22 Prof. Challis on the Central Motion of an Elastic Fluid, 



a great variety of phsenomena of light, which is one of those 

 forces, by the hypothesis of a highly clastic medium pervading 

 space, it is not a little surprising that an explanation of the cor- 

 relation of the several forces shoiild not have been sought for in 

 the existence of this medium, which would seem to be a vast 

 reservoir of force suflficient to account for all observed dynamical 

 effects. So long since as ] 840, in the Philosophical Magazine 

 for December of that year, I called attention, with implied refer- 

 ence to such a general theory, to the importance of giving an 

 answer to the following question : — If a minute spherical atom 

 were subject to the mechanical action of the vibrations of a very 

 elastic medium, like those which take place in air, would it, in 

 addition to a vibratory motion, receive also a permanent motion 

 of translation ? But I know of no attempt at the solution of 

 pi'oblems of this kind excepting one which I made in a paper 

 communicated to the Cambridge Philosophical Society, and 

 published in vol. vii. part 3 of their Transactions. By taking 

 into account the square of the velocity and condensation, I have 

 there arrived at the conclusion, that the small sphere would be 

 permanently moved in the direction of the propagation of the 

 vibrations. i\lthough, if I attempted the same problem now, I 

 should treat it in a different manner, the result, I have reason 

 to say, would be substantially the same as to the effect of the 

 terms of the velocity and condensation that arc of the second 

 order. I should also be prepared to indicate the circumstances 

 under which the motion of translation might take place in the 

 direction contrary to that of propagation. In a theory of phy- 

 sical forces the latter of these effects would correspond to attrac- 

 tion, and the former to repulsion. 



It must, however, be admitted that the great obstacle to this 

 kind of research is the very imperfect state of the mathematical 

 theory of the motion of fluids. The principles according to 

 which partial differential equations are to be applied, and their 

 solutions interpreted, are far from being well understood. Having 

 given attention to this department of applied mathematics a great 

 many years, I am fully sensible of the. difficulties which beset it, 

 and am able to point only to a few results of my researches which 

 appear to be satisfactorily established. Those which may be 

 considered of chief importance rest upon the following prin- 

 ciples : — (1) The motion of a fluid, so far as it is not arbitrarily 

 impressed, but results from the mutual action of the parts of the 

 fluid, obeys the law of continuity. (2) Those circumstances of 

 the motion that are not arbitrary cannot be inferred from the 

 arbitrariness of the functions which integration introduces. The 

 first of these principles is made the foundation of a new hydro- 

 dynamical equation, which may be called the equation of the 



