DYNAMICAL PRINCIPLES TO PHYSICAL PHENOMENA. 
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components, yl, ym, yn, parallel to the axes of x, y, z respectively. We are at liberty 
to do this, as y is evidently a vector. If we take Ampere’s theory of magnetism, 
yl, yin, yn will be proportional to the excess of the number of normals to the planes 
of the currents round the molecules which point in the positive direction of the axes 
of x, y, z respectively over those which point in the corresponding negative directions. 
If £ has the same meaning as before, ylfj, ym£, yng will be the components of 
magnetisation in the directions x, y, z respectively. It is proved in Maxwell’s 
‘ Electricity and Magnetism,’ vol. ii., art. 634, that if we have currents whose 
components parallel to the axes of x, y, z respectively are it, v, w, placed in a magnetic 
field, the kinetic energy of the two 
= || | (F it + Gv +LLt>) dxdydz .(103) 
where (‘ Electricity and Magnetism,’ vol. ii., art. 405) 
(104) 
where p is the reciprocal of the distance of the point where the components of 
magnetisation are y£l, y£m, y£n from the point where the components of current are 
u, v, w. To apply Lagrange’s equations we must see what T', the function which 
takes the place of T in the modified Lagrangian equation, becomes in this case, as we 
saw before that some of the terms occurred with opposite signs in T and T'. 
Suppose that in the expression for the kinetic energy we have the terms 
■gA^r + B<£t \ ' .(105) 
and that <£ is a gyroscopic coordinate, then 
T'=T—<£<*>.(106) 
where <t> is the momentum corresponding to <f>, so that, considering these terms alone, 
fi>=A^H-Bi p .(107) 
rrv 
Cfi 2 
Substituting for we find 
