/=1 , 



PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 

 r=0 ... V— lcos| — - — \- x\ 



595 



— cos 



Also 



cos 





r = l 



Sir 



therefore the four values of 



d 



dx^ 



cos X are 



=fc cos I -^ — \- x\ , d=z v—1 cos ( — -j~ + -^ ) 

 and a trial of any other values of r and r' will shew that these are the only re- 



sults. 



Again 



d 5 cos X 

 d x^ 



= I cosr + / . -5 + \/ — lsinr + /-^ I cos (/_/+— -j — 



+ X 



Let 



y = gives cos I V x\ 



r = 2 



/=2lr=\ 



L-=2 



(cos-^ + \/ — Isin-g-j cos ^— + a; j 



/ 2-^ ,-—. . 277 \ /Stt \ 



( cos— ^ + V — lsin-Y-1 cos (-g- + a; j 



(cos-^+AZ-lsin-^ j cos (--«- + ^) 



( cos-g- + V-lsm— ^j cos ( -g- + a; 1 



-cos(|- + :.) 



/ 2 TT / — - . 2 TT \ / TT \ 



( COS— g— + V-lsm— g- j COS ( — ^ + X j 



_cos(-|l+:.) 



f cos-g- + V-lsin— g-j COS (— + x\ 



d^ cos a; 



which are the nine values of , i • 



dx^ 



They may be written more briefly thus : 



cos(|- + :r), -cos(|+x), -cos(-^+^) 



(cos-^dbV^siny^ cos (^ + xj, ^cos^±a/-1 sin-g-j cos (-^ + A 

 and / cos-g-rfcV-lsin-g-j cos (^-^ + a;j 



VOL. XIV. PART II. 



5p 



