190 proceedings: philosophical society 



with respect to z after putting /(a/3) = 1 and writing down the values 

 of the Jacobians. In particular, if the strengths /(a/3) of the two sources 

 are constants which are equal in magnitude but different in sign, then 

 as and 0' approach one another the total electromagnetic field is in 

 the limit equivalent to the electrostatic field of a point charge, the 

 magnitude of the charge being the limit of the product 00' and the 

 strength of one of the sources. The potential energy of an electro- 

 static field can thus be supposed to arise from the individual and mutual 

 energies of two interfering radiant fields whose singular lines overlap. 



When the strengths of the two consecutive sources 00' are not con- 

 stant and not equal in magnitude, we obtain a type of electric point 

 charge with two singular lines attached to it, the charges on the two 

 lines being generally variable and together equal and opposite to the 

 variable charge associated with the singular point. The case in which 

 the charge on each singular line is the same is of chief interest. 



Interference, or a cancelling out of singularities, can also be obtained 

 with two point charges of this general type even when they are at a 

 finite distance apart, provided their singular lines overlap. There 

 must also be a simple relation between the magnitudes of the two charges 

 at associated times; this indicates that it may be possible to give a 

 mathematical proof that the mean value of the electronic charge is 

 the same for all electrons. It is thought that this phenomenon may 

 have some relation to chemical saturation. The present theory may 

 be extended to the case in which the sources or point charges are mov- 

 ing and the singular curves are not straight lines pointing in opposite 

 directions but are moving and changing in shape. The appropriate 

 solution of Maxwell's equations is again of the type (1) but a and /3 

 are now defined by the equations. 



[X ~ *(«)]' + [y - V («)? + [«-$■ («)] 2 = C 2 [t - af, a<t, 



= , k{a) [x-£(a)]+m 1 (a)[y-ri(a)] + n 1 ia)[z-t (a^-cp^a) (t-a) 

 Zl (a)[x-Z(a)}+m (a)[y—o(a)]+n (a)[z-U<x)]-c(t- a ) 



where £ (r), rj (r), f (r) are the coordinates of the source at time r and 

 l (a), li (a), ra (a), Wi (a). n (a), Wi (a), pi (a), are functions of a con- 

 nected by the equations 



l\ + m\ + n\ = p\ l x (a) £ ( a ) + m x (a) r, (a) + ?l l (a) f (a) - C Pl (a) = 

 ll + ml + n\ = 1 Z Zj + w m x + n n 1 = 1 



This theory may be developed and applied to problems of atomic 

 and molecular structure. Thomson's Faraday tubes are regarded 

 as singular curves of generalized point charges and an arrow may be 

 used to signify the direction of the flow of energy along a Faraday 

 tube. The result of chief importance is that an even number of sin- 

 gular curves should be supposed to start from each point charge, the 

 number being proportional to the mean value of the charge. It is 

 suggested that the valency electrons in an atom are each doubly con- 



