.2 6o 



NA TURE 



[August 26, 1909 



J070 electromagnetic uiiits. The positive charge carried 

 by each a particle has been deduced by measuring the 

 total charge carried by a counted number of a particles. 

 Its value is g-3Xio-''° electrostatic units, or 3ixio-'° 

 -electromagnetic units. Substituting this number in the 

 value of c'lm, it is seen that ni, the mass of the a particle, 

 -is equal to 6-ixio-"' grams — a value in fair agreement 

 with the number previously given. 



I trust that my judgment is not prejudiced by the fact 

 .that I have taken some share in these investigations ; but 

 the experiments, talien as a whole, appear to me to give 

 an almost direct and convincing proof of the atomic hypo- 

 .thesis of matter. By direct counting, the number of 

 identical entities required to form a known volume of gas 

 .has been measured. May we not conclude that the gas 

 is discrete in structure, and that this number represents 

 .the actual number of atoms in the gas ? 



We have seen that under special conditions it is possible 

 .to delect easily by an electrical method the emission of a 

 rsingle a particle — i.e. of a single charged atom of matter. 

 This has been rendered possible by the great velocity and 

 energy of the e.xpelled a particle, which confers on it the 

 power of dissociating or ionising the gas through which 

 it passes. It is obviously only possible to detect the 

 presence of a single atom of matter when it is endowed 

 with some special property or properties which dis- 

 1;inguishes it from the molecules of the gas with which 

 Jt is surrounded. There is a very important and striking 

 method, for example, of visibly differentiating between the 

 ordinai-y molecules of a gas and the ions produced in the 

 gas by various agencies. C. T. R. Wilson showed in 

 1897 that under certain conditions each charged ion became 

 a centre of condensation of water vapour, so that the 

 presence of each ion was rendered visible to the eye. Sir 

 Joseph Thomson, H. A. \\'ilson, and others have employed 

 this method to count the number of ions present and to 

 ■determine the magnitude of the electric charge carried 

 "by each. 



A few examples will now be given which illustrate the 

 •older methods of estimating the mass and dimensions of 

 ■molecules. As soon as the idea of the discrete structure 

 ■of matter had taken firm hold, it was natural that attempts 

 should be made to estimate the degree of coarse-grained- 

 -ness of matter, and to form an idea of the dimension of 

 molecules, assuming that they have extension in space. 

 Lord Rayleigh has directed attention to the fact that the 

 _earliest estimate of this kind was made by Thomas Young 

 In 1S05, from considerations of the theorv of capillarity. 

 Space dons not allow i'.,e to consider the great varietv 

 of methods tliat have later been emploved to form an 

 'idea of the thickness of a film of matter in which a 

 molecular structure is discernible. This phase of the sub- 

 ject was always a favourite one with Lord Kelvin, who 

 •developed a number of important methods of estimating 

 the probable dimensions of molecular structure. 



The development of the kinetic theory of gases on a 

 ■mathematical basis at once suggested methods of 

 •estimating the number of molecules in a cubic centimetre 

 •of any gas at normal pressure and temperature. This 

 number, which will throughout be denoted bv the svmbol 

 "N, is a fundamental constant of gases; for, according to 

 the hypothesis of .'\vogadro, and also on the kinetic theorv, 

 all gases at normal pressure and temperature have an 

 "identical number of molecules in unit volume. Knowing 

 the value of N, approximate estimates can be made of the 

 ■diameter of the molecule; but in our ignorance of the 

 constitution of the molecule, the meaning of the term 

 ■diameter is somewhat indefinite. It is usually considered 

 to refer to the diameter of the sphere of action of the 

 forces surrounding the molecule. This diameter is not 

 necessarily the same for the molecules of all gases, so 

 that it is preferable to consider the magnitude of the 

 ■fundamental constant N. The earliest estimates based on 

 the kinetic theory were made by Loschmidt. Johnstone 

 ■Stoney, and Maxwell. From the data then at his dis- 

 j;osal, the latter found N to be i-qxio". Meyer, in his 



Kinetic Theorv of Gases," discusses the various methods 

 ■of estimating the dimensions of molecules on the theorv, 

 -and concludes that the most probable estimate of N is 

 •fvixio". Estimates of N based on the kinetic theorv 

 -are onlv anoroximate, and in manv cases serve merelv to 

 NO. 2078, VOL. 81] 



fix an inferior or superior limit to the number of the 

 molecules. Such estimates are, however, of considerable 

 interest and historical importance, since for a long time 

 they served as the most trustworthy methods of forming 

 an idea of molecular magnitudes. 



A very interesting and impressive method of determining 

 the value of N was given by Lord Rayleigh in 1899 as 

 a deduction from his theory of the blue colour in the 

 cloudless sky. This 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 atmo- 

 sphere 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 avail- 

 able. Lord Rayleigh concluded that the value of N was 

 not less than 7x10". Lord Kelvin in 1902 re-calculated 

 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 

 diftlcult to estimate with accuracy the correction to be 

 applied for this effect, but it will be seen that the un- 

 corrected number deduced by Lord Kelvin is not much 

 smaller than the most probable value 277x10^° 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 liow 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 investiga- 

 tions of Perrin on the law of distribution in a fluid of a 

 great number of ininute 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 experi- 

 mental 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 = 2-56xio" 

 has been obtained by the direct method of counting the 

 particles and determining the corresponding volume of 

 helium produced. .-Xnother very simple method of deter- 

 mining N from radio-active data is based on the rate of 

 transformation of radium. Boltwood has shown by direct 

 experiment tiiat radium is half transformed in 2000 veai^s. 

 From this it follows that initially in a gram of radium 

 0346 milligram breaks un per year. Now it is known 

 from the counting method that 3-4x10"' a particles are 

 expelled per second from one gram of radium, and the 

 evidence indicates that one a particle accompanies the dis- 

 integration of each atom. Consequently the number of 

 a particles expelled per year is a measure of the number 

 of atoms of radium present in 0-346 milligram. From this 

 It follows that there are 31X10"' 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 3-1 X 10". 



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 bv the Ion, pro- 

 duced in gases by o ravs or the ravs from radio-active 

 substances. On modern views, electricltv, like matter, is 

 supposed to be discrete in structure, and the charge carried 



