190 Dr. Norman Campbell on the 



second from the last 5. The differences between the 

 resulting values of b and c obtained from these two parts 

 of the observations differ by far more than the probable 

 error ; this difference is an indication that the formula 

 applicable to the observations with small values of y is 

 not applicable to the observations with large values. It 

 is not strictly legitimate to apply the same values of b, c, m 

 to all the observations. And if: it is not legitimate, of 

 course the method of Z.S., which divides the observational 

 material into two parts and assumes that the equation is 

 equally true for all of them, will give a result different 

 from that obtained by the methud of L.S. which treats 

 that material as a whole. If our object is merely to 

 represent the observations as nearly as possible by a con- 

 venient empirical formula, it may certainly be better in 

 such cases to employ the method of L.S. : a closer fit is 

 likely to be obtained. But then the problem is not one 

 of pure physics, which is not concerned at all with merely 

 empirical formulae ; neither method of adjustment has in 

 such cases any true validity at all, for the adjustment itself 

 is fundamentally false. And if the object is merely to 

 obtain an empirical formula it may be urged that, though 

 L.S. gives a closer fit, it is scarcely worth obtaining at the 

 expense of the enormously greater labour. 



It may be noted that, for comparison, the observations of 

 Examples 1 and 3 have been divided similarly into two parts, 

 each of which is adjusted separately by L.S. The results 

 are given at the foot of each table. It will be seen that in 

 these examples, where the equations do fit the observations 

 (although the equation of Example 3 is also empirical), there 

 is very much less difference between the values given by the 

 two parts of the observations. (The value of m for the second 

 half of Example 1 is subject to a very large probable error, 

 as may be seen by examining the observations on which it is 

 based ; the differences are not at all inconsistent with the 

 applicability of the same constants to the whole of the obser- 

 vational material.) 



5. Some further considerations. 



These examples — and a great many others have been 

 -examined — show that the method proposed is perfectly 

 practicable and that it does not lead to results differing 

 very greatly from those of the method of L.S. And that 

 proof, as I hold, throws the task of justifying their action on 

 those who continue to emplo}^ a method which is admittedly 

 invalid theoretically and exceedingly cumbrous in practice. 



