PROFESSOR TAIT ON IMPACT, II. 385 



ments of 3 which have been recently made for me, by a statical process, by Mr Shand. 

 In what follows, I shall assume that the values of D have had this (positive) correction 

 applied. 



By the help of (4) we now have, for the time of compression, the expression 



<J 



dx 



VDl _ a4_ (M# - F)(D - x)j A 



Except for the very small values of D, we may neglect the last term under the radical, 

 and the expression, slightly diminished in value, becomes 



The numerical value of the integral is approximately 1'5. For any one substance the 

 time of compression is therefore inversely as the fourth root of D ; and, of course, 

 directly as the square root of M. But we may also write the expression, by means of 

 equation (5) above, in a form which applies to all substances for which the elastic force 

 is in the sesquiplicate ratio of the distortion, viz. 



1-5 D 



This result lies just half-way between the limits, D/V and 2D/V, assigned (from general 

 considerations) in the first part of this paper. 



With the data for the first fall of the quadruple mass in the experiment last referred 

 to, this expression becomes almost exactly s '01. The value of e is about 0*77, so that the 



whole time of impact should be f 1 ~H q . 77 ) S, 01, or s- 023 ; while the experimental 



value of T is S, 0211. But, in consequence of the quantity 9, above spoken of, all the 

 measurements of arcs from which T is calculated are necessarily too small. Add to C, 

 as measured, the product of 3 by. the sum of the two tangents, as given in the table ; 

 and diminish R by the amount 3; the observed time becomes S, 0224; so that the 

 formula gives a tolerably close approximation. 



If we bear in mind that the values of D ought to be increased by the quantity 3 ; we 

 see at once the reason, already referred to, for the apparent falling off of the values of e at 

 low speeds, when they are calculated from the values of H given in the tables. 



Among the practical applications of the results above, we see that when a nail is 

 driven, say by a ^-lb. hammer moving at the rate of 10 feet per second, the time of 

 impact being taken as S, 0004, the time-average force is some 300 lbs. weight. If the 

 head be one-tenth inch square, this corresponds to a pressure of more than 2000 

 atmospheres. 



