[ 3836 ] 
XXXIX. Note on the Radiation from an Alternating Circular 
Electric Current. By Prot. W. McF. Orr, M.A.* 
1. JN this Journal of December 1903, p. 670, formule are 
given for the magnetic force at a great distance 
from a perfect conductor in the form of a very thin circular 
ring which carries an alternating current. I did not then 
notice that these formule can be expressed very simply in 
terms of Bessel’s functions: I understand that the connexion 
had been noticed, though not definitely stated, by Dr. 
Pocklington (see ‘ Nature,’ Mar. 26, 1903) : it may, however, 
be worth while investigating more fully the expression which 
can thus be obtained for the rate of radiation of energy. 
2. In the notation of the former paper, in case of a current 
of the type C, cos (es +«Vt)+C, cos (—xs+«Vt), where s 
denotes distance measured along the ring from a fixed point, 
we have for the components of magnetic force at a point which 
isata large distance R from the centre of the ring, and whose 
colatitude and longitude measured from the point s=0 are 
0, d, respectively, the equations 
a2=—oR-1 cos 0} C, sin «(ad + Vi— RB) 
—(—)C, sin «(—ap+ Vt—R) 5 P,(8) f, 
B2=—aR~! cos 0} OC, cos «(ad + Vt—R) 
+ (—)°C, cos «(—agd + Ve—R) A (9), 
y2=oR- sin 6} C, cos «(ad + Vt—R) 
+ (=)°C, cos «(ap + Vi—R) } (8), 
where 
+7 
F,(@) =| cos f cos a (y+ sin Osin w)dyp, 
T 
+7 
f, (8) =| sin Y sin o(y+ sin 6 sin rd, 
and xa=o =any integer, a being the radius of the ring. 
3. The relation ca=o=an integer holds, approximately, 
for some of the free periods {, which were more immediately 
referred to in the previous paper ; if, however, the current 
oie / ay 
is of the type C, cos (p’+«Vt) + C, cos (— od’ + xVt), 
* Communicated by the Author. ; 
+ The accidental omission of a factor x from the ex i 
ressions 
«(t+ap+ Vé—R) is here corrected. - : 
J The equation determining the free period appears, however, for 
every value of o to have an intinite number of roots; and there appear 
to be modes of free motion corresponding to the case o=0, one of the 
corresponding values of « being a pure imaginary. | 
