364 KELATIVE MOTION AND UNIVERSAL GRAVITATION. [CH. XIII. 



to reconsider the statements of the Principles of Conservation of 

 Momentum and of Moment of Momentum. These principles 

 were stated in Articles 111 and 112 for the motion of a system in 

 a given field of force, and they hold provided the field of force is 

 subject to certain conditions. They consequently imply that the 

 frame of reference has been so chosen that the field of force obeys 

 the conditions, and of course it is understood that the frame of 

 reference has been so chosen that the Postulates of Mechanics 

 apply to the system under discussion. We accordingly arrive at 

 the following statements of these principles : 



(1) When the motion of a system can be referred to a frame 

 for which the Postulates of Mechanics are applicable, and which 

 is such that the field of force relative to the frame gives rise to 

 zero resultant force in a -direction fixed relatively to the frame, 

 the linear momentum relative to this frame resolved in this direc- 

 tion is constant. 



(2) When the motion of a system can be referred to a frame 

 for which the Postulates of Mechanics are applicable, and which 

 is such that the field of force relative to the frame gives rise to 

 zero moment about an axis fixed relatively to the frame, the 

 moment of momentum relative to this frame about this axis is 

 constant. 



It is worth while here to remark that if one frame has been 

 chosen for which the Postulates apply they will still apply to a 

 new frame moving relatively to the first with uniform velocity in 

 a direction fixed relatively to the first, and if either of the above 

 principles has an application to the former frame it has an applica- 

 tion also to the latter. 



Now when any system can be treated as independent (Article 

 286) both the principles apply to it, and the moment of momentum 

 about any axis fixed relatively to the frame of reference, and the 

 linear momentum in any direction fixed relatively to the frame 

 of reference are constants. Taking the origin of the frame of 

 reference at the centre of inertia of the system, we see that the 

 linear momentum in any direction is zero. On the other hand 

 the moment of momentum about any axis being the moment of a 

 couple (of vectors localised in lines), the moment about any axis 

 is the resolved part of an unlocalised vector parallel to that axis. 



