14 PROCEEDINGS OF THE CANADIAN INSTITUTE. 
Therefore 
rm) PEF PN 
oo RX PN” 
the relation on which is based the definition of nodal points. 
It would seem preferable, however, after having proved the 
existence oO nodal oa We +, to reverse these steps, and from. 
BE 
ox = Tae to deduce — oo FR? &e. 
21. Again, if w at N gives w’ at N’, 
OF shes, Ii. 
BN ARAN; 
Therefore 
WwW pie Ww 
PF 
that is, the apparent magnitude of w at F is equal to that of w 
at EF’. 
22. If w at S gives w’ at S, then (Fig. 7) from the similar triangles. 
SNS, SF’X, XFS we have 
w NS es SF 
ih Ney ASE aah ck 
In like manner if w at S’ gives w” at S’ we have 
Oe EEN 
a9 Gi NSE 
Hence from the last two relations 
w w’ wo" 
pes en 
23. If w at K gives w’ at F, and w at EF’ gives w” at K’, then 
(Fig. 7) 
o SNK ex 
oN a oy, 
and 
w NE’ FE’ 2h 
i N’K’ eo 
t Vide Helminoit7, ‘opt saiiietolosinia: Dp. 75. 
