.4*| 52 2°
SW ! 58.3 [60 .1*| 64 .2*/ 66.4 || 57.0 | 60.8 [58.3 | 55.8

wsw_ || 64.2 | 64.4 | 64.6 | 63.4 || 67.2 | 69.1 | 69.2 | 61 3

Ww 68.0 (65.4 | 73.4 | 66.3 Weza7 i756 | Nzauon menime
wnw |l'64.7-|68 .4 | 74.4 |63°.9 ||62 0 |71.3 | 74.5 | Game
Nw || 568.7 (68.4 [71 <4 |e2)20 || 53.7 |eeu4 les ci |/P5omee
NNW 56 .5* | 68 .2 | 68.1 | 61 .5°|| 48.3 | 60.2 | 62.0 | 47.9

Mean || 70°.9 | 729.2 | 72°.8 | 73°.3 | 579.1 | 64°.1 | 63°.8 | 59°.2

Ii appears from the average values for all directions taken together
that the specifie angle of deviation is greater in spring and summer
for the landstations de Bilt and Maestricht but that, at the maritime
stations Helder and Flushing, as also at Groningen, this difference
is slight or nihil, while for Helder they are of opposite sign. This
result cannot be considered as final owing to the small frequencies
of some directions, and although for some directions the rule holds
good (e.g. for NW and NNW directions, Table VII), it fails for others
e.g. the K. direction.

( 873 )

TABLE VII. Mean specific angle of deviation for
NW and NNW directions of the gradient.

Winter Spring | Summer | Autumn
= 1 ]
Groningen 59°.8 67°.6 68°. 1 | 58°..5
Helder Oat Wee tO d Tee 6 | 65 .9
de Bilt | 54 .8 | 58022 59 .8 50 .8
Flushing ! DilpO 68 .3 69 .8 G22
Maestricht 1 51 .0 62 .3 65 .1 50) -2

The question in how far the distribution of winddirections in
different seasons may cause a difference between the average angles
of deviation can be answered by calculating not the specific means,
in which every direction is regarded as equivalent, but by giving
to each direction the weight of its frequency.

The values thus computed and shown in table VIII apply to the
period March 1904—December 1910 and the winddistribution during
these years.

TABLE VIII. Mean angle of deviation according to the frequencies
of direction, 1904-1910.

Winter Spring | Summer | Autumn | Year

|
Gronisent | 610.8 | 740.5 | 700.1 680.1 | 70°.2
Heldera Sail) gide.5e.| (166 Tome atin 0L Wi IG
de Bilt 60 .8 69 .0 6.8 | 60.3 63 .6
Flushing |) 65.3 Tie Chalpeizes7 a) 88... 6a.
Maestricht 53.5 62.9 | 61.9 | ee eee

|

It appears then that, with the only exception of autumn for Helder,
the average angles of deviation in spring and summer are actually
larger than in winter and autumn and that this phenomenon must
be principally ascribed to the distribution of winddirections.

As the meteorological conditions are extremely variable, a period
of seven years (1904— 1910) is decidedly too short to furnish wind
frequencies for different seasons which may be considered as normal
values, it is interesting to apply the results of tables V and VI for
Helder and Flushing to two series of wind observations extending
over 25 years and made on board the lightvessels Terschellingerbank

58*

( 874 )

and Schouwenbank situated in the vicinity of the two landstations.
Table IX shows the windfrequencies for magnetic directions, the
average deviation being 14° (Westerly).

For application to the data of this table, the angles of deviation
corresponding with magnetic winddirections are given in Table III
for Helder and Flushing.

TABLE IX. Frequencies of winddirection at two lightvessels,
pro 1000, magnetic.

Terschellingerbank Schouwenbank

18841908 1882—1906
Digeton|| w | spr. [Sune] a | w | ser [Sam | a
G | o4 | 51 | 56 | 27 || 15 | 28 | 36 | 18
N a7 Vest elas, etea alleraoi| es alee tetas
NNE 16 | 41-| 46 | 23 || 20 | 62 | 62 | 32
NE || 36 | 92 | 61 | 36 || 31 | 138 | 101 | 48
ENE 23) (1952.01) 405) 220i van |, aslo tals
E mises 95) 4! fol 59 ll a7) ede alae ates
ESE || 47 | 32 | 20 | 45 || 57 | 30 | 23 | 56
se || a0 | 45 | 29 | @ || 62 | 36 | go | 55
SSE | 35 | 22 | 18 | 43 | 36 | 24 | 18 | 34
S | 80 | 42 | 28 | 81 | 71 | 39 | 28 | 61
ssw || 64 | 34-| 26 | 53 || 93 | 39, | 28 | 72
SW “133 122 | 115 | 100 || 139 | 86 | 68 | 111

WSW || 64 | 58 86 62 713) 102) |. 132 70
W |} 138 | 84 | 111 125 82 71 | 130 90

NW Taha aS) OL 9] 484 a ||) WT 56 Gree eas
NNW Soni! 40 Neto 9 42 Neco. eae aes

The computation leads to the following results:
Winter Spring Summer Autumn Year
Tersehellingerbank 74°.5 77°.8 78°.5 75°.6 76°.59
Schouwenbank 10:0, 7329) 903.20) wale Oana ne
It appears then that, although at Helder ‘the specific angles of
deviation are greater in winter and autumn than in summer and

spring, still the total means follow the general rule, owing to the
distribution of the wind in the different seasons.

The angles of deviation as computed in this manner for Terschel-
lingerbank are much larger aid probably more accurate than those
derived from the semidiurnal variation of wind and_ barometric
height; from which we may conclude that these variations are
influenced by various disturbing elements so that a direct application
of theoretical reasonings is premature.

Physics. — “Contribution to the theory of binary mixtures.” XVIII.
By Prof. J. D. van ver WaAats.

(Communicated in the meeting of January 27, 1912).

In the preceding contribution some points have been mentioned
which deserve a fuller elucidation, and the discussion of others was
omitted, which I will now take in hand. In the first place it seems
desirable to me to discuss more fully in how far the course of the
isobars in connection with well-known properties of the spinodal
curve is sufficient to enable us to decide beforehand whether three-
phase pressure will occur for a mixture with minimum 77,,, so that
we need not attribute its existence to other unknown causes, and
that accordingly the existence of three-phase pressure must not be
considered as an anomalous phenomenon.

In the preceding contribution the question was put as follows:
has the spinodal line on the liquid side for mixtures with minimum
Ty one value for w where = is equal to O for this line, or are
there three values for « where this is the case, always for given 7°
Thinking that the calculation would not be feasible, I had intended
to try and answer this question for myself by a graphical way. And
I had come to the conclusion that the existence of 3 values had to
be expected 1 if the place where 7); is minimum is close to the
side, 2 if the range of temperature for 7% is not too small for the
components, and 3 especially if the value of the ratio of the critical
pressures of the components is /arge. And strictly speaking, calculation
is not feasible yet, and this will continue to be so until the equation
of state is known with perfect accuracy. Probably the intricacy of
the calculations will then prevent us from obtaining a result. But
if we content ourselves with an approximate calculation, and if the
quantity 4 is kept constant in the equation of state, and if quasi-

( 876 )

association is left out of account, an answer may be found to the
raised question in a simple way, which will enable us to see which
of the three causes mentioned which would promote the existence
of three-phase pressure, would have to be called the real one after
all. And. already in contribution [I I indicated the real cause.

For a mixture with minimum 7), there is always at least one
value of 2, for which for constant 7’ the pressure possesses a
maximum value in a point of the liquid branch of the spinodal line.
This point lies in the double point of the isobars. So it is required
for this that this double point exists. And as this point lies on that
side of the z-value for minimum 7%, which lies nearer to the
component with small value of 6, and not far from this value, we
are sure of the existence of this double point for the mixture ether-
water, at least at temperatures which do not greatly exceed the
minimum critical temperature of the mixtures, or which remain

: f : ' dp dp
below it. In this double point the two lines i = O and e) =")
dv) ax) y
intersect, and it follows immediately from the course of the isobars
that if we follow the line = = 0, the value of the pressure is a
= C
maximum, both for the liquid branch and for the vapour branch,
in the two points in which the said two branches intersect. :

If for the different values of w we draw this pressure for the
liquid branch, we should obtain a line with a greatest value, touching
the p of the loop-isobar. Whether this contact may be taken in the
mathematical sense of the word, is after all of no importance for
our purpose. There would probably occur a discontinuity in this

: ‘ : ._ dp ' its
p,v-tigure for the course of the line a 0. Also the spinodal line
passes through that point, and so this has certainly one point in

d,
common with the line ==!) As for the rest the spinodal line lies
av

Pa: : :
everywhere outside the line 0. the question might again be
v
‘put if it touches this line in the mathematical sense of the word.

This, however, is not of importance for our purpose either. But it
; dp . ; y
seems probable to me that the line spe in the v,c-figure is con-
av

tinuous in the considered point, but the spinodal line discontinuous,

: ; eee. ap ;
because it has only a single point in common with —-=0. On the
av

(877 )

d : :
other hand the line == 0 is discontinuous in the p,e-figure, and
av

3 ; : dp
the spinodal line continuous. Then 7 would really be = 0 for the
av
the spinodal line in the mentioned point, as I have always put in
my former communication. But as I observed already above these
problems are not of practical importance for the investigation which

I wanted to carry out’).

\) A discussion carried on during the correction of the proof, but which has
not led to agreement, has even led me to doubt the continuity of the v,x-figure

d : :
for the line 7=0 in the double point of the isobars. In this double point both

v

dp . 0
dv and dp are zero, and a assumes the form 0°
av

It is true that for the determination of the loop-isobar we have started from
dp x :
the value - =0; but this does not alter the fact that in the result repeatedly
Uv
new values appear for some quanlities, which at first we had not assigned to them.

: dv dp } Sah ee
As an example I mention a) . On the line = =O this quantity is infinite,
Av av

Pp

and on the line = 0 it is 0. The result is that in the’ point of intersection 2
dx

: 4 d’y
more new values ap,ear besides. In the same way the quantity E ] . On the
OES
P

first line it is infinite. Moreover if is equal to O in the double point, and has
besides two more new values.
There are oiher difficulties attached to the existence of this point. The quantity
GEN Se ee dp i?
iz is infinitely great on the line | =0, and it is equal to zero on the

da ] pT adv

spinodal line. What is its value in the point that these two lines have in common?

dp
dv dx
As d

v . . .
~—] =—-~,>—~ we find the ratio of the quantities to which we had intended

x Ptah he dp
dv),

to assign but one value equal to O, infinite, or zero, or equal to two different
values.
I have finally, however, convinced myself that also the spinodal line in the

; : beat : Be fu
v,a-figure is continuous and touches the line = = 0 in the double point of the
dv

isobars. A proof of this has been furnished to me in the discussion mentioned

in this note, but-this proof seemed to me only valid when a priori we assume

the continuity of the spinodal line in the v,x-figure. | have now convinced myself

of the contact in the mathematica! sense of the word by the following consideration,
It follows from the eqration of the spinodal line that;

( 878 )

Only, now that I do eall attention to these questions, I think that

dp é 2 \ de)»
dv dv }p

dw dp 2
dae iC oe (=)

Up dv
or if = —=(0) & =o. Then the two branches of the p-line, which lie both on
av

dx},
the left of the double point, are considered as belonging together, as should be

done. Now:
dp
dv dx),

dx, 7 dp
dv ),

And numerator and denominator being equal to zero:

d*p (dv d*p

eS +- =

dv __ dadv\ da) sin dx

dx}, = d*p dv ce d*p

dv? \ dz), pin dedv

But because ee) =o, the denominator is equal to 0.

do = do dp
dx) spin aaa

And so there is nothing left but to assume for both lines, viz. spinodal and

And then:

d
@) = 0 discontinuity in the p,x-fizure, or to investigate this.
av

ps 10
This proof would not be valid if a was really indefinite in the double
av
point. But as appears in the differentiation of p with respect to v, x being kept
constant, this quantity does not admit of any indefiniteness.

Now we can easily derive:
dv 4 dv
dz»), dx,/), :

=) dv 1
da, Oe dx a 2
dv dv re.
when {| —— } and | —— ] represent the directions of the two branches of the
1 2

dv
addy Ax»
p-line in the double point.
And finally it has appeared to me that for every line that passes through the

2

dp . ap .
double point, the value aD is O, and that for the line ou =0O the value of saa it

da dv da?
not infinitely great, so that also in the p,a-figure the spinodal line is continuous.
So we must consider the double point, also for the direction of the X-axis, as
two coinciding points,

( 879 )

I ought to point out that the differential equation of the spinodal line :

pee aelan"
da? )yT dx ) spin\ dx? ]»T

does not justify us, as I putin my previous communication, in putting

aS diss eaes
equal to O in the considered point. Then — is, indeed, = 0,
Be

da 1 dx
2 I
but then it is perhaps also logical to put = infinite.
; dx*,T
1 7 : dp
If we put 7 above (7)1),in, then both the line = =——\()Seands the
v

spinodal line have split up into a lefthand and a righthand part.
Then there may be indicated two values for 2, on either side of the
# Of ( Tyi\min, between which there lie neither binodal nor spinodal
lines, and also two values of xv, wider apart, inside which the line
#0 no longer exists. And also the double point of the isobars,
v

which lies on the side of the component with the smallest value of
6, has been shifted further to the side of that component. But at the
value of 7’, which is equal to the critical temperature of the remarkable
point, the limits of 2 between which there are no binodal lines, no
spinodal lines, no points of the line 2 0, have overtaken each
other. On the side of the component with the greatest value of 6
that component has perhaps long been reached, but on the other
side the said limit has extended to the double point of the isobars.
In the z of that point we find then: 1 an extreme point of the line
7 0, and that one for which the liquid branch and the vapour
v

branch have merged into each other; 2 an extreme point of the
spinodal line, and that one, at which the liquid branch and the
vapour branch have united; 3 a similar point for the binodal line;
4 a double point of the isobars.

In the v,2-diagram the 3 first-mentioned lines have a vertical
tangent, and also one of the branches of the loop isobar. So it is,
indeed, a point with remarkable properties from a mathematical point
of view, and no less from a physical point of view. It is a point in
which a binary mixture behaves exactly as if it were a simple sub-
stance. It is that point that I have always called the remarkable
point in the previous communication. The plaitpoint temperature of
this point satisfies the same relations as the critical temperature of

( 880 )

. a 8 ay , mn 8 ay
a simple substance. So we can put ae for R7).and the value 5— =
at Oy 20 by

dp . ;
for px. At that temperature and in that point “P is then with perfect
ax
a6

certainty equal to O for the spinodal line, and ( 4 = 0. though
Ak pr

dv ae ae
— is infinite.
dx? ],T

Now it was the question in the preceding communication whether

= for the liquid branch of the spinodal line could, moreover, be
equal to O in two points of the said spinodal line that lie further,
and then in two heterogeneous plaitpoints. By a graphical way I
concluded to the existence of a point for the case ether-water where
the spinodal line would possess a minimum value of p and so where
a plaitpoint of the 2°¢ kind would be present. But as the existence
of this plaitpoint required that another plaitpoint of the 1st kind
was to follow later, | have assumed this existence as a certainty,
though I must confess, that I could not have concluded to it from
the course of the isobars alone. This is what I meant when I said
above that besides the course of the isobars also the knewledge of
properties of the spinodal line is wanted. I have since tried if the
existence of that plaitpoint of the 1s* kind, where p again possesses
a highest value, could be derived from the course of the isobars,
without our having to take into aecount a property as the one
mentioned. But this attempt has failed. And I have been confirmed
in the conelusion that as I had already put in Contribution II, the
circumstance from which the necessity of the existence of the two
heterogeneous plaitpoints ensues, is to be found in the existence of

aw ; 2 ; dp
the curve |—— ]=0, which intersects the line —=0O. As may be
;

dx* J oT dv
seen from fig. 8 of Contribution II, the spinodal line is suddenly
pushed far back to smaller volumes or greater pressures over a

‘d?w
certain width in consequence of the existence of the curve (

= | ==(0):

Qe” / oT

But from the plaitpoint of the 2°¢ kind to the component with the

greatest value of 6 the spinodal line continues to pursue its usual

ih ==!0: An
dv

this it was exactly what I had sueceeded in concluding from the

isobars. That the said curve still exists at temperatures above 7%, for

course, and remains at a-small distance from the line

( 881 )

l : ; :
ether and still euts =? is to be ascribed to the difference in the
v

size of the molecules of water and ether. I have discussed this curve
and its influence in Contribution III.

There it can appear how difficult it is to account for its influence
in the different cases. The temperature of the disappearance of this
curve, at which it has contracted to a single point, is in the notation
of Contribution II]

aa

Fe dx? —")
. MRT, = — a(l—a ——.
b (1+ y)?
If according to the little table occurring in this contribution we
take with the ratio of the size of the molecules 5, for z a value
somewhat smaller than 0,4 and y somewhat greater than 0,358, we

: ie 1 dether 4, +a, —2a,
find for

: a value of about
(7 kether 2 by Cether

aa]

2 fe
. This may

yield a value for which is greater than 1; but this formula

lanl

kJether

is entirely based on the approximate equation of state, and can only
be considered to give more or less an idea of the value of 7). Yet
the great ratio of the values of 6 seems to be the main cause of
the existence of the three-phase tension, by the side of the value of
la

a Whether there may be more causes for the appearance of two
heterogeneous plaitpoints, I do not know. I ean only state that up
to now I have not yet been able to find another cause for it; at
least for plaitpoint lines which join the two critieal points. And the
situation of the two plaitpoints is quite as it follows from fig. 8 of
contribution Il. The plaitpoint of the 1s* kind lies on the side where
the pressure of saturation at given 7’ is smallest, and the plaitpoint

2

; aw F
of the 2™¢ kind on the other side of ae u =O. So for ether and water the
AX

1st plaitpoint on the side of the water.

Also the coincidence of these plaitpoints is to be expected accord-
ing to this figure. So the point P,, at the temperature at which
dw : : oo dp :

—~=(), which lay entirely inside — =O at still lower 7’, gets
da? ; z dv vk
outside it for the first time. So this takes also place in the covered
region. Then the points recede further from each other with rise of
T. The point P.q above the critical temperature of ether and above
the temperature of the transformation when the transition from main

( 882 )

plait to branch plait has taken place, occurs when the plaitpoint of
the 2™¢ kind coincides with one of the 1st kind belonging to the
plait which makes its appearance for the first time in the critical
point of ether. I thought in contribution II that I had to find a par-

: : : dy ; :
ticularity in the behaviour of aS 0 also for this coincidence ;
x

but erroneously, as I have seen now. This coincidence must take
2

place with increase of the temperature, just when = () continues to
v

ae Gl
get further and further outside = 0, of course contracting more
: ;

2
and more then, and approaching to a single point. If a= 0 con-
Ca

d
tinues to get outside oO the two plaitpoints which lie on the
v

right and on the left of this curve according to contribution II fig. 8
move further and further away from each other. The lefthand plait-
point of the first kind approaches more and more the lefthand com-
ponent, in our case water. The righthand plaitpoint, viz. that of the
second kind, approaches the second component more and more, in

: Seah: dv dv d?v ‘d?v
our ease ether. In this plaitpoint | — } =| — ] and | — | =| —
dx } dx }g dc* ]y dx” }

according to the description in contribution II. But there is, moreover,
intersection of the p- and the g-line, so that the g-line on the left
side, before the point of contact, has greater volume than the p-line,
and afterwards smaller. I point out, what is perbaps superfluous,
that according to fig. 8 the first component would have to be com-
pared with water. But with further rise of the temperature and the
ensuing further course of this plaitpoint of the 2°¢ kind to the side
of ether caused by this, a new plaitpoint, one of the 1st kind,
makes its appearance, when ,7’= (7'p)ether 18 reached. Starting from
this moment there are 3 plaitpoints present. For this new plaitpoint too

dv dv a? v\ dv Ae :
— )—{ — )and{ —- | ={ — ] and moreover there is intersection.
dz}, dx} q dai) du? q

Sut this intersection is opposite to the preceding. The course of this
new plaitpoint is of course so that it moves further and further
away from the ether side, and approaches the plaitpoint of the
2ed kind.

Before the appearance of this third plaitpoint there existed only
2 plaitpoints at all temperatures above that of Pa,, a pair of hete-
rogeneous ones. I purposely say a pair, to express in this way that

( 883 )

they belong together, and together give rise to the binodal curve in
the v,z-figure which I shall call the binodal of Korteweg. And this
figure is then the representation of a branch plait, indicating partly
equilibria which are to be realized, and partly hidden equilibria.
Then the top must be found in the neighbourhood of the top of
aw
dx?
larger and larger dimensions with rise of 7’ — I should almost
say, it strives to become the only figure of equilibrium and it will
succeed. But before this has come about, a great deal must happen.
It is required for this in the first place that a new plaitpoint of
the 1st kind makes its appearance, and that is the critical point of
ether. To bring this about it is necessary that such a new plaitpoint
appears; for to be the only figure of equilibrium the plaitpoint of
the 1s* kind must get rid of the plaitpoint of the 2»¢ kind — and
this can only take place when the latter can unite to a pair with
a plaitpoint heterogeneous with it. Not immediately when this third
plaitpoint appears, is this new pair formed. It is required for it that
the temperature has been reached at which the transformation of
branch plait to main plait has taken place. At this temperature the
intermediate plaitpoint, that of the 2°¢ kind has got detached from
the first plaitpoint, and it has gone to the 3°¢. Now the first plait-
point has got rid of the heterogeneous plaitpoint, and has become
the top of a main plait. But now too this is not the only equili-
brium. There is still three-phase pressure and the main plait must
still get rid of the branch plait"). And also the way in which it gets
rid of it, has still a history. Properly speaking it has already got
rid of it, at least for the stable region, when the third plaitpoint has
got on its visible circumference. Then it is to all appearances
entirely master of the field, and the three-phase pressure has dis-
appeared. But internally, so in the region that is covered by what
has now become main plait, the two plaitpoints still exist which
must be considered as a pair from icansf Before this pair can be
annihilated by their being united to a double plaitpoint, they had
both to get into the hidden region, because a plaitpoint of the 2°4

= 0, and is then Jefthand plaitpoint of fig. 8. This figure assumes

1) That this transformation temperature is necessary, and has a rather great
significance, is Clear. But up to now I have looked in vain for the considerations
in consequence of which the way to determiné them mathematically, would be
clearly indicated. It appears, indeed, from fig. 5 or fig. 2 (These Proc. VII p. 626)
that at this temperature the point where the binodal line produced in the covered
region e. g. AB, meets the line BC, will have to lie on the spinodal line, but it
does not seem feasible to me to express this in mathematical form.

( 884 )

kind can never be found outside such a region. And at last at the
temperature of P.a, the plaitpoint that lies close to the top of

——= 0, is entirely master of the ground. Perhaps already at this

7

; drxyp
moment or soon after the whole line -— — 0 has already contracted
da*

to a single point, and then disappeared, and everything behaves
then as if there had never been three-phase pressure.
This description holds exactly for the system ether-water, but it

must be modified for other eases. Thus in eases in which both
2

: ‘ ay
P. and P.q lie above 7), the temperature at which aa gets
az

., dp os a
outside ae oO will lie above 7;,, and so also nearer the tempera-
v

{ure at which it disappears. But for the rest no modifications need
be applied to the above given description than those that naturally
follow from this.

Before 1 drop this subject, I will make one more remark. In
this description we have always started from the thought that a
plaitpoint of the 2°¢ kind belongs to one of 1s kind to form a pair
with it. Such a plaitpoint can only leave the plaitpoint that is
heterogeneous with it if there is another of the 1st kind present in
the field, with which it can unite to a pair, and the temperature at
which this tan take place, we have called the transformation tem-
perature. And I have also wanted to make clear the necessity of
this transformation. Of course a plaitpoint of the first kind can be
present by itself, but never one of the 2nd kind. The observation
of this rule will often show us at a glance what 7x or p,7-figures
are possible or impossible for the course of the plaitpoints. Thus T
have mentioned as a mathematical possibility for a 7\x-figure with
a maximum in front and a minimum at the end, the case that 7%,
would be smaller than 7%. If we considee this case in the light of
the just-mentioned rule, we see that this must be considered impos-
sible from a physical point of view. If we design such a figure, it
appears that then only one plaitpoint would be found between the
two critical temperatures, namely one of the second kind. To con-
sider this possible would lead to an absurdity. Then there would
be three-phase pressure, but there would be no top for the elevation
above it or for the plait that hangs on it. In the same way ap, 7-line

: : : . dp ,
must be rejected, for which the value of - would be negative for
€

the middle branch, viz. that of the plaitpoints of the 2n¢ kind.

( 885 )

Gal

dp 5 ; dp 4
When mas negative, — and — have the reversed sign. Though
a av ap

then the 7,z-figure need not be rejected, this would, indeed, be the
case for the p,x figure and vice versa. From this ensues that where the
T,r-figure has a maximum value for 7) the p,a-figure will also
have to show a maximum for p. In the same way for the value of
v for the minimum.

I will avail myself of this opportunity to discuss another question
about the shape of the plaifpoint line, the solution of which is not
only of importance for the discussed case of ether and water, but
for all the cases, in which three-phase pressure is found. This
question was first suggested to me by the p,7-figure for the system
ether-water of the preceding communications, and that in the following
form: Should not a break be drawn in the p,7-curve for the plait-
points, which begins in the critical point of ether, in the point
where the p,7-curve for the three-phase equilibrium cuts the former
curve ?

As an argument in favour of the existence of such a break in
the course of the plaitpoint curve the consideration might be alleged
that the part of the plaitpoint curve that begins at the critical
point of ether, is still unaffected by the influence of the three-phase
pressure, while that part that lies above the line of the three-phase
pressure is to be considered as the locus of the tops of the plaits
which rise above the three-phase line. But I point out that this
would not only hold when the three-phase line cuts the plaitpoint
line, but also when it has a point in common with the plaitpoint
line, and ends or begins in it, and so the question would not
only have significance for our case, but everywhere where a three-
phase pressure must be drawn which connects the two realisable
branches of the plaitpoint line. That the plaitpoint line is greatly,
and sometimes exceedingly greatly modified by the causes, from
which also the existence of three-phase pressure ensues, appears
when we direct our attention to the realisable branch, which in the
case under consideration, ether-water, is the third branch that ends
in the critical point of water. This branch begins, namely, for
pressures which can be exceedingly small. But from this the existence
of sudden changes follows by no means in the direction of the
plaitpoint line, which would then also have to appear in the 7Z\z-,
and p,v-representations of this line. Of course now that there are
causes for the three-phase pressure, this plaitpoint line is different
from what it would be without the existence of these causes, but

( 886 )

then throughout its course. But the main features remain and
the modifications are of great importance only when a realisable
plaitpoint comes under the influence of a plaitpoint heterogeneous
with it. Thus the character of the plaitpoint line on the ether side
has been preserved till a plaitpoint of this branch, before or beyond
the remarkable point, has begun to form a pair with a plaitpoint of the
second kind — and on the other hand a plaitpoint of the branch on the
side of the water, when it had got detached from the heterogeneous
plaitpoint with which it had formed a pair till then, has begun to
exhibit the usual characteristic of a plaitpoint on the side of the
component with the highest value of 7%.

It may be of use on this occasion to examine the course of the
critical pressure equal to == for the mixture, if we assumed it to
have the cbaracter of a simple substance. For a mixture with
minimum plaitpoint pressure this locus for the points of the curve
formed by these points, begins in the critical point of ether and
then remains (see fig. 48) on the lefthand side of the first branch of
the plaitpoints to the remarkable point. There it coincides with this
point, and cuts the first branch’). All this time it remains hidden
by the liquid-vapour line, except in the remarkable point. When it
has passed this point, if continues to ascend to the eritical point of
the second component, and a point of this locus is hidden at given
temperature in the two-phase equilibrium that exists above the
temperature of the remarkable point on the water side, and
has been discussed above. So it also possesses a point in the
cusp which was repeatedly mentioned in the preceding paper. It is

ina
certainly remarkable that the only point of the locus Pi = on aa

that can, ever show itself, continues to show itself with the existence
of three-phase pressure. At higher temperatures it remains hidden
in the then still existing figure of equilibrium, which differs in form
according as fig. 48 or fig. 49 is followed. In fig. 49 it is an ordinary
two-phase figure, but in the case of fig. 48 it is at first still a figure
of three-phase equilibrium during a greater or smaller range of
temperature. In the case of fig.49 the temperature of transformation
lies of course lower than that of the remarkable point, but in the
case of fig. 48 this is not certain. So this temperature of trans-
formation, indeed, always lies above (7)i)min, but not always below

1) Perhaps I overlooked this intersection formerly too, and then I erroneously

supposed it lo be further to the left.

( 887 )

the mentioned temperature; always, however, on the branch that
runs from (T,1)nin to the point P.q (see fig. 52), either below the
point s, or somewhat above it.

The following remark may perhaps serve to show the correct use
of the Vv and the p,7-figure of the plaitpoints and the situation
of the plaitpoints with respect to the three-phase tension. If we take
a point of the three-phase curve in the p,7-figure, then the value
of 7 and the corresponding p of the three-phase tension is deter-
mined by this point, so that we can draw a straight line at the
height of the three-phase pressure, at this value of 7’ above a line
on which the value of x will be measured. The three values of z,
which exist at this 7’ and at this pressure, are then read in the
T,x-curve. If the gas phase comes first, as is the case in tig, 48,
when the chosen point of the three-phase tension lies between A
and £8, there are two elevations above the three-phase pressure,
which, of course, lie side by side. The height of these elevations is
then indicated by the p,7-curve, by reading from it, how high the
first and the third branch indicate the plaitpoint pressure at the chosen
value of 7. In this case there does not exist a plait which hangs
on the three-phase line. The basis of the first elevation has a breadth
equal to the distance of 2, from «z,, and that of the second elevation
equal to the distance of 2, from 2,, which distances are indicated
in the 7,«-figure at 7. If the gas phase lies in the middle, which is
the case in fig. 48 for points on the left side of A, and in fig. 52
for points below s,, there is one elevation above the line of the
three-phase tension, the basis of which has a breadth equal to 2,—z,, -
which is then the whole width, over which the three-phase tension
extends. But moreover, there is a plait which hangs down over a
width 2,—a,. The tops of these plaits are again determined by the
p,T-curve. lf we had chosen the point A itself, then 2,—zx,=0, and
we have the discussed cusp. If we had chosen a point in the three-
phase tension line of the p,7-curve, which belongs to a temperature
smaller than (7'pi)min , there is only one elevation, and instead of the
plaitpoint of the plait which hangs down, we then have a point of
the vapour tension line of ether, which we must think added in fig. 48.

Of course we can also proceed in the same way in the cases
represented by figs. 49, 50, and 51, to which might be added a
figure representing the termination of the three-phase pressure above
the remarkable point. Whether all these eases will occur, is not to
be decided beforehand. But the case represented by fig. 48 is the
least simple one, and that to such a degree, that it seems more and
more improbable to me that it will occur.

59

Proceedings Royal Acad. Amsterdam. Vol. XIV.

( 888 )

For the determination of the temperature of the point P,, of
fig. 52, we have 3 equations:

(dp aw 1? J? z J2
a = 0; z u = 0 and ae x< ma lt a al a
dv ]a1 du* J» T dx* ) Tt \dv* ).T dx’? ),.7¢ \dvdx ) 7

The last of these three equations supposes that the three-phase

: aw ; dp
pressure begins as soon as the cure = O gets outside (Z)=0
ip v)2T
and expresses that these two curves touch. Compare fig. 8 of Con-
tribution II, in which, however, water has been chosen as first
component. Then the contact of the two curves takes place in a

av

ike es ee d* a’

point in which — is positive, and is negative, —— being posi-
dv* dvd da*

d*y

tive and negative. The latter quantity being equal’ to

aAvae

ap ap : MRI
oe ricollnas positive. If we introduce the value of

, in these
dit se (v—b)

d
functions, as it follows from Gre we find the following four
aU) rT

conditions for the point Pay:

2 3
ye ae
db da
du 1 da
AOD a
db?
(=) 1—22

=

(v--b)>~ «? (1—a)?

db?
(=) 2 il eRe
v(v—b)~ 4a de?
But though it is not difficult to derive two equations for the

determination of the value of v and x of the point ?,», the intricacy
of one of these equations hampers the determination of these two

and

db
qnantities themselves. We see, however, that as aa is
ax

ereater, the more easily these 4 conditions will be satisfied *). The

1) This latter part has already partly been treated in Contribution II, but the
conclusions drawn there, rest on insufficient grounds. That long before 7), for
water the non-miscibility has ceased to exist, has not been sufficiently kept separate
from the existence of non-miscibility at Z), for ether.

( 889 )

two equations for the determination of v and w are:
(v — by? ae Gigs A
x“ (1—2) Ze) ee COE 2a da

‘db’? db\?
1—22 (v——b)? 3b—v Ae dx) 1 da
Ns. zs Rp O) wis aoe ae

and

is a(1 =i oe ee & ps a ae
db
dx 1 da 1 da 1 d’a
+ 2 — —
v @ ax? a de a dx

Tt is of course not our intention to accurately determine the
systems of values for v and z, which satisfy these equations, as
our whole solution must only be considered as an approximation.
But the following course might be taken to indicate in the first

v—b : : P
place the value of —— as function of « at least approximately.
.

. v—b\? :
If we put (=) = Z, then according to the first of the above
v

ewe

x 5 + wv —- Qa da?

equations :

and according to the second equation:

ae

a dex?

dec

db
ae J2da ldalda 1-20 (=y 3b-v

ve? adxe aduada« aa(=a)?

db
If we substitute the value for —,;— as it follows from the first
v

equation, for this quantity, we get:
db da

dx \1 d'a | GD 4 de (v-b v-b\? 1 1-22 /v-b\? 3b-v
» (a dx? v J a(1-a) a (1a) z) x?(1-z2)? on v

Taking into consideration that x will not differ much from 34, it
appears from this last form that:

L a »—b\? 6
ae ates

(890 )

db
and by equating ~~ from the two equations, we find :
v
S00 dat ail 1—22 3b—»)?
gal? tes le ate |
a de a(l—e) a(1—a)? v ai2: “Z

~ Qa da? a(1—a)

67 1 az
F

l—2z) wn dz?

If we transfer the numerator of the 1st member as denominator

to the 2°¢ member, the ist member may be represented as a curve,
3

which we need only follow for values of 7 greater than sae) oe

a dx’?

This curve begins infinitely high at this value and runs asymptotically

to Z=o. The second member may also be represented as a curve,

which begins infinitely high at Z=0, and cuts the Z-axis at
“4 1 @a rata :

as Sa at a value that is 3 times as great as the abscissa

of the valne at which the Js* curve lies infinitely high. So it appears

v—b : ;
that two values for ( ) or Z satisfy. The first, which we want
_
: z(1—a) 1 dx
to know, is somewhat larger than ——-—~——., and the second,

6 a dx”

2

pees yp :
which belongs to the position in which —- =O touches the line

da?
dp _ : .
= 0 externally, is somewhat smaller than 3 times this value. As
av
Mw : ; a pe 2
a rule —3 = 9 will undoubtedly differ littie from a’ point there. Of
AL

course, if we can express v and a in this way, one more equation
would have to be used to determine 2.
On the supposition that « differs little from } we find about:

Z Ge (=)= 8 a,+a,—2a,,
A Srmr s TIS) 9 >
v 24a,+a,+2a,,

v—b : :
So the value of —— depends in a high degree on the value of
;

2a,,. With 2a,,—=a,-+ a, we should even find v—b =0, and so

v—b 1
also 7=0. With a,,=0 we should find call With

v
a,+74, | fi | v—v 1 d T 1 T
( = =———$ we should nna ——-=>=— an —=z-+k-
in j e shou : 3 5 k

( 891 )

The second point of intersection of the curves for the determina-

v—b\? aN:
tion of ( ) has no meaning for the determination of the point
v

Pa, nor for the determination of the point P.2, but might serve
to get to know the temperature at least by approximation, above
which the branch of the plaitpoint line, which belongs to the second
component, will assume a normal course.

The two curves which serve to determine the value of 7. need
not necessarily intersect. The two points of intersection may e. g.
coincide, or the two curves may not even come in contact with
each other. When the two curves touch or are not at all in contact,
this means tbat the plaitpoint line has a normal character through-
out its course, and that there can be no question of three-phase
pressure. As the two points of intersection lie further apart, the
temperature range for the three-phase pressure is more considerable.
Inversely also a’ very limited range of temperature is possible for
such a pressure, or this can disappear entirely.

The condition whether or no three-phase pressure occurs, might
also be expressed more directly in the following way. If the point,

F ; aw : : :
in which the curve aia = 0 has contracted to a single point, lies
&
., ap ; Be
outside — = 0, there is three-phase pressure; if it lies inside — =0,
v av

there is no three-phase pressure. The transition case requires that

d,
the point lies exactly on f=0.
av

In contribution LI the value of xz, v, and 7 has been caleulated

hig. eat? : ; :

for the point in which = O has contracted for given value of

b, MRT 2a
(a aS (Cae

transition case. But the values of 7. x7, and-v oceur in such an

=O, we should have the condition for the

nee oars id
intricate shape, that the substitution in —P —( does not lead to
v

clear results.

Then the course to find the relation which must exist between
the quantities 6,, 6,, a,, a, and a,, would be this that after elimi-
nation of 7, which is easy tc perform, also the quantity v were
eliminated from a third power equation in v and two second power
equations in v. Then we have two relations in a2, and the constants
that determine the properties of the substance. Eliminating « finally

( 899 )

we have the relation between the constants of the substance, which
contains the criterion for complete miscibility.

In the notation of contribution II] we ean write the condition for
non-miscibility, at least in the discussed cases as follows :

a, +a, — 24a, = 4y*

l—2 en 1
a, a + a,=— + i Ty
a ' 1—2#«
, : f : ay
If we take the sign >, this equation expresses that ee!
av
. . dp - :
disappears outside ae: That this does not always mean three-
av

3

phase pressure at the temperature at which -~ = 0 vanishes, has

av
appeared again here, and this had already been pointed out in cons
tribution II. The three-phase pressure can, namely, already have ceased
ae: dy ’ ; :
to exist, in consequence of the Aa = 0 disappearing above 7%.

ax*

If the sign < holds, there is no three-phase pressure. The quantities

—b :
y and « depend on Pare in this equation of condition. So by the
)
1
side of the ratio of the size of the molecules, also the value of
a, + a, — 2a,, is decisive for miscibility or non-miscibility.
According to the. representation at which we have now arrived,

2

dp
= 0 touches —=0
da dv

the temperature P.g is that at which

inside the latter line. At higher 7 there is intersection and three-
2

Dabur
= 0 disappears, three-phase pressure has ceased
av

io exist; and this may happen before one of the components is in
the critical state. This case was treated before in these contributions,
But if this disappearance does not take place until above the critical
temperature of the component with the lowest value of 7;,, the
three-phase pressure also continues to above this temperature. So if

phase pressure. If

, Pw P
three-phase pressure occurs, the intersection of —~-=0O and = 0
ax av

appears always to be the cause.

( 893 )

Physiology. — “On the comparative nocuousness of concentrated
and diluted arsenobenzene solutions. The dilution to be applied
in intravenous injections.” By Dr. Cuarirs Fieic (Montpellier),
Lauréat de l'Institut et de ’Académie de médecine de Paris.
(Communicated by Prof. H. J. Hampurcer).

(Communicated in the meeting of December 30, 1911).

I pointed out last year that though some authors, particularly
K. Aut, K. Taner, R. Donor, C. FrannxeL, and C. Grouven had
applied the acid solutions of 606 in intra-muscular or even intra-
venous injections (discontinuing them immediately in the latter case)
none had used then for the intra-venous injection the dé/wted acid
solution and, as an outcome of clinical results which authorized me
in doing so, I have been the first to recommend strongly the appli-
eation of strongly diluted acid intra-venous injections. The preparation
of the solution is very simple; it is sufficient to dissolve 0.50 or
0.60 gr. of 606 in from 350 to 500 gr. of artificial serum at 7 per
1000 for which it may be found useful to substitute, especially in
cases in which chlorine may be kept back in the system, by an
equal volume of isotonic or paraisotonic serum where glucose has
been substituted for chlorine (glucose at 40—47 per 1000). The in-
jection itself is as simple as an ordinary injection with artificial serum.

From a therapeutic point of view the method is extremely active
(FLeic, Dunot); according to Dunor and others its therapeutic activity
is even far superior to that of the alkaline method.

1 have expressly stated that the innocuousness of the injection was
due to its great dilution, and I have attributed the unfavourable
symptoms observed by the authors after the intra-venous acid injec-
tion, to the solutions being too concentrated. These symptoms, charac-
terized in the first place by congestion of the blood in the head,
difficult breathing, an intense feeling of anxiety, vomiting, diarrhoea,
ete. are entirely different from the weak reactionary symptoms
(hyperthermic symptoms, shivering) which attend properly diluted acid
injections. The latter grow much slighter or disappear even entirely
if, as has been advised by WecHseLMann, only nevly distilled ?) water

1) These reactionary phenomena which are especially due te water which has
been sterilized a long time alter it was distilled, must, as has been yery well
understood by Wecusetmann, be attributed to decomposition products of animal and
vegetable origin in water, which has been distilled Jong before, which products ave
set free by sterilization. | have ascertained that they are by no means due, as one
might be led to believe, te the aetion of the CO,, which such water may contain,

( 894 )

is used in preparing the artificial serum. On the other hand the
troubles caused by the injection into the veins of too concentrated
solutions of 606 are of a far more serious nature. FramNKEL and
GrovuveN have even published a case in which death followed in
about three hours and a half, after the injection, and yet in this case
a certain amount of soda (entirely insufficient, however, to neutralize
the acidity) had been added to the solution, used for the intra-venous
injection.

These very marked differences between the clinical results of
concentrated and diluted acid solutions made it interesting to study
experimentally the toxicity of solutions of different concentrations
and to trace the cause of the fact why the concentrated solutions
ave hypertoxical. This research was even very important, as it might
serve to combat the error of certain authors who, having applied
concentrated acid solutions in intra-venous injections with injurious
and even mortal results, have believed themselves entitled to do
away entirely with the intra-venous acid method, a method which,
when applied under the conditions pointed out by me, presents
only advantages and seems to be superior to the others. After the
publication of my first results (November 1910) the method has been
employed with great success and in a great number of cases by
Dunor (from the end of May 1911) who after having given up the
concentrated intra-venous acid injection, to replace it successively by
the intra-muscular acid injection, and the intra-venous alkaline in-
jection, has been induced on his part (at the advice of Eariicu, and
probably without knowing my first researches) to try and afterwards
to apply systematically, the intra-venous acid injection in strong
dilutions. Sinee then other authors have followed the same method
and their results only show its value.

Of the experimental researches which I have made on the com-
parative nocuousness of concentrated and diluted acid solutions I
shall summarize here only the chief results as regards the toxicity
of acid solutions of 0.60 gr. on 400 ce., injected into the veins of
rabbits and does, and of acid solutions, at the rates of concentration
in which they were at jirst used by Dunot, and by Fraunken and
(ZROUVEN.

The doses injected into the veins by Dunor went from 0.50 gr.
to 1 gr. of 606, dissolved into 1 ¢.c. of methyl-alcohol, the whole
diluted to a volume of 30 ¢.c. by means of artificial serum. I have
thus studied the toxicity of the most concentrated solution, that is
lo say 1 to 80 (with or without methyl-aleohol),

( 895 )

The dose injected by Frawnkun and Grovven, more especially in
their mortal case, was 0.40 er. of 606 dissolved into 1 e.c. of

N
methyl-aleohol to which were added 1 or 1.5 ce. of NaOH 0

(on an average 1.2 cc.) the whole being brought with distilled
water to a volume of 15 cc. I also have studied experimentally
the toxicity of this solution (with or without methyl-alcohol).

In order to be exact and to facilitate comparisons I shall add the following data.
The acidity in HCl of the solution 1 to 30 of Dusor amounts to 5.10 gr. per

2 ; aeeee N|
1000 and that of the solution of Franken and Grouven (with iee. 2°NaOH a)

is 3,91 per 1000; that of the solution diluted to 0,60 gr. of 606 to 400 c.c.,
which represents a type of a diluted solution is only 0.23 gr. per 10001);

As the toxicity of the acid solution is due above all as we shall see, to the
phenolic functions of OH of 606 much more than to the acidity in HCl, and more
exactly, to their degree of concentration in the solution, it may be interesting to
give the concentrations in —OH per 1000 for the three types. These concentra-
tions are for the first solution 2,233 —OH per 1000 c.c. ; for the second 1.733 gr. ;
for the third 0,100 gr.

It follows that in the solutions of Dunot and of Frarnket and Grovven the
concentrations in acidity or in phenolic function are from 17 to 22 times as strong
as in solutions of the diluted type.

We may finally point out that the doses injected into man per kilogramme
(taking an average weight of 65 kilogrammes) were in the mortal case of
Fraenket and Grovuven 0.006 gr., and 0.0153 gr (the highest limit) in the case of
Dunot, where the injection was attended by a “tableau assez impressionant”.

From the numerous experiments on their toxicity which I have
made, it follows that the solutions of Dunor and of FraenkeL and
GROUVEN are much more poisonous than the solutions diluted to
0.60 gr. per 400 c.c., the latter being already much less poisonous
than the solution of 0.60 gr. per 200 c.e.

On an average the immediate tovicity of the first two may be
fixed at from 0.006 gr. to 0.010 gr. per kilogramme of rabbit ?) ;
that of the latter at 0.130 gr. that of the most diluted solution at
0,180 gr., the immediate’ toxicity of the latter is therefore from
about 20 to 30 times lower than that of the concentrated solutions
used by above-mentioned authors !

1) These acidities are calculated whilst taking for the formula of dichlorhydrate
of dioxydiaminoarsenobenzene the formula (C,2H,,N,0,As, .2HCl + 2 H,0), given
by Euruicu,

*) The toxicity of 606 being very great when applied in these concentrations,

only trifling differences can be established in the toxicity of solutions with and
without methyl-alcohol..

( 896 )

When studying these values and comparing them with those
mentioned before we are immediately struck by the fact that the

toxicity of these last solutions — and not the toxicity after a long
time, but the zmmediate tovicity is represented :
1 — in the case of FrannkeL and Grovven’s solution by a figure

equal or very nearly equal to that representing the dose injected per
kilogramme into man ;

2 — in the case of Dunor’s solution by a figure evidently lower
than the mavimum dose which he says he has injected into man
per kilogramme.

On the other hand when studying no longer the immediate
toxicity of the two types of concentrated solutions, but their secon-
dary toxicity, that means to say that, relating to the dose which
kills the animal after a somewhat longer time (from 12 to 24 hours
for example) I have ascertained that the dose grows. still much
smaller.

Finally when studying the effect on dogs and rabbits of the same
solution, injected 7% equal or somewhat smaller doses than those
injected by the authors into man (holding in view the difference in
weight) I have ascertained that these doses were invariably and
often immediately mortal, in the case of the solution 1:30, and
nearly always mortal in the case of the other solution.

From these facts I think I may draw the following conclusions :

1 — It is not at all surprising that the case of FRAmNKEL and
Grovtven proved mortal after a very short time; there is no reason
to assume, as the authors have done, an excessive sensibility of
the patient to the action of arsenic, as death was not due to acute
arsenic poisoning (contrary to what they believe, and as I shall
prove lower down) but simply to the solution being too concen-
trated ; it is very surprising that the two other cases, treated by the
authors, have not had the same fatal ending.

2 — It is in the highest degree surprising that the patients injected
with the Dunor-solution have shown only the symptoms mentioned,
and that “le tableau assez impressionant’’, described by the author,
has not ended in death, as the dose injected per kilogramme was
0.153 gr. whilst the dose, dimmediately toxical for the animal, is
upon an average 0,010 gr., that means to say 15 times as weak.
And our astonishment increases if we remember, as I observed
before, that the secondary toxicity is represented by a still smaller
figure | According to several experiments, too numerous to be classed
as exceptions, the figure in question, calculated for a man weighing
65 kilogrammes, would come to a toxical dose somewhat less than

( 897 )

0.50 gr., that means to say less than half the maximum dose which
Dunort says, he could inject man with.

As, however, the immediate toxicity of the two types of solutions
studied, was for the dog sometimes lower than for the rabbit, one
might be inclined to infer from this that man, nearer to the dog in
the zoological seale than to the rabbit, is less sensible to 606 than
the animals. But this supposition, not very likely at first sight, is
decidedly wrong, for when experimenting with diluted solutions
(either alkaline or acid) it is discovered that animals, in proportion
to their weight, can bear without any trouble, doses of 606 much
greater than those which would cause the first symptoms of poisoning
in man.

Scientifically it is therefore incomprehensible, I should almost say
inadmissible that into the veins of man may have been injected several
times and without fatal results such a considerable amount of 606
(1 gramme) in such a concentrated solution as the one described
(1 fo 30). It is in every respect to be regretted that no detailed
clinical observations have been published for the cases in question.

We shall realize still better how well founded these conclusions
are if we consider the nature of the disorders attending concen-
trated acid intravenous injections.

In the experiments relating to zmmediate tovicity death is caused
by acute asphyxy with more or less general convulsions. At the
autopsy the heart may beat still, but the lungs are marked by
hemorrhagic points and in some places by large violet coloured
zones of infarcts in connection with emboli throughout the vascular
part of the organ. The right cavities of the heart and the large
bloodvessels entering it, contain blood which, if not coagulated, can
be made to coagulate very easily: mm vitro. If this blood is spread
in a thin layer over the sides of a glass, we can discover without
difficulty, even with the naked eye, little clots, in the centre of
which we see a yellowish precipitate, originating as we shall see in
the action of 606 on the albumenoids of the plasma. The nervous
centres may also be subject to emboli or infarcts. The same facts may
be observed in those cases where, though the doses injected were,
in proportion to the weight of the animal, not so great as those
with which man was injected, death has nevertheless been the con-
sequence.

In the experiments relating to toxicity after a longer period, the
animals die after having shown an increasing difficulty in breathing,
in connection with either acute congestion and oedema of the lungs

( 898 )

or pneumonia or broncho-pneumonia. At the autopsy pulmonary
lesions are discovered analogous to those which have just been des-
cribed when discussing immediate toxicity, but with a permeability
‘of the lung to air, the smaller as the survival has been shorter ;
large zones of red hepatization are met with, and often the bronchia
and the trachea are filled with a fine spume and a considerable
amount of fluid oedematous transude, and sometimes in the pleura
itself a sero-fibrinous very slightly hematie fluid is met with. In
those cases in which death followed after a few days it was found
that to the preceding lesions others were added of a more distinetly
infectious nature (grey hepatization for instance).

One or two weeks after the injection we also observe diffuse pul-
monary lesions even in those animals (more especially in dogs) which
were injected with doses too slight to cause death, and which,
though losing flesh temporarily, only showed passing symptoms of
dyspnoea.

In the 3 kinds of cases quoted we have to do with troubles and
lesions of a mechanical’) origin owing to the considerable precipi-
tation in the blood of 606, injected in too strong a concentration.
This fact can very well be explained at the hand of researches
made on the arsenic compound, found in the blood, after the acid
intravenous injection.

In a former treatise I pointed out, in the first place that the
precipitate caused in the blood by the acid solution of 606, was by
no means due to the acidity in HCl of the solutions; I believed
moreover I had to admit, as a result of reactions I had studied
between the salts of the form CO,NaH of the blood and 606, that
the latter precipitated in the blood in the form of an insoluble base

+ 2 Ui 2
ie BS nee ee me NH i but further researches have shown
OH OH
me that the precipitates, produced in an albuminous medium, are in
reality more complex than my initial scheme indicated, and that
moreover, probably to a great extent, reactions took place between
the phenol group —OH of 606 and. the albuminoid substances of
the blood, so that the precipitate formed, far from being exclusively

1) It must be noted that in the case of sub-cutaneous acid or alkaline injections
in toxical doses, frequent congestive lesions in all the principal interior organs
have been pointed out by different authors. Especially in experiments on the
Guinea-pig Desmoutizre and Paris have found little hemorrhagie centres in all the
inner organs. Probably the nature of these lesions is akin to that of lesions of

the same kind, caused by intra-yenous injections of toxical doses.

( 899 )

INE
due to the base OH >... . represents perhaps almost exclusively

a phenolic combination of albumenoid. *)

This precipitate, at any rate when it is formed in a concentrated
solution of 606, takes the form of compact clots not easily divisible
into smaller particles: hence its physical state does not fulfil the
conditions I specified in 1907 in connexion with my method of
insoluble intra-venous injections, which conditions would be necessary
in order that its being set free in the current of the blood should
not give rise to the formation of emboli.

When on the other hand the same precipitate is formed under
the influence of a sufficiently diluted solution of 606 (0.60 gr. to
400 ec. for instance) it presents itself in a much finer state of divi-
sion, and is from a physical point of view much better suited than
ihe former, owing to its mechanical fitness for the blood and the
possibility of its passing the smaller blood vessels and the capillaries.

This explains why the toxicity of the diluted acid solution is much
weaker than that of the concentrated solution: the reason being that
the noxiousness of a mechanical kind is much less in the diluted
solution.

A noxiousness of this kind, however, also manifests itself in these
solutions, as was shown by the condition of the lungs of those
rabbits on which their immediate toxicity was tried and the intense
dyspnoea, observed at the time of the injection, but this noxiousness
makes itself felt only for much more considerable doses of 606 than
the doses therapeutically used on man; the limit of mechanical
noxiousness is far distant from the limit of the maximum therapeutic
doses; so that for man these doses possess practically no toxicity.
The serious dangers of the concentrated acid solutions form in no
way an objection to the method by which strongly diluted acid
solutions are employed, which method, owing to its great therapeutic
activity should be applied more and more.

It is interésting to observe that the most poisonous factor, from a
pharmacodynamic point of view, of the dichlorhydrate of dioxy-
diaminoarsenobenzene in acid solutions is not due to the acid, for
the catastrophes observed are especially of a mechanical kind, as a

1) The reactions are also complicated as regards the much weaker precipitation
of weakly alkaline solutions. A more detailed account of the precipitates caused
in the blood by alkaline and acid injections will be found in my treatise: “La
méthode des injections intraveineuses acides d’arsénobenzol a forte dilution, au
serum artificiel ordinaire et au sérum achloruré glucosé.” (Maloine, éditeur.
Paris. 1911).

( 900 )

result of the precipitate which was formed, and we have seen,
that hydrochloric acid plays no part in the precipitation. I may
expressly state that this is also the case in a concentrated solution,
such as the solution 1 to 80, corresponding to an acidity in HCl of
5.10 gr. per 1000, as an HCl-solution of 5 per 1000 does not pre-
cipitate blood-serum; moreover the amount of HCl, fixed in even
strong doses of 606, is not great enough to be poisonous.

Hence the most directly towical function of arsenobenzene in con-
centrated acid solutions is the phenolic function OH, the coagulating
effect of which on the albuminoid substances of the blood results in
evils of a mechanical kind, evils manifesting themselves immediately,
that is to say before the chemical toxicity of the arsenic complex has
set m.

The preceding remarks on the nature and the great danger of
the disorders and injuries which follow rapidly upon intra-venous
injections of acid solutions of concentrated 606 show that I was
fully warranted in emphasizing how difficult it is to understand that
the injection of large doses of these solutions should not have been
attended with graver troubles, ending more frequently in death, than
those which have been published. Viewed in the light of the above
investigations, I have a right to be surprised at the scientifically
inexplicable discrepancies between the experimental and the published
clinical results.

The former are at any rate highly instructive. They mark in the
first place the highly important part played by dilution in the dimi-
nution — practically it might even be said in the removal of the
toxicity. This fact should be known to all therapeutists, for it is far
from new, but though, as far as I am concerned, | have always
acted upon it, whenever I have applied clinically the results of my
experimental researches‘), yet I have often seen it misappreciated

- or at least forgotten — by eminent clinical lecturers. Therefore
I purposely recommend it again and should wish to see it applied
in all cases in which the intra-venous injection implies the use of
a substance (of an artificial or biological origin) which, when applied
in concentrated solutions, perhaps might be given in doses, which

1) Cf., especially for intra-venous injections of bloodserum, the following treatise:
Cuartes I'Lera, “Sur les injections de solutions isotoniques de chlorure de calcium
ou de sérums fortement calciques, de solutions isotoniques ou hypertoniques de
sucres et sur l’ingestion ou les lavements d’eau abondants, avant el aprés l’anes-
thésie chirurgicale.’’ Académie des Sciences et Lettres de Montpellier, 7 Juin 1909,
et Presse médicale, 29 Janvier 1910, 69—72.

(901 )

would not exclude the possibility of toxial symptoms. Another
advantage of diluted solutions may be found in the necessarily much
greater slowness with which the solution enters into the blood; this
slowness may be attended in some cases by phenomena denoting
rapid adaptation, which phenomena, according to their internal
mechanism may be reduced to Rocur’s tachysynethy or to CHAMPY
and Gtny’s tachyphylaais or to Ancen, Bouin, and Lamsert’s skepto-
phylaxis. Moreover I have advised, when applying solutions of 606
to carry out the diluted injection itself always very slowly.

Although the dilution is a factor which diminishes the toxicity, it
should not be carried too far: the therapeutic activity of the 606
injected being, as 1 have shown, to a certain extent connected with
its temporary insolubility, and the latter bears a direct proportion to
the length of the period during which the substance is in the orga-
nism and an inverse proportion to the rapidity with which it is
eliminated’), too strong a dilution, which would cause too rapid a
solubilisation of the precipitate and leave the arsenic compound for
too short a time in the tissues, would diminish its therapeutic activity
too much. It will also be found advisable, in the case of 606 not
to go beyond a dilution of 0.60 gr. per 500 ce. so as not to make
the organism lose the benefit of the most favourable condition brought
about by the jirst precipitation.

Finally the facts which I have discussed enable us to explain
various cases in which death followed sooner or later after the
injection (from a few days to more than two weeks) and which
have injudiciously been ascribed to some other cause than to an
action of 606.

When examining the symptoms of these cases, we read that the
patients have died of disorders of an intermittent nature, sometimes
affecting the lungs, sometimes the nerves, whilst the autopsy shows
lesions of the same nature as those which I deseribed as following
upon too concentrated injections. As some precipitate may be caused
by the contact of blood even with alkaline’) solutions, the mechanical
nocuousness may be taken as a factor having caused lesions which
are fatal in the long run, and a connection may easily be established
with the experiments quoted above, in which death followed only
after a few days; this factor has certainly intervened in some cases

1) These facts explain why alkaline solutions have a weaker therapeutic activity
than acid solutions: in the case of the former the insolubility in blood exists only
to a small extent, and the arsenic is, as I have observed, much more rapidly
eliminated.

2) This precipitation increases as the alkalinity of the solution decreases.

( 902 )

in which the solutions used were not sufficiently diluted. Thus it
may easily be understood that only moderately strong concentrations
may cause insignificant pulmonary lesions, attended by no fatal
consequences whatever, in the case of sufficiently strong persons, and
be attended on the other hand with the gravest results for other
individuals in a state of local or general debility.

For the details relating to the experiments on toxicity mentioned
here, and a general study of the acid intra-venous method, I beg to
refer to the geveral survey already mentioned in this paper.

(Physiological Laboratory of the Medical
Faculty at Montpellier).

Geology. — “On an essential condition for the formation of over-
thrust-covers.” By Dr. B. G. Escuer. (Communicated by
Prof. Dr. G. A. F. Monmneraarrf).

(Communicated in the meeting of January 27, 1912).

E. Have*) has called the attention to the fact that only such
territories as were formerly occupied by geosynclinals give occasion
to the formation of over-thrust-covers. I suppose I can point out a
second condition that evidently must be satisfied, that tangential
propelling-forces form a mountain-system, built of over-thrust-covers.

Comparative studies in the Western Alps prompted me to point
out *), that the hereynic folding of the sub-structure of the present
Northern border of the Alps was the cndirect cause of the formation
of the alpine covering-system of the Western Alps in the tertiary period.

Whilst formerly a resistance of the Central Plateau of France
of Vosges and Schwarzwald was spoken of I think I have
proved, that not these parts of the hereynie mountains in Europe,
stiffened by a previous folding, offered resistance to the alpine
propelling forces, but other parts of the preatriasic folding-mountain
system of Central-Europe, situated more E., 5.E. and S$. The Eastern
South-Eastern and Southern border of the hereynie mountains
of Central-Europe was evidently formed by the autochthonie ‘“Zentral-
Massive” of the West-Alps: Mercantour, Pelvoux, Belledonne, Grandes-
Rousses, Mont Blane, Aiguilles Rouges (++ Dents de Moreles), Aarcentre.

1) E. Hava. Traité de Géologie.
*) B. G, Escuer. Ueber die praetriasische Faltung in den Westalpen ete. Diss.
Zurich 1911.

(903 )

That a part of the Alps was already folded in the hercynic orogenetic
period, and that this folding did not take place at one time, but
was performed in two phases’) that can clearly be distinguished, has
lately been proved by M. Lueron*) for Mont-Blanc, Aiguilles-Rouges
and Aar-centre. Lugnon speaks even of a regional division into zones,
of which one was folded by the ‘phase ségalaunienne’ (= prae-
Stéphanien) the other only by the “phase allobrogienne’ (= prae-
triadic). This regional ‘dualisme’” may be correct for Mont Blane,
Aiguilles-Rouges and Aar-centre, Lucron has still to afford sufficient
proof for the existence of these two folding-mountain-systems for the
Franco-Italian Alps.

Most authors agree about the resistance of a mountain system
that has already been folded, to a second folding.

The fact that a plate that has already been folded offers resistance
to a second folding in another direction’) may be a mechanical
explanation for the case that the direction of the strikes of the two
foldings form an angle. In nature however it often occurs that these
two directions run almost parallel, and then of course this explanation
cannot be applied. It seems however quite natural, that a folding
stiffens a certain part of the earth-crust, and that such a territory
afterwards offers a greater resistance to a second folding in the
same direction, than another part lying behind it that has not yet
been folded. The absolute resistances are here of course not of as
much interest as the relative ones, and as, at a subsequent tangen-
tial propelling force, the part that has not yet been folded, offers
less resistance in the beginning, a folding will here of course likewise
take place. That folding can last here at least as long as the now
folded beds offer the same resistance as, in their time, the previously
folded beds, lying before them, could offer.

After Pauntcxe*) has proved by his splendid successful experi-
ments, that if, at the experimental tectonics, really forces are applied
and suppositions made that are somewhat in conformity with those
occurring in nature, good results may be expected, it is, in my

*a) M. Luceoy. Sur l’existence de deux phases de plissements paléozoiques dans
les Alpes occidentales. Comptes Rendus de l’Acad. d. Scienc. Paris 30 Oct. 1911.

5b) M. Luazon. Sur quelques conséquences de l’hypothése d'un dualisme des
plissements paléozoiques dans les Alpes occidentales. Comptes Rendus de !'acad.
d. Science Paris 13 Noy. 1911.

4) Cu. Tu. Groornorr. Verslag v. d. geol. excursie naar de Zwitsersche
Jura en het Alpengebied. Bijlage bij het Jaarboekje 1909 v.d mijnbouwkundige
Vereeniging 1909. :

5) W. Pautcke. Kurze Mitteilungen ueber tektonische Experimente. Jahresber.
d. Oberrhein. Geol. Vereins. Neue Folge. Bd. 1. Heft 22. p. 58—66. 1911.

60

Proceedings Royal Acad. Amsterdam. Vol. XIV.

( 904 )

opinion, not impossible to study with the help of such apparatuses
as Pauncke used, experimentally the influence of an old folding on
a new one.

From the most recent researches in the Western Alps follows
that the Helvetian covers are but small slides compared with the
Penninian covers. According to E. ARrGAND ‘) these are stowed agaist
Mont-Blanc and the Aar centre, whilst the Helvetian covers were
slid over these autochthonic centres.

Lucron*) and Arpenz7) suppose that the Mont-Blane-centre and
the Southern (Protogin)-territory of the Aar-centre have partly been
slid over the Aiguilles-Rouges and over the Northern border of the
Aar-centre lying to the N.W. and N.

This overthrust took place during the Alp-folding in the tertiary period,
but according to Lucron*’) it was only restricted to the South-western
hereynie chain (chaine allobrogienne) whilst the autochthonic terri-
tory lying more northward is separated from it by the alpine syn-
clinal of Chamonix and its continuation: Oberer Jungfraukeil-Ferni-
gen-Windgallenmulde ’), and was not slid by the alpine folding.

Whereas Herm *) and Surss*) suppose that at the tertiary folding
the autochthonie centres were forced upward, a supposition supported
by Kk. Tonwinski'’), on the authority of local tectonic researches, I
am of opinion*) that the vaults in the autochthonic centres were
already extant before the tertiary Alp-folding, and Arprnz’) is like-
wise of the same opinion: “Die Massivwoélbungen sind dagegen in
ihrer Anlage alteren Datums’’ ‘).

Though there may be perhaps some objection to the view that
the vaults in the bereynie southern border were extant before the
alpine folding, a view that is a.o. supported by the fact that between
Belledoune and Mercantour local slide-covers occur (Devoluy, Embru-
nais), yet it may be admitted as certain, that the covering mountain
of the tertiary Alps has been slid against and over a territory, that
had already experienced an older orogenetic movement and was
already folded at the end of the Carbon-period.

BrrrraNp, who eompared the Glarneralps with the great over-thrusts
in the Carbonbasin of North-France, gave the first stimulus to the

6) —. Araanp. Les nappes de recouvrement des Alpes pennines etc. Beitrige
z. geol. Karte der Schweiz. Neue lolge. 31 Lief. 1911.

7) P. Arpenz. Der Gebirgsbau der Zentralschweiz. Protokoll d. Sitzung vom
. Dec. 1911 der Naturforschende Gesellschaft. Ztirich.

5) Aus. Herm. Eclogae geol. helvy. Vol. IX. p. 43. 1906.

9) E. Sunss. Das Antlitz der Erde. Ill Band. 2e Halfte. p. 124. 1909.

10) K. Topwinskt. Die grauen Hérner. Vierteljahrsschrift der Ziircher Naturf.
Gesellschaft 1910.

=

( 905 )

development of the theory of over-thrusts in the Alps. Since this theory
gained ground in the territory of the Alps and the hereynic folded
beds in North-France and Belgium were in their turn compared with
the mountain-system of the Alps.

Fourmarier'') points to some tectonically corresponding features
of Ardennes and Alps and discusses in this connection a. 0. the fan-
shaped folds. Groornorr *) compares the three territories: Alps, Chain
Jura, Table Jura with North-France (over-thrusts) the folded Carbon
of South-Limburg and the flat Carbon of North-Brabant.

It seems to me that there is another important conformity in the
fact that likewise in the Ardennes an older folded chain of moun-
tains is lying under the over-thrusts**). Most likely the Southern border
of the Caledonie mountains is extant here, against and over which
the herecynic mountains formed over-thrusts. In this territory we find
likewise evidently .a resistance caused by already folded beds (here
caledonic folded Cambrium-Silurian beds) against a later folding, by
which a cover-structure (here a hereynic one) was formed. Whereas
consequently in the Alps a previous hereyniec folding was the indirect
cause of the formation of a later alpine structure of slides, the
Ardennes are to be regarded as a territory in which likewise two
orogenetic movements took place, here however the younger of the
two movements, by which the over-thrust-structure was formed,
coincides with the old folding of the Alps.

Great over-thrusts have Jong since been known in Scotland. E. B.
Bainey **) gave lately a description of a very complicated over-thrust-
structure SE of Loch Linnhe, showing great conformity with the
profiles through the Western Alps. This territory belongs to the
caledonic mountains of Western-Europe, i.e. to the Northern part.
The general direction of the strike is here SW—NE. According to
BrrtrRanp **) lie to the North-West of this territory the hwronic moun-
tains, which were folded in the algonkium. Evidently there is here
likewise a relation between the appearance of an over-thrust-struc-
ture and a previously folded mountain-system lying before it. Here
the first folding however took place during the huronic period, and
the territory, stiffened by it, formed a buffer with regard to a sub-
sequent folding which threw up, here in the caledonie period, a
slide structure.

11) P. Fourmarrer. La tectonique de l’Ardenne. Annales d. |. Soe. géol. d. Belg.
t. 34. mémoires 1907.

12) EK. B. Battey. Recumbent folds in the schists of the Scottish Highlands.
Quart. Journ. Geol. Soc. pp. 586—620 1910.

18) M. Berrranp. La chaine des Alpes et la formation du continent européen,
Bull. de la Soc. géol. de France, 3e Serie, T, 15. 1887.

60*

( 906 )

As early as 1887 Burrranp’*) published two maps with the
Northern frontiers of the caledonic and hereynie foldings in Europe
and partly those of North-America. As an important acquisition since
that time may be regarded the description of the over-thrust in

eons
ae

_ Fig. 1.

( 907 )

Scandinavia, where caledonic masses have been slid over huronic
territories to the SE. To my knowledge the latest map concerning
this subject is to be found with E. Have*) (1st Vol. p. 209). Only
the Northern frontiers of the caledonie and hereynic foldings. in
Western- and Central-Europe however are indicated here, whilst for
the formation of over-thrust-structures in Western and Central Europe
evidently the Southern frontiers of these foldings are. of importance.
For this reason I indicate on the annexed map (Fig. I) very sche-
matically, besides the Northern frontiers, likewise the Southern fron-
tier of the hereynie folding of the Alps, and the presumptive Southern
frontier of the caledonic folding in the Ardennes, and of the huronic
folding in Scotland.

I represent myself a profile of North-Scotland over the Ardennes
to the inner-border of the Alps, in the main as fig. 2 in which
those parts that are not occupied by over-thrusts, are represented
much fore-shortened.

An essential condition for the formation of overthrust-structures
is mm my opiniun, the existence of a mountain-system folded in a
previous orogenetic period and afterwards abraded, that served as a
buffer against the ensuing folding.

In Fig. I. I have indicated the southern frontiers of the huronic
and caledonic mountains for part of Western-Europe, these frontiers
being for the present entirely hypothetical. The older foldings have
only been observed before i.e. in the cases discussed here to the North
of, the overthrust-structures, whilst I have admitted in analogy
with the Alpine-mountains, that the older foldings extend to some
distance southward under the slide-covers. The map and profile are
meant to elucidate the principle I pronounced here. | am very well
aware that in reality the circumstances are much more intricate.
So I am convinced that hkewise at the inner-border of the Alps a
remainder of a hercynie mouniain-system is extant (Manno *), and
that the mesozoic sediments of the Alps are inclosed between two
already hereynic folded territories. A similar old folded territory
may perhaps likewise be found to the South of the over-thrusts of
the Ardennes (there caledonic) and to the South of the Scottish slide-
covers (there huronic); but for the present we are still fully
uninformed in this respect.

That part of the earth-crust which we contemplated in profile
Fig. 2 shows, in my opinion accidentally, a regular repetition of
over-thrusts that have been slid in a Northern direction. Somewhat
more to the South in the territory ofthe Mediterranean, the directions

( 908 )

SE “Alps Jura Ardennes Scotland N

LEG, vavatavavivaVavilavavavieavavaval Bm = TM VAVAVAVAY UV SAI UU L
as A —_ Ar. Sy cee
alpine hercynic caledonic huronic
IV Il II
Fige2:

of the Alpine foldings show great variety ; in Scandinavia the caledonic
territories have been slid in a 8. E. direction.

With the notion that in the tertiary period the Alps come, as it
were, between the two clamps of a set-screw is necessarily united
the hypothesis that the Alps were passive during the alpine move-
ment, and the seat of the active force originating e.g. in the con-
tractive strains, was more in the depth. 1 suppose that these forces,
working in the depth, were transferred to the surface by the old
already folded and abraded remains of the mountains, and that the
young level sediments were squeezed between two such stiffened
territories which had be2n pushed towards each other. When the force

. in the depth continued for a considerable time, and consequently the
two stiffened -territories were pushed closely together then an over-
thrust-structure was formed (vide Fig. 3).

A. Territory of the active forces 1. before the folding.

B. Territories previously folded 2. after slight folding.

C. Territory of the young sediments 3. after strong folding.
Fig. 3.

The movement towards each other of the old, already folded
remains of the mountains may, in my opinion, be explained by
tangential, but also by centripetal movements. In the former case we

( 909 )

can imagine, that the remains of the mountains are firmly united
with the actively working zone, in the second case we need not
make this supposition.

Only if we admit, that the active forces do not lie in the folded
beds themselves, the use of compressive machines is allowed in the
experimental tectonics, for there the folded beds are likewise passive
during the folding.

Amsterdam, January 16, 1912. b. G. Escuer.

Astronomy. — “Star systems and the Milky Way’. By Prof. J. C.
KAPTEYN.

(Communicated in the meeting of January 27, 1912).

In the November-meeting of last year, I tried to show that there
is an evident relation between the Milky Way and the star-streams.
The relation consists in the fact, that the motion in the great star-
streams relatively to the centre of gravity of the whole system is
perfectly, or very nearly, parallel to the plane of the Milky Way.
This is true separately for the stars of the B, A, and G types. Con-
sequently it is true also for the relative motion of these several
streams and it was this relative motion which was then particularly
considered.

I have found since that this approximate parallelism with the
plane of the Milky Way subsists for the motion of a// the somewhat
rich systems for which sufficient data are available.

Relatively to the centre of gravity of the whole system let:

h =~yearly linear motion of the solar system ;
8 = galactic latitude of the Apex of this motion;

V = yearly linear motion of a determined stargroup ;
B = galactic latitude of the true vertex (convergent) ;
and furthermore, relatively to the solar system:
» = yearly linear motion of this same: group:
6 = galactic latitude of the apparent vertex (convergent).
Then py is the resultant of V and —A.
Therefore, if we project on the normal to the Milky Way,
Dain O= hoin JB: 4 8 ee a)

For the coordinates of the Apex let us adopt:

a = 269°0 d= + 32°0, consequently 8 = + 23°0.
For / the best available value must: be that which CampBeLL has

( 910 )

produced from his rich — untortunately to other astronomers still
inaccessible — storehouse of radial velocities:

h=A9)9. kal p: see:
The equation (1) thus becomes:
» Sin == —— (Cae Wesin Bi ale cece e(e)
lor those groups for which our present data are more or less
reliable we find the following values of », resp. » sin 6. I add the
values of V sin £B, furnished by (2), i.e. the component of the true
velocity at right angles to the Milky Way.

Group v p sin b V sm B
Hyades 45.6 — 3.4 kil. + 4.2
Ursa Major 18.4 — 11.1 — 3.5
Seorp-Centaur 18.8 — 6.7 + 0.9
Perseus 18.0 — 41 + 3.5
G I 32.6 — 84 — 0.8
A I 27.7 — 6.05 + 1.5%
He I 22.0 — 6.7% + 0.8°
G Il 18.4 — 8.5 — 0.9
A Il 24.5 -—— 10.25 — 2.65

= 20)5 + 0.35

The uncertainty

a in the position of the vertices ;

b in the group velocities » ;

c in the direction and amount of the sun’s velocity ;

d in the position of the Milky Way,
is still considerable. Presumably the values found for V sin B are
not or hardly greater than their uncertainty. They are smallest for
the best determined groups.

This result, if confirmed by further observation, must be of great
importance for the investigation in detail of the cosmic motions. For
it would enable us to find out all the elements of the stream-motion of
any small local group of stars showing common proper motion. We
might thus hope to find out any differences in the motion of parts
of the stellar system situated in different quarters of the sky or at
different distances.

As an example take the Pleiades.

(911)

I find stv stars for which the radial velocity has been measured.
In the mean of all we get:
a1900 61900 u p 0 corrected
8" 40™ + 23°53’ 0/053) 158° + 5.5 kil p.s.
in which w represents the total proper motion, p its angle of posi-
tion, @ the corrected radial velocity. Direct observation gave + 9.8
for this velocity, but the Pleiades are Helium stars and it has been
found that these require a correction of — 4.3 kil. p. sec. which
not improbably may be due to pressure shift. By the use of the
just mentioned working hypothesis that the true motion is parallel
to the Milky Way, I derive from these data:
Direction of the motion (relatively to the sun) towards the point
of the sphere 5> 28" W— 38°7; stream-velocity 15.0 kil. p. sec;
parallax 0’’018, consequently distance 181 light-years.

In addition to my communiation at the November meeting, [
wish to draw attention to two more facts which seem hardly recon-
cilable with Eppineron’s theory.

1st. The fact that according to Eppineron’s and our own deter-
minations, neither do the elements of stream II for the A stars
coincide with those of the G stars, nor are they intermediate between
these and the elements of the 4 stream.

2°, The fact that, according to a provisional investigation, the
average value of the radial velocities of the A, /’, G, K-stars with
insensible astronomical proper motion, corrected for the sun’s motion
through space and taken all positively, does not coincide with and
is much in excess of that for the helium-stars. This result, if it is
further confirmed, would at least prove that, even in the regions of
space more remote than the bulk of our helium-stars, the motion of
the stars is still dependent on their spectral class.

It seems desirable to wait for some additional materials which
will very soon be available, before discussing these points further.

Finally, in order to prevent misconstruction, it may be well to
remark that, where I concluded to expansion of matter, I meant
expansion in a determined direction.

Such an expansion does not in the least exclude contraction in
other directions. On the contrary. In my opinion there is good reason
to assume that the kinetic energy of the system is increasing. If this
is the case and if there is no action from without, we cannot but
admit contraction of some sort.

(912)

Botany. — “On the cell-wall of Closterium together with a consi-
deration of the growth of the cell-wall in general.” By Prof. C.
vAN WisseLincu. (Communicated by Prof. J. W. Mou’.

(Communicated in the meeting of January 27, 1911).

Investigations of Fiscuer, Havuprrieiscu, and Lirkemi.urr.

Although the interesting Closteria, which occur commonly in
ditches and pools, have frequently been investigated, yet only a
smail number of investigators have studied in detail the structure of
the cell-wall in Closterium, the cell-division and growth in their mutual
relationship. There are only three prominent investigators, namely,
Fiscuer '), HauprrieiscH*), and Litkemtiier*). Their publications
give evidence of serious investigation.

Some time ago when I studied karyokinesis in Closterium Ehren-
bergii Menegh. and Closterium acerosum (Schrank) Ehrenb., the cell-
walls with their peculiar appearance also attracted my attention,
and consequently I studied the work of the investigators mentioned
above. But their explanations did not satisfy me, and hence I also
made a special study of the structure of the cell-wall, the cell-division
and the growth in both these species.

I will briefly mention the most important results of the three
investigators referred to. LitkemtLier succeeded in distinguishing
two Jayers in the thin wall of Closterium, an inner one, which
showed a distinct cellulose-reaction with iodine and sulphuric acid,
and an outer one which only gave a weak cellulose-reaction or none
at all. Lirkemttier also showed that whenever the cell-wall is
coloured yellow or brown in consequence of an iron content, the
outer layer must be considered to be that which contains the iron.

As is well known, Closteria mostly show a peculiar marking of
the cell-wall, namely longitudinal lines, dots, and transverse lines.
According to Hauprrieisca and LitkemtLier the longitudinal lines
are caused by the presence of delicate alternating ribs and furrows.
In Havpre.uiscn’-opinion what presents the appearance of a dot,
is in reality a depression or pit in the cell-wall, and he holds that,
in addition, real pores occur in the cell-wall, namely, at the ends
1) A. Fiscubr, Ueber die Zellteilung der Closterien, Bot. Zeitung, 1883, No. 14,
p-. 225.

2) P. Haverrieiscu, Zellmembran und Hiillgallerte der Desmidiaceen, Inaug.
Dissert. 1888.

5) J. Liirkemiitter, Die Zellmembran der Desmidiaceen, Beitriige zur Biologie
der Pflanzen, 8. Bd. 1902, p. 347.

(913 )

of the cells where, according to Kiss '), they are of great impor-
tance to the mucilage secretion and movement of Closterium. LUrke-
miter does not mention any depressions or pits in the wall; in his
opinion the wall possesses real pores.

The transverse lines are limited in number. They mostly occur
only in the middle of the cell: sometimes there is only one: some-
times several are present. According to the investigators mentioned,
there is found in the so-called belted Closteria, in addition to the
lines in the middle, a transverse line at a relatively great distance
from the middle, about half way between the middle and the end
of the cell, in one, or, as more often happens, in both halves of
the cell. Lirkreminier states that pores are absent from the parts
where the transverse lines occur. According to Havuprreiscu the
arrangement of the transverse lines in the different species is so
constant that they can very well serve for the systematic classification
of the genus Closterium.

In the opinion of the three investigators the transverse lines show
where the different parts constituting the cell-wall come into contact.
For all three hold that the wall of Closterium consists of pieces of
membrane of differing length. According to Hauprrietscn and Lirkr-
MULLER the pieces of membrane fit into each other with oblique,
bevelled edges. These pieces of membrane have been given different
names. The small circular pieces in the middle of the cell are called
by Havprriersca and Lirkemtiier “Querbinden” (transverse bands),
the large end pieces ‘Schalen’’ (shells) and the large cylindrical pieces
between the “Querbinden” and “Schalen” which occur in the belted
Closteria, are called ‘“Giirtelbander” (belts).

The same three writers hold that the transverse lines arise through
two different processes, namely, by cell-division and by a process
to which Fiscuzr has given the name ‘‘periodisches Erganzungs-
wachstum”’ and which depends on the intercalation of a new cylindrical
piece of membrane. In the cell-division ‘‘Querbinden” and transverse
lines arise in the middle of the cells; in the ‘“periodisches Erganz-
ungswachstum” “Giirtelbander” and also the transverse lines between
the middle and the ends of the eells are formed. In some respects
the conclusions of the three investigators differ from one another.
FiscHeR assumes that before the beginning of the formation of the
transverse wall begins, the cell of Closterium constricts itself some-
what in the middle and that soon after that on the right and left
of the constriction a circular tear appears in the wall and that the

1) G. Kueps, Ueber Bewegung und Schleimbildung der Desmidiaceen, Biologisches
Centralblatt, V. Bd. Nr. 12, 1885, p. 353.

( 914 )

wall opens. Thus two circular openings would arise. On the short
circular piece of membrane which has been cut out, the forma-
tion of the transverse wall begins which grows further inwards
until the protoplast is divided into two. Whenever the cell of Clos-
terum divides into two daughter-cells, the transverse wall splits and
the short, dissected piece of membrane to which the transverse wall
is attached. The process begins at the periphery and continues
inwards. The walls of the new cell-halves, arisen by fission of the
transverse wall, grow out rapidly during and after the fission.

In Havpreiuiscn’s opinion the cell-division in Closterium does not
always take place in the same way. He distinguishes between species
of Closterium with and without “Querbinden’’. In the latter in cell-
division the two shells separate somewhat and a new, very short cylin-
drical piece of membrane becomes intercalated. On this new piece
of membrane the transverse wall appears which grows forward in
the manner described above. In the Closteria with ‘Querbinden” the
two shells do not separate but a circular tear appears in the youn-
ger shell close to the older one. Where the tear has appeared, the
wall opens and a very short cylindrical piece of membrane becomes
intercalated. On this new piece of membrane the transverse wall
appears. The further process of cell-division takes place in both
species in a corresponding manner. In fission the short, cylindrical
piece of membrane is first divided into two, and after that fission
of the transverse wall begins, which process continues inwards.
When the cell-division is completed, the new cell-halves develop to
their normal growth.

LirvkemiéLiEer calls attention to the fact that the place where the
cell-division is to take place, is already indicated in advance.
This place is in the younger half-cell close to the older one, and
there is a feebly marked fold at this place in the cell-wall, called
“Ringfurche’ by Lirkemtnier. The only transverse line, which the
younger cell-half shows, is caused by this fold. It is only absent in very
young cell-halves, in which the wall is not yet completely developed.
At the point of the “Ringfurche” the cell-wall broadens out somewhat
and the transverse wall appears, which grows inwards until the proto-
plast is divided into two. Then the transverse wall splits, whilst
the cylindrical membrane tears, at the point at which the transverse
wall is attached. From each half of the transverse wall anew mem-
brane-half arises. LirkemiLier does not believe that in cell-division
the cell-wall opens, through the formation of one or two circular
tears. Nevertheless he agrees with Havprvieiscn that cell-division leads
to a union of younger and older parts of the cell-wall, that these

( 915 )

parts fit into each other with bevelled edges and that the older
part of the cell-wall overlaps the younger.

The three investigators have arrived at the following results with
regard to the origin of ‘Giirtelbander” (belts). According to Fiscuer
after the cell-division of belted Closteria the new cell-half is not
yet similar to the old one; it consists only of a shell piece and as
yet possesses no belt; in the new half-cell at a little distance from
its base intercalation of a cylindrical piece of membrane takes place,
which develops into the belt of the new half-cell. In this process
a circular tear also appears and the wall itself opens at the
place where the new piece is intercalated. The description, which
Havptr.eiscu gives, of the formation of the belts, agrees in the main
with that of Fiscngr. In Lirkemtier’s opinion no tear appears near the
base of the wall of the new half-cell, but a fold of the cell-wall
(Ringfurche) develops, which grows into a cylindrical piece of mem-
brane, namely the belt.

Vhe present investigation.

Attention may be directed to the following points which concern
the methods of investigation I have followed. I employed living as well
as fixed material. As fixing solutions FLemmine’s mixture (osmic acid
0,5, chromic acid 0,9, glacial acetic acid 6, water 120) and absolute
alcohol were used. The fixed and the fresh material were treated
with different reagents, such as a solution of chromic acid (from
20 to 50°/,), ScnuLrze’s macerating fluid (warming with potassium
chlorate and nitric acid), iodine in potassium iodide solution and
slightly diluted sulphuric acid (of 76°/, and of 55'/,°/,, 4 parts by
weight of 95°/, to 1 part by weight of water and 9 parts by weight
of 95°/, to 1 part by weight of water); the Algae were also warmed
in glycerine to 300°, and stains were also employed, especially
ruthenium red in a weak solution of ammonia. Generally different
methods of investigation were combined.

The Closteria were grown in ditch-water, not only in wide-
mouthed bottles and in dishes but also separately on microscope
slides. In the latter case they were examined daily, and in that
way various measurements were obtained; finally they were treated
with reagents in order to determine exactly what changes the cell-
wall had undergone.

The following pages will principally be devoted to an account of
the results obtained in this inquiry, whilst I intend to explain the
foundations on which they rest more completely elsewhere.

( 916 )

In the first place it must be pointed out that I cannot agree with
the view of Fiscnrr, Havuptrieiscu, and Lirkemtnier according to
which in Closterium the cell-wall is composed of various pieces
of membrane joined together (Schalstiicke, Querbinden, Giirtelbander)
which fit into each other with sharp edges and have been formed
separately at various times by the protoplasm. On the contrary, |
have come to the conclusion that the wall of Closterium must be
regarded as one whole. It is composed of various superposed layers.
The innermost enclose the whole protoplast, whilst the outermost
only partly cover the underlying ones. In agreement with this the
cell-wall is not everywhere equally thick. It does not arise piecemeal,
but develops as a whole from the protoplast, out of which layers
of cell-wall successively originate. The transverse lines show the
parts where the older layers, which only partly cover the younger
ones, cease. By using reagents it is easy to show that the innermost
part of the cell-wall, which is rich in cellulose, uninterruptedly
encloses the whole protoplast. lt already follows from this faet, which
escaped the attention of earlier investigators, that the cell-wall does
not consist of separate parts.

The innermost layers of the cell-wall are the youngest and the
richest in cellulose, the outermost are older and in them the cellulose-
content is greatly diminished. Using iodine in potassium iodide
solution and slightly dluted sulphuric acid the stratified structure of
the cell-wall and the differing cellulose-content of the innermost and
outermost layers are clearly seen. The cell-wall swells considerably
on being treated with sulphuric acid, especially the outermost part,
whilst the cells as a whole contract. In the presence of iodine the
wall is at the same time coloured blue. The innermost part that
extends uninterruptedly along the whole protoplast, becomes dark-
blue. The outermost layer gives no cellulose reaction; it is stained
yellow by iodine and extends continuously over all the layers of
the cell-wall. Between the innermost part of the cell-wall which is
rich in cellulose and the yellow-stained peripherai layer, lies a
portion poor in cellulose which takes only a light blue stain. In
Closterium acerosum there is sometimes no cellulose-reaction at all
to be observed directly under the peripheral layer.

With some preparations, it can be seen that the innermost part
of the cell-wall, rich in cellulose, as well as the outermost part
which is poor in cellulose, consist of different layers. Evidently the
layers, in proportion to their age, undergo a chemical modification ;
the cellulose-content becomes smaller; the cellulose gives place to a
material which gives no cellulose-reaction and the tendency to swell

( 917)

up considerably in sulphuric acid increases. Also to some extent a
coalescence of the layers takes place. In the outer portion they are
not so easy to distinguish as sometimes in the inner portion.

In the outermost layer, which is stained yellow by iodine, another
modification has moreover evidently taken place, in which more
external factors have come into play. Transverse lines are clearly
seen on the cell-wall after treatment with iodine and sulphuric acid.
The older layers which lie over the younger ones project somewhat
and at the base of the older layers the underlying younger ones
are poorer in cellulose; the wall there is more subject to modifi-
cation; in consequence of this the blue-coloured wall shows light
lines along the older layers, which project somewhat.

With respect to the dots and the longitudinal stripes, I observe
that I could see them best with different focussing. The dots were
then most clearly seen on the outermost part of the cell-wall and
the longitudinal stripes in the innermost part of it. This observation
is not in agreement with the view of LitkemMULLER, in whose opinion
the dots were produced by pores, but it is more in accordance with
that of HavprrLeiscn, who speaks of depressions or pits. The fact
that the lines are most clearly visible in the innermost part of the
wall is hard to reconcile with the view of the investigators who
maintain that the wall is provided with peripheral ribs and furrows.
I may remark with respect to Closterium acerosum that the dots
are absent from the parts where the transverse lines oveur.

Like Lirkemiiier [ am of opinion that the part where cell-division
is to take place is already indicated beforehand on the cell-wall.
The cell-wall there shows a pronounced modification. In my opinion,
L&rKeMULLER’s explanation of the phenomenon is, however, not tenable.
According to this author, the cell-wall forms, at the place of division,
a small fold directed inwards, so that there appears to be a slight
thickening on the inner side and on the outer side a furrow (Ring-
furche). Lirkemtrner obtained his results with dead material. With
fixed and other dead material I also have observed at the place of
division a little fold in the cell-wall, but never with living material,
and hence I do not think that in living specimens any fold of the
cell-wall occurs at the place of division. My own conviction is that
the cell-wall in the part under discussion has undergone an important
change. It shows there a transverse line which can be distinguished
from the other transverse lines. The cell-wall at the altered place
is poorer in cellulose and less strong. After treatment with iodine
and somewhat diluted sulphuric acid a light line ean be noticed.
During treatment with reagents (chromic acid) it often happens that

( 918 )

the cell-wall tears at the place of division. The little fold seen in
dead material is also probably connected with the fact that the cell-
wall at the place of division is less strong.

It is easy to answer the question why no fold is to be observed
in living material. During life the wall is stretched by turgor, so
that no fold is to be expected. To this I must add that in fixed
material I have sometimes seen much larger folds of the cell-wall,
namely, in the younger, still thin walled half of the membrane.
The cell-wall then showed a triple circular fold. In living material
such folds do not occur either. This strengthened my belief that the
little fold also first appears after death.

In connection with the fact that in Closterium the part at which
cell-division is to take place is determined beforehand and that at
this place the cell-wall shows a marked modification, I will here
describe results which I obtained formerly with Spirogyra. As in
Closterium, so in Spirogyra the formation of the primary transverse
wall begins on the mémbrane cylinder opposite the nucleus and then
continues inwards, until the protoplast is divided into two. In Spi-
rogyra, the part. where the formation of the transverse wall is to
begin, does not show special characters in the cell-wall, yet by a
series of centrifugal experiments I’) have proved that the place is
already determined before the beginning of the nuclear-division, by
the influence which the nucleus exerts. I am inclined to attribute
the like kind of influence to the nucleus of Closterium. The important
modification of the cell-wall at the place of division in Closterium
is connected with the subsequent separation of the daughter-cells.

In Closterium I could demonstrate no cellulose in the primary
transverse wall. It is characterised by a greater solubility in chromic
acid solution. When the primary wall has been formed, a layer of
cell-wall; rich in cellulose is produced in each daughter-cell; it
surrounds the whole protoplast and covers the old cell-wall and the
primary transverse wall. This new layer of the cell-wall is produced
by apposition. Results in agreement with this were earlier obtained
by me with Spirogyra. *)

In Closterium a fission of the cell-wall follows the thickening of
the primary transverse wall. At the modified part the old cell-wall
is stretched until it tears asunder and then the transverse wall splits.
It is the primary transverse wall which splits. The process begins
') Zur Physiologie der Spirogyrazelle, Beihefte zum Bot. Centralbl. Bd. XX1V
(1908), Abt. I. p. 165.

2) Over wandvorming bij kernlooze cellen, Reprint, Bot. Jaarboek, Vol. 18,
1904, p. 11 and 12. Zur Physiologie der Spirogyrazelle, 1. c. p. 174.

(919)

on the old cell-wall and continnes inwards. At the place of division
a slight constriction occurs which slowly becomes more marked. It
is peculiar that the new part of the cell-wall which is thus exposed,
i.e. the split transverse wall, shows a sharp contour in contradistine-
tion to the old cell-wall, and this is probably to be ascribed to the
fact that the old wall is more modified chemically. The two halves
of the transverse wall assume during fission a convex position with
regard to each other; finally they separate. In the fission of the
cell-wall which is induced by a chemical modification, turgor also
plays an important part. Without the action of turgor it is difficult
to imagine that the thin halves of the transverse wall could take
up a convex position with regard to one another. Through the same
force which brings this about, the old wall tears at the modified
weak part and the transverse wall splits.

Nothing can be traced of the occurrence of circular openings
(Fiscuer, Hauprrierscn) in the old cell-wall and of intercalation of
a new, narrow annular piece of membrane which projects (FISCHER).
When the old wall tears each daughter-cell has already a new wall,
so that when cell-division proceeds normally, no openings can arise
in the cell-wall. The occurrence of openings in the wall is moreover
hardly tenable. As a consequence of turgor the protoplasm would
pass out and a speedy death of the protoplasm might be expected.
Princsurm ') has also previously assumed that in the cell-division
of Oedogonium the wall opens by means of a circular tear, but later
investigations have shown that this does not take place in Oedogonium.’)

When the cell-division is finished, the halves of the transverse
wall grow out quickly to the new halves of the cell-wall. These soon
approximate in shape and size to the old halves of the cell-wall. The
wall of the young halves is at first very thin. Later the difference in
thickness between the new and the old half becomes smaller, some-
times indeed it is no longer of any significance. Chemical modification
seems to take place quickly in the new halves of the cell-wall.
Quite soon with iodine and slightly diluted sulphuric acid the thin
peripheral layer which is stained yellow, can be distinguished, as well
as the subjacent layer poor in cellulose and the innermost layer which
is rich in cellulose. When the daughter-cells are still connected, the
peripheral layer can already be demonstrated. When the wall becomes
older and thicker, the peculiar markings on it become visible, namely

1) N. Prinasuem, Morphologie der Oedogonien, 1858, Pringsheims Jahrb. f.
wiss. Botanik Bd. I. p. 13.
2) CG. van Wisseuinen, Uber den Ring und die Zellwand bei Oedogonium, Bei-
hefte zum Bot. Centralbl. Bd. XXII (1908), Abt. I. p. 182.
61
Proceedings Royal Acad. Amsterdam. Vol. XIV.

( 920)

the longitudinal lines and in Closterium acerosum also the dots. It
has already been stated above that the chemical modification also
causes the disappearance of the dots at the place of the future cell-
division, Consequently the old cell-wall has no dots round its edge.
While the new membrane-half acquires dots, no new ones develop
at the part where they have disappeared. In consequence there occurs
on the border of the old and new membrane-half, a small strip
free from dots.

With regard to the question how the growth of the cell-wall in
Closterium must be interpreted, the following remarks may be made.
Apposition, addition of new layers of cell-wall substance must certainly
be assumed. This is in agreement with the stratified structure of the
cell-wall and also with some observations concerning its development.
How, for example, can the existence of the layer of the cell-wall
rich in cellulose in the daughter-cells after the formation of the
primary transverse wall be explained without accepting apposition ?
For one cannot believe that one and the same layer at one place
develops by intussusception from the primary transverse wall which
contains no cellulose and in another part develops from the old
cell-wall. Less easy to answer is the question whether in Closterium
intussusception, intercalation of new material in the already formed
cell-wall, takes place. Superficial observation might cause the
impression that intussusception is very probable on account of the
rapid surface growth of the thin wall of the new cell-half. Ido not
think, however, that it is necessary to postulate intussusception in
the case of Closterium. Nevertheless the growth of the cell-wall
cannot be completely explained by apposition. There is no doubt
that in the development of the cell-wall an important modification
takes place in the layers already formed by apposition. The new
layers rich in cellulose are produced by apposition on the inner
side of the cell-wall. Slowly they become poorer in cellulose and
richer in a substance which does not give a cellulose reaction. In
agreement with this layers rich in cellulose are found on the inner
side of the cell-wall and others poor in cellulose and free from it
are found on the periphery. The chemical modification makes the
wall more extensible, consequently turgor can contribute to the increased
size of the cell. In order that the wall may retain its required
strength, if must be strengthened on‘the inner side by new layers.
From this it follows, that by rapid surface growth as in the case
of the new membrane halves, chemical modification and apposition
must also be intensive. I believe that apposition is considerably
stronger in the new membrane halves than in the old ones, for

(921 )

when the surface growth of the new halves ceases, probably in
consequence of the increase in volume of the cell and resultant
decrease in turgor, then especially a growth in thickness occurs and
the difference in thickness between the two halves of the wall be-
comes much. less.

A study of cell division in Closterium makes it specially clear that
in the development of the cell-wall, chemical modification is of great
significance. At the place of the cell-division chemical modification
of the cell-wall is very extensive; it here produces not only stretching
of the cell-wall, but even the tearing asunder of the old cell-wall.

Apposition of new cell-substance, chemical modification of that already
formed and finally turgor are the three important factors in the
development of the cell-wall in Closterium. With respect to intussus-
ception, its occurrence can neither be proved nor disproved. It is not
necessary to accept it in order to explain the development of the
wall in Closterium.

The conflict between the adherents of the intussusception theory
and those favouring the apposition theory of growth of the cell-wall
has in my opinion formerly often been so unproductive because the
chemical nature of the cell-wall and especially the chemical modifi-
cation which it undergoes has received little or no attention. Neither
apposition nor intussusception can alone completely explain the deve-
lopment of the cell-wall.

When the “Urmeristem’” of a vegetation-point is compared with
the ‘“Dauergewebe” of the adult organ which arises from it, it is
impossible with the help of the intussusception- or apposition-theory
to form a conception of the growth of the cell-walls and even, when
one accepts both processes, no satisfactory explanation of the deve-
lopment of the cell-walls and tissues results. If, however, continuous
chemical modification, as well as apposition, is assumed, then the
explanation of the phenomena observed does not any longer present
insurmountable difficulties. It may now be accepted with certainty
that the stratified composition of the cell-wall has its origin in the
fact that on the inner side layers are successively formed by the
protoplasm, which layers cover one another. If these layers under-
went no chemical moditication, it eould not be explained why, for
example, the outermost layers of the cell-wall of many parenchy-
matous bark-cells show a much weaker cellulose-reaction than the
innermost-layers and sometimes seem to be quite devoid of cellulose
content. Where the cells are in contact with intercellular spaces, one
can sometimes observe that the outermost of the layers containing
cellulose have been modified to a varying extent, so that the self-

61*

( 922 )

same layers in one place still show cellulose reaction and in another
place do not. In some tissues it appears as if the cells in agreement
with the old conception are imbedded in intercellular substance.
Frequently it is no longer possible in adult tissue to recognise
sister-cells, although this would present no great difficulty if no
modification of the cell-wall had taken place. If can easily be ima-
eined that by chemical modification of the cell-walls the relationship
of cells is effaced.

Although I am inclined to believe that generally apposition, modi-
fication and turgor play a great part in the growth of cell-walls,
yet I also think that. intussusception is not always excluded; thus
for example, in the cuticularisation of cell-walls containing cellulose
it is necessary to assume intussusception. *)

In Closterium, no growth in length of any importance can be
observed in either the old or the new full grown halves of the wall ;
nevertheless a considerable increase in length can frequently be noted
in some individuals. The phenomenon is caused by a process which
investigators have called “periodisches Erganzungswachstum”. It
amounts to an addition to the cell-wall of new pieces of membrane.
Opposite the nucleus, the cell-wall undergoes a modification, which
is similar to that which happens to the cell-wall before cell-division.
At the modified part the cell-wall becomes stretched, whilst on the
inner side it becomes strengthened by new layers through apposition.
The old layers of the cell-wall finally tear asunder and the under-
lying new cell-wall is exposed. It shows a sharp outline just as
the cell-wall which was laid bare in cell-division. Whilst the
thin, new, weaker piece of the wall is stretched by the influence
of turgor, the cell-wall becomes strengthened on its inner side
by apposition. In this manner a whole new piece of wall is inter-
calated. An opening of the cell-wall, as Fiscuer and Havuprr.erscu
maintain, takes place no more than in cell-division, for, when the
old layers are torn asunder, anew wall is already present. After inter-
calation of a new piece, the cell-wall shows two new transverse
lines. The walls of the older cell-halves are thicker and project somewhat.

Between cell-division and intercalation of a new, cylindrical piece
of membrane there are some important points of agreement. The
process in both cases is induced by a modification of the old cell-
wall, which finally tears asunder, after a new cell-wall has been formed.
In both cases, rapid surface growth of the newly exposed parts of

1) G. vAN Wisseninaw, Over Cuticularisalie en Cutine. Reprint from the Proc.
Koninkl. Akad. v. Wetensch. Amsterdam, 2nd Sect. D. Ill, N® 8, p. 26. Sur
la culicularisation et la cutine, Extrait des Arch. Néerl. T. XXVIII, p. 32.

(923 )

the cell-wall takes place. The processes take place at the same places
in both cases, namely opposite the nucleus in the younger half of
the cell near the older half or in the middle of a new intercalated
cylindrical piece of membrane also opposite the nucleus, always
therefore in parts where the cell-wall is younger and thinner. Cell-
division is distinguished from intercalation in that it is accompanied
by division of the nucleus and the formation of a transverse wall.

It has been stated above that the intercalation of a new, cylindrical
piece of membrane can also take place in a similar piece of membrane
which has already been intercalated. This process can therefore be
repeated in one and the same cell. Cell-divisions and intercalation
of pieces of cell-wall are not processes which regularly alternate in
a certain group of Closteria (belted Closteria), as the three investigators
already mentioned have imagined. In the species I have studied both
processes occur; sometimes there are 10 or more successive cell-
divisions without any intercalation. It may also happen that after
repeated cell-divisions intercalation of a new piece of membrane takes
place a few times in succession. The name “periodisches Ergénzungs-
wachstum” is not correct.

As already described, the transverse lines which the cell-wall
shows; arise by cell-division and by intercalation of new pieces
of cell wall. As Lirkemiituer has observed the young individuals
which arise from spores originally possess not a single transverse
line and later one transverse line only at the place of future cell-
division. At this stage one cannot therefore distinguish an older and
a younger cell-half, but this is possible in the daughter-cells, where
the cellwall at the border between them shows a transverse line, whilst
later the young cell-half at the place of division also shows a
transverse line which can be distinguished from the first-mentioned
one. Ai each cell-division there is cut off from the wall of the
younger cell-half a short piece, which remains connected with the older
one. The daughter-cell with the oldest half of the ceil wall possesses
after each cell-division a strip more than its mother-cell. In this way
cells with 10 or more median transverse lines can be formed.

By intercalation of pieces of membrane cells arise which show
transverse lines at a considerable distance from the middle. It must
be borne in mind that the two processes can alternate with each other
in various ways, that the pieces of membrane which in cell-division
are cut off from the younger half may be of different sizes, that the
mother-cell in cell-division is frequently divided into two unequal
parts, that intercalated pieces of membrane can grow to different
lengths and that in general, in proportion as the parts of cell-wall

(924 )

are older, they are also thicker and the marking on the cell-wall
is more distinct. Moreover the growth in thickness of some parts
of the cell-wall sometimes shows abnormalities, so that it may happen
that younger parts have thicker walls than older ones and give a
stronger cellulose-reaction (sometimes in Closterium Ehrenbergii). When
all this is taken into account, it is clear that the cell-wall in Closterium
even in one: and the same species shows an enormous diversity,
especially with respect to the number and position of the transverse
lines or the length of the parts of the cell-wall and the thickness
of the cell-wall in different parts. For this reason I cannot agree
with Hauprrirtiscu’ that the arrangement of the transverse lines in
different species is so constant that they can serve for the systematic
classification of the genus Closterium.

Chemistry. — “On the system: Water — Alcohol — Manganous
sulphate.” By Prof. F. A. H. Scurememakers and Dr.
J. J. B. Dewss.

(Communicated in the meeting of January 27, 1912).

The equilibria occurring in this system are represented in fig. 1;
the points IW and dA indicate the components water and alcohol,
the third apex of the components-triangle which is not drawn here
therefore represents the J/nSO,. The temperature axis is taken
perpendicular to the plane of the eomponents-triangle.

The curve A/ situated in the side plane MnSO,—A— T of the
prism is the solubility line of the anhydrous MnSO, in absolute
alcohol; as this salt is practically insoluble in absolute alcohol the
curve f/ must lie in very close proximity to the axis A 7 of the prism.

The equilibria occurring in the binary system: water — InSO,

( 925 )

have been investigated by F. G. Corrreti'); these equilibria, so far
as they are required in the ternary system are represented in fig. 1
by the curves ab, bc, and cd situated in the side plane MnSO,—W—T.

The curve aé indicates the solutions saturated with MnSO,.7 H,0,
the curve dc those saturated with MnSO,.5H,O0 and the curve cd
the solutions saturated with MnSO,. H,0.

The equilibria occurring in the ternary system are represented
by the surfaces situated within the prism, their intersecting lines and
intersecting points:

abuku’e is the saturation surface of the MnSO,.7 H,O0
efv’u’ and bevu ,, ,, - en ASO ea see)
fgmdevkv’ i ss ee sae SO ee)
ghim eee - He ree we ie OM
kuvkv’w’ » 5 binodal surface.

In order to facilitate the survey, the figures 7, 5, 1 and O are
drawn on the saturation surfaces, and the letter 5 on the binodal
surface. For the sake of brevity we will call the salts in future J/n, ,
Mn,, Mn, and Mn,.

The saturation surface of the A/m, consists of two parts separated
from each other; the one to the left indicates the saturated solutions
of Mn, rich in water, the one to the right those rich in alcohol.

The binodal surface 4 should be imagined to be divided into two
parts by the critical line AA,; with each solution L, of the one
part, a definite solution ZL, of the other part can be in equilibrium.
The binodal surface therefore represents the two-layer systems L,-++ L,.

The intersecting lines of the saturation surfaces of a solid substance
form the saturation lines representing the solutions saturated with
two salts.

ew’ and wb is the saturation line of Mn, + Mn,
jor and. ve 45. 4; sp » » Mn, + Mn,
gin eds s ene) Ae ins:

The intersecting lines of the binodal surface with the saturation
surfaces of the solid substance represent the conjugated liquid-pairs
which are saturated with a solid salt. Because as seen in fig. 1
the binodal surface intersects each of the saturation surfaces of M/n,,
Mn, and Mn, in two curves, it follows that one series of liquid-
pairs is saturated with MZ/n,, another series with Mn, and a third
series with Mn,. In fig. 1 are represented :

1) F. G. Corrrent, Journ. Phys. Chem, 4 637 (1900).

( 926 )

the liquid-pairs saturated with M/n, by Ku and Ku’

” ” ” ” ” Mn, ” uv ” wy!
L, AIHA /

” ” ”» ” ” Mn, ” vK, ” v HG,

Each of the points « and w’ is the intersecting point of the bino-
dal surface with the saturation surfaces of Mn, and Mn,. These points,
therefore represent a liquid pair Z,-+ L, saturated at the tempera-
ture 7, = Ty with Mn, + Mn, or, in other words, the system :

Mn, + Mn, + Lu + Lu

The same is true for the points v and v’ which at 7, = 7, repre-

sent the two liquids of the equilibrium :
Mn, + Mn, + Ly, + Ly

The saturation line of Mn, + Mn, consists (experimentally) of the
two parts ew’ and wb; as, however 7, = T, , the complex Mn, +
Mn, + L, traverses an uninterrupted temperature series; the solution
however, changes its composition abruptly, at 7, = 7, from L, into
Ly, or reversedly so. The same is true for the complex Mn, +
Mn, + L in the points v and v’.

From the composition of the solutions Z, and ZL, it follows that
at 7,,= 7, the reaction:

Mn, + Lw 2 Mn, + Li

Mn, + Mn, + Ly | Mn, + Mn, + Ly
Mn, + Ly + Ly | Mn, + Lu + Ly
occurs.

From this reaction it follows that from 7,—= 7, one saturation
line of Mn, + Mn, must proceed to a lower, and another one to a
higher temperature. Further, it follows that the liquid-pairs saturated
with Mn, occur below and those saturated with Mn, above 7, = Ty .

From the composition of the solutions LZ, and Z, it follows that :
at 7,= T, the reaction:

Mn, + Ly 2 Mn, + Ly

Mn, + Mn, + Ly | Mn, + Mn, + Ly
Mn, + L.+ Ly | Mn, + Ly + Ly

occurs. The situation of the curves proceeding in fig. 1 from the
points » and v’ is in accordance with this reaction.

From the figure it follows that the dissociation region, if we only
consider stable conditions, extends from 7;=5,°3 to T;,=48.5°.
Between 7, and 7), a separation into two liquids in the stable con-
dition is possible, below 7; and above 7%, this is, however, no

longer the case and, as has been confirmed experimentally, only a
separation in the metastable condition can take place.

In general the mixtures: water + alcohol + salt, in which the
separation only takes place in ternary solutions, exhibit a minimum
critical mixing temperature. That is to say that below this critical
temperature no dissociation into two liquids can take place; above
this temperature, however, decomposition may occur,

For instance, in water-alcohol mixtures A.NVO, can cause disso-
ciation only above 79.5°, NH,NO, only above 67.6°, (NH,),SO,
only above 8°, and Na,CO, only above 27.7°.

Similar systems with a maximum eritical temperature, namely with
a temperature above which no separation can any longer occur have
to our knowledge not yet been found. In the system water-aleohol
-MnSO,, however, now investigated by us, not only a minimum
critical temperature 7, but also a maximal critical temperature 7',,
seems to exist.

Mn, If we project the special curve
kuvk,v'u’ on the plane of the
components-triangle JV/—A— Mn,, we
obtain something as in fig. 2. The

K triangle, however, has only been

K drawn partially in this figure. The

projection of the special curve con-

Ww A sists of two conjugated branches

Fig. 2. which form a closed curve of a pecu-

liar form; the arrows indicate the direction in which the tempera-
ture increases.

Each of the branches £4, must, of course, exhibit a discontinuity
in two points corresponding with the temperatures 7, and 7, ..

If we intersect the spacial representation by planes perpendicular
to the temperature axis, we obtain the isotherms; these have been
determined at 50°, 35°, 30° and 25°. A few points of the isotherm
of O° have also been determined.

The isotherm at 50° can be represented schematically by the
curves dm and ind and the isotherm of 0° by the eurves ae, ef, tg

and gh. A few other isotherms are represented in fig. L by the
dotted curves.

( 928 )

Bio-Chemistry. — “On the action of some carbon derivatives on
the development of penicillium glaucum and their retarding
action in connection with solubility in water and in oil.” By
Prof. J. Borsexen and Mr. H. Warrrman. (Communicated by
Prof. A. F. HoLieman).

(Communicated in the meeting of January 27, 1912).

Le

In our previous communication *) we have shown that there exists
no essential difference between the benzene derivatives investigated
by us, as regards their action as retarding, as well as nutrient
substances for the penicillium glaacum.

The compounds readily soluble in oil exert a retarding action even
in small concentrations, whereas with substances sparingly soluble
in oil, this retardation only occurred with higher concentrations, but
all these substances which dissolve fairly readily in water give, finally,
a development although with compounds like salicylic acid, benzoic
acid and the tolaylic acids, this takes place only with very low
concentrations at which a vigorous vegetation is excluded owing to
the small total quantity of organic nutriment.

In each case we may take it for granted that all these substances
are capable of providing the penicillium with carbon-containing
material, if we only take care (by the choice of a fitting concen-
tration) that the organism cannot overload itself with the same.

Our Continued investigation has shown that the penicillium is not
very particular as to its food, but that it is capable of development
in solutions of nearly all the carbon derivatives.

Even chloroform, formic acid, methy! alcohol and carbon tetra-
chloride, given as exclusive carbon-containing nutriment, cause growth
and, therefore, can yield the material from which the penicillium
constructs its undoubtedly very complicated system of organic
compounds.

Only a few derivatives of the highest oxidation stage of carbon,
such as carbon dioxide and urea are unsuitable.

The results are shown in Table I. For the description of the
experimental process we refer to the first communication.

If we survey these experiments which have been collected in this
table at random from a much greater number, we notice in the
first place that by far the greater number, chosen from the most
varying groups of organic compounds, can promote the growth,

1) These Proc. of December 30, 1911, p. 608.

( 929 )

TABLE 1. Development of the penic. gl. on different carbon compounds. The inorganic nutri-
ment consists of 4/g9°/) of potassium phosphate, 3/9)°%) NHgCl and 1/9) °/) of magnesium
sulphate; ¢ if not stated otherwise = 21°—22°,

Quantity of solution = 50 ce.

Compound
formic acid
acetic >
palmitic »
cerotic »
stearic >
oxalic >
malonic »
sebacic »
succinic »
|glutaric >
d tartaric »

| formaldehyde
| methyl alcohol

| ethyl alcohol

glycol

| glycolic acid
| lactic »

| chloroform

| CCl,

CoCly

| CCIBr: CHCI
CCIH: CCl,

|

|
benzene

naphtalene
anthracene
phenantrene
pyrene
znaphtoic acid
| « naphtol

|p >
i

| cetyl alcohol

olive oil 1)
urea
glycerol !)

|

'p-phenolsulf.ac.
>

NEES
ieee
Ted ic coo Dea
Petting a 3?
| 2) 10 2+ |34+-
| 3| 2 ? Pate
| 4 Davee Bate
5 De eae
65.544 [64+
| 7/5.5/4+ [644
|} 8|5.5\44+ 64+
| 9] 6 j44- l64—-
10} 4 |44+- j6+4
11) 51 24 [344
(OG |p =
13/3.5\2+ I3+
114/200 /24+ [3+
15| 4 |2+ [3+
ea 3-4
litg|) Bay pe eae
18|10.5/24+ |g
119) 21 j2+ l6--4-—
| 20 Pr fe
| 21 De te
22) nea
3) eo
i = 4
25 B®
96/35/24 '3-1
27| 55 |24- [344
Nee
28 apple saat
be |
90)) yi eetes alae:
30 5? |g4
31] (5 2 (8+
|
32 —
33| 5 |B 7+
BA Gin 5 wi
35; 8 |5— |T—
36 8 2— 4—
37 24 i444
38)(010) (24
39] 42 21 [g4—1
40 | 261 )2-- |84—--—-+
41 |1073)24++-/34+-+
42 |1403/24 +4344
saat |

4+. 10+
fae see
4+ 10+
44 10+
4 10
is ras
[+
11 strong
Mette
a=
Bf 124-4
7
1+
14++
7 v. strong
6+
|9 strong
ran 30-+-++-F
10-+-
10+
10+
10-+-++
See
5+4+
6+ +--+
94+ — |14++
++ 44+
9— 14—
9— 14—
es 3044
| [14 strong
6= as
/
jj Strong fot y, strong
4 v. strong|7
4 str. <39/7 str.som. 39)

Development after a given
number of days

Remarks.

( The pieces do not }3 and5

(perceptibly dissolve. { fairly

| » » > » { wellsol.
> > > » Jin oil

| Temperature of the room.

» > » »

( Division factor oil: water

( 03
» » 2 US VERY,
> > > § small

Insoluble in oil.

Development remains slight.

» »

One dr. which does not quite diss. |
|

> » » » » » » |

The sulphonic acid group also |

proves no hindrance; in our

|) first investigation we had,

|| presumably, started from an

|| impure preparation.

One drop.

Benzene mixes with oil in all

proportions.

Of these hydrocarbons were

| added quantities of 1,5—8
mg., which, however, did

| not dissolve.

|

Naphtalene is very readily so-
luble in oil.

|; Very readily soluble in oil.
_) Division factor between 76-102.
| Both naphthols are percepti-
bly soluble in water.
| ( Fairly soluble in oil; percep-
( tibly soluble in water.
| One drop.

1) The research of A. Roussy C. R. 153, 894 (1911) on the life of fungi on fats and fatty
acids gives no pure result, as in the nutrient base tartaric acid was present which, as is weil
known, (and we can confirm this) forms a suitable source of carbon.

Owing to the presence of this acid, the growth on dilute glycerol solutions has escaped him;
he has only noticed a harmful action of 10 to 12%, of glycerol which is not to be wondered
at, as we found already a slight diminution with a + 30/, solution (No. 42).

( 930)

Besides carbon dioxide itself, formaldehyde, pyrene, urea and also
the two naphthols cause no development.

As regards formaldehyde we are going to extend the investigation
to still lower concentrations; urea is very closely allied to carbon
dioxide, and the two naphthols have a particularly favourable division
factor oil: water, while they are still very perceptibly soluble in water.

In the second place it strikes us that there are some compounds
such as palmitie acid, stearic acid, benzene, naphthalene, cetyl alcohol,
and olive oil, whose division factor olive oil: water is undoubtedly
much larger than that of salicylic acid and benzoic acid and which,
evidently, can yet promote the development of the mould.

These substances, however, are distinguished from the above strongly
retarding substances (to which belong also the naphthols) by their
extremely sparing solubility in water.

In order to demonstrate the significance of the rapid dissolving
of the substances in water in connection with their nutrient or
retarding action, we are obliged to consider the quality of the proto-
plasmic wall which those substances must traverse in order to be
absorbed in the organism. Let if be presupposed that a too large
concentration of any substance whatever will cause a retardation
of the growth. Without further arguments as to the possible
structure of the protoplasmic wall we may well take it for granted
that it must not be put on a line with a layer of oil, without
further evidence. ;

So long as it forms a part of the living organism it must be
regarded as a wall limited by an aqueous liquid, and therefore as
a membrane which, in a certain sense, is protected by a layer
of water.

If we were dealing with an oily layer immediately accessible, all
substances readily soluble im oil, and particularly those insoluble in
water, would penetrate and exert their retarding action.

{On the other hand, substances insoluble in oil would be unable to penetrate
and thus serve as a nutriment. This point, which may be connected with the
differences existing between lecithin-cholesterol mixtures and true oils, will be
disregarded for the present].

This, however, is evidently incorrect, for the higher fatty acids
(which are very sparingly soluble in water) naphtalene, cetyl alcohol
and olive oil itself, which dissolve in oil freely or very readily, do
not act at all retardative on the growth of the peniccdlium and, on
the whole, form in the long run a fairly good organic nutriment.

(931 )

This behaviour may be explainéd very readily when, as stated
above, we suppose that all the substances before they arrive at the
protoplasmic wall must traverse a layer of water; the substances
very sparingly soluble in water can perform this only in an extremely
tardy manner and the concentration of these substances in the
protoplasm can, therefore, increase bat very slowly. If, when the
concentration in the protoplasm is but small the organism can use

up these substances —- and the penicillium seems capable of this
in a very high degree — they may act as an organic nutriment.

The substances which are readily soluble in water but very sparingly soluble
in lecithine etc. such as (presumably) succinic acid, glutaric acid ete, will, of course,
be prevented by this last property from rapidly overloading the organism. If these
can be readily assimilated they will form a good carbon-containing nutriment.

Not merely the great division factor lipoid: water marks a sub-
stance as a narcotic, but it must be capable of entering rapidiy into
the organism and, besides a rapid and ready absorption in the
protoplasmic wall proper, a decided solubility in water is therefore
required ').

From this and the previous investigation it follows that from any
organie substance devoid of any particularly pronounced basic or
acid properties we may predict*) whether it will exert a strongly
retarding action on the growth of lower, organisms. If so, it must
be (a) somewhat soluble in water and (/) dissolve considerably more
in oil than in water °).

Il.

In order to confirm the results obtained and the conclusions drawn
therefrom, by a larger number of experimental data we have extended
our investigations over a large number of saturated fatty acids
with normal carbon chain.

These offer the great advantage that, in this series of substances
we have at disposal a material of which, while retaining analogous
chemical properties, the physical characters, so far as the solubility

1) Whether colloidal solutions must be regarded here as distinct from true
solutions must be decided later.

») This prediction, of course, only relates to aqueous solutions; as soon as
much fat is present, for instance in butter, the retarding substance, on account of
the large division factor will accumulate in the fat and can only act in a retard-
ing manner for so far it is still present in the water-phase. We will refer to
this question later on account of its practical importance.

in water
nuous modification.
The preparations,

TABLE II.

phate, 4/9)°/) ammonium chloride and !/

and oil is concerned,

which

( 932 )

we have used,

0/
50 /0

undergo from term to term a conti-

were mostly obtained

Development of the penscillium in solutions of !/5)°/) potassium phos-
magnesiumsulphate which con-

tain the saturated fatty acids as exclusive organic nutriment.

T= 20°—21°; quantity of liquid =50 c.c.
| Maxim. |
quant Development after 4
(eempadne) Nin me a given number of days “ment | Remarks
— —— — 7 ————S 7 ———— —————s —!S — eae = —— eee
Pail Gl eee iL 6+ 104
icacid | 2) 45 j2— |4— 6? 10? Smal
formic aci higitnget ines f= fA 10 | development
7 ie (ee ae e ule ;
|; 44 10 j2+ |44-+ 6++4-4 - fairlystrong, acetic acid does not.
acetic acid | 5} 50 |2? /4+-- 6 strong s‘rong | 50—99 dissolve inolive oil,
6; 99 Pes 44+ <N05) joa jfairly strong) in all proportions
Ne vile site Pes
| |
7] 9.5)2+ |44+ nee ho | dissolves in olive
prop. acid 8| 48 |2— (4+ Raa! Eee +48 oil in all propor-
Oh 96 i2—= 2 14— 6+ 10+ tions
mu le le = i Ra eS
Oeil PES ek 6+ j10 | some-
nbutyr.acid] 11) 55 |2— /4— 6+<11 baie what >
12) 110 |2— |4— 6— ‘10 0— | <85
13} 8.3/34+/5++ t+ [lot ++
14, 90.333? |5+ ‘T+slight 10+ far
valeric acid) 15) 95.433— |5+<14 7+ 10+ below »
16; 208.4\3— |57 1? 10 — 90.3
(Hexoic) | 17) 221.13— [5— 1— 10—
‘caproicacid 181 drop27 4++ 6+++ | 9 strong >
19}2 drops |2— |4? 6+ 9+
| |
ieee tal eee a
ar | ey, Lee | ‘2 drops no longer
heptoicacid ao Grenier = Ia By | dissolved entirely
| | in water
(0X53 (9 A eR aes ae 7 —e= | a Sa
caprylicacid 221 drop2+ 44+ 6++-+ | 9 strong
23/2 drops |2— |4— c= | 9—
eee aa & meri na] = 7 = Pe =a 7e3 -
nonoic acid 241 drop2— 4? 6+ | 9+ +4 >
2? drops ae \|4— oe | 9— |
“(Decoic) | | = - Of the other fatty
capric acid | 26) = -+| ++ 1 -+4+4)) strong acids a small quan-
lauric acid | 27, | § ++ +4 ++-+)| strong — tity no longer dis-
myristicacid, 28 ES a7 +-+- strata ++ solves in water.|
palimiticacid: 29) \ = 2+)) 4 + 6 + 9 + The solubility of
Stearic acid | 30)| = || + -+ 4 a5 palmitic acid and
arach. acid 31} 5 ;/) + + | |} not observed | stearic acid in olive
cerotic acid) 32) 5, +) | + + + | oil isstill very con-
| 3 | | siderable > 0,49)
(aoe | | (of palm. acid > 1)

|
|

( 933 )

from Kannpaum; of the lower fatty acids the concentration was
determined by titration, whereas the higher ones, if perceptibly
soluble in water, were weighed out.

In the case of the practically insoluble acids a little of the snb-
stance was added; on sterilising they did not perceptibly dissolve. Of
the acids soluble in water different concentrations were investigated
in order to determine, if possible, the maximum of development.

For the rest, we refer to our first communication.

When, for a moment, we exclude formic acid, we notice thatthe
fatty acids behave exactly as was to be expected from their solubility
in water and in oil.

Acetic acid, favoured by its solubility in water, can serve as an
exclusive carbon-containing nutriment up to fairly high concentration.

The concentration of maximum growth is situated about as high
as with p- and m-oxybenzoic acid (see previous communication).

With propionic acid, n-butyric acid and n-valeric acid which are
miscible with oil in all proportions, this maximum is situated much
lower.

As they dissolve sufficiently in water, they can act either as a
nutriment or as a retarding agent according to the concentration.

This is still very plainly perceptible with the acids C, to C,
included ; in very low concentration they give an excellent development
but very soon, however, the maximum is attained, so that ina very
dilute but still saturated solution (<2 drops to 50 ce.) no, or but
little, growth takes place.

From capric (Decoic) acid upwards nothing more is noticed of a
retarding action. Notwithstanding the undoubtedly very high division
factor oil: water they all cause development.

Here, the solubility in water has become so trifling that the
organism can no longer absorb the fatty acid rapidly (see previous
communication).

As the penicilliam can use up this carbon-containing material also,
it becomes assimilated before the unfavourable concentration in the
organism is arrived at.

As is to be expected, the growth becomes less marked with the
increase in the number of carbon atoms (see palmitic compared with
laurie acid) nof owing to a strong decrease of the solubility in the
fatty portion of the organism but, in the first place, to the gradual
diminution of the solubility in water, which so impedes the entering
into the organism that the assimilation can only take place with
slight rapidity.

( 934 )

As regards the formic acid, the less favourable development might
be due to the hydrogen ions. This, however, is not the case with the
‘smaller concentrations as shown from an investigation as to the
retarding action of the H-ions (see later).

It is much more likely that the’ slow growth is due to the simple
construction and the high state of oxidation of this acid. An assimi-
lation in the organism is here attended with grave difficulties.

We, rather, ought to be surprised to find that the penicillium is
capable of development in a solution of formic acid as sole organic
nutrient, of forming spores, ete.

In the higher concentrations this slow assimilation must also play
a role, because in such a case the organism, not being able to use up
the formic acid quickly enough, will be overloaded and the deve-
lopment will cease.

We notice, indeed, that the maximum development is sitnated
much lower than in the case of acetic acid, although the division
factor oil: water will, presumably, be smailer.

Summary.

An investigation was instituted as to the influence which certain
carbon derivatives, when given as exclusive organic nutriment exert
on the growth, and the retardation thereof, of the penicillin glaucum.

Here it was shown :

1. That the development may be induced by the majority of the
carbon derivatives investigated, which belong to widely different
groups of compounds.

2. That the growth takes place readily on compounds fairly soluble
in water but not,-or but slightly, soluble in oil.

3. That the growth only takes place at very low concentrations
in the case of compounds which are more readily soluble in oil
than in water, whereas at somewhat more considerable concentrations
it is retarded or does not take place at all.

4. That this growth is not considerably interfered with when the
solubility in water is exceedingly small even though the solubility
in oil be very considerable.

5. That this growth is very weak or imperceptible :

a. on compounds nearly insoluble in water,

b, on simple highly oxidised compounds such as earbon dioxide,
urea and formic acid.

¢. on some compounds which readily dissolve in oil and are also
soluble in water to a not ineconsiderable extent, such as the naph-
thols, carbon tetrachloride, formaldehyde (3).

( 935 )

We have endeavoured to explain these facts by assuming that the
organism is protected by a layer of water through which it has to
be reached by the nutrient as well as by the retarding substances.
In the case of substances soluble in water it will depend mainly on
their solubility in fat whether they will penetrate the organism
rapidly and eventually overload the same.

a. If they are absolutely insoluble in water they will have neither
a nutrient, nor a toxical action.

b. If they are very little soluble in water but fairly so in oil
(cetyl alcohol, palmitic acid, naphthalene) they will have a nutrient
but no toxical action.

c. If they are considerably soluble in water, but still much more
so in oil, they can act as a nutrient in small concentrations only ;
at higher concentrations they cause retardation.

d. If they are readily soluble in water but very little so in oil,
they cannot act as a toxical substance, but only as a nutrient.

Finally, we have drawn from this the conclusion that an anti-
septic ') must have a large division factor oil: water, also a sufficient
solubility in the last solvent.

Delft, January 1912. Org. Chem. Lab. Techn. University.

Astronomy. — “Calculations concerning the central line of the
solar eclipse of April the 17th. 1912 in the Netherlands’.
By Mr. J. Werper. (Communicated by Prof. E. F. van pr
SANDE BAKHUYZEN).
(Communicated in the meeting of January 27, 1912).

Although the central line of a solar eclipse is given in the astro-
nomical ephemerides through many points on the surface of the earth,
it may be useful for the observation of the approaching eclipse to
communicate a few results which have been calculated for Holland
in particular. Owing to the small width of the zone of annularity
in Duteh Limburg the data given in the almanacs for this eclipse
are not sufficient to predict whether or no a particular place will be
situated within this zone; this is obvious as the differences between
the different calculations surpass the width of the zone.

This disagreement arises principally from the differences between
the geocentric places of the moon which have been adopted for the
calculations; the employed values of the ellipticity of the earth have
had some influence too.

1) No strong acid or strong base is meant here, but a chemically-indifferent
substance.
62
Proceedings Royal Acad. Amsterdam. Vol. XLV.

( 936 )

For the basis of my computation I have employed the HansEn-
Nrwcoms values, for the longitude, latitude, and parallax of the moon
taken from the Berliner Jahrbuch, but with some corrections added
to thom. The longitudes have been increased with the sum of 1. an
empirical correction deduced by Prof. E. F. v. p.S. Bakuuyzen from
Newcoms’s results of the occultations and from the Greenwich obser-
vations up to 1910°), 2. a few theoretical terms of short period,
according to Nrwcomp?) Rapavu*) and Hii1*), partially modified
according to E. F. y. p. 5. Bakuuyzen’s results from the observa-
tions*) and 38. the corrections deduced by the latter, dependent on
perigee and eccentricity °). The corrections to the latitudes proceed
partly from those to the longitudes, partly from those to the node
and the inclination of the moon’s orbit. The deviation in latitude
between the centre of gravity of the moon and its centre of figure
to the amount of —1".00, incorporated by Hansen in his tables,
I have kept unaltered according to E. F. v. p. S. Baknuyzen’s in-
vestigation’). The parallax constant has been increased with + 0".37
according to Newcomsp and BATTERMANN *).

The formulae for the moon’s places adopted by me are:

1=1(B.J.) + (1 + 0.110 cos g + 0.008 cos 2g) .{ + 772 + 1”.69 sin D
— 0.38 sin 2D — 0'.24 sin (D + g') + 0'.09 sin g' + 0".16 sin (D — g)
— 0.21 sin (2D — g)} — 0".43 sing — 0".17 cos g 4+ 1.28 sin fg + 217°
+ 19.36 (t — 1876.0)} + 0'.82 sin {g + 198° —9°.67 (t--1876.0)}

+ 0.45 sin (4 cosg = UB.J.) + 9".55

b= 0)(B.J.) + Ai sinu + (9".55— AQ) XK 0,09 cos u = b(B.J.)—0".10.

n= 27 (B.J.) + 0.37.

The angles in these formulae, have for the mean time of my
computations, 1912 April the 17th 14/11" mean time Berlin, the
following values : -

mean anomaly of the moon — 278.4
mes vs 5 ng SUNN g-— 103.8
longitude of the ascending node = 214
angle from node to perigee ® = Vad
angle from node to the sun’s perigee w’ = 260.0

1) Proc. Acad. Amsterdam 14 1912 p. 686 et seq.

2) Investigations of Corrections to Hansen’s Tables of the Moon p. 37 (1876).
8) Annales Paris. Mémoires 21.

4) Papers Americ. Ephemeris 3 Part 2.

6) Proc. Acad. Amst. 6 1903 p. 370 et seq. and p. 412 et seq.

6) Ibid.

7) Proc. Acad. Amsterdam 14 1912 p. 692 et seq

5) Beobachtungs-Ergebnisse der Kéniglichen Sternwarte zu Berlin N° 18 p. 12.

( 937 )

mean elongation of the moon from the sun
gto—yg—w’=D= i714

mean longitude of the moon C

mean argument of latitude C= § Se]

In the formula for /, ¢ is expressed in years, here 1912.29; in
that for 6 I have adopted as corrections to the inclination and the
longitude of the node

Ai =— 0"A0
A y= + 10".50
according to E. F. v. p. S. Baxauyzen Proc. Acad. Amst. 6 p. 426.

For the ellipticity of the earth I adopted the mean of the values
according to Hetmert’) and to Hayrorp’). My computations have
been accomplished with log(1—c) = 9.9985 385 corresponding with
the ellipticity 1: 297,65.

For the calculation of the width of the zone of annularity there
is also needed the ratio of the radius of the moon to the equatorial
radius of the earth. For this ratio I have employed Jog s = 9.435 3888,
which, adopting as mean parallax of the moon 57' 2'.65, corresponds
with a radius of the moon of 15’ 32”.68. The last value, which 1
take from Prof. E. F. v. p. S. Bakauyzen, is founded on the results
of heliometric observations (by BrsseL, WicuMann, and Harrwie) and
of occultations, (some occultations of the Pleiades and those calculated
by L. Srruvr and Barrermann), the former of which gave 32".75,
the latter 32'.65.

The geocentric longitude /', latitude 4' and distance of the sun
f' and the obliquity of the ecliptic « have been taken from the
Berliner Jahrouch; further I adopted Avuwers’ value A’ = 15'59".63
for the mean radius of the sun and 8'.80 for the solar parallax.

Calculation of the central line.

According to Hanskn*) we have the following relations between
the co-ordinates of a given place on the surface of the earth and
those of the sun and the moon, if these bodies seen from that particular
place seem to be in contact with each other.

1) Sitzungsber. Berlin. 1901 p. 328.
*) J. F. Hayrorp, The figure of the earth and isostasy (1909).
Supplementary investigation (1910).

8) P. A. Hansen, Theorie der Sonnenfinsternisse und verwandten Erscheinungen.
Abhandl. d. K. Sdcus. Ges. d. Wissensch. IV (1858) p. 305—334.

62*

( 938 )

9, = Pcosh — Qsinh — cos py sin (¢ 4+ Aa’) =usind
$, = Psinh + Qeosh — {(1-e) sin py cos d' — cos py sin d' cos (t + Aa')} = u cos 0
us sec f + {|Z — (1 —c) sin py sin d' — cos py cos d' cos (t+ Aa’) taf.
The factor 1 + 2 which still appears in these formulae of HaNnsrn
and through which the influence of the atmospheric refraction is
brought into account, could here be neglected.
In these equations the quantities P, Q, and Z depend in the
following way on the co-ordinates of the sun and moon.
__ cos b sin (—2') ne sin (6 —8') Go (6 —B’) cos (I—2')

ee VA,

sin x sin x sin x
sin 8".80 sin 8".80
1— 7 = (ll) | 1 + ——— be 30—1 (bos nitee aie
( i( uy a? : ( ( tg pars)

The quantities 0’, Aa’, and h refer to the direction of the straight
line between the centres of the sun and moon. The declination of
this direction is d’ and if to its right ascension a’ we add Aa’, we
obtain the right ascension of the sun. For the point on the celestial
sphere whose co-ordinates are a’ and d’, h is the angle between the
hour-cirele and the circle of latitude. The quantities d’, Aa’, and h
are calculated from the co-ordinates of the sun and moon and the
obliquity of the ecliptic by means of the auxiliary angles da’, d’, and
h,, in the following way :

Psinh, + Qeosh,

tg «| = cos & tgl' j=) R . 8".80 + b' cosh,
Posh, — Qsinh sinh
iq d' =tge sina’ Ad = —_~_—__.. 8".80 + B! .
R' cos d cos d
sin h, = sin € cos a’ h=h, + sind’ (Aa’).

The quantities g, and ¢ depend on the time and the place of

observation, since we have .

ig ~, =(l—c)tgqm and t=r-+a
where g and 4 denote the geographical latitude and longitude of
the place of observation and r is the true solar time for that meridian
from which 4 is reckoned as eastern longitude.

The angle 7, which appears in the 3"¢ of Hansry’s equations only,
is the semi-angle of the cone which is in contact with the sun and
the moon; for an apparent external contact the value of /, which
we shall denote by /, is determined by :

aS sin A' + ssin8".80 .
sin fe SS in
: R' sin x — sin 8".80
while for an apparent internal contact, the corresponding value /; is
determined by :

(939)
sin A' — s sin 8".80

sn f. = — — ——_— sin x.
i R' sin x — sin 8".80

For other phases of the eclipse the angle f may be determined,
when time and place of observation are known, as a third unknown
quantity, together with the angles uw and 6, from Hansen’s three
fundamenial equations’). By means of this angle the phase of the
eclipse is obtained by calculating the quantity m from:
sin f

sin a

sin mA' =

(R' sinw — sin 8".80) — s sin 8" 80,

and the fraction of the apparent diameter of the sun which is
eclipsed by the moon *) will be
4 (1 — m)

If we define the angle f as a continuous variable, the three
fundamental equations hold good for all phases of the eclipse. The
quantities w and 6 determine the position of the place of observation
relatively to the straight line through the centres of the sun and
moon, i.e. to the axis of the shadow-cone; w is the perpendicular
distance of the place of observation from this axis and @ is the position-
angle of the great circle, parallel to the plane going through the
hadow-axis and this place, in the point of the celestial sphere, the
co-ordinates of which are a’ and J.

The central line of an eclipse is the curve on the surface of the
earth along which that surface is intersected by the axis of the
shadow. Therefore for the points of this line we have «=O, so
that the line is determined by the equations ?, = O and 0, = 0, i.e. by:

cos p, sin (t + Lea’) = P cosh — Q sinh
and

(1 — ¢) sin py, cos b' — cos ip, sin d' cos (t + Aa’) = Psinh + Qeosh.

Suppose the perpendicular distances from all points on the
surface of the earth to the plane of the equator to be enlarged in
the ratio fee, then this surface becomes spherical. By giving
corresponding displacements to the centres of the sun and moon we
somewhat simplify the problems exclusively regarding the central line.

If the declination of the direction of the axis of the shadow,

1) In this way we always find two values for the angle f, the sum of which
is equal to the apparent diameter of the moon with negative sign. We have always
to take the greater of the two.

*) For annular as well as for total phases the physical interpretation of the
expression } (1—m) is no louger the same.

( 940 )

tang Jd!

1—e
The right ascensions are not altered by our transformation, neither
are the geographical longitudes. The co-ordinate @, takes the place
of the geocentric latitude.

now also altered, is denoted by 6 , then we have tang J';=

If we replace V (1—-c)? cos? d' + sin? d', by w', then
sin J’ = wi! sin d', and (1—c) cos d' = w' cos d'; .
After the introduction of the auxiliary quantities U and M, which
are computed by the formulae:

Has and M= PsecH oer | (2!)

we obtain as equations of the central line:
cos p, sin (t + La’) = M cos (H + h)

M
cos J’, sin pp — sin d'; cos Pp, cos (t + Aa') = — sin (H +4 h).
w

By subtracting the sum of the squares of the two members of
these equations from unity, we find:

sin d', sin py + cos d', cos py, cos (t + Aa’) =z, ,

an equation, the 24 member of which is the positive root of an
expression which may be computed by means of the formulae (//).

Fe cos? 3 2 =I ML 4 FP ' sin? (H+ DE. (ED)

If further we calculate the auxiliary quantities w', U, and N
fulfilling the conditions
1 M sin (H+h
ih oe gg ie ce
Vi-F' w' zy
then the geographical longitude is given by the equations
M cos (H-+-h)

Oe) z, cos (U-+ J’)

and 2= (¢+Aa')—1t— Aa’. (IV)
and the geographical latitude by :
1
ig p= poe tg (U-+-d';,) cos(t+ Aa’). « . . . (V)

With this set of formulae I calculated the longitude and latitude
of two points in the central line for two moments, one 5 min.
mean solar time after the other. In the results following below we
have 7) = 0°32"26°.20 Amsterdam mean time = 0"12™545.06

( 941 )

Greenwich mean time, and the geographical longitudes are given
relatively to the signal of the Dutch Survey at Ubagsberg *).

Times Geogr. long. E. of Ub. Geogr. lat.
7, +07 — 2° 28'11".9 TOO A Odeo wile)
T, + 5" +0 13 56.5 Ot PSHE. Sons, WGz)

The first point C, is still far in Belgium and the second lies
already in Germany. In order to determine better the central line
for Limburg I have calculated a third point C,, which comes into
the axis of the shadow one minute earlier than C,, and I obtained

Time Geogr. long E. of Ub. — Geogr. lat.
T, + 4™ — 0° 19'53".3 SOF SON 220 cae CC)

This point C, is still situated in Belgium, but near the Limburg
frontier. By interpolation between these three points the following
values were found for the longitudes and latitudes which hold good
for the topographical and military map of Holland ’).

Geogr. long. E. of Amst. Geogr. lat.
0°.45' 50°.50' 38.3

50 53 12.8

fey 55 46,7

10 58 20.1

5 Hl O 53.0

10 3 25.2

15 5» 56°9

Computation of the place where the vertex
of the moon’s shadow leaves the earth.

The solar eclipse of April 17 will probably be distinguished by
the peculiarity that in the central line at first it is annular, later
on it becomes total, then to grow annular again. One of these points
of transition, viz. where the total eclipse becomes annular, will be
“situated in Belgium, if the above mentioned values of the apparent
radii of the sun and moon are accurate. First I shall derive the

1) The difference in longitude between Berlin and Ubagsberg (7° 26'34".9) I took
from the determination of the differences of long. between Ubagsberg and the
observatories at Bonn, Géttingen and Leyden: Veréff. K. Preuss. Geod. Inst. Tele-
graphische Lingenbestimmungen in 1890, 1891 und 1893; and Publication de la
Commission Géodésique Néerlandaise: Déterminations de la différence de longitude
Leyde-Ubagsberg, etc.en 1893.

*) From the last mentioned publication I also derived the latitude of Ubagsberg,
in order to reduce the computed latitudes to those of the topographical map
which are in accordance with the “Meetkunstige beschrijving v. h. Koningrijk d,
Nederlanden.”

(949 )

time of this transition ; subsequently the point where it takes place.

1 : : :
If ——, a and J are the geocentric spherical coordinates of the
Sin IU

, a and Jd’ the selenocentric ones of the vertex of the

moon and

sin f,
shadow, both referred to the equator and the equinox, then the
rectangular geocentric co-ordinates of this vertex are :

8
—— cos J cos a + —— cos d' cos al
SIN Ie Sin 7.
v
- 0 8 pies 1
y= - cos Dd sin a@ 4+- ——— cos 0 sina
Sin sin f.
sind
ae Dano at
>= - sin 5 + —— sind
sin It sin f.
i

In these expressions I substitute for the declinations the quantities
dé, and d',, just as I have done before, so that here the auxiliary quantity
w= V(1—o)*cos? d+ sin? dD has to be introduced.

At the times of transition the vertex of the shadow falls on the
transformed surface of the earth, the sphere with radius 1, hence

2

32 3 = —
Seq 4 a
(io)
From this equation we derive:
f w ne sw ;
(1—c)? = ——_ + ——~ 2 ———-—— {cos dj vos J; cos (a —a) +-
sin” I sin® f. Sin © sin f.
Si 4

+ sin d; sin d'y} .
by which the time of transition is determined.
For the angle w between the directions (@ d,) and (a' d‘;) the relation
cos YW = cos dy cos b', cos («'— a) +- sin dy sin ',,

holds good and from this we find

“OL NG P
w + sw'—— | — {(1—c) sin a}?
1 sin J,
sin? — py = - see Gen (A)

2 sin x

4 sw w' ——

sin f.

J;

Another form for the angle y is found by using the expressions
Poosh — Qsinh=YP and Psinh + Qcosh=4, which occur in
Hansun’s fundamental equations.

jp, O, and 7 are the rectangular co-ordinates of the centre of the
moon referred to axes through the centre of the earth as origin,

( 943 )

The axis of Z has been taken in the direction (a'd') and the axis
of $ perpendicular to the plane of the declination-circle a’.

After having applied the transformation described above, which
reduces the surface of the earth into a sphere, we can adopt a
system of rectangular co-ordinates analogous to the former. The
co-ordinates of the displaced centre of the moon with reference to
these axes are distinguished from the corresponding co-ordinates of
the real centre of the moon by the index /.

So the axis of 7, is parallel to the direction («' 6';) and the axis
of }, is perpendicular to the plane of the declination circle a’. The
radius vector ef the centre of the moon after the transformation is
denoted by &y.

The following relations hold between these quantities with and
without the index /.

Sy , ,
Y= : ——— : hook u obs w q
uw l—e (l---ce)sina
ya) ;
Since si? y= =» we thus derive:
Ry

- a) (1-9
a G ot Sire | sin? gr
: Ww w
As $= Mcos(H +h) and 2= M sin(H + hk) we find:
2 1
see gals ( —_ 1) sin® (a+n| M?=1—2,,
o w

so that for the calculation of y we can also employ the equation

ie a —— =

1

nye ee : V1—27 eG colic (AEG

The instant at which the transition from totality into annularity takes

place is that for which the formulae (VI) and (VII) give the same

value for yw. I calculated 3w for the time 7, 7+ 4 min. and

T,-+ 5 min. from both these formulae and found, interpolating for
the minutes between 7’, and 7’, + 4.

Time a8 from (V1) _ from (VII)
T, +0 min. 0°18'44" .69 0°18'21" .05
Po a ee 42° .59 29 .88
oe eee 43 .49 38 .85
» +3; 44 .40 47 .98
5 4 «, 45.30 57 25
oe aes 46 .20 TOMGEGe

These values are equal at 7), + 2™335.9,

( 944 )

For this instant I have now calculated from the formulae (/) to
(V) the place of Co on the central line where the totality passes
into annularity, and obtained for the geographical length east of
Ubaesbere and for the geographical latitude of this point:

y= NS EES
po= 50°25/34".0.

Calculation of the angle at which the limiting-lines of the
area of internal contact on the surface of the
earth intersect each other in Co.

The equations which are satisfied at the limiting-lines, are:

¢,7 + 9,?7=w* and vee + ae = ie
if in the expression for wu we replace the angle / by /.

The first equation follows from Hansrn’s fundamental equations.
When in that equation the expressions for %,,¢,, and w have been
substituted, it gives the relation between 2,47 and the moment at
which the. internal contact occurs at the place of observation (Ag7).
In the limiting-lines this equation will hold for two consecutive
moments. From this condition follows the second equation which
is derived from the first by differentiation with respect to the time.

At the point Co the three functions ?,,%,, and w are equal to
zero for the time 7’, + 2™33s.9. In the vicinity of this point at a small
distance Z and at a time differing from the first by the small quantity
T, it is sufficiently accurate to use linear relations for the computa-

0 0
tion of the 3 functions. Hence we may pnt ?, = ae L+ ous vis
P OL O or 0

and the same will do for ?, and w.
As all partial derivatives appearing in these equations relate to

0p
the point O, I shall henceforth simply write ee ete. instead of

09,)
Vi a etc.

After the substitution of the linear expressions for ?,,9%,, and wu,

the equations of the limiting-lines become:

00,\? do, \° Ou ‘tn > (9%, 9%, 00,00, du du rp
Ge) + (gen eee er oe ar ea

a0.) (ON ei al eee
*iGr)+ Gr) “(Gr |=

and

( 945 )

02,0¢, Of, O07, Ou Ou op, \7 og, \? Ow \*).
ST ale a7 L+- ral euak ae-a 7 =0
OL oT OL or OLOoT Ge 07 oT

We now eliminate from the two equations the relation of L to T
and thus we obtain an equation between the differential co-eflicients
which after reduction becomes :

& 0, Oo, == (; Didu du ot) + (= Ou du 00, “) (VILL)
OO TO Oly NOTA OL 0 NOL OF YOor

In developing -the terms of this equation, I assume the linear
element Z to lie in an arbitrary azimuth A on the surface of the
earth transformed into a sphere.

Then we find :

0¢ 2
oe =cos A and ar ee P; sin A

0¢ + Aa’)

d(t+Aa') d(r+Ac’)
Ole le dT
By differentiation we find for the derivatives with respect to L:

a 15771 p, sin(t + Aa’) cos A — cos (t +- Aa’) sin A

0D,

ae

Further we have = 1 and for

I put x.

— {(1-e) cos d' cos pz + sin D'sin pz cos(t + Ax')} cosA-sind'sin(t+-Aa')sinA

u , 5 ' . r ' > ns ‘
== taf (1—e)sind cos p,—cosd'sin p cost+Lea')} cosA + tg fcosd'sin(t+Aa')sin A

and for those with respect to 7:

0 d)y

Tea — % c08 py cos (t + Ac’)

i) dd 16!

— on x Psin d' + (Z + 8 cose f.) =

Ou at, dZ \ Fi Ms dé' df;
or of, Tap eco =a — s cose f.

The last two derivatives have been simplified by means of the
relations 2, = 0, ?, = 0 and wu = 0, which hold good for the point Co.
Attributing to the linear element Z the azimuthal direction of the
central line on the sphere <A,, and denoting the derivatives with

0g
respect to “Z in this ease by 73 et seq., we find the following

c

equation for the determination of A,:

09,0, 09,00, _ :
om nor . . . . . . . (ZX)

( 946 )

Substituting the following relations :
09, 09, L- 09, 0?, L,
IF 3. ORT Stan eae
from which the equation (IX) can be derived, in the expression in
brackets in the first member of (VIID, we get
0,09, 0¢,00,\L.
G OL ee

09, OP, 02, 09,
Here aL, and az. are the same functions of A, as va and a

are of A. We further find by developing :
0,00, 09,0,
OL,0L oOL,0L

sin d' sin gy —(1-c) cos d' cos pz cos (t+ La’)! sin (A-A,)

The expression between {} is equal to —w’z, according to former
notations, hence :
09,00, 09,00, Le

: SO Vt) 3 xX
OL oT oLor Wen eaei op Cy

Employing the numerical values which I needed for calculating
the position of the point of transition, I first solved the equation (1X),
from which I found :

A, = 50°.5'46''03.

Subsequently I replaced in the equation, which followed from
(VIII), the angle A by 4 = A— A,, and obtained for the caleula-
tion of 4 an equation of the following form :

¢,” sin? A = (ec, sin A + d, cos A)? 4+ (c, sin A + d, cos A)?
with the following numerical values of the co-efficients :
¢, = 6138".9 ¢, = — 7".24 c, = — 10".24
d, = + 9".80 d, = — 13".09.

For the solution of this equation I first computed the auxiliary
quantities C=c,? —c,’—c,*, D=d,?+ d,? and H=2(¢e,d,+c¢.d,);
afterwards the angles 6B and I’ from the formulae :

: 10D a E
sin B= + —_—_——. and tg r=———
(C+D)?+ E* C+D

and finally found these two solutions :

A,=+4(84+T) and A, =— }(B—T)
The numerical calculation led to :
A, = + 0°9'3"1 and A;=— 0°9'10"3

So the central line almost bisects the angle between the limiting-
lines in Co. East of this point the north limit deviates a little more
from the central line than the south limit. The angle between the

( 947 )

two limiting-lines in point Co is 4, —A,— B; so that for this angle
the result of the calculation is: B=0°18'18".4.

Measured on the surface of the sphere the distances of C, and C,
from Co amount to 2338" and 3985", so that according to the adopted
data the width of the annular zone at these points comes respectively
to 12”.4 and 21”.2 or 380 and 650 meter.

: = Le
From relation (X) we find co-efficient ¢, = w’z; — T 3 accordingly
Li, on ; = 3 Oe ues :
i ee the velocity Vo, with which in Co the shadow-axis moves
WZ
I

along the central line over the surface of the earth. For points in
the central line near Co the duration of the totality or annularity

is given by:
Ou Ou \A op, \? (0¢, a
2{ Vo + — :
( ON a) (Se) ss (52)
& 22) ae (@
or oT OL
The value of this expression is in casu: 0.00542 7’ and from this
it follows that the annularity lasts 0°47 in C, and 0%.80 in C;.

Calculation of the differential coefficients of the geographical longitude
and latitude of the points in the central line with respect
to the longitude, latitude, and parallax of the moon.

In these calenlations we may neglect the very slight variations
of the quantities Ae’, J’ (or d';) and h in consequence of small
variations in the places of the moon. In the differentiation I have
therefore treated them as constant quantities.

From formula (IV) for tg (¢-++ 4a’) we deduce

oda dj) dY
sin 2(t + Aa') Pp 8 4

, Where } = Mcos (H + h) (see form. IV)

9)
and Y= Neos (U +- d';) = z;cosd'; — — sin d';, hence
w

sin J,

dY¥ = cos d', dz; — tad

; 5:
From the relation z,;? = 1— jj? — —, we obtain
w

dz, = — ie dy —
Zz] w' <7
the values of the differentials dY and dz,, we find dd expressed in

d\) and dQ as follows:

2 da Peosd'; xX
saan = (ot et) a+ ae
sin 2 (t + Aa’) p Yz; Yew

—d, and, substituting in the formula for da,

( 948 )

where 2, sin d'; + — cos db‘; = X= Nsin(U + d')) =sing,
w
In order to profit as much as possible by the quantities already

aX: ¢
calculated I substitute ~g(U-+d',) for ¥ and tg (t + Aa’) for 2
by employing the differential relations
d\) = cosh dP — sinh dQ en dQ = sinhdP + cosh dQ
and by introducing the auxiliary angle u, variable between — 90°
and -+ 90°, which is determined by

tg w= w' cotg (U + Jd’) a + cos d', tg (t + Aa’) (XIa)
we may reduce the differential expression for da to:
Seo
a= HT sin (t+ Aa’) tg (U +0',) {sin (uh) dP + cos (uth) dQ) (XJ)
w 2]

For the deduction of the corresponding differential expression for
the geographical latitude, it is necessary to eliminate dp;, dD, and d)
between the equations

dp _ dy

sin 2—p gin 277
and

rE d 5

cosd', =Qsind', sin d',
: dD -
w wo 27

cos prdp; = dX = (
a
and the expressions formerly found for d and d}. To simplify
the second equation I employed the relation
cos b'; D sin d'y a

w! wz, wiz;
The introduction of the auxiliary angle v variable between — 90°
and + 90°, according to the formula
w') sin J!
gu. — oe = fi
)
also simplifies the calculations. We then find:
sin 2—p cos (t+ Aa’) ‘ ;
S— — {— sin (v — h) dP -+ cos (v — h) dQ (XII)

d U
sin 2p, wey, cosy

(XZ/a)

For the calculation of the differentials dP and dQ 1 have employed
the following approximate formulae

dP=Zdl—Ptgbdb—Pcotgadx . . . (XIIT)

20 Zdb—Qcoigadm .. . (XIV)

The numerical values of the partial derivatives of 2 and gy with

respect to /, >, and a have been calculated for the two instants

T,-+4 min. and 7,-+ 5 min. This calculation gave the following result :

for 7, +4 min. for 7, + 5 min.
ON erate
= = 1G _ yey _ = NGS st 4 74.1
— 21.2 "fF _ _ 502 | <= — 232 °F — _ 50.6

For a given longitude we find for the differential variation of

sin® ¢f

the latitude of the central line (dy) —=dp — da cos —/ cotg A :
stn opy

where A denotes the azimuth of that line in the point (4,7). In the
present case we find for the two instants
(dp) = dp — 0.516 dd and (dp) = dp — 0504 da
From the above mentioned values of the partial derivatives of
g and 4 with respect to /, 6, and a we finally derive for the time

7, +4 min. :

(dp) = — 28.1 di + 83.3 db — 39.3 dz,
and for the time 7’) +5 min.:
(dp) = — 22.7 dl + 82.8 db — 38.9 dz.

As may be seen from these differential formulae, it is in parti-
cular the latitude of the moon that influences the situation of the
central line. The empirical correction of —1'.0, applied by Hansen
to the latitude of the moon diminishes with 1'23" the geographical
latitudes of the central line of this eclipse in our country; this cor-
responds to a transposition of 2,5 K.M. towards the south.

If it appears that corrections are necessary for the places of the
moon accepted by me for these calculations, there will be no diffi-
culty in computing their influence on the position of the central line.
I myself am not able to give any corrections with any certainty.
The only thing would be to take into account the influence of the
height above sea-level, owing to which the geographical latitudes for
given longitudes are about 2”.1 per 100 M. smaller.

Postscript.

When I commenced these calculations Prof. E. F. v. p. SANDE
BAKHUYZEN’S investigations into some points, regarding the longitude
and latitude of the moon‘), were not yet completed. In the mean-
time the results he arrived at appeared to agree well with the
values I employed. The sum of all the terms of short period in the

1) Proc. Acad. Amst. 14, 1912, p. 686 et seq.

( 950 )

longitude according to Brown, which were also calculated, amounts,
however, when we add to it the influence of the adopted corrections
of perigee and eccentricity, to + 0".67, i.e. 1".10 less than the value
I derived from the originally adopted formula. The previous investi-
gation of Prof. BakyuyzuN into the observations of the moon up to
1902 led him to believe that the co-efficient of sim g, which is of special
importance here (as we have g = 278°) would be in 1912 at least
—0".6 greater than its theoretical value, using also the adopted values
for the corrections of perigee and eccentricity. From this remark a value
of the longitude results, which is + 0".6 greater, so that the most
probable correction of the longitude I employed would be — 0".5.
Thus we should have d/ = —0".5 and db=—0".05, hence (dp) =
+ 7". In more than one respect, however, some uncertainty remains.

>

Anatomy. — “On the structure of the Dental system of Reptiles.
By Prof. Dr. L. Box.

(Communicated in the meeting of January 27, 1912).

If we compare the dental system of mammals with that of reptiles
two points of difference come especially to the front. One of them
bears a more physiological character and regards the fact that with
mammals, as a rule, the dental shelf gives off only two series of
buds, one for the milk-set and another for the permanent set. With
the majority of reptiles on the contrary a shedding of teeth takes
place several times during their life-time, though among this
group of vertebrates species are known to us, where the shedding
of teeth does not take place at all, or is restricted to a special part
of the dental system, as may likewise be the case with mammals.
These however are exceptions and in general the dental system of
mammals as diphyodont (in some cases monophyodont) is placed
over against that of reptiles as polyphyodont. It is pretty well the
current view that the diphyodontism of mammals must be derived
from the polyphyodontism of the lower vertebrates, and it is sup-
posed that the number of renewals of the dental system was gradually
reduced from many to a few, whilst the duration of the existence
of the teeth was lengthened. Only a few authors take a different
stand-point, and are of opinion that the shedding of teeth of mammals
should be a property obtained by that group of animals themselves,
and the primitive mammals should consequently have been mono-
phyodont (Lecue).

The second point of difference is of a more morphological nature.
The dental system of mammals namely is, save a few exceptions,

(951 )

built of more complicated teeth. The crown shows two or more
cusps. In the first case both cusps, the lingual and the buccal, can
be well developed, and at first view the tooth is to be recognized
as a bicuspidal one, or the lingual cusp is so much reduced that
the tooth becomes apparently monocuspidal as with caninus and
incisivi. By the variation in the number of the cusps the teeth of
the dental system of mammals present a great diversity in the shape
of the crowns, the set is anisodont, contrary to the more isodont
set of reptiles, whose teeth are in general of a more equal and
simple conical form.

There are different views of the way in which the anisodont
dental system of mammals has developed out of an isodont primi-
tive form.

Two theories on this subject have their supporters and_ their
opponents. The so-called conecrescense-theory teaches that the com-
plicated mammal tooth developed itself by fusion of a number of
cone-teeth of reptiles, each cusp of such a tooth should represent
a primitive cone tooth. The differentiation-theory on the contrary
teaches that every mammal-tooth, however complicated it may be,
should be homologous with one single cone-shaped reptile-tooth, the
crown of which lost its simple form and developed a more com-
plicated relief.

Herewith the two chief points of difference between the dental system
of reptiles and the dental system of mammals are indicated as briefly
as possible. With the formation of the dental system of mammals
from that of reptiles, a polyphyodont isodont dental system was
transformed into a diphyodont anisodont one. Is there any relation
between these two points of difference? In my opinion too little attention
is paid in literature to this question. When animadverting on the
formation of the complicated form of the tooth, the question whether
there may be some relation between the fact that the tooth becomes
complicated, and the diminution of the number of tooth-generations
from several to two, is not referred to at all by the differentiation-
theory, and hardly ever by the conerescence-theory. It is true that
every now and then the supporters of the concrescence-theory express
the view that the fusion of several cones to one whole must have
diminished the number of tooth-generations. Rds has tried to give
a scheme of this phenomenon. I suppose that this essay is to be
regarded as incorrect, but I refrain from further criticism. I entirely
chime in however with the principle of which this essay is the
expression. For I hold that for the derivation of the mammal dental
system from the reptilian dental system, one must try, as much as

63

Proceedings Royal Acad. Amsterdam. Vol. XIV.

possible, to find a process of transformation, by which the two chief
characteristics of the mammal dental system are derived from a
single cause. I think I have succeeded in this attempt. I could how-
ever only come to the solution I have found of this problem, after
I had come to the conviction, especially on account of researches
about the development of the dental system of reptiles, that our
conception of the structure of this system must be rather importantly
modified. It is my intention to restrict myself in this communication
to this fundamental point of my theory, in order to explain in a
subsequent communication the relation existing, in my opinion, between
diphyodontism and polyphyodontism, and how the relation between
the diminution of the number of tooth-generations, and the compli-
cation of mammal-teeth must be understood.

The dental system of most of the now living reptiles consists of a
sometimes great number of little teeth, placed in a single straight
line in the upper- and underjaw. Besides these teeth we find with
several species, especially with those having lived in former periods,
other teeth in different skeleton parts of the roof of the mouth (Pa-
latinnm and Vomer), but as these have not been inherited by mam-
mals, we can leave them out of discussion, and restrict ourselves to
the rows of teeth united with the jaws.

I should like to indicate a dental-system, the teeth of which are
placed in a single row as a monostichical one. And if we regard
the grouping of the teeth in the skull of a reptile, this term might
justly be applied to such a system. But if we carefully examine the
development of the dental system of reptiles, we discover symptoms
that seem to place that system in a somewhat different light, and
that awake the supposition that the simplicity of the rows of teeth
of reptiles is only a semblance, or to express it more correctly forms
a secondary situation which renders the real character of this dental
system irrecognizable. As it is, my researches with regard to the teeth
of the vertebrates convinced me that this dental system is not a
monostichical system, but what I wish to call a “distichical” one.
Though the teeth stand in a single row, they must after all be regard-
ed as belonging to two rows, the elements of which have second-
arily been placed in one single row, because they have interposed
themselves between each other. This fact has as yet not been recog-
nized because teeth that in reality were not replacing-teeth, have
been considered as such. If onee the attention has been fixed on
this primary distichism, the development of the dental system of
reptiles teaches still more: namely that originally the dental system
of reptiles was not a distichical one, but even a “tristichical” 1. e,

( 953

that this dental system is to be deducted from a form in which the
teeth stood in three parallel rows, an outer, a middle, and an inner
one, consequently a circumstance as is known to us with anamnio-
tes. Of these rows the outer one however has become rudimentary
and is still found with several of the now living reptiles in the form of
abortive teeth, which offer a much more primitive mode of develop-
ment, never function, and are very soon removed or resorbed. Con-
sequently only two rows remain, an outer one and an inner one,
which I shall distinguish as the ‘eaostichos’ and the “endostichos”
whilst I shall distinguish the just mentioned row that has become
rudimentary as the ‘parastichos’. I shall now briefly demonstrate

ce

my views.

There exist about the development of the dental system of repti-
les already several researches. For instance of Résr (Crocodile, Cha-
maelaeon) Lrecue (Iguana) Harrison (Hatteria) Levy (Anguis, Lacerta).
In how far my views deviate from those of these authors will soon
be apparent.

In my elucidation I shall proceed from the dental system of a
Crocodillus porosus having sixteen teeth in the upper-jaw. I can
directly corroborate for this form an observation of Rése that with
this group of reptiles directly from the mouth-epithelium, consequently
not from the dental shelf a number of rudimentary teeth is formed
on the spot where the dental shelf is connected with the mouth-
epithelium. Lecur found these teeth likewise with Iguana, and Har-
RIsSON with Hatteria, and myself observed them with Lygosoma. I
differ in my view of the value of these teeth in so far, that they
form for me a rudimentary row — the above-mentioned “parasti-
chos”, whilst Roész and Lecke conceive them as a rudimentary first
generation of teeth. It must be well understood that to both authors
the notion of rows of teeth is unknown. I shall not expiate further
upon this difference of view.

When comparing the sixteen enamel buds in the teeth-shelf I was
struck by the fact that they behaved differently with regard to that
lamina. Some were placed at the buceal side of the peripheric half,
whilst the tooth-papilla formed by the mesenchym grows from
aside in the enamel-organ. A second group of lamina buds was
formed at the free border of the lamina
and the tooth-papilla grows in the
thickened rim of the shelf. Fig. 14
shows the diagram of a section of the
dental lamina with the two types of
Fig. 1. dental-organs. Further I give in Fig. 2, as

63*

an elucidation, a series of sections
of a dental organ developed from
aside of Crocodillus porosus, and in
Fig. 3 another of an organ originating
in the border. In this series also an
abortive tooth was found. If now we
carefully observe the formation of all
16 teeth, it appears that there is an
undisturbed regularity in the suces-
sion of the two groups, for, without
exception, they alternate. A lateral
bud is succeeded by a terminal one,
which is again succeeded by a lateral
one and so on, Seen from the buccal
plane a part of the teeth-shelf would
have, with regard to the arrangement
of the buds, an appearance as it is
sketched in Fig. 4. This alternation
of the dental organs with reptiles
was already known in literature. In
his extensive and exact description
of the dental system of Hatteria

Harrison emphatically points
to this phenomenon. What
is now the relation between
these first developed teeth,
of which those placed more
to the surface, indicated in
Fig. 4 by a—d, are a little
more developed than those
indicated by 1—4? The an-
swer to this question indicates
the fundamental difference
between the current view and
mine. In the opinion of Résx,
of Scuwazpp, and likewise of
Harrison, the teeth a—d
belong to the first generation,
and after having been used for
a short time they will be dis-
placed by the teeth 1—4.
Consequently the latter form
already the second teeth-
generation,

In this process tooth a would be replaced by tooth 1, tooth 6 by
tooth 2 and so successively. I shall immediately prove that this
conception cannot be correct. The mutual relation between the eight
teeth sketched in Fig. 4 is of a wholly different nature. We have
io do here with two rows of four teeth, which are not to be regarded

as first and second gene-
rations, for the teeth 1 to
4 will not displace the teeth
a—d. In their further de-
velopment every time a
tooth of the row 1—4
Fig. 4. penetrates between two
teeth of the row a—d. Consequently instead of there being quest-
ion of a first and a second generation, we have here two primary
rows, the teeth a—d and the teeth 1—4 are entirely equivalent. In
its first development the dental system of the Crocodillus is conse-
quently distichic, the teeth a—d represent the first generation of the
exostichos, the teeth 1—4 the first generation of the endostichos.
This structure-principle of the dental system of the Crocodillus
can however not be observed in a more advanced stage of develop-
ment, because the teeth of the two rows unite in a single line with

the border of the jaws.

In order to confirm my view that in the first stage of development
the dental system of reptiles consists of two rows of teeth running
parallel and not of two generations, I refer in the first place to
Fig. 5 in which a horizontal section through the upper jaws and the
teeth in a young stage of development of Lacerta is represented. In
the section both the premaxillary and the maxillary ones have been
struck. We shall restrict ourselves to the origin of the maxillar
teeth. Touching the maxillary bone we find three teeth, a, 6 and c.
As the direction of the section is somewhat slanting, the teeth
have been struck in a different level. These three teeth belong to
the exostichos. Alternating with these there are three teeth, indicated
by 1, 2, 3. According to the views of Rose and other authors these
teeth, belonging to the inner row or endostichos, should form the
second generation of the teeth a, 6, and c, they should displace the
latter. But from the figure it is, without more, clear that this view
cannot be correct, that 1, 2, and 3 cannot become the substituting
teeth of a, 6, and c, but will, between the latter, grow together
with the maxilla.

It is true, that here likewise the teeth a, 6, and ¢ are a little
more developed than 14, 2, and 8, but the difference is so slight,

( 957 )

that on this ground already it might be doubted if in reality there
exist here two generations. Consequently Lacerta appears to lave
likewise a distichical dental system, and ‘both the teeth a, 6, and e
and the group 1, 2, and 38 represent a first generation, the former
of the exostichos, the latter of the endostichos. In Fig. 5 the origin
of a second generation is perceptible indeed, though in a young
stage of development. In the section of the dental lamina we see
namely the origin of three teeths.

It is these teeth that at their further development, whilst moving
towards the maxilla, will displace and substitute the teeth a, d, and c.
These three teeth indicated as a’, 6’, and c' form the second generation
of the exostichos. In this preparation a second generation for the
endostichos had not yet originated. In several reptile-embryos I found
similar phenomena as in Lacerta. It is self-evident that for such like
observations horizontal sections through the origin of the dental
system are preferable. In Fig. 6 we find such a section through the
premaxillar dental system of Lygosoma olivaceum.

The section is in a_ transversal direction somewhat slanting, so
that on the right half of the figure the origin of more teeth is struck
than on the left side. In the median line lies the unpaired tooth.
The exostichos consists on both sides of two teeth a 4 and ec d, and
the endostichos of an equal number 1 2 and 8 4. It is likewise
clear in this section that 1 2 3 and 4 are not the substituting teeth

( 958 )

of a 6 c and d, not a second generation, but a first generation of an
independent row. They will soon have shoved between the elements of

Fig. 6.

the exostichos. In this preparation the second generation both of the
exostichos and of the endostichos had originated already. The teeth
a’ b’ c’ and d’ form the second generation of the exostichos. Exactly
as with Lacerta also with Lygosoma a tooth is not displaced by another
lying askance before or behind it, consequently not by an alternating
tooth, but by a tooth originating directly behind the tooth that must
be substituted. In our subsequent communication we shall revert to
this point, as, with regard to the shedding of the teeth of mammals,
it is not devoid of interest. Of the endostichos the second generation
has likewise originated; on account of the slanting direction of the
section its elements are only visible in the right half of the figure.
It is the two teeth which, still connected with the dental lamina, are
situated to the right behind the teeth 8 and 4.

Consequently it is very evident that Lygosoma possesses a distichical

( 959 )

dental system. Whether this property of structure is still peculiar to the
dental system of all reptiles, must be proved by subsequent investi-
gations. Perhaps these will show that it is not the case. In my
Opinion e.g. it is doubtful whether the dental system of Calotes, of
which I give a horizontal section in Fig. 7, is of a distichical nature.

I do not find an indication of it in the stage represented here.
Neither was there any vestige of substituting teeth. It may certainly
be imagined that, with some groups of reptiles, one of the two
rows is checked in its origin and development, which would render
the dental system monostichical. That this circumstance does not
occasion a suppression of the shedding of the teeth requires no
further argument.

We fixed already the attention to the fact that in its origin and
development the exostichos is somewhat in advance of the endostichos,
If this relation is not disturbed by later influences, the renewal of
the teeth in the exostichos will also every time take place a little
earlier than in the endostichos. A beautiful example of this fact is

sketched in Fig. 8. It regards the premaxillary dental system, as I
found it in a skull of Tupinambus nigropunctatus. The teeth of
this part of the dental system are regularly provided at their rims
with two notches. Besides the unpaired tooth standing in the median
line, one finds on either side five premaxillary teeth. And now it
is very interesting to see, that, regularly alternating, a still intact
tooth and an already partly resorbed tooth with an underlying
substituting tooth succeed each other. Here has evidently the chro-
nological difference in origin and substitution of the elements of
the two rows been preserved in such a degree that in this part of
the full-grown dental system the composition from two rows can
still be demonstrated.

( 960 )

This latter. fact seems finally to be especially distinctly the case
with Hatteria, as here according to Harrison’s ') representations and
description the teeth differ in size, so that regularly a large and a
little tooth alternately succeed each other. Harrison’s very accurate
description of the development of the dental system removes every
doubt that the two sorts of teeth belong to a different row. Yet this
naturalist has neither ‘been able to free himself from the notion of two
generations, and consequently describes as a peculiarity of the
dental system of Hatteria that, what he calls the teeth of the second
generation do not seem to displace those of the first generation, but
the latter give way and receive the elements of the second generation
among them. The dental system consists consequently, as tbe author
expresses himself, of two dentitions: “The teeth which are developed
on the dental lamina during the incubation period and which function.
during the early life of the living animal, are almost certainly the
members of two distinct dentitions, the later teeth instead of displa-
cing the earlier coming to alternate with them”. (lc. p. 202). The
distichous character of the dental system of Hatteria appears likewise
from the further details in the development which Harrison informs
us of, but into which I do not enter here.

As I hope the given examples are indeed sufficient to show that
our conception of the dental system of reptiles needs modification.
It will be necessary to distinguish in it a functionary and a genetic
structure. According to the former the dental system consists of a
single row of teeth, but the history of the development teaches that
this condition is not a primitive one, and that this simple row is in
reality a compound one built of two primary series to which, with
different species (Crocodillus, Iguana, Lygosoma, Hatteria) at the
lateral side another rudimentary. row is joined, the elements of which
develop themselves in the same way as with amphibia. This new
aspect on the one hand connects the dental system of reptiles more
closely with that of the Anamnia, and forms, on the other hand, a
point of issue for a modified conception of the relation between the
dental system of reptiles and that of mammals. .

With regard to the first part I remind of the fact that especially
with the tailed amphibia ‘“Polystichism” of the dental system is by
no means rare. Now we can imagine that, with regard to the
maxillar dental system, this Polystichism, through diminution of the
rows, has become a Tristichism, respectively a Distichism. The way
in which this diminution was accomplished is closely connected with

1) Quarterly. Journal of mier. sc. Vol. XLIV.

( 964 )

the way in which, with reptiles, a dental lamina has been developed.
As a rule it is represented, as if a fold of the epithelium had pene-
trated into the jawmesenchym. I do not think that this view is entirely
correct, but I suppose that the dental lamina has been developed
because both in the upper-jaw and in the lower-jaw in medio-
lateral direction, a fold of the mucous membrane has overgrown
the area in which the teeth were developing. This area was, as it
were, operculated. In order to prove this view I could add several
observations, but I restrict myself to simply mentioning it in order
to revert to this point at length elsewhere. We only call the attention
to the faei, that by this conception of the origin of the dental-
lamina it is clear, why teeth never originate from the medial sur-
face of this lamina. By this operculation the formation of enamel-
organs became possible. Now I imagine that with reptiles two primary
rows of teeth came to development in this operculated area whilst
a third outside row was not overgrown and remained at the surface. The
elements of this series — indicated above as “parastichos’ — preserved
the primitive character of their origin and developed themselves like
the teeth of amphibia. These simple teeth however gradually lost
their function on account of the greater strength of the elements of
the two operculated rows. This short indication of the velation
between the dental system of reptiles and that of lower vertebrates,
may suffice here. I intend to develop my views about the relation
between that of mammals in a next communication. Only for com-
pleteness’ sake be communicated here as the essential part of my
views that, in my opinion, mammals have inherited the distichism
of the dental system of reptiles, and that this distichism comes to the
front here in a much more distinct form namely as the lactal teeth
and the permanent teeth. In my opinion the lactal dentition represents
the exostichos of reptiles, the permanent dentition the endostichos
whilst the so-called prelactal dentition must be derived from the
parastychos. Consequently there would not exist the least relation
between the diphyodontism of mammals and the polyphyodontism
of reptiles.

( 962 )

Mathematics. — “On some relations between Bessel’s functions”.
By Prof. W. Kapreyy.

1. When 7 and s are real numbers and
(1 Nem OND) B= «cos w
the following expressions
S = cos ra cos s% +- cos r8 cos sa
T = sinra sin sB + sin rp sin sa
may be developed in trigonometrical series.
For, writing
ra + sB = re sin w +- sax cos wW = @ cos (w—¥)
from which

r

O=« Vr? +s? tgp = —
8

the equations
2S = cos (ra + 88) + cos (ra—sfB) + cos (rB+ sa) + cos (73—sa)
2T = cos (ra—s8) — cos (ra+s) 4+- cos (rB— sa) — cos (78+ sa)
may be reduced by means of the known series
cos (ra+-s8) = cos [9 cos (w—g)] = I, (e) — 27, (9) cos 2 (w—g) +
+ 21, cos 4 (w—gy) —
cos (ra —s8) = cos [9 cos (w+-y4)] = I, (0) — 22, (@) cos 2 (w+) +
+ 2T,cos4(w+g)—...
cos (r3-+-sa) = cos [o sin(w+q)] = T, (0) + 27, (@) cos 2 (M+ 9) +
+ 27,cos4(w+g) +...
cos (rB—sa) = cos [9 sin (w—y)] = T, (@) + 21, (Q) cos 2 (w—y) +
+ 2I,cos4(w—gy)+.
Thus we obtain
28 = 47, (o) + 8, (g) cos 4y cos dw 4 87, cos 8p cos 8H + .
and in the same way
2T=B8T, (y) sin 2g sin2w4+ 8, (Q) sin Oy sin 6H +-8T,, (Q) sin 10g sin 10@ }-
2. We may also express the quantities S and 7’ by multiplication
of trigonometrical series.
For if
FT (e)=4.4, + a, cos# + a,cos2a+...
= hb, sinw-+ b, sn 2x4...
gy (7) = 3a’, +a, cose + a’, cos2a +...
their product may be represented in one of the following forms
f (x) p (e) = 4A, + A, cosa + A, cos2e-+...
F (2) 9 (a) = B, sin a + B, sin 2a +...

( 963 )

where ')

n

wo
==, SS! fl Sia !
A, = 4 =a m &i—m + 3 = (Gn An-+n + Am a m-n)
0 i
n a
ae Sen '
By > = Om On—m + is = (a m bmn — bn mtn ).
0 1

These coefficients may be written more compactly by observing
that a=) —\a;,, d=, —a>,.0=, ——_ 0, ‘and 6, = 0:
Hence

0 n
Shi a] uf) a '
= (a m &m-+n =|- An a m+n) = m &na—m
—n 0
0 n
! afl = =! od)

= (a m Omtn — bn a m+n) =2 2a bn—m

n 0

—/

and
= 1 !
4A, = = Em (a m “in-+-n + An & m+n )
—n
= ' '
4B,, > Em (a m Dintn —. bn a m+n)
ae
where €, represents the value 1 if m= —n, —n+1,...— 2,—1,0

and the value 2 if m=1,2,3...

3. Now let us apply these formulae in the first place to expand
S in a trigonometrical series.
Multiplying
41, (rv) + I, (rx) cos 2w + I, (rx) cos4w +...
} cos s3 == 41, (sv) — IL, (sx) cos 2w + I, (sa) cos dw —...

we have, m being an even integer

4 cos ra =

Im = Im (72) in = ene Tn (sa)
therefore, writing the product

1 1
Te OE RESTS i + A, cos 2w + A,cosdw +...

the coefficients A are determined by

m n

4A, = = (aye Em [Lm (82) Intu(ra) + (122 (rz) Im4tn(sx)].
In the same way supposing

1 1
Ten 78 cos sa = i A', + A’, cos 2m + A',cos4m +...

1) Proceedings of the .aeeting of Febr. 29, 1908.

( 964.)

we have

m n

4 Al, = S (1)? €a Ln (72) Inn (60) + (1)? Ln (82) Im-tn(r2)) 5

—n
and adding the two results

m

4 (Ay + Any = {1 + (—Y AS ()) 2 Em [Ln (8) Ltn (re) +

a Din (ra) Lmtn (sw) ].
Therefore, if m has the values 2,6,10,... this coefficient vanishes,
and if n= 0,4, 8,... we obtain

m

2 (An+ AG) = = (—1)2 En Lm (sx) Inn (rz) + In (rz) Iinten (sx)].

—n
Hence, writing
L1S=C,+ 2C,cos4w + 2C, cos8w +...
the coefficients are determined by
ic) ) 3
2 C4g = (1)! €0p [Lop (8@) Lop 4g (rz) + Lop (ra) Top-+4q (82)].
—29
Comparing this, with the first expansion
1 S—TJ, (0) + 22, (@) cos 4 cos 4w + 27, (9) cos 8p cos 8w +...
2 0 \S 4S 8 AN p
we obtain the remarkable relation

L4q (# Vir +s?) cos 4q p= 4 SS (=e &9) [Top (sw) Lop tag (t@) +

—2q

+ Lop (ra) Top4oq (sz)] - (1)

r

A
where ig p=;.
8

fd
In the special case that rs, we have y= is and cos 4q g=(—1)),

sO

(—1)1 Lag (2 V2) = ES (—1)" 8p Lop (v2) Lop44q (72);

—2q

which gives for g=0

Tene) = > aby 2p L? op (re).

c=)

a result which may be verified by expanding I, (eV 2) by NeuMANn’s
method in a series of the form

Ife V2) = a,1,%(2) + a,F,%(2) + 0,1, + ---

4. To determine in the second place 7’ we multiply the series

( 965 )

4 sin ra = I,(re) sinw + I,(rz) sin 3w + I,(ra) sindw +...
4 sin s8 = I,(sx) cos w — I, (sa) cos 3m + I, (sv) cos5w—...
which, compared with the notations of Art. 2, give
m—I
i =) (Ehiew ss (S21)8 Or na)
m being odd in this case.

Therefore writing
7 sin ra sin s8 = B, sin 2m + B,sindwo -+....

the coefficients are determined by

m—\ n

4B, = S (—1) 2 & [fm (se) Intn (v2) — (1)? In (r)Zn4n(see)] «

aaah

and in the same way
ri sin sa sin r8 = B', sin2w + Bi, sindwo +...

where
m—l n

4B, = S (—1) 2 &n [Ln (2) Intn (sz) — (—1)? Ln (sx) Intn (r2)].
hn

Hence

n m—l

4 (By + By!) = {1—(—1) 23S (—1) 2 En [Ln(s2)Zn-fn(r)-+Lnr2) Inn (sar)].

vanishes for n=O, 4, 8.. and reduces to
m—l

2(B,+B'n) = S(—1) 2 eal Ln(se)Tmtu(re) + In(ra)Im+n(sie)
—— Te

for the values n = 2,6,10,...
From this we may infer that
47T=D,sin2M+ D,sin6o + D,,sin1l0w +...

where

1D — G1 \eop4[ Top 41 (sir) Zop44gpa(rx) + Lop 41 (rx) Lop-4sq-+s (sr)]-
—2q—

Comparing this result with the first expansion
4 T= 21,(v) sin 2p sin 2m + 2, (v) sin by sin 6w +...
we find the identity
L4g42 (aV 7? +5?) sin (4q+2) p=
ey (—1)'e,41 [Lop 41(s@) Lop 44q-4e(rx) + Lop ire) Lo) 449-43(sv)] - (2)
—2q—

which gives for r=s

( 966 )

Lagp2 (02) = © (—1Peap 4 Lap 41 (60) Lappin (ra)
—29

and reduces to
I (ar/2) = = Dirt Top41(sa)Lop+3(r2).
if ¢—10:
5. It seems desirable to verify the two formulae (1) and (2). This
may be done in the following way.

The first member of (1), considered as a function of 2, satisfies
the differential equation

d*y 1 dy oi
Be ! =)
dx? oF Fy Fe +(r+e ty =

therefore the second member must also satisfy the same equation.
To prove this we put

Lop(rv) = urp , Lop(sx) = vap
then it is evident that

d?U2p 1 durp 5 4p*
— r°— oo 0
da? a du + (: x? dre

d? voy 1 dvop 5 4p?) 0
dx* Hee dx eile 2? aie

1
Now, if = be represented by D, we will apply the operation
wv

1 169?
p+ lp + (#48— a)
a a

on the general term

Uap Vpt4g 1 2p Urp+44q
of the series in the second member of (1).
Determining in the first place

1 16q°
D? + —D-+| r+8*? = —- }; (uopvop44q) = My
41} v

we have
D?(uspv2p+449) = U2p dD vop+4q +- 2 DurpDvop+s4q + Vapt4q Dury
1 1
er D(uspvop+4q) = a (u2pDv2p4-4q oe vop44q-Durp)

so by addition
1 2-49)?
tno Derby + 5 Dray) = (‘ ui fay" — «roped

&

( 967

; 1. eee
V2p+47 Pr usy = = Duy —A = r- U2pV2n4-4q-

a
Therefore
8p? -+-16p Ss
Wf pclae = Pq U2, Vp+4g + 2 Dus, Dv, 449

vu

which is reducible to

M, = 1s (uap—1 v2p44q—1 + Uap V2%p-44941)-
by the known properties of the functions w and v

ra

_
2puiry = > (uap—1 + Uopfi) Dur, = > (tep—1 — Uy-+1 )
~_ _

8

&
5 (Coptaq—1 SF vep+4g+1)

G
<

(2p; £9) v2p-Hig =

s

Dovop,44q = 9 V2p+t4q—1 — V2pt4q+1)-
In the same way, putting

M,=)D +

D pe let 169") , 6
=F U +s a = “a? ) (v2p+-4q voy)

Lv
we get
M, = 78 (U2p4ag—1 Voy—1 + U2pf4g-1 V2p-+1 )-
Hence, if P represents the second member of the equation (1)
we have proved that
urs ae

da? a2 dx

16q°
Pee ee
2

TS 2 :
= 5 = (1) &)[uap—1 vapt4g—1 + Mappi VaptagH + uept4g—1 Y2p—1 +
2 — 99

F U2pt4qt1 apt |
Developing this series we obtain
U—4g—1 V—1 + U—4g+) VE -- U1 V—4g—1 + U1 V—4g41
— (UHagti M1 + U—4943 U3 + 1 V—4gti + Us V—4¢+3 )
+ (W—4g43 U3) + U—4g45 U5 + U3 Vi4gts + U5 V—4745 )

+ (u—s5 v4g—5 + U—3 V4q—3 + U4g—s V—5 + U4g—s v3
— (u—3 V4g—3 -- U—1 V4qg-1 + UW4g—s3 V—3 + Udg—1 V1
+ (W—1 Mtg—1 + U1 Mapp =F U4y—1 V1 + U4g41 21 )
2 (u] vigt1 + U3 V4g43 + Usq41 V1 + Mags Us )
+2 (us vig43 + U5 V4gt5 + wagts v3 + wags U5 )

64
Proceedings Royal Acad. Amsterdam. Vol, XLV.

(968 )

Observing that
u_p = (—1)" Un and V—» = (—1)r Un
it is easily seen, that the preceding series vanishes, which gives

a@P 14dP 169°
+ Hl ois pe eip=y
ve

da? a dx

and thus
Pe Coie Vr? + 83)
for the second integral is out of the question.

To determine the constant C, we must compare the coefficient of
x 4q a 4q me
e) in P with the coefficient of (=) in Cly, (ar? + 8”), the lat-
re ts?)2q
(itaea) C.
(49)!

av \19
To obtain the former we may observe that @ only will be

ter being

found in these terms of P

1 @
9 = (—1)P €2p [Lop (sa) Lop44g (v2) +- Lop (ra) Lop tag (82)]
—24

where &, has the value 1 for all the terms existing.
By changing p in —p, this expression may be written
29
is = (—1)P [1—2p (sa) L4qg—2p (v2) + Lop (7x) L4q—2) (se)]

or
2q

ae
5 = (—1)? [Lop (sx) L4q—sp (72) + Lop (r@) L4qg—2p (se1)].

Expanding the functions in this expression the coefficient of

a \47,
==) as found to be

1 sp rig—2p pp siq—2p

1)p
(2p)! (4q—2p)!

9°

a

ows

or

87 49 (4q—1) 4q (4q—1) (49—2) (49—3) |
- 1 — 7 Ati —... aA9
al 2! 4] Z |
i
where 4 =—.
§
Now

4q(4q-1 49(4q-1)(49-2)(4q-3
(1payi 4 (1-iay'r= 2] 1- (EY) 5.4 Ae Det tba]

ad 4]
or, supposing

( 969 )

1 + ia = Vi+2? (cos p + isin 7)
zi 1 — 2 =V1+2! (cos p — isin g)

4q(4q—1 4q(4qg—1) (4g—2) (4g—3
(14-22)"9 cos 4g y= 1- esta jae zn dis LY Gen Ea is

a) ! man
thus the required coefficient may be written
47 (r? + s?)*9

(4g) ; (14 47)29 cos 4qqy = CoE cos 4qy

—..+ 244

where
e
===
s

Comparing both coefficients we have

22 2\2q 2 22) 29

iia 8 C= Sane ai cos 4qy4

(49)! (49):

or
C = cos 4qy
and _ finally
Ie == Shy (aV r? + s?) cos 4q¢

which proves the identity (1). In the same way the formula (2) may
be verified. :

6. From the formulae of Art. 1 we may at once deduce definite
integrals for Bessel’s functions of order 4g and 4q + 2.
For these give immediately by integration between the limits 0

wu
ade
an 4

Wee é _——
al S cos 4quadw = = Ly (@ Vr? +s?) cos dog

0

1 ce * u in eet ee
xf T sin (4qg+2) odw = ok Tgq40 (x Vr? + 8?) sin (4q9+-2) ¢
0

sO when r=s

a
of cos (ra sin W) cos (ra cos w) cos 4gay = = cos (qx) T4q (ra V2)

0

7

ae , : x
At sin (rx sin W) sin (rx cos @) sin (4qg4+2) o = rn L4g42 (ra/2).
0

64*

Physics. — “Vhe imagneto-optic Kerr-effect in ferromagnetic com-
pounds and alloys.” II. By Dr. Srantsuaw Loria. (Communica-
tion from the Bosscna-Laboratory). (Communicated by Prof.
H, pu Bots).

In a previous paper ') I communicated to the Academy the results
of an experimental investigation of the polar Krrr phenomenon in
ferromagnetic compounds and alloys and promised an extension of
the investigations. Among the results presented at that time the
following are to be considered.

1. The dispersion curve of the polar Kerr-effect in the cases of
cupri-ferrite (CuO . Fe,O,) and of naturally occurring magnetite
(Fe,O,) in the region of the visible part of the spectrum (436 yu to
668 uu) exhibited points of inversion similar to those previously esta-
blished by Ineursoui.?) for magnetite and nickel in the infra-red
region (Lu to du).

2. The rotation, produced in the magnetic field, of linearly polarised
monochromatic light perpendicularly reflected initially increases pro-
portionally to the field and then, notwithstanding a further increase
of the field, attains a maximum constant value.

The purpose of the further investigation was the elucidation of
the physical meaning of the points of inversion in the dispersion
curve of the Kerrr-effect obtained from the experimental results. In
other words to search in the first place for any regular relation
between this. peculiarity of the dispersion of the magnetic Krrr
pbenomenon and the other optical and magnetic properties of the
substances concerned.

To solve this question it becomes necessary to know the refrac-
tive and extinction indices of those substances for which these cha-
racteristic points of inversion in the Kerr phenomenon have been
observed. It was justifiable to expect that perhaps the position of the
points of inversion stood in close relation to the form of the usual
dispersion curves. In conjunction with C. Zakrzewsx I have carried
out the optical investigations in the cases of cupri-ferrite, of magne-
tite and of invar. The measurements yield the elements of the ellip-
ticity of parallel light reflected from the mirror. The procedure was
the same as that previously used by C. Zakrzewsk1*).

1) Sr. Lorta, These Proc. XII, p. 835 (1910).

2) L. R. Inarrsoin, Phil. Mag, (6) 11 p. 41 1906 and 18 p. 74 1909.

3) © Zaxerzewskr; Bull. Acad. Cracov. (A) 22 p. 77, 1910; Sr. Loria and
C. ZAKRZEWSEI: |. c. p. 278.

(971 )

As a conclusion from these measurements for the questions we
are now concerned with there can be no suggestion of a direct
simple connection between, on the one hand, the points of inversion
of the magnetic Krrr-effect and, on the other hand, the dispersion
of the optical constants. Neither the dispersion curve of the refractive
index nor that of the index of extinction show any characteristic
indication in those parts of the spectrum where the above mentioned
inversion points occur. Taking into consideration the quite sufficient
accuracy of these measurements it becomes necessary to search for
the explanation of the inversion of the Karr effect in another
direction. In the following some new results will be brought to bear
upon the matter.

By means of the apparatus described in my first publication and
using the same method and procedure, the Kerr polar rotation was
examined in its dependence on the wave-length of the light and on
the intensity of the magnetic field. The measurements extend over the
region of the spectrum between 436 uu and 688 au; the field em-
ployed was varied between U,9 and 21 kilogauss.

The choice of suitable materials for observation was determined
by the above mentioned and still undecided question. The following
are the substances examined :

1. Pure artificially prepared magnetite (Fe, O,) for which I am
indebted to the friendliness of Prof. P. Wuiss. The specimen was
that which Weiss had employed in his magnetic observations. Ac-
cordiug to his results the saturation value of its magnetisation is
AiO> DC. 255. -):

2. Pure nickel (by Murck), also one of the pieces magnetically
investigated by Weiss and for which he gives the maximum value
479.0 ¢.g.s. for its magnetisation.

3. <A nickel mirror from the collection of the Bosscha-Laboratory
which nominally contained 99°/, Ni. :

4. Jron-nickel alloys of the compositions 73 Fe + 27 Ni and
74.6 Fe + 25.4 Ni respectively, which were placed at my disposal
by Dr. S. Hi.perr.

5. Ferromagnetic manganese which was also placed at my disposal
by Prof. Weiss and had been magnetically examined by him.

6. Haematite (Fe,O,) (Kakuk Berg, Hargitta Gebirge in Sieben-
biirgen) obtained from the Comptoir Minéralogique Suisse, in Geneva.

To the above named gentlemen, who have by their friendly loan
of the materials made these experiments possible, I beg to express
iny warmest thanks.

NP WEIss, Journ. de Physique (4) 9, p. 373, 1910,

(972 )

In order to facilitate a clear analysis of the results obtained I will
divide them into two sections. In the first the question of dispersion
will be considered and in the second that of saturation.

DIsPERSION CURVES.

1. Magnetite. The optical constants were first determined by
ZEEMAN ‘) for a natural crystalline surface (Pfitseh, Tyrol) of unknown
orientation; they are given in table 1, being the principal incidence
J and azimuth /7, from which the refractive index 2 and the extinction
index # are now calculated from Drupx’s equations”) to a second
approximation, Mr. pe Haas being so good as to carry out the cal-
culations.

TABLE 1
3 ; =
| J | H n x
|
434 68°27 10°10 2.36 | 0.32
589 | 68°27’ 8°48" 2.41 | 0.27
656 | 68933’ |! 71955! 2.45 | 0.25

Measurements with two other crystals gave appreciably the same
values.

In conjunction with Zakrzewski, according to the method already
referred to, I found the following values.

TABLE 2.

ASO | 62°45) ||, 0828
589.6 | 2.42 | 0.23
665357) 2245) i 10421

The numbers hold for an octahedral plane of the same erystal as
that used by me in the magneto-optical experiments; the polish was
incomplete and even with the naked eye irregular fissures and pores
were to be seen; the mirror was cleaned with toluol vapour; the
azimuth of the plane of incidence was without influence.

1) P. Zeemsn, Versl. Afd. Nat 3 p. 230, 1895.
*) P. Drupe, in Handbuch der Physik 2. Aufl. 6 p. 1298 seq., 1906.

(973 )

There is obviously rather a good agreement of the values and
although differences of about 15 °/, in the indices of extinction exist
they can be attributed to the lack of cleanliness of the surface.
Corresponding to the. smaller conductivity, the index of absorption
is appreciably smaller than in the case of metals.

Although the regular magnetite, as is known, exhibits itself as
aeolotropie in its ferromagnetic and probably also in its elastic pro-
perties yet it is difficult to assume the same in purely optical
processes. In any case, up to the present, only two optical constants
have been postulated for regular crystals and for isotropic bodies.
To examine the magneto-optical effect in this relation the above

mentioned artificial magnetite — obtained by calcination of ferric
oxide Fe, 0, —- was ground to a small plate and attained a somewhat

dull polish. In this case there could be no uniform orientation of
the mirror, at most only a minute crystalline structure.

Nevertheless the dispersion curve obtained showed quite the same
characters as in the case of perpendicular reflection from a natural
octahedral surface of the crystalline magnetite. The results of the
measurements are collected together in table 3.

TABLE 3.

= = Funct (4) | Magnetite | ) = 18.8 Kgs.
- : :
N | i(%7) | A(mm) | =(Minutes) | de

|
14 436 = Weel |) es cic + 0.15 =ca 3,
| |
i} | GRY |) ea a —= 3.60,
15 471 = TO. = Te

Hamp |) a sei Ne yey |
15 510 | + 9.9 | + 1.53 |
16pe e 5S0en | ees O0e eet aL!

2 | 56 | +286 | 4+ 4.49)

12 | 560 | +431.0 | + 4.80

2 | 610 | 433.2 | 45.14

17 637 | + 31.5 | + 4.88! |

iG) | 6sce fp eeoran | c= aisar | 00,04 ca0.00,,

The vertical column denoted by JN gives the number of ihe readings
belonging to one series; 2 gives the wave-length of the light used

in aw; A gives the double rotation, as read off directly from the
scale in mms., produced by a commutation of the current in the
electromagnet. The fourth column gives the mean value of the simple
rotation &.

To characterize the exactitude of the measurements I have calculated
the mean error for the points lying on the borders of the spectrum
used, and this is given in minutes and percents respectively in the
fifth column.

As is to be seen from fig. 1 the rotation, which is negative for

aia EEE

12 IGHREEL | ~

Bsccecreeceeeeceeeeeet eztristieresssiss:

aalsiziela if SLL ajalslabate Tr fapele fete |

ae sage! SnaeEr 4cnSBe aan HEH FH

geadasestatey eaectasorantetarertatarectasectotonantets
i Tt fala ele |

=? [shelatelalsiaie ime i a ialzilalel

ie ip BE EEEEEEEEEEEEE! ia SH Tey sacs

sie ceacasa:cdseeseeeescareceascecaerecseassesaeezecs

430 440 450 460 470 ¢80 490 S00 SO S20 S30 S40 S50 Séo 570 38 30 G00 610 6270 Glo bao 650 60 £70 Bo 690 Huse}

Fig. 1

436 uu, decreases rather rapidly with increase of wave-length, becomes
zero in the neighbourhood of 492 au, then becomes positive until for
615 wu it atiains a rather flat maximum and finally slowly decreases.
If one compares the shape of this dispersion curve with that of the
natural magnetite crystal it is seen that the general characters of the
two curves are the same, the only differences being that the zero
and maximum. points are displaced towards greater wave-lengths
by 30 to 40 wu. :

2. Nickel-steels. Until the present I had only investigated “invar”
containing 36°/, Ni. The interesting magnetic properties of this
alloy demanded an investigation of the Kurr-effect in nickel-steels of
another composition. In particular those alloys of the two metals,
which at ordinary temperatures appear feebly or not at all ferromagnetic,
deserved a closer observation.

Nickel-steel with 25,4°/, Ni, whose magnetical properties have
been tested by Hitpert and CoLver—Guaverr') is at ordinary tempe-
ratures as good as non-magnetic. None the less it shows a distinet

') S. Hitrerr and EF. Corver—Gravert, Zeitscbr. f. Elektrochemie 17 p. 750, 1911.

(975 )

Kerr-effect. The sign of the rotation through the whole of the visible
spectrum is negative. The dispersion curve has a similar form to that
of invar. Steel with 27°/, Ni, which also at ordinary temperatures
shows hardly any magnetic effect, behaved similarly magneto-optically.
The sign of the rotation here again is negative for the whole range
of the visible spectrum. Its absolute value is even greater than in
the case of the rather strongly magnetic invar. The shape of the
dispersion curve is very similar to that of the 25,4 °/, nickel-steel,
the difference being that the rotation changes somewhat less with
the wave-length. The results of the measurements of the rotation as
a function of the wave-length for the two nickel-steel alloys are
collected together in Tables 4 and 5 and also shown in fig. 2.

: Lt zz 1 a
Cor [SUA AE TS

Fig. 2.

TABLE 4.
«= Funct (‘) | Fe—Ni 27°/, | g=14.4 Kgs..
N 2(4¥) 4 (mm) : (Minutes) | Ge
15 | 436 | — 8.2 | —13.67 | +0.13=ca0.9%/
10 | 453°| — 99.6 | — 13.88
Where | = oarey | == a.e6r|
10 | 510 | —99.5 | 15.42! |
10 | 565 | —105.0 | —16.27
10 | 589 | —106.1 | —16.45' | +0.04=ca0.3%
10mm! 589 —104.5 | —16.19'
io | 688 | —104.9 | — 16.25'

The existence of the Kerr-effect in nickel-steel, whose magneti-
sation according to Hipxrt’s results has an extremely low value is
most surprising. Moreover pu Bots‘) had previously found a quite

‘)H. pv Bors, Phil. Mag. (5) 29 p, 304, 1890.

( 976 )

TABLE 5.

Oe el
e— Funct Q) Fe-— Ni 25.49 9 D Sie) Kgs.
N | 4(¢#) 4 (mm) = (Minutes) d=
10 436 — 68.6 | —10.63' | +0.08=ca0.7/,

| |
10 510 | — 82.4 | —12.75
10 589. | = 9210 | ==-4439" ||) 4.:0:07—=ca0e50),
| | |
10.-| 637-1) O64 als ==142 99!
10 688 | = O51 i) —2aaaza!

analogous result for twelve per cent manganese-stee! whose permea-
bility amounts only to about 1,01. The value of the negative rotation
varied from point to point on a highly polished mirror relatively to
different surface elements of the same piece, the rotation amounting
to one third of the maximum rotation for iron. These effects were
then attributed to inhomogeneity of structure as was borne out by
a metallographical examination by simple methods. Such results
— as also the opposite behaviour of Heusier’s alloy — may offer a
certain interest when applied to the theory of alloys and to metallo-
graphy although the method is hardly sufficiently simple for frequent
application. The physical interpretation however involves great diffi-
culties owing to the assumption of the continuity and homogeneity
of the substance, which is in general tacitly assumed.

SATURATION CURVES.

1. Nickel-steel with 25,4°/, N?. The mirror had the form of a
circular disk of about 25 mm. diameter and 2 mm. thickness. The
conieally bored pole end-piece had a vertex semi-angle of 55°—57),
The boring at the end remote from the mirror had a diameter of
6,3 mm., and at the end nearer to the mirror a diameter of only
3,6 mm. The distance of the pole end-piece from the mirror was
about 1 mm.

The form of the function ¢() is determined by the numbers
contained in table 6.

As is to be seen the negative rotation increases proportionally with
the field. Up to about 17 Kgs. there is searcely a distinct trace of
saturation to be noticed *),

1) | am compelled to take this opportunity of correcting an assertion appearing
in a paper by S. Hirerr and FE. Corver—Guaverr. They state there “The optical

(3ST)

TABLE 6.
o= funck (s))| Fe—Ni 25.40% | 1 = 589 ve
a : = . |
N | D(Kgs.) A (mm.) | (Minutes) | de
{oe ese cle eecrsrom Namrata alt soc03= scat.
10 | CES AN ACA (GN Mp ae ge Oise ORT
fOr ieeseonll) "sol | == 560" (= WO
10) \torss | = 64.9" | 10.06" 0.06=,, 0.6,
10 | 13.0 | —80.9 | —12.50' 0106 90557,
10 | 14.9 | —92.0 | —14.32 Odi v0.5.
10 | 16.0 ors | iso | 0,00 ., 014,
0 | i6-€ | —102.7 | —15.92 | 0.00=,,0:5,,

| | | |
2. Nickel-steel with 27°/, Nv. The mirror was a circular disk of
6 mm. diameter. All the other experimental conditions were as above.
The results are contained in table 7.

TABLE 7.
c= funct.(s)| Fe—Ni 274 = | 3 = 589 ms

N | o(Kes,)| Q(mm.) | = (Minutes) | de

faielercesa | 43a ==sgi6o™ | 0.05 cae Ye
eet | eae (ee Thar Qrdd== ke
12 1.8 shi =~9103) |) 0.04, 2
2 | 20] —23.2) —3.50 (MS eI ey
Oo ew | eee ae | Ee Ghoge=at eon
eo (ee | tee | Dake (ini sa
fon} riavae I =Sgaek Ve 10741" (069) Ins
(Onl ier eens | ot. 0,
1m |e 14 te tons! | rigi4s' OLos= 0:3
10 | 15.4 | 109.7 | --16.99" Qh0g==*,/0:5)
10 | 16.3 | —111.6 | —17.29' 0.09= ,, 0.5,,

investigations of the Kerr-effect which Dr. Lorta carried out gave a saturation
intensity of only a few units’. The statement of Hitrerr is, as he himself agrees,
due to a misunderstanding and does not correspond to the above facts.

(978 )

Up to about 10,5 Kgs. the rotation increases proportionally with the
field. In the region of the stronger fields the tendency to a saturated
condition becomes evident. Up to 17 Kgs. this state was however
not attained.

14 4 (Ags)

Fig. 3.
3. Nickel. Measurements carried out with a nickel mirror (a cir-
cular disk of about 18 m.m. diameter) belonging to the collection
of the Bosscha-Laboratory, gave the following results (Tab. 8, Fig. 3):

TABLE 8.
: = funct( ) Ni (B. L.) | | A=47 Tee
ao ss
N | @(Kgs)| 2 (mm) : (Minutes) de
15 |. 1.0%| - == 90.7 || — 4,58! |) 5 003= exer 7,
15: | S60) “25.0. | 9071 Mie SS
15) | oaogs Saou || Sedan Ne how ead aes
1505) 16:20)| fv tO on ere, 0.0715 /0.0>
180 “10,4 | Seal lor Nee Ah
iS. | a208' | 256-28 |) —Siesco: O00 == tacts
20 | 13.6 | —56.1 | — 8.88" 0.08 San

( 979:)

The maximum rotation, for 4—=477 uz, amounted to ¢, = 8,9’.

If the abscissa of the point of intersection of the two straight lines
(Fig. 3) be denoted by a, then w/ta = 550C. G.S.

As a result of direct magnetic measurements, as stated above, WEISS
gives for his nickel tested at 18°

A= 09,0 Cr Gas.

I have therefore repeated my measurements for the nickel specimen
placed at my disposal by Prof. Weiss. The mirror had the figure of
a rectangle, about 6mm. long and 3mm. wide, but was not quite
regular in form. It was still small enough to allow some doubt to
subsist as to how far the results are interpretable. The configuration
of the field right on the surface of the mirror is influenced by the
form of the bored pole end-piece as well as by its distance from
the mirror; the choice of the two conditions is more or less at the
disposal of the experimenter.

First measurement: The end-area of the pole end-piece (V) was
circular and of a diameter of approximately 5 mm.; the boring was
rectangular, about 2,5 mm. broad and 4 mm. high, the distance of
the mirror amounted to about 1,5 mm. The results are collected
together in Table 9, and Fig. 4.

Fig. 4.

Ror 580 ase, — ie. and 2/640 CHG. S:

Second measurement: Here the same conical bored pole end-piece
was employed as in the case of the investigation of nickel-steel.

The results are given in Table 10 and Fig. 5.

( 980 )

TABLE 9.

2 = funct () Ni (WEIss) I | 2 = 589 vy

N |(Kgs)| (mm) |< (Minutes oz

5 1.5 = OA | — 1.46° | 4+0.09=ca6 %
10 2.7 — 16.4 | — 2.54 | 0.08= >3 »
TN 828501) 122 \o-nll 500m tee nOMl == res)
10 | 5.5 273015 all = 15 020 | Le MOM is Oa
10 | 69 | — 40.6 | — 6.30 0.1 = » 1.5»
1G) Set |p cesta | ees: Ot 5 ut3s
10°) a3 — 50.5 | er Be 0.08=>1 »
10 | 15.3 = 50 sie ees 0.15= »2 »
109 |) 16a |) 950 | == TID! 0.15= >»2 »
i) IP UGE = 50.8} | == NiO} 0.1 = » 1.3»

TABLE 10.

«= funct. () Ni (WEIss) II | = 589 vu

N_ | (Kgs.)} A (mm.) | (Minutes) de

|
12 | 1.49 — 10.5 | — 1.62) | +0.03=ca2 %
| |

13 Meso = 203 = "3.14" 3)) (0c06——,,e2o ae
12 leet e6 — 31.1 | —4.82' | 0.04=,, 0.8,,
5 | 7.2 4° —443 — 6.86" | | 0;06—— 0.8"
is. |) ai — 52.9 —(8.20' |) “40:07, 0:4;,
14 etges — 58.3 — 9.02! 0.05= ,, 0.6,
11 | 19.7 | —58.2 | -— 9.02! 0.04= ,, 0.5,,
10 | 21.0 — 58.4 — 9.05! 0.07= ,, 0.8,,

2 Sli)

In this case for 42= 589 up: €, — 9,0’; and 2/42 = 640C.GS.

4. Magnetite. The measurements were performed on the same
mirror as that for which the dispersion of the Kerr-effeet has been
given above; it shewed many fissures and pores. According to Weiss

the saturation value of the magnetisation of this magnetite is

6,5 C.G.S.

Nin == 47

The first series of measurements was carried out with A= 589 uu.
As is known the rotation in this region of the spectrum is positive.
From the numbers given in Table 11 it is found that

€m = + 4,7’ and x/4a = 370 C.G.S.

TABLE 11.

= funct. ()
N_ | §(Kgs.)
12 0.9
12 2.2
15 3.2
15 5.0
10 1.3
15 9.0
12 11.4
14 17.0

i
J

Magnetite (WEIss)

A (mm.)

+ 4.64 |
+ 14.0
+ 20.8
+ 27.0
+ 30.7
+ 30.4
+ 30.5
+ 30.5

= (Minutes)

Se Oy 12!
EO iT!
tee Ga!
+ 4,18)
+ 4,75!
+ 4,71’
+ 4.72!
Sop

4 = 589 vy.

0206755
0.04=,
0209",
O;05—",,
0304s,
0.05= ,,

0.05" 5,

+0.04=ca6 op

Polly
1.3,,

2
1
1

”

( 982 )

This value does not agree with the results of the measurements
I have previously carried out under the same conditions but in the
region of negative rotation. If one measures the dependence of
the Kerr rotation on the field for 2 = 436 uu i.e. in the region of
negative rotations, the following numbers contained, in Table 12,
are obtained.

TABLE 12.

e = funct. (\) Magnetite (WEISS) | 2 = 436 ve

N “g(Kgs). A (mm.) = (Minutes) | oz

he ey Ss Oe | — 1.03 | +£0.05 =cad %

id] Bt eS a oral ssi 005= = fae,

Ve Neca | soe ears |) as,

16 ees al = 20, |e ereron all Soke eee eme

ulesp eo escdl 2 heel ates Bist

12 10.7 — 29.3 = Aba!" S|) © 0 s4— Sas

e| atbe2sleeesolor 8 =n to! | iss a

15 ¢| 06.7) i), 329.8 y| ——-4i61e ||) (0L07—= desy
These give ¢,—= — 4,7’ and 2/4 7= 450 C.G.S.

5. Manganese. For a ferromagnetic specimen of this element
Weiss and KameruincH Onnes found a specific magnetisation up
io about 2,5 C. G. S. In relation to the Kerr-effect it gave a
negative result in so far that the rotation cannot in any case be
greater than 0,35’. *)

6. Haematite (specular iron Fe,O,). pu Bots *) had already in vain
searched for an effect in the case of a mirror normal to the optical
axis. The mirror investigated by me was also parallel to the base
surface and reflected perfectly without however being magneto-optically
active. According to the investigations of Kunz *) this is also rather

1) P. Weiss and H. KamertingH Onnes, These Proc. XII, p. 657, (1910).

H. Benrens arrived at the same negative results in the case of the Kunpt-
Effect. Dissert., Miinster 1908,

2) loc. cit. § 18.

8) J. Kunz, Neues Jahrb. f. Mineral. etc. 1 p. 62, 1907.

( 983 )

improbable. With regard to my earlier negative result for ilmenite
no pains were taken to obtain mirrors of different orientation.

The last described measurements in the region of saturation are
only to be regarded as preliminary experiments which I had regret-
tably to discontinue owing to external circumstances.

The conclusion arrived at previously by bu Bots viz.: that 7/4 = Sin
must hold in the first place for an indefinitely extended plane mirror
of physically as well as chemically homogeneous material, which is
uniformly magnetized normally; also the thin glass test-plate used must
in the whole beam of lght measure a_ normal field equal to the indue-
tion inside the metal of the mirror, on account of normal econti-
nuity. Neither the nickel-steel as an alloy of complicated structure
nor the magnetite on account of its many fissures and pores
satisfy the first condition. So there remains only the metallic
nickel. How far the departures from the assumed configuration
influence the saturation curves in this case cannot be estimated
without further investigation; an opinion on this question can only
be based on rather tedious preliminary experiments.

Physics. — “On the solid state. I. — Mon-atomic substances.” By
Dr. L. S. Ornstein. (Communicated by Prof. H. A. Lorentz).

Already a considerable time ago G. Mim developed a theory of mon-
atomic solid substances by the aid of the statistical considerations of
BottzMann'). He derived the condition for the coexistence of solid
and gaseous phases, and determined the equation of state (equation
of compressibility) by the aid of the method of the virial. By the
aid of the theory of canonical ensembles the same results may be
reached in a somewhat simpler manner. Shortly ago Griineisen *)
derived the equation of state for a mon-atomic solid substance in an
analogous way as Mie, introducing, however, the hypothesis of PLANck’s
energy-quanta. It is, however, not devoid of interest to examine how
these matters may be treated by the aid of the canonical ensembles
modified in so far that PrLanck’s hypothesis is taken into account,
because then also the coexistence of phases is easy to examine.

lt is true that if the ensembles are modified in this way, we are
no longer allowed to suppose without further proof that ¥ (the
statistical free energy) is identical with the thermodynamic free energy,

1) Ann. der Phys. 11 1903 p. 675.
2) Phys. Zeitschr. XII p. 1023. Zur Theorie einatomiger Kérper.

Proceedings Royal Ac.d. Aimsterdain. Vol. XLV.

( 984 )

because for the proof of the identity of these quantities we make
use of the supposition that the systems. of nature are mechanical in
this sense that their movements are controlled by Hamiiron’s equations,
which cannot be the case for the systems for which the hypothesis
of Puanck holds. I shall, however, suppose in this communication
that we are allowed to apply to the modified ensembles all the
arguments which are of force for the ensembles of Gipps. On a
later oceasion I shall try to show on what premises this is allowed.

1. Consider a system built up of mon-atomic molecules. We suppose
that these molecules exert attractive powers on each other up to
distances that are large with respect to their mutual distances. We
shall further suppose that they repel each other with very great
foree when their distances are small. We may leave undecided
whether only adjacent molecules exert this repulsive force on each
other or also those lying further apart.

We consider a gramme molecule containing N molecules. The
volume be v.

Now we suppose with Min that the nature of the solid state
consists in this that in this state the only movement is such that the
molecules can execute vibrations round stable states of equilibrium.
In the state of equilibrium the molecules form some net of a regular
distribution through space, e.g. a cubical net.

So the energy of the considered system can be brought into the
form: minimum potential energy plus energy of the vibratory motion.
The energy at the boundaries is disregarded. It is natural to represent
the minimum potential energy by :

Nae NGS

v gin

Mim has demonstrated that the energy can be brought to this form
if we suppose the repulsive forces to be proportionate to a negative
power of the distance.

The condition that this energy is minimum for the given volume
leads to the equation:

av -l = Bin
If we apply this for the absolute zero (v = v,), we find:
@ um") = Bim.
a relation which Grinrisen derives as the condition that the pressure
is zero at the absolute zero of temperature.

I now consider a canonic ensemble of the modulus @ (@ =

( 985 )

if 7 is the absolute temperature and F the gas constant for a grammes

molecule).

When £ represents the energy and da an element of the 6.V
dimensional extension in phase for the displacements from the positions
of equilibrium and the corresponding moments, Y is given by:

Ve E

for which in our case may be written:
yr Nea N2B Etr Etr

ae + = = ts
, (@) =, vO vO fr oO a= cfe oO d2.

Now the supposition may be introduced that the energy of the
vibrations can only be whole multiples of the indivisible unity
of energy «. I shall follow Ezrnsrein’s method of representation.).
In the first place it may then be assumed that the integrations
with respect to the coordinates and moments need be extended over
only very narrow regions in the neighbourhood of 0, ¢, 2¢ ete. In
the second place we suppose that the system can be taken as con-
sisting of 3.V independent resonators. If in a definite case n, of
these resonators possess an energy ke, we may represent the con-
tribution to the integral for this case:

2 ny &k
3N ae G
A ie oF
k=1
ri ONE

If we take into consideration all the states in which 7; arbitrary
molecules have the energy /e they yield a contribution:

npek

(3N)! creed
(oye Uf

If we examine for what combination of the nz this isa maximum
we find:

nN = ae

a, determined by means of =n, = 3N, becoming :
—e/O
peed Zara a

1) Ann. der Phys. 22 1997. See Postscript.

( 986 )

The contribution of the most frequently occurring system becomes :
VoaN aot et A

—— = — ¢/@\3N >;

Vein e se / )

from which follows by summation with respect to all possible values

of VR:
aN? BN?
y =e
= 0 e vO nape @ 43N
: a5 — ¢/@Q\3N
(1 —e a )
or
N? N?2 —s/0)
Dap 2 NN ONS oe @tnaiesee ©) 4) aaaIvelag el

v ym

ae OW nes
If we apply £E= w— On we find for the mean energy 1
0O&

= BRS
Si Orme
BES
suite ; . : R
If » is the frequency of the vibrations, so that aah then:

:
= 3K By %
ees | od T,

i TG

el —]
from which follows the value for the specific heat given by E1ysrein.
Ow
To find the pressure we have to determine am In this we should
v

bear in mind that » is dependent on v.

iG RR a 1
On the supposition that the repulsive foree varies as ——, Mir has
pom

determined the frequency of the vibrations; he finds for it:

N?23.3m.3m + 1
(20y)) === —~ 4
M om+"ls

in which J is the weight of a molecule. If we apply this, we get:

2 Ov 2\oul
—_ — =([m+—]—.-
yp Ov 3] v

Making use of this result we find for the pressure:
aN? mBN°* ] dhpy

P=- ; - oe ee =
yp? pa+l p 9
guieen

(m + */s)

( 987 )
r
= aN* i m3.N* fi om + “fot

vy? ym-+l a 6

0

a formula which perfectly agrees with that given by GriNrtsen.
For T=0 we find p=0, when between a, 8, m, and v, the given
relation exists.

If we do not make any supposition on the dependence of » on»,
we find:

tke
ONE Age 4 TO Die (i IT
— = Cyrat.
/ y? p+ yp Ov i
0
Just as in the derivation of the specific heat A drops out of the
formula. A is supposed independent of 2

2. Coexistence of vapour and solid substance on the supposition
that the vapour is an ideal gas.

Suppose 7 molecules to be in a volume v. Consider the system in
which », molecules are found as solid substance in the volume
v,, n, molecules as gas in the volume v,. We have v, + v, =v,
n, +n, =n. The number of such systems in a canonical ensemble
amounts to:

: Hone
Yy — — as 6
Ton tow Vi" OD Aan
oe (Q2@M)2 ue
n,!n,! Che —€/0)3n,

To find the most frequently occurring system, and so the real one,
we must examine when this number will be maximum, varying the
v’s and the n’s. This yields the conditions:

Pi —P2 ;

; 2n, [a 3
—l g ologeAw—=n oi ogi (li eam c) i) + —{— — AS =
og ny, + og J ( ) 0 2, ym

3
— logn, + log v, +S log 22OM.

In these relations which are sufficient to determine everything,
A occurs. In this we find a way to indicate the value of A. For
high temperatures the second condition may be replaced by that
found by Muir, as everything referring to the theory of energy-
quanta must disappear then; for this if is necessary and sufficient that

( 988 )

ele
=a

a result which was to be expected *).

h

As a condition that the system is really maximum we find among
others :

Ps =o

dv

3. Coexistence of two solid phases. Let us suppose that two
solid phases are possible, so that there exist two different nets of
minimum potential energy.

These may differ as to the values of a, 8, and vr, and also with
regard to m a difference is possible, though improbable. I shall
distinguish the phases by the indices 1 and 2. Let us again sup-
pose that there are 7 molecules in the volume v, which are distri-
buted over the volumes v, and »v,, so that they contain n, and n,
molecules.

For the number of such systems in a canonical ensemble, we find :

2 2 f 2 f 2
w an, Bin, an, Bin,
! =
LO 2219 v,@ v,O0 v,™Q
in
Ni Wes
1 1

(a — e— 81/0) 3m (1 -— e— &:/0 31g

The search for the maximum system again yields the conditions
of coexistence; they are, as is easily seen,

Pi =P:

eats 2 wv v ops 1
= log Ny — 3 log (1 ae) “/) at Nn: E . B )

O \v, Vz Mz

If we apply this at the absolute zero, we find:

ny (« 8, )= Ny (« B,

Mee ake Sn il are 3? Tp ete aaa ’
a ny — 1 ; 3 My—1
Vio Yio! Vs0 Vo9 ?

Making use of Grinetsen’s condition we can write for this, putting

the densities 9, and. g,:

1 1
0, a. ( L— ae hee 0, a,{ 1 — =
: 1 2

0, a, = 0, ay.

The entropy of a gramme molecule is for the two phases:

1) See’Postscript.

( 989 )

dw
I= 90
x ey, 3 N E, ee
y, = — 3 Nlog (1 —e /@) + ———— 3 Nlog A,
28/0 — 1 2)
NGA ie nego Ossie ots Es 13 N log A
1 — se OPLVALOD, —e -3/ © -= 3 N log A.
2 ©2/0 — | oO

Which yields at the absolute zero:
fj, =" WE
So the theorem of heat of Nernst holds for the systems described
above.

Postscript. We can derive ¥ in a similar way if we make use
of the suppositions made by SOMMEREFLD').

Then we have to take as non discernible regions in the two
two-dimensional spaces that correspond to every degree of freedom
of a resonator such regions that the energy lies between / ¢ and
(i +1) «. If we introduce this in the formula for ¥, we get:

kD): E Nj;
yw Na N’ 8B | ie to) dh
ee sy Ou) Orn la “a ; (3 N)!
nye!

2 ip = BIN

If we substitute (4+ 4)e¢ for £, in the integrals which are to
be extended over a region /, and if we determine the maximum
in the usual way, we get:

k Sip ols
nk = G4 h € VO)
a being given by
é
(1 =)
‘Ca——
JE
he 20
This yields for W

‘i N’a N’B 3NE
Z Sa. DUNK. TeaGY AE
eat ee vO v@n 7 % 20

(1, — /)8N

1) Phys- Zeitschr. Ail 1911, p. 1057.

( 990 )
So there is agreement with what precedes, while A becomes = h.
We find for the mean energy:

3 Ne 3 Ne

2
OS

i

the result also given by SomMMeRrELD and PLaNck in his later consi-
derations.

Now Prof. Lorentz fixed my attention on the fact that Poincaré,
has made the remark that we are not justified in identifying the V
resonators of 3 degrees of freedom with 3 NV resonators of one
degree of freedom. I will show in what way we can meet this
difficulty.

The energy of every resonator may be represented in the form:
l 2 2 2 di me} 2 oh —— E
Bn (Pip sea teietse) tate a (5.7 + §,7 + §3") =

(p are the moments, § the coordinates with respect to the positions
of equilibrium). Now this energy can amount to 0...¢.. 2¢ ete.
According to the hypothesis of the energy-quanta there is no diffe-
rence between the systems for which the energy of the resonator
lies between O and ¢, € and 2e, ke and (+ d)e.

The extent of the region in the 6 dimensional space where the
energy is smaller than /, amounts to:

1 U3
6

The content of the shell for which the energy lies between /e and
(k + 1) amounts to:
1 ks*

By ae

If we consider that «= /», we find for the extent of regions of
equal probability
evita

whe

In such a region we may put the energy (4 -+ 1/,) «. Thus we find
for the contribution to w of the system where the energy for 7
resonators amounts to (4: --1/,) €

—_ (+ fla) E\"%
ww oom
—_ 1 Mike 9
5 5 ey A so. =

je

This yields for the most frequently occurring system

( 991 )

_ Ie
ne ake oO 5
while
SE /
=== —I7¢ 6)
ae 20(44, )

N=-

(ee

which is easily found if we bear in mind that:

he & 2¢
ae SO) 0° / io) )
Ske = 6 (1 +6 +e a
&

For small values of @ the formula deviates from the one given
before because then we may put:
BE &
PxG W@\=4
N=ae 20 (1 a)

For the mean energy we find for small value of @

3} 4deNe £/0

(om)

This value differs from Ernsrrin’s by a numerical factor. Funda-
mental modifications, however, need not be applied, in consequence
of this, to the above considerations.

Groningen, Febr, 1912.

Astronomy. — “Further researches into the constant term in the
latitude of the moon according to the meridian observations
at Greenwich”. By Prof. E. F. van DE SANDE BAKHUYZEN.

Since my previous communication about this subject in the Pro-
ceedings of last December, I have continued my investigations. I
was brought to it principally by the entirely different results found
by BarTeRMANN from his 8 great series of occultations of 1884—85,
1894—97, and 1902—03. I therefore resolved also to discuss the
Greenwich observations for the years 1883 (the first year in which
Newcomb’s corrections have been introduced into the Nautical Alma-
nac) up to 1894 and further to subject the systematic corrections of
the declinations to a close revision.

in doing this [I found to my regret that a mistake had slipped

( 992) )

into my reduction to Neweomb’s fundamental system*). I had
taken the differences Greenw. 1900 — Newc. Fundam. on page
31 of the introduction to the 2>¢ 9 Y. Cat. for the differences hold-
ing good for this catalogue, and had not noticed that on p. 2% is
said that for ¢his comparison the catalogue had first been reduced
to “Pulkowa refractions” and colatitude 21".80. The correction of this
mistake has altered the results of the previously diseussed years
with about 0.3.

First of all I will now revise my discussion of the systematic
errors of the Greenwich-declinations. Of course I was quite conscious
that for the present I could not think of a treatment of this
important subject, even aspiring to thoroughness. For my present
purpose, however, the determination of the mean declination-error
of the moon over many years, I believed that a very summary
treatment would be sufficient, also because it was not my intention
to obtain absolute places, but only places reduced as well as possible
to Newcoms’s system.

1. Systematic corrections of the declinations determined at Greenwich.

The different elements of these corrections I shall discuss succés-
sively.

Division-errors. In 1898 a new determination was accomplished
of the division-errors for every 1°, and account was taken of corrected
values for these errors for the observations of 1897 and following
years. The Greenw. Obs. of 1897 and the introduction to the 24
10 Y. Cat. contain tables of the corrections consequently to be ap-
plied to the observations of 1880—96. The mean value of these

!) | take this opportunity to observe that another slight inaccuracy has been
committed in deriving the differences between the computed R. A.-of the moon
and the results of the meridian observations at Greenwich, communicated in my
previous paper. It is due to the fact that I took the results for the years
1895—1909 from the first of the two tables contained in the volumes of the
Greenwich Observations, in which the observations are compared with the caleu-
lated places, not for the real but for the calculated moment of transit through
the Greenwich-meridian. All my ¢ « must therefere be diminished with about the
28th part of their amount. Hence the real mean values of az, i.e. the values of
the corrections to the mean longitude, become for the last two years:

A Naur. ALM. d Ross
1909.5 + 5".96 — O17
1910.5 + 7.27 + 0.91
Assuming also for 1912 A Ross = + 0".9, then we find for this year A Navut.
Atm. = + 7".6 as far as regards the correction to the mean longitude.

The influence of this mistake on the yearly means for 44 is practically zero.

( 993 )

corrections between N.P.D.65° and 115° amounts, however, only

to —0".02 (to —0".04 between 65° and 90°; to + 0.01 between
90° and 115°) and might therefore be neglected. ‘i

Zenithpoint. At Greenwich the values for the zenithpoint are dedu-
ced partly from nadir determinations, but chiefly from direct and
reflexion-observations of stars. Between the zenithpoints determined in
these two ways Zy and Zs there exist, however, systematic differ-
ences which are found different for different periods. These differ-
ences seem partly to be dependent on the errors of the micrometer-
screws in the microscopes and in the telescope. According to a very
recent investigation by W. G. THackrray'), however, they seem also
partly to be due to personal bisection-errors of the observers.

In the 3 following periods the following mean values for Zs—Zy
were found :

1869-1685 Zein = 0.40
1886—1891 0 .00
1892 —1909 —0 80

In each of these 3 periods the results of the separate years agree
very well inter se. Between the first and second periods, in Dec.
1885, new steel micrometer-screws were applied to the microscopes,
while in Oct. 1891, the micrometer-screw in the telescope was re-
placed by a new one and the objective was repolished. Moreover, in
1892 great changes took place in the staff of observers (comp. THACKE-
RAY p.’ 182), which have certainly influenced the value of the Zs—Z y
too. No influence, however, can be traced of later changes in 1902
and following years, owing to which none of the observers of 1892—
1901 has observed at the transit-circle after 1905. In the table
given by Tuackwray I namely find :

1892—1901° Mean Zs—Zy —0O"'.32
1902—1905 —0. 26
1906 —1910 —0. 27

It is therefore not quite clear in how far personal influences have
played a part in these differences and further the question remains
whether these have chiefly influenced the nadir-determinations or
the observations of the stars. Meanwhile, at Greenwich, the zenith-
points have always been principally based on the Zs derived from
the direct and reflexion observations of north and south stars. Before
1886 the mean difference between the Zs and the Zy was applied
to the Zy. Later on in forming the zenith-points a weight 4 was
assigned to the Zs, and only a weight 1 to the Zy. From 1897

1) Monthl. Not. 72 p. 178, Jan. 1912.

( 994 )

again a correction of — 0".25 was applied to the nadir determinations
when only these were available.

As far, however, as by this method of reduction we have not yet
obtained a declination-system that is homogeneous for the different
years, we can only take into account the remaining discrepancies by
applying for the periods of the 3 catalogues 1883—86, 1887—96,
1897—1905 and for the years 1906—O9 the mean corrections to a
fundamental system.

Flexure-corrections deduced from the differences R—D. As regards
the two periods 1897—1905 and 1906—09, I have kept to the
method explained in my previous paper; i.e. for the first period I
applied corrections in order to reduce the results to the flexure
+ 0".60 sin z and for the second, for which this value had already
been used at Greenwich, no further correction was applied.

For the period 1883—86 the employed co-efficients of sim z for
the direct observations were resp. + 0.69, + 0".66, + 0".69 and
+ 0".69, while also for the 10 Y. Cat. + 0".69 is used. A further
correction seemed unnecessary.

Finally, for the period of the 2»¢10 Y. Cat. 1887—96 the following
flexure-formulae were originally employed:

1887 + O0".68 sinz 1892 + 0'.58 sin z

wa), ie 930.70).
89 +0. 68 ,, A SEOs a
§0 20.56 =. 95°40) 4a
O1eU0NS4:, ORe2L 04am

In forming the star-places of the 2Ȣ 10 Y. Cat. the separate
annual results have been used without further correction. While the
mean of the 10 co-efficients amounts to +- 0.58, I have also reduced
the declinations of the moon of each year to the flexure -+-O0".58 sin 2.

The flexure-formulae derived from the R—D always contain also
a constant term which has to be regarded as a correction to the
adopted zenithpoint. This is always small, however, and amounts
till 1891 to about —O".01, afterwards to about -+- 0".05. For our
purpose we need not consider it.

According to THACKmRAY’s investigation the personal errors of the
observers would seem to depend also on the zenith-distance and thus
to give rise to apparently different flexure-values. We can only
attempt here to obtain final reductions to a fundamental system,
which hold as well as possible for the average observer.

Colatitude and Refraction. From 1883 to 1905 the colatitude
21.90 has been used without alteration and also the refraction of

the Tab. Reg. These values have also been employed for the forma-
tion of the three catalogues.

In 1906, however, the “Pulkowa refraction” has come into use
and as a consequence of this 21.80 has been adopted as colatitude.
For the difference between the two systems we find from the Table in
the Introduction to the 2°99 Y. C. p. 20.

N. P. D. Mean difference
New Syst. — Old Syst.
66° to 114° + 0".34
G2 Ls +. 0. 35
2 OS + 0, 32

For the annual means of the declinations of the moon I have
adopted + 0°.34.

Since 1902 corrections have been applied to the annual results
for the variation of the latitude according to A1Brecut. For the
formation of the 2°¢9 Y.C. also the results of the years 1897—1901
have been corrected for it. For my annual means, however, these
corrections have but littke importance as appears from the following
annual means of the reductions holding for Greenwich, i.e. of the
values of ALBRECHT’s 2 + 2.

aH — z
41900 —0".03
1901 +0. 04
1902 +0. 03
1903 +0. 05
1904 HEN 02
1905 —0. 01
1906 — 0. 05

I have paid no further attention to these reductions. Their influence
on longer periods and therefore also on the catalogue-com parisons
may be entirely neglected.

Reduction to Newcomb’s Fundamentalsystem. The last two Green-
wich-catalogues have been compared there with Newcoms’s Funda-
mental catalogue for 1900 and the results of these comparisons have
been given in the introductions to these catalogues.

From these I find the following mean differences in which Gr.
1900 red. means the declinations of the 24 9 Y. C. reduced to the
new system with Pulkowa refraction, and Gr. 1890 the deelinations
of the 2°¢ 10 Y."@.

(996 )

Newe. Gr. 1890 Newe.

IN, 1E% 4D). — —
Gr. 1900 red. Gr. 1900 Gr. 1890
65°52 + 0".14 + 0.07 = 01.31
60 —120 + 0. 10 + 0. 06 + O. 31
70s ((0) + 0. 16 +0. 10 of 0. 30

I adopt for my purpose the mean values between 65° and 115°
and now find first of all from the 2"¢ column and the differences
New Syst. —- Old Syst. given above:

Newe.—Gr. 1900 + 0".48,

Adjusting this value with the other two we finally obtain :
Newe.—Gr. 1900 + 0'.45
Newe.— Gr. 1890 + 0 .34

Further I adopt as reduction on Newcomp for the years 1906—
1909 + 0".45—0".34, and according to the introduction to the 2"4
10 Y. C. we find as mean differences between Gr. 1890 and the
LORY Ca—sGre sl SSOy:

NPD: 652 =1115°2 Gre 1S80=—Gr, 1890) —02208
60 —120 ==0308
CO) — AAO == (ON ill

I thus finally adopt :

Newe.—Gr. Obs. 1906—09 + 0.11
Newe.—Gr. 1580 + 0. 42

Resuming what we have found in this paragraph, we have to
apply to the Greenwich-declinations of the moon: 1. the above given
reductions to Nwwcoms, 2. for 1887—1905 reductions owing to
flexure, and 3. for all observations corrections to reduce the results
to the corrected value of the parallax-constant given im my previous
paper.

2. Investigation into the declinations of the moon.

sesides extending my previous investigation to the years 1883—
1894, I have also repeated the discussion for the years 1895—1902,
in order to accomplish it in the same way as for the other years.
The former method of investigation had this advantage that, besides
the constant error in latitude, also the periodic errors, dependent
on the argument of the latitude were introduced as unknown quan-
tities. On the other hand no attention was paid to possible personal

( 997 )

errors of the observers. The comparison of the former results with
the present ones thus gives us some information about the influence
of the method of investigation on the obtained results.

I compared the new results, ie. the mean of the three mean
values formed in the previously indicated way, with those derived
in my paper of 1903, and I found differences oscillating between
— O'10 and + 0".12, while the mean difference for the 8 years
amounts to + 0.01 only. The outcome is therefore very satisfactory
and also for 1895—1902 I have exclusively employed the new
results.

In the following Table I the results have been collected of the
observations of the limbs for the 27 years from 1883 to 1909.
The 2"¢ to the 4 columns contain the annual means formed in
the 3 ways, the 5" gives the mean of these three. Further the

systematic corrections have been put down in the 6 column and
the 7 contains the corrected Ad = Obs. — Naut. Alm.

Table II contains the results of the observations of Mésting A,
which have been derived in entirely the same way as those for
the limbs, as 1 now ealeulated also for the crater mean values after
the 3°¢ method, i.e. from the means for the different observers
separately. The columns of tables I and If wholly agree.

Besides deriving the mean results as they are collected in Tables
I and I, I have also combined my results in another way, viz. by
keeping those of the different observers separate but combining their
results for the different years. For those observers who only oceasion-
aly made observations, | combined these in one group under the
heading “Others”, just as had already been done for the formation
of the annual means in ihe 3" way, and as is generally done at
Greenwich. Otherwise some few observations, which moreover are
likely to be less accurate, would become too preponderant.

The mean results derived in the last way follow in Table II for
the obs. of the limbs, in Table IV for those of Mésting A. The
former contains, besides the results for the mean of both the limbs,
which had first been corrected for the systematic errors for each
year, also those for half the difference between the two, hence for
the radius of the moon according to each observer. Also the Ad of
Table IV had first been corrected for the systematic errors for each
year. The weights given in Table III are the quantities nn’ : (n + n’)
where » and x’ are the numbers of observations for each limb.
In order to make the weights in Table IV comparable to the
former, the 4" part of the number of observations has been taken
for these.

( 998 )

TABLE I. Observations of the limbs.

A 34 (North-limb + South-limb) A3

| 1 | a 3 Mean Cor corr
—o’73 | —o"s9 | —oves | —0'77 | +0770 | —0-07

1884 |.—0.60 | —0.60 | —0.59 | —0.60 | +0.70 | +0.10
1885 | —0.64 | —0.54 | —0.72 | —0.68 | +0.70 | +0.07
1886 | — 0.67 |. = 0,69 | —<0s7se ul =o-700 | s0-m0 0.00
1887 | —0.69 | —0.88 |; Soe |) 0.78: | =0;70° |, =-0702
(868:| 1/36; | —=sc3t ee=ttesie ny =-0-33 8) gee a) epee
18801 —0.81 |) 0/67) esoreo00|) Soca | 420:70.) 0.07
1800] 10.93 i 50%60™ |) =“058e~ |) =Soncont | <tioscoeule oes
1891 |. =0.45" |'-—10.60" |) —0:48" | ==0-5i1 "|| 420.501" | 0708
1802 "0/247 1) 008 “1/2 0832 Vaio |e oreo eon
1803 | —0.44 | —0.51 0.49 0.48 | +0.71 | +0.23
1804 | —0.52 | —0.46° ||. 0.55:-| 0-51 | 420160) | Sor00
1995 | —0.16 | —0.49 | —0.08 | —0.24 | +0.49 | 40.25
1896 | 40.44" | 130.93, | 0.31) |tee0.33 |! 20146) eenomg
1897 | +0.34 | +0.34 | +0.22 | +0.30 | +0.35 | 40.65
1898 |. 0.08 || ==0:10) ||, 0.10: \/9=F 0303 ))) 1-095) 1108
1899 202 Wee | Sen | SMe | +0.45 | +0.19
1900 | —0.74 | —0.54 | —0.66 | —0.65 | +0.52 | —0.13
19010 |u=-0.53.1) 0,66. lt ="063" | |S 0c61 ei e0sel 0.00
i902 | 0:30 20:25 )| “20.36 "| 0. si. 2p 0.47 some
1903] ==0:26" | =20:16 . |= 0.26 |="0.23" | =o dual eeoras
1904] —o.11 | —0.26 | —0.21 | —0.19 | +0.54 | +0.35
19¢5 | —0.36 | —0.28 | —0.49 Weairicce | utp afee a,
1906 | —0.07 0928) ie 0.28 — 0.21 | + 0.39 +0.18
1907 | —0.53 |) — 0.28 ||, — 0:51 |) —=Sovae ee eonsons | = 0Kts
1908 | —0.09 | —0.12 | +0.25 | +0.01 | +0.39 | 40.40
1909 | —0.19 | —0.05 — 0,24 | —0.16 +0.39 | +0.23

1905
1906

1907
1908
1909

TABLE II.

Observations of Mésting A

Mean
0°23

— 0.08
— 0.73

+ 0.02
—0.07

( 999 )

TABLE III. Observations of the limbs.

Observ. | Period | weigtt) aSSS | Nt

83—01
83—92
83—90
83—91
91—03

03—08
03—09
03—05
04—09
SE
BE
Others

TABLE 1V. Observations of Mésting A,

Observ. Period | Weight Ad

RC 05—09 | 15 | — 0"65
Ww 05—09 | 16 | + 0.76
E 509] fe | Ee O17
JS 05—08 SF |= .0.57

BE 06 and 09 4 + 0.36
Others 05—09 | 5 + 1.12

Proceedings Royal Acad. Amsterdam. Vol. XLV,

( 1000 )

The resulis as arrived at in the tables I-IV now must be examined
more closely. Looking first at the annual results of tab. I, we
notice some fluctuations in it. These may be partly real, because
they may contain inequalities of long period of the form dd =
— 0.20 s sin (a—x), — in which 2 is the longitude of the perigee and
y a slowly varying angle, which are, due to inequalities in longitude
of the form d/=ssin(g-+- x) caused by the action of the planets
and not included in Hansgn’s theory. So from the Jovian evection a
term of 18 years’ period with a co-efficient of more than O".2 must
proceed, from a perturbation by the Earth and Venus a term of 95
years’ period with a co-efficient of O'.13 and from another perturb-
ation by Jupiter a term of 7 years’ period with a co-efficient
cye (OO):

Probably, however, the greater part of the fluctuations alluded to
is due to personal bisection-errors. This appears from table III, and
especially if we consider the results of each observer for the sepa-
rate years, which are not given here. From these it is evident that
often considerable personal differences exist between the different
observers, and not only for the }(N—S), but just as well for the
1(N +S). E. g., for observer W the 8 results for A 4(N + S$)
from 190209 lie between ++ 0".22 and + 1".82 and for R.C. the
7 vesults from 1903—09 between — 0".02 and — 1".27, while the
6 results of J.S. from 19083—08 are situated between — 0'.64 and
+0".95. For the 13 chief observers with weights of at least 19,
i.e. with at least 60 observations, I further found as mean deviation
of their results for A 4(N+ 4S) by comparing these with the mean
of the 13, + 0.31, while their mean error, according to the agreement
of the different years inter se would amount to + O".14 only and
the mean error of the annual means, (generally from fewer observations
than the “personal means’’) is found to be, by comparison with the
general mean, + 0.27.

Also for the observations of Mésting A it appears that the personal
errors may reach amounts that cannot be neglected. The two
observers W. and R.C. found e.g. from the crater-observations the
same deviating results as from those of the limbs.

[ have now derived final results from those of the 4 tables as
follows. From those of table l I first formed mean results I, II] and
Ill for the 3 nine yearly periods and from these the general mean

1) In my investigation of 1903 it seemed to me that for these inequalities theory
and observation did not completely agree. Lately a new investigation into this
subject has been started at Leyden using the Greenwich observations of the last
years,

( 1001 )

1V, but also a mean value ‘/,1-+ 411-+-3/, 11=V_ in order to
eliminate a periodic term of an 18 years’ period. From table III I
combined the results of the 13 chief observers with equal weights
(VI) and added to those of the “Other observers” the results of the
4 observers with weights 1—5, which until now had been kept
apart (VII). Finally [ combined the vesults VI and VII with weights
13 and 4 to a general mean VIII. For the crater observations |
simply formed mean values from the resp. 5 and 6 results of the
tables Il and IV.
In this way I found :

Observations of the limbs:

I 1883—1891 A d= — 0".09

Il 1892—1900 + 0 .32
Il] 1901—1909 + 0 18
iV='/,1+ 1+ Ill) +0 14
V=>'/,1+7/, 0+ 7/, Ill + 0 18
VI 13 chief observers +0 14
VII other observers +0 34
VIlIl=7/,, 43 & VI+ 4 VII) + 0 19

Crater observations :
IX All the years 1905—09 Ad=-+ 0".20
X All the observers +0 .20

I would consider the mean of the results V and VIII as the
final result of the observations of the limbs and the mean of IX
and X as that of the crater-observations. Since these 4 results prac-
tically agree, I find at last:

A d Hansen = + 0".19

And as the mean correction of the declinations is = 0.96 X the

mean correction of the latitude, my result is

4A 8 Hansen = + 0".20

In the course of my investigation | was checked several times
by circumstances which would make its results less accurate. Espe-
cially the personal errors in observing the limbs of the moon and
also those in bisecting Mésting A brought a very uncertain factor in
the problem, Still the agreement found finally between the results
of the different computations and in particular between those from
the observations of the limbs and of the crater would make me
believe that, owing to the long period and the many observers, the

( 1062 )

uncertainty was lessened to such a degree that my final result
would still to some extent be reliable. There is one circumstance,
however, preventing this. My result cannot be made to agree with
that which BarrnrmMann derived from the accurate treatment of his
3 large series of occultations.

According to a personal communication which Prof. BarteRMANN
was kind enough to send me, he found, after a revision of his cal-
culations and a homogeneous reduction to Newcome’s fundamental
system, as results from his 3 series of observations :

1884—85 Ag= +1".04
1894—-97 + 0 .63
1902—03 + 0.99

Mean AB = + 0".89

He thinks that the 2nd result might still need a positive correction.

Thus the results obtained by the two of us differ O".7 and this
difference cannot be explained by casual uncertainties alone.

Prof. BarrrrmMann drew my attention to the different nature of
the two limbs of the moon and observed the possibility that the
very mountainous south limb might be always observed too far
south by meridian observers. Occultations and meridian observations
would then not only yield a different diameter of the moon but
also a different centre. The difficulty remains, however, that the
observations of Mésting A lead to the same centre as those of the
limbs. This would mean that also in making the micrometric deter-
minations of the crater the south limb would have been taken too
far south. A study of the selenographic determinations and of Hayy’s
investigations will be necessary to settle this point. That a large
personal error would have remained in the mean result of the
crater-observations by all Greenwich observers seems to me not
very probable in itself. It becomes very improbable, by the fact
that the corresponding observations at Greenwich and at the Cape
both reduced to Boss’ system, have led to a value of the parallax
constant which cannot be far from the truth.

Postscript.

Thanks to Prof. Dyson’s great kindness I have received from him
the mean results yielded by the just completed reduction of the
R. A. of the moon, observed at Greenwich during 1911. I take this
opportunity to communicate this important item for the knowledge
of the place of the moon on April 17.

( 1003 )

From 124 observations of the limbs there was found 4e = + 0°.603
and from 80 observations of Mésting A Ae = + 0°.640, so that
since 1910 the error in longitude has again increased considerably.

Probably these results have to be regarded as ‘apparent errors”
and must therefore be lessened with a 28 part of their amount.
Since I had not paid attention to this circumstance in discussing the
results of former years (comp. note in the beginning of this paper),
the then derived differences between the results of occultations and
meridian observations, are not quite accurate. Moreover I did not
feel justified now in employing the difference, derived from the whole
period 1847-1908, also for the reduction of the last years, since
it obviously did not hold for these. | now adopt, according to the
last years only, as reduction for the observations of limbs and crater
resp. 0”.00 and —O".20. Thus I obtain as correction to the mean
longitude according to the Naut. Alm. or Newc. I:

1908.5 AN. [=+6".04

09.5 +6 43
10.5 47.75
11.5 42By89

Extrapolating with the mean difference per annum between 1908
and 1911 —-+ 0".95, I find as correction to the mean longitude
for 1912.3 + 9".65. In order to obtain the correction to the true
longitude on the day of tne eclipse, I add to it + 1".33, as equation
of the centre, corrections of the elements and perturbations, thus
obtaining finally + 10".98.

As correction to the latitude I now find: 1 as a consequence of
the corrections to the longitude and to the longitude of the node
+ 0".03, 2 for a perturbation-term —O".08, and 3 as correction
to HaNsen’s constant term according to the occultations after Bar-
TERMANN’S calculations + 0".9, according to the Greenwich observa-
tions after my calculation + 0.2.

We thus obtain :

1912 April 17.0 Az=+11".0
Ag@=+0".85 or +015.

( 1004 )

Physics. — ‘Magnetic Researches. V. The initial susceptibility of
nickel at very low temperatures.’ By Ap. PERRIER and
H. Kamertincno Onnes. Communication N°. 126a from the

Physical Laboratory at Leiden.

§ 1. Introduction. To establish the general law for the effect of
temperature upon magnetic phenomena is a much more complicated
problem in the case of ferromagnetic substances than for substances
whose susceptibility is independent of the field; for, with ferro-
magnetic substances — even when an investigation is being made
ot the influence of change of field upon susceptibility at constant
temperature a distinetion has at once to be drawn between three
entirely different cases. The region of weak fields is identified by a
practically total absence of hysteresis: in the region of moderate
fields the susceptibility changes very rapidly and hysteresis plays an
all-important part; while in the region of strong fields or of satura-
tion magnetisation changes but very little further with change of
field. The intricacy of the general problem embodying these successive
cases as well as various further peculiarities 1.a. the irreversibilities
depending on temperature and on time arises from the very
nature of ferromagnetism itself. In these circumstances, therefore, an
experimental investigation as well as a theoretical treatment of the
whole problem of the change of ferromagnetism with temperature
can hardly be treated otherwise than by a systematic subdivision
of the investigation into various sections each of which can be
treated separately. The natural method of treating the problem seems
to be to ascertain the temperature functions which hold good through-
out each of the regions, and in that case the two extreme regions
are obviously the easiest to investigate, for then at least one of the
phenomena, hysteresis, is no longer of any account.

The investigation of one of these extreme regions, that of satura-
tion, has already been pretty well completed, not only at high but
also at very low’) temperatures. The results then obtained were used
by Werss in the research which led him to the important discovery
of the magneton. In his recent dissertation Raponavovircu has worked
in the other extreme region, that of initial susceptibility (i.e. suscepti-
bility in weak fields) but only at temperatures above 0° C. His results,
which were obtained exclusively with nickel, led principally to the
following result.

1) P. Weiss and H. Kamerunen Onnes, Comm. N°, 114 from the Physical
Laboratory at Leiden. (These Proceedings’ XII p. 649).

( 1005 )

If / is the magnetisation induced by a field of strength H, then,
for fields below 0,5 gauss about, and at constant temperature,
/=aH-+ bH
or
a -- bH
RapovanovitcH has now found that between 17°C, and the Cur
point @ and 6 are determined for nickel as functions of the tempe-
rature by

/ and /, are the saturation magnetisations at the experimental
temperature and at the absolute zero respectively, A and B are
constants. At the Curim point therefore a and 6 become infinite, while
they both vanish at the absolute zero; 6 is much smaller than a,
as long as we come not near the Curie point (at 18° C, 6 = 0,04 a).

The present paper relates to the susceptibility at temperatures
below 0° C. down to very low temperatures — the boiling point of
hydrogen — of the same nickel ring which was used by Rapova-
NovitcH in his research; for the use of this ring we are indebted to
the kindness of Prof. Wriss to whom we now wish to record our
thanks.

We wished to ascertain in the first place if the important deductions
concerning magnetisation in the neighbourhood of the absolute zero
to which the above formulae lead, are confirmed by experiment.
From the more general point of view indicated above, it is also of
importance to ascertain if all ferromagnetic magnitudes could be
expressed as junctions of the saturation magnetisation. And lastly
the result can be of fundamental importance in the physics 07 crystals,
for there are weighty reasons for ascribing ferromagnetic initial
susceptibility to a reversible twisting of the direction of magnetisation
in the elementary crystals as saturation is reached. A knowledge of
the susceptibility can therefore lead to a better grasp of the magnetic
structure of the crystal itself.

§ 2. Experimental method and results. We confine ourselves to a
very short description of the research the details of which we shall
publish in full later.

The ballistic method was used with a toroid built up of circular
plates of nickel. Absolute values were obtained by calibrating the

( 1006 )

galvanometer with a standard solenoid. The toroid, wrapped with its
primary and secondary winding, was placed in a large silvered vacuum
glass, into which a sufficient quantity of liquid gas was poured to
ensure that the liquid surface of the bath was well above the toroid.
The cryogenic part of the experiments gave rise to many serious
difficulties on account of the large mass of metal which had to be
cooled. For the measurements at liquid hydrogen temperatures the
toroid was first immersed in liquid air in the cryostat; the air wa.
then syphoned off, the cryostat evacuated and then filled with liquid
hydrogen.
The numerical results are collected in the following table.

INITIAL SUSCEPTIBILITY OF NICKEL.

Bath | if k

H=0
Ordinary temperat. | 291°K 3,045
| ( | 90 |. 0,955
| Liquid oxygen
| | 76,5 0,881

|
| Liquid hydrogen | 20,5 | 0,782

|
|
|
|

Each of the values given above is the result obtained from measure-
ments made with five fields between 0,017 and 0,090 gauss. The
quantity 6, which is extremely small even at ordinary temperature,
vanishes altogether at very low temperatures within the limits of
accuracy of the observations.

It is quite evident that with falling temperature a (or /) continues
to decrease regularly. Just as with regard to the value of 4, the results
with regard to a leave no doubt of good qualitative correspondence with
those obtained by extrapolation from the figures given by RapOvANOVITCH.
As for the quantitative correspondence *) it must be remarked that it
cannot, from the nature of the case, be well defined ; for it is a question
of a difference between 1 and a figure which at very low temperatures
differs from unity by a very small quantity. / and /, would have
to be known with very great accuracy before we could be at all

L é :
sure of the value of = —1. Taking the formula given by Ranova-

1) The difference of the absolute values at ordinary temperature obtained by
Rapovanovitcny from those given by us are caused by the change with time
of the magnetic properties of the nickel toroid (*Alterung”, “vieillissement’).
This change has been taken into account throughout our experiments.

( 1007 )

NovitcH, for a as a fnnetion of / to be correct, however, and using
it to determine / from our results, we find that between 90° K and
20° K the saturation magnetisation does not increase much more
than 0,0003, a result which is not inconsistent with what is accepted
on behalf of experiment concerning saturation magnetisation at low
temperatures.

Chemistry. — “On the activity of the halogene-dinitro-pseudo-
cumoles and their addition productivity with nitric acid.”
By A. Hurnper. (Communicated by Prof. A. F. Honteman).

(Wil! not be published in these Proceedings).

(March 28, 1912).

“

. : WACAA iw
= § ie tw Tey) 4 us) ours
= r 7
(é
'
:, yi 7
{ i a Eee y A Vt oe
Y Vales “7 h4 +h eri Fi pre
eat Ae : 3 Uo i ade a
. :
4 Sarre! Site : 1-90 p>
NY
~"
- 4 :
= a “
= 1h
An we eae
ri =
7 aol
=
y.,
'
? » -
-
A
é
"
‘
A ra

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING
of Saturday March 30, 1912.

Se —
0

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 30 Maart 1912, Dl. XX).

SiG) ANP BB aD ap Se SE

M. J. van Uven: “Homogeneous linear differential equations of order two with given relation
between two particular integrals.” (4th Communication). (Communicated by Prof. W.
Kartryn), p. 1610.

M. Sruyvarrt: “On the lineo-linear congruences of right lines and the cubic surface”.
(Communicated by Prof. Jan pre Varies}, p. 1018.

C. T. van Varkenpurc: “On the splitting of the nucleus trochlearis”. (Communicated by Prof.
L. Bork), p. 1023.

G. pe Vries: “Caleulus rationum”. (Communicated by Prof. Jan DE Vrigs), p. 1026.

F. A. H. Scurersemakers and A. Massing: “Some compounds of nitrates and sulphates”,
p. 1042.

L. van Irartzie: “On Dipterocarpol”. (Communicated by Prof. A. P. N. Francuimonr), p. 1044.

L. van Irarrre and M. Kersoscu: “On Minjak Lagam”. (Communicated by Prof. A. P. N.

FRANCHIMONT), p. 1047.

J. D. vAN DER Waats: “Contribution to the theory of binary mixtures”. XIX, p. 1049.

E. H/Biicuner: “Investigations op the radium content of rocks.” III. (Communieated by
Prot. A. F. Hortemay). p. 1063.

J. Borsrxen: “The configuration of benzene, the mechanism of the benzene substitution and
on the contrast between the formation of para-ortho- and of metasubstitution products”.
(Communicated by Prof. A. F. Horteman), p. 1066.

8. J. pe Lance: “The red nucleus in reptiles’. (Communicated by Prof. C. Wink er), p. 1082.

J.J. van Laar: “On the value of some differential quotients in the critical point, in con-
nection with the coexisting phases in the neighbourhood of that point and with the form
of the equation of state”. (Communicated by Prof. H. A. Lorentz), p. 1091.

M. W. Berierrmncrk: “Structure of the starch-grain”, p. 1107.

J. D. van DER Waats Jr.: “On the law of molecular attraction for electrical double points”.
(Communicated by Prof. J. D. van per Waats), p. 1111.

J. Borsexen and H. Waterman: “Action of substunces readily soiuble in water, but not
soluble in oi/, on the growth of the penicillium glaucum”. (Communicated by Prof.
M. W. Betserinck), p. 1132.

C. J. van VaLkenpure: “Caudal connections of the corpus mammillare”. (Communicated by
Prof. C. Winker), p. 1118.

Jan DE Vries: “On two linear congruences of quartic twisted curves of the first species”,
p- 1122.

K. Martin: “Further considerations about the geology of Jaya”, p. 1129.

Erratum, p. 1129.

Proceedings Royal Acad. Amsterdam. Vol. XIV.

( 1010 )

Mathematics. “Homogeneous linear differential equations of order
tivo with given relation between two particular integrals’. (4
communication). By Dr. M. J. van Uven. (Communicated by
Prof. W. Kaprteyn).

(Communicated in the meeting of February 24, 1912).

In the preceding communications we have discussed the parity of
function / (7) in connection with the parity of the functions « (7)
and y(r). It then became evident that the same function / (zr) deter-
mines two mutually semi-equivalent curves /’ (wv, y) =O when it is
a univalent even function of 7.

Let us now suppose that /(z) is determined as root of even power
out of a certain function of +; then to the same curve /' (x, y) = 0
belong two opposite functions /, from which ensues that 2 (a, 7) = 0
is then semi-equivalent to itself.

We shall occupy ourselves in the following, in connection with the
remark made here, in particular with algebraical curves / (a, y) = 0.

Just as in equation (31) and (382) (1st communication page 398)
we have expressed / in the integrals 2 and y, we shall now also

. af

give / =— such a form.

at

We shall make use of the following abridgments:
= P, F, — %, F,,

|

D = (®), F, — (®), F,

os
S

With the aid of this we can write equation (31) in the form
G = F.H— 3H F..
We then find

7 dl jj da ii dy (n —1) Fe j * ‘ i _ @-1) FAT
de desl de | (stn, a

If we caleulate /, and JL, out of (32), we shall finally find :

dl (n-—2)*

dv 22F.H?
For J? we can write

OL) Gee sah 2 = ee ee

Meal eT a :

In the supposition that /*(a, y, 2) = 0 is an algebraical equation

(4P HF .Hi2k2HH-6F HF -3F 2H 43H? FP). (51)

we shall arrive by eliminating the homogeneous variables a, y, and z
out of (51), (52), and F(a, y, 2) =O at a rational equation between
lesand ols

i= wif),

( 1011 )

If the solution is

Biya tates Lh an) 163)
we then find r+ out of
t—T =i a == KOH(WA) Rees oie or toed (ae)
Ee) WAU)

and /(r) by reversing the function 2 (/).

As ¥ (/*) is an algebraical function t is an algebraical integral-fune-
tion of /, and /(t) is the reverse of it.

If we take 7? = Vand /= Y as rectangular coordinates then

P(X, ¥)=0
will represent some algebraical curve.

We can conjugate the curve ®(Y, Y) =O to the system of all
curves /(wv, y) =0 which are mutually equivalent. A curve F’, (v7, y) = 0,
which is semi-equivalent to /“= 0, determines an opposite 7, hence
an equal Y and an opposite )’. The curve /’, =O conjugate to
®, = 0 is thus the image of &—O with respect to the Y-axis.

The curve ®=0O, which is conjugate to a curve / =O semi-
equivalent to itself, is therefore symmetrical with respect to the Y-axis.

We shall now give a somewhat extensive treatment of the case
in which “= 0 represents a conic. j

By means of a homogeneous linear substitution (if necessary with
complex coefficients) we can always make one of the points at infi-
nity to be in the direction of the }-axis. In this case the equation
F (wv, y) = 0 is linear in y and the equation y= (x) is rational, so
that operation with the equations (20),(21), and (22) (1s" communica-
tion page 366) gives rise to few algebraic complications.

However as we have our formulae ready for / and / expressed
by means of the implicit equation /’ (a, y,2)—=0O we shall, likewise
with a view to greater symmetry, make use of the unsolved equation
IG Re

Beforehand we remark that not all conics can be transformed into
each other by means of homogeneous linear substitutions. For, only
those conics can be transformed into each other by means of these
substitutions where the anharmonic ratio d between the points S, and
S, at infinity and the points of contact R, and FR, of the tangents
out of the origin have the same value; in other words: equivalent
conics have equal Jd.

We shall now first express the value of d in the coefficients of
thes equation” F = 0.

The anharmonic ratio 6=(S,S,, R,R,) is the anharmonic ratio
of the four rays which join these points with a fifth point of the

67*

(1012 )

conic ov of the four points which their tangents describe on a fifth
tangent of the conic. Let us take as fifth tangent one of the tangents
OR, out of OY, then the point of contact A, must be considered as
point of intersection of OR, with itself. The second tangent OR, out
of O intersects OR, in O. Let us moreover call S,', S,' the points
of intersection of OR, with the asymptotes of S\% and S° then we
can write

Jb —(S/S2 Ra) NS ie tO)

Salina

33 2
or, because S,' &, = — SR,
Y u"@)
foe AC
J = — a,
S'0
_ = She ee
rhe ratio 579 Can now be replaced by the ratio of the abscissae
1 u
wv, and v2, of S,' and S,', so that we find as simplest expression
Ww, aed
SSS OE VA Ae ee oe
v

The conic may be represented by the equation
F' (x,y,z) =a, a? + 2a, vy + a,,y? + 2a,,72 + 2a,,yz +4,,27=0. (56)

We now put

acy Wee. ney | == (AN

A131 Ass: As ;

and we indicate the subdeterminants of @,,...a,, respectively by
A,,...A,,. The pair of asymptotes is then represented by the equation

+ | 9 sate a 2 ¢ — » | 4 iil
ay, 0? -+ 2a, wy + a,,y* + 2a,,a2 + 2a,,y2 4- («., \: === 0)

Wak
The points of intersection of this pair of lines with the line
y = me

through O are now determined by

A ee: A
(@,,7° 2am ay, jue 4h 2(a,,m Ir A, ,)@2 = (+ =a | : Sa iW (57)
wes

If the indicated line through O is to touch the conic, then m

must satisfy

*— 2A, m+ A,, =0,

Or
2) 2 5) 2
(452433 — Ug, ) mM” — 2 (Gy 5g, —G, 455) m + (@,,@33—45 )= 0,

Or

( 1013 )

(a,,m -f- Gea —=0i(Ge.m- | Aa mda) te 5s (58)

Out iof (57

Gand ee

) and (58) follows for both roots #,:2, and v,:2, or

(w, =f &)° =

(a,,m--a,,)* Wes = 4,,4,,
Ae e,

= — =e
(qj, -2a,.m-—-a,,) | a,,;— —

hence

(a,—2,)* Be?
and, on actount of (55),
1—d\7 evale os r
(a) =. See ee ed)
From this ensues
1—d, 1—d,
——-=+t+2 , ——=—Af,
1+d, iO.
so
fe iter
= 1a a — ele (60)

So we find as was to be expected two reciprocal values for d.
Equivalent conics have equal J, therefore also equal 2. So for equi-
valent conics holds

Gas‘tas = constant.
A

To investigate how the value of d depends on the form of the
conic and on ifs situation with respect to the origim and of the line
at infinity we can invert the relative situation of conic and origin.
So we base our considerations on a fixed conic and we have then to
investigate how the value of d depends on the situation of the point
O thought as variable with respect to the fixed conic.

We take for the conic of reference the hyperbola

sey al

If later on we wish to transfer our results to the ellipse, we have
but to suppose / imaginary.

If 2; y,: are: the coordinates of point O, and z,, 7, and x,, y, those
of the points S,' and S,', then holds

Dees

t Ema OS, =. 2 = Ys —Yo
5 >) SS SS
OS,' v,— Xo Yi —Yo

s0

( 1014 )

(l-+d)a,=du,+2, , (1+d)y, = dy, + 4,.

Because (v,, y,) and (v,, y,) le on the asymptotes and their midpoint

fi +e, YitY. ; 6
( eS = ) on the conie, we find

)
ras va)

vy yy £ ps Yo (2+ w,)” (y, +y,)? Px

— ’ — a ’ ae. ae ie Cie 4,

a b a b a* b?

from which ensues

Ue, WY a 15)
(he i
so that z
ais o ? By ine ie » af 1&3 Ye x” Ya
seis (ae ce OU ee 7 eg Did | eee ee -( = —-* )=4¢:
Nie) i ia) iG =| ( a” b? } G Lb? :
or
one We 4S
se Se Ss PI 6 6 oe a 4 (OIL)

a (me (haaay
So points O of equal d lie on a conic similar and homothetie to
the come of reference.
In this way we can represent the values of Jd in connection with
those of & and 2 in the following plan:

| | |
I Ml jy eis Tee VI at val Vile
oeet = [= | |

k| =» | >-% <0) 0.) >0<¢41] 41 |>4+1,<+0] Fo

ee Ze (=)
y +n i cta>+]1 41 SE Ny S30) 1) 2,0 << <wolia +a

| se i

Petes Ley | SS thei | 0 SS) Se +1 |e 0<y <a all

|
> | 4 A 2 2 | tit |
ey =e <=+1>-—® Ti << ares) ap ll ap € ",U<Cv<cr — ol
i}

For the parabola A,, = 0, hence 4=0, so always d, =d,=+ 1.
For the hyperbola we find the following state of affairs :

I. At infinity J,=—1 Ik
Il. in the domain of the con-
jugate hyperbola SN) , —1>d,>— a;
Ill. on the asymptotes di=0 5 Oh ==S= OR
IV. between the asymptotes and
the curve 0<d<+1 » + oe >d,>+1;
V. on the curve d=+1 , O,=-+1;

VI. attheconcave side of thecurve d, =e—¥ , 0 p<, det} << p<m.

( 1015 )

For the ellipse holds:

Vil. At infinity Jd,-=—1 oo — 1;

V1. outside the curve Jes ea 0, dail 1,70 0,
V. on the curve d=+1 Se ale

IV. inside the curve +1>0,>0 » +1<d,<4+ @w;
Ill. in the centre J—=0 eee Ge

We shall now determine the form of the function /(7).
From (53) follows:
Fy =2 (4,,0--4,,y+4,,2) , Fy, = 2 (a,,0-+4,,y-+-4,,2).

Ne 5) . Ne 6)
FF, =2(a,,0-14,,y+4,,2) = 29-
) ~
a, » 2a,, , 2a,,
ERO eed al =O Ne, i —— ON ey 0.

PA Tey NTI rele

F.= Fy2Fy — Fy2Fr=4{a,, (@,.¢+4,,9+4,,2) —4,,(4,,7+4,,y+4,,2)}=
=4(A,,¢—A,,y).

=(F 2), Fy—(FyFi=8}4,5(4,,¢ + 4,59 +4552) +A, (a,,¢+4,,y +a

3°
== Oi (Giang + 4,,4,5)@ -F (4,,4,; + @,,4,,)y + (@,,4,3 + 4,,4,5)2 j=

—8{—@,,A,,« —a,,4,,y + (A—a,,A,,)z}—8 (Az — A,,9).
pe ee ere 2h. A?(A 2ait sea e, (A,,v—A, 7)”
22g A} egh :
—3.21!. A*g (Az—A,,g) + 3.2"°. A? ( A,,e— Att)
a eT B88 zgA? Teas
eT (Me ays = 29 (z= As a)

We now find:
(A,,@—A,,y)? + eae =

= (A,,°+4,,°A,,) «? + 2 (—A, sas) | a,,4,,4,,) vy + ( faa ae aoe
+ 2(a,,4,,4,,—Aa,,) ez 4-2 (a,,4,,4,,—Aa,,) yz + (A,,4,,°—2Aa,,)°—

= (a,,4,,—A) (a,,%7+ 2a,,7y +4,,y7+ 2a, ,v24 2a,,yz-+4,,2°) — Aa,,2°
=(a,,A,,—A) #—Aa,,2’,
or, because (w, y, 2) satisfy = 0,

(A,,ca—A,,y)? + A,,9°—2 Age = — Aa,,2’.
Hence we find ,

g
Ite sons (—A Peli i 24qz—Aa,,2? )s ee Ure ao (62)
= zg
Ae ; <
T= Sys (AR gt——Aakreayin ag ons Ss 4 (68)

By elimination of g we find

( 1016 )
ne “n QR 72 ‘ a,,A,,
36 7? =J* — 367° + 324( 1 ——__],_ . . . (64)
He
or, on account of (59),
36 1a (18)
bet @)
6 === eles esa

or

6dL
as) == -—__—__— re ayo ((0)
PA eae 1 8)
So / proves to be an elliptic function of r.
If we introduce /* = w as variable we find:
36 172? — T° — 36 I* + 324 (1—2?) 7’,
or
du? ;
9 (3) =u — 36 + 324 (1—a’*) u
dt
= u{u — 18 (1+4)} fu — 18 (1—a)},
thus
= 3du
C= se $$. — —_——__— ,
ne uw fu — 18 (1+-A)} ju — 18 (1—a)}
The singular points are now u,=o, u,=0, u,=—18(0-+4),
w, = 18 (1—2).
One of their six anharmonic ratios is therefore
UW, 1—A
Mal ee ig
The anharmonic ratio of the elliptic function «= /* = Q(@) is
therefore equal to the anharmonic ratio of the four characteristic
points iS.>, S,7> fy les of othe: conics) 21 — 10!
Evidently the invariant of this elliptic function is:
4 (S?—d +1)? (1-+322) (A+ 8a,,4,;)°
— O7 dla) =. QU aay a? ee Tale ee
Before transforming the elliptic integral we shall first investigate

(67

(68)

in what case it degenerates. Degeneration takes place, when the
du ! ‘
equation oa 0 has two coinciding roots. This occurs :

1. When 20; thus do) =o, = — 1: in) this) caseieither@,, —0
holds or A,, = 0, i.e. either the conic passes through O, or it touches
ihe line at infinity, in other words it is a parabola. These two types
of curves are not equivalent, but they are semi-equivalent : so they
have opposite functions J. This now coincides with the fact, that for

(TON)

1—( the form under the sign of the root in (66) is a perfect square,
so that two separated functions / appear. To distinguish the types
—0 and A,,=0 properly we shall return to the equations (62)

a3 <~33

and (63). For a,, = 0 these take the following forms :
2AI? = 9 (—A,,g4 2A2),
azAT = 3A,,9-

By elimination of gy we find

3

51 cha a a 2 (69a)
so
> 6d1 [
=i, = Se SLAY ip —,
18—I* 3Y2
or
CE

T= + 3/2. tanh ae DOVES Le = ean 0b)

If on the other hand we put A,, =O, then (62) and (63) pass into
gl? = 189 — 9a

3379

2ql = -— 34,42.
Elimination of gy now leads to
Giga? = ASME et yet. 8s (690)
from which ensues
~ 6d IT
t-—-Tt, = — | = -=—/2.tanh-! = :
J 18 --L? ay2
or
9 Teas =
[= — 3/2. tanh wa seer (d0u)
La
2. A second case of degeneration appears when A=-+ 1 (or4=— 1),

so for 6, =0, d, =o or J, =o, d,—O; in this case we have
a,,4,,—A or a,,4,, + 4,,4,, =90; the geometric meaning of this
is that QO lies on one of the asymptotes (for the ellipse in the

centre). The equation (66) now runs :
dl 6

T—T, = — - === a sin!
IV T7236
so that
{ 6
[= + ———_... (71)
sim (rt—t,)

3. When at the same time a,, =O and A,, =O holds, i.e. when
the conic is a parabola passing through QO, then the equation (62)
furnishes

SOA

This result has formerly been found (see 2"¢ communication page 590) ;

we can regard it as the combination of (70a) and (70b) for 1, = co.

( 1018 )

Mathematics. —— “On the lineo-lincar congruences of right lines
and the cubic surface’. By Myr. M. Sruyvarrr at Ghent
(Belgium). (Communicated by Prof. Jan pr Vries).

(Communicated in the meeting of February 24, 1912).

1. In pursuing our studies on the geometrical interpretations of matrices
whose elements are algebraical forms‘), we have been led to deduce
certain consequences of a’ wellknown theorem of Geometry of 7
dimensions.

The theorem runs *):

“Tf in space of 7 dimensions S, two simplexes with +1 vertices
“are reciprocal polars with respect to a quadratic variety, the spaces
“S,-9 common to the homologous limiting spaces S,—; of the two
“simplexes are such that every right line resting on m of these
“spaces rests also on the (7 + 1)”.

Let us apply this to the space S, and to the quadratic variety Q of
this space giving the properties of the ordinary ruled space ; the limiting
spaces 5S, of two simplexes with six vertices, reciprocal polars with
respect to the ‘quadratic variety. Q, furnish, by their intersections
with this @, varieties being the images of six pairs of linear complexes

in such a way that two complexes taken in the two rows and with
different indices are always in ¢nvolution; it is known that this notion
has been introduced into science by Mr. F. Kien.

The theory of ScHLArLt mentioned above indicates that every line
of SS, which rests on five of the spaces common to the homologous
limiting spaces S, also rests on the sixth,

Now, there exist such lines, at least in infinite number on the variety
(J itself, for the lines of a quadratic variety of S, form asystem ° ;
hence there is at least a finite number which verifies five conditions *).

On the other hand the right lines of the variety Q furnish plane
pencils of lines in ordinary space‘). Hence the plane pencils at
least in finite number which contain a ray of five out of six lineo-
linear congruences c; = c;’ = 0 contain a vay of the sixth.

In particular if the coniplexes c;,c'; are all special, their axes form

1) M. Svuyvaprr, Cinq Etudes de Géométrie analytique, applications diverses
de la théorie des matrices et de |’élimination, Gand, Van Goethem, 1908.

*) Cf. Scaudrii, Journ. f. Math. t.65;L. Berzouart. Rend. circ, mat. Palermo
t. 20; M. Sruyvarrt, Rend. R. Ist. Lomb, 1911.

8) Cf. KE. Berrini, Introduzione alla geometria projettiva degli iperspazi,... Pisa,
Spoerri, 1907, page 181.

+) Cf. E. Bergin, Joc. cit. page 136.

( 1019 )

a double six of a cubic surface and we see that ihe plane pencils
which contain a ray of five out of the six congruences ¢;= ¢cj= 0
also contain a ray of the sixth.

2. The investigation of the plane pencils containing a ray of 7,
congruences with distinct directrices has been made for n= 3 by
Mr. J. Neupere') and for n=3,4,5 by Mr. Jan pr Vris ’).

For the case of three congruences the problem consists of the
study of the planes which cut the three pairs of directrices accord-
ing to two homologous triangles. Mr. J. Neusere has found that
these planes envelope a surface of the 4° Class, whilst the centres
of homology describe a surface of order four reciprocal to the
preceding. This surface of order four contains as simple lines the
three pair of directrices of congruences and the three pair of rays
common to two of these congruences.

It is perhaps suitable to make known a method with the double
advantage of solving the problem at the same time for three, four,
or five congruences and of giving an analytical representation serving
for a later eventual study. Let us designate by

y + lz, y + mez’, y" + nz"
a variable point on a directrix of each of the three given congruences ;
the other directrices shall be determined by the intersections of planes :

Oxi),
pea= ll),

ihe == 0), i Se \).,
bixe— 0 ie = 0),
Let « be the centre of a pencil to be found; the plane of this
point and of the line a) has as equation
axb, — arbx = 0
and it cuts the line yz ina pomt 1 whose parameter / is determined by
ay by — drby + I(azb; — a,b:) = 0;
so the coordinates of this point Z are:
Li = yi(azbz — azbz) — 2; (a,b; — aby) ==) (00) Ul, 2).
This point, as well as the analogous points J/, NV, and the point «
are in the same plane, hence
yi (a:bz —a,b:) — 2} (ayb, — a,by)
| y', (ay 6, —a',b') — 2'; (ay: b's —a', by)
| yi (ably — abr) — 2" (alyrb"y — ab" yn)
| Es
1) Mathesis, 1903, page 105.

*) Proceedings Kon. Ak, t- Wet, Amsterdam, 1911 page 239.

|
| ——1() Ps

( 1020 )

This is the equation of the loeus to be found. This surface of
order four forms a particular case of that which was investigated
by- Mr. F. Scuur in his Habilitationsschrift*) and which is the locus
of a point whose homologous ones in four collineations are in a same
plane. The fact that the fourth of these collineations is the identical
transformation does not harm the generality and supposes only a
convenient choice of points of reference; but the first three collinea-
tions are three very special ones, for they make always a point of
a line yz, or y’2’ or y’’2’’ to correspond to each point.v of the space.

The following are some consequences :

I. If we give four or five lineo-linear congruences with distinct
directrices, the same reasoning substitutes for the determinant /’,, a
matrix with four columns and five or six rows of linear forms, a
matrix which in general annuls itself respectively for a curve of
order *) ten or for twenty isolated points. *)

So, “the locus of the centres of the plane pencils which contain a
ray of four lineo-linear congruences is a twisted curve of order ten ;
and there are twenty plane pencils each containing a ray of five
lineo-linear congruences.”

These properties have been geometrically demonstrated bij Prof.
JAN DE VRIES.

If. The determinant /’, annuls itself visibly for the points of

"

the six lines ah, a’b’, a'b", yz, yz’, y'z". By hypothesis two of these
lines do not meet; if, for instance a) and vz had a common point,
it would be a node on F,.

IH. If in the determinant /#’, we omit one of the first three rows
e.g. the third, we have the locus of the point « collinear to the
corresponding points 4 and J/; this matrix with twelve linear ele-

/

and
their two transversals. In general a matrix of twelve linear forms

ments represents therefore four right lines ab, a’b’, yz, y’2

annuls itself for a twisted sextic of genus three; so, in this repre-
sentation the curve can break up into four straight lines and their
two transversals.
From this results also that the couples of rays common to the
given congruences taken two by two are simple right lines of F,.
If in the determinant /’, we omit the last row we find the locus
of a point « for which the corresponding points 1, 47, NV are col-

1) Math. Ann. t. 18.

*) Cf. M. Sruyvaerr, Cing Ltudes... p. 37 where various properties have been
indicated of the curve resulting from the representation by matrix and finding
their application here; for shortness, sake we omit these developments.

3) M. Stuyvaert, Cing Etudes... p. 15.

( 1021 )

linear; this locus breaks up into a twisted cubic accompanied by
its three bisecants ab, a’b’, a’’b’’.

If we add to the determinant /’, a row of constants «,, @,, @,, @,
forming the homogeneous coordinates of a point @, we find a
matrix annulling itself for a curve of order six, locus of the point
w the corresponding points 4, .1/, N of which lie with point 7 in
the same plane passing through a.

IV. Jn the reasoning which has revealed the locus of the vertices
of the plane pencils containing a ray of three, four, or five lineo-
linear congruences it suffices to call w; the coordinates of the plane
of such a pencil, to express that this plane contains w and the corre-
sponding points 4, /, N,..., then to eliminate the w to have the
system of the planes of the pencils; we find a determinant or
matrices with linear elements in ~ analogous to the formulae men-
tioned above; their duality is complete.

3. The preceding calculation may be done in different other ways
and notably in such a manner that it is unnecessary to use the directrices
of the congruences and therefore neither to suppose them distinct.

We silently pass by these other processes and we restrict our-

selves to the investigation of a special case, the one where — the
congruences (1), (2), (3) having distinct directrices which we shall
designate by a, 6; a®), 62); a®, b) — the line a meets

(

b@) and 0), just as a@) meets 6 and 60), and a®) meets 6
and 62 (but a meets neither 6, nor a2, nor a®, ete.).

The right lines a b2) a) bY a® 6 taken in this order forma
skew hexagon. Let us project it out of a point -/ of the corresponding
surface /*,; the rays issuing from ./ and resting respectively on a
and 6, on a) and 6°), on aS) and J@) are in the same plane;
hence, in the projected hexagon the intersections of the opposite
sides are three points in a straight line; the projected hexagon is a
hexagon of PascaL; its vertices are on a conic; hence J is the
vertex of a cone of order two passing through the six points (a b©)
and reversely. The surface /’, is the locus of the vertex of a
quadratic cone passing through six points and we know that
it is of order four and has the six given points as double points,
that it contains the 15 lines joining these points two by two and
the LO intersections of two planes determined by the six points
distributed in two. triplets.

Let us now take a double six on a cubic surface

a’) a2) a® a® a®) a®

AY)- 62 63) 6H 62) 4

( 1022 )

In retaking the analysis of the preceding number or in imitating
the reasoning of Prof. Jan pe Vrivs, we recognize that the pairs 1,
2, 3 or 1, 2, 4 or 1, 3, 4 or 2,3,4 furnish every time a surface /,
analogous to the one defined aboye and that these surfaces have in
common a curve of order ten, c,,; that if we set apart three by
three the pairs 1, 2, 3, 4, 5 we have ten surfaces /’, having in
common twenty points, vertices of plane pencils having a ray resting
on a) and 6© (¢=1, 2, 3, 4, 5).

But by virtue of the property given at the commencement of this
paper each of these twenty pencils contains also a ray resting on
a8) and 5©).

4. To wind up with let us consider once more the skew hexagon
a) b2) a3) 6) a6) of the preceding number, whose edges we sup-
pose to lie on a general cubie surface #, and let us find the inter-
section of this surface /’, with the surface /’, locus of the vertices
of the quadratic cones passing through the vertices of the hexagon
(by supposition no four of the six vertices of which lie in the
same plane).

Of the 25 right lines of /, only nine are on /,, namely

a), 80, a®, $2, a®, G@)

aye) = a2 = 0; a@b© = aS 0, as SaOE@) = 0;
where we indicate by a?) = 0 the equation of the plane passing
through a and 6%,

In reality 1 the nine lines differing from @@,, 6°), a®, 62), a®, 6,
joining two nodes of /,, ave not on /,, for a cubie surface without
a singular point cannot bear three concurring right lines; 2 if the
plane determined for instance by the line a and the point (6% a)
intersected still /°, according to two right lines, ene of these would

(2)

pass through (4 a@ and through this point there would be three
right lines on /’,; 8 remains the 25 right line g of /,, intersection
of the planes through the alternating vertices of the hexagon. We
state without difficulty that if cannot meet any of the right lines
common to /’, ov F,, otherwise the hexagon would have four copla-
nary vertices, it cannot be moreover on F’,, otherwise it would inter-
sect the plane a 6% or one of the lines common to /’, and F,.

The intersection of /’, and /’, completes itself by a cubie e,.
The right line g of F, intersects /’, three times in points which
are not on the lines common to the two surfaces; these points are
thus on c,; from this ensues that this cubic is plane and non-dege-
nerated.

2))

The line connecting the point (a 4 with the point (@@® 0) is

( 1023 )

entirely on /’, and intersects /*, on the cubic ¢,; the same remark
holds for the right lines (a) 6) (a 6) and (a 6@)) (a® 6!) ; the
three points obtained in this way determine the plane of c, and
consequently this curve itself, as it is a plane section of F,.

In any case we must show that the three points under considera-
tion are not in general collinear.

Indeed through the six edges of the hexagon we can lay a pencil
of cubic surfaces. The three diagonals connecting the opposite vertices
intersect still one of these surfaces in three points situated according
to what precedes in a plane passing through the intersection of the
planes laid through the alternating vertices of the hexagon ; we have
there a pencil of planes cutting the three diagonals in triplets of
points which are not always collinear, for then it would be the same
with the alternating vertices of the hexagon which has been excluded
by hypothesis. And yet two planes of the pencils touch the hyper-
boloid determined by the three diagonals and they furnish three
collinear intersections.

We can consider if we like these remarks as properties of the
skew hexagon.

Ghent, January 1932.

Anatomy. — “On the splitting of the nucleus trochlearis.” By Dr. C.
T. van VALKENBURG. (Communicated by Prof. Dr. L. Bonk).

(Communicated in the meeting of February 24, 1912).

In a previous communication *) I called the attention to the fact
that in man (fetus, new-born, grown up) the nucleus of the trochleary
nerve need not consist of a continuous column of cells. In many
cases its continuity is interrupted: a smaller distal part is separated
from the more frontal nucleus principalis by a zone in which no
rooteells are found. The human material I dispose of, is by no means
sufficient to venture a valuation of the percentage of the cases in
which such a splitting is extant. It seems however that we had
better call it the rule than an exception. *) Besides from the nature
and situation of the cells of the caudal nuclenspart the connection

1) GT. vy. VatkensurG; Nucleus facialis dorsalis, nucleus trigemini posterior,
nucleus trochlearis posterior. These Proceedings June 25, 1910.
*) U. Tsucnipa: Ueb. die Ursprungskerne der Augenbewegingsnerven ete. Arb.
a. d. hirnanatom. Institut in Ziivich. Heft Il 1906. On page 35 this author
values the number of cases in which the nucl. IV is split at 20 to 309/). In my
opinion this number is too low, | find also the ‘hiatus’ always in the distal part
of the nucleus, T. finds it frontal, medial or distal.

( 1024 )

of the latter with nucleus principalis trochlearis is directly proved
by the possibility of following a separate nervestem which in its
sagittal course through the central substantia grisea of the aquaeductus
Sylvii situated ventrally from the other trochlearyfibres, unites with
the latter at its emersion, after having likewise been crossed in the
velum medullare anticum.

The situation of nucleus and root of the fourth pair of nerves to
the right and to the left is never identical. The above-mentioned
discontinuity is found either exclusively or much more distinctly at
one of the two sides than at the opposite one. As long as their number
is not much greater, the fact that, in the cases known to me, this
was always the left side, does not give me a right of generalising.

For a comparison I have investigated the structure of the nucleus
trochlearis in representatives of various classes of mammals, especially
with a view to the presence or the absence of a nucleus trochlearis
posterior.

I examined: a marsupial (didelphys marsupialis) an anodont (myr-
mecophaga jubata) three rodents (lepus cuniculus, cavia cobaya, mus
musculus), three carnivores (phoca vitulina, felis domestica, canis
familiaris) a monkey (oedipomidas oedipus).

Of all these animals only the rabbit showed a nucleus trochlearis
posterior; I found it in two of the six series of the brains of this
animal that the ‘Centraal Instituut voor Hersenonderzoek”’ possesses.
In the other rodents that I examined 1 did not find it (the Institute ~
possesses several series of the mouse).

The list on p. 1025 represents the relation — in sagittal dimension —
existing between the nucleus posterior and the nucleus principalis of
both before-mentioned rabbits. As preparation 1 is indicated the most
distal section, in which the nucleus trochlearis posterior is found.
The sections have been stained according to the VAN Gigson method. They
alternate with sections treated according to Pat's method, which of
course have not been used in counting. Their thickness is 30a. It
is obvious that the numbers of the rootcells found in a section have
no absolute value.

The counting was done with a magnification Zeiss Oc. 2 Obj. A.
No difference was made between distinctly polygonal and apparently
more oval rootcells.

The unequal number of preparations in which a nucleus trochle-
aris is found may be explained by the difference in size of the two
animals, perhaps likewise by individual difference. The distal boundary

both of the nucleus posterior and of the nucleus principalis —
is perfectly sharp. The frontal boundary is exceedingly indistinct on

( 1025 )

account of the gradual transition into the nucleus oculomotorii. The
latter begins — from behind — to show cells which are situated
dorsal from the nucleus trochlearis in the central grey substance

Rabbit 1 Rabbit 8
left right left right
Preparation 1 3 i) 0) 5
2 6 0 0) 7
3 6 0) 0) 13
4 4 0) 0 8
nf 5) 2 ©) ) 10
af 6 0 0) QO 2
. i 0) @) 0 0
5 8 0 0 0 0
s 9 0) 0) 0 0
> 10 0 0) O QO
5p 14 0) 6 0) 0
5 12 @) 6 1 3
- 13 i) 4 11 L5
- 14 0) 0 36 32
53 a (ts) 0) 0) 39 36
fe 16 0) 0 52 54
‘ 17 Seay med 60 | 56
2p 18 3 22 63 66
- 1.9)})) AG 2S) 55 69
af 20 ryt 45 50 49
‘ PAL ? P 28 26
12 37 54
25 23 47 52
24 56 54
<1 25 45 39
i, 26 395 37
96 27 32 38
oe 28 21 28

» 29 14 16
2 30 7 10

ventral from the aquaeduectus Sylvii, these are very well to be
distinguished (separated) from the nucleus trochlearis. The number of
cells that are situated on the place of the nucleus trochlearis increases
already after a few preparations, so that it cannot be decided how
ereat the oculomotoriusingredient of the nucleus is now, no more
can the exact place be assigned where oculomotoriuscells begin to
mix with trochlearic elements.

Remarkable is the very lateral situation of the nucleus trochleavis,
not on the most lateral part of the fasciculus longitudinalis posterior
but very distinctly 'aterodorsally from it, a little imbedded in the

68

Proceedings Royal Acad. Amsterdam. Vol. XIV.

( 1026 )

marrow fibres that are found there and border the central grey sub-
stance. This strongly lateral situation is less pronounced in man
though extant in principle, as appears from the figures subjoined to
my previous Communication (L.c¢.).

As to the nucleus trochlearis principalis, its situation corresponds
to a high degree in all examined animals. In its entire length however
it is imbedded in a more lateral part of the fasciculus longitudinalis
than with rabbits. Slight local differences — apparently depending
upon a stronger dorsal curvature of the posterior longitudinal bundle —
occur however. Only in the cat the gradual transition into the nucleus
oculomotorii is missing. The most distal cells of this nucleus are not
situated strictly dorsal from the place where the nucleus trochlearis
was found, but almost in the prolongation of the latter. Only a few
preparations farther frontal these cells pass into elements situated
dorsomedially that have been developed in the mean time. In the
dog the medial nucleus part however is found already in the same
level where the nucleus trochlearis is still present. The transition of
the latter into the lateral cells of the oculomotorian nucleus is gradual,
as in all other examined animals (with the exception of the cat).

At last I still fix the attention to the great asymmetry of the split
nuclei trochleares of the two rabbits which is distinctly expressed in
ihe above lists. In rabbit 1 to the left a nucleus posterior “lagging
far behind’, to the right another lying only 180 w farther caudal.
In rabbit 8 to the left no splitting at all, to the right a very distinct
one, which caused the formation of a nucleus posterior comparatively
very rich in cells.

No certain information can be given about the significance of the
phenomenon which I could only ascertain in man and rabbit. It seems
only clear that by the distolateral direction of the trochlearic-root
the situation of the nucleus trochlearis is at least partially determined.

Mathematics. “Calculus rationum”. By Dr. G. Dr Vrins. (Com-
municated by Prof. Jan pr Vrigs).

(Communicated in the meeting of February 24, 1912).

So far mathematicians have adhered to the opinion that an operation
of the fourth vank would teach nothing new; this opinion was in
part founded on the conviction that base number and exponent of
a power cannot be submitted to the commutative, associative, and
distributive properties. I have done away with this objection by
introducing the notion “medtwal power of two numbers’.

Doing so I have at the same time indicated the means of intro-

( 1027 )

ducing operations of an arbitrary rank for which the above mentioned
properties hold.

I hope I have opened a new field of investigation. The future
must show whether it is ofimportanee. At all events the considerations
have led me to investigate groups of transcendent curves, to a logical
classification and to a new analysis of them.

T have the outcome of my tnvestigations in manuscript, the contents
of which I wish to sketch in some lines. Starting from the algebraical
part | arrive in connection with the above mentioned analysis to the
geometrical applications. Only the operation of the fourth rank will
be under discussion and for the rest only considerations relating to
two variables will be allowed.

§ 1. If a power is submitted to a new involution the exponents
may be mutually interchanged. In this truth hes practically the validity
of the commutative property. Only a symbol is wanting for the
continual involution together with the settling of a base number to
determine univalently the mutual power of numbers. If we choose
for this e then the forms in their simplest shape appear. This suppo-
sition is made in the following, whilst the Nap. logarithm shall be
indicated by L.

“The mutual power of two numbers is the power of e having the
product of the logarithms of those numbers as exponents.”

If we put .

7 —) Cae sper 10
we shall write:
Ly >= Ch = gly = y Le — Yl.

That for the mutual power of more numbers also the associative
and the distributive property holds, will need no reasoning.

In a form as

U = 2,452

we shall call w, y, and ¢ efficients.

§ 2. A continued involution or evolution with equal exponent is
called “gradation” and the upper exponent appearing here gradation
index. The symbol used for it follows out of:

ne P —n —n
ee) 5 ese "= "(e).
These can be summarized in the form
"(x)= el'x,

68*

( 1028 )

“A continued mutual power with equal ef ficients ts called gradation”.
The inverse operation is called “descension’’.

“The it descension of a number is the number which put to the
nu gradation furnishes the original number”:

The descension will be indicated by an inverse rootsign; a
distinction of power and root descension is superfluous. The forms

n
n U P
n v— PE
Cah Ce eh a e= A(e)

a n
can therefore be written as
n
pas Vie,
n
When introducing negative and broken indices of gradations
everything can be summarized in "(v).
The gradation has the precedency of the involution, the evolution

of the descension.

§ 3. For a first consideration it is desirable to allow only positive
base numbers. By means of the operation, however, complex powers

may appear. Thus the number

1 .
I —e’
2 @
will prove to act here the partof *—1 in common mathematics.

The elementary operation is multiplication; when comparing two
quantities we must therefore pay attention to their ratio. For the
construction of figures the axes of coordinates are divided in such
a manner, that the successive abscissae (and ordinates) form a geome-
trical series. The lines drawn through the dividing points parallel
io the axes form a net of coordinates which shall be called ‘‘jield
of ratio” (in contrast to the wellknown “field of difference’).

For constructions it is advisable to take as base a number differing
but litthe from unity.

Just as the difference of two numbers is bivalent this proves
likewise the case with their ratio. Referring to what HotEL’) says
about operation-modulae we shall assign the same absolute value
(in a rational sense) to

= and a
y a“
(Numbers smaller than unity have for the field of ratio the same

1) Cours de calcul infinitésimal 1; § IV ete.

( 1029 )

meaning as negative numbers for the field of difference). The fo!-
lowing can serve as a confirmation of the assumed:
WE ae! and Teh
y fi ie ay

§ 4. Out of the delinition of mutual power follows that only one

indirect operation can be deduced from this, viz. :
Ly Lx
ea ee eae

If we use the word “matual root’ there is still ambiguity. The
absolute value of the two mutual roots (represented as follows):

Ly Lx
“ly =t1 “a: yjeSvy
must, however, be regarded as an equal one for the fie!d succeeding
the field of ratio. We might call the former the root of «to ¥.
It is useful to give forms as
ee
cS ‘e=—l(2)
the name of “reciprocal power”.

For gradations and descensions we might mention a series of
properties corresponding entirely to those for powers and roots. The
further development of rational algebra is analogous to ordinary
algebra. So we can speak here of a gradation binomium, of remark-
able roots, continuous roots, etc. In the geometrical part of course
the logarithmic proportion

ao==c d
comes to the foreground. And for different base numbers the form
(Lu: y=! Lu: Ly
is of importance. Likewise is of importance for geometry: ‘the
middle descent of two numbers”. This is the number whose 24 ova-
dation is equal to the mutual power of the two numbers.

As was to be expected this is independent of the chosen base
number. So if instead of e we take the base number «@ then, if we
introduce this as index,

A(t, ”)a= AY r)e-
2 2

This property corresponds thus to the property that the geometrical
mean is independent of the chosen unity. Further on holds

uw > A (uy).
2

§ 5. The question arises whether in the equation

( 1080 )

4 ="(a) — ep" |
when y and p have an assumed value, there is always a value to
be found for n. To show the possibility of this we have but to
follow the reasoning of the algebra handbooks for the existence of
logarithms. The immensurability of this number is, however, in
eeneral of a different order from that of the logarithms.

If mn is ealled the second logarithm of y then this number is not
definite until a definite value is indicated for p. The simplest assump-
tion is pe. There the e® power of e shall be taken as “dase
power.”

If now immensurable numbers are allowed as index of gradation
the result is regarded as limit to which a descension (changing in a
definite manner) of a gradation tends, and as definition of the 24
logarithm follows:

“The 24 logarithm of a number is the number indicating to which
gradation the base power must be brought to furnish the given number.”
The four principal properties are:

LL (u,v) = LLu + Liv; LL" (u)=n. Llu;

1
LL(u\v)=Lilu— Lin; LLAu=—. Llu.

n n
By the introduction of the notion “mutual gradation” of two
numbers the difference between the two indirect operations which
are deduced out of a gradation disappears. If we put

7

RS (Ag

p 1 PSS

then w and y can be interchanged in the following equation (their
mutual gradation)
2 [jy] = ay) = LLy(a) = Ly
This form is equivalent to
LLz=LLe. ly.

The mutual gradation as starting point leads to the investigation
of the “rootfield”. For this the evolution is the elementary operation.
The operation of the fifth rank following out of this shares the fun-
damental properties of the operations of lower rank.

Just as operations of an arbitrary higher rank may be introduced
and may give rise to the investigation of definite groups of curves,
operations of a rank lower than the first may also be introduced
geometrical considerations may also be connected with these.

§ 6. The equation of the curves of the first gradation is found

( 1034 )

by elimination of m out of the following two
v=." and aj==—aror.
For the construction of the points we must make use of different
base numbers for abscissa and ordinate, unless the logarithms of the
base numbers (a and 6) used have a mensurable ratio.

Y¥ ne

oe

FR.
i, 4
(pence
A m

eee
eae
iv

ny

P,P BP RP

mili
Taal
ee

ral

RP, 8,
nies

OLN

eS
WAZ

ig. 1. f

The lines of fig. 1 are drawn on this supposition ; the above mentioned
ratio is 3 for AB; 4 for MD: 4 for ME; 2:3 for FG and —3
for HJ. In the field of ratio the lines whose equation is:

Yo @, |
are the simplest; they shall be called “rationals”. They have the
form of parabolae or hyperbolae according to their “director exponent”
4= Lh: La, being positive or negative. So

( 1032 )

Lb
7 Waa ee

represents the part cut off the line a—4J, counted to M(1,1). The
lines w=1 and y=1 must be regarded as axes. They divide the
positive field of ratio into four quadrants which are unequal, but
which must be considered as equal in a rational sense (as will be
evident later on); c=0O and y=O correspond to — o in the field
of difference. Lines with equal director exponent are ‘rational equidi-
stant’. A pencil of straight lines through O (rationals for which 2 = 1)
intersects two equidistant rationals in corresponding points. If the
points of intersection of a selfsame rational are joined, then the cor-
responding figures are similar. So we might say that equidistant
rationals are pacallel in the smallest parts.

For «,=1, ¥,=1 the lines shall be called central rationals; they
correspond to the right lines in the field of ratio drawn through the
origin of coordinates. Rationals with mensurable director exponent
find a continuation in one of the three other fields of ratio.

§ 7. The director exponent of the rationals has a simple geome-

trical meaning. Out of the equation
ym or Dy=2La 4- Im

we find for it
dly = 1 dy
— ‘i ae @R , f =a
that is “the ratio of abscissa to subtangent.” For points of equidistant
rationals with equal abscissa the tangents pass through one and the
same point of OX (fig. 2); for given value of ordinates they inter-
sect each other in one point of OY. Furthermore all rationals divide
the rectangles of coordinates proportionally, so that the director exponent

can be regarded as ratio of two integrals. Calling the parts ./, and
c fo) to}

J, in which the line divides a rectangle (/) we find

a] Jin
— | udy : { Ok = Hao done
Ce Oe

As now the differences of the terms of a geometric series form

V]

again a geometric series that ratio also holds for area differences
and -differentials :
4— LJ, _ dd,
[Aa fr
For 4>>0 the strips lie outside each other; for 4< 0 overlapping
takes place (fig. 2). Here
Ao AOB

( 1033 )

represents the director exponent of the 8 equidistant rationals OW,
OP,, and “OP;.

LS

Z\

éy (LLU

ee

N
i\_\

Za

CLL Z/NZAASs

\
AN
KHAN

i
b
tal

As we ean also write

Ye | vs,

aaa | — e

Yr\%1
a rational is a line for whieh the mutual root of the ratio of
coordinates of two points is constant.

§ 8. In the field of proportion coordinates and areas are quantities
of the same exponential order. The area of the rectangle of coordinates
determined by the point:

IP (a? OR) AS) n= (a0).

The rational laid through this point and through P,, contains
likewise P,,4,- The area of the rectangle of coordinates determined
by this point is:

Imn-tn == (abn ==sd Ey Gh

so it is deduced out of a multiplication. Furthermore the coordinates
can be regarded as areas namely of rectangles having the coordinates
as base, the distance between OX, and OX (resp. OY, and OY)
as height. A point is not yet determined by the area of a rectangle of
coordinates only (equilateral hyperbola), an element for the direction
must also be known. Tc a sum in the field of difference always

( 1034 )
corresponds a product here; likewise with the geometrical sum:

r+ iy the geometrical product : ay =J.
This determines the situation of the point entirely.
To the geometric sum:
a ar Tyna ly r ,) ate i (Y¥ +-Y2)

corresponds here the geometric product :

eS Ch = (ee) o (OLN) ec
In fig. 3. this product has been construeted in two ways. The

™& he

i

Fig. 3.
points MP,P,P, form a rational parallelogram whose rational through
M and P, determines the diagonal. The rational distance between
M and P, must therefore be regarded as product of the distances
between Jf and P, and Jf and P,. So

ay’ and ey7'
are conjugate values whose product and mutual power are real; viz.
aa sand: 2(z)ia(@):
When treating the analysis we shall define the “rational angle” ;
for a preliminary transition to polar coordinates we can put:
avy = reose Hsing ,
out of which follows for rational distance (radius) and rat.- tangent:

PAB) 8. WeSC? «

)

( 1035 )

The first relation is the equation of the rational (or logarithmic)
circle; the second equation represents the rational of the centre with
director exponent tg y. If we introduce for the rat. tangent fy rat e
and for the exponential quantity the letter «w (meaning follows) we
can then write (exchanging tg rat by -tr):

ye =tru.

According to definition the logarithmic cirele is now the locus of
the points possessing equal rational distance to a definite point (here
M); this point is called centre. This has given an extension to the
notion of ratio; this more general notion we shall. eall “shew ratio”.
It is measured along the rational through P and J/; the measure is
the alveady mentioned radius 7 which is called the ‘modulus’, whilst
to w the name of “argument” may be given.

§ 9. The properties of the rational goniometric functions are
founded on the consideration of the logarithmic circle with radius ¢
(represented in fig. 4). In the geometry of differences we arrive,
gradually moving along a circle, from the value + 1 to —1 ‘and
back; the absolute value of the difference does not change then.
Here the logarithmie circle leads gradually from the value e to e—,
where the absolute value of the ‘“ratio” remains constant. Let us yet
mention as particularity that in J/ the differential coefficient of the
rationals is equal to the director exponent.

If we now allow the rational radius to revolve around J/, then
this coincides in 4 positions (P,, P,, P,, and P,) with the axes;

( 1036 )
here- the rational direction is identical to the direction of the line.
Following GRAssMANN’s notation for the field of ratio we might write :
Pie Me ie Ean place cn ee

To arrive now from the value

at the value:

we must allow the index of gradation to vary continuously from
0 to 1. If by this change the index has reached the value 4 (resp. — 4),
then the direction as well as the rational direction seen out of M
is halved. Considered in this way the points P, and P, are therefore
determined by

¢ and e—.

In all intermediate positions the exponent is complex. For all
poihts of a logarithmic cirele the modulus is constant with variable
argument. Here we have the widest definition of the notion “ratio”.
For two diametral points is

O="@.

Also to the areas of the rectangle of coordinates (or the partial
one separated by the rational) is applicable:
ays MN ler tyes
If the radius of the log. circle is one, then by
*(x) *(y)=1
is represented the point J/, so that for all values of y holds:
p11)" =1.

The directed area represented by P,g,(1 is therefore

.
ie x 1 ’
ihe one belonging to P, is

eal

3

§ 10. Although the curves of the field of ratio ought to be compared
io the rationals, a good idea can be formed of their course by the
comparison to straight lines. When tracing the inflectional points we
must frequently strike into a particular path. As example the log.

( 1087 )

circle will be investigated in its simplest position. Out of the equation :
*(a) -*(y) =*(7)

follows by differentiation

LV:
y= ——— ae (Le. Ly. Ley—(Lr)’}.
y w® (Ly)?
LA any

As y cannot become zero, « and Ly not ®, the inflectional point
condition is :
Ger yay —— Ger:
If we now introduce the area of the rectangle of coordinates, then
A Oe
furnishes, connected with the identity, where for convenience, sake
we write L?2v for (Lax)?, the condition :
ee i Ot 7 —"
There are six inflectional points when
r> Vs,
is satisfied.
The value of 7, for which two more inflectional points exist, is
deduced from the necessary condition for real values
L?(ay) 2 4Lex . Ly.
In connection with the inflectional point condition this becomes:
L*r :
————— > 4x. Ly,
Lia. Ly . :
from which ensues

3 (ee ee
Le. Ly < Fy 7 L'r and Ley > B-4L?r..

For decreasing value of 7 the two inflectional points therefore
coincide into a stationary point, if

< 8 2 Basar
Lr = Day — 2Le Ly = 207;

so that the radius of the /og. cirele is then:

Mii aoe

§ 11. For the study of the general equation of the 2°¢ gradation
comprising all logarithmic conics we should first have to treat the
rational displacement and rational revolution round the axis. As this
would lead us too far, I restrict myself to the logarithmic parabola
and Jog. equilateral hyperbola.

The rational translation offers no great difficulties in this way ;
the logarithmic circle given by

( 1038 )

will pass by means of the translation of the axes from w= a, y= 6
into the above mentioned form. The figure changes then according
to the assumed notions, but as figure of the field of ratio it remains
congruent {to itself. The congruence in the field of ratio is equal to
the similarity in the field of difference, when the translation takes
place along straight lines through O; in general it takes place along
arbitrary rationals, so that the notion of similarity must be extended,
where the skew ratios come into consideration.

Whilst now in general the points of the logarithmic curves are
constructed by means of a logarithmic line, they can be found in
simple position by means of rectilinear constructions.

§ 12. If we draw in the field of ratio a series of lines whose
equation 1s:
Cp.
and then, with the aid of a pencil of rays through QO the points
P), Pi; Py, Po, Ps, P3,P-3.2 > and. likewise 9; QQ 1,250 =o
on the above mentioned lines, we then find ordinates given by means of:
Yn = Yo"
by elimination of m out of these equations (regarding «, and y, as
variable coordinates) we find the equation :

Cd

<

— =e r[eeen]
2 Re

Fig. 5.

( 1039 )

y 2/2
i —a |
Yo vy

The points P form part of the logarithmic parabola: the points
(J of the anti-parabola, having as parameter the reciprocal value of «.
For 2=y, =1 we find the abscissa of the point of inflection out of

From this we can see that the anti-parabola has always two in-
flectional points; for the rest the condition for the existence of the
inflectional points is for the former 7 > e*. As locus of the in-
flectional points we find 7? .w2:¢. At the interpolation the centre
O displaces itself along the X-axis.

§ 15. Likewise the points of the logarithmic equilateral hyperbola

ae

Ya a
A | ‘ =.

Fig. 6

( 1040 )

and of the conjugate hyperbola can be immediately constructed, when
OX, and OY, are the asymptotes; the equation is then
why =2@)2 or Gal by Sai.

In this form it belongs to the curves of gradation; those are the
simplest lines in the rootfield. In case the exponent be 2, the net of
coordinates of the rootfield can be found by means of compasses and
ruler. (The construction is not mentioned here). By OX, and OY,
the positive field of ratio is divided into four rootfields; in these lie
the branches of the logarithmic hyperbola and the conjugate one. In
fig. 8 the above mentioned line is drawn, likewise the one with the
base number a? (resp. a—*). For the points A and B holds:

9 nr - ot
OA,=a?’ ; OB,.=a-.

The log. hyperbola is satisfied by: ve=at®, 0

A g ee naa +o Iie
The conjugate one is satisfied by: «=a? ; y=at?
5 ) Y

Inflectional points appear in all root quadrants except the first. In
the points # the line passes continually into the conjugate one. The
locus of the inflectional points is aye. Out of the fact that inflee-
tional points are present follows already, that the curves touch the
z- and y-axis in /; this is also to be seen algebraically in a round-
about way. So

y' = — (Ly: Le)
seems to be indefinite in £. By the substitution :

2 — sg

in which p is a constant, the differential quotient becomes :

1
ee cre
For <= —O that form is not any more decisive but taking
1

we find for u=-—
lim y' lim [ p¥:(4 wv? + 1— sd ur-(u? + 4))] = 0.

§ 14. The investigation of the log. ellipse is again simplified by
connecting p with two log. circles, whose radii are equal to the half
axes. The simplest position is indicated by

*(e\a).*(yb)=e or (the)? + (bLy)* =1.

The points of the line are points of intersection of the above
mentioned circles with central rationals; the construction is based on
the substitution : ;

( 1041 )

UA, Cru; if, sil,
cr and sr representing the rational sinus and cosinus. Of importance is
still the log. equilateral hyperbola in the position answering to:
(a) "(Y= "(3

it can be found by elimination of n out of:
n

@iy=ba, cyan
and is in this way constructed by points. This one as well as the
conjugate one contains one inflectional point on each branch. Out of
the condition for inflectional points it is evident that there is also one
in O. If the line and its conjugate form one line, this is a cusp. As
however the line in the 3° field of ratio (3° quadrant of difference)
can be brought to the same form, viz:

(cy), (@:y)= 7)

by means of power decomposition, ( can just as well be regarded
as inflectional point.

§ 15. When reducing the general equation of the 2°¢ gradation
we must have besides a translation also a rotation round the axis.
The coordinates lose the rectilinear form, are measured as rational
distance along rationals. The connection between old coordinates and
new ones is then established by means of rational projection. The
new axes are central rationals in perpendicular position, whose director
exponents therefore satisfy: 1+ 44 = 0.

Fig. 7

Proceedings Royal-Acad. Amsterdam. Vol. XIV.

( 1042 )

Naming the new coordinates (§, 7) we find :

Ss —— “eos y 4 ysen 7 , 1 — ces ¥ 4 sin ¥

whilst for the rational distance to J/ holds:
O= (5) = 1(0]) — ee) =(@)
We must continually keep in view that rational distances are
ratios; in the lack of a denominator we must assume 1 for it. If

CP is an arbitrary rational through P, then — just as for rectilinear
axes — the ratio of the parts into which Ob, PA,. is divided by

this, is constant.
: 1
Let us call 4 the director exponent of MZ, thus — a of MH;

then PB, and PA, are given by:
1
y =a 5 y=qr 2.
Let furthermore that exponent be « for PC, then
J, = ay (u—a):(L+p)(1-+2) 3) Je ay(1+dAp):(1+p)(1—A),
holds, when we put : Ob, PCO Je and OCPAL OJ.
If 4 and uw are moreover replaced by tgq and tyy, then follows
from this :

ap

AM
J: Je tg (p—y )-u( 2).

which rélation passes into the known one for gy = 0.
Finally we meution still that the connection between old coordi-
nates and new ones can be given by one formula:

i aeanhye -1)
i ==> oy :
With respect to the new axes the rational equation takes the form :

1—nsoe—% (out of y==mar)
in which we put for 7:

moos ¥ | ecos (Y—9),

=
>)

Chemistry. — “Some compounds of nitrates and sulphates”. B
Prof. F. A. H. ScareinrmMakers and A. MAssInK.

(Communicated in the meeting of February 24, 1912).

As has been known for a long time, several hydrated double salts
can be obtained from solutions containing NaNO, and Na,sO,. It,
therefore, was deemed important to investigate how the nitrates and
sulphates of other metals, in the first place those of the alkali group
would behave in this respect. The behaviour of NH,NO, and (NH,),SO,

( 1043 )
has already been investigated previously '); Mr. Massink has now
also investigated the double salt formation between the nitrates and
sulphates of Lithium, Sodium and Potassium. In order to investigate
this double salt formation the isotherms were determined in the re-
spective ternary systems and the compositions of the solid phases were
deduced therefrom with the aid of the “residue-method”’.

We will not now discuss these isotherms, which sometimes present
very peculiar forms, but will restrict ourselves solely to the solid
phases.

LiNO, — 1i,SO, — H,O

It appears from the investigation that at 35°, besides the components
LiNO, and Li,SO, and their hydrates LiNO, . '/,H,O and Li,SO, . H,O,
two double salts, namely

BiINORS eobhi SO. 2H. O
and LiNO, . 11 Li,SO, .17H,O
may also occur as solid phases in equilibrium with saturated solution.
NaNO, — Na,SO,— H,0.
At 20°, besides NaNO, and Na,SO,.10H,O, the double salt
NaNO, . Na,SO, . H,0
also occurs as a solid phase.

At 35° is found, besides the two anhydrous salts NaNO, and
Na,SO, also the anhydrous double salts :

3NaNO, . 2Na,SO,
and 3NaNO, .4Na,SO,

The double salt found at 20° and no longer existing at 35° was
already known and agrees in its composition with the mineral
Darapskit *). Contrary to the statement that this compound is readily
soluble in water, it follows from the isotherm at 20° that, at this tem-
perature, it is decomposed by water with separation of Na,SO, . 10H,O.

The existence of a double salt :

NaNO, .Na,SO, . 1'/,H,0
is also recorded *). In a continued investigation of this system at other
temperatures this double salt may perhaps also be found.

KNU, — K,SO, — H,O

As solid phases at 35°, only the anhydrous components KNO,
and K,SO, have been found.

1) F. A. H. Scoretnemakers and P. H. J. Hoenen. Chem. Weekbl. 6 p. 51. (1909).

*) NAUMANN —ZiRKEL. Mineralogie p. 574 (1901).

5) Dammer. Handbuch der Anorg. Chemie (1894) II. 2. p.171. Marranac. Ann,
des Mines [5] 12 44.

69*

( 1044 )

NH,NO, — (NH,),SO, — H,0")

Besides the two anhydrous salts NH,NO, and (NH,),SO, there
occur also at 0°, 80° and 70° the two anhydrous double salts

2NH,NO, . (NH,),SO,
and 3NH,NO, . (NH,),SO,
as solid phases.

So far as they have been investigated up to the present, the
ammonium salts behave quite differently from the potassium salts
and in their behaviour show more resemblance with the lithium
and sodium salts.

These investigations are being continued at other temperatures and
also with nitrates and sulphates of other metals.

Chemistry. — “On Dipterocarpol’. (Preliminary communication)
By Prof. L. van Irani. (Communicated by Prof. A. P. N.
FRANCHIMONT).

(Communicated in the meeting of February 24, 1912).

In the investigation of the balsam of Dipterocarpus Haseltii and
D. trinervis (Minjak Lagam) a substance was obtained in well-defi-
ned crystals.

When the balsam is mixed with petroleum ether, the solution
decanted and the remainder extracted with petroleum ether until
nothing more dissolves therein 34°/, of the balsam is left behind
in the form of small white crummy pieces, mixed with small
particles of wood. On boiling with aleohol and filtering, a liquid is
obtained from which on cooling, colourless erystals are deposited
to the extent of 19°/, of the original balsam.

The crystals have a melting point of 128° which by repeated
crystallisation from alcohol, may be raised to 184°—135°, but then
remains constant. On warming with alcoholic potash and subsequent
crystallisation from alcohol the melting point also remains constant

The substance obtained gives the colour reactions characteristic for
phytosterols, with acetic anhydride and sulphuric acid, with chloro-
form and sulphuric acid ete. As it differs, however, in more than
one respect, from the known phytosterols, it will be designated
provisionally by the name of Dipterocarpol.

1) I. A H. ScureineMAKerS and P. H. J. Horney. |.c. Determination of the
isolherm at 30°. A. J. G. pe WaAt. Dissertation, Leiden 1910; determination of
the isotherms at 0° and 70°.

( 1045 )

Dipterocarpol forms colourless biaxial crystals showing double
refraction and straight extinction. They are readily soluble in chlo-
roform, ether, and acetic ether, but with difficulty in cold alcohol.

At 130° they lose no water of crystallisation.

In the elementary analysis the following results were obtained :

combustion with copper oxide : combustion with lead chromate :
C = 80.78 80.68 80.69 80.53
Be 11643 11.41 11.45 11.35

Average: C 80.67 H 11.41.

In the determination of the molecular weight, according to the
method of the lowering of the freezing point. was found M = 483.

The formula C,, H,,O, requires C. 80.59, H. 11.44 and a mole-
cular weight of 402. The values found are, therefore, sufficiently
in agreement therewith.

Dipterocarpol is dextrorotatory ; @p (determined in chloroform)
+ 64.68,

In the ordinary way of acetylation by boiling with acetic anhy-
dride and sodium acetate, in which the time of boiling was much
varied, no crystallisable acetyl] derivative could be obtained ; also
none with acetic anhydride and sulphuric acid or zine chloride.
As phytosterols are generally so readily acetylised, dipterocarpol
therefore forms an exception.

When dipterocarpol is heated with sodium acetate and acetic
anhydride for 3 hours at 160°, the contents of the tube when cold
solidify to a crystalline mass from which, after washing with water
may be obtained by reerystallisation from alcohol, colourless crystals
showing double refraction and straight extinction and melting at
69°—70°.

These crystals form the anhydride of dipterocarpol.

In the elementary analysis was found :

I II The formula C,, H,, O requires :
C 84.74 84.20 84.37
H 11.82 11.36 11.47

Dipterocarpol anhydride is also formed together with diphenylurea
by heating dipterocarpol for a short time with phenylisocyanate.

When dipterocarpol is dissolved in benzene and shaken for 6 or
7 hours with Kiliani’s chromic acid mixture, it is converted into a
ketone (dipterocarpone) which can be obtained from alcohol in well-
developed crystals.

Dipterocarpone forms pillar-shaped, pointed rhombic erystals
melting at 183°—184°. They contain no water of crystallisation and

( 1046 )

give, on application of the well-known phytosterol reactions, less
intense colorations than dipterocarpol and its anhydride. The latter,
in. particular is characterised by very strong colour reactions.

In the elementary analysis was found :

I II The formula C,, H,,O, requires :
C 77.85 77.45 77.88
H 10.43 10.58 10.66

The molecular weight was found to be: 409; the calculated molecular
weight 416.

When dipieroearpone was dissolved in benzene and again shaken
for 6 hours with the chromic acid mixture it could be recovered
unchanged from the benzene solution. The melting point was found
to be 182°—188° and the C-content and H-content 77.69 and 10.30,
respectively.

Dipterocarpone is dextrorotatory ; @? (in chloroform) = + 71.08°.

From the dipterocarpone was made an oxime by means of hydroxy-
lamine hydrochloride and potassium hydroxide. This oxide is only
very little soluble in aleohol and is best recrystallised from glacial
acetic acid. It then separates in microscopic small crystals which
melt at 249°—250° with decomposition.

The nitrogen content was found to be 3.5°/,. The formula:
C,, H,, (NOH) requires 3.48 °/,.

When dipterocarpole is dissolved in glacial acetic acid and oxidi-
sed with chromic acid we again obtain dipterocarpone m.p. 1838°—184°.
A solution of dipterocarpol in acetone is not acted upon by potas-
sium permanganate. .

The action of bromine did not lead to the formation of a ery-
stallised product. Only amorphous, resinous substances were obtained,
with evolution of hydrogen bromide.

On treating a solution of dipterocarpol in carbon tetrachloride
with Wus’s iodine monochloride solution a little more than 3 atoms
of halogen was absorbed. The halogen not only acted additive, but
also caused substitution. On adding water to the iodised liquid,
fumes of halogen-hydrogen were noticed.

In the reduction of dipterocarpol with sodium in boiling amyl
alcohol, no erystallised dihydro-product was obtained, but only an
amorphous resinous mass.

As the result of this preliminary investigation it may be stated
that dipterocarpol is a phytosterol of the formula C,, H,,O, from
which one molecule of H,O can be readily eliminated.

Leiden, February 1912.

( 1047 )

Chemistry. — “On Minjak Lagam.” By Prof. Ll. van [rani and
M. Kersoscn. (Preliminary communication). Communicated
by Prof. A. P. N. FRaNcamont).

(Communicated in the meeting of February 24, 1912).

1. In the literature of the last 60 years mention is made repeat-
edly of a balsam called by the name of Minjak Lagam, which is
obtained from Sumatra. The balsam is occasionally described as a
liquid, oily product, in appearance much resembling oil of copaiba,
sometimes as a mass of a dirty white colour and tallowy consistency.

From the oily balsam Haussner ‘Archiv. der Pharm. 21, 241, 1883)
isolated a hydrocarbon from which he prepared a hydrochloride of
the formula C,, H,,.4 HCl, m.p. 114°.

2. It is generally stated that the Minjak Lagam is derived from
Canarium eupteron Miq. Provisionally this origin must be accepted
for the liquid variety of the balsam. There is, however, some reason
to believe that the balsam is not derived from the said Burseracae,
but froma Dipterocarpus.

Both kinds of balsam have been investigated by us.

The liquid variety happened to be in a collection got together by
bE Vrikse during a journey in the Dutch East Indies (about 1857).
As to the botanical origin, the bottle was labelled Canarium eupteron Miq.

The more solid variety was procured through the mediation of
the department of Agriculture in the Dutch Indies and was obtained
from Central Sumatra. At first, the botanical origin was unknown,
but the investigation by Dr. Janssonius of Groningen of the woody
particles which occurred in the balsam shows that this must have
been derived from a kind of Dipterocarpus; this was confirmed by
the determination of herbarium material obtained with great trouble.
The determination executed by Dr. VaLeron and Dr. Suirn at Buiten-
zore showed Dipterocarpus Hasseltii Bl. and Dipterocarpus triner-
vis Bl. to be the parent plants.

3. The balsam of Canariuin eupteron Mig. is thin-fluid; odour,
taste and faint greenish fluorescence remind of oil of copaiba. The
behaviour towards solvents is about the same as that of copaiba.
Mixed with an equal volume of carbon disulphide the balsam gela-
tinises so that the tube can be inverted without the contents running out.

When the balsam is heated in a waterbath it turns viscid at 80°:
when cold the contents are found to have gelatinised. Probably, this
phenomenon is due to polymerisation. In connection with the fact
that a similar behaviour on warming is stated of some Dipterocarpus
balsams, and also with the similarity with oil of Copaiba quoted

( 1048 )

above, a new investigation as to the origin of the liquid Minjak
Lagam appears to us to be desirable.

This Minjak Lagam consists largely of compounds indifferent to
alkalis. The acid-number is 10.45; the saponification number 14.8.
The amount of volatile oil which can be passed over with water
vapour amounts to about 49°/,. This oil is colourless, has a density
of 0.9051 (15°/15°) and a refraction of 1.4972 (24°); in a 10 cm.
tube the rotation amounts to —7.5°,

On fractional distillation, fully 93°/, of the oil pass over between
258° and 261°. Of this fraction the following constants were obtained:

Boiling point (corr.) 261°—263°.

Rotation in 10 em. tube —7.46°.

Refraction 1.49935 (16.5°).

Density -0:905 @*°/,;°):

This fraction appeared to consist entirely of caryophyllin.

On combustion, 206.7 mG. yielded 668.1 mG. of CO, and 220.
mG. of H,0O.

Found. Saleulated.
C 88.10 °/, 88.15 °/,
H 11.96 11.85

The molecular weight determined by the lowering of the freezing
point in benzene was found to be 205 (caleulated for C,,H,, —204).

The identity of the hydrocarbon with caryophyllin was further
established by the formation of the caryophyllin alcohol (m.p.
92°—94°) and of the splendidly blue nitrosite (m.p. 111°—112°).

The occurrence of such a large quantity of caryophyllin in the
liquid Lagam balsam justifies the supposition that this is not derived
from a Burseraceae, but from a Dipterocarpus.

Up to the present caryophyllin, in large quantity, has only been
met with in oil of cloves and in oil of Copaiba.

As to the botanical origin of the balsam and the composition of
the resin contained therein we hope to be able to communicate later.

4. The balsam of Dipterocarpus -Hasselta Bl. and D. trinervis Bl.
These two trees mutually differ so little that they are regarded by
some botanists as belonging to the same species.

The balsam forms a dirty white mass, which it is almost impos-
sible to pour out; small woody particles are present, also a little
water. The odour is disagreeable, reminding somewhat that of oil
of Copaiba.

On distillation with water, 2 samples of the balsam yielded
10.5 °

and 22°), of voiatile oil respectively.

iu Qu

( 1049 )

This oil was colourless and viscid and had somewhat the odour
of oil of Copaiba.

Density 0.9132 (*°°.,°); refraction 1.50137 (16.5°); rotation in
10 cm. tube —- 9.75° (15°).

When rectifying the oil water was split off. The oil was, therefore
heated for some time with metallic sodium and then distilled. The

1590

following data were obtained:

Boiling point (corr.) 261°— 264°.

Rotation in 10 e.m. tube —8.9° (15°).

Refraction 1.50029 (16.5°).

Density 0.9065 (**°/,,°).

By the formation of the blue nitrosite (m.p. 112°—118°) the iden-
tity of the oil with caryophyllin could be demonstrated, so that
this hydrocarbon also occurs in large quantity in the balsam of
Dipterocarpus trinervis Bl. and D. Hasseltii BI.

About that balsam it may yet be stated that, besides a resinous
body, not yet investigated, 19°/, of a crystallisable phytosterol occur
therein.

Leiden, February 1912.

Physics. — “Contribution to the theory of binary mixtures.” XIX.
By Prof. J. D. van pik WAALS.

In Contribution X (These Proc. XI p. 317) I occupied myself
with the conditions for the existence or non-existence of a locus for

: ee : : d*w ‘Ow
the points of intersection of the two curves ( —— | == Oland ie ==!
v QUES ios

da?

I had been induced to do so by a remark in Contribution II,

; aw F
Where it had appeared to me that when —~=O gets outside
av
aw San eet
== O at a certain value of 7’, this gives rise, at least asarule, to
av

the existence of a heterogeneous double plaitpoint, and so to the
existence of three-phase pressure. So long as the former curve
remains at all temperatures inside the region in which —— remains
av

negative, this double plaintpoint does not occur, and there is no
question of a complication in the ordinary transverse plait, and three-
phase pressure will not be found.

But I did not bring this problem to an end then. Occupied with

( 1050 )

other questions, I put off the further discussion again and again to
a future opportunity, and never gave the simple representation which
may be given of the existence or non-existence of three-phase
pressure, and never discussed on what circumstances about the
properties of the components the existence of three-phase pressure
depends.

The case that I treated at length, is this for which the auxiliary
quantities ¢, and ¢, are positive, and the points of intersection of
the above-mentioned curves have a closed figure as locus. In this

Pw Pup

case there are two temperatures at which = = 0 touches > = 0.
At the lower of these two temperatures begins the existence of the
two plaitpoints, which originally still lie in the covered region (e.g.
the point Pa, of fig. 52. Contribution XVII). And not before somewhat
higher temperature does three-phase pressure begin to appear (e.g.
at the temperature of the point Q, of fig. 52). For the meaning of
the higher of these temperatures I must refer to preceding Contributions.

I have not treated the case that the quantities «, and «, are
negative. It does not offer, however, any yreat difficulty. That then
there certainly exists a locus for the equations of the two mentioned
curves, is clear from the equations of Contribution X, e.g. (3), (3),

and (y). The value of.v, at which this locus begins or ends, is given by :

b? c
2 = 1—a(1l—a)-

z (db a
b?-+u(1—2) ( ;
aX

(db\
¢ ae e

‘ v(1 — 2) =

a = /db 2 ~
lb? +2 (1—«) k
da

If we leave the factor a1—.), which has no practical importance,

or

out of consideration, this condition becomes :
¢ (n—1)?
qu ec G eae

And the locus is found on that side of this value of 2, for which

c (n—1)?
a 1+ (n?@—1)2’

or for whieh
a ac tamer
C = (n—1)?

( 1051 )

As I already observed in Contribution X, the case 1 << nm (l—w) ¢
is left out of consideration in all these derivations. This is of little

a
importance and can be treated separately. Now — may be represented
,

2 P a 2
by a curve which begins at «=O with the value —, and termina-
3
a, d*a : ae :
tes at «=1 with the value —. As i = 2¢ is positive, this curve
é av
has its convex side turned downward. The second member of this latter
inequality may be represented by a straight line. So there is centainly

: : s s a, n° a 1
intersection of these two lines, when *>>——— and ~< =
¢~ (n—l1)? e ~(n—1)?
a, n(1+6,) a, 1+e, ;
or reversely. But.as we put ——— — and —=—— the for-
3 c (n—1)° ¢ (n—1)°

Iner supposition implies ¢, positive and «, negative.

The reverse supposition, which will have a far greater chance to
occur with great value of 7, implies ¢, negative and &, positive. On
both suppositions the equation 3’ or y of Contribution X has a posi-

wv . . . .
tive root for = 5 when the sign > in it is replaced by =.

—w
2 é 4 , dp dy P
The Jocus for the intersection of = =O and —- = O begins at
ax~ ave

this value of .V, and lies for the latter case, viz. e, negative, between
this value of V and N =o. If the case «, negative and ¢, positive
should be possible, this locus occurs between WV =O and the value
of NV at which the two lines intersect, so on the side of the com-
ponent with the smaller size of the molecules. But both for W—=0O
and for No, or what is) the same, for z=0 and a=1, the
equation @ of Contribution X shows that » = 6, and that the inter-
section of the two mentioned curves begins already at 7’= 0. This
means that the point P., of fig. 52 does not begin only ata certain
value of 7’, as we thought probable for the mixture water-ether,
bat that it has descended to the absolute zero of the temperature,
which we thought probable for the case watei-mercury.

If the two quantities ¢, and «, are negative, the straight line extends

, 7 a
over the full width from «=O to z=1 above the curve , and
Cc
: ; eee . 2 lw ¢ Up ‘
the locus of the points of intersection of — =O and —— —Otakes

aL” av
up the full width. A case which will probably not oceur, but that
we shall yet include in owr further considerations as not impossible.

( 1052 )

Summarizing we may put that if the components of a binary mixture
possess such properties that the values of ¢, and «, considered as
ordinates of points, lie in the quadrant in which ¢, and «, are positive,
the mixture cannot present three-phase pressure until above a
certain value of 7. If the points, of which «, and ¢, are the ordinates
do lie in that quadrant, but in that part that is situated below the
part QRP of the parabola of fig. 86, there is still three-phase pres-
sure, but it begins above a certain value of 7. For the other points
of this quadrant three-phase pressure is entirely wanting. According
as the points indicated by ¢, and «, still lie below the part of the
parabola, but approach it, the temperatures between which three-
phase pressure exists, lie closer together. For the points of the branch
QRP the two temperatures of the points P,, and P.4 of fig. 52
coincide, and so properly speaking there exists no longer three-
phase pressure.

If we consider it only as a mathematical problem, the space in
which ¢, and «, are negative is 3 times as large as the space in
which «, and e, are positive and which represent cases of complete
miscibility ; and the space in which ¢, and «, are positive, and yet
three-phase pressure is possible between two given temperatures, is
only an insignificant part of the whole region. To conclude to
the chance for the occurrence of these three cases merely from this
is, however, entirely unjustifiable. It follows from the restriction
ensuing from the condition that a, and a, be positive, that neither
&, nor «, ean descend below —1. This in itself already restricts
the number of cases in which three-phase pressure can already occur
at 77=0, to a high degree. But moreover in consequence of the
non-occurrence in nature of different mathematical possibilities for
the value of the quantities on which «, and ¢, depend, whole series
of points represented by ¢, and ¢, are excluded. Thus the whole
number of the points which lie below a line drawn in fig. 387 from
O’ at an angle of 45° with the axes will be excluded, if a value of
Shire ¢ F F 3
—=>Sn does not occur for a substance with a size of the mole-
Pr,
cules mn times greater, as is probable at least for the substances
which we generally know as liquids. Further we must exclude very
high values for ¢, and ¢«,, unless for very high values of n, and
also very small values for 1+ ¢, and 1+, unless for very small
values of n — 1.

The quantities which serve to determine ¢, and «, are according
to the definition the value of a,, a@,, 2, and, because also / occurs in
e=a,+a,—2a,,==a,-+a,— 2 aa,, also this latter quantity.

( 1053 )

In Contribution X fig. 37 [ have given a construction which

enables us with given value of m and / to see at a glance which of

the 3 mentioned cases, either complete miscibility or the two cases

,

a
of incomplete miscibility, will occur at given value of — or n

a, es

Besides the parabola of fig. 36 we have then still to constrnet the
curve of the second degree :

4n? 7? (1+e,) (1+¢,) =(2n +6, +n’6,)?,. . . . (1)
the equation of the parabola being rendered by :
4n? &, 8, = Se (€, +n? &,)}7. 5 No, Ty So moe (23)

The curve of the second degree, represented by (1), is a parabola
when /—1, an ellipse when /< 1, and a hyperbola when /> 1.

As it is possible to give an answer to all questions without
difficult caleulations when 7—1, I shall start with this supposition.

The parabola represented by (1) is then exactly the same as that
represented by (2) with only this exception that the points of the
former parabola are found by displacing those of the latter in a
negative direction both in vertical and in horizontal sense, by an
amount of + 1. In fig. 37 an ellipse has been drawn, so /< 1 was
supposed. It cannot be difficult to think this too transformed to a
parabola, in which case the branch which has now been drawn a
a little to the left of O, must pass through that point, as has been
indicated by the dotted line of fig. 36.

If in fig. 87 we trace a line from point O’ to an arbitary point

> : : » 2 Mies 3
of the curve drawn in this figure, 7° Tue cotp represents the
TS
4, Vk, Oi at :
value of —= hae If this line is made to rotate round the point 0’
oF ky

. «hie :
as centre, successively all the values of 7. ae represented from a
Ie
to 0. Now we have only to determine where the point lies in
which such a line intersects the curve of fig. 87 to know whether

yp)

at the given value of » and /, and the value of a determined by
ky
the direction of the line, the binary system will possess perfect
miscibility or only incomplete miscibility.
So long as for /=1 the value of ¢ is smaller than 45°, the
points of intersection of the line with the curve lie in the region

é ; Tih,
in which ¢, and &, are negative, and so with —*>>n there is incom-

yy

ky

( 1054 )

plete miscibility already at the absolute zero. If the line is made to

ie
rotate further upwards, and so = is made to descend below 7,
hey

the extremity of this line gets into the region where ¢, and «, are

positive, and there is still incomplete miscibility, but it does not
begin until above 7’=0. This continues to the point where the
eurve of fig. 37 intersects the parabola of fig. 386. At the value of
i that belongs to this point, the points P., and P.q of fig. 52
ti,
coincide, and on still further rotation of the line and so on
decrease of —* no plaitpoint of the 2"¢ kind exists any longer, and
1
there is complete miscibility. On still farther rotation of the line,
when igg=n, we get equality of 7, and 7Z;,. If gpv=n’,
T,,.——; this direction concides with the direction of the axis of
: n

.

the parabola of fig. 36, and in the case of /=1, also with that of

fig. 37. Then the values of #, and «, would be infinitely large, and

the physical possibility of the occurrence of such a case exists only

if 2 should be =o. On still further rotation the line would inter-

sect the ¢,-axis, and so ¢, = 0. Now the parabola of fig. 37 cuts the
2 | 2

é,-axis ina point where ¢, = 4 (n—1), and so mine) ——— i=
l+es, 14-4n?—4n

n Skies n
————— and we find for — a value equal to ——_. On still
(2n—1)* Snes (2n —1)°

further rotation the complete miscibility stops again, and so at

Die n

lie <n

for the case = 1. But it is not very likely that the case that a

there is again three-phase pressure already at 7’= 0

substance with a molecule 2 times as large would possess a critical
temperature 7 times smaller, should exist,

Now that we have to do with an intersection of two equal
parabolae with parallel axes, the place of the point of intersection can

be easily caleulated, and so also the value of Tat which the com-
key
plete miscibility sets in, ean be indicated.

Assuming an arbitrary value of / for the determination of the
points of intersection of (1) and (2) for the sake of further investi-
eation, the following equation may be derived :

4n? (1—/?) (1+ ,) (1+-8,) = (n—1)* 4- 2(n*—1) (€,—-n’e,) - (8)

This equation is obtained when the difference of (1) and (2) is

{ 1055:5)

subtracted from the identity :
dn? (1+ £,) (1+ €,) — 4n°e,e, = 4n® 4 4n’e, +- dn’e,.

If now 7=4, we find : Coen
— Te i =: . And as:
now , we find ¢, —n’e, 3m)
n—l=Ve,+nVye,
for the branch of the parabola of fig. 86 which les below the line
(n—1)?
PQ, Ve, —2 V8, will be equal to — amb 1)’ or
aeee ( yt n—1
“ at = =
Ua 2(n--1)
and
(x —1) i
2n Ye, = (n-—-1 ii 4+ -—-—
ote sence)
or
(n+ *)
Ve, = an +1)
and
(3n-+1)
DV, ee)
z ; Try
From this ¢, and ne, , and so also i can be determined.
ky

Ui
The thus determined value of —~ is of a complex form, and
ky
depends on 7 in this way:

(n—1)? (8n-+-1)?
n —=> -
Tr. 16(n+-1)° n
aie 4 (n—1)°
PS a RTEERE
16(n4+-1)°

This value is smaller than 7. With increasing value of n it becomes a

(n+ 3)?

smaller and smaller part of 2; for somewhat greater than 20 it becomes
equal to 1, and for still greater value of n it descends even below 1.
: : a, Vy
When / deviates from the value 1, the caleulation of — or —
a, Tires
the limit at which complete miscibility sets in, is not very well

feasible. It is then prevented by the difficulty to determine the place

for

of the points of intersectien for two curves of the second degree,
which is then only possible by solution of a 4% power equation.
I need, however, hardly point out that at any rate the possibility
remains for an approximate determination by means of graphical
construction.

It remains, however, also then easy to determine the said value for

( 1056 )

the limits of incomplete miscibility from 7’— 0. For then only the
points of intersection with the axes need be determined.

Let us begin with the case /< 1, in which case the curve of fig. 37
is an ellipse. Then there can only be intersection with the ¢,-axis,
and only between the values of ¢, lying between O and 4n (n—1).
The way in which these values of ¢, depend on / and n will then
be found by solution of (1), if we put ¢,—=0. And so by the aid
of the equation :

Al? n? (1 + €,) = (2n 4 €,)?.

Then we find:

= On (En 1) = el Via On) ee)

n—l)?
( ie the ellipse no longer cuts the

&)

2n—1
ieee OL tl
n n

2n—1
region where &, is positive. So for a value or /?< —

no com-
n?

ahd

pee ee: a I
plete miscibility is possible, whatever the value of ~~ or n—~* should
a, Ty,
i

be. But for a value of /* between 1 and —— part of the ellipse
n

gets into the region where «, is positive. If this whole part of the
ellipse should lie above the branch QP of the parabola of fig. 36,

a, 5 C a 5
two values of — would be indicated between which complete mis-
a

1
cibility would oceur. But if this part of the ellipse should remain
entirely below the branch QP, no complete miscibility is possible,

a, 2 ; ‘
but there are two values for ~ to be given between which incom-
a ¥

1

plete miscibility exists, which, however, begins and ends only above
T=0, as is represented in fig. 52. There is, however, still a third
and a fourth case possible, in which the said part of the ellipse inter-
sects the branch PQ of the parabola of fig. 36, either once or twice.
Which of these four eases will occur depends on / and n. Always
the part of the ellipse that lies above the branch PQ will indicate
complete miscibility, and reversely.

We shall proceed to investigate in what way the 4 cases mentioned
depend on / and n, knowing from the above that /? must be

2n—1
n?
2n—l
If 7 is exactly equal to ———, the two points of intersection of
ea

the ellipse and the ¢,-axis are equal according to (4), they are namely

( 1057 )

equal to 2(n—1) as can also be derived from (4). So if the first of
the 4 eases mentioned can occur, this value must be larger than
that of OQ in fig. 36. And so:

2(r=— 1) >(@ — 1)’

or
5 > nN.
= ees 2n—1
Not until /° has become somewhat greater than ——— does part
ne

of the ellipse appear in the positive quadrant and when /* has become

/

equal to the value of 7’ which follows from (1) when we put ¢,=0

and &, = (n—1)’ viz.: :
(w+ 1)! B
— = = - »
4n? [1 + (n—1)?|
the third case occurs, and the branch QP is cut onee. For n= 2
there is no great difference between these two values of 7*.
24 29
The former amounts to —, and the latter to —.
32 32
5 = < 4 x F 2u—1
If on the other hand n> 3, for which again the quantity ——
ne

corresponds as minimum value of /°, the second case occurs for somewhat
greater value of /*. It is again possible to increase 7° so greatly
that the value of (5) is reached, and so the third case can oceur
again. But moreover the value of / can be chosen such that QP is
not only intersected once, but even twice; then 7° must be, indeed,
2n-—]

chosen above aiat but remain below (5). It is not easy to deter-
mine within what limits for the value of 7° this double intersection
will take place. For this it would again be necessary to indicate
the place of the points of intersection of an ellipse and a parabola.
That this presents difficulties is to be regretted, because the possibility
or impossibility of this double intersection must decide whether or
no complete miscibility is still possible for the chosen value of 7 and
/. As transition case we have then to examine, what the value of /?
must be for chosen value of 7 if the ellipse is to touch the parabola.

We might also put the problem that is to be solved thus: where
for given value of 2 does the point lie in which the value of 7? is
ininimum on the branch of the parabola of fig. 386, between Q and
R, and what is this minimum value? Between this minimum value
and the value of (5) the parabola is twice intersected by the ellipse.
It is self-evident that we eannot introduce the restriction (between
Q and f) at once into our solution, and that we should really propose

70
Proceedings Royal Acad. Amsterdam. Vol. XIV.

( 1058 )

a more general problem, viz. to seek the points in which the
value of /? becomes minimum or maximum, when the whole parabola
of fig. 36 is followed. For the points that lie in infinity this value
=1, as appears from (1), when in this equation we neglect the
value of m and 1 by the side of the infinitely great value of ¢, and
we,. and then put ¢,=n’s,. If we follow the lefthand branch of
the parabola beginning infinitely high, ? begins with 1, and reaches
again the same value in the point #. Between les a minimum value
which still lies above Q for 7 < 38, but lies between Q and FR for
n>. On the righthand branch there hes a maximum value for /,
beyond the point 2. Yet we shall give an answer to the proposed
que:tion in which it seems as if it only holds for the portion of the
parabola between @ and P, because the minimum of / that lies on
this portion of the parabola, is only of direct importance. So for this
purpose equation (3), which only holds for points which are common
to the ellipse and to the parabola, will serve. By making use of
the relation which holds for the portion PRQ of the parabola, viz.
Ve, +2Vve,=n—1

we write (3) as follows :

4(1—I*)(1 + ¢,) (x? 4 n°e,) = (n—1)* + 2(n—1)* (n+1)(Ve,—nye,)
or

4(1—l?)(1+8,) (vn? +n?¢,) = (n—1)* + 2 (n—1)? @+ 1) (r-—1—2nye,)
or

4(1—2)(1+.¢,) (n?-+ ne.) = (n —1)* .8n+ 1) -——4(n —-1)? (rn + 1) nye, .

If we now also substitute ¢, = [(n—1) —nys,]’, we have a 4"
power equation for the determination of mVe,. If we put m/e, =.,
this equation has the following form :

Viet (ge ayaa Cee Ce UU Oe NG peal) ee
yl +-n? (n—1)*| — 40-2) — 2x i 1-1) 402)
+ a? \(n? +1) + (n—1)?}? — 2(m—1) a? + et =0 . . (16)

If this equation is represented by a curve, the second differential
quotient is always positive, and so it can possess at most two real
roots. If the known term is negative, there is only one positive root
possible for me,, and then we have the case that we had mentioned
as the third ease. If on the contrary the known term is positive,
and moreover the factor of 2 negative, the 4t case is possible. The
transition of the known term from positive negative takes place
when 14 i? has the value corresponding to the Q of fig. 36.
Equation (6) becomes then :

n(n? 1) (rn —3
2p pane o A ein? +1 + (n=1)} — 2(n—1)2* + of =0 (7)

( 1059 )

Then there is a root #20, and so long as 7 >>3, another root
which is positive. If 28, there is a second root =O, and then

the ellipse touches the parabola of fig. 86 in the point Q. Forn < 3,
there would still be a negative root for x, and this root wonld refer
to the point of intersection of the ellipse with the branch of the
parabola above the point @, but this intersection is immaterial for
our problem. If, however, >> 3, there is besides the root «= 0
another positive root, which then indicates the intersection of the
ellipse with the branch PR of the parabola.
If we put «= 4, (7) becomes in numerical values :
— 144 262 — 62° + «#’ =0
there is then a root between O and 1, viz. about 0,6. For n=5
(7) becomes :
— 40°/, + 42% — 8a? + 2’ = 0
then there is a root that does not differ much from 1.
At any rate « must be smaller than that of the point F.
For a value of ne, between O and the positive root of (7),and

a, 2 7 :
the value of «e, and —, answering to such a value, there will still

a
1
be complete miscibility for the chosen value 1 — /.
If we now take / smaller or 1 —/ greater, the known term of

(7) becomes positive, and the possibility exists that (7) possesses two
positive roots for «, the first somewhat ereater than O, and the
second somewhat smaller than the above calculated value. And we
may decrease 7? so much that these roots become equal. Then the
complete miscibility has quite disappeared. The ellipse no longer
cuts the branch QP of the parabola, but touches it. The point in
which this contact takes place, is then the point of the branch QP
of the parabola in which / is minimum.

If we write (3) in w, and differentiate logarithmically with respect
to / and «, keeping 7 constant, and if we then put d/? = 0, 1 — P
is eliminated, and we obtain the equation for the determination of
the value of w, at the place where for given value of 2 the value
of ? is minimum or maximum. We then get after some reduction :

F : 3 (8n+1)
2 }[(w—1) — a] (nr? +a") — ev [1 + (n—1—2)?}} = 1))) Se yy
Kt ) | ( + ) | ( ) i (n As 1)

— (n? +27) [1 + (n—1—2)"] = 0
or

n? (n—3) (n? +1) (n—1)(8n+]) a ,
ED) — 2 Gea (n? +- 1 + (m —1)3} +

( 1060 )

zis _(8n+1) ;
si Bas Kia nae rad
bo yet 1)
Boe vera ipre="

This equation too can have two real roots at the most, as the
second differential quotient is always positive. There is always a root
for a greater than that which belongs to the point A, for the value

3n+1 :
(n — 1) ———_, while z can always be taken so

4(n+-1)

large that the value is positive. This value belongs to the maxi-
mum of ?, and is of no importance for our investigation. But
then there must be a second positive root, at least when the
known term is posifive. And it is this second root that we
seek. This root is =0,ifm—98, and to this we already concluded
above. If <3, this root is negative and then this means that
the minimum of / lies on the parabola of fig. 36 above the point Q.
I have determined the numerical value of « for m=44 and n=5.,

is negative with v=

For n= 4 the ree becomes :
27,2 — 101,4 ¢ +- 61,1 2? — 19,8 «* + 324 = 0

The root is then about equal to —, and lies then almost halfway

oo |

the above determined value of the point of intersection, viz. 0,6,
which, however, was then determined only approximately for the
corresponding value of 1— P.

If we wanted to determine not z=nVe,, but Ve, itself, we
should have to divide the successive coefficients successively by 2*, 1°
ete. And for increasing value of m the equation converges then to:

13 :
5 8 (e') + = PY —T@) + 8) =0.

a a

This equation can be written :

, 1 + : IL 1 )
se) (5 a G — 7 + 7 = ()).

So the value of We, for the minimum of /? will approach to
for increasing value of n, while that for the maximum approaches
to J, so to that of the point P of the parabola of fig. 36. The

value of Ve, for the point & approaching to rr the point R

will always continue to lie between the maximum and the minimum

( 4064 )

value of /?. The values of /* corresponding to x =— and a’=1
vo
are 0 and o.
Before concluding the description of these ellipses I will first discuss
as an example the case already repeatedly treated by us of ether
and water. We shall begin with determining «, and «,, putting 2—=5.

a, 1
For the determination of «, we must know —=——————__,

. a, Tk, 4 2 — 7s
The quantity —=n aS known, and the choice of / is not doubtful.
a, Is
é 2n—1 : : } :
For # =——— the mixture would lie on the border of the region,

ne
in which complete miscibility begins already at 770. We have
arrived at the conclusion that this is not probable for this mixture
and so we have to put / > 0,6. But / cannot be much greater, for
2
already for /= — the point «¢,, ¢, lies in the region of complete
oO
miscibility. If we put = 0,61, we calculate «, = 6 and s, = 0,008
or ne, 0,2. With these values we can calculate the limits of x

: : : Dae _ ow
between which the locus of the points of intersection of —. = 0
au
dw : : ‘ f eee
and —— = 0 is contained, and then we find «#,=0,98 and 7,—0,383.
ae”

So the locus of the points of intersection lies almost entirely on the

. - . . . & .
ether-side. To this conclusion the consideration that v7, = an night
LN)

. . . n Ps
already have led us, from which we at once derive Gal = (!-«,)(1-«,).
a

We obtain the second relation from the first by changing » into
—, €, into «,, and 2 into 1—x.

With these relations we write:

And so 2,7, very great with respect to 1—2,)(1—z,).
But though the given values are correct on the whole, yet there
is a circumstance which shows that they should be somewhat revised

( 1062 )

’ oe
If we examine for the loeus contained between «——0.98 and

as : F : aw
vw 0,383, how the intersection is of the two curves = = 0
ae
Zp :
and —— —0, it appears that at the highest temperature, when these
av~
a : : é ch
curves touch, 7 =O must still exist, because for n—=5 or more
7

accurately 25,5, this curve disappears for a value of « that is

bya ay :
smaller than «= 0.383. If we then draw —— =O at the contact, it

must necessarily lie in the region where = Q is negative. And
Ov

then it would also disappear in that region, which must not be the
case for that high value of 2. This compels us to consider 7 = 0,883

too great. But in the caleulation of «= 0,383, we had put n= 5

>

and for n=5,5 we obtain for water and ether a higher value of

ais m
and a smaller one of wv.
ay
Thus I have once more returned to a thesis which I have expres-
: _ yp
sed more than once viz. that the disappearance of —— =O in the
av”
ary bi etre
region where mets positive, would be the criterion of three-phase
ave

pressure. | have, however, not yet quite succeeded in proving this thesis.
I am of course convinced of the validity of the application of this
thesis in our case. But T am not yet perfectly convinced of the
validity in all possible cases. At all events we can here use, this
thesis to calculate the value of / from:

aa (ik — iq) Ay?
al 2 1-+ 4g

kK? l

ole ee ies us 1 a |/2 ve 3 }
= Y a’ 1+? vy a, Lh? Ia, \

and from this we calculate /< 0,64.

Moreover it should be borne in mind that by a thesis as: “the
existence of three-phase pressure depends on the circumstance whether
dp ; ay, fe ke less
—— = () disappears in the region where —— is positive or negative’,
du? dv*

( 1063 )

not what I shall again call the mathematical possibility of three-phase
pressure can be meant. This exists of course for all values of 7 and /.
But I hope to return to this question later on. The possibility will
have to be considered whether if 7 is small not naturally only great
value of 7 will occur, and if then all arbitrary values of a, and a,
may be chosen. (To be continued.)

Chemistry. — “Jnvestigations on the radium content of rocks.” UI.
By Dr. E. H. Bicuner. (Communicated by Prof. A. F. Honnrman).
(Communicated in the meeting of February 24, 1912).

According to the method described in my first communication ‘)
on this subject I have now investigated a number of rocks which
are partly originating from the isle of Borneo and the Moluccas and
partly from the Dutch province of Limburg.

a. Borneo and Meluceas. Prof. Wicumann of Utrecht was kind
enough to present me for this purpose with a number of rockspeci-
mens from the museum of his laboratory, which were for the greater
part collected by Prof. Morencraarr curing his scientific exploration
of Central Borneo. I take this opportunity to openly thank Prof.
WicuMann for his kindness.

The results of the investigation, expressed in 10—!? gr. of radium
per gram of rock, are given in the following table.

Amphibole biotite granite, Karangan near Toemb. Temangooi 10,0

Amphibole granitite, Soengei Menjoekoei 153
3iotite amphibole andesite, S' Tebaceng 0,8
Amphibole andesite, 5%? Embakoe doubtful
Garnet andesite, Boekit Oejan 1.4
Amphibole andesite, Boekit Ampan 0,8
Amphibole andesite, S‘ Tepoewai 1,6
Biotite amphibole dacite, Riam Toentoen 2,8
Olivine diabase, Riam Pandjang iL gt
Rhyolitic pitehstone, 5 Kawan 0,7
Vitrous amphibole dacite, S** Embakoe 0,9
Diorite porphyry, S* Sebilit — - ies
Diorite porphyry, N* Gaang 0,6
Andesitic amphibole porphyry, Boekit Sedaroeng 1,4
Norite, St Menjoekoei 0,7
Andesite, Isle of Sangi 43
Augite andesite, Isle of Ternate 1,3
Pitchstone, Tandjong Hatoelawe, Amboina 0,5

1) Proc. XIII, 359 (1910), second commun. XII, 818 (1911).

( 1064 )

The table gives rise to some remarks. The general average
amounts to 4,73.10~—1? er. and thus agrees closely with that found
previously for the rocks from Sumatra, namely 1,65.10-12 er.
It also tallies fairly well with the mean of all the igneous
rocks investigated which amounts to 1,4.10-1% in a number of
104 specimens; in this calenlation, however, are not included’
the figures obtained by Jory. As I remarked previously '), Joty
always finds higher numbers than other investigators; these without
exception give average values varying from about 1 to 2, but as
ihe result of the measurements of 126 rock specimens, JOLY arrives
at a final figure of 7. Lasy, in a very recent publication *) rightly
concludes that it would be desirable to have Jony’s measurements
repeated by another investigator, so that this great difference may be
explained. The only specimen that far exceeds the average is the first-
named granite; here again we fird to some extent a confirmation of
the fact that granites often show a higher radium content. On the
other hand we find the andesite (N°. 4) where the presence of radium
remained doubtful, by which | mean that the figure is smaller than
0.3 (in the usual measure). If I am not mistaken, the only other
example of an igneous rock where radium cannot be detected in this
manner, is a basalt from Ross Sounp *).

The differences shown by specimens of a same rock but derived
from different localities are not smaller than those which oceur
between rocks of a different character, so that a connexion with the
nature of the rock does not seem to exist.

I will also correct a mistake which has slipped into the first
communication. There the basalt of the voleano Asar is stated to con-
fain 13,0.10—- er. of Ra. This figure was much larger than was
ever found in other specimens of basalt (the average amount is
only 0.6) and seemed suspicious. A fresh quantity of this basalt
has, therefore, been dissolved and investigated in the usual manner
with the result that now only 0.5 was found, quite in agreement
with the other results. Presumably, the original solution had become
contaminated in some way or other with a trace of a radium salt
and, of course, the merest trace of this is sufficient to vitiate the result.
The risk of such an error is hardly avoidable, when one is occasionally
concerned with radium preparations. I have, therefore, now taken the

1) Handelingen 13e Ned Natuur- en Geneeskundig Congres 111, p. 374; also
compare my second communication in these Proce.

*) Le Radium, IX, 21 (1912).

8) Fuercuer, Phil. Mag. 21, 770 (1911).

( 1065

precaution, to make a determination in duplicate, when the figures
are exceptionally high, and have only trusted the figures when
concordant.

b. Limburg. \n the discussion following the reading ofa paper on
this same subject at the ‘“Natuur- en Geneeskundig Congres” at
Groningen, Mr. Warerscnoor van per Gracut inquired, whether
there was likely to be a connection between the radium content
and the depth, at which the specimen was taken. In order to test
this idea experimentally, this gentleman placed at my disposal an
excellent material, namely a series of carboniferous rocks obtained
from a deep bore near Baarlo in Northern Limburg.

They consist of very sandy shales and quartziferous sandstones,
which are met with at different depths from 685 to 1398 M.

The results are given in the subjoined table.

Bore near Baarlo, depth 685 M. . . . 1,0
25 < 7 a COURMES a x, 0)8
; > ‘ Pe OQSe Mis ae ht Ad
- “0 4 rp pl yp ES le 1
53 ; 3 IPP le ee
> ‘ ie AOU epee Ol
2 ; Peet Oo) ME coe SOS
3 a (SO 7S Me ey = Ol3

These rocks may, therefore, be classed in general amongst those
poor in radium, with the exception of n°. 5. It will be interesting to
ascertain whether from a geological point of view also this rock occupies
a special place.

But in regard to the particular question asked I do not think
a sharp conclusion can be made. Rocks found at depths below
1223 M. appear, as a rule, to contain less radium than those met
with at smaller depths; but there, as well as at 850 M., we finda
specimen with a content of 0,8. A plain connection, in the sense of
a regular increase, or decrease of the radium content is not noticed.
In order to resolve this question it will be necessary to investigate
similar material from a great many other borings. Joty has in
fact, started this already; in his work Radioactivity and Geology
(p. 60) we find the radium content of shales, from the BaLrour-
Bore in Fifeshire, found at depths between + 700 and 1000 M.;
the quantity of radium met with varies from 3,5 to 4,1 and is
fairly evenly distributed over the whole series. Only one exception
occurs; at a depth of + 800 M. a carboniferous limestone is

( 1066 )

found with the figure 10.9; so at a comparatively small depth we
find a very high radium content. But at 40 M. lower and at
100 M. higher the tigure 8.5 is observed. Another example is also
mentioned by Joniy; recent coral-rock from the Funafuti Bore at
depths of 225 M. to 300 M. also shows but small differences without
a definite relation. | now call attention also to the fact, that in my
investigation of limestones and marbles, I have found already that
the figures for the radium content in the succeeding ancient deposits
were absolutely irregular; consequently we may arrive at the pro-
visional conclusion that there exists no relation between depth and
radium content. In this direction the investigation of plutonic rocks
is also a desideratum.

It will be noticed that the average figure in this series also comes
to 1.6 or, if excepting no. 5, to 0.8. The order of magnitude, there-
fore, remains the same; if, however, we compare these figures with
the average figure 4,5, given by Joty as the mean of 46 sedimentary
rocks, we are again struck by the remarkably high figure, always
obtained by this investigator.

In conclusion I wish to express my hearty thanks to Mr. Warer-
scHooT VAN DER Gracnt for his friendly cooperation.

Inorg. Chem. Lab.
University of Amsterdain.

Chemistry. — “The conjiguration of benzene, the mechanism of the
benzene substitution und on the contrast between the formation
of para-ortho- and of metasubstitution products.” By Prof. J.

Bouseken. (Communicated by Prof. A. F. Honurmay).
(Communicated in the meeting of February 24, 1912).

I. In consequence of the almost synonymous title of the eommuni-
cation of Dr. T. van pur Linpen (Dec. 30, 1911) I wish to make
a few observations in order to explain my stand-point in this matter.

Ist. For this purpose it is desirable to explain the reasons which
make me prefer the original ring of KKKULE as symbol for benzene
and all its derivatives to any other configuration, so long as one
starts from the hypothesis of the four valencies of carbon of constant
direction.

To begin with, all the representations in space, where the six
carbon atoms are not supposed to be in one single plane, may be
rejected because the optically active substitution produets, then to be

expected, have never, as yet, been noticed.

( 1067 )

Of all symbols, only those call for discussion in which the hydro-
gen atoms are distributed quite symmetrically.

Of these, there are only two that take due account of all the
properties of benzene; they are the well-known rings of K&KULE
and of ArMsTRONG-y. Banynr.

The first is based entirely on the tetravalency of carbon; if is a
consistent continuation of the symbols of all compounds which con-
sist exlusively of carbon and hydrogen; it accounts for most of the
properties of benzene and may be applied directly to all condensed
systems.

It gives us, however, no. satisfactory elucidation of the relative
saturation of benzene and of the uncertainty as to the existence of
possible isomers (such as two ortho-derivatives). ArMsTRONG has
endeavoured to overcome these difficulties by proposing the centric
formula. This has been accepted by von Banyrr on account of the
sharp. difference between benzene and the true unsaturated di- and
tetra-hy droderivatives. é

It needs, however, no comment that with the introduction of the
common bond of all carbon atoms towards the centre — in fact a
new kind of bond — no explanation is given of the deviations met
with in benzene; they are symbolised and there the matter rests.

An explanation can only be expected when apart from the ring-
systems, One arrives at a casual relation between the stability of the:
benzene and of a definite grouping of six carbon and six hydrogen atoms.

A step in the right direction has been made by Tuienr. If we
divest THteLe’s work from hypothetical arguments, it remains firmly
established that, in a conjugated system, the unsaturation is aceumu-
lated in the termini.

In the benzene ring, which is an endless conjugated system,
such an accumulation is not to be expected; each carbon atom will
therefore, possess quite as much, or as little, unsaturation and a
strong decrease of the additive power might be caused thereby,
Although we can well understand that the regularity of the distri-
bution can make the same less pronounced, this view yet gives us
no satisfaction because eyclobutadiene and cyclooctotetraene then ought
to possess an unsaturated character quite as slight as that of benzene,
which certainly is not the case with the first as it has never
been obtained as yet, and as regards the latter, it has been proved
quite recently by Wiiistarrer and Waser (B. 44 pg. 3423) that it
behaves as a very unsaturated substance.

This renders it probable that the ring with alternate double and
single bonds cannot explain satisfactorily the relative saturation of

( 1068 )

benzene. In so far, I agree with Wintstarrer and Waserr (l.c.), not
however, with their idea that the ring of K¥KuL¥ ought to be replaced
by that of v. Baryrr.

For as little as it is to be understood why, among the endless conju-
gated systems, the 6-ring only should occupy such a prominent place
is it to be understood why only this rag and not all the other ring
systems should possess centric bonds.

There is, however, another circumstance owing to which the ring
of KxKULK, as regards its stability in space, is distinguished favour-
ably from all other unsaturated ring systems; it has the smallest
ring tension.

For if we adhere consistently to the conception of the valencies
of constant direction, the angle between the sides of the benzene
hexangle amounts to (860°—109° 28°) : 2 = 125°16’. The ring tension
according to von Banyer is therefore 2°38’, i. e. much smaller than
that of the saturated 6-ring*).

dvery other condition of the bond between the atoms situated in
one plane, therefore also and in a very strong degree, the central
one (for so far as it signifies an attraction between atoms, and it
surely can mean nothing else) is more unfavourable.

In Kiéxutés benzene ring there is, therefore, in each of the apexes
but a slight ring tension while also in none of the apexes an excess
of unsaturation is present. So long as the conception of the four
valencies of constant direction is adhered to, this symbol is more
capable than any other of accounting for the slightly pronounced
unsaturation of benzene.

The second difficulty, that more derivatives are possible than have
actually been found, is of less significance. In other cyclic and non
cyclic substances one has so often been obliged to assume a very
readily miutual shifting of double and single bonds with a simulta-
neous displacement of H-atoms that, in my opinion such shiftings
in the benzene ring (where a displacement of atoms is not even
necessary) may be accepted without any hesitation.

Of course, it speaks for itself that in accepting KKKULK’s ring, it
is not taken for granted that this represents the true condition of
ihe molecule.

Our representation remains defective, bat the cause of this is
situated deeper; it roots in the unsatisfactory conception of the valencies
of constant direction.

1) The tension caused eventually by the double bonds acts perpendicularly to

the ring-plane and so does not influence the real ring tension.

( 1069 )

Il. Tuer, in order to arrive at an explanation of the unequal
distribution of the unsaturation noticed by him in a conjugated
system, has started the hypothesis that each doubly-linked atom
possesses a certain residual-valency which remains free at the terminal
carbon atoms, whereas these residues would neutralise each other
in the middlemost atoms.

With this, Tmimre abandoned the valency theory ; this is shown
strongly in the benzene ring proposed by him where each carbon
atom obtains five valencies.

ArmstronG and y. Batyrr also abandoned the valency theory to
some extent by introducing an entirely new kind of bond between
all carbon atoms simultaneously.

Both efforts, from their very nature are undecisive, but they must
be looked upon as an awakening as to the imperfection of the con-
ception of the valencies of constant direction which threatens to
strand on the properties of benzene.

I have come to the conclusion that indeed. the ordinary theory
of valeney should be shelved, but this should be done in a consistent
manner.

A. Werver in his well-known treatise on the theory of affinity and
valency (Vierteljahrsschrift d. Ziivich. naturf. Gesell. 1891) was the first
to conceive the fundamental idea of an affinity working in all directions
(Universal). In his “Neuere Anschauungen” 2nd Ed. p. 81 he gives
the following definition: ‘affinity is an attracting force working
regularly from the centre of the atom towards the surface’ and
further “valency is an empirically obtained numerical relation,
independent of valency units, in which the atoms combine with
each other.” It is a pity that these fairly sharp definitions lose
somewhat of their significance by the introduction of the idea of the
attracting surfaces (Bindefléche) in order to illustrate the amount of
the affinity fixed.

The distinction into chief and auxiliary valencies, which must play
an important role, particularly in the inorganic symbols, is also, in
my opinion, a less fortunate one; it must cause arbitrariness and
confusion.

But these are, comparatively, trifles; it must be admitted that the
acceptance of the idea of the universal affinity has facilitated in a high
degree the survey of the inorganic compounds, while it has given
to the organic compounds a rational foundation. z.

The carbon atom can group four atoms around itself thus forming
a tetrahedron.

When only three atoms are fixed by the carbon atom they will

( 1070 )

place themselves with the carbon in one plane in such a manner that

the carbon arrives in the centre and that the other atoms group
themselves around it in as regularly a manner as possible.

But in such a complex there remains a tendency to completion.
(This has already been felt by Wottaston in 1808 for the case
of all the combinations of a central atom with three others grouped
around it).

If, for whatever reason, the total completion cannot be attained,
a 6-ring, in which all lines between the centres of the cyclic atoms
and the atoms directly combined thereto make the equilibrium angle
of 120°, will amongst all conceivable constellations, be the most equi-
librated condition in which six carbon and six hydrogen atoms can
place themselves. With this representation all carbon atoms as regards
their insaturation become quite equal as this is distributed evenly
over the whole of the molecule.

] pointed out some time ago (Rec. 29, 86) that for the retention
of two homonymous atoms such as, for instance, of two nitrogen
atoms in the molecule N,, we must assume a certain inequality or
contrast, as otherwise they would not attract each other so energe-
tically.

As these atoms, however, must possess in regard to third ones a
same difference of energy, this inequality must be of the same nature
as that between two optic isomers.

We can imagine this’ inequality to be caused, for instance, by an
adverse movement of the corpusculae.

If this idea is applied to the benzene
O ring this inequality might be symbolised
with the annexed figure.

By means of this — and this is an

y

(( ) @)

(Sa. A) important advantage over the ring of
)

?) ee K¥KULE — not only the contrast between

ortho-para and meta would be shown,

ee (~ but also the equality of the two ortho-

OO) ea ) placed carbon atoms. Each substituent
) ~ will accentuate the contrast.

Hence, by a combination of the Werner

— fundamental principle of the universal

affinity and my idea as to the contrasts

—— also between homonymous atoms — we arrive at a symbol

which keeps account with all the properties of benzene and also

with its relative saturation. For owing to the completely equilibrated

position of the C and H atoms all tension is removed and owing

( 1071 )

to the even number of carbon atoms the said contrasts may be in
a condition of almost complete equilibrium ‘).

Il. Let us now consider how we must conceive the benzene
substitution. For the moment it does not matter much whether we
choose the symbol of K&éKULE or the one proposed by me.

In any case we know for certain that it is a molecule in a con-
dition of a relatively low chemical potential so that each change in
the configuration or condition of bond must cause a rise in the
potential. Now, the mixture of C,H,br + HBr will certainly lie again
on a lower potential plane in regard to the mixture of C,H, + Br,
because the reaction in presence of a little powdered iron takes place
with a considerable evolution of heat, but in order to arrive in that
new condition, a resistance has, evidently, to be overcome, as this
reaction takes place with extreme slowness without the presence of
a third substance.

This resistance may be due to the bromine as well as to the
benzene: here it is only rational to look for it in the benzene more
in particular because ali other unsaturated hydrocarbons of a similar
simple construction are brominated very rapidiy. If now we were
dealing with an immediate exchange this resistance could not be
expected to that extent (and this applies very generally to substitu-
tion reactions, see below). If, however, we accept an ‘addition’, this
behaviour then follows directly from the consideration that the stable
equilibrium will then have been disturbed altogethey. The regularity
of the affinity distribution as well as that of the spacial distribution
is destroyed.

It is, therefore, no matter of surprise that this condition of a much
higher potential will be attained only by an extraordinarily small
number of molecules and will not be permanent because this additive
product may make room immediately for the mixtures of C,H,Br-- HBr.
Only the simultaneous attack on all unsaturated carbon atoms —
formation of a hexabromide — leads to a condition whose potential
can be smaller than that of the mixture of bromine and benzene.

In benzene hexabromide the molecule has reached an equilibriam
comparable to that of benzene, owing to its condition of saturation
and also to the largely (though not completely) equilibrated spacial
distribution of its atoms.

Now this is what T. van per LinpeEn (l.c.) has noticed. On adding
to benzene an insufficiency of halogen he obtained a product consist-

1) The predilection in nature for a compound with an even number of carbon
atoms may perhaps be attributed to this same more complete saturation.

( 1072 )

ing of bexahalogen benzene, anyhow it did not contain appreciable
quantities of the above mentioned intermediate products.

It is also evident why, with the aid ofa catalyst, the hexa-additive
product did not show in the least a particular inclination to eliminate
hydrogen as this splitting uff reaction will be accompanied, parti-
cularly at the commencement, by a rise in the potential.

Van per Linden argues that the role of the catalyst will consist
chiefly in this, that from eventually formed additive products such
as C,H,Br, it will accelerate the elimination of the halogen hydrogen
molecule, but to me this appears to be incorrect.

In my opinion its action will really consist in this that it promotes
the entry of the bromine into the benzene in such a manner that,
the simplest additive product is formed first; the elimination of
the halogen hydrogen molecule from this first additive product in
connected with so large a potential fall that the aid of a catalyst
is not required here.

It speaks for itself that in the method employed by van pur LinDEN
none of the additive products were met with.

From my above explanation it follows — and this has also been
proved experimentally by van pbER LinpEN — that without a benzene

catalyst benzene itself will undergo substitution with extreme slowness.
The chance of forming the first additive products is too small and
the chance of retaining them will undoubtedly be less still as they
may pass into a more stable condition in two directions '). On the
other hand there will be more chance of obtaining the said additive
products of less completely equilibrated condensed systems in which
the conversion of hydrocarbon into a dihydro-product means a less
great disturbance in the said equilibrium.

Naphthalene, phenantrene, and anthracene give us at onee the
desired examples thereof and also the proof that catalysts are by no
means necessary for the elimination of the halogen hydrogen molecule
because this splitting off readily takes place without a catalyst.

I, therefore, consider it probable in a high degree that in the
formation of a monosubstitution product of benzene a temporary
additive substance is formed.

The question, however, now arises: What will be the configuration
of this ephemerie product ?

If we accept the symbol of KEKULK (or the one proposed by me)

') When this exit is closed by the choice of the acting molecule the first additive
product can be isolated. Indeed o- and terephthalic acid give, on reduction with

sodium amalgam first of all the dihydro-produets,

( 1073

the product obtained by the bromination of chlorobenzene ought to
possess the adjoined configuration *).

eee Van per Linpen thinks that a configuration like this
| ISBr.

might yet have been expected because the elimination of hydrogen

is excluded because in his opinion, in the bromination

-Cl of chlorobenzene, the formation of o-dibromo- in presence
Wy hin, x A :
\7Z ~Br. of 0-chlorobromobenzene has never been noticed, which

chloride from the above molecule is at least quite as probable as that
of hydrogen bromide.

To this one might reply that there has never been made a serious
search for the presence of these products. The otherwise so carefully
conducted experiments described, for another purpose, by T. van
pbeR Linpen in his dissertation (p. 71—90) admit the possibility of
the presence of traces and cannot very well be accepted here because
catalysts have been employed and these. as 1 will explain presently,
are sure to modify the course of the reaction *).

So long as it has not been proved with positive certainty that
with benzene as well as with the other condensed systems not a
trace of dichloroderivative is formed when the monobromo-substitution
product is chlorinated, the possibility of the above contiguration may
not be rejected *).

But even if this did not succeed I still believe I must adhere to
an analogous configuration of the additive products even though the
additive molecular parts therein must not be assumed to be wholly
equivalent to the atoms or atomic groups already present in the
benzene. I remind here of the conversion of maleie acid into fumario
acid with the assistance of HBr, in which case must also be assumed
an influence of HBr on maleic acid without this leading to the
formation of bromosuccinic acid.

In case only such influences or shifting products ave present, we
should almost be inclined to think that we may assume with equal
right a direct substitution and to this conclusion van per Lripen
arrives at the end of his argument (l.¢. p. 745).

Yet, as we explained above, this is not the same. The — for-

1) Howteman and Boesexen, Proc. 1909. p. 535.

9

2) I found some time ago that ethyl bromide when heated with aluminium
chloride causes the formation of ethyl chloride, whereas Mr. Srecrer has found in
iny laboratory that FeCl; reacts with ethyl bromide with formation of ethyl chloride,
ferrous bromide and free bromine.

8) An investigation in that direction has already given the result that p-dibromo-
benzene gives with chlorine without a catalyst, an elimination of very large quan.
tities of bromine. The existence of a primary addition product, if not proved, has
been, therefore, rendered very probable.

71

Proceedings Royal Acad. Amsterdam, Vol. XIV.

(1074 )

mation of shifting as well as of true additive products must be
accompanied by a considerable rise in energy and will, therefore
take place very slowly, if it takes place at all. The assumption of
similar products fully explains the extreme slowness of the substitution
reactions of benzene (and of all substitution reactions) if we take
great care that no benzene catalyst is present.

IV. This naturally leads me to the question: In what does the
action of catalysts consist? A catalyst can cause a modification in the
condition of benzene as well as in that of the acting molecule.

When it exclusively renders active the last molecule, when we
may think of a dislocation of this molecule, it becomes evident tbat
the benzene still wholly equilibrated, will be attacked in its entirety
and yield a hexa-additive product. From benzene and chlorine or
bromine, under the influence of light or of bypohalogenie acid. will
therefore be formed exclusively benzene hexachloride (bromide). The
number of these cases will, however, be limited because some of
the stronger catalysts also act on benzene.

Substances such as AICI,, FeCl,, 50, which so eminently promote
the polymerisation and monomerisation of unsaturated compounds
will undoubtedly exert on beuzene a shifting action.

Let us imagine the catalyst entering somewhere into the benzene
vine; the second molecule which can also have been made active
will then be able to act there. No longer the entire ring but a
single point thereof will be attacked owing to this change of equili-
brium. As the catalyst can facilitate afterwards the elimination of
molecules such as HCl, HBr, and H,O, the formation of a monosub-
stitution product is to be expected.

The following will show that the action of the catalyst is based
in the first place on a ‘shifting’ in the benzene.

With Mr. Singer, ' have studied the ethylation of chlorobenzene
and noticed that under the imfluenee of the mercuric-aluminium
chloride couple?) ethylene is rapidly absorbed by chlorobenzene. The
latter may also be obtained but not so rapidly by the action of
ethyl chloride on chlorobenzene when hydrogen chloride is eliminated.

Darzens (C.R. 150, 707, 151, 758) has found that with tetra-
hydrobenzene and acetyl chloride under the influence of AICI, the
reaction did not proceed further than to the hydrochloride of tetra-
hydroacetophenone

C,H,, + CH,COCI = C,H,, CICOCH,

10

1) The intensifying action of this is based on the formation of mercurous-alu-
minium chloride which being soluble in chlorobenzene, increases the concentration

of the catalyst. Gutewiren B. 87%. 1560 (1904).

(1075 )

and that the unsaturated ketone could only be obtained by heating
this hydrochloride with chinoline at 180°.

Prins and T (Rec. 80, 158) have found that although C,Cl, can
unite with chloroform to heptachloropropane, yet no perceptible
elimination of hydrogen chloride takes place at the boiling point of
chloroform. This starts very slowly at 80° and only becomes more
considerable at 250°, a temperature at which the elimination is very
perceptible even without the presence of AICI,. It will be noticed
that all depends on the relative energies which take part in the
reaction. If the elimination of the halogen hydrogen molecule is
accompanied by a potential fall it will take place. Catalysts such
as AICI, ete. evidently do not promote this part of the reaction to
any extent and this is easily comprehensible because in most cases
a previous potential rise is not required here.

But with C,H,Cl, ~ C,H,Cl, +38 HCI it may be assumed that
this is the case’) because at the parting of the irs? molecule of HCI,
the molecule passes into a condition of much less stability both as
regards the unsaturation and the spacial distribution of the atoms.

From all this it follows that the catalyst starts with the rendering
active of the benzene and that in consequence of the disturbance of
the -equilibrium caused by the catalyst, a monosubstitution product
is to be expected.

The entering molecule is also rendered active. By a series of in-
vestigations I have endeavoured to prove that substances as AICI,,
FeCl, etc. render the molecules active by a dislocation (which may
lead to dissociation); for instance, I have been able to demonstrate
that a substance like SO,Cl, reacts as entire molecule and also as
a mixture of its products of resolution.

In the case of hepiachloropropane, I bave noticed that the elimi-
nation of HCI ete. is, finally, also accelerated, as this, in presence of
much AICI,, commences at 80° at which temperature the deeompo-
sition, without catalyst, is hardly perceptible. Under the influence
of ecuprous chloride this decomposition takes place, at 300°, undoubt-
edly somewhat more rapidly than without a catalyst.

Hence, the separation of the eventually formed first additive product
of the benzene is sure to be more difficult in the presence of a
catalyst than without one.

On the other hand there remains the possibility of isolating the
products of conversion which are to be expected such as dichloro-

1) The observations of T VAN DER LINDEN l.c. make it however more probable
that C,H;Cl; -+-8HCI possesses more free energy than C;H,Cl,. (Note in the English
Ed. of these Proc. only).

71*

(1076 )

benzene, from bromobenzene and chlorime. They, however, annot
be of service to prove the existence of primary additive products,
because the catalyst itself has taken part in the reaction.

The reactions which we have considered up to the present proceed,
withont a catalyst, either not at all or extremely slowly ; some, however,
are known that can take place very rapidly even without inten-
tional addition of a third. substance (or foreign energy); to these
belong the ‘nitration’ and to a certain degree the “sulphonation”.

It must, however, be observed that the velocity is largely dependent
on the concentration of the acid so that it mereases in a much
stronger degree than corresponds with the strength of the acid.

This can be explained in a very simple manner by assuming that
in nitric acid and in sulphuric acid a catalyst is present; this will then
be the anhydride N,O, and the anhydride SO, of which we know
for certain that they ave present in small quantities and in the free
state in the 100°/, acid. Here the catalyst and the substituting
molecule are to a certain extent identical.

it is known indeed that fuming sulphurie acid is a considerably
more active sulphonating agent than the ordinary 98°/, acid and,
in the acetylation, | have been able to demonstrate that sulphuric
acid may be put on one line with AICI, and Fe Cl,.

The dilution previous to, or during the reaction decreases first of
all the concentration of these powerful catalysts. During the reaction
this decrease will be extremely strong because the catalyst itself is,
in the first place, fixed by the benzene and afterwards also by the
water generated. This, of course, causes that the course of the
nitration is very complicated and proceeds in the end much slower
than at the beginning.

But in the nitration in presence of a large excess of sulphuric
acid and nitric acid we can expect a more regular course of the
reaction because the condition of the nitration mixture, and conse-
quently the concentration of the catalyst, then remains practically
unchanged .

Catalysts such as SO,, AICl,, N,O,, FeCl, etc. may, therefore,
be considered as substances which attack the benzene molecule ina
definite place, thereby causing a disturbance of the equilibrium which
renders possible the formation of labile addition compounds which
may afterwards be converted into the much more stable monobenzene
derivatives.

Naturally this does not explain the action of the catalyst. We do
not understand why the condition of benzene should be modified by
AI Cl, and not by bromine alone. In order to solve this we cannot

: ( 107)

restrict ourself to the study of the system benzene + catalyst, on one
side, and of the mixture of catalyst + substituting molecule on the
other side, but by an efficient combination of the phenomena observed
in these two systems we must arrive at a satisfactory elucidation of
the progressive change of the reaction.

Let us now consider the case where one of the H-atoms of ben-
zene has been replaced. In the benzene there is now a disturbance
of the equilibrium so that the unsaturation cannot any longer be
equally distributed.

In the ring of K¥KULK (as explained previously by HoLLeman and
myself) as well as in the ring proposed by me the carbon atoms in
the ortho- and para-position must be distinguishable from those in
the meta-position.

By Horneman and me (I. ¢.) it has been assumed that when the
eroup entered renders the benzene more liable to attack we may
then expect an addition to the double bond and the conjugated
system, so that in the main para-oriho-substitution will take place.

In the reverse case, however, this addition will be retarded; an
addition to the third double bond takes place which will cause the
formation of meta (in presence of ortho)-derivative. VAN per LinpbEn
thinks he must conclude from his experiments that chlorobenzene is
attacked less rapidly while it is yet substituted ortho-para. Although
I quite agree with Horimman (Verslag 30 Dec. 1911) that these
experiments are not comparable because in the bromination of ben-
zene a powerful catalyst, NaObBr, was present, but none in the case
of chlorobenzene, I still feel convinced that the sulphonation, acetyi-
ation and benzoylation of chlorobenzene proceed slower than those
of benzene in otherwise comparable conditions. Yet, | do not agree
with Van per Linpen that the whole hypothesis as to the cause of
the contrast between ortho-para and meta should now be rejected.

It wants a not principiant modification and a considerable extension
by keeping account also with the nature of the entering molecule in
regard to the substituents already present.

Two points have to be kept in view.

Ist. Each group X in the nucleus causes, just like a catalyst a shifting
of the equilibrium owing to which the benzene will asa rule be more
readily attacked, and at the same time the contrast between ortho-
para and meta is formed or accentuated.

2d, In consequence of the nature of the acting molecule in regard
to the substituent XN already present the privilege accorded to the

( 1078 )

ortho-para-positions (1) can be opposed, to finally make room for
meta-substitution.

Luplanation. According to this view there are at work two influences
independently of each other; the first is the disturbance of the equili-
brium caused by X whieh will be different from group to group
but will always give preference to the carbon atoms in the ortho-
para-position, just as a catalyst renders active the place where it
has attacked the benzene molecule.

The second influence which can act in the same or in the opposite
direction is determined by the affinity of the already present group
X towards the entering molecule Bb.

Of this, we can discern three cases.

A. The affinity of the acting molecule B for X is very great. B
will then act in the first place, on X, and be retained therein after
which the action ceases.

For instance. The reduction of the nitro-group, oxidation of the
SH-eroup, bromination, under definite conditions, of the alkyl group ete.

B. The aftinity of the acting molecule B for X is less considerable
so that, at most, labile additive products can be retained.

The group B will then further accentuate the disturbance of the
equilibrium caused by X alone, and the molecule enters into the
nucleus ortho-para.

For instance. Chlorination of sulphides, amides, bromides, iodides ;
hydrogenation of ortho- and terepthalie acid, oxidation, under the
influence of potassium hydroxide, of nitro-compounds, mercuration
of acids ete.

C. The affinity of the acting molecule B for X is not present.

X will then oppose the addition and substitution ortho-para so
that the influence of the disturbance of the equilibrium can be lessened
or destroyed by this adverse action so that the meta-substitution can
become predominant,

or instance; Nitration, sulphonation, and chlorination of mitro-
compounds, sulphonic acids and carboxylic acids, but also hydro-
venation of amide and oxy-compounds.

Up to the present one has almost entirely overlooked the influence
of the entering molecule and this is chiefly caused by the fact that
among the acting molecules mainly those have been studied whieh
are mutually of the same nature (H,SO,, HNO,, Cl,, CH,COCI ete.).

If, however, one considers the effect of other molecules such as
mereurie compounds, hydrogen, potassium hydroxide, hydroxylamine
etc, the substitution representation becomes quite different.

In the above survey, I have included all cases ina general scheme

( 1079 )

from which it is seen that the reactivity of the substituted benzene
is dependent on the substituent as well as on the acting molecule
and that the type of the substitution will depend on this mutual and
common. influence.

I will illustrate this with a few very striking examples.

I. The nitro-group in nitrobenzene renders the molecule much less
accessible for nitric acid, sulphuric acid, chlorine, bromine ete. and
in agreement therewith we obtain with the last mentioned molecules
a meta-substitution.

Nitrobenzene, however, is very strongly attacked by potassium
hydroxide and, as was to be expected, we obtain orthonitrophenol.
s-Trinitrophenol is very readily oxidised in alkaline solution.

The nitro-group does not render the benzene molecule absolutely
unattackable. As soon as it is acted upon by molecules that possess
some affinity to the nitro-group, the ortho-positions become accessible.
Quite in harmony herewith is the behaviour of substances such as
o-chloronitrobenzene and particularly of pierylehloride. The chlorine
atoms present therein are not as a rule readily substituted but are
replaced by molecules such as H,, NaOCH,, KOH, NH,C,H, ete. ete.
which are driven by the nitro-group in the ortho-para-direction.

The objection raised by van per Linpen (Le. p. 741) to this sub-
stitution in connection with our theory is therewith quite neutralized
and at the same time these substitutions are the cases which he has
searched for and which we can formulate as follows:

Te 7 i LOCI
Ce -. | seein = i + NaCl.

Th N:
NOs oN \ 7 NO;

Il. The COOH -group directs nitric acid, sulphuric acid, the halogen
molecule towards the meta-position; the nitration, sulphonation, and
halogenation proceed again much slower than of benzene and toluene.

But we may not characterise the influence of the carboxyl group
as a generally retarding one. Benzoie acid and, in a still higher
degree, the phthalic acids are more readily reduced than benzene
and aniline: in regard to hydrogen, aniline is therefore more firm
than benzoie acid.

In agreement with my explanation, von. Baryur (Ann. 251, 264
and 269, 192) found that the carbon atoms at which the carboxy!
groups are situated, i. e. 1.2 or 1.4 gave the expected additive
product. Orthophthalie acid gives primary 43.5 dihydro 1.2 dicar-
boxylie acid.

This again is a case which van brER Lixpen has searched for,
namely of the isolation of the primary additive products,

( 1080 )

The separation could of course, be expected sooner than in the
ease of a dibromo or dichloro additive product because there exists
here no other exit towards the stable benzene derivative, except
either by the loss of the hydrogen absorbed or of the entire car-
boxyl group.

[ call attention to the fact that from Banywr’s research (l.c.)
it follows that there exists indeed a certain affinity of the hydrogen
for the carboxyl groups, as beside the hydro-acids other products
are also formed, such as phthalide at which the side chain has been
attacked.

Ill. A very illustrative case is the hydrogenation of a@-naphtyla-
mine. The amido group is considered to be the one that renders the
benzene molecule extremely aecessible; this also is caused by the
affinity of this group for the great majority of the entering molecules.

in harmony therewith, it directs almost exclusively towards ortho-para.

This, however, may not be generalised. In regard to the hydrogen
molecule it behaves differently. Aniline is not at all readily reduced
and the resistance is evidently of such a nature that in a binucleated
system such as naphthalene, the unsubstituted nucleus is more readily
reduced than the substituted one. As «-nitrcnapthalene directs the
second nitro-group towards the other nucleus, @¢-naphtylamine directs
the hydrogen to the same.

Just by overlooking the influence of the acting molecule, these cases
were considered as exceptions and it was endeavoured to find an
explanation in the indirect substitution described by Bianksma (Ree.
a YS8i-and 23; 202).

This means to say that the acting molecule tirst enters the side
chain then to pass into the nucleus. On studying more carefully the
cases wherein a similar course of the reaction has been noticed, such
as in the chlorination of acetanilide, one was able to prove (J. C.S
95, 1456) that the chlorine atom only then enters the nucleus quite
as rapidly as in the direct chlorination, when a substance like HCl
is present which again liberates the chlorine atom. The formation

of chloroacetanilide ean, therefore, by itself, never explain the ortho-
para substitution. We must, however, attribute that formation, like
the ortho-para substitution, to a same cause, namely to the influence
of the group NHCOCH, on the chlorine molecule.

When this side chain substitution gives rise to the formation of a
relatively very stable compound such as C,H;CH,Br, this willatonce
be noticed and Honteman has quite rightly pointed out that the for-
mation of these produets cannot explain the ortho-para substitution in
the nucleus.

( 1081 )

As has been observed, this explanation lies in what happens before
that substitution, viz. in the influence of the acting molecule on
the group X.

The cases of true, indirect substitution, in which this linking or
decomposition product is changed into the nucleus substitution pro-
duct, such as, for instance, in the halogenation of acetanilide or of
diphenyl sulphide (Ree. 29, 315), the chlorination of iodobenzene
etc. ought hence to be classed under heading A as well as B. In
a certain sense they are placed between the two.

The acting molecule has so much affinity to the group X that it
can either unite (or react) with it, or else enter the nucleus.

Benzene catalysts will, in such cases, lead the acting molecule
undoubtedly to the nucleus, whereas the substances or energies
which render the entering molecule active will facilitate the chain
substitution.

The bromination of toluene gives us a very good instance thereof;
under the influence of catalysts as FeCl,, AICI, ete. the action of
the group X on the nucleus is strengthened and ortho-para substi-
tution occurs; on the other hand, light and heat promote the chain
substitution. :

The nitration of toluene also comes under the same point of view.
When we-dilute the acid to such an extent that not a trace of
N,O, can be present, then, and particularly at a high temperature,
the chain substitution will gain over the nucleus substitution and
phenylnitromethane or benzoic acid will form.

The indirect substitution as suggested by BLANKsMma is therefore
not directly related to the nueleus substitution. But still we may
say, that the same cause which originates this indirect substitution,
namely the affinity of the group X for the acting molecule, promotes
the para-ortho substitution.

It appears to me that this contemplation, which is nearly entirely
based on a single assumption, namely of the shifting of the equili-
brium caused by a molecule or part of a molecule which finds
itself in a more or less solid combination with the nucleus of the
benzene, and which keeps account with the influence of this group
on the acting molecule, has placed the question of the substitution
on a rational foundation.

Delft, 18 February 1912.

( 1082 )

Anatomy. — “Vhe ved nucleus in Reptiles’. By Dr. S. J. pp Lanen.
(Communicated by Prof. C. Winker).

When studying the midbrain of Reptiles I was struck, first in
Lacerta agilis, by big multipolar cells, which I found in the region
of the most frontal oculomotor roots and which had much resem-
blanee with the multipolar cells of the red nucleus such as are
known in mammals.

With this aim in view, it was not difficult to state the same group
of cells in other reptiles.

The group of cells, determined in this way, was localized almost
in the same region, which von Monakow') and Harscurk *) have
given for the magnocellular part of the’ nucleus ruber, only with this
difference, that the fibres of the oculimotor roots do not run through
the nucleus as we see it in mammals. Consequently there is a little
dislocation of the whole nucleus in a lateral direction, which can find
an interpretation by the fact, that in mammals the second part is
situated laterally from the magnocellular part and therefore the former
part is displaced in higher vertebrates to a medial position,

In the Varanus Salvator it seemed as if there were also a parvo-
cellular part of the red nucleus, situated lateroventrally from the
magnocellular part and extending towards the front. On more exact
examination the above mentioned interpretation appeared not to be the
correct one, for it was very improbable, that in the lower vertebrates
we should find some parvocellular group of the red nucleus, this
group being one of the connexions of the neocortex with the lower
parts of the central nervous system and reptiles having no neocortex.
It is rather to be granted, that the conclusion of HatscHrk is true
when he says, that both parts of the red nucleus in mammals show
us variations relative to the higher ov lower place in the system,
occupied by the animal we have to examine. He has stated, that
the magnocellular part is diminishing in higher mammals and_ that
in man we can find back but a rudiment of this magnocellular part.
This rudiment is situated near the oculimotor nucleus and among
the rootfibres. In man the magnocellular part, in which the tractus
rubro-spinalis originates, is localised in a more candalr egion than the
part we are accustomed to call in man the nucleus ruber and which is
composed exclusively of small cells. Therefore the highest mammal

1) CG. von Monaxow. Der rote Kern, die Haube und die Regio subthalamica bei
einigen Siiugetieren und beim Menschen. Arb. a. d. Hirnanat. Inst. in Ztirich 1910.
2) R. Harscuex. Zur vergleichenden Anatomie der Nucleus ruber tegmenti. lest-
schrift z..Meier. d. 25 j. Best. d. Neurol. Institut an der Wiener Universitat 1907.

( 1083 )

has a great development of the parvocellular part of the red nucleus
and only a rudiment of the magnocellular part. This is the reason
of the fact that the tractus rubro-spinalis in man is also rudimental.
Moreover we find in the localisation of both parts the reason, that
tumors in the nucleus ruber in man but seldom cause degeneration
of the rubro-spinal tract, unless the tumor has a caudal extension by
which the rest of the magnocellular part is destroyed.

Descending in the series of mammals we see the parvocellular part
diminishing, the magnocellular part growing on the contrary. With
good reason v. Monakow calls the parvocellular part “the cortical
part”? of the red nucleus. He means that this part by its connexion
with the neocortex is changing in size relatively to the extension
of the neocortex, hence it is diminishing in the lower vertebrates with
smaller evolution of the neocortex.

Fig. 1.

Section of the midbrain of Lacerta agilis.

In reptiles the cortex cerebri having hardly any but genuine olfactory
qualities (it may be that we can suppose in some of the highest
reptiles an indication of a neocortex in the thalamo-striato-cortical
tract) we might expect only the pars magnocellularis of the red
nucleus to be developed.

( 1084 )

Subjoined I have collected some sketches of the principal represen-
tatives of reptiles. In all of them the bigness of the cells and their

Wig. 2.

Section of the midbrain of Varanus Salvator.

‘aracteristic multipolar form are clear. It makes an impression as if
scattered reticular cells as they are found everywhere in the reticulum
(See van Horve.’s article) ') have concentrated in one place by a
biological stimulus and in this way have formed a nucleus.

By the wealth distinctly of fibres in this region it was impos-
sible forme to see which fibres descend from the nucleus cau-
dally ; therefore I have no right to speak of a tractus rubro-spinalis.
Perhaps (and I am sure it will be as [ think) it will be possible

1) J. J L. A. Baron vin Hoevett. Remarks on the reticular cells of the oblon-
gata in different vertebrates. Kon. Acad. vy. Wetenschappen 1911.

( 1085 )

io show us this tract also in reptiles by experimental degenerations.

In fig. 1 1 have sketehed the nucleus ruber of Lacerta agilis,
such as we find it in rather a great series of sections coloured after
the method of Nissi. The section is taken from the middle part of
the midbrain, there, where the tectum opticum shows its greatest
development. It shows the frontal beginning of the oculimotor
nucleus. So we have here the frontal pole of the red nucleus.

I give also the nucleus at its greatest development, somewhat more
-caudally (fig. 2). Here the oculimotor nucleus is distinetly divided
in its three parts and laterally from the place, where the root fibres
are going out of the central trunk we find a great deal of big mul-
tipolar cells, being of the same type as those we have seen in

ea —
\
\
\
ace :
ai ;
*.
7 \ /
\ - “
oe SNe /
fia 8 aN /
: Ss y
y - kNrub /
\ i a
NY Sy 4
N /
\ ~
ae Je
LE
a4
~— aa
fig. 3.

Nucleus ruber in Boa constrictor.

Lacerta. It is clear, that here the nucleus is situated more ventrally
than in Lacerta, but partly we have to seek the reason of this
localisation in the fact, that this section is a more caudal one. This

( 1086.)

very distinct preparation is coloured with an infusion of elderberries
according to a method, which soon will be deseribed by C. U. ArtEns
IXAPPERS.

Figure 38 shows the nucleus in boa constrictor. The section is
coloured after the method of van Girson. There aremuch fewer cells
than in the former species of animals, but the form of the cells and
their localisation just vear the oculimotor root fibres make the
identification with the former groups of cells undoubtfal.

Mueh clearer is the sitnation-in the Alligator sklerops (fig. 4). The
Central Institute of Brain research has a very beautiful series in

Vig. 4.

Nucleus ruber in Alligator sklerops.

two colours (vAN Ginson and Wnhicurt-Par). The localisation of the
distinctly cireumseribed group of cells near the roots of the nervus

oculimotorius makes the diagnosis very easy.

( 1087 )

Also in the lower reptiles we can find back without difficulty the
group of cells. In fig. 5 1 sketched the situation in Testudo graeca.
Here also we find the oculimotor nucleus in the section and we see

Fig. 5.

Nucleus ruber in Testudo gracea.

several big multipolar cells, united to a distinct nucleus. The prepa-
ration is coloured with cresylviolet.

To my knowledge the red nucleus has never been described in
reptiles yet. by the annexed figures I think IT have demonstrated
with sufficient certitude the existence of the magnocellular part of
the nucleus ruber in reptiles.

dut it is not only in reptiles that I found the red nucleus, also
in amphibians it is possible to see a distinetly circumscribed nucleus,
localized absolutely in the same way, so in the region of the root-
fibres of the oculimotor nerve. It is again the same reticular
elements which have concentrated to a nucleus. In fig. 6 I give a
section of the brain of Rana, showing very clearly the group of cells.
Two sections more caudally we find the frontal pole of the oculimotor
nuclens, whilst the oculimotor roots are going out of the central
trunk, as we can see in the control-section, which is coloured after

( 1088 )

the method of Weicurr-Pat. In this section, only the cells are
coloured and therefore the rootfibres are invisible.

When for the identification we use the scheme of TretsaKorr )
such as he made it for Ammocoetes, we see, that he mentioned a

i

ESN are sat ps”

F eo

a siege

AEE

Fae

Hypothalamus

. Pe

Fig. 6.

Nucleus ruber of Rana.

mesencephalic group of reticular cells, except the more caudal groups
of reticular elements which all have been refound by van Horvert.).

In this lowest vertebrate the group consists of few very big mullti-
polar cells, which we may consider as the prototypes of the magno-
cellular part of the nucleus ruber and which we can find back in
all fishes. The cells are always localized in the region of the oculi-

') D. Trersakorr. Das Nervensystem von Ammocoetes. If. Gehirn. Arch. f. mier.
Anat. und. Entwicklungsges.

2) Loc. cil.

( 1089 )

woo
Fig. 7.

Fig. 8.
Nucleus ruber in Ciconia alba.

Proceedings Royal Acad. Amsterdam. Vol. XIV,

( 1090 )

motor rootfibres. As a specimen I give here a sketch of Selache
(fig. 7) where on both sides we find two big multipolar cells.

To show the situation in birds and the transition to the lower
mammals I add two figures.

dst a bird, 2°¢ one of the lower mammals.

[ chose the Ciconia alba, having a very fine series of this bird (fig. 8),
but it is very easy to find back the red nucleus in all other birds.
I saw it in Columbus, in Casuaris, in Spheniscus.

At last the form as it is to be seen in the opossum (Didelphys
marsupialis) (fig. 9).

IT am of opinion that in all these cases the identification is so
easy and so simple, that all confusion on this point is excluded.

\ al “N

= \ ey

—} <2 es
Fig. 9.

Nucleus ruber in Didelphys marsupialis.

( 1091 )

Physics. — “On the value of some differential quotients in the
eritical point, in connection with the coexisting phases in the
AA ye of that point and with the form of the equation
of state.’ By J. J. van Taar. (Communicated bygrot. Hear

LORENTZ).

1. In some previous papers we showed that the densities d, and
d, resp. of the liquid and vapour phase in the immediate neigbbour-
hood of the critical point are represented by the expressions *) :

de Weta 1—m: L B(1 m) + y (1 —- m)'2 + d(1 — mj? +...
d,=1—at ep (len) == (lm) a 12d (=e)

(1)

so that for values of m= 7’: 7; near 1 the quantities d, — 1 and
1 —d, are of the order of magnitude “1—-m, and not of the order
P“{—m (van perk Waats, These Proc. XIII, p. 116 and 1259) or of
B4 om (GorpHAMMER, Z. f. phys. Chem. 71, 577 (1910)).

In his “Thermodynamische Theorie der Capillariteit’” (1893) van prr
Waats also gives the correct expressions (see p. 44), and finds the
value 2 for a@ with the ideal equation of state, and the value 3,5
for real (normal) substances — quite in accordance with what we
found for them (loc.cit., ef.. These Proe. XIV, p.487) where the value
3,6 is given). For Blagetene eee @ may even be put 3,9 (see further).
Also Martuias (Ann. de Toulouse V) gave as empirical formulae the
theoretically correct ones.

For substances for which the ideal equation of state would hold,
we find loc. cit.

2 13 128 1359

> 17500"

The coefficient « indieates the divergence of the phases in the critical

point; the coefficient 3 is nothing but the coefficient of divection of

the so-called straight diameter ’/, (/,-+-d,) = /(m) in that same point.
When we pass from the ideal equation of state to the real one,

8 inereases from 0,4 to about 0,9, whereas «@ inereases from 2. to

about 3,9.

2. We shall now demonstrate that the expressions (1) will hold for
any form of the possible equation of state, and that d, —1 and 1—-d,

would only be of the order / 1—m, when in the eritical point not

1) See among others These Proc. XIV, p. 438 et seq., 563 et seg. and 574

72%

( 1092 )

9 3 4
only oe and zn are equal to O, bul also we and as And as the
av ave av av
latter is evidently an impossibility (for then there would be relations
between the coefficients of the equation of state), ¢@,—1 can never
be of the order of magnitude ” 1—m either. Other exponents, like
Py —m, are of course quite excluded.
For if we put quite generally
Tesla) s
we have, when ¢, 7, and m_ represent resp. “reduced” pressure,
volume and temperature, in the neighbourhood of the critical point :

1
e=1-+ E (m-1) + &; int) | 4- E é€,2(n-1)?+ &",,,(n—-1) (m-1) +
1 1 mt
se él (m1) | 4- E é)a(n—1)?§ + ete. | + ete.

Of 0g
In this ¢', represents [{ - ; €, represents | — }; €.a represents
On] i Om) fy

(= )
S| ee
On? / pr

The determination of the coefficient @ will require no other diffe-
rential quotients than the above mentioned ones. In this ¢, and ¢",2 are
both =O at the eritical point, so that by equation of the vaiues
of « in the two coexisting phases

1
é”.;(m—l) ce 1) —(n, | 1 F el. j- 1)*—(n, 1 | =. = 0

remains, because also the terms with only m—tL and (m—1)? vanish

in consequence of the equality of the temperainre.
If we now put:
De arg ae ates Se pelle (ot aa Se ne OC
in which t represents a power of 1—m as yet unknown, we get

nN, — l SSan Bi? == 05) 1= — (at— f'r?...) = —8,,

and hence:

|
&!y 1, (m—1)(6,4+-0,) + F é"n(*, 16>) +...=9,
j

or
] 6°. +63
Ee (—=7) == ee eel
6 O40,
Now evidently (the higher powers we shall want presently) :
6,4+6,=2atr,.; 6, — 6? 408? ..; OF + Or =—2a'r*.

CO, — 6, = 6e'Br* 2.3, 0, — 0", S80 Ba 590, Oe

( 1093 )

so that

+B, sae
———_—— = "t"
0,46,
Hence we get:
1
eo (1 —m)— Sea (Chih Ob CHOOT Ukia eee so: (9)
5

so that it now appears with the utmost clearness that t* must be
of the order 1—m, and so t of the order = 1—m.

Even if nm, were =1-+ er.., n,= 1—uc't.., in which a’ is not =a
(which, however, is impossible: see also These Proc. XIV, p .4839 and
440), even then t would appear to be of the order ! 1—im according to
the above. For then 6, +6, would be =(a+a)rt.., #, +6, =

6°. ae (3
= (a@* + «*)r*.., and - hence ——— (G2 — oe) t, so that
!

‘ils 6,
the conclusion would remain the same.
as bits 0°8 of
Only when also 2, ie. 3 were = 0 — but then é4 would
On -
also have to be =O on account of the form of the critical isotherm

(which of course runs from p=o to p=0O) — only then we
should have:

Ag
SW) (ra) ae | Beem Ni (O27 \ lee

1 ‘ : : :
-f 24 Ee (m—1)(4°,4+6*,) +. e + 190 él5(6°,+6°,) + ete. = 0.
But from this would follow :
(m—1) Ee .2at. | a i 50° ae (2a a) ees 0)

and so 1—m would be of the order 1‘, i.e. t of the order » 1—m.
So for this the (impossible) epi besitos é
required ')

wr wn

yw and é”,.= 0 would be

3. Let us proceed after these considerations to the expressions for
the coefficients @ and '.
As now henceforth t* can be replaced by 1—m, (@) passes into
" 1 m 2
& vt Fa € ya’,
6
after equation of the coefficients of the different powers of 1—m.

(22° £°..)

: te 2 1 1
1) If only BAS 0, we should have got — ¢ AG » —$+) instead of 5 ant os

24?

hence as 4; —54, = 8@6';*, 1—m is again of the order 74,

( 1094 )

from which follows:

a iy oo ao oo (Eb)
E ys
being the quite general formula for the coefficient ¢, whatever may
be the form of the equation of state «= /(m,n) *).
What follows may serve as a control. The ideal equation of state

eel a Sm 3
a v—b ot ey sae 3n—1 7?
gives for the different differentialquotients :
0g 24m 6) | s02e 144m 18 | d8¢ 9x 144m 72
dn (8u—1)? urs ental (n=1)) nt | dnt (n= " as
O*¢ 9X 12 « 144m 360) 07e 24 O88 144
Ont (Bn—1)> Ss |ndm ~~ (Bn —1)*|On70m (8n—2))
So this becomes for 7). :
éy = — 6 + 6 = 0 e's =18 — 18 = 0] 2" = — 81 72
eA 486 — 1360 — Ione, —= = Oe 37 — 1S.
Thus we find for «? according to (4):
6 & 6
i Ee 4

hence «= 2, as it should be.

If in (@) we also take the terms with r' into account, we get an
eqnation between the coefficients «, 8’, and y’. So we cannot deter-
mine p’ from this. For this we shall have to find the relation of
coexistence between the two phases. This is found from (se, denotes
the pressure of coexistence)

no—l

With
fF 1
eé=1+ é(m—1)4+ [Fer )((2— 1) = en (m1) | ao

a | 1
+ | P é!”ys(n—1)* -+ 5 é!y2.4(m —1)? (m—1) 4+ — "2 (~—1) (m—1)? + 3 (a)

1 wm
34 € ys(n—1)* +

= /

Uf
a 6 es (m1) | So
)

this becomes:

') Gf v. p. Waans, Capillariteit, p. 44.

( 1095 )

Pes «a — 1 \
& = 1+ €)(m—1) + Ea ayaa = eae ayy 9° (m=) | +
4 4 3 3 3 22
a E e583 aoe + : a2 4 poe *(m-1) 4 iene 45 m-1)?+- },(6)
3 1 2 l 2 1
te I Oe Ons
deg ea (matt [+ 58 nie 048, =e

as (n,—1) — (m—1) = 6, + 9,, (%,—1)* — (1 =
(see above).

6?,—4? , ete.

If in (@) we substitute successively m, and n, for 7, and then take
half the sum, we get:

-

ei Cree O-68e |
+ ae 7 — os Se —— eae 1) T 5 =e! ‘ost? = er + \.(a’)

2 2

! " Ope 1 ” 2 \
eé=1 +4 €)(m—1) +} &2, =a ls w(m—1)? | +

+ — : é'"y3(m-1)* lage oo ae

Equation of (6) and («’) now yields with 1 m = — (m—1) = 7’:

, [162-9 9,-6,] 1, [14,6 6,°-8,

mie gitwgy mae aires | arelnae a
ed ORS Cae si ia he 16,°—6,* 6-6,

ier 6,48, a haewlt O10 — it

1, [16,°+0,5 -0,¢14.4 :
De Cy ts vi 5 a48 = == ae | +. Nie

With the values of 6,-+ 6,, 6?, —6’,, etc. given above in §¢2
this becomes (the coefficients of ¢",, and &pe are evidently = 0):

] 1 1
ae ob | @ Be —isacp es. || ———ellane* 3 Cw — 07th
6 2 : :

1 Pal
+ pat E at —a's | = 0,

because evidently (6*, + 6*,):2= a'r‘. In this way we only get
the terms with tr‘, and find:

1 11) iid U 1 we q 1 mo
aa eae + 3 pa? — 30 Sais 05

hence finally :

( 1096.)

= Se a ee LD

in which @ is given by (1).

So the expression derived by van per Waats (Capillariteit, p. 44),
Viz. p' =e" 9,285, is inaccurate on account of the neglect of the
term with ”. Besides, the conirol by means of the ideal equation
of state confirms this. As we put n,=1+ar+ #'r?.., d. =

—
= 1 — at + Br .., evidently

b=a— 8,
because d, = 1: 7,.

2
Now by means of the above given values of the differential-
quotients (4° = 4) we find from (2):

»
18 — —. 126 d
4 i) 28 Rea)
tay Wares SU eg 5 ee
o 2,
giving B=4—3—-=—-—, in accordance with what we found before
fa) ca)

(see § 1). S

Van DER Waats’s expression would have given an entirely erro-
neous value for Pp.

4. The value of the characteristic function.
If we put
m dé.

e dm
we sball understand by the ‘characteristic function” g the value of:
f—-l1 6
aie ae a Bi
of which we know that it is equal to 1, when the quantities @ and
of the equation of state do not depend on the temperature 7’ (or
a only linearly on 7’). But in any other case y will no longer be
= 1, but it will be represented in the neighbourbood of the critical
point by
g =1+A(1—m),
in which we shall determine the coefficient 2.
In our previous paper (These Proc. XIV, p. 777) we have viz.
already shown, that when the said suppositions are fulfilled, formula
(8) given there holds, viz.

( 1097 )

T dpe a
A = =1- ’
p di pv,vs
tse
tee m dé. SE ine a d,d,
; ێ dim a

when «, denotes the pressure of coexistence, through which we

Rc COLE eee Om ;
distinguish —— from . So we have also:
n

dm Of
3 a
ia
PRUE

hence
a —1 _ 4,4,
Tk— 1 é

in other words g=1.

If, however, «@ and 4 are also functions of the temperature, we
have generally according to (4) of § 3, taking the values of 0,+46,,
etc. into account, and disregarding all the powers of im—1 higher
than the second :

! 1 " U 1 " 2
&o = 14 &)(m—1) + ae vt» 28-T7(m—)) -+- et (m—1)?* | 4-

1 1 i
ae |) a CGE = eto, <a-t(m— lL). . Sate
T 24 U t + 6 it ( ) =f 120 4 € ;

or as t? = 1—m = —(m—1):

i 1
&. = 1 + &;(m—1) + |= Evin (i — lee A mt | -

i 1 nr 29! 2 1 wr 2 2 1 my o
+ a 3a? B' (m-1)? — ale 22, 0" (m=1)*.. | + 120° 4a‘ (m-1)?.

From this follows:

dé, ' " ! "
=e; + | 26", 8) (L—m) — e'2 (L—m) | +
dm ie
l me 2 y 1 wr ° I reve
dL | 5 é'3a° p'(1—m) 4 3? ood aa = 60° "4 a4 (l—m),
1. e.

dé, ; " " l " 2a) 1 " 1 '
— == ¢', — (l—m) & p—2E ys, -} hy ya Pee ve a? tara ease

dm 5

t

a) u" ! 1 mt U :
In this — 2 &",, 6 + ae yas =0 according to the formula (1) tor

« derived above, so that we keep:

( 1098 )

dé. ; 1 rr 1 5 " ] ues
SS SS th Cees é Lt SS Ss a? é€ .
dm ; ( 3 e 20

Further according ito formula (2) we have:

l Pei! 1 mr ! 1 "tr
SS hh SS € 3 p — E yt,
20 2 2

so that we get:

dE, ! " | 2 " ! a]
— = Ey — (rn) | Wea — a? (Fe 8) Bel Galil
dm 6 Me

or as @ "5s = 6.e"., according to (1), also
,

dé. ' " HAS) 1 my !
== €,— (1 —m)| ©» — fe’, — — a? "p22, | = &', — wo (1—m), 5 (@)
dm 6

(08
in which «&; =| ) ; | with the ideal equation of state, where
kr.

Om
(see above) &"p = 0, &".,, = — 6, #"», = 18, w becomes =
18 : 1 108 3
== () = (=—6) —— .4, 18 SS = — = 19 = 9 = |.
5 6 5 5
So Ff ; m dé, dé, j= find
9o tor — <= — se we tnd proper iy
Sk € dm / py. dm a!
i

)
r

The value of this iss= —=4 for the ideal equation of

3 — a
state, and becomes = 7 for all ordinary normal substances.

As m= 1— (1—m) and «=1—+' (1—m), we now get for gy:

1 — (1-—m)

ae €; —w(l—m)}|—1

1 -— &', (1—m) ee 1 — #; (l—m)
S- —— ~ x ———
: a 1— (a*—28) (1—my'

seeing thatd,d, =[1 +a 1—m + B11 —~m)| [1 -a1—m+
+ ¢(1—m)] = 1 — (a?—28) (14 — m).
After some reduction this becomes:

ey — w (1—m) —1 1
¢=- X 9
Te) 1 — (a* — 28) (l—m)
or
o
] — ——— (1—m)
€1 —l
0S =1+4A(1—m). : (4)

1 — (a? — 28) (1— -m)

As now 4=0 with the ideal equation of state, ie. with that in
which @ and 4 are no functions of 7 (or a only depends linearly
on 7), in this limiting case must hold ;

( 1099 )

o a
——_ —= a — 26.
& i—1
: ; dé, . es
But as w is evidently = - = fy. we may also write for this:
: dm }).; ‘
idk
Ue <5
== = & — 28 ;
Sk-—1

which relation was derived in my preceding communication (These
Proce. XIV, p. 779). But in all other cases 4 is not equal to 0,
and we have:

Gre (Ge = 26\n ee = 2 Te stg (5)

From (4) we see also that » cannot b=1+'1—m — ¥%,
(1 — im), i.e. of the order / 1 — m near 77%., but must be of the order
1—m. I poimted this already out in my preceding communication
(loc. cit. p. 778, footnote). So though the empirical formula for ¢
drawn up by v. pb. Waats very well renders the values following
from Youne’s tables — theoretically if cannot be upheld.

5. After the above derivations we may proceed to determine the
values of some differential quotients for a normal substance as e.g.
Fluorbenzene. From Youne’s tables (Dublin Soc. June 1910), the
following values of m, «, d,, d,, '/,(d,-+.,), ‘/,(d,—d,) and ¢
have been calculated. (See p. 1100).

For 7). has been found 286°,55; for pe YounG gives 33912 mm.
of mercury; for d, the value 0,5541 has been assumed. The values
of # are those which can be calculated from the vapour pressure
formula

_l—m
— loy €¢ — tI > —=
m
ie nee &€ dé, : ,
The values of f—=— — have been calculated as follows. From
m dm :
the above tormula follows:
1 de, F l—indF
edm m? | m dm’
so that we get:
mde, F dF
— = (1 — m) :
edm m dm

A minimum (/'= 6,67) is observed in the values of / at m=0,77.
If we had continued the table up to m= 0,45, F would already
have increased again to 7,11. The value of ¢ at first rapidly in-

( 1100 )

ee Se

m é dy dp "p(y + d)l"p (di —ay)| F |f= at) ¢

0.6309 0.01902) 2.682 0.008144 1.345 1.337 |6.773 | 10.80 1.41

0.6488 0.02604 2.645 0.01086 1.328 1.317 6.740 10.44 1.41
0.6667 0.03471 2.607 0.01422 1.311 1.296 |6.723 10.11 1.41
0.6845 0.04547 2.569 0.01844 1.294 1.275 |6.706 9.822 1.40
0.7024 | 0.05865) 2.529 | 0.02357 1.276 1.253 6.694 9.547 1.39
0.7203 0.07460 2.488 0.02974 1.259 1.229 6.685 9.293 1.38
0.7381 | 0.09354) 2.447 0.03716 1.242 1.205 6.678 9.053 1.37
0.7560 | 0.1159 2.406 0.04600 1.226 1.180 6.678 8.837 1.35
0.7739 0.1424 | 2.362 0.05625 1.209 1.153 6.672*| 8.617 1.35
0.7917 | 0.1722 2.317 | 0.06814 1.193 1.124 6.685 8.425 1.34
0.8096 | 0.2066 2.270 0.08221 1.176 1.094 6.705 8.270 1.33
0.8275 | 0.2470 | 2.219 | 0.09873 1.159 1.060 6.708 8.095 1.32
0.8453 | 0.2919 2.166 | 0.1182 1.142 1.024 6.728 71.937 1.30
0.8632 | 0.3426 , 2.112 | 0.1403 1.126 0.986 6.759 7.804 1.30
0.8811 | 0.3996 2.052 | 0.1668 1.109 0.943 6.797 7.690 1.29
0.8989 0.4637 1.987 0.1987 1.093 0.894 6.833 7.579 1.28
0.9168 |20.5355 | 1.917 | 0.2373 1.077 0.840 6.882 7.487 1.26
0.9347 0.6165 1.837 0.2847 1.061 0.776 6.921 7.388 1.24
0.9525 | 0.7065 | 1.740 | 0.3463 1.043 0.697 6.972 7.305 1.22
0.9704 | 0.8069 1.621 0.4335 | 1.027 0.594 7.036 7.250 1.18
0.9883 0.9205 1.450 0.5744 1.012 0.438 6.98% 7.071 1.11
1.0000 1.0000 1.000 1.0000 1.000 0.000 — | — 1.00

creases from m1, but then more slowly, and it seems to approach
asymptotically to about 1,5. Its course is very well represented by
VAN ppR WAAts’s formula, but as we already stated, near 7),q—1

is not of the order “1—m, but of the order 4 — m.

renders the course, may appear from the following table, p. 1101,
Whereas the agreement between the calculated and the found
values of g--1 at m=0,70 and 0,86 is perfect, the discrepancies at
m=0,97 and 0,99 amount to about 10°/,.
From the values of mm and & occurring in the table, we can now

( UhO1Ey)

m e | Found
0 | —0.50 =1.50 ==

0.7024 1 + 0.543 — 0.149 = 1.394 1.39
0.8632 1+ 0.370 — 0.068 = 1.302 1.30
0.9704 1+ 0.172 —0.015 = 1.157 1.18
0.9883 1+ 0.108 — 0.006 = 1.102 1.11

easily calculate, making use of the six values of m from 0,8632 to
0,9525 (the last ineluded) ;

&, = 1 — 7,065 (1 — m) + 19,8 (1 — m)? — 24,0 (1 — m)*,
so that we have:

; ' ! = VANE " DME, ;
(PSS == (005 1 Oe ==(1 |} =O
‘ oN dm? J ey.

7

a: ee ee : ;
So 6,6 is found for = | win the ideal equation of state this
Higa Z

E 9.6
Valiess) = ——— —o-2) |.
x ‘
Let us now determine the values of the coefficients « and 3 in
the expansions into series for d, and d,.
With */, d,+d,) = 8 (1—m) + d(1—m)? we calculate from the

table for m = 0,8632 etc. the following values :

(2) Nc} J = 0,055.
And from */, (d, — d,):“ =a -+ 1-—m y (1 — m) + «(1 — m)? we
can calculate :
— 3,9 a Mid)533 4 oe
Now the value of Bp’ = «a? — B (p’ is the coefficient of 1 —m in

n,=1+ah1—m-+ p’ (Ul —m)+..., see above) becomes:
B = 15,2—0,9 = 14,3;
which for the ideal equation of state = 4— 0,4 = 3,6, so exactly
the fourth part.
And for « — 23 we find 15,2—1,8='13,4. | With the ideal eqna-
tion of state 4— 2 * 0,4 = 3,2 is found for the value of a? — 26).
For 2 we find now according to (5):
24= 13,4 — 6,6 = 6,8,
so that according to (4) close to 77:
g = 1+ 6,8 (1m).

( 1102 )

So for m= 0,9883 ¢ would be =1-+ 6,8 & 0,0117 = 1,08, and
for m=0,9704 ¢ would be =1+ 6,8 x 0,0296 = 1,20 (found 1,11
1,18). So A=6,8 is possibly still somewhat too low, but it is also
possible — and this I think more likely — that the values of d,
and d,, found experimentally near the critical point, are not quite
accurate, in consequence of which gy is found too high. So most
likely the value of the product d,d@, is too low, on account of the
density of the liquid phase being measured too small in consequence
of imperfect nomogeneity (presence of vapour bubbles), or because
the thickness of the capillary layer, which is of measurable dimensions
at the critical point, has not been taken into account, in which layer
the density is of course smaller than in the homogeneous liquid phase.

In consequence of this the locus ‘/, (7, + d,)—=f(m) deviates
seemingly too much to the liquid side quite near the critical point,
and accordingly the abrupt deflection of this locus close to 7, found
by Youne, Carposo and others, would disappear, when the density
of the liquid phase could be measured more accurately.

: : Ore
6. The value of the differentialquotients «',, = = ) and
kr

08s
‘ \On20m
near the ertical temperature. Those for C,H, not being at my
disposal, I could only make use of Dorsman’s data (Thesis for the
Doctorate) for CO,. For 33°41 he finds e.g. »= 75,30, 76,10,
S01, 449 and 343. From this we can calculate

2 ) may be calculated from data of isotherms quite
kr

oie :
WTO, YES > 10 =

dp .
that f for ¢ = 488 (the volume on the isotherm of 33°,1 that agrees
av

with the critical volume) has the value — 0,01245. From this the

438 aeielih (0s ¥
value — < —- 0,01245 = —- 0,0747 follows for ( } (the critical
ine On 33,1
pressure is viz. = 73).

So we have (31°,1 is the critical temperature) ;

Og Aoks — 3
—0 ; = — 0,0747 (both for v= 2).
On) 314 On / 33,1

Hence (the absolute temperature at t= 382°,1 is 805,2)
O*& 0,0747 t Wd
se =— 6 ONS SS — 4.
er Ondm J p> 2

We saw above that the ideal equation of state gives for this —6.
From the same data the value 0,00007432 can be derived for

( 1108

d*p , abs :
at v= 438 and 33°. [The data can viz. be rendered by the

2

dv*
formula p = 76,10 — 0,0)163 (v —— 449) + + 0,00003716 (v — 449),

2
7 2

€ )
from which easily ; and z . for v = 438 can be derived].
ap QAv-

QQ

Okt: 458
So for an we find ” $< 0,0000743: ==0,1953. Hence we have:
(ie

On-

078 0° + 4
—. ==) # : =(0,1953 (both for » = v,),
On? /3),1 On* 33)

and from this follows :

n r Oe 0,1953 :
Ett = — ae 3.0552. —=29°8.
On?0m / hey 2

For the ideal equation of state we find 18 for this.

Now in virtue of considerations which will presently be explained,
we shall raise the values —11,4 and 29,8 to —-12 and 36, as
these values cannot differ much from double the values in case the
ideal equation of state is used. It follows also from the nature
of the above indicated calculation, that the found values — 11,4 and
29,8 cannot lay claim to very great accuracy

Now we ean also find the values of ¢,:; and é’,,. From (1)
follows viz. :

Gene 6X (—12 a

i — 2 = = jee er
The ideal equation of state gives about double the value, viz.— 9.
We find further from (2):
1 " a rout of €
Te oi Ol 4 — Ble" = 36—14,3 (— 4,7) = 108,2,
hence

Cy sO Deeley sl Oe

for which with the ideal equation of state also about double the
value is found, viz. 126.

Finally we can calculate e"» = =(5 =) from &” = w = 39,6, in
Om? /),

which @ is represented according to (3) by
w= &'p—p't' op / Fore.
So we find:
en = 89,6 + 14,3 x (—12) + 1/, X 15,2 X 36,
or
é"2 = 39,6 — 171,6 + 91,2 = — 40,8

( 41104 )

The value of this differentialquotient is = O with the ideal equation
of state. The great negative value of ¢’» for real substances points
Bey: : da
as we shall presently see — to a great positive value of Fa
7 at

We have now the following survey (all this at 7%).

| LE
2 2 | gi—pt_ ele’ —e— | et, let 7 = wy) er Pe [Fe g2—9 8 5
z ei a ie ; Tk Sate | J x6 ; | rt ws CoS a8 |: /.

like
3.9.0.9 143 dl —4I 39.6 —12| 36 |—4.7| 68 |134 | 6.6 |6.8
[2 |04 3.6 4 0 9.6 —=16 18) }=9 91126) |) 3!2 1 3:24 Toy

The lower series of values refers to the ideal equation of state.
We may add the following remarks to what precedes. According
to (5) we may write for 2:
ee (a? —28) (fua—1) — fx
Ware

The numerator of this is = (a@* —28) (f,—1) — (€"e2—p'e"n¢-—?/ 7 8'"'02),

as) (=) ——@. But as jr—er, and sl——«—-s. we may also
write for this:

— ee + at [ (1) + eon + 1/4 804 | — B [2 (€—1) + eet |

Now with the ideal equation of state 40 (see above); and this

is what we expected, for then the above form becomes:
0 + a7 (8-—613).— B (6—6),

Both e’» and the coefficients of @ and 3 are then, namely, = 0.

jut with the real equation of state the value of this form is :

41 + a? (6—1246) — B(12—12),

so that the coefficients of @ and 3 would be again —0O. It is not
difficult to find a cause for this.

ob ; 0b
Te (he ave, _= 6, is verysmall( just as— = 6'y is slight}, we
o7 % : Ov %
y 0p f ; ; Rel (|,
may write for —, following from p = —— —-, i.e.
: oT P= ty) Gs

so that

(1105)

0*p 2A 0*p 6A
overs = Ty? ~ duo VY Toe
: ; aon da ,
in’ which A=a—Ta', and a represents Rr Hence we have at 7):
a

le ) e& ) A;
a == —} =1+ =
Om / fey p OL Jz, PRU ke

and so the well known relation (only now we have A, instead of «,
A;

ee ara

PLY Ie

But at 7). we have also, according to what we found just now.

ee aN oe 2Ag Thre _ oH eae, :
aS eae Tyo, Die Pkg eae
i 0" 6A, Tyv7z 6A; —
= — = Dot VBE = PRO k a oa

So the coefficient of «@ in the numerator of the above expression
for 2 passes (with small value of 6',) really into
(Cie ieee Croll) MEG) e— 0,
the coefficient of 3 then also passing into
2 (e', —1) — 2 (', —1) = 0

That the quantities &)—J, 6", and ee, have double the value of
| t 2

those for the ideal equation of state, is owing to this that where the

critical pressure is always about '/,, ag: be’, &:— 1 with vg = rb,
passes into
, Ap 27
é,—1= -
A): a

[ine thse Ale ia —— le CL alee) se lis nOwenalsOn ele ay Iseesmieall
compared with a,, unity may be written for Ap,:ay by approxi-

mation; so that then «,— 1 would become — 27:7° for the real
equation of state with r= 2,114 = 27:45—6, and = 27:9=>3
for the ideal equation of state. And as really the value 6 is found
for «, —1 = f, — 1, a’, (and also b';) must really be exceedingly small.

In any case (for small 6’, &")¢ = —2(e— 1) by high approxima-
tion, and hence = — 12, which is the reason that above we raised
the value — 11,4 found for «",, from experimental data to — 12.

Reversely the slight difference between the two values justifies the
supposition that 6% is really very small. But as then too ¢”,2,=
= 6 (*,— 1) = 36, we have found a sufficient ground in this to raise
the value 29,8, i.e. 380, which was calculated from only few expe-
rimental data, to 36,
73
Proceedings Royal Acad. Amsterdam. Vol. XIV.

( 1106 )

The numerator of the expression 4 now passing into — ep, we
get simply :
él
A= ees Teowcwes Gxcw temic ec. > 465)*))
from which then 2—=40,8:6=6,8 follows, as above.

‘ , : R Ce Op
8. As for small b', we may write —— — — for

: (see above)
v—bh Vv OT j

0°» a
— becomes == — — (if namely 6"; is also small), henee
oT? v
i Ore a", Tie
& — = = —— = —="5
Om? J pe vk Pk
So we get for A with f,—1 = e;—] = Ax: pyv, (see above):

A=- —.~ ‘
ao —T): Ab
when we substitute its value for A,. If we put

UG Oe =a phe, SGP RO GR Cleo
we get:

because a’, must be exceedingly small (see above). As now the value
6,8 was found for A, this comes to this that @; is almost 7, so
yreat positive (i,e. Tg? x (a'r: ay).

Summarizing everything that we investigated in the above and in
previous papers, we come to fhzs conclusion that the deviations from
the ideal equation of state chiefly find their explanation, besides in
the association of the molecules, in the following circumstances :

9

OD
1. That with small value of — the valne of ass is yreat. In con-
Ov v

sequence of this vy, becomes = 2,14, instead of v;, = 3b, for the critical
volume.
Ob 0%) da dat
—, —, and — the value of —
ot OF? dt dt
is great. This aceounts for the great increase of the characteristic
function gy (which has the value 1 at 7%) in the neighbourhood of 7°.
In conclusion we poimt out that for the determination of the values

wn

2. That with small value of

" wn

of eo. and é', the knowledge of the values of 6", and b

i ous
required, and so without the complete knowledge of the quantity 4
as function of » we cannot possibly predict anything regarding the
ow and eo. That these values are about half the ideal

v

mr

values of «
values from this would follow among others that 026", would be

not far from 1. Clarens, March 1912.

( 1107 )

Botany. — “Structure of the starch-qraim’. By Prof. Dr. M. W,
BELIERINCK.

If one gram of potato-starch is boiled with LOO eM? of distilled water
this is just sufficient to bring the grains to their maximum of swell-
ing and make the starch take up about 70°/, of the water so that
if remains suspended and cannot precipitate, as the swollen grains
touch one another. Each grain swells thereby to a somewhat irre-

0

%y

gular globule whose diameter is about 3.5 times that before the
ebullition. Whether the boiling lasts shorter or longer is of no con-
sequence. If more water is used for the boiling no further swelling
takes place; when left to sedimentation the liquid above the starch
colours but feebly blue with iodine.

When a microscopic preparation is made, containing but few
starch-grains, and a strong tannin solution flows sideways under
the cover-glass, the following is seen (compare the figure).

EXPLANATION OF THE FIGURE.
Magnified 200 times.

Potato-starch after projonged boiling and treatment with a tannin solution The
erains are by the boiling changed into little vesicles with dissolved contents. The
wall of the vesicles consists of amylocellulose (amylopectose), the contents of gra-
nulose (amylose), the latter being precipitated by the tannin.

At the moment the tannin comes into contact with them, the grains,
which at first sight seem homogeneous, show a very distinct mem-
brane through which the tannin easily diffuses to the inside where
it directly forms a characteristic precipitate. When using a more

73*

( 1108 )

(ilnte solution’) this precipitate consists of litthe droplets in very
lively Brownian movement and with a more concentrated tannin
solution, of solid particles, adhering together and filling up the
whole inner space of the vesicle. This experiment is so simple and
convincing that it cannot be doubted for a moment but the boiled
starch-egrain consists of a solid, sac-shaped, quite closed wall, con-
taining a liquid.

Ilow it is possible that this fact seems unknown | caunot under-
stand, but I have nowhere found it mentioned in the extensive lite-
rature about this subject.

The liquid in the vesicle is a granulose solution, or as is said

c

it the present day, an amylose solution, containing 0.6 gram of the
lev. origipally used, which diffuses but with difficultly through the walls
info the surrounding water. If, however, the boiled starch is rubbed
fine with sand the delicate sacs burst and the granulose solution
diffuses in the water, which then becomes intensely blue with iodine.

That the wall consists of a very soft substance may be observed
as well by its great variability of shape at pressure, as by the ease
with which it is distended to short threads by moving the cover-glass,
to which it adheres, when touched by it. When the boiled starch-
erains are washed out during some days with water constantly
renewed, it is possible finally to obtain the vesicles without
their contents and filled with water only ; after drying they weigh
O.4 er. if one gr. of starch has been used. With iodine they colour
lighter than the granulose and somewhat violet. When preserved
they become partly soluble in water containing chloroform. By leu-
kodiastase they are easily converted into maltose and dextrine, quite
like granulose; by erythrodiastase a little less easily, but a marked
difference does not exist. *)

If the boiling is effected not in distilled but in canal water, the
starch shows a strong disposition to precipitate whereby after 24
hours a layer results of 1/, to 7/, of the whole volume if again
1°/, starch is used. If 4°/, starch or more is boiled in canal water

1) Very much diluted tannin solutions give no precipitate at all with starch- or
evanulose solutions.

) By leukodiastase 1 understand the slowly diffusing diastase secreted by the
cerms of germinated corn-grains, which on slarch-gelatin plates, when treated with
iodine, produces diffusien fields which remain uncoloured. By erythrodiastase the
more quickly diffusing diastase of the endosperm of the grain, which on the said
plates - after. treating with iodine, is vecognisible by the erythrodextrine reaction.
WusMAN (De diastase beschouwd als mengsel van maltase en dextriase, Amster-
dam, 1889) called leukodiastase ‘“dextrinase” and erythrodiastase ‘‘maltase”’, but

these lerms-are not well chosen.

( 1109)

no sedimentation at all occurs, the swollen grains again touching one
another. The precipitation may be caused in the starch boiled with
distilled water by addition of dilute solutions of salts, acids, or alkalies.
At 0,001 °/, a slight contraction of the vesicles is already. visible
and it reaches its maximum at about 0,1 °/,.7) With still stronger
concentrations an accrease in thickness of the precipitated layer is
observed, probably because the vesicles then lose somewhat of their
weight in the heavier liquid. *) As non-electrolytes such as cane sugar,
urea, aethylaleohol, and methylalcohol, even in 1°/, solutions, cause
no sedimentation at all, it is evident that we have to deal here
with an ionreaction, which perhaps will prove to be very well apt
for exact measure. Aethylaleohol ef 5°/, and methylaleohol
of 6°/,, however, distinctly bring the vesicles to precipitation, but
then the superstanding liquid becomes rather turbid, the dissolved
eranulose precipitating also. Above 10°/, methylalcohol the precipi-
lation is complete.

If the starch is boiled in dilute salt solutions, the volume of the
sediment after standing is as large as if the salt had been added
later to the starch boiled in distilled water.

When the sedimentation is caused by ammonium sulphate it is
easy to show that as well the ammonium as the sulphuric ion are
present in stronger concentration in the precipitate than in the liquid
above it.

The foregoing is quite in accordance with the results of an in-
vestigation of Mme Z. Gatix-Grozewska.*) By extraction of starch
with dilute caustic soda she obtained a soluble substance, amylose,
and .an insoluble rest of amylopectose in about the same proportion
as the above (0.6 and 0.4). Her view, however, of the localisation of
the two constituents is another than that which follows from my
observations.

She says that amylopectose forms little scales or sacs, evidently
corresponding with the layers of the stareh-grain, so that this con-
stituent would occur as well within as outside the grain, whilst,
according to my experience, the whole inner portion dissolves in
boiling water and is homogeneous, the outerwall only being insoluble
and thus materially different.

1) No great difference in the thickness of the precip:tated layer (ca. 4m. from
a liquid layer of 17 cM.) was perceptible after 24 hours at room temperature
when using 0,1 "/) K,HPO,, KCl, Na Cl, (NH,), SO, CaCl,, Al, Cls, K NOs,
HCl, or Naz COs.

2) More dilute solutions of sugar and urea do cause some sedimentation for a
not yet explained reason. Stronger solutions do the same perhaps because of conta-
mination by electrolytes.

3) Comptes Rendus T. 146 p. 540, 1908.

( 1110 )

The words “amylose” and “amylopectose” have first been used
by L. Maquenne and E. Rovux,’) but they consider both these sub-
stances as perfectly mixed and say: “L’empoix d’amidon est constitué
pur une solution parfaite @amylose, épaissie par lamylopectose”’
(l.-G.- pag.. 21:9).

That Magumynn, even after the communication of Mme Gatin-
Gruzewska, had by no means the view here given follows from the
observations which he adds to the said communication. 7)

The change of the terms ‘“amylocellulose” and ‘“granulose’, so
long existing in the literature, into “amylopectose” and “amylose”
by MAQuENNE, seems not necessary.

The difference between the walls and the contents of the starch-
grain probably reposes on incrustation. We have namely to think
the surface of the grain as consisting of the albuminous matter of
the amyloplast mixed with the secreted eranulose by which the thus
formed mixture has become insoluble in boiling water. This would
be in accordance with the general observation, that incrusting sub-
stances highly alter the solubility of bodies susceptible of imbibition,
of which the lignified and = suberified cell-walls of plant cells and
tanned leather are good examples. This conception would lead to the
conclusion that the amyloplast does originally incrust the membrane
of the starch-grain, but later draws back from it, wherewith the
change of amylocellulose (amylopectose) into granulose (amylose)
would correspond.

If this view is right the quantity of albuminous matter, which
occurs in the membrane, must be very small, for in the rate of
nitrogen no distinct difference between amylocellulose (amylopectose)
and starch could be found, in both cases it being about 5 milligrams
per 100 grams of dry matter.

MaQurnNE says that his amylopectose is not coloured by
iodine; the amylocellulose (amylopectose) obtained from starch after
extraction of the granulose (amylose) in the manner here described,
proves to colour violet blue with it. It is not impossible that in this
case, too, a kind of incrustation should oceur, namely of an adsorption
of granulose in the amylocellulose wall, which then itself would in
pure condition remain unecoloured by iodine.

All other species of starch examined by me behave in the same
Way as potato-starch.,

1) Recherches sur l’amidon et la saccharification diastasique. Ann. d. Chimie et
de Physique, Se Série, T. 9, pag. 179, 1906.

*) Observation sur la Note de Mme Gariy-Gruzewska. Comptes Rendus T, 106
p. 542, 1908.

( dis)

Physics. — “On the liw of molecular attraction for electrical
double points”. By Prof. D. J. vax per Waars Jr. (Communi-

cated by Prof. J. D. van bER Waals).

Prof. Reincanum was so kind as to point out to me two ervors
which occur in my communication under the above title *).
In the first place the fornfula for € on page 154 I. c. must be:

_ mM, —________
€=—=—_V4 cos? 9 4+ sin® 0
r

il :
The factor —, oceurring l.c. in this formula and in all formulae
vo

derived from it, has been inserted erroneously.

But moreover and this is a more serious error — the chance

that the angles y and @ lie between definite limits, must be repre-
sented by:
: ni? vs VB eos? +1
CS ri sin gdy sin Vdd e mt

It is not allowed to omit the constant C as I did I.c. This constant
can of course be determined by means of the consideration, that the
sum of all chances is equal to unity. So we find:

CS

ad

i sin gd ¢ sin Odd oa

00

After a deduction analogous to that which was performed I.c. we
easily find :

m
where ¢ —.
Pl

So we get for LH:

1) These proceedings, XI p. 132 and 315.

ELE

i : 2 : 2m?
lor =—(0) i.e. c= this becomes — =
Fe
9 4
. } 2m
For =o i.e. c=O0 it becomes F= -
nt

If we want to find the mean foree in the direction 7, we must
differentiate the value of the potential energy with respect to—r
before performing the integrations. This comes to multiplying it by

>

This factor remains unaltered by the integrations; so we find

é : Om? m*
for the mean force in the two cases respectively — and — 2 TE
My conclusion Le., that the mean foree would vary more rapidly
with the distance than */,7, proves not to be correct: for ¢t—o it
varies as '/,7, at lower temperatures it varies less rapidly. These con-
clusions however only hold for densities, which are so small, that
interaction of more than two molecules at the same time need not
be faken into consideration. If we take this circumstance into con-
sideration we shall undoubtedly again find a more rapid decrease of
the force with the distance.

Biochemistry. -~. “Action of subsiances readily soluble in water,
but not soluble in oil, on the growth of the penicillium
ylaucum®?. By Prof. J. Bousexen and Mr. H. Warrrman. (Com-
municated by Prof. Brtuerincr).

le
The influence of the hydrogen-wons.

In our previous communications ') we have made mention of two
kinds of retarding substances. The first kind to which belong salicylic
acid and butyric acid, penetrates on account of its great solubility in
oil, coupled with a sufficient solubility in water, too rapidly into the
organism and causes it to be overloaded.

The second kind to which belongs formie acid is much more
readily soluble in water than in oil, but ean only be used up very
slowly so that an overloading is still possible.

As, both with salieylic acid and formic acid an injurious action
of the hydrogen-ions was not exlnded, owing to their great dissocia-
tion constants, it had to be determined by a special research at what
concentration the hydrogen-ions beeame a hindrance.

1) Proc. of Dec. 30 1911 p. 608 and Febr. 24, 1912 p. £28,

(1113 )

It may be observed here that with oxalic acid, malonic acid, tartaric
acid and lactic acid we had met with retardation phenomena which,
in our opinion, ought to be attributed to the action of hydrogen-ions.

These substances, readily soluble in water, but not at all soluble
in oil, exhibited, at definite concentrations, retardations which, from
their nature, were quite different from those observed with substances
soluble in oil.

These phenomena could be prevented by neutralisation ; on adding
an acid harmless in itself (gentisic acid) to a solution of tartaric acid
below the harmful concentration they could be revived.

3y calculation from the dissociation constants of the acids inves-
tigated and comparison with the action of a sulphuric acid solution
of definite concentration it could be demonstrated that these pheno-
mena were indeed connected with a definite quantity of hydrogen-
ions, and that this corresponded for the penicillium glaucum with
a concentration of about 1 * 10—-; in the case of the aspergillus
niger this concentration was higher, namely about 4.55 10-> in
grm. equiv. All this will be seen from a survey of the experiments.
(Table p. 1114.)

From this survey it is quite evident that the retarding action
observed with oxalic acid and tartaric acid must be attributed to a
definite concentration of the hydrogen-ions. To begin with, ammo-
nium oxalate is assimilated even af higher concentrations; the same
is the case with acid and with normal potassium tartrate II, 1V, V).

Further, a solution of ammonium oxalate does not affect the
growth of the penzcillium in p-oxybenzoie acid. (IX).

On the other hand, oxalic acid does retard the development of
the organism in p-oxybenzoic acid and even in concentrations lower
than usual (Compare VIII with I, for the hydrogen-ions of the
p-oxybenzoie acid, although themselves harmless, join those of the
oxalic acid so that the harmful concentration is attained sooner.

The same happens on adding together tartaric acid and gentisic
acid, both being below the injurious concentration; a harmful con-
centration is then reached (V1).

If, by making use of Osrwatn’s dissociation-constants of the acids
(for oxalic acid we have used the data of EnkLAAr (Chem. Weekbl.
8, 381 (1911)), we calculate from our observations the harmful
concentration of the hydrogen-ions we obtain:
d-Tartaric acid; K=0.097; harmful concentration = 500 me.

per 50 c.e.

From this about 0.8 > 10—-° m. gram equivalent.

Malonic acid; K=0A58; harmful concentration observed — 300

(4114 )

t= temperature of the room; 50 ccm. of a solution with usual inorganic nutriment.

Name of the | Conc. after inoculation observed after

N’.| compound. jinmg. 2|3)14] 5 | 6 |) 9 Remarks
a _idaysdaysjdays| days | days | days | ___
ae 9-2) 24 i a at Generally the deve-
17.5 | 219 ate lopment is slight.
97 ‘ : aie =i After some time a de-
ae) |= a ai cided yellow colour is
AE : A ; noticed in the concen-
| ene ale. a =. ie ar trations where a de-
97.5 ue 49 velopment is still
tot ee M noticed.
497 = — / After 25 days, no
| 1498 == _ development.
=" ie oo
a SEEDERS + ‘sii
Ammonium 30 +? +? ate Slight development
Il : 9 the strongest at the
oxalate. 102 > + ) + a | t teatin
300022 |e a6 argest concentration.
10 + ++ ao +--+ The retarding action,
51 + ++ ++ +++ therefore, commences
soos) LOL |) + 4+ ++ ++-+ above 300 mg.; with
Ill d. Tartaric acid 30! a a ar ne 500 mg. Mae very
eng is | pronounced in the
LOOT te 253 ee? +? | ae | first 5 days.
| 10 + ++ ++ |
cee st Rg 00 ia Ce ee ene Not the slightest
- | 500} t+) | [4 Ne
- \ retardation
. 10
y Potassium hy- 99 ar slate ilghe noticed.
drogen tartrate 560) |e ae Sista
~ \@.Tartar.acidto| “|| a eee eee ov Sarr ae Bisa)
which hasbeen 300 — — — — | 100mg. of gentisicy)
VI} added each | 500 | — | — — _ | acid added to little |
‘time 100mg. of 1001 — — = ob OMe
| gentisic acid. | : ve Meare 2
5 fs +
25 |+? -t
50 + te
VII Malonic acid th a civ
200 | + t+). ..... Maximum
300) | = ab
400 | — ate
1 ae ee | | aera
Oxalic acid to ; |
which has been, oe aot | Bi |
vip ,.added each gy, Bahl
time 150 mg. of} ¢) | _ || ee
p-oxybenzoic | oq | __
acid. | 150 =
| = | a teaet
Ammonium Te |
| oxalate to 40 | + | steels
IX which has been) 80 | + ++
added each 150 - ++
time 150 mg.of 300 9 + feat

p-oxybenz. acid.

( 1115 )

mg. per 50 cc. from which is calculated 1 >< 10->m. gram

equivalent.

Ovalic acid; the harmful concentration lies at 50 mg. per 50 ©¢.c.;
this agrees with a concentration of 1,2 > 10—° hydrogen-ions.
From this we may conclude that the retarding action becomes

very pronounced when the concentration of the hydrogen-ions

amounts to about 1 x 10~°; it is independent of the compound used.

Naturally, the observations only admit of an approximate estima-
tion, so in the calculation we could assume that the dibasic acids
employed had only resolved one hydrogen-ion.

Yet we have been able to use it for demonstrating that on adding
gentisic acid to tartaric acid the retarding action must start at a
concentration previously determined.

300 mg. of tartaric acid per 50 ¢.c. represent a concentration of
0,6 x 10—° gram equivalent of hydrogen-ions.

100 mg. of gentisie acid (A —0.108) represent fully 0.3 % 10->
hydrogen-ions.

Separately, both these substances are quite harmless (Proc. Dec.
1911, p. 615); when mixed they totally prevent the development
of the penicillium (V1).

Finally, we give a survey of the action of increasing quantities
of sulphuric acid added to 150 mg. of p-oxybenzoie acid, from
which it appears again that the harmful concentration lies between
Sed Om oranda saallOQsoe

| Observed after 72 days.

| Quantity of H»SO, H

| in mg. per 50 cc. in gram eq. 9 4 6 = eae Remarks. |
0 G08 seta Wot ted
2 1.8X10-6) + ++ 44+ | strane
5 310-6) + | ++ | +44 growth
8 b>< 1058) | 4-4] Yellow coloration
29 1.3<10-5| =| — oe Nees
47 19> 10—2) ee ey me ts
95 3:05< 16-51) — ey eee |
Added |
mM oriso me. | 1x09 | +] +4] ++ | ong

p-oxybenzoic acid | -|
in 50 cc. |

( 1116)

For p-oxybenzoic acid A = 0.0029 from which is caleulated, for
150 mg. per 50 ¢.c., a hydrogen-ion concentration of about 9 >< 10-7
(Gn round numbers 1 XX JO—*).

If we compare the action of the hydrogen-ions with that of sub-
stances like salicylic acid, the great difference is at once evident.

The retardation sets in fairly suddenly above a certain concentra-
tion and the development still taking place in unfavourable conditions
is readily distinguished macroscopically from the normal growth. It
looks as if the mycelium has been shrivelled and after some time
it turns orange-yellow. As this coloring matter diffases in the liquid
this becomes in the long run bright yellow.

If we ask wherein consists the harmful action of the hydrogen
ions we cannot answer this without referring to the protoplasmic
wall.

In our previous communication (Proc. Febr. 24, 1912, p. 950) we
have stated that this could not be merely an oily layer:

If, however, we look upon this wall as a very concentrated col-
loidal solutidn of a lJecithine-like substance in) which albuminous
matters are also present the rapid entering of the substances readily
soluble in fat or lecithine becomes, on the one hand, intelligible
while on the other hand, we can understand why the substances
readily soluble in water can also penetrate. *)

All substances that exert a decided action on the condition of the
wall will disturb its regular functions and thus cause a retardation.
Now it has been shown from a number of experiments that hydrogen-
ions are capable of coagulating colloidal solutions; for instance, this
is the case with lecithine solutions.

(J. Frimscamipr, Biochemische Zeitsch. 88, p. 344 (1912). Also
compare the researches of Micnarnis and his pupils, Bioch. Zeits.
19, 24, 27, 28, 29 and 380, particularly Micharnis and Takanasut
29, 439 and 380, 145).

Here, it was found that the maximum concentration for the coa-
culation of colloidal lecithine solutions was situated between 1 x 10-2
and 1% 10-4 and tbat if, on addition of solution of albumen,
was shifted towards the weaker acid concentrations.

It is now obvious to assume that the retarding action of the
hydrogen-ions exerted on the development of the penici//an glaucum,
1) The velocity with which the substances soluble in water can penetrate a
similar wall will depend on all kinds of circumstances not yet foreseen; in any
case it must be assumed to be much smaller than the velocity with which the
substances soluble in fat are absorbed, as in the opposite case the wall could

not be semi-permeable for substances like sugars, salt solutions ete.

( M474

will be connected with a coagulation phenomenon of the colloidal
plasmic wall.

The fact that the organism is here more sensitive than a com-
mercial preparation of lecithine will not be an obstacle to this
assumption. That this sensitiveness is also much dependent on the
special organism is evident from the fact, that the harmful concen-
tration of the H-ions with the Aspergillus niger lies at 4.5 x 10~°
therefore considerably higher than with the peniedlium (the tem-
perature being 32°.)

The last concentration 1 * 10 agrees with that stated by
Micnarnis and Takanasnr for the haemolysis of fresh blood corpuscles
in an isotonic medium and which is also attributed to the coagula-
tion of a stromatic substance.

The coagulation of these albumens is, however, again dependent
on their electric charge; if this is neutralised by taking up hydrogen
ions, then as M. and T. assume, they can no longer retain the hae-
moglobin and haemolysis sets in.

With the organisms investigated by us it can be very well possible
that the negative charge of the plasmic colloids (and here we need
not think of the wall only) protects them against the hydrogen ions
so long as the concentration remains below a certain limit. If this
limit is exeeeded, in other words if the isoelectric point is reached
a coagulation will take place and consequently a disturbance of the
function and retardation of the growth.

In this respect, the diffusion of the yellow colouring matter from
the organism in the surrounding liquid made us think somewhat of
haemolysis.

SUMMARY.

It has been shown that the retarding action of some acids soluble
in oil must be attributed to the hydrogen-ions.

The harmful concentration of the H-ions for the penied/iim glaucum
was determined at 1 % 10-5 grm. equiv. (for the aspergillis at
oe 1057):

It has been assumed that this injurious action was caused by a
coagulation of the colloidal constituents of the plasm.

In connection with researches of other investigators, it was sur-
mised that the coagulation was attended by a neutralisation of the
colloids having a negative charge by the hydrogen-ions with a
positive charge.
aie Laboratory Organic Chemistry
; Technical Uiaversity. Delft.

- Delft, March 1912.

( 1118 )

Anatomy. — “Caudal connections of the corpus mammillare’. B

.

-;
Dr. ©. T. van Vankenpurc. (Communicated by Prof. WinKLER).

Four connections of the corpus mammillare with other parts of
the brain are known: part of the fornixfibres unites it with the
ammon’s horn; the tractas Vicq p’Azyr with the nucleus anterior
thalami; the tractus Gupoen with the nucleus of the same name ;
the pedunculus corp. mamiillaris has a hitherto unknown destination.

This communication regards the two last-mentioned fibre-systems.

With regard to the origin and the extremity of either of these
there is no unanimity: whether the tractus GuDDEN originates or ends
in the nucl. tegmenti profundus; whether pedunculus corp. mam,
commences or finishes in the lateral nucleus of this ganglion, the
communications on this point disagree. A rabbit of a series of operated
animals had got an exceptional lesion. The pedunculus and tractus
GUDDEN were injured, whilst tractus Vicq@ p’Azyr and the fornix
remained unhurt. The animal was killed after half a year ; the examin-
ation of the brain that had been cut in a continuous series (coloured
after Pat's method, alternating with v. Girsoy’s)brought to light, with
regard to the mentioned tractus and nuclei, the following facts. The
knife that had entered from the dorsal side, had partly cleft a.o. the
diencephalon to the left of the middle line as far as the basis. In
this way the pedunculus corp. mammillaris was nearly sectioned, a
little distal from the lateral nucleus inammillaris ; the distoventral
direction of the seetion made it possible that the tractus GupDEN was
struck on the spot where it separates from the tractus Vicg p’ Azyr ;
only its most medial fibres had remained unhurt. The fasciculus
retroflexus (Mrynert) was entirely destroyed. Further the section had
gone through the most lateral part of the fasciculus longitudinalis
posterior, the commissura posterior and the splerium corporis callosi.
By hemorrhage the most medial ventral nueleus of the thalamus
opticus had been severely injured. More distally the wound gradually
retracted in a dorsal direction, going along the left edge of the central
substantia grisea of the aquaeductus Sylvii through the lamina com-
missuralis. The right half of thalamus and stem was completely
uninjured, so that the secondary degenerations could distinctly be
followed.

1. The examination showed that the pedunculus corporis. mam-
millaris, after its originally entirely ventral position — medially from
the pes pedunculi (pyramid tractus) — turns gradually partly medi-
dorsal. This part is placed dorsal from the lemniscus medialis arranged
in some thick Joosely cohesive fascicles. Towards the end of the

( 1119 )

diencephalon it becomes constantly more difficult to separate it from
the medial lemniscus, and apparently it ends near the cross-plane
immediately caudal from the nucleus trochlearis. It was however
impossible for me to get from my preparations a strong conviction
of this facet. On its way hither, already during its entirely basal
position healthy fibres add themselves to the degenerated bundle ;
these are not met with among the above-mentioned fascicles dorsal from
the medial Iemniscus. Presumptively they are partly originary from
the Jemniscus sensu strictiori, joining the pedune. ¢. mammillaris
(WALLENBERG) in the proximal protuberantial regions, and extending
partly towards the ganglion laterale? partly over it towards groups
of cells between fornix and tractus Vicq pb’ Azyr.

In my ease I could only follow fibres of the latter sort. The
absolute absence of large ganglion-cells, well preserved on the right,
proves that in reality the pedunculus ¢. mam. originates in the lateral
nucleus. It is an irrefutable fact that fibres situated laterally extend,
during the praepontine course of the ped. ¢. mam. from the latter
in the direction of the substantia nigra ventral from the lemniscus.
I intend to give further information about this connection in a
subsequent Communication.

2. The tractus Gudden (mammillo-tegmentalis), consisting of much
finer poorly medullated fibres had been primarily destroyed, as was
already noted, with the exception of the most medial part. The
secondary degeneration could be followed as far as the nucleus
Gudden (tegmentt profundus). The cells of this nucleus had moved
more closely together than in the healthy right side. At all events
it was not possible to discover a loss of cells of any signification.
Only a sinaller group of cells, more dorsal, situated nearly between
the parts of the fasciculus longitudinalis posterior had very considerably
diminished in number on the left side. As to the medial nucleus of
the mammillare, the left dorsal nucleus of it, with the exception of
a small part lying near the median line, had lost its ganglioncells.

It is obvious that we may conclude from this that the tractus
Gudden originates in the dorsal nucleus of the medial mammillar
ganglion; that this tractus ends in the nucleus tegmenti profundus
with the exception of its dorsal smaller part; that the fibres of that
tractus are arranged in the same way as they originate from the
mentioned dorsal mammillar nucleus, because only the medial cells
of those giving origin to the tractus Gudden, were preserved aeccord-
ing to the fact that only the medial part of the tractus mammillo-
teementalis had not been destroyed by the operation.

In my opinion it is prebable that the cells lying dorsal from the

( 4120 )

nuecl. tegm. prof. s.s. give origin to fibres, situated laterally in the
fascic. longit. posterior, having a frontal direction, as they had
primarily been destroyed near the nucleus oculomotorius.

About 80 years ago vAN GupbEN had already indicated the dorso-
medial nucleus mammillaris as the origin of the tractus called after
him, without finding however general agreement (vide e.g. KOLLIKER:
Gewebelehre).

The present standpoint is that of Casa according to whom the
tractus of Vicq pb’ Azyr and GuppEN originate from the same cells,
(fascic. mammillaris princeps); one part of the fibres goes in a fronto-
dorsal direction to the nucl. anterior thalami (Vicq pb’ Azyr) another
runs caudally to the nucl. Guppen (vide above). From the uninjured

state of the medial-ventral nuclei of the corp. mammillare in
agreement with the conservation of the tractus Vicqg p’Azyr — it

appears that the question is not so schematic as CaJaL represented
it in his drawing *') in which are represented fibres, originating in
the mammillare, dividing each dichotomically, producing in this way
ingredient parts for the two mentioned tractus.

In order to control my results obtained in the degenerative way
I examined embryos of rabbits of different ages.

I communicate here only what a specimen of 11 em. length and
another of 2'/, em. show. The brains of both embryos were, after
enclosure in paraffine coloured with cresylviolet by Dr. DrooGLEnver
Fortvuyn (frontal series).

Embryo 11 cm. Here principally all the relations so as they exist
in the fullerown animal can distinctly be found. With greater
distinctness however the separate connections of the tractus GUDDEN
and Vicg pb Azyr with the mammilare can be observed. Dorso-
proximal from the latter the two systems are united. The most
median part of the apparently common stem radiates first downward
as soon as the dorsal nucleus of the medial mammillare-ganglion
appears. An examination of the series in a caudal direction shows
that these fibres are the continuation of the tractus GupppN, which,
where the lateral (Vicq b’Azyr-) fibres run ventrally, appears as a
distinct tractus, passing the fascic. retroflexus at its medial side.

The dorsal nucleus of the medial mammillare has here the same
somewhat dish-shaped form as in the full-grown animal and lies on
the proximal half. The tractus Vicq pb’ Azyr first sends its lateral,
more distally the other fibres into the ventral part of the medial

') Text, del. sist. nervioso Tomo II, segunda parte, Fig. 636, pag. 746,

(1121 ) J

ganglion, in which they run for a short distance sagittally backward,
(just as the fascic. retroflexus does in the gangl. interpedunculare).

By the way I mention the very distinct radiation of fornix fibres,
in this stage of development, dorsal from the corp. mammillare to
the opposite side of the hypothalamus.

Embryo 2*/, cm. A fasciculus Vicg p’Azyr is still missing. The
corpus mammillare has only a very slight ventral curvation, in which
the ventral nucleus of the medial ganglion will be formed, its dorsal
nucleus however is very well recognisable. The tractus GUDDEN is
likewise perfectly distinct, passing on the typical point the fase.
retroflexus. As in the other embryo the lateral nucleus and the ped.
¢. mammill. are extant. Judging from such young stages one should
however not easily reckon this nucleus among the mamumillary
elements, as it is situated too lateral. The peduncle originates in it
strongly sagittally Gn the same way as in the full-grown animal)
and is therefore rather difficult to recognize.

The fact that only the tractus GubDeN is extant whereas the tractus
Vicq D’Azyr is missing, is a striking proof of the comparative inde-
pendence of these two bundles. The existence of the dorsal nucleus
is in agreement with this fact. Evidently Guppmn’s tractus is o/der
and its alliance with Vicq bAzyr is especially of a secondary,
topographical nature. It is possible that the lateral nucleus with
pedunculus corporis mammillaris, the dorsal nucleus of the medial
ganglion with tractus GuppEN, are of an older date than the ventral
nucleus of the medial ganglion with which part of fornix and the
tractus Vicq p’Azyr are connected A system of fibres perhaps homo-
logous with the pedunculus ¢. mam, with a very similar originary
nucleus is already known to comparative anatomists, in many fishes
(teleostei) [according to a communication of Dr. Ariens Kappers| ;
this is not the case (hitherto) with the tractus mammillotegmentalis.

According to the majority of authors it is an undeniable fact, that
in submammalia nothing is found either of a corpus mammillare
sensu strictiori or of a tractus Vicq p’Azyr. This exeludes likewise
the possibility of the existence of fornixfibres that might unite the
ammon’s formation with the medial ganglion of the mammillare.
They radiate all towards the hypothalamus, in correspondence with
the majority of the fornix-ingredients in rabbits, which run towards
the crossed hypothalamus (and tegmentum. ?)

74
Proceedings Royal Acad. Amsterdam. Vol. XIV.

( 1122 )

Mathematics. — “On two linear congruences of quartic twisted
curves of the jirst species”. By Prof. Jan DE Vrigs.

In a communication in the Proceedings of this Academy (Vol. XIV,
p. 255) I have considered the congruence generated by the curve
of intersection of two quadries each of which belongs to a given
pencil. This congruence is of the first order and of the first class.

In the following pages will be treated properties of two other
congruences of quartic twisted curves also of the fist order but
of the second and third class.

1. We consider a pencil (7*) of quadrics ¢* passing through the
conics @?, 3’, and a pencil (y*) of cubic surfaces y* the base curve
of which breaks up into @ and a twisted curve y’. By the inter-
section of each surface g* and each surface g* a congruence I of
quartic twisted curves oe" of the first species is generated.
Through an arbitrarily chosen point passes one surface of both
so Tis linear or of the first order.

2

Through any point C of y' passes one surface y? of (7?) eon-

4

pencils and therefore one 9° ;

taining %' curves 9 passing through C’; therefore y* may be called
a singular curve, Ca singular point of the second order.
Also 8° is singular; through any of its points B passes one surface

‘ cutting BG in B; so B is a singular

6° containing all the curves @
point of the third order.
Finally « is singular too. For a g? and a g* touching each other |
in a point A of «@ have a o0* passing through A in common. By
making to correspond to each surface y* the surface g* touching
it in A, the pencils, brought thereby in projective correspondence,
generate a surface @ with «* as nodal curve and A as triple point,
1

containing o' curves o* cutting « in A; so A and a are singular

of order five.

2. On an arbitrary straight line / the two pencils determine two
involutions /*, /*; as these involutions admit two common couples,

4

{ is bisecant of two e* and therefore I a congruence of the

N
second class.

Any generator s of one of the g* is cut by (y*) in an involution

/* and therefore a singular bisecant. All these lines s form the

congruence (2, 4) of the lines cutting « and 8? in two different
points.

The planes «, 8 bearing «’, 6 form together a surface g? inter-
sected by any g* in the combination of a line « with a cubie curve

( 1123 )

of 8 having with that line one point in common. Every line of
8 is a singular trisecant; for it has three points in common with
each of the a! degenerated curves 0‘ determined by (g’) and (a, ’).

A straight line ¢ of any ¢' not meeting «@ is cut by (v’) inan J*
and therefore a singular bisecant. It has three points in common
with y’ and intersects « on the line of intersection @ of y* and a@.
This line @ is met by ten lines of ¢*; all these lines are trisecants
of y’. Moreover a is cut in its point of intersection with y‘ in five
other triseeants. So the singular bisecants ¢ form a ruled surface
of order fifteen with y7 as fivefold curve.

3. Let x be the order of the surface 4 formed by the curves
o* meeting the line 7. Then the surfaces 4 and 4’ corresponding to
/ and /' have in the first place the 7 curves 9* in common, meeting
/ and /. Through any other point of their intersection passes a 0‘
meeting / and an other 0‘ meeting /'; therefore the residual inter-
section can only be composed of singular curves. As / cuts the
surfaces a‘, 8°, and y?, corresponding according art. 1 to points
A, B, C of a?, 8, y', into 5,3, and 2 points respectively, a?, 6’, y’
are respectively fivefold, threefold and double curves on 4. So for
the determination of # we find the relation ') # =4a-+ 5* >< 2+
+ 3?x<2+4-2?7 giving «= 12.

We can verify this result as follows. If we make to correspond

* meeting one another on

to each other any two surfaces g¢* and ¢
/ we generate a correspondence (3,2) between them; thereby the
points of an other line m are arranged in a (6,6)-correspondence,
any coincidence of which is a point of intersection of two surfaces
gy? and g* having a point of 7 in common, and therefore a point
of an @* resting on J. Therefore 4 is of order twelve.

Besides the three multiple curves above mentioned 4 admits still
as double curves the two e* with / as bisecant.

4. On a plane ¢ the congruence I determines a quadruple invo-
lution. If the point ZL describes the line / of y the three points
joined to £ by a quadruple will generate a curve 4*' determined
- by the surface 4"? corresponding to / (art. 3).

Among the points of intersection of / and 2™* the two couples of
points of the @* for which / is a biseeant present themselves ; the
remaining seven are points of coincidence, i.e. points of contact of
g with curves g*.

1) The surfaces 4 have been used in a similar way by EK. Veneront, Sopra
alcuni sistemi di cubiche gobbe (Rend. Palermo, XVI, 210).

(Hage)

The curve of coincidences q*, locus of these points, is obviously
also the locus of the points of contact of the curves g? and ¢* of
the pencils determined by the pencils (y*) and (g*). These pencils
have two base points A,, A, in common, whilst (vy?) admits still the
base points 5,, B, and (v*) the base points C;, (4 = 1, 2,.. 7). Through
Dy, passes one curve g;" containing «' quadruples with the common
point 4,; one of these groups has a double point in 4;, from which
ensues that £5; lies on g?. In an analogous way C belongs to oo!
quadruples lying on a g;° and is therefore likewise a point of g’.
Finally A; is a triple point of g’ and belongs to x’ quadruples
situated on the curve g*, in which @;° (art. 1) meets y. So_the
points of contact of the plane gy with curves 0% lie on a curve of
order seven with two threefold points.

). We will now consider the branch curve, i.e. the locus of the
couples of points completing the coincidences to groups of the qua-
druple involution.

Any curve g* is touched in the double points of the /* deter-
mined by (g*) on g® by six curves ¢*. By a quadratic transformation
with A,, A,, 5, as fundamental points we find that g* is touched
by eight conics g*. So by considering as conjugate to each other
two curves ¢*,g* touching one another a correspondence (8, 6), is
generated determining on any line m a correspondence (16, 18). The
curve of order 34 generated by the two pencils breaks up into the
curve of coincidences gy’ counted twice and the branch curve ¢*°.

By drawing m successively through Az, by, Cy, we find respectively
an (8, 12), an (8,18), a (16, 12). Taking into account the known multi-
plicity of these points on ¢* we come to the result that ¢*° passes
eight times through A;, siv times through 5;, four times through Ch.

6 By using once more a quadratic transformation with the funda-
mental points A,, A,, 6, the curve of coincidences ¢’ is transformed
into a curve a having likewise triple points in A,, A, and passing
through 5, and through the points B',, C, corresponding to B,, Cy.
The pencil (y*) passes into the pencil of lines with vertex B’,,
whilst the pencil (7) is transformed into a pencii of quartic curves
y', the base of which consists of double points in A,, A, and the
points B,, C,. Obviously a7 is the polar curve of 5’, with respect
to (yp'), i.e. the locus of the points of contact of the curves ys! with
tangents passing through 4',. The class of 2’ is 30; to the 28 tan-
gents concurring in 5’, belong the lines through A,, B,, C’, (in
each of these points a curve y' is touched by the corresponding

( 1125 )

line through 4',). According to the definition of the polar curve the
18 other tangents are inflectional tangents of as many curves tpt and
therefore curves yp‘ corresponding to conics y* osculated by a ¢’.
So the quadruple involution contains 18 groups with three coinci-
ding points. In other words, each plane is osculated by eighteen
curves Q*,

The curves gy’ and g*° will touch each other in 18 points. In the
base points A, B,C they have2*3*«8+2x6+7xk4=88
points in common. The remaining 16 points of intersection form 8
couples of coincidence and belong to eight quadruples. Otherwise,
each plane is bitangent plane for eight curves 9'.

7. Let us now consider the bisecants of the curves 0* through a
point P and the surface +, locus of the couples of points S in
which they meet these curves’). The curve GS through P is projected

from P by a cubic cone o*, the edges of whieh touch = in P;
P is a threefold point of Y. Each line through P contains moreover
two couples S; so = is a surface of order seven.

On each edge of o° still lies a second couple of points S ; so these
couples generate a curve o* of order six. As o*? and =" with the
common curves ¢4, and 6° can have furthermore only straight lines
in common, we find that eleven singular bisecants pass through P.
To these belong the two common transversals s of a and }* (art. 2);
on the other ones (v7) and (/*) must determine the same /?, therefore
they must meet y’. So there is still a congruence of order nine of
singular bisecants with y' as director line.

An analogous consideration furnishes with respect to a congruence
of twisted curves 9” of order o and class ¢ the result that a point
P bears in general o (n—1)? + (n—2) singular bisecants 2). So this
number is independent of the class.

However we must remark that this consideration does not hold
for o=1, ¢ >1 and n=2; for then the cone projecting the conic
through P out of P becomes a plane and the curve of intersection
lying in this plane will also pass through P. But then the singular
bisecants are lines of the surface enveloped by the planes of the
conics and in general they form no congruence.

The surface =7, contains the singular curve y‘, for through each
point C passes one 9‘ cutting CP a second time. However the singular

1) For bilinear congruences the surfaces © have already been used by VeneRont
(lic. p. 212),

2) For o=1, c=1 this number is n?—n—1. It was found in an analogous way
by Veneront (lc. p. 212).

( 1126 )

curves a’ and §? are nodal curves of 2", each of their points A (4)
bearing two curves 0* with APP) as bisecant.

Any 9* has in common with 2%, the two couples of points on
its two bisecants through P. Every other point of intersection is
evidently singular. As the 8 points of intersection with @ and (}?

have to be counted for 16, these conics being nodal curves of ="

e’ must have eight points in common with y’. So the curves e* of
Vr have eight points in common with y', four points with a and with 3°.

8. The points of contact of the tangents through P to the surfaces
gy’? and g* lie on the polar surfaces Z* and H° of P with respect
to these pencils. In a point A of @ a ¢g’ is touched in such a manner
by a gy’ that the tangent plane passes through P; but in general
the tangent in A to the common o* does not pass through P. The
surfaces 77? and 7°, touching each other along a@’ have still a curve
x** in common, which passes through P and through the points of
contact of tangents through P to curves e*, From this ensues that
the tangents to the curves o* of TV form a complex of order ten.

Any plane through P cuts >%, in a curve o’ with a triple point
in P and four double points on @* and 8, and therefore of class 28.
Of the 22 tangents through P ten belong to the complex of the
tangents of I. The remaining 12 coincide in pairs to double tangents
of o’, i.e. in lines on which the involutions determined by (v*) and (¢?)
have two coincided pairs in common, so they are cut by only one
ge’ in two points. Evidently the lines possessing this property form

a complex of order six.

9. The surface 1’? corresponding to a line / (§ 3) is cut by a plane
according to a curve 4" passing respectively 5 times, 3 times, 2 times
through the base points Az, By, Cy. (art. 4). So it has in common with
the curve of coincidences yg’ in the base 2x5x3+2X3-+7 X2=50
points; so there are 34 points of contact of gy with a curve 0‘
cutting 7; in other words, the curves e* touching a plane form a
surface of order 34.°*)

The surface « corresponding to a point A of a@* intersects ~ ina
curve, passing twice through Az, and once through 4;, Cy, and
having therefore besides these points still 5 & 7—2« 2x 3—2
—7= 14 points in common with gv’. So the surface g** mentioned
just now meets 14 times the conic a’; this agrees with the fact

1) This shows once more that the branch curve is a 4%, for the surface under
consideration has with » in common the curve of coincidences counted twice.

(entse

that the curves y' and °°, common to g and g*' pass together 14
times through A;,°).

In the same manner can be shown that 3 is an eightfold curve
and y’ a sixfold curve of @*’.

The curve of coincidences yp’ of a plane y has in its points of
intersection with a’, 6’, y’ evidently 2x 14«3+2x8+7x<6—=142
points in common with g**; in each of the remaining 96 points a

e* touches w. So two arbitrary planes are touched by 96 curves ot.

10. Let us now consider the projective nets of quadrics represented by
hay - Or + ye’; =0 and Af, + wg, tt vh*, = 0.

The congruence IF of the quartic twisted curves o0*, forming
intersections of corresponding surfaces, is //near. For through any
point Y passes the curve determined by the relations

i a*y + wb, -+-v yl) and gee +ug, +vh?, =0.

But under the condition

ay b*y Cy

Me | nT ee 0
| fry gy Wy
Y is a singular point bearing o!' curves 9%.
| ab : lac | ; ; J :
Ase |) oh = Orand)|) ~ = 0 determine two quartic surfaces
lig Lede
; : Bee : ; | Be
having in common the curve a= 0, 7=0 not lying on ; ==\()}
event

+12

the locus of the singular points is a twisted curve o* passing through
the 16 base points of the two nets.

Evidently o'* is the partial intersection of the quartie surfaces
determined by

Oe Bey | Gh Sas a
| a’y b*y cy (= 0, | a, By cy =e
fy GIy h’, fy Py h?, |

For these surfaces have in common the curve of the congruence
T determined by

Mates Beak
[zs VE bay (= Sand A=) <a 1B)
Cop patos |
and the curve 6’ denoted by M—=0.

1) In connection with this it must be remarked that in art. 8 of my communi-
cation quoted above an error has slipped in. The surface 424 mentioned there

passes six times through the curves 64 and 6's. So only 72 curves p4 touch two planes.

( 1128 )

Out of eA ==)0 andy ih 0 stollowseAy— Ox0oraj—10 —1ee— OF
out of A’=0 and JF= 0 follows*A\—=0 ‘org =). — 0 2aS0
4=0 and 6” have, besides the 8 base points of the first net, 16
points in common lying at the same time on A’ = 0. Consequently
each curve 9‘ of I cuts the singular curve 6? in sixteen points.

41. On the line UV represented by «, =u, + ov, the nets

Aa’, =O and =1/’,=0 determine the pairs of points
3 3

=k (ay + 2 dyty ar 07a") =) ey h (Gia Se 20fuso sis of?) = 0.

vo >
These two equations will determine the same pair, if the relations
A Gig =O DF i May Oy eh a Oe ay
3 3 3 3 58 3
hold. Eliminating 2, u, » we find the relation
ae tay Oni Hin O Pu Cite OU Lars
|
, . |
hydy — Ofuty buby = 6 dude CiCh—— OO Reh 05
ay— 6 fu b°,, — 69", ce, — oh’,

which proves that UV is bisecant of three curves 04; so the con-
gruence is of the third class.

12. Through a singular point S pass o' curves o* lying on a
surface ', generated by two projective pencils of quadrics and
having therefore a node in_S.

The surface 4 formed by the o* having a point in common with
a line / passes four times through o*, for 7 cuts 2* in four points.
So the order w of 4 can therefore (§ 3) be deduced from the equation
xv = 47+ 192 giving « =16. So. two lines are met by sixteen 0.

The o* cutting / meet any plane y through / in three points more
lying on a curve 4’; among the points common to / and 4'* occur
the three couples of points which / has in common with the curves
e* of which it is a bisecant; in each of the remaining 9 points @ is
touched by a curve e*. Soa plane ts tangential plane for nine curves @'.

The quadruple involution which the curves 0* determine in @ has
therefore a curve of coincidences g° of order nine. This curve is at
ihe same time the locus of the double points of the net of quartic
curves determined by

Us B v |
Opes b,? Cra i = 0
Se’ 92° h, ;

As this net admits 12 base points (points of intersection of gy and

o) g? has tevelve double points.

( 1129 )

Geology. — “Further considerations about the geology of Java.”
By Prof. K. Martin.

(This communication will not be published in these Proceedings).
ERRATUM.

In the Proceedings of the meeting of Dec. 30, 1911, p. 678,
line 18 from the bottom: for IX read XII.

(April 25, 1912).

ae

“

KONINKLUKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING
of Friday April 26, 1912.

DoCe

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Vrijdag 26 April 1912, Dl. XX).

Gi@OiENe NE ES:

V. E. Nrerstrasz: “Some calorimetrical investigations relating to the manifestation and amount
of imbibition heat in tissues”. (Communicated by Prof. H. ZwAARDEMAKER), p. 1130.

F. J. J. BuyrenpisK: “On the ciliary movement in the gills of the mussel”. (Communicated
by Prof. H. J. Hampurcer), p. 1138.

D. F. Torrenaar: “On the influence of the earth’s rotation on pure drift-currents”. (Com-
-manicated by Dr. J. P. van DER Srok), p. 1149.

C. P. Conen Stuart: “A study of temperature-coefficients and van *r Horr’s rule’. (Com-
municated by Prof. F. A. F. C. Went), p. 1159. (With one plate).

JAN DE Vries: “On a congruence of the second order and the first class formed by conics”,
p- 1173.

C. U. Armns Kappers: “The arrangement of the motor nuclei in Chimaera monstrosa compared
with other fishes”. (Communicated by Prof. L. Boxk), p. 1176.

J. E. pe Vos van Sreenwisk: “Provisional results from calculations about the terms in the
longitude of the moon with a period of nearly un anomalistic month, according to the
meridian observations made at Greenwich”. (Communicated by Prof. E. F. van pe SanpE
BakKHUYZEN), p. 1180.

W. Karrreyn: “New researches upon the centra of the integrals which satisfy differential
equations of the first order and the first degree”, p. 1185.

W. H. Juuius: “Preliminary account of some results obtained by the Netherlands Eclipse
Expedition in observing the annular solar eclipse of April i7th, 1912”, p. 1195,

A. Sirs and H. L. pe Leruw: “Confirmations of the theory of the phenomenon allotropy
Il”. (Communicated by Prof. A. F. Horremay), p. 1199.

J. D. vAN Der Waats: “Contribution to the theory of binary mixtures”. XX, p. 1217.

A. F. Horteman and J. P. Wisavr: “The nitration of ortho-chlortoluene”, p. 1230.

~J

wr

Proceedings Royal Acad. Amsterdam. Vol. XIV.

( 1130 )

Physiology. — “Some calorimetrical investigations relating to the
manifestation and amount of imbibition heat in tissues”. By
Dr. V. E. Ninrstrasz. (Communicated by Prof. ZwAARDEMAKER).

(Communicated in the meeting of February 27, 1912).

Amongst the numerous physico-chemical processes which throw
more light upon the nature of function, an important place has been
occupied of late years by imbibition *).

We mean of course the real molecular swelling, mostly viewed
as a diffusion phenomenon ’), not the capillary or endosmotie imbi-
bition. As a point of departure for some investigations in this diree-
tion we took imbibition-heat, other characteristics of the swelling viz.
volume-contraction of the entire mass of substance + water*), and
swelling pressure, being more remotely connected with the nature
of imbibition.

Keeping in view the fact that most ealorimetrical determinations
take up much time, we did not take the ice-calorimeter, generally *)
adopted for this purpose, but followed a method which, to a great
extent, obviated this difficulty, and moreover, allowed of the deter-
minations being made at the temperature of the room.

Our method was in principle a bolometrical one; the heat devel-
oped was measured by resistance-modifications in a thin copper-wire
isolated with silk and wound bifilarly (thickness 0.1 millimetres),
resistance 25 Ohms). We used two bolometers as much Jike each
other as possible (6, and 4, in the figure, length of tube 14 e.m.,
inner diameter 1,9 ¢@.m., outer diameter 3 c.m.); the side was formed
by a Dewar’s glass, which made the isolation as perfect as possible.
These were taken up as branches in a system, based on the prin-
ciple of Wukatstonr’s bridge, and had each as a counter-resistance

') W. Ostwaup, Koll. Zustand der Stoffe, Oppenheimer’s Hdb. d. Biochemie.
Bd. 1. p. 839.

L. MicuaAgis, Physik. Chemie der Kolloide in Handbuch Physik. Chemie und
Medizin, Koranyi und Richter. Bd. IL. Leipzig 1908.

M. H. Iiscorr, Das Oedeem. Dresden 1910.

H. Frrunpuicu, Kapillarchemie. Leipzig 1909.

*) J. Reinke, Untersuchungen tiber die Quellung einiger vegetabilischer Substan-
zen. Botanische Abhandlungen. Bd. IV. Heft 1.

8) The substance itself of course increases in volume.

‘) O. KrumMmAcueEr, Ueber die Quellungswiirme des Muskelfleisches. Zeitschrift
fiir Biologie. Bd. 52 Heft 4 und 5.

y. D. Honye, Opzwelwarmte der lenszelfstandigheid, Ned. Tijdschrift v. Genees-
kunde, 28 Oct. “11.

( 1134 )

a thin copper wire wound on a bobbin (w, and w,) and a thin
niccoline -wire, any part of which could be added to the’ resistance

Wy

by means of a movable post, enabling us to fix the resistance at
the length required. These two counter-resistances could undergo
with respect to each other some modification in size by the insertion
of a round compensator c of Du Bois Rrymonp, which on being
turned effected another division of the lengths of the two parts to
be passed by the current (S= key, G = galvanometer).

The Derwar’s glasses were placed in a cube shaped calorimeter
(length of the ribs 42 em.) consisting of two layers, an inner layer
of cork (thickness 3.5 cm.) and an outer layer of wood. A cover of
the same materials closed the whole. The Drwar’s glasses, fixed in
a wooden stand, had been placed in the middle of the calorimeter
on a narrow horizontal plank, the round extremity of which pierced
the calorimeter on one side, and was connected with a wooden
handle, which rendered it possible to make the whole revolve round
a horizontal axis. An advantage of this was, that whilst the calori-
meter and the Derwar’s glass were closed, it was possible to effect
the contact between tissue and fluid in the manner to be described below.

On either side the counter-resistances had been fastened to the
inside on a little plank. The round compensator stood apart, likewise
in a secluded space. It was covered by a glass plate, provided with
a little opening from which a magnifying glass projected, which

75*

( 1132 )

allowed the divided scale to be read off accurately. The turning was
‘effected by means of two cords, wound in different directions round
the axis; these on being drawn rotated the divided seale in opposite
directions. As these cords (like the current-wire) passed out through
Openings in the side, it was possible to effect the rotation with the
box closed. In the same way the wire-connections of the calorimeter
passed out.

All these were united, according to the above-mentioned plan, on
a system of posts fastened on the outside (see fig.). It goes without
saying that tnorough isolation was necessary against the changes in
the temperature (wadding, felt) for the counter-resistances inside, as
well as for the connections outside.

The bolometer itself was composed as follows (see fig.). On the
bottom of the Drwar’s glass (0) were the clew-shaped ') copper wires,
whieh were wound bifilarly. The two ends were led upward through
a thin glass tube (jp) (fastened to the side with sealing-wax) and
were connected by means of a thicker copper-wire with the posts.

The Drwar’s glasses were closed by means of an india-rubber
stopper, to the bottom of which a hook was attached on which the
little pail (¢) was hung, destined to contain the tissue to be experi-
mented upon. Before the experiment began this had to remain of
course above the level of the fluid in the tube (dimensions of the
pail were: height 2.5 cm. outer diameter 1 ¢m.).

Thus it was possible, the bolometer being closed, to wait till the
needle of the galvanometer was at rest, a state of perfect equilibrium
having set m; then the handle was turned, which caused the pail
to drop from the hook bringing it into contact with the fluid. Pail
and bolometer-wire always came down immediately in the same
position, side by side.

In order to determine the amounts of heat we did not make use
of the deviations of the galvanometer needle, but of the extent to
which the compensator had to be turned in order to keep the needle
al zero. The divided scale of the compensator rendered it possible
io read off this change. For shortness, sake we shall henceforward
call the round compensator of pu Bois RryMonp measuring-wire. It
goes without saying that the relations between the volumes of heat
developed, were different from those indicated by the measuring: wire
(the measuring-wire . forming only a small part of the counter-

1) Al first we used a copper-wire, wound spirally on a pin 5 em. high, in the
middle of which the tissue came down. Its sensibility was, however, 5 times

smaller than if the clew form was adopted, so that the latter was always used.

( 1133 )

resistances), and that every point had to be separately determined.
More will be said about this later on.

Now we intended to collect by means. of the imbibition heat some
data relating to the imbibition of different tissues of different animals.
For this purpose we chose the fresh-water mussel, the rabbit, the
pigeon, the neat.

Anodonta fluviatilis has two adductors, the central yellow part
of which has the function of a fast muscle, whilst the peripheric
white part may be for a long time in a state of tonns*). The parts
of these muscles also differ histologically.

Since according to ENGrLMANN the contraction is attended by a
water displacement in the muscular fibrils, it is conceivable that the
colloid substances of the hypothetical inotagmas absorb this water.
It might be supposed then that in such muscles more substances
liable to swelling are found than in the peripheric parts of the
muscle, which are in a state of autotonus.

We experimented upon chopped up tissue, which was then exposed
for half an hour to a hot current of air (40° C.) and was further
dried during two days in a vacuum-exsiceator at 40°.

We then obtained a fine powder of which we established the
amount of water lost, by weighing it before and after it was dried.
When it was left longer in the exsiccator, this loss increased at most
with 1—2°/,.

It is generally held that an arithmetrical decrease of water-percentage
causes a geometrical increase of imbibition-heat. Here, however, the
differences in water-percentage, during the various determinations of
one tissue, were so small that they could not be recognized as
influencing the results any more than the small temperature changes
during the experiment (the extremes were 10 and 14° C.).

We subjoiu the relative results of 10 series of experiments on
anodonta-organs, both for the tissue-powder and calculated for the
fresh tissue from these values, and the loss of water caused by
exsiccation, which was known. To facilitate comparisons we fixed
the value of the fast musele at 100 whilst the other results were
reduced in the same proportion. Our determinations were always
made with doses of 50 milligrammes and we took the average
scale-movement of the measuring-wire. In this way a slight mistake
is made as these deviations are not quite proportional to the heat
developed, but in the case of small differences this is not of much
importance.

1) J. Parnas, Energetik glatter Muskeln. Pfliiger’s Archiv., Bd. 13°.

( 1134 )

The time taken up by the experiment was 3, at most 5 minutes,
after that no more heat was taken up. We always worked with
equal volumes of fluid, the other conditions being likewise always
the same, so that, to compare the results, the capacity for heat of
the apparatus need not be taken into account. We may safely assume
that with heat-quantities such as these the distribution of heat over
copper-wire, fluid and glass is always effected in the same way,
when the experiments are carried out in this manner.

Fresh water mussel.

Relative and average values of the imbibition-heat of:

yellow white organ
(fast) (autotonous) lever of mantle corpus
muscle muscle S0janus

a. tissue-powder 100 80.9 71.7 65.1 36.5 38.3

db. calculated for
fresh tissue . 100 80.3 40.2 il gil 44.9 47.8

c. loss of water
by exsiccation 842°/, 83.5°/, 90.6°/, 88°/, 80.6°/, 78.9°/,

We observe indeed distinet differences and that most between the
muscle-tissue on the one hand and the other tissues on the other.

These differences are still more manifest in the fresh tissue.

The difference between the two kinds of muscles exists so far that
the fast muscle swells most, but it is too slight to admit of general
conclusions being drawn from it as to the nature of the functions.

From the results obtained with dry powder it might further be
inferred that the secretion or excretion organs such as liver and organ
of Bojanus contain these substances in a higher degree than the other,
more indifferent, organs. Possibly this may be connected with the
secretory function of these organs; it may be conceived that the
process of imbibition is of importance as a preparation to further stages.

Under exactly the same conditions the following series of expe-
riments was carried out with the organs of the rabbit.

The loss of water caused by the exsiceatory process varied in
different organs from 77 to 83°/;. We subjoin again some average
relative results. On every organ at least 10 determinations were
made (10—18).

( 1135 )

Rabhit.
Relative and average values of the imbibition-heat of:
white muscle red muscle kidney brain __ liver

a. tissue powder . 100 LO4.7 126.1 91.2 94.1
6. calculated for . 100 114.4 114.4 78.3 93

fresh tissue
c. average loss of 78.6°/, 16.62/59) © 60:68/) soit 18:97)"

water by exsic-

cation

Here we find the differences between the tissues not so ereat as
with anodonta; moreover we find, besides the muscles, especially the
red one, the swelling of the kidneys at the head of the list; for the
dry tissue it is even greatest. The swelling of the liver too, is above
that of the central nerve-system. As in the case of anodonta we see
here too that the secretion (excretion) organs have a relatively great
imbibition-heat.

In order to be able to put absolute values by the side of these
relative ones, various methods of measurement were adopted. The
most satisfactory was that effected by Jounn’s heat.

For the current-circuit to be constructed the various wire-connec-
tions were chosen in such a manner that their resistance could be
neglected; besides, however, a thin isolated niccoline-wire of a given
resistance was also inserted into the cireuit; this wire, wound in a
spiral of no great height was put on the bottom of the pail.

Thus the spiral had exactly the same position as the tissue-powder
in the experiment.

This resistance had been taken up into the circuit by being soldered
to two thicker varnished wires, which issued from between stop-
per and glass side, and which were connected with the current-
circuit by means of posts.

We had to experiment of course with such currents that their
heat-development caused deviations on the measuring wire of about
the same magnitude as those effected by the tissue-imbibition.

From the preceding determinations with glass-powder we knew
approximately how much heat was set free at a given deviation)
and could therefore establish, starting from the physical formula: heat =

7? Qt, the quantities we had to deal with. The duration of the

4.2

current was fixed at 3 minutes, that is the time during which heat
is still absorbed. The resistance of the niccoline-wire was 21 Ohms

( 1136 )

at a thickness of 0.15 millimetres and a length of 40 centimetres.

At a temperature of 14° C.") we now got at a current-strength
(7) of 30, 40 and 50 milliamperes (m.a.) deviations on the measu-
ving-wire of 46, 66 and 105 division-marks respectively. These
deviations, therefore, increased proportionately more than the strength
of the current and less than its square, which might indeed be
expected.

Of the deviations between two determined points which were
pretty close to each other, we found the absolute value by linear
interpolation. The trifling mistake thus made, could not be of much
importance.

We saw that for the white muscle tissue of the rabbit the average
deviation was 68.5, that is about as great as the one obtained at a
current of 40 in.a. at the absolute determination (66). As, however
dissolved and_ jelly-like substances gather on the clew of the bolo-
meter, causing the deviations on this side to be 2 or 3 times
smaller than on the other’) the determination of the absolute
value *) must always take place immediately before or immediately
after a series of experiments.

In the following series of experiments made with the muscle-tissue
of the pigeon and neat, we made, therefore, an absolute determina-
tion in connection with every series and under the same conditions.
Of the pigeon we used three kinds of muscles viz. the smooth tonic
stomach muscle, the heart muscle, and a striated thoracal muscle and
compared these values, both as regards their relative and their abso-
lute imbibition-heat. In these experiments we used doses of 100

!) The current being the same the deviations increased somewhat at the ganging
when the temperature fell.

2) When it is thoroughly rinsed and left in water for one day, the old sensibi-
lity of the wire is restored, as compared with the other side. In the long
run, however, some decrease seems to take place on both sides possibly by
defects of the isolation manifesting themselves.

3) This method we also applied in determining the effect of the volume of the
fluid in the Drewar’s glass. It was found to be very small.

We mostly put on both sides 10 cm®. into the tebe. but double this volume
and a current of 40 amperes had no effect on the deviations. Also when we took
4 times this volume (5 and 20 em*.) and a current of 109 m.a. the effect remained
doubtful, at any rate but slight (a difference of only 4 division-marks). Hence -
the capacity for heat of that part of the fluid which was heated is at any rate
but small, and moreover always the same; as we may further assume that the
relative distribution of the heat over copper-wire, water and glass is always the
same for the quantities of healt under consideration, it is unnecessary. to pay any
further attention to the capacity for heat of glass and water,

(41375

milligrammes; in the case of -pigeon I we made for every muscle
10 determinations, for pigeon II 5.

Pigeon I

stomach heart thoracal
muscle muscle muscle
a. average relative
ViQIUCS om coekr ot acu: 100 90.2 89.9
6. absolute values per
1 gramme of tissue-
POWGCEE . ve.ck 8.1 fe 7.0 gramme-calories

It follows from the above figures that the tonic smooth stomach
muscle has a somewhat greater imbibition-heat than the others,
whilst there is no marked difference between the imbibition heat of
heart-muscle and thoracal muscle.

Pigeon II.

stomach heart thoracal
muscle muscle muscle
a. average relative
VALLES seo Mae 100 86.9 97.8
6. absolute values. . 10.2 8.5 9.9 gramme-calories

Here too the stomach muscle has the greatest imbibition-heat though
the difference with the other values is smaller. The thoracal muscle
has a somewhat greater imbibition-heat than the heart-muscle.

The average absolute vaiues of the two series are therefore 9.15,
7.8 and 8.5 gramme calories.

Finally we shall compare these absolute values with those which
were obtained by KrumMAcHER') by means of Bunsmn’s ice-calorimeter
as modified by Scnunten and Wartna, so that an opinion can be
formed about the two methods. KruMMAcHER determined the imbibition-
heat of the musculus glutaeus max. of a newly killed neat (killed
one hour before); we did the same and proceeded as before.

As an average of 10 determinations with 100 milligrammes of
tissue-powder we found per gramme of muscle-tissue an imbibition-
heat of 11.6 gramme-calories. }

KromMacurEr found for dried muscle tissue, which, for the rest had
been left unchanged, 8.3 gramme-calories, for flesh which had been
extracted first 13.1 gramme-calories.

1) O. Krummacuer. Ueber die Quellungswirme des Muskelfleisches, Zeitschrift
fiir Biologie, Bd. 52, Heft 4 und 5.

(-1135")

Our values are between these; somewhat greater, however, than
his for flesh which had only been dried. Our method is superior
to his in the following respects: ;

1. the imbibition takes place at a more physiological temperature.

2. the determination takes much less time; 4 determinations can
be made in one hour.

Only further researches can bring to light the best method of
investigation; for the present it seems to me that the advantages
mentioned are of some importance.

The great amount of imbibition-heat developed even by inconsiderable
volumes of tissue, is at all events remarkable.

Conclusions.

1. In a dried state the organs of anodonta as well as those of
warmblooded animals are found to be liable to imbibition, which
imbibition is attended by a considerable development of heat.

2. Generally speaking the muscle-tissue develops the greatest heat;
then follow kidney and liver.

3. Between muscles contracting rapidly and those contracting more
tonically (white and yellow adductors of anodonta, heart- and stomach-
muscle of pigeon) the differences in imbibition-heat are too slight to
be of much value for contraction theories. At any rate it is not found
that muscles with rapid contraction always develop the greatest heat.

4+. The amount of imbibition-heat is for muscle-tissue of the pigeon
on an average 8.5 for that of the neat 11.6 gramme-calories.

5. Advantages of the bolometrical method are a more rapid
determination, and imbibition at a more physiological temperature.

6. The sensibility of the method is very great, one division-mark
on the measuring wire denoting on an average 1 or 2 hundredths
of a gramme-calorie.

Physiology. — “On the ciliary movement in the gills of the mussel’.
By Dr. F. J.J. Buyrenpuk. (Communicated by Prof. Hampurenr).

(Communicated in the meeting of February 24, 1912).

Since the time when VALENTIN ') enumerated four chief forms of
ciliary movement viz. the motus uncinatus, vacillans, undulatus and
infundibuliformis, deviating forms of motion have been described by
other investigators. Although even the untrained observer can, upon
the whole, recognize these forms of ciliary movement in various

1) Varentin. Flimmerbeweging In Waeners Handbuch der Physol. Bd. J p.
484—516.

( 1139 )

objects, the further description of them, as given by Vatentin and
others, is subject to the greatest difficulties. An estimate as to the
frequency of the ciliary movement can be formed with only a
moderate degree of certainty, even by the best observers. Martivs °),
however, applied the stroboscopic method in such a manner that the
rapid rhythmical movements can be studied more easily. If we light
up the cilia for a short time, every time when they are in the same
position, then it seems as if the cilia are perfectly motionless. Now
if the number of illuminations is greater than the number of periods
of the ciliary movement, then it seems as if the cilia make a very
slow periodical movement. According to Martius’ description a slow
wave-like motion runs over the series of cilia. Already at the inves-
tigation of this author, however, the drawbacks of the stroboscopic
method made themselves felt. The rapidity of the ciliary motion is
either such that even at a very short exposure only a hazy picture
is formed, or the vibration is so irregular that the moment of the
exposure corresponds every time with another position of the cilium.
Hence neither Martius nor any other investigator gave an accurate
description of the ciliary movements, based upon observations with
the stroboscopic dise *).

Therefore I gladly availed myself of an opportunity to study in
the “Institut Marry”
the mikro-kinematographic method. I chose for the object of my

the ciliary motion of the mussel, by means of

experiments the gills of the mussel as it appeared to me that in
other objects, for instance the epithelium at the bottom of the mouth
of frogs, the cilia were much smaller, and that especially one row
of them could not be obtained so easily in a preparation. For the
purpose I held in view, a thin preparation, with cilia which were
placed not too close together, was highly desirable.

The apparatus at my disposal was a kinematograph moved by a
motor. To intercept the light a revolving dise was used, placed
immediately before the film; this dise had a slit which could be
regulated, so that the exposure could be reduced to 0,001 second.
This short exposure could only be applied when the object was
slightly magnified, (apochromatic objective 16 millimetres) as the light
which was concentrated on the preparation by means of an are

1) Marius. Verhandl. der physiol. Ges. zu Berlin Archiv. f. (Anat.) und Physiol.
Physiol. Abl. 1884 p. 456—460.

2) L. Butt writes for instance (Travaux de l’assoc. de I’ Institut Maney 1910 Tome
JI p. 51), *Son emploi (de la méthode stroboscopique), toutefois, est assez restreint,
puisqu’elle ne fournit des resultats précis que lorsqu’ il s’agit de mouvements
absolument périodiques”’.

( 1140 )

lamp with an objective-condenser of Zeiss, was found to be too
weak when the preparation was strongly magnified. A second dise
placed with its slit between lamp and microscope was likewise
moved by the motor, so that the object was exposed as short as
possible to the intense light and heat of the are-lamp. Yet it was
found in my experiments that a heating of the object could not be
avoided. Especially whilst a suitable part of the preparation was
looked for and during the adjustment, the heating was such as to
render a further investigation of the motion impossible. On the other
hand the ciliary motion remained unimpaired if the heating was
compensated by a thin chamber, placed between condenser and
object, in which ice-water was circulated. This chamber consisted of
a brass ring, into which two thin brass tubes had been soldered,
which was closed at the bottom by a slide, and at the top by a
cover glass. The preparation was placed immediately on the cover
glass, and covered with another glass.

In spite of all these imperfections I succeeded in obtaining good
pictures, which could be of use in the analysis of ciliary vibrations.

ENGELMANN observed already that, besides the motus uncinatus,
the motus undulatus is very often met with in the mussel. In
explanation he writes on this subject +): “Obschon nun eine derartig2
Form (motus undulatus) wenigstens bei sehr biegsamen langeren Cilien
in derselben Weise, wie die erstbeschriebene (motus uncinatus) durch
aktive Bewegungen ausschliesslich an der Basis hervorgerufen sein
konnte, so lehrt doch das Vorkommen hakenformiger Kriimmungen
und das mitunter zu beobachtende Schwingen ausschliesslich der
Haarspitzen bei ruhendem Basalstiick, dass die Haare auf allen Punk-
ten ihrer Linge aktiv contraktil sein kOnnen”.

Whilst the motus uneinatus can be sufficiently accounted for by
a movement at the base, this ‘‘whip-like’” movement seemed to be
more® complicated.

If we examine a preparation of the gill of a mussel, then we
shall mostly see the cilia move backward and forward, perpendica-
larly on the plane in which the cilia are placed. Only in some
places they move in the plane of the cilia. Although as a rule a
motus uncinatus is to be observed then, yet it appeared to me as
if a kind of wave-like motion was also observable. I have repeat-
edly kinematographed such rows of cilia, but the rows in_ the
immediate neighbourhood disturbed the analysis of the movement.
Yet I could very well recognize the motus uncinatus from these
pictures. | cannot, however, describe it better than in the words of

1) ENGELMANN, Handbuch der Physiol. van Herman. Bd. I 1879. p. 387.

( 1141 )

ENnGELMANN: “das Haar kriimmt sich wahrend der Vorwiirtsbewe-
gung stark concav, etwa wie ein Finger by starker Beugung’’.
Sometimes, however, I succeeded, after long seeking, in finding
in a preparation a cilium standing alone, which was mostly much
longer than the other cilia. Such a cilium made then sometimes
very regular whip-like movements. The entire period of such a

Fig. I.

movement is represented in Fig. I. The length of the whole period
is 7/,, sec., the characteristic difference between forward and back-
ward movement is already visible. This was still more manifest in
another film, made of another preparation. It shows the nature of
the movement very distinctly. The number of pictures taken, amounted
to 28 per sec.; the magnitied pictures had been obtained with
apochromatic objective 8 m.m. and projection-eye-piece No. 2, the film
being about */, metres away from the eye-piece. The movements
of the cilium had been made much slower by the refrigeration, and
the periods took somewhat less than one second. By projecting a
series of photos of this film at one place on paper, the drawings
in Fig. II, IY, IV, and V were obtained.

Let us now view Fig. Il and IV. Although not alike they are
of exactly the same type. The outstretched cilium, a smail part of
the basal part of which is visible, begins to bend, traversing whilst
it is stretched out a circle segment, the basal part being approxi-

( 1142 )

mately the centre; evidently the place where the cilium enters the
cell-tissue is not the centre of the movement. When part of the

movement has been performed, ‘the cilium looks like a stick, stuck
into the ground in a slanting position. The point round which the
circular motion takes place lies deeper in the tissue.

The simplest explanation is to assume that the tissue before the
rootlets, by being contracted, causes the rootlets, and with it the
whole cilium, to undergo this circular motion. The part of the cell-
tissue which in the case in question is the probable cause of it,
bas been shaded in Fig. II to V.

The rapidity of the forward flection of the hair in slight at first,
increases fast, reaching its maximum between positions 4 and 5,
31 and 32. respectively ; then the rapidity decreases fast again. It
is difficult to ascertain at what point in the movement the greatest
amount of labour is performed, as for a strictly mechanical (hydro-
dynamic) analysis too many data are still wanting. Presumably the
greatest amount of labour is done at the point where the rapidity
is greatest, at least if the curvature backward, coinciding with it,
is supposed to be due to the resistant force. As at this time, moreover,
the amount of fluid displaced is greatest, the labour performed will

( 1143 )

have been all the greater at this stage. The positions 9 to 16, and
33 to 38 respectively, correspond in my opinion more or less with
a period of rest, during which the slight and especially irregular
movements downward would have to be explained from a passive
motion of the cilium, caused by the fluid.

How the bent down cilium is raised again the figs. II] and 1V
demonstrate. Examination of the positions 17, 18, 19 and 39, 40,
41, 42 respectively, reveals a curve setting in at the rootlet. From
the shape of this curve, but more especially from the backward
movement of the point where the cilium enters the tissue, it may be
inferred that the starting-point of the upward movement is found
in that part of the cilium which is enclosed within. the cell. From
the positions 19 and 42 a contraction wave runs to the top of the
cilium. This contraction wave, however, is of a peculiar kind. That
half of the cilium which is turned away from the direction of the
movement, is found to contract in its suecessive parts. This contrac-
tion can only result in the erection of the cilinm, as if cannot bring
about a shortening of the whole. The velocity of the propagation
is not a perfectly uniform one, but it seems to increase towards the
top. Whether this is due to mechanical causes or is to be looked
upon as being peculiar to the contractionwave in these cilia, is
difficult to decide. When the cilium is erect, the downward movement,
described above, sets in again.

To give a clearer insight into the mechanism I have added a

schematic drawing in Fig. VI. @ represents the point of entrance of

( 1144 )

a cilium, drawn in a bent down position, whilst it is in eourse of
erection, 4 is the non-contractile part, which, besides this one, also
has the following properties. It is flexible to the left, in the figure,
inflexible on the other side, incompressible length-wise. We can, there-
fore, aptly compare this half of the cilium by a long bag, filled with
fluid, being non-elastic on that side which is always exposed to the
pressure of the fluid. That side, however, which joins the second
contractile part of the cilium is elastic. c. Represents the contractile
part of the ciliam, in which « number of contractile elements (ino-
tagmas) have been drawn. /, in position 8, represents an inotagma
which has just shortened itself and is now in tonus. e is the succeed-
ing element, which is stretched and about to shorten itself; @ an
inotagma which is. still in a state of rest and will be stretched by
the contraction of ¢. The shaded parts S,S,.S, represent the proto-
plasm of the basal-border which contracts rhytmically. If we assume
that the motus uncinatus is caused by such a mechanism as the one
described here, then it need only be supposed that part 6 of the
cilium is less flexible, and that hence part c, (which is stretched out
in its full length in position 2) contracts entirely when the contraction
in S relaxes. We arrive then at the simple conception that the co-
ordinated movement of the cilia is effected exclusively by the contrac-
tionwave in the hyaline border. The contraction of the successive parts
causes the bending down of the backward cilia ; the cause or stimulus
of their erection must be sought in the relaxation of these contractile
parts. Besides those mentioned here, many observations lend support
to this supposition. Krarr*) for instance found that stimuli are also
transmitted through places where the cilia moved no longer. Hence
he concludes: ‘Die Coordination beruht nicht bloss auf einer ausseren
sondern wesentlich auch auf einer inneren, von Oberzelle zu Unterzelle
statifindenden Reiziibertragung beziehungsweise Leitung’. Vierworn *)
demonstrated that the ciliary organs of ctenophora never moved
unless a slight quantity of protoplasm was fixed to them.

On the other band it seems that flagelli, tails of spermatozoa ete.
can make movements independent of the body *). Moreover it should
be observed that the movements of only the tops of the cilia seem
to prove that exceptions to this movement-scheme may oceur, a/though
under abnormal conditions.

To effect a forward movement of the fluid, whilst the cilia only
move to aud fro, the forward movement must be more rapid than

1) Krarv. Pfliiger’s Archiv. Vol, 47. pp. 196—235.

2) Verworn. Pfl. Archiv. Vol. 48 pp. 149—181.

5) See Piitte’s Ergebnisse Physiologie. Vol. 1, 2. pp, 40 and foll.

( 1145.)

the return one (ENGELMANN) '). Krarr estimated at a retarded ciliary
motion in the mucous membrane of the mouth of the frog the ‘Vor-
schwung viel schneller (vielleicht fiinfmal so schnell) als der Riick-
schwung”’. Besides by a difference in velocity, the mechanical effect
on the surrounding fluid may be brought about by a difference in
the manner of movement of downward and upward stroke, of which
our case forms an example.

I have also tried to trace in my film this difference in velocity
when forward and backward stroke were symmetrical.

It appears that the cilia could be measured most easily on those
films on which cilia had been photographed which move in a direc-
tion, perpendicular to the row of cilia. Although at these measure-
ments it was found that the frequency of the ciliary movement was

not great as a rule (2—5 per second) yet at this small frequency
the velocity of the forward movement was so great that it was difficult
to draw from my films (28 photos per second) accurate conclusions
as regards this matter.

I, therefore, gladly availed myself of the photos of the ciliary
motion in the gills of mussels which M. Noaugs, technical assistant
at the Institut Marey, kindly put at my disposal *). These photos
had been made at a velocity of 120 per sec., and were perfectly
clear. I take this opportunity of offering again my hearty thanks to
M. Noeuks for his kindness.

The very difficult measurement of the cilia was made on the copies
of the film on bromide paper. By strongly magnifying them they

i ASBrir Ey I:

Numb.\length] | ate a et |e
ofthe of |N9° length|N». \length] N?. length N). length
|

photo cilium

N?. |length] N?. length

1 ict Bhale Patee LI 455) 555) 455) || 63 1.4] 71 3 719| 4.6
2 Wed LON 23 18} 4.5] 56| 4.4 | 64 1.4] 72} 3.4 ]|80) 4.6
3 sd 11 2.6 19%) 4550), 57) 3.6) || 65 1.4] 73 | 3.9 |81| 4.6
4 nd! 12 a4 NP 2OR i 451) 5892221) 66, 1.5] 74) 4.2 |82) 4.6
5 ileal 13) 4 21 4.5 | 59 1.4 | 67 1.5 ]-15 | 4.2 |83] 4.6
6 ey 14 | 4.5 | 22| 4.5 | 60 1.4) 68} 1.9| 76) 4.4
7 2 15) 4.5- | 23 | 4.5] 61 Wea) GON 22a fies le 4.6
8 2.1 16; 4.55 {|—| — | 62] 1.4|70| 2.4|78)| 4.6

1) Encetmann. Jenaische Zeitschr. |e.
2) For technicalities see the article of Mr. GARVALLO in the Travaux de I'Institut
Marey, I. 1909, containing also the picture of part of a film.

~l
oO

Proceedings Royal Acad. Amsterdam. Vol. XIV.

( 1146 )

could accurately be measured to '/,, of a m.m. It is often difficult,
however, to identify the same cilia on the successive photos. The
values found, were united in a table and then drawn on millimetre
paper. An example of the figures follows in Table I belonging to
Figs Vile

It was now found that the resulting curves could be reduced to
some types of which I shail give a few examples here.

If we look upon the movement of the cilium as that of a bar,
describing with one of its ends as a centre a certain angle to and
fro, then the values measured by me are only proportional to the
sines of the angles, which values when represented graphically might
give a correct picture of the movement. As, however, both from the
examination of the films and from all observations of ciliary motion
it must be presumed that the stroke of the cilia does not entirely
correspond with this simple form of motion, it seemed useless to me
io base any further calculations on the values arrived at. Likewise
speculations on the mechanical and hydrodynamical action of the
ciliary stroke t) must, owing to the great number of unknown factors,
be so inaccurate as to be absolutely unreliable.

In the first place the figures VII, VIIT, IX and X show that the

Wl

Ba

ex]

TA ‘31q

!) See avo. O. Weiss, Handbuch von Nagex Vol. 4 p. 679.

( 4147 )

downward movement is indeed much more rapid than the upward
one. It is true the proportion is not 1:5 (as stated by Krarr (Le

~ bo ww
) S S SS

-08

S

S
oe

TWA

but 3:10(11); 4:10(14); 2:8(6) in Fig. X on the other hand
2(3):5 and in Fig. X11:4 to

46
1:1'/,. To what extent this
20- irregularity has been caused by
abnormal physiological or me-
af chanical conditions is difficult
to trace. In the preparation of
a the mussel-gill hardly ever the
almost perfect regularity is to
see | A be observed, which characte-
HO BID SD ED SO. THD rizes the mucous membrane in
Fig. XI. the mouth of the frog.

This inequality is also met with when viewing the periods of rest.
The period of rest oceurs in Fig. VII almost entirely in the out-
stretched position of the cilium; in Fig. IX on the contrary, whilst
bent. In Fig. VIII and X the period of rest is divided and lasts
about as long in the outstretched as in the bent position.

This seems to be the rule according to my measurements.

The relation of the time of rest to that of motion may be seen
from the curves. As an average value I should fix it at 5:41. The
only conclusion which may safely be drawn is, that relatively the
period of rest as opposed to that of motion is much greater than for
instance with the heart, Yet in the normal condition stated here,

76*

modificati

72) 20

ons” may

FO

40

Fig. XII.

50

( 1148 )

STF SSe——a—a—aa—

60

manifest themselves. The three deviations whieh

Bo 90 40.
Fig. XML

must be defined sharply were probably caused by excessive heating.
They were :

1. Too great an acceleration of the frequency. If it increased
considerably (to 20 strokes per second) then it was at the expense
of the period of rest; moreover the movement grew more irregular.
The drawing in Fig. XII illustrates this phenomenon. In this abnor-
mal motion the difference in time of forward and return-movement
disappeared ; this occurred also in the second ease.

2. Movement of the tops of the cilia only. Fig. XIII gives an
instance of this. We see the regular vacillating motion, with motions

up and down which take up

equal period of rest.

10 20 JO 40 JO 60
Fig. XIV.

the same time, alternated with an

3. The combination of the
2 abnormal conditions. In Fig.
XIV _ a rapid, irregular motion
of the top of a cilium has been
drawn. Only the extreme fifth
part of the cilium is still in
motion (whether active or passive
cannot be ascertained).

Finally I beg to tender my
thanks to Dr. L. Bunn for his
great kindness in putting time

and materials at my disposal, thus enabling me to carry out this

investigat

Groningen, February 20% 4912.

ion.

( A149)

Metereology. — “On the Influence of the Eurth’s Rotation on pire

24 4 A l
Drift-Currents”. By Dr. D. F. Totnenaar. (Communicated by
Dr. J. P. VAN DER STOK).

(Communicated in the meeting of March 30, 1912).

The water of a laterally unbounded sea, initially at rest, is
supposed to be suddenly subjected to the influence of a wind of
constant magnitude and direction. Assuming a left-handed axial system
of which the Z-axis points vertically downwards, the current-com-
ponents « and v will have to satisfy the differential equations :

Ou Oru

= av + 6 —

OF 02”
a Ov ey P 0?v
a = — au -+ b ae

in which
a =2n sin.
nm = angular velocity of the earth — 7.3 x 10-5.
yg = geographical latitude.
i

0

je = viscosity coefficient of water

o = density.

Starting with the assumption of a sea of infinite depth, we have
the conditional equations: w=v—O0O tor t=O and, z=o. The
assumption of a constan€ wind, whose direction we take along the
Y-axis, may be expressed by the equations:

Ou ie k
Gols er Uhre:

2) = k r.
is ee bi a ma spe

if- V represents the magnitude of the wind and /: the external vis-
cosity coefficient.

The differential equations are solved in the simplest way by intro-
ducing a new variable w+ iv—=w, by which substitution they are
transformed into:

Ow ; O?w

a ae eae
Putting likewise 7 = W the conditional equations become: w= 0
for ¢= 0) and: forkg— oo;

see. S(t)

( 1150 )

“Ow
€ ae — tw —w,).
Oz 20 u

Putting w! =we'et, the equations change to
Ow’ b Ow! 9
Pye rsa Ms ee Oh al (2)

1 — OMtOra i Oeandis 60.

Ow" S) ;

Rahs:
- being = c.
uu
If we now introduce a function v, connected with aw! by
il (haat
qf =—wv + = — Sem hrs | ude Mush nee aneman ())
c 02

y will also have to satisfy the differential equation (2) and secondly
we must have

fp, =— wv, -—(Wet—w',) = — Weiat,
oy

: : 5 OD
Hence satisfies the differential equation ae ORG and y, is a
function of ¢.
The solution of this equation is known from the theory of heat-
conduction and is

ce 23

9, : Ser TIE |
g= =| Wem ua) aa, oe gee ae
Ve
Wot
Here JV is constant by assumption; if W, the magnitude of the
wind, were itself a function JI(‘ of t, we shold have under the

} This remark will

ar

sien of integration instead of JV: v(i— iF

be useful later on.
(3) gives

a
w= — cal q (aja
and_ finally
_ Ace? se) __ tai?
v=—_W Bw fon fe” Aas eh Cen
2) “bt

‘) Rremann—Wesrr. Partieile Different gleich. IL p. 106.

( 1154 )

The form of solution (5) gives rise to the following remarks: One
would feel inclined, since (5) holds for a sea of infinite depth, to
suppose that the solution for a sea of finite depth 2 could be given
in the same form, the upper limit of integration for 2 being / instead
of o, since the differential equations and other conditional equations
remain the same in this case. This conclusion would be wrong,
however; the modified integral would be found no longer to satisfy
the differential equation. The reason of this is found in the cireum-
stance that although the function ~ of eq. (8) must satisfy the same
diff. eq. as w’, this by no means involves that w' will satisfy this
diff eq. together with . On closer investigation this appears to be
the case only when the upper limit is infinite.

; ; : . : A
By introducing the new variable § and putting /7 = —— the
2V dS
solution (5) may be transformed into
i tetas
cece ~ 9 4be
t= ——— aaa 4—~ -dS
2V bx oi:
x naw 5 :
Now putting 2 = 265 OTE + ¢ )— 2cbht, we obtain:
a0y
te z 4a C— ie — oe ne 2 —¢c}—iar
; i eee Ue ieee Th Pe (Pe LB :
CV -- ———— d- VW — | ~ ——— djd&\6)
ke Tv, C 2 We s 2

0 0 1)

The solution for w was reduced to the form (6) in order to render
comparison easier with the solution, given for the same problem by
FrepHoiM') and which for various reasons seemed to me to be
theoretically inaccurate. For the assumption of a constant wind along
the Y-axis is expressed by FrepHoLm in the conditional equations

Ou Ov af : ’

— |)=0,(— ]=-— —, T being taken constant. To this form of the
ele eae
conditional equation he was probably led, because Ekman had already
found the solution of the stationary problem (in which the first
members of the diff. eq. are put zero). and had used the same con-
ditional equations as expressing a constant wind. Now these are
right indeed in the stationary problem. For it is always possible to
choose the axial system such that the Y-axis has a direction along
which the constant wind-velocity and the in this case constant surface-
current velocity have equal components. The }-axis then lies in the

1) Exman. On the influence of the earth’s rotation on ocean currents. Archiv for
Matematik, ete. p. 16. 1905.

( 1152)

direction of the yvelative motion of the wind with respect to the
water of the surface. It will presently be shown that in this case
also a similar choice of axes is not to be recommended. Still it is
iheoretically the correct expression for the existence of a wind of
constant direction and magnitude. But in the non-stationary problem
matters are different. Here also it is possible to choose at a certain
moment the axes such that the components of wind and surface
current along the X-axis are equal and hence the conditional equation

Oz
time, since now the current velocity is variable. Hence the condi-
tional equations only express the condition of a constant wind with
a variable system of axes. Since, however, the diff. equations only
hold for a set of axes fixed in the earth, FrEDHOLM’s solution cannot be
theoretically correct. FrepHotm indeed finds a solution for which the w
and v at the surface are, as we might expect, functions of ¢. Now
if we bear in mind that his conditional equations have no other
meaning than that the wind component in the X-direction is always
equal to that of the surface current and that the difference of these
components along the Y-axis remains constant, it follows at once
that his conditional equations really presuppose a wind which is
the same function of the time as the surface current.

Ou
( ‘2! holds, but this direction would have to rotate with the

Consequently, if FrepHonm finds

5a S eee

this solution can only be correct for the assumption of a wind, the
components of which must be given by
t

IE: b (sin aS
TE la
u a) Sit

t

Z if Sh b (cosas _.
V=—+- ell aqeatte:
k {u wT) $2

0

Comparing Frepsoim’s solution (7) with the solution (6) found by

: Tee h oN eie
us, and remembering that 77 and c=-—. it will be seen that
(t
the first part of (6) corresponds with FrepHoim’s solution and the
second part ought to contain the theoretically required correction.
Now the following reasoning suggests itself: If in formula (6) we

( 1153 y

suppose IV prot to be constant, but some function of ¢ (which would
modify this formula as explained under (4)) and if for this special
function of ¢ we take the above given expressions for U and VJ,
which according to me contain Frepyonm’s equations of condition
implicitly, we must obtain the solution of FRrepHoLm. After some
reductions of the integrals this appears to be indeed the ease.

In order to judge of the practical value of the correction, we
write (6) in this way:

eee —iaz 219-
‘ b fe 405 : =
ASSey Ge aaa (= ic 4hz di | dé
m Gil <
0 0 ‘
A
Introducing the variable Seeiryy cVbS we have for the sur-
2y bs

face current

t a
: NY Oe Bees peas
ie =e — | ——[ 1 — 22epb§ els f e—** da' | dé.
Md S 2
0

CV be

aD
7

Now Bnet fe-P dil is a function, the value of which is zero at
«=O, then rapidly rises and amounts aiready to 0.91 at «— 2
and then slowly approaches the value 1 for c=o. At «= 0.06,
however, its value. is only */,,. Now if ¢ is such that the cwds
belonging to this limit does not exceed 0.06, the correction may
practically be neglected. The data for a determination of cWbE are
very scarce, but still it is possible to state something about the
order of magnitude. This turns out, as will be explained presently,
to be of the order 10-7. Hence the correction may be neglected in
practice if cVbt << 0.06 or ¢< 4.10% i.e. about eleven hours. Thus
FrepDHOLM’s formula, although theoretically inaccurate, is practically
serviceable for studying the development of the current. Ifin formula
(6) without a correcting member we put HW’ not constant but a
function of ¢, the solution is, as we saw,

t ——~ — iat
Onaa(e e tbs ;
i | =| W(t—S) Sar ee ds,
es 4 G2
0

which formula would enable us to follow the development of the
current if we assumed a time-function for the wind, which would
then e.g. gradually increase or decrease.

Putting ¢= 2» in formula (5) we must find the formulae for the

( 1154 )

. . . t
stationary case. Introducing the quantity a’ = l/s we find:
cw
c+(1+ ia’
from which follows for the current components

eV

4 \alz
e—(l+da’z ‘

i

t= ———__———— gin (a'z + €) e— 22,
Va? + (a 40)?
l / cS a
where tg § = ——
ee a +e
Gly ie eee
Uv —— COS (a 2 +) ez

Var @to
Hence for the surface current

cV ee aeV
a Oe
Va? + (a+)? a* + (a+¢) uy
Pa = S98
(a'+-c) eV v
— rae

s

Val? + (a'-Fe)
If in the accompanying figure OV represents the magnitude of
the wind, OS, the surface current, “ VOS,=6. It is easily found

that

! i) »

fellate —= V and sin S,\VO= oe
Val + (@’+ 0)’

This shows that the terminal point S, lies on a circular are with
chord OV and apical angle 135°. S,V now represents the relative
velocity of the wind which Ekman took for )-axis in his solution
of the stationary case. Referring the result to these axes and putting

S,V = V’ we have:

eV! cV'
— = —a'lz pone Fale — 7S S'= 5°
Ce ya° cos (45—a'z) Ca ZA ASE 45
' c Va ! . 45 ! ! Cc aa
—— i pe 5—aez 7: —
0 meer a sir (45—a'e) oe onl
TI
on SSG!
SiG
aVva
i : P : a A ee RV age
These are indeed the formulae obtained by Ekman, if eV! =—— = —
{4 tt
‘ff

EkMAN’s choice of axes and his formulae in the shape My = Oh eats
{La

( 1155.)

the angle between surface current and relative wind velocity = 45°,
reckoned to the right for northern, to the left for southern latitude,
led him to the wrong conclusion that, since a becomes zero at the

, equator, the current there would
i become infinite and also that a
sudden change in the direction
of the current would take place
there. It is not difficult to see
now where the error in his
conclusion les. It is only as
long as one remains on_ the
same spot that the quantity 7’,
used by him, is constant; as
Ons soon as the results for different

: . kay 2 :
latitudes are compared 7 — £V' = — changes its value

Val? + (a'+-0)?

together with a’. And since 7’ becomes zero at the equator together
with a’, the result is by no means that the current velocity becomes
infinite, but simply that it becomes equal to V, as is obvious. At
the same time we see from the value of §, that at the equator §
approaches zero and that consequently the current, although rapidly,
yet gradually approaches the absolute wind velocity and begins to
deviate to the left for southern latitude.

If we put in the result for the stationary current velocity
If ad kV'yb ae car : go k*b

— ual 72 “var a=n2N | p—=o0 5 alu follows that ere b.

This now enables us to make an estimate of the value c?), which

we wanted for the correction of FrrpHoLm’s formula. According to

s

s$ S : a =
Monn’s observations aa is of the order 4 10-?, so that cb is

16 «10-+ 0.73 X 10 -i. e. of the order 10—", as we assumed.

The solution for a sea of finite depth was given by Ekman only
for the stationary case, neither does Frepnotm deal with the non-
stationary problem for this case. Since, as we saw, the theoretical
correction of FrepHotm’s formula may be practically neglected for
infinite depth, I felt justified in treating this case with FrEDHOLM’s

et Ou dv li
equations of condition (= = _ me the formulae with
the theoretically correct conditional equation become in this case
unnecessarily complicated for practical application.

( 1156 )

The differential equations for the case of finite depth remain the
same. The conditional equations now become
eee
Oz ue

0
u—v—0 at t=0 anl z=A, e
dz

The solution is here found, as in the hadeeots problem in heat
conduction, when the length of the bar is assumed finite, in the
form of a Fourier series. It runs:

mF 72? h
OY ievod a S eaten 2m+1)x2e 2m-+-1) 22
wH=fQ—— Se a cog : a { Aayeos a di(8)
m=0 et =
where
Ai@s 7) sinh. (1+ )a'(h—2)
2ua’ cosh, (+)ah

' being = Sa, Ae e This f(a) is the solution for t=, i.e. for the
a0

stationary problem. It is easy to show that this solution satisfies the
differential as well as the conditional equations.

Je) =

Since
h
f(2) cos ee tava CN ee sf C a) . 8 ( +iah Es
3 2 Qua’ Am La? + 4 (LIF a?
0

(8) may be written

na (2 1)2x20
217d : oe — pel 4} (2m+-1) ae
w = {(2) — — ew di Se 4le cos ———_——.. . (9)
: wh 0 2h

Now the summation in (9) may be reduced to another form. We
have namely : i

) is)
[y: > e-p(nty? = yf SESS Ss e ae cos gry 5)
q=

A n=—w 1
Putting likewise

Ps =
—~ > e-p(n+l—y? —1 ot S é€ *P (cos qv (1 —y)

TT p—=— w q=1
and subtracting, we find

Ye
wu

x
SS (e-P (2n--y)? — “e—p (2n-+1—y)")

n—=— ©

—_er? — — Qm-+1)? x? m2
—— o

ee z
= > (1 — cosgqn)e 4 cosqny=2De 4 cas (2m--1) ay.
q=1 m=0

1) Riemann—Weser, l.c. Il, p. 117.

( 1157 )

Zz h?
Putting y= — , p= — we have
" Qh’ b2
— (4nh+2)? —(Anh+2h—z)?
eee Da a Oe ag) thee / 5 45)
Se 4h? cos = = = = ; == 7 .
m=0 2h PI VAby fear Az Als
This transforms (9) to
— as —(4nh+42h—z)?
eo. AD ~
w= ee — ear qd}
Fe ) Ve fs Fur

Since af 7=0 w=0;) ee pus result is

v= | /— Jeane iad dj, 2 a eeu LG)

where —(Anh+2)?
Pon pis 040)
a
n==— © a'l2
r= eS Cap ae ie
n==— © 7 2

As the way, followed in deriving (10) is rather long, it may not
be superfluous to show that (10) satisfies the conditions of the
problem. That the expression satisties the diff. equat. needs no

—otepP
t ~*~ _jq)
e 4b)
further proof, as this is the case with any form (+ di.
: A /2

x

0
Besides at ¢=0, w=O and similarly w=0O for z=h, because
the solution has the form g(z) — ¢ (2h—z). It remains to be shown

Ow ant
that — = —= . Now:
0Z2=0 fl
Ou ed bi b
ae at === (VE)
Zz tu a
where ; t —(inh+=)?
Peal es eles e SEU, & \o
Boe 2a Aa

t f \
é, 5) a anh+2h—=)3
Q gs __ Gnh+2h—z) z) ; aR oe
— Seo

Now it appears that for z=O all the terms of Pand Q annul each

other excepting the term P for n=O, so that there finally remains:
(Anh)?

ia.

t a
Ow a We 3 Whe aad * +
Oze—0 pt x a as Game (EH)
0

(1158 )

The value of this integral is found by introducing the variable

A (4nh)? it Ow iT
v= ———._ equal to. — SOU = =
Aba b 022=0 uw

The solution (10) admits of a remarkable interpretation. The ana-
logon of the problem here dealt with in the theory of heat condue-
tion is to find the temperature in a bar of small cross-section of
length A, while at the end z=O a definite temperature interval
Ou Valea Ul =
i ca is a is maintained. Our result says that the temperature to be
found can be conceived as due to a distribution of an infinitely large
number of heat sources and sinks of equal strength.') The heat-sources lie

ates Orand zee [4k ji= 5 the sinks at z=2h(1+2n);=0. This
shows that with respect to the point z= the sources lie symme-
trically with the sinks, so that to every source at distance p cor-
responds a sink at distance —p and that consequently the tempera-
ture (and by analogy in our problem the current velocity) will
remain zero here, if it is zero at ¢=9. With respect to the point
z= 0, however, the heat-sources lie symmetrically to each other and
likewise the heat-sinks, while in addition there is one more heat-
source at the point 20. The symmetrical distribution of the sources
Ou

u 4
—=0, and also the sinks do not contribute

makes at this point )

Ou
ay at the point z= 0 there results only
Oz
the influence of the source there situated. Now this was calculated
al’
above and amounted exactly to ——.
Ul
For the surface current we find thus:

d 412 16h? 3612

iTy 6 fieaie = fs an gee
parle 1—2e 40 4. Q¢ 402 Qe 401 4+ ete. | da.

TVA: Bh
0

to this quantity, so that for

Comparing this expression with that of Fredholm for infinite depth,
we sce that it is equal to the surface current for infinite depth,
diminished by twice the current which in that case would exist at

depth z— 2h, increased by twice the current at depth z — 4h, ete.
As soon as 2 increases beyond a certain value, the current there

is quite negligible against the surface current. With increasing /
fewer terms will suffice and for 4 = only the first term remains,
being Fredholm’s formula for infinite depth.

1) W. Tuomson. Math. and Phys. Papers 2, p. 41.

( 1159 )

Botany. — “A study of temperature-coefjicients and VAN ’v Horr’s
rule.’ By C. P. Conen Srvart. (Communicated by Prof.
Be AG EC) Wann):

(Communicated in the meeting of March 30, 1912).

§ 1. Iniroduction.

In connexion with a number of investigations into the influence
of temperature on physiological processes, I have made a study of
the available data. At the meeting of the Dutch Botanical Society
in October 1911, I already communicated some of the results to
which the study of the literature had led me, and although the
further deductions are of a somewhat hypothetical character (for which
reason I have started an investigation to clear up some doubtful
points) I nevertheless feel it may be as well to publish already the
main results, because in the discussions which took place they suggest
some new points of view.

I may not omit to acknowledge here my indebtedness to Professors
Went and Conen for their advice and interest. *)

§ 2. What is van ’? Horr’s rule ?

In the literature of physical and physiological chemistry there is
found again and again the phrase “According to van ’v Horr for
every 10° rise of temperature the reaction velocity becomes twice to
thrice as great” (“R. G. T. rule’). It is the physiologists especially
who like to make use of the determination of the temperature-coeffi-
cient in order to decide from its magnitude whether a given process
is “chemical” or “physical”, and who to that end invoke the above
erroneously quoted rule. I shall endeavour to show that the formula
of van ’t Horr itself makes clear that the usual interpretation of the
“R. G. T. rule” with regard to the constancy of the coefficient rests
on a misunderstanding.

By temperature-coefficients I mean the quotient (Q) of two reaction-
velocities which are separated from each other by a constant interval
of temperature, usually 10°. Proceeding on the hypothesis that this
temperature-coefficient for every 10° increase equals 2—38 then it is
evident that this function may be graphically represented by a curve
ascending exponentially. “Bilden die Temperaturen eine arithmetische
Reihe, so bilden die Geschwindigkeiten eine geometrische” *). It is
clear, that, when the temperature-coefficients of this function are

1) The dissertation of Miss van Amsret, ‘On the influence of temperature on
physiological processes in yeast”, just now appeared, in which she makes a detailed
communication. To my regret too late for me to make use of it in this paper

2) Van ‘rt Horr-Conen, Studien z. chem. Dynamik 1896, p. 128,

( 1160 )

again plotted against the temperatures as abcissae, the new function
is represented by a line parallel to the abscissa, for the coefficient
is assumed to be constant.

It has long been known and moreover van ‘t Horr already
stated‘), that this coefficient is not constant, but that it decreases
when the temperature is raised and vice versa. But if the coefficient
decreases, then this signifies, that the reaction-velocity is diminished
and this again indicates, that the curve of the reaction-velocity és no
longer exponential.

Trautz and VoLKMANN *) were the first to pay full attention to the
lowering of the temperature-coefficients. In the saponification of a
large number of esters with Ba(OH), and NaOH *) they obtained
acceleration-curves (Pl. II, tig. 1) which agreed very well, and
which all possessed the peculiarity of showing a maximum at about
20° ; S08
10° and assuming 2 flat course at a high temperature of 49°"
The investigators then chiefly occupied themselves with the search
for a reason for this maximum at 20° and succeeded in finding one,

,

bags se ashe Bem : * oe
namely, an irregularity in the function —— (in which 1 = viscosity)
Bay Rae
and a maximum in see both at 20°. I will not here discuss the
aT?

formula they put forward; and only say that by the introduction of
dy ; :
—,, & maximum in the curve calculated was indeed obtained *).

Here again appears the long suspected connection between reaction-
velocity and internal friction, that has been regarded by many as a
postulate for formulating in absolute measure the reaction-velocity
of chemical processes *}. This however is not the point to which I
wish to call attention here.

Our ultimate aim is to establish the shape of the complete curve
of the coefficients in connection with the course of the complete curve
of reaction-velocity and temperature. Although this aim cannot at
present be attained, we may still begin by making some deductions
from the formula which already presents some properties of the

1) Studien, p. 128. Vorlesungen 1898, I. p. 224.

*) Zschr. f. physik. Chem. LXLV (1908).

5) Executed by Vorkmann, Inaug. Diss., Freiburg i. B., 1908.

*) See however v. Hateax, Zschr. f, physik. Chem. LXVII (1909), p. 179.

») The well-known analogy to Oum’s law. E.g. Nernsv, Theor. Chemie, 6. Aufl.
(1909), p. 672. Van ’r Horr, Vorles. I, p. 171.

( 1161 )

desired function, namely, the formula suggested by van ’r Horr ')
and simplified by ArrHENivs*)

dink A

a Oe)
in which =the reaction-velocity at a constant (abs.) temperature
7; on integration from 7, to 7’, this becomes

h, Tne
ln —— Al SS (2)
, TRE
k -
or, if -7,—7, = 10° and = = Q (coefficient)
vy
om :
7 = —_—_. 2
ihe (

5 ' Ties : ae
In the formula A is equal to "ot VAN “T Horr®) or 5 of ARRHENIUS‘)

and represents half the heat change (e.g. heat of dissociation). This
quantity is a function of temperature, but since i so to a much
smaller extent than the coefficient @ and since I only aim at a first
approximation, it will be supposed constant and 5500 eal. will be
substituted, which number is about the average of the values obtained
by VoLKMANN.

The Q-curve of course begins with 7’, = 10° absolute temperature.

Thus

104
Oto OF 3c
es) SC USS 0)
Lope — a1
log: Q., = 40
bg Oe, 12
logQ eG
log Q.5, = 0.628 One
log: Qs 07309 Or = 2. 04
log Q;5,; = 0.222 OL == OT
log Qigy == 0.047 Qiog = 1.1)
10A oe
log Qg =—_ = 0. Qa .00
720

The coefficient @,,, for aigae approaches very closely the value

1) Etudes de dynam. chim. 1884, p. 115. Studien, p. 127, 152.
2) Zschr. f. physik. Chem. IV (1889), p, 234.

*) Studien, p. 154. Ostw. Klass. 110, p. 29.

4) Immunochemie 1907,

~I
“I

Proceedings Royal Acad. Amsterdam. Vol. XIV.

( 1162 )

6.2 found by Prornikow'), but this is quite intelligible when it is
remembered that for this reaction and this temperature A equals about
6000. In the same way at 640°—719° abs. temp. Kooy’s *) coefficient
which is 1.17 at 700°, is connected with the value of A= 7790 at
that temperature. Further it is clear that the Q-eurve must take an
asymptotic course with respect tothe ordinate as well as to the abscissa.

The above figures seem to me to render obvious the meaning of
the critical passage *): “Bei der gréssten Zahl der bis jetzt in dieser
Richtung untersuchten Falle, welche sich auf das Temperaturinter-
vall O'—184° beziehen, ist nun sehr auffallend das Geschwindig-
keitsverhaltniss fiir 10 Grad Temperaturerhéhung etwa 2 bis 3 bei
gewoOhnlicher Temperatur, m. a. W.: eine Temperaturerhéhung
um 140 Grad verdoppelt, resp. verdreifacht die Reaktionsgeschwin-
digkeit”. Emphasis must be placed, not on “10 Grad Temperatur-
erhdhune”’ but on ‘“etwea 2 bis 3 bei gewdhnlicher Temperatur’.
It is indeed very curious that in curves of the most varied pro-
cesses in which A can have widely different values, and therefore
in the most diverse curves by far the larger portion of lines pass through
the rectangle which is formed by the abcissae 0° and 50° C. and
the ordinates (coefficients) 2 and 8. Whether the lines within the
rectangle descend quickly or slowly, whether they run through the
whole of its length or only touch one point of it, does not matter!
It is but a general principle, a rule , not a law.')

Now it would be of great importance to obtain an exact mathe-
Mg matical definition of the Q curve.

If we for tne moment imagine
the simplest case, namely, that
the X line (reaction-velocity) is
a straight line — which sup-
position, it must be here stated
emphatically, is purely mathe-
matical and completely inde-
pendent of any physical or phy-
siological-chemical hy pothesis —
then the Q curve is also a

simple function of temperature.

') Diss. Leipzig 1905. — Zschr. f. physik. Chem. LIll (1905), p. 630. —
If the formula of Arruenius is used instead of that of Berruenor, then Q =5.77
is obtained.

*) Diss. Amsterdam 1893. — Zschr. f. physik. Chem. IV (1889), p. 226.

*) VAN ‘2 Horr—Couen, Studien, p. 128.

( 1163 )

For, in general, if

Qs = (see fig. 1 in the text
k, J («)
: ] h nr + h) — i
then C— eae + [\ pA)
J («) J (2)
1, 4 fe +n-f0)
f (2) h
| (4)*)
— + —— .f (# 6 a M8 Cie, fo) is) -
J (#)
If one bears in mind that / is always supposed = 10° and that

f(«) is the smallest of the ordinates under consideration and may

be represented by A710, the latter general equation changes to
10 , .
Q= 1 + —— .. f(a). »- . -~. «. (8)

kT7-10
It is now clear what formula (5) tells us with respect to the
shape of the Q curve, when & is a linear function. For since
f («)=tgx =™m constant, hence

therefore (Q—1). /:7_10 = 10 m = constant.

Now since the function is according to hypothesis linear and since,
as is actually the case, it passes through the origin (i.e. at O° abs.
temp. £=0), 7-10 is proportionate to the absolute temperature,
and we may also write:

(— lie constant... a. i225, am-+ (6)

and from this again it at once follows that the Q curve is a rect-
angular hyperbola, of which the one limb asymptotically approaches
the y-axis (coefficient) and the other at distance 1 runs parallel to
the abscissa (abs. temp.). If both sides of eeuation (5) are multiplied
by ky-\o, it is at once seen that this hyperbolic shape is nothing
peculiar and only signifies that in a straight line the difference
between two successive £-values is constant.

The application of the result will appear from the following section.

1) Cf. v. Hasan, le. p. 168 a.f. “Die R. G.T.-Regel kann also héchstens
in der Form bestehen bleiben, dass sich die Temperaturkoeffizienten in dem
Gebiete der messbaren Geschwindigkeiten zwischen zwei und drei hiiufen” (p. 171).
-Also Trautz, Zschr. f. physik Chem. LXVI (1909), p. 506.

2) Instead of the elementary deduction given above, use can be made of the
Taytor’s theorem (Dr. M. J. vay Uven very kindly pomted it out to me) or of
the method in Gawotson Lehrb. d. Physik IIL (1905), p. 12.

hice

.

( 1164 )

I have already stated that the Q function for an exponential / curve
is a horizontal straight line.

If we attempt to establish the @ function for an arbitrary reaction,
the formula of van ‘rt Horr-ArruENius does not take us further.

What is the reason tor this? The sole and only reason is our
ignorance concerning the quantity A. For not until this quantity
becomes known as f(7’), is a conclusive opinion possible with respect
to the geometrical meaning of the formula in question. Therefore it is
above all necessary that the formula of van 7 Horr-Arrnentvs should
not be used to interpolate velocity-constants or coefficients (for these
should be obtained experimentally) but im order to discover the de-
pendence of A or w on the temperature. The determinations directed
to this end must be made at regular intervals (preferably from 1°
to 5°) because at the present time determinations at arbitrary tem-
peratures and interpolations with the formula of AkRruENius or
ByrtHeLor are of no value.

Now there are two standpoimts from which this problem can be
viewed. In the first place the formula can be considered as purely
theoretical (founded on thermodynamics) and then A can be identified
with half the heat of dissociation; if it turns out that the reaction-
velocity is governed by still more factors, then these must be idro-
duced into the formula. I have here in mind, for example, the
viscosity. Since the second law of thermodynamics only pronounces
on the possibility of energy transformations and not on the way in
which energy transformation comes about, and therefore not on the
loss of energy through friction, it is therefore intelligible that there
should be this omission in a thermodynamical formula. If, on the
other hand, we consider van ’? Horr’s formula as an interpolation
formula, viz. as an expression which agrees as closely as possible
with the observations, in which A represents a so-called interpolation
constant, that is to say, rather a note of interrogation than a ‘‘non-
variable’, then it must be our aim to break up this quantity into several
others, among which for instance the dissociation and the friction
might oceur.

It seems to me that there is much to be said in practice for the
latter view. In that case, however, there is absolutely no sense in
ceiving a single g-value for a reaction (at an entirely arbitrary tempe-
rature) as has been frequently done of late on the example of ARRHENIUS ;
indeed, it is a very rash generalization. This is at once obvious if
we construct for the experiments of Vo.kmann for instance, the
corresponding A-curves. It will be also clear from the next section.

As a matter of fact one may therefore say that any reaction (and

( 1165 )

not even necessarily a chemical process!) may be represented by
vAN “t Horr’s formula: it is only necessary to give suitable values
to the interpolation constant A. But in that case there is little
value in pointing out this ‘applicability’, as for instance in serum
reactions (experiments of Mapsen and others, and of Arrientus) ‘).

The results of our considerations may be summarized thus:

I. The curve representing for chemical reactions the relationship
between reaction-velocity and temperature is not an exponential
one; the relationship between temperature-coefficients and temperature
is hence not a horizontal line.

II. If the function of reaction-velocity is represented by a straight
line the curve of coefficients is a rectangular hyperbola.

If. Nothing definite can be said with regard to the true form
of the desired functions before the quantity A has been completely
defined.

§ 3. The temperature-coef ficients of vital processes.

After all that has been said above with regard to the fact that
temperature-coefficients of chemical processes generally diminish with
rise of temperature, it can hardly create surprise when it is found
that the processes in the living organism are equally subject to this
rule. Kanirz*) was the first to notice this and evidently regarded it
as an essential relationship, but it is obvious from discussions occurring
in the literature after 1905, that his remarks have remained quite
unnoticed, as (just to quote two recent instances) in the papers of
Miss van AmsteL and Professor van Iturson *), and the research of
Mlle I"tron *). The reasoning is as follows: “the rule of van ’r Horr
is not applicable to living processes, because the coefficient diminishes
and is too high at low temperatures and too low at high ones’. It
is hardly necessary to say that this conception should have been
already entirely abandoned. But, e.g., against Rureurs’s*, argument
(namely, that Trautz and VoLKmMANN had also found diminishing
coefficients — with which he did indeed hit the nail on the head)
van. Amster and van Irrrson defend themselves as follows °):
“Admitting that for physiological processes, also at harmless temper-
~ 1) Immunochemie 1907.

2) Zschr. f. Elektrochem. XI (1905), p. 689. See also Jost, Biol. Cbl. XXVI
(1906), p. 229. Afterwards Kanrrz, Biol. Gbl. X XVII (1907), p. 15 Conen, Vortrige
f. Aerzte tb. physik, Chem. 1907, p. 50.

3) These Proceeding». 1910, p. 227 and 598.

4) Journ. d. physiol. et d. pathol. génér. XIII (1911), p, 19.

5) Diss. Utrecht 1910, p. 152 These Proceedings 1910, p. 484,

6) L. c. p. 605.

( 1166 )

atures, the rule of van ’r Horr is of no consequence, what then
remains of BLAcKMAN’s theory?” Here all depends on what ts under-
stood by van *r Horr’s rule, which these processes are obliged to obey!

Recently a paper by Snyper’) appeared ”On the meaning of
variation in the magnitude of temperature coefficients of physiologice)
processes”. In this the principle of diminution is plainly stated and
supported by many numerical data. It does, however, seem to one
that all these figures, taken from the most complicated processes of
animal physiology, do not form any trustworthy foundation on which
to erect even a small structure of theoretical deductions. What,
however, deserves great credit is that, in collavoration with Top» °),
he at once made an attempt (in connection with VoLKMANN’s hypo-
thesis) to measure the change of viscosity of the body-fluids (dog’s
peptone plasma) under the influence of temperature. He finds a

Aan re A) ae Sees dy.
diminution of 4 with rise of temperature parallel to Ti for water.
¢

As usual, the observations are here also restricted “within physio-
logieal limits” while it is exactly the study of the phenomena of death
that can furnish most important data with respect to the condition
in which the wiakarmed protoplasm finds itself *). The extension of
the experiments to higher and lower temperatures, which is a com-
paratively small difficulty in the course of an investigation, should
make these experiments much more productive.

In view of the slight results which the above research has yielded
(BLACKMAN’s theory with all its appurtenances is clearly still unknown
in animal physiology *)) I may leave this and proceed to a survey of
the botanical publications from which data can be gathered for our
object. | add below a list of the literature I have used.

In my calculations and constructions | have proceeded from the
hypothesis that the figures given for the reaction velocities are free
from error. | am aware that IJ am thus guilty ofa heresy. My excuse
is in the first place that a critical selection is impossible because in
almost all cases the sources of error are not given, both as regards
number and magnitude. Moreover I wished to see what an exact
caleulation would yield from data, which in general could indeed

Amer. Journ. of Physiol. XXVIIE (1911), p. 167.

“) Ibid. p. 161.

8) See H. W. Fiscusr’s interesting paper, Beitr. z. Biol. d. Pfl. LX (1910), p.
133. Koll. Zschr. VIIf (1911), p. 291.

4) Héper in his comprehensive work (Physik. Chem. d. Zelle u. d. Gewebe, 3.
Aufl. 1911) still devotes only a single chapter to physiological-chemical kinetics,
and in this only a few words to the question of optima.

( 1167 )

vary in all directions. I believe I may say that the result which is
represented in the sub-joined Q-curves, justifies to some extent my
procedure.

And this for three reasons especially : firstly because the course
of the curves is very regular —- secondly because in those investi-
gations, especially those of Kuyper, in which account is taken of the
duration of warming (for which in animal experiments a// data are
wanting) the curves for one and the same duration of warming take
an accurately parallel course, and finally there is the more remar-
kable quality, that the course of the coefficient curves are of one
general type. This type can perhaps be best characterized by compar-

ing it to the well-known inflected gas-isothermals.

Although the following considerations apply to a greater or less extent
to all constructed curves, I shall always pay special attention to
KuypgEr’s curves (Plate I) since his figures (especially those for Pisum)
are presumably the most accurate which we possess with respect to
temperature-coefficients in physiology.

+104

+ 0.74.104

— 104

— 2.104
LON AZO 30a) Ao. 50
0 10 20 30 40
Fig. 2. A-curves for the respiration of Pisum
sativum (KuUYPER).
—lhours’ —2hours’ ---3 hours’ warming.

( 1168 )

The following peculiarities may now be noticed :
: 15°
1. Many curves have a maximum at —.

De

2. In successive hours the curves of the coefficients show a
tendency to pass from a gradual to a steep descent.

3. All curves show a tendency up to 35 or 40° to approach the
coefficient 1 asymptotically. Afterwards the direction changes to one
of rapid descent.

4. The curves of Nice, VeLTen, vAN RiJsskELBERGHE and RutGers
descend much more steeply than the others.

5. All curves descend much more rapidly than those of VOLKMANN °).

Further I have constructed from the five @-curves for Pisum the
corresponding A-curves with the aid of ARRueEnivs’ formula, for from
every value of Qa value of A can be calculated; from the latter
curves it is obvious that A is by no means constant and therefore
here also a previous remark on the rash generalization of A-values
applies. In fig. 2 of the text I have indicated the place where accord-
ing to ArruEnius *) “the” A-value lies, namely at w= 2A = 14800
(calculated according to CiaussEn *)). It will be seen that there is no
question of a real “mean’’, not even if we limit ourselves to ‘“inno-
cuous” temperatures. It is also seen that for supra-optimal tempera-
tures A soon acquires very large negative values. This results from

the formula nQ = 7a = since, when Q=1,A=0, and when
ib}
Q=0) A=— oe:

The latter result of course means that the respiration has stopped
and that death has occurred. The coefficient Q itself never becomes
negative.

We now proceed to a discussion of the property mentioned above
sub 1. Is the maximum which appears in many (Q-curves a real
maximum ? It occurs so frequently that we must consider it appears

according to a rule and we are at once reminded of the maximum
n°

which Trautz and VoLKMANN always found at 0° It should further

be noted that these authors leave open the possibility of the maximum
being somewhat lower, since they made determinations at intervals

Ss)

nN

1) The rate of descent could of course be again expressed by In_ practice
this, however, introduces large errors (compare vy. Ha.pay, 1.c.).

2) Immunochemie 1907, p. 88.

3) Landw. Jahrb. XIX (1890), p. 893.

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( 1169 )

of 10°*). It would be worth while to investigate this maximum also
foe physiological processes, in order to demonstrate a possible con-

: 1 aN ; A

nexion with ai Too much importance may, however, not yet be
a

attached to this maximum, since at O° the experimental errors may

4 ()\o
be considerable, and these errors influence the quotient a

As regards the second point, i.e. the decrease of the coefficients
in successive hours, we may note that the line of 1 hour’s warming
often shows (irregular?) oscillations, whereas the other lines generally
succeed one another more or less regularly. If we now bear in
mind, that VoLKMmaNy’s lines were yery slightly inclined, we obtain
the impression that the line for 1 hour's warming approximates to
those for reactions in vitro”) and that the subsequent lines deviate
more and more from this. This is exactly what Brackman has
asserted for reaction velocities and with him we may assume that
the correspondence would be complete if observations could be made
after an infinitely short time of preliminary warming.

It should be noted in passing that the construction of the Q-curves
affords a means of demonstrating almost imperceptible irregularities
of the k-curve. Since the various Q-curves are mereover directly com-
parable (assuming that the units are in -constant equal preportions),
in contradistinction to the f-curves, which change their slope in
accordance with a change in the choice of the values of the units,
the construction of the Q-curves is much more correct and important
than that of the k-curves. .

The third point deals with the asymptotic course when Q= 1.
In the preceding section we said that in reactions which are linear
functions of temperature the coefficient at 1 runs asymptotically, and
in agreement with this is the behaviour of the physiological coeffi-
cients at “harmless temperatures’. The upper limit of these tempe-
ratures varies between 25° and 40° according to the process and
the object. Starting from this temperature one conld draw further a
“theoretical” asymptotic line. (The same is seen in the A-curves.)
The explanation of this phenomenon is of course simply that at
infra-optimal temperatures the 4-curves frequently differ very little

1) Dissert. p. 25 Zschr. f. physik. Chem. LXIV (1908). *Wir sehen nur, dass
ein Maximum der Beschleunigung in der Nahe, wahrscheinlich unterhalb von 20
Grad liegt.”

2) Later physico-chemical investigations will be required to show whether my
generalisation from VOLKMANN’s experiments is justified,

( 1170 )

from straight lines. In that case the Q-curve must necessarily resem-
ble a hyperbola.
There are finally the fourth and fifth points. concerning the more

or Jess rapid diminution. The curve of NAGntt shows that the “abnor-
2 S
mally” high coefticient of Rurerrs for rie namely 6.75, no longer

stands by itseif but is even surpassed by the enormously high figure

9.33 for Nitella (which figure, it should be noted, was obtained by
( [e}

extrapolation from and is therefore probably too low). RurGeErs *)

fo}
attributed the high value of his coefficient to the cessation of growth
at O°. We are here at once reminded of the cessation of protoplas-
mic streaming and the very slight diosmosis at 0’. What is the cause
of this “Kéaltestarre’, which one is inelined to neglect as ‘freezing’?
What is more characteristic in the cooling of an emulsion-colloid
than the enormous increase in the increment /” (2), therefore also in
Q, of the viscosity ? *)

! am indeed convinced that by the investigation of the influence
of temperature on the viscosity of emulsoids, the mystery which
stil] surrounds heat and cold-rigor, will be solved, at least in part.
It is impossible to discuss this further, but I only desire to record
my scepticism as to the “chemicity” of a process possessing a high
temperature coeflicient. The real distinction between a (-curve
under purely physical influence and a purely chemico-physiological
one would perhaps become perfectly clear at once if one could
compare the two kinds of curves. It is, however, very remarkable,
that hitherto not a single case has come to light in which the coef fi-
clents throughout have “physical” values*) not even there, where a
purely physical influence might have been expected (e.g. protoplasmic
streaming, diosmosis). Now is it legitimate to refer this result without
further to a (chemical) metabolic influence ? That is indeed some-
what too simple. 1 entirely concur with SuTHERLAND*) in his severe
judgment: “/n order that the chemical theory of nerve-impulse may
prove helpful it must show in some reasonable way how the velocity of
propagation of a chemical reaction along a nerve can be proportional

1) Dissertation p. 183. These Proc. 1910, p. 479.

2) W. Ostwatp. Kolloidchemie 1911, p. 204, 221.

5) See the numerous instances cited by Sxyper. Univ. of Chicago Publ., Physiol.
If. (1905), p 125. Arch. f. Anat. u. Physiol., Physiol. Abt. 1907, p. 113. Amer.
Journ. of Physiol. XXIL (1908), p. 309.

') Amer. Journ. of Physiol. XXII (1908) p. 128.

(247d)

to the metaphorically so-called velocity of reaction at any point in
the nerve.”

In my opinion it is legitimate to “deduce” the chemical nature
of a process from the coefficient 2 to 3 only in such eases... of
which one can be certain in advance (respiration, assimilation). —

Finally I wish to indieate very briefly the conclusions to be
drawn from the above with regard to BLAcKMAN’s theory’), which
interprets the temperature optimum in physiological processes as the
resultant of a favourable and a harmful influence. This theory is
entirely based on the asswmption (found to be erroneous) that the
reaction velocity (/-)ecurve according to van “tT Horr is an exponen-
tial function; to this curve (“the line of zero time’) all the observed
reaction velocities are exterpolated, and if these extrapolated curves
end in the points ‘required by theory” the matter is sound, according
to Briackman, and van “t Horr’s rule also applies to harmful tem-
peratures.

BiackMAn’s theory has been controverted by van AmstrI. and VAN
Iverson (loc. cit.). These authors start with a totally different extra-
polation method and with its aid obtain results entirely opposed to
Biackman’s. This question cannot here be discussed further, and the
correctness of vAN AmstEG and ItrErson’s extrapolation method is
therefore also left out of consideration.

A different question, however, is, whether Bnackman’s method has
any use. Of course it has not. Since BLACKMAN extrapolates his heating
curves to a line which is not “chemical”, but quite imaginary and
arbitrary*), the end-points of these curves are as imaccurate as the
conclusions, which are drawn from the supposed agreement between
fact and theory, and the proof of his theory, based on these con-
clusions, is worthless. Is therefore his theory also worthless ?

No, at least I do not think so; only the validity of BLAcKMAN’s
theory cannot at present be proved. If the true curve were known
(but this awaits a chemical definition of A) then, and then only,
something might be attained by extrapolating. Meanwhile one can
only adduce grounds of probability. Some of these have already
been mentioned. A further argument results from the following con-
sideration. If the last portion of the /-curve, before the concave
bend, is produced rectilinearly and if we extrapolate to this, much
smoother curves are obtained than with BLAackMAN’s exponential line.
This is for instance well shown by Kuvyprr’s curves for Triticum ;
with Pisum a line is required intermediate between a rectilinear
1) Ann. of Bot. XIX (1905), p 281.

2) Kanirz, Biol. Ubl. X XVII (1907), p. 20.

( 1172)

and an exponential lengthening. Hence it follows that the sharp an-
tagonism between the lines of zero time of BLackMAN and of vAN
Amstren and van Itrrson is considerably lessened. It is clear, however,
that this gives scope for a most arbitrary procedure. There is no
positive proof.

It should be expressly pointed out that the above results in no
a merit based on his opposition

way diminish BLackman’s merit
to the general misuse of the terms ‘“Reiz” and ‘“Auslésung”’ as
meaningless principles’), thought to explain everything, and more
especially on the manner in which he traced a clear and logical con-
nection between the theory of reaction velocity in chemical and in
physiological systems, the theory of limiting factors and the theory
of the origin of the optimum. —

The above considerations may be summarized as follows :

I. The falling of temperature-coefficients with rise of temperature
is also the rule in physiological processes.

I]. Brackman’s theory, which is thus deprived of its “chemical
curve’ and its extrapolation method, is at present not susceptible
of proof.

Ill. Probably the study of temperature-coefficients will furnish
a better insight into the mode of action of temperature than that of
reaction velocity.

IV. Both the velocity curves and the coefficients point to a close
correspondence between physiological and chemic il processes.

V. This correspondence is, however, rendered less evident by the
influence of viscosity, which plays presumably a very important
part in the heterogeneous, colloidal protoplasm.

VI. The study of the influence of témperature on the viscosity
of colloidal systems will probably explain a large proportion of the
apparent deviations of vital processes from the course of chemical
reactions in homogeneous systems.

Utrecht, University Botanical Laboratory.

EXPLANATION OF THE FIGURES.
PLare lL. Fig. 1. Q-curves for the respiration of Pisum sativum (1—5 hours’

warming). According to Kuyrer, These Proceedings Vol. XII p. 219.
Ree. trav. bot. Néerl. Vil (1910), p. 164.

Fig. 2. The same for Triticum vulgare. According to Kuyrer, Proc, 1909.
p. 225 Ree. tray. bot. Néerl. VIL (1910), p. 194.

Fig. 3. The same for Lupinus luteus. According to Kuyrer, Proc. p 225
Xec. p- 190.

1) Nature LAXVILM (1908), p. 596.

( 1173 )

Praar Il. Fig. 1. Q-curves for the saponification of some acetic esters. According
to Votkmann, Diss. Freiburg i. B. 1908. ;

Fig. 2. The same for the evolution of CO, in alcoholic fermentation. Accord-
ing to v. Amsret and v. Iverson, Proc. XIII p. 233

Fig. 8a. The same for the geotropie sensibility of Avena seedlings. According
to Rureers, Proc. XI!T p. 476 Dissertation, Utrecht 1910, p. 92.

Fig. 3b. The same for the permeability of the medullar protoplasm of Sam-
bucus. According to vy. Rissserseraue. Ree. Instit. Léo Erréra, Bruxelles, V
(1901), p. 223 (by graphical interpolation in fig. 1).

Fig. 4a. The same for the velocity of streaming of the protoplasm of
Nitella synearna. According to N&ceut, Beitr. z. wiss. Bot. H. 2 (1860), p. 77.

Fig. 4b and 4c. The same for Chara foetida and Elodea canadensis, respec-
lively.According to Vette, Flora LIX (1876), p. 210 and 198 respectively.

Mathematics. — “Qn a congruence of the second order and the

Jirst class formed by comes.” By Prof. Jan DE Vruius.

The theory of the linear congruences of conics (congruences of
the first order) has been completely developed by Monrtrsano*)
(1892-—95). For the determination of the relations between the
characteristic numbers this author among others made use of two
auxiliary surfaces: the locus 4 of the conics meeting a given line
and the locus J of the conics the planes of which pass through a
given point. An extension of this method to congruences of higher
order remains infertile by the fact that in these cases a point common
to two conics is not necessarily a singular point. Until now general
considerations on congruences of higher order have not been published.

In these pages we consider a special congruence of order two
and class one, showing a family-likeness with the congruence (2,1)
described in 1908 by L. Gopravx ’).

1. The congruence IL under consideration consists of the conies
y° passing through a given point (, having three points in common
with a given twisted cubic ¢* and meeting a given line 7.

The locus of the conics passing through O and through any point
P and meeting g* thrice is a quadratie surface +*. By the points
common to 7 and &* two conies y* of I are individualized ; so P
lies on two-y? and TF is of the second order.

1) Atti Torino, XXVII (1892), Rend. Ist. Lombardo XXVI (1893), Rend. Napoli
(1895) p. 93, p. 155.

2) Sur une congruence (2,1) de coniques. (Mém. Soe. des Sciences du Hainaut,
6me série, t. X).

In 1904 we dealt with a special congruence (2,2), (These Proceedings Vol. VII,

p. 311).

( 1174 )

Moreover Tis of the /irst class, for an arbitrary line / determines
with QU one plane, containing only one conic y’.

If 7 passes through O it is a singular bisecant; the eonies y? with
/ as bisecant lie om a surface S* of which / is a nodal line and O
a triple point'). The straight lines of the plane (Or) are also singular
bisecants, this plane containing a pencil {y*).

The surfaces +? form a pencil, the base curve of which consists
of 9° and its bisecant 6 through O. Each * contains two systems
of y?; if R, and FR, are the points common to that ¥? and 7, these
two systems have OR, (resp. OR,) for bisecant. So ? is at the
same time the locus of the y* meeting twice a determined 7? lying on it.

The line 7 is touched by two 2*, any point P of one of these
surfaces is characterized by the property that the two y? through it
coincide.

The conies y* passing through any point S of 9? form a surface
?* with OS as nodal line and O and S as triple points; for the
bisecants ¢ of @® meeting 7 lie on a ruled surface of order four and
the two bisecants ¢ cutting OS in points different from S form with
SO two degenerated y’.

2. Each line ¢ determines one degenerated y*; the second line g
of that pair of lines joins O to the third point S of o* in the plane
(Od. The lines g generate a cubie cone with nodal edge 6, project-
ing ¢* out of O. Kach line g belongs to two pairs (g, ¢); the locus

2

of the point (y,f) 1s a twisted sextic.

The plane (Or) contains three lines d, = OS,. The bisecants f of
o* meeting d, generate a regulus; each (d, /f) is a y’.

Each plane through 6 contains a line ¢ meeting o* and7. A plane
through 7 contains three lines c. So the locus of the line ¢ is a
ruled surface of order four with & as triple line and 7 as single
director line. Each ¢ forms a y? with 0.

3. We now consider the surface A, locus of the y? meeting /.

The y? lying in plane (QO/) meets / twice and is therefore nodal
curve on 4; moreover this plane contains three lines g each of
which is eut by two bnes ¢ and therefore likewise nodal line.
Finally @ is double line teo. From this ensues that 4 is of order
twelve and admits in OU an eightfold point.

On this A’ the line 7 is double line and the curve y* fourfold
curve, as / has two points in common with any +? and four points
with any @*.

As the locus of the line ¢ is a ruled surface of order four, A”
: 1) Evidently £4 is at the same time surface M for any point /, and it passes

once through +.

(Airs)

contains. besides the six lines / indicated above, four lines ¢ and four
lines y. Moreover 4°? contains six lines f and three lines d as nodal
lines. Finally 4‘? contains four lines ¢ and the fourfold line 0d.

4. Let d be a ray of the pencil with vertex D lying in the
plane ¢&. Each line d is bisecant of one y*; the locus of the points
of intersection of d¢@ and y? is a curve of order four with Das node.
Through D pass six rays d each of which touches a 7’. So the

2

tangents of the 7° form a complex of order six.
From this ensues that the planes y of the y
a cone of class six, with (Or) as bitangent plane, the trace of this

> touching d envelop

plane with d being touched by two y’.

Any surface >‘ (art. 1) is cut by any line / in four points; the
planes y of the y* meeting / in these points pass through a ray of
the sheaf ©. So the planes y of the y* meeting / envelope a cone
of class four, admit also (Or) as bitangent plane, any y° lying in
that plane having 7 for bisecant’).

Both cones admit twenty common tangent planes, besides (07). So
there are fiventy y* meeting a given line and touching a given plane.

5. In any plane 2 the conics of the congruence determine a
correspondence (2,2). The two 2? touching 7 intersect 2 according
to two conics, each of which bears an involution of pairs P, P’;
the points corresponding to P(?’) coincide in P’ (P).

Let 7 be an arbitrary line of 2. The corresponding surface A’ is
cut by 2 according to a curve 4'° containing the points 7?’ conjugate
to the points P? of / in the correspondence (2,2).

To the points common to / and 4*° the points of intersection of /
and the y* of which / is bisecant belong; the remaining eight are
points of coincidence P— P’.

So the curve of coincidences is of order eight; the four points of
intersection of 4 with @* and & are threefold. points of it.

These four points are at the same time fundamental points of the
(2,2) and threefold points of the corresponding fundamental curves
of order four. Likewise the four points of intersection of 2 with 7
and the three lines / are fundamental points with conics as fundamental
curves.

1) The cones corresponding to / and /' admit 12 common tangent planes, besides
(Or). From this the order of A can be deduced once more.

( 1176 )

Anatomy. — “The arrangement of the motor nuclei in Chimaera
monstrosa compared with other fishes” By C. U: Anriéns Kappsrs.
(Communicated by Prof. lL. bork).

(Communicated in the meeting of February 24, 1912).

Examining the oblongata in different orders of fishes great differ-
ences are found in the topographic relations of the motor nuclei.

On the other hand there is a striking resemblance in the arrange-
ment of those nuclei within the limits of an order. Cyclostomi show
principal differences in this respect if compared with the Selachii,
and the oblongata of the latter is again very different from that in
Teleosts. Recently Droocirnver Fortuyn ') found that Ganoids (Amia
Calva) are again different from both.

These observations add to establish more differences between
classes and orders drawing the lines of limitation sharper.

In the end of last and the beginning of this year I had a chance
to examine a specimen of the order of Holocephali. This seemed
important to me because the animal (Chimaera monstrosa) represents
a separate order and because in several respects its brain stands in
between that of the Selachii and Teleostei.

I wanted to know: 1. If the arrangement of the motor nuclei
in the oblongata of Chimaera revealed such characteristics as should
be expected in a separate order; 2. if these characteristics stand
in between those of the Selachi and Teleostei.

Although I did not expect a great difference in the internal
structure of the oblongata with the Selachian type, on account
of the striking macroseopical resemblance between this oblongata
and the Selachian, my studies gave very interesting results, which
proved on one hand that also on account of the arrangement of the
motor nuclei in the oblongata Chimaera deserves a special place in
the classification of vertebrates and that on the other hand it stands
in between the Selachian and Teleostean type.

The facts are these :

The selachii have only a dorsal oculomotor nucleus ; Hurr*). A
real ventral nucleus as in Cyclosfomes or in Teleosts and Ganoids
(Amia Calva, Drooc.enver Forruyn) in not present. In this respect
Chimaera resembles the selachii. The IV nucleus has the same
features in Selachii, Holocephali and ‘Teleostii.

1) Notiz tiber den Eintritt der motorischen Nerven-wurzeln in die Medulla
Oblongata und die Lage der motorischen Kerne bei Amia calva. Folia Neurobiolo-
gica Bnd. VI, 1912, Heft J.

2) Notes on the trochlear and oculomotor nuclei and roots in the lower verte-
brates. Proceedings of the Koninl, Akademie vy. Wetenschappen te Amsterdam,
March 23, 1911 p. 897.

(ALEC

Also the Vt" nucleus of Chimaera has a great resemblance with
the dorsal V™ nucleus of Teleostei, as it is found in Lophius e.g.

The position of the VI cells in Chimaera stands in between the
location found in most Selachii and the one found in the Teleosts
in so far as they have a less dorsal position than in the former and
a less ventral position than in the latter. Division into two groups
as is frequently found in the latter does however not occur. The
nucleus is very diffuse, its cells are rather scattered.

The position resembles very much the one found in Amia Calva
by Droocierver Forrtvuyn (l.c.)

As I have already pointed out formerly ') the roots of the VI‘
nucleus in Chimaera come much nearer the VII root as is gene-
rally found in sharks. Also in this respect Chimaera approaches
the Teleosts. Not however in the number of rootlets which is even
more than in many sharks (6 or 7).

The most interesting topography in however exhibited by the VII
nucleus.

Whereas in all Sharks the VII" nneleus forms a continuous row
of cells with the IX" and X" root entrance, and keeping a dorsal
place, we found very regularly two facialis nuclei in Teleosts, one,
more frontal between the level of the VII and IX‘ roots, contain-
ing also the IX cells (as has been equally found by Trio’) and
another one caudally from the LX‘ root entrance, remaining conti-
nuous with the X cells*) and keeping a more dorsal position than
the VII—IX ecellgroup.

Chimaera exhibits a structure of the VII system, which has its
own special features, but in some respects resembles the Teleostean
character.

As in Teleosts there are two VII" nuclei in Chimaera, of which
one is located between the level of the VII and IX root, without
being connected however with IX cells and not exhibiting any
ventro-lateral shifting as the VII—IX nucleus in Teleosts generally does.

1) The migration of the bulbar V*, Vit2, and VII" nucleus in the series of
vertebrates and the differences in the course of their root fibers.

Verhandeling v. d. Kon. Akad y. Wetensch. te Amsterdam (Tweede sectie)
No 16, 1910.

2) Contribucion al Conocimiento del encefalo de los Teleosteos: Losnucleos
bulbares.

lo, 20 fascicolo, tomo VII 1909. Trabajos del laboratorio de investigaciones
biologicas de la Universitad de Madrid, p. 8 and 9.

3) Only in Gadus also this VIL nucleus was isolated from the X cells. Concern-
ing Lophius | refer to my paper in these Proc. 1910.

78
Proceedings Royal Acad, Amsterdam. Vol. XLY.

(inves)

The posterior VIL nucleus lies behind the IX rootlevel and in
about the middle of the bulb, being entirely separated from the vagus
nucleus. It is several times larger than the anterior nucleus. The
real vagus nucleus contains no VII elements. In so far a certain
resemblance with Gadus and Lophius is present as in those animals
the vagus nucleus is also free from VII elements. Specially Lophius
offers a point of resemblance as the posterior VII nucleus has a
more ventral position than the anterior VII nucleus in this animal.
It seemed probable to me that the posterior VII nucleus of Chimaere
contains at the same time the IX root to its origin with certainty.
The caudal part of the posterior VII nucleus is however a pure
VII nucleus again, the facialroot entering this nucleus in its frontal
and in its caudal part.

In so far the resemblance with the Teleosts is greater than one
would say at the first glance, because the sequence of cells in the
whole visceral system of this region in Chimaera is VII—IX—-VII—X,
just as in Teleosts, whereas in Selachii the primitive arrangement is kept:
VII—IX—X, being in harmony with the arrangement and sequence
of roots. The difference with the Teleostean topography would
consequently be only this that in Teleosts the 1X nucleus in combined
with the anterior VII nucleus, Whereas in Chimaera, it is combined
with the posterior VII nucleus.

Concerning the reason of the difference between Selachii and
Holocephali no definite opinion can be given at present. it may be
that it has to do with the innervation of the opereulum, but we
may not forget that Amia has also an operculum and that the
Selachian arrangement is kept there. Few words suffice for the arrange-
ment of the vagus column. Besides its freedom from facial cells its
strueture and length is the same as in the Teleosts. The vagal cell
column in Fishes offers generally very few differences.

The spino-occipital system remains. Its cells have a more dorsal
place in Selachii than in Teleosts and so they have in Chimaera. The
celleolumn is poorly developed in that animal reminding of the
scattered spino-occipital cells of Amia.

In Chimaera a more considerable overlapping of the vagus-column
and the spino-occipital column is found than in sharks or Teleosts.

At last I may mention that the topography of the large reticular
cells in Chimaera is about the same as has been described by
Van Hoivennt in the Selachii.') In the caudal part of the oblongata

1) Remarks on the reticular cells of the oblongata in different vertebrates.
Proceedings of the Kon, Akad, y. Wetensch, te Amsterdam. April Ao} he laly
p. 1048—1049.

(1179 »)

a large nucleus magnocellularis inferior is found, in the raphe extend-
ing laterad underneath the fasciculus, longitudinalis dorsalis in form
of “guirlande’. More frontally in the region of the octavus, V and
in front of the Vt, hardly any reticular cells are found in the
raphe, the greater part being scattered in the lateral parts of the
oblongata, forming the nucleus reticularis medius (octavus-region)
and nucleus reticularis superius (praetrigeminal region). The last
contain hardly central elements in contrary to the Reptilian, and
specially avian and mammalian nucl. retic. superius, which is clearly
divided into a dorso-central (nuecl. centralis) and a_ ventrolateral
(n. ventro-lat.) group.

Summarizing my results | may conclude: 1. that Chimaera also on
account of the topography of the motor root cells in the oblongata
and midbrain has a special place amongst the orders of fishes;

2. that it resembles in some points the Selachian in other the
Teleostean type, as has also been found in the forebrain of this
animal by CarPENTER and myself’).

The number of data which show that the nervous system of
Chimaera in many respects stands in between that of Selachii and
Teleostei, and sometimes reminds more of the Teleostean than the
Selachian type is enlarged by an interesting remark made by
Prof. G. Rerzivs (Das Gehérorgan der Wirbeltiere Teil I, 1881: Das
Gehérorgan von Chimaera monstrosa) who says ‘in sehr inter-
essanter Weise bildet das Gehérorgan der Holocephalen d. h. der
Chimaera ein Uebergangsstadium zu dem der Plagiostomen, ein Ver-
bindungsghed zwischen ihm und den anderen Fisschen’’. In a letter
which I received from Prof. Rerzivs in December 1908 he writes
“In letzten Sommer bekam ich ein ganz grosses Exemplar von
Chimaera und machte mir neue Preparate vom Gehérorgan, welche
sehr gut gelangen. Es ist wirklich merkwiirdig zu sehen, wie néher
das Organ steht an dem der Teleostier als an dem der Selachier’’.

It results from all this that my researches on the nervous system
of this animal give a further illustration of the interesting results of
the Swedish anatomist as also several somatic features of the Holo-
cephali prove their transitory character between the Plagiostomi and
Teleosts.

2) Das Gehirn yon Chimaera monstrosa, Folia Neurobiologica Bnd V, Heft 2.

78*

( 1180 )

CLEP

4

CHIMAERA

1

ue gy. ©,

T v@ we uX ores
COMmnLUS

‘EXPLANATION:

Vey)

f= -T (0 -TV G28-V MV ©23-V Be-K ZA-X COSpo

Topographic relation of the motor nuclei of midbrain and bulb in
regard ta the roots of the Ill, IV, V, VI, VII, IX and Spino-occipital
nerves in a Shark (Hexanchus) Holocephal (Chimaera) and a Teleost
(Cottus),

Astronomy. — Provisional results from calculations about the terms
in the longitude of the moon with a period of nearly an
anomalistic month, according to the meridian observations made
at Greenwich’. By J. E. pp Vos van Srernwuk. (Communi-
cated by Dr. E. F. van pg SanprE BAKHUYZEN).

(Communicated in the meeting of March 30, 1912).

In 1903 Prof. E. F. van pe Sanne Baknuyzen had come to the
conclusion that theory and observation did not perfectly agree about
the so called Jovian evection in the longitude of the moon; nor had
he been able to find in the observed places indications of another
inequality of the same kind caused by Venus and the Earth ').

*) Proc. Acad. Amsterdam 6, 1903 pp. 370 et seq. and 412 et seq.

CAt1Bi5)

The agreement as regards the Jovian evection was improved by
the introduction of a corrected value found by Hint for the perturb-
ations dependent on the ellipticity of the earth, and afterwards new
theoretical calculations of the amplitude by Newcoms, Hiiu, and Brown
yielded a value agreeing very satisfactorily with the results of the
observations’), but in the phase and hence in the length of the
period a deviation seemed to remain.

Recently Prof. Van pe Sanpe BaknvyzeN proposed that I should
undertake a new investigation into this question founded on a longer
series of Greenwich-observations than those used by him, and I
gladly assented.

Since EK. F. y. p. S. Bakuuyzen had discussed the years 1895
1902, the first thing was now to take the years after 1902 in hand
and further it was desirable to go back a little further than 1895,
in order to have at our disposal the results of an uninterrupted series
of eighteen years’ observations. This work has been only just begun
and if, notwithstanding this, I make bold to communicate already a
few provisional results, this is owing to the desirability of deriving
just now corrected places of the moon for the moment of the
approaching solar eclipse.

I shall therefore communicate here the results of a provisional
discussion of the 3 last years of the Greenwich-observations, which
were at my disposal: 1907 up to 1909. I derived from it the co-ef-
ficients of the terms with svg and cos g, which still had to be added
to Hansen’s longitude of the moon and compared these with the

sums of the corrections resulting from corrected values of the eccen-
tricity and longitude of the perigee according to BakuuyzEn and
from the perturbations by the planets according to Brown.

In my discussion of the observations | mainly followed the method
indicated by Newcome in his /nvestiyation just as Baknuyzen had
done; i. e. [| employed as‘ basis for my calculations directly the
deviations in R. A. For the present, however, I had to be satisfied
with a less rigorous course. The corrections of the co-efficients of the
great perturbations I adopted from Nerwcomp’s /nvestigation and as
co-efficient of the parallactic inequality I employed the value which
according to Hansen’s calculation would correspond to the solar parallax
8".80 (or 8".796), although this is no longer the case according to the
more accurate calculation by Brown. I did this because I could now
use extant auxiliary tables, while the influence of this inaccuracy

1) Newcomp found 1'.15, Brown 1.14, while E, F. v. vp. S. Baksuyzen had
derived 1.28 from the observations

( 1182 )

on my results could not be but slight, since the periods of these
terms are not commensurable with that of g.

An investigation into personal errors dependent on the age of the
moon offered little chance of success, as I had only the observations
of 3 years at my disposal. I therefore, after having corrected the
observations as indicated above, only applied a mean correction to each
category of observations in order to reduce the yearly mean of the
differences comp.—obs. to zero. I employed all the observations
made in the meridian including those obtained with the altazimuth
and thus had for each of the two instruments three categories of
observations, those of Limb I, of Limb II and of crater Mésting 4A,
i. e. six in all. [ formed for each of these the annual mean and
subtracted this from the individual Ae. I should certainly have done
better by leaving out of account the observations made at an age
of the moon less than 47.5 and more than 25°.5 (comp. the former
investigation by E. F. v..p. Sanpr Bakuuyzen), but of the 835 obser-
vations used, only 12 were in this case.

+ 0'87
2.55

Qi

2
3.

Pe

( 1183 )

The thus corrected and reduced Ae (obs. — comp.) were now
arranged for each year into 18 groups formed according to the value
of the mean anomaly: from g = 0° to 20°, 20°—40° ete. The means
found for those groups are found in the table on p. 1182.

The 18 results r obtained for each year have now been repre-
sented by equations of the following form

ecthsng+kcosg=r
in which ¢ stands for a constant deviation still extant in the results
of the year under discussion, while

dl = —hsing —k cos gq
represents the correction to be applied to Hanssn’s true longitude.

The weights of the values of 7 in one and the same year often
differ considerably, and these weights have to be taken into account,
if we wish to obtain a solution yielding the most accurate values
of h and &. This has been done for 1909 but for the two other
years the weights were momentarily neglected. Another solution was
also made for 1909 without taking the weights into account and by
comparing the results obtained in these two ways it appeared that
the influence of the omission probably is not great. I obtained with
and without weights for 4 resp. + 1.81 and + 1.69 and for
k+ 2"47 and + 2".20.

Adopting for 1909 too the solution obtained without weights the
following values are to be regarded as the results of this first investigation :

h &
1907.5 + 2.49 + 0".62
1908.5 + 1 .67 +1 .06
1909.5 =P 69 49 20

It stands to reason that from the results of only 3 years no imme-
diate conclusions can be drawn about the individual inequalities
influencing the / and &. The only thing I could do was to compare
my results with the co-efficients of sim g and cos g according to the
complex of the element-corrections as derived by E. F. vAN bE SAnpE
BakavuyzeN in 1903 and the perturbations as calculated by Brown.
I have extended this comparison of the empirical with the theoretical

values of —h and —& to the years 1895—1902 discussed by
VAN DE SANDE BAKHUYZEN ').

For the constant parts of —/ and — kT adopted — 4, = — 0".43
and —#,=—0O"17; and I borrowed the variable parts arising

from the differences between the perturbations BrowN—Hansen, from
BatterMann Beob. Ergebn. Berlin. 18 p.16—18. Of the perturbations
by the planets we have to consider those numbered 23—29; the

1) Proc. Acad. Amsterdam 6, 1903, p. 377.

( 1184 )

terms 1—7 cannot contribute noticeably to the / and /:, for reducing
these to the form asim(g—-+ x), the annual variation of x for N. 1
becomes 225°, for N. 5 330° and for the rest of the terms > 360°.
Further, of the perturbations by the sun N.39 has to be taken into
account and of those owing to the ellipticity of the earth N. 44.

These 9 terms calculated for the middle of each year were reduced
to the form a cos zy sing + asin x cos g, so that we obtain as computed
values

( —=)) comp. = = h, = = a cos x and \ Gon E)eomp. = —k, +2 a SIN,

The following table contains the values deduced from the abe
vations ( —A)ors, and (—*)o;, and the differences (——/)oos, — (—A)comp.
and ( =) ret ar (— We) corapes

| (= Bons. Oobs.~ Vcomp. Cc Ogos. —Ocomp.

1895. a jeee |) eZee 044 | = 40°43
1896. — 0.58 + 0.57
1897. | fe 0.16
1898. é | ri ot 0.49
1899.5 | 93 | 0. ‘S 1.13
1900. . D. 0 0.50
1901-5) -5|ee! al, | 210: 52 0.73
1902.5 | ; D. 0.59

1907. | ; ; 0.61
1908. | | 0.07

1909. : é 2 1.05

We now see that the differences between observation and com-
putation have still a systematic character. Yet we cannot deduce from
this comparison with any certainty an empirical correction to the
computed longitude of the moon for the moment of the solar eclipse
of April 17. For that moment we have g = 278°, so that especially
the value of / is of importance and it does not seem feasible to
extrapolate a value of (— /)ous. (— /)comp. for 1912.3

Prof. KE. EF. vy. bp. Sannin Baknuyzen’s opinion, (comp. J. Werepnr,
Calculations ete., Proce. Acad. Amst. 14 p. 950), based on his former
calculations, that the real value of 4 would probably be at least

O".6 greater than the computed one, is therefore not corroborated
by the results [ have obtained thus far,

(1185 )

. y ~ , °
Mathematics. — New researches upon the centra of the integrals
which satisfy differential equations of the first order and the
jirst degree’. (First Part) by Prof. W. Kaprnyn.

1. In a very interesting memoir’) “Determination et intégration
dune certaine classe d’équations differentielles ayant pour point singu-
lier un centre” H. Dunac has investigated the conditions which must
be fulfilled when the origin of coordinates is a centrum for the
differential equation

dy y+ax*t baytey’*

a) See
that is, when the general integral may be written in this form

ay + F, (ay) -+ F, (wy) +... = Const,

where #,(vy) represents a homogeneous polynomium of degree h.
Supposing that the coefficients are real or complex he shows that
the differential equation must be reducible to one of the following
eleven forms, where « and py are arbitrary constants

(e422? + way + vy") dy + (y+y?+uey+ve?)de=0. . . (1)
(e+ v* + 2ey4-y?) dy + (yty?+2ey+va?)dy=0. . . (2)
(Aras ay idy) -\(Gepye--waa)ida— OP. 5 «= (8)

1
(w+ 2a?—ay+ my’) dy + (+2 ~s) dz 005 7, *(4)
u

(G5 PH) GH) = (Os atar sem) cm ==) 6 5 A te a 6 6 6 IG)
(@--a*--y*) dy ++ (yluc?--2ey)de=0. .. . .. . (6)
(i= - GS OF) Cops’ (Waa \in—— 5 Se 6 op @ o 4 (UU)

(Gs ee EOP) Gin (ea) C5 5 eo oo G 6 5 o ()
(a--ry-+-uy’) dy + (y-aytuc’?)de=0 ..... . (9)
Ct = (Qa Res Ee) Ces 6 6 a Me 0 6 oe (ilk)
(ray eyo (yan dar On 2) eke coe. Ghd)

The object of this memoir is the same as that which we have
treated in our paper “On the centra of the integral curves which
satisfy differential equations of the first order and the first degree’’.
Ow point of view however was narrower than that of Dunac, because
we only considered real coefficients and real integrals. The object
of the present paper now is to extend our former results by adopt-
ing also the wider supposition that the coefficients as well as the
integrals may be either, real or complex. Our way of solving the

1) Bull. Sei. math. Paris (Sér. 2) 32, 1908.
2) These Proceedings 10 May 1911.

( 1186 )

problem, being very different from that of DuLac, leads to a new
classification of the results. Having obtained this we wish finally
to compare the two solutions.

2. Let the differential equation be witten in Porncari’s form
dy —a+aa*+2bayt+cy? —e#+V

dx ytaa®+2bay+ea? nye y+X (1)
which is different from the form adopted by Dunac, and let the co-
efficients be real or complex.

By substituting

§ = he + ky 4 — ke + hy
the form of the equation is not changed, for we get
dq —S a's? + 2p 'sy- yn

date 67+ 285y+y 777
where
(1? +k)? a = ah® +- (a 4+2b) Pk + (2b' +0) hk? +-c'k*
(h?--k?)? B = bh® — (a—b'—c) h’k — (a'+-6—e) hk? —O'k*
(A? Lh)? y = ch® — (2b—c+) hW?k + (a—20') hk? +-a'k*
(A? k?)? a = ah? — (a—20’) h?k — (2b—c') hk? —ch®
(1? 4-k?)? Bl = O18 — (a +b—c) Wk + (a—b'—c) hk? + bk
(2 Lk)? y' = ch*® — (28'+-0¢) Wk + (a +20) hk? —ak’.
Hence
(1? +k?) (a+y) = (atoh + @+eyk
(+B) (a +y7'/) = (+e) hk — (ato k

and
: h Sets! (a+c) (a tea) + (+e) (a'+y')
(ee (a te)? + (a' +c’)?
k _ @+e)(e+7)—@+9 @' ty)
aa ae (a fe)? + (a'--e')? ;

Now generally 2 and / may be so chosen as to satisfy two con-
ditions, for instance
a+y=0, a t+y=a
and thus the differential equation may be written in the simpler fotm
dy —« +t aa? + 2b'ey —a'y?
de -y fF ax* + 2bey + cy?
This general case we examined in our former paper. If however
(a0) + (a+)? =0
this reduction is impossible. In addition to our former paper we
therefore now must investigate the consequences of this supposition.

( 1187 )

Olin — ee ea)
the corresponding differential equation
dy -—a% + ala’ + 2b'ey — ay?
du = y as aun? + 2bey — ay?
admits three particular integrals of the form
y = Ac -— B
for, substituting this value and equalizing the coefficients of the
different powers of w in the two members, we have
—aA® 4+ (2b4a’) A? 4. (a—2b') A— a’ = 0
A? + 1 — {2ad? — 2 (b+a’)) A + 203 B=0
B\(aA—a’) B — A}=
which are satisfied by the roots of the cubic
a A* — (264 a) A2—(a— 26)A+ae=0

and by
aA

———
aA —a

In this case, the general integral may be written
(y—Ys)1 (y¥—Y2)? (YY —Ys)/# = const.

where y, 7,4, stand for the three particular integrals and A, A, 4,
are certain constants. To prove this, we may follow the way indi-
cated by G. Darpovux') in his fundamental memoir “Mémoire sur
les équations différentielles algébriques du premier ordre et du
premier degré”.

Writing the differential equation in homogeneous coordinates we
have

L (ydz—edy) + M (zd«—wdz) + N (ada —ydze) = 0

where
L= — 2b'x* + a ay — ay* + yz
M = ae? — avy — xz — 2by?
N = —- (a +20’) vz + (a’—2b) ye.
Supposing
of of Oa.
Hise + M FY: + N = IG ie

and replacing f by A; e—y—b;z, the funetion corresponding with
this value of f is easily found, for

A; L—M—RB; N = K; (Aj 2—y—B; z)
gives immediately

jee ( 2b +

ee) Bull Sci. math., Paris (Sér. 2) 2. 1878.

!
a

)« — (2b adj) y : (¢ = Ip 3)

437

( 1188 )

Remarking that z= 0 is a fourth particular integral, and putting
f=, we obtain a fourth value for
N

K, SS SS SS (a+ 20’) wv “ (ai—2b) y,

a

If now four numbers a, ¢, @,@, may be found such that

a, +a,+ta,+a,=0
and

ak, + 4,K, + a,K, + a,K,=0
the general integral may be written
(A, e—y—B, z)4 (A, @

or in inhomogeneous form

y—B,2)* (A, w—y —B, 2)%3 2% = const.

(y—y,)2 (y-—y,)2 (y —y3)’* = const.
where A,:A,:A,=—:—: —.

3

The numbers a, a, @, @, must satisfy the equations
ae, +a,+a,+a,=0

hence
a, <A,—A, a’ neg Mm IAG
a, ary A,A, a cy aah ae eo
a PARA a
So ‘| = SS Sas 54,4, D
, A,A, a n
« Ape a a
— | Eat 434, A, |:
(t, AVAL | ea a

D representing the determinant formed by the coefficients of the
first members of the three preceding equations.
After a slight reduction we find
A, = (A,—-A,) (@A,?— 2bA, —a)
A, = (A,-—A,) (@A,?— 204, —)
i (A,—A,) (aA,?—26A,—a).
For small values of w and y the general integral may be expanded
in the form
vy? 4+- fot, + 1... = Ttonst.
which proves that in this case the origin is a centrum.
4. Assuming in the second place a’ + c’ = 7 (a+ c), and referring
to our former paper, the origin will be a centrum if it is possible to
determine an infinite series of homogeneous polynomia P;, of degree

( 1189 )

A such that the following conditions are satisfied :

US ORY
e529 52= (stg) Ps

OP= OP) senha, Shoeey COX. < ov
Der or a sails dae Oe te a 5)?
CN ee
SAV uea OR: a2. Gai ethan) SF \ de =) ;

etc.
where P, = 2.
To expand the integral in the common form
vty? + Fi,4F,+....= Const.
we must observe that between the functions / and P the following
relations exist
(@Y¥ —yX) Pa-3 —(2? + y’) Pho + nF, = 0.

Considering now the infinite series of conditions we easily see that
ic is always possible to determine P, by the first condition. Proceeding
to the second it is evident that every constant factor of P, may be
omitted.

Writing therefore

Pi =p, trp, y
Py = — (0 + €) pHa
and putting
P= Hy tny
the second condition gives
g, = (34 + 2b) p, +p,
29, —2q,=(4b+2c)p,+ @at4d)p,
—g,=cp, + (264 3e)p,.
These equations can only be satisfied when
(Gat20 +op,+(@+2b+43c)p,=0
or introducing the values p, and p,, when
aa’ — ce’ = b(a + ec) —U' (a 4 ce).
From this condition and the given relation
a ¢ =2(a + o)
we deduce
a =b—i(b—c) , ¢=>—b+i(a+0)

Py, =—ilat b)
Pyaat+b.

( 1190 )

If therefore
a + b'=0

P, and all the following functions P, P,... vanish, which proves
that the origin is a centrum in this case.

To determine the integral we have

2(#Y—yX) + 3F,=—0
which gives
0}
vty x [a x* +- (26'—a) w*y + (c'—2b) wy?-—cy? | = const.
with
Gii==10 == (Qe! c)) eee Ota

5. When
a’ + ¢ =i(a+ec)
aa’ — cc’ = (b—ib') (a+)
and
ato == 0
the factor a + 4 may be omitted ; thus
P= ie +y.
Determining now /P,, the coéfficient g, may be chosen arbitrarily.
Putting g, = 0, we get
Pony tay
where
gq, =a —i(Ba4+2b/) g, = 2a + 3b' — id.
Assuming:
Pi=7, 2 +7, ey 4+ 7, ey? + 4, y?
P= s, e* + 8, xy + 3,07 477 + 3, zy® 8) y'
the following conditions give
Se Oh
2r, — 3r, = (8a-+ 40') g, + 2a' q,
3r,—2r, = (4648c') g, + (24+ 60’) g,
— 7, = 09, + (204-4) 9,
which always can be satisfied, and
8, = (5a420') r, + a'r,
2s, — 4s, = (8b 4+ 2c') r, + (4a4-40') r, 4 2a'r,
38s, — 3s, = Scr, + (66438¢c) 7, + (844+ 6b') r, + 3a’ 7,
4s, — 28, = 2er, + (46-+-4c) r, + (2a+80') 7,
—s, cr, + (26+5c’) r,.
which are impossible unless
(5a + 26'+ c)r, + (a'4+2b+4e') r, + (@4-2b'+40) 7, + (a +26+ Sc’) r, = 0.

( 1191 )

This condition may be witten
Ar, + B(2r,—3r,) + € (8r,— 27.) + D(—r,)=9
where
A = 5a +5 106 = 13¢'

B= — (54+2b'+0)
C=ai + 2b - de
D = — (13a+10b'+ 5e).

Introducing g, and q, this takes the form
g, {a A 4 (8a4 4b’) B+ (464-3) C + cD]
4 g, [2a' B + (2a+ 6d!) C + (2b4-4c’) D] = 0
or, eliminating @’ and c’
g, [— (80a? 4 40ab! 4 32ac + 12? 4+.20b'e+10c*) 4 i(12ab + 8be+ 400')]
+ gq [(12ab-+8be+ 4bb') — i (42a? + 44ab' + 28ac-+ 126"? + 168'e-+ 2c’*)] = 0.
To simplify this condition we write
9, [— (Ba + 8'+ 2c) (10a4+108'+ 4c) — 2 (b'—c)? + 4ib (Ba-Lb'+4 2c)]
+ q, [46 (8a +6'+ 2c) — i (8a 4 b'4 2c) (14a +10b') — 27 (6'-—c)?] = 0,
or
—2 (b'—c)? (9, +49.) +
+ (8a+ b+. 2¢c)[40(ig, + g,)—106'(g, 4 ig,) —10a(q, 4 tq.) — 4c, —4iaq, ] ——())
Now
Ab(ig, +-9,) — 4ceq,— 4iag, = 4(2a-+4 3b'—e) (9, + %4,)

— 2 (q,+ tq.) (a+¢) (8a — 26'4 5c) = 0

(a 4 c) [2b —a(a—c)] (26'—3a—5e) = 0.
This breaks up into three conditions which will be considered
separately.

6. When, in the first place
ate =i(a+c)
aa'—ee' = (b—ib') (a+-e)
atce=0
the second relation depends upon the first and the third.
This ease has already been considered in Art. 2.
7. Supposing secondly
ate =i(ate)
aa'— ce! = (b—ib')(a+-e)
2b =1(a—c)
which may be written

( 1192 )

2a'=i(a— 2b'+ ¢)
2c! = (a +26'+c)
26 = u(a—c)
then again the general integral of the corresponding differential
equation may be constructed from a system of particular integrals.
Substituting
y = Aw+B

in the differential equation we find that it is satisfied when

and A is the common root of the two cubics
cA® + (2b—c') A? + (26'-c) A+ ec = 0
cA® + (26—c') A? + (28'+a) A—a’ = 0.
Therefore
— (ate) A+a' +c = 0
which combined with the relation
a' +e! = i{a+e)

gives A=7 whence the corresponding particular integral may be

written
;
pe Oa -f Tae
C —2C
or
re 2i ;
OP iy LO a a
f a+2b'—c

This being the only possible integral of the first degree, now we
will try to satisfy the differential equation by an equation of the
second deeree
Aw + 2Hay + By? 4-2Ge2 + 2Fy + C=0.

Therefore y

Ba+Ay+G@ —a+a'e*?+2day4 cy?
~ Ae of By ue ime y Law 2419 bay+ cy?

must be equivalent with
(Av? +2 Hay + By? 4-2Gxe+-2Fy+C) (me+ny) = 0
Thus the following relations must be satisfied
aA+aH=mA
2bA + aH + 2b'H + a'B=2mH 4+ nA
cA + 2077 4- cH 4+ 20'B=mB + 2nH
cH + 3B=nB

( 1193 )

aG — HT + a F = anG
A + 26G — B + 20'F = 2mF 4+ AnG
H + eG + ¢F=2nFk
— Fk =m
=n:
The last two equations give mG + nk —0, therefore adding the
5h and 7" equations we get
(ate) G + (+e) F=0
which compared with the given relation
a+t¢=iato)

shows that we may take
Gest, 1S OSS SF 0
Considering now the 1", 4, and 5! equation we get

Sia Bi ae ia

m—a im—c

and substituting these values in the 2%, 3 and 6, we see that
m must be such as to satisfy the following three relations

a'(2b—im) aie. ;
ak + a+ 2b'— 2m = 0

m—«a im—c'
! !
ac c(2b'—m E ;
; iS Oe oe eat 0
m—a im—c
!
a c ef a f
— ——— | (a+ia' —2m) + 2(b+ib'—2im) = 0
m—a §wm—ce

The roots of the last equation are easily found, for
H = a + ta’ — 2m = 3 (a—c+2b'—4m) = — i (6 4-1b’—2im)
so a first root is
ie ata “a--2b'—c

n, =—
0 r)
4

4

and consequently the others

Ba+2b'te . a 2b ¢ =.

mm, == ————— n, = —————_ = 2am
1 2 : ¢

4 ; 2 4

Now im, does not satisfy the first and second equations, but m,
and m, do. Corresponding with m, and m, we have therefore two
solutions»

al neh c ; ‘ z
u == H, | ——— a? +- 2ey -—- —— y> | + 2a + 217 —_ = 0
vm, —C¢ nt

m,—a ome 7
lod
19

Proceedings Royal Acad, Amsterdam. Vol. XLV.

( 1194 )

u

a’ ¢
H, | —— «* + 2ey 4+ ———y? | + 2a + 2iy ——_ = 0:
im,—e m,

the last solution however may be easily reduced to

i 2
(« +iy —-— |= 0
‘ j 2m,

which is the square of the first particular integral, so that only one

integral of the second degree is left.

To construct the general integral from the two solutions found,

we write homogeneously
L(ydz—zdy) + M (zdx —xdz) + N (ady—ydx) = 0

where
L= — 2a — ec ay + ey? + yz
M = ad' # —aay — «z —2by?
N = — (a+ 2b) ez — (26+) yz.

Remarking that 2= 0 is also a particular integral and replacing fin

Oj, of of
L M—-+ N—=K,;
Ow + Oy ais Oz v
by p, wu, and z, we find the corresponding values of A’ to be
1
Kk,=— = (a+ 2b'+-c) a — iay
Y 1 ; Mic Se
K,=— = (a+ 65'—c) a — =) (5a 4-2b'— 3c) y
N ; l
Ka = — (a+ 2b') « — 5 (5a +2b'—c) y.

Now three numbers @, a, @, may be found which satisfy the

equations
CK Ke toh Ke)
or
(a+2b'+c) a, + (a+ 6b'—c) a, + 2 (a4 20') a, = 0
2a a, + (8a + 2b'—8ce) a, + (8a + 2b'—c) a, = 0
and
a+ 2a, + a, = 0
With these values
ct, 3a +2b'+-c a, a+2b'—c
Ct, - a —2b! + de a, - -a— 2b'4-8e ;

the general integral may be written

pr w%2 273 == const.

(1195 )

or returning to the inhomogeneous coordinates

a + D7 a+2b'— (J

———__ fi(a—2b' +c) a*—(a-2b'-c)ay 4 2iey} + a iy —
a—2b! —e : : ;

3a-+26'+¢
ee —_ = =—IC0NSUe

2 2} 2a+2b'+e
av + 1y -—- eT.
a+ 2b'—e

For small values of # and y the first member of this equation may
be expanded in the form
vty? + F, + Fy, +... = const.
which proves that in this case the origin is a centrum.
A remarkable case presents itself when
5a + 66'—c=0

for then

4 2 8
oe, = ——=—(a+ce) «,=——(+e) «,=—(+oe)
3 3 3
33
p=«+ty+
a--e
fate . i Bt
u— (ate) jo at ay + iy" +- 2(a@ + 1) — ——
2a—e 2a—e ate
and the general integral
pu = const.
Physics. — “Preliminary account of some results obtained by the

Netherlands Eclipse Expedition in observing the annular solar

eclipse of April 17, 1912.” By. Prof. W. H. Juttus.

The observation of the annular solar eclipse of April 17, 1912
near Maastricht was favoured by an exceptionally clear sky.

The general plan included:

1. Visual observations on contacts and on positions of crescents.

2. Exposures with the photoheliograph.

3. Exposures with the objective prism spectrograph.

4. Determination of the minimum value of the total radiation at

the instant of centrality.

Measurement of the entire process of radiation from the first

until the fourth contact.

6. Photometric determination of the varying intensity of the sun-
light from the first until the fourth contact for five spectral
regions of 30 A each.

. Observation of various secondary phenomena.

uo

<o*

( 1196 )

The full treatment of the observational data obtained by the
numerous (nearly 40) members of the expedition will of course
require a long time. Certain results, however, came out at once
with sufficient evidence to justify a preliminary communication.

To begin with we may safely conclude from the observations sub 1, 2,
and 3, that at our station the eclipse really was very nearly central,
corresponding to the prediction of the Leiden astronomers — al-
though the small corrections, necessary to determine a posteriori the
exact position of the line of centrality, are yet to be calculated from
these very observations.

With the objective prism spectograph (prismatic camera) Prof.
NwLaAnd obtained results even surpassing the expectation. Out of
five exposures two were made so near the time of centrality, that
both photographs show the hydrogen lines Hz, H:, H,, Ho, and
the calcium lines /7 and K as complete chromospheric rings ; besides,
thanks to the valleys and mountains of the moon’s edge, far over
a hundred lines are in evidence partly as FRavNnorer lines, partly
as flash lines. A careful study of this plate looks promising.

Special attention was given to the measurements of integral radia-
tion, because an annular eclipse was expected to separate the radia-
tion due to the entire solar atmosphere from the radiation due to
ihe .photosphere in a more convincing manner, than a total eclipse
could do.

The measurements sub 4 and 5 were made in duplo with two in-
dependent equipments: @) a thermopile (the same that was used in
observing the total eclipses of 1901 on Sumatra and of 1905 near
Burgos*)) in combination with a moving coil galvanometer of
Siemens & Harskn; 6) a bolometer with a quick, sensitive and dead-
beat galvanometer constructed by Dr. W. J. H. Monn.

As in arrangement a, after a sudden access or interception of
radiation, an interval of 10 seconds was required for the dead-beat
gealvanometer to attain its. final position, and because the annular
phase of the eclipse would probably last not much longer than one
second, the set of apparatus 6 was designed so as to become station-
ary in less than one second. “Dr. Moin had sueceeded in making
his bolometer and sensitive galvanometer answer this condition.

Both thermopile and bolometer were directly exposed to the sun’s
rays, Without intervention of any lenses or mirrors. The sensitiveness
of the arrangements was under easy control during the observations

') Total Echpse of the Sun. Reports on the Dutch Expedition to Karang Sago,
Sumatra, No 4 Heat Radiation of the Sun during the Eclipse, by W. H. Junius,
(1905). — Cf. also: These Proc. VII, p. 503 and 668 (i905 —1906).

(1197 )

by regulating resistances; if necessary it could be made such, that
“/rooooo Of the total radiation of the uneclipsed sun would have been
perceptible; but referring to the results obtained with the total eclipse
in 1905 at Burgos'), I expected the minimum not to fall below
/io000 ON the occasion of this annular eclipse.

The constancy of the zero readings of the galvanometers was all
that could be desired. During the whole lapse of time from the
first until the fourth contact visual readings on both instruments
were made at known epochs; moreover, the equipment allowed of a
continual photographic record of the motion of the galvanometer
coil to be made during an interval of 10 minutes including the
annular phase.

The principal result derived from the radiation measurements at
this eclipse is, that an wpper limit has been found, which the total
emitting and diffusing power of the entire solar atmosphere (the
so-called reversing layer, the chromosphere, and the corona together)
cannot exceed.

Indeed, at the instant of centrality, the sky being pertectly clear,
the photographically recorded radiation curve passed through a sharp
minimum, proving that the remaining intensity was less than '/,,,,
of the intensity of the radiation emitted by the uneclipsed sun.

After the readings furnished by equipment @ had been plotted
down on coordinate paper, the intensity curve came out so regular
and perfectly symmetrical in the same interval of LO minutes covered
by the photographic curve, that the results claim great trustworthiness.
In the visual curve the minimum ordinate did not correspond to
/eoo) Of the maximum radiation, but to */,,,,, and the curve was
somewhat rounded off as compared with the photographic record —
a natural consequence of the relative slowness of the apparatus a.

As the minimum value indicated by the quickest instrument must
come nearest to truth, we may conclude that this eclipse made the
integral solar radiation fall below */,,,, of its ordinary value.

Part of tbat remnant must still be due to the small uncovered
ring of the solar disk. Estimating the apparent surface of that ring
at */59, of the surface of the disk, its apparent radiating power pet
square unit at ‘/,, of the average intrinsic radiating power of the
disk (thus allowing for the decrease of brilliancy toward the edge),
we may admit, that at the epoch of centrality the photosphere was
still able to furnish us with '/,,,,, of the ordinary amount of radiation.
Thus no more than ‘/,,,,, of the sun’s total radiation toward the

2) W. H. Junius, These Proc. VIII, p. 672.

(1198 )

earth is left, as originating from the part of the so-called solar
atmosphere projecting outside the moon’s edge. Let us suppose that
atmospheric emission to proceed chiefly from the lower, thin absorbing
layer.

The next question is: what is the proportion between the volume
of the part of that lower atmospheric layer, visible during the annular
phase, and the volume of the half spherical shell from which, without
an eclipse, the radiation emitted and diffused by the same layer
reaches the earth. By simple considerations we feel that it would
scarcely be possible to put the value of that fraction lower than 7/,,;
so half the solar atmosphere radiates, at most, ten times as much
as the part visible during the annular eclipse.

Consequently: Less than */y5.. of the total (ultraviolet, visible,
and infrared) solar radiation proceeds from those parts of the celestia
body which le outside the photospheric level.

This result proves that it is impossible to maintain the theory, which
considers the photosphere to be a layer of incandescent clouds, whose
decrease of luminosity from the centre toward the limb of the solar
disk would be caused by absorption and diffusion of light in an
enveloping atmosphere (“the dusky veil”). For if this theory were
right, then, according to the calculations made by PickertNc, Wison,
Scuustpr, VoGEL, SreLiGnr, and other astrophysicists such an atmos-
phere should absorb an important fraction (*/, to */;) of the sun’s
radiation. Now, as the fraction emitted appears to be smaller than
/iyoo, and yet the atmosphere must be in a stationary condition, one
would be forced to conclude, that the main part of the absorbed
energy is continually being dissipated through space in some abso-
lutely unobserved form, This necessary inference not being acceptable,
we must look for another interpretation of the photosphere.

As to the measurements of radiation mentioned sub 5 we can
only state, for the present, that they ran well (although occasionally
slightly affected by some haze); we therefore may hope to deduce
from them, with greater accuracy than was hitherto attained, the
law of decrease of the integral radiation when passing from the centre
toward the limb of the disk.

The photometric observations (sub 6) made by Mr. B. J. van ppr
Praats included 480 settings, from which the distribution of lumi-
nosity on the disk for five different regions of the spectrum (closely
corresponding {to the regions selected by H. C. Voanr) has to be

computed,

( 1199 )

Chemistry. — ‘“Conjirmations of the theory of the phenomenon
allotropy.” Il. By Prof. A. Smits and Dr. H. L. pe Leeuw.
(Communicated by Prof. A. F. Hornirmay).

(Communicated in the meeting of March 30, 1912).

The investigation set on foot more than a year ago to test
the above-mentioned theory by different substances, the results of
which have already been communicated as far as the substances
mercury iodide, phosphorus, and sulphur ave concerned, has now
already advanced so far also with regard to some other substances,
that some results may be published.

As the investigation chiefly concerns the curves of heating and
cooling, we will first give some preliminary general considerations
about these curves. If we think the temperature (7))-axis to be the
vertical one, and the time (S) axis the horizontal one, we find as
temperature-time-curve a continuous line, which in the most favou-
rable case has a horizontal middle part.

If we consider the curve of heating
abed, and begin at a, we commence
with the curve of heating of the solid

1”

substance, and — will depend first of all
LS

on the quantity of heat that is supplied
per sec., and secondly on the specific heat
of the solid substance.

y

(fA
Before the point 6 is reached, = fie

as
creases continously to the value O, and
the cause of this is that the conductivity
of heat of the solid substance is not infi-

nitely great, in consequence of which

Fig. 1. melting sets already in in the outer layers,
before the mass in the immediate neighbourhood of the thermometer,
which is thought quite surrounded by the solid substance, has reached
the temperature of melting, by which at the same time the supply
of heat to the inner layers is greatly diminished.

This rounding, which takes place before the point 6, where the
horizontal part begins, has been reached, will therefore become the
greater as the conductivity of heat of the solid substance is smaller,
the specific heat smaller, and the supply of heat greater.

If once a liquid layer has been formed, we must allow for the
phenomenon of super-heating. Without any doubt the liquid which

( 1200 )

surrounds the solid substance in the experiment discussed here, will
always assume a higher temperature than corresponds with the
melting-point of the solid substance and now with a certain supply
of heat it will depend on the rapidity with which the heterogeneous
equilibrium sets in in the border layer, and also on the value of
the melting heat, whether the solid substance which surrounds the
thermometer will possess a constant temperature for some time.

If the heterogeneous equilibrium in the border layer was established
with infinite rapidity, a horizontal part of the curve of heating
would have to oceur even for the sma/lest melting-heat, and the
greatest supply of heat, if namely, as has been supposed from the
outset, the system behaved in a perfectly unary way.

It follows from this at the» same time, that when as is most likely
the case, the heterogeneous equilibrium in the border layer is not
established with infinite rapidity, a substance with small melting-heat
will be much sooner super-heated than a substance with a great melting-
heat, and if this phenomenon occurs a line will be found for which
dT
— has a positive value in all points instead of the horizontal portion.
as

Now, however, it has been supposed here that the substance behaves
in a perfectly unary way, and for this case we have arrived at the
conclusion that when a horizontal part is wanting in the curve of
heating, this must point to super-heating of the solid substance in
consequence of the retarded heterogeneous equilibrium. In most cases,
however, we are still entirely ignorant about whether a substance
behaves as a unary one or not under definite circumstances, and as
the horizontal part will also be wanting for the case that the sub-
stance does not behave in a unary. way in the heating-experiment,
but the heterogeneous equilibrium does set in rapidly enough, because
then superheating occurs in consequence of the retarded homogeneous
equilibrium, the curves of heating can teach us anything about the
behaviour of the substance only when the circumstances are made
as much as possible the same for different heating experiments,
while the previous history of the substance is greatly varied.

Before passing on to another subject it is still necessary to point
out about the curve of heating that though a horizontal part has

ale
appeared, there yet occurs a curvature at ¢ where G, increases con-
tinuously till all the solid substance has disappeared.

This rounding is owing to this that the liquid, which is certainly
superheated and will be the more superheated as the surface of the
solid substance decreases, comes more and more into contact with

]

( 1201 )

the sensible part of the thermometer (mercury vessel or windings of
the resistance thermometer).

Both roundings } and ¢ will be diminished
by slow heating, and augmented by greater
supply of heat. Moreover the rounding ce

VE may by greatly reduced by stirring, which
| circumstance is, however, expressly excluded
er : here.

aS Let us now consider the curve of cooling
\ abcd. This curve indicates the temperature-
\ time curve which we, get when a substance
\ behaves entirely as a unary substance, and
the heterogeneous equilibrium between tbe
| solid substance and tie border layer sets in
; rapidly enough for the loss of heat to be
compensated by the heat of crystallisation.
Starting from a we first get the curve of cooling of the liquid.

7

. . . . ¢
Before the horizontal part is reached, the value of —— becomes here

as
continuously smaller negative over a certain range of temperature,
because of the appearance of solidification in the outer layers already
before the liquid in the immediate neighbourhood of the thermometer
has assumed the temperature of solidification. So this phenomenon is
due to the insufficient conductivity of heat of the liquid.
If when the liquid round the thermometer has reached the tempe-

rature of solidification, the said compensation takes place, the curve
of cooling will present a horizontal part. Before the mass has,
however, become entirely solid, a change sets in, because the
thermometer comes more and more in contact with the solid sub-
stance, which for so far as it is not in direct contact with the liquid
will possess a lower temperature than the liquid, which will render
dT

— again continuously stronger negative, till the last trace of liquid

ds
has vanished.

If the heterogeneous equilibrium is not established with infinite
rapidity, the loss of heat can no longer be compensated by the heat
of crystallisation, in consequence of which the liquid in contact with
the solid substance is undercooled. In this case a more or less
descending line will be found instead of the horizontal part.

To simplify the case it has been supposed here that the substance
behaves as a unary one, which in reality is very doubtful, and
therefore we may not conclude when we find a curve of cooling

( 1202 )

without a horizontal middle part, that the heteregencous equilibrium
has not set in rapidly enough, for it is also possible that the
undercooling is partly or wholly to be attributed to the fact that the
homogeneous equilibrium does not set in, or in other words that the
substance does not behave as a unary one.

Accordingly to decide by means of curves
of cooling whether or no a substance be-
haves in a unary way, we follow the course

4 indicated just now in the discussion of the
curves of heating; during the solidification
the circumstances are made as equal as
Fi possible, whereas the previous history of the
substance is made very different.

If it is in any way possible, the substance
: a is then made to undercool a little in the
determination of the curves of cooling, and
then it is seeded in some way or other,
$$. because the maximum to which the tempe-

ae rature then rises in the subsequent solidifi-
Fig. 3 ma : ‘ : Spe
cation, can give very valuable indications.

The practically ideal curve has then a form as is indicated in fig. 3.
MERCURY.

In the first place we will communicate what results the investi-
gation of the element mercury has yielded, because this substance
is distinguished from other substances examined up to now by the
great chance it offers for an ideal behaviour when heated.

For mercury we meet namely with the case that even on a
considerable supply of heat a temperature-time curve is found with
a horizontal middle part, from which follows that the substance
behaves in a wnary way under-these, in general disturbing, cireum-
stances, and the heterogeneous equilibrium sets in with great rapidity
in case of heating.

So in a ease like this we need not apply the method mentioned
just now, for if a substance continues to behave in a unary way
when not only the previous history, but also the circumstances
during the melting are chosen different, this will certainly be the
case when a modification is applied only to the previous history.

Kig. 4 refers to an experiment, in which a wide test-tube, partially
filled with mercury, is heated from — 80° by being exposed to the
air. In the mercury a resistance thermometer had been placed which

( 1203 )

was inserted in one of the branches of a Waxatstone bridge. The
observation of the image of a Nernst-lamp cast by the mirror of

[ret PI cee
Fig. 4.

the galvanometer on a scale, enabled us to follow the change of
the temperature. From the readings, which were made every 10
seconds it appeared that the resistance thermometer, and so also the
mercury in the immediate neighbourhood, maintained the same
temperature for 95 seconds, which temperature is exactly the same
as that which is found, when solid mercury is melted in a bath of
low temperature, and for which —- 38°.80 was found with the gas-
thermometer. So in spite of the great difference in temperature
between the mercury and the surroundings no superheating of the
solid mercury took place.

The following fig. 5 shows the result that we obtained when we
rapidly heated mereury from — 80° in an air-jacket placed in boiling
water. It appears from the observations, which were recorded here
every 5 seconds, that the temperature now remained perfectly constant
for 45 seconds. The melting proceeded, indeed, more rapidly now,
in consequence of the gréat supply of heat, but in spite of this the
ideal course was observed, which points to a unary behaviour and
perfectly heterogeneous equilibrium.

Now it was to be expected, however, that the equilibrium of the

( 1204 )

substance mereury, which continued to behave in an ideal way under
greatly disturbing circumstances, might nevertheless be upset, when

=SB= /
vd
x
Sey
= Sebo a
-39°4
- Ya")
Fig. 5.

the disturbing influences are only made strong enough. To ascertain
this the experiment was repeated under much intenser circumstances :
a quartz tube with solid mercury of — 80° was suddenly placed in
water of 80° resp. in water of 100° without an air-jacket. We then
found the lines B and A fig. 6, the crosses indicating the readings
every 5 seconds. It follows from these lines that this experiment
was too much even for mercury, which was in no way astonishing.
As it now appeared that the previous history had absolutely no
influence on the shape and the situation of the curve, we thought
we were justified in concluding from this that the mercury had been
superheated here in consequence of a retardation of the heterogeneous
equilibrium.

In connection with what precedes it is exceedingly interesting to
see what was found in the determination of the curve of cooling.
Whereas it is exceedingly difficult to make the mercury behave in
a non-ideal way when it is heated, this is much easier to reach in
ease of cooling, and this is very remarkable, for the foregoing has

( 1205 )

perfectly convinced us of the unary behaviour of mercury, unless
in cases of very excessive treatment, so that the fact that a horizontal
middle part in the curve of cooling fails to appear under not extra-
ordinarily disturbing circumstances, must undoubtedly be attributed
to the too slow setting in of the heterogeneous equilibrium.

If mercury is cooled down in an air-jacket which is placed in a
bath of — 80°, we may succeed when the jacket is wide enough,
and the cooling in consequence of this takes place very slowly,
fo obtain a eurve of cooling with horizontal middle part, as Fig. 6
(readings every 40 seconds) shows, but as soon as the cooling takes

—35,80°

~ $04

-4r4

place somewhat more rapidly,
e.g. by the use of a somewhat
less wide air-jacket, the mereury
does not behave ideally, as
fig. 7 shows. The top, indeed
lies at — 38°,80 here, but a
purely horizontal part is wanting,
in spite of the comparatively
slow process of the solidification.
With a still narrower air-jacket,
the curve was much. steeper.

= 38 50°

So we arrive at the surprising
result that the heterogeneous

equilibrium between solid mer-
Fig. 7. cury and the border layer sets
in exceedingly rapidly in case of heating, but slowly in case of
cooling. It follows from this that superheating of the solid substance

( 1206 )

is not ascertained or only under very particular circumstances,
whereas undercooling of the liquid in contact with sold substance
seems to appear very easily.

ENE

In the second place tin was investigated, because the existence of
points of transition led us to expect here that the experiment might
be able to reveal the complexity of the system.

We expected this the more confidently, as phenomena have been
observed in the technique that point to this that the temperature of
the liquid tin at the moment of casting has an influence on the
properties of the solidified mass.

In Danmer’s “Handbuch der chemischen Technologie” this has
been expressed as follows. “Glanz und Festigkeit des Zinns hangen
von der Temperatur beim Giessen ab. Es darf weder so sehr erhitzt
sein, dass seine Oberflaiche in Regenbogenfarben spielt, noch so kalt,
dass sie matt ist. In beiden Fallen, zu heiss oder zu kalt gegossen,
biisst das Zinn an seinem Glanze und an seiner Festigkeit ein: im
ersteren Fall wird es roth, im letzteren kaltbriichig”’.

The apparatus used by us in the investigation of tin, has been
represented in fig. 8. The resistance thermometer has been ground
at c into the melting-vessel A, which consisted of not very readily

fusible glass. This ground joint is surrounded by a jacket, which

Fig. 8.

(1207 }

was filled with mercury, and was then closed by a layer of paraffin

The melting-vessel had been blown out to a diameter of 5 ¢.m.
at the bottom, there where the windings of the resistance thermo-
meter are found, so that this part could contain 250 gr. of tin. Above
this the vessel had been blown out to a still wider bulb 67), which
could be fused to a second bulb C by means of a capillary, which
was supplied on the opposite side with a second capillary.

Before it was fused to bulb 6, bulb C had been fiiled with pieces
of very pure tin, excellently prepared by Kannpaum. The only im-
purity it contained was lead, and only 0,04 °/,.

Then first of all the capillary g was connected with the Gaede-
pomp by means of an air-pump rubber tube, and so far exhausted
that a Geissler tube, which was permanently in connection with the
P,O,-vessel of the Gaedepump, no longer showed phenomena of
discharge.

Then the capillary g was melted off, and the bulb C was heated
to melt the tim that is in it. At the same time also the bulb
6 of the melting-vessel A was heated, and the whole apparatus was
held horizontal. The melted tin was now covered with a coat of
oxide, and the capillary / served to remove this before the tin
arrived in the melting-vessel A. If, viz., now the apparatus was
made to rotate a little round the resistance thermometer as hori-
zontal axis, the tin flowed from the buib C' through the capillary
f into the bulb 4, the coat of oxide remaining behind in C. The
melting-vessel remained in a horizontal position, till all the tin had
solidified in the bulb 4, after which the capillary 7 was melted off.

The tin filtered in this way was so perfectly free from the coat
of tin-oxide, that in its melted condition it looked quite like mercury,
and in solid condition it consisted of fine glittering crystals.

Of course we cannot guarantee that our tin was perfectly pure,
for though the solid tin-oxide had been removed, the tin will have
contained some tin-oxide in a dissolved condition. As this quantity
was, however, very small, and as it was at all events the same in
the different experiments, this circumstance did not afford an insuper-
able difficulty for our purpose.

Now the apparatus: was ready for the experiment, and was care-
fully immerged in a bath of melted potassium-sodium nitrate in
order to melt the tin, and make it flow into the widened part o.
The quantity of tin had been chosen so that the melting-vessel was

1) After the experiment the liquid tin was conducted to this bulb to solidify
here. This was done in order to prevent damage of the resistance thermometer
in the solid mass.

( 1208 )

filled up to the constriction between @ and % in a vertical position. ;

Now in order to find the poimt of solidification of tin for an if
possible unary behaviour, the melting vessel, which had only been
heated a few degrees above the melting-point of tin, was suddenly
conveyed to an air-jacket, which was found in another larger potas-
sium-sodium nitrate bath of a constant temperature = 220°.

The connection of the thermometer with the Wuerarstonr bridge
had already been effected before, and the image of a Neryst lamp,
cast on the graduated scale by the mirror of the galvanometer
showed, that the liquid undereooied on cooling. If the liquid was
lightly shaken, crystallisation set in, and the image rose to a maxi-
mum, where it remained immovable for more than 2,5 minutes ;

aSf

Fig. 9.

then it descended very slowly for a long time, after which it pretty
suddenly began to descend rapidly. The temperatuur-time curve that
follows from these experiments, which were repeated every 10
seconds, has been drawn in figure 9, in which only the observations
every 40 seconds are indicated to restrict the number of crosses.

It appears from this line that the solidifying mass round the
thermometer maintained the same temperature of 251.82° for more
than 2.5 minutes, and that it then slowly decreased to about 231.63°,
after which the temperature pretty suddenly decreased rapidly. As
it always appeared that the mass had already solidified for the
greater part at the moment that the slow decrease first commenced,
we thought that we had to conclude from the above very peculiar
line that the system really behaved in a unary way here on solidi-
fication, and that the slow decrease, which preceded the rapid

( 1209 )

decrease was not owing to the trace of tin-oxide, but had to be
ascribed to an exothermic process, which took place in the solid
mass after the solidification, which supposition was -corroborated by
the subsequent experiments.

Honsorn and Hennia'), who determined the point of solidification
of tin in an open vessel found 231.83°, when they used 1.5 K.G.,
a value which only differs 0,01° from ours.

If we use an open vessel, tin gets covered with a layer of oxide,
and strictly speaking, we do not determine the point of solidification
of pure tin, but the temperature of the eutectic point of tin oxide
— tin. Accordingly we might conclude from the exceedingly small
difference between Horsorn and Hennie’s result and ours that tin-
oxide dissolves exceedingly little in tin, and that it is not necessary
for the determination of the point of solidification to work in vacuum.

Yet for our purpose the determination of the influence of the
previous history of tin on its point of solidification, the vacuum,
and the absence of solid tin-oxide appeared an indispensible require-
ment, as with rapid cooling of liquid tin which had been heated
to a high degree exposed to the air, perfectly unreliable and widely
divergent results were obtained, whereas they were always the same
in vacuum and in absence of solid tin-oxide.

As in order to ascertain
the influence of the previous
history it is necessary to work
rapidly, and so also to make
the solidification take place
rapidly, first the curve of
cooling was determined of
tin that was heated only just
above the melting-point, and
was cooled simply by expo-
sure of the apparatus to the
air without jacket.

This experiment yielded
the curve as seen in fig. 10.
Of the observations, which
L were made every 10 seconds,

Fig. 10. only those of every 40 seconds
have been indicated. So the temperature remained constant for about
40 seconds, but the unary point of solidification could not be reached

') Ann. der Phys. 35, 761 (1911).

80
1oceedings Royal Acad. Amsterdam. Vol. XIY.

( 1210 )

in consequence of the more rapid cooling, though there was without
doubt a tendency to the setting in of internal equilibrium. The
maximum temperature here amounted to 231.74°, and so was 0.08°
under the unary point of solidification. Then the temperature first
decreased slowly to 231.6°, after which it decreased pretty suddenly
with continually accelerated rapidity, just as was observed in the
preceding experiment *).

After having obtained this result, we could proceed to the inves-
tigation about the influence of the previous history. The melting-
vessel was then heated to a temperature of + 300° and then cooled
as rapidly as possible to about 3° above the point of solidification
by a current of air produced by means of a foot-bellows. The further
cooling then took place without this means.

Fig. 11, which gives the result of this experiment, shows that

Ww

Fig. 11.

afier the solidification of the undercooled liquid had set in by means
of shaking, the temperature quickly rose to 231.98°, so 0.24° above
the temperature maximum of the preceding experiment, and even
0.16° above the unary point of solidification, but the fall of the
temperature was now very much quicker than in the former expe-

1) Thermo-currents were seldom noticeable with our resistance thermometers,
and when this was the case, the connection was made so that the effect to be
expected was diminished by the thermo-current,

(Elades)

riment, and so the curve deviates very much more from the ideal
curve of cooling than any of the other lines (the crosses mark the
observations every 40 seconds) '). Now it liad been proved that the
system tin, as had been expected, presents the same peculiarities as
phosphorus, though in a much less degree, which is not surprising,
because the point of solidification of tin lies so much higher, and
the transformations at that higher temperature will probably take
place pretty rapidly.

Finally we proceeded to the determination of the cnrve of heating
of tin which had _ solidified slowly beforehand, and had not been
cooled further than a few degrees below the point of solidification.

With slow heating in a wide air-jacket, which had been placed
in a nitrate-bath of -+ 300°, the curve represented in fig. 12 was
obtained.

Ae

Zax! £3496 :

£30

Fig. 12.

Characteristic is the long bend on the Jeft, which for a pure
substance with such a great conductivity of heat as the metal tin,
points to a conversion in the solid mass, which is accompanied by
an absorption of heat.

1) Here it deserves notice that the damping of the galvanometer was so perfect
that the image never passed through the zero-position, even though the mirror
moyed very rapidly at fiest,

50*

(1212)

An almost horizontal part was found at 231,92°, but this point
lies -+- 0,1° above the unary point of solidification.

As we have observed, tin can also melt in a unary way at
231,52° in case of very slow heating, but we must heat more rapidly
if we wish to get good regular lines, because else the temperature
depends too much on accidental disturbances; this is the reason that
the nitrate-bath had to be regulated at -- 300°.

The more rapid the heating is the more
gradually do the two parts of the curve of
heating, the righthand one and the lefthand one,
merge into each other, and with heating without
an air-jacket, so directly in the nitrate-bath of
300°, we obtained the curve as it is drawn in
fig. 13. The final melting-point here lies only
| 0,04° higher than in the preceding experiment.
So it has appeared from what precedes that
when we work rapidly the system tin betrays
its complex nature, as the theory of allotropy
fed us to expect in virtue of the three different
fia solid modification of tin.

234" L3G"

In connection with the said supposition that
the internal equilibrium in the solid state under
the point of solidification is subjected to a pretty

ae considerable displacement, some more experi-

Fig. 13. ments were made according to the capillary-
method of Socn. Powdery pure tin was put in very thin-walled
capillaries of about 0,5 mm. diameter. These capillaries were heated
in a bath of KNO, — NaNO, for some time ata certain temperature,
and then suddenly conveyed to another bath, the temperature of which
was varied till the tin was just gomg to melt after 10 seconds. The
result was the following :

Temperature at which the equi- Temperature at which the
librium of the tin had set in. | melting began after 10 seconds.

165° | 2380
200° | 237.5°
2980 2350

230° | 234°

( 1213 )

So the lower the temperature at which the tin has assumed its
equilibrium, the higher the initial melting point lies with very rapid
heating.

That the observed differences cannot be owing to the fact that
more heat is to be supplied to tin of 165° than to tin of 230° before
it melts, in consequence of the difference of temperature of 65°, is
at onee seen, as the initial melting-point appeared to have changed
only 0.5°, when the initial temperature was brought from 165° to
200°. This result, to which of course, only qualitatively value can
be ascribed, shows that really in the solid state, chiefly a little below
the point of solidification, a considerable displacement of the internal
equilibrium seems to take place ‘).

| Though the system tin seems

i! | to be so complicated that we

scarcely venture to assume any-
thing about the pseudo 7-2-
figure, we might now say this,
that when there were only two
kinds of molecules, the lines
for the internal equilibria in the
liquid phases and in the solid
phases might run as indicated

aa P eat
in fig. 14. So the quantity —
da

would differ in sign for the two
said limes, which, however, is
very weil possible.

Before leaving the system tin
we refer once more to what
one of us communicated in these
Proc. March 26, 1910 p. 77
about the metastability of the
metals, to which we can now
add that the supposition made

Fig. 14. there with regard to tin is
supported by the investigation communicated here to such an extent
that without any doubt the most obvious explanation of the so-called
recrystallisation is the transformation of a solid state out of equili-
brium to one of internal equilibrium, as the theory of allotropy led
us to expect. It follows from this theory that the phenomenon of

1) This phenamenon is also studied dilatometrically.

( 1214 )

recrystallisation will be of frequent occurrence, just as those which,
not very appropriately, have been compared to diseases by Conen. These
phenomena occur in more or less degree for every polymorphous
substance, and so it is absolutely senseless to assign a special place
fo tin on this account *).

W) AER:

The third substance subjected by us to an investigation was the
substance water. The experiments were made in open vessels, so
that the water contained some air, of which, however, not the slightest
disturbing influence was observed.

In the first experiment distilled water was put in a test-tube of
2.5 em. diameter, in which the resistance-thermometer had been
placed. The water was carefully made to solidify. For this purpose
the melting-vessel was first placed

in a second empty wider tube, and

el . then the whole was immerged in a
: / bath of common salt and ice. On
‘ut purpose we did not allow the tem-
rt perature of the ice to descend below
a Yiioe —0.3°, and then we conveyed the
Vit ade “4 melting-vessel with air-jacket to a

Fig, 15. water-bath of 30°.
In this way we succeeded in making the water melt ideally, which

clearly appears from the curve of heating of Fig. 15 (observations
every LO seconds).

This curve has namely a pretty long horizontal piece, which lies
exactly at O°.

That it is absolutely required to cool down the ice only very
litle below 0° in order to make the ice melt ideally, follows from
the figures 16 and 17. The line of Fig. 16 was obtained by keeping
the ice at —7° for some time beforehand, and then to convey the
melting-vessel with air-jacket into a bath of 30°, just as in the
preceding experiment. The result was now that the ice did not melt
ideally, but showed a clear melting range from —0.22 to —0,04°
and when the ice had been kept for some time beforehand at the
temperature of — 80°, the deviation from the ideal behaviour was
still somewhat greater, as fig. 17 shows, from which a range of

1) Gf. what Wyrousow says about this [Bull. Soc. fran¢. Minéral 88 296 — 300
Noy. (1910)].

Fig. 16.

Qs:
8

Vig. 17.

( 1216°)

melting-temperature follows from — 0.28° to —0,06°. So these
experiments afforded the proof that the substance water did not
behave as a unary one under these circumstances.

Finally the melting-vessel with
resistance thermometer was pla-
ced in liquid air, and water of
higher temperature, varying be-
tween 10° and 100° was squirt-
ed into the melting-vessel, in
which way we tried to bring
about a fixation of the internal
state in the liquid. If then the
jaar curve of heating was determined
in the described way the melting-
range appeared to be greater
than in the former experiments,
and the final melting-point
always lay above O° then. Fig.
18 shows one of these curves,
but we think that we cannot
attach so much value to this

Fig. 18. curve as to the preceding one,
because in this way of procedure the ice often possesses hollows,
which render the result Jess reliable.

The investigation of ice communicated here, however, shows with
the greatest clearness that the substance water is a complicated state,
and can easily be treated in such a way that it reveals its complexity *).

The investigation of the testing of the theory of allotropy will be
continued with different elements, and with both anorganie and
organic substances, the results of which will be communicated here

in due course.
Anorganice Chemical Laboratory

Amsterdam, March 29 1912. of the University.

1) The application of the theory of allotropy to the four modifications of ice will
be given later on.

( 1217 )

Physics. — <‘Contribution to the theory of binary mixtures” NX.
By Prof. J. D. vAN DER Waals.

In the preceding Contribution I repeatedly pointed out that not
all mathematical possibilities for partial miscibility really occur.
Among others the case of only partial miscibility seems to be
mathematically possible for all values of m and /, whereas for small
value of # this partial miscibility has only been seldom observed.
So if we want to find decisive rules for the occurrence of incomplete
miscibility, this seems not possible to me withort first having found
a rile for the determination of the quantity / in the formula
a,,’—la,a,. And this will no doubt require that we bave first sue-
ceeded in forming a clear idea of what the cause is of the attraction
of the molecules, so also of the cause which determines its value
for a simple substance. But though the knowledge of the properties
of the different mathematical possibilities, also im connection with
the temperature, is not sufficient — and not even the principal factor
that should be studied, still this knowledge is indispensable. And
therefore I will start with giving some results about this.

In the formula:
y—b)? db? c
(2 ) a ’) ee,
v (1—a) da a“

/

the projection on the v,z-plane has been given of the section of the
d’w ay aes

two curves ae O and = 0 at the different temperatures, though
v- AX

on simplified suppositions. Of course there might also be given two
such projections of this section on the v,7-plane and on the 2, 7-plane,
which would also be closed curves. but the formulae for-them would
not be simple, and so we shall not try to give them. In both there
would oceur a minimum and a maximum of 7) the minimum and
the maximum value of v or of wv being the same which also occur
in the v,z-prajection. If we imagine the three axes, an z-axis, a
y-axis, and a 7-axis, there is a closed curve in the space — and then
the differential equation of this curve is given by a relation between
dv, dx, and dT, which is derived from the simultaneously existing
relation between these three differentials for the two funetions

ay ap ee 4
——= (0) and —-=0. These two relations are:
dv? dx*
: aw ' dw dw :
= al IE iy SS Gp (I)
dT dv? ls dv* ao dx ie ;

and

( 438%)

Pw aw dy
IT + ——— dy + — dz=0
ide?" Avda eee
é : aw yp
If we take into account that fo = 0 and —- = 0 for the points
av Ak

of this section, we may also write:
2a dT d*p d*p

eh dai 0
Oat! dv’ dx dv
2c dT dp d*w

+ Pees Fy a
v y dx? du

We find for the relation between d7, dv, and dx then:

dT j ;
= T ae aL
dips dip | d*p 2a | 2a dp,
dv* dx dv dx dv p> v® dv? |
dp dp | iy 2¢ 2e d*p
adz* dx* | de® v | oda?
or
dT
—- dv da

a ———-—_ = - —_——_ == -— - sae (ll
d*p d*y ap Gp 2ad wp 2a ad*p 2a d*p sit dp (1)
dedi davdridat eda v dx dv v® du? “ y dv?

als

. a . r . . . .
If the denominator of wie equal to 0, then 7’ is either minimum

iS

or maximum; if the denominator dv is equal to 0, then v is either
maximum or minimum, and if the denominator of dz is equal to 0,
this holds for the limiting values of 2.

al

_ di
We may also write the denominator of at thus:

Up Bp | (dv\ dv
dv* des? du) 7 a 7 |?
beach: dv\' ;
indicating by {——] the tangent of the angle which the tangent to
ec) Tp

aw ‘ f dv
the curve —- =O makes with the z-axis, and by a the same
ax ak /]T

Sai dp 3 asl 2
quantity for the curve — 5 =0. For 7 minimum or maximum
av
these curves touch, and also the locus of the points of intersection

touches in that point. If at the minimum value of 7’ we draw the

( 1219 )

a’

three said curves in the v,v-projections, 7s =O lies in the neigh-
ae
bourhood of the point of contact little above »v—d, and with a cur-
dp a i aw ; : ;
vature —~ positive. The second curve —— =O, also with a slight
av Ge

positive curvature, but yet somewhat more pronounced than the
former curve, and finally the locus of the points of intersection, again
with a somewhat intenser positive curvature. But at the maximum
value of 7’ the relative position of the three said curves is another,
and there are even different possibilities.

d* yp d’w

First of all the relative position of —— =O and —.. = 0 may
av a

have remained the same, just as the sign of the curvature, and

there may only be a difference in the position of the locus of the

points of intersection, which has then the same point of contact as

the two said curves, but lies on the other side of the tangent.
aw ‘

Secondly the curvature of —--=0 can be of inverse sign in the
ae ist

dv
point of contact compared with that of = = 0, and have the same
ave

. . u . . . r €
sign as that of the locus of the points of intersection. Then —- = 0

av
must be quite contained within this locus at the moment of contact,
: : = ay :
and for higher 7’ the curve = =0 must disappear in the region
av
oe
in which

is positive, while in the former case this happens in
av

: ay , :
the region where —— is negative.

: z :

dv
This latter remark holds both if the second component, viz. that

with molecules of greater size, has a higher 7%, and when 7; should
be smaller than 7%, as for the system water-ether. But in all cases

; dee ; See
the value of the denominator of = in (1) begins with O at Tren.

)

2

: ; ‘ d*p d’p
and it ends with the same value at Zina. If —— and oe could not
6 av

“™/~ . . dv (*
become equal to O, the difference of the value of ( ) for the two
aLy/T

qj? 2

p ¢ - . . 7
curves REX and ao must begin with O for Trin, and end

dv? Ta

( 1220)

with O for Tig. So on that side of the locus of the intersections
where this difference is positive, there must be a maximum value
for this difference, and on the side where this difference is positive,
there must be a maximum value for this difference, and on the side
where this difference is negative, a minimum value. Now this diffe-
rence is positive on the side of the component with the greater size
of the molecules and reversely. But also if it should be possible that
dp a?

a E
- should be able to become equal to O, the same remark
aL”

and

av

yy

d7
holds for the denominator of qo Nia. that this denominator is always

positive on the righthand side between Zoy, and 7,7, and reversely.
jut we shall yet have io return to the value of the denominator of
ai dp Pp

¢
a beeause the faet whether Te and z B can become equal to 0,
ae~ av

is not entirely devoid of importance.
After this remark about the course of the value of the denomi-

dT
nator of “pe we may als make a remark about the course of the value of

the two other denominators in equation (1). First about the denominator
of dv. If this denominator is equal to O, 2 is either minimum or maxi-
mum. So if we examine the value of this denominator at the locus
of the points of intersection, this value will begin with O and end
again with O both on the lower and on the upper branch. On the
upper branch it is negative, and on the lower branch it is positive.
da

We can verify this by examining the sign of ora

The denominator of dv is O, when v bas minimum or maximum
value. Both on the righthand branch of the locus of the points of
os area Py
intersection of =0 and —=0 and on the lefthand branch

dv? aa

the value of this denominator begins with O and ends with O at the
minimum volume.

On the righthand side this value is always positive and reversely.

on at ies 7p
We can verify this either by examining the sign of Lo or by
Ld
* . . . dv . . . eo. .
examining the sign of for the locus of the points of intersection.
Av

We shall now have to show that really from the value of the
discussed denominators the above given sign of the value is to be

( 1221 )

aap dp dsp

’ 9 °
dv? dx dv da”

derived. For this it is necessary to know the values of

dy eae ; : :

and Te bearing in mind that we have to do with points for which
nts :

dy

dv?

For these values‘) we find the following. equations :

d*p 2a43)0—» |
(iam eg

\ db da
dp = 4a 3 a 1 dz}
6 See

db»? | ee TE)
d*p da da ¢
dat uF r(v-b) Qa
sa!

ap 2a 2 Ee, 1— 22
E 5S S00 Fix, 3 2 A
du v (v—d) z*?(1—a)?) |

:|

. . . . . a
With introduetion of these values the denominator of 7 has the

complicated form :

tN da {db\? ‘db

wt \ te pet leli oe: lé
w'(v ~ b) | v a v a\v

da

“da v-—b 3b—v fv—b\? 1—2ex
Lae arn ae v ai all

Gal

L
|
L
|

And the condition that the denominator of

be equal to 0, may

Git

be written as a third power equation in v, which in connection with
the second power equation in v which holds for the intersection of
aw dp : < : : :
iS 0 and ae oe can yield a relation in & for the determina-
ave a&

1) These values were already used in Contribution XVIII, p. 888, where however

db?
: da

the factor 2 has been omitted, which must be put for fe BF On account of this
v=

here is an error in the equation following there.

(1029) )

tion of the points where this denominator is 0. This relation in 2,
however, has such an intricate form as to render it useless. We

shall, however, return to this denominator later on.
r : 5 : a d*p dp
The denominator of dv is equal to 0, when — == ¢—.,

— Now
ve du? dv?

d*p . bes : aid : :
—~ is positive, so long as 7 <736. And though it is not impossible
av

e
that for limiting values for z the circumstance v= 3b, or even
v > 36 can occur, this is among the very exceptional cases. As
ee, ee eee 1
for the limiting values of « the value of —S——

) c ¢
i—e(+a=
a

9

the value of z(1—z) ~ must be Dis for v > 3b. For the present
a

$ d? i ele : ecwe
we shall not assume this case, but suppose = positive for the limiting
dv
values of w.
J2

: Up -. batt Gn
Then it follows immediately from this that also ee is positive for
Lv

es ; < : < GkF) dp
the limiting values of w From the given values for a and a
follows :
| (=) |
4a? du c } 2a 3b—v
oll s(o2) 7 al a ioe
or
db?
v(v—b) 2a 2a v—b
or
db»?
& c 2b
oad) 2aWEab
or

db = c
: = — by.
(G) a

And if we substitute this value of (

aoa E
— | in the equation of the

ae

curve for the intersections, we find back :

( 1223 )

2

Shs ‘ : Gh) Ps
That we were justified in calling the case that a < 0 for the
av

limiting values very exceptional, may appear in the following way.
Let us write:

or
a es er! 1
ce(l-a#) ce ¢ l—w
or
a Ba l+e, 1 n(l+e,) 1 1
cx(1—x) (n—1)? « (n—1)? 1—w«
For the limiting values of z:
Bolt ns, 1
—-+ —1=0.

(n—1)? a (n—1)? l—a@
And so we have for these values of z:
a 1 1 nr 1
cx(1—a) (n—1)? x a iS
For limiting values of « near O or 1 this value would be
very large. For the system water-ether we find with n=5}
and . about 0.36 a value about equal to 2.3 and for = 0.98 a
very large value — so that the inverse value is by no means greater

2
than 3 If one of the limiting values of a happened to be equal to

3
has the minimum value, then

: 1 n
the value of x, for which — + 5
wv Sth

a Lagan Geet eee ’
els 5; would be equal to | ——— ], and if this value is to be smaller than
CL =n tw

n would have to be greater than 10 for the accidental case of

5?

the coincidence of the two said values of w.
d wee Se db \*, c
The denominator of dv is positive so long as a) 8 greater than — bv.
ax a
If we put this condition in the equation of the curve of intersection,
we find:
v < 1
b
1

e
a(1—a) =

(gaa)

So the denominator of dv is positive throughout the lower branch
of the curve of intersection, and inversely, as we had predicted

da
above from the value of 7’ aah But on the other hand this also
(2)

f dT ;
shows that we have rightly made the denominator of “pr reverse its
ee dy d?yp
sign in the point where —- = Oand = () touch.

2 2
dv da
, : a dw d*p
Ihe denominator of dv is equal to O when ——— = —— fees
v? dx* dudv

After some reduction of this relation if we introduce the above given

dw dp : :
value of — and — ape eet of course the same equation as Is
av AXvav
7 PA he Reno Ca a ae
yielded by differentiating ———— +- —=—» with respect! to 2x;
~ #(l—a) da a

and putting the form obtained in this way equal to O. | fully dis-
cussed the equation, which we then get, in Contribution XI (1908)
and accordingly refer to this Contribution with an addition, however,
which is not devoid of importance. It refers to the discussion about
the obtained equation :

In this equation (These Proc. Vol. XI p. 429) the sign + must
be used in the numerator, when the value of v < 6,, and reversely.
I have now come to see that this may also mean that the sign
+ holds in the numerator for the determination of the minimum
value of v, whereas the sign — must be taken in the numerator
for the determination of the maximum value of v.

For the determination of the value of « for the minimum volume
the preceding equation may also be reduced to the form :

a(1—a)e
gee ve Wises
a Cx

or (n—1) vee in a = -——14 pee — 1, while the
cv (1—.) ¢(1—a)? eae

( 1295 )

sign between the two radical signs has tobe replaced by — for
the maximum volume.
By way of control I have calculated the different quantities in
this formula for a system that cannot differ much from the system
Vy

water-ether, and in this way computed the two values of — corre-

a

sponding to every value of 7. For the limiting values of «= 0,3 and

7] (* & . \ n° é,
0,97 we compute from 2,7, = ———— and from (1—z,)(1—a,) = ——_,,
(n—1)? (n—1)?

Wit 2 :
for n= —> the value of ¢, = 5,893 and ¢, = 0,0141 and n? «, = 0,426.

Atel Ite, 1. n?(l-+te I
Then the value of —— ee —-+ Cs :) - 1 is:
ca (l—z2) (n—1)f a (n—1)? 1—e
a
x a
cx (1—2)
(UX Omesccmeys pron sete. 2,294
Oa css Wardstac 2,374
Oc Sieaec wuss. 2,709
og Ges Sea Oe 3,352
On7e os 4,533
ORS eee asparctts 7,021
ODN ses sse = 14,517

From the equation:

=) | 1—2) | — () {1 + neal a]-+[1 + (x? — lhe] = 0
2 a

we find then for the following values of w the subjoined values of

v b
—and —:
b, b,
v b
; Ret ah
b, b,
0,3 4.4 235
0,4 7 and 3 2,8
0,5 7,6 and 3,4 aD
0,6 6,4 and 4,2 3,

We see from this table that the minimum volume will occur for
v about equal to 0,4, while the maximum volume occurs at x about

Te a
0,5. If we now also calculate aes —-—1 and nee
¢(1-2)? C=
we find:
SL

Proceedings Royal Acad. Amsterdam. Vol. XIV,

( 1226 )

a VA Eien ae
c(1-«)? (i

ONS ae, os ee ISA ODEN ees eon,
De tad Oo LING aio cot o AOR
Ofbaa eaten otc OC aay ee Os O.cl
OHO 5 Gc oa o CEG 5 oa oto a UCR)

If to the n-fold of a value of the second column we add a corre-
sponding value from the third column, and if we divide the sum by
n—1, we find beginning with a —0,8, successively the values
2.162, 2,437, and 2,87. From this we should conelude that the
minimum value of v lies just before «= 0,4. With the sign — we
find successively 1,42, 1,9645, and 2,602; and so the maximum
volume at 2 somewhat above 0,5.

But to conclude from this example that the maximum volume is
always greater than 6,, and the minimum volume always smaller,
would be just as rash as my conclusion in Contribution XI that both
maximum volume and minimum volume would always be smaller
than 6,. Probably the case may occur tbat they are both smaller
than 6,, and possibly also that they are both even greater than 6,.

If they are both smaller than 4,, the equation :

a (7

a
—1 -_——_ = ——— — ] =|
(n ay ‘ e(1—2)? Es Cin

must be satisfied for two values of x, for both with the sign +;
and if they could both be greater than 4,, then also if the sign
between the two terms of the second member has been replaced by
—. To examine what conditions the binary systems must satisfy for
one of these three cases to take place, we should examine the proper-
ties of the 3 functions which occur in this equation.

a

The first function — is infinitely great for «= Oand #=1,

ca (1—w)

and has a smallest value for certain value of 2. From the form :
eee MO wm (leben

(n—1)? iG (n—1)?_ 1—e

follows for the value of 2 at which the minimum occurs :

—1

eee y(l+e,)
= a nV (1+ 6,)
or a2 = 0,325. The minimum value itself is equal to :

WValatere niareen :
fm

( 1227 )

and is calculated from it equal to 2,265. Those numerical values,
of course, only hold for the system water-ether. So in the little
table on p. 1225 the first value still refers to the descending branch.

: a ;
The first term of the second member, viz. Vat — 1, begins
Cc —wv
5 n (Te
at 2a2—=0O with the value i Sw andmendseatea—1
Ko

with an infinite value. It is penne throughout, and nowhere ima-

mies
ginary ; the third quantity, viz. hs ——— ee
(n—1)? 2?

1+é, 1
becomes equal to O for «= = is = if al Tt begins
(n—2) (n—1 Nz

infinitely great, is descending rcs and becomes, as we shall
suppose, equal to 0; in that point its differential quotient is infinite.

If we write the equation which is to be satisfied, in the following
form :

2 yc ie ay oa
apa) o(1==2) 2 (eh Wave ee an

we can to decide which of the three cases about the value of
maximum or minimum volume is to be expected, in the first place
propose the question whether the first member is greater or smaller
than the second member for the value of x7, whieh makes the third
term equal to 0.

s ? y x : a,
For this value of w the first member is equal to — — (1--2)
c

i}

n 7 a a ae

and the second member — (1—.), and so we have
n—1 c(1—2)

to put the question whether

pea . SS 1
eters Wen, ie v ()

or
come ( => n? 1
il PGi jie
or
Le ee ae
Gat es << ED:

Or

( 1228 )

or

or

nV &, Z (n—1) — V1 08

Now for the system water-ether the sign < holds as «, is so
small, and this implies that for the mentioned value of x

a Ze n [Az a,
cau(1_—a) ~n—1 e(l—a)r

If this result is repre-
sented graphically, as
has been done in fig. 53,
the point P of the curve
G lies within the curve
A, and the ordinates of
& must be both aug-
mented and diminished

by an amount indicated
by the third curve C,
to intersect the curve
A. Then the point where
the curve JZ itself inter-
sects A must lie at a
value of a between that

x for which the volume
is minimum or maxi-
mum; and this is quite

in accordance with our former results for the system under consi-

ig. 53.

deration. And always when the point P lies within A, or when
nV e,<(n—!)—V 1+-¢,, the maximum volume will be greater than
4,, and the minimum volume smaller than 4.
But there are other cases possible for which :

We Sn 1 — ee
and then the result is different. Then the point P lies outside the
curve A. First of all we might think, that 5 had not yet intersected
the curve A before the point P, and then intersection with A can
only be broveht about by increase of the ordinates of B by a certain
amount in which case two points of intersection appear. Then both

( 1229 )

maximum and minimum volume are smaller than 6,, and this case
I had considered as the only possible one in Contribution XI. We
might possibly also think that the point P lies below A, but that
B had first intersected this curve twice, and then we might even
ask whether intersection with A might not be brought about both
by increase of the ordinates of 45 and by diminution with those of
C. Then we should get 4 points of intersection. But then the extreme
-values of « would have to be rejected as lying outside the locus of

F _ yw dw : ; .
the sections of ae and es = 0. That I think a closer investi-
gation necessary for this apparently unimportant matter is owing to
my desire to get more certainty about the mixtures of hydrocarbons
and alcohols. Are systems conceivalle for them which account for
the phenomena without it being necessary for us to attribute them
to an unknown abnormality of tbe alcohols? Would perhaps the
case v >, occur for them for both volumes?

So
TVs), = ea

for the systems for which the two terms in the second member of
the equation are connected by the same sign for maximum and
minimum volume, and also nye, << (n—1)—Ve, must hold. And
so there must be a perceptible difference between ¢, and 1+ ¢«, or
€, not much greater than 1, as for water-ether. It must be rather
smaller than 1; and «, must not be small, as for water-ether. If we
lower the parabola of fig. 36 in the direction of the &,-axis with
unity, the point ¢,,¢, must lie within the new parabola, but it must
remain below the original one. Only for values of 2 which are
greater than 2 does this new condition diminish the place for the
choice of the points ¢,,¢,. But if we put m< 2, the equation which
we have used to determine the value of « for the point P, could

Vil+e,)

no longer be satisfied. This value, equal to ——, would then be
7i—

greater than 1, and then no such point could be indicated between

«=0 and «=1. But this is a drawback only in appearance.
Nothing compels us to restrict the discussion about the equation:

a n tou 1 atte 3
— — ILS ——1
ca(1—r) =n—1 c(1—w)? n—1 cx*

to values of w lying between O and Lt. Only if we should find 2>1
we should have to reject a point for which «> I as irrelevant to
our question. But if the use of 2 > 1 should be objected to, we
might confine our consideration to values of 2 <1, but so near 4

>

( 1230 )

that the value of

far exceeds all other terms. It then appears
—w

that the value of the first member, in any case in which ¢, is posi-
tive, far exceeds the value of the first term of the second member.

Then the two values under consideration are:

a, n EA a,
— and —— —_—
c(1~«) n—Il c(1—«)?

If the two quantities are divided by the same factors, it appears
that so long as 1+ «, is > 1, the curve A lies above the curve B.
Also in a simpler way we might arrive at the result that if
Wie Sp il ee
both maximum volume and minimum volume lie on the same side
of a straight line v = +,.
If we write in
(v—b)? ole
a5 + C=) = oo
a (1—2) a
the value 6, for v, and seek the values of w, for which this then
holds, we get the equation:

2 \ 1+é, ne, | 1+ e,
«2 — x1 ———} + —___=— 0),
C (n—1)? 7 Gey (n—1)?
So the value of v= 6, is not Bea ite:

Pa gee iad
oe (ty ST ;

According to our above remark this condition is satistied for
n <2. Most probably this means then that all the values of v are
smaller than 6,. Then the case that all the values are greater than
b,, could not occur for n small; then the abnormality of alcohol
would consist in this that it behaves as if it consisted of very
great molecules.

Accordingly I have not yet succeeded in finding a system for
which the curve £ intersects the curve A twice in such a way
that also the phenomena of unmixing if 7 is not great, are accounted
for. For the present, however, I shall go on with the subject treated
in this and in the preceding contribution. ;

Chemistry. — “Vhe nitration of ortho-chlortoluene”. By Prot. A. F.
Houtieman and Dr. J. P. Wipaur.

(This communication will not be published in these Proceedings).

(May 23, 1912).

CONTENTS.

acETaBtLuM (On the relation between the symphysis and the) in the mammalian pelvis
and on the signification of the cotyloid bone. 781.
AcoUSTIC ENERGY (The effusion of) from the head. 758.
ADDITION (On the) and the additionproducts of chlorine to the chlorbenzenes. 837.
— propuctivity (On the activity of the halogene-dinitro-pseudo-cumoles and their)
with nitrie acid. 1007.
AIR MOTION (On the angle of deviation between gradient of atmospheric pressure and). 865.
ALCOHOL-manganous sulphate (On the system: water-). 924.
ALKALI- and earthalkali metals (Che permeability of blood-corpuscles in physiological
conditions, especially to). 122.
— merars (A remarkable case of isopolymorphism with salts of the). 356.
ALLOCINNAMIC AcID (Action of sunlight on). 100.
ALLoTROPY (The application of the new theory of) to the system sulphur. 263.
— (Das Gesetz der Umwandlungsstufen in the light of the theory of). 788.
— (Conformations of the theory of the phenomenon). II. 1199.
ALLOYS (The magneto-optic Kerr-eflect in ferro-magnetic compounds and). IT. 970.
AMINES and amides (On the action of oxalyl chloride on). 42.
Anatomy. ©. T. van Vatkenpurc: “The origin of the fibres of the corpus callosum
and the psalterium.” 12.
— ©. T. van Vatkenzpure: “On the mesencephalic nucleus and root of the nervus
trigeminus.” 25,
— A. J. P. van pen Brozk: “On the relation between the symphysis and the
acetabulum in the mammalian pelvis and on the signification ofthe cotyloid bone.” 781,
— L. Bouk: ‘On the structure of the dental system of reptiles.” 950.
— C. T. van VaLkexsure: “On the splitting up of the nucleus trochlearis.” 1023.
— §. J. vE Lanoz: “The red nucleus in reptiles.” 1082.
— ©. T. van VaLkensurG;: ‘Caudal connections of the corpus mammillare.” 1118.
— C. U. Arténs Kappers: “The arrangement of the motor nuclei in Chimaera
monstrosa compared with other fishes.” 1176.
ANGLE of deviation (On the) between gradient of atmospheric pressure and air motion, 865.
ANTHRAQUINONE (The course of the PZ-lines for constant concentration in the system
ether-), 183.
ANTIMONITE (Photo-electric phenomena with antimony sulphide). 740.

82
Proceedings Royal Acad. Amsterdam. Vol. XIV.

BI ClO NSD Gene nos s

ANTIMONY sulphide (Photo-electrie phenomena with) (Antimonite), 740.

ARBITRARY SURFACE (On the conoids belonging to an). Ist part. 481.

anGcon (The behaviour of) to the law of corresponding states. 158.

ARIENS KAPPERS (Cc. U.) v. Kappers (C. U. Artins).

ABSENOBENZENE SOLUTIONS (On the comparative nocuousness of concentrated and

diluted). 893.

Astronomy. H. J. Zwirrs: ‘Preliminary investigation into the motion of the pole of
the earth in 1907.” 2LL.

— J. C. Kapreyn: “The milky way and the starstreams.” 524.

— A. Pannekorxk: “A photographical method of research into the structure of the
galaxy.” 579.

— HE. F. van pe Sanve Bakuurszen: “Investigations into the empirical terms in
the mean longitude of the moon and into Hansey’s constant term in the latitude.” 686.

— J. C. Kapreyn: “Starsystems and the milky way.” 909.

— J. Weeprr: “Calculations concerning the central line of the solar eclipse of
April the 17th 1912 in the Netherlands.” 935.

— KE. F. van pe Sanpe Bakuutszen: “Further researches into the constant term
in the latitude of the moon, according to the meridian observations at Greenwich.” 991

— J, E. pe Vos van SreeNwiK: “Provisional results from calculations about the
terms in the longitude of the moon with a period of nearly an anomalistic month,
according to the meridian observations made at Greenwich.” 1180.

ATMOSPHERIC PRESSURE (On the diurnal variation of the wind and the) and their rela-
tion to the variation of the gradient. 48.
— (On the angle of deviation between gradient of) and air motion. 865,
ATOLLS (On the so-called) of the East-Indian Archipelago. 698.
AVENA (Investigation of the transmission of light stimuli in the seedlings of). 327.
BAK HUIJZEN (BE. F. VAN DE SANDE) presents a paper of Dr. H. J. Zwiers:
‘Preliminary investigation into the motion of the pole of the earth in 1907.” 211.

— presents a paper of Dr. A. Pannekork: “A photographical method of research
into the structure of the galaxy.” 579.

— Investigations into the empirical terms in the mean longitude of the moon and
into HansEN’s constant term in the latitude, 686.

— presents a paper of Mr. J. Wrepnr: “Calculations concerning the central line
of the solar eclipse of April the 17th 1912 in the Netherlands.” 935.

— Further researches into the constant term in the latitude of the moon according
to meridian observations at Greenwich. 991.

— presents a paper of Mr, J. E. pe Vos van Sreeywis« : “Provisional results from
calculations about the terms in the longitude of the moon with a period of nearly an
anomalastic month according to the meridian observations made at Greenwich.” 1180.

BARRAU (J. A.). The surfaces of revolution or quadratic cylinders of non-Euclidean
space. 148,
BENZENE (The nitration of), 837.
— (Lhe configuration of), the mechanism of the benzere-substitution and on the

contrast between the formation of para~ortho and of meta~substitution products. 1066,

CONTENTS. Iii

BENZENE DERIVATIVES (On the action of some) on the development of penicillium
glaucum. 608,

— HEXACHLORIDEs (On the) and their splitting up into trichlorobenzenes, 298.

BENZOIC acrD (On the chloration of). 684.

BENZOLSUBSTITUTION (On the magnetism of the) and on the opposition of the form-
ation of para-ortho-against meta-substitutionproducts. 684.

BESSEL’s functions (On some relations between). 962.

BEIJERINCK (M. W.) presents a paper of Prof, J. BozsexEn and Mr. H. Waterman:
“On a biochemical method for the determination of small quantities of salicylic
acid in the presence of an excess of p-oxybenzoic acid.” 604.

— presents a paper of Prof. J. Borseken and Mr. H. Waterman: “On the action

of some benzene derivatives on the development of penicillium glaucum.” 608.
— Structure of the starch-grain. 1107.

— presents a paper of Prof. J. BOESEKEN and Mr. H. Waterman: “Action of substances

readily soluble in water, but not soluble in oil on the growth of the penicillium
glaucum”. 1112.

BILINEAR COMPLEXES (The theory of) of conics. 550.

BINARY MIXTURES (Isotherms of diatomic gases and of their). VIII. Control measure-
ments with the volumenometer. 101.

— (Isotherms of monatomic substances and of their). X. The behaviour of argon
to the law of corresponding states. 158. XI. Remarks upon the critical temperature
of neon and upon the melting point of oxygen. 163.

— (Contribution to the theory of). XVI. 504. XVII. 655. XVIII. 875. XIX. 1049.
XX. 1217.

BINODAL cURVES (Some remarks on the direction of the) in the y-x diagram in a
three-phase equilibrium. 420.

BINODAL LINES (General considerations on the curves of contact of surfaces with
cones with application to the lines of saturation and) in ternary systems. 510.

BIOCHEMICAL METHOD (On a) for the determination of small quantities of salicylic
acid in the presence of an excess of p. oxybenzoic acid 604.

Biochemistry. J. Borsexen and H. WarerMan: “Action of substances readily soluble
in water but not soluble in oil, on the growth of the penicillium glaucum.” 1112.

BLoopcorPusCLES (The permeability of) in physiological conditions, especially to alkali
and earth-alkali metals, 122.

BOESEKEN (J.). The configuration of benzene, the mechanism of the benzene substi-
tution and on the contrast between the formation of para-ortho- and of meta-
substitution products, 1066.

— Action of substances readily soluble in water but not in oil, on the growth
of the penicillium glaucum. 1112.

— and H. Warerman. On a biochemical metiod for the determination of small
quantities of salicylic acid in the presence of an excess of p-oxybenzoic acid. 604.

— and H. WarerMan. On the action of some benzene derivatives on the develop-
ment of penicillium glaucum. 608,

— and H. Warerman. On the action of some carbon derivatives on the develop-

ment of penicillium glaucum and their retarding action in connection with solubility
in water and in oil. 928,

82*

Iv OoON TEN? S,

BOBSEKEN (s.), A. Scuwerer and G. F. van per Want. On the velocity of
hydration of some cyclic acid anhydrides. 622.
BOIS (H. E. J. G. DU) presents a paper of Mr. Morris Owen: “Thermomagnetic
properties of elements”. 637.
— presents a paper of Dr. Sr. Loria: “The magneto-optic Krrr-ellect in ferro-
magnetic compounds and alloys”. [I 970.

BOLK (t.) presents a paper of Dr. C. T. van Vatkenpure: “The origin of the
fibres of the corpus callosum and the psalterium”. 12.
— presents a paper of Dr. C. T. van VALKENBURG: ‘On the mesencephalic nucleus
and root of the nervus trigeminus”. 25.
— presents a paper of Prof. A. J. P. van pEN Broek: “On the relation between
the symphysis and the acetabulum in the mammalian pelvis and the signification
of the cotyloid bone’. 781.
— On the structure of the dental system of reptiles. 950. 7
— presents a paper of Dr. C. T. van VaLkensurG: “On the splitting up of the
nucleus trochlearis”’. 1023.
— presents a paper of Dr, C. U. Ariens Kappers: “The arrangement of the

motor nuclei in Chimaera monstrosa compared with other fishes”. 1176.
BORNWAT#R (J. Tu.). On the action of oxulylchloride on amines and amides, 42.

Botany. S. H. Koorpers: “A few observations on some new and little known cases
of Leguminosae with mechanically irritable leaves.” 132.

— W. Docrers van Leeuwen and J. Docrrrs van Leruwen-Reyxvaan; “On
the distribution of the seeds of certain species of Dischidia by means of a species
of ant: Iridomyrmex myrmecodiae Kmery”. 153.

— P. ©. van ver Wok: “Investigation of the transmission of light stimuli in
the seedlings of Avena’. 327,

— Tu. Wervers: “The action of the respiratory enzymes of Sauromatum venosum
Schott”. 370.

— ©. van WisseLincu: “On the cell-wall of Closterium together with a consi-
deration on the growth of the cell-wall in general’. 912.

— M. W. Beyerinck: “Structure of the starch-grain”. 1107. .

— C. P. Conen Stuart: “A study of temperature-coeflicients and van ’r Horr’s

rule”. 1159.

BROEK (A. J. P. VAN DEN). On the relation between the symphysis and the
acetabulum in the mammalian pelvis and on the signification of the cotyloid
bone. 781.

BROUWER (H, A.). On peculiar sieve structures in igneous rocks, rich in alealies. 383.

BROUWER (tL. B.J.). On the structure of perfect sets of points. 2nd Communication. 187.
— Continuous one-one transformations of surfaces in themselves. 4th Communi-
cation. 300.
BUCHNER (gf. H). Investigations on the radium content of rocks. III. 1063,
BUYTENDIK (F. J. J.). On the ciliary movement in the gills of the mussel. 1138.
CALCULUS rationum, 1026,

C.O (NMP NES ay

caRrBON (The system: iron-). 520.

— Derivatives (On the action of some) on the development of penicillium
glaucum and their retarding action in connection with solubility in water and

in oil. 928.
CARBONIC aActD (The phenomenon of condensation for mixtures of) and nitrobenzene

in connection with double retrograde condensation. 270.

CARDINAAL (J.) presents a paper of Prof. J. A. Barrau: “The surfaces of reyo-
lution or quadratic cylinders of non-Euclidean space”. 148.

CAUDAL connections of the corpus mammillare. 1118.

CELLS (The effect of substances which dissolve in fat on the mobility of Phagocytes
and other). 314.

CELL-wALL (On the) of Closterium together with a consideration of the growth of the
cell-wall in general. 912.

Chemistry. J. Tu. Bornwater: “On the action of oxalyl chloride on amines and

amides”, 42.

— P. van Rompureu: “ Additive compounds of m. Dinitrobenzene”, 46.

— A. W. K. ve Jone: “Action of sunlight on allocinnamie acid”. 100.

— A. Smits: “On retrogressive melting-point lines”. 170.

— A. Smits: “On retrogressive vapour-lines’. Ist. Communication. 177.

— A. Suits and J. P. Treup: “On the course of the PT-lines for constant con-
centration in the system: ether-anthraquinone”. 183,

— A. Smits and J. P. Treus: “Qn retrogressive melting-point lines” 3rd Com-
munication. 189.

— A, Smits and J. Maarse: “On the system: water-phenol”. 192.

— F. E. C. Scurerrer: “On the system: hydrogensulphide- water”. 195.

— A. Sirs: “The application of the new theory of allotropy to the system:
sulphur”. 263.

— T. van per Lrnpen: “On the benzenehexachlorides and their splitting up
into trichlorebenzenes”. 298.

— P. van Romurenu: “The essential oil of Litsea odorifera Val. (Trawas oil)”. 325.

— . M. Jarcer: “The photochemical transformations of ferri-trichloro-acetate
solutions”, 342.

— FE. M. Jarerr: “A remarkable case of isopolymorphism with salts of the alkali-
metals”, 356.

— P. J. H. van GINNEKEN: “Sugar solutions and lime”. 442.

— A. Smits and H. L. pe Leeuw: “On the system: sulphur”. 461.

— A. Smits: “The system iron-carbon”’. 530.

—F, E. C. Scurrrexr and J. P. Trecs: “Determinations of vapour tensions of
nitrogen tetroxide’. 536.

— F. M. Jarcer: “Contribution to the knowledge of the natural sulfo-antimoni-
tes”. 555.

— I. M. Janeer and H. 8S. van Kuoosrer: “Contribution to the knowledge of
sulfo-antimonites.” IT. 555,

VI CONTENDS.

Chemistry. J. Borsexen and Il, Warerman: “On a biochemical method for the deter-
mination of small quantities of salicylic acid in the presence of an excess of
p-oxybenzoic acid”. 604.

‘

— J. Borseken and H. Warerman: “On the action of some benzene derivatives
on the development of penicillium glaucum”. 608.

— J. Bonsexen, A, Scuwuizer and G, F, van per Want: “On the velocity of
hydration of some cyclic acid anhydrides”. 622.

— H. R. Doornsoscu: “On the iodides of the elements of the nitrogen-group”. 625.
— A. F. Houteman: “On the chloration of benzoic acid”, 684.

—'T. van per Linpen: “On the magnetism of the benzolsubstitution and on
the opposition of the formation of para-ortho-against meta-substitution products”, 684.

— H. Vermevien: “On some trinitroanizoles”. 684.

— FE. M. Jancer and J. B. Menke: “Studies on tellarium, Il. On compounds ot
tellurium and iodine’. 724.

— F. M. Jancer and J. N. van Kreoren: “The question as to the miscibility
in the solid condition between aromatic nitro- and nitroso-compounds”. IIT. 729.

— J. Ovre Jr. and H. R. Kruyr: “Photo-electric phenomena with antimony-
sulphide (Antimonite)”. 740.

— F. E. C. Scnerrer : “On-gas-equilibria”. 743.

— A. Smits: “Das Gesetz der Umwandlungsstufen in the light of the theory of
allotropy”. 788.

— Pu. Kounstamm and L. S. Ornstemn: “On Nernsv’s theory of heat and the
chemical facts”. 802.

— A. F, Hotteman. ”The nitration of benzene”. 837.

— T. van per Linpen: “On the addition and the addition products of chlorine
to the chlorbenzenes”. 837.

— FI. A. H. Scurememakers and J. B. Deuss: “On the system: water-alcohol-
manganous sulphate’. 924.

— J, Borsexen and H. Waterman: “On the action of some carbon derivatives
on the development of penicillium glaucum and their retarding action in con-
nection with solubility in water and in oil”, 928. ;

— A, Huenper: “On the activity of the halogen-dinitro-pseudo-cumoles and
their addition productivity with nitric acid”. 1007.

-— F. A. H. Scurernemakers and A, Massink: “Some compounds of nitrates and
sulphates”. 1042.

— L. van Irautte: “On dipterocarpol”. 1044.

— L. van Irauir and M. Kerposcu: “On Minjak Lagam’, 1047.

— E. H. Bicuner: “Investigation on the radium content of rocks”. LIT. 1063.

— J. Bérsexen: ‘The configuration of benzene, the mechanism of the benzene
substitution and on the contrast between the formation of para-ortho- and of
meta-substitution products”. 1066.

— A. Smits and H. L. pp Leguw: “Conformations of the theory of the pheno-
menon allotropy”. IL. 1199.

CONTENTS. vil

Chemistry. A. F. Hotueman and J. P. Wisaur: “The nitration of ortho-chlortoluene”.
1230.

CHIMAERA MoNSTROSA (The arrangement of the motor nuclei in) compared with other
fishes. 1176.

CHLORATION (On the) of benzoic acid. 684.

CHLORINE (On the addition and the additionproducts of) to the chlorbenzenes. 837.

CILIARY MOVEMENT (On the) in the gills of the mussel. 1138.

CLAY (J.). On the influence of electric waves upon platinum mirrors. (Coherer action). 126,

cLOsTERIUM (On the cell-wall of) together with a consideration of the growth of the
cell-wall in general. 912.
cLoubs and vapours (Electric double refraction in some artificial). 558. 2nd part. 786.
COHEN STUART (Cc. P.). v. Stuart (C. P. CoHeEn).
COHERER ACTION (On the influence of electric waves upon platinum mirrors). 126.
compounDs (Additive) of m. Dinitrobenzene. 46.
— and alloys (The magneto-optie Kerr-effect in ferromagnetic). II. 970.
CONDENSATION (The phenomenon of) for mixtures of carbonie acid and nitrobenzene
in connection with double retrograde condensation. 270.
CONGRUENCE (A bilinear) of quartic twisted curves of the first species. 255,
— (On the) of the second order and the first class formed by conies. 1173.
CONGRUENCES (On the lineo-linear) of right lines and the cubic surface. L018.
— (On two linear) of quartic twisted curves of the first species. 1122.
conics (‘The theory of bilinear complexes of). 550.

— (On the congruence of the second order and the first class formed by). 1173.

— (Surfaces, twisted curves and groups of points as loci of vortices of certain
systems of). Iste paper. 495.

conorps (On the) belonging to an arbitrary surface. Ist part. 481.

coRPuUS CALLOsUM (The origin of the fibres of the) and the psalterium. 12.

CORPUS MAMMILLARE (Caudal connections of the). 1118.

CORRESPONDING STATES (The behaviour of argon to the law of). 148.

COTYLOID BONE (On the relation between the symphysis and the acetabulum in the
mammalian pelvis and on the signification of the). 781.

CREATININ (The excretion of) in man under the influence of muscular tonus. 310.

CRENILABRUS MELOPS (Pleistophora gigantea Thélohan, a parasite of). 377.

CRITICAL POINT (On some relations holding for the). 771.

— (On the value of some differential quotients in the) in connection with the
coexisting phases in the neighbourhood of that point and with the form of the
equation of state. 1091.

CRITICAL quantities (The variability of the quantity J in van DER WaaLs’ equation
of state, also in connection with the). 278. Il. 428. IIL. 563. LV. 711.

CROMMELIN (c. a.) and H. KameruincH Onnes. Isotherms of monatomic sub-
stances and of their binary mixtures. X. The behaviour of argon to the law of
corresponding states. 158. XI. Remarks upon the critical temperature of neon
and upon the melting point of oxygen. 163.

Vill CONTENTS.

Crystallography. J. Scumurzer: “On the orientation of erystal sections with the help
of the traces of two planes and the optic extinction.’* 128.

cRYSTAL sections (On the orientation of) with the help of the traces of two planes
and the optic extinction. 128.

cubic surVvace (On the lineo-linear congruences of right lines and the). 1018.

cumotes (On the activity of the halogene-dinitro-pseudo-) and their addition pro-
ductivity with nitric acid. 1007.

curves (A bilinear congruence of quartic twisted) of the first species. 255.
— (On two linear congruences of quartic twisted) of the first species. 1122.

— of contact (General considerations on the) of surfaces with cones, with applica -
tion to the lines of saturation and binodal lines in ternary systems. 510.

cycLic acip anhydrides (On the velocity of hydration of some). 622.

DENTAL sySTEM (On the structure of the) of reptiles. 950.

peEuss (s. B.) and I, A. H. Scoretyemakers. On the system: water-alcohol-man-
ganous sulphate. 924,

DIAGRAM (Some remarks on the direction of the binodal curves in the v-a-) ina three-
phase equilibrium. 420.

DIA-MAGNETISM (On para- and) at very low temperatures. 115.

DIFFERENTIAL EQUATION (Homogeneous linear) of order two with given relation between
two particular integrals. 1st Communication. 391. 2nd Communication. 584. 3rd
Communication, 832. 4th Communication. 1010,

DIFFERENTIAL EQUATIONS (On partial) of the first order. 763.

— (New researches upon the centra of the integrals which satisfy) of the first
order and the first degree. Ist part. 1185.

DIFFERENTIAL QUOTIENTS (On the value of some) in the critical point in connection
with the coexisting phases in the neighbourhood of that point and with the form
of the equation of state. 1091.

DINITROBENZENE (Additive compounds of m.). 46.

DIPTEROCARPOL (On), 1044. F

piscHipIA (On the distribution of the seeds of certain) by means of a species of ant:
Iridomyrmex myrmecodiae Emery. 153.

pIsPERSION of hydrogen (The). 592. -

DIURNAL VARIATION (On the) of the wind and the atmospheric pressure and their
relation to the variation of the gradient. 4S.

DOCTERS VAN LEEUWEN (w.). v. Leeuwen (W. Docrers van).

DOORNBOSCH (H. R.). On the iodides of the elements of the nitrogen-group. 625.

DRIFT CURRENTS (On the influence of the earth’s rotation on pure). 1149.

pROSTE (J.), An extension of the integral theorem of FourrER. 387.

EARTHALKALI metals (The permeability of bloodcorpuscles in physiological conditions ;
especially to alkali and). 122.

PARTH’s ROTATION (On the influence of the) on pure drift-currents. 1149.

EINTHOVEN (w.) and J. H. Wierinea. On different vagus effects upon the heart

investigated by means of electrocardiography. 169,

CONTENTS. ; Ix

ELEcTRIc and magnetic forces (Considerations concerning light radiation under the
simultaneous influence of) and some experiments thereby suggested. Ist part. 2.
ELECTRIC WAVES (On the influence of) upon platinum mirrors. (Coherer action). 126.
PLECTRICAL double points (On the law of molecular attraction for). 111).
ELECTROCARDIOGRAPHY (On different vagus effects upon the heart investigated by
means of). 165.
ELEMENTS (Thermomagnetic properties of). 637.
EMPIRICAL TERMS (Investigations into the) in the mean longitude of the moon and
into Hansen’s constant term in the latitude. 686.
ENERGY (On the conception of the current of). 825. $28.
— and mass. 239. II. 822.
ENTROPY and probability. 840.
EQUATION OF sTaTE (Remarks on the relation of the method of Gipss for the deter-
mination of the) with that of the virial and the mean free path. 853,
— (On the value of some differential quotients in the critical point in connection
with the coexisting phases in the neighbourhood of that point and with the form
of the). 1091.
EQUILIBRIUM (Some remarks on the direction of the binodal curves in the v-x-diagram
in a three-phase-). 420.
ERRATUM. 238.
ESCHER (B. G.). On an essential condition for the formation of overthrust-covers. 902.
ETHER-anthraquinone (The course of the P7Z-lines for constant concentration in the
system). 183.
EUCLIDEAN SPACE (The surfaces of the revolution or quadratic cylinders of non-). 148.
FERRI-TRICHLORO-ACETATE solutions (The photochemical transformations of). 342.
risHes (The arrangement of the motor nuclei in Chimaera monstrosa compared with
other). 1176.
FIVECELL (The pentagonal projections of the regular) and its semiregular offspring. 61.
FLEIG (CH.). On the comparative nocuousness of concentrated and diluted arseno-
benzene solutions. 893.
FOURIER (An extension of the integral theorem of), 387.
FRANCHIMONT (a. P. N.) presents a paper of Dr. J. To. Bornwater: “On the
action of oxalyl chloride on amines and amides.” 42.
— presents a paper of Prof. L. van Irantre: “On dipterocarpol.” 1044,
— presents a paper of Prof. L. van Irauiie and M. Kersoscu: “On Minjak
Lagam.” 1047.
FREE paTH (Remarks on the relation of the method of Grpps for the determination
of the equation of state with that of the virial and the mean). 853.
GaLAxy (A photographical method of research into the structure of the). 579.
GALLE& (Pp. uw.) and J, P. van pur Stok. The relation between changes of the weather
and iocal phenomena. 856.
Gas-equilibria (On). 743.
casks (Isotherms of diatomic) and of their binary mixtures. VII. Control measure-

ments with the yolsmenometer. 10].
*

x CONTE N ® 9,

Gases (Determinations of refractive indices of) under high pressures, Lst paper. The dis-
persion of hydrogen. 592.
Geology. K. Martin: “Some considerations on the geology of Java”. 123.
— M. korperrserc : ‘Notes on the Sopoetan-mountains in the Minahassa”. Ist. part.
222. 2nd, part. 399.
— H. A. Brouwer: “On peculiar sieve structures in igneous rocks, rich in
alealies’. 383, .
— K. Marin: “On geological records on the south-west coast of New-Guinea”. 555.
— A. Wrcumann: “On the so-called atolls of the East-Indian Archipelago”, 698.
— Bb. G. Escupr: “On an essential condition for the formation of overthrust-
covers”. 902.
— K. Martin: “Further considerations about the geology of Java’. 1129.
G1iBBs (Remarks on the relation of the method of) for the determination of the
equation of state with that of the virial and the mean free path. 853.
GILLs (On the ciliary movement in the) of the mussel. 1138.
GINNEKEN (e. J. H. VAN). Sugar solutions and lime. 442.
GRaDIENr (On the diurnal variation of the wind and the atmospheric pressure and
their relation to the variation of the). 48.
— (On the angle of deviation between) of atmospheric pressure and air motion. 855.
Groups of points (Surfaces, twisted curves and) as loci of vortices of certain systems
of conics. Ist. paper. 495.
GRisiNS (G.). The permeability of bloodcorpuscles in physiological conditions, espe-
cially to alkali and earth-alkali-metals. 122.
HAAN (J. DE) and H. J. Hampurser. The effect of substances which dissolve in
fat on the mobility of Phagocytes and other cells. 314.
HAAS (M. DE) and L. H. Srerrsema. Determinations of refractive indices of gases
under high pressures. Ist. paper. The dispersion of hydrogen. 592.
HAAS (Ww. J. DE). Isotherms of diatomic gases and of their binary mixtures. VIII. |
Control measurements with the volumenometer. 101.
HAMBURGER (H. J.) presents a paper of Dr. Cn. Frere : “On the comparative
nocuousness of concentrated and diluted arsenobenzene solutions’. 893.
— presents a paper of Dr. F. J. J. Boyrenpiyk: “On the ciliary movement in the
gills of the mussel”, 1138,
— and J. pe Haan. The effect of substances which dissolve in fat on the mobility
of Phagocytes and other cells. 314.
HANSEN’S constant term (Investigations into the empirical terms in the mean lon-
gitude of the moon and into) in the latitude. 686.
HEAD (The effusion of acoustic energy from the). 758.
unart (On different vagus effects upon the) investigated by means of electrocardio-
graphy. 165.
uvat (On Nernst’s theory of) and the chemical facts. 802.
— runorem (On the inconsistency of my) and vAN perk Waats’equation at very

low temperatures. 291.
HELIUM (Further experiments with liquid), D, 118. BE, 204, F. 678. G, 818.

CONTENTS. . xI

HOFF’s (VAN ’r) rule (A study of temperature-coeflicients and). 1159.
HOLLEMAN (a. F.) presents a paper of Prof. A. Smrvs and J. Maarse: “On the
system: water-phenol”. 192.
— presents a paper of Dr. F. E. C, Scuerrer: “On the system: hydrogensulphide-
water”, 195.
— presents a paper of Prof. A, Smits: “The application of the new theory of
allotropy to the system: sulphur”. 263,
— presents a paper of Dr. T. van ver LinpeNn: ‘On the benzene-hexachlorides
and their splitting up into trichlorebenzenes”’. 298.
— presents a paper of Prof. A. Smits and Dr. H. L, pe Lezuw: “On the system:
sulphur’. 461,
— presents a paper of Prof. A. Smirs: “The system: iron-carbon’’. 530.

— presents a paper of Dr. F. &. C. Scuerrer and J. P. Treus: ‘Determinations
of vapour tensions of nitrogen tetroxide”. 536.

— presents a paper of Prof. J. Borsexex, A. Scuwrizer and G. F. VAN DER
Want: ‘‘On the velocity of hydration of some cyclic acid anhydrides”. 622.

— On the chloration of benzoic acid, according to experiments of Mr. J. Tu.
Bornwater. 684.

— presents a paper of Dr, T. van ver Linpen: “On the magnetism of the
benzolsubstitution and on the opposition of the formation of para-ortho- against
meta-substitution products’. 684.

— presents a paper of Dr. H. VERMEULEN: “On some trinitro anizoles”. 684.

— presents a paper of Prof. A. Smits: “Das Gesetz der Umwandlungsstufen in the
light of the theory of allotropy”. 788.

— The nitration of benzene. 837.

— presents a paper of Dr. T. van per Linpen: “On the addition and the addi-
tion products of chlorine to the chlorbenzenes”. 837.

— presents a paper of Prof. J. Borseken and’ Mr. H. Waterman: “On the action
of some carbon derivatives on the development of penicillium glaucum and their
retarding action in connection with solubility in water and in oil.” 928.

— presents a paper of Mr. A. Hurnprr: “On the activity of halogene-dinitro-
pseudo-cumoles with their addition productivity with nitrie acid.” 1007.

— presents a paper of Dr, E. H. Bicuner: “Investigations on the radium content
of rocks.” Ill. 1063.

— presents a paper of Prof. J. Borsrxen: “The configuration of benzene, the
mechanism of the benzene substitution and on the contrast between the formation
of para-ortho- and of meta-substitution products”. 1066.

— and J. P. Wisavur. The nitration of ortho-chlortoluene. 1230.

HOOGENBOOM (c. M.) and P. Zeeman. Electric double refraction in some artificial
clouds and vapours, lst part. 558. 2nd part. 786.

HOOGEWERFYF (s.) presents a paper of Dr, N. L. SounGeN: “Thermo-tolerant
lipase”. 166.

HOORWEG (J. L.). On the irritation-effect in living organisms. 7!.

XII COUNT i, Bt Shes

HUENDER (a.). On the activity of the halogene=dinitro-pseudo cumoles and their
addition productivity with nitric acid. 1007.

HYDRATION (On the velocity of) of some cyclic acid anhydrides, 622.

HYDROGEN (The dispersion of), 592,

HYDROGENSULPHIDE-water (On the system :). 195.

IMBIBITION HEAT (Some calorimetrical investigations relating to the manifestation and
amount of) in tissues, 1130.

INSULATING POWER (Note on the) of liquid air for high potentials and on the Kerr
electro-optic effect of liquid air. 650.

INTEGRAL THEORY (An extension of the) of Fourigr. 387.

INTEGRALS (Homogeneous linear differential equation of order two with given relation
between two particular). 1st Communication. 391. 2nd Communication. 584, 3rd
Communication, 832. 4th Communication, 1010.

— (New researches upon the centra of the) which satisfy differential equations of
the first order and the first degree. 1st part. 1185.

top:Des (On the) of the elements of the nitrogen group. 625.

IODINE (On compounds of tellurium and). 724.

TRIDOMYRMEX MYRMECODIAE EMERY (On the distribution of the seeds of certain
Dischidia by means of a species of ant:). 153.

1roN-carbon (The system :), 530.

IRRITATION-EFFECT (On the) in living organisms. 71.

ISOPOLYMORPHISM (A remarkable case of ) with salts of the alkali metals. 356.

1soTHERMS of diatomic gases and of their binary mixtures. VIII. Control measure-
ments with the volumenometer. 101.

— of monatomic substances and of their binary mixtures. X. The behaviour of
argon to the law of corresponding states. 158. XI. Remarks upon the critical
temperature of neon and upon the melting point of oxygen. 163.

ITALLIE (L, VAN). On dipterocarpol. 1044.

— and M. Kersoscu. On Minjak Lagam. 1047.

JAEGER(E. M.). The photochemical transformations of ferri-trichloro—acetate solutions. 342.

— A remarkable case of isopolymorphism with salts of the alkali-metals. 356.

— Contribution to the knowledge of the natural sulfo-antimonites I. 555.

- and H. & van KxoosrEr, Contribution to the knowledge of sulfo-antimonites.
I. 555:
—and J. RK. N. van Krereren, The question as to the miscibility in the solid

condition between aromatic nitro- and nitroso-compounds. IIL, 729.
— and J. B. Menke. Studies on tellurium. Il. On compounds of tellurium and
iodine. 724.
Java (On the geology of). 123.
— (further considerations about the geology of). 1129.
JONG (A. W. K. DE). Action of sunlight on allocinnamie acid. 100.
JULIUS (Ww. H.). Preliminary account of some results obtained by the Netherland
Eclipse expedition in observing the annular solar eclipse of April 17th 1912. 1195,
KAMERLINGH ONNES (H.). vy, ONNES (H. KAMERLINGH.).

CAO PND DE Ne LES « NII

KAPPERS (C. U. ARJENS). The arrangement of the motor nuclei in Chimaera
monstros; compared with other fishes. 1176.

KAPTEYN (J. c.). The milky way and the star-streams. 524.

— Starsystems and the milky way, 909.

K APTEYN (w.) presents a paper of Dr M. J. van Uven: “Homogereous linear
differential equation of order two with given relation between two particular
integrals”. Ist Communication. 391. 2nd. Communication. 584, 3rd. Communica-
tion. 832. 4th. Communication, 1010.

— On partial differential equations of the first order. 763.

— On some relations between Brsseu’s functions. 962.

— New researches upon the centra of the integrals which satisfy differential equations
of the first order and the first degree. 1st part. 1185,

KERBOSCH (M.) and L. van Ivature. On Minjak Lagam. 1047.

KERR-effect (Lhe magneto-optic) in ferromagnetic compounds and alloys. I. 970.

— electro-optic effect (Note on the insulating power of liquid air for high potentials
and on the) of liquid air. 650.

KLOOSTER (H. s. vAN) and F. M Jasneer. Contribution to the knowledge of
sulfo-antimonites. Il. 555.

KLUYVER (J. C.) presents a paper of Mr. Jj. DrostrE: “An extension of the integral
theorem of Fourigr.” 387.

KOHNSTAMM (PH.) and L. S. Ornsremn: “On Nernst’s theory of heat and the
chemical facts.” 802.

—and J. Cur. Reepers. On the phenomenon of condensation from mixtures of
carbonic acid and nitrobenzene in connection with double retrograde condensation. 270.

KOORDERS (s. H.). A few observations on some new and little known cases of
Leguminosae with mechanically irritable leaves. 132.

KOPERBERG (M.). Notes on the Sopoetan-mountains in the Minahassa, Ist part. 222.
2nd. part. 399.

KORTEWHG (D. J.) presents a paper of Dr. L. E. J. Brouwrr: “On the structure
of perfect sets of points” 2nd Communication, 137.

— presents a paper of Dr. L. E. J. Brouwer: ‘Continuous one-one transform- -
ations of surfaces in themselves’. 4th Communication. 300.

— and F. A. H. Scureryemakers. General considerations on the curves of contact
of surfaces with cones, with application to the lines of saturation and binodal
lines in ternary systems. 510.

KREGTEN (J. kg. N. van) and F. M Jascer. The question as to the miscibility
in the solid condition between aromatic nitro-and nitroso-compounds. 729.

KRUYT (H. R.) and J. Orie Jr. Photo-electric phenomena with antimony sulphide
(Antimonite). 740.

KUENEN (s. P.). Some remarks on the direction of the binodal curves in the v-z-
diagram in a three-phase-equilibrium. 420.

— Investigations concerning the miscibility of liquids. 644.

LAAR (J. J. YAN). On the solid state, VII. 84.

XIV CONTENTS.

LAAR (J, J. VAN). The variability of the quantity ’ in van DER Waats’ equation
of state, also in connection with the critical quantities. 278. II. 428. IIL. 563. 1V. 711.

— On some relations holding for the critical point. 771.

— On the value of sume ditferential quotients in the critical point, in connection
with the coexisting phases in the neighbourhood of that point and with the form
of the equation of state. 1091. ;

LANGE (s. J. DE). The red nucleus in reptiles 1082.

LAU & (M.). On the conception of the current of energy. 825.

Law of corresponding states (The behaviour of argon to the). 158.

LEAVES (A few observations on some new and little known cases of Leguminosae with
mechanically irritable). 132.

LEEUW (H. L, D&) and A. Smits. On the system: sulphur. 461.

LEEUWEN (W. DOCTERS Van) and J. Docrers vaN LEEUWEN-REYNVAAN. On
the distribution of the seeds of certain species of Dischidia by means of a species
of ant: Iridomyrmex myrmecodiae Emery. 153.

LEGUMINOSAE (A few observations on some new and little known cases of) with mecha-
nically irritable leaves. 132.

LIME (Sugar solutions and). 442.

LINDEN (T. VAN DER). On the benzene hexachlorides and their splitting up into
trichlorebenzenes. 298. :

-— On the magnetism of the benzolsubstitution and on the opposition of the form-
ation of para-ortho-against meta-substitution products. 684.

— On the addition and the additionproducts of chlorine to the chlorbenzenes. 837.

LINE SPECTRA (Summational and differential vibrations in). 470.
uines (The course of the £ 7Z-) for constant concentration in the system: ether-
anthraquinone, 183.

— (A quartic surface with twelve straight). 259.

— of saturation (General considerations on the curves of contact of surfaces with
cones, with application to the) and binodal lines in ternary systems. 510.

Lipase (Thermo-tolerant). 166.

Liaguip alk (Note on the insulating power of) for high potentials and on the Kerr
electro-optic effect of liquid air. 650.

LiQuIps (Investigations concerning the miscibility of). 644.

LITSEA ODORIFERA VAL, (The essential oil of) (Trawas-oil). 325.

LORENTZ (H. a.) presents a paper of Mr. J. J. van Laan: “On the solid state”.
VII. 84.

— presents a paper of Prof. W. Nernsr: “On the inconsistency of my heat theo-
rem and vaN per Waats’ equation at very low temperatures”, 201.

— presents a paper of Mr. J. J. van Laar: “The variability of the quantity 4 in
vaN pER Waats’ equation of state, also in connection with the critical quan-
tities”. 278. LT 428. IIL 563. [V 711.

— presents a paper of Mr, J. J. van Laan: ‘On some relations holding for the
critical point’. 771.

— presents » paper of Dr.-L. S. Ornsvern: “Entropy and probability”. 849.

CONTENTS. KV

LORENTZ (H. A.) presents a paper cf Dr. L. S. Ornsrern: “Remarks on the
relation of the method of Gisps for the determination of the equation of state
with that of the virial and the mean free path”. 853.

— presents a paper of Dr. L. S. Ornstern: “On the solid state I. Monatomic
substances”. 983,

— presents a paper of Mr, J. J. van Laar: “On the value of some differential
quotients in the critical point in connection with the coexisting phases in the
neighbourhood of that point and with the form of the equation of state’. 1091.

LORTA (sT.). The magneto-optic KEerR-effect in ferromagnetic compounds and alloys.
If. 970.

MAARSE (J) and A. Smirs. On the system: water-phenol. 192.

MAGNETIC FoRcES (Considerations concerning light radiation under the simultaneous
influence of electric and) and some experiments thereby suggested. Ist part. 2.

MAGNETISM (Researches on). II[. On para- and dia-magnetism at very low tempera-
tures. 115 LV. On paramagnetism at very low temperatures. 674. V. The initial
susceptibility of nickel at very low temperatures. 1004.

— (On the) of the benzolsubstitution and on the opposition of the formation of
para-ortho-against meta-substitution products. 684.

MAMMALIAN PELVIs (On the relation between the symphysis and the acetabulum in
the) and on the signification of the cotyloid bone. 781.

MAN (The excretion of creatinin in) under the influence of muscular tonus. 310.

MANGANOUS-SULPHATE (On the system: water-alcohol-). 924.

MARTIN (k.). On the geology of Java. 123.

— Further considerations about the geology of Java, 1129.

— On geological records on the south-west coast of New-Guinea. 555.

mass (Energy and), 239. If. 822.

MASSINK (a.) and F. A. H. ScuremseMakers. Some compounds of nitrates and
sulphates. 1042.

Mathematics. P. H. Scuoure: “The pentagonal projections of the regular fivecell and
its semiregular offspring.” 61.

— L. E. J. Brovwxr: “On the stricture of perfect sets of points.” 2nd Commu-
nication. 137.

— J. A. Barrau: “The surfaces of revolution or quadratic cylinders of non-
Euclidean space.” 148.

— Jan pe Vriks: “A bilinear congruence of quartic twisted curves of the first
species.” 255.

— Jan pe Vrigs: “A quartic surface with twelve straight lines.” 259.

— L. E. J. Brouwer: “Continuous one-one transformations of surfaces in them-
selves.” 4th Communication. 300.

— J. Droste: “An extension of the integral theory of Fourter.” 387.

— M. J. van Uven: “Homogeneous linear differential equation of order two with
given relation between two particular integrals.” 1st Communication. 391. 2nd
Communication. 584. 3rd Communication. $32. 4th Communication. 1010.

— P H. Scuoure: “The characteristic numbers of the prismotope.” 424.

XVI CRONE DE Ne DS:

Mathematics, Hx. pe Vuirs: “On the conoids belonging to an arbitrary surface.”
Ist part. 481.

— P. H. Scuours: “Surfaces, twisted curves and groups of pointsas loci of vortices
of certain systems of cones.’’ lst paper. 495.

— D. J. Korrewse and F. A. H. Scureinemakers: “General considerations on
the curves of contact of surfaces with cones, with application to the lines of
saturation and binodal lines in ternary systems.’ 510.

— D. Montesano: “The theory of bilinear complexes of conics.” 550.

—- W. Kapreyn: “On partial differential equations of the first order.” 763.

— W. Karreryn: “On some relations between BessEu’s functions.” 962.

— M. Srvuyvarrr: ‘On the lineo-linear congruences of right lines and the cubic
surface.” 1018.

— G. dE Vries: “Calculus rationum.” 1026.

— Jan ve Vrizs: “On two linear congruences of quartic twisted curves of the
first species.” 1122.

— Jan ve Vrigs: “On a congruence of the second order and the first class
formed by conics.” 1173.

— W. Kapreyn: “New researches upon the centra of the integrals which satisfy
differential equations of the first order and the first degree.” 1st part. 1185.

MEASUREMENTS (Control) with the volumenometer. 101.

MELTING POINT of oxygen (Remarks upon the critical temperature of neon and upon
the). 163.

MELTING POINT LINES (On retrogressive), 2nd Communication. 170. 3rd Communica-
tion. 189.

MENKE (J. B.) and FP. M. Jarcer. Studies on tellurium. II. On compounds of tellu-
rium and iodine. 724.

MERIDIAN OBSERVATIONS at Greenwich (Further researches into the constant term in
the latitude of the moon, according to the). 991.

— (Provisional results from calculations about the terms in the longitude of the

moon, with a period of nearly an anomalistic month according to the). 1180.
MESENCEPHALIC nucleus and root (On the) of the nervus trigeminus. 25. oy
Meteorology. J. P. van per Stox: “On the diurnal variation of the wind and the

atmospheric pressure and their relation to the variation of the gradient”. 48.

— J. P. van per Srox and P. H. Gau.i: “The relation between changes of the
weather and local phenomena”. 856.

— J. P. van per Srox: “On the angle of deviation between gradient of atmos-
pheric pressure and air motion’. 865.

— D. F. Toutpnaar: “On the influence of the earth’s rotation on pure drift-
currents”, 1149.

Microbiology. N. L. Souncen: “Thermo-tolerant lipase”. 166.
MILKY WAY (The) and the star-streams., 524.
— (Starsystems and the). 909.
mInAHASSA (Notes on the Sopoetan-mountains in the). Ist part. 222. 2nd part. 399.
MINJAK LAGAM (On), LO47.

CON TE NTS. XVIT

MIRRORS (On the influence of electric waves upon platinum) (Coherer action), 126.

MIscIBILItTy (The question as to the) in the solid condition between aromatic nitro-
and nitroso-compounds, 729.

— of liquids (Investigations concerning the), 644.

MIXTURES (The phenomenon of condensation for) of carbonic acid and nitrobenzene in
cormection with double retrograde condensation. 270.

MOGENDORFF (Ff. &.). Summational and differential vibrations in line spectra. 470.

MOLECULAR ATTRACTION (On the law of) for electrical double points. 1111.

MOLENGRAAFF (G. A. F.) presents a paper of Mr. H. A. Brouwer: “On pecu-
liar sieve structures in igneous rocks, rich in alealies. 383.

— presents a paper of Dr. B. G. Escurr: “On an essential condition for the forma-
tion of overthrust-covers’’. 902.

MOLL (J. w.) presents a paper of Prof. C. van WisseLIncH: ‘‘On the cell-wall of
Closterium together with a consideration of the growth of the cell-wall in gene-
ral”. 912.

MONATOMIC SUBSTANCES (Isotherms of) and of their binary mixtures, X. The behaviour
of argon to the law of corresponding states. 158. XI. Remarks upon the critical
teniperature of neon and upon the melting point of oxygen. 163.

MONTESANO (D.). The theory of bilinear complexes of conics. 550.

MOON (Investigations into the empirical terms in the mean longitude of the) and into
Hansen’s constant term in the latitude. 686.

— (Further researches into the constant term in the latitude of the) according to
meridian observations at Greenwich. 991,

— Provisional results from calculations about the terms in the longitude of the)
with a period of nearly an anomalistic month, according to the meridian observa-
tions made at Greenwich. 1180.

Moroz NucLEI (The arrangement of the) in Chimaera monstrosa compared with other
fishes. 1176.

MUSCULAR TONUS (The excretion of creatinin in man under the influence of). 314.

MUSSEL (On the ciliary movement in the gills of the). 1138.

neon (Remarks upon the critical temperature of) and upon the melting point of
oxygen. 163.

NERNST (w.). On the inconsistency of my heat theorem and VAN Der Waats’ equation
at very low temperatures. 201.

NeERNst’s (On) theory of heat and the chemical facts. 802.

NERVUs TRIGEMINUS (On the mesencephalic nucleus and root of the). 25.

NEW-GUINEA (On geological records on the south-west coast of). 555,

NICKEL (The initial susceptibility of) at very low temperatures. 1004.

NIERSTRASZ (Vv. E.). Some calorimetrical investigations relating to the manifest-
ation and amount of imbibition heat in tissues, 1130.

NIKIFOROWSKY (v.) — The effusion of acoustic energy from the head, according
to experiments of Dr. — 758.

NITRATES and sulphates (Some compounds of). 1042.

NITRATION (The) of benzenes. 837.

XVIII CONTENTS.

nirraTioNn (The) of ortho-chlortoluene. 1230.

nirric actb (On the activity of the halogene-dinitro-pseudo-cumoles and their addition
productivity with). 1007.

NITRO- and nitroso-compounds (The question as to the miscibility in the solid con-
dition between aromatic). 729.

NITROBENZENE (On the phenomena of condensation for mixtures of carbonic acidand)
in connection with double retrograde condensation. 270.

NITROGEN GROUP (On the iodides of the elements of the). 625.

NITROGEN TETROXIDE (Determinations of vapour tensions of). 536.

NocuousnEss (On the comparative) of concentrated and diluted arsenobenzene solu-
tions. 893.

nucLEus (The red) in reptiles. 1082.

on (The essential) of Litsea odorifera Val. (Trawas-oil). 325.

oLIE JR. (J.) and H. R. Kruyv. Photo-electric phenomena with antimony sulphide
(Antimonite). 740.

ONNES (H. KAMERLINGH) presents a paper of Mr. W. J. pr Haas: “Isotherms
of diatomic gases and of their binary mixtures. VILL. Control measurements with
the volumenometer. 101. ;

— Further experiments with liquid helium. D. 113. E 204 F 678 G 818.

— presents a paper of Dr. J. Cray: “On the influence of electric waves upon
platinum mirrors. (Coherer action)’. 126.

— presents a paper of Prof. L. H. Syprrsema and M. ve Haas: “Determinations
of refractive indices of gases under high pressures. lst paper. he dispersion of
hydrogen’. 592.

— and C. A. Crommeuin. Isotherms of monatomic substances and of their binary
mixtures. X. The behaviour of argon with respect to the law of corresponding
states. (Continued) 158. XI. Remarks upon the critical temperature of neon and

upon the melting point of oxygen. 163.
— and Apert Perrter, Researches on magnetism. III]. On para- and dia-mag-

netism at very low temperatures. 115. [V. On paramagnetism at very low tem-
peratures. 674, V. The initial susceptibility of nickel at very low temperatures. 1004,
optic ExTiNcTION (On the orientation of crystal sections with the help of the traces
of two planes and the). 128.
ORIENTATION (On the) of crystal sections with the help of the traces of two planes
and the optic extinction. 128.
ORNSTEIN (1. s.). Entropy and probability. 840.
— Remarks on the relation of the method of Gipzs for the determination of the
equation of state with that of the virial and the mean free path. 853.
— On the solid state. I. Mon-atomie substances. 953.
—and Ps. Kounstamm. On Nernst’s theory of heat and the chemical facts. 802.
ORTHO-CHLORTOLUENE (The nitration of). 1230.
OVERTHRUST-COVERS (On an essential condition for the formation of). 902.
OWEN (MORRIS). Thermomagnetic properties of elements. 637.

OXALYL cuLorIDE (On the action of) on amines and amides. 42.

CON T EN TS; XIX

OXYBENZOIC actD (On a biochemical method for the determination of small quantities
of salicylic acid in the presence of an excess of p.). 604,

OxYGEN (Remarks upon the critical temperature of neon and upon the melting point of). 163.

PANNEKOEK (A.). A photographical method of research into the structure of the
galaxy. 579.

para- and dia-maguetism (On) at very low temperatures. 115,

PARAMAGNETISM (On) at very low temperatures, 674.

PEKELHARING (C. A.). The excretion of creatinin in man under the influence of
muscular tonus. 310.

PENICILLIUM GLAUCUM (On the action of some benzene derivatives onthe development of). 608.

— (On the action of some carbonic derivatives on the development of) and their
retarding action in connection with solubility in water and in oil. 928.

— (Action of substances readily soluble in water, but not soluble in oil on the
growth of). 1112.

PENTAGONAL projections (The) of the regular fivecell and ifs semiregular offspring. 61.

PERMEABILITY (Lhe) of blood-corpuscles in physiological conditions, especially to
alkali- and earth-alsali-metals. 122.

PERRIER (ALBERT) and H. KamprtinaH Onnes. Researches on magnetism. II],
On para- and dia-magnetism at very low temperatures, 115, IV. On paramag-
netism at very low temperatnres. 674. V. The initial susceptibility of nickel at
very low temperatures. 1004.

pHacocytes (The effect of substances which dissolve in fat on the mobility of) and
other cells. 314.

PHENOL (On the system: water-). 192.

PHOTOCHEMICAL transformations (The) of ferri-trichloro-acetate solutions. 342.

PHOTO-ELECTRIC phenomena with antimony sulphide (Antimonite). 740.

Physics. P. Zeeman: “Considerations concerning light radiation under the simultaneous
influence of electric and magnetie forces and some experiments thereby suggested.”
lst part. 2.

— J. J. van Laar: “On the solid state.” VII. 84.

— W. J. ve Haas: “Isotherms of diatomic gases and of their binary mixtures.
VIII. Control measurements with the volumenometer.” 101.

— H. Kameruinan Onnes: “Further experiments with liquid helium.” D. 113.
E. 204+. F. 678. G. 818.

— H. Kameriincr Onnes and Abert Perrier: “Researches on magnetism. III.
On para- and dia-magnetism at very low temperatures.” 115. IV. ,,On para-
magnetism at very low temperatures”. 674, V. ,,The initial susceptibility of nickel
at very low temperatures.” 100+.

— H. Kamerutncu Oxnes and C. A. Crommettn: “Isotherms of monatomic sub-
stances and of their binary mixtures”. X. ,,The behaviour of argon with respect to
the law of corresponding states.” (Continued). 158. XI. “Remarks upon the critical
temperature of neon and upon the melting point of oxygen.” 163.

— W. Nernst: “On the inconsistency of my heat theorem ani van per Waats’

equation at very low temperatures.” 201.

XX CONTENTS:

Physics. J. D. van per Waats Jr: “Energy and mass.” 239. If. 822.

— Pu. Kounstamm and J. Cur, Reepers: “On the phenomenon of condensation
for mixtures of carbonic acid and nitrobenzene in connection with double retro-
grade condensation.” 270.

— J. J. van Laar: “The variability of the quantity 4 in vaAN DER WaaLs’
equation of state also in connection with the critical quantities.” 278. IL. 428.
DELS 563s eVienqiile

— J. P. Kuenen: ‘Some remarks on the direction of the binodal curves in the
v-a-diagram in a three-phase-equilibrium.” 420.

— E. E. Mocenporrr: “Summational and differential vibrations in line spectra.” 470.

— J. D. van per Waaus: “Contribution to the theory of binary mixtures.” XVI. 504.
XVII. 655. XVIII. 875. XIX. 1049. XX. 1217.

— P. Zeeman and C. M. Hoocensoom: “Electric double refraction in some arti-
ficial clouds and vapours.” !st part. 558. 2nd part. 785.

— L. H. Stertsema and M. pe Haas: “Determinations of refractive indices of
gases under high pressures. Ist paper. The dispersion of hydrogen.” 592.

— Morris Owen: “Thermomagnetic properties of elements.” 637.

— J. P. Kuenen: “Investigations concerning the miscibility of liquids.” 644,

— P. Zeeman: ‘Note on the insulating power of liquid air for high potentials and
on the Kerr-electro-optic effect of liquid air.” 650,

— J. J. van Laan: “On some relations holding for the critical point.” 771.

— M. Lave: ‘On the conception of the current of energy.” 825.

— J. D, van perk Waats Jr: “On the conception of the current of energy.” 828.

— L. 8. Ornstern: “Entropy and probability.” 840,

— L. 8. Ornstemn: “Remarks on the relation of the method of Gisss for deter-
mination of the: equation of state with that of the virial and the mean free path,” 853.

— Sr. Lorta: “The magneto-optic herr effect in ferromagnetic compounds and
alloys.” II, 970.

— L. 8S. Ornstein: “On the solid state. I. Mon-atomic substances.” 983.

— J. J. van Laar: “On the value of some differential quotients in the critical
point in connection with the coexisting phases in the neighbourhood of that
point and with the form of the equation of state.” 1091.

— J. D. van per Waats Jr: “On the law of molecular attraction for electrical double
points.” 1111.

— W. H. Junius: “Preliminary account of some results obtained by the Netherland

Eclipse expedition in observing the annular solar eclipse of April 17th 1912. 1195
Physiology. J. L. Hoonwee: “On the irritation-effect in living organisms.” 71.

— G. Gruys: “The permeability of blood-corpuscles in physiological conditions,
especially to alkali- and earth-alkali-metals.” 122.

— J. Cuay: “On the influence of electric wayes upon platinum mirrors (Coherer
action).” 126.

— W. Eitoven and J. H. Wrerrnea: “On different vagus effects upon the
heart investigated by means of electro-cardiography.” 165.

— ©. A. PekeLmanine: “The excretion of creatinin in man under the influence
of museular tonus.” 310,

CONTENTS. XXI

Physiology. H. J. Hamburcer and J, pp Haan: “The eflect of substances which dissolve
in’fat oa the mobility of Phagoeytes and other cells.” 814.

— H. Zwaarpemaker: “The effusion of acoustic energy from the head,
according to experiments of Dr. P. Nrk1rorowsky.” 758.

— Cu. Freie “On the comparative nocuousness of concentrated and diluted arseno-
benzene solutions. The dilution to be applied in intravenous injections.” 893,
— V. E. Nierstrasz: “Some calometrical investigations relating to the manitest-

ation and amount of imbibition heat in tissues.” 1130.
— F. J. J. Buyrenpux: “On the ciliary movement in the gills of the mussel.” 1138,

PLEISTOPHORA GIGANTEA THELOHAN a parasite of Crenilabrus melops. 377.

points (On the structure of perfect sets of). 2nd Communication. 137.

POLE of the earth (Preliminary investigation into the motion of the) in 1907. 211.

POTENTIALS (Note on the insulating power of liquid air for high) and on the Kerr
electro-optic effect of liquid air. 650,

PRISMOTOPE (The characteristic numbers of the). 424.

PROBABILITY (Entropy and). 849,

PsaLTerIuM (The origin of the fibres of the corpus callosum and the), 12.

QUADRATIC cYLIxpERS (The surfaces of revolution or) of non-Euclidean space. 148.

quantity J (The variability of the) in van Dek WaAaLs’ equation of state, also in
connection with the critical quantities, 278 If. 428. IIL 563. LV. 711.

quartic surrace (A) with twelve straight lines 259.

RADIATION (Considerations concerning light) under the simultaneous influence of
electric and magnetic forces and some experiments thereby suggested. Ist part. 2.

RADIUM CONTENT (Investigations on the) of rocks, IIT. 1063.

REEDERS (J. cHR.) and Pa, Kounstamm. On the phenomenon of condensation for
mixtures of carbonic acid and nitrobenzene in connection with double retrograde
condensation. 279.

REFRACTION (Electric double) in some artificial clouds and vapours, 558, 2nd part. 786.

REFRACTIVE INDIcEs (Determinations of) of yases under high pressures. Ist paper.
The dispersion of hydrogen. 592.

REPTILES (On the structure of the dental system of). 950.

— (The red nucleus in). 1082.
RESPIRATORY ENZYMES (The action of) of Sauromatum venosum Schott. 370.
rocks (On peculiar sieve structures in igneous) rich in alcalies, 383,
— (Investigations on the radium content of). I[L. 1063.
KOMBURGH (P. VAN). Additive compounds of m-Dinitrobenzene. 46.
— The essential oil of Litsea odorifera Val. (Trawas-oil). 325.
— presents a paper of Prof. F. M. Jarcer: “The photochemical transformations
of ferri-trichloro-acetate solutions”, 342.
— presents a paper of Prof. F, M. Jareer: “A remarkable case of isopolymorphism
with salts of the alkali-metals”. 356.
— presents a paper of Dr. P. J. H. vAN GINNEKEN : “Sugar solutions and lime”. 442.
— presents a paper of Prof. I, M. Jaraer: “Contribution to the knowledge of
natural sulfo-antimonites”, I, 555.

XXII c ON TEIN TS:

ROMBURGH (Pe. VAN) presents a paper of Prof. F. M. Jagcer and H. 8. van
Kuooster: “Contribution to the knowledge of sulfo-antimonites”. II. 555.

— presents a paper of Mr. H. R. Doornsoscn: “On the iodides of the elements
of the nitrogen group”. 625.

— presents a paper of Prof. F. M. Jancer and J. B. Menxe: “Studies on tel-
lurium. IT. On compounds of tellurium of iodine”, 724.

— presents a paper of Prof. F. M. Jarcer and J, R. N. van Kreeren: “The
question as to the miscibility in the solid condition between aromatic nitro- and
nitroso-compounds”. 729.

— presents a paper of Dr. J. Our Je, and Dr. H. R. Krurr: “Photo-electric
phenomena with antimony sulphide (Antimonite)”. 740.

SALICYLIC actbD (On a biochemical method for the determination of small quantities
of) in the presence of an excess of p.-oxybenzoic acid. 604.
sats (A remarkable case of isopolymorphism with) of the alkali metals. 356.
SANDE BAKHUIJZEN (E. F. VAN DE). V. BAKHUIJZEN (E. F. vAN DE Sanpe).
SAUROMATUM VENOSUM scHoTT (The action of the respiratory enzymes of). 370.
SCHEFFER (Ff. E. Cc.) On the system: hydrogensulphide-water. 195.
— On gas-equilibria, 743.
— and J. P. Trevup, Determinations of vapour tensions of nitrogen tetroxide. 536,
SCHMUTZER (J.). On the orientation of crystal sections with the help of the traces
of two planes and the optic extinction. 128.
SCHOUTE (Pv. H.). The pentagonal projections of the regular fivecell and its semi-
regular offspring. 61.

— The characteristic numbers of the prismotope. 424.

— Surfaces, twisted curves and groups of points as loci of vortices of ean
systems of cones, Ist. paper. 495.

SCHREINEMAKERS (ff, A. H.) and J. B. Deuss, On the system: water-aleohol-
manganous sulphate, 924.

— and D. J, Korrewsc. General considerations on ihe curves of contact of surfaces
with cones, with application to the lines of saturation and binodal lines in ternary
systems, 510,

— and A. Masstnk. Some compounds of nitrates and sulphates. 1042.

SCHWEIZER (a.), J. BorsekeN and G. F. van per Wanv. On the velocity of
hydration of some cyclic acid anhydrides, 622

SEEDLINGS of Avena (Investigation of the transmission of light stimuli in the). 327.

sEEDS (On the distribution of the) of certain species of Dischidiae by means of a
species of ant: Iridomyrmex myrmecodiae Kmery. 153.

SIHRTSEMA (L. H.) and M. pe Haas. Determinations of refractive indices of gases
under high pressures. Ist paper. The dispersion of hydrogen. 592.

SIEVE STRUCTURES (On peculiar) in igneous rocks, rich in alealies. 383.

SMIS (A.). On retrogressive melting-point lines. 170.

— On retrogressive vapour-lines. Ist Communication. 177.

— The applications of the new theory of allotropy to the system: sulphur. 263.

— The system: iron-carbon, 5380.

COUN EENe DS: XXIII

SMITS (a.). Das Gesetz der Umwandlungsstufen in the light of the theory of allo-
tropy. 788.

— and H. L. pe Leeuw. On the system sulphur. 461.

-- and H. I. pe Leeuw. Confirmations of the theory of the phenomenon allo-
tropy. LI. 1199.

— and J. Maansg. On the system: water-phenol. 192.
—and J. P. Trevun. The course of the P7'lines for constant concentration in the
system: ether-anthraquinone. 183.
— and J. P, Trevus. On retrogressive melting-point lines. 3rd Communication, 189.
SOHUNGEN (N. L.). Thermo-tolerant lipase. 166.

SOLAR ECLIPSE (Calculations concerning the central line of the) of April 17th 1912
in the Netherlands. 935.

— (Preliminary account of some results obtained by the Netherland Eclipse expedition
in observing the annular) of April 17th 1912. 1195.

SOLID CONDITION (The question as to the miscibility in the) between aromatic nitro-
and nitroso-compounds. 729.

SOLID sTaTE (On the). VII. $4.
— (On the). I. monatomic substances. 983.

SOLUBILITY in water and in oil (On the action of some carbon derivatives on the
development of penicillium glaucum and their retarding action with), 928.
SOPOETAN-mouutains (Notes on the) in the Minahassa. Ist part. 222. 2nd part. 399.

STAR STREAMS (The milky way and the). 524.

STAR SYSTEM and the milky way. 909.

STARCH=GRAIN (Structure of the). 1107.

STIMULI (Investigation of the transmission of light) in the seedlings of Avena, 327.

STOK (J. P. VAN DER). On the diurnal variation of the wind and the atmos-
pheric pressure and their relation to the variation of the gradient. 48.

— On the angle of deviation between gradient of atmospheric pressure and air
motion. 865.

— presents a paper of Dr. D. F. Totbenaar: “On the influence of the partis
rotation on pure drift-currents”. 1149.
— and P. H. Gauri. The relation between changes of the weather and local pheno-
mena, 856.
STUART (Cc. eB. COMEN). A study of temperature-coefficients and van ’r Horr’s
rule. 1159.

STUYVAERT (M.). On the lineo-linear congruences of right lines and the cubic
surface. 1018.

suBsTaNcEs (The eflect of) which dissolve in fat on the mobility of Phagocytes and
other cells. 314.

SUBSTITUTIONPRODUCTS (On the magnetism of the benzolsubstitution and on the oppo-
sition of the formation of para-ortho- against meta-). 64.

— (The configuration of benzene, the mechanism of the benzene substitution and

on the contrast between the formation of para-ortho- and of meta-). 1066.

sUGAR solutions and lime. 442.

SULFO-ANTIMONITES (Contribution to the knowledge of). 555,

XXIV CAOON TEN Ts:

SULPHATES (Some compounds of nitrates and). 1042.
SULPHUR (On the system:). 461. :
—- (The application on the new theory of allotropy to the system :). 263.
sUNLIGHT (Action of) on allocinnamic acid. 100.
surraces, twisted curves and groups of points as loci of vortices of certain systems
of cones. Ist paper. 495.
— (Continuous one-one transformations of) in themselves. 4th Communication. 300.
— of revolution (The) or quadratic cylinders of non-Euclidean space. 148.
— with cones (General considerations on the curves of contact of), with appli-
cation to the lines of saturation and binodal lines in ternary systems. 510,
SUSCEPTIBILITY (The initial) of nickel at very low temperatures. 1004.

SWELLENGREBEL (N. H.). Pleistophora gigantea Thélohan, a parasite of Creni-
labrus melops. 377.
syMeHysis (On the relation between the) and the acetabulum in the mammalian
pelvis and on the signification of the cotyloid bone. 781.
sYsTEM ether-anthraquinone (The course of the P/'\-lines for constant concentration
in the). 183.
— hydrogensulphide-water (On the). 195.
-- iron-carbon (The). 530.
— sulphur (On the). 461.
— sulphur (The application of the new theory of allotropy to the), 263.
— water-phenol (On the). 192.
— water-alcohol-manganous-sulphate (On the). 924.
TELLURIUM (Studies on). I]. On compounds of tellurium and iodine. 724.
TEMPERATURE (Remarks upon the critical) of neon and upon the melting point of
oxygen. 163.
TEMPERATURE-COEFFICIHNTS (A study of) and van “r Horr’s rule. 1159.
TEMPERATURES (On para- and dia-maguetism at very low). 115,
— (On the consistency of my heat theoremand yan DER WAALS’ equation at very low).201.
— (On paramagnetism at very low). 674.
— (The initial susceptibility of nickel at very low). 1004.
TERNARY SYSTEMS (General considerations on the curves of contact of surfaces with
cones, with application to the lines of saturation and binodal lines in). 510.
THEORY (The) of bilinear complexes of conics. 550.
— (On Nernst’s) of heat and the chemical facts. 802.
— of allotropy (The application of the new) to the system: sulphur, 263.
— — — (Das Gesetz der Umwandlungsstufen in the light of the). 788.
— of the phenomenon allotropy (Conformations of the). IL. 1199.
— of binary mixtures (Contribution to the). XVLE. 504, XVID. 655. XVIII. 875.
XIX. 1049. XX. 1217. iG
THERMOMAGNETIC properties of elements. 637.
THERMO-TOLERANT lipase. 166.
rissups (Some calorimetrical investigations relating to the manifestation and amount of
imbibition heat in). 1130.

GUOF NN, DeESNeD Ss. EX¥

TOLLENAAR (pd. F.). On the influence of the earth’s rotation on pure drift-cur-
rents. 1149,

traces (On the orientation of erystal sections with the help of the) of two planes and
the optic extinction. 128.

TRANSFORMATIONS (Continuous one-one) of surfaces in themselves. 4th. Communication.300.

TRAWAS-OIL (The essential oil of Litsea odorifera Val.). 325.

1

TREUB (J. P.) and EF. E. C. Scuerrer. Determinations of vapour tensions of nitrogen
tetroxide. 536.

— and A. Sirs. The course of the PZ lines for constant concentration in the
system: ether-anthraquinone. 183.

— On retrogressive melting-point lines. 3rd Communication. 189.
TRICHLOREBENZENES (On the benzenehexachlorides and their splitting up into), 298.
TRINITROANIZOLES (On some). 684.

TWISTED CURVES (Surfaces) and groups of points as loci of vortices of certain systems
of cones. Ist. paper. 495.

UMWANDLUNGSSTUFEN (Das Gesetz der) in the light of the theory of allotropy. 788.

UVEN (mM. J. VAN). Homogeneous linear differential equation of order two with given
relation between two particular integrals. lst Communication. 391. 2nd Commu-
nication. 584. 3rd Communication. $32. 4th Communication. 1010.

vaGus EFFECTS (On different) upon the heart investigated by means of electrocardio-
graphy. 165.

VALKENBURG (c. T. VAN). The origin of the fibres of the corpus callosum and
the psalterium. 12.

— On the mesencephalic nucleus and root of the nervus trigeminus. 235.

— On the splitting up of the nucleus trochlearis. 1023.

— Caudal connections of the corpus mammillare. 1118.

VAPOUR-LINES (On retrogressive). lst Communication. 177.

VAPOUR TENSIONS (Determinations of) of nitrogen tetroxide. 536.

vapours (Electric double refraction in some artificial clouds and). 558. 2nd part. 786.

VERMEULEN (u.). On some trinitroanizoles. 684.

VIBRATIONS (Summational and differential) tn line spectra, 470.

viRIAL (Remarks on the relation of the method of Gisss for the determination of the
equation of state with that of the) and the mean free path, 853.

VOLUMENOMETER (Control measurements with the). 101.

vortices (Surfaces, twisted curves and groups of points as loci of) of certain systems
of cones. Ist paper. 495.

vVOS VAN STEENWIJK (J. E. DE). Provisional results from calculations about the
terms in the longitude of the moon with a period of nearly an anomalistic month,
according to the meridian observations made at Greenwich. 1180.
VR1Es (G. DE). Calculus rationum. 1026.
VRIEs (HK. DE). On the conoids belonging to an arbitrary surface. -481.
VRIES (JAN DBE). A bilinear congruence of quartic twisted curves of the first
species. 255.
— “A quartic surface with twelve streight lines”. 259.
— presents a paper of Prof, D. Monrrsano: “The theory of bilinear complexes
of conics’. 550.

XXVI CONTENTS.

VRIES (JAN DE) presents a paper of Mr. M. Stuyvarrr: “On the lineo-linear
congruences of right lines and the cubic surface”. 1018.
— presents a paper of Dr. G. pE Vries: “Calculus rationum”. 1126.
— On two linear congruences of quartic twisted curves of the first species. 1122.
— On a congruence of the second order and the first class formed hy conics. 1173.

WAALS’ (VAN DER) equation (On the inconsistency of my heat theorem and)
at very low temperatures. 201.

— equation of state (The variability of the quantity 4 in), also in connection with
the critical quantities. 278. IL. 428. LIT. 563. LV. 711.

WAALS (J. D. VAN DER) presents a paper of Prof. A. Smirs: “On retrogressive
melting point lines”, 170.

— presents a paper of Prof. A. Smirs: “On retrogressive vapour lines. Ist Com-
munication”. 177.

— presents a paper of Prof. A. Smirs and Mr. J. P. Treup: “On the course of
the P7-lines for constant concentration in the system: ether-anthraquinone”. 183.

— presents a paper of Prof. A. Smits and Mr. J. P. Treus : “On retrogressive melting-
point lines”. 38rd Communication. 189,

— presents a paper of Prof. J. D. van per Waats Jr, : “nergy and mass”. 239, II $22.

— presents a paper of Prof. PH. Kounstamm and Mr J. Cur. Rerpers: “On the
phenomenon of condensation for mixtures of carbonic acid and nitrobenzene in
connection with double retrograde condensation”. 270.

— Contribution to the theory of binary mixtures. XVI. 504. XVIL. 655. XVIIL.
875. XIX. 1049. XX. 1217.

— presents a paper of Dr. F. E. C. Scnerrer: “On gas equilibria”. 743.

— presents a paper of Prof. Pa. Koanstamm and Dr. L. S. Ornstern: ‘NERNST’s
theory of heat and the chemical facts.” 802.

— presents a paper of Dr. M. Lave: “On the conception of the current of energy”. $25.

— presents a paper of Prof. J. D. van perk Waats Jr. “On the conception of
the current of energy. 828.

— presents a paper of Prof. J. D. van per Waats Jr.: On the law of molecu-
lar attraction for electrical double points”. 1111.
WAALS JR. (J. D. VAN DER) Energy and mass. 239. IT. 822.
— On the conception of the current of energy. 828.
— On the law of molecular attraction for electrical double points. 1111.

WANT (G. F. vAN DER), J, Bokspken and A, Scnweizer. “On the velocity of
hydration of some cyclic acid anhydrides, 622,

water (On the system: hydrogensulphide-). 195.

water-phenol (On the system:). 192.

wareR-alcohol-manganous sulphates (On the system :) 924.

WATERMAN (u.) and J. Borsexen. On a biochemical method for the determination
of small quantities of salicylic acid in the presence of an excess of p-oxybenzoic
acid. 604,

— Action of substances readily soluble in water, but not soluble in oil on the
growth of the penicillium glaucum. 1112.

— On the action of some benzene derivatives on the development of penicillium
glaucum, 608.

CONTENTS. XXVII

WATERMAN (u.) and J. Borseken. On the action of some carbon derivatives on
the development of penicillium. glaucum and their retarding action in connection
with solubility in water and in-oil. 928,

WEATHER (The relation between changes of the) and local phenomena. 856.

WEBER (MAX) presents a paper of Dr, N. H. Swen.encreset: ‘Pleistophora
gigantea Thélohan, a parasite of Crenilabrus melops.” 377.

WEEDER (J.). Calculations concerning the central line of the solar eclipse of April
the L7th 1912 in the Netherlands. 935.

WEEVERS (H.). The action of the respiratory enzymes of Sauromatum yenosum
Schott 370.

WENT (F. A. F. C.) presents a paper of Dr. W. Docrers van Leeuwen and Mrs. J.
Doctrrs vAN LreuweN—Reynvaan: “On the distribution of the seeds of certain
species of Dischidia by means of a species of ant: Iridomyrmex myrmecodiae
Emery.” 153.

— presents a paper of Mr. P. C. van per WoLk: “Investigation of the transmission
of light stimuli in the seedlings of Avena.’ 327.

— presents a paper of Dr. Tn. Wrevers: “The action of the respiratory enzymes
of Suuromatum venosum Schott.” 37).

— presents a paper of Mr. C. P. Conrn Stuart: “A study of temperature-coefli-
cients and van “© Horr’s rule.” 1159.

WiBaurt (J. e) and A. FP. Hottumay. The nitration of ortho-chlortoluene. 1230,

WICHMANN (C. &. A.) presents a paper of Dr. J. Scamurzer: “On the orientation
of crystal sections with the help of the traces of two planes and the optic
extinction.” 128.

— presents a paper of Mr. M. KorprBere: “Notes on the Sopoetan—mountains in
the Minahassa.” Ist part. 222. 2nd part. 399.
— On the so-called atolls of the East-indian Archipelago. 698.

WIERINGA (J. wu.) and W. Erntuoven. On different vagus effects upon the heart
investigated by means of eléctrocardiography. 165.

winxp (On the diurnal variation of the) and the atmospheric pressure and their relation
to the variation of the gradient. 48.

WINKLER (C.) presents a paper of Dr. S. J. p—E Lance: “The red nucleus in
reptiles.” 1082.

— presents a paper of Dr. C. T. van VaLkensur@: “Caudal connections of the
corpus mammillare.”’ 1118.

WISSELINGH (c. VAN). On the cell-wall of Closterium together with a conside=
ration of the growth of the cell-+wall in general. 912.

WOLK (P. C. VAN DER). Investigation of the transmission of light stimuli in the
seedlings of Avena. 327.

ZEEMAN (e.). Considerations concerning light radiation under the simultaneous
influence of electric and magnetic forces and some experiments thereby suggested.
Ist part. 2.

— presents a paper of Dr. E. KE. Mocenporrr. “Summational and differential

vibrations in line spectra’. 470.

XXVIIT CONTENTS.

ZEEMAN (P.). Note on the insulating power of liquid air for high potentials and on
the Kerr electro-optic effect of liquid air. 650,
— and C. M. Hoocrsoom. Electric double refraction in some artificial clouds and
vapours. Ist part. 558. 2nd part. 786.
Zoology. N. H. SwriuencresBer: “Pleistophora gigantea Thélohan, a parasite of Cre-
nilabrus melops”. 377.
ZWAARDEMAKER (H.) presents a paper of Dr. J. L. Hoorwee : “On the irritation-
effect in living organisms”. 71.
— The effusion of acoustic energy from the head according to experiments of
Dr. P. Nrkirorowsky, 758. ;
— presents a paper of Dr. V. E. Nrerstrasz: “Some calorimetrical investigations
relating to the manifestation and amount of imbibition heat in tissues”. 1130.
ZWIERS (ut. J.). Preliminary investigation into the motion of the pole of the
earth in 1907, 211.

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