p. F. EVERITT 
439 
Now enter the table twice using interpolation, once with ,^(1 — a) equal to 
"09750 and a second time with it equal to "10050, and we have 
i (1 - a) ri To 1-3 r,, ts t,; 
"09750 + -17228 +"15787 +"04779 -"06018 -"0GG93 + -00854. 
"10050 +"17014 +"15920 +"04567 -"06275 --06652 + 01111 
Multiplying the numbers in each column together, we find the eijuation 
"032000 = -009799 + •030345/- + "025 1 427-" + "002183r' 
+ "003776/-^ + "004452r'' + "000095/-'' ; 
whence, solving by Newton's method, 
?■ = -501. 
An illustration of the calculation of the probable error of r when found as 
above is given in Pearson's paper on p. 36. 
(6) Without interpolation. 
Using the same table as in example (a), we have as before 
^ + ^ = ■09750, ^ = -10050, t = -032000. 
N N N 
Entering the table with i(l — a) equal to '098 and "101 we have 
Ml-") n T2 Tj T^ T.-, r« 
"098 +"17292 + -15811 + -04744 --060(11 - -06687 + -00897 
-101 + 17678 +"15948 +"04531 -"06317 -"06644 +"01153 
Multiplying out as before 
"032000 = "009898 + •030569r + •025215r- + "002150r^ 
+ •003829r^ + "004443r^ + "0001 03r'' ; 
whence, solving by Newton's method, 
r = -498. 
This particular illustration, chosen so that the true values of ^ (1 — a) fall 
midway between tabulated values, shows the maximum error caused by working 
without interpolation for values of ^(1 — a) of "100, and in practically every case 
this error will be negligible when compared with the probable error of r. 
A study of the differences of the functions shows that for values of i (1 — a) 
greater than "100 the error introduced by working without interpolation will not 
be appreciably greater than in the example given and may quite easily be less ; 
for values of ^ (1 - «) less than "100 it will be desirable to use interpolation if the 
greatest accuracy attainable is desired, but even in very unfavourable cases such 
errors will rarely become as large as the probable error of the result. 
.56—2 
