CENTRE OF (H:\vn Y. 



c f ** -- 



J('-O" 



- da , <? , - ? v ex' 



\ v -v- a# = - (e c c e ) + - 



o - 



<V V ex' 

 ~ i' h l"' 



- 

 and = 



cx f 



134. If the curve be of double curvature, the formula- 

 (1) and (2) of Art. 132 still hold; in order to effect the inte- 

 grations we may use the formula 



dx 



and from the two equations to the curve we must fml j_ 



and ' : in terms of z. (See Integral Calculus, Art. 120.) For 

 example, in the helix 



x = a cos nz, y = a sin nz ; 



therefore 



If we take for the limits s = and s = 7<, we have 



_ a sin ?>// 

 = i 



- _ JV (t 4- nV) xdz _ /a cos nz <& 

 B ~~" 





 Similarly y = ^ - r 



