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BELL SYSTEM TECHNICAL JOURNAL 



That the deviations from the mean value of the deflections are 

 distributed in this, and in other cases, in close accordance with the 

 normal error function is illustrated by diagrams displayed in Fig. 5. 



The value obtained in Table I for the deflection at ^ = 270° is 

 shown again in Table II, together with the values similarly obtained 

 for the same bombarding potential at the other cardinal positions. 



24 2 5 26 27 28 2 9 3 0' 3,1 32 33 34 3 5 3 6 37 



24 25 26 27 28 29 30 3.1 32 3J 3.4 li 36 37 



Q 



2.4 2.5 2 6 27 2.6 2.9 3 31 32 3 3 3 4 3 5 3 6 3 7 



24 25 2 6 2 7 28 2 9 30 3.1 32 33 34 35 3.6 37 



Fig. 5 — Plots of all data taken at 77 volts for the four cardinal positions — 

 6 = 0°, 90°, 180°, 270°. The solid curves represent calculated normal error function 

 curves. The data plotted here are summarized in Table II. 



TABLE II 



Bombarding Potential 77 volts. Wave-length 1.39 A. 



Angle e 

 Odeg. 



90 



180 



270 



No. of Obs. 

 , ... 26 

 . ... 31 

 . ... 31 

 . ... 36 



Deflection 

 3.023 ± .026 

 3.057 ± .022 

 3.116 ± .027 

 3.104 ± .022 



The values of these deflections and their probable errors have the 

 characteristics of four measurements of one and the same quantity. 

 There are certain values of deflection common to two of the error ranges 

 but none common to three. This is the situation most likely to be met 

 with if we are measuring the same quantity in each case; the maximum 

 number of overlapping ranges should be one half the total number of 

 ranges. It is of some interest, however, to pretend that the different 



