740 



SGIENGE. 



[N. S. Vol. XII. No. 307. 



A DETERMINATION OF THE NATURE AND 

 VELOCITY OF GRAVITATION." 



The present note is to be taken as a sup- 

 plement to my previous paper on ' The Na- 

 ture of the Electric and Magnetic Quanti- 

 ties.' t A fuller development of the theory 

 of gravitation advanced by the writer is in 

 course of preparation. This will, however, 

 be delayed for some time, possibly for several 

 years, as it is desired to investigate certain 

 phenomena rather more accurately than 

 has hitherto been done, and at present the 

 writer is occupied with pressing work in 

 another line. 



It has seemed advisable, however, to 

 publish this determination of the velocity 

 of gravitation at the present time, and with- 

 out waiting to complete the fuller treatment, 

 for the reason that, as will be seen later, 

 the value obtained clears up a number of 

 perplexing optical problems, and removes 

 a number of obstacles which have hitherto 

 stood in the way of the development of that 

 branch of physics. 



On account of the fact that the writer's 

 papers on these subjects have unavoidably 

 been published in somewhat scattered form, 

 it is considered best to give a brief resume 

 of the work which forms the basis of the 

 method by which this velocity is deduced. 



In 1893 the writer perceived that Four- 

 ier's ' Dimensions ' could be developed into 

 a very powerful agent of research, and one 

 which should bear a relation to the usual 

 methods similar to that which Qualitative 

 chemistry bears to Quantitative. It was 

 for this reason that the name ' Qualitative 

 Mathematics ' was given to this new branch. 



As its name signifies, it is used, not for 

 the exact determination of numerical quan- 



* Being a supplement to ' A Determination of the 

 Nature of the Electric and Magnetic Quantities and 

 of the Density and Elasticity of the Ether.' 



\ Phys. Rev., January, 1900; and also of the earlier 

 papers: 1891-2, on 'The Laws and Nature of Cohe- 

 sion. ' 



titles, but for the prediction and classifica- 

 tion of phenomena.* 



It was first shown f that the nature of 

 electricity and magnetism was, at that time, 

 indeterminate, as all the electric and mag- 

 netic phenomena which we were able to 

 completely express dynamically could be 

 comprised in three qualitative equations, 

 whilst we had four unknown quantities. 



Then, by several methods, Williams's re- 

 sult, that either specific inductive capacity, 

 {h), or permeability (,a), must be a density, 

 the other term being a compliancy, was 

 confirmed. 



It was then further deduced that the one 

 which is a compliancy must decrease with 

 the first power, whilst the one which is a 

 density must decrease with the second 

 power, of the corresponding intensities, i. e., 

 if F be the electric potential difference per 

 unit length, and S be the magnetic poten- 

 tial difference per unit length, then if // be 



* Such a branch of mathematics is absolutely neces- 

 sary to supplement the work done by the other meth- 

 ods. For the latter can tell us nothing of the nature 

 of the cxuantity involved. Their very greatest strength 

 is their greatest weakness. The fact that a certain 

 function, which gives us the state of things at the end 

 of an organ pipe, also gives us the way a current of 

 electricity distributes itself near the end of a wire 

 dipping in a mercury cup is gratifying in its compre 

 hensiveness, but disappointing in that when we meet 

 that function, we do not know which of the many 

 possible phenomena it represents. Take, for instance, 

 our equations for light. They fit in with a simple 

 elastic-solid wave, and we have fallen into the habit 

 of speaking of light as really being such a wave, 

 and some eminent physicists, even, as I have pointed 

 out elsewhere, have fallen into the mistake of sup- 

 posing that the magnetic rotation of light neces- 

 sarily implies a rotation of the medium in a mag- 

 netic field, overlooking the fact that the whole 

 proof is based on this unfounded, and, as we now 

 know, certainly incorrect, supposition. All that the 

 equations really mean is that light is some kind of 

 periodic motion, but, if I remember rightly (as it 

 was some years ago that I investigated the matter), 

 there are eight kinds of periodic motion which can be 

 equally well represented by the light equations. 



-flbid., a,\so Elect. World, May 18, 1895. 



