340 Mr Vincent, Experiments on Impact. 



ird 4, 

 or Kg-fj , where d is the diameter of the dent and D is the 



diameter of the sphere. 



Thus the volume of the dent is proportional to the energy of 

 the ball just before impact. 



We may write then, using the above value for the volume of 

 the dent, 



Mu 2 _ ird* 

 2 _p, 32Z> W ' 



where M— mass of ball, 



u = velocity at impact, 

 p = a constant. 



If the other quantities in the equation are in C.G.S. units then 

 p is the force in dynes per sq. cm. which will make the lead flow. 

 The quantity p is also numerically equal to the number of ergs of 

 work done in making a dent a cubic cm. in volume. 



From equation (i) we have 



IQMD (uy 



v = ^r\d?)> 



which may be written 



p = ab 2 , 



where a = — and may be calculated from the dimensions and 

 mass of the ball. 



The value of b = -^ is obtained from the straight line A or B 

 on Fig. 6. 



For the ball used in these experiments a = S66 ; curve A 

 Fig. 6 gives b = 857, thus p = 6*4 x 10 8 dynes per sq. cm. 



For the curve B in Fig. 6, b = 1 140 and p = 11 x 10 8 . That is, 

 the pressure which is necessary to make the specimen of lead, 

 used for curve B, flow, is nearly twice as great as that necessary in 

 the case of the material used in the set of experiments shown by 

 curve A. 



The total upward force of the lead on the ball at any depth of 

 penetration I is 



irpr 2 = irpDl, 



