3(56 Dr. J. L arm or. Complete Scheme of Electrodynamie 



wards expand, transform, and even modify in detail. Although, 

 however, it is possible that we may thus be able ultimately to probe 

 deeper into the problem of aethereal constitution, just as the kinetic 

 theory has done in the case of atmospheric constitution, yet there 

 does not seem to be at present any indication whatever of any faculty 

 which can bring that medium so near to us in detail as our senses 

 bring the phenomena of matter : so that from this standpoint there 

 is much to be said in favour of definitely regarding the scheme of a 

 continuous rotationally elastic sether as an ultimate one. 



A formal scheme of the dynamical relations of free aether being 

 postulated after the manner of Maxwell and MacCullagh, and a 

 notion as clear as possible obtained of the sethereal constitution of a 

 molecule and its associated revolving electrons, by aid of the rota- 

 tional hypothesis, it remains to effect with complete generality the 

 transition between a molecular theory of the asthereal or electric 

 field which considers the molecules separately, and a continuous 

 theory expressed by differential equations which take cognizance 

 only of the properties of the element of volume, the latter alone 

 being the proper domain of mechanical as distinct from molecular 

 theory. This transformation is, as usual, accomplished by replacing 

 summations over the distribution of molecules by continuous inte- 

 grations over the space occupied by them. In cases where the 

 integrals concerned all remain finite when the origin to which they 

 refer is inside the matter so that the lower limit of the radius vector 

 is null, there is no difficulty in the transition : this is for example 

 the case with the ordinary theory of gravitational forces. But in 

 important branches of the electric theory of polarised media, some of 

 the integral expressions become infinite under these circumstances ; 

 and this is an indication that it is not legitimate to replace the effect 

 of the part of the discrete distribution of molecules which is adjacent 

 to the point considered by that of a continuous material distribution. 

 The result of the integration still, however, gives a valid estimate of 

 the effect of the material system as a whole, if we bear in mind that 

 the infinite term coming in at the inner limit really represents a 

 finite part of the result depending solely on the local molecular con- 

 figuration, a part whose actual magnitude could be determined only 

 when that configuration is exactly assigned or known. The con- 

 sideration of this indeterminate part is altogether evaded by means 

 of a general mechanical principle which I have called the principle 

 of mutual compensation of molecular forcives. This asserts that in 

 such cases, when a finite portion of the effect on a molecule arises 

 from the action of the neighbouring molecules, this part must be 

 omitted from the account in estimating the mechanical effect on an 

 element of volume of the medium ; indeed otherwise mechanical 

 theory would be impossible. The mutual, statically equilibrating, 





