June 14, 1907] 



SCIENCE 



945 



VALUES OF M'a AND JV'S, WITH LIMITING DECLINATIONS. 



Dec!, at whicli Term can amount to 0".005 



Ml = -\- da cos <5 



— 1 /2 rfa cos (5 dS 6 tan sin 1" 

 + 3/8 rfa cos rf dS^ sin^ I" 



— 1/6 rfa» coss (5 (tan^ 6 — 2) sin^ 1" 

 — 11/48 da cos (5 rfcSa tan 6 sin' 1'' 



+ 1/12 da^ cos» d dd tan 6 (tan^ 5 — 2) sin^ 1^' 

 + 19/128 da cos rf d6* sin' 1" 



— 1/16 da3 cos^ S dS^ (3 tan^ 6 — 4) sin* 1" 



+ l/]20dn6co3=<5(16 — 13tan2<J + tanM)Binn" 



Jlf, = + l/2(i52sin2i// 



— 1/2 da2 cos^ (! (tan' (5-2) sin" 1" 



— 1/8 da2 cos^ 6d6^5 tan^ d — 7) sin' 1" 



+ 1/24 da' cos* (5 (tan' (5 — 13 tan" (5 + 16) sin* 1'' 

 + 5/24 drf' sin' 1" 



jI/j = — da cos i! tan 6 sin l'' 



+ 1/2 (fa cos c'drfsin^l" 



— 7/8 da cos (5 (/(J^ tan 6 sin' 1" 



+ 1/6 (fa» cos^ 6 tan (S (tan^ 6 — 5) sin» 1'^ 

 — 1/12 (Za» cos' (S(i(J (tanM — 5) sin' 1" 

 + 23/48 da cos 6 d6' sin* l''' 



Jlf^ = da cos d sin^ 1'' 



+ 1 /2 (fa cos (5 d(! tan (5 sin' 1'^ 

 + 7/8 (fa cos tJ (f(52 sin' 1" 



— 2/3 da' cos' (J (tan2 6-2) sin' 1'' 



i!f5 = (f(5sin2 1'/ 



— 3/2 (fa2 cob' (5 tan (J sin' V^ 

 + 5/6 (f(J' sin' 1" 



— 1 /4 (fa2 cos' 6 d6 (5 tan' 6 — 7) sin' 1'' 



^1/5 = — da cos (5 (f (J tan 6 sin' 1" 

 + 1/2 (fa cos (!(f(i'sin* 1'' 

 + 1/2 fZa' cos' (5 tan' 6 sin' 1'' 



1/6 da'' cos' (5 (sec' (5 + 6) sin' 1" 

 2 (fa cos 6 d6 sin* 1" 



itf, 



Ms 



Jfg = (f(5'sin«l'' 



JVi = (f(5 



+ 1/2 (fa' cos' 6 tan (! sin 1" 



— 1/4 cfa' cos' (5 d6 (tan' (! — 1 ) sin' 1'' 

 + l/3(f(!'sin'l'' 



+ 1/4 cfa' cos' (! (f(i' tan (? sin' 1'' 



— l/ii da* cos' (5 tan 6 (tan' (! — 5) sin' 1" 



+ l/48(fa'coB'(5(i(5(tan'(!— 6tan'(5 + 5)sin'l' 

 + 2/15 (f(!5 sin' 1'' 



.Wj ^ da cos (5 tan 6 sin 1" 



+ l/2(facos(S(f<5sin'l" 



+ 7/8 da cos (5 cW tan 6 sin' 1'^ 



— 1/6 (fa' cos' (i tan (i (tan' 6 — 5) sin' 1" 



— 1/12 (fa' cos' (! (f(S (tan' (5 — 5) sin* V 

 + 23/48 da cos (5 (f(5' sin* V 



