Ximierical Calculation of the Jacobian Ellipsoids. 11 



Formula^ similar to (20) can be easily written down for ^'s; then 

 b.y means of them and (29), it may l)e verified that exactly the 

 same expressions as (21) hold good for «,, joa, i>z, £i, £2, £3- 



Again, the angles (p and (p are determined by the same equa- 

 tions as in (22), but the equation giving ■/ now transforms into 



siny = ( 3-5— jcosc. (38) 



Then, expression (23) for /2 also apphes in this case. 

 As to the second expression for il, put 



f7'= _^?^,- = l + 9/^-->25/^/'+ , 



' ^ ' '' ^nih^ 2 ' 2 2 



and let a new angle co^ be defined by 



(39) 



sm CO, 



/ 2t,'iT,v) \W 2^,cos(45°- a) cos(45°-/9 ) U 



then we have 



Lastly, the expressions for /^ and e given in (27) remain 

 unchanged, while that for l becomes 



3 / IK, \^_dA^ 



^ = 1—5 177/ ~V" 



(42) 



The method of §§ 7, 8 w^as applied for A=0"24— 0"6 at 

 intervals of 0'04; the last 11 row^s of Table I show the result. 



9. As an example, let A=0. Here, we may conveniently 

 proceed from the original equations (5), (6) and (13), which 

 simplify in this case thus: 



,->, = .:>., = COS-^, ft = l. 



£, = £., = sin ^, £:; = 0, 



