100 " Mr. HOLDITCH, ON SMALL FINITE OSCILLATIONS. 



From (23), Xi= Y = a, 



r, =0, 



y - V ^ _ _ ^ 

 '^'-^''dcp" d<p' 



jr = ^ - ^, = ^ - a, 

 d(p d<p 



v - V '^'y' _ fffl _ „ _ ^ 

 ^' - -^^ ~ d^i^ ' dcp dcl>'- ' 



d^_ _d^r,_d^ ^ 

 ' ~ rf^^ ' ~ d^' d<p ^ " '^ d(p' ' 



and it will be necessary to express ~ , -p^ , &c. in terras derivable from the separate curves ; 



dtp d<p 



let R and r be their radii of curvature at P; 



ds, . ds 



d^s, d^s 



let /?, = -77S , r, = -77S ' Sic. 



d9, d's, d^6-, 



~""^'d^d^-^'^°^^'d0^' 



Now d^ = d0 - d0, = d9 - d0 . - ; 



"^^^^ dtp d9'dtp R-r 



„, dr , dR ,„ dr d9 , dR dd, 

 d'a _ "d^ 'd(^ _ ' d9' dtp ' d9,' dtp 



d^ " (fi - r)'' ~ (fl - '•)' 



