Aug. i6, 1915 



Tensile Strength and Elasticity of Wool 



387 



statement as to their relative strength. To give definite information as 

 to their relative strength, when the averages and probable variations are 

 given, figure 3 has been devised, from which may be read the percentage 

 probability that one lot of fibers is stronger than the other; also, the per- 

 centage probability 

 that it is stronger by 

 any given amount. 



Suppose two sets 

 of observations give 

 Wj ± ^1 and tWj ± ^2 

 and we wish to show 

 the probability that 

 the first is greater 

 than the second by 

 an amounts. Know- 

 ing the probable 

 variation, r, a curve 

 can be drawn whose 

 highest ordinate is to 

 the ordinate of any 

 point whose abscissa 

 is X as the number of 



Fig. 4.— Curve of ordinary probability. The abscissae are taken as a 

 variation in strength of a given fiber from the mean strength of all the 

 fibers and the ordinates are proportional to the probability that such 

 a fiber exists. 



fibers whose strength is the average is to the number of fibers whose 

 strength is x more than the average. In this case, we take x to be 

 either a positive or a negative number. 



.47691"] 



The equation of this curve is y= ,— e~ L" 



'^i^/k 



Figure 4 is an 



illustration of this curve. 



The probability that the actual strength of fibers recorded as m^ + Tj 



is within dx oi m^ + x is 



r^-yJTZ 



[^]'. 



The probability that the strength of fibers given as in^±r^ is m^ + x+h 

 or just h greater than the other is 





[ 



4769(»»2— Wl+a+fe) 



Jdh. 



Hence, the probability that the fibers given as m^ + r^ have a real strength 

 m^ + x and the other just h greater is 



(.4769)= 



r^r^Tz 



[. 4769x 1 2 r 

 r2 le'l 



4769(^2— jrei+i+ A) 



J dx.dh. 



And the probability that the former has a strength m^ + x and the latter 

 a strength at least h greater is 



r^Yin 



