The Variation in Attraction Due to the Attracting Bodies. 209 



In Diagram 3 angle A C c or C c g corresponds to angle A C a of Dia. 5, 

 and angle A C 1 or C 1 g of Dia. 3, to angle B C b of Dia. 5. In triangles 



■p-2 



C c g and C 1 g (Dia. 3), c g = A cos 3, and 1 g = — cos 5. 



tan C c g : tan C 1 g :: f^cos 3^ : A cos 5 :: B- : A^ or tan A C a : tan B C b 

 :: B- : A^ 



B 

 Diagram 5. 



When the angles A C a and B C b become infinitesimal they are to each 

 other as their tangents. Therefore infinitesimal angle A C a : angle B C b :: 

 B= :A2 



The volume, then, of the wedge of the elipsoid measured by AxA'X 



ang^^a g^^^ls that measured by AxB'^X ^°g- ^ ^ib ^^ ^^^^ ^^ ^^^ oblate 



860° 360 



ellipsoid. Likewise obtaiuetl, in the case of the prolate ellipsoid: BxA-X 

 ang. A Ca —g^go y a ng. B Cb 



360= 360° . 



In Diagram 6 let A B A B be an ellipse having semi diameter C B equal 

 to (B), and B, b, B, b, a similar ellipse having C B, equ^l to (a ). also let 

 B, a B, be a circle with radius C B,. From any point P in line C B, pro- 

 duced, draw tangent lines P A,,, Pa, Pb,,, and from points of tangency A^,, 

 a, and b,,, draw CA,, Ca, and Cb^,, Draw C B , parallel to A,, P, and Ca , 

 parallel to b,, P. Then C A,, (A,,) and C B , (B,,) are semi conjugate diam- 

 eters in the one ellipse, and C b,, (b,,) and Ca,, (a,,) are corresponding semi 

 conjugate diameters in tlie other. 



14 



