ON CALCULATION OF MATHEMATICAL TABLES. 293 
paper already cited, reference may be made to two papers by C. W. Oseen.} No method 
of evaluating these functions is given, however. 
The function has been calculated from the expression 
Oy(z) = 1— SVE. (1 —8,.y) FESR - Sy 
for small values of y and w; and from 
Qy(e) = Ny(e) + 
for large values. 
2 (a e-* sinh (g? + cos vt. e*) dO 
TJ Oo 
By means of the recurrence formula, 
Qwale) =™ - Ay(e) — Qvi@) + ye’ 
=aN41 - Vv vl TX 
functions of higher or lower order may be found from the table below. 
4y | QOy(y). | QOy_a(v). | 4y Qy(v). Oy -a(v). 
| 0 0-000000 --+-0-636620 , 20 | —0-189267 : -+-0-028883 : 
. 1 —0-223134 -+-0:764280 21 | —0-176178 +-0:013998 
2 —0-388643 -+-0-801051 : 22 —0-152262 § —0-012517: 
3 —0-460801 -+0-729461 || 23 —0-:130347 | —0-:036507 
4 —0-438162 : +0-568656; || 24 —0-121139 : | —0:046406 : 
5 —0°351335 : -+0:-366713 | 25 —0:127483 : —0-039277 
| 6 —0-247796 : +0:181232 || 26 —0:143408 : —0-021774 
7 —0-171114 -+-0-056955 | 27 —0-158117 : —0-005646 : 
8 —0-144095 +0-010144 28 | —0-162347 : —0-000847 : 
9 —0-162886 -+-0-026096 : | 29 —0-153421 : —0-:010160 
10 —0-203545 : -+ 0-069837 | 30 —0-136283: | —0-028190: 
11 —0-236690 : --0-104088 31 —0-120215 : —0-044970 : 
12 —0-242467 ; +0:105767 |] o2 —0-113344 —0:051856 
13 —0-218764 : -+-0-073703 33 —0-118141 —0-046283 
14 —0-179525 +0-025095 34 —0-130374 —0-:032821 : 
15 —0-145256 : —0-016280 : 35 —0:141887 : —0-020161 : 
16 —0-131426 —0-033258 | 36 —0:145427;  —0-015975 
17 —0-140869 —0-023390 eco —0-138692 —0-022653 | 
18 —0:163728 : +0-001615: | 38 —0-125360 : | —0-036265 
19 —0:184111 : -+-0:023738 : 39 —0-112693 -—0:049134 : 
20 —0-189267 : +0-028883 : 40 | —0-107224 : | —0-054390 : 
Part III. 
Bessel Functions of negative semi-imaginary argument. 
Bessel functions of a negative semi-imaginary argument zV/ 1, Jo(z\ 45°) 
and J, (2\45°), from <=0 to z=10, by intervals of 0-1; communicated by A. E. 
Kennelly, Harvard University and the Massachusetts Institute of Technology ; also 
of their application to the determination of the alternating-current skin-effect im- 
pedance ratio Z’/R, of straight uniform round copper wires, remote from other 
active conductors, according to the formula 
B’ _#\ 48° To @\ 45°) 
2 Jy (@\45°) 
i (a) Uber die Elektromagnetischen Schwingungen an diinnen Ringen. 
(b) Uber das Elektromagnetische Spektrum eines diinnen Ringes. 
Archiv. f. Matematik, Astronomi och Fysik—Vol. 9. Nos. 12 and 28 1913-4. 
