QUICKEST DESCENT. 



Therefore 4gn XD-^Agmkn^ —^^ .v* 



^ . — , y nAU — wiAn 



which needs no correction. 



And, time through nn'=^= ^/'"^?".l7^^f !• 

 ' ° » 2n/^5'-\/(««AD— m.An,) 



In the same manner, 



time through n n = 9 r— 77 — t^t — ^ . / > 



2^^.;^(n.AD'— m.An') 



time through «L= ^^^^ '7,^\+,^ ' P^\J , 



^ 2V^. V(w.AD -m.An) 



and the time through Ln'= 2^^^\^^'! + ^' ^f > 



® VSf.-s/(n.Aiy— m.An') 



A %' being always nearly z= A L, when n is at 

 finite distance from A. 



Therefore, by substituting in equation (a) 

 V(n.AD— m.An) ~ 



V(n.Aiy-m.Ai/) 



