404 REPORT—1 883. 
the magnetism of one specimen of annealed iron wire from I= 1250 to I= — 1240, 
and back, the amount of work done against magnetic friction (apart from any 
induction of currents) was 1,670 centimetre-dynes per cubic centimetre of the 
metal. In hardened iron, and especially in steel, the work done is far greater. 
The effects of stress on existing magnetism and on magnetic susceptibility have 
been examined at great length. The most remarkable effects occur in wires which 
have been hardened by stretching. In these the presence of a moderate longi- 
tudinal tensile stress increases the magnetic susceptibility immensely for low values 
of the magnetising force, but diminishes it for higher values. It also increases, 
very greatly, the ratio of residual to total magnetisation; but both of those effects 
pass a maximum when the stress is sufficiently increased. 
The whole subject is much complicated by the presence of the peculiar action 
which, in previous papers, the writer has named hysteresis, the study of which, in 
reference both to magnetism and to thermo-electric quality, has formed a large 
part of his work. 
4. On Mawwell’s Equations for the Electro-magnetic Action of Moving 
Electricity. By Professor Firzceraup, F.R.S. 
Maxwell only once mentions this action in his ‘Treatise on Electricity and 
Magnetism,’ in § 768, although it is just as necessary as his displacement-currents 
in order to be able to consider all circuits as closed. 
The equations for the electro-magnetic field, § 618, are incomplete, for he intro- 
duces as the coefficient of ein the equations for the mechanical force -% 
ve a Ys 
and BAN, in its three components, while it would be more complete to have 
ae 
put in P, Q, 2 the complete components of the electromotive force. By so doing 
he would have introduced the terms c(ey) —b(ez), which are evidently the terms 
expressing the convective action. Maxwell himself practically makes this substitu- 
tion in §631 and deduces indirectly his electro-magnetic theory of light from the 
term — = thereby introduced. 
5. On the Energy lost by Radiation from Alternating Electric Currents. 
By Professor Firzceratp, B.S. 
I take the simple case of a small circular current. 
The components of the vector potential at any point must satisfy A?2"+ KpF'=0, 
while for points very close to the elements of currents they must be /’= po 
A 
‘ : 4. t 
Assuming the current simply periodic, ¢ = ¢, cos 2m vig then 
F cos 27 (¢— / Kp.) 
=plUu >= = pe? 
| t igs ds. 
; 
The energy in any element of the field is per unit volume = Fu + Gv + Hw, and as 
u - ph, &e., we can easily represent in the form of the square of the above 
integral the energy per unit volume, Estimating it for the case of a very small 
circular current, it gives for the energy at any time on a sphere of radius — 
E=(n dey) ee” Ry 
where a is the radius of the small circuit and ipa : 
The part of this independent of the radius of the sphere is evidently the radiated 
energy, and assuming it to move with the velocity of the waves, we find the 
energy radiated per second 
