Page:BatemanConformal.djvu/2

1908.] The group of transformations of this kind is known as the group of conformal transformations of space, it preserves the angles between two surfaces and changes a sphere into either a sphere or a plane.

The property, however, upon which the applications to electrostatical problems depends is that the transformations enable us to pass from one solution of the equation

to another.

Now the group of conformal transformations in a space of four dimensions possesses the analogous property in connection with the two differential equations

which are fundamental in the wave theory of light.

This has been known for some time, but the analysis given in § 2 will be useful in indicating the procedure to be adopted to obtain the relation connecting the two solutions for any transformation of the group.

In § 3 a particular solution of the first of the above equations is