386 Tables for Facilitating the Computation of Probable Errors 
have been tabled for n = 1 to 1000. Clearly for any even value of n between 1000 
and 2000 the value of Xi can be found from the value of %2 for ^n. Thus Xt. 
7i=1594 is Xi for ?i=797, and is found to be -01689. As the first difference for 
X« > 500 does not exceed -00002, and the second difference is zero to five figures, it 
will be clear that Xi can for odd numbers between 1000 and 2000 be found by the 
simple process of halving the sum of the adjacent values of %.2 for — and 
-|(h + 1). Further, for any even value of n between 1000 and 2000, may be 
found by halving the value of x^ 5"> ^^^d for any odd value of n between 1000 
and 2000 x^ ™iay be found by quartering the sum of the values of Xi for 2 
and ^{n + 1). Thus suppose n = 1731 ; we have ^{n — 1) = 865 and hin + 1) = 866. 
Hence = i('01622 + -01621) = -016215, and ;;^o =-JC02293 + -02292) = •0114625. 
The actual values are Xi = "016212 and x^ — '^^^'^^'^- Such differences will hardly 
ever have any statistical importance. To determine the probable error of the 
coefficient of variation we use Table III. Here we find 
tabled for values of V from 0 to 50. The probable error of Fmust therefore be found 
by taking out the value of Xi corresponding to the given value of n, and multiplying 
it by the yjr found for the given value of V by interpolation from this table. 
Thus suppose F = 28-65 for 583 observations. We have by the usual advancing 
difference formula {BiometriJca, Vol. ll. p. 175) 
-dr = 2418612 + -65 x 1-15861 - -^-^ x-01316 + '65 x ^35x 1;35 ^ .^^^^^ 
^ 2 2x8 
which evaluated by the Brunsviga = 24-93774*. Further, from Table II., x-^ = "01975. 
Thus the 23robable error = ^/^ = "49252. The value actually found by direct 
calculation is "49259, the difference, which is of no imjDortance for practical 
statistics, depending upon cutting off x-^ at the fifth figure. 
While Tables I. and II. are the work of the author, Table III. is due to 
Dr Raymond Pearl and J. Blakeman. All the values were found to seven figures, 
but it seemed sufficient for practical work to register them to five. 
* Actual value 24-937,739, so that tlie ^ table is amply sufficient. 
