

Matter and Force in Theoretical Physics. 471 



state of science demanded. As I have said before, I say again, 

 that I do not hold myself responsible for these hypotheses, not 

 perceiving how any others could be framed consistently with a 

 due regard to the antecedent and the existing state of physics, 

 and to the essential requisites of the foundations of science. 

 The real difficulty that stands in the way of the progress of 

 theoretical physics is a mathematical one — that of discover- 

 ing the true methods of applying differential equations of three 

 or more variables, and their integrals, for finding the mo- 

 tion and pressure of a fluid under given circumstances. This 

 is purely a matter of reasoning, and by reasoning only can 

 it be settled. It is in endeavours to surmount this difficulty 

 that I have for many years given attention to the mathematical 

 theory of the motion of fluids ; and though I have succeeded to a 

 considerable extent, I am well aware that much remains to be 

 done. In particular it may be mentioned that I have not ob- 

 tained an analytical expression for the quantity called h towards 

 the end of the article in the May Number, the determination of 

 which is of much importance relative to the theory of attractive 

 and repulsive forces. Having spent a great deal of time and 

 thought on these researches, I must now leave to others, who 

 may think it worth their while, the task of pursuing them 

 further. In the mean time I may appeal to the many explanations 

 of phenomena already effected by means of my Hydrodynamical 

 Theorems as evidence that the method of philosophy I have 

 pursued is the true one, and that I am justified in recommend- 

 ing it for adoption. It would be tedious to enumerate here all 

 the explanations to which I allude ; any one desirous to become 

 acquainted with them, and the various steps by which they 

 were reached, will find the requisite information in communica- 

 tions to this Journal extending through the last twenty years. 

 I will only advert to a few instances of explanations that are new 

 or of special importance. In the Undulatory Theory of Light 

 transverse vibrations are arrived at by reasoning from hydrody- 

 namical principles ; polarization is deduced (not assumed) ; the 

 direction of transverse vibrations relative to the plane of polari- 

 zation is ascertained ; reasons are assigned for the observed dif- 

 ferences between plane-polarized light, elliptically polarized light, 

 and common light ; the loss of half an undulation is accounted 

 for; and theories are given of Dispersion and Double Refraction. 

 For explaining phenomena of light, transverse vibrations, con- 

 sidered only to the first power of the velocity and condensation, 

 suffice. When the analysis is extended to the squares of the 

 velocities and condensations, it is shown that the sethereal waves 

 are capable of causing motions of translation of the atoms, and 

 thus producing, according to diversity of circumstances, the re- 

 pulsion of heat, the attraction of molecular aggregation, and the 



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