16 The Fmulameiital Problem of Practk al SUttutlcs 
(10) It will be seen from this paper that the next stage forward in the develop- 
ment of the probability integral must be (i) the issue of a table of the incomplete 
F-function. Such a table is now completed and arrangements are being made 
for its publication ; (ii) the issue of a table of the incomplete ii-function. Such 
a table presents grave disadvantages. It must be a table of threefold entry and 
this presents more serious difHculties than even those we have encountered in 
the table of the incomplete F-function, because (a) of the great extent of the 
computations requisite and {h) the great cost involved in publication even if 
completed. I should like to draw the attention of pure mathematicians to the 
following problem: Can the incomplete /)-function be expressed even approxi- 
mately in terms of a limited number of incomplete F-functions? 
Mr H. E. Soper, Miss M. Seegar and I have tried many solutions of this 
problem. None as yet with satisfaction to ourselves. It will not be easily solved, 
nor by the obvious methods of attack. Yet I am convinced that a solution is 
possible, if pure mathematicians of greater knowledge and larger inspiration will 
only deal with the matter. 
I have to acknowledge my great indebtedness to Mr E. C. Rhodes for numerical 
work and Miss A. Davin for graphical work on the illustrations of this paper, and for 
help in mechanical integration of the frequency curves. Such integration of course 
cannot be correct to the last figure. 
