m 



\ 



(E*) 



and therefore 



C ^v i(lV— W,) , r-v S(W— W) . Tv_ . 'i[W— TV,) 1 



~ to^ ^ 3« "^ S/3^ 3/3 "*' 3/33y 3y / ' 



f 1--V ^dj W- W,) , S^ , 1{W—W,) _3^ 3(^ — ^,) 7 



— is^Fy^ — §;;: "*■ s/ssy s/s + v sy r , 



By these equations the condition (^*), may be transformed into 

 the following : 



5« 3« ^ 3/3 3/3 ^ 3y 3y ^ ' 



To find the geometrical law expressed by this last formula, let us 

 take the given ray for the axis of z, and let us choose the planes of 

 xz, yz, in such a manner that the bisectors of their angles shall bisect 

 also the angles formed by the developable pencils ; we shall then 

 have, by the fourteenth number, E = E", that is • 



f^n {^x-^ + 3/3W — 3«3^ V3«» "^ 3^»y' 



and the formula {F*) will become 



3^' 



""'' ~ Xh^n ^n" W 3«V 3«' + 3/3* V3«J/3 3«3/3 3«^ 3/3' j 3a' +3/3' 

 or finally 



(G*) 



; (H*) 



r= r, (cos. «)' + rj (sin. «)', 



(I* 



