ra
The different regions with their limits, which occur in these
conditions, are represented in fig. 3 (Plate). The figure holds for
T,='/, T,, the values of g, and q, are expressed in multiples of 7;.
Let us subject the limiting-curves to a closer examination (see fig. 3).
a. Curve I, viz.
2(q,—417,,) (81)
1té:
According to (8) all the curves 7’7= f (2) with a concave beginning
will lie above this curve, with a conver beginning below it. For q,
must then be respectively larger or smaller than the values given
by the second member.
1p See Se
( 524 )
The curve will also yield g, = 0 for g, = 9, for which e? —1.
The initial direction is given by 9, = 4. (45°). Further for q, = 47,
ts 6,
is evidently also g,=47,, and for q,=%, e becoming = ©,»
g, will again be 47,. The curve I will therefore run pretty rapidly
asymtotically to the straight line g, = 47, for higher values of 4,
and will show a mazximum somewhere past g, = 47,. (JM, in fig. 3).
, ‘de
This maximum is represented by te =)
C
2
oe age 2 ee ee
J Yo 1 1 . a) 7
as: 02 = — wan according to (6). We have then:
2 1/
—fo . a :
(i+e ) Os OE Toe aa
3
= 6,
or Ge '’= 14 4T,—,
JT
(R= 2) Bie eae
or —- \ § — = 4 :
or Ch : -
From this we may find @, by approximation, so also q,,
is found from (84). As 9g, — 47, ae + Bw we have:
3
q = 4t $ate Par, 422 (4 —1-47,),
LAU a
2 6, ; vB
- —— 6) y 9 Vo
hence g, = 2q, — 47, —2—,
6,
” : 4 te
| ig gd. = 2a. — eth ees
71 “4, Te i
Now fig.3 holds for 7,—='/, T,, so (8a) becomes:
=e
GO, 4 FF
yielding #0, — 3,05. Consequently 9, = 26,7, = 6,10 7;.
according to (8b) 9, = 29, — 87, = 4,20 T,.
(8a)
and 4,
(80)
Further
Of the curve I (comp. 84) I have determined the following points
F 4 q:
With phe at gs 80. haat 0, == =o
1
ae
a
Qo 1 Pile? 1.65 bg, = 1,78 2, |\9,=7T, | 7 = 88,1'lg, — 4,17 7,
gre | 2,72 292° || a 54,6, 114
3 A 4,48 Ge a 20 te ee oe
bf ae Falko | Pipes} 15 ,,( 1810 | 401
Ge FZ 20,1 | 4,19 ,, | A | en 22000 4.00
Really the maximum lies just past ¢,—=67,. (We saw already
above, that for g, = 47, also 9g, = 47;,).
6. The curve II, viz
2(9,—47,)
Bake
This curve separates the curves 7 = (/ (7) with concave end (left
of this curve, because g, is then smaller than the second member)
from that with a convex end (right of the curve, where q, is larger).
For ¢,=0 also g,=0, as 6,=0; (imitial direction again
q, = 9, (45°)); for ¢,=4T, also g,=4T,, and for ¢,=—, g, will
(841)
=O
approach to 29, —47,, because ¢ ‘ approaches to 0. The mating
direction of the curve II is therefore given by 7, =24,, or q,='/2 4:
(26°,5). met
It will necessarily cut I. When 7,='/,7,, this point of inter-
section S, lies somewhat on the left of the maximum J/,. It is
found by combining
2 (q¢,—4T. 2 (q,—2T.
qs — AT. =f CP 2 CA )
and ee :
92/97, = rE 5 oF —h/97,
lte lte
By approximation we find g, = 5,907,, q, = 4,197, .
The further calculation leads to the following summary.
9, = 1T,\e '=0,61 |g, — 0,76 T,|\\q =8 Te - * — 0,02 (9, = 13,8 7,
as 0,22 3,64 ,, Le bad 0,011 rege
sae 0,135 Behe aa | sia Ba | 0,00 28,0 ,,
aa 0,08 7,56 4 {|| 20 4 0,00' 38,0 ,,
oer 0,05 > | |
Borg = 2h (=-47 } ee q. == 27 (see abov e).
c. The curve III, i.e
2(q, + 47,)
n=—47, +B...
( 926-)
For values of g, larger than the second member the beginning of
T=f (2) is concave; these curves lie therefore above the curve. In
the same way all the lines 7=//(2’) with convex beginning lie
below this curve.
Again q,=90, when ¢,=0 (initial direction 9,=4, (45°). When 4,
approaches to a, g, approaches to 29, + 47,, so the limiting direc-
tion becomes g, = 2 q, (63°.5). This curve lies entirely outside the
two first, more to the left.
Some points of the curve III follow.
9, =17,\e *=0,61 |g, = 2,207, |'q,=8 T,|e 7 = 0,02 |9, = 19,6 T,
aes 0,37 ae 10 0,01. PE ue
eS 0,13° (ea NN Aes 0,00. 34,0 ,,
pe 0,05 15,000] 1-0 S| 0,00. 44,0 ,,
d. The curve IV, i.e.
2(q, + 47,)
: (8/V)
eee
Te —— = ale alt
If g, is smaller than the second member, the end of T= f(2’)
will be concave; these lines lie accordingly eft of the curve; on
the right the lines 77= 7 (2') with convex end are found.
For 9, = 0 again g, = 0 (initial direction 9, = @, (45°)). fg, =o,
q, evidently approaches asymptotically to q,=—4T,, just as the
curve I approached asymptotically to ¢, =47,, when ¢g, =o. The
curve IV lies therefore only for a small part within the region of
the positive g,, and will therefore necessarily cut the g,-axis some-
where in S,, and yield a maximum value M, for g, before that time.
This curve too lies therefore entirely outside the preceding curves,
and again more to the left.
The g,-axis is cut, when (7, =—'/, T,)
je OF
qi | = 1 sn
Woe te — fps
/24
Rees pwc
or when
1 27; Se nh =e
; Oe
ew
iin 7
( 527 )
The maximum is found in exactly the same way as in I, and is
determined by
ee eT:
6,—e i ile Jo a ait a LSS)
to which belongs :
hele
ae 8
qs q1 T.—T, ( d)
If 7,='/, T,, then (8c) yields:
6,— e” ae! F
from which 6, = 0,567, or g, = 1,137,. According to (8d) we have:
g, = 29, — 27. = 0,26T,.
Further we have the following values for g, for increasing values
of 4q,.
9, =2T, le! =2,72|\q,— 0,16 7, ||g, = 10 7, |e! = 148|g, = — 1,847,
| :
4a | 7,39 = 0,575, || 15, 1810) Bg
| ||
6,,| 20,1 | 0,84 5; || |
Already at g,—=157, the limiting direction g,=—4/7’, (here
= —2T,) has been all but reached... 5
IV. So we have seen, that the four limiting curves (see fig.5),
which divide the g,,9,-space into different fields, radiate from the
origin (7, = 49, =) in the space. All of them touch in the origin
the straight line g, = g,, the former two on the right, the latter two
on the left. Only I is intersected by Il; IV falls for the greater part
outside the positive region; I and IV show maxima.
Below I and on the right of II lies the field A of the convex
shaped meltingpoint-curves.
Between I and II on the left of the poimt of intersection jS, lies
a small region B,, where the end of 7’= f(x) has become concave ;
on its right is the region B,, where the beginning of T= 7 (x) has
become concave.
Between II and III (on the left of S,, between I and III) lies
the field C, where 7’ = / (x) is concave throughout its course, 7’ = 7 (.c’)
convex.
Between IIL and the g,-axis (below S, between II] and IV) lies
the field D, where only the end of 77= 7 (x’) is still convex.
Finally there is still a very small region between IV and the
g,-axis, where the meltingpoint curve — both 7 = /(~) and 7’= f(’)—
is concave throughout its course.
If we assume a fixed value for 9,, e.g. ¢, = 937), and vary 7, from
( 528 )
O tot o, we pass successively through the four regions A, B,, C
and D. For g,=10 7, e.g. we should pass through the region B,
instead of through B,.
If g, is assumed to be constant, e.g. = 17), we pass successively
through the fields A, 5,, C, D and #, when gq, decreases from @ tot 0.
Fig.4 gives a representation of the first mentioned transition, viz.
10P-g a ols.
Between the meltingpoint-curves, marked 2,4 and 2,8 (so holding
for g,—= 2,4. and 2,877,), the transition from A to 4, (hatched) is
situated. Between 3,4 and 3,8 (see the hatched parts) is the transition
from B, to C. Between 7 and 8 (in this case for 7 = f(w’)) that
from C to D. Further the cases ¢, =1, 9g, = 2 (A), g, =5(C) and
q.= 3 T,
(Ss yCre ai Ly . 7 EX x ile ; | H | | |
Ae APE | OR lo.47, 2.87; |3.47,|3.87, |) 57, | He | oY GR RAIL
i | | | {
:
| z’=0.008| 0.015} 0.019 0.022! 0.626} 0.029
T0995 7.) |
0.038 | 0.051 | 0.057 | 0.069
0.08 Q.068| 0.079} 0.091; 0.41 | 0.12 | 0.16 b 0.21 | 0.24 | 0.28
| 2’ = 0.019! 0.038! 0.043! 0.052} 0.058 0.066| 0.080} 0.10 |
| | |
- |x=0.07| 0.14 | 0.16 | 0.185| 0.22 | 0.25 | 0.30 | 0.39 | 0.43 | 0.50
| | | | | /
|
|
|
|
| 0.13
~
~
=
—
0.13 | 0.16 | 0.17 | 0.19
0.67
| 2’ =0.039| 0.022| 0.072} 0.082| 0.03%} 0.10
0.36
20.114] 0.21 | 0.25 | 0.28 | 0.33 0.44 a 0.55 | 0.59
ie alee
| 2’ —0.053| 0.095] 0.11 | 0.12 | 0.14 | 0.15 | 0.18 | 0.22
0.80 ,, | | |
0.23 | 0.255
«=0.16 | 0.29 | 0.34 | 0.38 0.44 | 0.47 | 0.56 | 0.67
0.72 | 0.785
x’ =0.08?| 0.14 | 0.16 | 0.18 | 0.20 | 0.215] 0.25 |} 0.29 | 0.30 | 0.32
ST ier | |
|x =0,22 | 0 39 | 0.44 | 0.48 | 0.55 | 0.58 | 0.67 | 0.78 | 0.815] 0:87
nis ——___—_- 5 ba
| a’ =0.125| 0.20 | 0.23 | 0.25 | 0.28 | 0.29 | 0.33 | 0.36 | 0.38 | 0.39
O70. 244 |
a = 0.295! 0.48 | 0.54 | 0.59 | 0.65 | 0.69 | 0.77 | 0.86 | 0.89 | 0.928
| | }
=0.19 | 0.29 | 0.32 | 0.33 | 0.37} 0.89 | 0.43 |°0.46 | 0.47
Octo s . |
x =0.38 | 0.59 | 0.65 | 0.69 | 0.75 | 0.98 | 0.85 | 0.918} 0.928) 0.964
c' = 0.305! 0.43 | 0.46 | 0.48 | 0:51 | 0.525] 0.555) 0.58 |} 0.59 | 0:60
x =0.50 | 0.71 | 0.76 | 0.80 | 0.84 | 0.87 | 0.915) 0.969) 0.971) 0.986
/ | | <
rc’ =0.52 | 0.64 | 0.665! 0.695! OF.) OSes | Orie 0.755} 0.76
| | |
r =0.68 | 0.84 | 0.87-| 0.913} 0.927 | a 0.965 il 0.991) 0.997
, Li. ts" ghy them "Teta face | |
£4
( 529 )
qd: =10(D) have been traced. The curves 2,8 and 3,4 represent
therefore the type #, with convex beginning and concave end for
T= f(x). The calculations (according to formulae (4)) are summarized
in the annexed table, i.e. for 7,—= 4 7,, to which fig.3 applies.
With this change of 7, we do not enter the region /’; therefore
g, would have to be smaller than 0,26 7) (see above).
V. It remains to answer the question, to what modifications the
fields and their limits drawn in fig. 3 are subjected, when 7’,
not 4 7,, but eg. 0,9 T, or 0.1 T,.
The initial directions of the curves I to IV remain quite the same,
also the final directions, but between them there are some modifi-
cations; specially the place of the points of intersection and of the
maxima is changed.
a. If T, is no longer 0,5 7,, but e.g. 0,9 7,, so that 7, and T,
are very near to each other, we find for the maximum J/, from
(8a) and (80):
is
—4
Ge), = Bi 5 ag, = 2g, = 407,,
yielding 6, = 1,45°, hence, as 49, =4(5 — =) is now iar
i 20,2 7, Por g, we find then ¢, = '2,4 7.
The maximum has now got quite outside the limits of the values
of g which occur practically, so that the curve I now gradually rises
within these limits. (fig.5).
The point of intersection of I with II has not been displaced much.
We find now for itg, = 5,85 T, , g, = 5,55 T,, so that the value of
-_
gq, has remained nearly constant.
The consequence of the modified course of the curves I and II
is, that the region 6, has all but disappeared; on the left of S,
I and II nearly coincide; the region 6, has strongly diminished.
But also C and D have considerably diminished, so that the greater
part of the space is left for A and ZL.
The considerable increase of the region / is due to the fact, that
the point of intersection of the curve IV with the g,-axis lies much
higher than in fig. 3, and that the maximum has moved considerably
to the right. In fact. we find for the point of intersection mentioned :
Ls 3,67 n/
ELIE SN et ahaa me (ee eae
"1/187, 187,
l+e
q
from which
( 530 )
The maximum is given by (8c) and (8d), viz.
6, — ess 0.8 5 9, = 2¢,— 32423;
giving 0, — 1,125, so q, = 203 T°, 9, == Spee
In the following table some more data are given, which have been
used for the construction of fig.5.
Curve I alp=1 8 5 8 10 15 2 2% 30 40 50 100 150
1/7, =1,09 3,09 456 7,13 837 10,7 11,9 12,85 12,26 110 9,89 4,74 pe
Curve _ IT afp=1 2 4 6 8 W 1 0 30 40 60 100
92/7, =0,93 1,91 4,04 640 8,96 11,7 195 283 48,0 69,3 1125 196
Curve TIT m/p=1 2 4 6 8 10 1 20 30 40 60 100 |
n/7, =1,14 233 4,88 7,65 106 138 22,5 32,1 532 5A 120 203 \
Curve IV %/p=1 3 5 8 10 1 WO B 30 40 50 100 150,
92/7, =087 245 381 546 6,32 7,67 8,09 7,82 7,08 4,93 268 28 353)
b. Let us now take 7,—0,1 7,, so that the two temperatures
of melting lie very far apart. This case (see fig.6) agrees more closely
with that for which 7, —0,5 7; only the maximum of the curve
II has got nearer to g,=4 7,, and the point of intersection of II
with I has moved much farther to the right. This has made the field
B, considerably larger than in the case 7/7, = 0,5, which field had
nearly vanished for 72/7, = 0,9.
But nearly the whole of curve IV lies now outside the positive
region, so that the appearance of bi-concave meltingpoint-curves 1s
almost excluded.
The maximum of I| is determined by
G,--e _— 19 : IN —= 29,—2' |. 1Gt
9
yielding: 0, = 19. As 0, == ——s so. 9g, = 4"), 2g, Dene ee
: vi ; ; 0; Re
For the point of intersection of I] with I we find, as e~ is very
UF
large and e very small,
a AO i ee ee Oe 0,42 = Tae
The curve IV cuts the g,-axis, when
0,2 i. a See 3
Bil
2), fhe
be”?
i
7 q; :
so when 0,2e° = + 0,2,
("S01 >)
n 10
3) T, q)
or ee? *— — —_ —— ]
Susy
This give 71 __ 9. 903, hence g, = 0,0457
Dy fives 2) 7 ee IU ence Vy —_—_— 9» 0 ye
ou
The maximum is found from
=6j * of)
A, —e ae ee oy 0.0444 7 z.
This is satisfied by 6, = 0,1025, hence 7, = 09,0228 T,, 7, = 0,0012 T,.
We can further caleulate the following points of the four curves.
Curve I /7,= 2, 4/, 6), 8), 10/, 20,
hig 106" 197 93,15 368 9389 - 3,96._- 4,00
Curve Il n wis —— I/y 2/5 4/5 ¢/, 8/, 10/, 20/, 3 4
2/T,= 0040 014 048 O91 136 181 4,04 560 7,60
Curve TT 2/7 = % 2/y 4/5 6), 5), 10/, -20/, 3
i/p = IJ 211 383 489 (560 615 844 100
Curve IV 1/7.= “'b 2/, 7 aie ch tae 1), aH,
93/7, =— — 0,014 — 0,066 — 0,20 — 0,30 —035 —0,38 —0,49
c. Hence when we draw near to the limiting case 7, = 7), all
four eurves will evidently approach to the straight line 7, = 4,.
which euts the angle of the coordinates in two equal parts. Fig.5 is
to a certain extent already a representation of this case.
If, however, 7, is very small, so that 72/7, approaches to 0, then ]
passes evidently into the straight line 9, = 47, ; If into q, = 2g, ;
Hil into g,==0, so into the g,-axis; IV into g,= — 4T,=—0, so
again into the q,-axis. Of this fig.6 gives already an idea.
As to the two maxima and the two points of intersection, we
have finally the following summary.
My, M,
Ts/p =0 01 0,5 09 1140 O1 OO
a/r,—=4 42 6,1 262 © | 0 0,0012 026 82 o
n/T, — 4 4,0 4,2 12,4 we 0 0,0228 1,13 20,3 oa
S, S,
7/7, =0 0,1 0,5 0,9 1/0 0,1 ie oe %
fp = 7,6 5,9 3,85 4 = 0 0 0 0
n/7 =4 4,0 4,2 5,55 4 | 0 0,045 2,51 64,4 o
And in this way I think that the ideal case a= 0, a = 0 has
been sufficiently elucidated.
35
Proceedings Royal Acad. Amsterdam. Vol. VI.
( 532 )
Physics. — *Tsothermals of murtures of orygen and carbon dioxide.
I. The calibration of manometer and piezometer tubes”. By
W. H. Kersom. Communication N° 88 from the Physical
Laboratory at Leiden, by Prof. H. KameriincH Onnks.
(Communicated in the meeting of September 26, 1903).
§ 1. With a view to the investigations of isothermals, critical
and condensation phenomena, of which | hope to give the results in
a following paper, I have carefully calibrated a manometer and a
piezometer tube. The results of these calibrations have been reduced
according to a method to which Prof. Kameriincu Onnes has drawn
my attention, According to that method the bore of the tube is repre-
sented by some terms of a series of Fourtsr, the coefficients of which
are derived from the observations. Thus we start from a continuous
representation of that bore im opposition to the discontinuous variations
which we must adopt when we derive mean bores from the length
of the mercury column at different places, and regard them as bores
at the middle of the column. From the following may be judged
what can be reached by means of this method. *)
§ 2. The manometertube was constructed after the model described
in Comm. N* 50 of the Phys. Lab. at Leiden, ?) differing herein that
with a view to the higher pressures a ring was blown on to the
part 4,°%), thus preventing the tube from moving along the cement
in consequence of which the thinwalled part a, would be pressed
against the steel of the flanged tube, while the tube A, is bent
parallel to the length of the tube with the same purpose and in the
manner as has been described in Comm. N° 69 (These Proe. I] Mareh
30, 1901, p. 625). The stem (c, of fig. 4 Comm. N° 50), graduated in mm.,
had a leneth of 50 em., the innerbore was 0.83 mm., the outer bore
6 mm., the capacity of the reservoir a, was about 25 ce., the widened
part ¢/, above had an immer bore of 2.6 mm., an outer bore of 9 mm. and
had been taken so long that the manometer, filled with hydrogen, could
indicate pressures from about 60 to about 190 atmospheres. The upper
cylindrical part of the experimental tube for the investigation of the
') In consideration of the cireumstance that with these tubes observations have
been made which will form the subject of following papers, we shall give already
here for the sake of simplicity some data on stem calibration, together with some
remarks on the way in which the further data about these tubes are obtained.
2) These Proe. Il June 24, 1899, p. 29.
*) See plate I, fig. 4 of that Comm.
ae
( 533 )
mixtures was originally long 50 em. and divided in mm.’s, had an
inner bore of about 2.6 mm., an outer bore of about 7 mm.
The relation of the bores of the graduated parts of the manometer
tube and the experimental tube at different places was determined
by repeatedly moving a mereury column of about 10 em. length
over 5em. and then measuring its length. To effect this the manometer
tube was placed in a horizontal position and the places of the ends
of the merenry column were read with an eye-glass. We avoided
parallax by taking care that the nearest graduation on the g@lass
should be seen to cover its image on the mercury. For the wider
experimental tube this method could not be used owing to the
change of form of the mercury meniscus at the ends of the column
in consequence of gravitation. Therefore the experimental tube was
provided with a glass cock to which a narrow glass capillary had
been connected. From tlis the air escaped only slowly under the
excess of pressure of LO em. mercury. Then the tube was placed
vertically after a mercury column of the length mentioned had
been admitted. The latter could each time easily be moved over 5
em. and the position of the ends read.
Then a longer mereury column was admitted into the tube in order
to derive the mean bore from its weight. The bore of the above
mentioned tube under the great reservoir (/,), and also the volume of
the reservoir were then determined by weighing the mercury.
§ 3. As an instance of the process of the calibrations and the
(EA sth HE.
= ne |
MM j L hy
ee | 4
+ 6.90 1.40 | 10.11
9.96 | 41.33 | 0.04
14.989 | 44.31 | 10.09
198 | 11.30 | 40.01 |
4.76 | 11.30 | 0.01 |
1121S —0.11
|
t {
30.08 | 44.31 | +0.02
35.028 | 14.25 —0.04
39.90 | 11.20 —0.09
4h 29
mean: 11.29
( 534 )
ealeulations the data about the manometer will be given. The gia-
duated tube has been calibrated twice, in 1901 (1) and in 1902 (B).
I shall give here the data and the caleulations concerning cali-
bration B. Calibration A has been made in entirely the same way ;
the results of it will be given at the end of this paper and compared with
those of £B. Table I shows the results of the calibrations with the
mercury column; column .J/ contains the means, / the length of
the mereury thread, 4 the difference from the mean length. The
temperature could be considered as having remained constant.
T A Bia i aie
Ends of the mercury column:
Ist position: 3.795 49.98° temp. 20.7 |
2d » 30.35 in the graduated stem,... 9.25 mm. above
the division of the
thin capillary e, ; » 20.65
3d » 2.80 49.00 »- 20:0
Weight of the mercury (in vacuo): 3.3777 gr.
Caleulation :
Let » be the bore of the tube at an arbitrary place, indicated by
the coordinate xv (from O to 50). We may put:
=s, +d
where s, is a particular, normal, bore.
s
The volume between the 2 divisions p and gq will be:
q q q
Ve oa [ de =) (s, + d) dx = s, (q — p) + fa ds ./-.e
> P p
The length of the mercury column :
q—p=m+A4
if = the mean length (comp. table I). If 1, represents the volume
of the mereury column then :
q
Ve 38,m+ 5,4 +f the
P
We may choose s, so that :
Mk, == HA
then :
4 q
] .
A= ——fd.de= — { d’. da
ne e
p p
: d ;
| ia men If we knew the form of the function ¢', we might derive
( 535 )
a number of equations from table 1 to determine the coefficients
occurring there. Although the form of that function is unknown, yet
d' for wv between 0 and / must be representable by a series of Fourrer.
It may now be asked whether it is possible within the limits of the
accuracy given by the observations, to represent « by some terms
of a series of Fourmr. Therefore | have put :
Er din Pe Sax
d' = a’, cos + a', cos ee + a’, cos 7
/
where / is the length of the tube:
The term «@, is omitted, because, in connection with the cireum-
stance that 4 represents the difference between the length of the
mereury column and the mean length, we could expect beforehand
that it would become small.
qY
For —A4—{f{d.dev we then find, if we bear in mind that
P
q¢—p=m-+A, where A may be put small:
eet ee EL 4 x q+t+p
Ne ay | “a sim oT m + ZL eos ry, m) cos or
l bs 4 2m ¢ )
+ a’, = sin cs m + A cos ae m | COs : a (2)
A 3m 3a q+p
fa 5 f= sin Py m + A cos 3 sie COS 73 tion .
For the case under. consideration /= 50, m— 11.29, so that if
as in table I we put: — = ee
ae ol | iad Oy ea de
= A — tt, 11.05 + U.94 A | COS ie M
‘tee are eee
es }Lo.3i SE OREO AA | COS 7 M i + AS (lem
M.
3
cere | 9.28 + 0.48 A cos =
The data of table 1 now lead to the equations combined in table
Il: first I have derived from table I the values of L for M—= 10,
15 etc., as this offers some advantage in the calculations (the value
L with 176.90 is kept, as it did not seem advisable to me to
extrapolate as far as J/ — 5).
Giapic
TABLE IIL. TABLE II),
ede = 10.13 a 6.76 a’, + 2.49 a, SAAB
— 0.04 = 8.97 a, + 3.07 a', — 2.744, + 0.00 B',
en 6.510', == 03.07 ai, 2 8.esey — 6.248,
eae 3.264. 8.40 a, ee ae + 0.00 8,
— 0.01 — 0.00 a, — 10.38 a’, + 0.00 a, + 6.24 0’,
— 0.02 = — 3.19a',— 8.41 a’, + 7.9240, + 0.00 8,
Age GAT, — “805 a, eee — 6.25 8,
4909 = —" 8.88 o', + -3.04e, oa.) 4 ee
0.115 — — 10.420', + 8.330, — 5 42a, ee oe
By means of the method of least squares '), we find the normal
equations combined in table IV.
TABLE IV. TABLE IVé.
475.8 a, 17.920’, — 180.65 a', 4+ 3.8284—0 | = iegee
— 17.92a',+ 401.4 a',— 28.31¢,—0.6606=—0 | —60.338,
— 130.650’, — 28.31a', + 319.0 a’, + 0.0882=—0 | — 21.028,
[= 13.310',— 60330, —21.020'. ae0.69 00s. oe
These equations yield:
{ 4
a’, = — 0.00908 , |
a, == <-0,000964, 0) Be eae ee
a’, = — 0.00391 . j
sy means of the equation (8) we can now calculate the values of
£ for the different values of J/ in order to judge whether they
agree sufficiently with the values given by the experiment. Then in
the second number we may assign to 4 the values of table I, and
so use the coefficients given in table III, as these terms have little
influence on the result. It now appeared that it was advantageous
') Although each of the equations (3) contains 2 quantities deduced from obser-
vation, I have not applied here the method described in Supplement N° 4 to the
Communications from the Phys. Lab. of Leiden, These Proc. V Sept. 27, 1902 p.
236 on the reduction of equations of observations containing more than one measured
quantity, because M in comparison with /, may he supposed to be accurately known,
< pia
to add a fourth term to the equation (3), viz. one that contained the
72 OSE : - :
factor sin irr M. Independent of this, I had arrived at the same
conclusion in the ealeulation of the calibration A. Therefore | put :
27x Be a7 5a
d' =a’, cos = +a’, cox = + a’, cos + Be sin =... (5)
so that we had to add to the second member of (2) :
+ U', = sin > m + QJ cos = m | sin aa — (2b)
and to the second member of (3):
+ h', {6.24 — 0.20 A| sin = Pee oe ty a as (30)
To the equations of table III] we had to add the terms combined
in table III/, to those of table IV to the first members the terms
given in table 1V/, and also the fourth equation given there. These
equations gave :
a’, = — 9.00915
a,—= 9.000796 |
(0)
a’, = — 0.00402 |
b', = — 0.001048
By means of these we have derived from the equation (3) with
the supplementary term (3/) the values for 4 for the different values
of J/. The results are given in table V under the heading 4,, while
column 4, shows the observed values, and the last column contains
ee bo ia.
i :
vf en Pea.
| | ———
6.90 | +0403 | + 0.11 | — 0.007 |
10 + 0.069 | + 0.04 | + 0.029
15 40.0200 40.02 | 0.000 |
20 aa 0 O06 os 0.04 — (). 004
25 -O0S | +001 | + 0.005
30 | + 0.007 | +0.02 |. — 0.018
3 | — 0.0988 | —0.04 | 40.012 |
| 40 Be e073 | 0.09 + 0 017 |
| 45 — 0.117 — 0.445 — 0.002
Assis®)
the differences. From this we derive for the probable error: 0.009,
which with regard to the accuracy is permissible, so that the
equation (5) with the coefficients (6) well represents our observations.
From equation (1) follows for the volume between the divisions
O and Q:
ay
Vow, Jo fe an x
0
where Q’—Q+¢q and
Q
hs Os Oa QO 1a Oa da Q
=) d' da —| a'.sinan— 4+ —sinQ@n— + 38x on
=| {f Ls 2 es yee pee
0
Table VI gives for the values for @ from O to 50 the values
computed in this way for Q', the reduced readings. By means of
this table we may inter alia judge of the irregularity of the tube.
T A.B deck ae :
| oe eee 2, | Qo '\ g | Q | qa |
|
| 0 | 0.000 |} 47 | 16.878 || 34 | 33.864 |
| 1 | 0987 |) 48 | 47.978 || 35. | 34.866 —
| 2) 1.975 | 49 | 18.878 || 36 | 35.869
| |
| 3 | 9.968 | 20 | 49.878 |] 37 | 36.879
| |
# | 3.950 || 21 | 20.877 || 38 | 97.877
| |
5 4.938 || 22 |} 24.877 || 39 | 38.882
93 | 99 975° || 40 | 30.888 |
93.874 || 44 | 40.895
8 | 7.908
|
95 | 94.872 || 42 | 44.903
7] & 900 26. -| 2b 870e 43 42,911
10 | 9893 |] 97 | 96.868 |] 44 | 43.9905 |
—
_
_
—
—
0.888 || 28 | 27.867 || 45 | 44.931
|
| |
884 || 29 | 98.865 |] 46
—=
bo
—=
AS .9A2Q
|
13 | 42.881 || 30 | 99.864 || 47 | 46.954
14 | 43.879 || 31 | 30.863 || 48 | 47.966
15 | 14.878 S24 Bisab3 49
46 | 15.878 33 32.863 50
|
|
48 980
AY. 9938
The data of table I] enable us now to determine the normal bore s,.
By means of table VI we find for the reduced length of the mercury
column at 20°.6 C. the values :
46.232 cm.
46.215 em.
mean: 46.223° cm.
Hence at 20° C.: s, = 0.0053948 em’.
From the data of table Il we may also derive the volume of the
widened part (, (lig. 4 of Comm. N° 50). The bore of the capillary
e, Was measured with a microscope by comparison with a fine
graduation on glass by means of a micrometer eyepiece. The bore is :
0.000301 cm’*. We then find for the volume of the part d, between
the division 50 on the graduated stem and the mark on the capillary
at 20° C.: 0.14239 ce.
Using the value found for s,, we may derive from table VI the
volumes J’,& between the division 0 and the division Q, and then,
using the volume found for the widened upper part, the volumes
from division @ to the mark on the narrow capillary.
The calibration A has been made and reduced in entirely the
same way. The results of either are combined in a table which
indicates the volume for each centimeter division Q from O to 50.
Table VII is an extract from that table.
1p Ae ER — Vil.
« | a ee ee of, diff.
0 0.44161 04209 | O11
5 0.38487 G5) 8.45
10 | 0.35800 | 0.35872 | 0.20
15 | 0.33195 0.33183 | 0.47
| 20. 0.30441 0.30485 | 0.14
2 | 0.97731 0.27791 0.2
30 0.25028 0.25098 0.28
35 | 0.99357 0). 22400 0.19
40 0.19673 0.196905 | 0.09
45 | 0.46988 | 0.16970 | 0.19 |
50 0.44189 0.14939 | 0.35 |
Column V4 contains the volumes from the mark on the narrow
capillary to the division Q at 20°C., as resulting from the calibration
A, Vp as resulting from the calibration 4. The last column shows
the percentage differences. The mean percentage difference between
V4 and Vz in the complete table amounts to 0.19 °/,, for the part
from 0 to 41 inclusive, which only was used in the following
observations: 0.17°/,. For our purpose this agreement is sufficient.
From the fact that ]'z
accuracy might be iunproved by more determinations of s, and of
}"4 is always positive it follows that the
the volume in the widened upper part. I hope to revert again to
this subject in a following paper.
§ 4. To determine the capacity of the reservoir a, with 4, (see
fig. 4 l.c.) and also the bore of the part /,, the manometertube,
which at the end e, was provided with a cock with a fine point,
was exhausted by the mercury vacuumpump and then filled with
mercury in a reversed position until the mereury stood above at
7, (in the drawing below). A quantity of mercury was drawn
off twice and weighed so that we could determine the bore of /,
at different places. The level of the mercury in the tube was read
by means of a cathetometer. Then so much mereury was drawn off
that the mercury still stood in the graduated stem ¢,, and this was
weighed. This served) to determine the capacity of a, -+ 6,. The
following results were obtained: the portion 7, is divided into milli-
meters, the centimeterdivisions are marked from 0 to 6, O being
nearest to a,. It appeared that the bore could not be put constant;
I have put:
a7 1 aa a
and found :
a== 0.00585 7 %s;.== O3504 (emer
so. that
V,2— 0.3564 i + 0.0029 Q | Q.
Table VIIL (p. 541) contains the volumes from the division O to
the division Q at 20°C.
For the caleulation of the volumes of the menisci I have used
SCHALKWIJk’s table occurring in Comm. N°. 67°). For the volume
between the division O on 7, and the division O on ec, I found at
20° ©. : 25.024 ce. |
In the calibration of an experimental tube it will in general be
1) These Proc. III Jan. 27, 1901, p. 488.
( 544 )
TABLE VIII.
| Q V9
| 4 | 0 3574 |
5
| 9 0O 7 169
|
4 | 1.440 |
| ’
5 {8078 |
G6 | 2.4756 |
necessary to take into account an electromagnetic stirrer, consisting
of a soft iron rod in glass. in my case it consisted of a cylindrical
portion with two bulbs at either end. The bores were measured
with a micrometer screw, the length with a pair of sliding compasses.
Each time when the experimental tube had to be refilled with a new
quantity of gas, it had to be opened at the top in order to be
cleaned. Because the stirrer had to be brought in, it was not possible
to seal on a thin capillary as had been done for the manometer
tube. Nor could the stirrer be placed into it beforehand, as this would
be a hindrance in the cleaning and especially in the calibration with
mercury. The volume of the top portion was determined each time
after the measurements by cutting off so much from the top that on
that piece one division at least was well visible (the upper divisions
over a length of about 5 mm. were lost in the sealing). The fracture
was ground flat, the piece after being cleaned and dried was entirely
filled with mereury and the superfluous mercury was removed by
sliding a properly cleaned flat piece of glass over the ground off
end. The mercury was weighed, the position of the ground end
was observed with regard to the divisions of the tube with a cathe-
tometer and from this the volume of the top portion was derived.
Physics. — ‘‘J/sothermals of mixtures of oxygen and carbon diovide.
Il. The preparation of the mictures and the compressibility
at small densities.” By W. H. Kersom. Communication N°. 88,
continued, from the Physical Laboratory at Leiden, by Prof.
H. KAMERLINGH ONNEs.
(Communicated in the meeting of September 26, 1903).
§ 1. In this paper I shall deseribe the preparation of the mix-
tures of accurately known Composition in the mixing apparatus
( 542 )
deseribed by Kamertincu OnNneS and HynpMman, the determination
of the compressibility of carbon dioxide and some mixtures of earbon
dioxide and oxygen at ordinary pressures, together with the results.
§ 2. The substances. To obtain the carbon dioxide I used the
method followed in the Physical Laboratory at Leiden‘), which
together with the improvements made in the last years will be
described in a paper on the apparatus and methods used in the
Cryogenic Laboratory.
The purity of the carbon dioxide thus obtained appears from the
increase of the pressure at the condensation at 25°.5 C. which amounts
to only 0.07 atm.
The oxygen was prepared from potassium permanganate in the
way described in Comm. N°. 78, These Proc. IV, April 1902, p. 768.
§ 3. The preparation of the mirtures, the determination of the com-
position and the compressibility of the mirtures at ordinary pressures.
For the preparation of the mixtures I had at my disposal the appa-
ratus described in Comm. N°. 84, These Proc. V, March 19038, § 21. As
the operations required for the preparation of a mixture of accurately
known composition are deseribed there, I need not enlarge here on
the details of this subject. [ shall only mention that the apparatus was
connected by means of the cock 7, (see plate Il of that paper) to
the apparatus for the preparation of oxygen, by means of cock 7,
to the carbon dioxide reservoir, before which there was a drying
tube filled with phosphorous pentoxide, and also to the experimental
tube that had to be filled. After the mixture had been prepared, I
have investigated in the volumenometer /’ the deviation from the law
of Boye, in order to be able to express the volumes of my mixture
at high pressures in terms of the theoretical normal volume. Although
cae 1
for my investigation an accuracy of TI would have been sufficient,
| have gone a little further because in itself the knowledge of the
deviations from the law of BoyLr at ordinary pressures is important and
the apparatus without difficulty admits of a higher degree of accu-
racy. Taking all possible precautions an accuracy of ——— might
Y © T0000
. . 1
be reached. Yet I was satisfied with an accuracy of ———. To judge
“ , 5000 te
of this the following may serve :
') Comp. among others Kurnen, Arch. Néerl. t. XXVI, p. 3 and VerscHarreLt
Aittingsversl. Juni ‘95, Comm. N°, 18, Leiden.
( 543 )
Measurement of the volume :
In order to judge of the accuracy we shall proceed as if we
had to consider a quantity of gas measured in the first large bulb
kh,, above (see |. e. plate IH fig. 1). There the relative error is
largest as the small bulb 4, above is only used for auxiliary
measurements. The cathetometer used certainly reads well at 0.04 mm. ;
let the error be 0.02 mm. With a bore of 44, of about 200 mm,
F ae anes . We 95 Reese, ees
this gives an error of 4 mm’; on 250 ce. : 60000°
The height of the mercury meniscus read in the volumenometer was on
an average 0.140 em. I have supposed that the volume of the mercury
3
meniscus is found by multiplying the bore by 7 of the height. The
mean height undoubtedly lies between the half and the whole height (ef.
ScHALKWUK Comm. N°. 67, These Proe. IIT Jan. 1901 p. 488), so that the
; i aon : 1
error is certainly smaller than LT of the height, say ae Hence this
; 1
gives qg X10 mm.=—018 mm., on the volume an error of
36 mm* or ———. In order to reach an accuracy of
10000
more detailed investigation of the volumes of the mercury menisci
at this radius (7.8 mm.) would be required, in the way as SCHALKWIJK
le. has done for radii from 0.5 to 4 mm.
The variation of the volume due to temperature can accurately
be accounted for.
Variation of volume owing to difference of pressure in and outside
the volumenometer: ;
If we avail ourselves of the circumstance that the thickness of the
wall is small as compared with the radius, a calculation applied to
each bulb individually gives:
SV 31—u(pi—pe) Kk
Vi abe des ihe -
a
1
or for our case, putting: # = 6500 K.G./mm.’, uw = GT? with | ieee
mm., d=.0.5 mm.::
dV
SSeS 0.00000177 (p;i—pe)
if pi and p, are expressed in centimeters of mercury; so that for
JV 1 3 ; ; ; j
——=--———. For this a correction is applied
= =— ot. €M.: = 7
ae Be “= = 79000
( 544 )
hence the error of the correction owing to the coefficient not being
precisely known, may be neglected.
The volume in Lb above Lh,,,
by means of mercury, may be determined with sufficient accuracy
which could not be determined
volumenometrically, as we have to do with proportions of much
larger volumes.
Measurement of the pressure:
In most cases if will be possible to follow the rule of making
the adjustment of the mercury in the volumenometer at a mark so
that the pressure of the gas above if is not less than 0.5 atm. For
a measurement of the pressure 4 cathetometer readings are required;
let us put for the probable error of the result: 2><0.02—0.04 mm.;
this is on 40 em. : wate Only at the volumenometrical determina-
tion of the relation of //, and what is above it to 44, the pressure
was smaller, but this relation, being, as it has been said, only used
as an auxiliary quantity, need not be so accurately known. The
same may be said of the measurement of the remainder of the first
gas in /, after as much gas as possible has been transferred to
the mixing vessel /.
Although / had been accurately vertically mounted, so that the
mereury menisci of both “4,, and “£4, could be seen sharply without
altering the focusing of the cathetometer telescope, it yet appeared
that the windows “Lh, were not exactly vertical, but that they all
deviated from this position in the same direction at an angle estimated
at 0.2° by means of a level fastened at right angles to a flat piece
of steel. Therefore as the windows are not placed perpendicularly
to the line of vision of the cathetometer telescope, refraction occurs,
which causes an apparent displacement of the mercury meniscus of
n—l
ast:
cm., @d being the distance from the meniscus to the window,
n f
7 the angle of the normal on the window and the horizon, n the
refractive index of water. In our case (d= 8.6 em., n = 1.33) this
: ote 1
displacement amounts to: 0.0075 cm. This gives on > atmosphere an
eo ; te
error of aaa As we have to do with relations of quantities to each
0
of which a correction in the same sense would have to be applied,
the error in the result is smaller. If a higher degree of accuracy
is wanted, the angle formed by the windows and the vertical will
have to be determined more accurately, so that the correction may
be applied. For our purpose this was not necessary.
( 545 )
Correction for the temperature of the mercury :
[f the pressure amounts to say 0.5 atm., measured as the difference of
two mercury columns of 76 and 38 cm. respectively, the temperature of
the long column must be known precisely to within 0°.5, ifan accuracy
1
of .>=——
5000
mereury columns together with the thermometers are packed in wool.
The difference between the indications of the thermometer at the
lower end and at the upper end of the barometer Sar. did not as
is required. We must assume that this is possible if the
a rule amount to more than 0°.5 C., hence we may accept that the
uncertainty caused by this in the knowledge of the temperature did
not exceed by much 07.25 C. For the difference of the temperature
of the mercury in J/ and # a correction is applied.
The capillary depressions are largest in the volumenometer, and
of the order of say 0.07 mm. The uncertainty here is surely much
smaller than the errors resulting from the windows not being vertical.
Corrections for the difference in level between the meniscus in
Bar below, and in-J/, and also those for the reduction of the pres-
sure immediately above the mercury in / to the mean pressure of
the gas above it, may be applied with sufficient accuracy.
Measurement of the temperature :
During the time of one measurement (25 minutes) the temperature
by means of a thermostat of ScHALKWIJK*) can certainly be kept
constant at O0°.03 C., while if the water at constant temperature
flows rapidly enough through /, the temperatures at the lower and
at the upper end did not differ more. The temperature was read on
a thermometer 7/ connected with the stirrer Hr, which therefore
could be placed in different positions.. The thermometer was
graduated in 0°.05, so that O°.01 could be easily read; it has
heen repeatedly compared with a standardthermometer tested at
the Reichsanstalt. As therefore the error in the measurement of
temperature does not amount to 0°.038 C., the accuracy is certainly
0.03 : i
OY 300 = 10000
A portion of the volume (in the tubes Hbg, and Hby,, which
have an inner bore of 1.2 mm.) is not enclosed in the jacket. This
volume is a little less than 1 ce. For its temperature which is put
equal to the temperature of J/ a correction is applied. If in a
measurement in the first bulb £4, we assume that in the temperature
of that portion there is an error of 5°, the error in the mean
1) Comp. Comm. N°. 70, These Proc. IV May 25, 1901, p. 29.
. Date: 7 Feb. 703.
Time : 12.56. Nee |
Temp. bath ; 20.07. | |
69.500
69.373.
Mercury level in //,: Top 2-5
Mark 4 on fy,...... | 2.8 | 69. 405
OES sey a, RE: | 2.8 69.504
88586 ‘A
2.0 88 426
Manometer J: Top.....
ap peas
bo
_ Temp. J: 15.6.
Barometer Bar, :
Upper men.: Top... 3.2 78.372
Basis... 3.0 78 266
Lower men.: Top.... 2.2 — 0.5 + 0.052 —
ihe BasiSins ioe 2.2 | — 0.6 + 0.04
- Temp. Bar. below: 14.4 3
—_ above : 15.3
z can Lower men.: Basis. . | 9. ip ple les + 0.042
i Hope iw 1.5 | —0:5 + 0.0%
i Upper men. : Basis... V7 78.262
te ; thy SERB) eae ores 2.2 78.370
Manometer WV:
Temp.: 15.4.
Basin +. eae aewine 1.0 88. 420
POD tise cease ites 0.8 88.577
Mercury level in 2, : . ‘.
Mage-d tice eee or we ye
de em ee 22 69.400
Basis is ve fc hes 2.3 69.368 |
Le Re ae? | 2.3 69.494
Temp. bath: 20,08,
Time: 1.22.
a's ere
( 547 )
temperature of the whole becomes 0°.02 and may be disregarded,
especially in consideration of the fact that the difference in tempe-
rature between the jacket and the surrounding atmosphere as a
rile is less than 5° and therefore the error made will certainly be
smaller.
Hence only in very unfavourable cases the error in the result
5000” and we may expect that in most cases
the error will not exceed this amount.
will be larger than
To judge of the course of a measurement | have given in table [X
(p. 446) the experimental figures of an adjustement for the determi-
nation of the deviation from the law of Boyne of the mixture of
0.2 oxygen with O.8 carbon dioxide. Column Af contains the readings
of the level (see Comm. N°.60 These Proc. HI Sept. 29, 1900 p. 312),
/ the readings of the cathetometer.
The volumenometer had beforehand been calibrated with mereury
by Dr. C. Zakrzewski. Hence we knew at the same temperature the
volumes of the bulbs /,, measured between the middle marks on
the glass screens £y, and also the bores £b,, /b,, Eb,, Eb, Eb,
In the apparatus used the mercury could not be read while it stood
in £h,, because owing to a former manipulation in the blow-pipe the
hore at that place was not perfectly cylindrical. There the sum of
the volumes of the two neighbouring bulbs had been measured.
To test this and also to determine the volume of 44, with what
lies above it I have determined volumenometrically the relation of
the different volumes with dry air free from carbon dioxide. To
account for the deviation from the law of BoyLe I could make use
of coefficients of KAMERLINGH ONNES’') series:
Ba y
pra = oF es a ss a a == F =* es.
A A A A A
put kindly at my disposal, which accurately represent to within
0.2°/, the conduct of air as indicated by Amacar’s experiments. The
three first coefficients are for 20° C:
. 7 — 1.0738
Bsa = — 0.40495 x 10-3
C4. = o> OR(oox re":
We find for the relation of the volumes J’, and J, which are
filled with the same quantity of gas at the same temperature to
pressures p, and p, to the first approximation:
1) Gomm. N°. 71. These Proc. If June 29, 1901, p. 125.
: 36
Proceedings Royal Acad. Amsterdam. Vol, VL.
( 548 )
B.
Plt Epa, . eos ees
Ke Pi a
if p, and p, are expressed in atmospheres (0° C, 45° northern latitude).
A second approximation where the coefficient Cy would occur is
not necessary with a view to the accuracy required.
TABLE Xa. TABLE XA.
A Bel C BE |
A eS | ; 5 |
V, 5.01 El, | 0.00A085 |
| is
€. 18913 | 1.8910 _ 0.016 ib, 0.000675 |
: eae 0.000314
Vi 20e Os yee)
pe 1.9396 1.9400 | + 0.622 Bb, 0.000165 |
rs | I De |
Ys |4,9499 | 4.94205 | -— 0.072 ee ee
7, |
Table X shows the results of the calibration. There we have
called: V, the volume above /b,,, V, the one above b,, V, the
lib, «ete.
the volumes according to the mercury calibration, 5 according to
the
Column
one above Column A of table Xw gives the relations of
volumenometrical determination, C' the percentage differences.
I} of table X4 eives the relation of the volume of 1 mim.
of the indicated bore to the entire volume above it. It may be seen
that
following caleulations the mercury calibration has been adopted as
the agreement between the two calibrations is sufficient. In
being the more accurate.
For the calculation of the composition we derive from the meas-
the
(oxygen in carbon dioxide) are combined in table XL. A contains the
urements in volumenometerdata, as those for the mixture 0.2
data of the oxygen in the volumenometer, 5 refers to the oxygen
which has remained in /’ after the transference of the greater part
into FF’, C' veters to the carbon dioxide.
T2A=B G3.
A B C
Volume ..
Pressure..
‘Temperature
0.99979 /,
4) 396
19.81
0.98905 Vy
0.380
0.99994 V,
66.961 |
19.83
( 549 )
First of all we may derive from / the pressure which the remainder
of the oxygen would have exerted in the volume 0.99979 J, and
at a temperature of 19°.81 C. In this calculation the law of Borie
may be applied with sufficient accuracy. We then find: 0.022 em.
The pressure which the quantity of oxygen transferred to the mixture
would exert in the volume 0.99979 V7,, at 19°.81 C. is then represented
with sufficient accuracy by :
40.396 — 0.022 — 40.374 em.
The pressures of the oxygen and the carbon dioxide may be reduced
to the same temperature 19°.82 C., by deriving coefficients of pressure
variation from the series gives in Comm. N°. 71, or by means of
the value for oxygen 0.005674 found directly by Jonny, and the
value 0.003711 which follows from Crapruis’ data (Trav. et Mém.
du Bureau International des Poids et Mesures. t. I] p. 124) for the
“real” coefficient of pressure variation of carbon dioxide at 20° ©.
and an initial pressure of 1 atmosphere ‘).
We find for the oxygen: 40.575, for the carbon dioxide ; 66.959 em.
If p,, VV are the pressure and the volume of the first gas, p,, V,
of the second, it may be easily found that the number of molecules
of the first gas is proportional to:
pi V
By,
ae
1
Sas Py
that of the seeond to:
1 =f: arte Lh 4
ye
Where, at least with regard to the denominators, p, and p, are
expressed in atmospheres. We find from the data of Comm. N°. 71,
These Proc. Lil June 29, 1901 p. 130 and 132:
for oxygen :
V9) oe 1.074237
Bye ae io: 10-2.
1) We shall not consider here the variation of the coefficient of pressure-variation
with the initial pressure: this variation would be for a difference of 50 em. in
the initial pressure according to Cuapputs, | c¢., 0.000034, which with a reduction
of the pressure for 1° difference of temperature would give an error of only
sana: Keeping in view the fact that such large differences in the temperature
30000
do not occur, this may be neglected.
For earbon dioxide we may use the value derived directly from
observation which will be given later :
B Avg
=
Ay
These values may also be taken with sufficient accuracy for the
== =—— 0.00507n:
iemperature used (19°.82 C.). The composition of the mixtiure considered
is easily found to be: 0.19942 (oxygen in carbon dioxide).
§ 4. In the volumenometer | have determined the compressibility
at ordinary pressures as indicated in Comm. N’. 84, These Proc. V
March 28, 1903, p. 641, for the mixtures with molecular proportions
of 0.1994 and 0.3072 (oxygen in carbon dioxide), and also that for
the pure carbon dioxide. Although this has already been done by
Reenactt?), AMmaAGat?), Fucus*), Lepuc*) and lately by CHapptis’*) it
seemed to me important to make that determination with the same
earbon dioxide and in the same apparatus as for the mixtures, so
as to have the most favourable circumstances for the comparison of
the conduet of the mixtures with that of pure carbon dioxide.
Table XII gives the values directly derived from the observations
for volume, pressure and temperature belonging to each other. The
columns A. B and C refer to different adjustments with the same
quantity of gas. .
Tk Bo a heen
a. Carbon dioxide.
A B | C
Volume .:... 0.99969 V, | 0.99995 V, | 0.99958 VY,
Pressure... .. 47 264 Dx. 662 | 443.397 cm.
Temperature | 19.99 20.02 |. 49.97
4. Mixture with molecular proportion : ie = 0.1994.
dA B
| = ea SR a |
Volume..... | 1.00088 ¥, | 0.99934 7,
|
Pressure .... 97.708 |} 51.8178 cm.
|
|
‘Temperature 20.08 19.96
1) Mém. de Inst. de France. t. XXL, p. 329.
2) Ann, de Chim. et de phys. (4) t. 29, p. 246, 1873.
%) Wied. Ann. Bd. 35, p. 430, 1888.
4) Recherches sur les Gaz, p. S6.
5) Tray. eb Mem. du Bureau Internat, des Poids et Mesures, t. XII, 1908,
ce. Mixture with moleeular proportion : a = 0.5072.
} : A B oy
Volume..... 0.99975 ¥, | 0.99983 1, | 0.99972 F,
|
Pressure... .. 48 188 a9. 839 | 445.752 em.
| Temperature | 20.410 20.414 20.44
As an instance for the calculation we shall consider the last
mixture more in detail. First the pressures were reduced to. the
mean temperature 20°.15 C., by means of the “veal” coefficient of
poe ke Op oe .
pressure variation = (5) at 20°: 0.0034.7). This gave for A, B,
Pp O7
C, 48.193, 59.837 and 115.748 cm. respectively. If p,. V, and p,,
I", respectively represent a corresponding pressure and volume,
we have to the first approximation, which for our case is sufficient :
1 Ps. E, ro Bs
ae 7 ea ee ee Wee hk sy ay
A
Where p, and p, are expressed in atmospheres. From this we may
derive se In the cease considered we found:
ay
from A with C: aes = — 0.0035795
A,
pee et ln — 0.003407
mean: — 0.003493 at 20.13 C.
In the same way for carbon dioxide at 20°.00 C. :
from A with DB: es a
A’
Or: are ke Se — 0.005536
mean y = 0.005675,
and for the mixture 0.2 at 20°.00 C.:
Ba .
— = = — 0.003847.
AY
If the coefficient of pressure variation were known (mean coetti-
cient between O and 20°) we could easily derive 4, for the
different cases. For if for the mixture 0.3 at ¢= 20.13 in the equation:
1) Comp. p. 553.
B
PvaA = Ay + ar a . . . . . . . . (3)
we put v4 = 1, we obtain:
1+a,. 20,138 = A, + Ba,
if «, is the corresponding coefficient of pressure variation,
From the two relations between A4 and by, 44 may be derived
and then Ay, may be found from the relation’):
Ae AA. lea 0.0036625t) . «it 4 Tet, Seen
A difficulty arises from the uncertainty of @, for the mixtures :
an error in @, passes over into Ay, 20 times magnified. This may
be avoided in the following manner:
As normal temperature we shall temporarily adopt 20° C., and
then we write KAMERLINGH ONNES’ equation for the area of the
pressures considered here:
pV = Vins (ne a 2 oi af
V is the volume really occupied by the gas, V.y,, the normal
volume at 20° C., viz. the volume occupied by the quantity of gas
considered at 20° C. and 1 atmosphere
Now:
F ee 0.0086625 ; |
Ax = Axky ae eS ff
; eat 1B 1 + 20 X 0.0036625 |
AK,, }! + 0.004125 (20) i. +, a
A comparison with
Ba Vn
Ma Fi remetee| A VAG ae a
/ 4 | « ' V ( )
where J’y is the normal volume at O° C., gives the relations:
Ad» Vi == Age clas 8
Ba V3, = Bie are eee (©)
whence:
By BK
{2 == rE e ° . * e e . (9)
ne! : K
Hence it is given that for the mixture 0.3 at 20°.13C.:
Br
r — — 0:003498.
G K
From (5) follows, putting ¢— 20°.13 and V= Vy,:
1) Comp. Comm. N'. 71, These Proc. III June 29, 1901, p. 180.
1 +018 apx = Ax + Bx.
«kK represents the coefficient of pressure-variation of the mixture
)
he mean coefficient between 20° and 7), if the original pressure (at
20° C.) is 1 atm. From these two relations A, may be derived; it
must be remarked that now an error in @q passes over diminished
into the result. By means of (6) Ax, may be derived from Ax.
So 1 found for the mixture under consideration :
fore20". 15.0.2: AR 1.003969 , Ber = —.0.009521:
Further | accepted for a,x: 0.005445, found by linear interpolation
according to wv between the value 0.008454 for carbon dioxide derived
from Craprcis’ data, and the value 0.005423 for oxygen derived
from Joniy’s data. It then follows that Ax,, = 1.008524.
The different values thus found are combined in Table XIII.
T A Bol, BRUT
| ee ON Se | Weight. |
are rs |
Carbon dioxide | 1.00574 | 0 1 |
| 9
Mixture 0.2 | 4.00388 | 0.1994 | =
» 0.3 | 4.00352} 0.3072 ei
Oxygen | 4.00064 | 14
—
For oxygen Ax,, is derived from the data for Ay,, and L4,, given
on p. 549.
I have put:
sAg,, = 1+ a, (1—a)? + 24,, a 1—a) + @, 2’,
and have calculated the coefficients by means of the method of least
squares. There «ras compared with »lq,, —- 1 may be considered as
perfectly accurately known. I found:
i 0.00570
a, == 9.00142
a == 0:00065:
In table XIV (p. 554) the values (' derived from them are com-
pared with the values derived directly from observation 0.
In order to derive the coefficients A4, from the coefficients <1 x,,
an accurate knowledge of the coefficient of pressure-variation is
required, In a following paper, however, will be deseribed how the
coelficients A,,, may be used to derive from the volume of a gas
Carbon dioxide) 1.00574 | 1.00570 | 4- 0.00004 |
Mixture 0.2 | 4.00388 | 1.00413 | at 95 |
|
» 0.3 | 4.00852 | 1.00340 | + 12
Oxygen 1.00064 | 4.00065 | — 4
measured at about 20° CC the theoretical normal volume of that
quantity of gas (at O° ©).
Physics. — ‘“/sothermals of imictures of ovyygen and carbon dioxide.
ITl. The determination of tsothermatls between 60 and 140
atmospheres, aud hetiseen. —15 ‘Es and +60" ede By WE.
Kresom. Communication N°. 88 (8° part) from the Physical
Laboratory at Leiden, by Prof. H. KamErnincn Ones.
(Communicated in the meeting of October 31, 1903).
§ 14. During my measurements of the isothermals of mixtures of
oxygen and carbon dioxide it appeared desirable to take several
precantions and to make some modifications in the usual methods.
They will be described here in connection with and in behalf of
following papers on the results obtained.
§ 2. The arrangement. The manometertube and the experimental
tube which beforehand had been cemented into a steel flanged tube
(comp. Comm. N°. 70 V, These Proc. IV June 29, ’01 p: 107) were
placed into steel pressure eylinders. For the shapes of these see also
Comm. N°. 43, These Proc. 1 June 25, 1898, p. Se, fie. 2a ie
arrangement as drawn there has been modified, viz. the two pressure
eylinders into whieh the aforementioned tubes were placed were
entirely filled with mercury. They communicated at their lower ends
by means of a steel tube and of a steel T-piece with each other and
with a third pressure cylinder. This was filled partly with mercury
partly with glycerine. To obtain pressure, glycerine was forced into
it by means of a ScuArrer-BepeNBerG pump. This arrangement offers
the advantage that the tubes filled with gas do not come into contact
with the glycerine, and the mercury which is forced into the tubes
only slightly with the glycerine. In this way it was very easy to
redetermine the normal volume after lifting out the experimental tube
from the pressure cylinder, while the mercury menisci in the tubes
Eee
Ee
( 555
kept good during a very long time and no or very little soil was
deposited in the tubes.
The pressure cylinders and the connecting tubes had been well
‘cleaned beforehand with benzene, which was removed by heating
while air was sucked through. The connections were tightened by
leather washers soaked in paraffin. The packing which had to prevent
leakage of mercury along the pivot of the high pressure cocks through
which the mercury passed which was to be forced into the observation
tubes, consisted of rings cut from selected Spanish corks. During the
observations the two observation cylinders were disconnected from
that. where the pressure of the glycerine was transferred to the
mercury in order to be independent of leakage that might occur in
the pump or in the glycerine lead’). A perfectly tight fit of this
enclosed portion even at the highest pressures was secured.
§ =p The measurement of the rolumes. The determination of the
normal volume was made in the same way as has been described
in Comm. N°. 70 V. These Proc. 1V June 29, 1901, p. 107 and in
Comm. N°. 78, These Proc. VI April 19, 1902, p. 761, especially the
same precautions for the constant temperature and pressure were taken.
The normal volume was determined at least twice before and
twice after the measurements. It must be recorded, however, that
this was not done with the first quantity of carbon dioxide of which
the isothermals from 25°.55 C. to 37°.09 C. were investigated, because
the experimental tube had broken, while in the case of the manometer
we may profitably substitute a direct comparison with a standard
manometer, {0 which Comparison [ shall refer later.
I found for the normal volume of the hydrogen manometer :
22 Sept. ’O2: Dsed b= Ce:
23.494
55 rs Ma HS
12’ Nov. 23.220
As the first 3 measurements are not made in the bath of constant
temperature TI have in the calculation of the mean assigned the
weight 3 to ihe last determination and have adopted J7y = 23.210% ce.
From the following the advantage of a hydrogen manometer may
appear *). Most of the determinations with the first mixture (0.1
oxygen in carbon dioxide) were made with an air manometer. During
the experiments phenomena occurred which pointed to variations of
') Small variations of pressure could then be applied by screwing slightly in
or out the pivot of one of the fine high pressure cocks in the enelosed portion.
*) Comp. Comm. N°. 50, These Proc. II June 24, 1899, p 29.
the normal volume of this manometer. The manometer was removed
from the pressure cylinder and the normal volume redetermined, and
it appeared that from 22.114 ce. (May 9 1901) it had fallen to
22.056 ce. (Aug. 23 ’02). After this the manometer has been cali-
brated for the second time (calibration /) *) and filled with hydrogen;
of each of the isothermals determined some points have been tested
by means of the hydrogen manometer. Column (€' of table XV gives
the mean relation of the pressure measured with the hydrogen mano-
meter and that measured with the air manometer, where for the
normal volume of the latter we have taken the mean between
those before and after the experiments. Column A gives the date,
B the temperature relating to the isothermal.
TABLE XV.
A B. | C
20 June ’02 17.60 4.0020
20» » 90.29 | 4.0017
aS » » 94.99 1.0016"
D4 » » 99) 68 4S 42 O23
Ua Se 23.99 \. A 0013
Yb » » 95.290 |i 1.0019
mean : 1.0018
i
|
From column C we cannot derive a regular course in this short
period, so that for these isothermals [ have multiplied all the pres-
sures measured with the air manometer by the coefficient 1.0018.
On June 5, 6 and Aug. 21 points of the border curve have
been determined. These could only be brought to harmonize with
those determined later with the hydrogen manometer by multiplying
the pressures by coefficients which are combined in the following
fable together with that afore-mentioned. Hence this shows the course
of the variation during that period.
If we compare these figures with the values for the normal volume
before and after the measurements, it appears that almost the entire
variation has taken place during this last period. From May ’O1 to
') Comp. this Comm. |. p. 534.
TABLE XVI.
5/6 June ’02 1.0021%
90/26 » 5 et OOIS8
|
|
21Aug. > | 0.9997
June °02 the manometer was but seldom used, and the pressure
during that time was low, while the pressure in the months June
Augustus “O02 was often and during a long time from 60 to 125
atmospheres. Hence it seems that this variation is much greater at a
high than at a low pressure.
A similar variation of an air manometer with the time, probably
owing to the absorption of oxygen in the mercury, has also been
noted by Kurnen and Rosson (Phil. Mag. Jan. ’02 p. 150).
In the mixtures of the molecular proportions O.1 and 0.2 of
oxygen the variations of the normal volume were less than
1000 In
those cases we have accepted for the normal volume the mean
of the values before and after the measurements.
On the other hand, in a mixture with a molecular proportion of
0.3072, which for some weeks had uninterruptedly been exposed to
high pressure, the normal volume of 72.878° cc. before the expe-
riments (15 June °03) had fallen to 70.980 cc. after the experiments
(13 Aug.). It being highly probable that the variation of the normal
volume involves a considerable variation in composition, the results
of the measurements with this mixture which with regard to the end
condensation pressures and volumes extended to —14°.7 C., will
not be given here.
This also shows how very important it is that we should be
able to determine the normal volume after the measurements *),
From the observation of the volume oceupied by the gas at a
temperature of about 20° C. and a pressure of about 1 atmosphere
we derived the volume which the gas would occuppy at 20°C. and
Tatm. (75.9467¢m. mereury at Leiden, comp. Comm. N°.70, These Proce.
IV June 29, 1901. p. 111). Use was made of the coefficient of pressure
variation given in this Comm. II, p. 553, and the law of Boyne
was applied. By multiplication by the values of the coefficients
Ax, given in table XIV p. 554 under ( we find from this the
volume which the gas would have occupied if from an infinitely
1) Comp. Comm. N®. 50. These Proc. Il June 1899, p. 29, and N°. 70. V.
‘These Proc. IV, June 29, 1901, p. 107.
(995. )
large volume at 20° C. it were reduced to a pressure of 1 atm.,
and it had followed the laws of the ideal gases. We then find the
theoretical normal volume (at 0° C.) by means of the coefficient of
pressure variation (= coefficient of dilatation) for the ideal gaseous
state. As the calculations of the correction that according to Comm.
N’. 71 (These Proc. IV June 29, 1901, p. 125) must be applied to
the coefficient of pressure variation of pure hydrogen in order to find
that coefficient for the ideal gaseous state were not finished when I
began my calculations, | have adopted for this the value 0.0036625,
which in Comm. N°. 71 was given as a first approximation. The
corrections, however, which accordingly must be applied to the
results, will certainly lie far below the degree of aceuracy which I
could attain in my experiments of the isothermals at high pressures.
After what has been said on the calibrations’), the measurement of
the normal volume and the reduction to the theoretical normal volume
[ can confine myself to a short note on the measurement of the
volumes. The top and the base of the mercury were read with an
eye-glass, parallax was avoided in the way described before (Comp.
this Comm, [ p. 553). In this manner 0.1 mm. could be read. We
assumed that the mereury meniscus in the graduated stem of the
experimental tube has the form of a spherical segment, hence by
multiplication of the bore by half the height the volume may be
found with a sufficient degree of accuracy, our method of reading
considered. When the mixtures split into two phases, the position
of the liquid meniscus was also read. Corrections were applied for
the expansion of glass due to heat and to the inner pressure.
§ 4. The measurement of the pressures. The pressures were
measured with a hydrogen manometer, ranging from 62 to 196
atmospheres *).
In the first part of this Comm. (p. 932 ff.) | have discussed the
calibration, in § 8 of this paper the determination of the normal
volume. We need only add that the hydrogen was prepared as
deseribed in Comm. N°. 27 Zittingsversl. V, Mei 1896 p. 42.
From the means of the values of J74 and Vy of the table
from which table VIL forms an extract and from the normal volume
")
!) Comp. this Comm. [, p. 532. :
*) It appeared that the manipulations of the stems of the manometer- and the
piezometer tubes in the blow-pipe, as for instance the sealing of the top of the
latter, lad to be made with special care and the tube had to be cooled very care-
fully and slowly, else tensions will rise in the glass and consequently when high
pressure is applied (in these experiments 140 atm. was reached, the manometer
has stood 195 atms. several times) the tube will burst.
given in § 3, while the volume of the narrow capillary above
between the mark and the place where if is sealed was accounted
for, a table was derived. This new table gives for each division Q the
density d4 of the hydrogen when the mercury reaches that division
at a temperature of 20° C., expressed in terms of the normal density
(O° C., 1 atm. 45° N.L.) as unity. For the values of Q between
25 and 50 the table increases by 0.5; hence also for the higher
values of the pressure (as far as Q@ = 40) the error made by
interpolating linearly is less than 1 atin.
To derive from these densities the corresponding pressures we must
1
know the isothermal of hydrogen at 20° C. Measurements of this
have been made by ScHALKWUK; they do not, however, exceed the
density 54. An extrapolation from these observations for the densities
wanted is not allowed with a view to the mean error of his determination
of the (' of the series of KAMERLINGH ONNES (cf. SCHALKWIJkK’s Thesis
for the doctorate, p. 115). Observations at higher densities have been
made by Amacar (from LOO to 3000 aims.) The isothermal for hydrogen
at 20° C. derived from AmaGart’s data:
PUA gy) = 1.07252 + 0.0007194 14 + O.000000672 4?
(cf. ScHatkwik’s Thesis for the doctorate p. 121) does not agree,
however, with that from ScHALKWIk’s) observations. From these”
for instance, follows at d4=55: pv4,, = 1.11194 (cf. 1c. p. 124),
hence p= 61.157, whereas from the isothermal given by Amacar
we derive at p= 61.157: d4 = 54.897. ScHALKWiJk’s observations
have been made very carefully especially uis determination of the
normal volume (see Comm. N°. 70, V, These Proce. 1V June 29, 1901, p.
107). If with this we compare the way in which AmaGar has determined
his normal volume (Ann. de Chimie et de Physique, t. 39, 1893, p. 83)
it seems not entirely without reason if, while waiting for more
accurate determinations of the isothermals of hydrogen at higher
densities, we make those of AMAGar agree with those of ScHALKWIJK
“Ore ‘ D4.897
by multiplying all the volumes of the former by the factor ———
v0
So we obtain:
PUAgo = 1.0705 + 0.000717 4 + 0.00000067 (1.47.
To test this we compare the value of pry,, at d4 = 1, viz. : 1.0712
resulting from it, with the value of pe4,, which follows from
the value of the coefficient of expansion according to CHaApputs :
o
]
«, = 0.0036606 *), Via: 1.0732. The difference is — , so that the
1) See Scuatkwisk, Thesis for the doctorate p. 116.
( 560 )
equation found, which deviates from AmMaAGat’s observations at higher
ee 1 ;
densities ae does not deviate from the observations at smaller
D900
densities by more than =—
i 500
The following term in the series of KAMERLINGH ONNES would be
Da : Lats E
—. If we derive a value of )4 from the data given in Comm. N°.71,
vA
These Proc. IV June 29, 1901, p. 132, for hydrogen at O°C., 15°.4C.,
99°.25 C. and 200°.25 C., we find that this term for d4—=150
would yield in pra,,: 0.0009, so that if we omit this term at the
is made. As there exists
highest pressures an error of less than 7000
already some uncertainty about the exact shape of the isothermal,
I have omitted this term.
The values prg,, calculated thus for the different values of d4 of
the table mentioned at the beginning of this section, have been added
to this table together with the values for p derived from them‘),
When the isothermal of hydrogen at the densities occurring here
will be known more accurately, the pressures given here will require
a correction for which the afore mentioned table may be useful.
The temperature of the manometer differed at most a few tenths
of a degree from 20° C. The temperature coefficients for hydrogen
at 20° C. are found from the value of Aa, (given in Comm. N°. 71)
of the series of KameruincH Onnxes and AmaGat’s values of Ba and
(4 (given in ScHALKWik’s Thesis for the doctorate, p. 120), for the
femperatures O° C., 15°.4 C. and 47°.8 C., observing the reduction
mentioned to obtain the agreement with ScHaLkwisk’s isothermal.
TABLE XVII.
“Tiere
males:
200 0.714 | 150 | 0.531 100 | 0.349 |
19) 0.677 ! 140 -| 0.494 90 "| ~0.344
|
{RO 0.640 130 0.458
170 0.608 20 | 0.499
|
160 | 0.567 |} 410 | 0.385 G0
| |
!) This table has been given in my thesis for the doctorate,
|
.
ae
( 561 )
0
Column Ge) of table XVII gives the temperature coefficients thus
ar J,
found for the different pressures p.
Also a correction was applied for the difference in level of the
mercury columns in the manometer and the experimental tube, for
the expansion of the volume of the manometer tube cansed by the
inner pressure, and for the difference in capillary depression in the
two tubes. For the latter a separate experiment has been made to
determine the depression in a tube of the same inner bore as thie
manometer tube. This correction was 0.01 atmosphere.
The manometer was read in the same way as the piezometer
- (see p. 558). The level of the mercury in the manometer tube and
the temperature of this were read before and after the reading of
the meniscus and the temperature of the experimental tube. The
temperature of the manometer could be read to within 0°.05.
After the isothermal determinations the hydrogen manometer was
compared with the standard manometers (Comm. N°.50, Proce. June 1899)
which have been very accurately compared with the open manometer
by ScwatkwukK (Comm. N°. 67, Proc. Dec. 1900 and Jan. 1901,
Comm. N°. 70, Proc. May and June 1901). To render this possible
the hydrogen manometer had been constructed so that the lowest
pressure which could be read on it could still be measured with
the standard manometer IV‘). Table XVIII gives under the heading
A the pressure as measured with the hydrogen manometer used by
me, under the heading B the same pressure measured with the
standard manometer.
TABLE XVIII.
aw | B
|
| 64.04 | 64.040
| 64.02 | 64.024
Obviously the agreement is quite satisfactory. This comparison
comes in the place of the determination of the normal volume after
the measurements, and also of more determinations of the normal
bore of the graduated stem. (Comp. p. 540). As the there mentioned
mean percentage difference 0.19 °/, is principally due to the difference
') For the way in which this comparison has been made comp. VeRscHAFFELT.
Thesis for the doctorate p. 17,
between the two determinations of the normal bore, this comparison
highly improves the accuracy of the manometer.
The thermodynamical equilibrium in the experimental tube was
reached by means of an electromagnetic stirring apparatus; to
secure the equilibrium of pressure between the experimental tube
and the manometer [| waited 5 minutes after each adjustment before
reading. Of each isothermal two series of observations were usually
made, one beginning with the lowest and ending with the highest pres-
sure, the other in reversed order. Only rarely the results of these two
differed as much as = To judge of this see table XTX, which relates
”
to the isothermal for 22°.68 C. of a mixture of O.1047 oxygen in
earbon dioxide. Here 7 represents the volume, p, and py the corre-
sponding pressures in the two series, with a constantly rising and
a constantly falling pressure respectively, 4p the difference, rji,, and
Vig. the volumes of the liquid also in the two series, 4orj,, the
difference between them.
The agreement of the pressures is satisfactory, that of the volumes
of the liquid leaves to be desired. Although this is partly explained
by the circumstance that the volume of the liquid cannot be read
so accurately because the form of the meniscus is not so sharply
determined as is the case with mercury, and parallax could not
so easily be avoided as with the mercury menisci, if yet appears
that, if we desire to investigate this subject more fully, more care should
he taken to procure equilibrium by stirrmg and waiting.
§5. The constancy and the measurement of the temperatures. The
manometer was surrounded by a jacket with flowing water kept at
constant temperature by a thermostat, as described by ScHALKWIIK
Comm. N°. 70, Proc. May ’O1) with the modification in the thermo-
regulator described in Comm. N°. 78 (Proc. April 1902 p. 762).
In jhe same way the experimental tube was kept at constant
femperature by means of a second thermostat. This differed from
the former in the following respects:
The connection between the heating bath and the mixing bath,
the mixing bath and the connection between the mixing bath and
the observation bath have been insulated more carefully by means
of wool, paper and felt; this was necessary because greater differences
of temperature with the surrounding atmosphere occur here.
To the glass portion of the thermoregulator a side-tube with a
cock is sealed on, which facilitates the admission of a quantity of
mercury from a mercury reservoir, which by means of an india
rubber tube is connected with that side-tube, into the thermoregulator
——
(563 )
TABLE XIX.
“s fr Pf Ap Tl4r rig. f Arig
0.012159 | 58.66 58.60 | +0.06
41384 60.88 60.92 —0.04
|
|
40605 | 63.27 63.31 —0.04
0.009826 | 65.7% | 65.775 | —0.03
9047 | 68.26 68.31 —0.05
|
! :
| 8269 7090 | 70.9% | —0.04
/
|
|
|
)
7489°| 73.47 73.51 —C.04
67125 76.07 76.44 —.0%
59085 78.725 de. difference in saturationvolume:
5917? 78 .75° —Q.03 bec. —0. 000009
| 546 79.95° |-79.985 | —0.03 | 0.000217 0.000180 9.000037
| 5157 | 81.26 | 81.395 | —0.43 397 ete) \h eee 6
| 708 82..88° 82.895 = O12 583 ~ 29
4379 84. 70° 84.765 —=() 0G 746 672 oo 47
4309 | 85.05 | 591
4978 | 85.22 | | | 625
4258 85.35 | 288
4243 | 85.40 95
/
4A9| 85.54 | | | 125
reve 85.54 | | | @ce. difference in saturationvolume :
| 420° 85.52 | 10.02) ee. —0. 000005
194.64 1124.36 | 40.98
‘and hence the adjustment for different temperatures*). The narrow
4
part of the glass tube where the supply of gas is regulated, has
') A similar arrangement has been described by Friepuinper, Zeitschrift
fiir physikalische Chemie, Bd. 38 p. 401, 1901.
oT
Proceedings Royal Acad. Amsterdam. Vol. VI.
fenos: *)
been eraduated in mm. over a length of 4 em., which facilitates a
finer adjustment by moving up and down the supply tube.
For temperatures higher than 85° the water streamed succes-
sively through two heating baths, each provided with a thermo-
revulator; the first brought the water to 35° C., the second to the
desired temperature. To avoid exchange of heat with the surrounding
atmosphere the last bath was coated with asbestos, except where
it came into contact with the flames.
One thermoregulator had been constructed for higher temperatures,
filled with xylene and goes as far as + 90° C., the other for lower
temperatures was filled with benzole, of which the coefficient of
expansion was determined at 0.0011 and goes from —40 to+ 40°C.
For temperatures below that of the water supply, the water
streamed between the overflow and the heating bath through a zine
vessel insulated with felt, where small pieces of ice were continually
brought in.
By leading the water back to the overtlow after it has flown
through the observation jacket by means of a membrane pump *)
through tubes enclosed in wool, we could make measurements to
about 1°.9 C. For the experiments with the mixture 0.3, mentioned
in § 3, we used the current of solution of calciumehloride at constant
temperature, described in Comin. N°. 87, Zittingsversl Deel XI
Juni 1903 (see Pl. IL of that Comm., which shows the whole arran-
gement with the thermostat and the observation bath).
For temperatures above 380°, and also for temperatures as much
again below the temperature of the room, it appeared necessary
to replace the observation bath, which first consisted of a simple
vlass tube, by a vacuum jacket *). After this the difference in tem-
perature at 84°C. over a height of 33 em. without stirring amounted
to O'.02 C. Moreover we have always stirred before each observa-
tion. The water was insulated from the copper piece with which
the jacket was fastened to the steel flanged tube of the experimental
tube by a laver of sulphur. This prevented the cement from softening.
In order to prevent variations of temperature of the gas Compressed
in the experimental tube owing to conduction of heat along the
merenry column to the mercury in the compression tubes, we took
care that in the observations, where the mercury meniscus was lowest
the mereury column still stood over a length of 40 ems. in the jacket.
l) Comp. pe Haas, Thesis for the doctorate fig. I.
2) Comp. Comm. N°. 85, Versi. Deel XIE Juni 1903, p. 214. The case acting as
a spring was placed as low as possible to leave room for the coil which moves
the electro-magnetic stirrer.
'( 565 )
The temperature of the experimental tube was read with an eye-
glass to within O°.OL on an “‘Einschlussthermometer”’, divided into
O°.1, with a seale on milkglass. From time to time this was
compared at different temperatures with a similar thermometer tested
at the Reichsanstalt with the air thermometer, while the variation
of the zero of the latter in the mean time was accounted for and
also the temporary depression of the zero, which, after the thermo-
meter had for a long time been heated at 48° C., amounted to
0°.02* C.
6. Reduction of the observations. In cases where, in contrast
to the determination of the plaitpoint and the point of contact of
the mixtures and the critical point of carbon dioxide, the greatest
possible constancy of the temperature was not absolutely necessary,
the temperature during the determination of an isothermal which
lasted on an average from 3 to 4 hours was allowed to vary a few
hundredths of a degree. For the reduction to one temperature,
temperature coefficients for the different volumes were derived from
the observations.
In the two series, one at an always increasing, the other at an
always decreasing pressure, pressures were measured, corresponding
to different volumes, which in the two series differed but little.
Pressures were derived from them for the same volume and then
the mean was. found. When it appeared that these pressures agreed
sufficiently (comp. § 4) we have afterwards simply taken for two
corresponding points the mean of the volume and the pressure.
Physics. — “Lsothermals of mivtures of orygen and carbon diovide.
LV. Isothermals of pure carbon dioxide between 25° C. and
60° C. and between 60 and 140 atmospheres.” By W.H. Krrsom.
Communication N°. 88 (4 part) from the Physical Laboratory
at Leiden, by Prof. H. KammEruincH ONNEs.
§ 1. Reason for the investigation of carbon dioxide. Although the
isothermals of carbon dioxide have been extensively investigated by
Amacat, [| have yet determined a number of isothermals together
with its critical point. I was led to it by the following considerations :
Ist. it was desirable that I should be able to judge of the purity
of the carbon dioxide which I used for the preparation of the mix-
tures, and it seems that this judgment may best be derived from the
increase of the vapour pressure with condensation at a stationary
temperature *) ;
4) Comp. Comm. N°. 79, Proc. April 1902.
( 566 >
2nd_ difficulties had arisen about some quantities at the critical point
of carbon dioxide, which are important for the theory of the mix-
tures. Amacat, for instance, had determined the critical pressure at
72.9 atm., while Verscuarre.r from AmMAGat’s isothermals derived
73.6 atm."). Obviously this may give rise to an error in the deter-
mination of the data of the critical point of the mixtures, if as in
Comm. N°. 592) the logarithmical systems of isothermais are shifted
over each other. Moreover in Comm. N°. 75, Proc. Dec. 1901 p. 299,
for (=) at the critical point from AmaGart’s isothermals: 7.3
Or
had been derived: from his determinations of the saturated vapour
pressures: 6.5. This points to an uncertainty in the determination
of the critical volume. AmaGcar has determined the critical point
and the vapour pressures in different apparatus and hence probably
also with other carbon dioxide than the isothermals; by determining
the two in the same tube with the same carbon dioxide I hoped to
arrive at more certainty on these points.
3°. By comparing the isothermals of the mixtures after Raveau’s
method with isothermals of carbon dioxide observed in the same
experimental tube some systematical errors which might oceur in the
observations are eliminated from the determination of the critical
data of the mixtures. In this way an error in the determination
of the diameter of the graduated stem of the experimental tube
would have no influence on the critical pressure and temperature of
the mixture.
§ 2. In the following tables ¢ is the volume expressed in terms of
the theoretical normal volume, p the pressure in atmospheres (0° C.,
45° Northern latitude), vy, the volume of the liquid. The points of
the beginning and the end of the condensation are marked by the
letters be and ec. For the point 4¢ we adopted the point where
after having decreased the volume there appeared for the first time
With proper stirring a liquid ‘Schlier” on the wall, or after having
increased the volume with proper. stirring only such ‘“Seblier”
remained. These two points agreed sufficiently. The point ec could
be observed sharply, as with a small variation of the volume the
last part of the phase disappeared or reappeared. Especially here,
however, phenomena of retardation had to be avoided by forcible
stirring. J"), stands for the theoretical normal volume, the meaning
of Ag, is explained in the 2%4 part of this Comm., p. 552.
) Comp. Comm. N® 55. Proc. April L900,
*) Proc. Sept. 1900.
(O67 9
First carbon dioxide.
Before the measurements : My. = 71.020° c.c.
Ax,, = 1.00570
a. Isothermal of 25°.55 C.
No v | Pp pe tig
| 4 | 0.008573 | 63.12 | 0.54115 |
| 9} 7812 | 64.36 5028 | be
| 3 | T0AG | 64.42 4539 | 0.000420 |
| 4] al 64.44 AOL | 859
| 5 | 504 | 64 A 3545 | 0.001276 |
| 6| 4837| 64.40 | 315 | 1664
a 4068 | 61.39 | 2619! 9088
g| 3205 | 64.49 | 2065 | 9507
| 9| 3085 | 64.37 | » 1986 | £652
140} 2869 | ost | 1848 2)
4278 | 64.433) | 1025) ¢ |
12 | 2645 | zo. | 1876 |
13| - 2520 | 80.658 | 2033 |
| 44 | 2438 | 99.97 | 2967
45 | 9366 | 105.79 | 2503
16 |
2309 | 122.555 | 2830 |
| :
2970
1) We shall later revert again to the purity of the carbon dioxide, as it appears
from the increase of pressure at the condensation.
2) Here the liquid meniscus reached the part of the tube where through the
sealing in the blow-pipe the marks no longer were visible.
( 568 )
h. Isothermal of 28°.15 C.
ive 4 |p | BE | "liq
| 1 | 0.009238 — 63.4 0.5924
| 2 8565 | 65.19 5583
| 3 | 7807s| 66.755) 5212 | |
| 4 | 7030 | 67.995| 4780
| 5 | 6950 | 68.49 | 47395
6 | 6673 | 68.39 | 4564 | be
7 6300 | og.41 | 4310 | 0.(00290
8 | 5502 | 68.41 | 3764 oj
9 A712 | 68.438| 32248 0.001625
10 3974 | 68.48 | 9724 2189
11; 349] 68.45 | 2135 1)
4a! 3011 | 68 48. | 9060 | ec
43 og13 | 72.408; 2037 |
| 9670 | 78.55 | 2097 |
15 | 9546 | 89.54 | 9279 |
16 | 2446 | 103.47 | 2534 |
17 936) | 449.61 | 2834 |
18 9315 '| 136.58 3161 |
| | |
e. Bordereurve in the neighbourhood of the critical point.
Beginning condensation End condensation
aera oe [eae Bae
| Temp. | v 1 ae Temp. | v p
| a i
30.05 | 0.005594 | 71.47 } 30.41 | 0.003398 | 71.53
30.82 4833 | 72.725| | 30.81 3725 | 72.74
a |
, ad. Critical point:
Temp.: 80.98 Pressure: 72.93 Volume: 0.00443 *).
‘) Comp. footnote to the preceding table.
2) For the determination of this comp. § 5.
1 0,0L0068
2 0.009314
63.36
65,39
OF
ee ee)
3 | 8582 | 67.22 |
4 | 7809 | 6.085
5 | 7034 70.73
6 | 6975 | 74.95
7 5483 | 72.746
, 8 5102 | 72.87
9 KI77 | 72.93
10 4403 | 72.94
i Wh | 72.48
12 3959 72.96
430 3656 72.£95
(| 3906 | 73.53
it 3230 73.89
46 | 3051 | 75.43 |
147 | 2862} 79.48
| 18 | 2724 | 86.40 |
149} 2593 | 95.70 |
120) 9509 | 106.18
2| 2435 | 419.35
| 29 | 2362 | 138.65
0.
QO.
0.
0.
0.
0.
ho.
pe
6379 |
6090.
5769 |
D099 |
ANT
ADD
3988 |
3718
3214
3104
28885
2669 |
2423
26645 |
.2906%
J
0.010086 | 638
Isothermal of
31.89
87
0.009214 | 65.99?
9570 | 67.945
Tile ee, LOL OS
7017 | 71.68
6267 | 73.038
5598 | 73.94
B17 | 74.24
NT495| Th, 4A
43045! 74.56
2942 | 74.69 |
3610 | 75.00
3998 | 76.90 |
9883 | 82.02
DAT 89.90
|
9593 | £9.77
2503 | 114.45
2439 | 122.79
9377 | 136.71
iO).
CU,
~2365
2443
2587
.2790
fore -) .
g. Isothermal of 34°.02 C. h. Isothermal of 37°.09 C.
| No. | D RAE J | pe | | No. | v | p | pp
4 | 0.010067 | 65.48 | 0.6562 1 0.010863 64 56 | 0.7013
| 2 | 0.009337 | 67.295) 0.6283 | 2} 10093 | 66.£0 | 0.6752
| 3] 8560 | 69.49 | 0.5048 | 3 | 0.009339 | 69.99 | 0.6471
\ 4 | 7791 | 71.64 | 0.55845) | 4 | S54 | 74.73 0.61359, /
| 5 | 70238) 73.65 | 0.5173 | bs | 7810 7411 | 0.5788 | |
6| 6255.} 75.24 | 0.4712 | | 6 | | 7059 | 76.40 | 0.5394 |
| 7] 558€5) 76.605) 0.4926 | | 7 | 6987 | 78.585} 0.4940 | |
| 8 AG72 | 77.57%) 0.3624 back 55255| 80.47 | 0.4446 |
psa 20744) 78.385] 0.3148 | tO) AUTO) 82.40 | 0 aati
| 40 | 3243 | 81.41 | 0.26305 10 4011 | 83.89 | 0.3365
11 9955 | 86.16 | 0.2546 | |41 | 3930 | 88.89 | 0.2871
| 412 2746 | 95.02 | 0.2809 | 42 9799 | 103.08 | 0.2885
13| 9614 | 105.95 | 0.270 | 13) 9609 | 419.97 | 0.3112
14 2540 | 119.53 | 0.3000 | 144] 2495 136.01 0.3893)
15. | 2426 | 136.66 | 0.3316 = zt
Second carbon diovide *).
sefore the experiments: Vi,;7~ = 69.647 ¢.c., weight 2
Aiter: Ws z 62.629) 2 ayer
Mean bog be
2. Isothermal of 41°.95 C. k. Isothermal of 48°.40 C.
No | v Le ee | pe | No. | v | p | pe
1 | 0.011546 | 64.85 | 0.7487 | | 4 | 0.012311 | 65.20 | 0.8027
2 | 407945| 67.28 | 0 7262% | | 44572 1. 67°69) | Osveae
| 3} 40047 | 69.84 | 0.7014 | 3} 407875) 70.52 | 9.7607 |
4 | 0 C0911 | 72.78 | 0.6704 - 0.009970 | 73.61 | 0.7339 |
5-|. - 9486 | 75.48 | 0.6405 5 | 9932 | 76.61 | 0.7073
G61 7640 | 78.57 | 0.6003 6 | 8442 | 80.07 | 0.6769
7; 6915 | 81.34 | 0.5699 | 7 | . 7678 | 83.38 | 0.6402
8 G81 | 84.04 | 0.51945 8 | 6899 87.07 | 0.6007
9 5320 | 87.18 | 0.4638 | 9} 6118 | 90.90 | 0.5561
10 4530 | 90.13 | 0.40825 | 40 | D380 | 94.78 | 0.5099 |
i 3778 | 94.40 | 0.3555 414| 4570 | 99.62 | 0.4552 |
12 3087 | 105.01 | 0.3242 12} 3898 | 405.50 | 0.4033
143 | 9817 | 117.96 | 0.3393 13 31995 | 449.38 | 0.3736
114 9642 | 134.85 | 0.3563 | 144] 9864 | 185.56 | 0.3883
') Because the experimental tube has broken, the first quantity was lost. As,
however, the fracture occurred below the graduated portion of the stem, the
advantage mentioned in § 1, sub 3 remained.
/.. Isothermal of 57°.75
1 | 0.013174 66.27 | 0.8730
me 49356 69.20 | 0.8559
3 1586 FAAS 0.8363
4 AC807°| 75.42 | 0 8154
5 400095} 78 99 | 0.7506
6 0.009271 | 82:49 | 0.7648
q 8489 | 86.62 | 0.7347
8 | 7668 | 91.16 | 0.6990
SN 6930 95.73 | 0.6638
10 6113 | 101.32 | 0.6194
| 11 y | 4107.06" |20: 5754 |
| 42 4596 | 114.45 | 0.5960 |
| 13 3795 | 196.10 | 0.4786
| |
14 34915] 435.81 |-0.4647 |
|
|
§ 38. To simplify later calculations I have caleulated for the
isothermals e, 7, g, h, i, h, ¢ the values of pr for regularly increasing
1
densities E . Therefor each value has been interpolated from 4 points
v
derived directly from observation; only for the extreme values we
have interpolated between 38 points’). So we find the values given
1) For this we used the formula of Lagrange, which may be easily written in
the following form:
d—d, | , (d—d,) (d—d,) (d—d,)
— TF +), hes Pp. Jy +(P, ro ae )\—
d,—d, a) (b= dad)
—d,) (d—d,) (d—d,)
Po petroea EAU ss a Lhe
“te E De (d. ee ee ae
where
call gy a tte
at 7 ea
d,—d,
(Any ea 2 2 a
Coad
P represents pr, while — is represented by d. Supposing that @ lies between
i ; :
d, and ds, the two last terms of P become relatively small and they may be
easily calculated with a sliding-rule.
in table XN; the first column gives the different densities (expressed
in terms of the theoretical normal density), the following columns
pe each time for the temperature
mentioned at the head of the column.
the values of delonging to it,
is
Y ASB
Isothermals of carbon dioxide.
XX.
30. 982-3189? 4, 02 miUGe Al .$5° 48 10° Die
:
od is oa
80 0.8583
400 | 0.6355 | 0.6411 | 0.6528 | 0.6749 0.6997) | 0273497) 087203
420 | 0.5653 0.5745 | 0.5844 0.6036 0.6335 | 0.6742 | 0.7285
140 0.5037 0.5094 0.5240 | 0.54405 0.5746 | 0.6135 | 0.6743
160 0.4499 | 0.4566 | 0.4708 | 0.4918 | 0.5937 | 0.5640 | 0.6273
{80 | 0.4039 0.41065 0.4254 | 0.4466 | 6.4796 | 0.5212 | 0.5864
200 | 0.3646 | 0.3746 | 0.3863 | 0.4081 | 0.446°! 0.4847 | 0.5521
220 | 0.3314 | 0.3387 | 0.349% | 0.3754 | 0.4094 | 0.4536 | 0.52965:
940 | 0.3041 . 0.3109 0.3996 | 0.3477 | 0.38195| 0.4964 | 0.4991
960 | 0.2806 | 0.29875 | 0.3021 | 0.2243°| 0.354575| 0.4048 | 0 4812
980 0.2611 0.29680 | 0.£895>) 0.3052 | 0.3423" 0.3872 | 0.4692
200 | 0.2448 0.9521 | 0.2677 | 0.29155! 0.3302 | 0.3763 |
330 0.2333. 0.2410 0.2590 0.9835 0.32455) 0.3737 |
340 | 0.2273 0.2221 0.25549 | 0.9863 0.3255 | 0.8817 + |
360 0.2305 | 0.2401 | 0.9588 0.2900 | 0.3362
380 0.2497 «0: 9530.--0.2742 | 0 3073
400 0.2690 0.2800 0.30381 0.3376
420 | 0.24695! 0.3230
§ 4.
a and 4 in the following way: From the height of the liquid meniscus
ry, Was reduced to the same temperature for the isothermals
we directly derived the volume of the vapour phase: 7,9). If 7, is
the specific volume of the existent liquid phase, 7, the specific volume
of the vapour (as unity we always have here the theoretical normal
volume), we find:
LV yap. Vira: ( v, dr, vio de,
eg, A Vs— 0, \ Ca AT V—U, pw
After the vapour volumes have thus been reduced to one tempe-
rature, the liquid volumes are derived from this. We have assumed
in this that 7, and v, are functions of the temperature 7 only and
not also of v, as De Hern and others think. On this supposition
we can derive v, and v, from each pair of observations of ri, at
different + and at the same temperature. The values calculated thus
liq
have been combined in table XXI together with those derived directly
from observation.
TABLE XXI.
wo ee (3
Isothermal of 2: Isothermal of 28°.15 C.
| Nrs vi Vo Nrs. vy "9
2 0.CO07812 6 0.006673
3and7 0.002799 7736 7and9 0 003043 6680 |
4ands 9819 77122, Sand 10° 9998 6709 |
Dand9 9809 TAT 19 3011
44 2798 ae = =
te + = 1 ake oS Ae mean 0.003016 0. O06684 |
mean 0. 0028039 0 .007773° = == seis 3 i!
We see that no regular variation in the values of 7, and 7, can
be remarked, so that this justifies with regard to these experiments
our assumption of the dependence of v, and v, on the temperature
only.
In the calculation of the mean values of 7, and rv, in table XXI
we have accorded the same weight to the value borrowed directly
from mean of the values derived from the
other observations.
observation as to the
§ 5. For the determination of the critical point the following may
serve: The thermostat was adjusted at a few hundredths of a degree
below the critical temperature (the temperature above which no
stationary meniscus is observed). By letting a small quantity of water
of higher temperature into the mixing bath, the experimental tube
was brought to a few hundredths of a degree above the critical
and the substance was well stirred. Then the tempe-
If the volume lies between certain linits,
temperature,
rature falls. very slowly.
the following phenomena may be seen: A blue mist is formed which
( 574 )
at a definite place becomes denser and denser’). At a given moment
“strive” appear, the substance boils and rains, a meniscus is formed.
From the very first, the latter is perfectly sharp and flat, it remains
at the same place also. after stirring. The temperature was observed
immediately after the appearance of the striae, then the pressure and
the volume and then the temperature was determined again. So we
obtain the pressure for one or a few hundredths of a degree below
the critical temperature. For this a correction has been applied.
If we allow the temperature to rise, we still see a meniscus
during a considerable length of time after the temperature in the
bath has risen to a few hundredths of a degree above the critical
temperature. It disappears immediately, however, when we stir.
Hence this is no phenomenon of equilibrium.
So we could derive the temperature and the pressure directly
from observation. For the volume this was not possible, as owing
to the effect of gravitation the phenomena described above occur
at different volumes, so for instance in my observations with a
volume: 0.003924 (stirrer below), where the meniscus appeared
in the immediate neighbourhood of the top of the tube, and with a
volume 0.004281 (stirrer above) where the meniscus appeared 1 mm.
above the mercury.
The method generally used for the determination of the critical
volume consists in determining some liquid and vapour densities
at temperatures below the critical, and then using the rule of the
rectilinear diameter of CaiLnetet and Marnias. To this end we
have drawn on a diagram the densities resulting from the data of
§ 4, table XXT and § 2, ¢ as a function of the temperature, and
the diameter has been drawn on it. A deviation from the rectilinearity
could not be stated with certainty. For the critical density, expressed
in terms of the theoretical normal density we derive from this diagram
239, hence for the critical volume 0.00418.
dp Oy
Another method is this: At the eritieal point ) == aay
dd CoeL. 01 v
“y
(for the proof see for instance Comm. N°. 75).
a “dp rat
Mo determine (<= we have combined in table XXIT under O
( 5 :
\ 4 COCL
the vapour pressures resulting from § 2; for the temperatures 25°.55 C
and 28°.15 C we have taken the means from the different values
for the pressure.
') If the temperature is kept constant, the mist during a considerable length
of time (say 10 minutes) does not change to the eye.
( 575 )
TABLE XXII.
Temp. QO. C. O0=C:
D5) 64.40 64.41 + 0.01
28.45 OS .43 68.43 0.00
30.05 Taleras 71.44 == (hes
BOS Foe 720 = (()) (O:
30.98 72.93 |
If we calculate for the different values the coefficient 7 for van
pER Waats’s formula’):
p T—T,
log = wp ae
Pk i
we find with imereasing temperature regularly decreasing values of
jy. If in the development in powers of Ps take one term more,
so that we arrive at the formula:
ie Ce PRESET
log == ——— {| /+ 9 ——— |],
Pk | i i aay
and we calculate the values of 7 and g which give the best agree-
ment, we find very nearly g=//. Then I have put:
re i es grata ae
log —= f ———— +
eo) ee y ig
and found / = 2.914°. By means of this we obtain the values for
p given in column €. The agreement is quite satisfactory, only for
the temperature 30°.82 C. there is a considerable deviation : the same
is also found in the comparison of the saturation volumes so that
here we have probably to do with an error of observation.
From this we find at the critical point:
dp
d oil:
dT coer.
From the determinations of the isothermals we cannot with cer-
et ae (f Op
tainty derive a definite variation of | ~~] at the same volume with
. OE Ts
NS 7 U
the temperature, as may be best derived from table XX. Therefore |
ae |
have derived cad for the different densities from the isothermals
jie
of 30°.98 C. and 48°.10 C. and found the following values:
1) Continuitiit | p. 158.
100 0.581 200 1.403 300 9 304
120 0.742 990) Ae oT 320 2 G24
140 0.898 240 11s 340 3.066
160 1.066 260 1.886
180 {233 £80 2.062
If from this we interpolate in the same way as in § 9 we find that
0 2
ae — 1.610 for the density 225.50, to which belongs the volume:
rt ae
0.00445.
This value does not agree with that derived above from the densities.
The difference is larger than can be ascribed to the errors in the
observation. The deviation is in the same sense as follows from
AmaGat’s experiments. The following might serve as an explanation
of this difference :
According to a remark of Prof. KAMERLINGH ONNEsS from whom a
new paper on the cause of the deviations near the critical point may
be expected (comp. Comm. N°. 74, Arch. Neerl. serie IT, t. VI, p. 887)
the appearance of the mist in the neighbourhood of the critical
point seems to indieate that a part of the substance condenses round
numerous centra equally distributed over the whole space. That only
in this area this appears so distinetly, might be ascribed to the cir-
cumstance that here small forces are sufficient to cause great variations
of density. These condensations might have a perceptible influence
for instance on the saturation volume although the variation of the
pressure would not become perceptible in consequence of It.
In a comparison of mixtures with pure substances according to
the Jaw ef corresponding states we must disregard those conden-
salions, as they do not occur at corresponding points (in mixtures
near the plaitpoint). Hence our purpose will probably be served best
if we adopt for the critical volume: 0.00443, as this value according
to a thermodynamical relation results from determinations not so near
to the critical point, and where therefore particular phenomena which
occur i its immediate neighbourhood have played no part.
The following quantities are further fennd at the critical point,
which are necessary for the comparison of the observations with the
theoretical results of Comms. N°. 75 and N°. 81:
a) ) Ul: i 0 P :
ret Rede) Co )=— 269
(san), Bence (, Di (sie é ata
Here, in agreement with the value of the coefficient of expansion
for the ideal gaseous state accepted in this Comm. II, p. 558 we
have put: 7\= 273.04.
Physics. — ‘fsothermals of miLetures of oLrygen and carbon dioaide.
V. Lsothermals of mictures of the molecular compositions 0.1047
and OAI9IA of oxygen, and the comparison of them with those
of pure carbon diode”. By W. H. Kersom. Communication
N°. 88 (5% part) from the Physical Laboratory at Leiden by
Prof. KAMERLINGH ONNES.
(Communicated in the meeting of October 31, 1905.)
§ 1. The following sections contain the tables about two mixtures
of carbon dioxide and oxygen. For the meaning of r. p, Viiy, and
the determination of the 6.c.- and the ¢.c-points I refer to this Comm.
IV § 2. Of the end condensation point it should be remarked that over
a definite area below and above the plaitpoint temperature the meniscus,
in consequence of the effect of gravitation, disappeared in the tube.
The data about the plaitpoint were derived directly from the
experiment. On the phenomena near the plaitpoint I find the following
remarks among my notes of the observations: When the volume
increases from the homogeneous (liquid) state a blac mist gradually
forms itself. As the volume increases (small variations at a time)
this becomes denser. If the volume increases still more, layers of
different degrees of vefrangibility suddenly appear, which quickly
move among themselves. When we stir, however, they still dissolve
into the thickening blue mist. At a given moment, after the volume
has been increased again a little, these layers begin to concentrate
towards the middle of the tube, at the top and at the bottom it
( 578 )
becomes clear, small bubbles or drops are seen to move from below
and from above towards a certain point in the tube. At last-a
ineniscus appears there. This remains at that place. The temperature
at which these phenomena were observed was adopted as the plaitpoint-
temperature of the mixture considered, the volume and the pressure
as plaitpoint volume and pressure.
If the temperature is alittle higher, the meniscus appears lower
in the tube. The exact point where it appears cannot be observed
with certainty: drops are seen to move from above to below, and
bubbles from below to above more and more regularly towards one
place; at this place the meniscus will appear, but this place is rising
already before the meniscus has properly formed itself. When it is
formed, it generally still rises. If the temperature is still higher the
meniscus is distinctly seen to rise from the bottom of the tube. At
the lower end a quantity of liquid is gathered by the drops which
fall from the top to the meniscus. The same holds, mutatis mutandis,
for temperatures below the plaitpomt temperature.
Of the data about the point of contact only the temperature could
accurately be (to within O°.O1) derived from the experiment. To
determine the pressure some points at the beginning and at the
end of the condensation to within O°.1 of the point of contact
were observed; they were drawn and the point where the tangent
is at right angles with the axis of temperature was found. This
gave the pressure of the point of contact with sufficient accuracy.
Then the point of contact volume was deduced from the isothermal.
The molecular proportion of oxygen will be represented by w,
Vix is the theoretical normal volume, for the meaning of Ax
comp. this Comm. IL p. 552.
20
§ 2. first mirture of carbon dioxide and ovygen.
7 —— Onna y
Before the measurements: Viz" = 69.743. ce.
»
After A * COLT:
a. Border curve.
Beginning condensation. End condensation.
Temp. D p Temp. | D p |
17.53° | 0.008552 | 66.08 | 44.68 | 0.002597 | 85.52
17.63 8483 | 66.40 14.78 9757 | 87.09
19.48 7708 | 69.48 17.525 9949 | 88.95
20.19 7362 | 71.59 17.68 9986 | 88.29
90.98 | 7988 | 71.94 19.38 3195 | 88.465
21 48 | 6709 | 74.85 | 90.19 3292 | 88.35
22.06 | 6456 | 76.24 | 90.28 3323 | 88.35
92.38 6098 | 77.85 48 3664 | 87.35
22 83 | 5860 | 79.44 92.09 3880 | 86.58
99.87 | 5822 | 7996 | 99.43 4069 | 86.03
92.98 | 5697 | 79.95 | 22.80 | 4301 | 85.34
93.93 | 5366 | 81.46 | 92. 883 4394 | 85.42
99.98 4441 | 84.90
93.18 4663 | 84.16
b. Isothermal of 17°.60 C.
| No. v | p pe | Diig. |
| 1 | 0.011384 | 58.35 | 0.6642
| 2} 40605 | 60.46 | 0.642
3 | 0.009826 | 62.62 | 0.6153 |
4 9047 | 64.84 | 0.5866
5 9503 | 66.24 | 0.56395] de |
6 7489°| 67.85 | 0.5'82 | 0.000338
7 67125| 69.54 | 0.4668 | 574
8 6108 | 71.42 | 0.4344 826
f <9.) 5935 | 74.65 | 0.49595 879
40 5385 | 73.39 | 0.3952 | 0.001105
| 41 5157 | 74.26 | 0.3830 1194
19 | 44865 | 77.42 | 0.3460 4502
13 | 43795 | 77.68 | 0.3402 1556
14| 3482 | 83.35 | 0.9902 2189
45 | 9954 | 88.30 | 0.2608 | ec
16 9848 | 91.715) 0.2612
17 | 97195| 97.38 | 0.2648 | |
18 9572 | 109.13 | 0.2807
19 | WEG |
|
193.34 | 0.3042 |
!
38
Proceedings Royal Acad. Amsterdam. Vol. VI.
: SS Se ee ee ee ae
es ee eae oe ee ee oe ee
| a > pe toate
4 ~
4 ( 580 )
: c. Isothermal of 20°.29 C.
No. | v | p | pe | Viig.
3 4 | 0.011699 | 58.86 | 0.6886
oS 2| 414384 | 59 72 | 0.6798
E 3 40605 | 61 94 | 0.6569
gi | 4 | 0.009826 | 64.31 | 0.6319
x 5 9047 | 66.62 | 0.6097
6 8900 | 67.15 | 0.5976
. 7 8269 | 69.04 | 0.5709
7 8 7490 | 74.44 | 0.5348
E | 9 7291 | 71.98 | 0.5248 | be |
10 6713 | 73.07 | 0.4905 | 0.000267
q 44 | 59358 | 72.32 | 0.4470 5965
Za | 12 5157 77.9% | 0.40195 968 |
4 | 43 4468 | 89.88 | 0.3614 | 0.001360
| 44 4379 | 81.39 | 0.3564 4445
15 9640 | 85.85 | 0.3195 |. 2930
1G 3501 | 86.91 | 0 3043 / 540
4 | 47 9335 | 88.98 | 0.2944 | ec
| 48 3132 | 91.50 | @.2866
49 9959 | 95.64 | 0.2830
20 9897 | 97.76 | 0.2832
a 9759 | 104.46 | 0.28895
29 9613 | 114.89 | @.3002
im | 93 | 9597 | 125.128| 0.3162
d. ee! isothermal (21°.99 C.).
No. | D | p Se Brine a oS pe | Din
1 0. 019159 | 58.36 | 0.7096
: 2 41384 | 60 52 0.6889
3 | 0.009826 | 65.32 | 0 6419
2 4 8269 | 70.37 | 0.5819
5 6743 | 75.37 | 0 50595
6 6400 | 76.49 | 0.4891 | be
| 7| 5935 | 77.64 | 0.4608 | 0.000210
| 8 5157 | 80.34 | 0.4143 638
9 | 4379 | 83.76 | 0.3668 | 0.001169
) 10 3878 | &6.60 | 0.3358 | pp
. 1 3613 88.74 | 0 3206
; 42 3004 | 97.418) 0.2966 |
13 9769 | 109,96 | 0.3025
44 | 9598 | 14] 9808. | $288) Oe 98.75°) Osdats |
( 581 )
e. Isothermal of 22°.68 C.
| No. v | p | p | Lig
i —
4 | 0.012159 | 58.63 | 0.7129 | |
2 41384 | 60.99 | 0.6933
3 10605 | 63.29 | 0.6742 |
4 | 0.009826 | 65.76 0.6461" |
5 | 9047 | 68.285 | 0.6178
| 6 | 8269 | 70.92 | 0.5865
7 | 7489° | 73.49 | 0.5504
| 8 | 6712° | 76.09 | 0.5108 |
9 5913 | 78.74 | 0.4656 | dc
| 40 5546 | 79.97 | 0.4435 | 0.000198°
M4 | 5157 | 81.33 | 0.4194 400
42 | 4768 | 82.89 | 0.3952 5975
43 | 4379 | 84.735} 0.3744 709
14 | 4309 | 85.05 | 0.36645 591 |
15 4278 | 85.22 | 0.2646 625
16 4958 | 85.35 | 0.3634 288
17 4243 | 85.40 | 0.36235 951) |
18 4219 | 85.54 | 0.3609 425
49 4218 | 85.53 | 0.3608 | ec
20 30918 | 87.03 | 0.3474
24 3604 | 90.23 | 0.3252
99 3049 | 99.49 | 0.2025
93 9752 | 412.67 | 0.3401 |
24 9612 | 124.50 |
|
1) To explain the irregular course of vj, here, we refer to this Comm. III, p. 562,
while we remark that the variations of %, with the temperature and with the
volume become very large in this area, so that a small error in the latter may
‘give rise to a large error in the value of 7i;.
38*
( 582 )
J. Point of contact isothermal (23°.29 C.). g. Isothermal of 25°.20 C.
No. v p | pe | No. v | Pp | pp |
1 | 0.019150 | 58.95 | 0.7168) | 4 | 0.012159 | 59.81 | 0.7279
9 411785 | 60.04 | 0.70755| 2 41384 | 62.44 | 0.7074
3 11384 | 61 21 | 0.6968 | 3 10605 | 64.59 | 0.6850
4 40605 | 63.59 | 0.6744 4 | 0.009826 | 67.23 | 6.6606
5 | 0.009825 | 66.09 | 0.6404 | 5 9047 | 69.97 | 0.6330
6 9047 | 68.70 | 0.6215 | 6 8°69 | 72.78 | 0.6018
2 8269 | 71.34 | 0.5890 | 7 7490 | 75.69 | 0.5669
| s| —-74¢0 | 74.04 | 0.5545 | 8 67125| 78.59 | 0.5976
9 | 67125} 76.71 | 0.5149 | 9} 5935 | 81.69 | 0 4848
| 10} 5935 | 79.48 | 0.4717 | 10 5156°| 84.85 | 0.4376
au 5546 | 80.80 | 0 4481 | 1 4768 | 86.61 | 0.4430
| 12 5157 | 82.93 0.4241 12) 4379 | 88.70 0.3885
43 4768 | 83.78 | 0.3995 | 13 3 91°| 91 40 | 0.3648
| 14 4379 85.88 | 0.3761 | 14 3609 | 9497 | 0 3427
| 15 3991 | 87.97 | 0.4541 | 15 3229 | 101.13 | 0 3266
46 3605 | 91 26 | 0.3290 16 9846 | 114.98 | 0.3273
17 3046 | 101.03 | 0 2077 17 2710 | 124.35 | 0.3370
| 18 27915 | 112.40 | 0.3138 | :
“49 2646 | 124.08 | 0.3283 |
Point of contact:
0.005005
82.83 |
eee
This mixture has been prepared in a simpler mixing apparatus
than that referred to in this Comm. II § 3, and the pressures are
measured with an air manometer and then reduced to the indications
of the hydrogen manometer used later, as said in IIT § 38.
Of the border curve it may be remarked that below 19°.38 C.
the end condensation pressure decreases at a falling temperature,
which has not been observed by Verscuarre.t in mixtures of earbon
dioxide and hydrogen at the temperatures at which he observed.
Between the plaitpoint- and the point-of-contact-temperature there -
was retrograde condensation of the first kind (temporary liquid phase), -, Ke
me
i)
( 583 )
§ 3. Second inieture of carbon dioxide and oxygen.
g = 0.1994
Ax,, = 1.00413.
Before the experiments: Vi;~ = 69.608 cc’.
After __,, 69.555":,,
mean: 69.581° ,,
a. Border curve.
Beginning condensation. End condensation.
No. |’ Temp. = p | No. | Temp. v | p
| 4 | 10.06 | 0 .0092336| 66.35 Tt 10:09 | 0.003205 | 102.485
Zap- 12,456 81905) 71.57 2} 412.20 3633 | 100.055
3 | 14.425 Tb" hleas 3 | 14.44 39945 | 97.375
4} 16.01 5803 | 86.02 4} 16.00 A784 | 92.57
5
a 16.23 5530 | 87.84 | | | 16.22 5156 | 90.55 |
6. Isothermal of 9°.62 C.
No. D | p | pv | Vig
4 | 0.009795 | 64.05 | 0.6274
9 9M12 | 65.36 | 0.6152 | bc
3 8742 | 66.89 | 0.5881 | 0.000124
4 7918 | 69.46 | 0.5497 308
5 147 | 74.79 | 0.5131 470
6 6404 | 7%.92 | 0.4798 | | 672
7 5500 | 79.65 | 0.4381 909
8 AS. | 84.23 | 0.4052 | 0.001122
9 4022 | 91.55 | 0.3682 1464
10 3338 | 100.07 | 0.3340 2991
i 316% | 102.67 | 0.3248 | ec.
12 9874 | 412.50 | 0.3233
13 2742 | 121.35 | 0.3397
14 2699 | 125.18 | 0 3379 :
45 £632 | 129.33 | 0.3404 |
16 2581 | 135 67 | 0.3502 |
a NE
( 584 )
ec. Isothermal of 11°.35 C.
| Ne. | D | p | pe | Pig.
| 4 | 0.010341 | 63.46 | 0.6562
| 2} 0.009505 | 66.25 | 0.6298 |
3 8763 | 68.905| 0.6038
4 8629 | 69.37 | 0.5986 | dc
5 7950 | 70.95 | 0.56405| 0.000217
6 7203 | 73.535| 0.5997 384
7 6396 | 77 C2 | 0.4926 573 -
8 5608 | 81.14 | 0.4550 781 |
9 | 4829 | 86 40 | 0.4172 | 0.001097
10 | 4097 | 92.84 | 0.2804 4376
AA | 3712 | 96.79 | 0.3593 4707
42 3446 | 100.08 | 0.3449 2336
13 3397 | 100 89 | 0.3497 | e
14 3980 | 703.21 | 0.3385
45 3028 | 110.48 | 0.3345
16 9853 | 119.41 | 0.3398
47 9718 | 198.44 | 0.3491
18 96-1 | 137.56 | 0.3605
d. Plaitpoint isothermal (12°.51 C.).
No. | v | p | pe | Pig.
1 | 0.010259 | 64.42 | 0.6609
2 | 0.009570 | 66.77 | 0.6390
3 874 | 69.74 | 0.6096
4 8040 | 72.27 | 0.5814 | ac
Fé 7197 | 75.46 | 0.5409 | 0.000201
6 6378 | 78.56 | 0.50105 439
7 5597 | 82.66 | 0.4627 674
8 4772 | 88.24 | 0.4214 | 0.001044 |
9 3981 | 95.61 | 0.3806 1360
10 3606 | 99.65 | 0.3593 | pp
rw 3299 | 105.38 | 0.3476"
42 3057 | 112.34 | 0 3434
13 2870 | 121.71 | 0.3493
( 585 )
e. Isothermal of 14°.04 C.
No. | v | P | pr | "re. |
1 | 0.010318 | 65.06 | 0.6713
9 | 0.009504 | 67.91 | 0.6454
3 8726 | 70.87 | 0.6184
4 7926 | 74.06 | 0.5870
5 7272 | 7679 | 0.5584 | bc
6 7095 77.46 | 0.5496 | 0.000043
7 6337 80.59 | 0.5107 | 0.000265
8 56904 | 84.05 | 0.4786 457
9 4701 90.15 | 0.4292 786
40 4402 | 93.16 | 0.4101 888
44 4066 | 96.35 | 0.3918 933
42 3947 97.55 | 0.3850 | ec 1)
13 3700 | 100.97 | 0.3736
14 3987 | 109 15 | 0.3588
45 3002 | 118.66 | 0.3562
16. 9893 | 128.20 | 0.3619
Ibe Si ea le ee
f. Isothermal of 15°.41 C.
No. | v | P | pe | rig.
4 | 0.010276 | 66.02 | 0.6784
2 | 0.009515 | 68.77 | 0.6543°
3 8763 | 71.71 | 0.6284
4 7991 74.91 | 0 5986
a) 7159 | 78.62 | 0.5628
6 6435 | 82.05 | 0.5280 | be
! 5971 84.325 | 0.5035 | 0.000139
8
9
5604 | 86.34 | 0.4838 998
5099 | 88.71 | 0.4639 397
40 4997 | 90.31 | 0.4515 367
AA ugh | 91.44 | 0.4429 387
42 4667 | 92.81 | 0.4334 361
43. 4538 | 93.84 | 0.4258 973
44 4460 | 94.43 | 0.42415 164
45 4A | 94.87 | 0.4192 | ec
46 4045 | 98.88 | 0 4000
47 3692 | 103.36 | 0.3816
18 3953 | 413.06 | 0.3678
49 3908 | 122 03 | 0.3671
20 9821 | 133.47 | 0.3757
a" 9732 | 144.72 | 0.3872
ae oe Ee ee ee
1) Here we also had retrograde condensation of the first kind, although this
does not appear from the values given.
( 586 )
g. Point of contact isothermal (16°.27 C.). 1. Isothermal of 17°.66 C.
| No. p | p pe |
1 | 0.010312 | 66.345) 0.68415
2 | 0.009519 | 69.28 | 0 6595
3 | 8701 | 72.58 | 0.6315
4 7955 | 75 77 | 0.6028
5 | 7163 | 79.27 | 0 5685
6 | 6389 | 83.90 | 0.5316
7 | 5934 | 85.31 | 0.5105
8 5592 | 87.57 | 0.4897
9 | 5228 | 89.80 | 0.4695
10 | 4824 | 92.72 | 0.4473
11 | 4434 | 96.05 | 0.4959
12} 4031 | 100.54 | 0.1053
13 3647 | 106.62 | 0.3888
14 3284 | 14 98 | 0.3753
| 15 3053 | 122.99 | 0.3734
16 9857 | 133.275! 0.3808
va 2759 | 140.71 | 0.3832
‘Point of contact:
0.005322 | 89.20
| 7) P Pp v
|
4 | 0.010273 | 67.26 | 0.6910
2 | 0.009510 | 70.17 | 0.6673
3 | 8683. | 73.60 | 0.6391
| 4} 7920 | 76.98 0.6097
5 | 7161 ‘| 80.58°| 0.5774
6 6359 | 84.77 | 0.52905
7 5610 | 89.45 | 0.5001
8 4843 | 94.59 | 0.4584
9 4087 | 102.08 | 0.4472
10 3688 | 108.02 | 0.3984
rr 3280 | 417.36 | 0.3849
12 973 | 129.44 | 0.3848
3 9816 | 144.48 | 0.3976
§ 4. Coinparison of the mixtures according to the law of corre-
sponding states with carbon dioxide.
In Comm. N°. 59, Proc. Sept.
1900 methods are discussed for a graphical comparison of isothermals
of mixtures with those of a simple substance. Here as well for
er : . pv
carbon dioxide as for the two mixtures log’) was drawn as
a function of /ogv for the different temperatures. (For the absolute
zero we accepted — 273°.04 C.). If the law of corresponding states
also holds for mixtures of normal substances it must be possible to
live pressures occur, the drawing of /og
!) As the temperatures are so high that in the theoretical isothermals no nega-
wm
a offers no difficulty.
( 587 )
make the corresponding isothermals of the different diagrams coincide
by shifting them only in the direction of the /og v-axis.
I found that it was not possible to place the diagrams in such
a way over each other that the isothermals of the whole system
coincided ; I, however, sueceeded for the large volumes. According to
KAMERLINGH ONNES this signifies that in the mixture the coefficients
A,B,C,D,E,F of his series do not hang together with the coefficients of
the pure substance at corresponding temperatures in such a manner as
would follow from the law of corresponding states, but that for the
volumes where the terms with D, /, / in comparison with the others
are still so small that we may neglect the differences between these
terms and those given by coefficients which would obey the law
of corresponding states, the diagrams will coincide over such a large
range of temperature that 6 and C’ may still be regarded as corre-
sponding functions of temperature, hence a critical temperature and
a critical pressure holding for this range of volume and temperature
may be deduced from the law of corresponding states.
On the plate the diagrams are placed over each other so as
to give the best agreement for the larger volumes. In the hori-
i : 3 pv
zontal direction /ogv is drawn, in the vertical /og a The complete
lines refer to carbon dioxide, the dash lines to the first mixture,
the dash-dots lines refer to the second mixture. The points for
carbon dioxide are enclosed in circles, those for the first mixture in
triangles, for the second in squares. The different isothermals are
indicated by the letters a, 6, ete., with which they are communicated
in IV § 2 and V §§ 2 and 3. The pomts at the beginning and the
end of the condensation are marked by 6.c. and e¢.c.; they are con-
nected by curves which thus separate the homogeneous area from
the area where separation occurs. Finally the plaitpoints and the
points of contact are indicated by P and Ff, 4 is the point adopted
according to IV § 5 for the critical point of carbon dioxide.
It appears that the agreement for volumes larger than the critical
is_very satisfactory. In the smaller volumes, however, considerable
systematic deviations from the law of corresponding states occur.
We have already used these diagrams to determine the critical
temperature, pressure and volume in the sense as explained above
for the different mixtures. Although these results are satisfactory
they will not be given here, as more accurate results may be expected
from the same operations with diagrams projected on double the
scale for the part concerned.
If on a pT-diagram we draw the point of contact- and the plait-
( 388 )
point curves, they are seen to touch each other at the end .(critical
point of pure carbon dioxide) in agreement with Comm. N’. 81
§§ 9 and 14 (Proc. Oct. 1902). In the investigated part the curves
do not show the point of inflection found by VerscHarreLr with
mixtures of hydrogen and carbon dioxide (Comm. N°. 47 Proc. Feb.
1899); they are always concave towards the Z-axis.
Physics. — ‘‘/sothermals of mixtures of oxygen and carbon dioxide.
V. Lsothermals of mixtures of the molecular compositions 0.1047
and 0.1994 of oxygen, and the comparison of them with those of
pure carbon dioxide.” By W.H. Kezsom. Communication N°. 88
(6 part) from the Physical Laboratory at Leiden, by Prof.
IKAMERLINGH ONNES.
(Communicated in the meeting of November 28. 1903).
§ 5. According to § 4 (p. 586) the observations allowed of a
more accurate determination of the data for the critical point of
the mixtures for the range of the larger volumes and the range of
temperatures over which the observations have been made, in the
sense as it has been explained there, than it was possible from the
drawing given there. To this end diagrams were projected on
double the scale for the points in the homogeneous area for which the
volume is larger than 0.005; in these diagrams 0.0005 is represented
Ve
‘yy
by 1 mm. both for doy — and for logv. To determine the relation
of the critical pressures independently and to test the relation of the
critical temperatures of mixtures to that of pure carbon dioxide,
: : pr.
diagrams were constructed for the same area, where log Fis drawn
as a function of log p: here 1 mm. represents: on the Jog p-axis
v
0.00025, on the log Gaxis 0.0005.
al
§ 6. The diagram for the mixture which had been transferred on
tracing paper and in the middle of which a cross of axes was drawn
in order to permit an accurate judgment of the agreement of the
systems of axes for the two diagrams, was placed over the diagram
for carbon dioxide, so that the Jogv-, and log p-axes respectively
coincided, and then they were shifted until to the eye the isother-
mals of the mixture coincided with the system for carbon dioxide.
"~~ - =
W. H. KEESOM. Isothermals of mixtures of oxygen and carbon
dioxide. V. Isothermals of mixtures of the molecular com-
positions 0.1047 and 0.1994 of oxygen, and the comparison
of them with those of pure carbon dioxide.
400 -
| A
\
BA
N \
\ = 0104E
~~
\ >
200 | +
| \ Nee
300 FL. | : Pee o oe
5 | ‘ee a s a
i oe —
aoe 7 | r oS ee ia -
. 300 400 500 600 rele) 800 goo
Proceedings Royal Acad. Amsterdam. Vol. VI.
( 589 )
Then we measured off for the isothermals of carbon dioxide which
-lay between those of the mixtures, the situation of the former with
regard to the two neighbouring isothermals of the latter; this was
done for a number of points distributed at regular distances. Let
T, and 7, be the temperatures of the two neighbouring isothermals
of the mixture, and 7” the temperature which for the mixture cor-
responds to that of the isothermal of carbon dioxide considered, then
ep.
jeer Be
We assumed that the isothermals coincided best when the mean
square of the differences of gw and the mean g were as small as
possible.
Table XXIV, which refers to the comparison of the Jog j-diagram
of the mixture 0.1 with that of carbon dioxide shows in the 3¢ column
the afore-mentioned mean square of the differences, viz. for the
isothermals of 41.95° C. and 37.09° C. of carbon dioxide (after reduction
to the same temperature interval 7’,—7',) combined, for the different
superimposings of the coinciding systems indicated in the 1st column,
while 1.85 of the mixture coincided with the values of log p for
carbon dioxide given in the 2¢ column.
we obtain a great number of values for the relation g =
PBN BE i XING
It | 4.8850 | 0.012165
feniIte hy 48840) = 0.040535
lll | 4.8829 | 0.004783
Iv | 4.9821 | 0.004440 |
Vv | 4.8810° | 0.006221
os
Accepted; 4.88235
In table XXV we find the data for the critical points of the mixtures
thus found, combined with the data about the plaitpoints and the
points of contact, and also the critical points of carbon dioxide and
oxygen (the latter according to O1szEwskl). *)
1) It here appears that in the diagram given in § 4 (p. 587) in order to
obtain the best agreement for the area of the larger volumes, the isothermals of
the mixture 0.1 must be moved 5 mm. to the left, those of the second mixture
6 mm. to the right. The conclusions about the non-correspondence at the smaller
yolumes, however, still hold, the deviations even increase.
( 590 )
PAA Ee ioe B Se
Se | estaiceihs eel bie ee eneic (ne.
ait Pryi | Lor | Tk | Prpl | Par | Pork | Pzpl | Yar | Yak
| | | | :
0 304 .02/30%.02/304 02)72.93 72.93 72.93 | 0.00443
0.41047 | 295 .03/296 .33/ 285.68 | 86. 60/82.83 67.70 0.003878 |0.005005 450
| } | |
| | | | |
| 0.1994/2985 .55/989 31) 272.92|99.65/89.20) 67.30 3606 | D322 | 431
| 154.2 |154.2 (154 2 [50.7 |50.7 |50.7 | | |
esa | ea
The values of 7, derived from different diagrams and belonging
to different coinciding isothermals, did not differ more than 0.5 deg.
: ie ; 5
We-obtan~ for. ¢, = Wee for the mixtures 0.1 and 0.2 re-
oPrkUxk
spectively: 3.485 and 3.446, in sufficient harmony with the value
3.45, derived on p.577 of this Comm. IV for carbon dioxide.
About the critical data the following may be remarked: v,; shows
a maximum in the range investigated; for « between 0.1 and 0.2
por descends much slower than between 0 and 0.1; the same holds
in a less degree for 7%.
§ 7. To calculate the quantities introduced in Comm. No. 75, (Proce.
Dec. 1901):
il , De int Ip rck
—— one we rd , ete.
Ty \ de /r=0 Eee U6 45
I have represented several quantities of Table XXV as functions of «.
Observations for more values of « would'be required to determine
with some certainty how say v,, depends on w. As it appeared
that in consideration of the critical volume of oxygen, the data of
table XXV, could not be satisfactorily represented by a quadia-
tic funetion, I have added a term with «* and have derived the
coefficients from the data for carbon dioxide and oxygen (putting
herefor C’, equal to the value for carbon dioxide) and the two
mixtures. In this way I found:
Trt == Ty{1 — 0.6563 w + 0.8350 2? — 0.6715 2°}.
Pek = pe }l— 1.0871 «w 4 4.1885 2? — 3.40638 2°}.
Vek = ve {1 + 0.54225 w — 4.0310 a? + 3.2183° vt.
Papt = Ty {1 — 0.25792 & — 0.2349 a7}.
Pupl = pe {1 + 1.6639 @& + 1.5775 a? — 3.5462 2°}.
Trr = Ty. {1 — 0.2474 & + 0.0898 x? — 0.3352 2°}.
Poy == pe (fF 1.4963 2° — 1911S a 0 ee,
Ae
ee
( 591 )
The data about 7°; could be represented very accurately by a
quadratic function.
We may expect that for values of x outside the range of obser-
vation these formulae will show important deviations from the
experiment, because errors in the observations for «=0O.1 and
x = 0.2 pass over increased into the values for the other range. This
holds especially for 77, pre and v,, which are exposed to so much
more sources of errors than the other quantities.
§ 8. From the formulae given above we find:
Oe — 4 0871;
1 (dog 3
= al “) ) _ 0.54295,
Uk dx ]x—0
while « — 3 — 0.4808. That this value does not agree better with
the value of y found directly, while in § 6 we found that for the
Pxk Vek : F
—““ was properly satisfied, is due to
May (3
the representation by the above-mentioned functions, which may be
expected to show just at the limits the largest deviations with regard
to the differential quotients.
two mixtures the relation
7
, : : 1 dT’ zy
With a view to this the agreements between —— and
—"
eX. ae
ee Le fdn- 1 /dp;,
=) ) and between — (2% ) and ~( Sk ) must be
Ty \ de Jxr=0 pe\ dae Jx=0 pe\ dx Jr=0
considered as satisfactory.
; : jae a i Le
The values of @ and ? derived from the values of — :
DM re
1 (dpxp
and — (=) by means of the formulae (2a) and (24) of
Gee edt fe aan
Comm. No. 75 and the values found in this Comm. IV (p. 577)
Ox O'2
for the coefficients C,, |] and C, | —— ] occurring there, and
Or Owdr
PP t (ae; ‘ der
the values of «@ and ~p derived from — = and —
ys ‘ dx 0 da 70
(as according to Comm. No. 81, Proc. Oct. 1902, p. a the same
formulae hold for these quantities) have been combined with the
values derived from the critical points A in Table XXVI, where the
first column indicates from which point the data have been derived.
1) Comp. VerscHAFFELT, Comm. N°. 81, Proc. Oct. 1902, p. 325.
( 592 )
PAB. Br ACEVe.
Z }
| x | —0.6563 | —4.0874 |
P —0.6864 —1.2190 |
R | —0.6174 | —0.9892 |
For this application of the formulae of Comm. N°. 75 it should
be borne in mind that in the derivation of them we have used the law
of corresponding states, while in §4 (p. 587) it appeared that already
at the critical volumes deviations could be detected. As long as z,
however, is very small, the points 7? for the different mixtures will
lie in an area where according to KAMERLINGH ONNES (comp. § 4)
the law of corresponding states may be considered to hold at least
to the first approximation, so that then we find an ae and a @# for
the critical points for that area. The same may be said of the points
R. From the numbers given it appears that the values of @ and p>
with relation to those points, at least to the first approximation, agree
with those relating to the critical point of the mixtures for the area
of the larger volumes.
For the slopes on the p7-diagram for the plaitpoint- and the point
of contact curve with small «2, we find:
T;. ( dp Lye f di
= (4) apes yi, Mee 2 () = 6.0445
pke\di pl pie \ dT],
values which agree sufficiently.
For the slopes of the curves which in the same diagram connect
the points A and P we find:
For the mixture 0.1: ne cae == 2102)
Pypl = Tk
For the mixture 0.2: 2.561.
For the curves which connect A and R:
For the mixture 0.1; 2“? — 1.491
Day — Tk
For the mixture 0.2: 1.336.
From either side, therefore, there is an approach towards the value
1.610, which both quotients must have for very small 2.
§ 9. From the formulae given in § 7 it would follow that the
largest plaitpoint pressure to be expected in mixtures of carbon
dioxide and oxygen would be 132 atms. (with «—= 0.57), while the
largest value for 7',—T,; would be expected to be 15°.7 C. (with
ss
( 593 )
z= 0.63). The last value will probably be too large, as the curves
which, according to the afore-mentioned formulae, represent 7’, and
al as a function of «, and which for =O almost touch each
other, do not do so for «1 and hence for larger x yield too
large values for T7,—Toy1-
§ 10. Purity of the carbon dioxide. The values of a and 8 found
and the increase of vapour pressure found at 25°.55 C. with the
condensation: 0.07 atm. (comp. this Comm. IV, p. 567) allow us
to judge of the purity of the carbon dioxide used. By means of
formula (9) of Comm. N°. 79, Proce. April ’02, which for the unities
used in this paper may be written
(0,—v,) (Py— Ps) = Ar (e+ e-k—2)
if
A, = 14+ 0.0036625 ¢
and .
Eo -—p oY Cis!)
| pd? A;
we find, on the supposition that the admixture were oxygen, and
using for @ and the values derived from the point A:
x2 = 0.00027 .
§ 11. Retrograde condensation. In the annexed plate we give
for the two mixtures investigated curves which represent vj, as
function of v according to the tables given in sections 2 and 3
(p. 579 ff.). The curves for the different temperatures are marked by the
letters, by which the corresponding isothermals have been indicated.
k=
~The numbers on the plate hold for the unity 0.00001.
Physics. — ‘‘J/sothermals of mixtures of oxygen and carbon dioxide.
VI. Injluence of gravitation on the phenomena in the neigh-
bourhood of the plaitpoint for binary miatures. By W. H.
KrEsom. Communication N°. 88 (7 part) from the Physical
Laboratory at Leiden, by Prof. KamertincH Onngs.
(Communicated in the meeting of November 28, 1903).
§ 1. In this Communication V, § 1 (p. 577) it was remarked
that the liquid meniscus at the end of the condensation over a certain
range of temperatures appeared or disappeared in the tube. Kturnen
(Comm. N°. 17, Zittingsversl. May 1895) was the first who explained
these phenomena by the theory of van per Waats on the influence
of gravitation on the thermodynamic equilibrium in mixtures. (Contin. JI
( 594 )
p. 30). The following pages may show that there is also a quanti-
tative agreement between the phenomena and that theory.
§ 2. In the mixture with the molecular proportion 0.1047 of
oxygen the meniscus by increasing the volume at 21°.86 C. appeared
at the top of the tube, at 21°.94 C. it was formed at the mark
44.99 (stirrer below, mercury meniscus at 41.66); at 22°17 C. the
meniscus appeared at the bottom of the tube, at 22°.09° C. it was
formed at the mark 43.93 (stirrer below, mercury meniscus at 41.57).
The top of the tube was at the mark 47.40 (em).
In the mixture of the molecular proportion 0.1994 the meniscus
appeared at 13°.12 C. at the bottom of the tube, at 13°.07 C. it
appeared at the mark 38.5 (stirrer above, mercury meniscus at 37.4);
at 11°.89 C. the meniscus appeared at the top of the tube, at11°.92 C.
it appeared at 42.3 (stirrer below, mercury meniscus at 37.7). The
top of the tube was at the mark 42.97. We may assume that for this
mixture the limits between which the meniscus appears in the tube
are: 13°.10 C. and 11°.90 C.
In these observations the volume from the homogeneous state was
increased by small variations; in this case the meniscus even without
stirring appears quickly at its definite place, which is not altered
by stirring. If on the contrary we start from the state where separation
into two phases occurs and the volume is decreased, the meniscus
only disappears after stirring and then suddenly; hence it seems
that in the former case the equilibrium is established much sooner *).
§ 3. In order to be able to compare the observations discussed
above with theory, I have found what may be deduced for it if
x is supposed very small. It may be easily derived from conside-
rations of vAN pER Waats (Contin. II, p. 30 ff.) that the phases
which are in equilibrium are determined by the following pair of
equations :
M(1—2)+M,o(/Oypy Oy |
T : : M,——-M,) | —— }} odi
i Lv °F (5 ta ( 2 Fy AYE Ox ey u
M (1—2)+M,a/f 07» 0?
Fde= a : aye ras + (M,—M,) alld gdh
v Ov 0a: Ova:
Here y is the free energy for the molecular quantity of the mixture,
vy the molecular volume in ce., J, the molecular weight of the
substance of which the quantity in the mixture is indicated by «
ae
1) Compare with this what has been remarked in this Comm IV p. 574 about
the circumstance that the equilibrium was not immediately reached after the
heating of carbon dioxide at the critical point. Comp, also Gouy, C. R. t. 116,
p. 1291 and Maruias, Le Point critique des corps purs, p. 89.
‘
Se. <= |
iii
(aun)
(admixture), /, that of the other substance, while
= (Gr) (=) Gear)
The equations (1) determine on the w-surface a curve which
according to Kurnen (1. ¢. p. 6) I call the gravitation-curve’).
From (1) we derive:
M,A—«)+ Mx
dae (5) F v
dit gy On)» ($2) M,A—«)+ Mae & O7Y + (Mt, — re +)
Ov v Ow0r
ao a ee, dv On
From this equation it follows that at the plaitpoint —|{—}],
ditgr 1
: P
hence the gravitation-curve touches the isobar, and accordingly also
the spinodal curve, for which /=0O. Then also at the following
point of the gravitation-curve which passes through the plaitpoint,
dv
mae dv
to the first approximation —-— = | — }, or at the plaitpoint
div gy Ow pT
d?v 07x 2)
ligt Ou? ee :
By means of this we have for a point of the gravitation curve
which passes through the plaitpoint, in the neighbourhood of the
latter: 7
pod ecwn, gh (Oh) (BE) a (BEVOY go BEV) (BF
=3 010 \ (5) (Sas a aoe as) tara) de) ta)
in which equation the differential quotients of /’ and v must be
taken at the plaitpoint. If here we put w7,; small, we may reduce
this form using reductions as in Comm. N°. 75, § 7 (Proc. Dee.
1901), to the first approximation to:
0 PS \
1 MM Tele Ger
Le a ae \ ae Jr
2 wT pl (op)?
; Ow vT
in which relation the differential quotients of p must be taken at
the critical point of the simple substance.
+]
1) Comp. also Kuenen, |. c. Fig. 2.
2) This has been demonstrated for the gravitation-curve on the y-surface for a
constant mass in a different manner by Kuenen, |. c. p. 8
og
Proceedings Royal Acad. Amsterdam. Vol. VI.
( 596 )
If also in the second member of the equations (1) we put.” small
Wwe may integrate the latter to
(3). 3
M,
1 5 9 Tol = ~ gh | constant
‘Sai ap . 2
ait & Tl) (MRT, nH Eat (2)
From this equation we may easily derive the value of x7,; if the
mean composition Y, the height of the tube /7 and the place where
the meniscus appears are given, and hence also «7,;—_X, if this
takes place just at the top or at the bottom of the tube. Let 7’y,;
be the plaitpoint temperature belonging to the composition X, 7%; the
temperature at which the meniscus appears just at the top of the
tube, 7’,.,, the same for the bottom of the tube, then we obtain :
at oe Pin eo Sop Bi ge 2 ae, AT pt
| pl — Try f : 3 = ’
4A MRT, \0a)or (; ) dar
Vie
Te
Ov"
and for 7%; the same formula with the other sign.
If as in Comm. N°. 75, § 2 we introduce the law of corre-
sponding states this formula becomes :
2 pa = ee On AT xpi 4 3 MoH
via 7T X \p—ea ars = a ae (3)
PRL» C, ( )
Ow?
dd
upl
AL
where for we still could substitute the form given in Comm.
N°. 75 equation 2a.
§ 4. In the comparison of formula (8) with the observations
mentioned in § 2 1 have assumed that for the area of the plait-
points the law of corresponding states holds to the first approximation,
and I have taken for @ and 3 the values derived from the observations
of the plaitpoints (comp. this Comm. V, § 8).
On
For (53) I have taken the value —5.3 calculated by VerscHarrent
ae
(Comm. Suppl. N°. 6, Proc. June 1903, p. 121) from the series of KamEr-
s (0°n
LINGH ONNEs, which value with C,—3.45 *) gives ( C, (; ) = — 216%),
e
With the value 7 = 5.8 cm., and the critical density for carbon dioxide
1) Comp. this Comm. IV, p. 577.
“) Gomp. Gomm. N°. 75,, Proc. Dec. 1901, p. 307.
p ae Oo
Ta ens
M
— = 0.448, derived from the data of this Comm. IV, we find,
UE
supposing that formula (3) were to hold as far as the value 7 = 0.1047:
T spi — Poyl a Lt ae
The agreement with the value found in §2 (between 0°.15 C.
and 0°.31 C.) is better than might be reasonably expected with the
suppositions made. The circumstance that for the second mixture
1°.20 C. was found for this shows that for this value of « terms
with * etc. have already a preponderating influence.
Physics. — ‘“Hysteretic orientatic-phenoment.” By Prof. H. E. J. G.
pu Bors. (Communicated by Prof J. D. van per WaAats).
(This paper will not be published in these Proceedings).
(February 25, 1904).
KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,
PROCEEDINGS OF THE MEETING
of Saturday February 27, 1904.
QOS —s
(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 27 Februari 1904, Dl. XII).
Gi © BEE aro Abs:
H. W. Baxkuvis Roozesoom and A. H. W. Aren: “The melting point lines of the system
sulphur + chlorine”, p. 599.
A. W. Visser: “Enzymactions considered as equilibria in a homogenous system”. (Commu-
nicated by Prof. C. A. Lopry be Bruyn), p. 605.
A. J. P. vax pen Broek: “The foetal membranes and the placenta of Phoca vitulina.”
(Communicated by Prof. L. Bork), p. 610.
W. Karremn: “On the differential equation of MonGr’, p. 629.
W. A. Verstuys: “The singularities of the focal curve of a plane general curve touching
the line eat infinity > times and passing « times through each of the imaginary circle points at
infinity.” (Communicated by Prof. P. H. Scmours), p. 621.
W. A. Verstuys: “On the position of the three puints which a twisted curve has in common
with its osculating plane.” (Communicated by Prof. P. H. Scuourr), p. 622.
A. Smits: “A contribution to the knowledge of the course of the decrease of the vapour
tension for aqueous solutions.” (Communicated by Prof. H. W. Bakuuis Roozesoom), p, 628.
(With one plate).
H. Kameriincu Onnes and C. A. CromMerin: “On the measurement of very low temperatures.
VI. Improvements of the protected thermoelements; a battery of standard-thermoelements and ~
its use for thermoelectric determinations of temperature’, p. 642. (With 2 plates).
J. E. Verscusrrett: “Contributions to the knowledge of van per Waats’ /-surface. VIII.
The ¥-surface in the neighbourhood of a binary mixture which behaves as a pure substance.”
(Communicated by Prof. H. Kameriincu Onngs), p. 649. (With one plate).
The following papers were read:
Chemistry. — “The melting point lines of the system sulphur
+ chlorine.” By Prof. H. W. Baknvis Roozesoom and
fe He WwW Aran.
(Communicated in the meeting of January 30, 1904).
The boiling point lines of this system have already been described
at the meeting in May 1903. These led to the view that the com-
pound §,Cl, in the liquid and vaporous condition is but very little
dissociated and also that further compounds occur at a not too low
temperature in liquids with a higher proportion of chlorine.
40
Proceedings Royal Acad. Amsterdam. Vol. VI.
( 600 )
A closer study of the changes in volume which take place in these
liquids and of the velocity with which this happens has rendered
it probable that SCI, is chiefly formed and in addition also SCl,.
The equilibrium between $,Cl,, SCl,, 5Cl, and Cl, which takes
place in the liquids is not modified to any extent by cooling below
O° and remains totally unchanged at those low temperatures at
which these mixtures may deposit solid substances. This gives rise,
during the solidification, to very peculiar phenomena which, up to
the present, have not been noticed with other systems but which
may be explained by the views of the phase doctrine.
/o0
Bf)
S
ot iat
On the other hand nothing noteworthy occurs with mixtures con-
taining 50—100 atomic per cent of 5S. These behave entirely like
mixtures S.C], +8. The melting point of 5,Cl, (—80°) is lowered
by sulphur to F; the melting point of sulphur is also lowered by
5,Cl, from B (120°) to F.
At a low temperature the solubility of 5 in S,Cl, is very small.
The solubility or melting point line of 5 consists of two curved lines
( 601 )
FC and CB, which at C=96° join at an angle. The top line relates
to monoclinic, the lower one to rhombic sulphur.
Mixtures of O—50 atomic °/, sulphur may on cooling, give as
solid phases Cl,, S,Cl, and SCI,.
The manner in which they are successively deposited may be
best explained by first observing in what manner the solidification
of a mixture of these three substances would take place when the
SC], could be considered as an independent third component.
This would be the case if this compound did not dissociate in the
liquid condition and also was not formed from liquid $,Cl, and Cl,.
The system would then behave as a ternary system, the solidification
phenomena of which could only be completely represented by a
spacial figure.
We may also, however, disregard the constitution of the liquid
and express its gross composition only in Cl, and $,Cl, which is
all the more justifiable as there is no means of determining the
amount of SCI, in the presence of Cl, and $,Cl,.
We then obtain a representation in a plane (see fig. 2) which is
the projection of the spacial figure *).
In this figure EH and HA
are the solidification lines of
the binary mixtures SCI, and
Cl,, EK and KD those: of SCI,
and §,Cl,, AG and DG those
of Cl, and §,Cl,.
The ternary mixtures whose
compositions lie within the
region IHAG first deposit solid
chlorine, those in IKDG solid
S,Cl, and those in HEKI solid
SCl,. For each gross composi-
tion there exists a greater or
smaller series of molecular
_ arrangements which cannot be
ICL, Scly pee represented in the plane, but on
which the temperature at which
the one or other solid phase
commences to be deposited depends. (Some mixtures may even sepa-
rate more than one phase according to their molecular composition).
1)'We must then accept as components: 3 Cl, and S,Cl, in order that the
middle of the abscissa axis represents the composition SCI.
40*
( 602 )
This difference is further shown by the different crystallisation paths
which on further cooling are traversed by mixtures of the same
eross composition.
These crystallisation paths start in each of the regions mentioned
from the point representing the melting point of the solid phase,
that is from A, D and E respectively, and indieate the series of
mother liquors which remain, during a continued cooling, at each
temperature. The crystallisation paths in the first region end in HI
or IG, those for the second in KI or IG, for the third in HI or KI.
The lines I and I] schematically indicate two similar paths in the
last region, the vertical line EE’ is a third one which applies to a
liquid of the gross composition SCl,.
As soon as the crystallisation paths arrive at HI, KI or GI, the
subsequent solidification takes place along these lines, each time
with deposition of two solid phases: Cl, -- SCI, on HI, 5,Cl, + SCI,
on KI and Cl, +.5,Cl, on GI.
Finally the last liquid solidifies in 1 to a ternary eutecticum of
the three phases.
This would be the state of affairs if — as has been said — SCl,,
S,Cl, and Cl, were miscible in all proportions without transformation.
If, however, SCI, were a dissociable compound whose formation
and decomposition led to complete equilibria at all solidification
temperatures, then instead of the solidification deseribed another
would occur along the lines AH’, H’E’K’, K’D causing the system
fo appear as a binary one in) which occurs a compound which
enters into equilibrium with its Components in the liquid condition.
The position of these lines within the figure of the ternary system
is determined by the degree of dissociation of the liquid compound.
If this is extremely small, these lines approach to AH, HEK and
KD, if very large they approximate to AG and GD and the com-
pound does not appear as a solid phase. Solid Cl, is deposited along
AH’, solid SCl, along H’EH’K’, solid S,Cl,-alone K’D; HH” andake
are two eutectic points where complete solidification takes place.
These three lines are not only the first series of solidifying points of
the different mixtures, but at the same time the crystallisation paths
of all mixtures.
Now with mixtures of S,Cl, and Cl, neither the first nor the second
case is quite realised. At the low temperatures at which the soli-
difications take place, Cl,, S,Cl, and SCl, behave as independent
components ; for instance Cl, and $,Cl, may be mixed in the liquid
condition without entering into combination and in this way the
two solidifying lines AG and GD (fig. 1 and 2) of these mixtures
( 603 )
have been determined. Neither does SCI, undergo decomposition at
those low temperatures. If, therefore, it were possible to isolate pure
SCI,, all imaginable mixtures thereof with Cl, and $,Cl, or with
both might be obtained and the further portions of fig. 2 could then
be constructed. This, however, is not the case.
On account of the extreme minuteness of its crystals and the low
temperature at which crystallisation takes place, the compound SCI,
cannot be isolated in a pure condition and cannot, therefore, be
added in definite proportions to Cl, or 5,Cl,. By exposing various
mixtures of these compounds to temperatures of O° and higher it is
possible to cause the voluntary formation of those quantities of SCI,
which are in equilibrium with Cl, and 5,Cl, at the temperature
chosen. As these do not change much with the temperature, the
same series of mixtures is fairly well retained on cooling to the
crystallisation temperatures. The number of ternary mixtures whose
crystallisation may be investigated is, therefore, restricted to one for
each gross composition.
We, therefore, always obtain for the first solidifying points a series
such as AH’E’K’D in fig. 2, just as if we were dealing with a
binary mixture in which a dissociable compound occurred. If, however,
the equilibrium in the liquid does not change when Cl,, SCI, or
5,Cl, crystallises out, the system on solidification must behave as a
ternary one.
This should have appeared in practice by the fact that the curve
of the first solidifying points did not also represent the path of
crystallisation, and, therefore, the mother liquor left after cooling
each mixture to a lower temperature differed in composition from
that given by the point on the curve corresponding with the
temperature in question. Owing to the nature of the crystals,
however, it was impossible to remove the mother-liquor with a
pipette.
It was, however, possible to prove in the case of a liquid of the
gross composition SCI, that this does not completely solidify to SCI,
at EK’, but only commences to deposit SCI, at that temperature
(—30°), which quantity increases on further cooling, but in such a
manner that no complete solidification takes place below —80°. In
the points on both sides of E’ the continuity is still more pronounced
and this makes the accurate determination of even the first solidifying
points very difficult.
In the second place the solidification of the different mixtures
ought not to be complete in H’ or in K’, but only in I after traversing
the crystallisation paths H’'l and Kk’.
( 604 )
This is confirmed qualitatively but the exact determination of the
lines HT and K'l and consequently also of the ternary eutecticum
proved to be impossible. .
In this way no more was obtained than is indicated in Fig, 1,
namely the solidification lines AG and GD for the mixtures of Cl,
and S,Cl, in which no compound had formed and besides these the
series of the first solidifying points AH, HEK and KD for the par-
tially combined liquids formed at O°.
These lines therefore correspond with the accentuated lines in
Fig. 2. The true melting point of SCl,, without decomposition ot
the liquid (E Fig. 2) is therefore not yet known. If SCI, could have
been prepared in pure crystals, this might have probably been
determined as it would presumably be situated below the tempera-
ture where the liquid compound shows perceptible decomposition.
This is rendered more probable by the observation that notwith-
standing their minuteness the crystals of SCI, when rapidly heated,
are quite permanent up to — 20°.
Fig. 1 does not agree with fig. 2 in an important point. In
the latter DK is placed above DG, in the first DK is found below
DG. DG_ represents the lowering of the melting point of 5,Cl, by
added Cl, when this remains unchanged: Dk when a portion of it
combines with a part of the S,Cl, to SCI, according to the equation
§.Cl, + 3 Cl, = 2 SCI,.
If we now compare the total amount of the foreign molecules
which oceur along with the 5,Cl,, for the same total amount of
Cl,, these numbers are smaller in the case of a partial formation
of SCL, than when this is not the case. According to this supposition
DK ought to be situated higher than DG.
As in practice, the reverse position was found we must look for
a cause whieh may explain this fact. We find this by supposing
that besides SCI, there is also formed in the liquid a considerable
proportion of SCL, according to the equation
S.Ck Ch aes
By taking this view the number of foreign molecules mixed
with the S,Cl, becomes greater owing to the formation of SCI, than
without this.
The formation in the liquid of an amount of SCI, exceeding that
of SCL, which had already become probable by the dilatometric
experiments has, therefore, been confirmed. The slow: crystallisation
of SCL, will now be better understood; but the liquids between Cl,
and §,Cl, should now be considered not as ternary but as quater-
( 605 )
nary mixtures. If during the crystallisation SCI, in the solution does
not vield SCL, according to the equation
3 SCI, = SCI, + 8,Cl,
solid SCl, ought to be found somewhere on the way to complete
solidification. This point could not be decided.
Chemistry. — ‘“nzymactions considered as equilibria in a homo-
genous system.” By A. W. Visser. (Communicated by Prot.
C. A. Lopry pr Brtyy).
(Communicated in the meeting of January 30, 1904.)
1. A number of facts exist which indicate that the reactions
created by enzymes are reversible. Crort-Hin1') succeeded in partly
converting a concentrated solution of glucose into a disaccharide with
the aid of maltase and reversibly the disaccharide into glucose. He
supposed it to be maltose but afterwards EmMMERLING *) proved it to
be isomaltose; the fact however remains that maltase may cause
a reversible formation of polysaccharides. Recently, Crort-HiLu *)
has further proved that there is formed from glucose by means of
maltase a new crystallised biglucose called revertose, he thinks
it probable that also maltose may be formed ‘). KaAs?TLE and
LOEWENHART *) and afterwards Hayriot *) found that the fat-splitting
enzyme lipase is capable of resolving butyricester into butyric
acid and aleohol and on the other hand of forming the ester from the
decomposition products. EMMERLING’) noticed the regeneration of amygd-
alin from nitrilglucoside-amygdalate and glucose under the influence of
maltase. E. Fiscuer and FRANKLAND ARMSTRONG *) prepared with the
aid of Kefir-lactase a disaccharide from a mixture of galactose and
glucose called isolactose, which up to the present could not be
isolated in a state of purity. The same authors also found that
kefir-lactase forms a disaccharide from glucose alone and_ that
emulsin does the same from a mixture of glucose and galactose.
1) J. C. S. 78, 634 (1898).
2) Ber. 34, 600, 2206 (1901).
8) J. C. S. 83, 578 (1903).
4) All these experiments show that the substance supposed to be maltase still
contains other ferments.
®) Am. Ch. J, 26, 533 (1901).
6) GC. R. 182, 212 (1901).
7) Ber. 34, 3810 (1901).
8) Ber. 35, 3151 (1902).
( 606 )
From several experiments I have made, I think the conclusion
may be drawn that it is probable that saccharose may be rege-
nerated to a slight extent from glucose and fructose by means
of invertase, whilst it may be taken as proved with tolerable
certainty that salicin may be regenerated from saligenin and glucose
by means of emulsin.
If, with the usual precautions, a N/, solution of saccharose *) is
exposed to the action of invertase, the former is resolved into
glucose ++ fructose and the liquid shows a final polarisation
of — 3°.26°).
If a similar solution is inverted by N/, HCl the final polarisation
becomes — 3°.42.
A solution containing the same amount of glucose and fructose *)
as is formed after total inversion of a N/, solution of saecharose
also gives a final polarisation of — 3°.42.
A solution containing equal quantities of glucose + fructose and
which showed at the start a polarisation of — 12°.46 gave after
two. months action of invertase a polarisation of — 12°.29. These
experiments have been repeated a few times.
A N/,, solution of salicin, resolved by emulsin into saligenin and
glucose, gave a final polarisation of 1°.03 whilst a solution containing
as much saligenin and glucose as ought to be formed by the
complete decomposition of a N/,, solution of salicin shows a polari-
sation of 1°.18. Such a solution which contains the same amount
of emulsin as the N/,, solution of salicin gave after a month
a polarisation of 1°.03.
The formation of saliein, which shows that the reaction is
reversible, may be proved qualitatively in the following manner.
The glucose was got rid of as much as possible by fermentation
and after filterimg, the saligenin was completely removed by agitating
the solution with ether. The liquid was now concentrated to about
5 ¢c¢. on the waterbath. To one half of it was added a drop of
ferricchloride solution (1:10); this gave no coloration showing the
absence of saligenin, a mere trace of which would give a blue
coloration. The remainder was evaporated to dryness and gave
with H, SO, a red coloration (formation of rutilin). 0.5 ¢.e. of al °/,
bacterial action: all apparatus and utensils were also previously sterilised.
?) A Lippich-polarimeter was used. The readings were accurate up to 0°.02
and all observations were made at 25°.
°) I have to thank Mr, Atperpa van Exenstein for supplying me with these
perfectly pure sugars.
( 607 )
salicin solution and 1 gram of glucose was diluted with a 1 °/,
saligeninsolution up to 50 ¢.c.; the 0.005 gram of salicin present
could be detected in the manner described. Great care must be taken
to ensure the complete removal of the saligenin, as this also gives
a red coloration with strong H, SO,.
[ think these experiments warrant the conclusion that the
resolution of saccharose by invertase may be probably considered
as an equilibrium reaction and that this is tolerably certain in
the case of the action of emulsin on salicin.
As regards the last reaction, TAmMMann had come to the conclusion
that, although incomplete, it is not however a limited reaction, as
the limit did not undergo retrogression on adding the products of
decomposition. TamMann however has not worked with sterile
solutions so that, as others have already observed, his experiments
are not conclusive. Moreover, the figures found by TamMann for
the concentration in the condition of equilibrium at 0°? and 25°
differ not inconsiderably from my own.
2.. Dynamical researches as to the action of enzymes have soon
shown that certain decompositions do not proceed in such a simple
manner as in the case where acids are employed. Although
O’Suntiivan and Tompson first believed that the hydrolytic resolution
of saccharose by invertase is represented by the same simple
formula (for reactions of the first order) as that for the same
reaction by H-ions, TammMann and Dvuciavx have demonstrated that
such is by no means the case. This has been confirmed by subsequent
researches particularly by those of Henri. The reactioncoefticient of the
system saccharose + invertase calculated according to the logarithmic
formula appeared to increase; for the system salicin + emulsin it
appeared to decrease with the time. So TamMann comes to the
conclusion that the enzymes do not conform to the same laws as
the inorganic catalyzers and that these laws will not readily be
traced, and Ducnavx is of opinion that the laws of physical chemistry
do not apply at all to enzym actions.
As the dynamic investigation of the action of ferments had only
just commenced, these conclusions could hardly be accepted as final.
The exhaustive researches published in 1901 by Vicror Henri *)
and afterwards continued *) have indeed proved that the course of
ferment actions may decidedly be expressed by a formula. It has
already been observed that the resolution of saecharose by invertase
proceeds more rapidly than is expressed by the formula for reactions
1) Z. phys. ch. 39. 194 (1901).
2) Lois générales de l’action des diasases. Théses, Paris, Février 1903.
( 608 )
of the first order; it was therefore obvious to assume here an acce-
lerating autocatalysis, a reaction for which Ostwap *) had worked
out a formula. Henri has now followed this course indicated by
OstwaLp and deduced an empirical formula which, when applied to
his experiments led to coefficients which may be taken as practi-
cally constant for N/100 to N solutions. Henrt accepted a theory
of the mechanism of the action of invertase according to which the
ferment should enter into combination with saccharose as well as with
fructose (according to an equilibrium-reaction). By now trying diffe-
rent values for the equilibrium constants of these two reactions, he
arrives at two figures, the introduction of which into the formula
leads to the said constants. I believe to have succeeded in proving
that Henri’s views are not correct judging from his own experi-
mental data and from my own observations.
Recently Herzoc *), for the resolution of salicin by emulsin, (where
on applying the formula for reactions of the first order the coeffi-
cients regularly decrease) has applied Ostwatp’s formula for reactions
with negative autocatalysis *) to Henris and TAMMANN’s experiments
on the said reaction; he has found that this formula leads to
reaction coefficients which may be considered as constants. These
constants Change with the iitial concentration of the salicin solutions.
Hrrzoc however observes that Ostwawp’s differential equation for
negative autocatalytic transformations is incomplete ‘and that it
would be better to give it the form of a _ reaction of a higher
order’. This was already done by me some time ago.
3. Given the fact (now toleradly well substantiated) that enzym-
actions are equilibrium reactions, I have taken a view of the theory
of these decompositions different from that hitherto accepted and first
deduced formulae giving the relation between velocity of reaction
and chemical equilibrium. These formulae differ from those at present
applicated to this ease *); I have deduced them for mono-, bi- and
trimolecular equilibrium reactions *), first tested them in well-kwown
cases (ester formation; the transformation studied by KisvEr *) ete)
also by ScHoori’s observations on the action of sugars on urea *)
which I have myself extended and subsequently applied them to the
observations of Henri as well as to my own series of determinations
relating to the saccharose and salicin resolutions. The results of this
1) Lehrbuch, II, 2, 262.
2) These Proc. VI November 28 1903, p. 332.
’) Lehrbuch Il. 2. 270.
4) Osrwaup’s Lehrbuch Il, 2, 251, e.v.
6) Z. phys. ch. 18, 161 (1895).
6) Rec, 22. 31, Dissertation, 1902.
( 609 )
application are very satisfactory. I have further been able to develop
for the activity of the enzymes an intensityformula wherein, besides
the concentrations of the solutions, the constants found experimen-
tally occur and which I believe, gives a fair representation of the
quantitative progress of the enzym actions as studied by previous
observers and myself.
4+. These mathematical deductions and the details of the other
results obtained by me will be published fully elsewhere. [ may
only remark further, that my results show that, starting with a N/,
saccharosesolution (171 grams per litre) we arrive at a final con-
dition where fully 1 gram of saccharose still remains present. The
inversion therefore proceeds to an amount greater than 99°/,. This
seems also the case in the resolution of salicin.
My experiments further show :
1st. that the two ferments invertase and emulsin retain their
quantitative activity for some weeks in properly sterilised solutions.
2ed. that the average factor for the change of the velocity of the
saccharose decomposition with the temperature equals 2 for 10°
between O° and 25°,
3°. that by a change of temperature from O° to 25° the equili-
brium is displaced very little or not at all, which quite agrees with
theory as the caloric effect of the reaction is very small.
4th that at a definite temperature the change in concentration of
the enzymes has no influence on the equilibrium but only on the
velocity; the latter, as in other catalytic actions, is directly propor-
tional to the enzyme concentration.
5th. that as already observed by Henri, the intensity of the
invertase is smaller in proportion as the quantity of invertsugar,
present with the same amount of saccharose, is greater.
6. that the intensity not only depends on the quantity of invert-
sugar but also on the quantity of saccharose present in the solution ;
it is smaller when this quantity is greater.
This last conclusion does not agree with that of Henri (Theses,
p. 72) where he states that the addition of saccharose at the
commencement of a reaction has no influence on the velocity of the
inversion, but accelerates it when the addition takes place in the
middle of a reaction.
7, that, as duly required by theory, the reversal of the reactions
between glucose and fructose and between glucose and saligenin
proceeds very slowly and requires several weeks.
The results of Henri’s experiments are in accordance with the
intensity formula, which I have deduced.
( 610 )
Anatomy. — “Vhe foetal membranes and the placenta of Phoca
vitulina.’ By A. J. P. van pen Brork. (Communicated by
Prof. I. Bork).
(Communicated in the meeting of January 30, 1904).
Some time ago a seal in an advanced state of gestation was sent to
the anatomical Laboratory of the Amsterdam University. As neither
the foetal envelopes nor the placenta of the pinnepedal carnivores have
been described in detail, I was very gratified to be entrusted by the
Director of the Laboratory with the task of carefully examining these
organs. The preparation turned out to be in very good condition and
well enough preserved for microscopic examination.
Whereas a more detailed description wiil be published in another
place, the following may be given here as the principal results of
my investigations.
The gravid uterus was U-shaped, the convexity being on the eranial
side. The organ, which was somewhat flattened dorso-ventrally was
lying in transverse direction, so that the fundus uteri was situated
in the righthand part of the body. This U-shaped curve was ac-
companied by a twisting of the organ, so that the left ovarium,
entirely enveloped by an ovarial bag, was medially situated.
The greater part of the ligamentum latum had become absorbed ;
the ligamentum rotundum, a very powerful cord, ran from the front-,
respectively hind-wall of the uterus, that is: from the spot where
the ovarium was lying against the uterine wall, running down in a
slanting direction across the latter, towards the abdominal wall. The
ostium uteri, filled with a mucous clot, showed an aperture of +3 em.
Close to the top of this ostium, which formed an oval foramen in
the middle of the portio vaginalis, the foetal sac, rather strained,
could be felt. All this seemed to indicate that the animal, being in
labour, had gone ashore, when it was caught.
On opening the uterus by means of a longitudinal incision in the
organ, along the convexity, the following was noticed: The wall of
the uterus is extremely thin in proportion to the voluminous organ,
a little more than 1 mm., but increases in thickness towards the
vagina. The muscularis of the wall of the latter, however, is rather
thick (1 em.).
The chorion, as well as the placenta, is only loosely attached to
the walls of the uterus all over. It appears that the foetal sac reaches
down to the ostium uteri. On detaching the placenta I found septa
of cellular tissue adhering to the inner surface of the wall of the
uterus, which, just there, is somewhat thicker.
( 611 )
The placenta forms a perfectly closed girdle, situated about the
middle of the foetal sac, or, with regard to the uterus, in the
curve of that organ.
The uterine surface presents a lobated structure, the various irre-
gular lobes being separated by pretty wide fissures, and as moreover,
the placenta is comparatively thin, it is not very compact.
The circumference, measured at the surface of the uterus, is 66
em., the width, which is the same all over, 32 cm. The edges are
not stumpy and thick; rather thin. Several thick bloodvessels emerge
from the sides of the placenta, branching off into the chorion so
abundantly as to leave not a single part of it without a supply of
vessels. On splitting the chorion and the placenta along the convex
curve of the foetal sac, the amnion becomes visible. This is quite
disconnected. There was no direct contact between the two tissues
anywhere, nor with the placenta, the amnion not covering the foetal
surface of the placenta, but branching off at the placentary end of
the umbilical cord. The amnion, like a bag with thin walls, invests
the foetus pretty closely, especially along the back. Only behind
the tail-end of the foetus, which is turned towards the fundus uteri,
we find another part of the amnion that is not taken up by the
foetus, but filled with a substance that is soft to the touch. The
amnion is partly vascularized, partly devoid of any vessels ; especi-
ally in the immediate vicinity of the umbilical cord a vascular part
is noticeable. Here the amnion membrane seems also to be somewhat
thicker and to consist of two layers, which are moveable one over
the other. Here we find the umbilical sac, in the shape of an
elongated organ, connected with the amnion right along, lying against
this membrane.
As the amnion has not coalesced with the foetal surface of the
placenta, the latter can be at once examined after opening the
chorion. Of an insertion proper of the umbilical cord into the
placenta there can hardly be any question, the vessels dividing and
branching off long before they reach the placenta.
These ramifications enter the placenta at a rather considerable
distance from each other. Slips of the allantois, which lines the
placenta, cover these vessels, which therefore are found in dupli-
‘atures in this membrane as soon as they leave the cord. The
main canals of each of the two umbilical arteries branch off
into a girdle-shaped half of the placenta, and with fairly large
ramifications spread further into the chorion. When the convex
surface of the amnion is slit open very little foetal fluid runs out.
The foetus is found to be lying with its muzzle towards the ostium
( 612 )
uteri, its back turned upwards. It also appears that the available
space behind the tail-end of the foetus is filled up with about 3 liter
of lanugo, some of which was also adhering in places to the body
of the foetus. In the skin itself there were no remains of the lanugo-
covering, which consisted of short, straight hairs, all of the same
pearl grey colour. Speckled or black hairs were not found.
The umbilical cord has a length of only 12 em. so that the animal,
at the time of birth, is bound to pull out the placenta along with
the membranes. The skin is continued for about 1 cm. along the
umbilical cord, which is compressed sideways along its whole length.
Taking into consideration the thickness of the umbilical cord there
is only a small quantity of connective tissue. The three umbilical
vessels are not twisted around each other. The outer surface of the
umbilical cord is yellowish, shining, and feels hard.
A microscopical examination gave the following results:
The umbilical cord is covered with an epithelium forming a pave-
ment of several layers, which forcibly reminds one of the epithelium
of the epidermis. The lower layer of cells consists of high cells of
a somewhat cylindrical shape, lying close together, with large round
nuclei. Towards the surface the cells grow flatter, their limits being
well defined in the layers immediately following the basal one. As
the cells flatten down, the nuclei grow less prominent. Finally,
forming the outside layer, there is a horny surface with lamelliform
structure, in which, (by means of staining with haematoxyline) the
remains of nuclei can be traced in places. This horny layer is sharply
marked off from the epithelium-layer.
Where the amnion leaves the umbilical cord, this epithelium of
many layers changes into a simple epithelium.
In the cord itself there are in section five channels of unequal
width and with a wall of uneven thickness.
The two umbilical arteries and the vena umbilicalis have a very
thick muscular coating of circular muscle-fibres. The muscle-cells
show a lamelliform arrangement, the lamelli being separated by
connective tissue.
Elastic filaments cannot be traced, Towards their lumen the blood-
vessels are covered with an intima, which is not clearly defined
towards the periphery.
In the walls of the blood-vessels we find, almost right up to the
intima, the lumina of vasa vasorum, belonging to the system of the
vessels proper of the umbilical cord, to be mentioned presently.
A fourth lumen is that of the second vena umbilicalis. The wall
of it clearly shows an intima, round this there is a circular muscular
( 613 )
coating, and then, right round this, a coating of bundles of muscles
running lengthways, but not adhering close together. In the walls of
this vena I have not noticed any bloodvessels. In the lumen I found
here and there some blood-corpuscles. In following up this partly
obliterated vena towards the foetus, it is found to divide itself into
two branches shortly before the foetal insertion of the umbilical
cord; the two branches run together a little way down, then one of
them splits up again and three branches can be traced right up to
the front abdominal wall, where they lose themselves. Towards the
placenta this vena also splits up into ramifications, which grow finer
and finer and finally branch off into the tissue of the umbilical cord,
The fifth lumen in the umbilical cord is situated in the foetal half
between the two umbilical arteries ; towards the placenta these approach
each other and the vessel runs alongside of them. This lumen is
of an irregular shape, somewhat compressed and provided with an
epithelium composed of cells that are flattened and arranged in several
layers, the respective limits not being distinctly defined.
This lumen runs right through the cord till close to the placenta
where it suddenly stops. There is no communication between this
lumen and the yolksac. That we have here a continuation of the
allantois-channel is proved by its original position between the two
umbilical arteries, which position I also noticed inside the abdominal
wall. I did not notice any remains of a yolk duct with certainty.
The stroma of the umbilical cord consists of cellular tissue with
exceedingly fine fibrils pursuing a circular course. Underneath the
epithelial coating this circular direction is deviated from and the
curve becomes irregular. Round the vessels there is no distinct system
of circular fibres. Between the two arteries the character of the
stroma changes somewhat, it is of a looser construction and contains
a few longitudinal bundles of smooth muscular tissue. These can
best be seen by staining with polychrome methylen-blue (Unna) and
ean be traced right through the whole cord. By the side of this the
profusion of the bloodvessels belonging to stroma funiculi proper
seems remarkable.
These vasa propria funiculi umbilicalis ave met with right along
the funiculus, most of all in the foetal part. They appear to be con-
nected with the vasa of the subcutaneous cellular tissue of the abdo-
minal wall. Arteries as well as large veins filled with blood are
noticeable. The distribution is somewhat irregular. Especially round
the umbilical vessels they are heaped up together, entering the walls
close up to the intima. I have not been able to ascertain the existence
of a connection between the vasa propria funiculi and the vasa
( 614)
umbilicalia. As far as I know, a case of the presence of vasa propria
funiculi in any animal was not on record.
This isolated case suggests the general peculiarity of the vascular
system of seals, to which attention has already been drawn by
Hyer’). I may add that the immediately surrounding parts of the
allantois were also very rich in vasa propria, which, however, were
generally of smaller size.
A microscopic examination of the chorion, or rather of the wall of
the outermost and widest embryo-sac, shows us that there are two
layers, an outer one and an inner one, connected by extremely
loosely woven cellular tissues; between the two layers the blood-
vessels are situated. The outer, or uterine layer, the chorion proper,
is lined with a simple cylindrical epithelium about 20 uw igh. The
nuclei are oval-shaped and in the basal half of the cell; the proto-
plasm is finely granulated. Cell limits are distinctly visible. The inner
lining consists of one layer of flat cells with much-flattened nuclei.
The inner coat is nothing but the outer surface of the allantois.
(This connection will be referred to bye and bye). We cannot, there-
fore, call this membrane the chorion, strictly speaking, the name of
outer foetal envelope is more to the point. The bloodvessels in the
wall of this sae are of unequal caliber, in the centre, between the
two layers, larger vessels are met with, the arteries have a thick
muscular coating, smaller vessels are found partly in the stroma of
the allantois, in greater quantity however right under the chorion-
ectoderm.
Even with the naked eye an accumulation of small villi, conspi-
cuous by their velvety aspect, could be seen in some places on the
uterine surface of the outer foetal sac. A microscopic examination
confirmed that these were rudimentary villi. The epithelium did not
differ from the other parts, but the stroma was a much more com-
pact tissue and the interior was filled with very numerous capillaries
the central ones of which had a fairly large lumen.
The amnion, too, or rather the inner foetal sac, is found to consist
of two layers, lying against each other along the whole surface; only
where the wmbilical vesicle is situated they separate to envelop this.
The inner layer is covered with a cubic epithelium of 10 u., the outer
one is identical with the inner layer of the outer foetal sae and
must be considered to be a layer of the allantois. On comparing
foetal sacs of Phoca vitulina with those of other carnivores, Phoea
1) Hyrti. Ueber einige Kigentiimlichkeiten der arteriellen Gefissveriistelungen bei
den Seehunden.
Sitz. Ber. d. mata. naturw. Classe d. Akad. d. Wissensch. Vienna. Bi, XI, 1854,
( 615 )
is found to exhibit somewhat different conditions. In dogs, for
instance, according to the investigations of biscHorr*), SrRanL?) and
others, the allantois-sac forces its way between the chorion and the
amnion. While the allantois is thus making its way further and
further between the two membranes, gradually separating them
almost entirely, the edges of the allantois are coming closer together.
But these edges, according to the drawings of Biscnorr (l.c. Plate XV,
fig. 8) remain separated; according to STRAHL"), they establish contact
by means of cellular tissue, chorion and amnion being thus connected
at this point of contact. In Phoca I found neither the edges of the
allantois-sac, nor a connection like Srraun noticed in dogs; I must
therefore assume that in Phoca the development has gone a little
further and that through the elimination of the partition between
the two edges of the allantois-sac, mentioned by Srrant, the outer
and inner sac have become entirely isolated. The whole of the
original extra-embryonal coelom-cavity has in this way disappeared;
the space between the inner and outer foetal sac is the allantois-cavity.
I have already pointed out that the umbilical cord was connected
with the placenta by means of a so-called insertio velamentosa. The
vessels running towards the placenta or in the inverse direction, are
enclosed by the membrane covering the foetal side of the placenta,
viz. the outer layer of the allantois-sac, which continues on the
chorion along the edge of the placenta.
As far as the inner foetal membrane is vascularised, the vessels
show the same proportions as in the outer foetal sac.
The umbilical sac is situated in the inner wall of the foetal sac,
between the amnion and the allantois, connected by thin cords of
cellular tissue with both. It is a much-elongated, narrow bag, with
folded walls.
The walls consist of strongly vascularized connective tissue, its
limits are not sharply separated from the stroma of the amnion-
and allantois membranes. Only here and there we find the remains
of an original coating of epithelium. The bloodvessels, some of which
have a fairly large lumen, run almost entirely lengthways through the
organ. The majority of these vessels have a thick muscular wall and
were filled with blood. These vessels and the umbilical ones are
connected with one another.
With ‘regard to the placenta the following may here be stated.
1) Biscuorr, Die Entwickelungsgeschichte des Hundeéies.
2) Straut, Untersuchungen tiber den Bau des Placenta. III. Archiv fiir Anatomie
und Entwickelungsgeschichte. 1890.
S)l.G= pee oo:
41
Proceedings Royal Acad. Amsterdam. Vol. VI.
( 616 )
As already mentioned, the seal has a placenta zonaria, which, com-
pared with that of the dog or the cat, is of much looser construction.
The uterine side shows many more or less deep grooves, which
divide the organ into a number of lobes. The deeper grooves, as a
rule, run through the placenta in a longitudinal direction.
In the seal a green border-zone, such as we find described
in the placenta of several carnivores, does not exist. Yet there is
something like it. On detaching the placenta from the wall of the
uterus, one could see, even with the naked eye, that both edges
of the placenta were freely dotted with small, light-orange coloured
particles, some as large as a pin’s head; found, on examination, to
consist of bilirubine. This pigment was found in enormous quantities
and a microscopical investigation showed that the whole edge was
saturated with these orange coloured bits. Owing to them, the narrow
border-seam, instead of being a dark red, like the other parts of
the placenta, was of a dirty brown colour.
As far as the blood-pigment penetrates in the placentary tissue
— for these corpuscles may safely be taken to be transformed blood —
the whole tissue, when seen under the microscope, is tinged a light
yellow.
On following up this tinged zone under the microscope, we shall
see that along the outer edge the amorphous pigment is found in
ereat quantities, but no newly ejected blood is. found. Only at some
distance from the edge the clots of pigment become smaller, but at
the same time they are found to be lying in ejected blood that can
still be easily recognised as such, until finally, at the placental end
of the brown zone, the blood predominates and here and there a
elittering orange-coloured pigment clot is met with.
From this we may infer that the hemorrhage, during the devel-
opment of the foetus, first occius on the outer limits of the placenta
and gradually more towards the centre.
The bleedings at the edge are not the only ones I noticed in the
placenta.
In dogs, for instance, Srrani describes some so-called green islets
in the placenta, spots corresponding to the green edge-zone. These
islets do not occur in seals either, at least they are not visible
macroscopically. Under the microscope, however, we can see in
many places, under the foetal coating of the placenta, some uniformly
coloured light yellow spots. On close inspection if is seen that in
such places, situated immediately below the foetal surface, hemor-
rhage has taken place, and that round this seat of bleeding the
placental tissue is of a light yellow hue all over, Blood-pigment in
t Olt: )
amorphous condition I have not been able to trace in such spots.
The discoloration of the tissue may be explained in this way that
the blood-corpuscles give off their haemoglobine to the surrounding
parts and that this is absorbed gradually by the surrounding placenta-
tissue. This latter point is the most significant part of the process,
for, why should this surrounding tissue, which, unlike the corpuscles,
can hardly be regarded as having died off, absorb the altered blood-
pigment so uniformly? That we have here no post-mortem pheno-
menon appears clearly on examination of the blood-vessels at the
edge of the placenta. As already stated, this is of a more intense
yellow hue than that of the spots under the foetal surface, partly
through the more considerable amount of pigment. Now, we find in the
tissue of the border of the placenta, several vessels, the lumen of
which, in addition to blood-corpuscles, is filled with pigment. These
are foetal vessels. In the vasa umbilicalia I only found some blood,
but no pigment.
The presence of this pigment in the vessels proves, that this yellow
hue of the placenta-tissues is a vital reabsorption-process, and not
one of post-mortem diffusion. There is another fact in favour of
this view: it is my discovering (in the border-zone, where the
villi are not very much elongated and the villous epithelium, or
chorion ectoderm, is still intact), some distinct pigment-particles in
these cells, which had been absorbed from the pigment situated close
against this epithelium.
And on further comparing the structure of the placenta of Phoca
with that of fissipede carnivores (e.g. the dog), it is found that the
spongy layer is entirely missing; all along the thickness of the
placenta the same uniform structure is maintained.
The foetal surface of the placenta is covered with a layer of
the allantois, coated with a single layer of flat endothelium, as
already described. Underneath this, there is a thin layer of fairly
firm connective tissue, in which the larger ramifications of the umbilical
vessels are found.
From this tissue coarse septa of connective tissue find their way
into the placenta, which gradually diminish as they run towards
the foetal surface, although they usually succeed in reaching it. In
these septa the ramifications of the foetal vessels are found. Coarse
septa send out finer compartments in every direction. The coarser
ones divide the very compact mass of placenta into smaller sections.
From the maternal side too, some septa of connective tissue filling
up the aforesaid grooves on the foetal side of the placenta, enter
the latter; they are however less voluminous than those coming
41%
( 618 )
from the foetal side. The compact cellular tissue of the placenta
reaches right up to the wall; between the latter's coating of
muscles and the compact placenta tissue a very narrow, loosely
woven layer of connective tissue runs. In this layer, lying against
the muscular coat, we find the diameters of the very wide
uterine vessels and also in several places some uterus-glands. These
glands, in the shape of elongated tubes with short ramifications and
parallel with the surface of the uterus, are squeezed in between the
muscular coat and the placenta. They have a distinct lumen, the
epithelium is highly cylindrical. They are glands that have obviously
fully developed, but have not been invaded by villi. On the foetal
surface of the placenta moreover, distinct extremities of glands are
met with, which, like those just described, have bent round and
which run parallel with the muscular coat, in which a foetal villus
is plainly visible. These villi are not lying close to the inner surface
of the follicle, but are somewhat retracted from it. I did not succeed
in observing a distinct epithelium on these villi.
Some of these uterus glands appear in another form: the cells
have very much increased in volume, have swollen and are bulging
out in several places in the lumen. The protoplasm of these cells is
of a well defined reticular structure, the cell nuclei are in the basal
part of the cells. In the lumen of such glands we find some inde-
pendent cells, or combinations of only a few, some with nuclei,
the larger ones without any; moreover some conglomerations of
deeply stained fine particles may be observed here and there.
The compact mass of the placenta, when magnified, turns out to
contain a great number of bloodvessel-lumina, adhering close together,
each one of them surrounded by a distinct endothelium-wall. The
ramifications of the foetal vessels, together with some connective tissue,
run between these branches of the placental vessels. Forming a separating
laver between these two systems of blood-vessels, we find in the
greater part of the placenta one single layer of nuclei, situated in
a mass of protoplasm, in which, however, no cell limits could be
traced. This layer of nuclei, is to be regarded as belonging to a
syncytium. In some places I counted two, sometimes even more,
rows of nuclei between the branches of the placental- and those
of the foetal vessels, without my being able to say with certainty
which part of it should be taken to be of a syneytial character.
In the cases of suballantoidal hemorrhage and in the surrounding
parts, the nuclei of cells, lining the endothelium-walls of placental
vessels and the foetal villi adhering to the blood-mass, are of a
much darker hue than those of other parts of the placenta, As a
coating of these foetal villi I often observed a double layer of
nuclei, viz. a layer of flattened nuclei, lying close together, coating
the villus and, round this, a layer of round, large nuclei. Against
the latter layer the extravasated blood is found. Between the nuclei of
the inner series, cell-limits are sometimes noticeable (chorionectoderm).
Finally I want to offer a few remarks about the villi in the
border-seam.
The mass of coagulated blood found near the edge of the placenta,
and the bulk of which has the shape of amorphous, orange coloured
lumps, is mainly situated between two very long villi, running in
a slanting direction from the foetal surface of the placenta to the
wall of the uterus. From these villi and from the part of the
chorion that is lying between the bases of the two, a number of
shorter villi, with ramifications, find their way into the above
mentioned mass.
These villi are generally somewhat swollen and rounded off at
their extremities. They are all conspicuous by their profuse vascularity.
The chorion between the bases of the two villi just described is
covered with a layer of very darkly-stained nuclei, lying very close
together. It remains doubtful whether this was a syncytium.
The secondary villi, passing into the above mass also have such
a coating. In some cases two rows of nuclei could be seen on
the surface, while it seemed to me that the row of nuclei turned
towards the villus was not of such a dark hue as the outer one
turned towards the blood-mass. At the extremities of the villi the
nuclei are found to lie very closely together and to be more numerous.
Both in the protoplasm of the latter layer, covering the chorion,
and in that of the villi one observes accumulations of orange-
coloured particles.
Reabsorption of these corpuscles from the mass found in the border-
seam of the placenta is therefore effected by means of the coating
of the said layer of the chorion as well as that of the villi.
In one or two instances I found a coloured particle in the stroma
of a villus or in the capillaries running into it.
( 620 )
Mathematics. — “On the dijjerential equation of Monee” by Prof.
W. KaApreyn.
(Communicated in the meeting of January 30, 1904).
If we suppose that in the differential equation
Hr 4: OKs 3 1 es ee ee
H, K, L depend only on p and 4q, the necessary and sufficient condi-
tions for the existence of two intermediate integrals are the following.
In the first place H, A and ZL must be proportional to the second
differential coefficients of a function 6; thus
eS ee L
dT iT ea i piage iat ag a
O55) Sa eee, Ee
13 22
In the second place the function 6 must satisfy the differential
equation of the fourth order
2D(6 0? D 4 o?7D 4 ue 0S Oe
= 22 Op? 12 Op age ifs Og aa
=sle D\ 4, DW, 4 (oD :
=e fae = 2 Op Og Ge) | See (3)
eS VO Oia 4...
The general integral of this differential equation can be represented
by the following formulae :
where
Fea \
| dea Re Tare
14“—1
! !
yi
Via ae
u— UV
) i \ Sn
a 24 g' du — 2 fu ys” dv — (g' — fh’) (g' + wy’) —
e e
9 = 5
ae : |v —h)(g' —w) — (g—w) Y — M) |
where w and v indicate arbitrary parameters and
g=9) , h=h@& , G=H— » P= Hl)
four arbitrary functions, and
dy deg
/ Tait oe ae ta
If the conditions (2) and (3) are. satisfied the equation (1) will
possess the two intermediate integrals
ze—c gy" — Ww g' —= iy (1),
e—yy'—ah! =3(0)
Where 5 denotes an arbitrary function and w and + the functions
of p and q, derived from the equations (4).
In the particular case that the function @ satisfies the two members
of the equation (8) separately, we have to distinguish two cases
according to the double sign im
dD 6 2 os ahha — 6, Ove 0D
sR ae ES —=—= (0,
Og fs Op
The general integral can be written in both cases respectively
ES.
pj [ute = 9-)) HF (yu)
VW |
q= ys + (9)
A6=(2wy"'—4ugdt4o zw ryp— 2f( gq" = v)jupdu |
where g=g(w) has the same meaning as betore, whilst 7 and +
represent two new arbitrary functions of the arguments placed after
these symbols.
In these cases the two intermediate integrals are
epy(ug"’—a')— alu r" + 7") = & (u),
yt af (uve eo H=Slee +7),
the values of w and v being expressed in p and y with the aid of
the formulae (5).
The condition (8) appears, although in a different shape, already
in the excellent dissertation of J. VAnyi (hKlausenburg 1880).
Mathematics. — * 7% singularities of the focal CUTIVE of a plane
general curve touching the line at injinity 6 times and passing &
times through each of the imaginary circle points at injinity.”
By Dr. W. A. Versicys. (Communicated by Prof. P. H. Scnovurs).
(Communicated in the meeting of January 30, 1904).
In “Verhandeling’” 5 of the “Kon. Ak. v. W.” at Amsterdam Vol.
VIII, I have deduced some formulae expressing the singularities of
the focal developable and of the focal curve in function of the sin-
gularities of a plane curve having no particular position.
In a similar way it is possible to deduce the following formulae
expressing the singularities of the focal developable and of the focal
curve of a plane curve touching the line at infinity o times and
passing ¢ times through each of the imaginary circle points at infinity.
Let the plane curve be of order pg, of class v and let ¢ represent
the number of its inflectionai points. Then the singularities of the
evolute or of the cuspidal curve of its focal developable are the following :
rank, r= 2(u+ »v — 2e — 9)
class, m = 2p
number of stationary planes, 4 — 2¢
double osculating planes, G = v* — » — uw — 384 = 30° 4+ 28 — 6
stationary tangents, v = 0
double points, = 3(u—r)+-¢
double tangents, w = 0
order, n= 2 (3 u + 4 — 6e — 306)
stationary points 8 = 2 (64 — 2v 4+ 3 — 12e — 60)
stationary points not at infinity and not in the plane of the curve
B' = 2 (Su — 38y + 31 — 8e — 30)
order of the nodal curve « = 2 (uw -+ rv)? — 10u — 2v — 3t — Bue
— 4uo — 8re — 4ro + 8? + 80-1 26?
+ 20s + 106.
The chief singularities of the focal curve are:
order, n= 2m? + 4uy + vr? — Llu — vp — dt — 8ue — 40 — Bre — 2rd
+82? + 86 + o° +20 4+ 9o
rank, 7 = 4ur + r* — 4u — 4v — 8re — 2r0 — 30° + 8e + 50 :
number of stationary tangents, 7 =O
class, m = 6°? + buy + 4ute 4- 2re — 36u — 12y — 181 — 24ue
— buco — l2re — 4ro — 81e — 20 + 246? + 1286 — 86?
+ 60e + 280
number of stationary points 8B = 2 (84 + 4) (2u + vr) — 57a + 21y
— 2/0 — 48pe — louo — 12ve — Aba
— Sue — 26 + 4828? + 368s6 + 40?
+ 3686 + 9b6e + 400.
Mathematics. — “On the position of the three points which a
tivisted curve has in common with its ose ulating plane.” by
Dr. W. A. Verstuys. (Communicated by Prof. P. H. ScnovuTe.)
(Communicated in the meeling of January 30, 1904).
§ 1. Let d be the section of the osculating plane V in a point
P of the twisted curve C’ with the developable O of which C is the
cuspidal curve; then the twisted curve C and the section d have in
the point / only two points in common, that is they have in
P a contact of the first order.
( 623 )
The curve C has in P three successive points in common with
the plane V. The curve C’ is situated on the surface V, so the three
common points must lie on the section of VY with VV. This section
consists of the curve d and of the common tangent / in P of (C
and d, counting double. In the following way can be proved that
of the three common points only two lie on d.
Let us first take instead of a general curve a twisted cubic C,.
Let P be the origin; the property being projective the plane at
infinity can be chosen in such a way, that the curve is represented
by the equations
=o PSO —= eh
If now in point ¢=—O the curves (, and d, had three common
points then in the origin also the radii of curvature of the two
curves would be the same. Let # be the radii of curvature of
C, in P and ¢ the radius of curvature of d, in P, we then easily
find:
ans: ds* it (l+4+ 9¢*)*2
VEAP BRE CH Vk 868 + 8604
So for ¢=0 we find K=-—
The surface OU, is enveloped by the plane
e—3yt+32P —#=—0.
So the curve d, is enveloped by the line
—syt+3s2t—P—0
Consequently the equation of d, is
Oo
so the radius of curvature 7 = The curves C, and d, have in
the origin not the same radius of curvature, so they have not three
or more points in common.
Let p be the orthogonal projection of C, on V7 (7 = 0), then C,
has with p three successive points in common in P, for all points
which (, has in common with JV’ must le on the section p of V
-with the projecting cylinder of C,. The projection p has for equation
ae
, nee 1
-and so also the radius of curvature in the origin R= z showing
-
again that the curves p and C, have in the origin three points in
common.
( 624 )
bo
Out of the two values R=~— and »—=-— ensues that the section
bo
d, lies near P on the convex side of the projection p.
§ 3. The latter can also be proved as follows tor any curve
with the aid of Descriptive Geometry.
If we take the osculating plane J’, in any point of the curve C,
to be the vertical plane of projection and the normal plane of the
curve to be the horizontal one (plane of projection), then the vertical
projection p” is a curve cutting the axis perpendicularly in a common
point P and the horizontal projection p' is a curve having in P a
cusp with the axis for cuspidal tangent. Let us now construct
the vertical trace d" of OU. The vertical traces of the generating
lines of O lie on the tangents to p", thus all on the convex side
of p", whilst those traces are also situated on the same side of the
perpendicular on the axis in /?, where also p” and p’ are lying. So
the curves d" and p" turn the concave side to the same side, whilst
d" near P lies outside p". So the curves d" and p" have an even
number of points in common.
Thus if @ and d" had the three points of C) lying in J’, in common,
then also p" and ¢/ would have three points near ? in common,
So according to what was proved above p" and d” had four points
in common. That fourth common point of p” and dd” would, lying
on d", also lie on OV and would be the projection of a point Q of
the curve ( lying as near to it as one desires. So at the limit the
projecting line of Q would be a tangent of O. Thus near Pa tangent
of O might be perpendicular to the osculating plane JV’, which is
impossible. So C and (" have no three points in common.
§ 4. We can prove moreover as follows synthetically that the
twisted cubic C, has not three points in common with the trace ¢/,.
If (, and d, had three points in common at ? then ¢, and the
projection p, of C, on Vo out of any arbitrary point A would have
three successive points in common. This projection p, is a eubic
curve of class four. The three inflexional tangents of p, ave the traces
of the three osculating planes through A, thus they are also tangents
to d,. As the contact of the second order in ? must count for three
common tangents and each of the three inflectional tangents of p,
for two common tangents, two curves respectively of class two and
class four would have nine common tangents, which is impossible,
So the curves C', and d, lave at P no three points In common,
sO
( 625 )
§ 5. It follows from what was proved above for a twisted cubic
that also a general twisted curve ( has not more than two points in
common with the section d¢ of its developable ( and the osculating
plane WV. If C and d had three points in common, then (/ and
the projection p of C out of any arbitrary point A on the plane V’
of ¢ would have three points in common. Let (, be a twisted cubic
;
having in 7 six successive points in common with (. Now |” is
also the osculating plane of C, in P?; let d’ be the trace of the
developable O, belonging to C, and let p’ be the projection of C, on
V out of A. As the developables VU and OV, have five successive
generating lines in common, so ¢ and d have at least three succes-
sive points in common, whilst » and p' have six successive points
in common. Now, if d and p had three successive points 'n common
at P, this would also be the case with d’ and p'. According to the
preceding § the latter is not true, so C and d have neither three
points in common.
§ 6. The theorem can also be proved by searching for the points
of intersection of the cuspidal curve v or of the nodal curve § with
a second polar surface 4?0, just as Cremona did (CremMoNA—CURTZE;
p. 87—90). To simplify the matter I shall first apply this proof to
a twisted cubic, after which the proof for the general case can be
more easily followed.
Let us take for developable O' the surface consisting of a develop-
able OU, and of a quadratic cone A with vertex 7) passing through
the conic d, situated in the osculating plane*)” of P and on (,,.
The cuspidal curve of this surface of order six is tne cuspidal curve
C, of O,, so » = 3. The nodal curve & consists of d, and of a
curve of order six s. This curve s intersects the plane V of the
conic d, six times, three times of which in the points where d,
meets a generating line of V,, for which the tangent plane passes
through 7’, these three points being points of contact of double
tangent planes of ©’. Consequently s has in /P three successive
points im common with d,. Let A?V' be the second polar surface
for a point A lying in V. The order of A?’ is four.
In the formula of Cremona for §(@— 2) | have only to keep the
first and the third term, none of the singularities appearing on the
surface under consideration which are furnishing the other terms;
but a term P must be added for the particular point ? where
another third sheet of the surface O” passes through a plane curve
d, lying on O,. This singularity has not been considered by Cremona ;
( 626 )
it appears on the foeal surface of a plane or twisted curve touching
the plane at infinity.
So the formula of Cremona becomes :
s(o—- 2) = number of times that s meets the curve
of contact of A+ 324+ P.
The curve of contact of A consists of the generating lines of O”
of which the tangent plane passes through A. Of these generating
lines two are situated on the cone A, each of these meeting the
curve ys three times and two are situated on Q, as A lies on the
osculating plane J”; the latter meet s each one time. This number
of points of intersection of s with 4? Q’ is thus eight. According
to Cremona they must each be counted one time, so the first term is 8.
The section of QO” with JV" consists of ¢, and of the tangent in P
to d,, both counted double. So the second polar curve of A for this
curve or the section of |” with 4* 0’ consists of a curve of order
four, touching d, twice in /P, having thus with d, and with s
too only four points in common. The formula of CREMONA gives:
6S See ee
Consequently : 4 = 4.
The points 4 are the poimts outside ? where the cuspidal curve
meets another sheet. As (’, meets the cone A in all six times, C,
can meet the cone A in P only twice, so C, has also with the
curve d, lying on A but two points in common.
§ 7. If we had taken A outside the plane V" this change would
have had no influence on the number of points 2, but the term
issuing from the lines of contact would have been one more, so P
would in that case have counted for 3.
By applying the above used method to the nodal curve d,, we
find that 4* O’ of an arbitrary point A lying outside J” also meets
/, in three points. The singularity 2? counts for six points of inter-
section of the total nodal curve § with A* 0’, thus for as many
points of intersection as two points 4.
Out of the formula of Cremona for » (9 — 2) it is evident that P
counts for two points of intersection of the cuspidal curve C, with
ZL? 0’, thus also for two points 2. From what precedes ensues that
the cone A’ passing through d@, is an ordinary touching cone and
that the point of contact P counts in both formulae of Cremona for
two points A.
§ 8. Let the curve C’ be a general twisted curve of order vy. Let
‘
VY be its developable, the class u, the rank @ and let the order of
( 627 )
the nodal curve on ( be §. Let the number of stationary tangents
be @ and that of the double tangents w. Let P be an ordinary point
on C, / the tangent in P to C, V the osculatine plane in ?
and d the curve of intersection of |}” with the surface O. Let ce.
be a conic having at ?P five suecessive points in common with d.
Let 7’ be the vertex of a quadratic cone A’ passing through c, where
7 is arbitrary but taken in such a way that A’ cuts the curve Cin
none of its singular points. Let s be the curve of intersection of O
with A. This curve, of order 2, shows singular points: 1st in P;
2"' where C or a line 6 cuts the cone A’ (point P excepted), these
are cusps 42 on s; 3° where A meets the curve & or a line w:; these
pomts are on the surface Q’ consisting of OU and A’ triple points
t and nodal points on ys.
If we now determine the points of intersection of s with the
second polar surface 4° V' of a point A lying in V" then according
to Cremona the cusps 2 must count three times and the triple
points t, through which only two branches of s pass, must count
twice. in order to find out for how many points of intersection the
point ? must count, we consider the first polar curve of the section
of Y with V. This section consists of the right line / counted twice,
of the curve d and of the conic c,. So the first polar curve consists
of the right line / and of a curve of which one branch has five
points in common at ? with c, or with ¢ and of a branch touching
/ also in P and lying at ? between / and d. So the second polar
curve shows at / two branches touching c,. The two branches
of s passing through P touch / in P, and JV’ being also of both
branches the plane of osculation, they have both with |” or with
c, three points in common. Each branch of s through /? has thus
with 4? 0° in LP but four pomts in common, so that the point P
counts for eight points of intersection.
Besides meeting the curve s in these singular points of s the polar
surface 4? V’ meets it moreover in the ordinary points where s meets
the curve of contact of tangent planes through 1. These points
count according to Cremona each one time. The curve of contact
consists of two generating lines of A’ each meeting the curve s
o times and of (u—1) generating lines of V, as A is situated in the
osculating plane J’. These generating lines each meet s two times,
so that to determine 4 we arrive at the formula:
207=—344+45--4w+8+20+4+2(u—])),
« SG ee ee 25 cae Eee. oc 6) ae
a= Bio o—p—25—2H— 3}.
As according to one of the formulae of CayLry-PLUcKER
( 628 )
o? —-o—n—2§—20—3(74 A),
then
A=2rv+ 20—2.
So the curve (' meets the cone A’ outside P still 2 r— 2 ‘times,
and P counts for two points of intersection. So the curve C' also
ineets the conic c, lying on A’ only two times and consequently
the curve d, having with c, five points in common at /?, meets it
also only two times.
Chemistry. — “A contribution to the knowledge of the course of
the decrease of the papour tension for Aqueous solutions.”
By Dr. A. Smits. (Communicated by Prof. H. W. Baxatis
RoOZEBOOM.)
1. In 1788 BiacpEN') discovered the relation between the lowering
of the freezing pomt and the quantity of the solved substance.
Among the substances which he examined, were however also some,
which showed deviations, either in this sense that the lowering of
the freezing point increased more rapidly or in that sense that it
increased more slowly than the concentration.
Réporrr*), who quite ignorant of BLAGpEN’s work, made the
same discovery in 1861, and Copprt*), who ten vears later (1871),
continued RiporRerr’s investigations, came both to the result, that
deviations from the rule first discovered by BrLaGprEN, occurred both
in one sense and in the other. A disproportionately rapid inerease
of the lowering of the freezing point with the concentration was
found among others for Nabr, NaJ, CaCl, H,SO, and also for NaCl,
whereas for the nitrates of Na, NH,, Ba, Ca, Sr, Pb, Ag and for
Na,SO,, Na,CO,, NH,CNS the reverse was observed.
As an illustration of the course, as for Nabr etc. Réporrr had
already adopted the formation of hydrates. Copper assumed for the
deviations for -the nitrates, which are mostly anhydrous, that they
are modified by the action of water or by the fall of the tempera-
ture in a certain, not further defined way.
Results analogous to those of BLaGprn, RtpoRFE and Copprt were
obtained by ‘TAmMANN*) in 1887 when determining the decrease of
the vapour tension. TAMMANN found namely, that for most of the salt
1) Wied. Ann. 39, 1. (1890).
*) Pogg. 114, 63. (1861); ib. 116, 55 (1862); ib. 145, 599 (1871).
*) Ann. Chim. Phys. (4) 23, 366. (1871); ib. 25, 502. (1872); ib. 26, 98 (1872).
') Wied. Ann. 24, 523. (1885).
— =a
( 629 )
solutions the diminution of the vapour tension with increase of con-
centration increased more than the concentration, whereas for the
nitrates of K, Na and for KCIO, the reverse was observed. The
later investigations of Bremer'), HetMHonrz*), WALKER*) and Dirererict*)
gave the same result as those of their predecessors viz. this that in
general the diminution of the vapour tension increases more rapidly
than the concentration, and that the salts which form an exception
to this rule are chiefly the anhydrous nitrates.
Up to 1905 the determinations of the freezing point of salt
solutions of smaller concentrations than those which had been earlier
investigated, yielded the result, that the molecular lowering of the
freezing point decreases with increase of the concentration. As these
measurements were continued to the concentration of + 1 gr. mol. per
1000 er. H,O, it followed necessarily, that where the reverse course
had been ascertained by the earlier observers, a minimum value had
to occur in the molecular decrease of the freezing point, but for a
concentration which lay above that where the investigators of later
time had stopped. |
In 1896, however, I had come to the conelusion in the determi-
nations of the vapour tension by means of the micromanometer °),
that for dilute solutions, i.e. for solutions below the concentration
of 1 gr. mol. per 1000 gr. H,O, the molecuiar diminution of the
vapour tension creased with the concentration. This was found
inter alia for solutions of NaCl, KOH, H,SO, and CuSO,, whereas
for KNQ,-solutions the reversed course was found. This result was
therefore in perfect accordance with what had been found by my
predecessors for more concentrated solutions, but was directly opposed
(except KNO,) to the results of the determinations of the freezing
point.
The question was now: “Which results are the correct ones ?”
In the determination of the boiling point 1 hoped to find a means
to answer this question. After having applied some improvements
to the method and after having rendered myself independent of the
fluctuations of the atmospheric pressure by using a imanostat, | began
the investigations and the result was published in April 1900 °).
1) Rec. tr. Chim. 6, 122. (1887).
2) Wied. Ann. 27, 568. (1886).
3) Zeitschr. f. phys. Chem. 2, 602. (1888).
4) Wied. Ann. 42, 513. (1893); ib. 62. 616. (1897). Ann. phys. Chem. 27, 4. (1898).
8) Archiv. Néerl. (2) 1 (1897).
6) These Proceedings II April 21 1900 p. 635, April 20 1901, Jil p. 717. In the
same year (1900) Jones, Cuampers and FRazer eryoscopically found minima for
MgCl, and BaCl, lying at 0.1—0.2 gr. mol.
( 630 )
I arrived at the following result :
The molecular rise of the boiling point increased for solutions of
NaCl and KCI from the concentratien + 0.3 gr. mol. per 1000 er.
H,O, both towards higher and towards lower concentrations, or in
other words, the molecular rise of the boiling point proved to have
a minimum value lying at + 0.38 gr. mol. For the anhydrous
nitrates of K, Na, Ba, Ag and Pb, however, the molecular rise of
the boiling point proved, quite in concordance with the determi-
nations of the vapour tension, to continually decrease with increase
of the concentration.
The method which was the least accurate in appearance, proved
to be able to point out a mistake both in the method of the freezing
pomt and in that of the vapour tension. The first work was then
to force the micromanometer to greater accuracy by applying some
improvements, and then to repeat the experiments. In 1901") anew
series of experiments yielded really a result which qualitatively
harmonized perfectly with that obtained by means of the boiling
point method. For NaCl as well as for H,SO, a minimum occurred
in the molecular decrease of the vapour tension, lying at + 0.5 er.
mol. As before KNQO,-solutions gave a strong decrease of ¢ with
increase of the concentration.
In the same year KAHLENBERG?) found for solutions of NaCl,
KCl, KBr, KJ and MegCl,, that the molecular rise of the boiling
point increased continually with the concentration for the first and
the last salt from the concentration + 0.2 gr. mol. to = 5 gr. mol.,
whereas for KCl, KBr and KJ a more or less clearly marked
minimum was found.
Bitz *) was the first to confirm my results with certainty in 1902.
He found a minimum in the molecular rise of the boiling point,
not only for KCl and NaCl, but also for RbCl and LiCl. His deter-
minations of the freezing point of alkali chlorides showed only for
LiCl a continual increase of the molecular lowering of the freezing
point with the concentration; a minimum was not found, however,
for the chlorides of the alkali metals by this method. For LiNO,
and Libr Binrtz found a faint minimum, whereas for the chlorides
of the bivalent metals by the cryoscopie way very strongly pro-
nounced minima were found, mostly lying between 0.1 and 0.2 ger.
1) These Proc. IV September 28 1901 p. 163.
*) Journ. Phys. Chem. 5, 339 (1901).
3) Zeitsch. f. Phys. chem. 40 s. 185 (1902).
( 631 )
mol., which is in accordance with the observations of Jonrs, CHAMBERS
and FRAZER‘).
The first who by the cryoscopic way discovered minima in the
molecular lowering of the freezing point for chlorides of the alkali
metals below the concentration 1 gr. mol., were JonES and GrTMAN *),
who published their results in the newly published Jubelhand fiir
Ostwald. It is remarkable that working with the common apparatus
of BECKMANN these observers obtained more accurate results than Raovu
with his apparently ideal apparatus. For Raovuitr found for NaCl-solutions
up to the concentration 1 gr. mol. a regular decrease of the molecular
lowering of the freezing point with increase of the concentration.
2. After having thus shortly pointed out what the boiling point
method, the vapour tension method and the freezing point method
have brought to light for the study of the non-diluted solutions, [|
proceed to give the results of the determinations of the diminution
of the vapour tension of NaCl and NaNO,-solutions, made by means
of the méicromanometer, in which the aniline-water-manometer was
replaced by the manometer of Lord Rayixien *). It seemed namely
very desirable for the greater certainty of the results, to repeat
some measurements with another apparatus, the accuracy of which
did not differ too much from that of my manometer. Lord Rayirieu’s
invention was therefore very welcome to me, because his manometer
was stated to reach an accuracy of + 0.00045 m.m. Hg, and mine
had an accuracy of 0.00025 m.m. Hg.
Lord RayiricH’s manometer and the arrangement of this apparatus
has been represented in fig. 1 and 2. A is a barometer tube, which
branches into two parts at the top; the two branches are blown out
to two bulbs of + 25 mm. diameterat LA. In these bulbs extend
two finely drawn out glass points, which are ground off to a sharp
point at the lower end. On the tubes LL, of which the one more
to the left is split up into two branches, as is seen in the horizontal
projection, and which thus furnish three points of support, a glass
plate .V is laid which bears a mirror J/, whose front is silvered.
The glass plate .V is fastened to the three points of support and
the mirror J/ to the glass plate by means of water glass.
Lord Rayieien had connected the tubes CC with his apparatus by
means of straight glass tubes 3 meters long, but here some glass
spirals = 35 c.m. long have been added between them in order to
prevent any wrenching.
1) Amer. chem. Journ. 23, 89 (1900); ib. 23, 512 (1900).
2) Zeitschr. f. Physik chem. 46, 244 (1903).
3) Zeitschr. f. Physik chem. 37, 713 (1901).
42
Proceedings Royal Acad. Amsterdam. Vol. VL.
( 632 )
The manometer / with baro-
meter tube A is (see fig. 2) fastened
M. | Scie
in a groove of asolid board P by
means of Cailletet cement. This
board is part of an adjusting table
S, which can rotate round an
horizontal axis by means of the
screw 2. This axis passes through
the poimts of support of two sets
of screws Z, only one of which
is to be seen in the figure 2. The
mirror of the manometer has
the axis mentioned is parallel
to its front and coincides with
its middle. The air trap V, in
which the barometer tube ends,
is by means of an India rubber
tube provided with two clamps
(F and Hf and connected with a
mercury reservoir J. |
The principle, on which this
manometer rests, is as follows:
If the barometer tube is filled
with Hg as far as in the bulbs BB
and if the pressure is the same
in the two legs of the manometer,
we can cause the two glass points
io just touch the mercury mirrors,
which are now iw one horizontal
Pigiah:
plane, by using simultaneously the
clamp Hf‘) and the screw 2. This point can be very accurately
determined, as we can observe the reflected images at the same time
with the points and so it is as if we saw twice two points approach
each other. If the light of an incandescent lamp g, concentrated by
a lens, was thrown on the manometer through a mirror im, a great
accuracy of adjustment could be reached after some practice, when
1) The clamp G serves for the rough adjustment.
2) As it proved necessary to prevent heating of the manometer as much as
possible, a thick plate of asbesios 7 was adjusted between the incandescent lamp
and the manometer; in this plate a glass vessel # was fastened with a solution
of alum for the absorption of the rays of heat.
been placed in such a way, that.
—
( 633 )
the points were simultaneously observed through two magnifying
vlasses.
The position which the mirror J/ occupies in this adjustment,
so the zero position, could be accurately determined by means of a
scale and a reading telescope with a cross wire. If now a difference
in pressure was brought about e.g. such that the mercury mirror
in the left lee fell somewhat and that jn the right leg rose somewhat,
the adjustment of the two points on the mercury mirrors could be
again reached by turning the adjusting table, to which the manometer
is fastened, over a small angle to the left by means of the screw P,
for which at the same time the screw // was to be used, as the
bulbs LL are no perfect spheres, and have not perfectly the same
diameter either.
When the glass points are again placed in the required way and
the reading glass is again read, it is clear, that
we can calculate the difference in level of the
mereury mirrors in a simple way from the
angle of rotation, when we know the distance
é.1, between the glass points. If this distance is /,
ea the angle of rotation @, the difference in height
Fig. 3. between the two mercury mirrors is:
k=l sin a.
If we represent the deviation observed with the telescope expressed
in m.m. @ and the distance from the scale to the mirror J, then
a
a (
tg. ¢.= 3 for which we may write ty t= >, provided @ be very
: ) ‘ e , ‘
small.
As further for small angles sim @ = ty a, we may write in this case:
la
Be a a oie Ne oeeatiese ieee Mer
If the angles are too large for this assumption, we get the following
form for /:
la x a7
b= (1-+ 55) Se, wore Seem rae eee
The distance between the glass points was determined by means
of a comparator and amounted to 24.66 m.m. = /. The distance
from the scale to the mirror amounted to 2735 m.m. = 6.
It now proved that when the deviation @ was smaller than 100
m.m., formula (1) could be applied, whereas for larger deviations
formula (2) appeared to be required.
The accuracy of adjustment, obtained in this arrangement with
42%
( 6354 )
Lord Ray.eiGn’s manometer, appeared to amount to 0.1 scale division
or to 0.00045 m.m. Hg, whereas with my manometer it amounted
to 0.00025 m.m. He, as has been said before.
Fig. 4 represents the whole arrangement. A is the micromanometer,
B the antomatic mercury air-pump, C'’ the manometer of Lord
taYLEIGH and PD the reading glass with scale and mirror, a is a strip
of mirror, cut from a sphere. In the focus an incandescent lamp 6
is placed, over which a glass cup has been placed enveloped with
filtering paper. A parallel pencil of rays falls through the glass seale
e and is reflected by the mirror J/ from the manometer into the
reading glass /.
From this figure the connection of C with A through the long
glass tubes ¢ and 7 is also clearly visible. The results obtained by
this arrangement are summarized in the following tables.
T Asis 15 SB eee
Na Cl.
ea rides y ees) (SE P, *) | Po—P, N Dn
in er. mol, p. in mem. He inmm. He | t= Pe n 008316 ”
1000 er. HO of 0°. of 0°,
0.0441 0 00720 0.163 | 1.96
0.41073 O O1619 Of151 | 1.81
0.3823 0 05535 0.1447 1 740
0.6299 0 O9125 0.1449 1.742
Q OQSST 0.14564 0.1473 | lena
2 O476 Q.31017 0.1515 4 822
3.3524 0.53442 0.41594 4.947
With the aniline-water manometer the following results had been
before obtained.
We see from this that the tables I and Il harmonize very well
qualitatively ; both give a minimum vaiue of ¢ for the concentration
+ 0):5. of. mG.
That there are differences in many cases in the absolute values of
ris probably due to the uncertainty which exists in applying the
temperature correction when working with my manometer. In future
1) Pm = molecular diminution of vapour tension.
2) 0,08316 = theoretical mol, dimmution of vap. tens. at 0°,
Na Cl.
ee je aes Pn | p—p, W Pi
in gr. mol. p. in mm. Hg in m.m. Hg ‘= “Dp. nh U,URBIG
1000 gr. HO | of 0°. of 0°.
0.0591 0.00879 0.149 4.79
0 0643 0.00039 0.146 1.76
0 1077 0.01541 0 143 1,72
0 4597 0.06400 0.441 eof (8.
0.4976 0 OGIR7 0.4144 4.70
4 OS0S 0.45484 0 143 1 723
1, 2521 0.48014 0.4144 1.730
1 8298 0.26757 (). 147 1.765
2.1927 0.33406 0.153 1.832
4 6362 0.78345 0.169 2 032
it will therefore be advisable to place the manometer in a thermostat.
Up to this time the manometer was placed in a glass vessel, through
which the water of the aqueduct flowed. If a correction is rendered
unnecessary by keeping the manometer at constant temperature, the
greater sensitiveness of the aniline-water-manometer will be still more
apparent *).
For the comparison of the results of the determinations of the
vapour pressure with those obtained in a cryoscopic way, the results
of Raovir?), Jones and Grtrman and mine for NaCl-solutions are
placed side by side in the following table.
So Raovir did not find a minimum in the factor 7 in spite of his
1) After having read my publication in the Archives Néerlandaises, BareLit made
some measurements with a manometer which differed from mine only in so far,
that it was erected in reversed position, in order to make the closure with mercury
instead of with oil possible. This change was sufficient, as Prof. Cassuro,
under whose superintendence Bareitt seems to have worked, wrote to me, to omit
my name altogether in the publication in the Ann. de Chim. et de Phys. T. XXV
1902, though they used the most essential part of my work viz. a dilute solution of
Na OH, Naz CO. or glass, which causes the aniline to run in a tube of the aqueous
solution, and to which the great accuracy is actually due.
*) Zeitschr. {. Physik. Ghem. 27, 638 (1898).
( 636 )
2A i
Na Cl.
SEE
|
ig- JONES and
ip — SMITS.
GETMAN. |
Concentration ,?g— RAOULT. |
|
| |
Cen ee a Per cA
04 | 1-865 —- > eee | 1.81
05 | 41.86 | 1.804 | 4.74
1.0 | 4.838 | 1.906 | 1.77
2.0 | 2.007 1.82
3.0 | 2.490 1.92
|
ig = ‘ caleulated from the lowering of the freezing point
in > » » » diminution of the vapour tension.
method which seemed so very accurate, though he continued the
experiments up to the coneentration 1 gr. mol.; JONES and GETMAN,
however, found a strongly pronounced minimum lying at the con-
centration + 0.1 gr. mol., whereas the determinations of the vapour
tension give a minimum at + 0.5 gr. mol.
[ have already pointed out in a previous paper’), that only for
ihe case that we have to deal with exceedingly diluted solutions the
value of 7 calculated from the lowering of the freezing point must
be in harmony with that calculated from the diminution of the vapour
tension.
For the calculation of 7 from the lowering of the freezing point
the following equation is used:
ead.
fs ae ee
RL* mn
and for the calculation of ¢ from the diminution of the vapour tension,
ic AF
we applied the equation
Ap N
bp a he IS, Weal eC ae
Po
For exceedingly diluted solutions 7g = 7p or
Ap N Le ae
— Bs of i: ae =e . . . (3)
Po di 5) 7]
or
Lp mh eee
a Al 6. oars . . . . (4)
Po KT,”
1) These Proc. Ill, Febr. 23 1901, p. 507.
=— so Se
( 637 )
For not very dilute solutions this is however no longer the case
and as VAN Laar!) found, for them the following relation holds:
Pega Regen ° 5
oO” i 2 RT? : iy : x 7 % 4 - f ())
or
Ap. 1 (Ap! nae 5
sess ( Sar Se ae 8)
Po 2 [ Po Ri o. /
If therefore we wish to compare the results of non-diluted solutions,
we can e.g. calculate instead of 7¢—=/p according to (1) and (2) the
following values:
S {RANG
Bre To. x
Lp EfApy N
an i ot.
Po 2 Po 4 M
which theoretically must have exactly the same value.
I have already shown before *), that the error committed by putting
ig=tp instead of /g= /p for not very dilute solutions, is not
sensible before we reach the concentration + 1
lf a
or
or,
If we now compare the results obtained by Raovrt, Jones, Gur an
and myself by means of the factor /, we get the following table:
At Bey Boo,
Na Cl.
fia wes a aI
Concentration | /¢— Raovurt. | coe | I, — SMIits.
|
0.05 1.91 Aeon | 04.96
TAN eb MARE rie ST wi A
Coty St dessc” The 4008 1.75
1.00 | 1.86 | 4.031 1.80
2.00 | 2.064 1.88
3.00 : eae ee OS
It is obvious that the second column is now qualitatively in
concordance with the two following; also the factor / derived from
the observations of Raovit, gives a minimum, but it is very faint,
so faint, that it did not appear in the calculation of 7g (table IL) *).
1) Zeitschr. f. physik. Chem. 15, 457 (1894).
2) These Proceedings II, Febr. 23 1901 p. 512.
3) This has already been shown by van Laan in a somewhat different way.
(Archives Teijler 8 (1903) ).
( 638 )
We see further that the differences between the third and the
fourth column in this table are about as great as in table IV, so
that it is sufficient to calculate 7g and zp for a first investigation of
the concordance of the results obtained by different methods.
The investigation of NaNO,-solutions yielded the following result.
T 2A 1B as ae
Na NO,.
Concentration | Pa es Pin ‘
‘és es aa H H eer cree =
] or. mol. p. i ls of SS SS SS SS oer
rg nol. p in mm. Hg no m.m g Po 3 0.08316
1000 gr. 11,0 of O°. of O°.
0.0515 0.00718 0.143 i bea
0.0901 0.01257 0.139 1.68
0.3385 0.04578 Oneae 1.626
0.8328 0.11042 6.1326 4 594
2.8168 0.33126 0.1176 1.41%
4.0544 0 46119 0.11375 1.268
7.3151 0 79056 0.10807 1.300
It follows from this table, that the factor ¢ decreases continually
with NaNQO,-solutions.
Also Jones and German have observed the same course in their
determinations of the freezing point, which follows from the following
table.
flee Rial oa Dp Ship
Na NO,,.
Molecular
Concentration. freezing point t
depression
0 05 3440 | 1.85
0.10 3498 | 4 843
0.20 | 3.345 1.798
1.00 | 3.198 1.719
2.00 | 3.074 | 4.65:
3.00 2 969 1.596
( 639 )
3. The minimum in 7 may be brought about by the formation
of hydrates in solution. I showed already before‘), how great the
influence can be, which the formation of hydrates in solution can
exert on the course of the factor 7, specially with regard to not
very dilute solutions.
For very small concentrations, however, the number of water
molecules is so predominant, that the number of molecules withdrawn
from the solution, practically does not bring about any change in
the molecular concentration. Towards higher concentrations the in-
crease of the molecular concentration in consequence of the forma-
tion of hydrates augments continually, and so it may be assumed,
that for a certain concentration it has increased so much, that it has
become equal to the diminution of the molecular concentration in
consequence of the retrogression of the electrolytic dissociation. If this
is the case, 7 has reached its smallest value, and will increase
towards higher concentration, because the influence of the formation
of hydrates prevails more and more over the retrogression of the
electrolytic dissociation.
Besides the above mentioned formation of hydrates, we may gene-
rally assume auto-complex-formation and hydrolysis, so that probably
many electrolytes form a system so intricate, that some time will
probably elapse before the desired insight into it will be acquired.
Referring here to salts of strong bases and acids I could leave hydrolysis
out of account. The auto-complex-formation has not been discussed,
because it brings about a diminution of the molecular concentration,
and was therefore of no use for the explanation of the phenomenon.
4. Finally I will call attention to the very remarkable fact, that
solutions of NaNO,, which qualitatively behave in a very normal
way, do not follow the dilution law of OstwaLp, whereas solutions
of KNO, follow this law according to my measurements, and as the
deviations for NaNO, solutions lie in this direction that A’ increases
with the concentration as is seen in the following table, this points
to an influence as e.g. occurs for NaCl solutions, but in a much
smaller degree *).
1) Archiv. Néerl. (2) 1 (1897).
2) That KNOs,-solutions harmonize better with the theory than NaNO,-solutions
is in accordance with the results of experiments made by ABeaa and BopLanpeR
(Zeitschr. f. anorg. Chem. 20, 453 (1899)), from which could be derived, that the
tendency to complex-formation depends on the degree of the tendency to ionisation,
which latter tendency is indicated by the tendency of dissociation. The greater
the tendency to ionisation the smaller the tendency to complex-formation. According
to Witsmore (Zeitschr. f. physik. Chem. 35, 318 (1900)) the tension of disso-
ciation is for K =3.20 and for Na =2.82, from which would follow, that kalium
salts have a slighter tendency to complex-formation than natrium salts.
{ 640 )
Die Bs ea:
Na NOQ,.
From the determinations of the vapour tension at U°
with Lord RAYLEIGH’s manometer.
Degree of | 2
Concentration. Dissociation | cK —¢ coe
| : | Mi
0.0515 | 0.72 0.09
0.0901 0.68 0.16
0 3585 0.63 0.35
0.8328 0.59 0.72
From the determinations of the boiling point at + 100°.
0.0469
0.83 0.49
0.0852 0.81 0.28
0.4448 0.72 0.76
0.8630 Osa 4.50
TA Bie Ver
KNO,.
From the determinations of the vapour tension at 0° with the
aniline-water-manometer.
Degree of a2
Concentration dissociation K=¢,-—
az
GS 2
0.0400 0.81 | 0.441)
0.4450 0.58 0.42
0).5997 0.39 0.15
0), 9288 0 804 O42
From the determinations of the boiling point at + 100°,
0.4000 0.91 0.$22)
0.4994 0 74 A065
0.7486 0 67 4.02
0.9921 0.651 | 1.21
average 1.05
!) We must not attach too much importance to the absolute value of K, as a
slight error in the sensibility of the manometer appears in K greatly magnified.
2) By this method we cannot make use of more diluted solutions to test the
dilution-law, as the error of the observation has too much influence then. For the
concentration 0.1 gr. mol. per 1000 gr. H3O this influence is already fairly strong.
If e.g. for this concentration we had found a rise of the boiling point of 0.1°
instead. of 0.099°, we should have had z=0.93 and K = 1.98..
( 641 )
It is remarkable that the law of dilution proves to apply here
up to fairly high concentrations. It would therefore be interesting
to carry on the series towards higher concentrations to see where
the deviations begin to appear.
That the freezing point method is inferior to the vapour tension
method and the boiling point method with a view to accuracy
follows also from the fact, that no constant values for K can be
caleulated from the observations of Loomis, Jones and GETMAN, as
appears from the following table.
A Ra Be LX:
KNO,,.
From the determinations of the freezing point.
Dapres of | w2
Concentration. dissociation | K=€ Loomts !).
0.20 era 0.35
0.40 0.69 | 0.78
0.50 0.65 | 0.61 | JoNES and GETMAN.
1.00 | Oa | 0.44 |
The fact, however, that Brmrz?) obtained concordant results for
solutions of caesium nitrate by means of the freezing point method
justifies the hope, that when the experiments are made very carefully,
also by this method the law of dilution will prove to hold for
KNO,-solutions.
I have agreed with Dr. Binrz that he will examine the behaviour
of chlorates, perchlorates and permanganates with regard to the law
of dilution and I shall investigate the nitrates.
The above salts manifest little tendency. for complex formation and
are therefore the most suitable material for the above mentioned
purpose.
Febr. 1904, Amsterdam.
Chemical Laboratory of the University.
1) Phys. Rey. 3, 279 (1896).
2) loc. cit.
( 642 )
Physics. — *n the measurement of very low fem peratures. VI.
[improvements of the protected thermoelements : a hattery of
standard-thermoelements and its use for thermoelectric deter-
minations of temperature”. By HH. KaMertincH ONNkES and :
C. A. CROMMELIN.
(Communicated in the meeting of November 28, 1903).
§ 1. Lmprovements of the protected thermoelements. Comm, N°. 27
II (June °96) contains a description of the apparatus with which at
that time the thermoelectric determinations of temperature were
made. The measurements for the sake of which these determinations ‘
were made are not yet closed, because they have been repeated with 4
: : : ¥
constantly improved arrangements. In the mean time the thermo- |
electric determination of temperature itself has been improved. The .
experiments of Mr. HoniMann') have offered an opportunity for
remarks about some of these improvements. Yet up to now a com-
plete description of the modifications made since the appearance of
Comm. N°. 27 has been deferred. It is now given in the following
paper.
Zesides the “protected” (comp. Comm. N°. 27) observation-elements
we still use protected comparison- or standard-elements. We have also
retained the construction of both the observation-elements and the
comparison- or standard-elements, so that the two “limbs” (the
junctures with their protecting-tubes) can be immersed into steam,
ice or into some liquefied gas or other to test whether the element
is free of current with equal temperatures of the junctures.
For the observation-element we avail ourselves of a combination of
coustantin and steel to obtain a considerable electromotive force. We
found for it with constantin wire furnished by Harrmann and Braun
46 microvolts per degree (O°C.— + 100°C.) Kirmencic and CzErMak*)
give for constantin-iron 51, Crova*) 63, van AvBeL and Paiior*) 47,
H. Rupexs*) 53, Honpory and Wien*) 56, Keer *) 58, Fucus *) 54.
1) Bakxuvis Roozepoom. Proc. Vol. 5, p. 283, 1902.
Houumann. Zeitschr. f. Phys. Ghem. Bd. 43. 2. p. 129. 1903.
2) Kiementic and Czermax, Wied. Ann. Bd. 50, p. 174. 1893.
3) A. Crova, C. R. 125, p. 804. 1897.
') Van Avper and Pamtot, Arch. d. Sc. phys. et nat. Genéve Per. 3. T.. de.
p. 148. 185.
5) H. Rupens, Zeitschr. f. Instrk. Bd. 18 p. 65. 1898.
6) Hotsorn and Wien, Wied. Ann. Bd. 59, p. 213. 1896.
7) Kueiver, Arch. d. Se. phys. et nat. Geneve. Per. 3, T. 32, p. 280.
s) Fucus, Ueber das thermo-electrische Verhalten einiger Nickel-Kupfer-Legier-
ungen, Graz, LSS.
CC ——
es
( 645 )
Constantin and steel appeared to satisfy the requirements for thermo-
elements laid down in Comm. N°. 27. We succeeded in tinding
wires of which, after they had been treated as described in Comm.
N°. 27, the potential-differences at a temperature difference of 100° C.
amount to no more than 0.5 microvolt along the whole wire and at
the extremities over a length from 50 to 60 em. no more than
0.05 microvolt *).
In order to be able to test whether the element is free of current
a steel wire has been soldered on to each of the ends of the wire.
The junctures of the two steel wires with the copper leads are kept
at an equal constant temperature viz. 0° C. Each of these protected
junctures constantly kept at 0° C. has its own ice-pot which is mounted
insulated from the others (See fig. 1 Pl. | and compare with this
figs. 1 and 2 of Pl. I Comm. N°. 27).
As to the principal features the arrangement of the limbs like
that of the whole element has remained the same as in Comm. N°. 27.
The constantin wire, which like the German-silver wire might easily
be bent in sharp curves and then show disturbing electromotive forces,
is again protected by a thickwalled indiarubber tube connected
hermetically with the glass protecting-tubes of the limbs. Owing to
its elasticity the steel wire did not require this protection; a layer
of shellac protects it from rust (for a better protection of this layer
it may also be coated with a thinwalled indiarubber tube).
In the limb constantin-steel the constantin-wire (1 mm. thick, 0.25
2 resistance per m.) is enclosed in the inner glass tube (see fig. 2
Pl. | and comp. fig. 4 Pl. HI Comm. N°. 27), the steel wire goes
straight between the inner and the outer tube (see fig. 2 Pl. I and
comp. fig. 4 Pl. Ill of Comm. N°. 27). Owing to the small condue-
tivity it was not necessary to wind the steel wire round the inner
tube (see fig. 4 Pl. II] of Comm. N°. 27). For the limbs which are
always immersed in ice, a firm outer protecting-tube is very desirable
with a view to the circumstance that the ice must repeatedly be
packed together. Each ice-pot is enclosed in a protecting cone-shaped
piece of paste-board soaked in oil of which the lower rim stands in
in the water on its dish, thus forming an air-jacket round the ice-pot
which is closed at the bottom; yet in warm weather it is advisable
to pack the ice every five minutes.
Although to simplify the construction of the elements we have
1) The defects which were avoided in the treatment described in Comm. N°. 27,
have later been detected in thermoelements of the Phys. Techn. Reichsanstalt.
There the treatment considered has also been applied in following cases. (Cf.
Zeitschr. f. Instrk. Bd. 19. p. 249, 1899).
( 644 )
used tubes with two openings (see fig. 6 Pl. I) through which the
two wires of the element are drawn, yet in many of these tubes
tensions appeared, which proved an impediment to their being
operated upon.
Formerly it was very difficult to make a connection between the
copperblock (for the meaning of this ef. Comm. N’.27) and the protecting-
tube, which connection should not only be airtight, but which also
must allow of being placed into steam and at low temperatures into
different kinds of liquids. This difficulty has been entirely overcome.
In N°. 27 we have spoken of our intention to try, following the method
‘of Caitieter, and solder the copper block on to glass which to this
end had been platinized. In this we succeeded to perfection. The
glass tube is platinized at the end with platinum-chloride in the blow-
pipe while care must be taken that if remains perfectly cylindrical,
then it is coppered galvanically and tinned over an alcohol flame.
Then the thin upright rim turned on to the block, which is also
tinned and carefully cleaned, is pushed round the end after which
they are soldered together by means of resin asa flux. Then the -
cap, the juncture seam and the tinned glass together are galva-
nically platinized and gilt. In this manner an important improvement
has been obtained. The indiarubber protecting-ring which made the
limb much thicker is removed, the fit is perfectly tight and permanent,
the limb may be fastened into almost any apparatus and be immersed
into any liquid without the least fear of action on the wires or of
shunt-circuits anywhere between the two wires.
Platinizing and gilding are not always necessary. The thermo-
element used in the experiments of HoLuMann I|.c. was only tinned,
as acetaldehyd does not attack tin. If for one reason or other we
do not wish to bring the protected thermoelements into direct contact
with a liquid with strong chemical action in which it is immersed,
they are enclosed in a separate protecting-tube (see figs. 3 and 4,
Pl. I) terminating in a thinwalled copper cap soldered on to it in
the way as described above, into which the block of the thermo-
element fits exactly, and which cap is covered galvanically with a
suitable metal. This auxiliary means was for instance used here
in determinations of melting-points of mixtures of chloride and
sulphur by Mr. Arr. Between the limb of the thermoelement and
the protecting-tube provided with a platinized and gilt cap, a little
pentane was poured to fill up the space.
In addition to the description of Comm. N°. 27 we remark that
the airtight connection of the outer glass protecting-tubes with the
indiarubber protecting-tube has been made by means of indiarubber
(645 )
foil and indiarubber solution in one of the ways represented in
figs. 2, 3 and 5.
For the filling of the tubes we can recommend in general dry
hydrogen.
§ 2. Battery of standard-thermoelements. At the end of Comm, N°. 27
it was remarked that the comparison-thermoelement itself with
junctures placed in ice and steam, the electromotive force of the obser-
vation-element being expressed in terms of that of the comparison-
thermoelement, could be used as a standard. One of the junctures
is easily kept at 0° C. when the precautions are taken described in
Comm. N°. 27 and in this paper §1. As to the other which is placed
in steam we must make sure that in the boiling-apparatus described
in Comm. N°. 27 the water vapour flows out at a steady rate and we
must apply the small correction for the variation of the boiling-point
with the barometric height in order to easily reduce the electromotive
force to that which would be obtained if this juncture were kept
precisely at 100° C. If the metals do not undergo a secular variation,
we always have at our disposal a constant electromotive force
(although it cannot be reproduced with certainty independent of the
special apparatus) which is very appropriate for the calibration of
sensitive galvanometers in general, and has moreover the advantage
in thermoelectric determinations of temperature that it belongs to the
same size as the electromotive force to be measured.
It seems “that this idea has later been developed by the Phys.
Techn. Reichsanstalt ’).
At the time of Comm. N°. 27 (June °96) the comparison thermo-
element was compared at intervals with a standard-element (then
Ciark’s). On the whole it satisfied the requirements better than the
Crark-cell, which had to be replaced repeatedly, while owing to the
improvements of the protection of thermoelements we had obtained
comparison-thermoelements which could serve unaltered for indefinite
time. The favourable experiences made with the German-silver-
copper-element in Comm. N°. 27 led us to replace the single comparison-
or standard-thermoelement by a battery of 3 standard-thermoelements
each with its own boiling-apparatus and its own ice-pot, which are
mounted insulated. Two of those elements ?, and /?, are made of con-
stantin-steel, the third Q, is the afore-mentioned German silver-copper-
element with a3 times smaller electromotive force than that of ?, or P,.
1) Vgl. Zeitschr. f. Instrk. Bd. 17, p. 174, 1897.
Idem Bd. 18, p. 183, 1898.
Idem Bd. 22, p. 149, 1902.
Idem Bd. 23, p. 174, 1903.
( 646 )
By means of an elements-switch of which the arrangement may be
seen without further description from Pl. I fig. 7 and PI. II, we
can switch the single elements or combinations of them in series or
in opposition and obtain electromotive forces in the ratios of
1, 2, 3, 4, 5, 6, 7 which by the central commutator of the elements-
switch are connected to the galvanometer wires (@ in a positive or
negative sense. The elements-switch has been made of galvanoplastic
copper (mounted on ebonite) and packed in a case with cottonwool
so that there electromotive forces are excluded.
The electromotive forces mentioned cover at intervals of about
30 degs more than the whole range of temperatures below 0° C.
Therefore in the measurement of a temperature we can each time
use a very near combination of standard-thermoelements for comparison.
§ 3. Determinations of the electromotive forces of the observation-
element. In Comm. N°. 27 the observation- and the comparison-
element were compared by means of the deflections which they
produced successively on the same galvanometer. This deflection-
method must always be applied whenever the determinations must
he made quickly. For these determinations of the deflection the
string-galvanometer of ErtHoven') which owing to its sensibility
and independence of magnetic disturbances would for the rest be
probably also very suitable for thermoelectric determinations, would
have the advantage above other galvanometers that the indications
are instantaneous. An opportunity to test this instrument has not
yet presented itself.
In determinations, however, where we especially want to observe
fluctuations of the electromotive force about an almost constant value
a compensation-method offers large advantages. Jn order to avail
ourselves of the advantages offered by the circumstance that the
electromotive forces to be compared are approximately equal, the
switching in opposition of the observation- and the comparison-
element was rendered possible in Comm. N°. 27, where the battery
of the standard-elements of the nearest electromotive force would
then be used. To the arrangement of Comm. N°. 27 for measure-
ments of deflections an arrangement has been added which allows
of a determination of the electromotive force of the observation-
element at perfect compensation by means of a zero-method. Thus
the comparison of the standard-element with the Criark-cell of the
arrangements of Comm. N°. 27 by means of the deflection-method
is left out. In this case the element must give a very small but
1) Proc. 1903—1904 p. 107.
( 647)
perceptible current while its resistance, owing to the variations
which it undergoes, must always be determined separately. The
connections which instead of this are added to that of Comm. N°. 27
are in principle the potentiometer-arrangement and have been drawn
diagrammatically in the annexed figure *).
3 eT Weston batt
UU |
A | |B | Mest
NG, es ve.
ae ( fs)
Soi 1 a te
— UNAISINA I Ass nn WAV yp a
/ a, A; i NK
| ace |
ES a were ————_______._.._
Sy
In the circuit of an accumulator (with a negligible resistance)
three resistance-boxes R,, R,, R-. and a fixed resistance FP’ are
introduced, of which the first serves to regulate the resistance in
the whole cireuit, the second and third serve as shunts for two.
circuits A and B in which the observation-element and the battery
of comparison-elements are inserted, while the third, a resistance
of 8000 2 tested at the Phys. Techn. Reichsanstalt serves as a
shunt for the circuit C, in which is inserted a battery of Weston-
elements. These side circuits may be connected to the galvanometer,
each by means of its own commutator with mercury contacts (as
described in Comm. N°. 27 see pl. V) and be commutated in order to
read in how far we have attained the desired zero-adjustment by
regulation of the different resistances and to. apply a correction for
the deflection which might have remained.
The principal resistance-boxes are adjusted by means of plugs like
the auxiliary boxes arranged in parallel for the finer adjustment.
This is preferable to an adjustment with a slide-wire where also
small differences remain’). As the F,, 2, and &, are known approxi-
mately beforehand, (with an adjustment at — 116°C. about 7290 2,
40 2 and 40 2 respectively) the current given by the Weston-
elements will always be very small. In order to make it still less
1) Cf. for instance JAzcer, Die Normaleleménte, p. 100.
Dewar and Femina, Phil. Mag. (5), 40, 95. 1895.
*) Cf. Lesretpt, Phil. Mag. Ser. 6 Vol. 5. p. 668. 1903.
45
Proceedings Royal Acad. Amsterdam. Vol. VI.
( 648 )
disadvantageous five of those elements, in order to obtain an
equal distribution of the current each with a series-resistance of
5000 2, are connected parallel to each other. Finally, when the
adjustment is obtained, the battery which has served in the regulation
is replaced by altering a plug in the commutator, by a battery
arranged in the same way, which serves for the measurements.
The peculiarity of this arrangement is that we can make imme-
diately after each other all the readings required for the measurements
by handling the commutator-boards (comp. successively Pl. V Comm.
N°. 27) and without making other contacts than those of mercury ; this
would be impossible without the commutators and the current-rever-
sers with mercury-contacts. This again reveals the great advantages
which these apparatus offer for similar measurements. It seems,
however, that little attention has been paid to them.
The whole arrangement with 6 current-reversers 1, 2, 3, 4, 5, 6
and 4 commutators A, B, C, D for both deflection- and zero-method
as it has become now may be easily seen on Pl. Il. The current-
reversers and commutators with mercury-contacts have been indicated
by three and four parallel lines respectively.
1 serves to connect one of the two galvanometers, that of Harr-
MANN and Braun, described in Comm. N°. 27 or a magnetically
protected galvanometer of Du Bors and Rusens.
2 and 4 to switch the galvanometer on to one of the three
branches A, B, C,
3 to switch the battery of comparison-elements on to the branch
A or on to B,
5 to introduce the observation-element and the comparison-battery
separately or in series or in opposition (cf. 3),
6 to introduce either the observation-element or the comparison-
elements.
A, B and C make and reverse the connection of the three circuits
with the galvanometer, JD reverses the accumulator. The commutators
and the current-reversers, like the Werston-battery have been packed
in cottonwool, placed together in large cases. Only the tubes where
the contact of the mereury is made by handling the commutator-
board (see Pl. V Comm. N°. 27) project beyond it.
( 649 )
Physics. — “Contributions to the knowledge of vax pur Waats’
w-surface. VUI. The w-surface in the neighbourhood of a
binary mixture which behaves as a pure substance.” By Dr. J. B.
VERSCHAFFELT. Supplement n°. 7 to the Communications from
the Physical Laboratory at Leiden by Prof. H. Kamerninen
ONNES.
(Communicated in the meeting of October 31, 1903).
General part.
Distillation of a mixture without its composition being altered,
and reversely also condensation of a mixture by decrease of volume,
without variation of pressure, quite as a pure substance, can only
occur at one special temperature. Experiments of KugNEN') have
shown for the first time that this phenomenon may be observed in
the neighbourhood of the plaitpoint of the mixture; this circumstance
has been theoretically investigated and explained by van DER WaatLs?).
If a mixture behaves as a pure substance just at the plaitpoint
temperature the critical point of the homogeneous mixture, the critical
point of contact and the plaitpoint coincide at a same point which
may therefore properly be called the critical point of the special
mixture and of which I shall represent the elements, as for a simple
substance, by 7%, pz and vy.
Then according to VAN DER Waais*) we have at the plaitpoint
(=), = 0. Hence the isothermals of two neighbouring mixtures
at the same temperature must intersect in pairs, so that the system
of isothermals of the mixtures at the critical temperature of the
special mixture must agree with fig. 16 of my paper in these Proce.
Oct. 25 1902 p. 345. In the annexed figure a similar system of
isothermals is drawn according to observations of Quin? ‘) with
mixtures of hydrochloric acid and ethane.
Although the special mixture behaves as a simple substance at the
critical point, yet it does not follow from this that its border curve
on the p, v, ¢ diagram may be found in the same way as for a
simple substance, i. e. by making use of the theorem of Maxwet.-
Ciavusius. For just below the critical temperature the pressure no
longer remains unchanged during the condensation and the expe-
rimental isothermal is no longer perfectly parallel with the v-axis,
1) Phil. Mag., 40, 173—194, 1895. Comm. phys. lab. Leiden, n°. 16.
2) Arch. Neéerl., 30, 266, 1896.
3) Contin. II p. 116.
4) Thesis for the doctorate, Amsterdam 1900.
( 650 )
though the variation of pressure is vanishingly small. Consequently
the system of isothermals satisfies the law of corresponding states,
but the border curve does not necessarily do so. Hence we shall
see that for the border curve this is only the case to a first and
a second approximation.
The w-surface. 1 shall represent by a, the composition of the
mixture which behaves as a simple substance. In the neighbourhood
of the critical point the system of isothermals of this mixture may be
represented by the equations (2) and (2’) of my paper in these proc.
Oct. 25 1902 p. 321; for the rest all the considerations of sections 2 and
3 of the same paper are directly applicable, except that z—a, must
everywhere be substituted for «7, and hence also 274.—k for x7. Thus
we find back, for the system of isothermals of the mixtures at a
temperature which differs little from 77, the equations (18) and (18’),
where x—azvy, is vanishingly small, but not z and «7, separately ;
f)
from the circumstance that at the critical point @ = 0, it also
Uv
Ov
follows that m,, = 0; and because m,, = px@—k,, 7,4 we must have:
3 my 0
ee Sa Ss << Sea
a Pk: Or k
Finally we may remark that whereas in fig. 16 (1. c.) the dotted line
which, agreeing with «<0, had no physical meaning, this line can
really exist here, since «<2, may as well be imagined as x > ax.
The equation of the y-surface may now be written in this case:
1 1
w= — m, (v—v7k) — an (v—v7,.)?— a Ms (v—vTr)* — z m® (v—v7z)*. -
: 1 “z—xzyz)* 2ap—--1 (x—az)’
1.2 a,?(1—az)? 2.3 «,°(1—axz)*
day —daz.+1 («—az;z)'
T 3.4 ai(1— a)! arc | (2)
where again a linear function of z is omitted, while m,, = pre, and
further m,,, m,, and m,, may be put equal to zero.
The border curve at a temperature T. In the same way as before ')
I find, putting
$(%,+%)—°m =P , 3(%,—-r71)=9
b(e,+2,)—omn = , $(,—#)=&
v, v, 2, @, representing the molecular volumes and the molecular
compositions of the coexisting phases, that
1) These Proc. V, Oct. 25 1902, p. 330.
2 mi, = 3
gas . (3)
30
: 1 oer ft 2
1 my, 2M, Ms o- gi Ma sy aes 3 ar" 30— ph ipwe
pf —-— ==. 4 Si! em (4
Ms sp 2kTm,, (4)
"ep (1-ax)
¥ 1 m,,m,, 2 i"; M:,
= ‘02 aie Al eases = ae
eed ie 3 Ms, a me, . 6)
ran See BT Ge a
m, Na
xy. (1-2xz)
1 m,,m,, 1 em yee :
Pe Pte en a - + —m2,,—— ] +). - - (6)
Meso 0 m 30
The relations (2) and (5) are the same as I have found before *)
for the special case m,, = 90, on the edge of the w-surface, while
the expression for ® becomes the same when we put 2, =O or
z= 1. 1 also find again for the border curve on the p,v diagram
of the mixtures at the temperature 7’ to the first approximation the
same parabola of the fourth degree: }
2 2 4
aise m7. im ms, Sm", %,, nes *
Pie = = (ois +. =a v—vUTE}-- (4)
ied, o> WM, a Ns
The plaitpoint, i.e. the apex of this parabola, coincides to the
first approximation with the point prz, VTL, v7Tk- According as the
factor between brackets is positive or negative this parabola is turned
upwards or downwards; in the first case the special mixture has a
minimum vapour tension, in the second a maximum vapour tension.
The isobars. If in equation (18) l.c. p. 327 we consider 2 and v
as two variable quantities depending on each other and p as a
parameter, this equation represents the projection of the system
of isobars on the wz, v-surface. If m,, were not zero this system
would resemble a system of isothermals with the point 77%, U7Tz
1) Of all the coefficients m which occur here I have formerly given the expres-
sions in the k’s and 2 and 6, except of mg, for which the expression follows here:
m,,— 8 pk + ky, @ (a—8) Ti + &, @” T;? + k,, a (a—8) v% Tr—k,, a Ty
or reduced:
1
——e [3 + a (a—p) Por == 2 a’ Pos == a (a—p) ae Pail:
2) These Proc. V, Oct. 25, 1902, p. 329.
( 652 )
as critical point’). Here it consists, in the neighbourhood of that
same point, in a double system of curves of hyperbolical shape,
as may be seen in the annexed figure, separated by two curves,
of which the equation is obtained by putting p—=pz,. To the first
approximation the system of isobars is represented by the equation
m,,(t—xTk)? + m,, (t—xTE) (v—vTKE) = p—pre, - - (8)
which represents hyperbolae, of which the one asymptote is:
mM,4
L—LT, —= — —(v—vTe) - . .. .
” 02
while the second, z—a7, — 0, may be written to the second (9)
approximation |
Ms 4
£—2£T;, = — — (v—v7z)* -
M4 J
_ The connodal line. In order to find the projection of the connodal
line on the «z, v-surface we eliminate p—pz7; between the equation
of the isobar and that of the border curve; we then find to the
first approximation
Mg «
(e«—z7,.) = — (UOTE) 6 ein oe
mM,
The critical point of contact, the apex of this hyperbola, coin-
cides, like the plaitpoint, to the first approximation with the point
UTk: UTk> PTk-
The border curve for a mixture x. If in the equation (8) we con-
sider « as constant and 7, hence x7, and v7; as variable, and if
finally we make use of the equation of state of the mixture
(equation (13) le. p. 825) to express 7’ in p and v, we obtain the
‘
1) The systems of isobars may then be written in the form:
z—=n, — n, (v—vz7z) + 2, (v—v7z)? +....
where the 7’s are stil] fictions of p, for instance:
t= Mog Noy (P—pTk) 5 Nos (p—prk)’ = ote piace
If the v's are expresscd in the m’s, we find:
meee Ag 1 ees } ads. Moo 0 as 51
Noo — Tk; tot — — . Noo ———— > ; 4 Nig — VU, Ns = “ei:
Mo m 01 m 01
2
, s Mos slg 4 M5 As 0 —_ m ll Mey
ty, — ne —— Si ; 5 Noo = 5 Ney = = = ; 9° ls. =e ee
01 M1 m 01 m 01
m m m
> F 30 11 30 40
RG I EE orc FW Tica , etc.
Yon m 01 Mo,
( 653 )
border curve of the mixture # in the p, v, 7’ diagram. To the first
approximation its equation is:
k 1 Ko (
Z eWeek ee 2 “EER
P—Pxk = —
11
as for a simple substance’). Hence to the first approximation the
border curve satisfies the law of cor responding states.
That the border curve, apart from the deviations existing already
in pure substances does not altogether satisfy the law of correspon-
ding states, has a double cause. It is not only for mixtures which
differ little from the special mixture 2, that the experimental isother-
mal shows a slight slope, but this is even the case for the mixture
a, itself; only at the plaitpoint temperature it is perfectly horizontal
so that already for the mixture wz the border curve must deviate
from the law of corresponding states. If as before!) we develop the
equation of the experimental isothermal :
Ee ie ho
we find:
1 m,,m,, k in" ,, m7, :
ie —— | ee 3 ——+-— ; (a x TI.) a
Ms, i) are,
Ems ae Ln m,.\"
neat pees MeL
, 3 M,, Diss Waa 2
—8m “Fi (v—v7p) (c—2«7Trx) + . (12)
gen ole’ Mm.
m*,, + —
Se ieee er)
and hence, for «= xz,
2 2
Lan m;; ae 1 a Pe
Mya Ye 2
ah
30 (v-v;,)
(L-T;)’
ar,
p=prth,, (te T;)—-8m’,,
+ (13
2 RT m,, Bo Are
ees
only for z,—=O or 1, that is to say for the pure su tances, the
third term is left out — and in the same way all the crms which
contain v—vk.
If now by elmination of 7—7;, between the eq: ation of state
of the mixture z;, (equation (2), l.c. p. 325) and the experimental
isothermal (10), we search for the border curve for that special
mixture, we see that the slope of the experimental isothermal only
influences the third term — viz. with (v—v;)* — in the development
(11) of the border curve, so that this border curve only to a third
approximation shows a deviation from the law of corresponding
1) These Proc. V, Oct. 25, 1902, p. 336.
m
( 654 )
states. Also for a neighbouring mixture this deviation is only percep-
tible in third approximation, while for mixtures with a small com-
position, i.e. on the edge of the y-surface, it exists already in second
approximation.
The cause of this smaller deviation in mixtures near the special
mixture must be looked for in the circumstance that those mixtures
in all their qualities deviate only in second approximation from a
single substance; thus we deduce from equation (11) that the critical
points: plaitpoint, critical point of contact, critical point of the homo-
geneous mixture and point of maximum coexistence pressure, differ
only in second approximation, so that the four curves (in the space
with p, v and 7’ as coordinates), which connect these critical points
of all mixtures touch each other at the critical point of the special
mixture, which in general is not the case at the two critical points
of the pure components.
Application to mixtures of hydrochloric acid and ethane.
The experiments of KuENEN with mixtures of ethane and nitrous
oxide, the first where the existence was shown of a mixture that
in its critical phenomena agrees with a simple substance, does not
allow us to form a complete image of the conduct of neighbouring
mixtures. Besides, his investigations were only aimed at the discovery
of the second kind of retrograde condensation, and the existence of
that special mixture was a new discovery, and not the object of the
investigation. Suitable data for our purpose are given by the measure-
ments of Quint on mixtures of hydrochloric acid and ethane; accord-
ing to Qurr the composition of the mixture which behaves as a
simple substance is «7, = 0.44, 1.e. 0.44 gram molecules ethane and
0.56 gram molecules hydrogen chloride. Mixtures behaving as a
pure substance have also been observed bij Causper*) in his experi-
ments with CH,Cl and SO,; as Cavsnr however investigated only
two mixtures of this binary system, his data are insufficient for
our purpose.
In order to proceed with the mixtures investigated by Quint in
the way indicated by KamErRLINGH ONNES, we must determine in the
first place the critical elements of the homogeneous mixture 7, por, Vok-
pv é
7 log p diagrams
it was sufficient, as in the case of my former investigations?) of the
Instead, however of drawing, the /og pv, logv or
1) Liquéfaction des mélanges gazeux, Paris, 1900.
2) Arch. Néerl., (2), 5, 644, 1900.
fe
abe ‘
( 655.)
mixtures of carbon dioxide and hydrogen to use the log p, log v
diagrams, as | found that not only the logarithmical diagrams of
the pure substances but also those of the four mixtures investigated
could be made to coincide with the iogarithmical diagram of carbon
dioxide by shifting them parallel to each other.
Unfortunately Quint made only few observations in the neigh-
bourhood of the critical point, a circumstance which rendered this
investigation rather difficult. For it is by means of those very parts
situated in the neighbourhood of the point of inflection that the
superimposing of the diagrams may be obtained in the most accurate
way, While in the area of the larger volumes a shifting within rather
wide limits does not cause a perceptible deviation of the superim-
posed diagrams.
bourhood of the critical point in the case of hydrochloric acid is to
be regretted because the difference between the critical point given
by Quint and that found by shifting is much larger than we should
expect, the diagrams covering each other in a satisfactory way. The
more so because, when for ethane and carbon dioxide the diagrams
are made covering each other in the observed area the critical points
too coincide.
Here follow the values found, for the different mixtures, as ele-
ments of the critical point of the homogeneous mixture:
Especially the want of observations in the neigh-
= = (pure HCl) 0 1318 0 4035 0 ,6167 0,714. (4 pure C,H,)
—— 42°.5 30°,0 26°,4 os
pek = 7} Svat. 05'.5 58 6 or ak
Urk = 0 00429 =0 00190 =§=0 00543 ~—— 0 —,00570
tpi== ss 51°33 43° 1 309,53 *27°,25 27°,37 319,88
pri 84,13 atm. 77 ,51 65 42 54 30 56 84 48 ,94
Drpl = 0 ,00380 0 00420 =O. 00471 0 00540 =—5_ 00576 0 00652
C.- 3 48 3 46 3 45 0 45 3,50
In order to make a comparison I have written in this table the
plaitpoint elements of the mixtures as observed by Quint, and in
RT) ee
which here
Prk Vrk
are about the same for all the mixtures, especially in the neigh-
bourhood of the special mixture. By means of Quinv’s data we find
however, for HCl, the much larger number C, = 3,71; this deviation
evidently must be brought in connection with the other one I mentioned
before.
the last line the values of the expression C’,—=
( 656 )
If we draw the ¢,, and ¢,,; as ordinates and 2 as abscis we obtain
two curves which obviously touch each other at one point; it is
difficult, however, to define this point of contact precisely. If the
same is done with p,¢ and py), the determination of the point of
contact of the two curves is even less certain, owing to the cireum-
stance that, according to the table above, for z = 0,4035 = piz > papi,
which surely follows from the inaccuracy of the method. And the
deduction of this point of contact from a graphical representation
of the 7, and v,,; is quite impossible because these volumes are
known by no means with sufficient accuracy.
Therefore it seems to me that the best method is that of Quint
who deduced the composition of the special mixture from the shape
of the plaitpoint curve by searching on this curve the point where
the bordercurve, which terminates at that point, touches the plaitpoint
curve. That point may be determined fairly accurately: we find
for its coordinates 7; —= 29°,0 and vo; = 63,8 atms., whence again
x, — 0,44 and vz = 0,00500.
By means of the graphical representations of the fx, Pre and Ox,
aL 1p »1-
I find in the neighbourhood of x; = 0,44, si 20, ih a
dx dx
Ivy, 5
and Baro 0,0020; hence «a = — 0,07 8B = + 0,50 and y=0,40, so
at
that the relations y= a—fin—- 7,3 are confirmed: in a satisfac-
a
tory way.
By means of Quint’s observations, by inter- or extrapolation, partly
also by using the law of corresponding states and the values of
teks Dek» Urk found above, I have drawn the isothermals for the 6
z-values considered, at the critical temperature 29°.0 C. of the special
mixture « — 0.44. Those isothermals are represented in the annexed
figure, which thus shows the p-v-diagram of the mixtures at the
temperature 29°.0 C. The dot-dash line is the critical «= 0.44 with
the critical point in C. The isothermal «= 0.40 is a dash line in
the unstable part; owing to their small curvature the experimental
isothermals are represented by straight lines. The border curve is
a complete line like the observable parts of the isothermals.
Under the p,v-diagram I have represented the projection on the
p, e-surface. The critical isobar (63.8 atms.) is represented by a dot-
dash line; some other isobars are drawn, like the projection of the
connodal line (also projection of the afore-mentioned border curve),
while the isobars in the unstable part, i.e. within the projection, are
dotted. The temperature 29° being lower than the critical temperature
of pure ethane (31°.88), the connodal line consists of another part,
which I have not drawn, however, in order not to make the figure
uselessly intricate. This second piece should have its apex, the critical
point of contact, at about v7, —= 0.92, and v7, = 0063, and would
intersect the axis r=1 at v= 0.00472 and v = 0.01081.
To this second piece of the connodal a second border curve cor-
responds which would begin at a height p = 46.1 (maximum tension
of ethane at 29°.0 C.) and terminate at the plaitpoint p7,; = 51.2,
vtpi = 9.0063. But this border curve too I have omitted like the
isothermal of pure ethane.
At the lower part of the figure it may be seen that the isobars
in the neighbourhood of the critical point C, indeed to the first
approximation, are hyperbolae of which one of the asymptotes, which
agree with the critical pressure, is parallel to the v-axis, the other
cuts this axis at a given angle. To the second approximation the
first asymptote is a parabola which coincides with the projection of
the connodal line.
It were useless to investigate whether indeed the border curve is
of the fourth degree and the connodol of the second degree; for this
the data are not numerous enough and the drawing not sufficiently
accurate. But it is obvious why the border curve should be of a
higher order than the connodal. The p, v, z-surface, of which the
projections on the surfaces p,v and 2,v are shown in the fig., is in
the neighbourhood of the critical point a saddle-shaped surface, which
at the upper part of the figure is seen parallel to the tangent surface
at the point C. The isothermals of the mixtures «= 0, «— 014
and «= 0.40 are situated on the slope turned towards us; the latter
over a fairly extensive range (of large volumes to about 2 = 0.006)
forms nearly the border of the surface; the critical isothermal lies
just beyond that border, but becomes visible at Cand remains visible
for small volumes. The isothermals «= 0.62, 7=0.71 and x=1
occur on the back of the p, v, z-surface, yet for small volumes they
become visible. The parabola:
2 2 — re
which envelops the isothermals in the neighbourhood of the point C
(l.c. p. 344 and fig. 16) is the apparent outline of the surface in
that neighbourhood.
The lower part of the figure represent the surface seen from above;
the isobars are there level-curves. The critical isobar forms a loop
which agrees with the described shape of the surface. A section of
a horizontal surface situated a little higher consists of two pieces,
( 658 )
of which one, lying within the loop is closed. Within the loop
therefore, the surface shows an elevation of which the top almost
agrees with «= 040, v= 0.06, p= 63.9. For higher horizontal
surfaces the section consists of one branch only. For horizontal
surfaces corresponding to p < 63.8 atm.. the sections also consist in
one branch which surrounds the critical loop.
From «=O the bordercurve occurs on the front of the p, v, a-
surface, but reaches the border almost at the volume 0.008, then
occurs on the back where it remains until the point C, and returns
to the front. At the point C’ the osculation plane to the border
curve, at the same time the tangent plane to the surface, is horizontal;
the projection on the «,v-plane shows the border curve more and
more in its true shape the more we approach the point C; whereas
in the upper projection that border curve is seen more and more in
an oblique direction and finally in a tangent one, so that it must
appear flattened, which accounts for the higher order of the border
curve in that projection.
(March 23, 1904).
KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,
PROCEEDINGS OF THE MEETING
of Saturday March 19, 1904.
_—— SOG
(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 19 Maart 1904, Dl. XII).
= = a
CON PEN P's.
A. F. Hotieman: “The nitration of Benzene Fluoride”, p. 659.
Jax Rurren: “Description of an apparatus for regulating the pressure when distilling under
reduced pressure.” (Communicated by Prof. S. HooGrwerrr), p. 665.
H. Kaweruincu Onnes: “Methods and apparatus in the cryogenic laboratory. VI. The methyl-
chloride circulation”, p. 668. (With 2 plates).
H. Kameriiscu Oyyes and H. Harrer: “The representation of the continuity of the liquid
and gaseous conditions on the one hand and the various solid aggregations on the other by
the entropy-volume-energy surface of Gipss”, p. 678. (With 4 plates).
P. vay Romevren: “On Ocimene.” (Communicated by Prof. C. A. Lopry pe Bruyy), p. 700.
P. van Rompveren: “Additive compounds of s. trinitrobenzene.” (Communicated by Prof.
C. A. Lopry bE Bruyn), p. 702.
E. Verscnarrett: “Determination of the action of poisons on plants.” (Communicated by
Prof. C. A. Lospry pe Brryn and Prof. HvGo pr Vrirs), p. 703.
W. Emstioven: “On some applications of the string-galvanometer”, p. 707.
A. F. Hotieman: “Action of hydrogen peroxyde on diketones 1,2 and on z-ketonic acids”, p. 715
L. E. J. Brovwer: “On a decomposition of a continuous motion about a fixed point O of S;
into two continuous motions about O of S,’s.’? (Communicated by Prot. D.J. Korrewee), p. 716
C. A. Losry pe Bruyn and L. K. Worrr: “Can the presence of the molecules in solutions
be proved by application of the optical method of TynpaLi?’ p. 735.
J. J. Buayxsma: “On the substitution of the core of Benzeng.” (Communicated by Prof
C. A. Lopry pe Bruyn and A. F. HoLtremay), p. 735.
The following papers were read:
Chemistry. — “Vhe Nitration of Benzene Fluoride.” By Prof.
A. F. HoLieman.
(Communicated in the meeting of February 27, 1904).
Dr. Brekman who made some communications in his dissertation
as to the above nitration came, although his experiments remained
unfinished, to the conclusion that in this case the isomeric mono-
nitrocompounds are formed in quite a different proportion as in the
nitration of the other halogen benzenes. As it appeared fo me very
a
Proceedings Royal Acad. Amsterdam. Vol. VI.
( 660 )
important to further confirm this statement and as Dr. BEEKMAN could
not undertake this himself, I have studied this subject once more
and now communicate the results obtained.
The difficulty which presented itself was that we were unable to
obtain benzene orthonitrofluoride so that it was impossible to apply
the methods which, in the case of the products of nitration of the
other halogen benzenes, lead to the knowledge of the proportion in
which the isomers are formed. Two observations by Dr. BEEKMAN
furnished us, however, with a key to find the said proportion. These
were: 1. the very ready transformation of benzene p-nitrofluoride
with sodium methoxide into the corresponding anisol; 2. the further
nitration of the benzene orthonitrofluoride present in the nitrating
mixture to benzene dinitrofluoride (Fl: NO, : NO, =1:2:4) which
compound has been obtained by Dr. BEEKMAN in a pure condition.
I convinced myself in the first place of the quantitative course of
the transformation of benzene p-nitrofluoride with NaOCH,.
1.8347 grams of p-NO, C, Hy. Fl = 13.01 millimols. were dissolved in a very
little pure methy!] alcohol, an equivalent quantity of sodium metoxide dis-
solved in methyl alcohol to the concentration of 0.75 normal was added
and the mixture was heated in a reflux apparatus for fully one hour in
the boiling waterbath. The liquid still possessed a faint alkaline reaction
but became neutral on our adding a trace of dilute acetic acid. On pouring it
into water a very beautiful white mass was precipitated which was drained
and then air-dried. Without being recrystallised it exhibited a melting
point of 52—53°, showing it to be pure p-nitranisol.
On the other hand in this dilution benzene metanitrofluoride is
but very little affected by treatment with sodium methoxide for one
hour in the boiling waterbath :
1.0842 grams m-NO, C, H,Fl=7.7 millimols. were mixed with 10c.c. of
Njj.09, NaOCH, this being the equivalent quantity, After being diluted with
water, the liquid was titrated back with 7.50 cc, of acid, theory requiring
7.7cc. Only 0.2 millimols of the compound had therefore, been decomposed,
or 2.6°/) of the total amount,
This renders it possible to quantitatively determine the amount of
benzene p- and m-nitrofluoride in a mixture of the two compounds
as shown by the following experiments :
a. 1.1040 grams = 7.83 millimols. of a mixture of 89°/, of the para and
11°/, of the meta compound were mixed with 10.1 cc. of 7/).09; sodium
methoxide and heated in a reflux apparatus for one hour in the boiling water-
bath, After being poured into water the liquid was titrated back with 0,8 cc,
( 661 )
of m acid corresponding with 0.82 millimols of meta if we apply the correc-
tion of 2.69, for the meta compound attacked. 0.82 millimols = 10.5°/,
of the meta compound.
b. 1.1250 grams = 7.98 millimols. of the said mixture were treated in
an analogouS manner with the equivalent quantity (16.9 cc.) of m/9.:
sodium methoxide. The liquid was then titrated back with 0.85 cc. of 7 acid,
corresponding, after applying the correction, with 0.87 millimols. of the meta
compound, or 10.9°/,. Taking the mean of these two experiments we find
10.7 °/, of the meta-compound.
Dr. Berkman had observed that benzene dinitrofluoride (Fl: NO, :
NO, = 1:2:4) is converted at 15° in a few minutes into the corre-
sponding anisol by the action of sodium methoxide. This e¢ircum-
stance might be taken advantage of for the quantitative determ'nation
of this dinitro compound in the presence of benzene p-nitrofluoride
if the latter should suffer no change. This was, indeed, the case:
1.0035 grams of the para compound were treated at 15° for 5 minutes
with 9.53 cc. of /).9, = 5 cc. n sodium methoxide. After being poured into
water the liquid was titrated back with 5 ce. of n acid.
A mixture of the two gave the following result:
1.1680 grams of a mixture containing 10.9°/, of the dinitro compound were
digested at 15° for 5 minutes with 17.6 c.c. of m/24. Na OCHs. The liquid
was then titrated back with 7.6 cc. of m acid; there was, therefore, present
17.6
a quantity of dinitro compound of mo — 7.6 = 0.7 millimols , or 0.1302 gram
corresponding with 11.1 °/, of the dinitro compound.
The above observations rendered it possible to quantitatively deter-
mine any benzene di- or metanitrofluoride eventually present in a
nitration product of benzene fluoride. In order to determine the
benzene orthonitrofluoride contained therein, | converted this into the
dinitrocompound by renewed treatment of the nitration product with
concentrated nitric acid. Dr. Berkman had found that a further nitra-
tion took place (as shown by the increased sp. gr.) when the said
product was treated for half an hour at O° with five times its weight
of nitric acid of 1.52 sp. gr., but that even after this treatment,
traces of benzene orthonitrofluoride may still be detected by boiling
the compound with aqueous sodium hydroxide which yields o-nitro-
phenol. On the other hand Dr. Berkman showed that pure benzene
p- and m-nitrofiuoride are quite unaffected by this renewed treatment.
In order to get a further and complete nitration of the ortho
compound, | prolonged the time of the renewed treatment with
nitric acid to one hour after first ascertaining whether benzene
44*
( 662 )
p-nitrofluoride is unaffected thereby. This did not seem to be quite
the case, so a small correction has to be applied:
a. 2.95 grams of pure p-NO;.C,.Hy.Fl were treated at 0° with five times
the weight of fuming nitric acid of 1.52 sp. gr. The compound rapidly dis-
solved without elevation of temperature. After one hour the liquid was
poured into ice water and the fluorine derivative was instantly precipitated
in a solid condition. When the liquid had become clear it was carefully
filtered and the mass was repeatedly triturated in ice water until] the
acid reaction had completely disappeared. It was then treated with 9.65 ce.
Of 7/}.; NaOCH; for 5 minutes at 15°. The liquid was then titrated
Q GEA
back with 4.77 cc. of m acid. This gives — 4.77 = 0.23 cc. of nalkali
consumed, corresponding with 0.428 gram of dinitro compouud, or 1.4 °/).
b. 1.732 grams ofthe para compound were treated in the same manner.
But after the acid had been removed by washing, the residue was melted
to a clear liquid by applying a gentle heat. It was then cooledin ice water
and again triturated and washed in ice water until the last traces of acid
had disappeared: it was then treated as in a. 10.48 ce. of 1/1.93 Na OCH,
were used and the liquid was titrated back with 5.3 cc. m acid; 0.1 cc. of
n alkali had therefore been absorbed corresponding. with 0.186 gram of
dinitro compound or 1.0°/,¢ The mean of the two determinations is there-
fore 1.2°/.
Being in possession of these data, I have now subjected the nitra-
tion product of benzene fluoride to the same test. Dr. Brrxman had
previously found that the nitration at O° with a mixture of 25 ce.
of nitric acid of 1.48 sp.gr., 5 ce. acid of 1.51 sp. gr. and 10 grams
of benzene fluoride yields a compound consisting solely of mononitro
compound (to judge from its percentage of nitrogen; found 9.95
calculated 9.93). 1, therefore, nitrated in the same manner and purified
the product, which in ice water is semi--solid, by first washing it
in ice water, being careful not to lose any oily globules, and then
with water at 20°, which caused the whole mass to melt to a homo-
genous liquid. After all acid reaction had disappeared the bulk of
the water was removed by means of a separatory funnel, the clear
pale yellow oil was freed from a few drops of adhering water by
means of a strip of filterpaper and then finally heated in a testtube
at 9O°—100° until it no longer became hazy on cooling. We may
assume that all the moisture has then been removed, likewise small
quantities of any unchanged benzene fluoride. The product so obtained
solidified after inoculation at 15°.7; a second preparation at 187.6.
It does not contain benzene dinitrofluoride :
1.4115 grams were treated for 5 minutes with 9.45 cc. of ”1/,.9, sodium
methoxide. The liquid was titrated back with 4.9 cc, 7 acid, or 9.46 72/;.9g acid,
( 663 )
But on the other hand it contains benzene metanitrofluoride :
a. 5.208 gram of the nitration product = 36.9 millimols. were heated
with the equivalent quantity, namely 78.5 c.c., of 7/3... sodium methoxide
for one hour in the boiling waterbath. After being poured into water, the liquid
was titrated back with 1.5 cc. n acid; this after correction corresponds
with 0.2170 gram of meta compound or 42 "9.
b. 5.817 gram of the nitration product — 41.3 millimols were treated in
the same manner with the equivalent quantity, namely 79.7 cc. of 7/;.9s
sodium methoxide. The liquid was titrated back with 1.55 c.c. n acid;
which after correction for tne attacked meta compound (2.6 °/,) corresponds
with 0.2243 gram, or 3.9%) meta compound. The mean of the two determi-
nations is, therefore, 4.1 °/.
In this determination of the quantity of meta compound it has
been assumed (and such is very probably the case) that the benzene
orthonitrofluoride present in the nitration product also reacts quanti-
tatively with sodium methoxide.
By renewed treatment of the nitration product with concentrated
nitric acid in the manner described, its solidifying point does not
perceptibly alter, for it was found to be at 18°.8. This had already
been noticed by Dr. Berkman. Still, the twice nitrated product now
contains benzene dinitrofluoride:
a. 1.0015 gram of twice nitrated product was left in contact for 5 minutes
at 15° with 8.45 cc. of /;.9,; sodium methoxide. The liquid was titrated
back with 3.9 cc. m acid. Therefore, alkali absorbed = — 3.9 =0.5 cc.
nm alkali = 0.093 gram dinitro compound, or 9.3 °/5.
b. 2.264 grams were treated in an analogous manner with 10.15 cc. of
n/j.9, sodium methocide. The liquid was titrated back with 4.25 cc. nacid.
10.1
Alkali consumed, therefore — — 4,25 = 1.06 cc. corresponding with 0.197
gram, or 8-7 °/) dinitro compound. The mean of the two determinations is,
therefore, 9.0 °/.
Now we have seen that by treating pure benzene p-nitrofluoride
with strong nitric acid for one hour 1.2°/, undergo further nitration.
In the twice nitrated mixture there is present 9°/, of dinitro- and
4°/, of meta compound '), therefore 87°/, of para; 1.2°/, of this
represents 1°/, of the whole. This quantity of 1°/, must, therefore,
be deducted from the amount of benzene dinitrofluoride found, in
order to obtain the quantity which owes its existence solely to the
1) 9.0°/9 dinitro = 6.4°/, mononitro. By subsequent nitration, 100 parts of the
once-nitrated product increase to 100 + (9.0—6.4) or 102.6 parts which contain
4.1 parts of meta, or 4°.
( 664 )
subsequent nitration of the benzene o-nitrofluoride. This, therefore,
amounts to 8°/,, corresponding with 6.1°/, of ortho compound. Accor-
ding to the above the composition of the nitration product is therefore :
6.1°/, benzene ortho nitro- Pages) Being formed by nitration of ben-
4.1° / » meta a zene fluoride at 0° with the concen-
69.8", 5 +para 5 | tration of the acid stated on p. 662.
The composition of the twice nitrated product was found to be
9°/ of benzene dinitrofluoride, 4°/, of meta- and 87°/, of para com-
pound. This was easily controlled by making an artificial mixture
having this composition as all the three components were at disposal.
Its properties must then be identical with that of the twice nitrated
product. And indeed, the solidifying point of such a mixture was
found to be 18°.7 and 18°.9 whilst that of the said product was at
18°.8. According to BrEKMAN’s data’), the sp. gr. of the artificial
mixture should amount to 1.27738, whereas 1.2791 was found for the
twice nitrated product. This higher figure is, probably, to be attri-
buted to the fact that the corrections to be applied are somewhat
uncertain so that the results could only be accurate to within about
1°/,. If this should cause a little excess of dinitro and a little defi-
ciency of meta compound, the sp. gr. will be at once seriously
affected, whilst the solidifying point does not perceptibly alter. In
0
fact, an excess of 0.8°/, of dinitro compound is sufficient to explain
ihe difference in the sp. gr.
I have also endeavoured to nitrate benzene fluoride at —30°,
using the same acid mixture employed in the nitration at 0°. On
-adding the fluoride drop by drop to the acid cooled to that temperature
it dissolves with a dark brown colour causing but little rise in
temperature, just as had been observed in the nitration of benzene
bromide. After all the benzene fluoride had been added, the colour
gradually began to fade and when the nitration vessel was removed
from the refrigerating mixture and its contents reached a temperature
of about —20°, the liquid soon became pale yellow and the temperature
rose to about + 10°. It, therefore, appears that the velocity of
nitration at —30° is already considerably retarded, as the intro-
duction of each drop of benzene fluoride at O° is accompanied by
a very perceptible caloric effect. The solidifying point of the product
which was collected in the way described, was situated at 19.°1,
from which it may be concluded that it differs but little from the
product obtained by nitration O° This can only contain about 1°/,
less of by: “products.
1) Sp. gr. meta 1.2532; para 1.2583; dinitro 1.4718, all at 840.48.
( 665 )
' >
Let us now see what the quantitative determinations of the nitration
products of the halogen benzenes have taught us:
iC, Bo Rhe| CoH! Or |. C,H, Br. | C,.H, J
OUGNG: Seer | 6.41 99.8 3 Ye: 34.2
) |
meta. =... | £4) | O.3(2)|)" 0139(2)} | = platen
temp. O°.
HALAS see
where it is attached to a weight 7,
which runs along a seale fixed to the tube Qa.
—-
The flask is packed in the same way as the ethylene boiling vessel
(Comm. N° 14) first with nickel paper and then with several layers
of wool, the number of layers increasing at the colder parts, as can
be seen from the drawing PI. I. They are contained between varnished
and nickelled paper as is seen in Cj, C;, C., C, Fi, Fi, Fy, while
horizontal strips of felt, dotted in the drawing, prevent convection
currents. These various layers form airtight compartments, which
are connected together by means of small tubes C,, C,, while the
whole airtight space is connected with the atmosphere through a
drying tube F/. The outer surface is painted white.
§ 2. The methylchloride cycle. A short description of this is
desirable. The liquid methylchloride is preserved in the tubulated
condensor ©, which is cooled by running water. Its pressure is
measured by the manometer and its level can be seen in the level
glass ©,, with blow-off cocks as used with water boilers (to make
a reading the connecting tube for liquid methylchloride ©,, must be
cooled with ice as shown diagrammatically on PI. II (for farther par-
ticulars the quoted description of Martutas p. 383 N° 2)). A large
cock ©,, protected by a filter (shown l.c. as N° 9) makes it possible
to shut the condenser off immediately by a small movement, even when
a strong stream of methylchloride is sent through the condenser. This
cock is followed by a regulating cock ©,, to which the tubes for
liquid methylehloride are connected. The latter run to:
1s. the refrigerator D, which is used to obtain liquid nitrous oxide,
either in the manner given in Comm. N° 51 Sept. ’99, or by drawing
it off into a vacuum vessel U from which the nitrous oxide can
be siphoned over into other vacuum vessels and thus be brought to
apparatus arranged in other rooms.
As far as the nitrous oxide circulation according to Comm. N° 51
is concerned the mercury and auxiliary compressors (Comm. N° 54)
can be used as & in place of the BrotnerHoop of Comm. N°. 51.
The various pieces of apparatus, for which the nitrous oxide in %
is used, are generally connected to the tube App and the sack &
from which the gas can be repumped into B. Plate II shows the
use of a small 2°K.G. cylinder 8 of the kind usually used in this
laboratory for this purpose.
2d. other apparatus formerly described e.g. one of the cryostats
(Comms. N° 51 and 83),
3d. the boiling vessel for the preparation of liquid ethylene €
Pl. II as described in § 1, either directly or through the regenerator
€’ where the methylchloride is cooled by cold vapour coming from
another vessel and passing from Jn to Ex,
45
Proceedings Royal Acad. Amsterdam. Vol, VI.
( 676 )
4th. an apparatus gy which will be described in detail in the following
section and intended to deliver a stream of calciumchloride solution
at a low but very constant temperature.
We may consider the methylchloride vapour which streams out
of these refrigerators and regenerators. In the case 3 above (some-
times also in case 2 for which the connection %; serves) it would
be sucked by a BurckHarpDT—WEIss vacuum pump %, installed in
the manner given in Comm. No. 83. From here it would travel to
one of the conjugated pumps of the Société Génevoise 3, mentioned
in Comm. No. 14, which receive the vapour from the BurcKHARDT
or from all other apparatus (D Pl. II and further indicated under 2).
This pump % may for another example take the vapour directly from
the boiling vessel © (see Pl, IJ and Z Pl. I) as well as between the
high and low pressure cylinder from the branch tube , which too
allows gas to be pumped from one of the four above mentioned
sacks , in which the methylchloride can be preserved for a short
time and of which only one is represented on Pl. I, while other
sacks can be connected to apparatus from which methylchloride
escapes under constant pressure. The pump is provided with an
indicator on the low pressure cylinder, a vacuummeter between
the high and low pressure cylinders and a manometer on the high
pressure cylinder, besides several cocks which are required for
pumping, drying and filling with methylehloride. The vacuum meter
¥my indicates the pressure of the gas which enters the high pressure
cylinder. From the cylinder volume and the number of strokes one
ean derive the volume of gas and reduce it to that under normal
conditions moved in the cycle, so that the velocity with which the
liquid in the refrigerator evaporates can be followed.
In addition a safety valve Sw is added to the high pressure cylinder
principally to protect the condensor &.
The methylehloride which can escape from this safety valve is
passed into the above mentioned sacks §. Usually, all the methyl-
chloride passes into the condenser, where it is cooled by running
water from the main. In between, an oil trap § is placed which
is slightly warmed by steam (see ©,c,), so that the transported oil
shall give up the dissolved methylchloride. The oil thus separated
by the change of direction is run into a flask 8. The last portion
of the methylchloride, freed here, is carried to the sack . At the
top of the oil trap, the gas is freed from the last traces of oil by
layers of felt and wadding contained between sheets of metal gauze.
(C.f. the oil trap of the ethylene circulation shown by Maratas l,c,
p. 383 fig. 1).
is
——
( 677 )
§ 3. Circulation of calcium chloride solution at constant tempera-
ture below zero C. The thermostat is similar to that described in
Comm. No. 70 III May ’01, but with the difference that at P, a
side tube with cock and mercury resevoir is introduced, so that the
regulator can be set for high temperatures (very well to 60° C.)
and also for a low one by the choice of a suitable fluid. The spiral is
filled with benzene and, instead of water from the main (as in No. 70),
a cooled stream of calcium chloride solution is run into the heating
vessel. The solution is contained in a vessel ® with filter and
float Na and is driven through the refrigerator €, and regenerator ©,
in which the methylchloride evaporates and thus cools the circulating
calcium chloride solution. This is caused to move by a force pump =
with valves €, connected to one of the conjugated compressors %
while a bent tube prevents the cooled solution from falling.
In the refrigerator the liquid methylchloride runs through the
tube €7, and regulating cock €,, to the inner space, while the
calcium chloride solution runs spirally in the outer. The liquid
methylehioride running into the refrigerator is cooled by the vapour
evolved, which escapes by a wider tube ©, to the regenerator, from
which projected liquid returns by a narrow tube &;. Finally the
danger which might arise when the cooled methylchloride, left
between the cocks d and the shut off cock of the tubing G, returned
to the ordinary temperature, is avoided by connecting a safety cap
with a closed tube ©; added above. At 12 Atm. the thin plate breaks
and sufficient space is produced without communication with the air.
The walls are all calculated to stand the ordinary pressure of the
methy|lchloride.
The pressure under which methylchloride
‘ evaporates must not fall below a certain value,
=, as the calcium chloride might then freeze out.
br It is kept constant by the pressure regulator &
Pl. II. When the pressure falls the mercury
rises in 6, see accompanying figure, and forces
the float a, upwards, so that the lever / rotates
about g and thus closes the suction channel by
the double valve h,h,. A safety tube & Pl. II
“ and a tube to receive spilt mercury complete
the apparatus. The properly cooled calcium
chloride solution runs from the refrigerator ©, to the thermostat XY,
where it is rewarmed to the required low temperature and conducted
to the apparatus which must be held at constant temperature.
On Pl. IL a piezometer surrounded by a vacuumglass is shown,
45*
where the outer surfaces are connected by the copper box used
for the vacuum jacket of Comm. N°. 85. This jacket remains
free from dew deposit, so that the divisions on the tube can be
clearly read. Above the liquid surface the vacuum tube is lengthened
by an ordinary tube of about 50 cm, so that the solution is protected
from the atmosphere by a layer of cold air.
The apparatus was e.g. placed once at about 25 meters distance
from the refrigerator, in another room. It would be less suitable
to convey the methylchloride itself over this long distance owing to
the increased danger from fire.
The calcium chloride solution had a specific density of 1.28, the
vacuum under which the combined pumps worked was set so as to
produce a temperature of — 45° C. in the refrigerator and remained
satisfactorily constant. The small pump moves about 2 liters of
solution per minute.
In order to keep temperatures below — 20°C. constant at long
distances by a methylchloride circulation, it will be necessary to
have a refrigerator with a greater cooling surface.
Physics. — Communication N° 86 from te Physical Laboratory
at Leiden. “The representation of the continuity of the liquid
and gaseous conditions on the one hand and the various solid
aggregations on the other by the entropy-volume-energy surface
of Gisps” (By Prof. H. KameriineH Onnzs and Dr. H. Harper).
(Communicated in the meeting of June 27, 1903).
§ 1. The meaning of the following research will be best made
clear by showing its relation to the former communications (66, 71,
74) from one of us (H. K. O.). Like these it: arises from the cer-
tainty that it is increasingly necessary to represent the experimental
values for an equation of state from a general point of view.
In the first place this research is connected with that of N°. 66 *)
on the reduced 4, €, v (y = entropy, € = energy, v = volume) Gipss’
surface formed after vAN DER WaAALtLs’ original equation of state.
The drawings of N°. 66 show that a ridge appears on the side
of small volumes on the Gipps’ surface given there, by shifting the
constant isotherm (fig. 1) of simple form (l.c. Pl. I and II), derived
from the above mentioned equation of state, along a vertical directrix.
1) KamertincH Onnes, Die reducirten Greps’schen Flachen. Vol. jub. Lorentz,
Archiv. Néerl. Sér. Il, T. V. p. 665—678. Leiden, Comm. n°. 66.
~
Fig. 1. Fig. 2.
This ridge — the liquid ridge — carries the liquid branch of the
connodal of the liquid vapour plait; the isotherms run over the
ridge from the vapour to the liquid side and from higher to lower
entropy (l.c. Pl. I, fig.1.). In the vicinity of the critical temperature
the ridge becomes broader and smoothes down into the double
convex surface (I. c. Pl. I, fig. 3) which further forward is everywhere
double convex. For lower reduced temperatures the ridge passes
nearly into an yeplane. The projection of the ridge on this plane
is a curve along which the inclination (tang—! = absolute temperature
T) decreases towards negative values of the entropy (see fig. 2). The
projection of a cross section of the ridge shows the rapid change
of the inclination in the v «plane (tang—! = pressure p) for a small
change of volume. The correspondence of the properties expansion,
compressibility and specific heat, for liquid and solid shows imme-
diately that the representation in the 4, ¢,v coordinatesystem of the
experimentally determined conditions, belonging to one of the solid
averegations of a material, can be supposed to belong to a ridge
corresponding to the liquid ridge. Also that other solid varieties
require further ridges. So long as we exclusively keep to the
experimentally determined values only narrow strips of these sup-
posed ridges are given for a short distance to the side of the tops
and thus form themselves isolated parts, not connected with the
vapour and liquid regions, of the whole Gres’ surface for the
special substance.
Tbe various ridges, if we for a moment admit their existence,
will be more or less shifted, according to the density, towards zero
volume (v) and according to the fusion and transformation heats
more or less to zero entropy (7). The difference in specific heat of
the modifications, will be given by a variation in curvature. Looking
( 680 )
from the side of large v, we
oe should see a succession of ridges,
= and where we for simplicity con-
sider the case of a single solid
bas state of aggregation, we should
, see the resulting ridge rising at
lower temperatures above the
Fig. 3. liquid ridge (ef. fig. 3).
To find the coexisting phases from the region a’ a" or from the
region 6’ with the vapour phase from the region c, one must lay
the common tangent plane on the curved surface in ¢ and the given
ridge. In the case that a rarefied gas phase occurs in c, the ridges
would be represented approximately by curved lines. This is then
also to be permitted in the search for the corners a and 6 of the funda-
mental triangle of the triple point. The general thermodynamical
character of a solid state occurring together with the VAN DER WAALS
state (liquid, gas and labile intermediate states) would be thus obtained
by representing it on a Gisss’ surface by a ridge of a somewhat
other position and form but generally analagous to the liquid ridge.
There is thus every reason to suppose that outside the region
of observations and towards the large volumes the first continuations
of the isotherms obey an analogous law as to form and change
of form with temperature as the liquid isotherms, and thus by
a slight extension really produce a ridge. This appears to be more
probable when one notices that there is also a ridge on the Gisss’
surface which does not correspond to the original equation of
VAN DER Waats where a and #6 are taken as unchangeable but
which belongs to the equation into which this changes when a and
4 are taken as functions of temperature and volume. Thus when
shifting the variable or corrected isotherms (cf. N°. 66 § 3 end) in
place of the original constant one a similar ridge as that which
we have considered would also be always formed, though the suc-
cessive isotherms are no longer equal and similar, but show a small
continuous change with temperature. In this way one cannot escape
the conclusion that metastable states occur at the side of the solid
state between solid and gas.
The observed part of the isotherm on the vapour side for tempe-
ratures far below the furthest limit of the observed undercooling of
liquid does not extend beyond the sublimation line. Still from ana-
logy with what is known for vapour at higher temperatures, it must
be assumed until the contrary is proved, that the Grsss’ surface extends
inside the sublimation line to metastable and even to labile equili-
ae
|
|
|
|
( 681 )
bria, not in principle different from those given by van per Waats’
theory. And very clear and special evidence must be brought forward
(which is not the case (cf. § 2)) to show that the two above men-
tioned parts of an isotherm must not be united.
Now, (cf. fig. 4) for a
substance which exists in
the liquid and solid states,
call cd and ef the portions
of the connodal of the liquid
and solid ridges, gh and ih:
portions of isotherms on the
liquid and solid ridges. It is
clear that ¢ and h may be
joined by a continuous line.
For the formation of two
ridges it is clearly only neces-
sary, that two isotherms g’h’, i’k’, should incline to the v-axis very
strongly, but still not differ much from the two preceding isotherms
gh, ik, and also that A’v’, hi should not differ much. With such
small variations resulting from the above mentioned controlled changes
of the isotherms with the temperature on the Gisss’ surface, we are very
familiar since the a and 6 of van per Waats are taken as temperature
functions. The difference between 7k and. the isotherm g/ is analogous
to the difference between the true empirical isotherm g/ and the simplest
form of isotherm given by van per Waats who has long shown
that 6 must necessarily be a volume function. The portion /z alone
appears tou have received a somewhat greater change which we may
ascribe to a further change of 6*) with the volume.
With this explanation of the cause for the displacement of the
isotherm on the Gisss’ surface we do not come into collision with
the assumptions of vAN DER WaAAaLs, who assumes that ) undergoes
a change in the fluid state owing to the compression of the molecule.
We thus only specify the possibility of a yet further change of the
same sort, which finally produces a new equilibrium between 4
and v in the solid state. Beforehand there can be no question of
explaining the solid state by referring it to the same processes as
those which exist in the liquid state. This can only be done when
the relation of the elasticity for instantaneous changes of volume and
the time of relaxation for the liquid and solid states are worked out
1) We use the a and 2 of van per Waats in the most general manner given
by this physicist.
( 682 )
and the great change of the time of relaxation with the above men-
tioned further change of 6 at the transformation from solid to liquid
is explained on the same grounds. Still keeping this in view we may
say that by prolonging the line /z till it reaches the solid state we
have given what van per Waats calls the equation of state of the
molecule.
Now it follows immediately from this representation that the form
of the connecting line 4z must be taken as dependent upon the tem-
perature and the inflection as decreasing and finally vanishing with
rising temperature. Thus the above consideration of the form of the
liquid ridge on the Grsss’ surface necessitates the assumption that the -
solid can be joined to the liquid ridge by a plait. This will be gene-
rally perpendicular to the v-axis and will end in a plaitpoint i.e. this
indicates the continuity of the gaseous and solid states of aggregation.
With these considerations we have not treated the question whether
the conditions in the plait which we assume to exist in the gap
between the two states of aggregation (c.f. § 2 for outside the plait)
are also conditions of equilibrium, labile or otherwise. We have
advanced no reason for this. This is as far as we know not done
by others either who have assumed the existence of similar condi-
tions *). In considering the vapour, we stated that there have not
been observed metastable states connecting the solid with the gaseous
and liquid states. However these appear very clearly and markedly
between the gaseous and liquid states, and have an important bearing
in the theory of vaN pur WAALS.
Also it is not unlikely that van per Waats has never in his
writings treated the continuity of the gaseous and solid states, and
has expressly kept it in the background, because the use of such
intermediate states as those above considered is only allowed theo-
retically when it is shown as VAN DER Waats did for the inter-
mediate vapour-liquid states — that these intermediate states may be
treated as conditions of equilibrium. However we do not propose to
determine “the molecular equation of state’ from a given mechanism,
but to seek for an empirical form for this from the known facts by
induction. In this case we must use the most obvious analogies as
indications and it is not allowed to deviate from the most simple
suppositions without proving each step. With variable molecules it
is probable that relations between entropy and volume can exist
other than those which van per Waats has already treated in
his equation of state based on the theory of cyclic motion. In order
1) See especially Ostwatp, Textbook of general chemistry.
te.)
( 683 )
to be able to fix a meaning for some of the conditions which according
to this possibility are suggested by us, we must suppose that the material
can suffer stresses with imponderable as well as with ponderable
mechanism. Thus we may obtain actual values for 9 as well as for v
at which we can keep the material homogeneous which in reality
would be impossible. No difficulty should arise if we in addition to
general assumptions suppose that the entropy can be kept constant.
We only extend to the imponderable mechanism what is generally
allowed for the ponderable, when one supposes the substance kept
homogeneous with constant volume in VAN DER WAALS labile conditions.
We have thus in the following set ourselves to model the parts
of the Grsps’ surface which are experimentally known, for substances
which exist in the solid state, to add to these portions the vapour
and liquid regions following vAN per Waats, and to combine the
region thus obtained with the solid ridge in such a manner that the
isotherms on the Gusss’ surface shall differ as little as possible from
the wnchanged isotherm of van per Waats, and the course of the
isotherm in the y v projection shall be as simple as possible. We have
e.g. excluded states on the surface where 7'’= 0 except at 7 = —
and have supposed that for every value of 7 and v only one value
of ¢ belongs.
It is clear that the problem formulated thus does not extend further
than the search for a continuous function, which for a known range
coincides with the Grsps’ surface and satisfies a given — but phy-
sically we hope happily chosen — criterion of simplicity. The solution
obtained from this determination has a certain value and forms a
continuation of the investigation of Comm. Nos. 71 and 74°), the
development of the equation of state in series.
There also the principal object was to produce a numerically correct
combination of the experiments independent of the thermodynamic
peculiarities of the substances treated. The solid state was at first not
considered in order to avoid a too large field. With this limitation
it appeared that the whole range of experiment for normal substances
could be expressed by a series condensed to a polynomial in powers of
1
e so that we could find exact valnes for p, for 4 = =|z —dv, for
= ef Te — r) (and other quantities e.g. w= — | pdv) for all
states within the region considered, without tedious calculations.
1) KameruineH Onnes. Ueber die Reihenentwickelung fiir die Zustandsgleichung
der Gase und Fliissigkeiten, Livre jubil. Bosscua Archives Néerl. (II) T, VI p. 874—
888, ‘01. Leiden Comm. n°. 74.
( 684 )
The extension of this idea to associated substances was necessarily
excluded since the law of corresponding states was taken as the
basis of the development. The existence of a maximum density for
water need then bring no difficulty for the representation of the
qo —Teenittd state in the consideration that in general p, and thus 7 also,
é 1
is given along an isotherm by powers of —. The question, if the
v
connection between 7 and v, which follows from the mechanism of
the liquid or gaseous states, can in general be given by expressing
1
7 in powers of —, could be left out of account. Now that we wish
Vv
to introduce the solid state into the polynomial — until now not used,
but after some change perhaps applicable for this purpose — we meet
the difficulty that with many substances solidification is accompanied
with increase of volume. For water, which falls in this case, the
question is treated more fully in §§3 and 4. Still if this case could not,
as we have supposed, be explained by association, and if in general
the complete knowledge of the mechanism of the solid state for the
isotherms of gas, liquid and solid leads to an implicit relation between
7 and v, still for one part of the range of it will be possible to
express this directly by one value in terms of v. It appears to us
to be quite possible that with certain normal substances p can be
1
empirically expressed in powers of — over the whole range under
v
consideration.
The Gippss’ surface, which we have constructed for this first class
of substances, will serve to give not improbable corresponding values
of p and v for an isotherm in the liquid-solid plait, and to permit
computation of useful values for the virial coefficients — the coeffi-
cients in a polynomial
BS oe,
les se Reape ete Perc a, tw, 6 Pia.) We
If we seek for the values which these coefficients can have, we
find a second connection between this investigation and Comms
Nos. 71 and 74. In both of these it is shown that values will be
found for the reduced virial coefficients of different substances, which
are sufficiently, but still not quite, equal. These differences in B @
ete. will just give the deviations of the various substances from the
law of corresponding states. They express parts of the molecular
interaction which cannot be explained or represented by the actions
of homologous points which last actions are those whose mechanical
( 685 )
similarity results in the law of corresponding states. The various
substances certainly differ widely in the solid state when they are
expressed with reduced coefficients. Thus the mechanical dissimilarity
of the actions of unhomologous points appears at once. When the
same isotherm passes through the gaseous liquid and solid states,
the higher coefficients of the polynomium must without doubt differ
considerably. It is thus to be expected that the lower coefficients,
will also exhibit certain but smaller differences, which are connected
with those in the higher coefficients. In this manner, in the compa-
rison of two substances, the deviations from the law of corresponding
states would be clearly connected with the solid properties of the
two given substances.
Further, as the virial coefficients give the deviations from the
BoyrLe Gay-Lussac law we may say that these deviatious do not only
express the properties of the liquid state as given by VAN DER WAALS
but also those of the solid state. Really a connection between the
deviations and the properties of the solid state is also implied in
VAN DER Waats’ last development of the equation of state after the
method of cyclic motion.
§ 2. The best possible connection of the known part of the solid
with the liquid ridge by a continuous surface has some similarity with
the use of the continuous line by which J. THomson connected the
liquid and gaseous states found by Anprews. Still there remains a
marked difference. THomson could start from the existence of a cri-
tical point. A continuous change from the solid to the liquid state
is not experimentally proved, it is doubted by some and as to the
crystalline modification it is directly contradicted by Tammany. If
TamMann’s theoretical considerations were correct, then it would already
be clear that we had produced only a simple empirical interpolation
when we intended to have constructed a group of intermediate states
which beforehand would be at least probable on physical grounds.
TamMMANN’s objections are certainly not conclusive. They rest in
the same way as our assumptions on extrapolations outside the
experimental region, and it appears that our extrapolation is more
probable than his. Also Tammann’s combination of the fusionline of
water, an associating substance, with that of other substances as if
they were two cases which could pass one into the other by change
of temperature and pressure, presents some important difficulties. We
have not to consider these conclusions so long as we exclude asso-
ciated substances and substances of perhaps very complicated character.
Instead of giving immediately a general treatment of cases so
( 686 )
different in principle, we confine ourselves to the simplest group
of substances.
For these we have constructed the representation which we shall
further develop in the following.
In agreement with TamMMANN, we also assume, although under-
cooling only occurs to a limited extent, that the liquid ridge
continues to very low temperatures (at first we may assume to the
absolute zero) states with increasing times of relaxation up to the
glass condition being encountered in passing over the ridge towards
decreasing temperature. Thus we do not come into collision with the
observations. Still we do not mean that it is quite impossible for
crystalline properties to be found on the glassy ridge e.g. at very low
temperatures. Further we do not suppose that the existence of one
such a ridge would exclude the possibility of other amorphous condi-
tions where other equilibrium relations between entropy and volume
could equally be found. Moreover it is highly doubtful if the term
amorphous does not include very various structures in the solid state,
so that it is certainly not necessary that an amorphous condition
should be present on the ridge where liquid would be found at a
higher temperature. As to the crystalline ridge, our whole represen-
tation makes it appear more probable to us, that the crystalline
ridge in the simplest case should run next to the liquid ridge down
to very low temperatures, than that it should follow Tammann’s ring
shaped form (c. f. § 4).
The process of transformation from the crystalline to the gaseous
(below the liquid-gas critical temperature, liquid) state does not at all
disagree with the usual assumptions concerning the molecular forces,
but is immediately to. be deduced from them. A very satisfactory
agreement with the suppositions would be obtained when the charac-
teristic difference between two ridges appeared to result from the
differences of density and entropy (specitic heat) of the modifications,
the crystalline or amorphous form taken by each of these modifications
being thermodynamically of secondary importance, so that for a first
investigation they would not come into account in comparison with
the change of properties of the solid phase due to differences of
density and entropy.
However it may be, we must certainly assume that the crystalline
form will result from the molecules being by choice oriented and
arranged in a given manner owing to the forces from the not
corresponding points. The directing and arranging forces will then
be different for different densities and entropies, whence the most
probably occurring orientation and arrangement will be different
hb! death
( 687 )
for different densities and entropies and the crystal form will be
different for various modifications.
The increase of the vibration energy will gradually efface the
mean predominant most probable distribution and orientation as the
crystal is raised in temperature and although the whole continually
approaches a uniform mean distribution and orientation still some
different groups will remain in arrangements of most probable predo-
minant distribution and orientation. In particular if this hypothesis
is applied to the case of a gaseous and a solid phase in equili-
brium which are brought together to a higher temperature, fresh
hypotheses must be made to render it clear that no identity of the
two phases can become possible and therefore no continuity of solid
and gaseous states will be found. Of course it does not matter if
the temperature under consideration is above the liquid-gas critical
point. Further there is no reason known why it should not be
allowed to extend the double convex part of the Gisss’ surface, —
containing essentially states of equilibrium, to higher temperatures and
pressures, so that it surrounds the critical point at the end of the plait.
Is is quite in harmony with our assumptions of § 1 that, in the
gaseous phase of a substance occurring also as solid, molecular groups
will at all times be found (produced always from different indivi-
duals) in which the particular attraction between not equivalent
points '), predominating in the solid state, will also be manifest.
Below a certain temperature it will then be necessary to momenta-
rily consider certain portions of the gas as crystalline. We are here
only following the method employed by Bottzmann for the deter-
mination of the equilibrium distribution, which is the most probable.
We apply it to a given density and velocity distribution but also
extend it to orientation and arrangement.
We have mentioned above the existence of more ridges which
appear successively on the Gusps’ surface towards the side of
diminishing volume. This case appears to us to be the normal one.
It is probable that the various solid modifications are not known for
most substances. If we further consider that a small change in the
course of the isotherms can cause one ridge to rise above another and
thus to represent more stable phases or not, it is not at all probable that
just those modifications of the various substances are known, which
belong to corresponding ridges. It is therefore, possible that in the solid
state the various substances would differ less than now appears to be
the case if one were acquainted with all their modifications; finally the
1) Comp. Retneanum, Drudes Annalen. 1903. 10 p. 334,
( 688 )
possibility remains that more liquid ridges could exist along which with
falling temperature the time of relaxation would not increase to the
value required for the solid state, while states of equilibrium between
the two are to be expected, so that the same substance could exist
in two liquid modifications.
The reasons why such a case is not known and why the various
solid modifications are usually crystalline, must be further explained
by a theory of the solid state.
§ 3. Following the lines developed we have constructed three
models of Gipss’ surfaces.
We have first considered an imaginary substance, which partially
‘corresponds with carbon dioxide, in the liquid state is in harmony
with vAN DER WAALS’ original equation, and which further can exist
in one solid (crystalline) modification. For the Gress’ surface of this
substance constructed according to our ideas, we have only considered
that portion where the fusion line of the substance is to be found.
This model serves principaliy to present clearly the views on the
solid state advanced in this communication.
Having assumed that we can express the character of the
peculiarities in the transition from solid to liquid by this model,
we have further constructed two others, which refer to the actual
CO, and on which all known thermodynamical properties are
expressed as numerically exact as possible.
One of the models represents the whole surface for CO, with the
exception of the portions for the ideal gas state and for very low
temperatures.
The second gives, on a necessarily larger scale, the region where the
transition occurs between the various modifcations with small volumes.
Finally another model has been formed which demonstrates
sufficiently, that taking it in general, a substance like water can be
represented in the manner followed by us. We mean that the
deviations which this substance exhibits can be brought into line
with the association. In general a liquid ridge which
: corresponded sufficiently with the vAN prR WAALS
, i equation of state, would be pressed upwards and
i towards decreasing volume by the association. This
*
7
1% i transformation is represented schematically in the y v
aaa projection by fig. 5. To the right lies the undisturbed
Pay a VAN pDrER Waats ridge, given by the portion where
nent
the connodal liquid-vapour, the curve drawn, runs
Fig. 9. to the left, the twisted ridge is again given by the
-
tl tt ae eS re Ns
( 689 )
altered portion, the two portions of the connodal solid-vapour are
again drawn (unfortunately the altered connection is omitted in the
figure). At m lies the maximum density of water under its own
vapour pressure. The preliminary model made by us serves to show,
that the most notable properties of H, O will be correctly given if
we consider the ice ridge as an ordinary solid ridge on the surface, and
the liquid ridge as changed by the last mentioned process owing to the
association.
We hope shortly to obtain models which will exhibit the trans-
formation of the different modifications or allotropic states as well as
the peculiarities of the expansion phenomena. In this way we hope
to contribute to a somewhat better insight, at least to a_ better
survey, of the thermodynamical character of the different substances.
However in addition to the questions relating to association there
are others, which have reference to mixtures, saturated solutions
etc., and which would necessitate a long investigation. We hence
think that the results now obtained from a sufficiently independent
whole to be published.
We have thus in the above made the meaning of our work
clear and can now proceed to describe the models somewhat more
fully and to show that the experimental data can really be obtained
on these surfaces.
I. THE SOLID-LIQUID PLAIT ON THE GIBBS’ SURFACE.
(Representation of the continuity of the solid and gaseous states).
The specific heat of the imaginary substance in the gaseous state
has been assumed to be equal to half that of liquid carbon dioxide:
the specific heat in the solid state as equal to that which is found
by employing Nreumann’s law. Also the substance obeys the VAN DER
Waals equation of state for carbon dioxide in the liquid and gaseous
States. It appeared useful to give for this model (pl. Il, fig. 1) front
and side elevations and plan (pl. III fig. 1, 2, 3, 4) with the lines
7 = const., v = const., 7’= const. (dashed lines) p = const. (dotted
lines), for which the drawings are sufficiently explanatory. The con-
nodal fluid (gas)-solid is drawn on this model and the coexisting
states joined by steel wires.
The principal difference between our representation and TAMMANN’s
is very clearly seen on comparing the plan (pl. II fig. 2) with his
figure (Drupe’s Ann. 3 p. 190).
This model is also useful for a comparison of our idea with the
well known scheme given by Maxwext (Theory of Heat, p. 207)
( 690 )
our plan is easily compared with the latter for the small volume
part. To find how our vapour plait will be connected with this
portion, it is only necessary to use pl. III fig. 2. The chief difference
is seen in the different forms of the spinodal line. Ours is given
by the dot-dash line of fig.6 and Maxwsrt1’s in fig. 7. Ours consists
of two portions which remain apart to the lowest temperature
WY Z
2, Z
Z Z
LYb- Z BZ
Z
Zz
Fig. 6. ied.
(T=0), while Maxwet.’s shows only a secondary loop. Quite
improbable are MAxweEtt’s isotherms. They show in the vapour plait
a point of inflection in the isotherms. Thereby they differ entirely
from the equation of state of vAN DER WaAatLs, which is certainly
qualitatively correct for vapour and liquid.
II. Tur Gipps’ suRFACE FOR CQ,.
(The general model).
This model was constructed by the help of the empirical equation
of state given in Comms. Nos. 71 and 74 with the assistance of the
thermody namical i mulae ore in No. 66.
E&yT — €K =f ars flag sa) (cz -*) dv
: dp
wr w= fee fi) ft)
Tk
whence
oats 6,+26,+ 46, peo c, +2¢,+ 4c
e=c¢,,(l — Ty) — pe s a == 5 ae ae
b, ie = 4—
perv % +2b,+ 40D, Pk t i
et v a
+.
2 v? 2° )
,
|
( 691 )
yf Vics UE: A amv Ik UE {s —t,—3 "h
| ae epl— Sin ta ——. |- at a - — a =) ee
Ty; Dy th, OE iy 2?
os Pk Vk c, —¢, —3¢, a Pk Uk Pape d, — 32,
2 Tp he 4T;, 25
& c ac
Pk Uk ti —k, an es Pk Uk hae 3 - LiF ae
ae Fe aN Ce oor eS Q)
As specific heat ¢, in the ideal gas state we have taken
0,17.419.10° — 71,2 * 10°"), and it is considered constant. For the
critical constants we have used
qr
== -304,5") pp — 13 1014 10F = T40.10° ———
em sec? .
from the experiments of AmaGcaT and
1, = 2.20 —— from the experiments of Kurnen and Rosson ’)
yk a7
cm
deduced by the law of the rectilinear diameter.
The assumed critical values give:
2 = 0,001044.
With (1) and (2) have been calculated
a) five points belonging to the ideal gas state, where v, is taken
as 180:
fy for £:==.0:40 By is 200
y = 43,1><105
s== sOU 10"
2. for ‘ = 0.60 aj == 180
mec te8 C10
= == 46 « 10°
en lor f= O68 vy = 180
ap a See OE
& =645610!
AD (os ee i — 180
yn == 108 >< 10°
Re Be ei
oe sort == 118 vy — 180
a == 1205
heey Wy pore | 91,
b) two points on the gaseous branch of the connodal line for which
KvurENEN and Rosson (loc cit) have given the values of 7 and v
1) Sufficiently near the value given by REGNAULT.
2) Kuenen and Rosson, Phil. Mag. 6 p. 149, 1902.
46
Proceedings Royal Acad. Amsterdam. Vol. VI.
o>) for w= O24 i 74
a) $= ba Sa .
E> = 61a 1"
1 dor == 4008 v= 119
Ber 10 Sot
Be =e, KE:
The first of these belong to the triple-point gas-liquid-solid.
c.) The points of the liquid state belonging to 6 and 7 are ealeu-
lated with the help of Kurnen and Rosson’s numbers for the heat of
vaporisation. We have found
6 1or £0 (14 Up = 0,85
4 —=— 10210:
€ = — 262 x«10'
9. for t = 0.68 vy == 0583
y =—122 «10:
é =— 304 x10!
In the same way taking into account the heat of fusion at the
triple point we find for a point belonging to the solid state.
1.0: forl t= OTIS “ar 3.068
5
S187 520
& —— 446 <10'
The model (see Pl. I! fig. 2) is constructed with
the values of v in ems —'/, of the above numerical values
1
” ” » WY, ”? —— sarge aersy Os ” ” 9
10°
1
” ” » & 5; » ==, 9108” 9 ” ” ”
According to TamMann two solid modifications of CO, exist so that
we must add two solid ridges (see Pl. II fig. 2) in addition to the
liquid ridge. We have assumed that Tammann’s 2"¢ modification lies
between the fluid state and the first modification, and we call TAMMANN’S
2>¢ modification A and his first £. The reason why we have assumed
this arrangement between the two solid modifications is the following :
TamMANN ') has determined the fusion line for the modification A as
well as for &, and also the transition line for the second modification.
dp
He found (see PI. I fig. 1) that the values of are greatest for the points
a
on the equilibrium line c, smallest for the fusion line a@ of the modi-
fication A and found between the two another locus for the fusion
line of the modification £. The same is also to be obtained from our
1) Tammany, Ann. Phys. u. Chemie 1899 Bd. 68 pg. 553.
( 693 )
model with the position of the ridges chosen, while it is at the same
time easy to see that by another arrangement the “3 for the three
lines will not agree so well either with TamMann’s values or with
our desire to make the course of the temperature line the simplest
possible. We hence consider that the arrangement of the ridges which
we have chosen agrees with the experiments and that thus the specific
volume of the modification A is larger than that of JB.
On this model the binodal for the liquid and gaseous condition
(line GL) is shown and also the gas branch of the binodal for the
gaseous state and the modification 6 (line GLz). The three points
belonging to the triple-point gas-liquid-solid 6 are joined two and
two by steel wires. The dashed line which passes through these
points is the isotherm of the triple-point, and close to this runs the
critical isotherm. The dotted line is the pressure line of the triple-
point. According to TAmMann’s values the solid phase of this triple-
point belongs to the modification 6, while the ridge of the A modi-
fication (see Pl. II fig. 5) lies below the fundamental plane of the
triple-point determined by Kurnen and Rosson. A tangent plane that
touches at more than three points, cannot be placed on our model
which is in agreement with the phase rule. In addition to the just
mentioned triple-point the existence of two others on our model, the
triple-point gas-liquid-solid A and the triple-point liquid with the two
solid modifications A and £ is rendered probable by TamMann’s
experiments.
On comparing our model with one constructed after the equation
of vAN DER WAALS, one sees that on ours the liquid ridge rises
more steeply from the critical temperature to the lower temperatures.
It hence follows that the specific heat of the liquid is too small on
the model after van pier Waats. The slow rise of the liquid ridge
in the latter has also the result that the heat of vaporisation is
too small.
Ill. THe Gress’ surFace ror CO, AT GREATER DENSITIES.
(Detail model of the liquid and solid states).
For the general model the specific heat at constant volume was
assumed to be constant in the ideal gas state. But for the construction
of the detail model, to be now described, we have been obliged to
consider the variability of c,. RecNautt and E. Wiepremann have
measured c, for CO, at one atmosphere pressure and various tempe-
ratures, and have expressed the change with 7’ by empirical formulae.
46*
( 694 )
The results of the two investigators agree well. If one seeks from
the empirical equation of state for 0°0 C. the correction which must
be made on c at one atmosphere to reduce it to the ideal state,
one finds 0.003 cal., which quantity lies within the limit of experi-
mental error. The correction is still smaller for higher temperatures.
We also find that the correction, which is necessary to reduce the
specific heat c, of aether found by E. WiepEemann to the ideal state,
is too small to come into account. The formulae given by Reenacit
and E. Wirprmann for the specific heat of gases and vapours are
thus applicable to the ideal state at least with close approximation.
Hence Lepvc’s contention’) is refuted that for substances which obey
to the law of corresponding states both c, and c, are constant in the ideal
gas state. From the experimental values of c, and the well known
R
relation c,—c, —=—, we can calculate the value of c, and its variation
m7
with the temperature.
Having found c, in this manner we calculated the corrections
which must be made to the equations (1) and (2) due to the variation
of c,. We find the following new values for the points on the liquid
branch at t=0.714 and t=—0.68 and for the solid phase at the
triple-point
points of the liquid state
Pion f= "O08 wear O88
4 == — 117><10°
——_ 286 10'
lh fort) "6714-0 0,85
y—=— 96105
& — — 245><10"
point of the solid state
If. for’ t'== @ 714-4 =— 0.676
4 = — 18010*
é = — 42010"
Now we must investigate the liquid range for higher pressures
more exactly and in the first place determine c,. This follows from
the formula
1) Lepuc, Recherches sur les gaz. Paris 1898 and 99.
( 695 )
by introducing the value of p from the empirical equation of state,
this gives
_ Lepe( PD mw LPR (mu) LPO (rx
it a Ray a geo ay dt? \ Fp rays ee
ede fo \' ay (eX? |
rag ae c) 3 ae (eb
for £ = 0.897 or’ 2 = 273 and v = 1,020 we find
6. ep = 0.0432
or, since at T —273' cyp— 0.1431 is
€3, = 01863
The point corresponding to v=1.02 and t=1 in the liquid
region is now found. This was obtained by the aid of the equations 1)
and 2) where the term ® must be certainly taken into account;
we find
lV. fort=1 yy = 1.020
y= 717T,,=— 42.10 *& 10°
e= 87, = — bia S16?
If we now assume that at the same temperature the difference
between the specific heats at constant volume in the ideal gas state
and for the volume 1.020, is constant and equal to £, we have
R
é—éT, = | ep dT — (= a t) (2-1: J,
rh
c k L
ol ey EAR (Biel: gees a | ee
ko T m Ty,
Tk
with which the following points for v= 1.020 are calculated:
V. for t=0.864 v, = 1.020
7 = jae ctor
e ——145x<10'
Nig sor e== bate oy, — 1-020
4 —— 28X<10*
€ ——33X10'
According to the numbers of KuENEN and Rosson the first of these
two points lies on the liquid branch of the binodal line.
The model Pl. II fig. 3 is constructed from the values for these
points.
The values of v used are 100 times the calculated
a Le tate dee i eee MOT wheal 652 4
Ere etn she! BO" ie ee is
( 696 )
Further, care has been taken to give the tangent plane the proper
inclination at these points in agreement with
"|
dg 0g
ome as ge ime yaw that temperature and pressure shall
have their real value.
On the given drawings (scale ‘/, of model) for plan and elevation
Pl. Ill, fig. 5 and 6 — one side elevation has been rejected as it
does not clearly show the course of the pressure and temperature
line — the behaviour of the line 7’ = const, p= const, v = const,
4 =—const and the position of the triple point can be seen without
further explanation. We draw attention to the intersection of the connodal
line S4 Sp by the connodal line S; Sg and further to the passage
of the isotherms over the connodal line and the crossing of the
isotherms with their corresponding isopiestics. In order to read from
the isotherms, given on the model, the corresponding values of p
and v, the diagram of the isotherms (see PI. I, fig. 2) was constructed,
which reminds one of the course of the isotherms derived from the
VAN DER Waats’ equation. The point 7, in this figure corresponds
to the triple point for liquid and the two solid modifications of
earbon dioxide. According to Tammann the pressure is 2800 K.G.
The point ALS, is the critical point of the modification A in the fusion
line. According to the model the critical pressure would be 6500 K.G.
and the reduced temperature 1.7,
The critical point GZ occurs so far to the right on this scale
(the unit of volume is equal to that of Pl. HI fig. 5 and 6) that it
cannot be represented in the drawing.
No critical pomt exists for the transition of Sg to LZ owing to
the interposition of the ridge S4. The binodal line on Sg and Z,
loses its physical meaning at a given position of the rolling tangent
plane. A continuous passage from Sz to S7z, is only possible through
the gaseous as an intermediate state.
An important result can be obtained from the foregoing. Whenever
substances exist whose molecules undergo changes in the transition
to the solid state, which are mechanically similar to those which
determine the condition of the two phases, these said substances
will also agree with the law of corresponding states in the solid
condition. An experimental investigation for the continuity of the
solid and gaseous states would be best made on the substance with —
the lowest critical pressure. If, for the moment, we assume that AH, and
CO, are sufficiently comparable from this point of view — at present
no better example is at hand —- the eritical point solid-gas should
be sought at about 1800 atm. and —210°C., and thus in possible
( 697 )
experimental pressure and temperature ranges. For many years a
similar investigation has stood on the program of the Leiden Labo-
ratory.
IV. Tae Gipss’ surrack FoR H,O vor GREAT DENSITIES.
(Model for the equilibrium of TamMann’s ice varieties and water).
The Greps’ surface suffers a deformation from association in the
case of water, and the general character of the change has been
already given in § 3 according to our views. Having once arrived
at a given idea about the general form, we can more exactly deter-
mine the form to be ascribed to the ridges according to this idea
by the help of the experimental numbers. The model that we have
obtained by our method is shown on Pl. I fig. 4. As Tammann has
already indicated, two other ice varieties (ice II and ice III) are
found, in addition to ordinary ice (ice 1). The general position of
the ridges belonging to these values follows from TAMMANN’s measu-
rements concerning the volume change and heat of transformation
for the transition of one ice variety into another or into water. If
we give the value O to the last and 1, 2 and 3 to the three ice
varieties, TAMMANN finds at 7’ = 251 (triplepoint water — ice J — ice LI)
Ay t= O44
Av,,; = — 0.05
Av,, = + 0.193
’,, = — 73 cal.
P= 10K 5
m=t+ 3
Also TamMANN finds that Av,, is very nearly equal to Av,,. We
have assumed that Av,, 1s somewhat greater than Av,,. We then
find the general arrangement given in Pl. IV fig. 1 for the water
and three ice varieties. The dashed line gives the isotherm through
the triple point water — ice | — ice III, the dotted line the isopiestic.
We have not taken these from pl. II, fig. 4, where no isotherms
or isopiestics are drawn, because this figure is not sufficiently worked
out for this purpose. We have drawn on Pl. IV. schematic figures
in order that they may be used in continual comparison with the
surface, whenever we wish to further explain the properties of the
-surface. From these we can show easily that they agree with the
model of Pl. II, fig. 4.
We now further specify our ideas for the modification O and 1.
Here = is negative for points on the binodal line, and this also
( 698 )
follows from the modei. In fig. 2 Pl. IV, let AA’ and BB' be a
pair of coexisting phases. A higher temperature belongs to AA’ than
to BB', while the pressure at AA’ is greater than that at BB’. If
we extend the fusion line of ice in the direction of falling pressure,
Ree . é. 4p
it is probable that for a given negative value of p, would change
dt
; , a ., op
its sign and become positive. Those phases for which ao 0 would
be determined by DD', LE’ and FF". The critical point water-ice I
would be found at G and would therefore present a negative value.
Poyntinc ') came to the same conclusion in a different way. A second
critical point at positive pressure, which is deduced by Poyntine
and also by Pranck’*) by linear extrapolation of the variation of
the latent heat of fusion, which is also given by us, becomes
impossible by the appearing of the other ice varieties, which we will
describe now. If we assume, returning to AA’, that by rolling the
common tangent plane to ('C’ in the direction towards 55’ on the
water and ice J ridge, we should also touch the ridge ice J//
dp ue
at '. Then = would be positive for water and ice ///, in agreement
dt
with TAmMann’s measurements. If now we suppose that ice //J is
non-existent, we may prolong the binodal line AC’ A’ C" to a little
over CC' which gives us continually lower temperatures and higher
pressures. For a given position the tangent plane will now also touch the
ice II ridge. Hence we obtain a lower temperature 7’, for this triple
point than for the triple point water —ice I— ice HI, while the pressure
is higher for 7, than for 7. This is also in agreement with TAMMANN’s
_ dp
results. In the same way for water — ice III and water — ice II is —- >.
t
According to our model the fusion curve of ice II has a termination
at higher pressures and temperatures and therefore we have assumed
that a critical point water — ice II exists.
Now we consider further the transformation line ice I to ice IL.
According to TamMann the heat of transformation from ice I to ice LL
is positive in the neighbourhood of the critical point 7’= 251° and
at lower temperatures negative. In order to be in agreement with
this, the ice I ridge has been given a strong curvature and the ice Il
ridge a weak (see fig. 3 Pl. IV where the elevation of the ridges
from the side of the ye plane is shown). Hence the course of the
1) Poyntine Phil. Mag. (5). 12. 1881.
2) Puancx. Wied. Ann. Bd. 15 p. 460, 1882.
H HAPPEL The representation of
d and gaseous conditions on the one
tions on the other by the
1g am
H. KAMERLINGH ONNES and
the continuity of the liqui
hand and the various solid aggrega
entropy-volume-energy surface of Gibbs.
? Co
fe ¢
fig. 2
Proceedings Royal Acad. Amsterdam. Vol. VI.
( 699 )
binodal curve is given by the line drawn in fig. 4 Pl. LV. It is easy
Ip : Ip
to see that now . < 0 at the triple point 251° and > O at lower
€ C
temperatures. The transformation line has thus the course drawn in
fig. 5 Pl. IV, which qualitatively is in complete agreement with
TamMANn’s determinations for this line.
The transformation line from ice I to ice Il is very similar to
that from ice I to ice III. Since the ice II ridge distinctly rises more
steeply than the ice Ill ridge the line of transformation from ice |]
to ice II is more curved than that for ice I to ice LI. The result
is that the line of transformation from ice I to ice II cuts, above
the absolute zero, the vapour pressure line of ice I, which runs very
close to the Z-axis (see fig. 6 Pl. IV). A triple point vapour
— ice I — ice II corresponds with this common point, this has not
been observed, but TamMann holds its existence as probable. Also the
transformation curve from ice I to ice Hl (Pl IV fig. 5) when
produced cuts the Z-axis. The common point then corresponds to a
negative temperature, and thus this triple point cannot be realised.
The curve of transformation from ice II to ice III was not deter-
mined by Tammany, but its course can be seen on our model.
From the model it follows that Tammann could obtain ice II by
cooling to — 80° C., while less cooling would be sufficient for ice III.
Owing to the form which we have chosen for the liquid ridge,
the expansion coefficient of water near 0° C. would be negative and
water would show a maximum density, while the expansion coeffi-
cient of ice would be positive, all in agreement with experiment.
The pressure lines for water (see fig. 7 Pl. IV) run in accordance
with this (at least near 0°) from larger to smaller value of v, and
simultaneously from lower to higher temperatures. The maximum
density of water, on our model, is shifted by increase of pressure
towards decreasing temperature, while at the same time it becomes
less marked and finally vanishes; also in agreement with experiment. *)
1) Amacat. Recherches sur les gaz.
v. p. Waats. Arch. Néerl. Vol. XII. p. 457.
Grassi. Ann. d. chim. 3. 31, p. 437. 1851.
( 700.)
Chemistry. — “On ocimene”. By Prof. P. van Rompurcu. (Com-
municated by Prof. C. A. Lopry pre Broyy).
(Communicated in the meeting of February 27, 1904).
At the December meeting 1900, I had the honour to submit to
the Academy a communication on the essential oil from an Ocimum
Basilicum L. which contains besides a large quantity of eugenol, a
hydrocarbon of the formula C,,H,, to which I gave the name of
Ocimene. The peculiar behaviour of that hydrocarbon reminded me
of the olefinic terpenes, discovered by Semmirr, of which myrcene,
isolated by Powrr and Kirper, was the best known. Ocimene,
however, did not appear to be identical with myrcene.
CHapman') has shown some time ago that the essential oil of hops
contains 40—50 °/, of an olefinic terpene which he considers to be
identical with myrcene. In his paper, CHapmMan disagrees with my
observation that myrcene is noi so changeable as stated by Powsrr
and Kisser. According to these investigators this substance becomes
polymerised after standing for a week, whereas I could preserve it
for months, of course in a properly sealed bottle. Cuapman refers to
a paper of Harries”) to show the unstability of myrcene. There we
read, however, only that the polymerisation “sehr leicht zu bewirken
ist durch langeres Stehen oder durch mehrstiindiges Erhitzen auf
300°”, whilst SemmieR*), in accordance with my observations, says
that he found it to be ‘‘iiberhaupt nicht so leicht veranderlich”.
The olefine terpene from hops has the power of absorbing oxygen,
like ocimene. In one of CHaApMAN’s experiments 16 cc. of oxygen
were absorbed in three days by 1 ce. of the terpene. I had already
found previously that myrcene does not absorb in the same time any
notable quantity (only fractions of a ce.) and, recently, on repeating
my experiments I found my previous observation confirmed. If,
however, myrcene was left in contact with oxygen for a long time
(in tubes 1.5 cm. in diameter) the volume of the gas began to de-
crease gradually, but with increasing velocity, so that after 16 days
30 ec. had been absorbed. Of a sample of ocimene which had been
kept in a properly sealed bottle for three years and had twice made
the journey to and from Java, 1 ec. absorbed 17.8 cc. of oxygen in
11 hours; in the case of this terpene I again noticed that after
1) Journ. of the Chem. Soc. Trans 1903. 83 p. 505.
2) Berl. Ber. 35 (1902). S. 3259.
5) Berl. Ber. 34 (1901). S, 3126.
>
( 701 )
oxidation had set in, the absorption proceeded more rapidly so that
on the second day, for instance, oxygen was being absorbed at the
rate of 2 cc. per hour.
Still, I should not feel justified in saying that hops-terpene and
myrcene are not identical, merely on account of the difference in
oxygen absorption, because further experiments have taught me that
under certain undefined conditions even this hydrocarbon may some-
times be left in contact with oxygen for a day without absorbing a
notable quantity’). But as soon as the absorption has commenced
it proceeds at a fairly rapid rate.
By the action of oxygen a colorless viscous substance is obtained.
I hope to refer to these experiments more fully later on.
In the same paper CHAPMAN expresses some doubts as to the
“chemical individuality” of ocimene. Although I have already pointed
out in my previous communication that the boiling point at 20 mm.,
the behaviour on distilling at the ordinary atmospheric pressure and
the index of refraction of ocimene and myrcene differ considerably,
I will now adduce additional facts which undoubtedly prove that
ocimene and myrcene are different compounds.
Mr. C. J. Enxnaar, who has taken up the study of ocimene in the
Utrecht laboratory, repeated in the first place the determination of
the index of refraction of this hydrocarbon and for a product care-
fully fractioned over metallic sodium he found np—1.4872 and
np = 1.4867, which values satisfactorily agree with 1.4861 previously
found by myself by means of another apparatus. For myrcene, Power
and Kreper have found np—1.4674 whilst I had, previously, found
1.4685.
SEMMLER (loc. cit.) has shown that myrcene is reduced by sodium
and aleohol to dihydro-myrcene. On applying this reaction to ocimene,
Mr. Enkiaar obtained a dihydro-ocimene, which not only differs
from dihydro-myrcene *) as regards boiling point, specific gravity
and index of refraction, but also by the fact that it yields with
bromine a crystallised additive compound. These investigations are
being continued.
1) Not improbably, traces of moisture or of products of oxidation exercise a
catalytic influence. A retardation was noticed when ocimene freshly distilled over
metallic sodium was placed in dry oxygen.
*) Dihydro-ocimene boils at 168° at 763 mm. At 21 mm. the boiling point is
65°. Sp. gr. at 15° 0.775. The boiling point of dihydro-myrcene is 171°.5—173°.5
at the ordinary pressure and its sp. gr. 0.7802,
( 702 )
Chemistry. — ‘Additive compounds of s. trinitrobenzene.” By Prof.
P. van RompurcH. (Communicated by Prof. C. A. Losry pr
BRUYN).
(Communicated in the meeting of February 27, 1904.)
A communication from Jackson and CLARKE') on additive com-
pounds of substituted nitrobenzenes and dimethylaniline and another
from Hissert and SupporouGH*) on. additive compounds of s. trini-
trobenzene and alkylated arylamines induces me to call attention to
the fact that I have been engaged for a long time with the study
of the additive compounds of m. dinitro- and s. trinitrobenzene. In
addition to those which I have described in former papers *) I have
prepared a large number of compounds with different aromatic amines
(such as toluidines, phenylendiamines, benzidine and their alkyl
derivatives) which will be fully described elsewhere as soon as the
crystallographic investigation of many of these products, kindly
undertaken by Dr. F. M. Jancur, has been concluded.
Besides with benzene and naphthalene‘), s. trinitrobenzene combines,
like picrie acid, with different aromatic hydrocarbons. It forms with
anthracene fine orange-red needles (m.p. 161°), with a methylanthracene
reddish colored needles (m.p. 138°), with phenanthrene an orange-
yellow compound (m.p. 168°)*) with jlworene a yellow compound.
In all these compounds we find that 1 mol. of s. trinitrobenzene
is combined with one mol. of the hydrocarbon.
s. Trinitrobenzene forms with a-bromonaphthalene a fine lemon-
yellow compound (m.p. 189°) and a similar one with dibenzylidene-
acetone.
Substituted aromatic amino-compounds such as anthranilic acid,
and its methylester, p. aminoacetophenone, ethyl m. and p. amino-
benzoate brought together with s. trinitrobenzene in alcoholic solution
readily form colored well-crystallised compounds, the first two of
which are colored orange and the others red. p. Aminobenzoie acid
combines less readily and I have not sueceeded in obtaining an
additive compound with m. aminobenzoie acid, which is a stronger
acid than its isomers.
Among the above compounds are some which will, presumably,
prove of importance in the hands of the micro-chemist for the
detection of certain substances.
1) Berl. Ber. 37, (1904), S. 177.
4) Journ. Chem. Soc. 83 p. 1334.
3) Rec. d. Trav. chim. d. Pays-Bas 6, 366; 7, 3, 228; 8, 274; 14, 69.
4) Hepp, Ann. d, Chemie 215, S. 376.
6) In the Dutch publication of this article, the melting point has been stated
incorrectly.
E703?)
Botany. — ‘Determination of the action of poisons on plants.” By
Prof. E. Verscuarrett. (Communicated by Profs. C. A. Losry
pE Bruyn and Hveo pe Vriszs.)
When a part of a living organ of a land-plant is placed in water
it usually absorbs water on account of the well-known osmotic
properties of the protoplasm and this absorption goes on until the
cell-walls allow of no further extension. The accompanying increase
in volume and the phenomena of tension in the tissue which may
result therefrom, have, since Huco pr Vriss laid the foundations of
the subject, given rise to many an investigation which it will be
superfluous to mention here again. Evidently this absorption of
water will also cause the weight of the fragment of tissue to increase
and it is easily understood that fairly considerable differences in
weight will arise as soon as the organ is somewhat rich in parenchym.
All this only happens however as long as the part of the plant
is alive. When a part of an organ that has been previously killed
is placed in water, no more water is absorbed; on the contrary,
since the semipermeability of the protoplasm has been destroyed,
the dissolved substances of the cell-sap diffuse out; with them part
of the water that stretches the cell-wall leaves the fragment of tissue,
and this latter diminishes in weight as well as in volume.
Hence it seems possible, by determining the changes in weight,
subsequent upon placing a plant-organ in water, to decide whether
this latter is alive or dead. If it turns out that no other cireum-
stances have a disturbing influence, we should have a new criterion
for determining the lethal limit of measurable external circumstances,
besides the diffusion of colouring matter at the death of plant-cells’),
used by Hugo pr Vrizs, and the non-appearance of the plasmolytic
phenomenon, recently applied by A. J. J. van pg Vexps?). In order
to test the practicableness of the method I tried to determine in
this way the toxic limit of a few substances and it seems to me
that this has been successful. Not every arbitrarily chosen plant-organ
can be expected to lend itself equally well for these experiments;
most of them proved serviceable, however, and as very fit for this
purpose I mention the potato-tuber, beetroot, fleshy leaves of Aloe,
juicy leaf-stalks like those of Begonia, Rheum and other plants.
One example may illustrate the proceeding and give an idea about
the observed differences in weight.
1) Arch. Néerl. VI, 1871.
*) Transactions of the four first Flemish Physical and Medical Congresses
(Dutch).
( 704 )
After a preliminary experiment had proved that the toxic limit
of CuSO, for potato lay below a concentration of 0,005 grammol.
per litre, four fragments of potato were dried with filtering-paper,
weighed, and placed in solutions of CuSO, containing:
a 0,001; 6 0,002; ¢ 0,003 and d 0,004 gr. mol.
The bits of potato weighed respectively :
a 3,715: 6'3,225- ¢ 2,860 and’ d°3,195"er.;
After having stayed in the solutions for 24 hours, they were
dried and weighed again, the results being:
a 4,620; 6 3,310; ¢ 2,895 and d 3,260 gr.
So they all had absorbed water; the toxic effect of the cupric
sulphate penetrating at the same time would now soon become
apparent, however. The bits were washed and placed in water from
the supply (water from the dunes); after 24 hours they weighed:
a. 4,670; 6. 3,350; c. 2,825 and d. 3,150 gr.
This time c. and d. had lost weight and this loss increased steadily
during the following day, whereas a and 6 went on absorbing water.
The toxic limit of CuSO, for bits of potato weighing 3—5 grammes
consequently lies, after 24 hours, between 0,002 and 0,003 grammol.
per litre, i.e. between 0,03 and 0,05 per cent (molecular weight of
Cu SO, = 159).
Henceforth a piece of tissue was considered undamaged if, after
having stayed in the poisonous solution for 24 hours and then for
another 48 hours in water (once or twice renewed), it had, at all
events, not lost weight, if it had not gained. It is obvious that in
these experiments only such organs can be used as will remain alive
for a fairly long time, when immersed in water. I can state concerning
potatoes, that normal fragments, placed in water which was daily
renewed, even after 18—20 days did not lose weight but absorbed
small quantities of water. It made no difference, at least within this
period of time, whether water from the supply or distilled water
was used. In all similar experiments the results obtained by weighing
are confirmed in a striking manner by the circumstance that bits of
potato, when they die off, turn dark-grey (conversion of tyrosine
into homogentisinic acid by enzyme-action). Also various other parts
of plants show some similar phenomenon which may serve as a
check, in tbe first place the diffusion of colouring matter, as with
red beetroot, Begonia and others.
In the manner described above, also the harmful limit of con-
centration may be determined of neutral mineral salts which in a
certain dilution are innocuous for a long time, but in more concen-
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( 705 )
trated solutions must necessarily become harmful if it were only on
account of their strong osmotic action on plant-cells; in other words,
it is possible to determine the toxic limit of plasmolysing substances.
In these cases the results of weighing are different in that the tissues
in the salt-solution obviously lose weight but recover weight again
when placed in water, if they have remained undamaged. If during
the deplasmolysis death might occur, this can afterwards be recognised
by a diminution of weight.
By this method I have been able to ascertain that the potato-
tuber is rather sensitive for plasmolysing agents. Pieces of this organ
appear to be damaged when they have stayed for 24 hours in
0.4 grammol. NaCl (2.34°/,), and are then placed in water. We
will not decide whether death took place already in the salt-solution
or on entering the water; sometimes, however, the grey discoloration
already began to appear in the solution. A solution of 0.3 grammol.
NaCl (1.75°/,) is perfectly harmless when acting for a day. Now
other parts of plants offer a much greater resistance to neutral salts.
The limiting concentration of NaCl for pieces of beetroot, e.g., lies,
when acting for a day, at between 1 and 1.5 grammol.; I did not
determine this limit more accurately. Similar values are furnished
by various other parts of plants, such as the tuber of Colchicum
autumnale, the leaf of Aloe dichotoma and Aloe succotrina.
For KBr, KNO,, the molecular concentration at which pieces of
potato begin to be injured is pretty much the same as that given
above for NaCl. For the present, however, it was not my intention
to extend this investigation to a greater number of salts, although
this would undoubtedly lead to many interesting results, also perhaps
concerning the action of ions on the living cell. It only must be
mentioned here that with glucose and saccharose, injurious effects
on pieces of potato began to be noticeable at a concentration of
0.5 or 0.6 grammol. which is only slightly higher than with NaCl.
Interesting observations on the action of sait-solutions on plant-
cells have been formerly made by J. C. Cosrerus'); although they
have not been repeated by the weighing-method, I must not omit
drawing attention to them, since they seem to point to a different
behaviour of the cells in the salt-solution, depending on the presence
or absence of oxygen, which may be of importance with regard to
what follows.
The determination of the lowest limit of concentration for which
substances are poisonous, led us to investigate whether this limit can
1) Arch. Néerland. t. 15. 1880.
( 706 )
be shifted by adding other compounds to the solution. This is indeed
often the ease, and so the weighing-method lends itself to a repeti-
tion of the experiments of KaHLENBERG and TrurE*) and those of
True and Gtks*) in which by a different method the toxicity of
metallic compounds was proved to be diminished by the addition of
certain salts. The case which I have examined a little more closely
does not concern a metaliic poison, however, but an alkaloid.
The lowest poisonous concentration of chinine hydrochloride for
potato is a very low one, namely 0.001 grammol. per litre *), the
action lasting 24 hours. All parts of plants which I examined, proved
to be about equally sensitive to this poison. The result of adding
NaCl in a certain concentration to the chinine solution, is that after
the same time, death occurs at a considerably higher concentration
of the chinine, this concentration
depending again on the amount
of NaCl in the solution. The figure
represents graphically this shifting
of the toxic limit. One sees from
it that by 0.2 grammol. NaCl per
litre the harmful concentration of
the chinine hydrochloride is raised
from 0.001 to 0.005 grammol.,
a further addition of salt acting
less favourably again. At 0.4 gram-
Paes eee eae es mol., as was pointed out before,
2 i “ yaci pure NaCl is injurious to the potato.
As far as I have been able to gather, the toxic action of chinine
hydrochloride on plants generally is modified in the same sense by
NaCl. At any rate I obtained the same results with pieces of sugar-
beetroot, the leaf-stalk of Begonia, fragments of the leaves of Aloe.
As the cells of the sugar-beetroot resist much higher concentrations
of common salt than those of the potato, it is not surprising that
also in the presence of more than 1 grammol. NaCl per liter the
antagonistic action towards chinine can be observed with this plant.
The diminution of toxicity, observed by the above-mentioned
authors when certain salts, harmless in themselves, are added to
metallic compounds, has been ascribed in most cases to the concentration
of toxic ions being decreased; their results agree with the connection
0,005
0,004
‘TyooapAy “UTUTT,)
0,003
0,002
0,001
1) Botan. Gazette. vol. 22, 1896.
*) Bulletin Torrey Botan. Club. vol. 30. 1903.
3) or 0,03965 °/); mol. weight of Cy9 Ha, N2 O23. HCl -+ 2 H,O = 396,5.
f-.
ste el | te:
( 707 )
between disinfecting power and degree of dissociation '), formerly
studied by Patni and Kronicg. Antitoxic actions of metal on metal
with animal cells as reagent, studied by Lors, proved however that
the explanation cannot always be sought in this direction’). So a
deeper interpretation of the case here mentioned must be put off for
the present, the more as, very likely, it will appear not to belong
to the domain of physiology but of chemistry.
The observations may be completed with the results of some ex-
periments with other compounds.
The toxicity of chinine hydrochloride for potato and for sugar-
beetroot is as clearly as by NaCl diminished by KBr, Li Br, Ca(NQ,),,
which are rather different salts. Glucose and saccharose, on the
other hand, have no influence whatever.
Also of another organic poison, namely oxalic acid, the action
proved to be partially neutralised by NaCl being also present in
the solution. Especially the sugar-beetroot gave very distinct results
here, although also with the potato the antitoxie influence of the
salt was clear. In a less degree, but yet in an unmistakable manner,
the toxicity ef oxalic acid is counteracted by saccharose.
Some experiments with a metallic poison (cupric salts) gave results
which were in general concordant with those of KaHLENBERG and
c
his collaborators.
Physiology. — “On some applications of the string galvanometer’’.
By Prof. W. Einrnoven. Communication from the Physiological
laboratory at Leyden.
In a former paper*) the amount of sensitiveness of the string
galvanometer and the time in which the deflections of the quartz-
thread are accomplished were mentioned and illustrated by a few
photograms. We = stated that with a feeble tension of the wire a
current of 10-!2 Amp. could still be observed and that with a
stronger tension, so that the movement of the wire is still dead-beat
and the sensitiveness is reduced to a deflection of 1 mm. for
210-8 Amp., a deflection of 20mm. requires about 0.009 seconds.
1) Zeitschr. fiir physikal. Chemie. Bd. 12. 1896. Zeitschr. fiir Hygiene. Bd. 25. 1897.
2) Prricer’s Archiv. Bd. 88. 1901. Americ. Journ. of physiol. vol. 6. 1902
Other observations belonging to the same category of animal physiology, were
recently made by E. Lesyé and Cu. Ricner rics, (Arch. internat. de Pharmacody-
namie. XII. 1903).
3) These Proc. June 27. 1903. p. 107.
Proceedings Royal Acad. Amsterdam. Vol. VI.
( 708 )
These data may be sufficient to form an opinion about the mstru-
ment in theory and to give an idea of its fitness for practical work;
yet on this latter point the applications alone can give full and
convincing evidence.
In what follows we intend to mention some of these applications.
Where the object is to measure very feeble currents no other
ealvanometer seems to equal the instrument we are considering. It
is obvious that theoretically there is no limit to the sensitiveness of
any arbitrary galvanometer for constant currents. One can indefinitely
increase the period of oscillation of the magnets as well as the
distance of the scale and so obtain any desired sensitiveness in theory.
sut practical difficulties soon draw a limit. One among other diffi-
culties is the inconstancy of the zero-point, which is influenced by
many circumstances and which causes the more trouble the more
the period of oscillation increases.
This is probably the reason why an electrometer is preferred toa
galvanometer when very feeble currents have to be measured, e. g.
when great insulating resistances have to be examined or the ionising
power of radio-active substances.
In the celebrated investigation by Mr. and Mrs. Crrte *), which led
to the discovery of radium, the radio-activity of various materials
was judged by their power to render air conductive; and the conduc-
tivity of the air was measured by means of an electrometer. The
electrometer had to be charged by a current, which passed through
a conducting layer of air, the rate at which the electrometer was
charged being a measure for the current.
Evidently if was not an easy matter tO measure currents in this
way; so Mr. and Mrs. Curm preferred a method of compensation
by means of a rod of piezo-electric quartz. The charge received by
the electrometer through the layer of conductive air was compensated
by a contrary charge derived from the quartz-rod. To effect this the
rod was subjected to a steadily increasing pull by continuously adding
weight to a scale suspended on the quartz-rod. In this way the
image of the mirror of the electrometer had to be kept at zero, the
increase of the pull during the time being the measure for the current
and in this case also for the conductivity of the air.
It is much easier to make these measurements with the string
valvanometer.
| connected the instrument with two brass plates A, and A,, fig. 1.
re
1) See eg. Mme Skiopowska Curae, Recherches sur les substances radioactives,
Annales de Chimie et de Physique 7, T. 30, p. 99, 1903,
( 709 )
Both plates were round, had a diameter of about 25 cm., were
insulated and mounted at a distance of about 2 cm. from each other ;
the laboratory-battery of about 60 Volts and a resistance of 1 Megohm
were inserted in the circuit from the galvanometer @ to the plates.
1 Megohin.
The sensitiveness of the galvanometer was adjusted at 1 mm.
deflection for 210-1! Amp., the time required for a deflection
being about 5 to 7 seconds. Now a round plate, covered over a
diameter of about 20 em. with powdered uraniun-trioxide (containing
water) was shoved in between CLO>)! Amp:
= 1.2 10'? Ohms or rather more than a million Megohms. An
insulating resistance of 6 >< 10'% Ohms ean be demonstrated with
the 60 Volts laboratory-battery by a lasting deflection.
We finally mention another application of the string galvanometer
for measuring very feeble currents, namely those which are caused
by atmospheric electricity. A spirit-lamp is held up on a long pole
in the open air. An insulated wire connects the flame with one ter-
minal of the galvanometer-wire, the other terminal being earthed.
Under these conditions one sees a lasting deviation of the galvano-
meter which diminishes and disappears as soon as the pole is lowered
and carried indoors, but which returns as soon as it is taken out
and held up again.
The deflection of the galvanometer in these experiments was
generally more or less oscillating on account of the wind causing
fluctuations in the contact of the flame and the end of the wire.
Besides for measuring feeble currents, the wire-galvanometer is
suitable in practical work for detecting small quantities of electricity
and especially for accurately measuring rapid variations of electric
tension or of feeble electric current. As the instrument for feeble
currents which is quickest in its indications, it will undoubtedly prove
useful for transoceanic telegraphy.
The smallest quantity of electricity that can be detected by it, can
easily be calculated. Let us imagine that a great resistance has been
inserted in the circuit so that the electromagnetic damping of the
moving wire may be neglected and that now suddenly a current of
constant intensity is sent through the wire.
The movement of the wire under these circumstances is accurately
represented in the formerly published photograms *). Theoretically the
wire will, at the moment the current starts, experience an electro-
magnetic force by which an acceleration will be imparted to it. Its
motion will be an accelerated one until a speed is attained such that
the resultant of the electromagnetic force and the tension of the wire
will make equilibrium with the resistance of the air,
) These Proc. June aly 1903. p. 107,
eit }
If however the tension of the wire is feeble enough, the duration
of this accelerated motion is very small compared with the total
duration of the deflection so that it may be neglected. We are then
allowed to speak of an initial velocity of the wire and may disregard
its mass. The initial velocity is proportional to the current and may
be estimated at about 20 mm. per second fora current of 10—-% Amp.
with an image as is obtained with our magnification ‘).
A current then of 10-% Amp. only needs to last for LS sec. to
cause a deviation of 0.1 mm. and as the photograms prove such a
deviation to be still visible, a quantity of electricity of 5 >< 10—!2
Ampere-seconds can consequently be detected. This quantity is equal
to the charge of a condenser of 1 microfarad at a potential of
510-6 Volts or to the charge of a sphere of 4.5 em. radius at
a potential of 1 Volt.
Since, as was pointed out above, the initial velocity is proportional
to the current, the deflection for a small quantity of electricity, will
entirely depend on that quantity itself, and it will make no difference
whether a strong current passes during a short time or a feeble cur-
rent during a longer time, if only the time of passage be small enough.
The properties of the wire-galvanometer lead us to expect another
very remarkable consequence. If the tension of the wire is increased,
the velocity with which a deflection is accomplished, will increase,
but at the same time the amount of the deflection for a given cur-
rent will diminish. Now it has already appeared from the photograms
that, provided the tension of the wire is not too great, the change
in sensitiveness is exactly inversely proportional to the change in
deflectional velocity, so that the initial velocity for a given current
is independent of the tension of the wire. From this we derive the
seemingly paradoxical result that under the condition mentioned the
deviation for a quickly passed, small quantity of electricity is the
same for any tension of the wire.
The facts are in complete accordance with this argument and for
an observer who is not accustomed to the instrument, it is very
curious to see, how with a relatively much greater tension of the
wire and a consequent great diminution in sensitiveness for constant
1) This amount of 20 mm. is only approximately true. I hope soon to be able
to deal more extensively with the movement of the wire under various conditions.
The influence of the viscosity of the air will then be compared with that of the
electromagnetic damping. It would be a decided advantage if the wire could be
placed in an air-tight space, which would enable us to observe its deflections either
in a vacuum or under increased pressure.
(712 )
currents, the sensitiveness for a quickly passed small quantity of
electricity remains nearly unaltered.
And the practical application lies at hand. Whenever rapid varia-
tions in electric tension have to be discovered and the disturbance
by slowly varying currents has to be avoided, a requirement which
frequently imposes itself in electro-physiological investigations, the wire
must be relatively strongly stretched.
The described sensitiveness for small and quickly passing quan-
tities of electricity, more even than its sensitiveness for constant
currents, makes the wire-galvanometer a suitable research-instrument
for a number of phenomena which are usually observed by means of
an electrometer.
If one end of the wire is earthed, the other joined to an insulated
conductor, e.g. a resistance-box, a rubbed ebonite rod, brought near
the resistance-box, will act by influence and easily drive the image
from the scale. A single advancing or receding movement of the rod
must obviously result in a double movement of the wire, since this
latter always returns to zero when the rod stops moving. At a distance
of a few metres, rubbing the rod with a silk cloth will still cause
deviations of the galvanometer, each single stroke of the hand ocea-
sioning ato and fro movement of the wire.
When I had laid aside the ebonite rod and the silk cloth and
came near the resistance-box with the hand only, a small deflection
of a few millimetres could still be observed. When quickly approach-
ing the hand, the wire showed a momentary deviation im one
direction, when quickly withdrawing it, in the opposite sense. Even
moving the fingers round one of the plugs of the resistance-box
caused the wire to move. It must be emphasised that the resistance-
box was not touched by the hand so that ordinary conduction
from the body through the galyanometer to the earth was out of
the question. .
I could not at once explain the phenomenon. My first thought was
that the body or at any rate the hand was charged to a certain
potential and like the ebonite rod drove electricity by influence
through the resistance-box and the galvanometer. But the potential
of one of the hands of an uninsulated person is too small to explain
the movement of the wire.
Also clothing, e.g. a woollen sleeve, appeared to play no part.
If a round metal disk connected to the earth by a conducting wire
and hence having presumably the same potential as the galvanometer
and the resistance-box, was suddenly brought near or removed from
(713 )
the latter, the same deviations were noticed as when moving the
human hand.
Also these deflections changed only litthke when the metal disk was
moved, after having been charged by a storage-cell to a potential of
+ 2 or —2.
The idea that the strange phenomenon had to be ascribed to
currents in the air which would ‘generate electricity by friction, had
to be rejected at once, as soon as, by means of a pair of bellows,
a powerful air-current had been directed against the resistance-box
without the wire showing the least motion. But in the end the
explanation appeared to be very simple. The ebonite plate of the
resistance-box has a certain charge and the lines of electric force
bend from the ebonite to the metal plugs. As soon as a conductor
now approaches, the lines of force are displaced and thus electricity
is moved from the metal through the galvanometer to the earth.
That this is the real explanation could be easily shown by rubbing
the ebonite of the resistance-box and so charging it to a higher
potential. When this was done the deviations became many times
larger.
An interesting proof of the usefulness of the wire-galvanometer
as a sensitive instrument which at the same time is quick in its
indieations, is afforded by the ease and accuracy with which it
registers sounds.
When a Stemens’ telephone is connected with the galvanometer,
the sound-vibrations falling on the plate of the telephone will send
induced currents through the wire, by which this latter will be moved,
As soon as a tone of arbitrary pitch is made to sound against
the telephone with constant intensity, the image of the wire broadens
in a curious way. In the bright field the narrow, black image is
broadened to a band of several centimetres breadth, which has a
light grey tint and whose appearance in the field is feebler as it is
broader. The middle of the grey band always corresponds to the
image of the quartz-thread in rest. The margins have a somewhat
darker delineation than the rest of the band.
This appearance is entirely explained by the circumstance that the
wire executes regular, rapid vibrations of the same rhythm as the
sound-vibrations striking the telephone.
One peculiarity has still to be mentioned. If a sound like @ or 0
is sung against the telephone-piate, one sees the grey band divided
into parts. Symmetrically with respect to the middle of the image,
within its real margins something like secondary and tertiary margins
( 714 )
are visible which admit of no other explanation than that the motion
of the wire, representing the sound in its fundamental and _ partial
tones, consists of a number of vibrations of different frequencies
and amplitudes.
We hope soon to analyse this phenomenon photographically. When
the intensity of the sound is changed, the breadth of the grey band
also changes immediately. And at the moment the sound stops, one
sees the narrow, black image of the wire standing perfectly still
again in the bright field.
When the telephone is replaced by a microphone and a suitable
induction-coil, tie same phenomena are observed; with these contriv-
ances however the arrangement has become much more sensitive.
Feeble sounds now give rise to considerable broadening and it is
surprising to see, how, when one speaks softly at a distance of one
or more metres from the microphone, the image of the wire reacts
powerfully on each word that is spoken or rather on each syllable
that is pronounced, but always immediately occupies its position of
rest as soon as the sound stops for a moment.
Feeble sounds, as e.g. the cardiac sounds of a rabbit are excel-
lently rendered by the galvanometer.
desides for the study of phonetics and of cardiac sounds, the wire-
galvanometer will find fruitful applications over an extensive range
of physiological research. We already communicated some results of
an investigation concerning the human electrocardiogram '). Besides,
an investigation of the nerve-currents is now in course of progress,
about which we will only mention in this place that the action-
currents of a nerve, resulting upon simple stimulation, can be shown
and registered in an excellent manner. As far as I know action-
currents of the ischiadic of a frog, arising by the stimulus at the make
and break of an ascending and of a descending constant current, have
never been observed hitherto. The string galvanometer shows them in
all their details as they must be expected according to PrLtGEr’s law
of contractions and the existence of which could until now only be
surmised from the observed muscular contractions. One also sees the
superposition of the phenomena of electrotonus on those of the action-
current, which need be no impediment to the interpretation of the
obtained curves. We seem to be justified in supposing that perhaps
new points of view will be opened about the manner in which the
nerve is capable of reacting on various stimuli.
Oe Bue
a i i
( 745 )
Chemistry. — “Action of hydrogen peroryde on diketones 1,2 and
on a-ketonic acids. By Prof. A. F. HoLLeman.
Some aromatic acids may be obtained by first thtroducing the
acetyl group by means of the reaction of Frirpen and Crarts and
oxidising this to the carboxyl group. In many cases, however, this
oxidation does not take place readily; the group CO.CH, yields with
comparative ease the group CO.CO,H but the further transformation
of the latter into the carboxyl group is often attended with great
loss. Even the method of HooGrwerrr and van Dorp, consisting in
heating the a-ketonic acid with concentrated sulphuric acid does not
yield the theoretical quantity. I have tried whether this transforma-
tion might perhaps be attained quantitatively by means of hydrogen
peroxide, according to the equation :
R.CO. CO,H R.COOH.
+ HOOH — + HOCO,H (= H,O+C0,)
This was indeed the case. Aqueous solutions of pyruvic acid,
benzoylformic acid, thienylglyoxylic acid when heated with the
calculated amount of 30 °/, hydrogen peroxyde (Merck) at once
eliminated CO and yielded almost quantitative amounts of acetic
acid, benzoic acid and thiophenic acid. From Prof. EyKman, | received
small specimens of four a@-ketonic acids which he is investigating
and these, when heated in aqueous or acetic acid solution with a
slight excess of H,O, also eliminated CO. On titrating the acids
obtained from them it was found that their group CO .CO,H had
passed into CO,H.
This result led us to suppose that «-diketones might also be readily
resolved by the action of H, O,,
R.CO. CQ.R'
+ HO OH
Some of the diketones, such as benzil, camphorquinone and
= R. CO, H+ R'. CO, d,
phenarthrenequinone were dissolved in glacial acetic acid and warmed
for some days with a small excess of 30 °/, H, O,. The expected
reaction took place almost quantitatively: it was remarkable that
campherquinone did not at once yield camphoric acid but first the
anhydrde, which was converted by boiling with dilute alkali into
camphoric acid.
Messis. J. Huisrnca and J. W. Berkman have carried out the
experiments.
Groningen, March 1904. Lab. Univers.
|
( 716 )
Mathematics. — “On a decomposition of a continuous motion
about a fived point O of S, mto two continuous motions
about O of SJs’ by Mr. L. E. J. Brouwer, communicated
by Prof. Korrewse.
(Communicated in the meeting of February 27, 1904).
Two planes in NS, making two equal angles of position are called
mutually “equiangular to the right” if one is (with its normal plane)
plane of rotation for an equiangular double rotation to the right
about the other one and its normal plane.
We will call the sides of one and the same acute angle of position
“corresponding vectors” through the point of intersection of twe
equiangular intersecting planes.
As is known a system of planes equiangular to the right or to
the left is infinite of order two. Of course a determined equiangular
system of planes to the right can have with a determined equian-
gular system of planes to the Jeft not more than one pair of planes
in common (two pairs of planes cannot intersect each other at che
same time equiangularly to the right and to the left); but one
pair of planes they always have in common. We will show how
that common pair of planes can be found.
A pair of intersecting pairs of planes of both svstems is of coirse
easy to find. We lay through any vector OC’ the planes belonging
to the two systems; their normal planes intersect each other in a
second vector OD. Thus OCD is one plane of position of those
two pairs of planes. In the second plane of position the four planes
furnish four lines of intersection, let us say OH, OF, OK, OG,
in such a way, that the considered pairs of planes must be OCH;
ODK and OCT; ODG. The following figures are supposed to be
situated in those two planes of position.
' D :
5
‘,
Fig. 1.
Let the pair of planes OCH; ODK belong to the giver system
equiangular to the right, and OCF; ODG to the giver system
equiangular to the left,
e717 )
The vectors in the second plane of position are drawn in such a
Way that either
\ OH > OC
, (1)
}OK > OD
is an equiangular double rotation to the right, or that such is the
case with
\ OH SOC
,OK > OD
We shall suppose the first to be true (the reasoning is the same
for the second case). Then
OF > OC
1OG = OD
is also an equiangular double rotation to the right; for, the planes
OFC and OGD ean be brought to coincide with these directions
of rotation with the planes OHC and OAD, having the directions
of rotation
OL > OC
|OK > OD
\ OF =F OC
| OG' + OD
is an equiangular double rotation to the left.
If farthermore OA and OF are bisectors of the angles HOF and
KOG, and 4 we have-made “COA! => 7 DOB > FYaA0A =
== POL = VARs == "7G 0B, then: the, pair of planes
{ AOA!
BOB
is a pair of planes of rotation as well for the equiangular double
rotation to the right (1) as for the equiangular double rotation to
the left (2). So it is the pair of common planes which was looked
for of the two systems of planes.
We shall think now that through two
arbitrary vectors OA and UF two planes
intersecting each other equiangularly to the
left have been laid; we shall now consider
more closely the position which two such
planes have with respect to the plane
OAL and its normal plane. We shall call
the indicated equiangular planes. to the left
a and 3; and indicate UAB by y and its
Fig. 2. normal plane by J. In fig. 2 the lines
drawn upwards lie in d and those drawn downwards in y.
(ito)
The plane OCC” is the plane of position of y and @, intersected
by y in OF, by a4 in OC. Fig. 3 is supposed to lie in that plane
of position. We have made fartheron in fig. 1 the angles A’OD’,
C’OD’, COD equal to 7 AOB =g, and the directions of rotation
indicated in those planes belong to a double rotation to the right.
Fig. 4 is supposed to lie in the plane ODD’, and the lines OG and
OG’ are drawn in it in such a way, that ODGD'G’ = OCFC EF’.
F.= ce! G D’
oe ee
¥ rs
0 0 D
Fig. 3. Fig. 4.
We shall consider the plane BOG more closely. Let us project
Ob and OG both on a, then it is not difficult to see that the
execution of those two operations, each of which is threedimensional,
gives as a result two lines OH and OA, mutually perpendicular
(see fig. 5, supposed to lie in a).
The projecting planes are successively: OF” (tig. 6) and OGA’
(fig. 7).
0 5 F A
=
H K
Ns H 0 A 8) E
Fig. 5. Fig. 6. Fig. 7
We shall directly see that OA and O/” are situated on diffe-
rent sides of OH, and OG and OA’ on different sides of OX,
and that ~HOB = /WOG, if we suppose ourselves to be successively
in the threedimensional spaces, in which the projecting takes place.
So we see that the plane BOG has two mutually perpendicular
vectors, making equal angles with @ and projecting itself on «
according to two perpendicular vectors namely OF and OG, projecting
themselves according to O/T and OX: the characteristic of equiangular
intersection.
Let us still examine of which kind that equiangular intersection
is; we shall then perceive that on account of OB being transferred
into OG by the equiangular double rotation
( 719 )
OF' — OA'
OH => OK
and this being of the same kind as
OF —» OA'
OA— OF
which in its turn can be made to coimeide with
OC' = OA'
OA = OC
by a single rotation about the plane OAA', the kind of equiangular
intersection is the same as the kind of the double rotation
OC' = OA'
OA = OC
which is to the left according to the data.
So the plane OBG is identical with the plane 2, for through OB
only one plane equiangular to the left with @ can pass.
ab
If we now introduce the notation Eq ) equiangular to the right”
ce
indicating if abcd denote four vectors through QO, that the planes
(ab) and (cd) are equiangular to the right and that the same double
equangular rotation to the right transferring @ into 4, also transfers
c into d, then
OA, OB
OF, OG
is equiangular to the right and the corresponding equiangular double
rotation to the right transfers @ into Bp. In other words we have
proved the
Theorem 1. If (
s) is equiangular to the right, then = is equian-
gular to the left; or in other words though less significant :
By an equiangular double rotation to the right any plane passes
into one equiangular to it to the left.
If we suppose three vectors ac (whose position of course determines
the position of S,) to have come after some equiangular double rotations
ab\ . :
to the right into the position de/, then Ce is equiangular to the left
ade
ac ; : ad ! ;
and equiangular to the left; so é ) equiangular to the right
. :
ap
ad 555)
and ( -) equiangular to the right, so finally
ad
ef
( 720 )
equiangular to the right; in other words the final position would
have been obtainable out of the initial posiuion by a single equiangular
double rotation to the right; with which is proved:
Theorem 2. Equiangular double rotations of the same kind form a
eroup.
Let us suppose given two equiangular systems to the right and two
vectors OA and OF through each of which we bring the planes
belonging to both systems; then the’ equiangular double rotation to
the left, transferring OA into U4, will transfer at the same time
the angle of position formed in OA into the one formed in OB, thus:
Theorem 3. Two equiangular systems to the right form in each
vector the same angle, which can be called the angle of the two
systems.
The obtained results we shall verify by deducing analytically
theorems I and 8, which deduction will also throw some more light.
Suppose a rectangular system of coordinates to be given in such
( OX be
Oe 0x
4
a way that
is equiangular to the right. The same then holds good for
( OX,, pi ee bee net
ORG ay: OX,; OX,
A vector @ through O we can determine by its four cosines of
direction @,, @,, G5, @,.
A plane passing through the vectors @ and 3 with direction
of rotation from «@ to ~p, is determined by its six coefficients of
position (i. e. projections of a vector unity) 2y55 2515 412+ Aras Aeas Aaa,
which are detined by the following relations, if we represent ¢,3,—a,(),
-
by 5:
a ene rere ne eevee oer ———————., ete.
a tame Be oe pee el a == ae 5 3 5 2
a 4 333° 7! S31 “hp Sre + Sis 2 ik 334
We must take the positive sign in the denominator, for A,, must
he positive, when the projection of @on OX, NX, to that of 8 on OX, NX,
rotates through an angle less than a in the same way as (LX, to
ON,; and in that same case §,, gives us a positive value. If we
how represent that positive root of the denominator by AY, then
S
, 32 “ 3;
a = 743, — sah etc.
; A K
An equiangular double rotation to the right can be given by the
(721)
system of equiangular planes of rotation to the right with direction
and the angle of rotation.
For all those planes of rotation
Past Avg
have the same values. These three values «,,@,,,, besides the
cosinus of the angle of rotation a@,, we can take as determining
quantities of the equiangular double rotation to the right. A rotation
<_2a is unequivocally determined by that (for, whether the angle
of rotation is a, which is left undecided by the value of the cosinus,
follows from the sign of the a,, a, d,).
Saat an arbitrary vector @ to be transferred by the rotation
into 3, then it holds good for each pair of vectors aj that:
a,@, —a, 8, + a,8,—a,8,=— K.a
a, 3, —a, 8, + a, 8,—a,8, = K.a,
a, Bp, — a, B, + 4,8,—a,8, = K.a
a, B, + a, 8, + 4; 8 + 4,6, = 4,.
If however we consider that A = + Vsin? 9, if & is the angle of
rotation, then A’ proves to be a constant for all pairs of vectors so
that we may regard A.a,, K.a,, A.a, and a, as determining quan-
tities of the double rotation which we shall call 2,, 2,, a,.,; and
we shall write the relations:
2 ets
— a, Pp, — a, B, + a, 8, + «,8,=—2, '
a, 2, Toy 3, mses Ps of as By = Es ]
(ZT)
ae ae
og Suen er By a, Bs + a; 8, — *; |
a Pr @, Bye, fp, + @, p, =
in which we have at the same time arranged the first members
according to 3,;3,.3;,3,. We now se as
B+ afta ft aVHK740,,7 +4,,.7° +4,.7+24,744,7% +4, +
+r Stas pe os a oer aes
WGN | ot See |) oe
= sin? } + cos? &
ail B
So we can regard 27,, %,, 7,7, as cosines of direction of a vector
through QO in S, and we can represent an equiangular double rotation
to the right by a vector through O in S,, which determines it
( 722 )
unequivocally. (A vector without length; lateron we shall determine
it, likewise unequivocally, by a vector with length, in JS;).
If we farthermore consider the determinant on the coefficients of
8,.3,,3,.3, in (/7) it proves to. satisfy all the conditions of an
orthogonal transformation.
We call that transformation with that determinant
—a, —a, +a, +a,
+a, —a, —a, +a,
6, = @, eee
+a, +a, +a, +4,
the (+7) a-transformation; it appears in the relations (//), if the
first members are arranged according to the cosines of direction of
the final position of the rotating vector. If they are arranged according
to the cosines of direction of the initial position the determinant of
the coefficients becomes
B, Bs a Bs ig B,
7 B; B, B, Parak B,
B, = B, B, B,
B, b, B, By
which we shall eall the (— 7) 8-transformation.
(Juite analogous to this we have for equiangular double rotations
to the left (9, 9, @,9,) bilinear homogeneous equations between the
cosines of direction of initial and final position of a vector, let us say
e and 3, which arranged according to the 8's, give as determinant
of the coefficients
a. ss a, — a,
a, =e, =-.e.
— a, a, a, —@,
a, a, a, ans
the (+ /) «transformation and arranged according to the a’s
Ps By 3,
= Bs vid B, PB, B.
By oe eB
2, By Bs By.
the (—/) 3-transformation.
We can now state the following:
If the equiangular double rotation to the right (2, a, 2, 7,) transfers
the vector (@, a, @, 4,) into (3, 8, 3, 8,) then the (+ 7) a-transformation
transfers the vector (7, 2, #, %,) into (8, 8, 8, B,)
aE eee
( 723 )
and the (—v,) §-transformation transfers the vector (7, 27, 7, 7,)
into (a@, a, @, @,).
Analogous to this:
If the equiangular double rotation to the left (g, 9, @; @,) transfers
the vector (a, a, a, @,) into (3, 3, 2, %,), then the (+ /) a-transformation
transfers the vector (9, @, @, @,) into (, 8, B, B,)
and the (—/) #-transformation transfers the vector (e, 9, 9, @,) into
(a, a, as at,).
Let us now suppose that S, has first an equiangular double rotation
to the right (x) transferring an arbitrary vector @ into #'; then an
equiangular double rotation to the left (@), transferring #’ into y, then
we can write:
x = [(+ re]? e=((—)rl?
(+ ye] - [(—Ar}e
where the form between {} denotes the determinant of transformation
having as first row the sum of the products of the terms of the
first row of [(+ 7) a] with the corresponding ones of respectively the
first, second, third and fourth of [(— 2) y], whilst the second etc. row
in a corresponding manner is deduced out of the second etc. row
of [(+,r) a] (all this in the way of forming a product of determinants).
If S, has first an equiangular double rotation to the left (g) transferring
a into @" and then an equiangular double rotation to the right (2’),
transferring 8” into y, we have:
e=[((+)a] RX F=[((—nNxe
x ={{(—r7] - (+ 9elhe.
—
But now
(+ ye] -(—)y=l-— 7] - (4 De)
which can be at once verified, so:
a = 2.
Thus:
If S, is allowed successively an equiangular double rotation to the
right (x) and one to the left (g) the order of the two rotations may
be interchanged. For, in both cases an initial position of a vector e
gives the same final position y.
And if we regard the quadruple a, #’, 6",y, then os is
yf
equiangular to the right, according to the rotation (a) and € 7
(3
equiangular to the left according to the rotation (eg); by which we
assuredly once more have proved theorem 1.
48
Proceedings Royal Acad. Amsterdam. Vol. VI.
( 724 )
Let us farthermore suppose (6) and (tr) to be two equiangular
double rotations to the right, transferring a given vector ¢ the for-
mer into &, the latter into 4. Then
o={G-H8s- =i ele
The same orthogonal transformation transferring o into §, transfers
zt into 7, so that the angle between $ and 1 is the angle between the
vectors o and t independent of the initial position «. As a special
case theorem 3 is included in this, for the case that the twe double
rotations take place about an angle $2; for then the angle between
$ and 7 is the angle of the two planes of rotation through ¢, proving
to be independent of «.
We have still to mention that theorem 1 in the second form is
entirely included in the applications of the biquaternions on S, as
given by Dr. W. A. Wurtnorr in his dissertation: “De Biquaternion
als bewerking in de ruimte van vier afmetingen” (the biquaternion
as an operation in fourdimensional space). For an equiangular double
rotation to the right is represented by Q.¢, +, (p. 127) where
Q represents a certain quaternion with norm unity.
This applied to an arbitrary double vector
@,&, + 4,8,,
changes it into
Qa,é, ar AE os
so it leaves the isosceles part of that double vector to the left
unchanged and so also the equiangular system of planes to the left to
which it belongs. This holds good for an arbitrary double vector,
so particularly for a plane.
Finally theorem 3 can be proved as follows:
If g and w are the acute angles of position of two planes, then
if we represent the coefficients of position respectively by 2’s and w’s:
cos ~P cos W = 4,, Usa ta Marrs rat Arg Mig tag Maa tes Hae =
= = (A,,+4,,) (u,; +44) aes = (4,; TAS oi My).
For intersecting planes with angle of position g:
cos p= & (45,4, 4) (Us Urs) = & (Ags 414) (Has Yaa):
So for two intersecting planes, belonging to two definite equiangular
systems to the right or two to the left
Vig ee age a oe and Bei iE as +i x
resp. BF a a and fetal an and cos gy —— 008 gy.
We shall now resume our geometrical reasoning dropped after
theorem 3. Let us take through O a definite vector OW in S, but
not movable with S, and let us represent each system of planes equi-
Pores)
angular to the right by the line of intersection of the plane through
OW belonging to it with S,1 OW. That S, is thus, entirely filled
with these representing lines which are in (1,1)-correspondence with
the represented systems of planes.
We shall call that S,;1 OW regarded as a complex of the rays
representing the equiangular to the right systems of planes, “‘the repre-
senting S, to the right of S,” or shorter “the S, of S,’. In the same
way we form the ‘“S, of S,’. Each pair of planes in S, is then
unequivocally determined by its representants in S, and S,and rever-
sely the pair of planes determines unequivocally its representants.
Theorem 4. An equiangular double rotation to the right of the S,
about a certain equiangular system to the right which double rotation
leaves according to theorem 1 the position of S; unchanged, givesa
rotation of S, about the representant of the system of the planes of
rotation over an angle equal to double the angle, over which the
equiangular double rotation to the right of S, takes place.
Proof. In the first place ensues from theorem
Th a 3 that the representants in S, keep making mutu-
ally the same angles; so S, has a ‘motion as a
nF solid”. We suppose through OW to be laid its
plane of rotation a in S, and its normal plane ~.
0
In fig. 8 we suppose the lines tending downward
¢ to lie in @ and those tending upward to lie in@
© whilst the indicated directions of rotation are
those of the equiangular double rotation to the
Ww’ right which we consider. Angle WOC'is made equal
Fig. 8. to } x. Then the S, is the S, through OC and
B. Let OP be an arbitrary vector in 8 and @ the angle, over which
the equiangular double rotation to the right takes place. The double
rotation leaves OC unchanged as representant of the equiangular
system to the right on (a8). Moreover it transfers OW into OW’ and
OP into OP’. If we then still make “ P’’OP’ equal to “” P’OP
we have:
OP, OP'
( ow. ee equiangular to the right, thus :
OB OP
OW, ey equiangular to the left, or also:
ORY, OP
ow' equiangular to the left, so at last
ieee.»
The plane POW giving OP as representant of its equiangular
system to the right before its double rotation, gives after that rotation
(transferred to P’OW") as representant OP’’ making an angle 29
with OP; so an arbitrary vector OP in S,1OC (the invariable
vector) rotates about OC over an angle 2¢, with which the theorem
is proved.
We can now say: For an S, moving as a solid about a fixed
point the position is at every moment determined by its “position
to the right” (the position of the S, moving as a solid about a
fixed point) and its “position to the left” (the position of S,). For,
if of two positions the pairs of planes through O coincide, then this
is the case too for all planes, thus for all rays too.
N.B. We can remark by the way, that in this way we have
proved quite synthetically that two positions of S, have a common
pair of planes, namely that pair, which has as representants the
axis of rotation of the two positions to the right and that of the two
positions to the left; so, taking into consideration that also the
common fixed point is always there (having as projections on the
positions of planes remained invariable the centres of rotation of
the projections of S, on it), that the double rotation is the most
general displacement of S,. However, until now we have occupied
ourselves only and wish to keep doing so with the motions of S,,
where always the same point ( is in rest.
For a continuous motion of S, the position and the condition of
motion are at every moment determined by S,and_S;; so the motion
of S, is quite determined by the motions of S, and S;; and at every
moment the resulting displacement of S, is quite determined by
that of S, and of S;, independent of the order of succession or
combining of the two latter; they have no influence upon each
other. We can regard a motion of S, as a sum of two entirely
heterogeneous things, i. e. which cannot influence each other in any
way or be transformed into each other.
We can proceed another step by indicating not only by a line in
S, a system of equiangular planes of rotation to the right, but
also by a line vector along it an equiangular velocity of rotation
to the right, that line vector being equal in size to the double
velocity of rotation of the double rotation and directed along the
vector moving with jS, in the direction of OW. Then equal and
opposite velocities of rotations to the right of S, are indicated
by equal and opposite vectors in 5S,.
Let OP. be such an indicating vector and OQ, and OS, two
mutually perpendicular vectors in the plane erected perpendicularly
727.)
to OP, in S, in such a way that
OP,, OW
A OS, )
is equiangular to the right, then to the equiangular double rotation
to the right of S,, indicated by OP, corresponds the rotation of S,
about OP. equal to the length of OP, in the direction of OQ, ~ OS,.
Let OP’. be another indicating vector and let us determine in an
analogous way OQ’, and OS',, then the orthogonal systems of vectors
OW P, Q, S, and
OWP', Q,S',
are congruent, can thus be made to coincide by a rotation of S,,
with OW, thus SS, too, remaining in its place, so that the indicating
vector OP, by a motion of S, in itself can be made to coincide
with the indicating vector OP’. in such a way, that at the same
time the directions of rotation of S, belonging to it coincide in the
normal planes. But then an indicating vector in S, represents that
velocity of rotation entirely in the way usual in space of three
dimensions, as also by its length it indicates the size of the velocity
of rotation of S, belonging to it; if namely we endeavour to regard
the definition of that usual mode of representation entirely apart
from the notion ‘‘motion with or against the hands” which is lacking
in S,; and say simply after having taken in that space a system
of coordinates OXNYZ: the vector of rotation will be erected to
that side of the plane of rotation, that for the plane of rotation
being by motion inside the space made to coincide with the plane
of YY in such a way, that the direction of rotation runs from OX
to OY, the vector of rotation is directed along the positive axis of Z.
For us that system of -coordinates in S,: OX,, OY,, OZ, has
been chosen in such a way that with OW it forms a system of
coordinates in S,, for which
OF.» O4; O2,, OX, OX OF;
on ony oe on fon a)
are equiangular to the right.
A vector along Q(X, then indicates a rotation of S, in the sense
a OY, = 02,
Entirely analogous reasonings hold good for S). It being however
more profitable to be able to say also for S;: a vector along OX;
represents a velocity of rotation of S; in the sense of OY;—~ OZ,
we must modify the preceding either by choosing the system
OX: Y;Z, W in such a way that
( 728 )
OF), OF
es en
is no more equiangular to the right, but to the left, or if we suppose
OY), OZ,
a)
to be also equiangular to the right, we must take as indicating vector
in S; that vector in the direction of which OW would move together
with |S,, not the one moving together with S, in the direction of OW.
We shall do the latter. The advantage of this choice will be evident
from what follows. |
We have still to remark, that if only the position of S, and S;is
determined, the position of S, ensues from it not in one, but in
two ways; for, a position of S, gives no other positions of S, and
S; as its “opposite position” for which all vectors are reversed ; that
opposite position can be obtained by an arbitrary equiangular double
rotation over an angle a; S, and S; then rotate 2 a and are again
in their former position.
But a continuous motion of S, out of a given initial position is
unequivocally determined by the given continuous movements of
S, and S; out of the corresponding initial positions. So we shall
have completely answered the question how a solid S, moves under
the action of determined forces if we can point out how S, and 5;
move under those actions; in other words if we can point out “the
cones of rotation in the solid and in space”.
APPLICATION. The Euler motion in S,.
The equations of motion for this have been given for the first
time by Franm in the ‘“Mathematische Annalen” Band 8, 1874 p. 35.
The system of coordinates OX, X, X, X, in the solid we shall
choose in such a way that the products of inertia disappear. We
shall suppose
OXF Ox,
OX,, "OX,
to be equiangular to the right.
And we choose OX, Y,Z, and OX; Yi Z in such a way that:
OX;, OR Okan 05.
ee ee
is equiangular to the right and
OX OR. Re
Cee
( 729 )
equiangular to the left, (from which ensues as a matter of fact
that also
OX, OF), (OX, oe)
Sie ae i a Ow
are equiangular to the right).
The systems OX, Y, Z and OX; Y; Z execute the motions of
S, and S; which are to be considered.
Let us farther call ,@,, ,@,,,@,,,@,,,.@,,,@, the components of
the velocities of rotation according to the system OY, X, X, X,;
and §,, Y,; P, the components of the velocities of rotation of S,
according to OX,, OY,, OZ, likewise w,,w,,w, the components
of the velocities of rotation of S; according to OX), OY), OZ. Then
we know the components of velocity of rotation to the right
OX 0X. OY,— OZ,
OX, —> OX, or according to OX.>0W
and analogues, and likewise the components of velocity of rotation
4 (,w, + ,,) according to
OX, > OX,
to the left 4(,@, — ,w,) according to OX,» OX, or according to
OY; — OZ,
OW > 0X; and analogues.
Therefore :
P, = 2; + 1, P, = 0; — 10,
9, = .©, + .o, b= == sor, =",
C= O35 Oo, wy, = ,W, — ,o,.-
The Euler equations of motion “in the solid” (giving the opposite
of the apparent motion of the surrounding space) follow more simply
than according to FrAHM out of the vector formula
fluxion of moment of motion = moment of force — rota-
tion X moment of motion ;
which is easy to understand for a three dimensional space as well
as for a four dimensional one,
(and where the sign X indicates the vector product)
For, “in the space” the fluxion of the moment of motion = moment
of force; but of this for the position in solid has already been
marked the fluxion wanted to keep the position constant in the solid,
i.e. the fluxion which corresponds to the rotation of the moment-
vector about the rotationvector and this is — rotation & moment
of motion.
Let us call the squares of inertia 2m,’ etc. P, etc. and let us put
( 730 )
P,+P,4+P,+P,=R
—P,+P,+ P,—-—P,=A,
PBS Pr 2 Sek
Pye says Sipe ay.
Then we can write the rotationvector in the form:
29,7 + ,0,j + 0,4 + h(,@,7-+ 0,7 + ,, 4)
or in the form
€(P.¢+ Pej t Ps*) + & (Wit + UI + Ys &)-
The notations 2 and « are taken from the above-named dissertation
of Dr. W. A. Wurtnorr; / is defined on page 67; €, and ¢, on page 78.
The moment of motion becomes
: nil P,) 05 0 BE ich, Fi A eee ee
+ AP, + P,) 10,4 +A, + Pd) 9.9 + Ce Py) 0.8
or in an other form
be, (Rp, + 4, w,)i+ (Rp, + A,w,)j + (Re, + Ay.) B+
4 he, (Rw, + A, 7,)i+ (Ry, + 4,9,)5 + (Ry, + 4,75) B-
If ¢ and w represent the rotation vectors in #, and R;, we can
write the rotation: .
é, p+ & wy,
and the moment
tR(e,p +e, v) + 4 &,- (Aw + 2, (A) g),
where the notation (A)p means: A, y,71-++ A, ¢,j + As &, &.
The first and strongest of these terms falls along the rotationvector ;
for a body with equal squares of inertia it is the only one; the
second, which, together with the A’s, becomes stronger as the body is
more asymmetric, we might call the “crossed moment” because its
right part is caused by the left part of the rotation and inversely.
Let us put finally the moment of force in the form ¢, "+ &, »,
where gw and py are threedimensional vectors ; then the above given
formula of the vector can be broken up into the six following
components, given successively by the coefficients of & 7, € 7, & J,
£, 9,6, kb, &, k.
Ry, + A.W, = 4, Gs — As Wa Ys + 2m,
Rp, + Ay 9: = A, 9. Vs — Aa Ps W + 20,
Ro, + A, y, = 4,9, 9: — 4. Gs + 2H,
Ry, + A, GP, = As Fs Wi — A, 9, Ws + 20,
Ry, + Ay, = A, p, gy, — AY, 9, + 2H,
Ry, + 4,9, = 4,9, ¥: — 4,9, W, + 20,
( 731 )
If we put R?—A,?=a, and RA, + A, A,=—45,, and if we
represent the vector a4, 9,7 + 4, ,j + 4; 9; *%, by (a) yg, we can write
the six equations of motion:
(a) p = V.(b)w.g + 2Ru — 2Av
(a) p= V.(b)p.w + 2Rv — 2Ap.
For absence of external forces:
(a) p=V.(K)y.g
’ (h)
(b= V.Og-y
In this form we can directly read:
1st. If in the initial position g =, then g remains equal to y,
i.e. if the initial rotation of S, is a rotation // to a principal space
of inertia, then the motion remains a rotation // to that space. The
equations of motion for that case can be reduced to a system to be
treated as the well known Euler motion in 8, when the forces are
missing.
29d, For unequal A’s “invariable rotating’? is only possible under
the following two conditions which are each in itself sufficient:
a. for g and w both directed along one and the same axis of
coordinate (X-, Y- or Z-axis of the representing spaces) i.e. for a
double rotation of 8, about a pair of principal planes of inertia;
6. for g=O or p=—O, i.e. for an equiangular double rotation
of Sy
It has been pointed out by K6rtrer (see ‘Berliner Berichte”
1891, p. 47), how a system of equations analogous with what was
given, can be integrated. (The problem treated there is the motion of
a solid in a liquid). According to the method followed by him the
six components of rotation can be expressed explicitly by hyper-
elliptic functions in the time. If however we have ¢,, Gs; Fs, Wy; Was Wy
expressed in the time, we have the “cones in the solid” for S, and
S; To deduce from these the “cones in space’ we set about as
follows. We notice that the moment of motion to the right Rg + (A) w
in S, remains invariable “in space’’ (in S; that vector changes of
course its direction, but there Ry + (A), remains invariable); calling
the two spheric coordinates (“polar distance” and ‘‘length’’) of y with
respect to Rp + (A) w during the motion of in space & and x and
remarking that each element of the “cone in space” at the moment
of contact coincides with the corresponding element of the “cone in
the solid”, we can express #, # and x in the time, with which the
fol}
“cone in space’ for S, is found. Analogously the “cone in space”
is determined for S,; with respect to Ry + (A)g.
We shall just show that as soon as two of the squares of inertia
P become equal, which means the same as two A’s becoming equal
we can do with usual elliptic functions only.
For instance let. A, = A,) thus also \as— a, = b,? for instance, thus for four real roots uw, << u, << u, << U,,
that course becomes:
a | =
Oh, eh EVD tps Sw (2b 2b:
u— U, -- 37, where sn = sn rf i ate 8 ( 3 1 )
ply— gl, 87 a,? a,
and pig Ug — Ups
Farthermore :
oe. b, 20; oP; > gw, Cos F
eg aL Oe a ea a
a%s ats 2fs
where the second member is a rational function of ¢, (w, can be
rationally expressed in ¢, according to (I), ,¢,’ according to (II),
2fs 2W; cos F according to (IV)), so that -, too can be expressed in ¢
by elliptic functions and by that the entire ‘cone in the solid” ;.and
further according to the above method also “the cone in space’.
The following special cases can very easily be traced to the end.
1st. The four squares of inertia are equal two by two. This case
is obtained by putting A, = A, — 0.
Then
aé.= hh — A,* b= KA,
24 Tt? tb 0!
And the equations of motion pass into:
a, 9, —0 a,y,—9
03.P5—0 5,0, —0
b, b,
> — tp _——
} a%3 ; : 43
from which we directly read, ¢,, ,g;, w, and ,y, remaining constant,
that the “cone in the solid’ for S, and for S; is a cone of revolution
with the X axis as axis of revolution. Farthermore the moment
( 734 )
Rg+A,y, to the right lying in
the meridian plane of g remains in
S, invariable. Thus ‘“‘in space” that
meridian plane rotates about the
vector Ry+ A,w,, by which the
“cone in space’ is known, and
likewise proves to be a cone of
revolution. Analogous for S;. Fig. 9
shows the two cones of rotation
in S, The outer cone is the
moving one.
2d, Three of the squares of inertia are equal and unequal to the
fourth. We take the axis of the unequal one as X, axis in S,. Then
Abe Als A= A; 6. > 62S Sa, = 6, = eee
equations (/) pass into
E vee
g—— V Ww. @
a
: b
w——Vg.yp
a
therefore g and yw are both perpendicular to y and to y, whilst pt+w=0,
so y+ w is constant and ¢ and yw are each for itself constant in absolute
value, so that they both rotate about their sum (‘in space’ that
vector of the sum has in general quite a different position for S,
than for S,) by which the two “cones in the solid” are determined.
“Invariable rotating’ of S, we have here wherever » and y,
y regardless of their value, coincide. To find
aT aaa the ‘cone in space” for |S,, we notice the
invariability in S, of Ry + Ay. ‘In space”
p rotates about Rp + Aw, for the angle
‘’ between those two vectors remains constant.
In S, rotates analogously “in space’’ w about
7 Rw + Ay. Fig. 10 represents the two cones
Fig. 10. of rotations in S,. (Here too the outer cone
is the moving one).
We remind the readers once more, that where we bring g and y,
as far as their positions in the solid are concerned, into relationship
with each other, we must of course in our mind make the positions
to the right and the left that is of the systems of coordinates OX,
Y, Z, and OX, Y, Z, to coincide with each other, so that but one
system of coordinates OX YZ is left (for instance for the equations
sa. Ss es Te ae 2 i
( 735 )
(h) this must be noticed); but in space (i. e. the S, 1 OW)
those systems of coordinates OX, Y, Z. and OX; Y; Z have at
each moment very definite positions differing from one another.
Chemistry. — Prof. C. A. Lospry pr Broyn read also in the name
of Mr. L. K. Wourr a paper entitled: “Can the presence of
the molecules in solutions be proved by application of the
optical method of Tyxpau.?”
(This paper will not be published in these Proceedings).
Chemistry. — Prof. C. A. Lopry pg Bruyn presents also in the
name of Prof. A. F. HoLLeEMAN a paper by Dr. J. J. BLANKsMa,
entitled: “On the substitution of the core of Benzene.”
(This paper will not be published in the Proceedings).
(April 19, 1904).
KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,
PROCEEDINGS OF THE MEETING
of Saturday April 23, 1904.
——_—— =00ce—-
(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 23 April 1904, Dl. XII).
C©) Se a EN ES:
Eve. Dvsors: “Facts leading to trace out the motion and _ the origin of the underground
water in our sea-provinees.” (Communicated by Prof. H. W. Baxuvuis KhoozEBoom), p. 738.
L. H. Sierrsema: “Investigation of a source of errors in measurements of magnetic rotations
of the plane of polarisation in absorbing solutions.” (Communicated by Prof. H. Kameruincu
ONNES), p. 760.
Frep. Scuvu: “An equation of reality for real and imaginary plane curves with higher
singularities.’ (Communicated by Prof. D. J. Korrewrec and P. H. Scnoure), p. 764,
C. A. Losry pE Bruyn and C. H. Sivrrer: “The BeckMAny-rearrangement: transformation
of acetophenoxime into acetanilide and its velocity”, p. 773.
C. L. Jenerus: “The mutual transformation of the two stereoisomeric pentacetates of d-glucose.”
(Communicated by Prof. C. A. Lorry pr Bruyn), p. 779.
Pp. H. Scuoure: “Regular projections of regular polytopes”, p. 783.
L. E. J. Brouwer: “On symmetric transformation of S, in connection with S, and §)”.
(Communicated by Prof. D. J. Korrewee). p. 785.
Pu. Konxstamm: “On the equations of Ciavstus and van DER Waats for the mean length
of path and the number of collisions.” (Communicated by Prof. J. D. van per Waats), p. 787.
Pr. Konxstamm: “On van DER WAAaLs’ equation of state.” (Communicated by Prof. J. D.
VAN DER WAALS), p. 794.
J. Revpter: Note on Sypnrey Youna’s law of distillation.” (Communicated by Prof. J. D.
VAN DER WAALS), p. 807.
H. A. Lorentz: “Electromagnetic phenomena in a system moving with any velocity smaller
than that of light’, p. S09.
E. Janyxe: “Observation on the paper communicated on Febr. 27 1904 by Mr. Brouwer:
“On a decomposition of the continuous motion about a point O of S, into two continuous
motions about O of §3’s.” (Communicated by Prof. D. J. Korrewxe), p. 831.
L. E. J. Brouwer: “Algebraic deduction of the decomposability of the continuous motion
about a fixed point of S, into those of two S,’s.” (Communicated by Prof. D. J. Korrewes),
p- 832.
A. A. W. Husrecut: “On the relationship of various invertebrate-phyla”, p. 839.
Max. Weser: “On some of the results of the Siboga-expedition”, p. 846.
L. Bork: “The dispersion of the blondine and brunette type in our country”, p. 846,
R. P. vay Carcar and C. A. Losry bE Bruyn: “Changes of concentration in and crystallisation
from solutions by centrifugal power”, p. 846.
C. L. Juncivus: “Theoretical consideration concerning boundary reactions, which decline in
two or more successive phases.” (Communicated by Prof. C. A. Lopry pe Bruyn p. 846.
The following papers were read:
49
Proceedings Royal Acad. Amsterdam. Vol. VI.
( 738 )
Geology. — “Facts leading to trace out the motion and the origin of
the underground water in our sea-provinces”. By Prof. Eve.
Dvnors. (Communicated by Prof. H. W. Bakauis RoozEsoom).
(Communicated in the meeting of June 27th, 1903).
As to the origin and the condition of the underground water in
our low-lands, we are, as vet, almost entirely in the dark; facts,
that might throw light on the subject, are almost entirely lacking.
The hazardous suppositions made on the subject by some, and
the extraordinary caution, which others thought necessary in practice,
prove this. Only lately Darapsky, in a dictatorially written article,
held forth that even now rivers of former geological periods
follow theit very same channels, but now as underground streams.
The underground water he considered as almost exclusively river-
water ').
Others have admitted powerful artesian currents from the eastern
high-land, without any decided facts supporting that opinion. Again
others fancied to have found the explanation in VoueeEr’s hypothesis,
on the condensation of vapour in the ground; a hypothesis, refuted
already a long time ago by no less an authority than Hann *). A single
phenomenon observed in one of the East-Frisian Islands, already
years ago observed in our own country, and explained, but now
forgotten, led some to imagine possibilities, as to the sea threatening
us also from below, a thing which filled them with anxiety. Not to
mention altogether absurd and physically impossible suppositions.
However it appeared to me that an earnest searching for facts,
could not but bring to light something that would give us a elue,
further to find our way in this important question, important both in a
scientific and a practical respect. Indeed, thanks to the kindness
I met from different sides, I was enabled, during these latter months,
to make a large number of observations and to collect facts which
show forth, in outline, the direction, the origin and the general
condition of the underground water in the main part of our
low-lands.
Since it will take some time fully to work out the results obtained,
the present circumstances make it desirable I think, already now, in
this short communication, to make known the most important of
!) L. Danapsky, Die Trinkwasserfrage in Amsterdam. Journal fiir Gasbeleuchtung
und Wasserversorgung. 46 Jahrgang, p. 468, sqq. (1903).
*) J. Hany, Zeitschrift fiir Meteorologie, 1886, p. 482—486,
( 739 .)
them. My researches were principally limited to the southern part
of the North-Holland low-lands, including the dunes, and the adjacent
parts of the provinces of Utrecht and of South-Holland. It is a
matter of course that also here | had to limit myself to the chief
points of the question.
In the last decennia, hundreds of borings have been done in the
polders, in the dunes and in the area between them by the corps
of military engineers and by others, with the object of making
fortifications or of obtaining fresh water. Down to a certain depth,
the constitution of the soil is consequently pretty well known, and some
deeper borings have tolerably well acquainted us also with the
constitution of the soil at greater depth. Sand is the chief substance,
alternating with beds of always very impure clay. Close to the
surface, pretty generally, a zone is found of clayey substances, (the
well-known ‘old sea-clay” of Svrarine), over considerable areas,
covered with a layer of peat, which clay, in the dunes, where that
peat is generally lacking, is covered with blown sand. Under the
finer sand of the upper-soil, often mixed with clay, in which occur,
in large areas, deeper layers of peat, there is a zone of coarse-grained,
often gravelly sand, not unfrequently containing pebbles. In the
west of the mentioned region, the top of that zone lies about 30 M.
+~AP. deep, or a few metres higher; in the east, near Aalsmeer,
Sloten, Amstelveen, Mijdrecht, Wilnis, Oudhuizen, it rises to 16 or
14 M.- A.P.; near Muiden and Nigtevecht as high as 10 or 8 M.
-~ A.P. and its reaches the surface further east. Under Amsterdam and
both south-east and north-east of it, the soil, on the whole, is much
richer in clay.
Also at greater depths, clay-beds occur, but never as unbroken
layers, extending over great distances; the most regular zone is
after all that of the so-called old sea-clay, near the surface. It is
besides of importance, that near our eastern frontiers much older
formations come to the surface, than have been found, some hundreds
of metres deep, under the lowlying lands in the west. This in itself
is a reason not to expect artesian water, from Germany, in our
western sea-provinces, to some hundreds of metres below the surface,
at least.
Of great significance for the problem is also the fact that more or
less pure clay rarely occurs. What is considered as such, on further
examination, (washing of a number of samples of different origin,
and especially chemical analysis, which analysis Dr. N. Scnoor.
was kind enough to do at my request) proved to consist for only
one third of clay at the most, generally for much less, even for only
49%
( 740 )
one seventeenth. The investigations by Prof. Sprixe?) have proved
the fact that, and the reason why, even very thick layers of im-
pure clay, e.g. the limon supérieur de la Hesbaye, let through water.
What then must we think of our clay, which, though technicians
will call it impermeable or “rich clay’’, likewise, for the greater part,
consists of sand !
The chemical analysis of specimens of the fattest clay-sorts selected
from their outward look, (a large number of such specimens being
at my disposal from a variety of borings) showed the real clay
percentage to consist of less than @ third: at Sloten (boring IV. 2,
at +M.—A.P.) and at Uitgeest (Station, at 43 M.— A.P.). Of about
a fourth: at Hoofddorp, Haarlemmermeer (at 6 M. and also at
34 M.—A.P.); at Amsterdam (Dairy at the Prinsengracht, at 9
M. -A.P.) and in the dunes, 3 K.M. west of Santpoort (at 40 M. ~A.P ).
Of about « jifth: at Amsterdam, (Dairy in the Second Spaarndammer
Dwarsstraat, at 3.5 M. — A.P.); at Harlem (Hagestraat, at 14 M. —A.P.);
at Hillegom (Treslong, at 14 M.~+ A.P.); at Beverwijk (Middle of
Breestraat, at 19 M.—A.P.); at Alkmaar (Station, at 22 M. ~ A.P);
in the northern part of the Watergraafsmeer polder (near the Ooster-
railroad, at 35 M.—+ A.P.); at Katwijk (875 M. South-West of the
water-tower of the Leyden waterworks, at 1.6 M. > A.P.). Of about
a siath: at Sloten (boring III. 1, at 5.50 M.-—> A.P.) and at Eertden-
koning, in the west of the Haarlemmermeer polder (at 19.5 M. —A.P.).
Of about a seventh: at Velsen (near Rosenstein, at 2.50 M. — A.P.); at
Katwijk (in the same borings, at 3.8 M.—~ A.P.). An eighth to a ninth:
at Beverwijk in the same borings at 5 M.—A.P.); at Amsterdam
(Prinsengracht, at 6 M.—+ A.P.) and in the Koningsduin near Castri-
cum (at 32 M.+A.P.). Of less than @ tenth: at Driehuis (Nunnery,
at 18 M.—A.P.). Of about a jifteenth: at Amsterdam (Second
Spaarndammer Dwarsstraat, at 62 M-> A.P.); at Hillegom (Treslong,
at 4M. A.P.). Of about a seventeenth: in the Watergraafsmeer polder
(at 8 M.+ A.P.). No clay at all, at Amsterdam (Second Spaarndam-
mer Dwarsstraat, at 48 M.->A.P.). The last specimen, looking like
fine-sandy clay, proved to consist of sandy caleareous tufa with
td Wg AeaoG,.
As to peat, experiments have shown to me that its impermeableness
1) W. Sprine, Quelques expériences sur la perméabilité de l’argile. Annales de
la Société géologique de Belgique. Tome 28, p. 117—127 (1901), and : Recherches
expérimentales sur la filtration et la pénétration de l'eau dans le sable et le limon.
Ibid, Tome 29, p. 17—48, 1892). Compare also the report of H. Rasozéer on those
investigations in: Bulletin de la Société belge de Géologie, de Paléontologie et
d'Hydrologie. Tome 16, p. 269—295, (1902),
( 741)
is equal to that of sandy clay, but that in another respect, it is
very different from clay, i.e. in its water-containing capacity. Whereas
clay, like sand, can contain water for scarcely more than a third
of the volume of the dry substance, non-cgmpressed peat can do so
many times over. Peat of the Rieker polder, near Sloten, on the
territory of the military water-works, was found to have a capacity
of holding water, nine times the volume of the dry peat; and the
water in it can, although slowly, yet freely move.
On the whole we have to deal with an upper-soil of finer, often
clayey sand water, and on which or in which, in most places,
enormous water-reservoirs occur: the peat beds, for even the com-
pressed peat contains still a large quantity of water. In the colder
(rainy) seasons the upper peat layers are not only always kept filled
with fresh water, but they can, though slowly, provide lower regions
from their water-store ; and along with the water, no doubt with carbonic
acid, which deep below will dissolve iron and chalk ; and methane
which, in the same way as carbonic acid, the more easily dissolves,
the higher the pressure is. Deep down the latter product of decaying
organic matter, cannot be formed, on account of the absence of
bacteria.
Those upper-layers, little permeable, more or less shut off the
zone of gravelly coarse-grained sand which at the bottom, in a
similar way but much more imperfectly, in its turn is shut off by the
irregular beds of impure clay and fine-grained sand, occurring there.
Under those conditions the vertica/ motion of the water, must on
the whole be difficult; at one place more and at the other less,
according to clay or sand locally prevailing and in proportion to
the latter being finer- or coarser-grained, whereas in the coarse-
grained medium zone or zones, horizontal motion is comparatively
easy ; that medium zone is therefore the great channel, and in
extracting underground water this “‘water-vein’” is generally found
at about 80 M.— A.P. or a little deeper still.
That indeed below that depth the underground water has an easy
horizontal passage, appears from the fact, that the height to which
the water ascends in tube-wells, driven below the upper-edge of the
coarse-grained bed, falls but little; whereas higher up in the fine-
grained sand, it nearly always is considerably higher, (i.e. excepting
the deep polders, where the deep water will naturally rise above
the surface of the soil).
As to fixing the direction in which the deep underground water
moves, a thing that will enable us to inquire after the existence of those
currents, supposed by some, and also the origin of the underground
( 742 )
water, the means to do so, although hardly ever applied, are evident.
Just as on the surface, it is the law of gravitation that also deep
below, gives to the water its horizontal course. The direction of that
motion, as caused by gravitation, can be demonstrated from the
inclination of the pression-line of the water, deep below, for that
motion can happen only from spots under greater, to those of smaller
pression. The vertical motion, under any given constitution of the
soil, can, as a rule, be inferred from the positive or negative character
of the pression below, with respect to the level of the water on
the surface.
When the water from the underground, freely rismg in a tube-
well, remains below the level of that in the upper soil, that vertical
motion can take place only in a downward direction — if at
any rate, then and there, a motion in a vertical direction on the
whole is possible, which is mostly the case. When, on the other
hand, the level of the water, in the tube-well rises higher than that
of the surface-water, as is the case in the deep polders, vertical
motion in a somewhat permeable soil, can take place only in an
upward direction. The quantity of chlorides in the water, determined
as chlorine, furnishes us with an other indication of the direction
of that vertical motion.
So the observation of the height to which the water ascends in
the tube-wells and the mutual comparison of the same, can teach
us much as to the direction in which the water moves. A great number
of those observations have enabled me to ascertain, that also deep
below, the motion of the underground water (uninfluenced though it
remains by small irregularities), depends on the shape of the surface.
In short, the direction is from the dunes to the lower regions ;
from the higher to the deeper polders, and any great unevenness of
the surface, makes its influence felt, already at a considerable distance.
In the dunes the deep underground water is under the highest
pressure ; in the deepest polders it ascends in the tube-wells to a
level some metres lower, although there it wells up above the
ground. Near a low-lying polder the water falls also in very deep
wells. So not only near the surface, but also deep below, there is
a motion from the dunes to those polders and also from the higher
to the lower polders.
Before communicating the observations, on which those results are
founded, 1 must specially state, that there are influences, which for a
time may more or less change the pression of the water in the
underground, as it appears from the rise or fall in the wells. In the
first place must be mentioned: rains, which make their influence felt
A hema
{ 743: )
almost immediately, which influence is far more powerful, than any
other. After the heavy rains in the fourth week of April 1908,
a number of deep wells on being sounded (Aprii 27%") showed a
higher level of 0.18 to 0.20 M. A week later it had sunk about
0.06 M., and only after the dry latter half of May, towards the
end of that month, it was again what it had been towards the end
of April, before the heavy rains. The rising of ihe deep well-water,
immediately after much rain, may be in part the result of the
greater ‘pressure of the upper-soil. In the same way, a train passing
over the railway-dike in the Watergraafsmeer polder, for a moment
raised the water 7 m.m. in a deep well, at a distance of 18 M.,
which well was 34.5 M. beneath the surface of the polder. Principally
ihe rain will increase the hydrostatic pression. In the second place,
changes in the pression of the atmosphere have a passing influence
on the level of the water in deep wells. Those changes make them-
selves felt at once, but that natural barometer is an imperfect one;
the effect of the changes in the atmospheric pression soon disappears.
For some hours however millimeters rising or falling of the quick-
silver have their equivalent in centimeters on the watergauge.
In the third place the low and the high tide of the sea, exercise
i negative or a positive pression on the deep underground water, i. e.
on those spots, which are not too far from the sea (3 or 4 K.M.
seems to be the utmost limit here). I have always taken those
circumstances in te account. For the rest, as far as necessary, the dates
of the observations are stated here. With a few exceptions, I myself
ascertained the ievel of the water (with respect to N.A.P., the new
water-mark of Amsterdam, as a standard) or it was done under my
control; some other results I hold from reliable sources.
In the dunes now, the pression of the deep underground water ascends
to about 38 M. above A.P. So on Maréh 30% 1903, in a well of the
Harlem waterworks sunk down to 53 M.A. P., situated in the
midst of the dunes, at 3 Kk. M. west of Sandpoort, and a little further
from the polderland, the level of the water was observed to be at
2.91 M. +-A.P.; in another well in the dunes, deep 45.5 M. = A. P.,
almost 2 K.M. further south, and at a distance of 2?/, K. M. from
the polderland, the water ascended to 2.19 M.-+- A. P. In a third
well, close to the water-tower near Overveen and 1 Kk. M. from the
low-lying lands, as deep as 54 M. ~ A. P., it rose only to 1.20 + A.P.
Those three wells are at a distance of 2'/, to 3 K.M. from the sea,
In another well, near to the Brouwerskolkje, sunk down to 70 M.~ A.P.,
(in 1890), at */, K.M. from the one near Overveen and less than '/, K.M,
from the low-lying land, the water had been seen to ascend to
( 744 )
0.30 M.-+ A.P. The boring-hole, although still in the dunes, being
comparatively low, the water rose here above the ground. The fact
that those four wells are situated in the dunes, together with their
comparative distances from the lower regions, distinctly make their
influence felt here.
Nearer to the inland dunes, the level of the water is every-
where lower than in the middle. On the 11% of April 19038, in
the Koningsduin near Castricum, the level of the water in two
wells, sunk down to 32 M.= A.P., was°1.195 and 1:23 M.+ AP.
They were at a distance of about */, K.M. from each other and
they were */, K.M. from the low-lying land; the distance from
the sea being 2°/, kK.M. On the same day the level of the water
was 0.29 M.-- A-P., in a well, deep 33 M.— A.P., near Sant-
poort, at the inland of the dunes and 2200 M. from the Zuid-
Spaarndam polder (the level of the superficial water or the Summer
Level here being 2.60 M.->A.P.), whereas it reached no higher
level than 0.055 M.-+ A.P. at Rosenstein, separated from the dunes
by the plain of Driehuis, and only 13800 M. from the Noord-Spaarn-
dam polder, (of the same depth as the polder of Zuid-Spaarndam).
Just as in the Brouwerskolkje near Overveen, the water rises
above the boring-hole also near Bergen, on the grounds of the
Alkmaar waterworks, in wells, only about 20 M. — A. P. deep,
for the reason of the dunes having purposely been lowered. Here
however, in the midst of high dunes and at */, kK. M. from rather
shallow polders (summer-level + 1.33M.), it rose to a level of 1.385 M.
+ A.P., on March dst 1903.
Ina well, deep 40 M.> A.P., on the grounds of the paper-manufactory
of the firm van GELDER & Sons, at Velsen, which well is situated at
1300 M. from the Noord- en Zuidwijkermeer poiders (having 2.40 M.
— A. P. Summer-Level) the water on April 14% 1903, had a level
of 0.26 M.+ A.P. without, for 53 hours, there having been any
pumping, neither there nor at any of the other wells. Under meteor-
ological conditions which admit of comparison, a well, deep 44 M.
— A.P., near the small steam-mill, in the Meerweiden, on the North-
Sea Canal, had a level of 0.485 M. — A.P., it being situated
only 3870 M. from those polders and between two shallower ones
(— 0.50 and + 1.40 M. Summer-Level). In the Zuidwijkermeer-
fort, situated in the polder of the same name, a well, 45 M.—> A.P.
deep, had on March 8 1902 a level of about 0.80 M. — A.P.
Here we distinctly see the lowering of the level of the water in
deep wells, from the dunes to the polders, which shows a horizontal
motion in that direction.
The same appeared, still more distinctly, south of Harlem, through the
influence, which the extensive Haarlemmermeer polder, with its outlying
polders, eastward, has on it; the summer level of those polders,
which together cover 42000 H. A., being about 5 M. or more under A.P.
At Aerdenhout a well, 82 M. > A.P. deep, showed a level of
0.52 M. + A.P. on May 5 1903. We may admit that at the time
the level of the other wells was being ascertained, it must have
been here about 0.40 M. + A.P. This well is 3600 M. from the
Haarlemmermeer poider and only 350 M. from the Veenpolder
(Summer-Level ~- 0.75 M.). A well at Heemstede, on Kennemeroord,
deep only 26.8 M.—> A.P.; but sunk down into the gravelly sand,
had on June 2°¢ 1903 a level of 0.575 M.—A.P. That well,
although in the inner-dunes, lies only 2200 M. from the Haarlem-
meer polder. Another well, some 100 M. north of the Common-Hall
at Heemstede, at about 13800 M. from that polder and. still in the
inner dunes, had on May 29%, a level of 0.78 M.-> A.P. In a third
one, nearly 30 M.-> A.P. deep, situated within the precincts of the
community of Heemstede, but at only 440 M. from the Haarlemmer
polder, on Bosbeek, at the border of the inner dunes, and under
meteorologic conditions admittting of comparison, the level of the water
was 1.29 M.— A.P. A well on the Leyden Canal, deep 32 M. — A.P.,
near the remise of the Harlem Electric Tram, on April 9% 1908,
had a level of 0.225 M. > A.P. This well, within the Veenpolder
(Suminer-Level ~ 0.75 M.), lies one side at 3700 M. from the encircling
canal of the Haarlemmermeer polder, but also at only 1400 M. from
the Noordschalkwijk polder, (Summer-Level~} 1.25 M.) and the other
side about 1 K.M. from the dunes. A well near the Harlem Gas
Works, in the Veenpolder (+ 1.40 M. Summer-Level), 1700 M. from
the encircling canal of the H.M.P., had, on March 51st 1903, a level
of about 1.00 M.— A.P., and in a well on the grounds, reserved
for the Harlem Abattoir, the level on April 4! was 1.08 M.—> A.P.
This well lies in the Roomolen polder (Summer-Level ~ 1.25 M.), at
1300 M. from the encircling canal of the H. M. P.
On the other hand in a well at Hillegom (behind the building of
the Hillegom Bankvereeniging), sunk down to 389 M. > A.P.,
1200 from the Haarlemmermeer polder, the level of the water on
April 8 1903 was only 1.20 M.~> A.P. Although equally far from
that polder as the well near the Common-Hall at Heemstede, the
distance that separates this well at Hillegom from the central range
of dunes, being 2900 M.; that at Heemstede only 1650 M. The
upper-soil moreover at Hillegom is much richer in clay than that
at Heemstede, the deep underground water consequently on the first
( 746 )
mentioned spot, being much more under the influence of the pression
which makes itself felt in the H. M. polder.
At only 1125 M. north-east of the well at Hillegom, but BOO M.
within the Haarlemmermeerpolder, at “‘Eert-den-Koning”, a well
has been sunk down to 26.3 M. + A.P., in which on April 21%,
(before the heavy rains of the last weeks of that month), the level
of the water was 2.57 M. + A.P. The cause of such a difference
is some 1500 M. greater proximity of the centre of the Haarlem-
mermeer polder. In the midst of that polder, at Adolfshoeve, on
the east Hoofdweg, 890 M. southwest of the Vijfhuizer Dwarsweg,
I saw the water ascend only to 4.70 M.+A.P. in a well, deep
34 M.—A.P., sunk down below a bank of clay. slightly less deep.
Probably the rains of a few days before, had raised the water a
decimeter above its dry weather level. At Hoofddorp I found on
May 8 1903 a level of 5.038 M.—-A.P., in a well only 18.5 M.>
A.P. deep. Although less deep than the other wells, also this was
sunk into the less fine sand, and near the top of the coarse-grained
sand, beneath the less permeable upper-soil of fine sand and clay.
If the well had been sunk below the clay-bank and 34 M.-> A.P.
deep, the water no doubt would have risen a little higher. So the
result is, that in the midst of the Haarlemmermeer polder, the under-
ground water, from under the deeper lying clay, can ascend half a
metre above Summer Level (this being 5.20 M.— A.P.), on the other
hand, from under the clayey top-layer. it can rise but little above
it. The pression it acquired in the dunes and in the surrounding,
shallower polders, on its way to the H.M. polder, is in the middle
of it, at 18.5 M.— A.P., almost entirely lost; and at 34 M. — A-P.
reduced to about half a metre. so it can rise but little above
the surface underground water, whereas at ~Eert-den-Koning’, the
ascending capacity of the water rising from 26 M. — A.P. is 2.63 M.
above Summer Level, or about 1.50 M. above the grass-land of
the polder. The upper-soil, we must bear in mind is half permeable,
and on its way to the middle of the polder, the water gradually
loses more or less its ascending-capacity. Consequently also, the water
cannot horizontally move further east, for then it would have to
move to parts, where there is more pression.
That indeed the difference in pression between the surrounding
higher parts and this deep polder, is the cause of the motion,
appeared from observations taken on other spots round the Haarlem-
mermeer polder, and in the deep polders more east, adjacent to it,
including the large Mijdrecht-polder.
North-east of the Haarlemmermeer polder, in the Rieker-polder,
( 747 )
a great many wells have been sunk for military purposes, most of
which wells are about 50M. > A.P. deep. The levels in them were
repeatedly sounded by me, which, considering their large number,
led to important results. Specially of great significance is what those
soundings teach us, as to the direction in which the deep underground
water moves. Subjomed table, in which, as much as possible, only
wells of corresponding depths have been put down, entirely confirms
what I found elsewhere.
Those soundings were done on June 5 1903. The distances of
the wells to the H.M.polder itself, one will get by adding 80 M. to
the figure that expresses the distance between them and the encircling
canal. |
Distance in M., to Level of the water
Number Depth, the encircling canal in the well,
of the well. in-M.— A.P. from the H. M. P. m Mo — A.P:
ie, 8 56.5 25 3.00
reals 47.0 50 2.99
20 49.8 ae 2.985
| 45.6 100 2.995
| NO a 47.2 367 2.94
10 ad 525 2:91
21 51:5 750 2.835
23 52.3 795 2.83
25 52.9 840 2.82
35 55.0 1090 2.81
36 54.0 1120 2.80
od 50.6 1145 2.80
40 52.8 1225 2.78
Here clearly comes out a motion of the deep underground waiter,
from the higher polders, north of the Haarlemmermeer polder,
towards this deep polder. On 1200 M. of distance there is an
inclination of 0.22 M., or 1,8: 10000, whereas in other directions,
there is no regular inclination. That indeed no general motion from
east to west or vice versa is to be thought of, naturally follows
from the comparison between the level of the water in wells thus
situated. For instance from the following row of wells, all at 25 M.
trom the encircling canal of the H. M. polder.
( 748 )
Number Depth Distance in M. Level,
of well. in M.—A.P. from well II. 5. m Ma Ale
if a 56.3 0 3.025
6 39.0 50 2.98
7 40.1 100 2.98
8 56.5 150 3.00
10 46.5 250 2.99
12 30.0 318 3.005
14 44.0 380 3.025
nis 38.0 595 3.01
At the same time the fact stands forth that, once a level reached
under the fine-grained and clayey upper-strata, further differences in
depths are of little consequence.
Comparison of the other soundings will show forth the same for
either statement.
The average level of last mentioned 8 soundings, in wells at
25 M. distance from the encircling canal, is ~ 3.00 M., so equal
to that in well Il 8 which we used as starting-point in the first table.
Though there is no great current in the one or the other direction,
vertical on the one towards the H. M. polder, (so from east or west,)
there seems to exist a slight local motion from the Nieuwe Meer
(level about — 0.60 M.) to the west (Summer Level of Rieker polder
~ 1.80 M.), as may be seen from the comparison between wells,
situated at increasing distances from that small lake, but pretty well
at an equal distance from the H. M. polder.
Number Depth, Distance in M., Level,
of well. in M.— A.P. from the N. Meer. in Mi. SAE
Ls 48.5 60 2.935
2 48.7 90 2.9939
3 50.5 110 2.925
4 51.0 135 2.932
7 52.8 220 2.955
8 5 ies 235 2.95
i) 50.0 235 2.955
LO 49.5 235 2.96
12 41.3 300 2.98
Il 14 44.0 690 3.025
——— ar ie ile
( 749 )
The real existence of the above indicated motion, from the
shallow polders, north of the H. M. polder, towards the latter, is
confirmed by observing the level in a well, sunk down to 32.5 M.
—A.P. under the direction of Dr. ALEXANDER KLEIN, near the
“Huis de Vraag’’, between the Rieker polder and the Sloter binnen-
and Middelveldsche combined Polders (Summer Level — 2.15 M.),
not far behind the Vondel Park. On June 16% 1903, I found the
level to be 2.46 M. + A.P. The well lies 5100 M. from the H. M.
polder, or about 1800 M. further than well [Hk 40, in the Rieker
polder. So also here there is an inclination of about 1.8 : 10000.
Also towards the polders which le eastward, adjacent to the
H. M. poider, and hydrologically one with it, the motion of the
water, deep down, is from the higher to the lower ones. This was
shown by soundings, done on June 24% 1903, in wells, all sunk
down to about 30 M. — A.P. and belonging to fortifications south-
east of Amsterdam. There appeared to be an impelling force in that
deep water towards the Groot-Mijdrecht polder (where they keep the
water to a Summer Level of — 6.60 M.).
The following small table, concerning observed levels on August
26" 1903, shows this :
Distance to the Level,
Groot-Mijdrecht Polder in M. > A.P.
Fort near Nigtevecht 7 KM. 1.775
Mil. Post near Oostzijdschen Watermill 5.5 _,, 2.01
Fort near Abcoude aa a
a De Winkel Dakss, 2.29
3. 3 ~betshol i ee 4.43
The fact that the inclination of the pression-line is specially great
here, near the deep polder, and also from Nigtevecht to the Oost-
zijdschen Watermill, must, I think, be attributed to the greater height
to which the gravel-diluvium rises in this part, a thing to which
attention has been called, already at the beginning of this paper.
The influence of surface-water can therefore make itself felt comp-
aratively strongly, when locally rapid changes occur; at Botshol,
on account of the neighbourhood of the deeper polder, and at
Nigtevecht on account of the rising of the upper-part of the deposit
of coarse grained sand, which at a comparative small distance, east
of Nigtevecht, at certain spots, even reaches the surface. The reason
being that the artesian regularity of pression, to which the deep
( 750 )
underground water is submitted, is broken by those local irregularities
of the geological structure.
That we have not to think of strong currents of the deep under-
eround water, in a general direction for all, but of currents, dependent
on the local form of the surface, may finally be confirmed by
soundings in two wells, sunk also under the direction of Dr. KLEIN,
in the Watergraafsmeer polder (Summer Level ~ 5.50 M.). One of those
wells, in the north of that polder, near the Ooster-railway, at 250
M. north-west of the so called Poort, deep about 39.5 M. = A.P.,
had on June 18 1903 a level of 3.215 M.—A.P. In another,
presumingly 385 M.-> A.P. deep, in the south of that polder, near
the Omval, the level was 3.125 M.— A.P., on June 23¢ 1903. The
latter lies 5 K.M. almost straight east, from that near the “Huis de
Vraag,” which in its turn hes 2.8 K.M. east, but a little towards
the north, from well III. 40, in the Rieker polder.
Another well, about 25 M.-—- A.P. deep lies, in the south-west
corner of the Bijlmermeer polder (Summer Level > 4.80), at 4 K.M.
north-west of the well near the Oostzijdsehen Water-mill, 4.8 K.M.
south-east of that near the Omval and 11 K.M. from the Bullen-
wijker and Holendrechter polder (Summer Level +3.35 M.). This
well had, under the same meteorological conditions, a level of 3.075
M.~+ A.P. At the well-known boring done by the corps of military
engineers, at Diemerbrug, near the Weesp turnpike, beyond the
northern extremity of the bBijlmermeer polder, the level of the water
in the well, then 73 M.— A.P. deep, was 2.51 + A.P. on Oct. 18%
[888. That well was 2 k.M. from the eastern border of the Water-
graafsmeer polder.
Consequently the result of the different observations is, that there
is not a general, so called ‘‘artesian’ current from east to west
or vice versa, in the region between Amsterdam and the H. M.
polder, neither south-east of Amsterdam; those found, are but special
currents originating in local differences of height of the surface and
directed towards the Haarlemmermeer- and adjacent other deep polders
and towards the Watergraafsmeer-, the Bijlmermeer- and the Holen-
drechter polders.
Another result is the conclusion we may draw, as to the direction
of the vertical motion of the underground water, by comparing the
different levels of the water in the deep wells with that of the
varying levels of the underground water rising from smaller depths
and with the highest level this reaches. In short in the shallow
polders, in the dunes and in the area between them, the direetion
appears to be downward; in the deep polders, on the other hand,
(751)
such as the Haarlemmermeer polder and the adjacent deep ones,
upward. It is a wellknown fact that the water in deep wells rises
above the surface of the underground water and above the grass-
land of the deep polders. In polders of smaller depth, the deep
wellwater remains below the surface. Likewise the ascending
power of the water, as a rule, gradually diminishes towards the
middle of the deep poiders. In higher parts, such as in the dunes
and in the flat sandy adjacent area, the surface of the wunder-
ground water is considerably higher than the level of the water
in the deep wells. So here we find increase of pression from
below upward, and descending movement of the water. In the
dunes near Castricum the level of the surface of the underground
water is about 1.30 M. higher than that reached in the deep
wells; at Santpoort, at the inland side of the dunes, the difference
even being 1.80 M.
In connection with the above indicated conditions, especially in
the colder seasons, when the underground water is generally fed
with the water penetrating the soil from the rainfall, the dunes,
the shallow polders and the intermediate area will get a fresh
supply of water, whereas there is always a loss by the pumping in
the deep polders, to which, certainly in no less degree than to the
sea, there is a constant affluence. The underground water not being
of distant origin, it can as a matter of course be derived only from
rains on the spot itself, or at a small distance.
Just a passing remark in connection with the results arrived at,
to call the attention to the drying out of the dunes and especially
of the lower stretches of land west of the H. M. polder. This drying
out, i.e. considerable lowering of the surface-level of the underground
water, actually noticed for already halfia century, has repeatedly been
attributed to the waterworks in the dunes for the water-provision
of Amsterdam; to my opinion however it is in the first place
due to the draming of the Haarlemmermeer, just half a century
ago, from which event dates the powerful subterranean current
from the dunes to the deep extensive Haarlemmermeer — polder.
Especially in the lower tracts from Ziuidschalkwiyk to Bennebroek,
up to a few kilometers from that polder, the drying out process
has made itself felt, on account of clay above the coarse-grained
sand being almost entirely lacking. In those parts the water in the
ditches, when there is no fresh artificial in-flow, will soon sink down,
actually making its way under the encircling canal of the H. M.
polder, as is proved by the considerably lower level in part of
that region’). Ever since, a few years ago, the level of the H. M.
polder was lowered 0.30 M., the level of the water in a pond, 4 M.
higher, at Meer-en-Berg, and 400 M. outside the polder, was observed
to be lowered as much. From this we can imagine how powerful
the influence of a lower level of 5 M. must have been at the
time when the Lake of Harlem was being drained dry.
As to the motion of the deep underground water, at the side of
the dunes, facing the sea, I have been able to make only a few
observations. The great uniformity with which the dunes border on
the sea however, in connection with the other results of my investiga-
tion, permit drawing pretty safe conclusions from them, as to the
general condition.
A well known fact is that the superficial water flows from the
dunes towards the sea, just as it does inland from the dunes to
ihe adjacent flat area and the polders. A remarkable proof of the
water flowing from the dunes to the sea, is the welling up, at
ebb-tide, of fresh water on the beach, north of Noordwijk-aan-
Zee. Puddles and furrows form themselves, from which, as long
as if is ebb, not unlike rills, fed from sources, large quantities
of water, only partly consisting of salt-water, flow. towards the sea.
Particles of clay brought up with the water and found in the ripple-
marks on the beach, suggest the presence of a clay-bed, close to
the surface, through interruptions of which the welling up of the
water takes place. On March 27% 1903, at 11 a.m., it being low-
tide, about 9 hours after high-tide, (the wind 8.S.E.), I scooped
opposite strand-pole N°. 78, from such a rill, about 200 M. long,
(the debit of which might be calculated to be in the least 7 M*® an
hour), a sample of water, which proved to contain 11550 mG. of
chlorine the Liter. So for '/, it was fresh- and for ?/, sea-water,
and hourly more than 2.3 M* fresh water found its way into the
sea, through that litthe ebb-rill. The great uniformity now with which
the dunes slope down to become beach permit us to accept as
a general though in most cases invisible fact what here, through
local circumstances, happens visibly.
Another proof for the considerable flowing down of fresh surface-
water towards the sea, furnished to me a stone-well at the foot of the
dunes, on the beach at Zandvoort, from which the fishing-smacks
take their water-store. The bottom of that well is 0.72 M. ~ A.P.,
1) That also from the encircling canal itself, which is about 3 M.— A.P. deep,
the water is sinking down, is proved by the fact, that near the Cruquius, the
level is always some centimeters lower than in the Spaarne and in the canals
of Harlem.
( 753 )
i. e. 0.04 M. above average low-tide mark, and’ 4.0 M. below
high-tide mark. On Febr. 18% 1903, at 4.20 p.m., it being low-tide,
the quantity of chlorme of the water in that well, was 291 m.G.
the Liter. On Mareh 6 1903, at 10.380 a.m., about three hours after
high-tide, the level of the water in that well was 0.95 M. + A.P.
or 0.76 M. above the sea, at that moment.
Also in the deeper, coarse-grained sand-layers, there is a main
current of fresh water towards the sea. In a well in the dunes,
350 M. from the sea (low-water line), on the Kerkplein at Zandvoort,
sunk down to 28.38 M.— A.P., the level of the water on the 14‘ of
April 1903 was as follows :
At 430 pm. 1445 M.-+ AP.
d gi) MAF
1.520
39
~
Os) =
So a distinct influence of the high-tide, which at IJmuiden rea che
its highest level, 1.43 M.--A.P., at 4.55 p.m.; at Zandvoort presum-
ably 8 minutes earlier, is evident.
The next day, in the same well — the deeper one of the two —
the level of the water was found to be:
At 12 o'clock 1.28 M.+A.P.
3, 42:85 pm. 1.24
penta ee Th 22
we ‘Gout thew
esteem Bangs ys, Lee
1.193
: 1.205
ree age mee 1 20
Comparing the above figures with those of the self-registering
tide-gauge at IJmuiden, it appeared that the influence of the tide
makes itself felt 40 minutes later in that well, situated 350 M. from
the sea. The sudden way in which the gradual rising of the water
stopped at 3.5 p.m. was found to correspond with the somewhat earlier,
change in the level of the sea, the difference in time corresponding.
At IWJmuiden, 1.30 p.an., the low-tide level was observed to be
0.76 M.= A.P.. So the water in the well was 1.95 M. higher. At
high-tide however, it was at that time, but about 0.10 M. above the
level of the sea. So the amplitude of the tide influence in the well,
50
Proceediags Royal Acad. Amsterdam. Vol. VI.
( 752 )
was then about 0.34 M. But the tide rose then unusually high
(0.55 M. above the average high-tide mark) the low-tide mark being
then just the average one. I think I may estimate the average vertical
amplitude in the well to be, at the most, 0.30 M., and believe pretty
near to hit it, when accepting 1.30 M.-+ A.P. as the average level
in that well, or 1.50 M. above the average sea-level.
When considering the motion of the deep ground-water, in the
direction of the sea, caused by the hydraulic pression in the dunes, we
must not overlook the much greater specific weight of sea-water. A
column of sea- water 30 M. deep, (with a specific weight of 1.0244, on the
average, as that of the North-sea-water), will be kept in balance by a
column of fresh water, about 0.75 M. higher. No doubt however the
depth of the fresh water, in the coarse-grained sand below it, is much
greater than 30 M.— A.P., without any considerable decrease in the
ascending power. A direct proof of this is the small percentage of
chlorine of the water in the deep well in the Kerkplem, amounting
only to 45 m.G. p. Liter, and that in the well on the beach,
30 M. deep, about 250 M. more south, was 52 m.G. the Liter. In
statistic equilibrium, 1.50 M. above the average-level of the fresh under-
ground water would correspond with a depth of 61.5 M. But on
account of the motion of the fresh water we have here to deal with
a condition of dynamic equilibrium; the pressure at great depths
consequently is not ‘simply settled by the height, to which the
water ascends higher up, in the ground, However below 30 M. (in
the coarse-grained sand) there will be little difference, so we cannot
but accept, that an extra-pression of 1.50 M. of the sweet ground-
water, apparent from the level the water reached in the tube, will
correspond with a depth of about 60 M. > A.P.; taking in con-
sideration the decrease of pression downward, we may safely state
the depth to be 50 a 60 M..— A.P. One thing is sure, the water
which rises from about 30 M. > A.P., has still ascending power
above the level of the sea. This may be distinctly observed in the
well, sunk on the beach, although being 300 M. nearer to the
low-tide line, a considerable decrease can be noticed. At that small
distance, the deep underground water in the dunes has already, for
the greater part, lost its ascending power and we may accept that
not far out into the sea, if is entirely gone. That strong pression-fall
must be principally attributed to tide-fluctuation, which every time
renews a fourth of the water in the sand, as far as that fluctuation
makes itself felt; apparently (the well in the Kerkplein shows it) at
a rather considerable distance, from the sea. But also the fact that
the beach slopes down at Zandvoort the depth of the sea, 400 M,
( 755
)
from the low-tide line, being 2.5 M.; 1200 M. beyond that line,
5 M. below A.P. and that the fine-grained sand intermixed with
clay of the original upperlayers for a great part will have been
replaced by coarser sea-sand, must considerably have contributed
towards greatly increasing the pression-fall of the deep underground
water, at the sea-side. At high-tide the flowing off however is very
small, and all things considered, the flowing off of the water from
the dunes, at the polderland side, certainly will not be less considerable
than that towards the sea.
But let us drop this subject, too few facts being at our disposal
to judge of that complicated process, and watch the influence of the sea-
water at a greater distance from the coast. There can exist no doubt
as to the underground of our low-lands being soaked with sea-water. In
none of the borings executed in the last scores of years, if only deep
enough earried through, the proof of it was lacking; more or less deep,
according to circumstances, but the underground water showing an ever
increasing quantity of salt, highly exceeding that ofall polders ditches
or canals, exceeding even that of the Zuiderzee. In or near the dunes,
one must go much deeper to find sea-water, than in the polders;
and in the polders, on higher ground, as a rule, deeper than in those
lower situated. In the Brouwerskolkje, at a depth of 72 M. > A.P.,
the percentage of chlorine did not exceed that of surface dune-water,
neither was this the case in wells of the Harlem water-works, deep
54 M. — A.P.; nor in the one, in the dunes at Elswout, 80 M. ~ A.P.
deep; nor in the Rieker polder at more than 50 M.—+A.P. Near
the Huis-de-Vraag, in the north-east corner of the Rieker polder,
down to 32.5 M.— A.P. only 34 m.G. chlorine a Liter was found;
at 46.5 M.—A.P. not more than 81 m.G.; and near “Het Kalfje’,
on the Amstel, south of Amsterdam, at 351 M.-—> A.P., only 47 m.G.
a Liter. At Purmerend, situated in shallow polders, with Summer
Levels of 1.25 to 1.60 M.—A.P., but surrounded by the deep
Purmer- (Summer-Level —- 4.47 M.), the Beemster- (S.L. + 4.00 M.)
and the Wijdewormer polder (S.L.-> 4.50 M.), the water rising from
50 M. — A.P., has a quantity of only 45 m.G. of chlorine a Liter. The
well-water at Schermerhorn, in shallow polders, between the deep
Beemster- and Schermer polders, at 76 M.— A.P. deep, contains 170
m.G. chlorine a Liter. Although the underground water in those
deep polders, on the whole is brackish, the quantity of chlorine
was only 192 m.G. a L. in the Purmer polder, at about 1 K.M.
from the encircling dike, in the direction of Purmerend on the Wester-
weg, and 600 M. north the church. Similar fresh deep underground
a0*
( 756 )
water is also found in the south-east corner of the Beemster polder,
opposite Purmerend.
On the whole west of the Haarlemmermeer polder, in wells not
greatly exceeding 30 M. in depth, the underground water is equally
fresh as dune-water, also at Heemstede and at Hillegom and in some
of the shallow polders near Haarlem. At great depth, there is in
those parts a considerable increase in the quantity of chlorme. Near
ihe railwaystation of Vogelenzang, between the Leidsche vaart and the
rail-road, at 1600 M. from the Haarlemmermeer polder, at a depth of
88M. A.P., it amounted to 184.6 m.G. a Liter, it being only 35.5 m.G.
a Liter at 25 M.~> A.P. Near the villa Bennebroek, 650 M. from the
Haarlemmermeer polder, 47 M.~> A.P. deep, it contained 99.4 m.G.,
and at a depth of 89 M., 245 m.G. chlorine a Liter; on Bosbeek,
in the parish of Heemstede, being only 440 M. from that polder, at
about 380 M.+A.P., 58 m.G. a L. Numerous instances may be
brought forward of the quantity of salt in the underground water
growing with its greater depth, and at a higher level, as one draws
nearer to the deep polders. A well-known fact is, that in consequence
of the flowing down of the underground water from off the dunes,
the water of the neighbouring low-lands, up to quite a few kilo-
meters’ distance, may be fresh. More considerable and noticeable at
greater distance however, is that down-flow deep in the ground.
Close to the steam-nill for the draining of the land, in the Meer-
weiden near Velsen, at: full '/, K.M. from the dunes, the under-
ground water, 28 M. below A.P., contained 30.5 m.G. chlorine and
at 44 M. below A.P., 65.4 m.G.; and even 1 K.M. more east,
within the precincts of the fort, in the western corner of the Zuid-
wijkermeer polder (S.L.-—- 2.40 M.), at 34 M. > A.P., only 60 m.G.; at
45 M.—+ A.P., on the other hand, 603 m.G. chlorine a Liter. In
the midst of the dunes themselves the ground-water seems to get
brackish only at about 150 M. below A.P.
Of special significance is the fact, already stated above, that the
underground water in the deep polders is growing salter at a much
higher level. So at Eert-den-Koning, only 300 M. within the Haarlem-
mermeer polder, at 26 M.> A.P., the underground water had 367m.G.
chlorine a Liter. Similar conditions are generally prevailing there. That,
generally speaking, the higher percentage of salt cannot be attributed to
water from the canals (‘““‘boezemwater’’), so cannot have got in from the
surface, may in the first place, be proved from the fact, that the
water in shallow polders, in many places, down to considerable
depths is as perfectly sweet as that in the dunes, although one can
prove that there is no communication with the dunes; in the second
( 757 )
place, that within those polders, just as outside them, but already
at a higher level, the water deeper down will be found to have a
higher salt standard. At Hoofddorp the quantity of chlorine, at
18.5 M.—A.P., was 202 m.G. a Liter; at 28 M.— A.P., 260 mG.
and at 38 M. > A.P., 993 m.G. With such a rapid increase as in
the last 10 M., unmixed sea-water may be expected, at little greater
depth.
No doubt can be entertained as to underground sea-water and
fresh water in our sea-provinces balancing each other in a way, as
indicated by Bapoy Guysex and HerzperG'), very much however
modified, in general and in special cases, by the general geological
structure with its local modifications. There is no ground for fear
of the sea-water coming up from below, in part of the dunes, in
which the underground water has been lowered down to the sea-
level; the very fact that there are polders, which already for
centuries lie below it, and still have fresh water, down to great
depths, and that even of the deepest polders the upper-soil, several
scores of metres deep, is much more soaked with fresh than with
salt water, refutes that fear.
Remarkable however is that at Hoofddorp, although situated in
the midst of the Haarlemmermeer polder, the deep underground water is
less salt than at Eert-den-Koning, near the edge of the polder, and
less still so than some kilometres north-west of Hoofddorp, e.g. on
the farm Mentz, where a deep well, presumably equally deep, has
water containing 6535 m.G. chlorine a Liter, i.e. 24 times the
quantity of that at Hoofddorp. Differences in the condition of the
sub-soil are evidently the cause of those differences in the salt quantity.
In the shallow polders, on account of the direction downward of
the vertical motion, also the water from the canals (“‘boezemwater’’)
may be the cause of rendering the deep underground water salt,
when locally the structure of the soil does not prevent it.
Bearing in mind, for the motion of the underground water, the
significance of the different heights of the polders, and not forgetting
the irregularities in the extent, the thickness and the comparative
pureness of the clayey beds, also irregularities in the vertical distri-
bution of the water and in the composition of it may be explained.
1) W. Bapon Guypen in: Tydschrift van het Kon. Instituut van Ingenieurs L889,
p. 21; Herzeernc in: Journal fiir Gasbeleuchtung und Wasseryersorgung. 1901,
p. 815 s.q.q. I count myself happy to have pointed out in lectures, conversations
and letters this forgotten merit of one of our engineering-officers, in consequence
of which remembrance Mr. GC. E. P. Rissis and Mr. R. p’AnpRimontr have, in
their publications given due uonours to our compatriot.
Intermixing with water, richer in salt, both from above and from
below, may consequently be hindered or furthered by it, also the
oozing in of fresh water; the different mixtures, as an other conse-
quence, being able to move horizontally in the one or the other
direction, or be prevented to move at all, which explains the different
levels they reach.
The hypothetic currents can be dispensed with to explain the
existence of fresh water, between 385 and 50 M. — A.P., in the old
boring at Sloten, so often urged in proot of powerful subterranean
water-currents of distant origin. Of the above mentioned wells in
the Rieker polder, those, most west, are only 800 M. east of the
boring of 1887. The different levels observed in the wells at Sloten
can in reality be due only to local motion, in the direction of the
shallower polders (with their higher upper-pression) to the deeper
polders, where the pression from above is less powertul. The fresh
water, everywhere found there at great depths, down to 50 M. > A.P.,
can find its origin only in those shallow polders themselves. The very
position of the old boring at Sloten, at a corner of the shallow
Rieker polder, between two deep polders (the H. M. polder and the
Middelveldschen Akerpolder (S. L. — 4.20 M.)), explains the irregu-
larities of composition observed there in the vertical distribution of
water, and thus it is, with the boring near Diemerbrug, outside the
north corner of the deep bijJmermeer polder (S.L.—> 4.20 M.). At about
250 M. + A.P. water of a somewhat lower standard of salt (mini-
mum 1192 m.G. a Liter) was found; no fresh water, as DaARapsky
lately held forth. Considering what influences are at work in the
distribution of the water in our soil, one can but see natural
phenomena in all those deviations.
Considering the geological condition of the place itself and of its
surroundings, the occurrence at Wijk-aan-Zee, both of fresh water down
to 31 M. ~ A.P. (47.8 m.G. chlorine) and of its getting brackish, already
at 50 M. > A.P. (851 m.G. chlorine) may be easily explained; also
the presence of a layer of fresh water, between the sea-water, in
the sub-soil of [Jmuiden.
In this discourse on some general features of the movement of
the underground water in our lowlands the question ‘remains to be
settled, how it is that some shallow polders, of which the canals
and the ditches like those of other, deeper polders, are mostly filled
with brackish water, can furnish fresh underground water.
In the first place the answer will be that, by no means, all
surface waters of the polders are brackish. Even in the H. M. polder,
I found, also at dry seasons, in some places fresh surface water
755 )
containing only 78, 60, 35.5 mG. of chlorine a Liter. Holes made
in the midst of deep-polder meadows often fill with fresh water,
even when a long period of absolute dry weather precedes the
digging of them; so in the Purmer-polder, near the above mentioned
deep well, on May 13 1903, the water in such a hole, dug about
1.80 M. deep, contained only 72.6 m.G. chlorine a Liter, the
adjacent ditch water having 407 m.G. Near Hoofddorp, in the
H. M. polder, in the midst of the Slaperdijk, 250 M. southwest of
the Hoofdvaart, after weeks of dry weather, in a hole, the Corps
of military engineers had dug, down to 0.40 M. below polder-level,
water oozed in, which contained not more than 102 m.G. chlorine
a Liter, still that dike (the summit of which is about = A.P.)
over all its length stretches between two canals 10 a 15 M. wide,
only 40 M. apart and always filled with brackish water, 1 or 41.5 M.
deep. The water of those canals at that moment contained 5141 m.G.
of chlorine a Liter. The level of the water that had gathered in
the hole, was O.11 M. Iigher than that in the canals and at that
time they were even considerably higher than they had been the
last month. But those are deep polders, in which the vertical motion
of the underground water is from below upward. What to think
now of the water that penetrates the soil of the shallow polders ?
The extent of the land, in the polders, generally exceeding that -of
the water at least 25 times, and the level of the underground water
in rainy seasons, being considerably higher than the neighbouring
ditch water, consequently the fresh water will filter down, in a far
greater proportion than the brackish, the surface of which forming
but an insignificant portion of that of the fresh water fallen in the
meadows. The water of the canals (‘‘boezemwater’’) consequently can
but little add, in those rainy seasons, to the salt-standard of the
underground water. In the dry season, on the other hand, the land
drying out, water must be let in; the soil is then absorbing brackish
water from the canals. In fact, however, even such shallow polders,
as the Rieker polder and those of Purmerend, which possess fresh
underground water below the recent more or less impermeable strata,
have brackish underground water near the surface, all the year round,
Nevertheless, to my opinion, a great number of phenomena point to
the supposition of the deep fresh underground water, found in some
of our shallow polders, which have brackish underground water
near the surface, being due to rainfall on the spot itself, or at a
comparative short distance. This question will be the subject of a
further communication.
Considering the facts communicated here, in connection with others,
€ 760 )
concerning the quantities of water which from the rainfall penetrates
the soil, it need not be further demonstrated that in the sub-soil under
the dunes, under the adjacent flat elevated area and under some
shallow polders, drinkable water is and will not be lacking, in the
main land of the provinces North- and South-Holland, superficially
judging so little favoured in this respect, and with two fifths of the
population of our country. That the velocity with whieh the deep
underground water can move through the coarse-grained sand, is quite
sufficient to make it possible to procure it from the sand in large
quantities, a great number of facts prove it. I will mention but one,
that of the paper-manufactory at Velsen, of which the six wells,
encompassing an area of 0.85 H.A., every 24 hours, on the average,
furnish at least 2200 M* of fresh water or nearly as much as the
town of Harlem wants and about a tenth of what Amsterdam
consumed during these latter years. And those wells furnish water,
which shows no. signs as yet of a too slow horizontal motion ere
long being likely, by disturbing the natural equilibrium of the under-
eround fresh and salt-water, to convert the pumped fresh into salt-
water. On the contrary the water of the oldest well, full six years
in use, has grown a little sweeter still.
Physics.
of magnetic rotations of the plane of polarisation in absorbing
solutions.’ By Dr. L. H. Siertsema. (Communication N°. 91
from the Physieal Laboratory of Leiden by Prof. H. Kammriinen
ONNES.)
“Tnvestigation of a source of errors in measurements
(Communicated in the meeting of January 30, 1904),
In a great number of measurements of the magnetic rotation of
the plane of polarisation it was found, that this rotation assumes very
large values in the neighbourhood of an absorption-band. Similar large
values were found by me in an investigation on the negative mag-
netic rotation of potassium ferricyanide ') in dilute solutions. These
results agree with the new optical theories which yield for the
magnetic rotation the dispersion formula: ’)
e Aa dn
; : dn
since the quantity Pa also assumes a large value near a band.
Oh
tl) Arch. Néerl. (2) 5 p. 447; These Proc. 1901/02 p. 339; Comm. Phys. Lab.
Leiden N°, 62, 76,
*) These Proc, 1902/03 p. 413; Comm. Phys. Lab, N° 82.
( 761 )
Much attention should therefore be paid to the fact that Bares *)
has made measurements with solutions of cyanine, fuchsine, litmus
and aniline blue, from which it would follow that these large
rotations did not exist, whereas ScHuMAuss*) with these very sub-
stances has found very large rotations. According to Bares these
large differences are caused by a source of error which arises from
the circumstance that for these measurements we make use of light
of which the intensity varies with the wave length"). He shows
that both with the half-shadow method, and with that where we
adjust on a dark or a bright band in the spectrum, great errors may
be made as soon as we arrive at a region where the intensity-curve
of the light used shows a considerable decrease, and that this may
produce apparently large rotations.
As this source of errors might also occur in my measurements
with potassium ferricyanide, it seemed important to me to investigate
in how far this may have had a disturbing influence, and thus in
how far the large rotations then found would have to be ascribed
to it.
With the method involving the use of a dark band in the spectrum,
the source of above errors comes to this, that as soon as the intensity
of the light on the two sides of the band is not the same, we are
inclined to wrongly adjust the middle of the band, and to displace
it too much towards the dark side. For we may suppose that for
an adjustment we, as a rule, search for two points on the borders
of the band which are of equal intensity and then adjust between
them. It must be noted that attention has been repeatedly drawn to
this source of error *) although, as far as I know, an experimental
investigation of the errors which may so arise was first made by
Batrs*). A theoretical solution would be possible in the manner
indicated by Bares, but this requires a knowledge of the intensity-
curve of the spectrum which is seen by the observer in the absence
of the magnetic rotation. Moreover we ought to know which of
the intensities on the edges is used by the observer to determine
the middle of the band, and this especially will partly depend on
the observer. An experimental determination may easily be made.
We need only produce a spectrum with a movable dark band and
1) Bares. Ann. d. Phys. (4) 12 p. 1091.
2) Scumavss, Ann. d. Phys. (4) 2 p. 280; 8 p. 842; 10 p. 853.
3) Bares. Ann. de Phys. (4) 12 p. 1080,
4) Gernez. Ann. éc. norm. | p. 12 (1864).
Van Scuatk. Thesis for the doctorate. Utrecht 1882 p. 30,
*) Bates |. c. p. 1086,
( 762 )
examine it while the light passes or does not pass through an
absorbent substance. The apparent displacement of the band near
the limit of abserption must then immediately appear.
For my measurements with potassium ferricyanide I have made
use of rotations of 11° and higher. A quartz plate 0.4 m.m. thick,
cut at right angles to the optical axis was now used and with it a
similar rotation is obtained near the limit of absorption. This plate
preceded and followed by a nicol was placed between the collimator
and the experimental tubes, which moreover were mounted in precisely
the same way as they were for measurements of the rotation in
potassium ferricyanide. A large number of adjustments have been
made by rotating one of the nicols, one set where the experimental
tube was filled with a ‘/,°/, solution of potassium ferricyanide, and
one with water instead of the salt-solution. The calibration of the
spectrum was made as before with a mercury arc lamp. The following
values have thus been obtained, as means of pairs of adjustments:
band with
nicol water solution
din py
83°O" 629° 650
82°30’ 611 612
82°0’ 593° 5935
81°30’ 577 O77
81°O’ 5625 565
80-30’ 549 549°
SO°O’ 538 538
12-30’ 525 526°
79°O’ 515° 516
78°50’ 5125
18°45’ 510°
78°40’ 509
78°35’ 508°
78°30’ 505 905°
78°25’ 504
78°20’ 502°
78°15’ dOL
78°10’ S00
78°5’ 498
78°O" 495°
77°30" 486°
7450! v7
(limit of absorption, about 481)
The annexed figure represents
graphically a part of these read-
ings for both sets. The irregular
differences, may apparently be
ascribed to errors of observation,
which near the limit of absorp-
tion will be somewhat larger
than at other places, owing to
the smaller intensity of the light.
They do not amount to much
more than dau. A deviation
of the kind whieh we might
expect from the source of errors
supposed by Barrs, would reveal
itself, near the limit of absorp-
tion, in a displacement of the
band towards this limit. Such
+ series, with, water a displacement is not at all
o J . solution ; : "
‘ indicated by these observations.
= Umit ontahenoption Let us consider what apparent
'
displacement must have taken
place, to account for the anomalous rotations which are found in
the measurements. This may be found by supposing for a moment
that the rotation of the sait is normal, and by putting it equal to
that of water. If for instance we start from the value g,,=7.1 for
2, = 606") and we call 2, the wave-length, where the band ought
to have appeared with the solution, if it appeared with water at
4, = 519, then we find by a simple calculation 4, = 509, while we
have observed 2, = 500. According to what has been said before a
displacement of the band of 9 wu cannot be apparent. Hence the
validity of the results obtained before is not affected by the error
supposed by Barns.
1) Comm. N°, 76 p. 4; Proc. Royal Acad, 1901/02 p. 340,
( 764 )
Mathematics. — ‘An equation of reality for real and Lnypinary
plane curves with lugher singularities”. By Myr. Frep. Scuvn.
(Communicated by Prof. D. J. KortEwne.)
(Communicated in the meeting of March 19, 1904).
For a plane algebraic curve having an equation with real coeffi-
cients only and possessing no higher singularities than the four of
Prickrr, Kir ') has deduced (as an extension of relations of reality
found by ZevTHEN in a C) the equation
nt Pe 2s" bag og" 2A 2) eee
where
n is the order, / the class of the curve,
3 the number of real inflexions,
# the number of real cusps,
vr’ the number of real isolated bitangents and
dé" the number of real isolated double points.
This equation of Kiem can be extended to curves with higher
smgularites and it then becomes most remarkably simpler and
merariably holds good also for curves in whose equation imaginary
coefficients appear, Which is not the ease with the equation of KLEIN.
The equation found by me runs as follows :
fil ES ocak 1 eshte. adi VL teste eee
Here ='7, denotes the sum of the orders of the singularities with
real point, X'v, the sum of the classes of the singularities with rea/
tangent. By an element of the curve I understand in the following a
pomt of the curve together with the tangent belonging to it, exclu-
sively as forming a part of one branch of the curve, which can
be represented by one single Puisrvx-development (with exponents
fractional or not). The element I call a singularity: 1st if point or
tangent or both are singular, or 2°¢ if point or tangent or both
belong to several elements of the curve, or 3'¢ if the point is real
and the tangent imaginary or reyersely,
If through the same point more branches pass, we call the point
a manifold singular point; this is to be regarded so many times as
a singularity as there are branches passing through it. Correlative
to this is a manifold singular tangent.
}) F. Kets, Eme neue Relation zwischen den Singularitiiten emer algebraischen
Curve. Math. Ann., Bd. 10 (1876), p. 199.
a
( 765 )
With Priicker') we understand by the order ¢ of a single sin-
gularity the number of the points of intersection coinciding in the
(singular) point with an arbitrary line of intersection through that
point. If eventually more branches pass through the singular point,
we must of course count those points of intersection only, which by
a slight displacement of the intersecting line are found on_ the
branch belonging to the singularity in question. Correlative to the
order is the class v of the singularity. This class is at the same
time equal to the number of points of intersection approaching the
(singular) point along the branch in question with an intersecting
line passing through that poimt and about to coincide with the (sin-
gular) tangent.
If we regard this last quality as the definition of the class of
a singularity, then the development in point coordinates with the
(singular) point as origin and the (singular) tangent as axis of «
itv
becomes y= au ; + ...., after having given all exponents an
equal denominator though as small as possible (for a small value
of « gives ¢ small roots y, on the contrary a small value of y
gives ¢-+-v small roots ~). If farthermore Y and Y are the line
coordinates of the straight line 7 + Y.«—+ Y = 0, then the development
the correlativeness of ¢ and +. At the same time it is evident from
this that order and class of a singularity can be read immediately
from the corresponding development, from those in point coordinates
as well as from those in line coordinates.
In (2) X't, denotes a summation with respect to the singularities
with real point, Xv, to the singularities with real tangent, where
a manifold singularity must be taken into consideration as many times
as it possesses single singularities. Here not only the higher and
PitckeEr-singularities must be counted, but also those elements of
the curve, the counting of which has an influence on the equation
(2); thus also those elements (¢= v= 1) of which the point is real
and the tangent imaginary or reversely. It is clearly indifferent
1) J. Pricer. Theorie der algebraischen Curven. Bonn, A. Marcus, 1839, p. 205.
2) O. Srouz. Ueber die singuliren Punkte der algebraischen Functionen und
Curven. Math. Ann., Bd. 8 (1875), p. 415 (spec. p. 441—442),
H. G. Zeutuen. Note sur les singularités des courbes planes. Math. Ann. Bd.
10, p. 210 (spec. p. 211—212).
H. J. SrepHen Swirg. On the Higher Singularities of Plane Curves. Proc. London
Math, Soc,, Vol. 6 (1874—75), p. 103 (spec. p. 163—164),
( 766 )
whether we do or do not include entirely real or entirely imaginary
non-singular elements among the +’-signs.
The equation (2) holds good for curves with inagmary equation
as well as for curves with veal equation.
Now follow the chief poimts of the deduction of the equation
discussed. This will be given more minutely in my dissertation ’)
still to appear.
To this end we shall treat in $1, 2 and 3 the relation (2) for
curves with real equation, taking that of KLEIN as our starting
point. In § 4 we shall indicate it for curves with imaginary equation
too, and in § 5 we shall transform it to other forms.
§ 1. Curves with real equation and with no other manifold
singularities than double points and bitangents.
For the present we shall take a one-sided point of view where a
curve is regarded as a locus of points.
If the curve has higher unifold singularities we dissolve them.
This means that we bring about such a small vea/ modification in
the equation in point coordinates with preservation of the order,
that the higher singularities disappear without PLOcKER-point-singu-
larities (cusps and double pomts) taking their place (but of course
inflexions and bitangents). After this dissolution, where we assumed
the Précker-singularities already present to be remaming, we apply
the equation of KLEIN.
To this end we must consider how many isolated bitangents and
how many real inflexions appear in the dissolution of a higher
singularity. In two ways isolated bitangents can be formed, namely
Ist in the dissolution of a real singularity, i. e. a singularity
whose corresponding singular branch is real, 24 in the dissolution
of two conjugate imaginary singularities; here point as well as
fangent must be imaginary, as otherwise we should be treating a
manifold singularity, which we exclude from this paragraph. Of
course real inflexions can arise only from the dissolution of real
singularities.
By dissolving the singularity the class of the curve undergoes
an increase 7. Here d represents the reduction of class of the singu-
larity (called by Swira, Le., p. 155 the diserimimantal index) i.e. the
1) Over den invloed van hoogere singulariteiten op aanrakingsproblemen van
vlakke algebraische krommen. (On the influence of higher singularities on problems
of contact of plane algebraic curves.)
( 767 )
multiplicity of the singular point as point of intersection of the curve
with the first polar of an arbitrary point.
INFLUENCE OF A REAL SINGULARITY. Suppose when dissolving a
real higher singularity with a reduction of class d,, we arrive at 3,
real inflexions and 1, isolated bitangents. The class then becomes
kk +d so that ensues from the equation of Kier, if for simplicity’s
sake we think the curve to possess but ove higher singularity :
n in p oF at" = By oe 2 =k so d, ar x sal 20".
What the value is of 3, and of t’, separately, depends upon the
manner of dissolution. If however we apply the above equation to
curves formed in different manners of dissolution, we find that
B42", has always the same value, called by me the reduction of
reality of the singularity. In my dissertation I shall deduce out ofa
definite) manner of dissolution for that reduction of reality the
value d, + v,—t#,, which causes the latter equation to become
n+p 4 2r°+%,=k+x 4 26"+4,*'). . . . (3)
INFLUENCE OF TWO CONJUGATE IMAGINARY SINGULARITIES. As we exeluded
_ —
1) This equation agrees with the index of reality given by A. Bratt (Ueber
Singularitiiten ebener algebraischer Curven und eine neue Curvenspecies. Math.
Ann., Bd. 16 (1880), p. 348, spec. p. 391) based upon the decomposition of the
higher singularity in Piicxer-singularities. A. Gavitey (On the Higher Singularities
of a Plane Curve. Quart. Journ. of Math., Vol.7 (1866), p. 212, Collected Math.
papers, Vol. 5, p.520) has namely shown, although in a not entirely satisfactory
way, that the Pricker-equations as well as the equation of deficiency keep holding
good for curves with higher singularities, if we regard such a singularity as equi-
valent to %* cusps, 6* inflexions, 3* double points and +* bitangents. For «* and 6*
CAYLEY gives
x*=t —1 , Pr=v—1 Se Ws so oo
and he indicates how 3* and r* can be deduced from the Puiseux-developments
in point and line coordinates.
Later on fuller proofs for the results of Caytey have been furnished, among which
that of StepHey Sairn excels for its simplicity and rigorousness (I. ¢., p. 153— 162),
based upon the line of thoughts of Caytey. For the CayLey-numbers of equivalence
Smita introduces (l.c, p. 161) the names cuspidal index, inflexional index, nodal
index and bitangential index and among them he finds a simple relation (1. ¢., p. 166).
Britt has shown that this Caytey-equivalence does not only completely satisfy the
Pritcker-equations and the equation of deficiency, but that it is possible to deform
the curve retaining order, class and deficiency in such a way that the higher singu-
larities are decomposed into the equivalent ones of Pricker. Bruty calls this opera-
tion a deformation of the singularity (I. c. p. 361). Already Caytey (On the Cusp
of the second kind or Nodecusp. Quart. Journ. of Math., Vol. 6 (1864), p. 74,
Collected Math. papers, Vol. 5, p. 265) gives for the case of a ramphoid cusp an example
of a such like deformation although he does not emphatically draw the attention
to the fact that class and deficiency remain unaltered.
In an elegant way Britt indicates further algebraically, that for every real defor-
( 768 )
from this paragraph the manifold higher singularities, point and
tangent of conjugate imaginary singularities must both be imaginary.
If we decompose those singularities into the equivalent ones of
Picker in the manner indicated by Britt (see note), thus without
changing order and class of the curve, then of those PLickER-singu-
larities point as well as tangent are imaginary, as was also the case
with the original singularities. So no PL¢cKER-singularities are formed,
which appear in the equation of Kien, so that that equation inva-
riably holds good for a curve, possessing only higher singularities
of which point and tangent are both imaginary.
Comprising the results of this paragraph, we thus find fora curve
without manifold higher singularities the equation
n+ p+ 2c" + Dv, => k+ x'+ 2d" 4 Dt, . . «. (8)
where the summations must be extended only to the real higher singu-
larities.
§ 2. Curves with real equation and with
\ /
manifold higher singularities.
If the curve has manifold higher singularities, we can imagine
that these are driven asunder in the separate singularities in such
a way by a slight vea/ modification in the equation of the curve
retaining order and class of the curve, that its singular points and
tangents all differ, but without the nature of the separate singularities
having undergone a change. This operation which I shall explain
more minutely in my dissertation for the case of one manifold
singularity only, I eall the despersion of the manifold singularity ?).
mation of a higher singularity «*! — 6*! + 2 (3*" — c*") retains the same value,
which he calls the index of reality of that singularity. Here «*’, B*', 3*”, <*!
represent the numbers of the real cusps and inflexions and of the isolated double
points and bitangents, generated at the deformation. How large those numbers are
separately depends on the manner of deformation.
This however is not a new result, but an immediate consequence of the equation of
Kieiw if after various deformations we apply it to a curve possessing at first but
one higher singularity.
Britt (l.c. p. 391) says he intends to point out elsewhere that the index of
reality of a singularity (however, this must run: of a vea/ singularity) amounts
to x*—f*, so according to (4) to ¢— v. In connection with
n+ B+ Qe" + BY + De™ = Kh + xe! + 23" 4+ 4! 4 D5"
the equation (3) follows immediately from it. However | am not aware where
Britt gives the promised proof.
*) So here we leave the one-sided point of view of the beginning of § 1.
( 769 )
By this dispersion however new isolated double points and isolated
bitangents are formed, but the higher manifold singularities disappear,
so that the equation (5) is applicable, provided among J” and rt" the
newly generated isolated double points and bitangents are counted
These however can be formed only as points of intersection and
common tangents of two conjugate imaginary branches.
Here are three cases to be distinguished with respect to the reality
of the two pomts and tangents of the manifold singularity consisting
of two conjugate imaginary branches. The case already discussed, that
the points and the tangents are both imaginary, does not give rise
to a manifold singularity, so it does not come into consideration now.
Ponts OF CONTACT REAL, TANGENTS IMAGINARY. From both branches
being conjugate imaginary ensues that the points of contact coincide,
but that the tangents differ. If the order of each of the singularities
is ¢, then both branches intersect each other in ? coinciding points,
which after the dispersion of the singular points cause # double points
to be generated. If that dispersion takes place, as we keep assuming,
in such a way that the equation of the curve remains real, then the
singular points become conjugate imaginary, whilst the singular
tangents remain imaginary. So after the dispersion we get singula-
rities which have no influence on the equation of Kier. However
we have got another ¢ double points of which ¢(¢—1) are imaginary
and ¢ are isolated. The latter is easy to understand by causing the
¢ coinciding tangents of each of the singularities to diverge a little
before the dispersion, by which each of the two singularities changes
into a common f¢-fold point with separated but slightly differing imagi-
nary tangents. The ¢ tangents originating from the one singularity
are conjugate to those of the other. With the dispersion the ¢ pair
of conjugate imaginary tangents give ¢ isolated points, whilst the
remaining double points become imaginary.
After the dispersion of the singular points by which the number
of isolated points has become Jd” +¢ and the number of isolated
bitangents has remained invariable, we find by applying the equation (5)
me So = bE x + 2d" +2) + Se.
For this again we may write :
rarer se Sg ae Ue get Ot. Sate | I aay
if we but extend ='t, to those higher singularities of which the point
is real but the tangent imaginary.
POINTS OF CONTACT IMAGINARY, TANGENTS REAL. This case is quite
correlative to the preceding. Now the points of contact are different,
whilst the tangents coincide. Out of this common tangent is formed
ot
Proceedings Royal Acad. Amsterdam. Vol. VI.
(770 )
by the dispersion of the singular tangents v* new bitangents, of which
v are isolated. So for this case too the equation (5) holds good if
we but extend +'r, to those higher singularities of which the point
is imaginary but the tangent is real.
POINTS OF CONTACT AND TANGENTS BOTH REAL. Now point and tangent
of both imaginary singularities coincide. So the two branches touch each
other. This may be an ordinary contact or a higher one, as the
Puisrux-developments of both singularities correspond in the first terms
(which are then real); the unequal terms are conjugate imaginary.
If ¢ and v denote order and class of each of the singularities and
e a number which need not be known more closely, the numbers
D and 7’ respectively of the coinciding points of intersection and
of the coinciding common tangents of both branches amount to
D=F se, ;
(ie ee Ee “pl
This ensues from a relation which always exists for two singular
branches touching each other between the numbers D and 7, namely
T— D=(8,* + 1) (6,* + 1) — («,* + 1) («,* + 1),
where 3,* and 3,* denote the inflectional indices, z,* and z,* the
cuspidal indices of both singularities *). This relation was first deduced
by STEPHEN SwitH (l.c., p. 167). If according to (4)') we express
the indices in order and class of the singularities, we find
T — D= 0,0, =t ts
or, “as:an- our ‘case 7, == i, = 1 and 0, 2=0;=;
T—DPD = v*.—’,;
2
from which ensue the two equations (6).
If therefore we disperse both singularities in such a way that the
singular points and tangents begin to differ, this causes point and
tangent to become imaginary, whilst D new double points and 7
new bitangents appear. If among these are D" isolated double points
and 7” isolated bitangents, then
Pot es
By es
which [ shall prove more minutely in my dissertation.
sy the dispersion of the singularities the numbers of the isolated
double points and bitangents have become dé"+t-+c' resp. t’+r+e'
So the equation (5) gives .
m+ P+ 2(e"4v+e)4 By =k x4 2(e"+t+e)4+ 2 ‘3
So before that dispersion
Ree
1) See note p. 767—76s,
( aii)
nt+Pt2e"+ Do, Sk4+2 +204 Vt... . (5)
where the two summations must also be extended to the imaginary
singularities with real points and tangents.
§ 3. Proof of equation (2) for a curve with real equation.
The considerations of the two preceding paragraphs all lead up to
the equation (5) thus holding good for every curve with real equation
and with higher singularities. The summations must be extended
only to the Aigher singularities, namely %’/, to those with real points,
y’v, to those with real tangents.
The equation (5) can be considerably simplified by including also
the PLitckrr-singularities among the ’-signs.
InrLtexion. For an inflexion we have t=1, v=2. If we omit
Bp’ but extend ’t, and Y’v, to the real inflexions then in (5) due
consideration is taken of the presence of those inflexions.
Cuse. For this ¢= 2, v=1, so that for the cusps the same holds
good as tor the inflexions.
IsoLATED PpoINT. An _ isolated point is formed by two conjugate
imaginary elements, of which the points are real, thus coinciding,
the tangents imaginary, thus differing. For each of those elements
¢—v=1. If we extend the summations to the isolated points, this
has no influence on S"v, (the tangents being imaginary), whilst on
the contrary '/, increases with 2d". If now in (5) we omit the
term 20", but extend 7, to the isolated points, the equation remains
frue.
ISOLATED BITANGENT. This is formed by two elements (f= v= 1)
with real tangents and imaginary points of contact. For this holds
good the correlative of what was observed for an isolated point.
So if the summations are extended also to the PLiéckrr-singularities
the equation (5) becomes
Rl ees JF ! é
Ye ee oe he gh ncn ge ee
where, if one pleases, every other element of the curve may be
included among the +'-signs.
§ 4. Proof of equation (2) for a curve with imaginary equation.
To prove the relation (2) for a curve with imaginary equation,
we write it in the form :
J =k—n+t+ art: ad PAC =p
So we must show, that also for a curve with imaginary equation
J has the value zero. Let g+7y—O0 be the equation of that
51*
( 772 )
curve, were g and y possess but real coefficients. For that curve J
has of course the same value as for the curve p—iyw=—0O, e.g.
the value -/,.
For the curve g? + w? = 0, consisting of the two first-mentioned
curves, J has thus the value 2./,, as J consists only of terms, which
are formed additively for a degenerated curve out of the corresponding
terms of the partial curves. The equation of that curve is however
real, so that the relation (2) is applicable to it. From this ensues
a 2S, ==! 50 J =):
This proves, that / has the value zero for the curve g+7y~=0
too, and that for this the equation (2) also holds good.
For this deduction we have tacitly made the supposition that @
and w have no common divisor, as otherwise the curve g?+y?=—0
would possess a part counting double and thus an infinite number
of singularities. If g and yw have such a common divisor, that is if
the curve degenerates into a curve with real equation and into one
with an imaginary one, the relation (2) still holds good. For, as we
have seen, this is the case for the two partial curves, from which
ensues by addition the corresponding equation for the total curve.
Kuen (l.¢., p. 207) finds by applying his equation to the curve
gy? + uy? =—0, for a curve with imaginary equation, of which the p
real points and the + real tangents are not singular, the relation
t-Pr Sk pl lL
This equation can be immediately deduced from (2).
Farthermore ensues from (2):
The equation (8) of KLE for imaginary curves holds good also
if that curve possesses real singular points or real singular tangents
if only they count for as many real points or tangents as is indicated
hy the order resp. the class.
§ 5. Other forms for the equation (2).
The equation (2) can be reduced to still other forms. The PLicker-
equation 3 (4 —n) =~ — x becomes namely for a curve with higher
singularities 3 (k — n) = p—x-+ J (3,*—=,*), or according -to (4)')
3(k —n) = B—x+ D(vr,—4), where the Y-sign must-be extended
to the /igher singularities, the real ones as well as the imaginary
ones. By including the PLtcker-singularities, and if one likes also
the ordinary points of the curve, under the +-sign the equation
becomes
!) See note p. 767—76s8.
(773)
a Re Pe we et OB)
The equation of reality (2), ean thus be written in the following
form:
SS \ ~ sels » 7 Sl fe 7
= t, — &v, = 3(2 t, — = »,). Bera (os Os a ee
If farthermore 2” ¢, indicates a summation over the ¢maginary
points, "vr, over the tnaginary tangents, then Yt,=+'t, + >"t,, ete.
so that (10) becomes
ier kee Ce ee ee)
The equations (2), (9) and (10) are of course but different forms
for the same relation of reality.
Sneek, March 1904.
Chemistry. — Professor Lospry pr Bruyn presents communication
N° 7 on intramolecular rearrangements: C. A. Lospry pe BruyN
and ©. H. Sivirmr. “The BrecokMany-rearrangement ; trans for-
mation of acetophenoxime mto acetanilide and its velocity.”
(Communicated in the meeting of Febuary 27, 1904).
Among the many intramolecular rearrangements known in organic
chemistry, the one associated with the name of Brckmayn belongs
to one of the most important series on account of the extent of its
region and its scientific significance. As is well known, it consists
in the transformation of the oximes, under the influence ofa certain
number of reagents, into the isomeric acid amides, for instance :
R,CNOH — RCONHR. Its extent is obvious if we remember that all
ketones and aldehydes are capable of yielding oximes and that a
large number of these, particularly of the ketoximes, can undergo
the rearrangement. Its scientific importance is chiefly due to the fact
that its application to the stereoisomeric ketoximes has been the means
of determining the configuration of those stereoisomers, in this manner :
RCR’ RCR’
| — RCNHR’ and || — RHNCR’
NOH Q) HON 0
The rearrangement generally takes place under the influence of
different reagents such as sulphuric acid, hydrochloric acid, phos-
phorus pentachloride and -oxide, aecylehlorides, acetic acid with its
anhydride and HCl, zinechloride, alkalis. As these substances are
always applied in relatively large quantities, it is thought most pro-
bable, that the actual rearrangement nearly always relates to inter-
(wire)
mediate products, additive compounds or derivatives of the oximes,
which occasionally have been separated '). These intermediate products
then contain a negative group’ (or the group OK) attached to the
nitrogen which changes place with the C-combined alkyl- or aryl-
group. On subsequent treatment with water the amide is generated.
We then have ;
RCR’ RCR’ RCX+H,O RC=O
Le tee TL Goal eee ea ee el ee
NOH NX NR’ NHR’
That hydroxyl] itself can assume the function of the group X which
changes place with R’ is shown by the interesting observations of
WerRNER and buss’), Werner and Skipa*), Posner‘) and Auwsrs
and Czerny °), who have noticed some cases of the BECKMANN-rearran-
gement in the absence of any reagent. Dibenzhydroximic acid
CC HC0L0 Can:
i)
obtained from chlorobenzhydroximie acid
NOH
C,H, C.Cl by means of silver benzoate, melts at 95°; according to
6 oO . ©
Nou
Werner and Buss it changes after some days spontaneously into its
isomer C,H,CO.NHOCOC,H, m.p. 161°; on heating this takes
place more rapidly. Possner observed that o-cyanobenzaldoxime
changes into ifs isomer when simply heated above its melting point ;
it first melts at 175°, then solidifies and finally melts again at 203°,
Here we consequently have the direct conversion :
JANG HC SH ACH NC .C, H, COH
pases eet r eS NC. G, H, CO Nil)
NOH NH
Finally, Avuwers and Czerxy have found that 0-oxy-m-methyl-
benzophenonoxime: HO.H, CC, H, C-C, H, partly undergoes the
a
BECKMANN-rearrangement when submitted to distillation.
These observations from Werxer and his pupils, of Posner and
of Avwers and Czerxy are of fundamental importance for the under-
!) Beckmann for instance (Ber. 19. 988) obtained C,H; CCl: NCgH, from (CgH;)2 C:NOH
and PCI;. It is very probable that (CQH,); G@: NCI is formed first as an intermediate
product.
*) Ber. 27, 2198 (1894).
3) Ber, 32, 1654 (1899).
4) Ber. 30, 1693 (1897).
5) Ber. 31, 2692 (1898).
bo it3s)
standing of the mechanism of the Brckmany-rearrangement. They
prove that this important transformation is most decidedly a real
intramolecular rearrangement, which may oceur in some cases with
the oxime, but in the majority of eases with derivatives in which,
instead of the OH-group, another negative group or a halogen has
been attached to the nitrogen. In that case the change from IL into
III represents the actual rearrangement.
Avuwers and Czerxy have already pointed out that the above rearran-
gement caused by distillation deserves the closest attention. They are
of opinion that this observation leads to the view that the BrckMANN-
rearrangement is a catalytical process which is in accord with
BECKMANN’s own ideas. But is it permissible to speak of a catalytic
process when the catalyzer is wanting? And do not Auwers and
CzeRNY withdraw their own statement when they say that “es sich
vielmehr handelt um die directe Ueberfiihrung eines weniger stabilen
System in ein stabileres?”’
The BrckMANN-rearrangement has not, up to the present, been
subjected to a dynamical investigation. Such a study is not rendered
less desirable or less important by the fact that, as a rule, the
rearrangement of the intermediate product and not that of the oximes
themselves will be investigated.
The oxime which has been studied in the first place is aceto-
phenonoxime of which only one form is known and whieh quantita-
tively passes into acetanilide. Its configuration is therefore :
C.H,—C—CH, — C,H,. HN. COCH,.
|
HON
The rearrangement, which Beckmann found to take place under
the influence of concentrated sulphuric acid was studied in the first
place. Before starting it was necessary to work out an analytical
method allowing the quantitative determination of the resulting anilid
in the presence of the unchanged oxime. After several preliminary
experiments it was found that the anilide formed on adding water
was completely hydrolyzed by boiling for a few hours and that the
acetic acid could then be distilled off and titrated; the excess of
oxime did not interfere. We have in consequence determined the
velocity with which the anilide was formed. In carrying out the
experiments 2.5 grams of the oxime were dissolved in 50 or 100 ce.
of sulphuric acid, previously heated to the temperature at which the
experiment was made (60° or 65°) and at detinite periods a certain
quantity was pipetted off from the bottle (which was placed in a
thermostat) and analysed.
( 776 )
The reaction proved to be one of the first order, the velocity constant
did not change with the concentration; so it is a monomolecular
one. At 65°, for instance 4; = 0.0019 for a solution of 2.5 grams of
the oxime in 50 as well as in 100 ce. of 93.6°/, sulphuric acid (time
in minutes; transformation of */, of the oxime after 160 minutes).
The transformation velocity increases with the concentration of the
acid as shown from the following table:
Temp. 60°. Velocity- Time of 7/,
Concentration H,SO,. constant. transformation.
93.6 0.0011 275 min.
94.6 13 232
97.2 38 75
Lo 70 45
At 65°, a 86.5°/, sulphuric acid gave a constant of 0.0006 (time
of '/, transformation = 501 minutes). When using 99.2°/, acid at 60°,
practically all the oxime had been converted after 15 minutes.
The influence of the temperature is apparent from the following
figures :
at 60°, 93.6°/, HSO, £=0,0011; 946°), H,S50,,. 4==000ms
65°, $3 = 3 = 10,0089 ~ x = 0,00
The temperature-coefficient for 10° is therefore about 3.
A solution of SO, in chloroform did not appear to cause any trans-
formation of the oxime.
The results of this research therefore confirm the view that im the
3ECKMANN-transformation we are dealing with a real intramolecular
rearrangement. Even if the application of sulphuric acid should cause
the formation of an intermediate compound (which has not yet been
positively proved, but which is very probable’) ) our experiments
show that this formation (or the conversion T into II) takes place
With immeasurably great velocity. The very perceptible development
of heat which occurs on mixing the oxime with the concentrated
sulphuric acids also points to this facet.
Addendum. Of late years, Srimauirz and his coworkers (Amer.
Chem. J. 1896-19038) have been engaged in the study of the
BeckKMANN-rearrangement. In my opinion Stinenitz’s ideas cannot be
accepted in their entirety. Recently this chemist has given a summary
of his conclusions in a separate article “on the BeckMANN-rearrange-
1) If to an ethereal solution of the oxime is added a solution of sulphurie acid
in ether, a precipitate is obtained the nature of which will. be investigated,
(CCC)
ment” (Amer. Chem. J. 7, 29.49 (1903)). He then arrives at the fol-
lowing views.
The analogy of the LlorMaNN-transformation of the amides into
amines with the BrCKMANN-rearrangement (an analogy first pointed
out by Hoogrwerrr and van Dorr (Rec. 6.373, 8.173 ete.) ) and
the fact that the acid azides of Curtivus are converted with elimina-
tion of nitrogen into the same isocyanates which occur as inter-
mediate products in the Hormann-transformation, induces STimeGLirz
to attempt to explain these reactions from a same point of view.
He believes that in the three above transformations there must be
formed intermediate molecule-residues containing univalent nitrogen;
with the azides for instance CH,CO.N.N, > CH,CO.N + N,; with
the bromoamides for instance, CH,CONHBrSCH,CO.N + HBr. These
molecule-residues are then supposed to be converted straight into
the isocyanate: CH,—CO .N—=sCONCH,. In order to arrive, in the
transformation of oximes into amides, at such molecules with univalent
N-atoms, Srimeuitz assumes that first of all HCI is attached to the
oxime Owing for instance to the action of PCI,. R,C = NOH+ HCl
> R,CCI—NHOH,; this additive compound under the influence of
PCI, then loses one mol., of water and gives R,CCI—N which
molecule-residue is then supposed to be converted into RCCI=NR,
which on treatment with water yields the amide.
Now, first of all it is difficult to see where the HCl, which gets
attached to the oxime, is to come from; if is of course known. that
some oximes yield with PCl, compounds such as R,C CIN with
formation of HCl, but this is not the formation which Srinenirz had
in mind. We also fail to see how sulphuric acid, acting as dehydra-
ting reagent will, in the rearrangement, cause a mol. of water to
be first attached and then to be again eliminated; neither do we
understand how the transformation under the influence of, say, P,O,
or ZnCl, can be reconciled with the ideas of Stimenitz. Finally,
Stinciitz himself admits of his own theory that “it does not agree
so well with the more obscure relations of the theory of stereo-
isomerism of ketoximes and their influence on the rearrangement
of these isomers. It
Tr
s hoped that future work will remove this
difficulty’. (Am. Ch. J. 7, 29, 67). The difficulty is this, that Stmenitz
theory utterly ignores a fact of fundamental importance, namely the
formation of two different amides from the stereoisomeric ketoximes;
these according to StTincnitz ought to lead to the same intermediate
product from which the same amide only could be formed. And
finally the transformations of an oxime into the isomeric amide
Without any reagent whatever, gs observed by Werner and _ his
(778)
coworkers, by Possyer and by Avwers and Czerny are directly
opposed to his representations.
In his last theoretical paper, Srieciirz attributes the transformation
of some more hydroxylamino-derivates to the intermediary formation
of molecule-residues with wunivalent. nitrogen; he ineludes all these
under the name of ‘BECKMANN-arrangement”.
I think, IT have shown that this classification is not permissible.
If it were so, the HorMann-transformation might claim priority over
the “BrckMANN-arrangement’, which is of more recent date.
In order to avoid confusion I think it absolutely necessary to let
each of the said transformations retain its Own name and to treat
them as separate reactions. In the Curtics-transformation CH,CON .N,
—= CONCH, + N,, the assumption of the intermediary occurrence of
a molecule residue CH,CO.N is permissible; in the Hormany-reaction
CH,CONHBr — CONCH, + HB, such is possible but not necessary,
Br . C—OK
inay also have been formed as an intermediate product
NCH,
(Hanrzscn); finally we may admit in the BrckMANN rearrangement.
R.C.R’ ~ R.C— X — RCOH (= RCO. NHR’ .)
NX NR’ NR’
a same mechanism as in the HorMany-transformation, but according
to my Opinion, not the presence of a moleculeresidue with univalent
nitrogen.
The physico-chemical investigation of the BrokMANN-rearrangement
is being continued.
Lopry DE Breyy.
Amsterdam, February 1904. Oigan. chem. lab. of the Univ.
!) X =Cl, Br, OH or SO,H [respectively H,SO,], OCOCH,.
(7799)
Chemistry. — Prof. C. A. Lopry pe Brvyy presents communication
N°. 8 on intramolecular rearrangements: C. LL. Junaies. “The
mutual transformation of the tivo) stereoisomerie pentacetates
of d-glucose.”
(Communicated in the meeting of March 19, 1904),
1. It is well known that the esterification of alcohols by means
of acetic anhydride is accelerated in a high degree by the presence
of catalyzers and this of course also applies to the sugars. But if
is a remarkable fact that in the case of these polyhydrie alcohols
We arrive at various isomeric pentacetates according to the nature
of the eatalyzer. The investigations of FRaxcHimont *) and of HrrzrE.p *)
have shown that, when dry sodiumacetate is used as catalyzer, we
obtain a product melting at 154° (3), whilst according to Erwie and
KGnia@s *) treatment with ZnCl, yields a product melting at 112° («).
After Francuimont had proved that these two compounds were in
reality isomeric’) {the first was formerly thought to be a diglucose-
octacetate} this chemist supported the view that they may be best
represented as derived from the so-called oxide-form of glucose *).
The two pentacetates will then be stereoisomers as the oxide-form
of glucose, which contains one asymmetric carbon atom more than
the aldehyde-form, must give rise to two isomers.
As in the case of the two methylglucosides*) we arrive, on applying
ToLLENs’ glucose formula, at the following constitution of the
pentacetates :
AcO — CH — CHOAc
—0O-
The existence of two isomers is explained by the fact that the
CHOAe — CH — CHOAe — CH,OAc®)
terminal C-atom on the left appears as a new asymmetric atom.
2. It was known that the p-isomer formed by sodiumacetate is
1) A few years ago, Tayrer described a third isomeric glucosepentacetate
m.p. 86) (Bull. 18. 261 (1895). My investigation has led me to the conclusion
that this isomer does not exist but is a mixture of the other two,
*) Ber. 12. 1940.
3) Ber. 13. 265.
4) Ber. 22. 1464.
5) Recueil. 11. 106 (1892) Recueil. 12. 310.
6) These Proc. June 24 1893.
7) E. Fiscner B. 26. 2400 (1893).
8) Ac = CH; — CO.
( 780 )
converted into the other compound by boiling its solution in acetic
anhydride for a short time with a little ZnCl,.
I have made a closer study of this transformation; it is caused by
an intramolecular migration at the terminal asymmetric carbon atom.
One might feel disposed to explain the transformation in an acetic
anhydride solution by an addition and subsequent elimination of
a molecule of the solvent, sach as FiscHeER supposed to happen in
the mutual transformation of the two isomeric methylglucosides +).
This view, however, becomes untenable as the transformation can
also take place without the presence of acetic anhydride. Then
Lopry p& Broynx, by simply melting the p-isomer m.p. 134° with dry
ZuCl,, at once obtained the other compound m.p. 112°. T also succeeded
in causing the same transformation ina chloroform solution contaming
SO,. On shaking chloroform with fuming sulphuric acid, a portion
of the SO, passes into the chloroform. This solution has been found
to aeeelerate many reactions by catalytical action. A solution of
the B-pentacetate in CHCL, which contained 18.8 milligrs. of SO, per
ce. at first rotated but slightly towards the right; after a short time
its rotatory power had increased. The SO, was now removed by
means of dilute alkali and the chloroform distilled off. The residue
was recrystallised from alcohol and in this way the pure a-isomer
m.p. 112° was obtained.
3. As in the case of the two methylglucosides, the final con-
dition in the transformation between the two stereoisomers is here
also an equilibrium; the limit however is— situated close to the
form melting at 112°. A’ solution prepared by dissolving 5 grams
of B-pentacetate in 100° ce. acetic anhydride (containing 2 grams
of zinechloride) showed an initial rotation of + 1° (polariscope
Scumipr and Harxscu; JO em. tube). On keeping this solution at
35°, the rotation increased with measurable velocity and finally arrived
au + 14°.5. In the case of a quite similar solution of the a@-isomer,
having an initial rotation of -+- 16°.3) the final rotation was also
+ 14°.5. From this we calculate that in the condition of equilibrium
there exists 88°/, of the @ and 12°/, of the p-compound. The former
could in facet be isolated in a pure condition: in addition also some
erystals which melted at 95——-98° and eontained both isomers.
4. By determining at definite times the said changes in the rotation
the velocity of the mutual transformation could be measured.
It conformed with the formula for the unimolecular reversible
1) Compare my communication, these Proc, June 27, 1903,
€ 7an*)
d oP. a. Ory !
transformation ; for ; la. ——') was found a constant value whieh
a a Oe
a
was the same in the case of either isomer.
This average value representing the sum of the velocity constants
of the two contrary reactions is 0.0095 (the time expressed in hours
and using ordinary logarithms) at 35° and a concentration of 2°/, zine-
chloride. At 45° and 2°/, ZnCl,, the average constant was 0.028. The
temperature coefficient of the transformation for every 10° is, there-
fore, 3.01. Further determinations were also made with 1"/, solutions
of zincchloride at 45° and the constant was found to be 0.0135.
This seems therefore to be proportionate to the concentration of
the catalyzer.
d. Besides these two isomers, Tanrer (Bull. 1895, 18, 261) ima-
gined to have found a third glucose-pentacetate.
On treating glucose with acetic anhydride and a little zinechloride
and recrystallising the product from alcohol, he obtained from the
mother-liquor crystals with [a], = + 59° at 62°. This substance had
no sharply defined melting point situated below the melting points
of the above isomers. As he could not effect a further sepa-
ration of these crystals by recrystallisation, he took it to be a third
modification with a melting point of about 86°, but still occluding
a small quantity of the other two, which it was difficult to get rid
off. It is however obvious that this so-called third modification is
only a mixture of the other two, which is deposited from an alco-
holic solution saturated with both compounds. The following facts
are im favour of this view.
Ist. If it were a third isomer, it might be got perfectly free from
the others by recrystallisation and present a definite melting point.
Qed. Tf we make a mixture of the isomers melting at 134° and
112° so that [@|p = 60° the product will show the same melting-
traject as that of Tanrer*), namely 91—94".
34, A solution saturated with both isomers, and a saturated
solution of Tanrer’s product appear to contain the same amount of
pentacetate. | have used 50°/, alcohol as solvent. On shaking at 25°
with an excess of the two pure isomers a solution was obtained
containing 3.08—3.10°/, of pentacetate; Tanrer’s product similarly
treated gave a solution containing 3.13—3.14 °/).
1) a2» is the rotation in the condition of equilibrium, z) the initial rotation, z
the same at a stated period.
*) Mr. Tayret had the kindness to forward a specimen of his preparation to
Prof. Lopry pe Bruyn. With this sample the experiments have been made.
It is therefore not a matter of doubt that a third isomer does
not exist but that it is a mixture of the other two *).
The two stereoisomeric methylglucosides may be converted into the
corresponding pentacetates and conversely, the latter into the former *).
The «-glucoside corresponds with the pentacetate m.p. 112°, the
p-elucoside with the pentacetate m.p. 134°. It is therefore as well
to indicate the two pentacetates, respectively, with @ and ~, as has
in fact been done in the said article of BeHrenp and Roru.
6. The mutual transformation of the methylglucosides and pent-
acetates throws a new light on the phenomenon of the multirotation
of sugars. We may accept as the most probable explanation of this
phenomenon a mutual direct transformation of the two stereoisomeric
modifications which must exist according to ToLLENs’ glucose formula.
The recently published investigations of Fraykuanp ArMsTRoNG*) and
of Brnrenpd and Rorn*) have furnished strong arguments in favour
of this view.
But it must be remembered that ToLLeNns’ formula does not express
the aldehydic properties of glucose; one is therefore inclined to
assume that in a glucose solution there must occur also molecules
in the aldehyde-form, or molecules which contain 1 more H,O with
the group HC(OH),. One may then also come to the conclusion
that this hydrated aldehyde-form does not act as an intermediate
product in the transformation between the two stereoisomeric oxide
modifications *), but that we have here a complete analogy of what
takes place with the glucosides, namely that, although a direct trans-
formation takes place between the stereoisomers, there also occurs
a quantitatively imsignificant, secondary reaction involving addition
and elimination of the solvent. These reactions will then all be in
equilibrium with each other. This poimt, I will also try to’ elucidate
experimentally °).
1) This view is also held in a quite recently published article of BeEHREND
and Rorn Ann. 331, 359.
?) E. Fiscuer and E. Franxitanp Amsrronea. Ber. 34, 2885.
3) Journ, Chem. Soc. 838, 1305. 1903.
4) Ann. 331, 359.
5) Compare Marrix Lowry, Journ. Chem. Soc. 75, 212, (1899). 83, 1314. (1903).
6) Several chemists (v. Lippmann, Chemie d. Zuckerarten II, 130, 990. Ber. 29,
203, Trev, Z. f. phys. Ch. 18, 193, Soon, C.R. 182, 487), and myself (Ber. 28,
3081 (1895) ) have expressed the opinion that with the three [z|p’s of -- 106°,
+ 53° and --22°,5 known for glucose, correspond three modifications, namely
two oxide forms and one aldehyde form, After the research of Mr. Juxerus on
the methylglucosides and the pentacetates it is practically certain that the [e]p of
( 783 )
The particulars of this research will be published later on elsewhere.
Amsterdam, March 1904. Organ. Chem. Lab. of the Univ.
Mathematics. — ‘“Reyular projections of regular polytopes.” By
Prof. P. H. ScHoure.
We consider for this end the three regular polytopes u1,, Br, C;,
of the space S, with dimensions, which correspond respectively
to the tetrahedron, the hexahedron and the octahedron of our
space and setting aside the polytope 4, with its exceedingly simple
properties we treat some special cases of the following two. general
theorems relating to A, and C,, of which the proof will be given
elsewhere.
Eheore m ;I.
“Let mm represent $n or 4(n--1) according to the number of
dimensions 7 of JS, being even or odd.”
“Construe in m planes «@,,@, . . @ congruent regular polygons
with n+l [or 27] sides; let g be the circumradius of those polygons.”
“Let us take in each of those planes a vertex of the polygon as
the origin O and a definite sense, in which distance is counted from
this origin to any other vertex along the circuit.”
“Let us place at the remaining vertices the numbers 1, 2
in such a way that the number jp is put in a, near the vertex which
is distant from the vertex O in the sense assumed in «@ a number
pk jor p (2k—1)| sides. In other words: let us place in «eg, moving
round from O in the indicated sense the numbers 1, 2 in such a
way that when continuing to a following number we skip 4—1
[or 2(4—1)| vertices. Here the polygon in «em can be reduced as far
. _ ntl at Bie
as the numbering goes to a regular polygon with or — | sides,
| . 1 Y
each vertex of which bears g numbers, as soon as / and w+1
53° belongs to a condition of equilibrium between the two oxide forms. The
question put to me by Messrs. Benrenp and Rors in their recent paper (Ann.
331, 309) has therefore now been answered. My former contention that glucose
with [@|o+ 106° might crystallise from a solution in which it was not present
(namely, from glucose with a [z|p+ 53°) is, of course, no longer tenable. It is,
as Bb. and KR observe, a question of the relative solubility of the two or three
isomers able to be converted into each other. | had already shared this view for
a considerable time. Lowry and Ir. Arnmsrronce have also expressed the opinion
that it is a question of equilibrium. As stated above, Mr. Junaivs will try to determine
the precise nature of this equilibrium. Lo ps8:
( 784 )
[or 2h:
odd n the polygon is reduced in @, in this respect to a linesegment
long 29 bearing at one end the even numbers 0, 2, 4, .. . and at
1 and 2n| have the greatest common divisor g. And for
9?
the other the odd numbers 1, 3, 5
“Let us replace for odd # the just mentioned linesegment 20 by
a linesegment eo) 2 bearing at its ends the same groups of numbers.”
“Let us place for even # the mm planes and for odd n the m—1
planes and the linesegment g¥ 2 in such a way in the space S, that
in a common point they are rectangular to one another.”
“Then the n+1 {or 2n| points 7; of that space the projections of
which on these mm elements coincide with the vertices numbered
with 7, are the vertices of a regular polytope A, with length of
edges oVn+1 [or C, with length of edges @Vn].”
This double theorem where with respect to the continuous bifur-
eation “this [or that\”’ we must either always read this placed
before the brackets or always that placed inside the brackets,
reminds one of the decomposition of the general motion in |S, into
m components for even 7 in 7 rotations, for odd 7 in m—1 rotations
and a translation. This remark is important with respect to the
decomposition of the groups of anallagmatic motions belonging to
Aj. and.e,,.
Theorem II.
“Let S,-1 and S, be two spaces rectangular to each other in a
point and let Sop represent the space determined by them.”
(1)
“Let us, take in Sp) @ regular polytope Aes in Sp a regular
ar
poly tope c, having both as the index (1) indicates unity as length
of edges.”
“Let us number the p vertices of A, 4 with the pairs of numbers
(O, p), G,p +1), (2, p + 2),.-- (p—1, 2p—1) and let us assign to
each of the 2p vertices of C, one of the numbers 0, 1, 2,... 2p—14
under the condition that the p diagonals bear at the ends again the
pairs of numbers (0, »), (14,p + 1), 2(p + 2),- . -(p—t, 2p—1).”
“Then the 2p points P; of Ss, 1, whose projections en S,p—1and S)
coincide with the vertices of Apt and G, bearing the equal numbers,
(V2)
form the vertices of a regular polytope As, —; with length of edges
(1)
V2 which projects itself on S,—1 according to two comeiding Ages
(1)
>
and on ip according 10 a Cp
By this simple theorem we are enabled to deduce the proof of
]
;
‘2
we weet aig
( 785 )
theorem I for the polytope C;,, out of the one for the polytope An.
By repeated application we arrive at:
oh we of the space Sa) can project itself on a definite
system of mutually rectangular spaces S,y—1, S,g-2,..-5,,5,,5,
gil ~ 3) 274)
respectively according to a Cri , two coincided C 4-2 pre
V2) (1) e's
27-3 coincided Cy, 27-2 coincided squares Cy, and 27—! conicided
. (1) ”
linesegments C) ”
Mathematics. — “On symmetric transformation of S, in connection
with S, and S).? By Mr. L. E. J. Brouwer. (Communicated
by Prof. D. J. Korrrwne).
Let us for the present occupy ourselves with a particular case of
symmetric transformation — the reflection, and let us investigate its
influence on S, and S;. As WS, and .S are independent of the choice
of a system of axes, we make a suitable choice by selecting the
XxX,
cosines of direction of a vector before the reflection ; 8,, 8, 8,, 3,
axis along the axis of reflection. Let us call a,, @,, a,, a, the
those after it; let us moreover represent a,' a," —a@,'a," etc. by
6, etc, and p, 8,’ —8,' 8B," ete. by x, etc: and let us call 2,, ete.
the coefficients of position of a plane with sense of rotation included
before the reflection and u,, etc. those after it. Then:
CS B,
a= 3B,
rs igen = lala ©
CC ae B,
Gai = %,, Si, = Kis
S31 —— han S43 Sn Maa
5, Aaa Ss, ——T om hed
V 5703 +8751: +8715 4871448704483 Has tH’: ik Hag Se as. era Oe
So also:
~
as = F2; 14—— — Pia
As, = Us: Ay, — esd
7 le 7! Ae y Pp ee (s4
52
Proceedings Royal Acad, Amsterdam. Vol. VI.
( 786 )
OF:
“par 4.4 = ths fy Az = Ars = {454
As, = = As —= (43, — [hg, As, =a das —= Hs T Lag (a)
ee a His Hs, Ax = As = Uy, 34 |
Now however
are the eosmes of direction of the representant of the system of
planes equangular to the right with 4 with respect to a system
of coordinates OX, Y,Z, taken in S,, as that was defined (These
Proceedings Febr. 1904, page 729).
And likewise
Ae. Ios
We must further add to the numerator the volume of the distance
spheres, lying within other distance spheres, which quantity has been
twice instead of once subtracted in the term 24. We geet then
the form
ll b : _ bn
1—>—4 Bl+....4N—
1 = ait
Fale A SY 3 eae Ls Wie eae
Ma ooo ee ee > eat
a ane nn o Sri = ae te.
where 7 is a finite number; for a point cannot lie in more than a
finite number of distance spheres at the same time; as van LAar *)
has made probable, in not more than twelve. We must however
keep in view, that the quantity v which occurs in 2, does not
represent the volume v but the available volume and that this quan-
tity would therefore have to be determined from the equation of
the nt degree:
hb? dy, G8 a hn
\
= Fat ge 2
LG. %,, rete est
There is not much to be said about the coefficients, occurring in
the quantity 8. As Bonrzmann*) has shown they need not change
their signs, on account of the circumstance mentioned by him, as
we should expect if we did not take this circumstance into account.
So is eg. as BottzMann has shown, C, not negative, but positive.
For the present there is not much chance that further coefficients
will be determined on account of the exceedingly laborious caleula-
tions, which would have to be carried out. Yet formula (4) may
already in this form be of use for the question of the derivation
of the equation of state.
1) The developments of Botrzmany’s theory of Gas, p. 148 et seq. further con-
tinued, lead to the same form.
2) Arch. Teyter (2) VII last page.
8) These Proc. | p. 390.
( 794 )
Physics. — “On van per WaAaLs’ equation of state,’ by Dr. Pu.
KkouNsTAMM. (Communicated by Prof. vAN DER WAALs).
§ 1. The way, in which we have to take the extension of mole-
cules into account for the derivation of the equation of state, has been
repeatedly a subject of discussion. It is known that, in order to avoid
the introduction of repulsive elastic forces and therefore the apparent
contradiction with the supposition that only attractive forces act,
VAN DER WaAats has, in the first derivation of his equation, not allowed
for this extension by means of the virial, but by quite other means. This
departure from the path first taken was disapproved of by Maxwe..'),
and strongly condemned by Tarr*), who himself from the equation
of the virial had arrived at an equation of state, as also Lorentz
had derived, viz. :
a pt i h
¢ == a — 7 1 _— 3 . : . . F . (1)
More than ten years ago an interesting controversy was carried on
between Tair?), RayLeigH*) and Kortrwere*) on the value of this form
in comparison with the original form :
(ct NC Oe RE a snl -pg ee
Whereas Tait considered an equation of the form (1) as the only
correct one and the derivation of van per Waats as decidedly
wrong, because it could never lead to this form, Korrrwre thought
that he could prove, that on the contrary the final result ought to
have torm (2), a form which he greatly preferred. This preference,
Which is not to be justified from a purely mathematical point of view
as the two formulae are identical when we take only the terms of
h
the order — into account — and the terms of higher order are
s
neglected in both cases — may be easily understood when we con-
sider that we have here to do with physieal problems. For whereas
from the form (1) neither the existence of a minimum volume, nor
1) Nature 10, p. 477.
*) Nature 44, p. 546, 627; 45, 199.
5) Nature 44, p. 499, 597; 45, 80.
4) Nature 45, p. 152, 277.
(13)
that of a critical pomt can be derived’), it is known that equation
(2) indicates both, thongh not numerically accurate; one of the nume-
rous cases, where the equation of VAN per WaAAts is a safe guide
for the qualitative course of the phenomena, though it is unable to
represent them quantitatively. Korrrwre derives, therefore, from the
equation (1), (2)?) by putting as it was deduced by van pER WaAALs
VV 227s?
and himself ” =-———— for the value for the number of collisions
v—D
: VV 2ans* Ms
instead of P= ————, which value was used by Tart and Lorenvz.
v
This discussion has not led to a perfect agreement, any more than
a later discussion carried on between BoitzMann*) and VAN DER
Waats ‘) about the corrections, which are to be applied to the value
of 4, which is put constant in (1) and (2) and equal to the fourfold
of the volume of the molecules. As is known, JAGER*) and BourzMann *)
ab
found by first approximation 4, = 6, (: Sa -) for the > from (1);
:
17h
VAN DER Waats /, = ips (: *\ ao ) for that from (2): afterwards
P
SP 2 8
= i : ; ab
VAN DER Waars Jr.‘) has found for the latter b=, (2- )
‘ Sr
in a different way, so that his result, as far as the terms of the order
b Lb?
: ca -, are concerned, agrees with that of JAGeR and BorrzmMann. In
his publications which have appeared since *), his father has pro-
nounced himself ‘inclined to acknowledge */, as the correct value.’
but it is not doubtful for an attentive reader, that this “inclination”
leaves ample room for doubt, both with regard to the value of the
3
s?
coetficient and to the following coefficient p, which was given
on one side as 0.0958, on the other side as 0.0369,
1) Evidently Tarr has not seen this, but he thinks that the peculiarity of form
(2) exists in this, that it is a cubic with respect to 7; evidently on account of
the part which the three sections of the isotherm with a line parallel to the
r-axis, play in the theory of van per Waats. But he overlooked, that every valid
equation of state will have to represent these three volumes.
*) See also van pekR Waats: Continuitiit 1899, p. 60.
3) These Proc. I, p. 598.
*) These Proc. I, p. 468.
5) Wien. Sitzungsber. 105, p. 15.
6) Gastheorie, p. 152.
7) These Proe. 5, p. 487.
on~
3) These Proc. 6, p. 155,
( 796 )
Now it has clearly appeared of late, of how preponderating an
importance the knowledge of these corrections is for an accurate
equation of state. In the first place Brinkman’) has succeeded in
proving, that the behaviour of air at O° between I and 3000 atms.
can be very accurately represented by means of coefficients which
do not differ considerably from the values found by BourzmMann;
then vAN DER Waats?) has proved — as van Laar*) had done
before that with the aid of these corrections the critical coefficient
‘RT 4 Z %
becomes ( ye 3.6 and in this way one of the great discrepancies
pr).
hetween theory and experiment seems to be removed. And this last
result makes it again clear, how great from a physical point of
view, the difference is between an equation of form (1) and (2),
though from a mathematical point of view they may be identical by
first, second and further approximation. Already a long time ago
Dinrerict') proved, as lately Happrn’) has also done, that with an
equation of the form:
: =A ely Faw l \ , bh I? } :
Ge ae “Tr ele le ay ‘; |b eee
ihe critical coefficient can reach at the utmost the value 3 with the
theoretical values of the coefficients, and that this form can therefore
never represent the experimental data. It seems therefore not devoid
of interest to me, to examine the different derivations of the equation
of state, in order to find which form must be taken as the correct
one. This investigation will at the same time enable us to form an
opinion about the difference between BoLTZMANN and VAN DER WAALS.
§ 2. As is well-known, the proof which van per WAALS originally
gave for his equation of state, rests on two theorems, the first of
which is explicitly stated, the other is assumed without argument
as self-evident. The first theorem states, that the number of collisions
in a gas with spherical molecules is represented by the before-
: : VY 22ns*
mentioned formula ? = ——
Now I have already pointed out
Ua
in a former paper’), that this formula is inaccurate, and must
!) These Proc. VI, p. 510.
2) Botrzmann-Festschrift, p. 305.
*) Archives Teyler (2) VII.
4) Wied. 69, p. G85.
5) Drude 13, p. 352.
6) These Proc. p. 787.
( 797 )
' 114
: . : /2ans? 8 wv
be changed by first approximation into P = —-—-— Ts aes
v )
1~2
F ate [2a ns? ab
neglecting the terms of higher order ? = -———-—_{ 1 + — — ]}.
;
The other theorem says that the pressure on the wall (or an
imaginary partition) is inversely proportionate to the mean length of
path. Already KorrrwrG') has felt an objection to this theorem, and
has therefore looked for another way of deriving the equation of
state; though convinced of the validity of the theorem, vAN DER WAALS”)
has later on given another proof, because he considered this theorem
as a not to be proved dictum. After the appearance of the already
cited paper by VAN DER Waats Jr., however, it is in my opinion
beyond doubt, that this theorem does not contain an unprovable truth,
but — at least in the terms given here — a provable untruth. For
it says the same thing as the statement, that the pressure exerted
by the collisions on the distance-spheres per plane unity is equal to
that on an imaginary or real wall. It seems to me, however, that
VAN DER Waats Jr. has convincingly proved, that when the terms
b
of the order — are taken into account, the relation between these
i
pressures defined in the usual way, is 1 — : is
If this result is combined with the just mentioned value for the
number of collisions, which determine the pressure on the distance-
spheres, it is seen, that also in this way the fourfold of the volume
of the molecules is found as first correction, but for the present this
does not teach us anything about the final form, because in the
communication of VAN DER Waars Jr. the relation of the pressures
is not given in its true form, but developed to an infinitely extended
series with neglect of the higher powers, which are, however, material
to the determination of the final form.
In order to derive the final form, we may, if we want to avoid
speaking of repulsive forces, make use of the method based on the
increase of the transport of moment brought about by the collisions.
We start in this from the observation, that the quantity of motion,
which, bound to the molecules, generally moves on with the velocity
of them, proceeds in a collision over a certain distance with infinite
1) Verslagen der Kon. Ak. Afd. Natuurk. Tweede reeks, X, p. 362.
*) Continuitéat 1899, p. 60 cf.
( 798 )
velocity which is best seen by imagining a central shock, in whieh
both molecules pursue their way in the direction from which they
came, but adopting each other's motion. It is therefore just as if
they have passed through each other with infinite velocity and as
if further nothing has happened, so also as if the quantity of motion
of whose motion the pressure of the gas is a consequence —
does not move with the velocity of the molecules, but as if with
every mean path which is described, a distance is saved, which is
a mean of the distances of the centres of the molecules in collisions.
If the distance obtained in this way is '/, sV2 for every mean path of
r
then the increase of the pressure is:
V 2a01s*
a 1 D
| a. : + 3 mY = /
Y ied LPO )
SS EE Se
] v
iY 2 sens?
If the mean path. when we take into consideration that the
; : ss v h
distance spheres cover each other, is ———— , wherep=g| — },
V2 ans* v
b
then the factor which we must take into account is 1 + —~?, and
v
we get the strictly accurate equation :
a RP b-
P aa ” == eS ] at = B ° e . . ; . (4)
The tran of thought which we have sketched here in a few
words, and from which G. JAGER (loc. cit.) arrived for the first time
; 3) ) .
at the correction term =0,(142—) has already been rigorously
:
developed by Korrrwre'), but he seems to have come to another
resulf. This disagreement is, however, only seeming. KorTEWEG
says”): “the sum of all the distances saved by collisions is therefore
4. APr cos «dt*). The sum, however, of all the distances with whieh the
J bd
P molecules approach the plane A in the time dt is evidently
Pv cos € dt.’
Now it is beyond doubt-in my opinion, that if a number of mole-
cules in the time df by their own velocity pass over a way Pu cos & dt,
1) Verslagen der Kon. Ak. Afd. Natuurk. Tweede reeks X p. 362.
=rihaeGs p. 369.
be . |
) A= in our terminology; v represents the velocity of the molecules in
Kir
KORTEWEG’S paper.
( 799 )
and at the same time a way 4.A/’» cos & dt is saved by the collisions,
those molecules seem to move with a velocity Prcosedt(1 + 4A),
and so the number of collisions has increased in the same ratio.
KorrewrG, however, continues: ‘In order to obtain therefore the
same number of collisions with the plane 14, the molecules will
only have to pass over a way Pv cos edt, instead of over a way
Pv cos € (A — 4A) dé, in other words, the number of collisions of this
system increases in the ratio (1 — 44): 1.” Now between the two
results there is only difference of order r and in so far as we wish
to neglect the quantities of this order, Korrmwxa’s result may cer-
tainly be accepted. If, however, we wish to solve the problem
rigorously, the first result alone can be accepted.
For Korrewrka makes it appear, as if — taking into account the part
of the way being saved — an equally Jong way is described in the
time (1—4A)dt, as in the time dt without doing so. Now in the
last case the molecules pass over a way /r cos édt in the time df,
so. Pycos edt (1 —44A) in the time (1 — 4A)d¢. In the time d¢ there
is saved 4APvcosedt, in the time (1 — 4A)(/t therefore (1 — 4.1)
4 APv cos edt; so the distance, passed over in the time (1 — 4A)d¢
by saving way and really moving together is somewhat slighter
wiz. 16 A* Pecos edt) than that passed over by the real motion alone
in the time cf).
1) Perhaps Korrewea was led when drawing up the formula mentioned in the
text by the solution of the problem in one dimension which he has given in
Nature (loc. cit.) later on. He finds there — perfectly accurately — for the time
passing between two collisions against the wall of a row of 7 particles of diameter
A which can move over a total distance LZ with a velocity V:
This formula reminds us more of Korrewea’s result than of ours, really however
it agrees with the latter, not with the former. For, if we determine the ratio of
the number of collisions with and without saving way, it is Q = ae Now Lis the
?
total distance over which the molecules can move, so the path described by their
own motion + the path saved: mA is the path saved. So Z corresponds with
(1+ 4A) Prcosedt, na with 4 A Pv cos: dt; so the ratio of the collisions is here
: p ; ; L—n
again (1+ 4 A): 1. To Korrewea’s result 1 : (1L—4 A) would the formula Q = = =
Li — 4 IA.
- : ' : HA :
correspond, which agrees with the first as to the terms of the order L , but which
is certainly not sérictly accurate.
It is true that with the formula for one dimension, with regard to its physical
meaning, an equation of state agrees, in which a quantity is subtracted from the
volume which is a function of 6 and v, not a formula of form (1); but we shall
see that our formula derived in the text, leads also to such a final form.
( 800 )
§ 3. So we arrive at equation (4) without making use of the
equation of the virial and without speaking of repulsive forees. That
the introduction of these and the determination of the so-called
“repulsive virial” in the same way as has been done by Lorentz,
Tarr and BonitzMann, leads to the same result, is easy to see, if we
V2 ans? V2 ans? | .
put everywhere —— $ instead of -————— for the number of
v v
collisions in the formulae used by them. The expression 8 does not
depend on any of the integrations and the repulsive virial yields
h 4
therefore RZ — 3 instead of RT —. This is easy to understand, even
v v
without following the proofs of Lorentz and BoirzMann, for it is
clear that the term which is introduced into the equation of the
virial through the collisions, must be proportional to the number of
those collisions, as two collisions can never be of a different kind‘).
It seems therefore as if theory really leads to the form expected
by Tarr and Dinrerict, which conforms so little with the experiment.
In reality, however, the result is quite different. For — as I pointed
out in my other communication — 2 has by first approximation not
ab
the form: 1+ a > as JAGER and BoLrzMann generally write, but we
e v
8 v
find in the way first indicated by Crausius —— > for it, and only
)
by carrying out the division and by neglecting the terms of higher
uD ;
order, we get the form 1+ a a As | showed, we get, taking the
fo} yh, ;
terms of higher order into account :
VaAsb b? hn
esas caine AE 2) per Ne
ve o 2 vy” pn 3
jeg b&b 17B? b* rn jn (°)
ey 160 Se ead bess
where # is a finite number.
Now it is true that the other coefficients of this series, C, and B
excepted, are unknown, and we might conclude from this, that it
must therefore be indifferent for the present, whether the equation
of state is written
') Konrewea and van per Waazs have also made use of this property in their
derivation of equation (2) from (1), mentioned on p. 795.
( 801 )
11}? L? ht
b == |- B— }-
a RT | 5 v 0” ve 6
(> r 7 Fg ae CORE eee
| o— Qh } - } C,
16 v v?
or
a RT \ ' 1 h ' 5 5? ' > /? } (7)
13 — le - Sian en eee
P t yy? r | Y 8 »? : v? |
but this conelusion would be unjustifiable. For it is possible, nay
even probable, that the coeflicients of numerator and denominator in
(6) decrease rapidly; it is therefore possible, that the true form is
accurately represented by a quotient of two forms, which have each
only three or four terms; from this follows by no means, that also
in the form (7) we should get a close approximation with three or
four terms, for the coefficients of the higher powers in (7) do not
depend only on the coefficients of the Aigher powers in numerator
and denominator of (6), but they are also functions of the coefficients
of the lower powers 1; *'/,; 2; ‘'/,,; and in such a way that they
do not become zero, when the coefficients of the higher powers in
(6) do so. Now the difference between (6) and (7) vanishes, of course,
for such large values of v, that the series (7) converges strongly,
but for the critical volume and even more so for liquid volumes tlie
difference is very pronounced. This appears already from the simple
fact, that a form as (6) ean easily yield a minimum volume; but
(7) only when an infinite number of terms is taken into account.
And also the before mentioned difference between the results of
Dirrertct on one side, and van Laar and van per Waats on the
other side, prove how careful we must be with the introduction of
simplifications which seem perfectly allowable.
§ 4. Also the other ways proposed for finding the equation of
State, arrive at similar final results.
This is easy to see for the most direct way, indicated by BontzMaNn ‘).
For it is clear, that his formula (4), which leads to the form:
‘ a\v—2b ies
(p+3 ——=RT .......@
requires another correction on account of the fact that the distance
spheres cover each other partially. The numerator of this fraction
1) Gastheorie p. 9.
99
Proceedings Royal Acad. Amsterdam. Vol. VI.
( 802 )
becomes then identical with the denominator of the fraction from (5).
In the denominator we get a correction for the part of the eylindre
y, which falls within more than one distance sphere, or as we may
also say, for the part of a surface -l, which is found within more
than one distance sphere, if we define this surface A by the condi-
tion, that it is found everywhere at a distance s from the outer
surface. We shall call this surface A henceforth ‘surface of impact”,
hecause the foree which in a collision acts on the centres of the
molecules, acts in this surface. The determination of the numerical
value of the further coefficients seems an exceedingly elaborate work,
at least BoLTzM\NN announced already in the Lorentz volume of the
Arch. Neéerl. that he would have this calculation carried out for the
next coefficient, but this caleulation has not yet been published. It
seems, however not doubtful to me, that also the numerical value
must be the same as the value found in other ways. At all events
the final form becomes also by this method
on 17)? 2 hn
AY Gate Cera eS)
ieee aaa ee ere tee
Leo ey ee
rh pit
in which » represents a finite number.
Now it is not difficult to show that the only remaining method
for deriving the equation of state, which led to the correction '7/,,,
must lead to exactly the same equation as (9), when its principles
are consistently applied. As is known, this method assumes, that
the pressure is to be integrated not only over the volume v, but
also over half of that of the distance spheres: 4, because a molecule
whose centre has got on a distance sphere, is subjected to exactly
the same force as when it has got on the surface of impact (the
volume enclosed by the surface of impact may be put =v). The
volume of the distance spheres, however, is really smaller than h,
hecause some distance spheres coincide, and we get therefore *):
u 17 i? ok
p+ | Ct 4 os) aR , i)
yp o2 Uv F ‘
Now van ver Waats Jr. (loc. cit.) has already pointed out, that
it is tacitly assumed here, that the surface of the distance sphere
which is found within another distance sphere experiences a pressure
= 0, and that therefore, for the sake of consequence, also the parts of
the surface of impact falling within distance spheres, must be supposed
1) Continuitaét 1899, p. 65.
( 803 )
to experience a pressure =O. He has, however, not worked out
this thought further; as it seems to me, because he has not fully
appreciated the ideas which led his father to the correction ‘7/,,. He
has, therefore, substituted for this view, another, undoubtedly correet
one, but he has not explained, how the former might be completed in
order to yield also the true result. If, however, we make use of
the observation made by him, then it is clear that the pressure
au
which seems to be P= p ++ “2 per unit of surface when we. think
it as working in the usual way on the total area of the surface
of impact 0, must be really larger in the gas, viz. equal to
ial S
paca 771
7}
, When this pressure p' acts only on the /ree surface O”.
Now it is clear that this quantity is which hereby gets into the
denominator of the first member of the equation of state is identical
with the quantity introduced by BoLtzMaNn in this place. For he,
too, determines this denominator by examining what part of the
surface of impact falls within the distance spheres. This shows us
at the same time another point. In the few words which van DER
Waats') bestows on this derivation of the equation of state, he says,
that the pressure is not to be integrated over the total volume of
the distance spheres, as we might expect, but over half of it. Now
I have been struck with this from the beginning, and I have tried
to find the reason in vain. Jt appears from what precedes that we
have really to integrate over the total volume and that VAN DER
Waats has only introduced the division by two as compensation for
the circumstance overlooked by him, but which we take here into
219
2 av
account. So he got »—#, instead of ———, which evidently does
v0—OD
not make any difference by first approximation. But already the
second approximation cannot properly be found in this way.
It appears now, that we must integrate the pressure p’, determined in the
way above indicated, over the whole outer surface, that of the distance
spheres included in so far as they fall outside each other?), and that
1) Continuitit 1899, p. 62.
*) The iogical inference from this theorem: that the true equation of state is found
by assuming that every surface element, lying either on a plane or a curved wall,
experiences a pressure: p' per unit of surface provided it does not lie within a distance
sphere, in which case the pressure must be put equal to 0, would involve, that
we did not mtegrate the pressure over the available volume (volume diminished
by the free volume of the distance spheres), but that another correction was applied
53*
( 804 )
the axiom from which vAN DER WAALS started, viz. that we must
equate the pressure on the distance spheres and that on the outer
wall, is true, if only we apply it to the pressure p’. This result is
only in apparent contradiction with the result of van per Waats Jr.,
that the pressure ? on a fixed plane wall stands to the pressure P'
©
,
on the distance spheres in the ratio of 1: 1 — mae For these pressures
»
P and P' have been found by supposing the quantity of moment
furnished by the wall (and the distance spheres) in the collisions to
be distributed over the fota/ surface, so by assuming that every
surface element contributes an equal amount to the impulse; the
pressure p' of which there is question here, and which proved to be
the same for both, is found on the other hand by supposing, that
only the mean /ree surface contributes to the quantity of motion,
and that the rest is therefore subjected to a pressure = 0.
From this follows:
Se free area ot surface of impact — (1 ca S
~!’ total area of surface of impact v
_ free surface of distance spheres 11+
| ge P = Sa a ee 1 — — —
total surface of distance spheres 8 v
11d
! 1 Sak
iP 8 v Oo b : ; _
and so = = 1 — — — with neglect of the terms of higher
ss b ov :
pee
order.
The importance of the proof completed in this way, lies for me
in the fact, that it makes use of the idea of systems of molecules
whose intra-molecular forces need not be introduced into the equation
of the virial, provided we adopt the pressure integrated over the
whole volume of these systems in the virial. I need not point out
the great advantages of such a point of view, already cursorily
mentioned by vax per Wa ts in his dissertation, and later worked
out; the communications of VAN DER Waals on the equation of state
and the theory of cyclic motion are striking evidences of its value.
Now it is true that there is a difference between our case and
the cases, to which this view is applied in the communications
in connection with the volume of the distance spheres, which are cut by the sur- _
face of impact. This correction would come to an increase of the volume to be
integrated with that part of the distance spheres that is found between the surface
of impact and the outer wall, but it is clear that this volume may be neglected
with the same right as the total volume enclosed by those two surfaces,
( 805 )
mentioned. For in the latter we suppose the existence of really
permanent systems of atoms, whereas in our case two molecules
Whose distance spheres cover each other partially, and which are
therefore thought as a system, remain only together for an exceedingly
short time. But we see that we get to the right result by assuming,
that also the part of the surface of impact lying within the distance
spheres, is part of a ‘system’, and that therefore the foree exerted
on if, does not count’). This result isa priori by no means improbable,
for this part of the surface of impact has exactly the same essential
property as the other parts of ‘‘systems’’ viz. of falling within distance
spheres, whereas in the communications mentioned this hy pothesis
for the surface of impact was not necessary, because there the
systems are characterized by other properties which do not distinguish
the surface of impact viz. that it is part of the same system for a
comparatively long time.
§ 5. The result obtained in the preceding §, enables us now to
use also the first method of reasoning of VAN Der Waats for the
determination of the final form without making use of the virial.
For we have seen that the pressure P on the wall, when the
pressure on the distance spheres P' is determined by
free ae meat me
P total “e? of surface of umpact Pe
p< tes. ue eS
~——- surface of distance spheres
total
Now the pressure on the distance spberes is, as appears from
Ciausivus’ formula for the length of path, proportional to:
free
——— surface of distance spheres
total
available volume
so that we find from this for P:
free : y
——— area of the surface of impact
, total
| eects pee
available volume
') The real significance of the introduction of these systems may be expressed
in this way, that we think the situation of one given moment as fixed, and take
info account the systems of more than one distance sphere formed in this way.
This removes also what is paradoxal in the supposition (see v. p. Waats Jr. loc.
cit. p. 644) that the pressure is 0 in those places which have just experienced a
collision or will soon experience one, viz. the points in the distance spheres. For
in this fixed state those points are really exempted from collisions from all other
molecules than those belonging to their system, and whose pressure may therefore
be considered as an intra-molecular force.
( 806 )
The signification of 7 we find by equating the volume of the
molecules to zero; it appears then, that 7= FT, so that the equation
of state becomes
available volume — RP
=. — i
free :
Yotal “ec of surface of impact
identical with (9).
Equation (10) shows us at the same time, what is the physical
significance of the quantities used by van per Waats Jr. in his proof
with the aid of the virial. For he integrates the pressure P over the
volume 7, the pressure P’ over the volume 4, so that the equation
of state becomes:
tree : 3
surface distance spheres
(»+ =| ee pe caake = RT ae
2 free : : +
area of surface of impact
total
which is, moreover, at once seen, when we read the cited paper
attentively. (Specially p. 492).
Though it is not clear to me, why we must integrate here over
half the volume of the distance spheres, I must acknowledge that
the result — to which we can also get without the proof in question
by simply putting the results (6) and (9) identical — is correct. For
calculations formula (11) which agrees closest with the original form
of vAN DER Waats, may be of use. I had hoped that [ should be
able to use the formula obtained in this way for removing the
remaining discrepancies between experiment and theory, at least
” . (Ta
partially, specially the great difference in the value of ( *) :
pé a
As yet these efforts have not met with the desired success, and it
is obvious, that this will not be possible, before we know e.g. the
numerator of (11) much more accurately than we do now. It is clear
that this numerator in virtue of its physical signification, can never
become zero for volumes larger than the minimum volume; now we
: : 11d
know this numerator only in the shape 1 reteoite expression
which becomes zero tor very much larger volumes, nay even for
the ordinary liquid volumes. For these volumes therefore the appli-
LEA
cation of the correction 1 — ra will be injurious, instead of advant-
ageous. Not before the mathematical form of two of the three quan-
( 807 )
WF free free ae a
tities : surface distance spheres ; area of surface of impact:
total total
available volume, is more accurately known, we shall be justified
in expecting better concordance of experiment and theory.
Physics. — “Note on Sypxry Youne’s law of distillation.’ By
Miss J. Revpier. (Communicated by Prof. J. D. VAN DER
WAALS).
Some time ago SypNrEY YounG gave a law of fractional distillation’),
which seems very strange at first sight. According to this jaw in
distillations with an efficient still, the weight of distillate coming over
below the middle point of the boiling temperatures of the components
would be almost equal to the weight of the most volatile component,
also when the separation is far from perfect. This concordance
would be so close, that Youne could even base a general law of
quantitative analysis on it, at least for substances whose boiling
points were not too near to each other. Now it seemed, however,
unlikely, that this law should always hold, quite independent of the
nature of the Zv-curves and of the composition of the mixture
from which we = start. Therefore | have distilled some mixtures,
inter alia also with Youne’s evaporator still head.
| began with some of the examples chosen by Youne, and I found
really that they confirmed the law. Then I tried to determine the
limits of its validity by taking a mixture with very steep 7’v-line,
so that I could closely examine, what happens, when the distillation
is broken off above or below the mean boiling point. I took for
this benzene (boiling point 79°,6) and aniline ‘boiling point 180°)
and began with such a composition, that the imitial boiling point
lay wready above the middle point, thinking that Youne’s law would
be sure not to hold in this case. Yet also now the law was confirmed,
but the process of the distillation revealed also the character of the rule.
For it appeared that independent of the composition of the mixture,
even when it consisted of 4 °/, benzene and 96 °/, aniline, and so
0
a thermometer, which IT had placed in the liquid, pointed to almost
180° already in the beginning of the distillation, the temperature in
the still head remained constant at 79° for a long time, and rose
then suddenly very rapidly to 180°, so that the distillation might
have been broken off with the same result very far above and
1) J. Chem. Soc. 81 752,
( 808 )
below the middle point 129°\8. It appeared in other words, that
with Youna’s still head an almost perfect separation was reached
already in a single distillation. That the law under consideration
holds in this case, is self-evident.
| found also there where the 7'r-line is less steep, as for benzene
and toluene, that the thermometer remained in the neighbourhood of
the boiling point of the most volatile substance during the greater
part of the distillation, and then suddenly rose rapidly, quickly passing
through the middle temperature, so that here too the breaking off
at the middle temperature is not essential.
Where it is essential as with distillations with less efficient stil
head or for mixtures with very flat) Zv-line, the law does not
hold. As an instance I give the three following distillations, the first
of which, where a mixture with very steep Zv-line is distilled with
the evaporator, conforms to the law; whereas the second, where the
same mixture is distilled with an ordinary straight tube and specially
the third where a mixture with flat 7’-line is distilled with the
evaporator, deviate from the law.
Weight of the
ie oT : me over below midde
Still head. Component Boiling point | components [OME d
temp. im gr.
in gr.
— a ——> ec SF Ch Om Oe es ees sn eee es sn ee nn nw... nn eee ee
Evaporator jenzene 79°.6 6O.S8 1¢@ 60,6
Toluene 110°,8 34,6
Straight
‘abe jonzene 719°.6 30,0
Toluene 110°.8 500 } M2
. yp “| strs -=—- = --
Evaporator an fone 4d 4 0 11,4 1077
chlorate
Benzene
In aecordanee with this Youne himself gives his law only for
mixtures which are not difficult to separate distilled with an efficient
still head.
[ think that IT am justified in coneluding that the law is simply
based on the separation of the mixture in its components, and that
we have to inelude under what Youne calls: a far from perfect
separation, only those cases, where at the end of the distillation a
small fraction of the most volatile substance is left in the recipient
( 809 )
and a small fraction of the least volatile is present in the distillate.
That the two quantities will then differ little in weight and therefore
the deviation from the law is comparatively small, is not strange in
my opinion.
I think to have shown in this way, that Youne’s rule is a proof
of the excellent way in which Youne’s still heads work, but that
from a point of view of quantitative analysis we must only take
this rule as an application of the most obvious Operation, viz that of
separating a substance in pure state froma mixture and then weighing
it separately.
Physical Lab. of the University. Amsterdam.
Physics. — ‘“Hlectromagnetic phenomena in a system moving with
any velocity smaller than that of light.” By Prot. H. A. Lorentz.
§ 1. The problem of determining the influence exerted on electric
and optical phenomena by a translation, such as all systems have in
virtue of the Earth’s annual motion, admits of a comparatively
simple solution, so long as only those terms need be taken into
account, which are proportional to the first power of the ratio
between the velocity of translation w and the velocity of light c¢.
w?
Cases in which quantities of the second order, i.e. of the order —,
. c
may be perceptible, present more difficulties. The first example of
this kind is Micurtson’s well known interference-experiment, the
negative result of which has led Firz Grratp and myself to the
conclusion that the dimensions of solid bodies are slightly altered
by their motion through the aether.
Some new experiments in which a second order effect was sought
for have recently been published. RayiriGH*) and Brack?) have
examined the question whether the Earth’s motion may cause a
body to become doubly refracting: at first sight this might be
expected, if the just mentioned change of dimensions is admitted.
Both physicists have however come to a negative result.
In the second place Trovron and Nose *) have endeavoured to
detect a turning couple acting on a charged condenser, whose plates
make a certain angle with the direction of translation. The theory
‘) Rayteien, Phil. Mag. (6) 4 (1902), p. 678.
2) Brace, Phil. Mag. (6) 7 (1904), p. 317.
*) Trouron and Nogie, London Roy. Soc. Trans. A 202 (1903), p. 165.
( 810 )
of electrons, unless it be modified by some new hypothesis, would
undoubtedly require the existence of such a couple. In order to
see this, it will suffice to consider a condenser with aether as
dielectricum. It} may be shown that in every electrostatic system,
moving with a velocity w'), there is a certain amount of ‘“electro-
magnetic momentum’. If we represent this, in direetion and magni-
tude, by a vector ©, the couple in question will be determined by
the vector product *)
yy 50] 9 GS. Fs See ae ae ee
Now, if the axis of 2 is chosen perpendicular to the condenser
plates, the velocity w having any direction we like, and if 7 is
the energy of the condenser, calculated in the ordinary way, the
components of @ are given") by the following formulae, which are
exact up to the first order:
2U 2U
§.. — —_ SY, ee Ss
6, = ans, 6, = et ©, 0,
Substituting these values in (1), we get for the components of
the couple, up to terms of the second order,
20 2U
Wy We, — — We Wz, 0.
c
2
a2
€
These expressions show that the axis of the couple lies in the
plane of the plates, perpendicular to the translation. If @ is the angle
between the velocity and the normal to the plates, the moment of the
couple will be — w? sim 2a@; it tends to turn the condenser into such
(
a position that the plates are parallel to the Karth’s motion.
In the apparatus of Trovton and Nosrir the condenser was
fixed to the beam of a torsion-balance, sufficiently delicate to be
deflected by a couple of the above order of magnitude. No effeet
could however be observed.
) 2. The experiments of which T have spoken are not the only
reason for whieh a new examination of the problems connected
with the motion of the Earth is desirable. Potrncark*) has objected
') A vector will be denoted by a German letter, its magnitude by the corre-
sponding Latin letter.
*) See my article: Weiterbildung der Maxwetu’schen Theorie. Electronentheorie
in the Mathem, Eneyclopiidie V 14, § 21, a. (This article will be quoted as M. E.)
*) M. E, § 56, c.
4) Powcarsé, Rapports du Congrés de physique de 1900, Paris, 1, p. 22, 23.
( 811 )
to the existing theory of electric and optical phenomena in’ moving
bodies that, in order to explain Micnkenson’s negative result, the
introduction of a new hypothesis has been required, and that the
same necessity may occur each time new facts will be brought to light.
Surely, this course of inventing special hypotheses for each new expe-
rimental result is somewhat artificial. If would be more satisfactory,
if it were possible to show, by means of certain fundamental assumptions,
and without neglecting terms of one order of magnitude or another,
that many electromagnetic actions are entirely independent of the
motion of the system. Some years ago, I have already sought to
frame a theory of this kind’). I believe now to be able to treat
the subject with a better result. The only restriction as regards the
velocity will be that it be smaller than that of light.
§ 3. I shall start from the fundamental equations of the theory
of electrons *). Let 0 be the dielectric displacement in the aether,
the magnetic force, @ the volume-density of the charge of an
electron, » the velocity of a point of such a particle, and f the
electric force, i.e. the force, reckoned per unit charge, which is
exerted by the aether on a volume-element of an electron. Then,
if we use a fixed system of coordinates,
div 0 = By dir fy ye
rot fy = — (d + Oy).
5 ee ete |
rot d = — — fy,
ia
= >) 4 —[v. b].
I shall now suppose that the system as a whole moves in the
direction of « with a constant velocity mw, and IT shall denote bij u
any velocity a point of an electron may have in addition to this,
so. that
9, =w-- uy, ty =-Uy, Y2 = Uz.
If the equations (2) are at the same time referred to axes moving
with the system, they become
1) Lorentz, Zittingsverslag Akad. v. Wet., 7 (1899), p. 507; Amsterdam Proe.,
1898—99, p. 427.
2) M. EL, § 2.
( 812 )
dw) = @, div h = 0,
Ob- 05, 1/0 P “ee l |
fee : — : 1 Ree ee, fy
oy 02 c (5 a =A ¢ Q (we + Uy );
05, Oh- Pay | 0 i
Oz. a ae & : =) Oy SE ae
My Oe ¢ eeys fpliae
Ou Oy c \ Ot Ow ce
00- 03, Lal 0
cemic wag sD) De»
0d, 0d. 1 fo 0
a oa sta "aa .
1
fz — Dx + Fi (uy h- = ue h, );
c
‘ 1 1
i, = oy — = whe + = (u, hy — u, bz),
: 1 LS
f. = d. + — wh, + — (1 by — ty br).
€ c
§ 4. We shall further transform these formulae by a change of
variables. Putting
c? Z
ae ae ke,
C7 —w"
(3)
and understanding by / another numerical quantity, to be deter-
mined further on, I take as new independent variables
a = k l av b y — Ly 9 Z' == i <5
1 k uw hk uw
d',. == d, ; 0’, Sa d, ae a ay i v- +. -_— h, ‘
[? -? ‘ e [? Ap:
1 hk mu I: TG
l) A — 4 ly, 9 ly Ui — P fy / -+ Pe Og . i) S = esi fy. Se dy e
/? ‘ [? ¢ [? ¢ f
for which, on account of (38), we may also write
w w
dD. — EY, , d, = ke (+ ae ke } dD = ke (*. = “Hy )
c c .
bz == y's, by = a (s Me 2s hs ) em ie (. + =e )
C ce.
P
( 813 )
As to the coefficient 7, it is to be considered as a function of w,
whose value is 1 for «=O, and which, for small values of 2, differs
from unity no more than by an amount of the second order.
The variable ¢’ may be called the “local time’; indeed, for 4 = 1,
/— 1 it becomes identical with what I have formerly understood by
this name.
If, finally, we put
1
LB OQ — 0 rat . . . . . . . ° (7)
k? = = w', , ku, =w,, Bs Sy oP tN
these latter quantities being considered as the components of a new
vector wu, the equations take the following form:
“rat wu’, ' ‘
die Sel ee 5 at) == 0;
ty
t! { ! 1 dd’ ’ ! Q
ro —— ——— oO ul - “ ° . é e
) c or . ( )
1 oh’
i
ie c Ot
1 Ul ' Ul t 2 Ww Lj !
ie Fb Er. : (u,h.— wh, +P. = (u', 0, + u’. d',),
2 2 1 > ; Bw
te Gln nis) lb, ee
x k > k c h c? ; ,
f i? 8g P 1 ( ! f ' ! [ ! ) P w ' db!
2 ES SS Ss i iil lid | ee TS
Zz p Dx + I ; Wa Dy y Ya Bios uu; 0 -
The meaning of the symbols div’ and rot’ in (9) is similar to that
of dw and rot in (2); only, the differentations with respect to 7, y, 2
are to be replaced by the corresponding ones with respect tor’, y’, 2’.
§ 5. The equations (9) lead to the conclusion that the vectors
db’ and §' may be represented by means of a scalar potential g’ and
a vector potential a’. These potentials satisfy the equations ')
a 1 0%’
A —p — ba. ia ed QO, . ° . . . . (11)
t a’ 1
| edt WORE aa =e ay ae ee re (12)
and in terms of them 9’ and §' are given by
1) M. E., §§ 4 and 10,
( 814 )
] any ‘are uw ron
= — = de grad lags arad Qay + . . . (15)
c Of : ty
bh’ = rot' a’, = ‘ . . - ° F (14)
g* 0? 0?
The symbol Z' is an abbreviation for .—~ +4- and grad'g’
+- .
On”? On"? © O02"?
Og! dg’ Og’
denotes a vector whose components are coy re
Ow Oy’ Oz
. The expression
grad a, has a similar meaning.
In order to obtain the solution of (11) and (12) in a simple form,
we may take ww, 4,2) as the coordinates of a point 7” in a space
S’, and aseribe to this point, for each value of ¢, the values of
Q,u.g.a, belonging to the corresponding point P (x, 7, 2) of the
electromagnetic system. For a definite value / of the fourth independent
variable, the potentials g’ and a’ in the point 7? of the system or in
the corresponding point 2’ of the space S', are given by ')
1 xi. 4
g=— (Sas. . ois eit
1 pond Pee |
ee [Fas > a
Axe r
/
Here dS’ is an element of the space S', 7’ its distance from
’ and the vector
/
ge’ uw’, such as they are in the element dS’, for the value ¢’ —— of
c
and the brackets serve to denote the quantity @
the fourth independent variable.
Instead of (15) and (16) we may also write, taking into account
(4) and (7),
ee eo
v= | iS... | 4
dn r
a eT es
gf st oe a AL ed
Ame x”
the integrations now extending over the electromagnetic system itself.
It should be kept in mind that in these formulae +’ does not denote
the distance between the element ZS and the point (x,y, 2) for which
the calculation is to be performed. If the element lies at the point
(v,, Y,,2,), We must take
de (w—wa,)? + (y —y,)? -+ (e- =2,)":
It is also to be remembered that, if we wish to determine yg’ and
1) M. E., §§ 5 and 10.
( 815 )
a’ for the instant, at which the local time in P is ¢’, we must take
0 and ow’, such as they are in the element @S at the instant at
.
which the loeal time of that element is / — —
c
§ 6. It will suffice for our purpose to consider two special cases.
The first is that of an electrostatic system, i, e. a system having
no other motion but the translation with the velocity 7. In this case
wu’ = 0, and therefore, by (12), a’ = 0. Also, ¢’ is independent of ¢’,
so that the equations (11), (15) and (14) reduce to
A'p =— 0; | (19)
> —— grad. ¢g', f' — 0. \
After having determined the vector 0’ by means of these equations,
we know also the electric force acting on electrons that belong to
the system. For these the formulae (10) become, since u’ = 0,
iy 2
= = I= d', fy —— k d'y, fz — a ee . . . . . (20)
The result may be put in a simple form if we compare the moving
system S with which we are concerned, to another electrostatic
system 2’ which remains at rest and into which > is changed, if
the dimensions parallel to the axis of « are multiplied by 4/, and
the dimensions which have the direction of 7 or that of z, by /,
a deformation for which (4/,/,/) is an appropriate symbol. In this
new system, which we may suppose to be placed in the above
mentioned space S$’, we shall give to the density the value 9’,
determined by (7), so that the charges of corresponding elements of
volume and of corresponding electrons are the same in + and &".
Then we shall obtain the forces acting on the electrons of the moving
system 2, if we first determine the corresponding forces in ", and
next multiply their components in the direction of the axis of . by
2
P, and their components perpendicular to that axis by a This is
conveniently expressed by the formula
7 - I ~ a
B=(% py a ie ad eee
It is further to be remarked that, after having found »d’ by (19),
we can easily calculate the electromagnetic momentum in the moving
system, or rather its component in the direction of the motion.
Indeed, the formula
( 816 )
OM f
6= ftr.o)as
shows that
4 eS'¢
ee | (d, hb: — d- h,) dS
=== (
Therefore, by (6), since h! =
kl
= | (bd, * +p.")dS./. (22
2
‘
kltw fC.
oS. = | (d,7 + d-") dS:
§ 7. Our second special case is that of a particle having an elee-
tric moment, i. e. a small space JS, with a total charge fe dS =k
7
but with such a distribution of density, that the integrals fe wdS8,
4
fe yd 8, fe S have values differing from 0.
‘ e
Let X,y,z be the coordinates, taken relatively to a fixed point A
of the particle, which may be called its centre, and let the electric
moment be defined as a veetor » whose components are
.
Pz = | oxdS, py =r oy dS, i. = | ozds.... . ieee
d vps << d i i d As
F — Eh Ol, ae, = Py =) 04, 28, i =— [e wdS . (ea
dt . ‘e dt et dt -
Of course, if X, y, Z are treated as infinitely small, uy, uy, we must
he so likewise. We shall neglect squares and products of these six
quantities.
We shall now apply the equation (17) to the determination of
the sealar potential g’ for an exterior point P (7, y, 2), at finite distance
from the polarized particle, and for the instant at which the local
time of this point has some definite value ¢. In doing so, we shall
give the symbol |g], which, in (17), relates to the instant at which
'
,
‘| . . . . . . . .
the local time in dS is ¢ ,aslightly different meaning. Distinguishing
z
by 7’, the value of 7 for the centre A, we shall understand by ,@|
the value of the density existing in the element dS at the point
r
(x, Y, Z), at the instant ¢, at which the local time of A is ’——.
c
It may be seen from (5) that this instant precedes that for which
we have to take the numerator in (17) by
j w kr j—r' : 8 oe dr KS Or" Or’
2 ——___. — #? _-x-+——( x — — + Z—
€ eh C Ps c Ow ay. 0
units of time. In this last expression we may put for the differen-
tial coefficients their values at the point AL.
In (17) we have now to replace [oe] by
do et Or' 07" dr’ \ [ 00 pa
lel +H ox 2] 45 = (xx He agen ae =) eI Nee
do ' : ist re
where 7 relates again to the time ¢,. Now, the value of ¢ for
which the caleulations are to be performed having been chosen, this
time ¢, will be a function of the coordinates «, y,z of the exterior
point P. The value of {@] will therefore depend on these coordinates
in such a way that
d[o] k 1 Or' [ 0g
i .. Wimoe Ei oe
by which (25) becomes
,w. [90 d[Q] d[e] d[Q]
[el +e ex | 32] — (x Ou y Oy ge Oz
Again, if eee we understand by 7 what has above been
1
called 7’,, the factor — must be replaced by
7
t
,
1 ore l a KI 07 1
iar os ~v5(5 he eye
so that after all, in the integral (17), the element d Sis multiplied by
Lo| = [| 0xle] 9Oyle] 9 Zl]
7" Ot Ox Oy 7 dz 7'
This is simpler than the primitive form, because neither 7’, nor
the time for which the quantities enc!osed in brackets are to be
BY }2 w
taken, depend on w, ¥, 2. Using (23) and remembering that fi odS=0
we get
apt, [me] L peledy 2d, atop
cra 4ac*r'| Ot 4a lov r' Oy x
a formula in which all the enclosed quantities are to s a for
the imstant at which the local time of the centre of the particle is
'
PP
pe SRD
€
We shall conclude these calculations by introducing a new vector
yp, whose components are
o4
Proceedings Royal Acad, Amsterdam. Vol, VL.
( 818 )
Pr = klpr, Py —l py, 2 lpe, . . « - (26)
passing at the same time to .’,7/’,2',/ as independent variables. The
final result is
pf a Bal eed Gel Pal ee
— Ager’ ot Aa lode’ -' oy dz’ (7
As to the formula (18) for the vector potential, its transformation
is less complicate, because it contains the infinitely small vector w’.
Having regard to (8), (24), (26) and (5), I find
i Opal
4Aacr Ot
The field produced by the polarized particle is now wholly deter-
mined. The formula (13) leads to
ee eee eee oR lem eee! s
Sis 4axeot? + 1 4 wee | de’ r a a dz’ or!
and the vector §' is given by (14). We may further use the equations
(20), instead of the original formulae (10‘, if we wish to consider
the forces exerted by the polarized particle on a similar one placed
at some distance. Indeed, in the second particle, as well as in the
first, the velocities ' may be held to be infinitely small.
It is to be remarked that the formulae for a system without
translation are implied in what precedes. For such a system the
quantities with accents become identical to the corresponding ones
without accents; also 4;=1 and /—1. The components of (27) are
at the same time those of the electric force which is exerted by one
polarized particle on another.
'
=
(27)
§ 8. Thus far we have only used the fundamental equations
without any new assumptions. I shall now suppose that the electrons,
which I take to be spheres of radius R in the state of rest, have
their dimensions changed by the effect of a translation, the dimensions
in the direction of motion becoming kl times and those in perpen-
dicular directions / times smaller.
jer ee
In this deformation, which may be represented by G —, 7,
kh tae
each element of volume is understood to preserve its charge.
Our assumption amounts to saying that in an electrostatic system
~, moving with a velocity aw, all electrons are flattened ellipsoids
with their smaller axes in the direction of motion. If now, in order
to apply the theorem of § 6, we subject the system to the defor-
mation (A/,/,/), we shall have again spherical electrons of radius 7,
( 819 )
Hence, if we alter the relative position of the centres of the electrons
in by applying the deformation (4/, /, /), and if, in the points
thus obtained, we place the centres of electrons that remain at rest,
we shall get a system, identical to the imaginary system ’, of
which we have spoken in § 6. The forees in this system and those
in + will bear to each other the relation expressed by (21).
In the second place I shall suppose that the forces between unchar-
ged particles, as well as those between such particles and electrons, are
influenced by a translation in quite the same way as the electric forces
in an electrostatic system. In other terms, whatever be the nature of
the particles composing a ponderable body, so long as they do not
move relatively to each other, we shall have between the forces
acting in a system (2") without, and the same system () with a
translation, the relation specified in (21), if, as regards the relative
position of the particles, =’ is got from Y by the deformation (A/, /, /),
Lh
or = from ' by the deformation (F 7? +)
We see by this that, as soon as the resulting force is 0 for a
particle in =’, the same must be true for the corresponding particle
in +. Consequently, if, neglecting the effects of molecular motion,
we suppose each particle of a solid body to be in equilibrium under
the action of the attractions and repulsions exerted by its neighbours,
and if we take for granted that there is but one configuration of
equilibrium, we may draw the conclusion that the system ’, if the
velocity ™ is imparted to it, will of self change into the system
+. In other terms, the translation will produce the deformation
ptt
Moe by:
The case of molecular motion will be considered in § 12.
It will easily be seen that the hypothesis that has formerly been
made in connexion with MicHELson’s experiment, is implied in what
has now been said. However, the present hypothesis is more general
because the only limitation imposed on the motion is that its velocity’
be smaller than that of light.
§ 9. We are now in a position to calculate the electromagnetic
momentum of a single electron. For simplicity’s sake I shall suppose
the charge ¢ to be uniformly distributed over the surface, so long
as the electron remains at rest. Then, a distribution of the same
kind will exist in the system SS’ with which we are concerned in
the last integral of (22). Hence
54*
and
e
oS. = PC hs lw.
It must be observed that the product 4/ is a function of w and
that, for reasons of symmetry, the vector © has the direction of the
translation. In general, representing by w the velocity of this motion,
we have the vector equation
e?
§ = a tt ree Aree le
62acR oem
Now, every change in the motion of a system will entail a cor-
responding change in the electromagnetic momentum and will there-
fore require a certain force, which is given in direction and mag-
nitude by
dS
aS ee, ee
we a Ki
Strictly speaking, the formula (28) may only be applied in the
ease of a uniform rectilinear translation. On account of this circum-
stance — though (29) is always true — the theory of rapidly varying
motions of an electron becomes very complicated, the more so, because
the hypothesis of § 8 would imply that the direction and amount of
the deformation are continually changing. It is even hardly probable
that the form of the electron will be determined solely by the
velocity existing at the moment considered.
Nevertheless, provided the changes in the state of motion be suf-
ficiently slow, we shall get a satisfactory approximation by using (28)
at every instant. The application of (29) to such a quasi-stationary
translation, as it has been called by ABRAHAM’), is a very simple
matter. Let, at a certain instant, j, be the acceleration in the direction
of the path, and j, the acceleration perpendicular to it. Then the force
® will consist of two components, having the directions of these acce-
lerations and which are given by
% = ta: ond ee a
if
2 r . 5 2
a ta sl ee and m, = oe ees + - Spee
bach de back
Hence, in phenomena in which there is an acceleration in the
') Apranam, Wied. Ann, 10 (1903), p. 100,
( 821 )
direction of motion, the electron behaves as if it had a mass m,, in
those in which the acceleration is normal to the path, as if the
mass were m,. These quantities m, and m, may therefore properly
be called the “longitudinal” and “transverse” electromagnetic masses
of the electron. I shall suppose that there ts no other, no “true? or
“material” mass.
mw?
Since & and / differ from unity by quantities of the order —, we
9?
c?
find for very small velocities
e?
m, = mM, = broth
This is the mass with which we are concerned, if there are small
vibratory motions of the electrons in a system without translation.
If, on the contrary, motions of this kind are going on in a body
moving with the velocity w in the direction of the axis of z, we
shall have to reckon with the mass m,, as given by (30), if we con-
sider the vibrations parallel to that axis, and with the mass m,, if
we treat of those that are parallel to OY or OZ. Therefore, in
short terms, referring by the index + to a moving system and by
=' to one that remains at rest,
mS) = (ent) (2), ee en)
aU
§ 10. We can now proceed to examine the influence of the Earth’s
motion on optical phenomena in a system of transparent bodies. In
discussing this problem we shall fix our attention on the variable
electric moments in the particles or “atoms” of the ~ystem. To these
moments we may apply what has been said in § 7. For the sake
of simplicity we shall suppose that, in each particle, the charge is
concentrated in a certain number of separate electrons, and that the
“elastic” forces that act on one of these and, conjointly with the
electric forces, determine its motion, have their origin within the
bounds of the same atom.
I shall show that, if we start from any given state of motion if
a system without translation, we may deduce from it a corresponding
state that can exist in the same system after a translation has been
imparted to it, the kind of correspondence being as specified in
what follows.
a. Let A’,, A’,, A’,, ete. be the centres of the particles in
the system without translation (2'); neglecting molecular motions
we shall take these points to remain at rest. The system of points.
( 822 )
A,, A,, Ay, ete., formed by the centres of the particles in the moving
system 2, is obtained from A’, A’,, A’, ete. by means of a deformation
Loe mer
& qT ~} According to what has been said in § 8, the centres
will of themselves take these positions A’, A’,, A’,, ete. if originally,
before there was a translation, they occupied the positions ,, .A,, A,, ete.
We may conceive any point /” in the space of the system +" to
be deplaced by the above deformation, so that a definite point ? of
corresponds to it. For two corresponding points /” and P we shall
define corresponding instants, the one belonging to /”, the other to
P, by stating that the true time at the first instant is equal to the
local time, as determined by (5) for the point /, at the second instant.
3y corresponding times for two corresponding particles we shall
understand times that may be said to correspond, if we fix our
attention on the centres A’ and A of these particles.
}. As regards the interior state of the atoms, we shall assume that
the configuration of a particle A in = at a certain time may be
Poet
derived by means of the deformation ( 7 7) from the confi-
guration of the corresponding particle in ”’, such as it is at the
corresponding instant. In so far as this assumption relates to the form
of the electrons themselves, it is implied in the first hypothesis of § 8.
Obviously, if we start from a state really existing in the system
~’, we have now completely defined a state of the moving system +.
The question remains however, whether this state will likewise be
a possible one.
In order to judge this, we may remark in the first place that
the electric moments which we have supposed to exist in the moving
system and which we shall denote by », will be certain definite
functions of the coordinates 7, y, 2 of the centres A of the particles,
or, as we shall say, of the coordinates of the particles themselves,
and of the time ¢. The equations which express the relations between
y on one hand and «, y, z, ¢ on the other, may be replaced by other
equations, containing the vectors p’ defined by (26) and the quantities
w’,y’,2’,t’ detined by (4) and (5). Now, by the above assumptions
a and #, if in a particle A of the moving system, whose coordinates
are ©, y, 2, we find an electric moment »p at the time ¢, or at the
local time ¢’, the vector p’ given by (26) will be the moment which
exists in the other system at the true time ¢’ in a particle whose
coordinates are x’, y’, 2’. It appears in this way that the equations
between p’, 2’, y’, 2’, ¢ are the same for both systems, the diffe-
rence being only this, that for the system +’ without translation
( 823 )
these symbols indieate the moment, the coordinates and the true time,
Whereas their meaning is different for the moving system, p’, 0, y/, 27, U
being here related to the moment »p, the coordinates wv, y, 2 and the
general time ¢ in the manner expressed by (26), (4) and (5).
It has already been stated that the equation (27) applies to both
systems. The vector d’ will therefore be the same in >’ and X,
provided we always compare corresponding places and times. How-
ever, this vector has not the same meaning in the two cases. In +’
it represents the electric force, in it is related to this force in
the way expressed by (20). We may therefore conclude that the
electric forces acting, in + and in Y’, on corresponding particles at
corresponding instants, bear to each other the relation determined by
(21). In virtue of our assumption 4, taken in connexion with the second
hypothesis of § 8, the same relation will exist between the “elastic”
forces; consequently, the formula (21) may also be regarded as
indicating the relation between the total forces, acting on corresponding
electrons, at corresponding instants.
It is clear that the state we have ele to exist in the moving
system will really be possible if, in + and 2’, the products of the
mass m and the acceleration of an electron are to each other in the
same relation as the forces, i.e. if
[es g2
mj (2) == (". rs “| UL j (=’) ° ° ° ° ° (52)
Now, we have for tbe accelerations
ea ara ice -
Di ee (=), - 6 2 + « « (83)
as may be deduced from (4) and (5), and combining this with (32),
we find for the masses
m (=) = (Kl, kl, hl) m €')
If this is compared to (81), it appears that, whatever be the value
of /, the condition is always satisfied, as regards the masses with
Which we have to reckon when we consider vibrations perpen-
dicular to the translation. The only condition we have to impose on
/ is therefore
d(klu
(lw) oe
dw
But, on account of (3),
d(kw)
dw
— and
) are certain functions of the time, then the same system after it
has been put in motion (and thereby deformed) can be the seat of
a state of motion in which, at the corresponding place, the com-
ponents of p’, d’ and b’ are the same functions of the local time.
There is one point which requires further consideration. The values
of the masses m, and m, having been deduced from the theory of
quasi-stationary motion, the question arises, whether we are justified
in reckoning with them in the case of the rapid vibrations of light.
Now it is found on closer examination that the motion of an electron
may be treated as quasi-stationary if it changes very little during
the time a light-wave takes to travel over a distance equal to the
diameter. This condition is fulfilled in optical phenomena, because
the diameter of an electron is extremely small in comparison with
the wave-length.
§ 11. It is easily seen that the proposed theory can account for a
large number of facts.
Let us take in the first place the case of a system without trans-
lation, in some parts of which we have continually »=0, >= 0,
6=0. Then, in the corresponding state for the moving system, we
shall have in corresponding parts (or, as we may say, in the same
parts of the deformed system) p' = 0, 0’ = 0, l’=0. These equations
implying » = 0, }=0, § =0, as is seen by (26) and (6), it appears
that those parts which are dark while the system is at rest, will remain
so after it has beem put in motion. [ft will therefore be impossible
to detect an influence of the Earth’s motion on any optical experi-
ment, made with a terrestrial source of light, in which the geome-
trical distribution of light and darkness is observed. Many experi-
ments on interference and diffraction belong to this class.
In the second place, if in two points of a system, rays of light
of the same state of polarization are propagated in the same direction,
the ratio between the amplitudes in these points may be shown not
to be altered by a translation. The latter remark applies to those
experiments in which the intensities in adjacent parts of the field
of view are compared.
The above conclusions confirm the vesults | have formerly obtained
by a similar train of reasoning, in which however the terms of the
second order were neglected. They also contain an explanation of
MICHELSON’s negative result, more general and of somewhat different
form than the one previously given, and they show why Ray rien
and Brace could find no signs of double refraction produced by
the motion of the Earth.
As to the experiments of Trouton and Nosiz, their negative result
becomes at once clear, if we admit the hypotheses of § 8. It may be
inferred from these and from our last assumption (§ 10) that the only
effect of the translation must have been a contraction of the whole
system of electrons and other particles constituting the charged
condenser and the beam and thread of the torsion-balanee. Such a
contraction does not give rise to a sensible change of direction.
It need hardly be said that the present theory is put forward with
all due reserve. Though it seems to me that it can account for all
well established facts, it leads to some consequences that cannot as
yet be put to the test of experiment. One of these is that the result
of MicHELSON’s experiment must remain negative, if the interfering
rays of light are made to travel through some ponderable transparent
body.
Our assumption about the contraction of the electrons cannot in
itself be pronounced to be either plausible or inadmissible. What
we know about the nature of electrons is very little and the only
means of pushing our way farther will be to test such hypotheses
as | have here made. Of course, there will be difficulties, e.g. as soon
as we come to consider the rotation of electrons. Perhaps we shall
have to suppose that in those phenomena in which, if there is no
translation, spherical electrons rotate about a diameter, the points of
the electrons in the moving system will describe elliptic paths,
corresponding, in the manner specified in § 10, to the cireular paths
described in the other case.
§ 12. It remains to say some words about molecular motion. We
may conceive that bodies in which this has a sensible influence or
even predominates, undergo the same deformation as the systems of
particles of constant relative position of which alone we have spoken
till now. Indeed, in two systems of molecules +’ and Y, the first
without and the second with a translation, we may imagine molecular
motions corresponding to each other in such a way that, ifa particle
in X has a certain position at a definite instant, a particle in Y
occupies at the corresponding instant the corresponding position. This
being assumed, we may use the reiation (83) between the accelera-
tions in all those cases in which the velocity of molecular motion
is very small as compared to w. In these cases the molecular forces
may be taken to be determined by the relative positions, indepen-
dently of the velocities of molecular motion. If, finally, we suppose
these forces to be limited to such small distances that, for particles
acting on each other, the difference of local times may be neglected,
one of the particles, together with those which lie in its sphere of
autraction or repulsion, will form a system which undergoes the
often mentioned deformation. In virtue of the second hypothesis
of § 8 we may therefore apply to the resulting molecular force
acting on a particle, the equation (21). Consequently, the proper
relation between the forces and the accelerations will exist in the two
cases, if we suppose that the masses of all particles are influenced
hy a translation to the same degree as the electromagnetie masses of
the electrons.
§ 13. The values (80) which I have found for the longitudinal and
transverse masses of an electron, expressed in terms of its velocity, are
not the same as those that have been formerly obtained by ABRAHAM.
The ground for this difference is solely to be sought in the cireum-
stance that, in his theory, the electrons are treated as spheres of
invariable dimensions. Now, as regards the transverse mass, the
results of ABRAHAM have been confirmed in a most remarkable way
by IKXAUPMANN’s measurements of the deflexion of radium-rays in
electric and magnetic fields. Therefore, if there is not to be a most
serious objection to the theory I have now proposed, it must be
possible to show that those measurements agree with my values
nearly as well as with those of ABRAHAM.
1 shall begin by discussing two of the series of measurements
( 827 )
published by KaurMaxn') in 1902. From each series he has deduced
two quantities y and 6, the “reduced” electric and magnetic deflexions,
w
which are related as follows to the ratio @=—:
c
C U7] .
Bah, WO= Ee (34)
Here y (8) is such a function, that the transverse mass is given by
3 e ~,
m,=— . —— w(8),- - « «» « » « (89)
4° 62c?R
whereas 4, ank /, are constant in each series.
It appears from the second of the formulae (80) that my theory
leads likewise to an equation of the form (55); only ABRAHAM’s
function yw (8) must be replaced by
ap ee
a es Bp):
vo
Hence, my theory requires that, if we substitute this value for
yw (8) in (34), these equations shall still hold. Of course, in seeking
io obtain a good agreement, we shall be justified in giving to /, and 4,
other values than those of KAUrMANN, and in taking for every measure-
ment a proper value of the velocity w, or of the ratio B. Writing
sk,, —k’, and #' for the new values, we may put (34) in the form
1? 4 2 «
PS ak S MD os Bk Fe
7
and
bes ?
(he 6°) ae :
KAUFMANN has tested his equations by choosing for /, such a value
that, calculating 8 and 4, by means of (34), he got values for this
latter number that remained constant in each series as well as might
be. This constancy was the proof of a sufficient agreement.
I have followed a similar method, using however some of the
numbers calculated by Katrmany. I have computed for éach measure-
meut the value of the expression
Hel = By PG) Hy eo FF Oe
that may be got from (387) combined with the second of the equations
(84). The values of w(3) and £, have been taken from KavrMany’s
tables and for 3’ I have substituted the value he has found for 8,
multiplied by s, the latter coefficient being chosen with a view to
se Sola
') Kaurmann, Physik. Zeitschr. 4 (1902), p. 58.
( 828 )
obtaining a good constaney of (88). The results are contained in the
following tables, corresponding to the tables [1] and LV in KavrmMann’s
paper.
III. s = 0,933.
6 v(B) m4 B' kg!
0.851 2.447 1.721 0.794 | 2.246
0.766 1.860 | 1.736 : 0.715 | 2.958
0.727 1.78 | 41.73 | 0.678 | 9.956
0.6615 1.66 | Lidar FSO Ot | 2 256
0.6075 4.595 | 4.655 | 0.567 24175
IV. s = 0,954.
<= —— ———
B (6) | ke B' ke!
ee oe oe =" lesneees — = eS
0,963 Sea | 8 12 0.919 10.36
0.949 2.86 | 71.99 | 0.905 9.70
0.933 2.73 | 7.46 | 0.800 | 9.98
0.883 2.31 | 8.32 | 0.842 | 410.36
0.860 2 A995 | 8.09 0.820 | 10.15
0.830 2.06 8.413 0.792 | 10.23
0.801 1.96 8.13 0.764 10.98
0.777 1289 8.04 0.744 | 10.20
0.752 4-83... 11-8302 Oia 10.22
0.732 4.7% | 7.97 0.698 | 40.48
The constancy of 2’, is seen to come out no less satisfactory than
that of /,, the more so as in each case the value of s has been
determined by means of only two measurements. The coefficient has
been so chosen that for these two observations, which were in Table
Ill the first and the last but one, and in Table IV the first and the
last, the values of 4’, should be proportional to those of /,.
I shall next consider two series from a later publication by KAUFMANN’),
which have been caleulated by Renew?) by means of the method of
1) Kavemany, GOtl. Nachr. Math. phys. KL, 1903, p. 90.
2) Ruxce, ibidem, p. 326.
( 829 )
least squares, the coefficients 4, and /, having been determined in
such a way, that the values of 4, calculated, for each observed §,
from KAvFMANN’s equations (34), agree as closely as may be with
the observed values of 7.
I have determined by the same condition, likewise using the method
of least squares, the constants @ and 4 in the formula
Ui == as? — bo! ;
which may be deduced from my equations (56) and (37). Knowing
a and 4, I find B for each measurement by means of the relation
C
B=Va-.
y
For two plates on which KavurmMann had measured the electric and
magnetic deflexions, the results are as follows, the deflexions being
given in centimeters.
I have not found time for calculating the other tables in KAUFMANN’S
paper. As they begin, like the table for Plate 15, with a rather
large negative difference between the values of 4 which have been
deduced from the observations and calculated by Rung, we may
expect a satisfactory agreement with my formulae.
§ 14. I take this opportunity for mentioning an experiment that
Plate N°. 15. a= 0,06489, 4 = 0,3039.
| D | B
: ¢ IGateulated | - | Calculated | | Calculated by
Observed. | by R. | Diff. | by a | Dit: 4} = : ‘
| | | | om need
0.1495 | 0.0388 | 0.0404 | — 46 | 0.0400 | — 419 | 0.987 | 0.951
0.199 | 0.0548 | 00550 | — 2] 0.0552 | ==) Bl VG. 96% | 0.918
0.2475 | 0.0716 | 0.0710 | + 6| 0.075 | + 1| 0.930 | 0.881
0.296 0.0806 | 0.0887 | + 9| 0.085 | + 1!/ 0.899 | 0.842
0.3435 | 0.1080 | 0.1081 | a5) Af | 0.1090 | —10| 0.3847 | 0.803
0.391 | 0.1290 | 0.1297 pos 7 | 0.1305 | — 15 0.804 | 0.763
0.437 | 0.1524 | 0.4597 | — 3 0.4532 | — 8| 0.763 | 0.727
0.4825 | 0.1788 | 0.4777 | +41] 0.4777 | +44] 0.72% | 0.692
0 | | 0.660
5963 | 0.9033 | 0.9039 | — 61 0.9033 | 0} 0.688
( 830°)
Plate N°. 19. a = 0,05867, 6 = 0,2591.
% | B
; |
; Ghsecve: ee Dirt. oe Dit. | ae Ss
ee ea
0.1495 0.040% 0 0388 + 46 0.0379 +25 | 0.990 | 0.954
0.199 0.0529 | 0.0597 | 4+ 2) 0.052 | 47 | 0.969 | 0.998
0.247 | 0.0678 | 0067 | + 3] 0.0674 | +4 | 0.939 | 0.888
| |
0.296 | 0.0834 | 0.082 | — 8} 0.084% | —140 | 0.902 | 0.849
0.3435 | 04019 | 0.1022 | — 3| 0.1096 | —7 | 0.862 | 0.811
0.391 0.1219 | 0.192 | — 3! 0.199% | —7 | 0992 | 0.773
0.437 | 0.1499 | 0.1484 | — 5] 0.4437 | —8 | 0.782 | 0.736
0.4825 0 1660 0.1665 — 5 0.1664 | —"4 | 0.744 | 0.702
0.5265 0.1916 0.1906 = $10, 0.192 | 444 | 0.709 | 0.671
has been made by Trovuton’) at the suggestion of Firz Grra.p, and
in which it was tried to observe the existence of a sudden impulse
acting on a condenser at the moment of charging or discharging;
for this purpose the condenser was suspended by a torsion-balance,
with ifs plates parallel to the Earth’s motion. For forming an
estimate of the effect that may be expected, it will suffice to consider
a condenser with aether as dielectricum. Now, if the apparatus is
charged, there will be (§ 1) an electromagnetic momentum
2U
>
6} —— wD.
c
Terms of the third and higher orders are here neglected). This
momentum being produced at the moment of charging, and dis-
appearing at that of discharging, the condenser must experience in
the first case an impulse — @ and in the second an impulse + 6.
However Trovuron has not been able to observe these jerks.
| believe it may be shown (though his calculations have led him
fo a different conclusion) that the sensibility of the apparatus was
far from sufficient for the object Trovuron had in view.
Representing, as before, by Ll’ the energy of the charged condenser
') Trovrox, Dublin Roy, Sec. Trans. (2) 7 (1902), p. 379 (This paper may also
be found in The scientific writings of Firz Geran, edited by Larmor, Dublin and
London 1902, p. 557).
( 831 )
in the state of rest, and by (’-+ UL” the energy in the state of motion,
we have by the formulae of this paper, up to the terms of the
second order,
an. expression, agreeing in order of magnitude with the value used
by Trocron for estimating the effect.
vr
The intensity of the sudden jerk or impulse will therefore be — .
w
Now, supposing the apparatus to be initially at rest, we may
compare the deflexion «, produced by this impulse, to the deflexion
a which may be given to the torsion-balance by means of a constant
couple A, acting during half the vibration time. We may also
consider the case in which a swinging motion has already been set
up; then the impulse, applied at the moment in which the apparatus
passes through the position of equilibrium, will alter the amplitude
by a certain amount ? and a similar effect 3’ may be caused by
letting the couple A’ act during the swing from one extreme position
to the other. Let 7 be the period of swinging and / the distance
from the condenser to the thread of the torsion-balance. Then it is
easily found that
e ¢ <0"
ene KT w
According to TrovTon’s statements (7’ amounted to one or two
ergs, and the smallest couple by which a sensible deflexion could be
produced was estimated at 7,5 C.G.S.-units. If we substitute this
value for A and take into account that the velocity of the Earth’s
motion is 3 x 10° ¢.M. per sec., we immediately see that (39) must
have been a very small fraction.
(39)
Mathematics. — “Uhservation on the paper cominunicated on
Febr. 27% 1904 by Mr. Brocwer: ”On a decomposition of the
continuous motion about a point O of S, into two continuous
motions about O of S,'s.” By Dr. E. Janyxe. (Communicated
by Prof. D. J. Kortewese.)
The above mentioned paper is connected with investigations of
Frerp. Caspary and with works published by me in the years
1896—1901. Mr. Brouwer not referring to these, I take the liberty
to remark the following: Problems of the theory of the thetafune-
tions on one hand and of mechanics on the other hand have led
( 832 )
me to relate the rotation in S, to two rotations in S,. The relations
between the elements of the four-dimensional rotation and the elements
of the two threedimensional rotations belonging to it have been
explicidy pointed out by me in ‘“Sitzungsberichte der Berliner
Akademie” of July 30% 1896 and in the “Journal fiir die reine
und angewandte Mathematik” Vol. 118, p. 215, 1897. I have
particularly found that the components of the velocity of the first
rotation are easily deduced from the components of the velocity of
the two others (compare also my lecture at the ‘“Naturforscher Ver-
sammlung’” at Hamburg 1901: “On rotations in fourdimensional
spaces,” (Ueber Drehungen im vierdimensionalen Raum).
Mr. Brouwer arrives in his paper also at these results though in
a different way, namely geometrically, whilst I have worked alge-
braically. Mr. Brouwer arrives at a decomposition (“Zerlegung”) of
the fourdimensional rotation into two threedimensional ones, whilst
I use the expression coordination (“Zauordnung”).
Berlin, March 28%, 1904.
Mathematics. — “Alyebraic deduction of the decomposability of
the continuous motion about a fixed point of S, into those of
two S,s’. By Mr. L. E. J. Brovwrr. (Communicated by
Prof. KorTEWwEs).
As the position of S, is determined with respect to a fixed system
of axes by siv independent variables and that of S, with respect to
a fixed system of axes by three independent variables we understand
at once that in an infinite number of ways two S, motions can be
coordinated to an S, motion, so that position and velocities of S, are
determined by position and velocities of the two S,’s. On such a
coordination Mr. JAHNKE has been engaged in the papers mentioned
above and has deduced the relations between positions and veiocities
of S, and the two S,’s. Interpreted geometrically his coordination
amounts to the following: Let us suppose in S, a fixed system of
axes X, X, X, X,, and a movable one Y, Y, Y, Y,; let us con-
sider the part equiangular to the right of the double rotation, which
transfers Y, Y, Y, X, into Y, Y, Y, Y,; let us add to it an equal
equiangular double rotation to the left (namely equal with respect to
the system of axes Y, VY, NX, X,; only with respect to a definite
2 1
1
system of axes can we call an equiangular double rotation to the
right and one to the left equal); the resulting rotation becomes a single
( 838 )
rotation parallel to the space Y, NY, .Y, which would transfer the
system of axes .Y, YY, Y, into an other 7, 7, Z,. Thus to each
position }” with respect to XY, Y, Y, , answers a position 7 with
respect to .Y, Y, X,, and by interchanging right and left, in an
analogous manner a position (7 with respect to Y, , Y,; and we
may consider the positions 7 and // as coordinated to the position )’”.
Not immediately to be seen are the two following properties of
the S, motion geometrically deduced in what was communicated in
the February meeting.
Ist. The continuous motion of S, can be decomposed, that is:
independent of the choice of a system of axes two definite three-
foldly infinite motion groups exist in SS, in such a way that an
arbitrary motion can be composed out of two motions each of which
belongs to one of the groups mentioned.
Qed. The continuous motion of S, can be decomposed into two
S,; motions, that is, two twodimensional manifoldnesses (namely
those of the systems of planes equiangular to the right and to
the left) exist in S, in such a way that each of the motion
groups mentioned transforms the elements of one of them into
each other and leaves the other unchanged; to which further-
more we can allow twodimensional Euclidean stars to answer in
such a way that to congruent combinations in one of the manifold-
nesses congruent combinations of the Euclidean stars correspond,
that to the corresponding motion group of S, answers the motion group
of the Euclidean star movable as a solid and that to congruent
combinations in the motion group of S, answer congruent combinations
in the motion group of the Euclidean star movable as a solid: reason
why we may call the two twodimensional manifoldnesses fivodiinen-
sional Euclidean stars and the motion groups of S, transforming them
Euclidean threedimensional motion groups about a piced pout.
We shall now see how we can arrive algebraically at both results.
Mr. JAHNKE takes from Caspary the so called ‘Elementary trans-
formation” (see a.o. Jahresbericht der Deutschen Mathematiker-
Vereiniging XI, 4, 1902, p. 180 and F. Caspary, Zur Theorie der
Thitafunctionen mit zwet Arqumenten, Cretix’s Journal, vol. 94, page
75), which has the property that an arbitrary congruent transformation
of S, can be replaced by two successive elementary transformations.
The name “Elementary rotation” (Elementardrehung) of Mr. JAHNKE
seems to me less fortunate, because it is asymmetric transformation,
not a rotation. The real meaning of the “Elementary transformation’
will be made clear furtheron. For the present we remind the readers
of its determinant type (see Jahresbericht, 1. ¢., page 180).
55
Proceedings Royal Acad, Amsterdam. Vol. VI.
, ake *, a,
1 rr 5 ‘a
~ ae 1 7 3
5; 2 . . . . > (I)
—7, a, 1 Tw,
X, TU, aX, —#,
and we notice that it does not represent a group and does not
possess any threedimensional properties (it does after composition
with itself, compare for instance the theorem of Mr. Janyke, Jahres-
bericht, l. ¢., page 182: “Jede endliche Drehung im &, lasst sich als
eine Zusammensetzung aus einer Elementardrehung im #, mit sich
selbst auffassen’”’’); which operation is for the rest bound to a once
chosen system of axes).
We shall now deduce two different determinant types likewise
determined by a system of cosines of direction %,, 7,, 7,4, which
do represent a group and have threedimensional properties. Those
will be the determinants of equiangular double rotation to the
right and to the left.
Let us solve the a@’s out of the equations (/7) (see Proceedings of
March 19%, 1904, page 721); then we have
PFE, ge — he hp re \
ieee een Chee aetna os. kag) See (a).
berg Es Gy ot a le
a, = 2,8, — *, 8, — x, B, — x, B,
Thus the determinant type of the equiangular double rotation to
the right is
7, NX, —H, = ee
— FH Mi 4 ig 1 |
3 4 1 2
. . -})
a, —, x, , |
ea | et eee 1%,
Directly can be verified that this determinant type forms a group.
Likewise we deduce for the equiangular double rotation to the left
(7, x, 7, %,), transferring the vector (@, @, a, a,) into (@, 8, B, B,), the
relations :
1— — %, 8, — “2, Bs + 1, B, + x, B, |
= Xf; a Be
ee es
re a,—— zB, —2, 8, — 7,8, — 2, 8,
1) “Each finite rotation in S, can be regarded as a composition of an elementary
rotation in S, with itself,”
— SS
i
( 835 )
from which ensues the determinant type for equiangular double
rotation to the left:
—x, —27, a is
1, —%, —2 x |
; : S| Oe eR.
—X, a, —42, on
—a, —7, —2, —2,!
and for this too the property of a group can be verified.
If we call (I’) the determinant type formed by interchange of the
rows and columns of (1), we can remark :
If we reverse the signs in the bottom row of type (ID type (1’)
appears.
If we reverse the signs in the last column of type (III) type (I)
appears.
If we ask ourselves whether each arbitrary congruent transformation
can be replaced by the succession of a transformation (III) and a
transformation (Il) the answer must be affirmative; for we shall have
but to take those transformations (III) and (II) belonging to the
transformations (I) which when successively applied transfer the
given initial position into the given final one. (For those two ways
only the intermediate positions will differ in as far as they will be
each other’s reflection with regard to their _Y,-avxis.)
This is the algebraic proof of 1°.
At the same time it has become evident that the meaning of
the type (I) is an arbitrary equiangular double rotation to the
right preceded by a reflection according to the .Y,-axis (that is the
X,-axis of the initial position) or an arbitrary equiangular double
rotation to the left followed by a reflection according to the X,-axis
(that is the Y,-axis of the final position), and that the meaning of
the type (1) is an arbitrary equiangular double rotation to the right
followed by a reflection according to the Y,-axis or an arbitrary
equiangular double rotation to the left preceded by a reflection according
to the _Y,-axis.
Thus according to a preceding communication made in this meeting
of the Academy (see page 785) it has been proved that the types (I)
and (I') represent the most general symmetric transformation of S,,
of which the determinant type has been simplified only by particular
choice of the system of coordinates.
We shall now give a proof for 2°.
Out of the relations (a) for equiangular double rotation to the
ww ue
20*
( 836 )
right we deduce, representing for shortness’ sake a’, a’, — a’, a’, ete.
by §:, Gic; 6.6 ,— Pip. cle. by zy ee
S93 (% 7 +4 )Xast (WRF Hy sho + (3% — MyM) g— (Ay + Hs Vag
+ (7+ 1) + (Hg — HM a,
§ 5, (41%, — 7H Asst hrs? Vhs: — (5 1 ha +
(23+, % fis Ks4)
§ (7, +20 Nas tH dt (1% 3— 2H ,)(Xe +X.) +
+ (73° fa (AYP Ae Va
—— (0,° 1-7) host I ha (4 + 2%) hed
+ (70, — 7% X12 +Fs5)
Yas ( 2, — 4%) ast Xad— (As +8 hart +H Wat
+ (2,0, +2, 1 )(X1a+Hs4)
& = (27,, +77 )\Xas tis) + (45% — 2,2) Ns +2) —
(0 Py hat (A + haw
from which ensues:
EE (219 2 Hy has thas) + 2( + 5% Ns t+ he)
+ 2(2,%, —9 7X12 +Xs,)
€,,4§.,=2(9,7%,—2%,%,) sth) + (4 4+2,'—2,— 2, Wa Phd tT
Ff 2(2,% +, \ fre + ha4)
E +8, 2(r, 8, 42,2) Hast tr + 2( 5% — 7,2 )Xsr + Xa
+ (9,74 22 — 9 — 2, Vs +h)
= ==, a
Gu — Sis — X38 — Mis
S51 ae So4 = Xa. — Kas
wae? - par ini Sie
Sie S34 — ais hs4°
So also if we eall 4,, ete. the coefficients of position of a plane
before the equiangular double rotation to the right and wy, etc. the
coefficients of position after it:
4,44, (22 +97 — 2° — 7,’ )\(Uas tia) + 2(2,%, +20 ,)(%, +b) +
2 (20,0, — 7, )(M, Fils 4)
Ag A, =" (2,2, — 1% ,)(Uas +H) + Fo? — 2 *)(U,, +H)
+ 2( 2077, + EH My Mss)
As A, ,=2(2,7,+7,%,)(U,, +41) + 2(%,%,— 7, %,)(Uy, +H.) +
+(9,° +27 —2,?—%,’)( 1. Has)
Ass ae Ay, = Uss — Ui
As — 4eg = Msi — Mag
A, — Ay = Bye — Bee
(-837))
In an analogous way we deduce from the relations (4) for an
equiangular double rotation to the left the following relations between
the coefficients of position of a plane before and after the rotation:
Ass + fig = Mas H+ bag
As, + As, = Ur + Mas
Ais + Aa, = Ua + Ua
dys 4, $82 — Hr,’ — 2," (Us — By.) + 2( F431 — Ua) +
+ 2(% 7, — 7% ,)(U,.—Us,)
Ay 4, = 2(%, 1, — 1% V3 — Hy 4) ih (2? 4 72 —1,°— 2's. — ba) +
+ 2(27,77, +, %,)(U,.—Us,)
4, a— 45,2 (7,0, + ,0,)(U,3—Hy,.) + 2(2,%,— 2, 2%,)(U,,—B a) +
ar Ey — 2
As now (4,, + 4,,)? = land XS (4,,—4,,)? = 1 and the determinant
nitaZ—x7—a,* 2(2,2,+2,7,) 2(7,7,—7,7,) bed
2(2,%,—27,7,) x +a7—ai—a 2(2,%,127,2,) | (Ly)
2(9,7,+27,7,) 2(,%, —21,%,) x,°+2,'
represents the general congruent ea eae Meo
about a fixed point expressed in the four parameters of homogeneity,
we can regard the motion group with the determinant type (ID
as a congruent motion group of the twodimensional Euclidean
star of the (4j-+4g4)’s and the motion group with the determinant
type (IJ) as a congruent motion group of the twodimensional
Euclidean star of the (4,-—A,4)’s; namely according to the determinant
type ([V) about an axis with cosines of direction
leaky Ty x,
Vie 40- ws, Vie?
over an angle equal to 2a arc COs X,.
Let us call the S, of the (4;.+4a4)’s “the representing space to the
right” or the S, of S, and the S, of the (4c—Ans)’s the “representing
space to the left” of the S, of S,, then we find that to two equiangular
double rotations to the right (left) (7,' 7,' 2,' 2,/) and (2," a," 7," a,''
of S, whose angles of rotation are are cos 2, and are cos x," and whose
systems of planes of apt make an angle with each other equal to
eyes bor
are coe gaia est =, (see Proceedings, March, 1904, page 724)
VYi—z,” . V1—
correspond two rotations ie S, (S)) over angles 2 are cos 2’, and 2 are cos x,",
x,'x,"+2,'x,"+a,'x,"
Vi—2z,” . Vi—a,"
whose axes make an angle equal to are cos
( 838 )
with each other. So to congruent combinations in the group of
the equiangular double rotations to the right (left) in S, correspond
congruent combinations in the motion group of JS, (Sj. As moreover
the
As3 =e As
Ass ei Ass
Ars =e As
of a plane are the cosines of direction of the representant of the
system equiangular to the right with that plane with respect to the
system of axes OX, Y,Z, (defined Proceedings March1904, p. 728),
and likewise
Ass Sie a
a5; = Aas
A, po. Ass
the cosines of direction of the representant of the system equiangular
io the left with that plane with respect to the system of axes
OX, Y,Z (defined in the same place) the S, and S;introduced just
now prove to be identical with those introduced here formerly (see
Proceedings March, 1904, p. 725) so that they represent not only
by their motions the equiangular motion groups of S, to the right
and to the left, but also by their vectors the systems of planes equi-
angular to the right and to the left (with direction of rotation) of
S, and so that the angle of the representing vectors is the angle of
the systems of planes themselves.
So also to congruent combinations in the twodimensional mani-
foldness formed by the equiangular systems of planes to the right
(left) correspond congruent combinations in JS, (S,). This is an algebraic
proof for 2"¢. to its full extent.
This deduction has at the same time made clear the meaning of
the four parameters of homogeneity for the general congruent three-
dimensional transformation about a fixed point, namely the cosines
of direction of the vector indicating the corresponding equiangular
double rotation to the right (left) of au jS, of which this S, is
the S,.(S) and the system of axes in S, the system OX, Y,Z,
(OX; Y; Z).
( 839 )
Zoology. — “On the relationship of various invertebrate phyla.”
By Prof. A. A. W. Husrecar.
In an elaborate paper entitled “Beitrage zu einer Trophocdéltheorie,”’
published in 1903 in the 38th volume of the “Jenaische Zeitschrift
fiir Naturwissenschaft,’ Prof. Arnoip Lane of Ziirich (p. 68— 77)
gives a clear exposition of what has been, in his opinion, the phy-
logenesis of the Annelids.
In this pedigree he places, beginning with a protocoelenterate,
a ctenophore-like being, a plathelminth, an intermediate form resem-
bling a triclade, an animal in the shape of a leech which already
possesses metameric segmentation and finally a proto-annelid,
The grounds on which he bases this phylogenesis, compel us to
acknowledge important relations between these animal groups. But
whether this kinship testities to a descent in the order given by Lang,
or whether the order has for the greater part been a reversed one,
deserves to be examined more closely.
In my opinion there Ctenophores should not be placed at the
beginning of the series, nor are they to be considered as links between
Coelenterates and worms, but they have to be looked upon as animals,
which form the last offshoots of an evolutionary series, leading from
the Annelids via the Hirudimia and the Plathelminthes. Of these
latter there have been some which gradually assumed a pelagic
mode of life and have become Ctenophora, the external resem-
blance of which with transparent jelly-fish seemed to justify their
being placed by the side of the Coelenterates.
Let us first test the grounds on which that combination has until
now been defended (see e.g. G. C. Bourne in Ray Lankester’s
Treatise on Zoology, 1900).
The presence of a gastro-vascular system and the absence of an
independent coelom, as well as the presence of a subepithelial
nerveplexus are characteristics which can be found not only with
the Coelenterates, but also to a great extent with the Plathel-
minths,
The tentacles of the Ctenophores have quite wrongly been compared
to those of the medusae, while the analogy of the adhesive cells
of the Ctenophora with the nematocysts of the Cnidaria is also
defective. And if nematocysts should be found in some Ctenophora,
no conclusions should be based on this, because they also occur in
Molluses, Plathelminths and Nemertines.
The absence of nephridia, the general structural proportions and
the gelatinous composition of part of the organism are details which
( 840 )
by no means interfere with a view which would see in the Cteno-
phora Plathelminths that have become pelagic.
That the connection which Haxrcken intended to establish between
Coelenterates and Ctenophora, when describing Ctenaria ctenophora,
is an imaginary one, has already repeatedly been shown, so e. g.
by R. Hertwie (‘Jen. Zeitschr”’. Bd. 14, p. 444), G. C. Bourne
(I. c. p. 445) and others. The first-mentioned author says emphati-
cally (1. e. p. 445): “Die Ctenophoren sind Organismen welche sich
yon den iibrigen Coelenteraten sehr weit entfernen.”” Also KorscHELT
and Hriper in their excellent handbook on the embryology of the
invertebrates are inclined (p. 100) to look upon the Ctenophora rather
as an independent branch of the animal kingdom, the connection of
which with that of the Coelenterates lies far backward. On the other
hand they point out unmistakable relations between the phylogenesis
of the Ctenophora and that of the Bilateria (Annelids, Arthropoda,
Molluses ete.). They expressly add that the side-branch of the animal
kingdom on whieh the Ctenophora are placed cannot be consulered
as having furnished a starting-poit for higher animal forms.
Ctenoplana and Coeloplana are consequently not considered by
them as advancing steps of development in the direction of the Plat-
helminths, but as aberrant, creeping Ctenophora. LaneG himself has
acknowledged on page 72 of his great handbook that the place
of the Ctenophora among the other Cnidaria is a very problematical
one and that their embryology distinguishes them from all Cnidaria.
So there can be no doubt, considering all this, that the tie
which nowadays keeps together the Ctenophora with the Coelente-
rates has of late years been considerably slackened. One effort and
it may be entirely removed °).
What on the other hand have we to. think about possible relations
between Ctenophora and Plathelminths? These relations appear espe-
cially striking to those who have oecupied themselves with the
embryological development of both classes.
Thus SeELeNKA has already in 1881 summarized this analogy under
twelve heads (zur Entwickelungsgeschichte der Seeplanarien, 5. 288).
Also Lane in his monograph on Polyeclads (1884) has emphatically
pleaded for that relationship, although in a separate paragraph he
acknowledges the existence of real difficulties. Also in his most recent
paper he adheres to the same opinion.
The discovery of two very peculiar genera of animals has still more
1) A paper, published very recently in the Zoologische Anzeiger (Bd. 27, p. 223)
on a new, much simplified Ctenophore, does not, as its author Dawyporr sug-
gests, strengthen the bond between Coelenterates and Ctenophora.
ee el
( 841°)
emphasized the problem of the relationship between Ctenophora and
Plathelminths, I mean Ctenoplana and Coeloplana. In different degree
they unite properties of both classes as has already been clearly eluci-
dated by their discoverers: Korornerr and KowaLewsky. Yet neither
Bourne who prepared the Ctenophora for Ray Laykester’s large
Textbook of Zoology, nor Korscuett and Heimer in their handbook
mentioned above, nor Wininy, who lately studied Ctenoplana in a
living condition, are really convineed of the possibility of a derivation
of Plathelminths from Ctenophores, in which case these two genera
should have to be considered as intermediate forms in that direction.
So WILLEY e.g. points out that if is not very probable that littoral
forms would have sprung from pelagic ones, whereas generally
the contrary is observed. This would according to him have been
a reversion of the natural sequence. The future will show, in
my opinion, that the difficulties mentioned, and raised by such able
experts, will for the greater part vanish as soon as relationships
“against the grain’, i.e. in the timnatural order, are no longer
accepted, but when both genera are considered as gradually mutating
Plathelminths which are already fairly on the way of assuming
etenophoran habitus,
From what precedes we may at any rate infer that whereas the
Coelenterate relationship of the Ctenophora has faded, their compa-
rability with the Plathelminths has come to the fore.
The data for judging in how far a derivation of the Annelids from
Plathelminths might be possible are given in extenso especially in
Lane’s earlier and later publications, more particularly in his well
known Gundapaper (1881) of which he has given an improved and
partly modified edition in his most recent essay, quoted in the
beginning. So I need only refer to this latest paper here.
I for my part must now try to show that a derivation im. the
opposite direction presents no difficulties. We then should look upon
Plathelminths and Ctenophores no longer as ancestral forms but as
modified and in many respects unilaterally modified descendants of
~a more primitive, Annelid-like type.
Lane has already in his Polyelad-monograph (p. 674) openly
declared himself against such a view. Yet in the twenty years which
have since elapsed, various considerations have changed and it seems
that CaLpweLt’s view (Proc. R. Soe. 1882 no, 222) has become
more probable again, according to which “there is a presumption .
that in fact Platyelminths are degenerate Enterocoeles.”’
1 should be willing like to undertake the defence of this thesis
and to see in the Plathelminths degenerate forms in whieh the
( 842 )
coelom has almost entirely disappeared, while the genital apparatus
has obtained a maximum degree of complication.
At the outset it seems to me to be less probable that at the base
of the pedigree of the Annelids such animals should stand like the
hermaphrodite Plathelminths with their ovaries, testes, vitellaria, so
greatly varying in size and shape; with their shell-glands, ootype,
clirus, penes, uterus, spermatheca, ete., not even to mention the
vitello-intestinal, the Laurer- and other canals. Does not this very
complication force us to place such animal forms rather in the
peripheral branches than near the root of any pedigree ?
On the other hand we can state that in those Polychaeta which
have retained archaic characters, such as Polygordius, Protodrilus and
Saccocirrus, various peculiarities draw our attention which in Plathel-
minths are further developed. So the phylogenesis of the Plathel-
minths would not necessarily have to be so long, via Polychaeta,
Oligochaeta, Hirudinea, but the type of Plathelminths might already
at an early period have been a deviation of the original coelomatous
ancestral forms, while in the course of this evolutionary process also
the present Oligochaeta and Hirudinea might have sprung off laterally.
Meanwhile the stronges argument for the degeneration of the
Plathelminths seems to me to be found in their early ontogenesis.
When we consider this in the light which not long ago especially
American workers have procured to us, we ought to pay attention
to the phenomena of ce//-lineage: the descent of special groups of
tissue from certain mothercells. Winison, Coxkurx, Mrap and others
have shown us the way here.
Of paramount importance is the fact that Annelids (Polychaeta
Oligochaeta, Hirudinea) and Molluses in those earliest phases of
development show a striking uniformity and that e.g. in all of them
the couple of mothercells of the so-called mesoblast-bands, within which
the coelom and metamerism appear first, originate in a_ similar
manner from one cell, the oldest, unpaired, mesodermic mother-cell,
belonging to the 64-cellular cleavage phase.
This cell lies in the second quartet of cells reckoned from the vege-
tative pole and is produced by a plane of division slanting to the left.
The next cleavage always divides this cell into a right and left
mesodermic cell; these two develop into the paired mesodermic bands.
All this is always observed in the animal phyla above-mentioned. Con-
cerning the Plathelminths Lane provided us already twenty years ago
with extensive data, which however do not constitute an unbroken
series such as is necessary for establishing the cell-lineage. Such
a series was given us a few years ago (1898) for Leptoplana
( 843 )
by E. B. Wirtsox (Annals of the New-York Academy of Sciences,
vol. XI p. 15). From his publication we may conclude as follows:
1. That a cell-couple as represented by Lana for Discocoelis, is
also present in Leptoplana, which Mrap has compared to the mother-
cells of the mesoblastbands of Annelids and Molluses, although from
this cell-couple 710 mesoblast develops i either YJOnUs of Plathelminths.
2. That, moreover, with Leptoplana, four cells of the second cell-
quartet (counted from above) become the mother-cells of “larval mesen-
chym’, that they remove to the interior and that by further subdivision
they gradually furnish the whole mesoblast of Leptoplana. This origin
of the mesoblast in Plathelminths was also already known to LANG.
3. That also with Molluses (Unio, Crepidula) and probably also
with certain Annelids (Aricia), beside the two symmetrical mesoblast
bands still another source of mesoblastic tissue occurs, which is
directly comparable to the source of larval mesenchym mentioned
in 2, and that also these mesenchym mother-cells originate from cells
belonging to the ectoblast quartet, as with the Plathelminths.
4. That consequently it may be considered a settled fact that
with Annelids and Molluscs the mesoblast has a twofold origin ').
Conkhin (Vol. XIII, Journal of Morphology, p. 151) has emphasized
that thus mesoblast is furnished by each of the four quadrants,
viz. the mesenchym by the micromeres of the second quartet
of A, B, and C, the mesoderm-bands by D.
This latter phenomenon is always connected with lengthening of
the body and with teloblastie growth, even with animals like Lamel-
libranchia and Gastropoda, although the latter are not generally
Jooked upon as longitudinally developed forms. From this Conkiin
justly inferred that the radial mesoblast has a still more primitive
character than the bilateral.
Whoever considers more closely the correspondence here noticed
in the development of the Polyclada with that of the Annelids and
Molluses, will have to acknowledge that only that solution can be
satisfactory which considers the two ceils, mentioned in 1, as the last
remnant of the no longer fully developing mesoblast-bands with
the degeneration of which the disappearance of the coelom and of
a distinct metamerism has gone hand in hand.
1) 1 may briefly call attention to the fact that I also pleaded for a manyfold
origin of the mesoblast with mammals, on account of what had been found in
Tarsius (Verh. Kon. Ak. v. Wet. Amsterdam, vol. VIII n’. 6 1902, p.69) and that
I concluded from it that the mesoderm is not equivalent to the two primary germ-
layers, but that Kuervenpera was right when he qualified it as a complex of
originally independently developing organs.
( 844.)
To Jook upon them as potential mother-cells of those mesoblast-bands
would be against all known laws of heredity, where in all other points
there is so great a resemblance, also with regard to the mesenchym,
between this 64-ceilular stage and that of Annelids and Molluses and
where it would be entirely impossible — supposing evolution to have
followed the line: Coelenterates, Ctenophora, Plathelminths — to
derive the mesoblast-bands, which must anyhow lie accumulated in
the cells mentioned, from these preceding ancestral forms. On the
other hand it can easily be understood that these bands have gradually
assumed their present form and peculiar characteristics in the long
(and to us unknown) series of the ancestral forms of Annelids,
Molluses and Polyelada, and that with these latter and still more
with the Ctenophora (which have an ontogenesis so much resembling
that of the Polyelada,) the part played by these mesoblastic mother-cells
has again receded to the baeck-ground.
We must then, especially on account of what ontogenesis has
taught us, consider the Plathelminths as degenerate descendants of
Coelomata and so the = strobilation of the Cestoda, which are still
further degenerated by parasitism, again falls within the reach of an
explanation which would homologize it with the metamerie structure
of the Annelids.
How the gradual reduction leading from Polychaeta via Oligochaeta
and Hirudinea to Plathelminths, has left its traces in all the different
organs and tissues I will not develop more extensively here; I may
suppose these poimts to be generally known.
It is obvious, after what has preceded, that we ought not to attempt
to derive the metamerism of the Annelids from the pseudo-metamerism
of the Turbellaria as Lane does. I prefer to accept the hypothesis
formulated already in 1881 by Sepewick, according to which a longi-
tudinally extended, actinia-like being, possessing wormlike free motility,
formed the starting-point. Gradually cyclomerism was converted into
bilateral symmetry and linear metamerism, in the same way as now
already certain Actinia show a tendency to bilateral symmetry.
Ep. vAN BenepEn afterwards indicated (1894), though only in an
oral adress which has never been published, how SxpGwick’s view
might be extended to the Chordates. In 1902 in the ‘‘Verhandelingen”’
of this Academy, I have tested the possibility of applying Srp@wick’s
theory to the facts that are revealed to us by the development of
mammals. And the facility with which the explanation of Sepe@wick
can be extended both to Vertebrates and Invertebrates, is undoubtedly
an argument in its favour.
Lanc and Harscurk object that a prolonged actinialike being would
it tee
( 845 )
also. have possessed unpaired tentacles and an unpaired gastral division
in the median line. They forget that such an unpaired medial coelomic
cavity is already present in Balanoglossus and that LANGERHANS
(‘Zeitschr. fiir wiss. Zool.” Vol. 34. 1880) and Goopricu (Q. J.
Microsc. Se. Vol. 44, 1901) have also shown the existence of an
unpaired coelomic cavity in Saceocirrus, while cases of unpaired
median sensory spots could be enumerated in Coelomata. The well-
known antithesis of headsegment and pygidium as compared with
the trunk in the bilaterally metameric Coelomata is an argument
that goes far to meet Lane’s and HarscuEK’s contention.
Neoformation of segments, still pretty equally distributed with the
cyclomeric Coelenterates, but there also already variable, occurs with
the Coelomata exclusively at the posterior end and with many of
them only during embryonic life.
If we assume in accordance with E. van Brnepen (see Verh. Kon.
Akad. v. Wet. Amsterdam. Vol. VIII p. 69) that the stomodaeum
of an actinia-like ancestral form has been the precursor of the chorda
dorsalis, beside and above which the nerve-ring unites to a spinal
chord, while under it a connection between the stomodaeal fissure
(the chordal cavity) and the gastral diverticula (coelomic cavities)
can be observed, then it follows from this that the ancestral forms
of the aquatic Chordata are moved about in the water in a position
different from that of the ancestral Articulates by 180°. The mouth
of the Chordates would then have arisen later as a new formation,
as has already repeatedly been asserted. It is an undoubted simpli-
fication of our phylogenetic speculations if we are entitled to look
for this difference in orientation already in very early ancestral
forms and can so avoid Grorrroy St. Hinaire’s error who shifted
the process of reversion to a much later stage of development.
If thus the phylogenesis is very considerably shortened, I may
call attention to the fact that even with respect to the mammalian
foetal envelopes, I showed in the above-mentioned publication the
possibility of a similar shortening of their phylogenesis, by not
admitting that these embryonic coverings have originated from those of
reptiles and birds, as was done until now, but by considering them in
direct connection with larval envelopes of invertebrate ancestral forms.
In the grouping of bilaterally symmetrical, coelomatic animals
(resp. of such as have lost their coelom again) which has here
been attempted, important phyla (Nemertea, Nematoids’ Prosopygii,
Chaetognatha, etc.) have been left out of consideration.
There are still too many gaps in our knowledge of their anatomy
( 846 )
and their development, to enable us to form a correct judgment
about their exact position. .
With regard to the Nematoda I want to add that to me it seems
io be an error to look upon the parasitical Nematoda as descended
from those which are nowadays found living freely in the sea or
in fresh water or in moist soil. All these latter are far too uniform
to allow us to look upon them as ancestral forms. This phylum can
be better understood, when we consider the parasitical forms as the
older primitive ones and on the other hand derive the free-living
forms from them, as parasites which have adapted themselves
secondarily to a free existence. What the origin of the parasitical
Nematoda in their turn may have been remains an open question
for the present.
Of what has been briefly summarised above, I hope to give a
more elaborate exposition in the current number of the ‘“Jenaische
Zeitschrift. fiir Naturwissenschaft” which is now going through the
press, in which periodical also LANnG’s paper, which induced me to
write this article, appeared. To that number I refer for further
particulars.
Zoology. — Prof. Max Weber reads a paper: “On some of the
results of the Siboga-Expedition.”
(This paper will not be published in these Proceedings),
Anthropology. — Prof. L. Bonk reads a paper on: “ The dispersion
of the blondine and brunette type in our country.”
(This paper will not be published in these Proceedings).
Chemistry. — Prof. C. A. Losry pr Bruyn also in the name of
Dr. R. P. van Carncar presents a paper on: “Changes of
concentration in and crystallisation from solutions by centri-
Sugal power.”
(This paper will not be published in these Proceedings).
Chemistry. — Prof. C. A. Lopry pr Bruyn presents a paper of
Mr. ©. L. Juneis: “ Theoretical consideration concerning boundary
reactions which decline in two or more successive phases.”
(This paper will not be published in these Proceedings).
pa] |
(May 27, 1904),
CON: Pee: Nes.
ARSORPTION-COMPOUNDS which may change into chemical compounds or solutions. 368.
ACETANILIDE (Transformation of acetophenoxime into) and its velocity. 773.
ACETOPHENOXIME (Transformation of) into acetanilide and its velocity. 773.
acips (Action of hydrogen peroxyde on diketones 1, 2 and on z-ketonic). 715.
— (On the compounds of unsaturated ketones with). 325.
Arrica (Contributions to the determination of geographical positions on the West-
coast of). II. 426.
AFTER-IMAGES (On tactual). 481.
AGGREGATIONS (The representation of the continuity of the liquid and gaseous con-
ditions on the one hand and the various solid) on the other by the entropy-
volume-energy surface of GrpBs, 678.
AIRMANOMETER (The determination of the pressure with a closed). 510.
ALBERDA VAN EKENSTEIN (w.). Dibenzal- and benzalmethylglucosides. 452.
auLoys (The course of the melting-point-line of). 21.
Anatomy. A. J. P. van pen Broek: “The foetal membranes and the placenta of
Phoca vitulina.” 610.
Anthropology. L. Bork: “The dispersion of the blondine and brunette type in our
country.” 846,
apparatus (Description of an) for regulating the pressure when distilling under reduced
pressure. 665. .
— (Methods and) used in the Cryogenic Laboratory, VI. The methylchloride cir-
culation. 668.
AQUEOUS SOLUTIONS (A contribution to the knowledge of the course of the decrease
of the vapourtension for). 628.
ascus-ForM (The) of Aspergillus fumigatus Fresenius. 312.
ASPERGILLUs fumigatus Fresenius (The Ascus-form of). 312.
Astronomy. FE. F. van pE Sanpe Bakuuyzen : “Investigation of the errors cf the tables of
the moon of Hansen-Newcoms for the years 1895 —1902.” 370. 224 paper. 412. 422.
— C. Sanpers: “Contributions to the determination of geographical positions on
the West-coast of Africa.” IT, 426.
ATEN (a. H. W.) and H,. W. Baxuuts Roozesoom. Abnormal solubilitylines in
binary mixtures owing to the existence of compounds in the solution. 456.
— The melting point-lines of the system sulphur -++ chlorine. 599.
t
56
II CO NT) BeNe Ts:
BACTERIA (On the) which are active in flax-rotting. 462.
BAEYER’s tension theory (A quantitative research concerning). 410.
BAK HUIS ROOZEBOOM (H. W.) presents a paper of J. J. van Laan: “The course
of the melting-point-line of alloys.” 3rd communication. 21.
— The boiling-point-curves of the system sulphur and chlorine. 63.
— presents a paper of Dr. A. Smirs and L. K. Woxrr: “The velocity of trans-
formation of carbon monoxide.” IIL. 66.
— presents a paper of J. J. van Laan: “On the possible forms of the melting
point-curve for binary mixtures of isomorphous substances.” 151. 22¢ communi-
cation. 244.
— presents a paper of Dr. A. Sarvs: “The course of the solubility curve in the
region of critical temperatures of binary mixtures.” 171.224 communication, 484.
— The phenomena of solidification and transformation in the systems NH, NO,,
Ag NO, and KNO,, Ag NO. 259.
— The system Bromine + Iodine. 331.
— The sublimation lines of binary mixtures. 408.
— presents a paper of J. J, van Laan: “On the shape of melting point-curves
for binary mixtures, when the latent heat required for the mixing is very small
or = 0 in the two phases.” 518.
— presents a paper of Dr. A. Sirs: “A contribution to the knowledge of the
course of the decrease of the vapour tension for aqueous solutions.” 628.
— presents a paper of Prof. Euc. Dusors: “Facts leading to trace out the motion
and the origin of the underground water in our sea-provinces.” 738.
—and A. H. W. Arex. Abnormal solubility lines in binary mixtures owing to
ihe existence of compounds in the solution, 456.
— The meltingpoint lines of the system sulphur + chlorine. 599.
BAKHUYZEN (E. F. VAN DE SANDE). See SanpE Bakuuyzen (K. F. van De).
BaTrery (A) of standard-thermoelements and its use for thermoelectric determinations
of temperature. 642.
BECK MANN-rearrangement (The); transformation of acetophenoxime into acetanilide
and its velocity. 773.
BEEKMAN (J. w.) and A. F. Hoxtemay. Benzene fluoride and some of its deri-
vations. 327.
BEHRENS (vu. H.). The conduct of vegetal and animal fibers towards coal-tar
colours. 325.
BEMMELEN (J. M. VAN). Absorption-compounds which may change into chemical
compounds or solutions. 368.
BEMMELEN (Ww. VAN). The daily field of magnetic disturbance. 313.
BENZALMETHYLGLUCOSIDES (Dibenzal- and). 452.
BENZENE (On the substitution of the core of). 735.
— perivatives (Crystallographic and molecular symmetry of position isomeric). 406.
— FLUORIDE and some of its derivations, 327.
— (The nitration of). 659.
© ON FT 8 NOP Ss. rit
-BENZIDINE (The transformation of). 262.
BEIWERINCK (M. W.) and A. van Denpen. On the bacteria which are active in
flax-rotting, 462.
BIERENS DE HAAN (b.) (Extract of a letter of V. W1Luior on the work of);
“Théorie, propriétés, formules de transformation et méthodes d’évaluation des
intégrales définies.” 226.
BINARY MIXTURE (The y-surface in the neighbourhood of a) which behaves as a pure
substance. 649.
BINARY MIXTURES (The equations of state and the y-surface in the immediate neigh-
bourbood of the critical state for) with a small proportion of one of the compo-
nents (part 3). 59. (part 4). 115.
— (On the possible forms of the melting point-curve for) of isomorphous substances.
15], 2nd communication, 244.
— (The course of the solubility curve in the region of critical temperatures of).
171, 24 communication. 484.
— (The sublimation lines of). 408.
— (Abnormal solubility lines in) owing to the existence of compounds in the
solution, 456.
— (On the shape of meltingpoint-curves for) when the latent heat required for
the mixing is very small or=0 in the two phases. (3 communication), 518.
— (lsothermals of gravitation on the phenomena in the neighbourhood of the plait-
point for). 593.
BLANKSMA (J, J.). On the substitution of the core of Benzene. 735.
BLONDINE and brunette type (The dispersion of the) in our coantry. 846.
BOEKE (J.). On the development of the myocard in Teleosts. 218.
BOILING-POINT CURVES (The) of the system sulphur and chlorine. 63.
BOIS (H. E. J. G. DU). Hysteretic orientatic-phenomena. 597.
BOLK (L.) presents a paper of A. J. P. van DEN Broek: “The foetal membranes
and the placenta of Phoca vitulina.” 610.
— The dispersion of the blondine and brunette type in our country. 846.
BONNEMA (J. H.). A piece of lime-stone of the Ceratopyge-zone from the Dutch
diluvium. 319.
Botany. C. A. J. A. OupEMans and C.J. Kontne : “On a Sclerotinia hitherto unknown
and injurious to the cultivation of tobacco” (Sclerotinia Nicotianae Oud. et Koning).
48. Posteript. 85.
— Pu. van HakreveLD: “On the penetration into mercury of the roots of freely
floating germinating seeds.” 182,
— G. Grisys: “The Ascus-form of Aspergillus fumigatus Fresenius.” 312.
— C, A. J, A, OupemMans : “Exosporina Laricis Oud. — A new microscopic fungus
occurring on the Larch and very injurious to this tree.” 498.
— E. Verscuarre.r : “Determination of the action of poisons on plants.” 703.
BOULDER-CLAY BEDS (Deep) of a latter glacial period in North-Holland. 340.
BOUNDARY REACTIONS (Theoretical consideration concerning) which decline in two or
more successive phases. 846,
56*
IV € 0 NP ENE.
BRINKMAN (c. u.). The determination of the pressure with a closed airmano-
meter. 510.
BROEK (4. J. P. VAN DEN). The foetal membrane and the placenta of Phoca
vitulina. 610. -
BROMINE ++ lodine (ihe system). 331.
BROUWER (L. £. J.). On a decomposition of a continuous motion about a fixed
point O of S, into two continuous motions about O of S$,’s. 716. Observation of
Dr. E. JAHNKE. 831.
— On symmetric transformation of S, in connection with S, and Sz. 785.
— Algebraic deduction of the decomposability of the continuous motion about a
fixed point of S, into those of two S,’s. 832.
BRUNETTE TYPE (The dispersion of the blondine and) in our country. 846.
BRUYN (Cc. A. LOBRY DE). See Lopry pe Bruyn (C. A,).
BUYS-BALLO? medal (Extract from the Report made by the Committee for awarding
the). 78.
CALCAR (Rk. P. VAN) and C, A. Losry DE Bruyn. Changes of concentration in
and crystallisation from solutions by centrifugal power. 846,
CALIBRATION (The) of manometer and piezometer tubes. 532.
CARBON DIOXIDE (Isothermals of mixtures of oxygen). I. The calibration of manometer
and piezometer tubes. 532. If. The preparation of the mixtures and the com-
pressibility at small densities. 541, ILL. The determination of isothermals between
60 and 140 atmospheres, and between — 15° C. and + 60° C. 554, IV. Isother-
mals of pure carbon dioxide between 25° C. and 69° C. and between 60 and
140 atmospheres. 565. V. Isothermals of mixtures of the molecular compositions
0.1047 and 0.1994 of oxygen, and the comparison of them with those of pure
carbon dioxide. 577. VI. Influence of gravitation on the phenomena in the neigh-
bourhood of the plait point for binary mixtures. 593.
— (Isothermals of pure) between 25° C. and 66° C. and between 60 and 140
atmospheres. 565.
— (Isothermals of mixtures of the molecular compositions 0.1047 and 0.1994 of
oxygen, and the comparison of them with those of pure). 577.
CARBON MONOXIDE (The velocity of transformation of). I. 66.
CARDINAAL (J.) presents a paper of J. van DE GriEenD Jr.: “Rectifying curves.” 208.
CENTRIC DECOMPOSITION of polytopes, 366,
CENTRIFUGAL POWER (Changes of concentration in and crystallisation from solutions
by). 846.
CERATOPYGE-ZONE (A piece of limestone from the) of the Dutch diluvium. 319.
Chemistry. J. W. Diro: “The action of phosphorus on hydrazine.” 1.
— J. W. Commenix and Ernst Cowen: “The electromotive force of the
DanIELL-cells.” 4.
— J. J. van Laar: “The course of the melting-point-line of alloys” (3"4 com-
munication). 21.
— H. W. Baxuvis Roozesoom: “The boiling-point curves of the system sulphur
and chlorine.” 63,
CONTENTS v
Chemistry. A. Smirs and L. K. Woxrr: “The velocity of transformation of carbon
monoxide.” LL. 66.
— C. A. Lopry be Bruyn ‘and C. L. Juncius: “The condition of hydrates of
nickelsulphate in methylalcoholic solution.” 91.
— ©. A. Losey DE Bruyn and C. L. Juxezus: “The conductive power of hydrates
of nickelsulphate dissolved in methylaleohol.” 94.
— ©. A. Lopry bE Bruyn and L. K. Woirr: ‘Do the [ons carry the solvent
with them in electrolysis.” 97.
— On intramolecular rearrangements. N°. 5. C. L. Junius: The mutual transfor-
mation of the two stereo-isomeric methyl-d-elucosides.” 99. NO. 6. H. Raven.
“The transformation of diphenylnitrosamine into p-nitroso-diphenylamine and its
velocity.” 267. N°. 7, C. A. Lopry pe Bruyn and C. H. Suurrer: “The Brcx-
MANN-rearrangement ; transformation of acetophenoxime into acetanilide and its
velocity.” 773. N® 8. C. L. Juneics: “The mutual transformation of the two
stereoisomeric pentacetates of d-glucose.” 779.
— S. Tymstra Bz.: ‘The electrolytic conductivity of solutions of sodium in mix-
tures of ethyl or methylaleohol and water.’ 104.
— J. J. van Laar: “On the possible forms of the meltingpoint-curve for binary
mixtures of isomorphous substances.” 151. 22¢ communication. 244.
— A. Smits: ‘The course of the solubility curve in the region of critical tem-
peratures of binary mixtures.” 171. 2"¢ communication. 484.
— A. F. HoLLEMan: “Preparation of Cyclohexanol.’’ 201,
— H. W. Bakuuis RoozEBoom; ‘“The phenomena of solidification and transformation
in the systems NH, NO;, Ag NO, and KNO,, Ag NO,.” 259.
— A. F. Hoieman and J. Porrer van Loon: “The transformation of benzidine.” 262,
— 8. Hoocewerrr and W. A. van Dorr: “On the compounds of unsaturated
ketones with acids.” 325.
— Tu. H. Benrens: “The conduct of vegetal and animal fibers towards coal-tar-
colours.” 325.
— A. F. Honteman and J. W. Beekman: “Benzene fluoride and some of its
derivations.” 327,
— H. W. Bakkurs Roozesoom: “The system Bromine + Iodine.” 331,
— kh. O. Herzog: “On the action of Emulsin.” 332.
— J. M. van BemMeLen: “Absorption-compounds which may change into chemical
compounds or solutions.” 368,
— F. M. Jarcer: “Crystallographic and molecular symmetry of position isomeric
benzene derivatives.” 406.
— H. W. Baxuuis Roozesoom: “The sublimation lines of binary mixtures.” 408.
— A. FP. Hotteman and G. L. VorrMan: ‘‘A quantitative research corcerning
BakyeErs’s tension theory.” 410.
— W. ALBERDA vAN EkeEnsTEIN: “Dibenzal- and benzalmethylglucosides.” 452,
— ©. H. Siurrer: “The transformation of isonitrosoacetophenonsodium into sodium
benzoate and hydrogen cyanide.” 453.
YI CONTENTS.
Chemistry. I]. W. Bakuvrs Roozepoom and A. H. W. Aven: “Abnormal solubility lines
in binary mixtures owing to the existence of compounds in the solution.” 456.
— J. J. van Laar: “On the shape of meltingpoint-curves for binary mixtures,
when the latent heat required for the mixing is very small or =O in the two
phases.” (3™4 communication). 518.
— H. W. Bakuurs Roozesoom and A. H. W. Aten: “The meltingpoint lines of
the system sulphur -+ chlorine.” 599.
— A. W. Visser: “Enzymactions considered as equilibria in a homogenous
system.” 605.
— A. Smits: “A contribution to the knowledge of the course of the decrease of
the vapour tension for aqueous solutions.” 628.
— A. F. HoLteman: “The nitration of Benzene fluoride.” 659.
— Jan Rutten: “Description of an apparatus for regulating the pressure when
distilling under reduced pressure.” 665.
— P. van RompurcH: “On Ocimene.” 700.
— P. van Rompurcu: “Additive compounds of s. trinitrobenzene.” 702.
— A. F. Hottrman: “Action of hydrogen peroxyde on diketones 1,2 and on a-
ketonic acids.” 715.
— C. A. Lopry pz Bruyn and L. k. Woirr: “Can the presence of the molecules
in solutions be proved by application of the optical method of TynpaLL.” 735.
— J. J. Buanksma: “On the substitution of the core of Benzene.” 735.
— ©. A. LosBry DE Bruyn and R. P. van Catcar: “Changes of concentration in
and crystallisation from solutions by centrifugal power.” 846.
— ©. L. Junerus: “Theoretical consideration concerning boundary reactions which
decline in two or more successive phases.” 846.
CHLORINE (The boiling-point curves of the system sulphur and). 63.
— (The meltingpoint lines of the system sulphur ++). 599.
CIRCLE POINTS at infinity (The singularities of the focal curve of a plane general curve
touching the line at infinity ¢ times and passing ¢ times through each of the
imaginary). 621.
cLAUSIUS and VAN DER Waats (On the equations of) for the mean length of path
and the number of collisions. 787.
COAL~TaR-coLouRS (The conduct of vegetal and animal fibers towards). 325.
COHEN (ERNST) and J, W. Commettn. The electromotive force of the DaNnrELL-
cells. 4.
COLLISIONS (On the equations of Cuausius and vaN DER Waats for the mean length
of path and the number of). 787.
COMMELIN (J. w.)and Ernst Conen. The electromotive force of the Danie.t-cells. 4.
COMPLEXES of rays (On) in relation to a rational skew curve. 12.
COMPONENTS of a quadruplet (On the double refraction in a magnetic field near the). 19.
compounbs (On the) of unsaturated ketones with acids, 325.
— (Absorption-compounds which may change into chemical) or solutions. 368.
— (Abnormal solubility lines in binary mixtures owing to the existence of) in the
solution, 456,
CONTENTS. Vil
compounps (Additive) of s. trinitrobenzene, 702.
COMPRESSIBILITY (The preparation of the mixtures and the) at small densities. 541.
CONCENTRATION (Changes of) in and crystallisation from solutions by centrifugal
power. 846,
CONDUCTIVE POWER (The) of hydrates of nickelsulphate dissolved in methylalcohol. 94.
conpuctivity (The electrolytic) of solutions of sodium in mixtures of ethyl- or methyl-
aleohol and water. 104.
conics (On systems of) belonging to involutions on rational curves. 505.
CONTINUITY (The representation of the) of the liquid and gaseous conditions on the
one hand and the various solid aggregations on the other by the entropy-volume-
energy surface of Gibs, 678.
CONTINUOUS MOTION (On a decomposition of a) about a fixed point O of S, into two
continuous motions about O of S,’s. 716. Observation of Dr. E, Jaunke. 8381.
— (Algebraic deduction of the decomposability of the) about a fixed point of S,
into those of two 8,’s. 832.
course (The) of the melting-point-line of alloys. 21.
— of the decrease (A contribution to the knowledge of the) of the vapour tension
for aqueous solutions. 628.
CRITICAL sTaTE (The equations of state and the y-surface in the immediate neigh-
bourhood of the), for binary mixtures with a small proportion of one of the
components (part 3). 59. (part 4). 115.
— (The equilibrium between a solid body and a fluid phase, especially in the
neighbourhood of the). 230. 224 part. 357.
CRITICAL TEMPERATURES (The course of the solubility curve in the region of) of
binary mixtures. 171. 224 communication. 484.
CROMMELIN (c. A.) and H. KameriincH OnneEs. On the measurement of very
low temperatures. VI. Improvements of the protected thermoelements; a battery
of standard-thermoelements and its use for thermoelectric determinations of tem-
perature. 642.
CRYOGENIC LABORATORY (Methods and apparatus used in the). VI. The methylchloride
circulation. 668.
CRYSTALLISATION (Changes of concentration in and) from solutions by centrifugal
power. 846.
CRYSTALLOGRAPHIC and molecular symmetry of position isomeric benzene derivatives, 406,
cuBIc cuRVE (The harmonic curves belonging to a given plane). 197.
curvE (The singularities of the focal curve of a plane general) touching the line at
infinity ¢ times and passing < times through each of the imaginary circle points
at infinity, 621.
— in 8, (PLicker’s numbers of a). 501.
CURVE IN space (The singularities of the focal curve of a), 17.
cuRVEs (An equation of reality for real and imaginary plane) with higher singila-
rities. 764,
— (Qn systems of conics belonging to involutions on rational), 505,
— (Fundamental involutions on rational) of order five. 508.
VITi AON OPS Bees:
curves (lhe harmonic) belonging to a given plane cubic curve. 197.
— (Rectifying). 208.
CYCLOHEXANOL (Preparation of). 201.
DAILY FIELD (The) of magnetic disturbance. 313.
DANIELL-CELLS (The electromotive force of the). 4. /
DECOMPOSABILITY (Algebraic deduction of the) of the continuous motion about a fixed ;
point of S, into those of two S,’s. 832. /
DEKHUYZEN (Mm. c.) and P. VeErMaat. On the epithelium of the surface of the
stomach. 30.
DELDEN (a. vaN) and M. W. BetsErtnck. On the bacteria which are active in |
flax-rotting. 462. |
DIBENZAL- and benzalmethylglucosides. 452.
DIFFERENTIAL EQUATION (On the) of Monee. 620.
DIKETONES 1,2 (Action of hydrogenperoxyde on) and on g-ketonie acids. 715. a
DILUvIUM (A piece of Jime-stone of the Ceratopyge-zone from the Dutch). 319.
DIPHENYLNITROSAMINE (The transformation of) into p-nitroso-diphenylamine and its |
velocity. 267. .
DISPERSION (The) of the blondine and brunette type in our country. 846.
— of light (Lhe periodicity of solar phenomena and the corresponding periodicity
in the variations of meteorological and earth-magnetic elements, explained by
the). 270.
D1ITO (J. w.). The action of phosphorus on hydrazine. 1.
DORP (W. a. VAN) and 8S. HoogEewErFr. On the compounds of unsaturated ketones
with acids. 325.
DUBOIS (EUG.). Deep boulder-clay beds of a latter glacial period in North-Holland. 340.
— Facts leading to trace out the motion and the origin of the underground water
in our sea-provinces. 738.
DIJK (G. VAN) and J. Kunst. A determination of the electrochemical equivalent of
silver. 441.
EARTH-MAGNETICAL elements (The periodicity of solar phenomena and the corres-
ponding periodicity in the variations of meteorological and), explained by the
dispersion of light. 270.
EFFECT (A new law concerning; the relation between stimulus and) (6 communi-
cation). 73. he
EINTHOVEN (W.). The string-galvanometer and the human electrocardiogram. 107.
— On some applications of the string-galvanometer. 707.
EKENSTEIN (W. ALBERDA VAN), See ALBERDA VAN EKENSTEIN (W.). F
ELECTROCARDIOGRAM (The string-galvanometer and the human), 107. |
BLECYROCHEMICAL equivalent of silver (A determination of the). 441. if
ELECTROLYSIS (Do the lons carry the solvent with them in). 97.
ELECTROMAGNETIC phenomena in a system moving with any velocity smaller than that
of light. 809.
ELECTROMOTIVE-FORCE (Lhe) of the Danie.u-cells. 4.
EMUISIN (On the action of). 332,
CO N TEN Ds: Ix
ENTROPY-VOLUME-ENERGY SURFACE of Gress (The representation of the continuity of
the liquid and gaseous conditions on the one hand and the various solid aggre-
gations on the other by the), 678.
ENZYMACTIONS considered as equilibria in a homogenous system. 605.
FPITHELIUM (On the) of the surface of the stomach. 30.
EQUATION OF conpDITION (The liquid state and the). 123.
EQUATION OF REALITY (An) for real and imaginary plane curves with higher singu-
larities. 764.
EQUATION OF STATE (On VAN DER Waals’). 794.
EQUATIONS (On the) of CLaustus and van pER Waats for the mean length of path
and the number of collisions. 787.
EQUATIONS OF STATE (The) and the -surface in the immediate neighbourhood of the
critical state for binary mixtures with @ small proportion of one of the compo-
nents (part 3). 59. (part 4). 115.
EQUILIBRIA (Enzymactions considered as) in a homogenous system. 605.
EQUILIBRIUM (The) between a solid body and a fluid phase, especially in the neigh-
bourhood of the critical state. 230. 2nd part. 357.
ETHYL- or methylalcohol (The electrolytic conductivity of solutions of sodium in
mixtures of). 104.
EXOSPORINA LARICIS OUD. — A new microscopic fungus occurring on the Larch and
very injurious to this tree. 498.
FIBERS (The conduct of vegetal and animal) towards coal-tar-colours. 325.
FLAX-ROTTING (On the bacteria which are active in). 462.
FOCAL cURVE (The singularities of the) of a curve in space. 17.
— (The singularities of the) of a plane general curve touching the line at infinity
o times and passing < times through each of the imaginary circle points at
infinity. 621.
FOETAL MEMBRANE (The) and the placenta of Phoca vitulina. 610.
FRANCHIMONT (a. P. N.) presents the dissertation of Dr. F. M. JageEr: “Cry-
stallographic and molecular symmetry of position isomeric benzene derivatives.’ 406.
ruNGUs (A new microscopic) occurring on the Larch and very injurious to this
tree. 498.
GaSEOus conditions (The representation of the continuity of the liquid and) on the
one hand and the various solid aggregations on the other by the entropy-volume-
energy surface of Gisss, 678.
GEEST (J.) and P, Zeeman. On the double refraction in a magnetic field near the
components of a quadruplet. 19.
GEOGRAPHICAL POSITIONS (Contributions tc the determination of) on the West-coast
of Africa. {I. 426. j
Geology. J. H. BonnemMa: “A piece of lime-stone of the Ceratopyge-zone from the
Dutch diluvium.” 319.
— Eva. Dusois: “Deep boulder-clay beds of a latter glacial period in North-
Holland.” 340.
x CONS Ee Ne TES:
Geology. Eve. Dusois: ‘Facts leading to trace out the motion and the origin of the
underground water in our sea-provinces.” 738.
G1BBs (The representation of the continuity of the liquid and gaseous conditions on
the one hand and the various solid aggregations on the other by the entropy-
volume-energy surface of). 678.
GLACIAL PERIOD (Deep boulder-clay beds of a latter) in North-Holland. 340.
cLucosE (The mutual transformation of the two stereoisomeric pentacetates of d-). 779.
GLucosIDES (The mutual transformation of the two stereoisomeric methyl-d-). 99.
GORTER (a.). The cause of sleep. 86.
GRAVITATION (Influence of) on the phenomena in the neighbourhood of the plaitpoint
for binary mixtures. 593. :
GRIEND JR. (J. vAN DE). Rectifying curves, 208.
GRIJNS (G.). The Ascus-form of Aspergillus fumigatus Fresenius. 312.
HAGA (d.). Extract from the Report made by the committee for awarding the Buys-
BaLLot medal. 78.
— presents a paper of G. van Disk and J. Kunst: “A determination of the electro-
chemical equivalent of silver.” 441.
HAMBURGER (H. J.) presents a paper of E, Hexma: “On the liberation of trypsin
from trypsin-zymogen.” 34.
HAPPEL (H.) and H, Kamertinen Onnes. The representation of the continuity of
the liquid and gaseous conditions on the one hand and the various solid aggre-
gations on the other by the entropy-volume-enerey surface of GipBs. 678.
HARREVELD (PH. VAN). On the penetration into mercury of the roots of freely
floating germinating seeds. 182.
HEKMA (k.). On the liberation of trypsin from trypsin-zymogen, 34.
HERZOG (Rk, O.). On the action of Emulsin. 332.
HOLLEMAN (A. F.). Preparation of Cyclohexanol. 201.
— The nitration of Benzene fluoride. 659.
—- Action of hydrogen peroxyde on diketones 1,2 and on g-ketonic acids. 715.
— and J. W. Beekman. Benzene fluoride and some of its derivations. 327.
— and J. Potrer van Loon. The transformation of benzidine. 262.
—and G. L. Vorrmayn. A quantitative research concerning Batyer’s tension
theory. 410.
HNOMOGENOUS SYSTEM (Enzymactions considered as equilibria in a). 605.
HOOGEWERFF (S.) presents a paper of Jan Rutren: “Description of an apparatus
for regulating the pressure when distilling under reduced pressure.” 665.
— and W. A. van Dorp. On the compounds of unsaturated ketones with acids. 325.
HUBRECHT (A, A. W.) presents a paper of Prof. Hans Srrauu: “The process of
involution of the mucous membrane of the uterus of Tarsius spectrum after
parturition.” 302.
— On the relationship of various invertebrate phyla. 839.
HYDRATES of nickelsulphate (The condition of) in methylalcoholic solution. 91.
— (The conductive power of) dissolved in methylalcohol. 94.
HYVRAZINE (The action of phosphorus on). 1.
—— —————-~*
CONTENTS. XI
HYDROGEN CYANIDE (The transformation of isonitrosoacetophenonsodium into sodium
benzoate and). 453.
HYDROGEN PEROXYDE (Action of) on diketones 1,2 and %-ketonic acids, 715,
HYSTERETIC orientatic-phenomena. 597.
INTEGRALES DEFINIES (Extract of a letter of V. Wiiuior on the work of D. Brerens
pE Haan: “Théorie, proprictés, formules de transformation et méthodes d’éyalua-
tion «les). 226.
INVERTEBRATE PHYLA (On the relationship of various), 839.
INVOLUTION (The process of) of the mucous membrane of the uterus of Tarsius spec-
trum after parturition. 302.
INVOLUTIONS (On systems of conics belonging to) on rational curves. 505.
— (Fundamental) on rational curves of order five. 508.
IODINE (The system Bromine +-). 331.
tons (Do the) carry the solvent with them in electrolysis. 97.
ISOMORPHOUS sURsTANCES (On the possible forms of the meltingpoint-curve for binary
mixtures of). 151. 2nd communication. 244.
ISONITROSOACETOPHENONSODIUM (The transformation of) into sodium benzoate and
hydrogen cyanide. 453.
ISOTHERMALS of mixtures of oxygen and carbon dioxide, I, The calibration of mano-
meter and piezometer tubes. 532. IJ. The preparation of the mixtures and the
compressibility at small densities. 541. III. The determination of isothermals
between 60 and 140 atmospheres, and between — 15° C. and + 60° C. 554.
IV. Isothermals of pure carbon dioxide between 25° C. and 60° C. and between
60 and 140 atmospheres. 565. V. Isothermals of mixtures of the molecular com-
positions 0.1047 and 0.1994 of oxygen, and the comparison of them with those
of pure carbon dioxide. 577. VI. Influence of gravitation on the phenomena in
the neighbourhood of the plaitpoint for binary mixtures. 593.
JAEGER (F. M.). Crystallographic and molecular symmetry of position isomeric benzene
derivatives. 406.
JAHNKE (E£.). Observation on the paper of Mr. Brouwer: “On a decomposition
of the continuous motion about a point O of S, into two continuous motions
about O of 8,’s. 831.
JULIUS (Ww. H.) presents a communication of J, W. ComMELIN and Ernst Conen:
“The electromotive force of the Danreut-cells.” 4.
— Extract from the Report made by the Committee for awarding the Buys-BaL.ot
medal. 78.
= The periodicity of solar phenomena and the corresponding periodicity in the
variations of meteorological and earth-magnetic elements, explained by the dis-
persion of light, 270. :
JuNG1US (c. L.). The mutual transformation of the two stereo-isomeric methyl-
d-glucosides. 99.
a
— The mutual transformation of the two stereo-isomeric pentacetates of d-glu-
cose, 779.
MII C80 ONT Ren se
yuNG1Uus (c. 1.). Theoretical consideration concerning boundary reactions which
decline in two or more successive phases. 846.
— and C. A. Losey ve Bruyn. The condition of hydrates of nickelsulphate in
methylalcohoJic solution. 91.
— The conductive power of hydrates of nickelsulphate dissolved in methyl-
alcohol. 94.
KAMERLINGH ONNES (H.) presents a paper of Dr. J. E. VERsCHAFFELT: ‘“Con-
tributions to the knowledge of van per Waats--surface. VJI. The equations
of state and the y-surface in the immediate neighbourhood of the critical state
for binary mixtures with a small proportion of one of the components (part 3).
59. (part 4). 115. VIII. The y-surface in the neighbourhood of a binary mixture
which behaves as a pure substance.” 649.
— presents a paper of W. H. Kersom: “IJsothermals of mixtures of oxygen and
carbon dioxide. I. The calibration of manometer and piezometer tubes. 532.
lI. The preparation of the mixtures and the compressibility at small densities.
541. III. The determination of isothermals between 60 and 140 atmospheres, and
between —15° C. and + 60° C. 554. LV. Isothermals of pure carbon dioxide
between 25° C. and 60° C, and between 60 and 140 atmospheres. 565. V. Iso-
thermals of mixtures of the molecular compositions 0.1047 and 0.1994 of oxygen
and the comparison of them with those of pure carbon dioxide. 577. VI. Influence
of gravitation on the phenomena in the neighbourhood of the plaitpoint for
binary mixtures.” 593.
— Methods and apparatus used in the cryogenic laboratory. VI. The methylchloride
circulation. 668.
— presents a paper of Dr. L. H. Siertsema: “Investigation of a source of errors
in measurements of magnetic rotations of the plane of polarisation in absorbing
solutions.” 760.
— and C. A. CromMMELIN. On the measurement of very low temperatures. VI.
Improvements of the protected thermoelements; a battery of standard-thermo-
elements and its use for thermoelectric determinations of temperature. 642.
— and H. Happex. The representation of the continuity of the liquid and gaseous
conditions on the one hand and the various solid aggregations on the other by
the entropy-volume-energy surface of Gipss. 678,
KAPTEYN (W.). On the differential equation of Monee. 620.
KEESOM (W. H.). Isothermals of mixtures of oxygen and carbon dioxide, I. The
calibration of manometer and piezometer tubes. 532. II. The preparation of the
mixtures and the compressibility at small densities. 541. III. The determination
of isothermals between 60 and 140 atmospheres, and between — 15° C. and
+ 60° C. 554. IV. Isothermals of pure carbon dioxide between 25° C, and 60° C.
and between 60 and 140 atmospheres. 565, V. Isothermals of mixtures of the
molecular compositions 0.1047 and 0.1994 of oxygen, and the comparison of them
with those of pure carbon dioxide. 577. VI. Influence of gravitation on the
phenomena in the neighbourhood of the plaitpoint for binary mixtures. 593.
CO NFER? 8. XII
KETONES (On the compounds of unsaturated) with acids, 325.
F : ? Uy eS
KLUYVER (J. c.). Series derived from the series me 305.
KOHNSTAMM (PH.). On the equations of CLausius and VAN DER WAALS for the
mean length of path and the number of collisions, 787.
— On VAN DER WaAALs’ equation of stute. 794.
l
KONING (c. J.) and C. A.J, A, OupEMaNs. On a Sclerotinia hitherto unknown
and injurious to the cultivation of tobacco, (Sclerotinia Nicotianae Oud. et
Koning). 48. Posteript. 85.
KORTEWEG (bD. J.) presents a paper of L. E. J. Brouwer: “On a decomposition
of a continuous motion about a fixed point O of Sy into two continuous motions
about O of S,’s.” 716. Observation of Dr. E. Jaunke, 831.
— presents a paper of Frep. Scaun: “An equation of reality for real and imaginary
plane curves with higher singularities.” 764.
— presents a paper of L. E. J. BrouwEr: “On symmetric transformation of 8, in
connection with S$; and Sj.’ 785.
— presents a paper of L. E. J. Brouwer: “Algebraic deduction of the decompo-
sability of the continuous motion about a fixed point of 8, into those of two
8,’s." 832,
KUENEN (J. P.). On the critical mixing-point of the two liquids. 387,
KUNST (J.) and G. van Dix. A determination of the electrochemical equivalent of
silver. 441.
LAAR (J. J. VAN). The course of the meltingpoint-line of alloys. (3rd communi-
cation). 21.
— On the possible forms of the meltingpoint-curve for binary mixtures of isomor-
phous substances. 151. 2nd communication. 244.
— On the shape of meltingpoint-curves for binary mixtures, when the latent heat
required for the mixing is very small or =0 in the two phases. (3rd communi-
cation). 518.
LATERAL AREAS (Something concerning the growth of the) of the trunkdermatomata
on the caudal portion of the upper extremity. 392.
Law (A new) concerning the relation between stimulus and effect. (6th communi-
cation). 73.
— of distillation (Note on SypNEY Youna’s). 807.
LENGTH OF PATH (On the equations of CLaustts and vAN DER WaALs for the mean)
and the number of collisions. 787.
LIGHT (Electromagnetic phenomena in a system moving with any velocity smaller than
that of). 809.
LIME-STONE (A piece of) of the Ceratopyge-zone from the Dutch diluvium. 319.
LINE AT INFINITY (The singularities of the focal curve of the plane general curve
touching the) ¢ times and passing ¢ times through each of the imaginary circle
points at infinity. 621.
XTV: EoNTEN TSS.
11QUID and gaseous conditions (The representation of the continuity of the) on the
one hand and the various solid aggregations on the other by the entropy-volume-
energy surface of GrBBs. 678.
Liquips (On the critical mixing-point of the’ two). 387.
LIQUID sTATE (The) and the equation of condition, 123.
LOBRY DE BRUYN (C. A.) presents a paper of J. W. Dito: “The action of phos-
phorus on hydrazine.” 1.
— Do the Ions carry the solvent with them in electrolysis, 97.
~
— presents a paper “On intramolecular rearrangements,” N°. 5. C. L. Junetus:
“The mutual transformation of the two stereoisomeric methyl-d-glucosides.” 99.
N°. 6. H. Raken: “The transformation of diphenylnitrosamine into p-nitroso-
diphenylamine and its velocity.” 267. N°. 7. C. A. Lospry DE Bruyn and C, H.
Siurrer: “The BeckmMaNN-rearrangement ; transformation of acetophenoxime into
acetanilide and its velocity.” 773. N® 8. C. L. Junerus: “The mutual trans-
formation of the two stereoisomeric pentacetates of d-glucose.” 779.
— presents a paper of S. Tymsrra Bz.: “The electrolytic conductivity of solutions
of Sodium in mixtures of ethyl- or methylaleohol and water.” 104.
— presents a paper of Dr. TH. Weevers and Mrs. C. J. Wrevers—-pE Graarr:
“Investigations of some Xanthine derivatives in connection with the internal
mutation of plants.” 203.
— presents a paper of W. ALBERDA vaN ExkeENsTEIN: “Dibenzal- and benzal-
methylglucosides.”” 452. .
— presents a paper of ©. H. Sturrer: ‘The transformation of isonitrosoaceto-
phenonsodium into sodium benzoate and hydrogen cyanide.” 453.
— presents a paper of A. W. Visser: “Enzymactions considered as equilibria in
a homogenous system.” 605.
— presents a paper of Prof. P. van Rompureu: “On Ocimene.” 700,
— presents a paper of Prof. P. van RomBurGH: ‘Additive compounds of s. trinitro-
benzene.” 702.
— presents a paper of Prof. EH. VerscaarreLr: “Determination of the action of
poisons on plants.” 703.
— presents a paper of Dr. J. J. Buanxsma: “On the substitution of the core of
Benzene.” 725.
— presents a paper of C. L. Junerus: “Theoretical consideration concerning
boundary reactions which decline in two or more successive phases.” 846.
— and R, P. van Catcar, Changes of concentration in and crystallisation from
solutions by centrifugal power. 846.
—and C, L. Junerus. The condition of hydrates of nickelsulphate in methyl-
alcoholic solution, 91.
— The conductive power of hydrates of nickelsulphate dissolved in methylalcohol. 94.
— and L. k. Wotrr. Can the presence of the molecules in solutions be proved
by application of the optical method of TynDaLL? 735.
LOON (J. POTTER VAN). See PorreR vAN Loon (J.).
CON TEN TS. xv
LORENTZ (il. A.) presents a paper of A. PANNEKOEK: “Some remarks on the
reversibility of molecular motions.” 42.
— Electromagnetic phenomena in a system moving with any velocity smaller than
that of light. 809.
MAGNETIC DISTURBANCE (The daily field of), 313.
MAGNETIC FIELD (On the double refraction in a) near the components of a quadruplet. 19,
MAGNETIC ROTATIONS (Investigation of a source of errors in measurements of) of the
plane of polarisation in absorbing solutions. 760.
MANOMETER- and piezometertubes (The calibration of). 532.
MARTIN (k.) presents a paper of J. H. Bonnema: ‘‘A piece of lime-stone of the
Ceratopyge-zone from the Dutch diluvium.” 319.
— presents a paper of Prof. Eva. Dusois: “Deep boulder-clay beds of a iatter
glacial period in North-Holland.” 340.
Mathematics. J. pe Vries: “On complexes of rays in relation to a rational skew
curve.” 12:
— W. A. Verstuys: “The singularities of the focal curve of a curve in space.” 17.
— Jan pe Vries: “The harmonic curves belonging to a plane cubic curve.” 197.
— J. vAN DE GrRIEND Jr.: “Rectifying curves.” 208.
-— Extract of a letter of V. Wrinror on the work of D. Brerexs pr Haan:
“Théorie, propriétes, formules de transformation et méthodes d’évaluation des
intégrales définies.” 226.
33
— J. CG. Kuuyver: “Series derived from the series pm) 3052
m
— P. H. ScHoure: “Centric decomposition of polytopes.” 366.
— P. H. Scyoute: “PLicKker’s numbers of a curve in 8.” 501,
— Jan ve Vries: “On systems of conics belonging to involutions on rational
curves.” 505.
— Jan pE Vries: “Fundamental involutions on rational curves of order five.” 508.
— W. Kaprteyn: “On the differential equation of Moner.” 620.
— W. A. Verstuys: “The singularities of the focal curve of a plane general curve
touching the line at infinity ¢ times and passing ¢ times through each of the
imaginary circle points at infinity.” 621.
— W. A. Versiuys: “On the position of the three points which a twisted curve
has in common with its osculating plane.” 622.
— L. E. J. Brouwer: “On a decomposition of a continuous motion about a fixed
point O of S, into two continuous motions avout O of S,’s.” 716. Observation of
Dr. E. JaAHNKE. 831.
— Frep. Scouu: An equation of reality for real and imaginary plane curves with
higher singularities.” 764.
— P. H. Scnourr: “Regular projections of regular polytopes.” 783.
— L. I. J. Brouwer: “On symmetric transformation of $, in connection with
S; and Sj.” 785.
xVI CO N ENF 3.
Mathematics. L. E. J. Brouwer: “Algebraic deduction of the decomposability of the
continuous motion about a fixed point of S, into those of two S,’s.” 832.
MEASUREMENT (On the) of very low temperatures. VI. Improvements of the protected
thermoelements; a battery of standard-thermoelements and its use for thermoelectric
determinations of temperature. 642.
MEASUREMENTS (Investigation of a source of errors in) of magnetic rotations of the
plane of polarisation in absorbing solutions. 760.
MELTINGPO!NT-cURVE (On the possible forms of the) for binary mixtures for isomor-
phous substances. 151. (2nd communication). 244.
MELTINGPOINT-cURVES (On the shape of) for binary mixtures, when the latent heat
required for the mixing is very small or = 0 in the two phases. (3rd commu-
nication). 518.
MELTINGPOINT-LINE of alloys (The course of the). 21.
MELTINGPOINT-LINES (The) of the system sulphur + chlorine. 599.
meRcuRY (On the penetration into) of the roots of freely floating germinating seeds. 182.
METEOROLOGICAL and earth-magnetical elements (The periodicity of solar phenomena
and the corresponding periodicity in the variations of), explained by the dispers-
ion of light, 270.
Meteorology. Extract from the Report made by the Ccmmittee for awarding the Buys-
Bator medal. 78.
METHODS and apparatus used in the cryogenic Laboratory. VI. The methylchloride
circulation. €68.
METHYLALCOHOL (The conductive power of hydrates of nickelsulphate dissolved in). 94.
— and water (The electrolytic conductivity of solutions of sodium in mixtures of
ethyl-or). 104,
METHYLALCOHOLIC SOLUTION (‘The condition of hydrates of nickelsulphate in). 91.
METHYLCHLORIDE circulation (The). 668.
Microbiology. M. W. Berterinck and A, vaAN DeLpen: “On the bacteria which are
active in flax-rotting.”’ 462.
MIXING POINT (On the critical) of the two liquids. 387.
mMixTurEs of ethyl- or methylaleoho! and water (The electrolytic conductivity of
solutions of sodium in). 104.
— (The equations of state and the y-surface in the immediate neighbourhood of
the critical state for binary) with a small proportion of one of the components. 59.
— (Isothermals of) of oxygen and carbon dioxide. I. The calibration of manometer
and piezometertubes. 532. II]. The preparation of the mixtures and the com-
pressibility at small densities. 541. ILL The determination of isothermals between
60 and 140 atmospheres, and between — 15° ©. and + 60° C. 554. IV. Iso-
thermals of pure carbon dioxide between 25° C. and 60° C. and between 60
and 140 atmospheres. 565. V. Isothermals of mixtures of the molecular com-
positions 0.1047 and 0.1994 of oxygen, and the comparison of them with those
of pure carbon dioxide. 577. V1. Influence of gravitation on the phenomena in
the neighbourhood of the plaitpoint for binary mixtures. 593,
CONTENTS. XVII
MIXTURES (The preparation of the) and the compressibility at small densities. 541.
— ({sothermals of) of the molecular compositions 0.1047 and 0.1994 of oxygen,
and the comparison of them with those of pure carbon dioxide. 577.
MOLECULAR composiTions (Isothermals of mixtures of the) 0.1047 and 0.1994 of
oxygen, and the comparison of them with those of pure carbon «lioxide. 577.
MOLECULAR MOTIONS (Some remarks on the reversibility of). 42.
MOLECULES (Can the presence of the) in solutions be proved by application of the
optical method of TynDaLL. 735.
MOLL (J. w.) presents a paper of Pu. van HaRREVELD: “On the penetration into
mercury of the roots of freely floating germinating seeds.” 182.
MONGE (On the differential equation of). 620.
motion (Algebraic deduction of the decomposability of the continuous) about a fixed
point of S, into those of two S,’s. $32.
— (Facts leading to trace out the) and the origin of the underground water in
our sea-provinces. 738.
motions (On a decomposition of a continuous motion about a fixed point O of S
into two continuous) about O of S,’s. 716. Observation of Dr. E JaHnxe. 831.
MUCOUS MEMBRANE (The process of involution of the) of the uterus of Tarsius spec-
trum ufter parturition. 302.
MUTATION of plants (Investigations of some Xanthine derivatives in connection with
the internal). 203. '
MyocakD (On the development of the) in Teleosts. 218.
NITRATION (The) of Benzene fluoride, 659.
NORTH-HOLLAND (Deep boulder-clay beds of a latter glacial period in). 340.
NUMBERS (PLicKER’s) of a curve in S,. 501.
OCIMENE (On). 700.
ONNES (H. KAMERLINGH). See KamerLinco Onnes (H.).
OPTICAL METHOD of TyNDsLt (Can the presence of the molecules in solutions be proved
by application of the). 735.
ORIENTATIC-PHENOMENA (Hysteretic). 597.
oRIGIN (Facts leading to trace out the motion and the) of the underground water
in our sea-provinces. 738.
OSCULATING PLANE (On the position of the three points which a twisted curve has
in common with its). 622.
OUDEMANS (c. a. J. A.). Exosporina Laricis Oud. — A new microscopic fungus
occurring on the Larch and very injurious to this tree. 498.
—and C. J. Konine. On a Sclerotinia hitherto unknown and injurious to the
cultivation of tobacco (Sclerotinia Nicotianae Oup. et Konrne). 48. Posteript. 85.
OXYGEN and carbon dioxide (Isothermals of mixtures of). I. The calibration of mano-
meter and piezometertubes. 532. II. The preparation of the mixtures and the
compressibility at small densities. 541. III. The determination of isothermals
between 60 and i40 atmospheres, and between — 15° C. and + 60° ©, 554,
57
XVIII ClOCNGTREENEL 3S.
LV. Isothermals of pure carbon dioxide between 25° C. and 60° C. and between
60 and 140 atmospheres. 565. V. Isothermals of mixtures of the molecular com-
positions 0.1047 and 0.1994 of oxygen, and the comparison of them with those
of pure carbon dioxide. 577. VI. Influence of gravitation on the phenomena
in the neighbourhood of the plaitpoint for binary mixtures. 593.
oxYGEN (Isothermals of mixtures of the molecular compositions 0.1047 and 6.1994 of),
and the comparison of them with those of pure carbon dioxide, 577.
pANNEKOEK (A.). Some remarks on the reversibility of molecular motions. 42.
PEKELHARING (C. A.) presents a paper of Dr. M. C. Dexnuyzen and P. VERMaatT:
“On the epithelium cf the surface of the stomach.” 30.
— presents a paper of Dr. R. O. Herzoe: “On the action of Fmulsin.” 332.
PENTACETATES (The mutual transformation of the two stereoisomeric) of d-glucose. 112.
pertopicity (The) of solar phenomena and the corresponding periodicity in the
variations of meteorological and earth-magnetic elements, explained by the
dispersion of light. 270.
pHasEs (Theoretical consideration concerning boundary reactions which decline in
two or more successive). 846.
PHENOMENA of solidification (The) and transformation in the systems NHy NO,, Ag NO,
and KNO;, Ag NO;. 259.
PHOCA VITULINA (The foetal membrane and the placenta of). 610.
pHosPHorus (The action of) on hydrazine. 1.
PHYLA (On the relationship of various invertebrate), 839.
Physics. P. Zeeman and J. Geesr: “On the double refraction in a magnetic field near
the components of a quadruplet.” 19.
— A. PanneKoEK: “Some remarks on the reversibility of molecular motions.” 42,
— J. E. VerscuarreLt: “Contributions to the knowledge of vAN DER Waals
y-surface. VII. The equations of state and the y-surface in the immediate neigh-
bourhood of the critical state for binary mixtures with a small proportion of one
of the components. (part 3). 59. (part 4), 115. VIII. The p-surface in the neigh-
bourhood of a binary mixture which behaves as a pure substance. 649.
— J. D. van per Waats: “The liquid state and the equation of condition.” 123,
— J. D. van per Waats: “The equilibrium between a solid body and a fluid
phase, especially in the neighbourhood of the critical state.” 230, 2nd part. 357.
— W. H. Junius: “The periodicity of solar phenomena and the corresponding
periodicity in the variations of meteorological and earth-magnetic elements,
explained by the dispersion of light.” 270.
— J. P. Kuenen: “On the critical mixing-point of the two liquids.” 387.
— G. van Dik and J. Kunst: ,,A determination of the electrochemical equivalent
of silver.” 441.
— C. H. Brinkman: “The determination of the pressure with a closed airmano-
meter.” 510,
CONTENTS xIX
Physics. W. H. Kersom: “Isothermals of mixtures of oxygen and carbon dioxide. 1. The
calibration of manometer and piezometer tubes. 552. {L. The preparation of the
mixtures and the compressibility at small densities. 541. ILI. The determination
of isothermals between 60 and 140 atmospheres, and between — 15° C. and
+ 60° C. 554. IV. Isothermals of pure carbon dioxide between 25° C. and 60°
C. and between 60 and 140 atmospheres.” 565. V. Isothermals of mixtures of
the molecular compositions 0.1047 and 0.1994 of oxygen, and the comparison of
them with those of pure carbon dioxide. 577. VI. Influence of gravitation on the
phenomena in the neighbourhood of the plaitpoint for binary mixtures,” 593.
—H. E. J. G. pu Bois: “Hysteretic orientatic-phenomena.” 597.
— H. Kameriincu Onnes and C. A, CrommMenin: “On the measurement of very
low temperatures. VI. Improveinents of the protected thermoelements; a battery
of standard-thermoelements and its use for thermoelectric determinations of tem-
perature.” 642. .
— H. KamertincH Onnes: “Methods and apparatus used in the cryogenic Labo-
ratory. VI. The methylchloride circulation.” 668.
— H. Kameritncu Onnes and H. Happex: “The representation of the continuity
of the liquid and gaseous conditions on the one hand and the various solid
aggregations on the other by the entropy-volume-energy surface of GrBps.” 678.
— L. H. Srertsema: “Investigation of a source of errors in measurements of
magnetic rotations of the plane of polarisation in absorbing solutions.” 760.
— Pu. hounnstamm: “On the equations of CLausius and vAN DER Waals for the
mean length of path and the number of collisions.” 787.
— Pa. Kounsramm: “On van DER Waals’ equation of state.” 794.
— Miss J. Reupier: “Note on SypNEy Youne’s law of distillation.” 807.
— H. A. Loxentz: “Electromagnetic phenomena in a system moving with any
velocity smaller than that of light.” 809.
Physiology. M. C. Dexuvuyzen and P, Vermaat: “On the epithelium of the surface
of the stomach.” 30.
— E. Hexma: “On the liberation of trypsin from trypsin-zymogen.” 34.
= J, kK. A. WERTHEIM SaLomonson: “A new law concerning the relation between
stimulus and effect” (6t? communication), 73.
— A. Gorter: “The cause of sleep.” 86.
= W. Etnraoven : “The string galvanometer and the human electrocardiogram.” 107.
— J. Boexe: “On the development of the myocard in Teleosts.” 218.
— G, van RignBerk: “On the fact of sensible skin-areas dying away in a centri-
petal direction.” 346.
— ©. Wivkier and G. van RisnBerk: “Structure and function of the trunk-
dermatoma.” IV. 347.
— C. Winter and G. van RiunBerK: “Something concerning the growth of the
lateral areas of the trunk-dermatomata on the caudal portion of the upper
extremity.” 392.
— J. K. A. WerrHemm Satomonson: “On tactual after-images.” 481.
— W. Etnruoven: “On some applications of the string-galvanometer.” 707.
Xx Goax?t? END s:
PIEZOMETERTUBES (The calibration of manometer and). 532.
PLACE (f.) presents a paper of Dr. J. Boeke: “On the development of the myocard
in Teleosts.” 218.
PLACENTA (The foetal membrane and the) of Phoea vitulina. 610.
PLAITPOINT (Influence of gravitation on the phenomena in the neighbourhood of the)
for binary mixtures. 593.
PLANE OF POLARISATION (Investigation of a source of errors in measurements of mag-
netic rotations of the) in absorbing solutions. 760.
PLANTS (Determination of the action of poisons on). 703.
— (Investigations of some Xanthine derivatives in connection with the internal
mutation of). 203.
PLtcCKER’s numbers of a curve in S,. 501.
point O of S, (On a decomposition of a continuous motion about a fixed) into two
continuous motions about O of S,’s. 716. Observation of Dr, E. JANKE. 831.
— of SS; (Algebraic deduction of the decomposability of the continuous motion
about a fixed) into those of two 83’s. 832.
pornts (On the position of the three) which a twisted curve has in common with its
osculating plane. 622.
poisons (Determination of the action of) on plants. 703.
POLYTOPES (Centric decomposition of). 866.
— (Regular projections of regular). 783.
POTTER VAN LOON (s.) and A, F. HoLteman. The transformation of benzidine. 262.
PRESSURE (The determination of the) with a closed airmanometer. 510,
— (Description of an apparatus for regulating the) when distitling under reduced
pressure. 665.
PROJECTIONS (Regular) of regular polytopes. 783.
quapruPLeT (On the double refraction in a magnetic field near the components of a). 19,
RAKEN (H.). The transformation of diphenylnitrosamine into p-nitroso-diphenylamine
and its velocity. 267.
REARRANGEMENT (The BECKMANN); transformation of acetophenoxime into acetanilide
and its velocity. 773.
PEARRANGEMENTS (On intramolecular). No. 5. C. L. Junezus: ‘The mutual transfor-
mation of the two stereo-isomeric methyl-d-glucosides.” 99. No. 6. H. RakEn:
“The transformation of diphenylnitrosamine into p-nitroso-diphenylamine and its
velocity.” 267. No. 7. C. A. Lopry bE Bruyn and C. H. Swurrer : “The Brck-
MANN-rearrangement: transformation of acetophenoxime into acetanilide and its
velocity.” 773. No. 8 C. L. Junerus: “The mutual transformation of the two
stereoisomeric pentacetates of d-glucose.” 779.
REFRACTION (On the double) in a magnetic field near the components of a qua-
druplet. 19.
REUDLER (J.). Note on SypNEY Youne’s law of distillation. 807.
REVERSIBILITY (Some remarks on the) of molecular motions. 42.
CONTENTS. XXI
ROMBURBGH (P. VAN). On Ocimene. 700.
— Additive compounds of s. trinitrobenzene. 702.
Roots (On the penetration into mercury of the) of freely floating germinating seeds, 182.
ROOZEBOOM (H. W. BAKHUTS). See Bakuuis RoozeBoom (H. W.).
RUTTEN (JAN). Description of an apparatus for i es the pressure when
distilling under reduced pressure. 665,
RIJNBERK (G. VAN). On the fact of sensible skin-areas dying away 1m a centripetal
direction. 346.
— and C. Winker. Structure and function of the trunk-dermatoma. IV. 347.
— Something concerning the growth of the lateral areas of the trunkdermatomata
on the caudal portion of the upper extremity. 392.
SANDE BAKHUYZEN (E. F. VAN DE). Investigations of the errors of the tables of
the moon of HanseN-NEwcoms for the years 1895—1902. 370. 24 paper. 412. 422.
— presents a paper of C. Sanpers: “Contributions to the determination of geogra-
phical positions on the West-coast of Africa.” II, 426.
SANDERs (c.). Contributions to the determination of geographical positions on the
West-coast of Africa. IT. 426.
SCHOUTE (P. H.) presents a paper of Dr. W. A. VersLuys: “The singularities of
the focal curve of a curve in space.” 17.
— Centric decomposition of polytopes. 366.
— P.tcker’s numbers of a curve in S,. 501.
— presents a paper of Dr. W. A. VersLuys: “The singularities of the focal curve
of a plane general curve touching the line at infinity ¢ times and passing ¢ times
through each of the imaginary circle points at infinity.” 621.
— presents a paper of Dr. W. A. Verstuys: “On the position of the three points
which a twistéd curve has in common with its osculating plane.” 622.
— Regular projections of regular polytopes. 783.
SCHUH (FRED.), An equation of reality for real and imaginary plane curves with
higher singularities. 764.
SCLEROTINIA (On a) hitherto unknown and injurious to the cultivation of tobacco
(Sclerotinia Nicotianae Oup. et Konine), 48. Postcript. 85.
SEA-PROVINCES (Facts leading to trace out the motion and the origin of the under-
ground water in our). 738.
SEEDS (On the penetration into mercury bes the roots of freely floating germinating). 182.
SERIES derived from the series > —~’. 305.
SIBOGA-ESPEDITION (On some of the es of the). §
SIERTSEMA (L. H.). Investigation of a source of errors in measurements of mag-
netic rotations of the plane of polarisation in absorbing solutions. 760.
SILVER (A determination of the electrochemical equivalent of). 441.
SKEW CURVE (On complexes of rays in relation to a rational). 12.
SKIN-AREAS (On the fact of sensible) dying away in a centripetal direction. 346.
SLEEP (The cause of). 86.
SXII CO NTE NTS:
SLUITER (c. H.). The transformation of isonitrosoacetophenonsodium into sodium
benzoate and hydrogen cyanide. 453.
— and C. A. Lopry pe Bruyn. The BreckMaNn-rearrangement ; transformation
of acetophenoxime into acetanilide and its velocity. 773.
sMITS (A.). The course of the solubility curve in the region of critical temperatures.
of binary mixtures. 171. 224 communication. 484.
— A contribution to the knowledge of the course of the decrease of the vapour
tension for aqueous solutions. 628.
— and L. K. Wotrr. The velocity of transformation of carbon monoxide. II. 66.
sopiuM (The electrolytic conductivity of solutions of) in mixtures of ethyl- or methyl-
alcohol and water. 104.
SODIUM BENZOATE (The transformation of isonitrosoacetophenonsodium into) and hydrogen
cyanide, 453.
SOLAR PHENOMENA (The periodicity of) and the corresponding periodicity in the
variations of meteorological and earth-magnetic elements, explained by the dis--
persion of light. 270.
SOLIDIFICATION (The phenomena of) and transformation in the systems NH,NO,,
AgNO, and KNO,, AgNO. 259.
SOLUBILITY CURVE (The course of the) in the region of critical temperatures of binary
mixtures. 171. 224 communication. 484.
SOLUBILITY LINES (Abnormal) in binary mixtures owing to the existence of compounds
in the solution. 456.
sOLUTIONS (Absorption-compounds which may change into chemical compounds or). 368..
— (Changes of concentration in and crystallisation from) by centrifugal power. 846.
— (Investigation of a source of errors in measurements of magnetic rotations of the
plane of polarisation in absorbing). 760.
SOLVENT (Do the Ions carry the) with them in electrolysis. 97.
SOURCE OF ERRORS (Investigation of a) in measurements of magnetic rotations of the
plane of polarisation in absorbing solutions. 760.
STANDARD-THERMOELEMENTS (A battery of) and its use for thermoelectric determinations.
of temperature. 642.
STIMULUs and effect (A new law concerning the relation between). (6th communi--
cation). 73.
STOK (J. P. VAN DER). Extract from the Report made by the committee for
awarding the Buys-BauLor medal. 78.
— presents a paper of Dr. W. van BemMeELen: “The daily field of magnetic distur--
bance.” 313.
stomacH (On the epithelium of the surface of the). 30.
STRAHL (HANS). The process of involution of the mucous membrane of the uterus
of Tarsius spectrum after parturition. 302.
STRING-GALVANOMETER (The) and the human electrocardiogram. 107.
— (On some applications of the). 707.
SUBLIMATION LINES (The) of binary mixtures. 408.
SUBSTITUTION (On the) of the core of Benzene. 735.
CON TEN TS: XXIII
suLPHUR and chlorine (The boiling-point curves of the system). 63.
— + chlorine (The meltingpoint lines of the system). 599.
-sURFACE (Contributions to the knowledge of van per Waats). VII. The equations
of state and the g-surface in the immediate neighbourhood of the critical state
for binary mixtures with a small proportion of one of the components (part 3).
59. (part 4). 115. VIIT. The y-surface in the neighbourhood of a binary mixture
which behaves as a pure substance. 649.
SYDNEY youNG’s law of distillation (Note on). 807.
SYMMETRY of position (Crystallographic and molecular) isomeric benzene derivatives. 406.
— sulphur and chlorine (The boiling-point curves of the), 63.
SYSTEM bromine ++ iodine (The). 331.
— sulphur + chlorine (The meltingpoint lines of the). 599.
— (Electromagnetic phenomena in a) moving with any velocity smaller than that
of light. 809.
sysTEMS NH,NO,, AgNO, and KNO,, AgNO, (Ihe phenomena of solidification and
transformation in the). 259.
— of conics (On) belonging to involutions on rational curves. 405.
TABLES OF THE MOON (Investigations of the errors of the) of HanseN-Newcoms for
the years 1895—1902. 379. 2nd paper. 412. 422.
TARSIUS spectrum (The process of involution of the mucous membrane of the uterus
of) after parturition. 302.
TELEOsTS (On the development of the myocard in). 218.
TEMPERATURES (On the measurement of very low). VI. Improvements of the protected
thermoelements; a battery of standard-thermoelements and its use of thermo-
electric determinations of temperature. 642.
“TENSION THEORY (A quantitative research concerning Bafyer’s.) 410.
Terrestrial Magnetism. W. van BemMELEN: “The daily field of magnetic disturbance.” 313.
THERMOELEMENTS (Improvements of the protected); a battery of standard-thermoelements
and its use for thermoelectric determinations of temperature. 642.
ropacco (On a Sclerotinia hitherto unknown and injurious to the cultivation of)
(Sclerotinia Nicotianae Oud. et Koning). 48. Postcript. 85.
TRANSFORMATION of acetophenoxime into acetanilide and its velocity. 773.
— (The phenomena of solidification and) in the systems NH,NO,;, AgNO; and
KNO;, AgNO3. 259.
— (The) of benzidine. 262.
— (The) of diphenylnitrosamine into p-nitroso-diphenylamine and its velocity. 267,
— (The) of isonitrosoacetophenonsodium into sodium benzoate and hydrogen
eyapide. 453.
— (The mutual) of the two stereo-isomeric methyl-d-glucosides. 99.
— (The mutual) of the two stereo-isomeric pentacetates of d-glucose. 779.
— (On symmetric) of S, in connection with S, and 8S; 785.
XXIV = CeO, NOT -E NSE.
TRINITROBENZENE (Additive compounds of s.). 702.
TRUNKDERMATOMATA (Something concerning the growth of the lateral areas of the)
on the caudal portion of the upper extremity. 392.
— (Structure and function of the). IV. 347.
TRYPSIN (On the liberation of) from trypsin-zymogen. 34.
TWISTED CURVE (On the position of the three points which a) has in common with
its osculating plane. 622.
TYMSTRA BZ. (s.). The electrolytic conductivity of solutions of sodiuin in mixtures
of ethyl- or methylalcohol and water. 104.
TYNDALL (Can the presence of the molecules in solutions be proved by application
of the optical method of). 735.
uterus of Tarsius spectrum (The process of involution of the mucous membrane of
the) after parturition. 302.
VAPOUR TENSION (A contribution to the knowledge of the course of the) for aqueous
solutions. 628.
Vegetable Physiology. Tu. Werevers and Mrs. C. J. Weevers—pe Graarr: “In-
vestigations of some Xanthine derivatives in connection with the internal mutations
of plants.” 203.
vELocity (Electromagnetic phenomena in a system moving with any) smaller than that
of light. 809.
— of transformation (The) of carbon monoxide. IL. 66.
verRMAAT (p.) and M. C. Dexsuyzey. On the epithelium of the surface of the
stomach. 30.
VERSCHAFFELT (E.). Determination of the action of poisons on plants. 703.
VERSCHAFFELT (J. E.). Contributions to the knowledge of van DER Waals
y-surface. VIL. The equations of state and the y¥-surface in the immediate neigh-
bourhood of the critical state for binary mixtures with a small proportion of one
of the components (part 3). 59. (part 4). 115. VIII. The y-surface in the neigh-
bourhood of a binary mixture which behaves as a pure substance. 649.
VERSLUYS (wW. A.). The singularities of the focal curve of a curve in space. 17.
— The singularities of the focal curve of a plane general curve touching the tine
at infinity o times and passing ¢ times through each of the imaginary circle
points at infinity. 621.
— On the position of the three points which a twisted curve has in common with
its osculating plane. 622.
VISSER (a. W.). Enzymuactions considered as equilibria in a homogenous system. 605.
VOERMAN (s. L.) and A. F. Hoiieman. A quantitative research concerning
Baryer’s tension theory. 410.
yYRIES (J. DE). On complexes of rays in relation to a rational skew curve. 12.
— The harmonic curves belonging to a given plane cubic curve. 197.
— On systems of conics belonging to involutions on rational curves. 505.
— Fundamental involutions on rational curves of order five. 508.
CONTENTS. XXV
WAALS (VAN DER) (On the equations of Craustus and) for the mean length of
path and the number of collisions. 787.
— y-surface (Contributions to the knowledge of}. VIL. The equations of state and
the y-surface in the immediate neighbourhood of the critical state for binary
mixtures with a small proportion of one of the components (part 8). 59. (part 4).
115. VILL. The y-surface in the neighbourhood of a binary mixture which behaves
as a pure substance. 649.
— equation of state (On). 794.
WAALS (J. D. VAN DER). The liquid state and the equation of condition. 123.
— The equilibrium between a solid body and a fluid phase, especially in the
neighbourhood of the critical state. 230. 2nd part. 357.
— presents a paper of Prof. J. P. Kugnen: “On the critical mixing-point of the
two liquids.” 387.
— presents a paper of C. H. Brtxkman: ‘The determination of the pressure with
a closed airmanometer.” 510.
— presents a paper of Prof. H. E. J. G. pu Bots: “Hysteretic orientatic-pheno-
mena’. 597.
— presents a paper of Dr. Pa. Kounstamm: “On the equations of CLaustus and
vAN DER Waats for the mean length of path and the number of collisions.” 787.
— presents a paper of Dr. Pu, Kowystamm: “On van DER Waals’ equation of
state.” 794.
— presents a paper of Miss J. ReupLer: “Note on SypNeY Youna’s law of distil-
lation.” 807.
waTER (Facts leading to trace out the motion and the origin of the underground)
in our sea-provinces. 738.
— (The electrolytic conductivity of solutions of sodiam in mixtures of ethyl- or
methylalcohol and). 104.
WEBER (MAX). On some of the results of the Siboga-Expedition. 846.
WEEVERS (TH.) and Mrs, C. J. WrevERs—pr Graarr. Investigations of some
Xanthine derivatives in connection with the internal mutation of plants. 203.
WENT (F. A. F. C.) presents a paper of Dr. G. Gruns: “The Ascus-form of Asper-
gillus fumigatus Fresenius.” 312.
WERTHEIM SALOMONSON (J. kK. A.). A new law concerning the relation between
stimulus and effect. 73.
— On tactual after-images. 481.
WILLtoT (v.). — Extract of a letter of — on the work of D. Brerens pe Haan:
“Théorie, propriétés, formules de transformation et méthodes d’évaluation des
intégrales définies.” 226.
WIND (c. H.). Extract from the Report made by the Committee for awarding the
Buys—Ba ior medal. 78.
WINKLER (c.) presents a paper of Prof. J. K. A. WerrnHem Satomonson: “A
new law concerning the relation between stimulus and effect.” (6th Communi-
cation). 73.
XxVI C(O: Not EANSTTS-
WINKLER (C.) presents a paper of Dr. A. Gorter: ‘The cause of sleep.” 86.
— presents a paper of Dr, G. van Runperk: “On the fact of sensible skin areas
dying away in a centripetal direction.” 346.
— presents a paper of Prof. J. K. A. WERTHEIM SaLomonson: “On tactual after-
images.” 481.
— and G. van RisnBerk, Structure and function of the trunk-dermatoma. IV. 347.
— Something concerning the growth of the lateral areas of the trunk-dermatomata
on the caudal portion of the upper extremity. 392.
WOLFF (r. kK.) and C, A. Lopry pe Bruyn. Can the presence of the molecules in
solutions be proved by application of the optical method of TyNDALL. 735.
WOLFF(L. kK.) and A. Smits. The velocity of transformation of carbon monoxide. II. 66.
XANTHINE DERIVATIVES (Investigations of some) in connection with the internal muta-
tion of plants. 203.
ZEEMAN (pP.). Extract from the Report made by the committee for awarding the
Buys—Ba ior medal. 78.
— and J. Grest. On the double refraction in a magnetic field near the components
of a quadruplet. 19.
Zoology. Hans Srrauu: “The process of involution of the mucous membrane of the
uterus of Tarsius spectrum after parturition.” 302.
— A. A. W. Husrecut: “On the relationship of various invertebrate phyla.” 839
— Max Wesrr: “On some of the results of the Siboga-Expedition.” 846.
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