MR. G. F. C. SEARLE OR PROBLEMS IN ELECTRIC CONVECTION. 679 
(8.) The vector B, whose components are the values per unit of area of the line 
integrals of the vector A taken in right-handed directions round three infinitesimal 
areas in planes perpendicular to x, y, z , is called the Curl of A, and is denoted by 
B = curl A, Its components are 
-r, dA 3 d A 3 „ c/Aj dA A _ dA 2 dA 1 
1 dy dz ’ 3 dz dx’ 3 dx dy' 
The positive direction of the integration and the positive direction of B are related in 
the same way as the rotation and translation of a right-handed screw working in a 
fixed nut. 
(9) . From the definition it is plain that div curl A = 0. 
(10) . When any vector A changes with the time, the vector —, or A, denotes that 
CLU 
vector which would have to be compounded with the vector A at any instant in 
order to obtain the new value which A has after unit time, if the change is uniform. 
Its components are of course 
c/Aj f/A 2 dA s 
dt dt dt 
Mr. Heaviside has given a very useful chapter on the elementary parts of Vector 
Algebra and Analysis in vol. 1 of his e Electromagnetic Theory.’ I have followed 
his notation with the exception of writing the scalar product SAB instead of AB 
simply. But I gather that he would not object to this change.* An account of 
vector analysis on the same lines has also been given by Dr. A. Foppl.I 
Statement of Principles. 
3. In my investigation I shall follow Maxwell’s theory, but shall adopt the 
method, employed by Heaviside, Hertz, and others, of stating the fundamental 
equations in terms of the electric and magnetic forces. Quantities of the nature of 
potentials will be introduced during the course of the work, but this will be done 
simply to facilitate the calculations. 
The four principal quantities to be dealt with are : (1) the electric force E, (2) the 
electric displacement D, (3) the magnetic force H, and (4) the magnetic induction B. 
Since the medium is supposed to be homogeneous and isotropic, we have the relations 
D=bKE. (1), 
B = /xH 
* ‘Electromagnetic Theory,’ vol. 1, p. 304, also ‘ Electrical Papers,’ vol. 2, p. 528. 
t ‘ Einfiihrung in die Maxwell’sclie Theorie,’ Leipzig, 1894. 
(A 
