438 
MESSES. T. E. THORPE AHD J. W. RODGER OH THE RELATIOHS 
where V is now the volume of tlie liquid passing through the tube in time t. This 
formula was deduced for a circular tube of radius R, but it is almost impossible to 
obtain narrow tubes of perfectly circular section. The tube employed, as already 
stated, was elliptical. In such a case the semi-axes of the ellipse being A and B, 
Professor PiUCKER was good enough to show that in the above formula should be 
replaced by 
A^B' 
4 {A~ + B-) 
which, when A = B = P, is, of course, P‘^/8. 
Since observations were made at different temperatures, a correction for expansion 
of glass, and for changes in p, the density of the liquid, must be introduced into the 
formula. 
If A, B, V, I and p are determined for 0 °, if 9 be the temperature of observation, 
/S the coefficient of linear expansion of glass between 0 ° and 6, and s the volume which 
1 cub. centim. of liquid measured at 0 ° occupies at d, then 17 ^ the coefficient of viscosity 
measured at 9 will be given by 
(1 + Yp (1 + S/30) 
“ 4 (A3 + B2) /V (1 + (1 -f S^0) SttUs (1 + /3d) ' 
Neglecting quantities of the second order. 
■jriYBHjy 
— 4: (A3 + B3) lY 
SttUs 
(1 + 2 ^ 0 ). 
This formula may be written 
7]e = Kpt — I’p . 
1 + 2/30 
ts 
K and k are constants having different values for each limb of the glischrometer, 
and p is, of course, constant for the same liquid. 
1 2y8d could be taken with sufficient accuracy from a table constructed for every 
5 degrees ; .s was obtained from observations on the thermal expansion of the liquid. 
Details of the measurements made in order to determine the constants K and k 
have already been described. Their values are given by 
log Kl 7-140937 log /vy = 2-313429, 
log Kii = 7-120666 log = 2-333699. 
C)n the Mathematical Expression of the Pelation of the Viscosity of 
Liquids to Temperatures. 
Our observations on the several liquids were, as already stated, taken at intervals 
of temperatures varying between 5° and 15°. In order to obtain viscosity coefficients 
at any desired temperature from these observations, we have used both graphical and 
