TABLES OF NEPTUNE. 81 



The sum of to, 6, and the reduction to the ecliptic gives the true ecliptic longi- 

 tude of the planet, referred to the mean equinox of the date. 



Tables of the radius vector. 

 Table XVII. gives the values of 



i?a + 150, and B,,, + 100. 



The expressions for B^.i and R^,^ are given on p. 40, § 19, and the units are those 

 of the seventh place of decimals. R,,i + 150 must be multiplied by sin Z, and 

 B,,i + 100 by cos I, and the products included in the perturbations of log r. 



Table XVIII. gives the principal terms of the perturbations of the logarithm 

 of the radius vector produced by Uranus, as given on p. 41. The constant added 

 is 209. 



Table XIX. gives the perturbations of the same element by Saturn, namely, 



397 cos {S — N) 

 + 4:Cos2 (S — N) 

 + (const. = 400) 



Table XX. gives the perturbations of the same element by Jupiter, namely, 



701 cos (/—i\^) 

 + (const. =z 700) 



The units of these tables are those of the seventh place of decimals. 

 Table XXI. is formed of the four following quantities. 



1. A constant formed by applying the necessary corrections to the logarithm 

 of the mean distance. We have 



Mean motion, including its perturbations, 7864.935 



Secular var. long, epoch, + 21.443 



Elliptic mean motion, 7843.492 



To which corresponds log a z=z 1.4787334 



Constants of perturbations of log r (p. 31), — 5920 



Negative of constants added to Tables XVIII.-XX., — 1309 

 Constant to be substituted for log a in expression for log radius vector, 1.4780105 



2. The elliptic log r — log a, namely, 



+ .0000078 



— .0026857 cos I —.0025301 sin I 



— .0000014 cos 2 Z — .0000235 sin 2 I 



3. The effects of the perturbations of h, h and a during the same revolution to 

 which Table XV. corresponds, represented by 



^-^r- sni I ^^, cos l-\-o log a, 



sm 1 ' sni i ' 



if being the modulus of the common system of logarithms. 



H May, 1865. 



