Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/256

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equal to where is a numerical quantity which for simplicity we may make equal to unity.

We therefore put

Let

Then all the successive images of will lie on the arc .

The position of the image of in is where

That of in is where

Similarly

In the same way if the successive images of in , &c. are , &c.,

To find the charge of any image we observe that in the inverted figure its charge is

In the original figure we must multiply this by . Hence the charge of in the dipolar figure is

If we make , and call the parameter of the point , then we may write

or the charge of any image is proportional to its parameter.

If we make use of the curvilinear coordinates and , such that

then