PRESIDENTIAL ADDRESS. 379 
of the blue colour in the cloudless sky. his theory supposes that the 
molecules of the air scatter the waves of light incident upon them. This 
scattering for particles, small compared with the wave length of light, is 
proportional to the fourth power of the wave length, so that the proportion of 
scattered to incident light is much greater for the violet than for the red 
end of the spectrum, and consequently the sky which is viewed by the 
scattered light is of a deep blue colour. This scattering of the light in 
passing through the atmosphere causes alterations of brightness of stars 
when viewed at different altitudes, and determinations of this loss of 
brightness have been made experimentally. Knowing this value, the 
number N of molecules in unit volume can be deduced by aid of the theory. 
From the data thus available, Lord Rayleigh concluded that the value of N 
was not less than 7X10'*. Lord Kelvin in 1902 recalculated the value 
of N on the theory by using more recent and more accurate data, and found 
it to be 2°47x10*°. Since in the simple theory no account is taken of 
the additional scattering due to fine suspended particles which are un- 
doubtedly present in the atmosphere, this method only serves to fix an inferior 
limit to the value of N. It is difficult to estimate with accuracy the correc- 
tion to be applied for this effect, but it will be seen that the uncorrected 
number deduced by Lord Kelvin is not much smaller than the most probable 
value 2°77X10!° given later. Assuming the correctness of the theory 
and data employed, this would indicate that the scattering due to suspended 
particles in the atmosphere is only a small portion of the total scattering 
due to molecules of air. This is an interesting example of how an accurate 
knowledge of the value of N may possibly assist in forming an estimate 
of unknown magnitudes. 
It is now necessary to consider some of the more recent and direct 
methods of estimating N which are based on recent additions to our scientific 
knowledge. The newer methods allow us to fix the value of N with much 
more certainty and precision than was possible a few years ago. 
We have referred earlier in the paper to the investigations of Perrin on 
the law of distribution in a fluid of a great number of minute granules, and 
his proof that the granules behave like molecules of high molecular weight. 
The value of N can be deduced at once from the experimental results, and 
is found to be 3:14X10".. The method developed by Perrin is a very novel 
and ingenious one, and is of great importance in throwing light on the law 
of equipartition of energy. This new method of attack of fundamental 
problems will no doubt be much further developed in the future. 
It has already been shown that the value N=2°56x10'° has been 
obtained by the direct method of counting the a particles and determining 
the corresponding volume of helium produced. Another very simple method 
of determining N from radioactive data is based on the rate of transforma- 
tion of radium. Boltwood has shown by direct experiment that radium is 
half transformed in 2,000 years. From this it follows that initially in a 
gram of radium ‘346 milligram breaks up per year. Now it is known from 
the counting method that 3°-4X<10"° a particles are expelled per second from 
one gram of radium, and the evidence indicates that one a particle accom- 
panies the disintegration of each atom. Consequently the number of a 
particles expelled per year is a measure of the number of atoms of 
radium present in 346 milligram. From this it follows that there are 
35°1x10" atoms in one gram of radium, and taking the atomic weight of 
radium as 226, it is simply deduced that the value of N is 31X10". 
The study of the properties of ionised gases in recent years has led to 
the development of a number of important methods of determining the 
charge carried by the ion, produced in gases by a rays or the rays from 
radioactive substances. On modern views, electricity, like matter, is sup- 
posed to be discrete in structure, and the charge carried by the hydrogen 
atom set free by the electrolysis of water is taken as the fundamental unit 
