DYNAMICAL PRINCIPLES TO PHYSICAL PHENOMENA. 
341 
( 110 ) 
where r is the distance between the point where the magnetic force is required and 
the point where the components of the electric current are u, v, w. The expressions 
(110) agree with the ordinary expressions for these forces. 
Wiedemann has shown that an electric current flowing through a longitudinally 
magnetised iron wire twists the wire. This shows that the coefficient of the term we 
are considering is a function of the strain coordinates. Let us suppose that we have 
a current flowing through a straight longitudinally magnetised wire coinciding with 
the axis of x ; let a denote the twist of the wire round the axis of x, y the strength of 
the current, and or I the intensity of magnetisation, then we have a term in the 
expression for the kinetic energy of the form 
fipfoty .( m ) 
where f[a) denotes some function of a. 
We see by Lagrange’s equation for the coordinate a that the couple H tending to 
twist the wire is given by the equation 
yi-f\a)r]^y=f f (a)ly .• (112) 
If we apply Lagrange’s equation to the electrical coordinate we see that this term 
corresponds to an electromotive force E given by the equation 
E=-f{/G)I}.(113) 
so that if we twist a magnetised iron wire we shall get an electric current. This 
phenomenon has been observed. If we suppose that the intensity of magnetisation 
remains constant, equation (113) becomes 
■ E =-/»;f T .am 
or from (112) 
E y= —Clct 
2 Y 
MDCCCLXXXV. 
(115) 
