Equations of Propagation of Electric Wa ves. 



19 



5. Their formation is accompanied by the production of oil, which is 



not found in normal leaves. 



6. The presence of this oil suggests that events similar to those 



occurring in succulent plants are taking place, viz., reduced 

 respiration and the development of osmotically active substances 

 in excess. 



7. It is therefore probable that the intumescences are due to the 



local accumulation of osmotically active substances, produced 

 under the abnormal conditions, viz., reduced transpiration 

 and consequent lack of minerals, while carbohydrates are being 

 developed in excess. 



The Integration of the Equations of Propagation of Electric 

 Waves." By A. E. H. Love, F.E.S. Received December 29, 

 1900— Read February 7, 1901. 



(Abstract.) 



The equations of propagation of electric waves, through a dielectric 

 medium, involve two vector quantities, which may be taken to be the 

 electric force and the magnetic force ; and they express the rate of 

 change, per unit of time, of either vector, in terms of the local values 

 of the other. Various forms may be given to the equations, notably, 

 that employed by Larmor, in which the magnetic force is regarded as 

 a velocity, and the electric force as the corresponding rotation. In 

 this form there is one fundamental vector, viz., the displacement 

 corresponding to the magnetic force, regarded as a velocity ; and this 

 displacement-vector may, in turn, be derived from a vector potential. 

 Every one of the vectors in question is circuital ; and the several 

 components of them satisfy the partial differential equation of wave 

 propagation, viz., <f> = c 2 V 2 <£, c being the velocity of radiation. 



One way of integrating the equations is to seek particular systems 

 of functions of the co-ordinates and the time, which, being substituted 

 for the components of the vectors, satisfy the equations ; more general 

 solutions can be deduced by synthesis of such particular solutions. 

 Owing to the circuital relations, certain known solutions of the partial 

 differential equation of wave propagation are not available, for represent- 

 ing the components of the vectors. A very general system of parti- 

 cular solutions, which are available for this purpose, is obtained. These 

 particular solutions are expressed in terms of spherical harmonics and 

 arbitrary functions of the time; and. they can be regarded as generali- 

 sations of others, given by Lamb, which depend in the same way upon 

 spherical harmonics, and contain simple harmonic functions of the time. 

 By means of them, we can describe two types of sources of electric 



C 2 



