80 CONSTANT-VOLTAGE TRANSMISSION 



its electrostatic capacity appreciable, the accurate cal- 

 culation of the line can be obtained most easily by using 

 convergent series, as in Tables III and IV. By this 

 method the use of hyperbolic functions is avoided. 



Since the convergent series require the use of complex 

 numbers, which are distinguished by the use of the 

 letter "/," a very short outline of the rules for using 

 these numbers will be given, in order to make the in- 

 structions for the tables quite complete. 



Each of the complex quantities, Z = R+jX, 

 Y = G +y B, C -\- j D, etc., is composed of two parts, 

 the first, a "real" term and the second an "imaginary" 

 term, which is multiplied by the letter j. In adding 

 complex numbers, the imaginary terms must be kept 

 separate from the others. Thus, 



6 + y 2 added to 4 +/ 9 = 10 -\-j n 



In multiplying two complex quantities, one follows the 

 rules of ordinary algebra, j being treated as an algebraical 

 quantity which has the property that jxj = j 2 = i- 



From this it follows that, 



f = ~ J 



> etc - 



Thus (6 +j 2) X (4 +jg) is worked out as follows: 



6+JT2 



4+J9 



+ 24+78 

 - I8+./54 



+ 6 +./ 62 



