ON STANDARDS OF ELECTRICAL RESISTANCE. 117 
out the connexion between the electromotive force induced in the above 
manner and the fundamental equations adopted for the absolute system. The 
exact sense in which the terms are employed is defined in the accompanying 
foot-note, along with some simple corollaries from those definitions *. 
A current (C) in a straight conductor of length (L) crossing the lines of 
force of a magnetic field of the intensity (S) at right angles will experience the 
same force (/) as if all the points of the conductor were at the unit distance 
from a pole of the strength (8). The force in this case exerted on the magnet 
is, by equation (5), equal to SLC, and, conversely, an equal force is exerted by 
the magnet on the current. Hence we have equation (7), expressing the value 
of the force (f) exerted on a current crossing a magnetic field at right angles, 
FO Oe © gla LA ee WARS (7) 
Let us imagine this straight conductor to have its two ends resting on two 
conducting rails of large section in connexion with the earth, and let the whole 
sensible resistance (R) of the circuit thus formed be constant for all positions 
of the conductor. Let us further imagine the rails so placed that when the 
conductor slips along them it moves perpendicularly to the magnetic lines of 
force and to its own length. By experiment we know that when the con- 
ductor is moyed along the rails cutting these lines of force, a current will be 
developed in the circuit, and that the action of the magnetic force on this 
current will cause a resistance (f) to the motion (due to electromagnetic 
causes only); and, by equation (7), we find that this resistance f=SLC. 
Let the motion be uniform, and its velocity be called V; and let the work 
done in the unit of time in overcoming the resistance to motion due to elec- 
tromagnetic causes be called W; then W=YVSLC. But this force produces 
* Definition 1—A magnetic field is any space in the neighbourhood of a magnet. 
Definition 2.—The unit magnetic pole is that which, at a unit distance from a similar 
pole, is repelled with unit force. 
Definition 3.—The intensity of a magnetic field at any point is equal to the force which 
the unit pole would experience at that point. 
Corollary 1.—A pole of given strength (8) will produce a magnetic field which (if un- 
influenced by other magnetic forces) will at the unit distance from the pole be of the in- 
tensity S, 7. e. numerically equal to the strength of the pole; for, at that distance, the force 
exerted on a unit pole would, by def. 2, be equal to 8, and hence, by def. 3, the intensity 
of the magnetic field at that pomt would be equal to 8. 
Definition 4.—The direction of the force in the field is the direction in which any pole 
is urged by the magnetism of the field; this is the direction which a short-balanced, freely 
suspended magnet would assume. 
Rtemark.—The properties of a magnetic field, as shown by Dr. Faraday, may be con- 
veniently and accurately conceived as represented by lines of force (each line representing 
a force of constant intensity). The direction of the lines will indicate the direction of the 
force at all points ; and the number of lines which pass through the unit area of cross sec- 
tion will represent the magnetic intensity of the field resolved perpendicularly to that area. 
Definition 5.—A uniform magnetic field is one in which the intensity is equal through- 
out, and hence, as demonstrated by Professor W. Thomson, the lines of force parallel. 
Example.—The earth is a great magnet. The instrument-room, where experiments are 
tried, is a magnetic field. The dipping-needle is an instrument by which the direction of the 
lines of force is found. The intensity of the field is found by a method described in the 
‘Admiralty Manual,’ 8rd edit., article “Terrestrial Magnetism.” The number of lines of 
force passing through the unit of area perpendicularly to the dipping-needle in the room 
toust be conceived as proportional to this intensity, and the direction to correspond with 
_ that of the dipping-needle. The magnitude and direction of the earth’s force at a point 
are generally expressed by resolving it into two components, one horizontal and the other 
yertical. The mean horizontal component in England for 1862 was at Kew = 3°8154 
British units, or 1°7592 metrical ; 7. e. a unit pole weighing one gramme, and free to move 
_ in a horizontal plane, would, under the action of the earth’s horizontal force, acquire, at 
ee end 3 a second, a velocity equal to 1‘7592 metres per second. (Vide also Appendix C. 
to 12. 
