276-278] 



ROTATION OF THE EARTH. 



353 



free body falling from relative rest in the neighbourhood of the 

 place. 



We shall write W for the weight of the body, m for its mass, 

 and g for the acceleration due to gravity, and we shall regard the 

 Earth as a sphere of radius R and mass E attracting like a 

 particle of the same mass placed at its centre. We shall find 

 that W is not equal to the force ymE/R z with which the Earth 

 attracts a body, and we shall find that W is equal to mg. 



278. Weight of a body. The difference between W and 

 ymE/R 2 arises from the Earth s rotation. We may say roughly 

 that some part of ymE/R* is required to maintain the circular 

 motion of the body about the polar axis, and that the remainder 

 is the force W. 



Let X be the angle which the radius of the Earth drawn to the 

 place makes with the plane of the equator. The body describes a 



Fig. 84. 



circle of radius R cos X with angular velocity II, and thus the 

 acceleration ^Rf^cosX towards the axis must be produced by the 

 force of magnitude W supporting the body, and the force ymE/R 2 

 towards the Earth s centre. 



Let I be the angle which the direction of W makes with the 

 plane of the equator. Then I is the (astronomical) latitude of the 

 place. 



