84 



TABLES OF NEPTUNE. 



take the arguments from Tables I.-IV. more than once in three or four, or even 

 five, years. The intervals of computation are first to be chosen, and need not be 

 less than 180 days for the heliocentric place. Then comjDute the values of I, y, 6, 

 and the arguments for the first date of the series, and again for a date an integral 

 number of intervals (not generally exceeding ten) later. The longitudes and 

 arguments for the intermediate dates may then be found by continual addition 

 of the differences for 180 days (if this is the interval) from the bottom of Table I. 



§ 39. Examples of the use of the tahles. 

 As a first example, we will compute an ephemeris of the heliocentric positions 

 of Neptune for the years 1865 to 1868 inclusive. The intervals of computation 

 will be 180 days, and we commence with the date 1864, Oct. 13, and end with 

 1869, March 21, between which are nine of the" assumed intervals. We first 

 compute the epochs and arguments for the extreme dates as follows : 



1. For 18G4, October 13. 



Table II., 1864, 



Table III., Year 0, Oct., 



Fact. X 9, 

 Table IV., Day 13, 



I 



5 40 58.30 



1 38 19.86 



.14 



4 18.39 



228 



y 



54 54.37 



7.88 



0.35 



e 



130 15 49.25 



29.82 



— .01 



1.31 



Arg. 1 



91.96 

 1.75 



0.08 



2 



199.49 



8.37 



0.37 



Epochs & Args. 1864, Oct. 13, 



7 23 36.69 



228 



55 2.60 



130 16 20.37 



93.79 



208.23 



Arg. 



Table II., 1864, 



Table III., Year 0, Oct., 



Table IV., Day 13, 



3 



243.86 



23.47 



1.03 



4 



5 

 19 



1 



5 



206 



10 







6 



193 



7 

 



7 



93.9 



48.8 

 2.2 



8 



250 



25 



1 



9 



237 

 22 

 "l. 



For 1864, Oct. 13. 



268.36 



25 



216 



200 



144.9 



276 



260 





2. For 1869, M 



ARCH 21. 









Table II., 1868, 



Table III., Year 1, March, 



Fact. X 8, 

 Table IV., Day 21, 



I 



14 25- 17.73 



2 32 31.25 



.19 



7 10.64 



228 



y 



55 36.39 

 12.23 



0.57 



130 1 



d 



8 28.26 



46.25 



— .01 



2.18 



Arg. 1 



101.30 

 2.72 



0.13 



2 



244.11 



12.98 



0.61 



For 1869, March 21, 



17 4 59.81 



228 



55 49.19 



130 1 



9 16.68 



104.15 



257.70 



Arg. 



Table II,, 1868, 



Table III., Year 1, March, 



Table IV., Day 21, 



3 



369.03 



36.41 



1.71 



4 



104 



29 



1 



5 



260 



16 



1 



6 



228 



10 







7 



353.9 



75.7 

 3.6 



8 



385 

 39 



2 



9 



353 



34 



2 



For 1869, March 21, 



7.15 



134 



277 



238 



33.2 



26 



389 



