NORMAL VARIABILITY 



93 



These values are plotted in the accompanying 

 diagram (Fig. 6) as vertical distances above a base 

 line. The figure obtained by joining together the 

 points thus arrived at may be observed to show some 

 resemblance to the previous Figs. 4 and 5. 



The three series of numbers already given are those 

 which are obtained on expanding the expressions 

 (1 + 1)2, (i + i) 3 , (i + i) 10 < In general the probabilities 

 of the various possible combinations when n coins are 

 tossed simultaneously are given by the expanded value 

 of (i + i)*. 



Quetelet has worked out the relative probabilities of 

 the most frequent combinations in the case of 999 coins 

 simultaneously tossed i.e., the expanded value of 

 (i + i) 999 . A few of these values are given in the 



following table i 



TABLE III. 



It may thus be seen that the likelihood that a result 

 appearing in any given throw will show a still greater 



