ELECTRIC AND MAGNETIC INDUCTIONS IN THE SURROUNDING FIELD 281 
Modification of the Third Principle. 
The third principle admits of similar analysis, according to which we may regard 
the magnetic intensity along a closed curve as due to the cutting of the curve by 
tubes of electric induction. If we regard the line integral of the magnetic intensity 
round a tube of induction as measuring the magnetomotive force—employing a useful 
term suggested by Mr. Bosanquet —we may put the modification in the following 
form :— 
Whenever magnetomotive force is produced by change in the electric field, or by 
motion of matter through the field, the magnetomotive force per unit length is equal to 
477 X the number of tubes of electric induction cutting or cut by unit length per second, 
the magnetomotive force tending to produce induction in the direction in which a right- 
handed screw would move if turned round from the direction of the electric induction 
towards the direction of motion of the unit length relatively to the tubes of induction. 
This is the most general form of the principle, but we shall only require the more 
special statement which immediately follows from it : that the line integral of the M.I. 
round any curve is equal to 477 X the number of tubes passing in or out through the 
curve per second. 
We have reasons exactly similar to those given in the last case for supposing that 
any change in the total electric induction through a curve is caused by the passage 
of induction tubes in' or out across the boundary. The alternative that change 
takes place by propagation from the ends, seems inconsistent with the theory of the 
transverse flow of energy. 
I shall postpone the discussion of the modifications of the general equations of the 
electromagnetic field following from these changes in the fundamental principles, and 
proceed to discuss the bearing which they have upon the nature of currents in 
conductors. 
A straight wire carrying a stead,y current. 
Let AB represent a wire in which is a steady current from A to B. The direction 
of the electric induction in the surrounding field near the wire, if the field be homo¬ 
geneous, is parallel to AB. 
Let E be the value of the electric intensity, or the difference of potential per unit 
length perpendicular to the level surfaces, and let R be the resistance of the wire per 
E 
unit length. Then C = p where C is the current, and C is uniform throughout the 
circuit. The magnetic intensity in the immediate neighbourhood of the wire at a 
2C 
distance r from the axis of the wire is —. 
r 
The hypothesis proposed as to the nature of the current is that C electric induction 
tubes close in upon the wire per second. The wire is not capable of bearing a 
