TABLES. 



203 



Table 6. 



Values of the Probability Integral for Argument 



0.4769 



of measurement = the Probable error 



; that is, when the unit 



Multiples 























of the 

 Probable 



•o 



•1 



•2 



•3 



•4 



•5 



•6 



•7 



•8 



•9 



Error. 



























o-oo 



0-65 



o-ii 



0-16 



0-21 



026 



0-31 



0-36 



0-41 



0-46 



1-0 



•50 



•54 



'58 



•62 



■6o 



•69 



•72 



•75 



•78 



•80 



2-0 



•82 



•84 



•86 



.88 



•89 



•91 



•92 



•93 



•94 



•95 



3-0 



•957 



.964 



•969 



•974 



•978 



•982 



•985 



•987 



•990 



•992 



4*0 



•9930 



.9943 



•9954 



•9963 



■9970 



•9976 



•9981 



•9985 



•9988 



•9990 



5-0 

 infinite 



•9993 

 1-000 



•9994 



•9996 



•9997 



•9997 



•9998 



•9998 



•9999 



•9999 



•9999 





Tables 5 and 6 show the proportion of cases in any Normal 

 system, in which the amount of Error lies within various extreme 

 values, the total number of cases being reckoned as 1 - 0. Here no re- 

 gard is paid to the sign of the Error, whether it be plus or minus, but 

 its amount is alone considered. The unit of the scale by which the 

 Errors are measured, differs in the two Tables. In Table 5 it is 

 the " Modulus," and the result is that the Errors in one half of the 

 cases, that is in 0'50 of them lie within the extreme value (found by 

 interpolation) of - 4769, while the other half exceed that value. 

 In Table 6 the unit of the scale is 04769. It is derived from Table 

 5 by dividing all the tabular entries by that amount. Consequently 

 one half of the cases have Errors that do not exceed 1*0 in terms of 

 the new unit, and that unit is the Probable Error of the System. 

 It will be seen in Table 6 that the entry of "50 stands opposite to 

 the argument of 1'0. 



If it be desired to transform Tables 5 and 6 into others that shall 

 show the proportion of cases in which the plus Errors and the minus 

 Errors respectively lie within various extreme limits, their entries 

 would have to be halved. 



Let us suppose this to have been done to Table 6, and that a 

 new Table, which it is not necessary to print, has been thereby pro- 

 duced and which we will call 6a. Next multiply all the entries in the 

 new Table by 100 in order to make them refer to a total number 

 of 100 cases, and call this second Table 65. Lastly make a converse 

 Table to 65 ; one in which the arguments of 65 become the entries, 

 and the entries of 65 become the arguments. From this the Table 7 



