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The special purpose of this note is to make clear that the fifth fundamental equation of electromagnetic theory may be derived from the four field equations and the principle of relativity without making any arbitrary convention as to the mass of a moving body. It is quite unnecessary to place the transverse mass of a moving body equal to ${\tfrac {m_{0}}{\left(1-\beta ^{2}\right)}}$ and the longitudinal mass equal ${\tfrac {m_{0}}{\left(1-\beta ^{2}\right)^{\frac {3}{2}}}}$. The simple relation for the mass of a moving bod $m={\tfrac {m_{0}}{\left(1-\beta ^{2}\right)}}$, which was derived directly from the principle of relativity by Lewis and Tolman (loc. cit.) and from ideas of light pressure by Lewis (loc. cit.) is sufficient.

The fact that the fifth equation can be derived by combining the principle of relativity with the four field equations is one of the chief pieces of evidence which support the theory of relativity.

University of Michigan,

Ann Arbor, Mich.,

November 11, 1910.