154 
Mr Pocklington, The Natural Units 
the molecule in this state is roughly constant. Excluding 
hydrogen and water, it varies from 3 3 x 10 4 for nitrogen to 
7 - 6 x 10 4 for ammonia. The square of the geometrical mean is 
25 x 10 9 cm. 2 /sec. 2 The geometrical mean of the selected values 
of quantities measured in cm. 2 /sec. 2 is 3‘5 x 10 10 cm. 2 /sec. 2 
According to Quincke* the surface tension of liquids divided 
by their densit}^ ranges between 22 and 88, with only a few 
exceptions. The geometrical mean is 44 cm. 3 /sec. 2 
The tensile strength of materials has no lower limit. Its 
higher limit is found in steel and is l'4x 10 10 dynes per sq. cm. 
Critical pressures vary from 2 x 10 7 for hydrogen to T9 x 10 s for 
water. Young’s modulus and the modulus for volume elasticity 
of liquids have much higher limits, 2 x 10 12 and 3 x 10 11 . Probably 
in order to obtain the physical constant that we require we should 
replace the length or volume that occurs in the numerator of the 
expression for the modulus by the sum of the intermolecular 
lengths or by the co-volume ; these last-named quantities being 
unknown, we cannot make use of the coefficients of elasticity. 
The mean of the values retained is 3‘7 x 10 8 gm./cm. sec. 2 
The coefficient of viscosity has no greater limit, its lower limit 
is found in ether, ’003 gm./cm. sec., if we disregard the case of 
liquefied carbon dioxide, which appears to be exceptional. 
6. Let us now choose l, m, t as new units of length, mass 
and time. The centimetre will now be l/l units of length, and 
similarly for the others. To find the values of the various 
quantities in the new units we have only to write l/l, 1/m, 1/t 
for cm., gm., sec. Equating the new values to unity we have 
l 3 /m = 7, 
P/t 2 = 3-5 x 10 10 , 
P/P = 44, 
m/lP = 3-7 x 10 s , 
m/lt = 3 x 10 -3 . 
These equations are not consistent. Solving them by the 
method of least squares on the assumption that equal pro- 
portional errors of the right-hand sides are equally probable, 
we have, 
l = 4'0x 10- 8 , m = 1-4 x 10- 23 , t = 5'5x 10" 13 . 
The values of the quantities in question in terms of the new 
units are T5, 6'6, *21, '33, 4 - 7. 
The fact that these numbers are all near to unity tends to 
confirm our original hypothesis. We may note that the weight 
of an atom of hydrogen as deduced f from experiments on the 
* Smithsonian Physical Tables, p. 129 (1896). 
t J. J. Thomson, Conduction of Electricity through Gases, p. 130. 
