Reprint of Papers On Electrostatics And Magnetism

Cover Reprint of Papers On Electrostatics And Magnetism
Reprint of Papers On Electrostatics And Magnetism
William Thomson Kelvin
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, d (il) and therefore the total amount of matter on this face will be By determining in a similar way the final quantities of matter on the other faces of the parallelepiped, we find that the total amount of matter to be distributed over its surface is - 2 f^ + ^ + ^l a/37 - Now as the parallelepipeds into which we imagined the whole mass divided are infinitely small, we may substitute a con- tinuous distribution of matter through them, in place of the superficial distributions on their faces ...which have been de- termined ; and in making this substitution, the quantity of matter which we must suppose to be spread through the in- terior of any one of them must be half the total quantity on its surface, since each of its faces is common to it and another parallelepiped. Hence the quantity of matter to be distributed through the parallelepiped a/3 7 is equal to (d (il) d (im) d (in) \ dx dy dz Besides this continuous distribution through the interior of the magnet, there must be a superficial distribution to represent the un-neutralized polarity at its surface.

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