444 



DR W. PEDDTE ON 



For all values of x from 0' to 1 this point lies between r<f> and rd, provided that 



we have 



1 



m> 



I' 



When the stage (p on the inward motion is reached, all such groups exert outward 

 force, and their average stretch is 



lfm + 1 , ,1 lr 



The total outward pull due to them is therefore 



M+i J n 2 m m{7n + l) 



(10) 



the summation being with respect to m. 

 When we have 



1 



m< -, 

 P 



we must take the fraction x so that its largest value is given by r(p + xr(pjm = rO, i.e., 



Then the number of groups 



x — mip 



rd> r6 - rd> 



vmp — -. r-r = v ^ 



m(m + 1 ) m + 1 



break in the range r(p to rO with an average stretch \(r0 — r<$>). Hence their outward 

 pull is 



i_i— S%i?rdr.-Mre-r$f. . • • • • ( n ) 



i m + 1 ./ 2 



In the case of the remaining number 



(1 -"^tStT) : 



r<f> rd ' 



m m+1 



we have to consider the w th break. Now the m th break of a group which broke at 

 r(p/(m+ 1 ) + rnpr($>lm{m + 1 ) occurs at onr9j(m+l), so that the average stretch for this 

 number is 



1 



2 



_ in in + 1 J 

 Hence the total inward pull of these groups is 



v /'o_...;.. A™"'^ 



A -J 



?u ?« + 1 



(12) 



