September 3, 1909] 



SCIENCE 



297 



set free one gram of hydrogen in electro- 

 lysis, it can be deduced that Ne = 1.29 X 

 10'° electrostatic units where N, as before, 

 is the number of molecules of hydrogen in 

 one cubic centimeter of gas, and e the 

 charge carried by each ion. If e be de- 

 termined 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 electrolyzed, 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 

 consequently the weight, was deduced with 

 the aid of Stokes's formula by observing 

 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 de- 

 termined. 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 

 3.0 X 10"'" electrostatic units. The corre- 

 sponding value of N is about 4.3 X 10'°. 



"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 utilized by Sir 

 Joseph Thomson to measure the charge e 

 carried by each ion. When the expansion 

 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 = 3.4 X 10-'°, H. A. Wilson e = 3.1 X 

 10-'°, and Millikan and Begeman 4.06 X 

 10"'°. The corresponding values of N are 

 3.8, 4.2 and 3.2 X 10'° respectively. This 

 method is of great interest and importance, 



as it provides a method of directly count- 

 ing the number of ions produced in the gas. 

 An exact determination of c by this method 

 is, however, unfortunately beset with great 

 experimental difSculties. 



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 Ehrenhaft on the Brownian 

 movement in air shown by ultra-micro- 

 scopic 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 aJso 

 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 4.6 X 10-'°, and thus N becomes 2.74 X 

 10'°. 



A third important method of determina- 

 tion 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 de- 

 termining the total charge carried by a 

 counted number of a particles. The value 

 of the charge on each a particle was found 

 to be 9.3 X 10-'°. 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 

 4.65 X 10-'°, and of N 2.77 X 10'°. This 

 method is deserving of considerable confi- 

 dence as the measurements involved are 

 direct and capable of accuracy. 



The methods of determination of e, so 

 far explained, have depended on direct ex- 

 periment. This discussion would not be 

 complete without a reference to an impor- 

 tant determination of e from theoretical 

 considerations by Planck. From the 



