experiments, we get results more or less resembling those 

 indicated by theory, and the concordance improves as 

 the number of throws of the coins is increased. 



Curves of a similar type are obtained when inde- 

 pendent measurements are made of any physical 

 quantity, such as the height of a mountain. The 

 individual measurements are subject to many sources 

 of error. Usually some errors tell one way and some 

 the other, and we get the majority of the results near 

 the average value. But occasionally, all or nearly all 

 the errors chance to fall on the same side, and we get 

 a solitary result differing much from the mean, just 

 as about once in 1000 throws all our ten coins fell head 

 upwards. 



While the general type of curve is maintained in 

 all such measurements, its exact shape depends on 

 the accuracy of the observations. In those physical 

 measurements where great exactitude is possible, nearly 

 all the results would closely approach the mean. The 

 curve, therefore, is high in the middle, and falls 

 rapidly on each side. If large errors are unavoidable, 

 the number of observations which differ widely from 

 the mean increases, and the curve flattens and broadens. 



Similar phenomena also appear when measurements 

 are made of biological quantities. Fig. 2 shows the 

 variation in measurement of the chests of a large 

 number of Scottish soldiers. It illustrates clearly the 

 concentration in the number of men near the mean 

 value of about 40 inches, and should be compared 

 with the theoretical curve of frequency given in Fig. I . 



Again, Fig. 3 represents the variation in length of 

 the fruits of three varieties of Evening Primrose 



