SOLIDS ON SURFACES. i I ) 



elements ds, ds, of the curves traced on the two surfaces by 

 the point of contact P, and that dx, dx', dx", dx„ dy„ dz,, an 

 proportional to the cosines of the space and body axe-angles 

 of this element, we have the two equations (18) 



Ldx-hL'dx' + L"dx" = o: 

 L,dx,-+- 31, dy -\-N,bz, = o. 



But the variational equations of the given surfaces an 



dK, s dA', . dK, » 



dF<^ +^°>+ sf^/= °- 



which equations, to subsist simultaneously with the other two, 

 require that we should have (19) 



Whence /, ^(« + £ + g) = *X> + £"+i") = 



. . fdh ,/A ,/A"-\-' 



Similarly /,-= (^ + _-+___) . 



