176 
Oti Expansions in Tetmchoric Functions 
was not necessary to repeat them. In all these tables, in the row s = 0 we have 
placed 1(1 — a) in the column containing the tetrachoric functions and it is only 
necessary to draw attention to the ftxct that in the next column the negative sign 
in —a^Tg does not apply to the first term ^(1 — «). The tables will then be easily 
TABLE I. 
/•29 -t ^.48g— X 
Jo r(49) 
as 
Tetrachoric 
Terms in 
Value of Series 
s 
Functions r. 
Series - a^Tg 
up to term Tj 
0 
1 
00000000 
+ 
•0025551 
+ -0025551 
•0025551 
1 
0 
00000000 
+ 
•00791545 
— 
— 
2 
0 
00000000 
— 
•01567180 
— 
— 
3 
0 
11664237 
+ 
•02210325 
- 
•0025782 
- ^0000231 
4 
0 
02499479 
— 
•02189644 
+ 
•0005473 
•0005242 
5 
0 
00638743 
+ 
•01259137 
•0000804 
•0004438 
6 
0 
03228531 
+ 
•00159776 
•0000516 
•0003922 
7 
0 
01785148 
•01140536 
+ 
•0002036 
•0005958 
8 
0 
00840223 
+ 
•01000967 
•0000841 
•0005117 
9 
0 
01470566 
+ 
•00006659 
•0000010 
•0005107 
10 
0 
01282194 
•00849985 
+ 
•0001090 
•0006197 
11 
0 
00895618 
+ 
•00711870 
•0000638 
•0005560 
12 
0 
01042333 
+ 
•00164419 
•0000171 
•0005388 
13 
0 
01079260 
•00754632 
+ 
•0000814 
•0(106203 
14 
0 
00962776 
+ 
•00418464 
•0000403 
•0D05800 
15 
0 
01015854 
+ 
•00374438 
•0000380 
•0005419 
16 
0 
01102777 
•00640271 
+ 
•0000706 
•O0OG125 
17 
0 
01128126 
+ 
•00094254 
•0000106 
•0006019 
18 
0 
01209893 
+ 
•00523425 
■0000633 
•0005386 
19 
0 
•01345974 
•00422873 
+ 
•0000569 
•0005955 
20 
0 
•01483350 
•00218561 
+ 
•0000324 
•0006279 
21 
0 
01660082 
+ 
•00525599 
•0000873 
•0005407 
22 
0 
01901932 
•00110396 
+ 
•0000210 
•0005617 
23 
0 
02196131 
•00426227 
+ 
■0000936 
•0006553 
24 
0 
•02561864 
+ 
•00346981 
•0000889 
•0005664 
25 
0 
•03033429 
+ 
•00205905 
■0000625 
•0005039 
26 
0 
•03631783 
•00439701 
+ 
•0001597 
•0006636 
27 
0 
•04391748 
+ 
•00042653 
•0000187 
■0006449 
28 
0 
•05371111 
+ 
■00393217 
•0002112 
•0004337 
29 
0 
•06638572 
•00244866 
+ 
•0001626 
•0005963 
30 
0 
08285325 
•00248099 
+ 
•0002056 
•0008018 
True value •0005850. 
understood, but, in order that a better appreciation of the results uiay be obtained, 
the value of the series up to a certain term has been plotted against the number 
of that term. A line, drawn across the paper and corresponding to the true value 
of the integral, shows how much the value of the series is in excess or defect of the 
true value of the integral. The various points have been joined by continuous 
wavy lines but, of course, these lines have no real physical meaning. However, by 
joining the points, the graph will, we think, convey a better idea of the variation 
