ii4 Mr. Christie on the mutual action of 
theoretical results, it is better to adopt in a more general way 
the principle to which I have referred. 
According to this principle, the magnetism in the ring will 
not be developed with the greatest intensity in the point 
which is vertical to the pole of the magnet at any instant, but 
in a point at a certain distance behind it ; and in every point in 
advance of this, and likewise in those behind, magnetism will 
be developed with an intensity depending upon their distances 
from the pole of the magnet. In the points behind, the 
intensity will be greater than, what I have termed, the inten- 
sity due to the distance of the magnet ; in those in advance > 
less : but the same distribution of magnetism in the ring will 
constantly follow the magnet, during its rotation under it 
with the same uniform velocity. The effect of the magnetism 
in the points behind the pole of the magnet will be, to urge 
the ring with a constant force in the direction of rotation ; 
that of the magnetism in those in advance, to urge it in a 
contrary direction, likewise with a constant force : so that the 
ring will be urged in the direction of rotation with a force 
which is equivalent to the excess of the former force above 
the latter. We may therefore assume that the whole force of 
the parts of the ring in advance of the magnet will be 
destroyed by the force of only a portion of the part behind; 
and that the ring is continually urged in the direetion of 
rotation by the undiminished force of the remaining portion of 
the part behind: so that to obtain the force of the whole, 
we shall have to integrate from one extremity of this portion 
to the other. 
Let r be the radius of the circle described by the poles of 
the magnets, or the radius of that circle in the ring vertically 
