308 ' PHILOSOPHICAL TRANSACTIONS. [aNNO 1669. 



1. Therefore^ if the power or force V move the weight P, then the force 

 m V will move m P, other circumstances being alike, as suppose through the 

 same space in the same time, that is, with the same celerity. 



3. Also, if the power move the body through the length L in the time T, 

 then in the time w T it will move it through the length n L. 



A. Therefore, if the power /^ in the time T, move the body P, through the 

 length X, then the power m V, in the time n T, will move m P, through the 

 length n L ; and consequently, as VT, the product of the force and time, is to 

 PL, the product of the weight and length, so is m 7i FT to mnP L. 



5. Because the degrees of velocity are proportional to the lengths or spaces 

 run over in the same time, or, which is the same thing, reciprocally propor- 

 tional to the times of running over that length ; it will be, as tj^ : C :'. -^-tf : - C; 



that is, the degrees of celerity are compounded of the direct ratio of the lengths 

 and the reciprocal ratio of the times. 



6. Therefore, because V T -. P L \\ m n V T : m n P L, it will be, as 



V;~ :: m/^:^j,-; that is, V: PC:: m F : mPC = mP X C = 



P X mC. 



7. That is, if the power F can move the body P with the celerity C, then 

 the power m /^will either move the body P with the celerity m C, or the body 

 m P with the same celerity C, or lastly, any body with such a celerity that the 

 product of the body and celerity he m P C. 



8. And on this principle depends the construction of all machines for facili- 

 tating motions, viz. that in whatever ratio the weight is augmented, in the very 

 same ratio the celerity must be diminished ; so that the product of the celerity 

 and the mass, to be moved by the same force, may be still the same, as suppose 

 F': PC:: F:mP X- C= PC, 



in 



9. If the body P, moved by the power F", with the celerity C, impinge di- 

 rectly against a quiescent body m P, (not obstructed) they will move on toge- 

 ther with the celerity j—- C. For, because the power is the same, the greater 

 the mass that is to be moved, so much the less must be the celerity ; namely, 

 as V \ PC'.: V \ — ^ — P y^rr-T — C =■ P C. Consequently the impetus 

 of the one body (that is, the product of the mass and velocity) will be 

 — i— P C, and that of the other --i— mP C. 



10. If a body P, moved with a force V, and celerity C, be impinged on by 

 another body m P, moving the same way, but with a greater celerity n C, (and 

 having therefore the force mnV), then they will both move on together, with 



