OUTLINES OF NATURAL PHILOSOPHY. 



one another, so that a more correct equation is 

 obtained than any one of those of which it is com- 

 posed. 



.'(no 



Some combinations of the equations, however, are 

 more advantageous than others. A good rule to 

 be followed in the selection of them, is to unite 

 in one sum all the equations in which the co-effi- 

 cients of the same unknown quantity, A for in- 

 stance, are the greatest, ordering it so that all those 

 co-efficients may have the same sign. Do the 

 same with respect to B and C, and the other quan- 

 tities to be found. Thus, each of the unknown 

 quantities will appear in one of the equations with 

 the greatest co-efficient possible, and will be de- 

 termined from the cases in which it had the great- 

 est share of the total effect. 



Suppose the general formula to be 



y . A sm x 4- 15 sm r, 



and that from observation we have eight values of 

 x and j/, viz. 



Values of x. 

 140 

 135 

 130 

 125 

 120 

 115 

 110 

 105 



Values of #. 



73'.5 



80.2 



87.0 



94.1 



99.5 

 104.5 

 107.5 

 110.2 



- - <V! 



1 Hence, 



