440 TRANSMISSION 



If now we set other lines like the following at 2 

 ai a A a 1 a 2 



*! b B V P 



then we know from the table that the chances are 4.5 to I 

 that the true position of AB is not outside the lines a 1 l^ 1 and a 2 lP, 

 each removed twice the probable error from the determination. 

 Probable error of mean. The probable error of the mean is 

 based upon the standard deviation, as we notice by the following 

 formula : l standard deviation 



^nean = 0.6745 / , , . 



Vnumber of variates 

 or E M = db 0.6745 ~~/=' 



Substituting for the case in hand, we have 



1.28 



V327 



The student cannot fail to notice the overwhelming influence 

 of numbers in controlling the value of E, or to realize that if 

 the number of determinations should become infinite, E would 

 become zero. 



Probable error of standard deviation. According to methods 

 of deduction, to be discussed later, the probable error of any 

 determination for standard deviation is found by the follow- 

 ing process : divide the standard deviation by the square root 

 of twice the number of variates and multiply the result by 



In the case in point we have 1.28 as the standard deviation 

 with 327 variates. Substituting these numbers in the formula, 



we have 1<2 g 



E^ = 0.6745 = 0.034 . 



V 2 x 327 



1 See C. B. Davenport, Statistical Methods, p. 15. The method by which the 

 constant 0.6745 is obtained will be explained in the Appendix. 



2 The formula for probable error of standard deviation is 



Eff = 0.6745-^. 



v 2 n 

 See C. B. Davenport, Statistical Methods, p. 16. 



