TABLES OF NEPTUNE. 83 



But if tlie date is earlier than 1779 or later tlian 1943, P^^ and P^j must first 

 be corrected from Table XIV. 



Write these four products under each other, remembering that their algebraic 

 signs will be the same as those of the sine and cosine of I and 2 I, unless the cor- 

 rections make P^^ or P„j negative. Write under them the fifth quantity, 6vi. 



Enter Tables VI. to XIII. inclusive, with the arguments at the top of each. 

 Take out the eight remaining values of Sv. 



Enter Table XV. with I, first reducing the minutes and seconds to decimals 

 of a degree, and take out the corresponding equation by interpolation to second 

 differences. 



Under these fourteen quantities write I and y, add up the sixteen lines, and call 

 the sum u. 



Under u write 6 ; enter Table XVI. with t(, (reduced to hundredths of a degree) 

 as the side argument, and the year as the top argument, and take out the reduction 

 to the ecliptic. Add it to u and Q, and the sum will be the heliocentric longitude 

 of Neptune referred to the mean equinox and ecliptic of the date. 



Enter Table XVII. with argument 1, and take out the values of R,,x and i^^.i- 

 If the date is previous to 1779 or subsequent to 1943, multiply the values of 

 Ai^..i and AP^.i from Table XIV. by 10.53, and correct R,x and R^^ as follows : 



i2,i by 10.53 AP,i, 

 i2,,iby — 10.53 AP,.i, 



adding the units of these products to the last figures oi R^x and R^i. Then multiply 



Rs,i by sine of I, 

 R^i by cosine of I, 



and write down the products with the algebraic sign of sine I and cos I respectively. 



Enter Tables XVIII. to XX. with their proper ai-guments, and write the results 

 under the products thus found. 



Enter Table XXI. with the argument I, and take out the corresponding number, 

 the first two figures of which are at the top of each column. Write it so that 

 the last figure (the seventh place of decimals) shall be under the last figures of 

 the former numbers. 



The sum of the six numbers thus found will be the common logarithm of the 

 radius vector of Neptune. 



Enter Table XXII. with argument 1, and take out B^^ and B^^. Multiply the 

 former by sin I and the latter by cos I. 



Enter Tables XXIII. and XXIV. with their proper arguments, and take out 

 the corresponding numbers, applying the proper algebraic signs. 



Take the sine of i from Table XXV., and multiply it by the sine of m {u having 

 already been found). 



The sum of the five quantities thus found, each taken with its proper algebraic 

 sign, will be the north latitude of Neptune above the plane of the ecliptic of the date. 



Thus we shall have the heliocentric co-ordinates of the planet. The computer 

 can then pass to the geocentric place by the method which he prefers. 



If an ephemeris is wanted during a series of j'ears, it will not be necessary to 



