COMET OF 1889-1896-1903 267 



October 26.5, was taken from the British Nautical Almanac, the 

 latitude and longitude being reduced to the mean equinox of 

 1 886.0. To find the derivatives of the quantities I took from the 

 Almanac a series of complete positions of the planet at four-day 

 intervals, reducing each to the same mean equinox. The lon- 

 gitudes, for example, were tabulated and the differences found 

 to the fifth order, and from these differences, by means of the 

 formulas for interpolation, was found the value the first differ- 

 ence should have at the required date. Dividing this by four, 

 was found very accurately the daily rate of change of the lon- 

 gitude, which is the derivative required. The necessary data for 



Jupiter ar thus : 



A= 197° 38' 31''. 19 



/3 = + I 17 46.32 



logr= 0.7368529 



M = + 0= 4'3i'^749 



\!i=— 0^^88125 



Alogr = — 0.0000025525 



From these the rectangular coordinates and their derivatives 



were easily computed, and subtracting these results from the 



corresponding quantities for the comet, as given above, I find 



for the coordinates and their derivatives of the comet relative to 



Jupiter, 



log x = 8.5690896 



log 7 = 9.4382768 



log z = 8.8665992 n 



dx 

 log ^=6.4384763 



dv 

 log;^ =7.3387872 



log "-," = 6.8180026 n 

 dt 



32. The elements of the orbit of the comet about Jupiter may 

 be found from the above coordinates and velocities by means of 

 the integrals derived from the equations of motion of one body 

 around another. These integrals are given by LaPlace ^ in the 

 following form : 



1 Mecanique Celeste, Livre II. 



