. Carnegie Institution of Washington publication. . B Fig. 70.—Example of graphical operations with three variables. A. Scheme of graphical table. B. o, J3, y, given fields. Construction of <p —f (alf 0, y). If we construct a graphical table as that of fig. 70 a for each of the curves a = const., we can thus find a complete system of points determining the course of the curves <p = const. 153. Vector-Algebra.—It will be of special importance for us to bring graphi- cal methods into application for mathematical operations concerning vector-fields. It will be useful and save circuml
. Carnegie Institution of Washington publication. . B Fig. 70.—Example of graphical operations with three variables. A. Scheme of graphical table. B. o, J3, y, given fields. Construction of <p —f (alf 0, y). If we construct a graphical table as that of fig. 70 a for each of the curves a = const., we can thus find a complete system of points determining the course of the curves <p = const. 153. Vector-Algebra.—It will be of special importance for us to bring graphi- cal methods into application for mathematical operations concerning vector-fields. It will be useful and save circumlocution when at the same time we introduce a few simple notations of modern vector-analysis.* A vector considered as a quantity which has both magnitude and direction will be denoted by a letter in heavy print. The corresponding letter in common print will denote its scalar value or tensor (intensity). The same letter in common print and with the suffix 5 will denote the projection of the vector on the direction 5. In the same manner we shall by the suffixes x, y, 2 denote the projections on the three rectangular axes x, y, and 2. Thus Vector. Tensor. Projection on direction s. Projections on rectangular axes. A B A B As Bs Axi Ay, AZ BX, By, Bz F F Fs Fx, Fy, FZ ?Compare: Gibbs-Wilson, Vector-Analysis, New York, Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Carnegie Institution of Washington. Washington, Carnegie Institution of Washington
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