456 Prof. J. Perry on Liquid Friction. 



where a = *009 and /c=l'33, That is, for low speeds we have 

 the law 



At the critical speed the law suddenly changes to 



which holds for all higher speeds which we have tried. The 

 ciitical speed 



and 



y c = an c 2 , or '009 n c 2 . 



It is to be recollected that p is too nearly constant for us 

 to say with certainty that a is proportional to p, as the theory 

 requires. The errors of observation were so great that it was 

 not worth while finding accurately the most probable values 

 of k and a. 



We wish it to be understood that our apparatus was very 

 carefully constructed, and great care was taken in making the 

 observations ; but it is our intention to pursue the investiga- 

 tion with apparatus much more carefully constructed. 



Vibratory Experiments. 



In designing the apparatus it was our intention to obtain (a 

 from the damping of the rotational oscillations of the suspended 

 cylinder about its vertical axis, the trough being at rest. We 

 meant in this way to obtain /jl for velocities very much smaller 

 than those which could be employed in our steady motion ex- 

 periments. A considerable number of observations were made, 

 but when we tried to make calculations of //, we found that our 

 mathematical difficulties were too great, and after many months 

 of effort we are forced to say that we are unable to utilize these 

 observations. In equation (4) assume that v = we iU , and iv 

 may be obtained in Bessel functions. Unfortunately, as there 

 are two surface conditions, both particular solutions of the 

 Bessel equation are necessary, and the work of reduction be- 

 comes very great. An approximate solution is obtained by 

 taking r=R + «z?, R being the radius of the suspended cylinder, 

 and taking the equation (4) to be 



dh-> 1 dv v p dv 



d? + Udx~W~ pit* ' ' ' (11 ^ 



Making this assumption in the case of steady motion, it was 

 found that it was sufficiently correct for practical purposes. 



