206 Prof. A. W. Pucker on the Density and 



part of the representation of the experiments, not a " hump " 

 upon a fundamental circle. 



The only case in which Mr. Pickering's point of view is 

 allowable is that in which the range expressed by the curve 

 assumed to be fundamental is very much greater than that 

 over which the assumed disturbance extends. In the case of 

 my equation this is not so. If the last term be omitted, the 

 curve fails to fit the experiments over more than half the 

 range to which it applies, and fails entirely outside that range. 

 The first terms have no sort of claim to be regarded as funda- 

 mental. All are alike empirical and must be taken together. 



Further proofs of the weakness of such arguments are not 

 wanting. If it is permissible thus to separate the terms of 

 the equation, we may treat them in other ways. 



The first part of my expression gives a straight line, which 

 expresses Mr. Pickering's results very well (and with a slight 

 modification would express them still better) between 46*94 

 per cent, and 58*94 per cent. Above the latter point a linear 

 equation does not suffice. As this point is close to one of 

 Mr. Pickering's breaks he might, by dividing my equation 

 thus, have argued that it proved the existence of this break ; 

 but by separating the terms in another way he has been led 

 to the opinion that this is the only break which the equation 

 satisfactorily bridges. 



A method of manipulating the symbols which leads to such 

 discordant results is self-condemned. When Professor Lodge 

 condemned in 'Nature' the use of empirical equations for 

 detecting discontinuities, Mr. Pickering disclaimed the method. 

 He is now using it in his defence. He makes different 

 equations of my one by leaving out various terms at pleasure, 

 and then proceeds to argue as though they had some physcical 

 meaning. 



(5) Mr. Pickering contends that my curve extends to so 

 small a distance beyond the first and last break alleged to 

 exist within its range that it cannot be regarded as having 

 bridged them. 



Had I started close to one of Mr. Pickering's breaks, he 

 would no doubt have argued that the fact that my curve did 

 not apply beyond it proved the existence of a discontinuity. 

 His conclusions would, however, have been disproved had I 

 shown that his experimental results could be equally well 

 represented by a series of discontinuous curves, each of which 

 began within the range of a part of the curve which he con- 

 sidered continuous, and bridged continuously a part which he 

 regarded as discontinuous. If these new curves had the same 

 average length as his own, the distances of their extremities 



