Page:CunninghamPrinciple.djvu/5

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542
 
Mr. E Cunnigham on the

Hence

and therefore

,

so that the longitudinal mass is equal to

It is the second term in this expression that is neglected by Abraham, and which he has to account for by assuming the energy of the electron to be made up of W together with a term not electromagnetic in origin.

We proceed to evaluate this expression in the two cases (i.) of a sphere with uniform volume density; (ii.) of a sphere with uniform surface charge.


(i.) Volume Distribution.

Hence

.