Remarks on the theory of the Resistance of Fluids. 277 



line of its motion, are at variance with each other. Correctly un- 

 derstood, these resuhs are in perfect accordance not only with each 

 other but with the common theory. They differ, it is true, not howev- 

 er in principle, but only in the nature of the quantity deduced ; a dif- 

 ference arising necessarily from the different circumstances taken into 

 the account by each of these gentlemen. Professor Wallace consid- 

 ers the number and effect of the particles acting at any instant, and 

 consequently the quantity which he deduces is the force of resis- 

 tance. Professor Keely and the common theory, consider the effect 

 and number of the particles encountered in a given time, and there- 

 fore the quantity which they deduce is the fluent power of resistance. 

 Professor Wallace makes the force of resistance, estimated in a di- 

 rection perpendicular to the plane, as the sine of the inclination. 

 Professor Keely and the common theory, make the fluent power 

 of resistance, estimated in the same direction, as the square of the 

 sine of inclination. Both these results are legitimate deductions from 

 the common theory, and if either of them were true, it wovdd fol- 

 low of course that the other must be true also. Unfortunately how- 

 ever they are neither of them true. The force of resistance is as 

 the square of the sine, and the fluent power of resistance is as the 

 cube of the sine of inclination ; as I think I shall satisfactorily prove 

 before I close. 



The common theory supposes the resisted body to move in the 

 fluid, to be equally submerged at every velocity, and to be resisted 

 only by the inertia of the fluid. As the objections I have now to 

 make to this theory lie to the argument and not to the hypothesis, I 

 shall take the same hypothesis. 



First. — Let the resisted body be a plane of given area, perpen- 

 dicular to the line of direction in which it moves. 



The velocity communicated to the fluid encountered by the plane, 

 is as the velocity of the plane. 



When any velocity is communicated to a given quantity of mat- 

 ter, the force into the time of its action, is as the velocity commu- 

 nicated. 



The time of the action of the plane on a given quantity of the 

 fluid, is inversely as the plane's velocity. 



From these three analogies, which need no illustration, I deduce 

 another viz. 



The force at any instant on the plane, is as the square of the velo- 

 city of the plane. 



