68 



MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES. 



Before forming the derivatives of the perturbative function, t 1 of the preceding series was 

 replaced by g' by means of the Besselian transformation, and the following quantities computed: 



| ( ^ ) 2 _ ,,^-r, ( V a )"= [9.5506691] +2 [8.294341] cos ( -2 [6.84032] cos 2 i 



- 2 [8.3S23S7] cos (- g') - 2 [6.46366] cos (- 2g') - 2 [4.8459] cos {- 3g') 

 - ^-^ ( T -, ) sin (/ +77') = [7.19762] - 2 [8.036580] cos (- g>) - 2 [6.41880] cos (- 2g') 



-2 [4.9771 1 cos (-3r/') 

 + 2 [8.590096] sin (—(/') + 2 [6.97240] sin (— 2g') +2 [5.5308] sin (— 3 g') 

 where the numbers in brackets are the logarithms of the coefficients. 



The required derivatives were then formed according to the equations 



r m ' i « \ . . 1 

 (')« n = 'Lsin-lHj)-( I] U 



fdO,\ ( m 1 / a V i ( 1/ r' y 1 / r y 2 ) 1 m' fa 

 ar \ ~dr ) = \ siul" \AJ \ \ 2\ a 1 J ~'Ia i \aJ \ — 2smT'l J 



„fdfl \ i ni' ./ <i v 3 i i sin J/ r'\ . , • • > 



<W> J sin 1»" J ( J ) } j -— UO 811 ^ +7/) ! +(J) 



-(H) 



