88 Sir J. Lubbock on the Perturbations of Planets 



Mr. Farley has calculated for me a table of the values of 

 these quantities for all the planets, and also for the comet of 

 Encke, the comet of Bieia, and the comet of Halley. 



ciR m' a' f gtt' 7- J, ,, , ui-^l 



— = r^ 0-2--, -cosff — »){! +>•} * >•. 



[X, }L r \^ r a ^ 'J 



l+P=l-^^{{^^Cos/-l3^sin/}f;cos/' 



+ {C^cos/+^rsin/}isin/'} 



+ 





cH ci' V 7' I r 



I call the quantities -^ cos/', -jSin/', - cos^ — sm/, -5, 



a'2 



--J25 &c. the elementary quantities, because they are the elements 



which, by means of various Combinations, form the disturbing 



function IL —z—, &c., and if the numerical values of the con- 

 ar 



slants are introduced before the development is begun are 

 alone required. Mr. Farley has calculated the coeflicients of 

 these quantities when they are developed in terms of the mean 

 motions for the planets, and also other tables for eccentricity, 

 •1, -2, ... . •?, which show the convergence to be so slight, 

 that such mode of development can only be employed when 

 the eccentricity is small. These tables have all been con- 

 structed by means of mechanical quadratures. These tables 

 are not wanted for the comets, because their co-ordinates 

 cannot be developed in terms of their mean anomalies in suf- 

 ficiently converging series. 



When the method of mechanical quadratures is applied to 

 the determination of the perturbations of comets, a correction 

 is required ; but when that method is used for the determina- 

 tion of coeflicients of this nature, the limits of the integral are 

 and 360°, and the correction vanishes ; so that by means of 

 several particular values, rigorous values of the coeflicients 

 are easily obtained. Nor does the width of the interval matter, 

 provided it is not made too large. It is difficult to give pre- 

 • cise rules to regulate the width that should be employed ; but 

 in the formation of these tables it was easy to employ various 

 modes of verification. As this inquiry is in its infancy, I 

 considered it sufficient to retain only those terms which are 



