53, 54] PRINCIPLES OF MECHANICS. UNITS AND DIMENSIONS. 101 



what acceleration the earth's pull would cause this mass to 

 receive, if allowed to fall. Experiment shows that in a given 

 locality on the earth's surface all bodies fall in vacuo with the 

 same acceleration. The value of this acceleration is denoted by g, 

 and its value at the sea-level in latitude 45 is 



OTY1 



#=980-606 '-. 



sec. 2 



Accordingly the force exerted by the earth on a mass of m grams 

 is mg dynes, or the 



weight of a kilogram in latitude 45 = 980,606 dynes. 



Now the value of the acceleration g is not constant, but varies 

 as we go from place to place on the earth's surface, ascend moun- 

 tains or descend into mines. Accordingly, the weight of a kilogram 

 is not an invariable, or absolute standard of force. At the center 

 of the earth, a kilogram would weigh nothing. Its mass is, how- 

 ever, invariable. The value of g at points on the earth in lati- 

 tude X and h centimeters above the sea-level, is given by the 

 formula, originally given by Clairaut*, 



g = 980-6056 - 2*508 cos 2X - '000003/L 



For further information with regard to units, the reader may 

 consult Everett's Units and Physical Constants. 



* Everett, Units and Physical Constants, Chap. in. 



