ASTRONOMY. 



There are two cases of this problem, one, when the 

 constant quantities are yet entirely unknown, ano- 

 ther, when they are already approximated, and 

 only require to be farther corrected. In the first 

 case, the process is very simple. 



235. Substitute the quantities known by ob- 

 servation for y and <r, in the given formula, 

 (each observation being supposed to afford a va- 

 lue both of x and of #), and thus, as many equa- 

 tions will be obtained, as there are observations. 

 Then let there be composed, from the addition 

 of these into separate sums, as many equations 

 as there are quantities to be found. The solu- 

 tion of these equations will give the quantities 

 required, and because, in a multitude of obser- 

 vations, the errors must in a great measure 

 compensate for one another, the results thus ob- 

 tained will be more accurate, cceteris paribus, the 

 greater the number of the equations combined. 



The postulate on which this rule proceeds is, that 

 though each of the given equations is incorrect, 

 on account of the unavoidable errors of observa- 

 tion, there is nothing that determines the amount 

 of the errors to be on one side more than another, 

 or in excess rather than defect. By adding a 

 number of the equations together, the errors may 

 therefore be expected, in part at least, to balance 



one 



