: 
ON THE FURTHER TABULATION OF BESSEL FUNCTIONS. 
95 
values of sin a, are given in Table III., and also those of log (—z sin ay), 
which latter series is useful for purposes of interpolation. 
TaBiE IIL.— Values of Q, (x) and log { —Q, (x)}, Se. 
a | Qo (x) \log (—Qpo (#)) | log (—sin ap) | —sina, | log(—«a sin a0) 
| 10 | —-012 428 881 | 2:0944,3 203 | 2-0946,9926 012,436,531 | T-0946 9926 
20 | —-006 240 9144 | 3°7952,4822% | 3°7953,1581 | 006,241,886 | 1:0963 4581 
80 —-004 163 9632 | 3:°6195,0688 | 3:°6195,3699 | 004,164,252 | 1:0966 5824 | 
| | | 
40 003 123 8578 | 3°4946,9125 | 3-4947,0820 | 003,123,980 1:0967 6819 
50 | —-002 499 4148 | 3:3978,3835 | 3°3978,4920 | 002,499,477 | 1:0968 1920 
i; 60 | _-002 082 9945 | 3:3186,8813 | 3°3186,9567 | -002,083,031 | 1-0968 4692 
70 | _-001 785 5309 | 3:2517,6737 | 3°2517,7291 | -001,785,554 T0968 7095 
80 —-001 562 3571 | 3: 1937,8030 | 3°1937,8454 | °001,562,372 | 1°0968 7453 
90 —-O00L 388 7884 | 3:1426,3609 | 3:1426,3944 | 001,388,799 | 1:0968 8195 
100 —:001 249 9268 5-0968, 8458 30968, 8729 | 001,249,935 | 1:0968 8729 
200 —-000 62 9908 | 4°7958,7363 | 4:7958,7431 | 000,624,992 | 1°0969 0431 
| 300 —-000 416 6640 £-6197,8598 4°6197,8628 | 000,416,664 | 1:0969 0753 
, 400 —-000 312 4989 44948,4849 4:-4948,4866 | 000,312,499 T0969 0865 
_ 500 —-000 249 9994 4:3979,3897 | 4:3979,3908 | -000,250,000 | 1.0969 0908 
/ 600 —-000 208 3330 | 4°3187,5806 | 4°3187,5814 | 000,208,333 | 1:0969 0939 
700 —-000 178 5712 |.4:2518,1141 4°2518,1147 | 000,178,571 | 10969 0951 
800 | —:000 156 2499 | 4-1938,1975 | 4:1938,1979 | 000 156,250 | 1:0969 0978 
900 | —:000 138 8888 | 4:1426,6723 | 4:1426,6728 -000,138,889 | 1-0969 0979 
1000 | —:000 124 9999 | 4:0969,0967 | 4:0969,0980 ' 000,125,000 | 1:0969 0980 
They have also obtained approximate expressions for a, for a few 
special values of ~ when « is very large. 
The extent to which these 
approximations can be depended on will have to be verified when the 
tables of a have been formed. 
these approximations until such verification can be made ; 
It seems better to postpone the report on 
but it may be 
stated that a good approximation to ay is ag=— = pe : to 
The following are accurate : 
ai=0, 
a3s=cot x 
as=cot eek aimee oe v3 
3 3 
The Committee desire reappointment, with a continuation of their 
present grant. 
APPENDIX. 
Report of the Committee appointed in 1906 to consider the Further 
Calculation of Bessel’s Functions. 
In the communication on this subject made to Section A in 1906, it 
was stated by Professor Lodge that the equation 
Det + Q,Q: ra =] ’ 
