208 



OBSERVATIONS OF THE TERRESTRIAL 



TABLE VII. (Continued.) 



The equations of condition (E) are of the first dimension with 

 respect to the two unknown quantities they contain, and may be 

 written 



ax + by = c ; (F) 



in which the values of a, b, and c (or of (p - /u ) cos A, A - A , and 

 h - h ), are given in the preceding table. In order to deduce the 

 most probable values of the two unknown quantities, these equa- 

 tions must be combined by the method of least squares. Accord- 

 ingly multiplying equation (F) by the coefficient of a? (a), and by 

 the weight (w) of the determination which it represents, and adding 

 the results, we have 



and, performing the same operation with respect to the coefficient 

 of the other unknown quantity, 



8 (icab) x 4 8 ( 



8 (wbc) . 



These are the two final equations which, by elimination, will fur- 

 nish the most probable values of the quantities sought. 



Let the values of x and y, obtained from these equations, be A 

 and B ; then substituting in (D), 



r cos u = A, r sin n - B ; 



