FRAME OF REFERENCE 35 



at the equator will appear to act on a spring balance with a force 

 equal only to the earth's attraction on 99 6 J grammes. 



A second set of errors would be introduced by referring motion 

 to axes in the earth's surface, these being caused by the change in 

 the directions of the axes. For instance, if we use the laws of 

 motion as though they were true for motion referred to axes fixed 

 in the earth, and apply these laws to the fall of a stone, we shall 

 find that the stone ought to strike the ground at a point vertically 

 below that from which it is dropped. If we allow for the rotation 

 of the earth, we shall find that the point at which the stone actually 

 strikes must be somewhat to the east of the point vertically below 

 that from which it started. 



The errors introduced by treating motion on the earth as though 

 it were motion with reference to axes fixed in space are, in gen- 

 eral, either extremely small or very easily corrected. We shall, 

 therefore, proceed at present by neglecting such errors altogether, 

 and shall apply the laws of motion to motion with reference to 

 the earth's surface. 



LAWS APPLICABLE ONLY ;ro MOTION OF A PAKTICLE 



26. There is a further limitation to the completeness of New- 

 ton's laws which ought to be noticed here. The second law would 

 lead us to suppose that from a knowledge of the force acting on a 

 body, and the mass of the body, we could deduce a definite accel- 

 eration of the body. But if the body is of finite size, the accelera- 

 tion will be different at different points of the body ; for example, 

 we have seen that, as a consequence of the earth's rotation, the 

 acceleration of a point at the equator of the earth is different from 

 that of a point at the North Pole. Which acceleration, then, is it 

 that is determined by the second law ? 



The answer to this difficulty is that the second law must be 

 supposed to apply only to particles, i.e. to pieces of matter so 

 small that they may be regarded as points. A moving particle has 

 a single definite acceleration, just as a moving point has. From the 



