294 Mr R. F. Qwyther, On the solution of the [May 25, 



put m for the density of the medium, but still the dimensions will 

 differ from those of the electro-magnetic system. Thus if 



dP 



a = "dt> 

 and a is of dimensions [M^ IT* T' 1 ], 



then v is of dimensions [M% 2/"*]. 

 Then as before the kinetic energy 



=|(r+^ 2 +n=^(« 2 +/3 2 +7 2 )=£.( a 2 +^+7), 



and potential energy 



m u, 



Wlth 7 = ^ ; 



but /J, is of [0] dimensions, therefore v is of [M *], which is contrary 

 to our requirements. 



(2) Mr Glazebrook has worked out another analogy in which 

 vdtj/dt = F, etc., founded on equations into which the electro- 

 motive force at a point is introduced as an impressed force but 

 not apparently related to the strain of the medium. So long as 

 linear equations only are used it is probable that other analogies 

 could be similarly worked out. Put 



i/| = F, etc., 



, , * dF 4tt/ 



therefore v% = -^ = - -j- , 



±(d^_dv\_dH_dG = 

 dt\dy dz) dy dz ^ ' 



.(24). 



We might by starting with the vector (f, 97, £) have proved the 

 equality of the quantities 



# + «■+?> «arf{g-*)\*a}i 



that is, 



1*£ (/ 2 + g* + /i 2 ) = A 2 {a 2 + /3 2 + 7 2 }, 



but these expressions would no longer be the kinetic and potential 

 energies of any actual motion. 



