ATOMIC WEIGHTS 



FOEMUL.'E FOR THE CALCULATION OF PROBABLE ERROR. 



The formula for the probable error of an arithmetical mean, familiar 

 to all physicists, is as follows : 



/ ^^ 



(1.) e = 0.67J 



Here n represents the number of observations or experiments in the 

 series, and S the sum of the squares 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 inversely proportional to 

 the square of its probable error. Let A, B, C, etc., be such means, and 

 a. h, c their probable errors respectively. Then the general mean is de- 

 termined by the formula : 



A + J. + ^ 



-^ + -^ + -1- 



a'' b- c2 



For the probable error of this general mean we have : 



1 



(3.) '- / 1 1 1 



Y «= b- c2 



In the calculation of atomic and molecular weights the following 

 formula are used : Taking, as before, capital letters to represent known 

 quantities, and small letters for their probable errors respectively, we 

 have for the probable error of the sum or difference of two quantities, 

 A and B : 

 (4.) e= 4/a^P 



For the product of A multiplied by B the probable error is 



(5.) e= V(A&)2 + (Ba)2 



For the product of three quantities, ABC : 



(6.) e= y(BC«)2 + ( AC6)2 + (ABc)2 



For a quotient, . the probable error becomes 



(r.) *"' 



/(tT 



