2 TRANSMISSION LINE FORMULAS 



and arithmetic only, they should be found useful by all 

 electrical engineering students and engineers. Groups of 

 problems with answers are added to provide practice in the 

 use of the formulas. The working formulas can be imme- 

 diately used by electrical engineers without the delay 

 caused by working out the true meaning and correct oper- 

 ation of long and intricate systems of calculation. They 

 are also arranged to require the minimum amount of labor 

 for routine work where many lines are to be calculated. 



The first method, which is described in Chapter III, is in 

 the form of a chart which gives the regulation or voltage 

 drop of a line, and which also shows directly the required 

 size of conductor for given conditions. 



In Chapter IV are given formulas for distribution lines 

 and transmission lines only a few miles long. These are 

 extended in Chapter V by means of the constant K to 

 apply to transmission lines of any length in ordinary 

 practice. 



For purposes of checking different formulas, and for 

 the calculation of extremely long and unusual lines, the 

 fundamental formulas of transmission lines are expressed 

 by rapidly converging series in Chapter VI. While these 

 series require much more arithmetical work than the K 

 formulas, they will give the exact results to any degree of 

 accuracy desired. The method of convergent series in- 

 volves the use of complex numbers, that is, numbers in 

 which "j" terms appear. They are easier to handle, 

 however, than logarithms, sines and cosines of angles, or 

 hyperbolic functions, and therefore the use of these other 

 mathematical functions has been avoided. 



Each of the above groups of working formulas is printed 

 in a table, ready for practical use. The tables will be 



