[946 
aditimi as to 
lity ; and in 
2/ 2 = 4(1 -x) 
+ iy)- 
the required 
946] 
NOTE ON THE THEORY OE ORTHOMORPHOSIS. 
423 
To show that this is so, call for a moment the right-hand side il, the equation is 
V(1 - v 2 ) = - iv> 
hence 
or 
therefore 
1 — 7] 2 = il 2 — 2£lir) — rf, 
mi v = H 2 -1, 
2i v = a -1 = M* ¡¿f+V(i - p)} + (¿f - vU - P)J, 
^ - (jfcr=+¿) ip=(;»/= - Y) VC 1 - 
_ + 4 (if. + 1) ft + (if* + 2 + ¿) (- f)■ - (Jf‘ - 2 + ¿) - (M‘ - 2 + T) p, 
that is, 
or say 
4p - 4p + 4 (jf • + T) ft = (jp - 1 
ili 2 / ’ 
p _ p+(jf.+t;) f, _ i f m * - 4T=» : 
MV 
viz. substituting for £, 77 their values, this is 
that is, 
or finally, it is 
as it should be. 
2 <* - f)+ (m‘+T) (*■+y) - i (jf > - Ty = o, 
; + 
1 = 0, 
Starting then from the relation 
«7 + V(i - »? 2 ) = di 2 fa’f + V(1 ~ | 2 )}, 
and writing 
№ = cos 21^1 log № + V(1 ~ I 2 )},