49 ' General Met hod for determining 



dent of «, are : 1st, the number i; 2d, the product of the 

 two numbers, i and i'j 3d, the products of the three num- 

 bers i, i\ i", &c. 



The coefficients of -J^/3, + P.^,- 5'./3, &c. in the part 

 multiphed by z, are: 1st, the sum of the two numbers 

 i and i' ; 2d, the sum of the products two by two, of the 

 three numbers /, i' , i" ; Sd, the sum of the products three 

 by three of the four numbers /, if, i', i'" , &c. 



The coefficients of —P.p>, + ^.|3, -5'./3, &c. in the 

 part multiphed by 2% are : 1st, the sum of the three num- 

 bers i, i', i" ', 2d, the sum of the products two by two of 

 the four numbers i, i', i" , i'" ', 3d, the sum of the products 

 three by three of the five numbers i, ?', i" , i"', i"" , &c. 



By worl<ing in the same way on the latitudes of the co- 

 met, its latitude, according to the number z of days since 

 the epoch, will be expressed by the following formula, 



7— /.Jy + i.i'.S'.y — i.i'.i"J'.y + r'.i' J". i"'.6*7— &c. 

 Coy-(; + /'').5'r + {'•«' + i.i" + l'.i").S^y) 



+ ». }. -0.t.i" + i.i'i'" +i.i".i"' + i'.t".i"')J*y}- . . .{q) 



Coy- (<■ + /'') 

 ( + &c. 



+ ^ • ) + i\r + i'.i"' + i"w"').5>-&c. ( 



This being done, we shall have a equal to the part inde- 

 pendent of z in the formula (p). 



By reducing into seconds the coefficient of z, and sul)- 

 tracting from the logarithn) of this number of seconds, the 

 logarithm 3-3500072, we shall have the logarithm of a num- 

 ber which we shall designate by a. 



By reducing into seconds the coefficient of 2% by after- 

 wards taking the logarithm of the double of this number of 

 seconds, and subtracting from this logarithm the following, 

 J -7855 594, we shall have the logarithm of a number which 

 we shall designate by l). 



We shall afterwards have 9 equal to the part independent 

 of z in the formula {q). 



Bv reducing into seconds the coefficient of z, in this 

 forinula, and by subtracting from it 3- 5500072, we shall have 

 the logarithm of a number which we shall designate by h. 



Bv reducing into seconds the coefficient of z^ in this 

 same formula, and by subtracting 1-7855894 from the loga- 

 rithm of the doubleof this number of seconds, we shall have 

 the logarithm of a number which we shall designate by /. 



It is upon the precision of the values of a, h^ k, and /, 

 that the exactness of the following method depends ; and 

 as their formation is very simple, we must choose and mul- 

 tiply the observations so as to obtain them with all possible 



rigour. These quantities are the difierentials ('-j:J^ vlF/ 5 



