70 REPORT—1899. 
what from that obtained by first finding the value of the function at ¢ 
and f by simple interpolation, and then interpolating P between these. 
On the whole we consider that methods of interpolating in the case of 
tables of double or multiple entry require a full discussion and treatment 
which would be out of place here. The chief source of error which will 
arise in using the present tables will, we believe, be the error of inter- 
polation ; but this error with caution will not, we consider, amount to 
more than 3 or 4 in the 10,000, an error which is of no importance in 
statistical investigations. 
F G H I 
© © © © 
(-1,-1) (,—1) (,=1) (2-1) 
0, 0 1,0 
(-1, Tae aebgetity gal 3g” 2,0) 
© wee eens igh eeeeee © e 
2 Rae = 
: Sek : 
e: ween eee eee OP wenn - 
i 
© - (°) 
S eS occ ee 4 7) K 
as ©, 1) ap ie 
© ©) © © 
R N M L 
(—1, 2) (0, 2) a, 2) (2, 2) 
(5) Should the G (7, v) integrals ever become, like the I'-integrals, of 
physical or mathematical importance, e.g. in relation to I-integrals with 
a complex variable, then the present table will serve as a skeleton table 
to be filled in for much smaller differences of 7 and ¢. The present 
determination of G (7, v) through a knowledge of H (7, 7), and the use 
of 10-figure tables like those of Vega, will serve for almost all purposes 
that are likely to arise, and even without such 10-figure tables for all statis- 
tical purposes. The latter were indeed those for which they were planned. 
To give greater accuracy for interpolated values we should have had to 
increase at least ten to twenty fold the 2,300 entries of the present table, 
and this could only be done by an amount of labour wholly incommensur- 
able with our initial aims. The table as it is has involved between five 
and six thousand independent calculations, and has consumed an amount 
of time and energy which, had it been foreseen—which luckily it was not 
—would probably have sufficed to discourage any attempt to carry out 
the work. 
