14 PROCEEDINGS OF THE CANADIAN INSTITUTE. 



Therefore 



«> _ PF _ PN 

 ^' ~ FX "~ PW" 

 the relation on which is based the definition of nodal points. 



It would seem preferable, however, after having proved the 

 existence of nodal points t, to reverse these steps, and from. 



U) U)' U) PF „ 



p^ = p7^.^o deduce -=-,&c. 

 31. Again, if w at N gives w' at N', 



RN R'N'" 

 Therefore 



U) <Jj' 



that is, the apparent magnitude of w at F is equal to that of o/ 

 at F'. 



22. If w at S gives w' at S, then (Fig. 7) from the similar triangles. 



SNS, SF'X, XFS we have 



«> _ NS _ /' _ SF 



In like manner if w at S' gives m" at S' we have 



w _ SF'_ /' 



«? ~" ^ ~ "SF • 

 Hence from the last two relations 



/' ^ SF "" SF ■ 



23. If w at K gives w' at F, and w at F' gives w" at K', then 

 (Fig. 7) 



«i _NK_F'X_/' 

 ^' ~ NT ~ FF ~ 2A' 

 and 



io _ NF _ FF' _ 2h 

 ~^' ~ N'K' ~ FX ~ 7 ' 



t Vide Helmholtz, Optique physiologique, p, 75. 



