REPORTS ON THE STATE OF SCIENCE.—1914. 
Neumann Cylinder Functions —continued. 
78 
x Yo(x) 
3°86 +0-015765 
3°88 +0:002917 
3-90 —0:009866 
3-92 —0-022579 
3-94 —0-035219 
3:96 —0-047781 
3:98 —0-060260 
4:00 —0-072653 
4:02 —0-084955 
4:04 —0-097162 
4:06 —0-109270 
4.08 —0-121275 
4.10 —0-133172 
4:12 —0-144959 
4-14 —0-156631 
4-16 —0:168184 
4:18 —0-179615 
4-20 —0-190919 
4-22 —0-202093 
4-24 —0-213134 
4-26 —0-224038 
4:28 —0-234802 
4-30 —0-245422 
4:32 —0-255894 
4:34 —0-266216 
4:36 —0-276384 
4:38 —0-286395 
4:40 —0-296247 
4-42 —0-305936 
4-44 —0-315458 
4:46 —0-324812 
4:48 —0-333995 
4-50 —0-343003 
4-52 —0-:351834 
4-54 —0-360487 
4:56 —0-368957 
4-58 —0-377243 
4:60 —0-385342 
4-62 —0-393252 
4-64 —0-400971 
4-66 —0-408497 
4:68 —0-415828 
4:70 —0-422961 
4:72 —0-429895 
4:74 —0-436629 
4:76 —0-443160 
4-78 —0:449486 
4-80 —0-455607 
4-82 —0-461520 
4:84 —0-467225 
4:86 —0-472719 
4-88 —0-478003 
4:90 —0-483074 
4-92 —0-487931 
4-94 —0-492574 
4:96 —0-497002 
4:98 —0-501213 
5:00 —0-505208 
5-02 —0-508984 
Y,(z) x Y,(@) Y,(x) 
+0-643933 || 5-04 —0-512543 +0-172467 
+. 0:640800 5-06 —0-515883 +0-161521 
+0-637444 5-08 —0-519004 | +0-150556 
+0-633868 5-10 —0-521905 | +0-139577 
+0-630073 5-12 —0-524587 +0-128587 
+0-626063 5-14 —0-527048 +0-117590 
+0-621839 5-16 —0-529290 +0-106591 
+0-617404 5-18 —0-531312 +0-095594 
+0-612760 || 5-20 —0-533114 | -10-084602 
+0-607909 || 5-22 —0-534696 +0-073619 
+0-602855 | 5-24 —0-536059 +0-062650 
+0-597600 | 5-26 —0-537202 -+0-051700 
+0-592146 | 5-28 —9-538127 +0-040771 
+0-586497 | 5-30 —0-538833 -+0-029867 
+0:580655 || 5-32 —0-539322 | +0-018994 
+0-574623 || 6-34 —0-539593 +0-008154 
+0-568403 || 5:36 | —0-539648 | —0-002650 
+0-562000 || 5-38 —0-539488 —0-013412 
+0-555415 5-40 —0-539112 | —0-024128 
+0-548652 5-42 —0-538523 | —0-034796 
+0:541715 || 5-44 —0-537721 | —0-045411 
+0-534605 5:46 —0-536707 —0-055970 
+0-527327 || 5-48 —0-535482 —0-066468 
+0:519884 || 65-50 —0-534048 —0-076903 
+0-512279 || 5-52 —0-532406 —0-087270 
+0:504515 || 5-54 —0-530558 —0-097566 
+0-496596 || 5-56 —0-528504 —0-107786 
+0-488525 || 5:58 —0-526247 —0-117929 
+0-480306 || 5-60 —0-523788 —0-127990 
+0-471943 || 5-62 —0-521128 —0-137965 
+0-463488 | 5-64 —0-518270 —0-147852 
+0-454795 || 5-66 —0-515215 —0-157646 
+0-446018 5-68 —0-511964 —0-167345 
+0-437112 5-70 —0-508521 —0-176945 
+0-428078 5-72 —0-504887 —0-186443 
+0-418921 5-74 —0-501064 —0-195836 
+0-409646 5-76 —0-497055 —0-205120 
+0-400255 5:78 —0-492861 —0-214293 
+0-390753 5:80 —0-488484 —0-223350 
+0-381144 5:82 —-0-483927 —0-232290 
+0-371430 5:84 —0-479194 —0-241110 
+0-361617 | 5-86 —0-474284 —0-249806 
+0-351708 || 5-88 —0-469202 —0:258375 
+0-341706 5-90 —0-463949 —0-266815 
+0-331617 5-92 —0-458529 —0-275123 
+0-321444 5:94 —0-452945 —0-283297 
+0-311191 || 5-96 —0-447199 —0-291333 
+0-300862 | 5:98 | —0-441293 | —0.299299 
+0-290461 600 | —0-435231 —0-306982 
+0-279992 6-02 —0-429015 —0-314590 
+0-269459 6:04 —0-422648 —0-322051 
+0:258867 6:06 —0-416134 —0-329363 
+0-248219 6-08 —0-409474 —0-336522 
+0-237519 6:10 —0-402674 —0-343527 
+0-226772 6-12 —0:395735 —0-350376 
+0-215981 6-14 —0-:388660 —0-357066 
+0-205151 6-16 —0-381453 —0-363595 
+0-194286 6-18 —0-374117 —0-369961 
+0-183390 | 6-20 —0-366656 —0-376164 
