IX. On Fluid Motion, so far as it is expressed by the Equation of 

 Continuity. By S. Eabnshaw, M.i\. of St John's College. 



[Read March 21, 1836.] 



The difficulty of this subject is so universally admitted, that I 

 hope it will be received as a sufficient excuse for bespeaking the 

 reader's indulgence should any thing occur, in the course of this 

 paper, which he may judge not sufficiently borne out by the argu- 

 ments on which it is sought to be established. 



*o' 



Though the subject of this communication is by no means new, 

 yet what is brought forward in it will be found to possess some 

 novelty both as to the results obtained, and the manner of treating the 

 subject. Hitherto, nothing more could be done, beyond investigating 

 the differential equations of fluid motion, than to endeavour to generalize 

 the results obtained from a particular integral of the equation of con- 

 tinuity d-,^(p +d/(p + d,'(p = 0. It is manifest, however, that the results 

 of such generalization from a particular case, how skilfully soever de- 

 duced, must at least be clogged with some degree of uncertainty, and 

 be therefore in some measure unsatisfactory. But in consequence of the 

 discovery of the general integral of the equation 



d/<p + d/cp + rf/0 = 0, 



not only is the difficulty of the subject shifted farther from the threshold 

 of our researches, being reduced to that of interpreting this integral, 

 but we are able to proceed with a much greater degree of generality. 

 Vor,. VI. Part II. Dd 



