On the general principles of the Resistance of Fluids. 137 



As the surface of the plane, by supposition, does not vary, the num- 

 ber of particles acting on it, therefore, does not vary, and the resist- 

 ance, consequently, is as the sine of the angle of inclination — the 

 number of the particles being the same at all inclinations, and the 

 force of each, varying as the sine of angle of inclination. Mr. Wal- 

 lace, to whom this correction is entirely due, then cites authors to 

 show that his theory agrees more nearly with experiments than the 

 old one. All authors agree that the resistance obtained by experi- 

 ment is greater than that deduced from the old theory, and as much 

 greater as the angle of inclination is less, in both of which points 

 does the new theory coincide with experiments. Indeed, Prof. Robi- 

 son, in speaking of the French experiments, (in the Art. Resistance, 

 in Encyc. Brit.) makes this remarkable observation : " The theo- 

 retical law, (the squares of the sines,) agrees tolerably with observa- 

 tion in large angles of incidence ; that is, in incidences not differing 

 very far from the perpendicular ; but in more acute prows, the re- 

 sistances are more nearly proportional to the sines of the angles of 

 incidence than to their squares," — thus actually recognizing this law, 

 without even hinting at the reason of it. The reviewer next observes, 

 that the force perpendicular to the plane may be resolved into two 

 others, one in the direction of the motion, which will vary as the 

 square of sine of inclination, (by the old theory it is as the cube of 

 the sine,) and one perpendicular to the direction of the motion, which 

 will vary as the product of the sine and cosine of same angle. This 

 latter force in boats moving on the surface of the water, acts in a di- 

 rection contrary to gravity, and being unopposed, tends to raise them 

 out of the fluid, and diminish the surface immersed. This upward 

 force, "which" says the reviewer "appears to be entirely overlooked 

 by writers on this subject," accounts for the diminution of the surge in 

 Fairbairn's experiments, and shows the incorrectness of an observation 

 of Dr. Lardner, (in Vol. XVII of the Cabinet Cyclopedia,) on the ad- 

 vantages of rail roads over canals, which is quoted by the reviewer. 



To illustrate the theorem of Mr. Wallace, I will investigate a few of 

 its simplest results in the resistance of fluids to bodies moving in them. 



To find the resistance to a solid of revolution, moving in the di- 

 rection of its axis of revolution. Let .r and y be the coordinates of 

 the curve, whose revolution generates the surface of the solid, their 

 origin being at the extremity of the axis. By the theorem, the num- 

 ber of particles that act on a surface is as its area, vvliile only their 

 force varies with the inclination. The number of particles, there- 



VoL. XXVIL— No. 1. 18 



