124 Mr. B. Moon on the Transmission, in one 



we must have 



F',(0 =^(0, 



t. £. we must have either (p , ((o)=0, or (f>'(t) + — 0' (a?) =0. 

 The first of these would give us 



which is obviously an inadmissible result. Adopting, therefore, 

 the alternative hypothesis, or 



and integrating this equation by Lagrange's method, the auxi- 

 liary equations for which in this case are 



we shall get 



= ^+ — dt } = dv, = da x9 



$ — <}> j \oc± —tj, v, u x >. 



But we have already seen that (/> is of the form shown by the 

 equation 



4>-<f>{M>oc } t) ; 



and these forms of <£ are incompatible except on the supposition 

 that cj)'(/.)=(j) , (x)=0 — in other words, unless we have 



F, (tew*,) =£'(©). 

 Therefore the first of equations (3) becomes 



</>(*>) =0, 

 or, which amounts to the same thing, 



w = 0, 

 or 



'v + a\og e u x =0 (7) 



When (?) holds, substituting in (1) we get 



du x a da. x 

 at a x ax 



