PROFESSOR Pearson's contributions to osteology. 461 



frequency polygon of the gross errors will be given by the 

 binomial (^ + ^y\ and when ?t, the number of elementary 

 errors, is indefinitely increased, will become a continuous 

 curve. This is the ' normal probability curve,' or the ' curve 

 of frequency of error.' It is of the type shown in fig. 3. 



Let QM be the ordinate about which the curve is symmetrical. 

 Then QM is the probability that half the number of elementary 

 errors are positive and half negative — i.e., that there is no gross 

 error. Or, in other words, QM is the frequency of the true 

 observation. Now if the ordinates corresponding to the terms 

 of the series (h + h)", where n is indefinitely large, be erected at 

 distances from a parallel axis, OY, proportional to the values of 

 the corresponding observations, then the distances between 



successive ordinates will be proportional to the elementary 

 errors. So that if PN be the ordinate through any point P on 

 the curve, PN is the frequency of a gross error proportional to 

 NM. 



If PN divides the area of the curve cut off between OM and 

 QM in half, then MN is called the probable error of the observa-' 

 tions. The total area of the curve is obviously proportional to 

 the number of observations. Hence the probable error is sucli 

 that the number of errors greater than it is equal to the number 

 less than it. 



It will be noticed that n being indefinitely great, the curve is 

 unlimited in either direction, and only meets the axis OX at 

 infinity. 



