796 Mr. H. T. Flint on Transformation of Equation of 



function, <E>, in the transformations of the restricted principle 

 of relativity ; for these are equivalent to 



where 



<|> = aii.+bij. + cis. + di^, .... (4) 

 a = &(ix— ivU), 

 b = i 2 , 



c = i.s, 



d = ^(iv^ + U), 



k = (I-, 2 )"*, 



v is the velocity of the second system relative 

 to the first measured in units in which 

 the velocity of light is unity, 



i = \/^T. 



It will be observed that (4) is not self-conjugate, and that 

 in this case the conjugate of <3> is obtained by changing the 

 sign o£ v. 



A vector, r, subject to <E> becomes a new vector, r', and the 

 operation is similar to the imposition of homogeneous strain 

 on an elastic medium. 



The usual way of expressing this is to state that r is mea- 

 sured by inhabitants of one system and r' by those of another 

 moving relatively to it with velocity v. 



By changing the sign of v we pass from r' to r, so that 



while 



r' = <£ . r, 



r = <E>\r', 



and since 



r = <£>-V 



I 



(4') 



where <3> -1 denotes the inverse of <I>, the conjugate of <£> 

 in this simple case is also its inverse. 



We may call <E> the strain function, in analogy with the 

 three-dimensional case. 



We now pass on to consider the stress function, #, 

 occurring in the dynamics of continuous media ; and 

 for full details of the expression of the equations of motion 

 in a form convenient for the Theory of Relativity, the 

 reader is referred to Laue's paper and Cunningham's work, 

 to which reference has been made. It will be sufficient to 

 state that just as the stress function (f> of the Theory of 

 Electricity may be expressed in terms of the p-components, 



