54 Ellery IV. Davis 



Rearrangement gives, respectively, 



(b' s ch 2 0" + b" a sh 2 6")x' s 



-\-2(a'b" — a"b') ch 0" sh 0"*'/ + (a' a ck 2 0" + a" 2 sh 2 0")/ 2 



= a' 2 b'"- ch 2 6" + 2a'b'a"b" ch 2 0" sir 0" + a" 2 &" a sh 4 6\ 

 and 



[(£' 2 + 6" 2 ) (ch 2 0" + sh 2 0")]l 2 + 2b'b" 

 + 4(a'&" — a"&') ch 0" sh 0"^ 

 + [ (V 2 + a" 2 ) (ch 2 0" + sh 2 0") ] v n - + 20'a" 

 = [ (a'b' + a"t") 2 (ch 2 0" + sh 2 0") + a'fc" + a"b'}-. 



Every element belonging to the locus is the intersection of a 

 curve pair 0' = constant with a curve pair 0" = constant. Thus. 



/V= o 



