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sions perpendicular to the motion remaining the same. If $\scriptstyle {m_{1}}$ and $\scriptstyle {m_{2}}$ are its longitudinal and transverse masses, and $\scriptstyle {m_{0}}$ the mass for infinitesimal velocities, we shall have

${\begin{aligned}&\scriptstyle {m_{1}=m_{0}{\frac {1}{(1-\beta ^{2})^{\frac {3}{2}}}}}\\&\scriptstyle {m_{2}=m_{0}{\frac {1}{\sqrt {1-\beta ^{2}}}}}\end{aligned}}$

where, for brevity, $\scriptstyle {\beta }$ has been put for $\scriptstyle {\frac {v}{\text{V}}}$. With this electron Lorentz has shown that no optical or electrical effects of motion through the ether can be detected.

The subject has been approached from a different standpoint, and treated in a very interesting and instructive manner by Einstein.^[1] His fundamental postulate amounts to a denial that it is possible to observe any effects of uniform convection through the ether in which all the bodies concerned (including the observer) take part. This he calls the Principle of Relativity; the significance of the name is that only relative motion of one portion of matter with respect to another, or of one electrical charge with respect to another, can produce any observable effect; uniform motion, relative to the ether alone, becomes as impotent, if not as meaningless, as absolute motion.

Einstein considers two sets of coördinate axes, one at rest in the ether ($\scriptstyle {x}$, $\scriptstyle {y}$, $\scriptstyle {z}$), while the other moves with the constant velocity $\scriptstyle {v}$ in the x direction ($\scriptstyle {\xi }$, $\scriptstyle {\eta }$, $\scriptstyle {\zeta }$). He defines carefully the meaning of "time" ($\scriptstyle {t}$ in the fixed system, $\scriptstyle {\tau }$ in the moving system) by means of clocks distributed at various points, some at rest with the fixed axes, and some moving with the moving axes. The clocks are supposed to be synchronized by light signals. By kinematic considerations he shows that, in order for the principle of relativity to hold, we must have,

${\begin{aligned}&\scriptstyle {\xi ={\frac {1}{\sqrt {1-\beta ^{2}}}}(x-vt)}\\&\scriptstyle {\eta =y}\\&\scriptstyle {\zeta =z}\\&\scriptstyle {\tau ={\frac {1}{\sqrt {1-\beta ^{2}}}}\left(t-{\frac {v}{{\text{V}}^{2}}}x\right)}\end{aligned}}$

where, as before, $\scriptstyle {\beta ={\frac {v}{\text{V}}}}$.

1. Ann. d. Phys., xvii, p. 891, 1905.