390 Intelligence and Miscellaneous Articles. 



ON THE MOLECULAR THEORY AND LAWS OF ELECTRICITY. 

 BY L. LORENZ OF COPENHAGEN. 



In a paper on the mechanical theory of heat*, M. A. Dupre* has 

 given a lower limit for the number N of molecules contained in a 

 milligramme of water, namely 



N>125xl0 



18 



that is, that the number is greater than 125 trillions. A similar 

 though somewhat higher limit may, I think, be deduced in an en- 

 tirely different and, as I think, very simple manner. 



For measuring the intensity of an electrical current I will choose 

 the electromagnetic unit, and as unit of the quantity of electricity 

 that which passes in a second through the section of a conductor 

 when its intensity is equal to unity. I take, as electricity which 

 has passed through, the sum of the positive quantities passing in the 

 direction of the current, and of the negative in the opposite direction. 

 The repulsion, F, of two electrical bodies with the quantities of elec- 

 tricity e and e 1 and the distance r is then expressed in absolute 

 units by 



r 2 

 in which 



«=31074X10 7 . 



Further, let the electrical tension of a body be that quantity which is 

 required to impart to the body the unit of the quantity of electricity. 

 Up is the electrical tension, e the quantity of electricity, pde is the 

 work required for the communication of the electricity de, and the 

 whole work A of the tension p and the corresponding quantity e is 

 determined by 



.= I pde. 



If, for instance, the quantity e is uniformly distributed upon the sur- 

 face of a sphere whose radius is r, the tension is 



r 



and the work represented by the electricity is 

 a _ °?^ *'__ pe 



The decomposition of a milligramme of water requires an amount 

 * Annates de Chimie et de Physique, vol. vii. (1866). 



