42 



From what has been said, however, it may be suggested 

 that the theory enables us by a simple construction to pass 

 from any one system of radiant energy to any other system. 

 For if the wave fronts of these respective systems be taken 

 and if the derived surfaces of these systems be used as 

 generators of a convolute surface, then the transition from 

 one wave system to the other can be effected by means of 

 the surface so described. 



It follows that the radiant energy which is dissipated in 

 the first system will be conserved in the second, and con- 

 versely, so that the two systems are finitely interdependent. 



^he case in which one of the generating curves is at an 

 infinite distance is peculiar, and again leads to a construction 

 for the convolute. 



Let PN (fig. 4) be the direction of the parallel rays^ and 

 Ox, Oy axes. 



Let V be (xr/), P (4,/) and < ?Tx = xP, < PS^ = .^ 

 then g/ - jj = (a; - ^)tan\// 11 



. 1 + tan ^ 



Eliminating y and tj from equations 11 and 12 



-^. —L,fiec\p= — x&ec\p 13 



. J. / SQC-4^d-4, f r -J'seC-d'd-d' 17, \ 



.. ^ = e ^ ^1 ~ I e •' ^ ^xsec\pd\p + c) 



