200 Conway—TLhe Partial Differential Equations of Mathematical Physics. 
But 
dy ! 0x’) 
r—— = —(a— wv) — — &e.; 
du ( ) j 
and, since the numbers are real, the square of this expression will be less than 
(re Wh 
OG 5 \* O25 \" 
Gaye Gey eo. .<t 
Hence, with this condition, we must have 
p= 0, 1.€. a= ZL 3 Vy = Bop &e. 3 
and hence u=¢. Hence the solution is infinite for all the values of the variables 
given by the equation 
SUAS, BS Gola), Cs, 
where 2',(¢)... denotes the result of writing ¢ for win #,... ‘To this type of 
solution we may give the name of Kinetic Function. For, if ¢ denotes the time, 
such a solution would have a singularity which was in motion. 
