280 REPORTS ON THE STATE OF SCIENCE, ETC. 
Table of ‘Converging Factors.’ 
x For B,(z) | For B,(x) 
6-0 0-504 : 0-567 
1 0-497 : 0-560 
2 0-490: 0-552 : 
3 0-483 : 0-545; 
4 0-477 0-539 
5 0-470 0-532 
6 0-463 : 0-525 
7 0-456 ; 0-518: | 
8 0-450 0-512 
9 0-448 : 0-505 : 
7-0 0-437 : 0-499 
Intermediate values of Q(x) and ©,(x) by intervals of 0-02 were thenfound by 
interpolation from central differences. The tables are given as calculated some years 
ago and are in substantial agreement with the values of the H, and H, functions in 
Watson’s ‘ Theory of Bessel Functions.’ The colon : represents half a unit approxi- 
mately in the last place of decimals, 
Lommel-Weber {2 Functions of Zero and Unit Orders. 
x Q(x) Q(x) Pecos i Q)(2) Q(z) 
0-00 | +40-000000 | —0-636620 0-70 | +0-421842 —0-535988 
| 02 | +0-012732 —0-636535 | -72 | +0-432506 —0-530358 
| 04 | +0-025460: | —0-636280: | -74 | +0-443056 —0-524592 
| 06 | +0-038182 | -—0-635856 | -76 | -+0-453489 —0-518692 
| -08 +0-050893 : —0-635262 || -78 | +0-463802 : —0-512660 | 
/ 0:10 | +0-063591 : —0-634499 | 0-80 | +0-473994: —0-506497 : | 
-12 | +0-076272: | -0-633567 | -82 | +0-484061: —0-500206 : 
14 -+0-088933 | —0-632466 -84 | +0-494002 —0-493790 
‘16 | +0-101570 —0-631196: | -86 | +0-503812: —0-487249 
18 | -+0-114179: —0:629759 | -88 | +0-513491 —0-480585 : 
0-20 +0-126759 | —0-628154 0:90 | +0-523035 —0-473802 : 
22 | +0-139304 ; —0:626382 | -92 | +0-532442 —0-466901 
| 24 | +0-151813 —0-624443: || -94 | +0-541710: —0-459884 : 
| -26 | +0-164281 : —0-622339 | -96 | +0-550837 —0-452754 
| 28 | +0-176705 : —0-620069: | -98  +0-559819 : —0-445512 : 
0:30 | +0-189083 —0-617635: | 1:00 | +0-568656 : —0-438162: | 
| -32 | +0-201410 —0-615038 | -02 | +0-577345 : —0-430705 : 
| 34 | +0-213683 - —0-612277 || -04 | +0-585884 —0-423144: | 
36 | -++0-225900 —0-609354: | -06 | +0-594270: —0-415481 : 
| +88 | +0-238056: —0-606271 | -08 | +0-602502 : —0-407719 | 
0-40 | +0-250149: —0-603027 | 1:10 = +0-610578 : —0-399860 
‘42 +0-262176: | —0-599624: | -12 -+0-618496;: —0-391906 : 
44 | +0-274133 - —0-596064 | -14 | +0-626254: —0-383861 
46  - +-0-286018 —0-592346 : 16 -+.0-633850 : —0-375726 
-48 | +0-2978296: | —0-588473: || -18 | +0-641283 —0-367504 
0:50 | +0-309556 —0:584446 | 1:20 | +0-648550 —0-359198 
52 | +0-321203 : —0-580265: | -22 | -+0-655650 —0-350810 
54 | +0-332765: | —0-575933: 24 40662582 —0:342343 : 
56 | +0-344239: —0-571450: | -26  +0-669343: —0-333800: | 
58 | +0-355622 - —0-566819 28 | +0-675933 : —0-325184 
0-60 | +0-:366911: | —0-562040 | 1:30 | -+0-682350; —0-316496 : | 
62 | +0-378103 —0-557115 | 32 | +0-688593 —0-307741 | 
64 | +0:389195 —0-552046 84 | .0-694659 - —0-298920 
‘66 +0-400184 | —0-546834 36 | +0-700549 —0-290036 
, ‘8  +0-411067: | —0-541480: +38 | +0-706260: | —0-281092: 
