10 REPORT—1848. 
given time, proportional to the square of the intensity of the current. For, what- 
ever be the actual source of the galvanism, an equivalent current might be produced 
by the motion of a magnetic body in the neighbourhood of the closed wire. If now, 
other circumstances remaining the same, the intensity of the magnetism in the in- 
fluencing body be altered in any ratio, the intensity of the induced current must be 
proportionately changed ; hence the amount of work spent in the motion, as it de- 
pends on the mutual influence of the magnet and the induced current, is altered in 
the duplicate ratio of that in which the current is altered; and therefore the amount 
of mechanical effect lost in the wire, being equivalent to the work spent in the mo- 
tion, must be proportional to the square of the intensity of the current. Hence if é 
denote the intensity of a current existing in a closed conductor, the amount of work 
lost by its existence for an interval of time dé, so small that the intensity of the cur- 
rent remains sensibly constant during it, will be k.#.d¢; where k is a certain con- 
stant depending on the resistance of the complete wire. 
Let us now suppose this current to be actually produced by induction in the wire, 
under the influence of a magnetic body in a state of relative motion. The entire 
mutual force between the magnetic and the galvanic wire may, according to Am- 
pére’s theory, be expressed by means of the differential coefficients of a certain 
“force function.” This function, which may be denoted by U, will be a quantity 
depending solely on the form and position of the wire at any instant, and on the 
magnetism of the influencing body. During the very small time dé, let U change 
from U to U+dU, by the relative motion which takes place during that interval. 
Then i dU will be the amount of work spent in sustaining the motion; but the 
mechanical effect lost in the wire during the same interval is equal to k i? dt; and 
therefore we must have 
idU=k? dt. 
Hence, dividing both members by ki dt, we deduce 
1 dU 
kin ee 
which expresses the theorem of Neumann, the subject of the present communica- 
tion. We may enunciate the result in general language thus :— 3 
When a current is induced in a closed wire by a magnet in relative motion, the 
intensity of the current produced is proportional to the actual rate of variation of 
the “force function’? by the differential coefficients of which the mutual action 
between the magnet and the wire would be represented if the intensity of the cur- 
rent in the wire were unity. s 
On a means of determining the apparent Solar Time by the Diurnal Changes 
of the Plane of Polarization at the North Pole of the Sky. By Professor 
WuearstTone, F.R.S. 
«« A short time after the important discovery by Malus of the polarization of light 
by reflexion, it was ascertained by Arago that the light reflected from different parts 
of the sky was polarized. ‘The observation was made in clear weather with the aid 
of a thin film of mica and a prism of Iceland spar; he saw that the two images 
projected on the sky were in general of dissimilar colours, which appeared to vary 
in intensity with the hour of the day and with the position, in relation to the sun, 
of the part of the sky from which the rays fell upon the film. The first attempt to 
assign a law to the phenomena of atmospheric polarization was made by Professor 
Quetelet of Brussels in 1825 in the following terms :—‘ If the observer consider him- 
self as placed in the centre of a sphere of which the sun occupies one of the poles 
the polarization is at its maximum at the different points of the equator of this sphere, 
and goes on diminishing in the ratio of the squares of the sines unto the poles where 
it is at zero.’ This law would be true did the reflected light proceeding from the 
part of the sky regarded arise solely from the direct light of the sun sent to that part ; 
but other secondary reflexions occur which complicate the result and give rise to 
the neutral points since discovered by Arago, Babinet and Brewster. But for the 
purpose of explaining the principle of the instrument now submitted to the examina- 
tion of the Section, we need not take into consideration the intensity of the polar- 
