THE R BIT OF U R A N U S. 19;-} 



Table XXI gives the corresponding coefficients for the action of Saturn, com- 

 puted from the expressions on p. 87 witli the addition of the following constants. 



Const, of (A.f.()) = 0".10 

 {b.s.l) = 3 .30 

 (Jj.c.l) = 3 .10 

 {h.s.2) = .20 

 (b.c.2) = .20 



Table XXII gives the coefficients for the action of Neptune from tlie formulae 

 on p. 87, all the numbers being multiplied by the factor 0.863 to reduce them to 

 the adopted mass of Neptune. The following constants are added : 



To (6.C.0) .... O'.OG 



(b.s.l) 1 .00 



(J.c.l) 1.20 



{h.s.2) .20 



(5.C.2) .20 



Table XXIII gives the secular and long-period terms for various epochs com- 

 puted from the formulae of p. 189. The sums of the several constants added in 

 the three preceding tables are here subtracted again so that these e.\pressions 

 become 



h.c.Q — Sc = 0".10 — 0".12r— .011r')>7 + .046r^;f 

 (h.s.l) — vc = _ 5 .00 — .227' — 0".05 T' + .975^77 + .221^;: 

 (&.C.1) — 2c = — 5.00 + 2.-47r+0.12r2 + .221^>7 — .975^x 

 (J).s.2) — 2c = — .46 — .017'+ .046,5)7 + -"H'^^ 

 {b.c.2) — 2c = — .41 + .127'+ .01 U^ — .046^;e 



Precepts for (he use of the Tables. 



E.xpvess the date for which the position of Uranus is required in years, months, 

 days, and hours of Greenwich mean time, according to tlie Julian Calendar if the 

 date is earlier than 1500, according to the Gregorian Calendar if it is later than 

 1600, and according to either calendar between tliese epochs. 



Enter Table I with the beginning of the century, and take out the values of g, 

 o, (,)', B, 6', and arguments 1 to 9. Multiply </ and (/ by the fraction of a century 

 corresponding to the date, and write the products with their proper algebraic signs 

 under a and d. If the calendar is the Julian, the century marked J" must be taken, 

 and if the Gregorian, that marked G. Between the dates 1752 and 1951 it is not 

 necessary to enter Table I at all. 



If Table I was not entered, enter Table II with the year, or the first preceding 

 year found therein. If Table I was entered, enter Table II between the year 

 1800 and 1896 as if the number of the century were changed to 18. Take out 

 the values of g, o, $, and the arguments, and write them under the corresponding 

 quantities from Table I. 



Enter Table III with the excess of the actual year over that with which Table II 

 was entered, and with the month. Write the corresponding values of g, o, 0, 

 and the arguments under the previous values. Multiply 6' by the fraction of a 



