

Prof. J. Perry on Liquid Friction. 449 



9 D 



The numbers headed - - n — - are intended to be corrections 

 n l + \ 



of D/(7 + \) for the constant speed of 9 revolutions per minute. 



We have plotted the numbers in the last columns of these 

 tables with upon a sheet of squared paper ; but it is 

 unnecessary to publish the resulting curves. We exhibit 

 them to the members of the Society. 



Knowing what has been done by Prof. Osborne Reynolds, 

 it seemed unlikely that one simple formula should satisfy 

 either of these curves ; that is, it was likely that in the Jower 

 curve there was some temperature for which the speed n=9 

 was a critical speed, and there was also a temperature for 

 which n=40 was a critical speed. We therefore used the 

 curves merely for small temperature-corrections in our other 

 experiments, in which we kept the temperature nearly 

 constant. 



It was therefore without much interest that, in preparing 

 this paper for publication, we tried to obtain empirical formulae 

 for these curves ; and at first we used, not the observations 

 themselves, but the observations as corrected by curves drawn 

 upon squared paper. 



When log(0 — 4*2) and log j—z- are plotted as coordinates 



of points on squared paper, we were astonished to find that 

 when n = 9 the points lie in two straight lines. The allinea- 

 tion of the points is very striking, even when the uncorrected 

 observations are taken, and leads to the following empirical 

 formula : — 



Letting cj> denote 0—4*2, and letting y denote D/(Z + \) 

 the torque as measured in degrees deflexion of pointer per 

 unit length of wetted cylinder ; then, at the constant speed 

 of w=9, 



?/<^> 1 * 349 = constant for temperatures above 40° C. 

 ?/(£ ' 686 = constant for temperatures below 40° C. 



On plotting log,?/ and log<£ for the constant speed ?i = 40, 

 the points are not found to lie so nicely in straight lines, but 

 there does seem to be some sort of discontinuity at a tem- 

 perature of about 45° C. 



At first we thought that these temperatures were the tem- 

 peratures at which the speeds n = 9 and ?i=40 were the 

 critical speeds, and we were greatly concerned because our 

 result seemed to be quite out of accord with the reasoning of 



