DYNAMICAL PRINCIPLES TO PHYSICAL PHENOMENA. 
321 
kinetic energy due to the kinosthenic coordinates enters with the negative sign into 
the equations of motion.] As we suppose that is the intensity of magnetisation, it 
is convenient to write (25) as 
(26) 
where B=A yf. 
If H be the external magnetic force, the work done when the intensity of mag¬ 
netisation is increased by S (y£) is —H8(rji) or as £ remains constant —HgSy, and 
thus Lagrange’s equations as modified by Routh give 
dt d v d v — ^ 
or when things have settled down to a steady state 
dV 
applying this equation to the term — VrC/B we get 
(27) 
(28) 
din 
b) dv f =H 
B J 
(29) 
Thus, since is the intensity of magnetisation and H the magnetising force, the 
coefficient of magnetic induction, which we shall denote by k, will be given by the 
equation 
B 
B 
2 B 
dB 
dr) 
1 i d lQ g B 
2 d log' 
(30) 
A.t present we shall only consider magnetic induction, and suppose that there is no 
permanent magnetisation in the part of the system which we are considering. 
[When a piece of soft iron is placed in a magnetic field where the force is, for the 
sake of simplicity, supposed to be parallel to x and equal to X, the energy is —IX 
where I is the intensity of magnetisation, since I = £ 77 , the energy =—f^X. 
Now when the energy is expressed in terms of the velocities, Lagrange’s equation 
gives 
d dT dT 
dt dx dx 
— external force parallel to x . 
(31) 
