Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/64

24 but at the origin these quantities become infinite. For any closed surface not including the origin, the surface-integral is zero. If a closed surface includes the origin, its surface-integral is $$4 \pi m$$.

If, for any reason, we wish to treat the region round $$m$$ as if it were not periphractic, we must draw a line from $$m$$ to an infinite distance, and in taking surface-integrals we must remember to add $$4 \pi m$$ whenever this line crosses from the negative to the positive side of the surface.

On Right-handed and Left-handed Relations in Space.

23.] In this treatise the motions of translation along any axis and of rotation about that axis, will be assumed to be of the same sign when their directions correspond to those of the translation and rotation of an ordinary or right-handed screw.

For instance, if the actual rotation of the earth from west to east is taken positive, the direction of the earth s axis from south to north will be taken positive, and if a man walks forward in the positive direction, the positive rotation is in the order, head, right-hand, feet, left-hand.

If we place ourselves on the positive side of a surface, the positive direction along its bounding curve will be opposite to the motion of the hands of a watch with its face towards us.

This is the right-handed system which is adopted in Thomson and Tait's Natural Philosophy, § 243. The opposite, or left-handed system, is adopted in Hamilton's and Tait's Quaternions. The operation of passing from the one system to the other is called, by Listing, Perversion.

The reflexion of an object in a mirror is a perverted image of the object.

When we use the Cartesian axes of $$x, y, z$$, we shall draw them