Xumerical Calculation of the Jacobian Ellipsoids 



â-'(v) = dßl1v)-d.ß.i:lv) = ;.//cos(«-,9)J 



(20) 



where 



;. = ^ 



cos a 



Hence (13) becomes 



., tan (a — ,5") 



,«o- 



taii'ia 



sin(a— y5) 

 sin 2« cos(« + y9) 



cos2acos;^a + ,9) 



^/2r) 



COS^Î 



£2 =, sin(V/ + ^9) 



sin 2a cos (a— ^5) 



^ o _ tan (a + ß ) 



tan 2« ' 



o_ sin2a sin(« + ji5') 



cos(«— /9) 



) (21) 



cos(a — /:^) 



From the definition of -v's and e's, it foUows that 



/V + V = l, (i = l,2,3); 



hence s^ can be found from />,., or vice versa. But, actually, these 

 six quantities were all calculated independently from (21), using 

 the above identities as a means of verification. 



6. Substituting in (5) the value of S given in (12), and using 

 (20), (21), we get 



îi = 



( 1 + 2 f ''- ^^"^ ^"- + ^^^ W 6 f ^'' ^^^ ^'^ + ^^ ^ 

 \ cos '2a J 



If, herein, we put 



tan^ = — =- 



V2o2cos(a + /î) 

 ^ \ cos2.i / ' 



sm;^ = 



•Si 



Idß.zp. 



■cos^, 



then 



(> = 3 



sin^ 



£^tan^ tan;/ 



(22) 



(23) 



The second form of expression for i?, viz. (0), can be treated 

 in the same manner: putting 



