82 TABLES OF NEPTUNE. 



4. The terms 



— 150 sin I — 100 cos I 



introduced to destroy the effects of the constants added to J^^i and R^^. 



Table XXII. gives the values of 5,,i and jB^.i (p. 40). The constant 0".30 has 

 been added to each of these quantities to render them positive. 



Tables XXIII. and XXIV. give the perturbations of the latitude produced by 

 Saturn and Jupiter respectively, no constants being added. 



Table XXV. gives the values of log sin i, to be added to log sin u in order to 

 obtain the elliptic latitude. They, as well as d, have been obtained from the 

 formulas 



sin i sin Q ^p -[-hp -\- 0".30 

 sin i cos Q ^q-{-hq — .30 



The values of hp and ^q being taken from the table p. 39, and the corrections 

 ± 0".30 being applied to destroy the effect of the constants added to B^^ and B^^. 



§ 38. Elementary precepts for the use of the tables. 



Express the date for which the position of Neptune is required, in years, months, 

 and days of Greenwich mean time, according to the Gregorian Calendar. 



If the date is between 1800 and 1955 inclusive, enter Table I. with the year, 

 or the first preceding year found therein, and take out the values of ?, y, d, and 

 Arguments 1-9 inclusive. Note also the value of P. If the date is not between 

 the above limits, enter as if the number of the century were 18. 



Enter Table II. with the excess of the actual year above that with which 

 Table I. was entered, and with the month. Write the values of ?, y, 6, and the 

 arguments under those from Table I. Multiply I' and 6', the former interpolated 

 to the day of the month, by P of Table I., and write the units of the product under 

 the hundredths of seconds of I and 6, paying attention to the algebraic signs. 



Enter Table III. with tlic day of the month, and write down I, &c., under the 

 former values. 



If the date is without the limits 1800-1955, enter Table IV. with the century, 

 write the principal quantities under their proper heads, as before ; multiply column 

 "Fact. T" by the entire fraction of the century repi-esented by the date, and 

 column "Fact. T'-" by the square of this fraction, and write the products under 

 their proper heads. 



Add up all the partial values of I, y, 0, and the arguments thus obtained, 

 attending to the algebraic signs of the products, subtracting from the arguments 

 as many times 400 as possible, and we have the final values of those quantities. 



Enter Table V. with the final value of Arg. 1, and take from it the five quan- 

 tities there found. Multiply the first four of them as follows, using logarithms 

 or natural numbers as may be most convenient : 



i^i by sine of I, 

 Pc.i by cosine of I, 

 P,2 by sine of 2 I, 

 Pc.2 by cosine of 2 I. 



