WORKING METHODS OF CALCULATION 



75 



calculated should be selected because they are of the 

 greatest engineering value, and not because they are 

 the most convenient to obtain. The results should not 

 be obtained by trial and error, but by a direct process of 

 calculation. Graphical methods should be supplemented 

 by mathematical methods for obtaining the same results 

 with greater accuracy. In the present case it may also 

 be noted that the results are obtained without using 

 tables of trigonometric functions of angles nor tables of 

 hyperbolic functions; however, tables of transmission- 

 line constants will be found convenient. 



With comparatively short lines, up to twenty or 

 thirty miles in length, the electrostatic capacity of the 



QR 



PR 



FIG. 9. Vector Diagram of A. C. Line with Leading Current, 

 Conditions Given at Receiver End. 



line may be neglected, and this greatly simplifies the 

 electrical formulas. The fundamental relationships of 

 the various electrical quantities connected with an 

 A. C. line, neglecting the electrostatic capacity, are com- 

 pletely shown by the vector diagram, Fig. 9, when the 

 load conditions are specified at the receiver end of the line. 

 This diagram is drawn for a leading current since, 

 with the formulas being considered, a leading reactive 

 current is taken as a positive quantity, and a lagging one 



