TABLES OF NEPTUNE. 77 



All these quantities have the same values as in 19, pp. 40 and 41. 



The elliptic values of the co-ordinates being thus corrected, we have the helio- 

 centric co-ordinates resulting from the concluded theory. 



To facilitate this computation, the following tables are constructed. They are 

 designed to give the means of determining, for any date between the years 1600 

 and 2000, the principal auxiliary quantities which will be needed in computing 

 the place of the planet from the above theory. Many of these quantities are 

 modified so that the computer shall be troubled as little as possible with difference 

 of signs. Thus, to all the quantities P s , P a R s , etc. constants are added so that 

 they shall always be positive, and so that the signs of the products which form 

 the perturbations shall be the same as those of sin /, cos I, etc. Again, constants 

 are added to all the perturbations of the longitude and radius vector, to make 

 them positive. 



37. Data given in the several tables. 



TABLE I. gives the values of the " epochs and arguments" for the beginning of 

 each fourth year from 1800 to 1952 inclusive, the years 1800 and 1900 beginning 

 with Greenwich mean noon of Jan. 0, and all the other years with that of Jan. 1. 



Pis simply the number of the four-year cycle before 1900, by which I' and & 



1900 Y 



of the next table must be multiplied, or - 7 , adding a unit for fractions. 



I is the mean longitude in orbit of Neptune, affected with the long-period per- 

 turbations of that clement, p. 39, and referred to the mean equinox of 1850.0. 



y is the negative of the longitude of the node affected by perturbations, counted 

 on the orbit of the planet from that point which is equally distant from the node 

 of 1850 with the equinox of 1850, and diminished by 1, the sum of the constants 

 added to the equations of longitude. 



6 is the longitude of the node, referred to the mean equinox of the epoch, and 

 diminished by 1', the constant added to the reduction to the ecliptic. 



In the arguments 1 to 9 inclusive, the circle is divided into 400 parts. Repre- 

 senting the mean longitude of a planet, referred to the equinox of 1850.0 by its 

 initial letter, the values of the different arguments are as follows : 



Arg. 1 = U N, 



" 2 = S N, 



" 3 = J N, 



4 = 2S N, 



" 5 = S, 



G = S 2N, 



" 7 = 2J N, 



S = J, 



" Q=J 2N. 



>> 



Thus, Arg, 1 gives the difference of the mean longitudes of Uranus and Neptune, 

 expressed in parts 100 of which make a quadrant ; and so of the other arguments. 



At the bottom of the table the expression A[}^)is the change in the longitude 

 or the argument during that 180 days which commences with 1850, Jan. 0. 



