COL 



which will move off with a velocity equal to that with which the first 

 moved. If they decrease in magnitude, they will all move in the direc- 

 tion of the first motion, the velocity of each succeeding body being- great- 

 er than that communicated to the preceding; and the contrary, if the 

 bodies increase in magnitude. 



Cor. 5. The velocity thus communicated from A through B toC, when 

 B is greater than one of the two A & C, and less than the other, exceeds 

 the velocity which would be communicated immediately from A and C ; 

 and is a maximum when B is a mean proportional between A and C. 



Cor. 6. If there be n bodies in geometrical progression, whose common 

 ratio is *, 



Cor. If the number of mean proportionals interposed between two 

 given bodies A and X be increased without limit, the ratio of A's velo- 

 city to that communicated to X approximates to the ratio of V X : V A. 



III. Of the impact of imperfectly elastic bodies. 



1. In the direct impact of two imperfectly elastic bodies A and B, if the 

 compressing force be to the force of elasticity : : 1 : e, 



A-f B ' 



. Br 

 A + B ' 



Cor. 1. The relative velocity before impact : do. after :;!:?. 



Cor. 2. In imperfectly elastic bodies A 2 -{- Bi 2 is greater than A a'* 

 4. Bb'*(See last Art. Cor. 3J 



Cor. 3. If there be n imperfectly elastic bodies in geometrical, progres- 

 sion, whose common ratio is r, 



Velocity of first : velocity of last : : (1 + rf " ' ," (I +e) w ~ *' 



IV. Of the impact of bodies against immoveable planes. 



1. When a perfectly hard body impinges obliquely on a perfectly hard 

 immoveable plane, after impact it will move along the plane, and velocity 

 before impact : do. after ; : radius : sin. of incidence. 



2. :If the body be perfectly elastic, the of incidence / of reflection ; 

 and velocity before incidence = velocity after. 



3. If the body be imperfectly elastic, the velocity before incidence C 

 velocity after reflection *\ sin. of / of reflection I sin. / of incidence; 



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