Hypotheses of Dynamics. 241 



a reference of motion to the fixed stars and the earth's 

 rotation. No doubt, in practical observation of motions on 

 the earth's surface or in space, we must still employ, im- 

 mediately, points fixed in the earth, or the fixed stars, 

 respectively, as reference systems, and the earth's rotation as 

 giving us our time-scale, applying to the crude observations, 

 when necessary, the corrections which may have been de- 

 termined. But the laws as expressed above both give a 

 theoretical justification of this course and indicate the way in 

 which the necessary corrections may be made more and more 

 accurate. If the laws of motion in the form referred to be 

 assumed, it may readily be shown that in the circumstances 

 in which we find ourselves, surrounded on all sides by bodies, 

 at vast distances, which are moving with velocities of apparently 

 the same order of magnitude as our own, these bodies may be 

 employed as a rough reference system ; that the earth, con- 

 stituted and situated as it is, must be rotating with a roughly 

 uniform angular velocity relatively to these bodies, and that 

 therefore we are justified for most practical purposes in using 

 the fixed stars as a reference system and the earth's rotation 

 as a time-scale. Moreover, with this assumption it becomes 

 apparent that the corrections to be applied to the crude 

 observations made relatively to this reference system and this 

 time-scale, must become more accurately known as we acquire 

 increased knowledge of the motions of the stars and of the 

 masses and motions of the members of the solar system*. 



It may turn out, of course, that the assumption on which 

 the above method rests is untenable, that in fact there may 

 be no axes by reference to which Newton's laws hold. In 

 that case other axioms will have to be formulated. Meantime 

 the above general form of the laws may be said, at least 

 qualitatively, not only to give us as a particular case the 

 empirical expression which they have at present, but also to 

 account for those of the past and to indicate the lines on which 

 we must work that they may be improved in the future. 



I mentioned above two legitimate ways in which dynamical 

 reference systems may be determined. The attempt has been 

 made to determine them in what seems to me an illegitimate 

 way, viz. by assuming a priori that such systems must have 

 certain characteristics, notably that they must have no rota- 

 tion. This is the only kind of method to which Prof. Lodge 

 seems to refer in the paragraph in which he gives a sketch of 

 the difficulties in the way of specifying axes (p. 7). It is 



* Thus this mode of expressing the relativity of the laws of motion 

 has, in addition to the advantages just mentioned, that which Mach 

 claims for his, that its tendency is to stimulate the progress of science. 



