163.

Hence it is quite conceivable that at some other time, under changed external conditions, every one of the systems of units which have so far been adopted for use might lose, in part or wholly, its original natural significance.

In contrast with this it might be of interest to note that, with the aid of the two constants $h$ and $k$ which appear in the universal law of radiation, we have the means of establishing units of length, mass, time, and temperature, which are independent of special bodies or substances, which necessarily retain their significance for all times and for all environments, terrestrial and human or otherwise, and which may, therefore, be described as "natural units."

The means of determining the four units of length, mass, time, and temperature, are given by the two constants $h$ and $k$ mentioned, together with the magnitude of the velocity of propagation of light in a vacuum, $c$, and that of the constant of gravitation, $f$. Referred to centimeter, gram, second, and degrees Centigrade, the numerical values of these four constants are as follows:

$h\&=6.415·{10}^{-27}\frac{\text{gr}{\text{cm}}^2}{\text{sec}}\mathrm{\backslash displaybreak}[0]$

k &= 1.34 · 10^{-16}\, \frac{\text{gr}\, \text{cm}^{2}}{\text{sec}^{2}\, \text{degree}} \displaybreak[0] \ c &= 3 · 10^{10}\, \frac{\text{cm}}{\text{sec}} \displaybreak[0] \ f &= 6.685 · 10^{-8}\, \frac{\text{cm}^{3}}{\text{gr}\, \text{sec}^{2}}\;.\footnotemark

F. Richarz and O. Krigar-Menzel, Wied. Ann. 66, p. 190, 1898. If we now choose the natural units so that in the new system of measurement each of the four preceding constants assumes the value $1$, we obtain, as unit of length, the quantity $\sqrt{\frac{fh}{c^3}}=3.99·{10}^{-33}\text{cm},$ as unit of mass $\sqrt{\frac{ch}{f}}=5.37·{10}^{-5}\text{gr},$ as unit of time $\sqrt{\frac{fh}{c^5}}=1.33·{10}^{-43}\text{sec},$ as unit of temperature $\frac{1}{k}\sqrt{\frac{c^{5}h}{f}}=3.60·{10}^{32}\text{degree}.$ These quantities retain their natural significance as long as the law of gravitation and that of the propagation of light in a vacuum and the two principles of thermodynamics remain valid; they therefore must be found always the same, when measured by the most widely differing intelligences according to the most widely differing methods.