INTRODUCTION. 



FORMULAE FOR THE CALCULATION OF PROBABLE ERROR. 



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

 to all physicists, is as follows : 



(1.) ^ = 0.6745 



\tt [n — I] 



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

 termined by the formula : 



A + _^ + ^ 



(2.) M ^ ^'^ ^^ '' 



a' ^ b- ^ c' 



For the probable error of this general mean we have : 



(3.) 



e 



I 



\i^ + i + ^ 



In the calculation of atomic and molecular weights the following 

 formulfe 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 : 



(•i-) e = V «' -f b'^ 



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

 (5.) e= i/(A(^)2-|-(Ba)2 



For the product of three quantities, ABC : 

 (6.) e = i/(BCa)^ + {KQbf + (AB^)- 



T> 



For a quotient, -v' the probable error becomes 



A 



