342 RADIUS OF CURVATURE. 



di/ d*ij 



Art. 201 the values of -/- and ^ . Substitute these values 

 dx aar 



in the expression for p in Art. 320, and we find 



P ~ fdr\* d*r ' 



1 ,. dr I du 



If r = -, then -^ = g-^, and 



u dv u? dd 



d*r _ 2 (du\* 1 d*u 

 ~d&'~u* (dd) u* dff* ' 



Substitute these in the above value of p ; then 



p = 



This result may also be found thus : 



dr 1 du 

 By Art. 321 P = ^ = -^^ 



By Art. 284 -* = 



therefore 3 -^ : 



dp o / cZ 2 ^ 



and -v- = I w + -^, 



P = 



1 



3 / - <* 1 



u*p 3 



d * U 



