292 MESSRS. PROUDMAN, DOODSON, AND KENNEDY ON THE DIFFRACTION OF 
Analysis of Results and Interpolation. 
(By A. T. Doodson.) 
4. A consideration of the results tabulated up to this point shows that for na = 9, 
10, they are not adequate for the complete representation of Y^ + Y/, Z 1 2 + Z 3 2 through¬ 
out the range of 6. Owing to the excessive labour involved in further computations 
from the original series, other methods were tried. The following sections are devoted 
to the discussion and presentation of this work. 
For values of 6, except those “ near ” 180°, the first approximation for large values 
of >ca, gives 
where 
Y, = — Zj = ttk« cos 0, 
Y 2 — —Z 2 — \kcl sin 0, b 
0 = 2cos ^ 0. 
*( 10 ) 
Consider then the functions 
= Yj — ^-/ca cos 0, 
*i 2 = Y 2 —|-na sin 0, 
£ = Zi + J/ca cos 0, 
£> = Z 2 + \r,a sin 0, 
( 11 ) 
which express the amounts by which the functions Y 1? Y 2 , Z l5 Z 2 differ from the 
values given by (10). These functions and their derivatives are calculable from the 
* Bromwich, loc. cit. 
