136 
On Polychoric Coeficients of Correlation 
Hence if and be found accurately the remaining T's can be determined as 
accurately as we please without reference to the t's. 
T, = T, = ^e-i^' (xix), 
But, 
V27r 
2; = V2 T,+To=- 
i^'^ dx 
.(XX). 
V27r J - co V27r 
Hence the tables of ordinates and areas of the normal curve readily provide jr^ 
and Ti to seven decimal places, and (xviii) provides the higher T's. These were cut 
down to five figures and an approximate check on their values obtained by (viii). 
As a matter of fact if r is of the order "50 we cannot hope to obtain more than 
three figure accuracy in r without going to higher t- and ^-functions than the 
sixth, especially when using (xvii). But three figiu-es in the correlation are usually 
adequate and the labour of computing is much increased if higher functions are 
used. Such must, however, be used if the correlation be sensibly higher than '50. 
The following table gives the ^ (1 + h's, H's, xs, t's, ^t's, T's, and ^T's for 
the a;-variate. 
TABLE I. 
•802 
•871 
-972 
1-000 
+ -84879 
+ 1-1311.3 
+ 1-91104 
+ 00 
•27827 
•21042 
•06425 
0 
k 
r-t 
T4 
T,-, 
- CO 
0 
■036 
■r79912 
•07908 
•358 
- •36381 
•37340 
•G22 
+ ^31074 
•38014 
•2-19667 
•91404 
•02553 +-56594 +-98333 : +1^44723 +2-29464 
0 
- -036 
--358 
- -622 
- ^802 
--871 
- -972 
-1 
0 
+ -07908 
+ -37340 
+ -38014 
+ -27827 
+ -21042 
+ -06425 
0 
0 
- -10060 
- -09606 
+ -08353 
+ -16701 
+ -16830 
+ ^08682 
0 
0 
+ -07221 
- -13226 
-•14021 
- -03176 
+ -02401 
+ ^06952 
0 
0 
- -00688 
+ -07952 
- ^07001 
- -10990 
- -08359 
+ ^01634 
0 
0 
- -04291 
+ -07579 
+ ^08432 
- -02041 
- -05839 
- ^03270 
0 
0 
+ -03654 
- -06933 
+ •06182 
+ -07319 
+ -03408 
- -03744 
0 
•036 
-322 
- -264 
-180 
•069 
-101 
-028 
+ 
•07908 
+ 
-29432 
+ -00674 
-10187 
-06785 
-14617 
■06425 
•10060 
+ 
-00454 
+ -17959 
+ 
-08348 
+ 
-00129 
-08148 
-08682 
+ 
•07221 
-20447 
- -00795 
+ 
-10845 
+ 
-05577 
+ 
-04555 
-06956 
•00688 
+ 
-08640 
- -14953 
-03989 
+ 
•02631 
+ 
-09993 
-01634 
-04291 
+ 
-11870 
+ -00853 
-10473 
•03798 
+ 
-02569 
+ 
-03270 
+ 
-03654 
•10587 
+ -13115 
+ 
•011.37 
-03911 
-07152 
+ 
-03744 
0 
-17827 
- -49385 
- -50388 
•56581 - 
-63299 
- -84922 
-1 
T., 
0 
+ 
•23690 
+ -29898 
+ ^29475 
+ 
•33853 
+ 
-33915 
+ -21135 
0 
T, 
0 
-18799 
- -00734 
+ ^00466 
+ 
-06947 
+ 
-12432 
+ -18307 
0 
Ti 
0 
+ 
•04848 
- -09506 
- -09186 
-10916 
-08255 
+ -06601 
0 
T-, 
0 
+ 
-07412 
+ -07799 
- -00511 
-06648 
-10343 
- -05518 
0 
0 
-08325 
+ -05616 
+ -05364 
+ 
-05379 
+ 
•01471 
- -08491 
0 
+ 
■07908 
+ 
•29432 
+ 
•00674 
■10187 
•06786 
- -14617 
•06425 
-17827 
■31558 
•01003 
•06193 
•06718 
- -21622 
•15078 
+ 
•23690 
+ 
•06208 
•00422 
+ 
•04377 
+ 
•00063 
- -12780 
•21135 
•18799 
+ 
■18065 
+ 
•01200 
-I- 
•06481 
+ 
■05485 
+ -05874 
•18307 
+ 
■04848 
•14354 
+ 
•00320 
■01731 
+ 
■02662 
+ •14856 
•06601 
+ 
■07412 
•06613 
■01310 
■06137 
•03695 
+ -04825 
+ 
05518 
•08325 
+ 
■13941 
•00253 
+ 
•00015 
•03907 
- -09962 
+ 
•08491 
