152 
Mr Pocklington, The Natural Units 
The Natural Units of Mass, Length and Time . By H. C. 
Pocklington, M.A., St John’s College. 
[Read 11 March 1907.] 
1. The units in terms of which physical quantities are 
usually expressed, those of the c.G.S. system, form a group the 
members of which are derived in a natural manner from three 
fundamental units, the centimetre, the gramme and the second. 
But these fundamental units are, from the physical point of view, 
not merely arbitrary but even of arbitrary orders of magnitude. 
They are indeed of the same order of magnitude as the smallest 
lengths, masses and times that are directly appreciable by the 
senses. We might choose as natural units of mass and length 
the mass of a hydrogen atom and its radius, but unfortunately 
these are not known with any accuracy, and moreover there is 
nothing to give us a corresponding unit of time. We prefer for 
the sake of uniformity to adopt an indirect method in each case. 
2. Our method for discovering the natural fundamental units 
is based on the hypotheses that all the properties of matter 
depend ultimately on the properties of some ether, and that this 
ether has a high degree of simplicity. A knowledge of the 
properties of this ether would (disregarding the difficulties of 
the mathematical analysis necessary) lead to a knowledge of the 
possible kinds of matter and their properties. The value of any 
given property (e.g. the tensile strength of a substance) would be 
given by an expression containing the numbers representing the 
various fundamental properties of the ether, raised to certain 
powers, and a numerical coefficient. The latter will never be 
very large or very small ; in the case of the simpler properties 
we may expect it to lie between 10 and j 1 ^, while in more com- 
plicated properties, such as second-order effects, we may expect 
a wider range. This theorem, which is of fundamental importance 
for our purpose, cannot be proved by rigorous methods, but one 
can convince oneself of its truth by examining a list of the 
formulae deduced from the assumptions of any theory. 
3. We can in general by choosing our fundamental units of 
mass, length and time make the numerical values of any three 
quantities equal to unity. If the ether has only three funda- 
mental qualities we can make the numerical values of the 
quantities defining them equal to unity, and the value of any 
quantity defining a property of matter will then reduce to the 
above-mentioned numerical coefficient, and so cannot differ greatly 
