Prof. Challis on Hydrodynamics. 209 



ing to these views, referable to setherial action of the first kind, 

 and the forces of electricity, galvanism, magnetism, and dia- 

 magnetism to setherial action of the second kind. I propose in 

 this communication to treat only of motions of translation of 

 a spherical solid produced by the vibrations of an elastic fluid. 



Here it may be remarked that the hydrodynamical questions 

 about to be discussed are such as can be answered by ma- 

 thematical reasoning alone. I assume that there will be no dis- 

 pute about the fundamental properties of the fluids; so that to 

 answer the proposed questions it is only required to discover the 

 appropriate mathematical processes. The same remark applies 

 to the questions discussed in the Numbers of the Philosophical 

 Magazine for June, August, and October 1862. What I have 

 now to say will consist in great measure of a revision of the 

 arguments contained in those communications, reference to 

 which will be made by citing the numbers of the articles (from 

 1 to 48) into which their contents are divided. I beg, therefore, 

 that the processes of reasoning employed in the present commu- 

 nication, as well as in the three j ust mentioned, may be regarded 

 quite apart from the physical applications which I have specified 

 above. Tt is very evident that the laws of the physical forces 

 cannot be referred to the motions and pressures of an elastic 

 medium, unless the principles and the methods of mathematically 

 investigating such motions and pressures be well ascertained 

 previously. 



On reviewing the contents of the article in the Number for 

 June 1862, I found nothing requiring notice before coming to 

 art. 10. Towards the end of that article the assertion is made, 

 as a consequence of antecedent reasoning, that " the propaga- 

 tion of a solitary wave is not possible." This conclusion is 

 drawn from a method of solving the problem of motion propa- 

 gated from a centre, to which objection cannot be taken by 

 those, at least, who maintain that there are not more than two 

 general hydrodynamical equations. Further, I have asserted 

 that " this conclusion involves another, that the variation of 

 the condensation from point to point at a given time cannot be 

 expressed by a discontinuous function ; for if that were the case, 

 the possibility of the uniform propagation of a solitary wave 

 would necessarily follow." And yet such discontinuity appears 

 to be matter of fact, judging from what is known by experience 

 to take place in air. The articulation of consonants and words 

 is evidence that we can impress on the air forms of condensation 

 not necessarily expressible by continuous functions. Moreover, 

 the principle I have employed in proving the law of equal pres- 

 sure, viz. that the parts of a perfect fluid are divisible without 

 assignable force by an infinitely thin partition, leads to the same 



Phil. Mag. S. 4. Vol. 30. No. 202. Sept. 1865. P 



