1067 
a. Water at 9°.6 C. (u —= 1,000, 4 — 0,01319 *) sf 
a= 0,01 x + 6,73. 10—° #°—3,06 } 10—-° 2, *) 
where «= Soe ‚ with 7’= 20,95 and: 0 = 0,1272. 
b. Benzene, at 9,°8 (u == 0,890, 4 = 0,00773) 
a= 0,01 # + 7,83.. 10—* 2? —3,00 .10-* 2* ,. 
with 7’= 20,86 and d= 0,0898. 
ce. Carbon disulphide, at 10°,8 (u =1,277, n = 0,003839) 
a = 0,01 « + 18,57. 10-64? — 13,65 .10-8 a§ + 4,0. 10-10 27, 
with 7’ = 20,83 and 0 = 0,0705. 
: fi : da 
moments at which two successive extreme elongations were reached =e, 
t 
Pp 
were all taken equal to 93 this is not absolutely correct: a mathematical investi- 
ea | 
gation shows, that the moment at which en =0 does not lie exactly halfway 
between the moments at which »—=O and that the small shift of the extreme 
points depends upon the amplitude. However in the present experiments — the 
damping being comparatively small-— the shift of the extreme points was within 
the limits of the errors of observation. We may also put it in a different way 
by saying, that the elongations were read at the moments (2n-+1) 3? which can 
also be represented by a series of the form (1), and these elongations did not 
differ perceptibly from the extreme values. 
1) The viscosities were calculated from the data 7,8, 7) = 20,65 at the ordinary 
temperature and 20.61 in liquid air, K = 573.5 at the ordinary temperature and 
571.0 in liquid air (see Comm. N°. 1490), and taking into account that the atmospheric 
air itself by its action on the part of the system which is not immersed in the 
liquid (mainly the cylinder) and the internal friction of the wire together accounted 
for a decrement 3, + 33 =0,00606 (see further down). 
2) It is clear that the coefficients in these equations are not exactly the same 
as would hold for a single spherical body; this can only be true in a very rough 
approximation, seeing that they refer to the complete oscillating system, of which 
the sphere only is immersed in the liquid. Moreover the coefficients (indirectly) 
undergo a modification through the influence of the internal friction of the wire, 
owing to k also depending upon it (directly according to Guye c.s. the internal 
friction of the wire does not give any higher terms than the first; comp. for 
instance Arch. de Genève, (4), 26, 136 and 263, 1908). However, it is impossible 
from the formulae to derive those which would hold for a single sphere, because 
there is no addilivity for the three sources of friction to a higher approximation 
than the first (see Comm. NO. 149d, IV, 5); it is obvious that, if the system could 
be subjected to the influence of the three frictions separately, formulae would be 
obtained with different exponents k and that these formulae would not be capable 
of being combined to a single one with one definite value of k. 
