XIV.] UNITS AND STANDARDS OF MEASUREMENT. 3r.9 



condition, namely, that it perseveres uniformly unless dis- 

 turbed by extrinsic forces. Now uniform motion means 

 motion through equal spaces in equal times, so that if we 

 have a body entirely free from all resistance or perturba- 

 tion, and can measure equal spaces of its path, we have a 

 perfect measure of time. But let it be remembered that 

 this law has never been absolutely proved by experience ; 

 for we cannot point to any body, and say that it is wholly 

 unresisted or undisturbed ; and even if we had such a body, 

 we shovdd need some independent standard of time to 

 ascertain whether its motion was really uniform. As it 

 is in moving bodies that we find the best standard of time, 

 we cannot use them to prove the uniformity of their own 

 movements, which would amount to a petitio princijni. 

 Our experience comes to this, that when we examine and 

 compare the movements of bodies which seem to us nearly 

 free from disturbance, we find them giving nearly har- 

 monious measures of time. If any one body which seems 

 to us to move uniformly is not doing so, but is subject to 

 fits and starts unknown to us, because we have no absolute 

 standard of time, then all other bodies must be subject to 

 the same arbitrary fits and starts, otherwise there would be 

 discrepancy disclosing the irregularities. Just as in com- 

 paring together a number of chronometers, we should soon 

 detect bad ones by their going irregularly, as compared 

 with the others, so in nature we detect disturbed movement 

 by its discrepancy from that of other bodies which we 

 believe to be undisturl)ed, and which agree nearly among 

 themselves. But inasmuch as the measure of motion 

 involves time, and the measure of time involves motion, 

 there must be ultimately an assumption. We may define 

 equal times, as times during which a moving body under 

 the influence of no force describes equal spaces ; ^ but all 

 we can say in support of this definition is, that it leads us 

 into no known diliiculties, and that to the best of our ex- 

 perience one freely moving body gives the same results as 

 any other. 



Wlien we inquire where the freely moving body is, no 

 perfectly satisfactory answer can be given. Practically 

 the rotating globe is sufficiently accurate, and Thomson 



' Rankiiie, Philosophical Magazine, Feb. 1867, vol. xxxiii. p. 91. 



