8 Trans. Acad. Set. of St. Louis. 



we arrive at the following formulas : 



-E^=^^^ + 2Ft:-{-B^-}-g. 



Now, it is obvious that — i?g, — R , — R^ are exactly the- 



components of the true force of gravity at the point (|, tj, ^). 

 If, then, we denote by V the ti^ue potential of the force of 

 gravity^ we shall have 



(16) F=^r+^^^n- <s>^^r;+^^^r-f-^p+^^2+/'^2+5^r. 



9. In conclusion let us have a glance at the relative value 

 of the several coefficients entering formula (16). As already 



remarked, the order of magnitude of ^c.„, ^ ^>- is that of 



" ^0' 770, ^0 



the principal terms in the expressions of the coefficients D^ 



M 

 E^ F^ that is, of the order of -^. The coefficient B and 



the secondary terms in the expressions of Z), E, F are of the 



M 

 order of the product of "w by the oblateness of the earth.* 



Hence, if the components of the solar and lunar attraction 

 are not taken into account when computing the forces of 

 gravity at a point on the surface of the earth, it is needless 

 to preserve any but the first term in the expression (16) of 

 the potential, which, then, reduces to the familiar form 



* In the units here selected the approximate values of — , _, (o"^ are: 



M 



Kg = 0. 000 001 5 , 



N 



gg = 0. 000 000 001 5 , 



fo^ = 0. 000 000 005 3 . 



It may, also, be noted that, approximately, 



€ = 0.0084 sin 2X and :^ sin e = 0. 000 000 006 sin 2X. 

 S3 



