380 TRANSACTIONS OF SECTION A. 
of quantity of electricity. On this view, which is supported by strong 
evidence, the charge carried by the hydrogen atom is the smallest unit of 
electricity that can be obtained, and every quantity of electricity consists 
of an integral multiple of this unit. The experiments of Townsend have 
shown that the charge carried by a gaseous ion is, in the majority of cases, 
the same and equal in magnitude to the charge carried by a hydrogen atom 
in the electrolysis of water. From measurement of the quantity of elec- 
tricity required to set free one gram of hydrogen in electrolysis, it can be 
deduced that Ne=1'29X10"° electrostatic units where N, as before, is the 
number of molecules of hydrogen in one cubic centimetre of gas, and e the 
charge carried by each ion. If e be determined experimentally, the value of 
N can at once be deduced from this relation. 
The first direct measurement of the charge carried by the ion was made 
by Townsend in 1897. When a solution of sulphuric acid is electrolysed, 
the liberated oxygen is found in a moist atmosphere to give rise to a dense 
cloud composed of minute globules of water. Each of these minute drops 
carries a negative charge of electricity. The size of the globules, and con- 
sequently the weight, was deduced with the aid of Stokes’ formula by ob- 
serving the rate of fall of the cloud under gravity. The weight of the cloud 
was measured, and, knowing the weight of each globule, the total number 
of drops present was determined. Since the total charge carried by the 
cloud was measured, the charge e carried by each drop was deduced. The 
value of e, the charge carried by each drop, was found by this method to be 
about 3°0X16—!® electrostatic units. ‘The corresponding value of N is about 
43x10". 
We have already referred to the method discovered by C. T. R. Wilson 
of rendering each ion visible by the condensation of water upon it by a 
sudden expansion of the gas. The property was utilised by Sir Joseph 
Thomson to measure the charge e carried by each ion. When the expan- 
sion of the gas exceeds a certain value, the water condenses on both the 
negative and positive ions, and a dense cloud of small water drops is seen. 
J. J. Thomson found e=3°4x10-'°, H. A. Wilson e=3°110—'9, and Milli- 
kan and Begeman 4°06x10—"°. The corresponding values of N are 3°8, 
4:2, and 3°2x10” respectively. This method is of great interest and im- 
portance, as it provides a method of directly counting the number of ions 
produced in the gas. An exact determination of e by this method is, how- 
ever, unfortunately beset with great experimental difficulties. 
Moreau has recently measured the charge carried by the negative ions 
produced in flames. The values deduced for e and N were respectively 
4°3x10-'° and 3:0X10”. 
We have referred earlier in the paper to the work of Khrenhaft on the 
Brownian movement in air shown by ultra-microscopic dust of silver. In 
a recent paper (1909) he has shown that each of these particles carries a 
positive or negative charge. The size of each particle was measured by the 
ultra-microscope, and also by the rate of fall under gravity. The charge 
carried by each particle was deduced from the measured mass of the 
particle, and its rate of movement in an electric field. The mean value of 
e was found to be 4°6X10—"°, and thus N becomes 2°74 X10". 
A third important method of determination of N from radioactive data 
was given by Rutherford and Geiger in 1908. The charge carried by each 
a particle expelled from radium was measured by directly determining the 
total charge carried by a counted number of a particles. The value of the 
charge on each a particle was found to be 9°3x16~—". From consideration of 
the general evidence, it was concluded that each a particle carries two 
unit positive charges, so that the value of e becomes 4°65X10-1°, and of 
N 2°77X10". This method is deserving of considerable confidence as the 
measurements involved are direct and capable of accuracy. 
The methods of determination of e, so far explained, have depended on 
