l68 PHILOSOPHICAL TRANSACTIONS. [aNNO 1726. 



Now the rule for finding the common velocity of non-elastic bodies, moving 

 the same way after the collision, is, to divide the sum of the quantities of 

 motion in the two bodies, by the sutn of the quantity of matter. It is also 

 granted, " that these bodies cannot mutually act on each other with the quan- 

 tity of motion common to both, sect. 215. The stroke therefore depends on 

 the relative velocity, which remaining, the intensity of the impulse will be the 

 same, in whatever manner the absolute velocities may vary. On this intensi 

 depends the intropression of the parts, which will therefore be always the same, 

 if two bodies impinge with the same relative velocity, whatever be the velocities 

 they move with." 



These principles furnish us with an argument against the new opinion. 

 For if it be true, then equal causes may have unequal effects, and that in their 

 own sense of an effect: the proof shall be taken from instances of the effects 

 of the collision of non-elastic bodies, whose respective velocities shall be 

 always equal. 



Let A and b denote two non-elastic bodies, of equal quantities of matter; 

 and let b be at rest, while a moves towards it with 8 degrees of velocity. 

 Here the common velocity after the stroke will be half the velocity of a before 

 the stroke, i. e. 4 degrees. Consequently the force in b thus communicated 

 by the stroke, will be as its square, or ] 6. 



Let B move forward with 2 degrees of velocity, and a follow it with 10 

 degrees; the respective velocity will be 8 as before; consequently the strokes 

 in both cases are equal. The velocity in b after the stroke will be half the 

 sum of the velocities before the stroke, or 6 degrees. 



According to the new opinion, the forces being as the squares of the veloci- 

 ties, the force of b before the stroke will be to its force after the stroke, as 

 the square of 2 is to the square of 0; i. e. as 4 is to 36. Subduct the force 

 in B before the stroke, from the force it has after the stroke, and we have the 

 degrees of force communicated by the stroke: which, if this opinion were 

 true, would be 32, i. e. just double the number of degrees communicated by 

 the same force in the former instance, which was but as l6. Thus equal strokes 

 produce unequal effects in our sense of effects. 



The following table gives several other instances. In the first three columns 

 are the velocities of the two bodies both before, and after the stroke; in the 

 two next, are the forces in b, both before and after the stroke; and in the 

 sixth, the difference of those forces, or the different degrees of force effected 

 by the same stroke; and in the last colunm, the proportion of those forces, or 

 effects of the cause or stroke. 



