422 



Profs. John Perry and W. E. Ayrton. [May 27, 



where r x is a constant for the material of which the particular block is 

 composed. Hence, combining (8) and (9) we have — 



u =~x + 1 dX ^ 



1 hi dt 



from which by denoting in the usual way an inverse operation 



V rj dt / 



The total distributed force v is of course equal to the sum of all the 

 forces ffjXj, &oX 2 , &c, so that 



/ f 1 j- 1 ^V 1 . / i _l i <*Y* ■ * 1 



V= < Ojl •+- I + M + I 1- • • • • CDC. > u, 



I \r x ~k Y dt) \r 2 k 2 dt/ J 



an equation between the force distributed over either of the parallel 

 planes, and the rate of motion of the planes relatively to one another. 



If any number of blocks are of the same material, or if, although 

 not of the same material, the ratio of r to h is the same in them, then 

 it is evident that for all such blocks there will only be one inverse 

 term of the above equation. Hence if there are n different materials 

 having different ratios of r to Jc, we have the general equation 



d n v . . d n ~ J v . . t dv . , 



dt n 1 dp- 1 dt 



du . . d n ~"u . d^u /1A . „ 



=c„« + c„_ w + . . +c 2 _+c 1 _ . . . (10).- 



In the preceding we have followed Professor Clerk Maxwell's 

 method of investigating the charge of a condenser, and the currents 

 flowing into it, the method of reasoning from our hypothesis regarding 

 the action of a viscous block being the same as his reasoning from 

 Ohm's law. From the form of the equation it is evident that the order 



* If we put m 1 =—, &c, and let 



s r represent the sum of products of m x , m 2 , &c, r at a time, 



s r p „ „ „ r at a time, but only such as involve m p , 



then the differential equation is evidently as follows : — 



, ,dv , cyd 2 v , , d n v f , ' ,\d u 



v + s — - + s 2 — + . . . . +s n — = s'ir-2 a v r v s' I — . 



dt d& dt* V pliJdt 



where a = + a 2 r 2 + + a n r n , 



Now if the body consists of only two substances, then we have 



, (r-i r 2 \ dv r x r 2 d?v , ■ x . f la.-, aX\du 



