4 ■ J. G. MacGEEGOE on THE 



a velocity which is uniform both as to magnitude and direction. Now velocity is a 

 relative conception, that is, it can be specified only by reference to a point and to lines or 

 axes through the point ; and the velocity of a body which is uniform relatively to one point 

 and one set of axes, may be variable if specified by reference to another point and another 

 set of axes. Hence if the first law be regarded as a definition, we require to consider 

 this body as not acted upon, or as acted upon, by force, according as we may happen to 

 specify its A'elocity by reference to the one or the other point and set of axes. Now, while 

 it is difficult, and indeed impossible, to express in words the ordinary conception of force, 

 this conception being given us by sense, it is clear that according to this conception a 

 body either is, or is not, acted upon by force. Its being so acted upon does not depend upon 

 our point of view. Hence the conception of force which is given by the laws of motion 

 regarded as forming a definition, is different from, and wider than, the ordinary con- 

 ception. 



In the remarks I have to make I shall employ the ordinary conception of force. But 

 let it be noted that ordinary is not synonymous with popular. That the ordinary concep- 

 tion is also the usual scientific conception, is shown by the fact that some at least of the 

 natural forces are held to be capable of being expressed as functions of the masses and the 

 distance, of the particles between which they act, mass and distance being quantities 

 which according to the usual conceptions of them do not vary with the point and axes by 

 reference to which positions, velocities and accelerations are specified. 



The Laws of Motion, when thus regarded as statements about the action of force, 

 may, so far as the translation of bodies is concerned, be considered either as generalisa- 

 tions established by direct though necessarily somewhat rough experiments, or as hypo- 

 theses made to explain phenomena and verified by means of the deductions drawn from 

 them. When, however, we come to study the effect of force in changing the rotation of 

 bodies or their state of strain, we assume the laws of motion to hold for the small parts 

 (particles or elements) of which we imagine the bodies to consist. And hence, since it is 

 impossible to make experiments on particles, without the aid of Maxwell's so far unem- 

 bodied demons, the laws of motion, as forming the basis of the whole science of dyna- 

 mics, must be regarded as hypotheses. 



The remarks I have to make on these hypotheses have reference to four points. First 

 I wish to consider whether or not the laws of motion may be made more precise in their 

 enunciation ; secondly, whether or not they are independent ; thirdly, whether or not they 

 are sufficient for the deduction of all the laws of abstract dynamics, and if not, what addi- 

 tion should be made to them for this purpose ; and finally whether or not the laws of 

 motion thus found necessary may be diminished in number. It is hardly necessary to 

 bring argument to show that the axioms of our science ought to be precise in their 

 enunciation, independent of one another, sufficient for the deduction of all propositions 

 applicable to natural forces generally, and as few as possible. 



That when regarded as statements about force the first and second laws of motion 

 are not precise in their enunciation, becomes obvious when we consider that, as force has 

 a non-relative character while velocity and acceleration vary in magnitude and direction 

 according to the point and the directions of reference, these laws cannot hold generally, 

 but only provided the motion of bodies be specified in a particvrlar way. It is important 

 therefore to determine what mode of specification of motion they imply. 



