136 On the general principles of the Resistance of Fluids. 



the wave or surge that rose in front of the boats, at velocities from 

 five to ten miles an hour, diminished rapidly or ceased altogether at 

 the higher velocities, from ten to thirteen miles. This result Mr. 

 Fairbairn considers as " very anomalous and contrary to all previous 

 theory," because it does not accord with the theorem that the resist- 

 ances increase as the squares of the velocities, but the reviewer points 

 it out as affording an instance of the necessity of uniting theory with 

 practice, and assigns a sufficient reason for it afterwards. He then 

 proceeds to lay down the general laws and principles on which inqui- 

 ries concerning the resistance of fluids depend. His first theorem is 

 the well known one, "If a non-compressible fluid act upon a plane 

 opposed perpendicularly to the direction of its motion, the force with 

 which it impels the plane, or acts upon it, will be as the square of the 

 velocity of the fluid." Under this, he remarks the corrections ne- 

 cessary to be observed in experimenting on this subject. The next 

 theorem is the one to which, particularly, I wish to call attention, as 

 it is an extremely important correction of a theorem which has been 

 adopted in all scientific works, from Newton's to the present day. 

 The old theorem is well known. It is this: "If the inclination of 

 the plane to the direction of the motion of the fluid vary, the resist- 

 ance perpendicularly to the plane will vary as the square of the sine 

 of angle of inclination." The demonstration is as follows. Since 

 the particles of the fluid strike the plane obliquely, their force per- 

 pendicularly to the plane will vary as the sine of angle of inclination, 

 by resolution of forces. The breadth of the column of fluid, and 

 consequently the number of particles striking the plane, also varies 

 as the sine of same angle ; the breadth being estimated perpendicu- 

 larly to the direction of the fluid. The resistance in a direction per- 

 pendicular to the plane, which depends on the number of particles 

 multiplied by their force in that direction, will therefore vary as the 

 square of the sine of angle of inclination. The theorem of Mr. 

 Wallace is this : If the inclination of the plane vary, the resistance 

 perpendicularly to the plane will vary as the sine of the angle of 

 inclination. His demonstration may be thus expressed. Since the 

 particles strike the plane obliquely, their force perpendicularly to the 

 plane, as in the former theorem, will vary as the sine of angle of in- 

 clination. But the number of particles striking the plane, he argues, 

 does not depend on the breadth of the column, but on the surface of 

 the plane, because the particles that act on the plane are those in 

 contact with it, and therefore their number is as its superficial area. 



