H. E. SoPER, A. W. Young, B. M. Cave, A. Lee, K. Pearson 375 
TABLE IX. Functions required in deter mining the " most probable 
value p of the Correlation. 
T 
^1 v) 
Ao [,r) 
•00 
0 
0 
0 
■05 
■02493,75000 
-•00615,64453 
-•00317,92000 
■10 
•04950,00000 
-■01175,62500 
-•00667,19813 
•15 
•07331,25000 
-■01626,62109 
- 01073,47255 
■20 
■09600,00000 
-■01920,00000 
-•01551,36000 
■25 
•11718,75000 
-■02014,16016 
- -02099,99084 
•30 
•13650,00000 
-•01876,87500 
- -02699,79938 
•35 
•15356,25000 
- -01487,63672 
--03310,98746 
■40 
■16800,00000 
- -00840,00000 
- -03874,08000 
■45 
•17943,75000 
+ -00056,07422 
--04312,99059 
•50 
•18750,00000 
+ •01171,87500 
- 04541,01563 
■55 
■19181,25000 
+ -02457,59766 
--04470,17533 
•60 
•19200,00000 
+ -03840,00000 
- -04024,32000 
•65 
•18768,75000 
+ -05220,05859 
-•03156,41987 
•70 
•17850,00000 
+ -06470,62500 
- -01870,45688 
•75 
•16406,25000 
+ -07434,08203 
- -00248,33679 
•80 
•14400,00000 
+ -07920,00000 
+ -01517,76000 
■85 
•11793,75000 
+ -07702,79297 
+ -03087,17070 
•90 
•08550,00000 
+ •06519,37500 
+ •03926,26688 
■95 
■04631,25000 
+ -04066,81641 
+ •03257,27752 
100 
0 
0 
0 
(13) On the Table for q„= I'sin"-'^ 4, d<f) 
While Table X, p. 377, gives the value of = \ sm"~^ cfydcf) to ten figures, 
. (I 
and therefore will be of use in calculating the values of the moments, the 
reader may be compelled to deal with values of n greater than those tabled, or 
even may need more than ten significant figures. The present values were 
calculated to twelve figures, by means of the simple relations 
1 
I2P+2 — liv 2]) +\ 
1 
lip+i lip 
7T 
with the control relation q^p x q2p-i = ^ 
q-zp-i > 
, and the occasional direct calcula- 
' 2;. 
TT 1 
2 2|7^ 1 
tion of individual g„'s to control the accuracy by use of Degen's Tables* and 
Briggs's Arithmetica Logarithmica'f. 
(2p) I - 
Since 
and 
22f {{p) !}2 2 
2p{2p)l ■■■ 
.(xcii). 
xcin 
* Tabularum ad faciliorem ct breviorem probabilitatis computationem utilium Enneas. C. F. Dcgen, 
Havniae, 1824. 
1 Londini, W. Jones, 1624. 
