Remarks on the theory of the Resistance of Fluids. 279 



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is as the sine of inclination. Therefore the poiver of resistance on 

 the oblique plane estimated in a perpendicular direction, is as the 

 cube of the sine of inclination. 



The fluent power of resistance, will also be as the cube of the sine 

 of inclination, for it will be as the product of force and velocity, and 

 the force is as the square of the sine, and the velocity estimated in a 

 direction perpendicular to the plane, will be as the sine and conse- 

 quently their product will be as the cube of the sine. 



I have now shown, if I mistake not, that the perpendicular force 

 on the oblique plane is not as the sine of the inclination, as found by 

 Prof. Wallace, and that the perpendicular ^ifew^ power of resistance 

 is not as the square of the sine, as found by Prof. Keely and the 

 commonly received theory, but that the former is as the square, and 

 the latter as the cube of the sine. 



It may be proper to remark here, that the common theory in pro- 

 ceeding to the determination of the above result, assumes that the 

 perpendicular force of each particle, is as the sine of inclination. 

 Sometimes this is given without illustration, as a self-evident step in 

 the argument; at others it is said to flow from the resolution of forces. 

 The propriety of referring to the doctrine of the resolution offerees 

 in this case, is not seen. There is no force until the particle acts, 

 and when it acts, the force is perpendicular to the plane, and there- 

 fore can require no resolution to bring it into that direction. But 

 there is a velocity which may be resolved, and from this resolved ve- 

 locity, the force may be deduced ; and this is the course I have pur- 

 sued. The course of the common theory, however, at this point, 

 though illogical, would involve no error, if it were true as assumed 

 by that theory, that the force of a particle in any direction is as 

 its velocity in that direction ; for we should in that case arrive at the 

 same result, whether we resolved a velocity and deduced a force 

 from it, or resolved some imaginary force that is assumed to be pro- 

 portional to the velocity. But when we consider the force to be as 

 the square of the velocity, as I have shown it to be, the mode pursu- 

 ed by the common theory tends to serious error. 



Third. — Retaining the same hypothesis, the next step is to deter- 

 mine the value of these several resistances, estimated in the direction 

 of the plane's motion. Prof. Keely pursues the subject in opposi- 

 tion to the views of Prof. Wallace, only to this point. Yet, this Is 

 the very point at which Prof. W. first begins to diverge from the 

 theory which Prof. K. defends. 



