440 
MESSRS. T. E. THORPE AND J. W. RODGER ON THE RELATIONS 
unsatisfactory. Graetz’s formula may be transformed into tlie preceding expression 
given Slotte on putting A = h, 6 = {C — c(h)/b, and — = a. 
In a subsequent communication, Slotte (‘ Beibl.,’ vol. IG, p. 182 , 1892 ) reviews 
the position of the question of viscosity as a function of the temperature, and 
concludes that none of the preceding formulge gives satisfactory results with liquids 
such as the oils where the viscosity alters rapidly with change in temperature. 
We had ourselves ascertained that an expression of the type given by Potseeille, 
even when four constants were introduced, failed to reproduce tlie results for water 
within the limits of experimental error. 
Slotte finds, however, that an expression of the form 
Vt = ^0/(1 + W' 
gives better results than any of the others. It differs from Poiseuille’s formula in 
containing in the denominator the general exponential term (l + ySf)" instead of 
1 + -j- 
We have employed this last expression given by Slotte as being the most 
satisfactory of those at our disposal. 
The formula may be written in the shape 
>? = c /(a + ty. 
In order to determine the values of the constants, two values of 77 , viz., and 7 ^ 3 , 
are chosen which correspond respectively wdth the temperatures q and q; a third 
value of 7 ^, viz., 7 ^ 0 , is then found from the equation, 
and the temperature q corresponding with this value 770 is found graphically, a and 
n are then deduced from the equations. 
ty - qq 
q + q — 2q 
log TJ-y — log 7^3 
log (« + q) - log (« + q) • 
In connection with each substance we give the data used in deducing the formula, 
c 
and the values of the constants for the expression 77 ^ = --A table is also given 
^ ' (a + ty ^ 
which contains the values of the constants when the formula is put into the shape 
77; = --Ww- file general apjjlicability of Slotte’s formula as a means of expressing 
77 as a function of the temperature is discussed at a later stage. 
Scheme of Work. 
With a view of testing the conclusions set out at length in the introduction tn 
this paper, and in particular of tracing the influence of homology, substitution. 
