FRAME OF REFERENCE 33 



The moon, in describing a circle round the earth, is believed to be acted 

 upon by the earth's gravitation in just the same way as the bullet. If no 

 force acted on the moon, it would describe a straight line ; as it is, it is 

 continually dragged down towards the earth, as we believe, by the 

 same force of gravitation as the bullet. Just in the same way, then, the 

 earth ought to experience an acceleration towards the moon. This accelera* 

 tion is one which admits of astronomical observation. 



24. In terms of ideas which have now been explained, the three 

 laws may be restated as follows : 



I. The normal state of a body is one of no acceleration. De- 

 partures from this normal state are produced by the action of 

 force. 



II. When a force acts so as to disturb the normal state of a 

 body, the force is proportional to the product of the mass of the 

 body by the acceleration produced. 



III. Forces occur in pairs, every action being accompanied by a 

 reaction, and each pair of forces being equal and opposite. 



FKAME OF REFERENCE 



25. In stating the laws of motion we have spoken of the motion 

 of a body without specifying the frame of reference relatively to 

 which this motion is to be measured. In practice, motion is gen- 

 erally measured relatively to the surface of the earth, whereas 

 Newton believed it to be possible to imagine a frame of reference 

 actually fixed in space, and intended all motion to be measured 

 relatively to this frame. Thus Newton's laws of motion apply to 

 motion referred to axes fixed in space, whereas what we require 

 to know, for all problems except those of astronomy, are the laws 

 of motion referred to axes moving with the earth. 



Let us first consider the effect of referring motion to a set of 

 axes moving with uniform velocity in a straight line through 

 space. A body under the action of no forces will have no accel- 

 eration in space, and, therefore, as the axes themselves have no 

 acceleration in space, will have no acceleration relatively to the 

 moving axes. Again, an acceleration has the same value whether 



