# A Kinematical Interpretation of Electromagnetism - download pdf or read online By Page L.

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We can write aT aT aT dT= -dx j + -dx z + -dx 3 ax] ax z aX3 It is clear that the right-hand side of this equation is a dot product. 74) Suppose that 2' is an arbitrary path between points a and b. Then integrating we have jb grad T. 75) a TCb) and TCa) are values of the field T at terminal points of the path. It means that the integral of grad T is independent of the path of integration, but it is defined by the values of T at the terminal points. In particular, for a closed path we have ¢grad T· d/= 0 This equation is of great importance in the theory of many fields.

V; we can write AV;gradT=~TdS, i = 1,2, ... V;. 87), written for every such volume, we have N N 2: t:. 88) S Taking into account that integration over every elementary surface S, is performed twice, in each case with dS having opposite direction (Fig. 10b), the right-hand side of Eq. 90) 34 I Fields and Their Generators It is proper to notice that both these equations are often used in the theory of geophysical methods. First of all they allow, in many cases, drastic simplification in the calculation of fields, replacing either a volume integral by a surface one or the surface integral by a linear one.

Also the field will be mainly studied in the vicinity of regular points where it behaves as a continuous function. However, we will pay some attention to singular points, lines, and surfaces, where the field behaves as a discontinuous function. As is known, continuity of a function T in the vicinity of a point p means that any displacement of the observation point p within an infinitesimally small area, results in an infinitesimal small change of the field T. If an infinitesimally small displacement ~ t of the point p along some line t leads to either a finite or an infinitely large change of the field ~T, the ratio ~T /~ t tends to infinity.

### A Kinematical Interpretation of Electromagnetism (1919)(en)(8s) by Page L.

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