270 POOR 



the rectangular coordinates, x' , j'' , .z' , of the comet referred to 

 Jupiter. Then to the elHptic elements of October 26.5 I ap- 

 plied the perturbations due to Jupiter for the same intei-val, and 

 thus found the osculating elliptic elements of the comet about 

 the sun for October 10.5. From these I then computed the 

 heliocentric coordinates of the comet and thence the rectangu- 

 lar coordinates, x" , y" , z" , of the comet referred to Jupiter. 

 Comparing the two sets of results thus found, I have as follows : 



These differences are all considerably less than a tenth of one 

 per cent, of the corresponding quantities, that in .:; being rela- 

 tively by far the largest. Such errors may well arise from the 

 unavoidable use of mathematical tables, and are small enough 

 to establish the substantial accuracy of both methods and 

 computations. 



33. Solar Perturbations, October to March, 1886. — During 

 the time that the comet was traversing the relative orbit about 

 Jupiter, the sun acted as a disturbing body and this action had 

 to be taken account of In order to do this I computed the 

 solar perturbations for the entire interval between October and 

 March, using an eight-day period. The method used in this 

 work was that of the variation of constants, the necessary 

 formulas being derived from the equations of hyperbolic mo- 

 tion as given by Watson. The quantities of which the per- 

 turbations were found are as follows : the four elements, tt, i^, 

 i, and e and the two auxiliaries, v and ^V (Watson's notation). 

 In this form I found the perturbations very easy of computa- 

 tion, and the method, on the whole, decidedly preferable to that 

 of the variation of coordinates, which I had used in a former 

 discussion of the same problem. The great trouble with this 

 latter method is that the indirect terms of the differential coef- 

 ficients, owing to the very small value of r, become large and 

 difficult to approximate. This necessitates the integration of 



