SECT. 1.] THREE COMPLETE OBSERVATIONS. 231 



may be put equal to I -\- n, may be determined. By reasonings analogous to 

 those which have been developed in article 140, will be obtained the equation 



_ R sin S sin (A D 5&quot;) , / , sin n \ &quot; 



~ H &quot;&amp;gt; rf ~\ H T R sin V l n ~&quot;~ n 



Let us designate the coefficient of n, which agrees with a, article 140, by the 

 same symbol a, and the coefficient of n r by ft : a may be here also determined 

 by the formula 



.g sin (* + Q 

 K sin V l n 



&quot;We have, therefore, 



Q = an 



which equation combined with these, 



P = ^ 



produces 



whence we shall be able to get /, unless, indeed, we should have ft = 0, in which 

 case nothing else would follow from it except P ==. a. Further, although we 

 might not have , 9 = (when we should have the third case to be considered in 

 the following article), still ft will always be a very small quantity, and therefore 

 P will necessarily differ but little from a : hence it is evident that the deter 

 mination of the coefficient 



P+a 



is very uncertain, and that /, therefore, is not determinable with any accuracy. 

 Moreover, we shall have 



V_ _P+ y_ P-\-a. 

 ~n~ (J n&quot; ~JP~ ~ 



after this, the following equations will be easily developed in the same manner as 

 in article 143, 



