384 PROFESSOR TAIT ON IMPACT, II. 



Hence, as F may be considered to be nil while the datum circle is being traced, we have 



for the correction, 3 suppose, to be applied to the tabulated values of D, that positive 



root of 



Mg-f(x) = (2) 



which vanishes with M. 



Integrating the equation of motion, we have 



M» 2 /2=MV 2 /2+(M^-F)a!-/(jc), . . . .' . (8) 



where V is the speed at impact, and f(x) vanishes with x. Thus, at the turning point, 



= MV 2 /2 + (M#-F)(D+a)-/(D+S). 



Now, by (2), we see that (Mg - F) is of the order f'(d) only, so that, when V (and 

 therefore D) is considerable, we may write this in the approximate form 



= MV 2 /2-/(D). 



This equation enables us to get an approximate estimate of the form of the function f. 

 A graphical representation of D in terms of MH, based on the various data of the experi- 

 ments of 22/6/91, below, on vulcanized india-rubber, gave three nearly parallel, but 

 closely coinciding curves, whose common equation (when the different values of 3 for the 

 different masses were approximately taken account of) was of the form 



MH a D* ; 



for the subtangents were 2* 5 -fold the abscissa;. Hence we are entitled to write (3) in 

 the tentative form 



Ma 2 /2 = MV 2 /2 + (M(/-F)a;-Acc l (4) 



Equation (2) now becomes 



M# = §A3^; 



whence 3 may be found, A being determined from one of the larger values of D (and the 

 corresponding kinetic energy) by the relation 



Mr/H = AD* (5) 



These give the approximate value 



6 . ■** d /2DV 



Tims I found that the values of D, for the experiment of 22/6/91 on vulcanized india- 

 rubber, must be augmented by nmi, 75, l mm, 2, and l mm, 9 respectively :— according as 

 the mass was single, double, or quadruple. These agree remarkably well with the 

 relative positions of the parallel curves already spoken of : and also with direct measure- 



