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



changes when all the vectors are subjected to the strain of 

 equation (4). 



D behaves like a f our-vector, so that we know that 6 . a, 

 where a is a four-vector, is itself a four-vector ; and therefore, 

 if b denote another four-vector, we have 



b . 6 . a = an invariant. 



It is to be remembered that a four-vector is denned to be 

 one which transforms according to the Lorentz-Einstein 

 equation : i. <?., according to equation (4'). 



If, therefore, 6 becomes 6 in the new system, and a and b 

 become a' and b', we have 



V.0.a' = b.0.a. ...... (9) 



Now 



b.#.a = 3>'b'. (0.a) by (4'). 



The brackets denote that (0 .a) is a vector, and hence 



by (3') 



<£>'.V.(0.a) = (0.a).<£>'.V 

 = V.<S>. (<9. a) 

 = b'.O>.0.a 



= b'.<£.0.<S>'.a'. 



Hence - , 



V.0.a'= b'.<S>.0.<£'.a', 



or, since a 7 and V are arbitrary four-vectors, the operation 



. = <E> . . <S>' (10) 



In the same way, by beginning with the left side of 

 equation (9) and following the same series of steps, 

 we find 



6. = <D'.0.O> (100 



These equations contain all the transformations of 

 pressures and energy-flow occurring in equations (6). 



If we require the transformation of any individual 

 component, we may obtain it by the following device : — 



From equations (5) and (6) we have 



q*x = ii • . i x 



for 



ij.fl.ii = ii.A^.i! 



= ii . A x = q xx . 



