THE ALTERNATOR. 23 



lems. The effects of distributed capacity cannot be ignored, how- 

 ever, in long transmission lines, and therefore the mathematical 

 treatment of the transmission-line problem stands by itself in the 

 theory of alternating currents. 



Direct-current problems and alternating-current problems con- 

 trasted. Direct-current problems are generally the finding of 

 one or two of the quantities, voltage, current and power, when 

 the other or others are given, and when the circuit conditions are 

 known. Alternating-current problems also are generally the find- 

 ing of one or two of the quantities, voltage, current and power, 

 when the other or others are given, and when the circuit condi- 

 tions are known. The difference between direct-current prob- 

 lems and alternating-current problems grows out of the fact that 

 in an alternating-current circuit the relation between voltage, cur- 

 rent and power, depends upon the resistance, the inductance and 

 the capacity in the circuit, whereas, in a direct-current circuit, 

 the relation between current and voltage is independent of 

 inductance and capacity. 



The relation between voltage and current in an alternating- 

 current circuit can be simply formulated only for the ideal case 

 in which the voltage and current are of the type which is repre- 

 sented by a curve of sines and when the capacity is concentrated. 

 Therefore in most alternating-current problems the voltage and 

 current are assumed to be of this type, which is called harmonic, 

 and the effects of distributed capacity are ignored. The concep- 

 tion of harmonic voltage and current is developed in Chapter III, 

 the voltage-current relation (harmonic) is discussed in Chapter 

 IV, and this ideal voltage-current relation is the basis for all of 

 the theoretical developments in Chapters V to XV. 



A discussion of non-harmonic voltages and currents is given in 

 Appendix B, and a discussion of the phenomena of distributed 

 capacity is given in Appendix C. 



6. Speed and frequency. The electromotive force of an alter- 

 nator passes through a set of positive values while a given group 



