356 NEWTON S PRINCIPIA. 



the error made by assuming the resistance to vary as the 

 surface is not very great, unless one of the surfaces is 

 many times larger than the other. Thus the French 

 experimentalists found this law in tolerable accordance 

 with their results. 



3. The resistance on an oblique plane does not vary as 

 square of sine of angle the plane makes with the direction of 

 motion. 



The French Academy experiments were made with ves 

 sels with wedge-like prows of various angles. If x be half 

 the angle at the prow, the formula 



E = P sin 2 + 3-15 3 



represented the resistance so exactly that the error was 

 always less than T n . 



Hutton found that the formula 



E = -84 (sin 0) 1 84 cos 2 



represented the resistance. 



Vince found the resistance did not vary as any con 

 stant power of the sine. Various other formulas have also 

 been given by Du Buat, Dr. Young, Eytelwein, &c. 



In the experiments of the French Academy, theory 

 gave a result for an angle of 12 only one fortieth of the 

 truth. In some experiments by Vince for an angle of 10, 

 the resolved part of the resistance in the direction of mo 

 tion was ten times that given by theory. 



4. The changes of resistance calculated by the theory 

 caused by changes of form are erroneous. The modifica 

 tion of resistance on any element produced by the near 

 presence of others cannot be neglected. 



If the formula of the experimentalists of the French 

 Academy be employed to calculate the resistance on cur 

 vilinear surfaces the results are altogether erroneous. 



Robbins found that the resistance on a sphere in air was 

 2-27 times the resistance on its great circle. Borda found 

 2 45. Hutton found 2 4. The ordinary law gives 2. 



