192 THE ORBIT OF URANUS. 



The formulae for the Tables are 



Equation of centre = 19352".()6 sin 



+ 567 .24 sin 



-f- 23 .05 sin 3j 



4- 1 .07 sin 4g 



-(- .05 sin bg 



Elliptic log. ? = 1.2833435 



.0003400 



.02036 18 cos g 



.0007 165 cos 2g 



.00003 18 cos 2>g 



.0000016 cos 4#. 



Table VIII gives the coefficients (v.c.O), (v.c.l), etc., for the perturbations of the 

 longitude and logarithm of radius vector produced by the action of Jupiter. They 

 are computed from the periodic terms of the formulae on page 83, with the addi- 

 tion of the following constants to make all the numbers of the table positive : 



Constant of (v.c.Q) = 55". 

 (v.s.l) = 6 . 

 (v.c.l) = 4 . 

 (v.8 2) = .20 

 (v.c.2) = .20 

 (p.c.O) = 1500 

 (p.s.l) = 150 

 (p.c.l) = 100 

 (p..2) = 10 

 (p.c.2) = 10 



Table IX gives the periodic part of the coefficients due to the action of Saturn, 

 taken without change from the expressions on page 84, together with the secular 

 variations, the latter including only the terms of (v.s.l), (v.c.l), (v.s.2), and (v.c.2), 

 which are multiplied by T and by sin A 2 or cos A* The coefficients of T are given 

 in the columns Sec. Var. and each number is increased by the constant 1".50 to 

 make it positive. The term 0".06T sin A 2 in (v.c.Q) is omitted entirely, as it will 

 not amount to a tenth of a second until after the year 2000. The constant terms 



added to the quantities. of these tables to make all the numbers positive, are: 



// // 



Constant of (v.c.O) = 30. 



(v.s.l) = 150. -f 1.50r 



(v.c.i) = 150. 4- i.sor 



(v.s.2) 130. -}- l.oOr 

 (v.c.2) = 130. -f 1-50 T 

 (v.s.3) = 8. 

 (v.c.3) = 6. 

 (v.sA) = 1. 

 (v.cA) = 1. 



