460 
PROFESSOR CAYLEY ON THE BICIRCULAR QUARTIC. 
33. We then have 
60 c + c' cos T + c" sin T * 
and the radical which multiplies da being 
= c+d cos T+c» sin T co ^ r ~ a » sin8T > 
the differential becomes 
dT Vfl 1 -fl a co 8 a T-a 8 8 in»T' 
( t + T +^ j ) ( c + ccosT +^ smT ) 2 V © 
that is 
dT Vfli- 0 2 c °s 9 T-^ sin 2 T 
^ ( a 4" cos T + a" sin T) 2 (6 + 6' cos T + b" sin T) 2 | \/ ® 
The denominator could, of course, be reduced to the form cos T, sin T) 2 ; but 
actual form seems preferable, inasmuch as it puts in evidence the linear factors 
— 7 == («+«' cos T -fa" sin T) + —^==(b-\-b' cos T-f sin T), 
V/+0 yg+9 
and there seems to be no advantage in further reducing the integral. 
