XII INTRODUCTION. 



FORMULA FOR THE CALCULATION OF 

 PROBABLE ERROR. 



Although the ordinary formula for the probable error of 

 an arithmetical mean is familiar to all physicists, it is per- 

 haps best to reproduce it here, as follows : 



Here n represents the number of observations or experi- 

 ments in the series, while S is the sum of the variations of 

 the individual results from the mean. 



In combining several arithmetical means, representing 

 several series, into one general mean each receives a weight 

 indicated by its probable error ; greater as the latter becomes 

 less, and vice versa. Let A, B, C, etc., be such mean results, 

 and a, b, c, their probable errors respectively. Then the 

 general mean is determined by this formula : 



(2.) M 



For the probable error of this general mean we have 



In the calculation of atomic and molecular weights the 

 following formulae have been employed. For assistance in 

 connection with them my thanks are due to Professors H. 

 T. Eddy and E. W. Hyde of the University of Cincinnati. 



Using, as before, capital letters to represent known quan- 

 tities and small letters for their probable errors respectively, 



