130 
MR. \V. F. SHEPPARD ON THE APPLICATION OF THE THEORY OF 
178'4 
163-4 
182-5 
159-7 
413-0 
378-2 
422-3 
369-5 
550-G 
504-4 
563-2 
492-8 
showing discrepancies in the actual table amounting to 
— 12-4 
+ 10-6 
— 2-5 
+ 4-3 
+ 14-0 
+ 0-8 
- 11-3 
1 
CO 
CJI 
- 1-6 
— 11-4 
+ 13-8 
- 0-8 
If rV represents any number in the calculated table, 
the corresponding v: 
nY"' will be found to be 
2730-4 
2811-4 
2708-5 
2831-7 
2060-0 
2127-2 
2049-3 
2142-5 
1075-0 
1725-4 
1662-2 
1737-8 
Multiplying each number 
in this table 
by the corresponding number 
“ calculated ” table, and dividi 
ng by 4378, we get the values of nY\'" 
111-20 
104-93 
112-91 
103-29 
194-90 
183-76 
197-67 
180-83 
210-73 
198-79 
213-83 
195-61 
Whence, from Table V. (p. 
159) the probable discrepancies are 
7-1 
6-9 
7-2 
6-9 
9-4 
9-1 
9-5 
9-1 
9-8 
9-5 
9-9 
9-4 
The ratios of the actual discrepancies to these probable discrepancies are 
- 1-7 
+ 1-5 
- 0-3 
-i- 0-6 
+ 1-5 
+ 0-1 
- 1-2 
— 0-4 
— 0-2 
— 1-2 
+ 1-4 
— 0-1 
Thus six out of the twelve ratios are numerically less than unity, and six numeri- 
cally greater, while the greatest ratio is well within the probable limit (§17). The 
hypothesis of independence in this case is therefore justified by the data.* 
Part III.— Application to Normal Distributions. 
§ 22. Probable Errors in Mean and in Semi-parameter by Different Methods .—Ii 
the values of a measure L are known to be distributed normally, the distribution is 
* The method of this section is an extension of the ordinary method (used largely by Professor Lexis 
and Professor Edoeavorth) for testing the “stability of statistical ratios,” 
