12 Mr. Tredgold on the Theory oj Hydro-dynamics. 



results derived from these propositions differ from the results 

 of experiment ; and it is so important that the resistances ot 

 fluids should be established on true principles, thatone naturally 

 expects, the subject to have been investigated with more than 

 ordinary care. Under such an impression it is not without 

 anxiety, as to the result, that I am about to call in question 

 the reasoning of these propositions. 



All the propositions alluded to, may be referred to Prop. 34, 

 book \\. of Sir Isaac Newton's Principles of Natural Philosophy. 

 Hence, if I succeed in showing that the demonstration of that 

 proposition is not correct, the rest must of course, in as far as 

 they depend on the same reasoning, have the same source of 

 error. 



The proposition is as follows : — " If in a rare medium, con- 

 sisting of equal particles freely disposed at equal distances from 

 each other, a globe and cylinder, described on equal diame- 

 ters, move with equal velocities in the direction of the axis of 

 the cylinder, the resistance of the globe will be only half as 

 great as that of the cylinder." 



The demonstration of this proposition in $ie Principles of 

 Natural Philosophy depends on its being proved that the effi- 

 cacy of a particle to resist the motion of a surface is as the 

 square of the sine of the angle of inclination of that surface to 

 the direction of its motion. Now I contend that this is not 

 true, but that the real ratio of the resistance is simply as the 

 sine of the angle of inclination. 



For let CD be the plane moving with an equable velocity, 

 in the direction AB, in a fluid at rest ; DF being the breadth 

 of the moving plane in a direction perpendicular to the direc- 

 tion of its motion, and CAB the angle the plane makes with 

 its direction. 



Let AB be the direct resistance necessary to render the 

 motion of the plane equable at the given velocity ; and draw 

 AE perpendicular to the plane, and BE perpendicular to AB ; 



then AE is the pressure perpendicular to the surface of the 

 plane, and the actual pressure of the fluid on the plane must be 



to 



