Remarks on the theory of the Resistance of Fluids. 281 



the last in the same ratio as I have found, viz., as the cube of the 

 sine. 



It is worthy of remark, that it appears from the results just dedu- 

 ced, that although ihe force of resistance in the direction of the plane's 

 motion, is less than that perpendicular to it, in the ratio of the sine 

 of inclination, yet ihe power Q.nd fluent power of resistance are not 

 only relatively, but actually the same in both directions. 1 may add 

 further, that this is a universal law of oblique action, and is in per- 

 fect accordance with the views expressed by me, in a communica- 

 tion to this Journal, Vol. xii, p. 338, in which among other things, 

 I endeavored to show that there is no loss of power in machinery, in 

 consequence of oblique action, unless it gives rise to an increase of 

 friction, or other resistances of an adventitious nature. 



Fourth. — We have hitherto, in speaking of the oblique plane, 

 supposed its velocity to be given, and its obliquity to vary. Let us 

 now suppose the obliquity to be given, and the velocity to vary. 



We have already seen that the force and velocity respectively, 

 perpendicular to the plane, are as the force and velocity respective- 

 ly, in the direction of its motion. We have also seen that the force 

 perpendicular to the plane, is as the square of the velocity in that 

 direction. Therefore the force is as the square of the velocity, 

 when both are estimated in the direction in which the plane moves. 

 In the same manner it might be shown that the power of resistance 

 in this case, is as the square of the velocity, and that the fluent pow- 

 er, is as the cube of the velocity. It will be seen that these results 

 correspond to those deduced under the first head — which they should 

 do ; for that is a case in which the inclination is given, viz., ninety 

 degrees. 



When both the obliquity and velocity vary, the resistances are 

 expressed, by combining the results found under the third and fourth 

 heads, viz. — 



Force of resistance is as square of velocity into the cube of the sine. 



Power of resistance is as square of velocity into cube of the sine. 



Fluent power of resistance is as cube of velocity into cube of the 

 sine. 



The common theory makes the fluent power of resistance as the 

 square of the velocity into the cube of the sine ; showing that though 

 by better luck than logic it deduced one correct result in a preceding 

 step, yet when in succeeding steps it comes to combine that result 



Vol. XXIX.— No. 2. 36 



