4 BEST AND MOTION 



reference. So also we could say that the fly was at rest) the car 

 being taken as frame of reference. Obviously any framework, real 

 or imaginary, or any material body, may be taken as a frame of ref- 

 erence, provided that it is rigid, i.e. that it is not itself changing 

 its shape or size. 



We may accordingly say that a point is at rest relatively to any 

 frame of reference when the distance of the point from each point 

 of the frame of reference remains unaltered. 



6. Motion relative to frame of reference. Having specified a 

 frame of reference, we can discuss not only rest but also motion 

 relative to the frame of reference. When the train has moved 

 a mile over the tracks we say that it has moved a mile rela- 

 tively to its frame of reference, the earth. When the fly has 

 crawled from floor to ceiling of the car we say that it has moved, 

 say, eight feet relatively to its frame of reference, the car. 



In fixing the distance traveled by the fly 'relatively to the train in an 

 interval between two instants t l , t%, we notice that the actual point from 

 which the fly started is, say, a mile behind the present position of the 

 train ; but the point from which we measure is the point which occupies 

 the same position in the par at time t 2 as this point did at time t r So, in 

 general, to fix the distance moved relatively to a given frame of reference 

 in the interval between times t l and 2 , we first find the point A which stands 

 in the same position relative to the frame of reference at time t 2 as did 

 the point from which the moving point started at time t^. The distance 

 from this point A to the point B, which is occupied by the moving point at 

 instant t 2 , is the distance moved relatively to the moving frame of reference. 



By the motion of a particle B relative to a particle A, is meant 

 the motion of B relative to a frame of reference moving with A. 



7. Composition of motions. Suppose that in a given time the 

 moving point moves a certain distance relatively to its frame of 

 reference, while this frame of reference itself moves some other 

 distance relatively to a second frame of reference, as will, for 

 instance, occur if a fly climbs up the side of a car while the car 

 moves relatively to the earth. 



Let us suppose that there is a frame of reference moving in 

 the plane of the paper on which fig. 1 is drawn, and that the 



