of Mass, Length and Time. 
153 
from unity. If the ether has more than three fundamental 
qualities, we cannot do as suggested above, but we can reduce 
the various constants to numbers that are either moderate or 
moderate multiples of powers and products of the new values of 
the outstanding qualities of the ether. The method can in any 
case only give the orders of magnitude of the units, but as will 
be seen, the admissible range of value is not great, less indeed 
than that of the earlier determinations of the atomic dimensions. 
4. The physical constants with which we have to deal are 
of two kinds, constants of nature and constants of particular 
substances. In the latter case we must have some method for 
obtaining a particular value from the many values for the various 
substances. We may reasonably say that hydrogen is marked 
out among the elements by being the first of the series, and that 
the formulae connected with that element must be the simplest, 
and hence that we should choose the constants connected with 
hydrogen. In many cases, however, this cannot be done, the 
constant in question not having been determined for hydrogen, 
and in any case we may doubt whether hydrogen is so pre- 
eminently fitted for our purpose that we may disregard the other 
elements. We therefore follow another plan. If a given constant 
appears to lie between two values, the geometric mean of these is 
taken ; if the range is from a finite number to either zero or 
infinity, the finite number is taken ; if the range is from zero to 
infinity, we cannot take any number to be a constant of nature. 
We first discuss properties that do not involve electrodynamics. 
5. The elements differ greatly in density, those of higher 
atomic weight having in general a greater density. The “ atomic 
volume” is more nearly constant. Now the graph of this quantity 
shows several minima of approximately the same value, while the 
maxima* differ considerably. We hence take the geometrical 
mean of these minima, 3'6, lO'o, 6’6, 8 - 3, 8'4, which is 
7 - 0 cm. 3 /gm. 
The heat of combustion varies considerably, but reasons are 
given in Watts’ Dictionary of Chemistry, vol. vn. p. 614 (1883) 
which lead one to consider 18000 cal./gm. as a constant of nature. 
In c.G.s. units this is 7 - 6 x 10 u cm. 2 /sec. 2 
The latent heat has no definite minimum. Its maximum 
value is found iu the case of steam, and is 536 cal./gm. or 
23 x 10 10 cm. 2 /sec. 2 
The absolute critical point of a substance divided by its 
molecular weight is fairly constant, and hence the velocity of 
* In the graph as usually drawn these appear to be chance points on asymptotic 
branches. If we plot the reciprocal of the atomic volume, especially if we plot it 
against the position of the element in the series of elements instead of the atomic 
weight (whereby we get a smoother curve), we see that they are really maxima. 
11 
VOL. XIV. PT. II. 
