交番電磁流界に於けるヴェクトル勢力の不生不滅連續

抄録

As a general case of an alternating current problem, an alternating electromagnetic current field is treated in which the rectangular components of each vector quantity, such as the density of electric and magnetic current, are considered as complex hormonic functions of time. Special attention is given to the problem of complex average power or vector power. As a method of analysis of such a problem, the symbolism of electrical vector power product, complex scalar product, complex vector product, etc, are proposed. The analysis is reduced to the calculation of complex effective vector fields and complex effecive scalar fields, that is, symbolic vector and scalar fields. This is an extension of the symbolic method to a space problem. The equations expressing the law of continuity of true electric current and true magnetic current and also Maxwell's fundamental equations of electromagnetic field are given in symbolic form. The phenomena of dielectric and magnetic hysteresis in revolving ellipsoidal electric and magnetic field is discussed under the conception of fundamental ellipse of the hysteresis loop, and the expressions of hysteresis loss and average stored energy in such fields are given in symbolic form. The symbolic vector fields of electric intensity and magnetic force are decomposed into curl field, divergence field and impressed field. This result is applied to the decomposition of vector power density and thus the fundamental equation of vector power in a complex harmonic electromagnetic current field is obtained in its symbolic differential form. Applying Gauss' theorem in the symbolic vector field of the vector power equation, it is converted into the following integral form.
This equation, by the author's opinion, can be best explained as a principle of continuity of vector power in an alternating electromagnetic current field. As a simple case of technical application of this principle, the vector power equations for network of linear electric circuit, linear magnetic circuit and linear electromagnetic circuit are deduced. (June, 1921)