282 Remarks on the theory of the Resistance of Fluids. 



with others before deduced, the first error becomes again involved 

 and destroys the truth of the result. 



In applying these results to a boat or other vessel, the plane we 

 have been contemplating may be considered a unit or given portion 

 of the area of the prow ; and consequently the several resistances 

 will be expressed by the results already found, multiplied respect- 

 ively by a quantity denoting the whole of that area. If however all 

 parts of that area be not equally inclined to the line of motion, the 

 mean cube of the sine of inclination must be taken. 



If the breadth of beam and depth of immersion be given, and the 

 form of the prow be that of an isosceles wedge, as was the case in 

 the experiments tried by M. Bossut at Paris, then the area of the 

 prow will be as the cosecant of the inclination, and the expressions 

 for the resistances will be as follovA^s : — 



Force of resistance will be as the product of square of the veloci- 

 ty, cube of the sine and cosecant of the inclination. 

 Power of resistance will be in the same ratio. 

 Fluent power of resistance will be as the product of the cube of 

 the velocity, cube of the sine and cosecant of the inclination. 



Since the sine of any angle is inversely as its cosecant, the product 

 of the cube of the sine by the cosecant of inclination is equal to the 

 square of the sine ; and therefore the square of the sine may be sub- 

 stituted for that product in each of these expressions. 



If the breadth of beam and depth of immersion be not given, the 

 area acted upon by the fluid will vary with each of these respective- 

 ly, other circumstances being given. Hence, when all the circum- 

 stances vary, except that the prow retains the form of the isosceles 

 wedge, the expression for the force of resistance, and also for the 

 power of resistance, will be, — the product of breadth of beam, depth of 

 immersion, square of the velocity and square of the sine ; and for the 

 fluent power of resistance, the product of breadth of beam, depth of 

 immersion, cube of the velocity, and square of the sine. 



These results, as I have already intimated at the commencement 

 of this paper, do not involve the whole resistance experienced by a 

 body in moving through a fluid, but only so much of it as arises from 

 the inertia of the fluid encountered. And therefore, since there are 

 other important sources of resistance, not taken into the account, 

 these results must not be regarded as being, in themselves considered, 

 of any practical value. A true and complete theory of the resistance 

 of fluids, is a great desideratum in mechanics, and I am not without 



