ASTRONOMY 



APPENDIX. 



ON THE METHOD OF DETERMINING BY OBSERVA- 

 TION, THE CONSTANT CO-EFFICIENTS IN AN AS- 

 SUMED OR GIVEN FUNCTION OF A VARIABLE 

 QUANTITY. 



Observation makes known the places of the heavenly 

 bodies only for instants, separated from one ano- 

 ther by certain intervals of time ; but the purposes 

 of science require, that they should be determined 

 for any time whatever, or for every instant. This 

 is rendered practicable by the consideration, that 

 the magnitude which determines the place of any 

 body, its longitude or latitude for example, is a 

 variable quantity, between which and the time (a 

 variable quantity also) a certain relation continues 

 always the same. This relation may therefore be 

 expressed by an equation, which, for every value 

 of one of the variable quantities, will give the cor- 

 responding value of the other; so that the one of 

 them may be assigned in terms of the other, or in 

 what is called a Function of it. The form of this 

 function is sometimes known from theory or ana- 

 logy, and at other times it is wholly unknown. In 



the 



