438 Prof. Challis on the Principles of Hydrodynamics. 



course it will be seen that I hold the direct contrapositive proof 

 to be of a different character from the direct positive proof. 

 "N^Tiat I have endeavoured to show is, that the difference of cha- 

 racter is not that which geometers in general attribute when they 

 lay stress upon the indirect proof by which they turn one form 

 of logic into another identical with it. So soon as a geometer 

 shall find out that he wants proof, as to a square inside a circle, 

 that what is out of the circle is out of the square, then, and not 

 before, will he be entitled to insist on the logician proving that 

 what is out of the genus is out of the species. 



I do not intend the preceding criticism to imply that I would 

 make any great change in Euclid. The best way to learn sepa- 

 ration is practice upon a mixed material, not observation of the 

 separation as already made. A teacher may, and should, call 

 the attention of his pupil to the distinction of the form of thought 

 and the matter thought on : but the compound product is the 

 material on which he has to work, and this is presented by Euclid 

 in its most natural form. 



November 1, 1852. 



LXX. On the Principles of Hydrodynamics. By the Rev. J. 

 Challis, M.A., F.R.S., F.R.A.S., Plumian Professor of 

 Astronomy and Experimental Philosophy in the University of 

 Cambridge. 



[Continued from vol. i. p. 241.] 



THE exposition of the principles of hydrodynamics which I 

 commenced in the Number of this Magazine for January 

 1851, and continued in that for March of the same year, I now 

 propose to resume, having been prevented by failure of health 

 and want of leisure from returning to the subject at an earlier 

 period. The propositions contained in the two former commu- 

 nications will be referred to as proved, and the notation there 

 adopted will still be employed, without further indication of the 

 meanings of the symbols. 



The tirst eight propositions, which were of a general nature, 

 applying equally to all perfect fluids, were followed by one 

 which related especially to incompressible fluids, and was thus 

 enunciated : " To determine the law of action of the parts of an 

 incompressible fluid on each other." The use of this proposition 

 in the solution of a few problems of fluid motion was then exem- 

 plified. I proceed next to the consideration of an analogous 

 pi'oposition relating to a compressible fluid ; it being essential, 

 according to the views already advocated, to deduce the laws of 

 the mutual action of the parts of the fluid on each other previous 

 to any determination of the circumstances of particular instances 



