136 Dr. H. Bateman on the 



The mean of these measurements is equal to 21'0609, 

 exactly agreeing with the value found by Fabry and Perot. 



It is to be remarked that we have here used only for 

 convenience sake one of the yellow lines of mercury as a 

 reference line; evidently the difference in wave-lengths can 

 be easily referred to standard lines of cadmium. We believe 

 that the present method can be applied to various other 

 purposes of accurate spectroscopic work. 

 August 7, 1913. 



XIII. The Classification of Electromagnetic Fields. By 

 H. Bateman, M.A., Ph.D., Johnston Research Scholar, 

 Johns Hopkins University *. 



§ 1. npHE field of the two vectors E, H will be called 

 JL electromagnetic when Maxwell's equations 



BH, BH y BE, 

 By B~-~Bi' 



3E Z BE y _ bh x 

 B# ' 3~ " ' 3* ' 



X 3E y BE Z __ , 



V d!/ 0? 



BH* 3H 3H 



3* + ~dy + 9- - "' 



> (1) 



BE, 



are satisfied for some real domain of the variables x, y, z, t. 

 In general these equations cannot be regarded as holding 

 for all real values of x, y, s, t, and the exceptional space-time 

 points or domains of such points are to be regarded as the 

 singularities of the electromagnetic field f. 



The simplest type of point singularity is one which moves 

 with a velocity less than unity, along an arbitrary curve. 

 If we solve equations (1) in the usual way with the aid of 

 four potentials A x , A y , A z , <1> satisfying the wave-equation 



-bx 2 + by 2 + ~dz 2 ~ bt 2 ' ' ' ' * (2) 

 and the relations 



a* + ay + a* + bt - a • • • (3) 

 a a z aA ;/ _ R aA^ a$ _ ^ 

 > " a. ~ M * 5 ~ar + ^ - _Jv: . (4) 



* Communicated by the Author. 



t We shall suppose that E X; TL X , &c, are one-valued functions of 

 a:, y, z, £ for the whole of the real domain of these variables, the point 

 singularities being- excluded. 



