BETWEEN THE VISCOSITY OF LIQUIDS AND THEIR CHEMICAL NATURE. 439 
algebraical methods. It may be convenient to discuss here the reasons which led to 
our adoption of the particular type of algebraical expression which we employ. 
Most of the formulEe which have hitherto been proposed have been devised from a 
study of the effect of temperature on the viscosity of water. Poiseuille {loc. cit.) 
used an expression of the form 
Vi — Vo/{^ d" 
0, E. Meyer (‘ Wied. Ann.,’ vol. 2 , p. 387, 1877) showed that although this 
formula gave good results for the temperature range over which Poiseuille’s obser¬ 
vations extended, namely 0° to 45°, yet for higher temperatures it was inapplicable. 
For such temperatures Meyer proposed the hyperbolic expression 
Vi = Vo/{^ + “0- 
To cover the entire temperature range from 0 ° to 100 °, Slotte (‘ Wied. Ann.,’ vol. 14, 
p. 13, 1881) suggested the expression 
Vi — ^/{^ ~\~ i) - 
which gfives numbers in fair agreement with the observed values. 
The preceding formulae were all deduced empirically and were applied only to a 
particular case. Graetz (‘ Wied. Ann.,’ vol. 34, p. 25, 1888), starting from Maxwell’s 
formula (‘ Phil. Mag.,’ (4), vol. 35, p. 129), rj = ET (in which E is the modulus of 
rigidity, and T is the time of relaxation, or the time which a stress excited in the 
fluid takes to fall to 1 /e of its original value), shows that as a first approximation 
Vi = A (d - t)/{t - Q), 
in which 9 is the critical temperature of the substance expressed on the centigrade 
scale, and h is an unknown temperature below the melting-point. A is a constant. 
In deducing the formula Graetz assumes that the viscosity of liquids is mainly due 
to molecular attractions, and that molecular impacts, which in the <^nse of gases are 
all important, play only a subordinate part in the case of liquids. It would follow 
from the formula that at the critical temperature 17 is zero, and at h is infinitely 
great. A and h have, of course, to be determined experimentally for each liquid. 
On applying bis formula to the results obtained by Pellstab and by Pribram and 
Handl, in which the temperature range did not exceed 60°, Graetz found that in 
some fifty cases it was satisfactory. In the case of the fatty alcohols and ethyl ether 
the formula was inapplicable. That Graetz’s formula appeared to fail in the case of 
ether was no doubt due to the imperfect data by means of which he tested it. We 
find that the formula rji = ’O 33338 (194‘4 — t)/{t — 227‘8) deduced from our observa¬ 
tions reproduces them with an average divergence of less than 0'3 per cent. For 
many of the other liquids, especially for water and the alcohols, the formula is 
