jgg THE ORBIT OF URANUS. 



cen wry after 1850, corresponding to the date with which Table II was entered, 

 and write the product under 0, or add it to it in writing 0. If Table II was 

 entered with a date before 1850, this product is negative. 



Enter Table IV with the day of the month and write down the corresponding 

 values of g, co, etc., under the former values. 



If the date does not correspond to Greenwich mean noon, the motion of g for 

 the hours must be computed from Table V, and the other quantities must be 

 interpolated to the fraction of a day in entering Table IV. 



Enter Table VI with the year, find by interpolation the values of g, and argu- 

 ments 1, 2, and 3, corresponding to the date, and write them under the former 

 values. 



Add up all the partial values of g, o, 0, and the arguments, attending to the 

 algebraic signs of the products. Subtract from the arguments as many times 600 

 as possible, and the results will be the final values of those quantities. 



Enter Table VII with g as the argument, the seconds being first reduced to frac- 

 tions of a minute, and interpolate the quantities E and log r. When g exceeds 180 

 the former quantity is to receive the negative sign; the latter is always positive. 



Enter Tables VIII to XVI inclusive with their respective arguments, and take 

 out the values of the quantities (v.c.O), (w.s.l), (w.c.l), etc., (p.c.O), (p.s.l), etc., so 

 far as they are found in the tables, writing the quantities having the same desig- 

 nation under each other. In Table IX the quantities Sec. Var. must be multiplied 

 by the centuries and fraction of a century of the actual date after 1850, and the 

 product must be included with the corresponding quantities, (v.s.l), (f.c.l), etc. 

 Before 1850 this product will always be negative; afterward always positive. All 

 the quantities taken from these tables are positive except (v.sA) and (.c.4) in 

 Table IX, which are negative. 



Add up all the partial values of (v.c.O), (v.s.l), etc., thus obtained from Tables 

 VIII to XVI, and from their sum take the corresponding quantities obtained from 

 Table XVII by intci-polating to the date. The required quantities are all given 

 in Table XVII fe ; Table XVIIa being only an expansion of a part of XVII & for 

 the present century. The final values of (v.s.l), (v.c.l), (w.s.2), etc., (p.s.l), (p.c.l), 

 etc., thus obtained are to be multiplied by the sines and cosines of the correspond- 

 ing multiples of </, in doing which four place logarithms are sufficient if the com- 

 putation is carefully made. The products are then all added together, and to g, w, E, 

 and (v.c.O); in the case of v, and to log. r, (p.c.O) in the case of p. That is, we 

 are to form the expressions: 



u = g -f-o -\-E-\- (v.c.Q) -\- (v.s.l] sin g -f- (v.c.l) cos g 



-f (v.s.2) sin 2j -f (v.c.2) cos 20 

 -f- etc. -|- etc. 



log r = log r (from Table VII) -f- (p.c.O) 

 + (p.s.l) sin g) + (p.c.l) cos g 

 -J- (p.s.2) sin 2y) -j- (p.c.2) cos 2g 

 + (p.s.3) sin 3<7) + (p- c - 3 ) cos %9- 



