§21-25] THE SATURNIAN SYSTEM. 



Jf 



2 -a 



irsin'qp (/ 0(0) + (Q (/ ( ) — g + rcos qp) 





 2© 



/o(o) r '" si " 2< P 



f h ( /»<„)— (,'-+(? rcos <r) 



2© 



J<i> 



i l> (f lea — (?+**) 

 r /o(o) 



2-3 2 



P4" = — i jT - J^l'll _ f 5 cos y log (/ 0(0) + o — r cos 9) 



t/0 /o(o) ^P 



— __ ft f J/^-ieWr 2 _ _2KH-r) ™ , 2i(f+ r) ™ 



— °J ? rf m r ^T (e + r)r r '.(»)• 



21. When the attracted point is so near the axis that the square of r can be re- 

 jected, the first term of R7 in § 16 is the only one which must be retained, and in this 

 case we have 



log(/. + ? — r 0089)) = log (/|™. + ? )-- r ' 



_ Qr(:- b) 





22. The attraction of the ring, perpendicular to its plane, and toward the plane, 

 is 



= - Dli 2 = *jT 



23. The integral of the value of D ff Z taken with reference to t, gives 



in which 



7 , 1 



24. The integration of q Z' 2 with reference to g gives 

 D, Z = Jc (Z02 — Z 21 — Z 12 -f- Z u ), 



in which 



Z2 —J j=f 2 -\-rcos(f>Jj 



=f 2 -\-r cos 9 log ( / 2 -)- Q — r cos 9). 



25. The final integration with reference to 9 trives, by means of the formulas of 

 §9, 



z = h {7Z — z% — 7/z 4- z;r), 



36 (279) 



