30 Rev. W. Whcwell on the principles (>f Dynamics, 



tlic moving force is as the pressure. And the same inference 

 may be extended to a body twice, three times, &c. as large, 

 by considering it as made up of two, three, &c. such bodies, 

 each acted upon by the same pressure. And thus this prin- 

 ciple leads directly to the third law of motion. 



The question, therefore, now becomes, whether the second 

 law of motion be included in the third .? and this is what the 

 foreign writers alluded to, assert, and pretend to prove. The 

 proof is of the following kind. 



Let a body be moving in a direction A B with any velocity 

 B C. At the point B let it be acted upon by any force in 

 the direction B D. It will descnbe an in- a b c 

 termediate line B E % the second law of '^^"X 



motion. But this intermediate direction is v_:^ 



also deduced from the principle that the D K 



velocity is proportional to the force, in this manner. 



The body being at B, and moving with the velocity B C, 

 is in the same condition as if it were at that instant acted upon 

 by a force which is represented by B C. But in that case it 

 would be acted upon by two forces represented by B C and 

 B D, and hence, by the statical composition of forces, it might 

 be considered as acted upon by a single force B E, the resul- 

 tant of B C and B D. Hence, since the velocity is propor- 

 tional to the force, the body will move in B E with a velocity 

 represented by B E. 



In this case we consider a velocity as depending upon a 

 force without any respect to the time ; and it is therefore clear 

 that the forces must be instantaneous or impulsive ; and that 

 this is the case will also appear from referring to the demon- 

 strations here pointed at. 



Thus Laplace, Mec. Cel. Ch. ii. Art. 5, assumes " f la force 

 dont un corps est anime en vertu de sa vitesse^'' and then com- 

 pounds such forces by the law of statics. It appears by the 

 proof that he supposes the force to be impulsive. (His object 

 is to prove by experiment that these forces are proportional to 

 the velocities.) 



Poisson, Dyn. Ch. ii. Art. 212. Takes, " un point sollicite 

 par deux forces, du genre de celles qui agissent instantanement 

 sur le mobile et qui Tabandonnent ensuite a lui-meme.'* He 

 then compounds these by the law of statical composition. He 



