200 MOTION UNDER CONSTANT FORCES 



Squaring and adding, and denoting the apparent weight, as usual, 

 by mg, we obtain 



m*g* = X 2 +Y 2 = ra 2 (<9 2 - 2<A G cos 2 X-f o>Vcos 2 X). (55) 



Taking the diameter of the earth to be 7927 miles, and the 

 value of G (the acceleration due to gravity at the North Pole) 

 to be 32.25, we easily find that 



~ = 290' 



The square of this is so small that to a first approximation it 

 may be neglected, and equation (55) may be written in the form 

 g G a?a cos 2 X. 



Thus the apparent weight in latitude X is less than the true 

 weight by mco z a cos 2 X, or about -%%-Q cos 2 X of the whole weight. 



The apparent weight does not act along the radius CP. If we 

 suppose it to act at an angle 6 with this radius, we obtain, from 

 equations (53) and (54), 



a _ Y _ ca?a cos X sin X 

 ~~ 



cos X sin X, approximately, 



giving the deviation of the plumb line from the earth's radius at 

 any point. 



FRICTIONAL REACTIONS BETWEEN MOVING BODIES 

 165. It is found experimentally that the relation 



(in which F, R are the tangential and normal components of the 

 reaction between two bodies) remains very approximately true 

 when the bodies are sliding past one another. The value of , 

 the coefficient of friction, is not quite the same as when the 

 bodies are at rest, the latter being always somewhat larger. 



Friction between two bodies which are sliding past one another 

 is called dynamical friction, that between two bodies at rest being 

 called statical friction. 



