350 



Mr Vincent, Experiments on Impact. 



The complete formula giving the relation between the volume 

 of the dent and the height of fall is probably more nearly 

 approached by any of the formulae 



pV=Mg{h-h}), 



pV = \M (u 2 - v% 



p(V+V'+V" + &c.) = Mgh, 



in which h' is the height of the first rebound, v the velocity of 

 rebound, V the volume of the 1st dent and V, V", &c, the 

 volumes of the successive dents. It seems then that the complete 

 law must involve a knowledge of the coefficient of restitution for 

 different velocities of impact. But this number e is more nearly 

 constant as the dents get smaller: that is to say the bodies suffer- 

 ing small permanent deformation have a nearly constant value for 

 e\ Thus the laws which we have seen are nearly obeyed for lead 

 would probably be obeyed with greater accuracy for brass, for 

 example, if we put in a term for e. Thus for steel balls falling on 

 brass it is probable that the formula 



pV = \Mn? (1 - e 2 ) 



would hold. 



Dents in Brass and Cast Iron. 



When " hard " steel balls impinge on surfaces of brass or of 

 cast-iron the diameters of the dents are found to be proportional 

 to the diameters of the spheres if the height from which they fall 

 is constant. 



The fourth power of the diameter of the dent is also again 

 proportional to the height if other circumstances are unchanged. 



These results follow from the numbers set out below. 



1 Hodgkinson, loc. cit. 



