449 REPORT—1883. 
= oi DGEE [20°C +) [sine cos 2e.E Fae 
— {2(p—-1) (p-2)-(2p- Dk} [sine cos 27.EF dx 
+ {4(p—2)—(2p—1)h} {sin ?-§v BFdx +4 [sin P-2x cos 2x.A*dx 
— 4n*| sin? cos 2u cos v.AFdx —(A*k + £)2 sin?-2x cos 22.A 
— {(1—pA?) cos 2a —(1 +2 sin? 2)A®}2 sin?-8x cos 2. EF | * ae 
1 
in?2c0s 2a..L°ae = — 
[sin or ; (p +2) (p+3)2k* 
[i pt+(pt+ 2)K*}2p|sin Px cos 22.E7*dx 
—{2(p—1) (p—2)—(2p—- ik} sine“ 00s 2x.E*de 
+ {4(p—2)—-(2Qp—1)k*} 
sin?~42,B?da + 4|sine-2v cos 20.A*da 
—4 sin?-x cos 2.A* 
— {(1—pA?*) cos 27 —(1—6 sin*x) A?}2 sin® x cos v.E*. a Pei 
In operating in the same manner with the reduction-formule Ixxiy., lxxvi., 
Ixxvi.*, lxxyiil., in the Memoir above referred to, the difference between the two 
should be taken the other way ; while afterwards the relation 
2 cos’*.v = cos” 2(1 + cos 22) 
should be made use of. It thus appears that 
eos” x cos 2v.F?dz = Gr Gane [ —(1- 2k*)*p* cos P—2x cos 2x. F "dx 
+ {2(p—1) (p—2) — (2p? —8p + 5)h?} feos cos 21.E "dx 
+ {4(p—2)-—(2p-7)k*} Jeos pty, Fda —4 [eos p—2x cos 2r.dx 
+2 cos?—x cos 27° AF 
+ {(1—/° —pA*) cos 2a + (142 cos®x)A*}2 sin x cos?“ 92 F ad nV 
i 1 
OE ean OEE a8 ot: FO: 
cos?v cos 2a. LFdx = Coe 73R 
[- {p—2(p + 1)k*}2p eos *xcos2v.EFdx 
+ {2(p—1) (p—2)—(2p?-8p + 8)K?} |cose—te cos 2v.EFdx 
+ {4(p —2) —(2p —9)k*] [eos p47, EF da 
- 4)eos P-*7 cos 2vA*dx — 4n|sin x cos?—"x cos 2x Fae 
+ (EB? + A?F)2 cos?-*2v.A 
—[{3(1 —2?) —pA?*} cos 2a + (1-3 cos? x)A*]2 sin x cos?*. EF | Se 
