294 REPORTS ON THE STATE OF SCIENCE, ETC. 
where z=XV/ 4rypo and numeric / 
Z’=linear impedance of the wire to alternating current, abohms-cm. / 
R =linear resistance of the wire to continuous current, abohms/cm. 
X =radius of wire, cm. 
Wea 
m™ =3-14159... 4 
1 
Y= apy of the wire, abmhos/cm., taken as 0-580 x 10™. 
re) = =resistivity of the wire, abohm-cm. 
yu. =magnetic permeability of the wire, taken as unity. 
@ =2nxf=angular velocity of alternating current, radians/sec. 
f =trequency of alternating current, cycles/sec. 
X’=linear reactance of the wire to alternating current, abohm-cm. 
Z_R’ € . x! 
on * 1? 
then the real term ad is taken as the skin-effect resistance ratio and the imaginary 
R 
term, 7. =~ is taken as the skin-effect reactance ratio. 
R 
Thus, for 2=3-0\ 45°, J,(3-0 \ 45°) =1-950192 796° . 51810 
J,(3-0\ 45°) =1-°799908 /15° . 71317 
and 1-318095-+7 0-950812=1-625244 735° . 80493 
7! 3.0\a5° 1950192 96". 51810, 
=1-318095+7 0-950812. 
Yn this case, the wire would offer an apparent resistance 31-8095 per cent. in excess of 
its continuous-current resistance. For the purposes of engineering practice, a much 
lower arithmetical precision would ordinarily suffice. 
The table was computed by Mr. P. L. Alger, in the electrical-engineering department 
of the Massachusetts Institute of Technology. 
References : 
(1) Jahnke and Emde ‘ Funktionentafeln,’ Berlin, 1909, p. 147, and (2) ‘ Experi- 
mental Researches on Skin Effect in Conductors,’ by A. E. Kennelly, F. A. Laws 
and P. H. Pierce, Proc. Am. Inst. Elec. Engrs., September 16, 1915, p. 1795. 
