240 THE REV. ROBERT HARLEY ON A CERTAIN CLASS 



-(25.3^-5. i3.2? + 3.r% 

 — 3(3—"^)^^ 



4'^H3*-^)^^=-(2^3S7-7.43^ + 3.ii^V 



+ (2^3^-5- 2. 3. 953"^ + 647.2?" -3. 707^)2/ 

 + (2 . 3\ 29 — 139^ + 3 . 'joc^)x ] 

 whence the resolvent 



+ 2(25~23<^)^ + 2/=I. 



10. For the quintic^, we have 



Ju « 



5^(4'-^)^=-y*+2/' + 2y + (2^5-% + 



5y(4^-^r^ = 5(2^-<2?)2/* + 2(2^ + ^)2/^ 

 -5(2^-3'^)y'-2"(26.3.5* 



5%'(4^-^)'^= -3(2« . 107-2" . f , 31.^4-17^%* 



-2". 3. 5 (2^3" -29.^)2/' 



+ 3-5(2'^5-2+. i3<3?4-7^')y' 



+ 2. 3(2". 5^7- 2.2593.2? 

 + 3.43i.2?"-2.3.2?^)2/ 



+ 2" . 3(2^ . 67-3 . 53<^+3'^>. 



54^(43 «^)4^= 2 . 3{(2" . 5 . 563-2^°. 54. 



dx^ 



x 



+ 5 . 2601^"— 2 . 5 . 13.2?%* 

 + (2". 5' -59-2'. 5 -323^ 



+ 5.7. 287^*— 2^ . s^^)y^ 



-(2''.3-5'-2^5-3i'^ 



-2.3-5.7^'-5.3i^V 



