76 REPORTS ON THE STATE OF SCIENCE.—1914. 
Yj (2) = Jy(z)  logar — Io(a))z —% + (1 +4) (Z) [1!2! 
& (1+4+4)(5) [21314... 
have been calculated by B. A. Smith for = 0-01 to 1-00 and 1-0 to 
10-2 to four places of decimals, and by J. R. Airey for x = 0-1 to 16-0 
to seven places. 
The following Tables have been computed from the relation 
Y,,(%) aa (log a Y) Jn(@) Zz G,(2) 
and verified by the method of differences. 
The interpolation formule for other values of the argument are 
2 3 2 
Yolo +h) = [1 - s + = 2+ | Yue) + [Fate] Lie) 
Yi(e ti) = [1 h_Fa- 2 bs Yi) + [= eon Y,(z). 
Tables of the Neumann Cylinder Functions. 
e | Ya) Yu(z) z | — Yo(a) Yi(z) 
0:02 | —3'911532 —50-044118 0-76 | —0-099484 —1-569515 
0-04 —3-217189 | —25-074360 0-78 —0-068482 —1-530927 
0-06 —2-809980 | —16-766014 0-80 —0-038237 —1-493705 | 
0-08 —2-520090 —12-620908 0-82 —0-008725 —1-457735 | 
0:10 —2-294335 | —10-139907 0:84 +0-020080 —1:422912 | 
0:12 | —2-109042 —8-490185 0-86 +0-048199 | —1-389144 | 
0-14 | —1-951600 —7-314934 0-88 +0:075652 | —1-356346 
0:16 | —1:814487 —6-435818 0:90 +0:102458 —1-+324442 
0-18 | —J-692861 —5-753809 0-92 -+-0-128635 —1-293362 
0-20 | —1-583421 —5:209517 0-94 +0-154198 —1-263043 
0:22 | —1-483817 —4-765173 0:96 +0-179162 —1-233429 | 
0-24 | —1:392318 | —4-395614 0:98 -+0:203539 —1-204467 | 
0:26 —1:307611 | —4-083430 1-00 +0:227344 | —1-176110 | 
0:28 | —1-228681 —3°816195 1-02 -+-0-250588 —1:148315 
0:30 —1-154725 —3-584806 1-04 +0:273280 | —1-121042 
0:32 —1:085096 | —3-382440 1-06 +0:295433  —1-094256 
0:34 | —1-019269 —3-203886 1-08 +0:317054 | —1-067922 
0:36 | —0-956809 | —3-045093 1-10 +0-338152 —1-04201) | 
0:38 | —0-897355 | —2-902869 1-12 +0:358737 —1-016496 | 
0-40 | —0-840601 | —2-774662 1-14 -+0-378815 —0:991350 | 
0-42 | —0-786288 —2-658408 1-16 +0-398393 —0-966551 
0-44 —0-734196 —2-552423 1-18 +0-417479 —0-942079 
0-46 —0-684132 —2-455317 1-20 +0-436078 —0-917912 
0-48 —0-635932 —2-365931 1-22 +0-454197 —0-894033 
0-50 —0-589450 | —2-283297 1-24 +0-471841 | —0-870426 
0-52 —0-544561 | —2-206594 1-26 +0-489016 | —0-847076 
0-54 — —0-501152 —2-135127 1-28 +0-505726 —0-823970 
0-56 —0-459125 | —2-068299 1-30 -+0-521976 —0-801094 
0-58 —0-418392 | —2-005598 1-32 +0-537771 —0°778438 
0-60 —0:378875 | —1-946580 1-34 +0:553115 —0-755991 
0-62 —0-340507 —1-890861 1-36 +0-568012 —0-733743 
0-64 —0-303222 —1-838105 1-38 +0-582466 —0-711687 
0-66 —0-266965 | —1-788017 1-40 +0-596481 —0-689814 
0-68 —0:231685 | —1-740338 1-42 +0-610060 — 0668116 
0-70 —0-197337 | —1-694840 1-44 +0:623207 —0-646589 
0-72 —0-:163878]] | —1/651320 | 1-46 +0-635925 —0-625226 
0-74 —0:131272 | —1-609599 1:48 +0-648217 —0-604021 
