WORKING METHODS OF CALCULATION 79 



The quadratic equation for obtaining Q, given in 

 (3), Table I, is to be used only when more exact results 

 are desired than can be obtained from the circle diagram. 

 This equation is derived directly from equation (i), of 

 this Chapter. While a quadratic equation may appear 

 forbidding at first sight, experience will show that it is 

 less labor to obtain at once a desired result than to 

 obtain it, perhaps only approximately, by a roundabout 



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

 Conditions given at Supply End. 



method of trial and error. The remaining equations of 

 Table I are obtained in the same way as similar equations 

 for varying- voltage lines.* 



The equations of Table II, where conditions are 

 specified at the supply end of the line, are very similar 

 to those of Table I. They depend, however, on a dif- 

 ferent vector diagram, which is shown in Fig. n. 



The equation for the receiver voltage derived from 

 the vector diagram, Fig. n, is similar in form to equation 

 (i) of this Chapter, and is 



&=(E 8 - P 8 R + Q 8 X)*+(P 8 X + Q 8 R)* . (3) 



When the line is long enough to make the effect of 



*See "Transmission Line Formulas," D. Van Nostrand Com- 

 pany, 1913. 



