ELECTROMOTIVE FORCE AND CURRENT. 21 



The distinction here alluded 'to has been carefully observed 

 in the text, but the difference between the electromotive 

 force due to resistance and overcoming resistance is sometimes 

 confusing to the student, on account of the loose use of the 

 terms often applied to them. 



Vector Diagrams. The method of representing variable 

 quantities such as currents and electromotive forces by 

 curves is exceedingly laborious, and consequently a more 

 rapid but equally complete method of representation is 

 usually employed. 



On page 7 was explained the method of obtaining 

 points on the curve of electromotive force. A point on the 

 curve was found corresponding to each position of the radius 

 P in Fig. 2 by marking off a height equal to the horizontal 

 projection N of P. The complete curve was determined 

 by imagining that P made a complete revolution of the 

 circle, and thus gave points forming one complete period of 

 the curve. 



By drawing the line O P of such a length that it represents 

 some number of volts to a fixed scale, and imagining it to 

 rotate about the end 0, it may be taken to represent the 

 varying electromotive force, without the curve obtained 

 from its successive positions being actually drawn. It must 

 then be remembered that the actual value of the variable 

 quantity represented by P may always be obtained by 

 measuring the length of the horizontal line drawn from to 

 .meet a vertical through P. The length of this horizontal 

 line is usually called the horizontal projection of P. The 

 length of P itself will be the maximum value of the variable 

 quantity represented by it. Its phase is represented by the 

 angle between P and the vertical through 0, while the 

 actual value of the quantity when in this phase is represented 

 by the horizontal projection of P in the position in which 

 O P is drawn. 



When drawing such a line to represent a varying quantity, 

 an arrow-head is shown at one end to indicate that this end 

 is to be taken as rotating about the other. Further, a con- 

 vention must be adopted with regard to the direction in 

 which rotation occurs. In the figures employed in this 

 book, the rotation will always be taken in a clockwise 

 direction. The rate of the imaginary revolution of the line 

 will be equal to the frequency of the current or electromotive 



