Proceedings of the section of sciences

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Huygens Institute - Royal Netherlands Academy of Arts and Sciences (KNAW)

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KNAW, Proceedings, edition 19 I, 1917, volume

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KONINKLIJKE AKADEMIE
VAN WETENSCHAPPEN,
"" . -:- TE AMSTERDAM -:-'.
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PROCEEDINGS 'OF THE,
SECTION' OF SCIENCES~
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,V'OL UME XIX ,
( ~, !ST PART~) "
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, JOHANNES 'MÜLLE~ ., . AMSTERDAM
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MARCH 1917 :=======
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,(Tr~nslaied) from: Verslagen van de,Gewone, Vergadering~1l der \Vis,. en
Natuurkundige Afdee!ing' XXIII xXly and DI. XXV.)
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, "KON INK,L IJI I{E: A'KA D E M;I E'. VA, N WETE NSCH. APPE N
TE··AMSTERDAM.
p Roe EED I NG S
\
\'} - VOLUME XIX
President: Prof. H. A. LORENTZ.,
: ~. Secretary: Prof. P. ZEEM·AN.
(Translated. from: "Verslag iran de gewone vergaderingen der Wis- en
Natuurkundige' Afdeeling," Vol. XXIV and. XXV).
·CONTENTS.
(J. VAl'! LAAR:, "On the Fundamental Values' of the Quantities.b and Va for Different Ellimen'ts,
in Connection with the Periodic System 11. Mercury and Antimonium. General Methods", p. 2.'
A. SCHIERBEEK: "On the Setal Pattern of Caterpillars:' (Communicated by Prof. J . .'F. VAN
BEMMELEN), p. 24.' " ,
Mrs. C E. ,DROOGLEEVER FORTUYN-VAN LEljDEN: "Some Observations on Periodic Nuclear Divi-
sion iu the Cat." (Communicated by Prof. J. BOEKE), p. 38. .
H. ZWAARDEMAKER, H. R. KNOOPS 'and M. W VAN DER BIjL: "The electrical phenomenon in c1oud- .
like' condensed odorous water vapours"" p 44 . . ' ' ,', '. , ,
H. M. DE BURLET and J. 1 J. KOSTER: "On ,the determination of the position of the maculaplanes
. and the planes of'the semicircular canals in the cranium". (Communicated by Prof. H. ZWAARDE-
MAKER), 'p. 49, " •
Miss E. T ALMA: "The inlluence of temperature ,on the growth of the roots of Lepidium sativum."
(Communicated by Prof. F. A. F. C., WENT); p. 61. , ' '
C. DE JONG: "Determination of the constant of. Precession and of the Systematic Proper motions of
c the stars, by the. comparison of KüSTNER's 'catalogue of 10663 stars with some zone-cataloglles
!' ' of the "Astronomische Gesellschaft"" (Communicated "by, Prof. E. F. VAN DE SAr'iDE BAK-
HUVZEN) p. 65. . '.... '.. .'.,.." .. ' , -
JAN DE VRIES: "Pencils of twisted cubics on a cubic surface", p. 97.
T. P. FEENSTRA: "A new group of antagonizing atoms". I. (Communicated by Prof. H. ZWAARDE-
MAKER), p. 99.
D. J. HULSHOff POL: "The relation of the plis de passage of GRATIOLET to the ape fissure."
(Communicated by Prof. C., WINKLER), p. 104. ,,',,' "
H,. J. HAMBURGER: ~Quantitative determination of .slight quantities of 504.. 11. Contribution to mi-
.. crovolume1rical analysis':, p. 115. c' , , .. ' , " ,
P. ZEEMAN: "Direct opth:al measurement of the velocity 'at the axis in' the apparatus for FIZEAU's
, experiment", p. ,125.. . ' " , ,
A. SM lTS and: A. . H; 'W. ,ATEN: "The Application of, the Theory of Allotropy to Electromotive
Equilibri<J,." V. (Communicated by Prof J. D. VAN DER WAALS), p. 133. ' , '
J D. R. SCHEFFER and F. E. C. SCHEFFER: "On Diffusion in Solutions." 1. (Communicated'by' Prof.
A. F.' HOLEMAN); p. 148.:; , , ", ",
, V. WILLEM: "The movements of the heart and the pulmonary respiration with spiders." (Commu-
'nicated by Prof. G. VAN RIJNBERK), p. 162.', " " , '\
A: A. GRüNBAUM: -"On the nature and p'rogress of visual fatigue.'~ (Communicated by Prof.
G. VAN RIJNBERK), p. 167. I,' "
W. REINDERS: "The system Iron-Carbon-Oxygen." (Communicated by Prof. J. BÖESEKEN), p. 175.
W. REINDERS: "Birefractive colloidal solutions." (Communicated by, Prof. j. 13öESEKEN); p. 189. '
J. DROSTE: "The field of a single. centre in EINSTEIN's theory of gravitation, and the motion of a
particle 'in th at field." lCommunicated by Prof. H. A. LORENTZ), p. 197. '
H. J. WATERMAN: "The Metabolism of Aspergillus niger." (Communicated by Prof. j. BÖESEKEN), p.215.
D. J. HULSHOFF POL:, "The ape fissure - sulcus lunatus - in man." (Communicated, by Prof.
. C. WINKLER), ,p. 219. ,,:: " , :,' .. ' "
BALTH. VAN DER "OL Jr.: "The currents arising in n-coupled circuits when the primary current is
: ,'suddenly broken or completed. ' (Comml\nicated' by Prof. . W H. JULIUS), p.,225. ," ,
1
Pl;oceedings Royal Acad: .Amsterdam. Vol. XIX.
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Physics. - "On t!te Fundam,ental ValuM of t!te Qual1,tities b ancl
Va fol" Dij/erent Elements, in Connection with the Pe1,iodic
System Ir. Mercu?'y anel Antimoniw"t},. Geneml A/et/wels". By
DI'. J. J. VAN L<\.AR. (Commllnicated by Prof'. H. A. LORENTZ).
,Communicated in the meeting oLMarch 25, 1916).
J. In oUt' foregoing paper 1) we have found that the values of b
and Va at the critieal temrerature can be built up aclclitively from
a few constant I fundament((l values fOl' the different elements. (See
the tables on p.1223 and p.1229 of the cited paper). '1'he elements . ÎI ~
H, 0, N, and 0 presented in this, as far as the val ues of bare
concemed, two different fnlldamental values (H even thl'ee), of ,,,hieh
the seeond may be considered as a contractio11 - about in the
ratio of 1/~1/2' 1 - of the fllndamentaI value. [For H the third-
,-alue is to the first as (l_l /'lll/2l 1]. The way in w hieh these
multiple values must be \lsed in the l'ecomtmction of the values of
band I/a of the dlffel'etlt chemiral combinations has been snfficiently
set fOl'th in the fiJ'st paper (henceforth to be indicated by 1). (See tile
different tables and the summa!')' on p.1234). With regard to the
values of V ((, we should pay attentIon to the fact th at fOl' compounds
as OH4, 0014' OHsOl, OHOI3 , 02Ha etc" and also for NHa and PHa,
Gerl4 and Sl1014' the central atoms do not take part in the attrac-
tion ; so t!lat In the reconstl'uetion the vaIlles of Va for 0, N, P,
Ge, Sn must all be put = O. Bllt for doubly bound 0 half the value
0= 1,55 IS found, and for the tripl)' bound 0 the full vallle 3,1.
(see furthel' again the tables, and also p. 1220-1221 and 1235;
also wlth regal'd to the two values fol' H).
Below we reproduce the two pl:incipal tables ~).
FundamentaJ Values tor bk X 105•
IH e= 105?
H =48,5 C = 100 N =85 0 =70 F = 55 Ne = 71 ?~
(34jI4) (15) (60) (50)
(SI = 155) P = 140 IS = 125 Cl = 115 Ar = 144
Ge = 210 (As = 195) Se = 180 Br = 165 Kr = 177
Sn = 265 Sb =250 (Te = 235) I =220 X =228
1) These Proc. of Jan. 29, 1916.
2) In the table for Va on p. 1229 Ne = 6,3 X 10-2 [= V (39,6 X 10-2)] bas
heen wl'iUen instead of Ne = 2,0 X 1O-2 l = V(3,96 X 10-4)]. Correct further on
p. 1224: H2 found = 976 instead of 1:)';'; on p, 1229: H2 found = 1,96 instead of
1,~5; on p 1237 read: neutralized in ordinary CilCUm&tances; "closed", as M.
expresse§ him~elr - would he free and "open".
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.)
In every ve1,tical column the inel'ease is therefol'e 55 units, wbile
in every horizontnl row the elecl'ease amounts 10 .15 units. The
values for Si, As, anel Te, WhlCh we have placeel hetween paren-
theses, coulel not be verified as yet by known rompounels, .the c;'itiral
elata of them being impcl'fectly known.
Fundamental Values for Vak X 102•
1 1 He = 0,8?
H=3,2 C=3,l N =2,9 o =2,7 F = 2,9? Ne =2,O?
(1,6)
P =6,4 S =6,3 Cl = 5,4 Ar =5,2
Se=7,1 Br = 6,9 Kr =6,9
Sb = 8,91 I = 8,8 X =9,1
If we add to this Hg = 11,0, as we shall immeeliately find, jt
may be said th at in the different hOl'izontal pl'Încipal series 'of the
perlOdlc system the values of ~/ a arc very neal'ly constant, the ratIo
in I'onnd numbers being (taking He = 1)
1 : 3 : 5 . 7 . 9 : 11,
We add that the values of b in the column of the halogens are
in exactly the f:,ame ratio as tbe vallles 1.2.3 4 (taking Cl = 110).
11. Before proceedIng to the ralculation of some new funela-
rnental vallles - In which some methoeIs wiJl be eliscussed fol' the
calculation of the vallles of IZ and b for substance'3 whel'e TI: anel
pk al'e unknown, and besieles of the unknown values of '1 anel
'c
]Jk themseh'es - we wlll make a few general remarks,
In the fit'st place we dmw attention to this, that when the above
,tables are lIseel to calrnlate the critical temperatlll'e and pressm'e
fol' elements, the cl,ttical data of whiclt are nnknown as yet, the
molecular state of these elements at '1 must be taken into account.
'0
Thus at the cl'itiral tempel'utul'e mel'clIry has long become Hg~,
Only at lowel' temperatul'es the mel'rllryvapou1' is = Hg\ on account
of the great volume, as IS knowIl. But at highel' tempel'alnres, whet'e
-tbe vapolll'volume gets smaller and smalleI', the assoriation to Hg~
incl'eases more alld more, and IS almast complete at '1'1.' Fol' mel'-
cnr}', namely, .just as fa I' same other associatmg substances the
jncrease of volume of the vapour tl'Ïllmphs on tlte deC1'~f1Se of tempe-
l'atul'e, and thel'efol'e I he association does not mcrease, but dec1'eases,
The same thing is probably the case fOl' water, but for this
snbstanre the fissociation at T,. (of tbe vapour namely) is still slight,
1 ~,
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wMle for mel'cury it is complete. To th is case belong those substances,
for wbich the heat of' dissociatioi1 q "of the double molecule& (i.e.:
the absol'oed heat in dissociation) is comparatively small or = 0 (at
anJ l~te '< fTk; hence fol' ordinat'Y substances < 7 Tb when q is
expt'essed in gl'. cal.). Acetic ~cid belongs to tile otllel' eategory of
substances, fOl' whieh the association in tlte vapour decreases on
increase of' tempel'atnre, till a minimnm is reaehed iJl the neigh-
bonrhood of '1'7,. At still higher tempel'ature the association in the
vapo1ll' increases, again. Here (below tile temperature of in \'ersiont
the temperatul'e-change thel'efol'e prevails over the volume-challge.
To 'this belong those substances, for which the heat of disso-
ciation of the double molecnles is eomparatively large (> 7 T7J.
Aceordingly mel'cury - and we shall also see this ronfil'med on.
other gronnds - is bimoleculm' at Tk .
re 1 8 ak 1 ale I
Now Rlle = -7). -b. Pk= -7 J. -2-' in whieb ). fol' substances with
2 k 2 bk '
high ditira] temperature bas the ]imiting vaIlle 27 /2~ I), so that VITi1h
R = 1 : 273,1 we ha\'e:
ak 1 ale I
TIc = 78,03 - Pk = --2. 1\
bk 28b "
lf now (Vale)1 = 11,0 X 10-2 ; (ble)l = 150 X 10-:; fot' Hgu as
we shall find pl'esent1y, then we get fol' Hgn :
1'k = 78,03 n 12510 X 101 Ple, 218 21251 X_ 104 , (r1
because for Hgn 1/a le = 17 (1/ ale)l' ancl also lik wiIl be = n (bkh
(possible contraction fot' bk exellicled).
,Hence we find:
T/o; = n. 6300 (abs.) P7c = 192 atm.
And as the critical temper'ature of merClll'y (see ~ 3) is lying with "" .
gl'eat pl'obability in the neighhourhood ot' 1260° (absolute) l), and
]
I)
. 1) For À we have llamely Cloun thed expres'sIO n À = -27- ( -y- )2,I. n w h'l Ch
8y-l y + I "
., (the reduced coefficient of direction ~f the straight line between Dk and Do in
a D, T-diagram, i. e. of the ideal "straight diameter") verges to 1. (Cf. These Proc.
of March 26, l 9 ! 4, p. 8 8, formula (18)). ~,
~) Not in all the tables Celsius degree~ are di .. tinguished from absolute tempe- o'l(.
l'atures with sufficient care in records of temperatures. Thus e.g. in the "Tables
annuelles" (which contain many errors also in other respects), 1 find continually ,
amidst l'ecol'ds of temperatures in Oelsius degrees, values which are meant in
absolute tempeÏ'lllure, without this being stated. For ,tbe critical temperature of
mercury 1 found the value ± 1270° C., given somewhere in tho'se tables. The
value is correct, bul lhe addition: degrees Celsius is fault)'. FOL' then Tk woultl
be aboul 1540Q absolute, whereas in reality ~h = 1260° absolute.
" 1 .!;.
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Pk being' about 200 atm., we find [besides total absence of an)'
contl'action of the b-value in the dissociation of Hgz, i. e. (b/c)2 =
2 X (b fc\] a value fOl' n which diffel's but very little from 2,
Fot' Antimonium, where (Vak\ = 8,9 X 10-2 and (bk)1 = 250xlO-5,
we should fiud Oll the- supposiiion of Sb l at T,~:
79,2
('l'k)1 = 78 X - X 101 = 247° (abs.).
250
lt IS found that the critiral temperatul'e of Sb is at least J 2900°
(abs.), so (hat at this temperature Sb would be associated ro about Sb12 •
Fo!' caJ'bon with (Va")1 = 3,1 X 10- 2, (b'c)1 = 100 X 10-5 we
should ha\ e found:
9.61 0
('1'k)1 = 78 X 100 X 101 = 75 (abs.),
' ...· hel'eas the critiral temperatlll'e of C iR certainly Iying above
6000° abs., so that for 1',,; cal'bon would at least have to be = Cw
And the same thing holds with respect to silicium and all the
metals I).
In the second place w.e draw atlention to this, that substances
like COl" SnCI 4 etc., where tbe attraction of the C- Ol' the Sn-atom
is cancelled, will ronsequelltly ha,'e a 1'etativel.~ 1010 criural tempe-
raiul'e. Thai is to say th at these and similal' slIbstances ~CH4' :NRp
PHs) would be JllUch less 'VVlatile at the o/'dinary temperature, ,,;rhen
the said circumstance wel'e Hot present.
Tbu& Vak = 0 + 4 X 5,4 = 21,6 for CCI4', whereas, ifthe attl'action
of 0 could makf' itself feit, Val: wOllld be = 24,7 (X 10-2), That
is to say: now a i& only, 467, wbel'eas ii would be 610 in case of
attraction of U, Hence in the latter case we ShOllld have fonnd for
'Tk the vallIe 556,2 lthe real value of Tk), multiplied by 610: 467,
0
sa that we "hould have found 726°,5 absolute = 453 C, instead of
0
283 0, The difference (170°) is very large.
For SnCl~, with t/ ak = 9 for Sn, the yalne of t/a l.; would have
been found 30,6 instead ot' 21,6, i. e. tllat of ale 936 instead of 467,
0
which would have brought Tk to 1189° abs. = 916 O. instead of
319° C., as it is now. Hence a difference of 600°,
If fo!' NHa the attracrion of the central O-atom could have made
itselr' felt,tllen t/ al;; would bave been = 2,9 + 3 X 3,2 = 12,5
iJlstead of 9,6, sa th at then Tk wOllld have rome from 40/?,0 to
1) In a following paper we shall ho wever, mentión - besides such a formidable
al:>sociatioll at 'l'k - anothcl' unexpected cil'cumstance, which call account for the
high critical teOlperature for metals and some metalloids.
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0 0
406 X (156 : 92) = 688 abs. = 415 C., whereas now the critical
tempel'atut'e of ammonia anI)' amounts to 133°. C.
And as last example CH4 • Here wit/i the atlraction of C Vak wOllld
_ be = 3,1 + 4 X 1,6 = 9,5 instead of 6,4, sa that ']'k would then
0 0
have become = 190,2 X (90 :~41) = 418 abs. = + 145 C., instead
of - 83° 0, as it really i8. ~
All these substanees therefol'e owè theü' l'elati ve volatiltty" resp.
lo\~' critical ternperatllre, to the cil'cumstance that the central atoms
Cafl110t make their attractive action felt towal'ds the outside, in consé·
q llenee of tbe absol'bing action of the sUl'l'ounding atoms. Substances with-
double Ol' multiple bindings (C2H4 , ü 2H2), where the attraetive action
eau opel'ate again full)' Ol' par/iall)' (see 1), wiIl, thel'efol'e, ät onee
be relatively less voIatiIe thaJl those of the ea,tegor)' eonsidered just nOlV,
UI, The critical values of mercury.
(I) Calculation of bk fi'om the deusities of t!te svlid ha logen cOlnZJoun,ds.
ACcol'ding to the propel'ty of the stl'aight diameter 1/2( dl + d2) =
= 1 + "I (l-m), henee at Iow temperatlll'es, where the (I'edueed)
density of tbe vapolll' cl2 eall be neglected:
cJ.-
dl = -.: = 2[(1 + r) - ymJ.
VI
1+"1
As now Vk = ~·bk = -- bh we .have .
Y ,
.2"1[(1 -+- y) -ym] [y ]
bk = '\ X = VI X 2{ 1 - -- 1n (1)
- 1 + r l+r
This fOI'rnula emtbles us to calcnlate ths \'alue of b7c fl'om VI (tbe
moleculaJ' volume of tbe li'l1.tid), when j' (coefficient of directiol1 of the
Rtl'aigt diameter) and m (the reduced tempel'atme) are lmown. And as at
low tempel'atures the volume of the solid phase wiII not differ rnueh
from th at of the liquid rh ase, the above formnla rnay be used by
(fjJproximation also fOl' the calcnJation of bI. from tbe molecular
volume of tbe solid phase.
Th'us tOl' Argon, where y = 0,75, b/~ = VI X 1,5(1-~/7m), !~'or
84°(abs,), i. e. at the triple point, the density is = 1,413, hellce
V1 = 39,88 : l,413 = 2ö,2. The valIIe of 111 is 84°: 151 ° = 0,55,
sa that bk = 28 X 1,15 = 32,4; i. e. cxpl'essed in the normal volume
Vo, 32,4: 22.,1.J 2 = 144 X 10-5, wltich is pel'feetly identieal with tlle
value of ble calculated dir'eetly fl'om Tk and pI. in Treatise 1.
The factor, therefore, by whieh VI is to be muItiplied to get bk,
is = 1,15.
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Fol' solid Oa:ygen the density at 21° is = 1.4256, hence VI = 32 :
: 1,426 = 22,4. The factor by w'hich. we must mnltiply, bas the value
1,5 with m = 21° : 126° = 1/6 and j' = 0,8, so that b,c becornes 33,6;
i. e. expl'essecl in Vo, ,33,6: 22-:1:12 = 150 X 10-:5. Detel'mined dil'ectly
in I fl'om Tk and ]Jk 1-:1:2 X 10-5 was found, so that the value of
h,c calculated from the solid phase (34° below the triple point) tums
out only 5 Ol' 6% too high.
The factor uy which VI must be multiplied to get bk, is thel'efol'e
vel'y val'iable, and depends in a high degl'ee on y and 111,. Fo!' m,etals
,ana salts, wbere Tk lies between 1000° and 3000° abs., y'iR generally
in the neigh bOll dlOOd of 1, alld then we become:
bic"> UI (2 -- m), . , . . . . . (la),
in whirh IJl vades fl'om I/a Lo l/lO> when VI is detel'mined at tbe
ot'dinal'Y tempel'ature (± 300° abs.). The factor, therefore, vades from
j,7 to 1,H. (The sign of inequality l'efel's to the fact that VI of the Bolid
phase is generally smaller than the val ue of VI' whicb wouid hold
at the same tempm'ature with I'egard to the liquid phase).
Now at Tt.. fol' HgCI 2 • HgBt" I alld. HgI 2 ROTINJANZ (Z. f. ph. Oh. \
87, p. 253) lias fOlmd I'esp. tlle vallles 976°, 1011° and 1072° absolute.
We maJ thel'efore put 1n = 0,28 Ol' 0,26, which makes the factor
2-m = 1,72' Ol' 1,74, Fl'om
\.7 kJ
bk= 22412 X D
1
follows thel'efol'e:
Fo!' HgOl.:
1,72 271,52
b,c = 22412 X 5,424 0,00384"
hence Hg = 38,*-230 = 154 X 10-5 •
}:I'Ol' HgBr~:
1,73 360.44
bk = 22412 X 5,738 0,0\0484,
which giyes Hg = 484-330:::-: 154 X 10-).
FOI' Hg12 (yellow) :
1,74 454,44
b k= -- X = 0,00582,
22412 6,060
glving Hg = 582-440 = 142 X 10 -5,
Fo!' Hg in compounds we can thel'efol'e assume about:
bk= 150 X 10-5,
Fol' mel'CUl'y it~elf we find from the density of liqnid mel'cul'y at ooe:
- 10