510 MR. A. E. H. LOVE ON THE SMALL FREE VIBRATIONS 



First, suppose we are dealing with an inextensible surface, then 



8 89 8? 



, a? ,817 a? 



By equations (5), since Z,Z 3 + mjrag + n^ = 0, and y a + m 2 7n 3 + n s n 3 = 0, 



X' - - K 3 * P (l>g) * _i_ 



h " 2 9 /9 8 3 + 9 



' . ISA a _ L _ , 



1 2 "r "" 



_ _ 



9/3 "r a (/8> a ay9 "" a (/s) a a/9 J ' 



1 [8 (/8) 88 8 (/8) aa8yS a (a/3) 3a 8/9 ' 



/ A 7, 3 



ft re 



( a /9) 8/S 3 "" 8 (a/3) 8/3* 8 ( 



Hence, taking the notation of SALMON'S ' Geometry of Three Dimensions/ chapter 1 2, 

 section 4, we have 



, > 



*! V F = ic',, h r h* G = K 2 , V*a E' = - 

 and the equation for the principal radii of curvature is* 



so that, if p'i, p' 2 be the roots of this equation, 



' X' - 1. .1 



'- P\ P\ 



P iPs 



Also 



*2 ^i + ^i 2 = K 'z ^'i + 'f'l 2 + K 2 Aj Aj K' 2 K 2 



Plp'a Pi Pa Pi Pa 

 * SALMON, p. 346. I have changed the sign of p so that the roots shall be the />, and />, of Art. 5. 



