REPORTS 
ON THE 
STATE OF SCIENCE. 
The Further Tabulation of Bessel Functions.—Report of the Committee, 
* consisting of Professor M. J. M. Hitt (Chairman), Dr. L. N. G. 
Fiton (Secretary), Professor ALFRED LopGE, and Dr. J. W. 
NICHOLSON. 
Ture Committee have made further progress with the calculations. Using 
the notation of previous Reports, values of Q,,(«) have been calculated for 
integral values of », from n=1 to »=6. These are shown in Table IV. 
below, together with the values for n=0, which are reprinted from 
Table III. of the Report of the Committee for 1907. 
From these the values of a (= sin-\(Q/R)) have been computed from 
n=0 to n=6. To these are added the values for n=}, 14, . . . 63, for 
which the semi-convergent expansions for the Bessel function terminate, 
which renders the computation easier. 
Instead of a itself, however, log {8va/(4n?—1)} has been tabulated in 
Table V. below. The reason is that this quantity is fairly adapted for 
interpolation both for intermediate values of « and for intermediate 
values of 7, as it varies comparatively slowly, especially for large values 
of x. For values of x greater than 1,000 (which is the largest argument 
in the table) log {8va/(4n?—1)} is very sensibly zero : in no such case does 
it differ from zero by more than about 1 in the sixth place of decimals. 
From log {8xa/(4n?—1)}, log a and hence a are readily calculated, 
J,(«) is then found from the formula 
log J,(a)=log {Ra/=} —} log «+log cos (e+a—7—n)), 
Tv a 
the values of log {R/ zt being taken from Table II. of the 1907 
TT 
Report. 
From the tables of the present Report and those of the 1907 Report 
the values of J,,(x) for values of n ranging from n=0 to n=64 at intervals: 
1909, D 
