92 CURRENT VALUE. 



would increase in the ratio of the square of the value of the 

 quantity being measured, if the deflection is proportional 

 to the deflecting force. In many instruments arrangements 

 are adopted by which a more even graduation is obtained 

 by making the deflection corresponding to a given force 

 smaller at higher points of the scale, or by arranging that 

 the action between fixed and moving parts becomes less as 

 the deflection increases. 



In order to make a distinction between the maximum 

 value of alternating currents, voltages, &c., and their effective 

 or virtual values, it is convenient to adopt the general 

 convention of indicating the maximum value by a capital 

 letter and the virtual value by the corresponding small letter. 

 Thus C, V, W represent maximum values ; 

 c, v, w are virtual, or R.M.8. values. 

 Consequently for harmonic wave form we have 

 C = *J 2 c V = f2v., &c. 



Example. As an illustration which should help to make 

 clear the subject of the preceding paragraph, we may consider 

 the relation between the reading of a Cardew voltmeter and 

 the voltage applied to its terminals. 



The Cardew voltmeter is of the hot-wire type, a long, thin 

 wire of high resistance being heated by the current passing 

 through it, and caused thereby to expand. The expansion 

 of the wire produces a movement in a fine cord attached to 

 a spring at one end of the wire, and causes the deflection of 

 a needle attached to a small pulley round which the cord 

 passes. The deflection of the needle is thus proportional to 

 the expansion of the wire, which is, in turn, practically propor- 

 tional to the rate at which heat is communicated to the wire 

 by the current passing through it. 



The rate at which heat is developed in the wire has already 

 been stated to be G*R joules per second. Since the value of C 

 is constantly changing in the case of an alternating current, 

 it is the average value of C" R, which represents the average 

 rate at which the wire is heated, and which, therefore, deter- 

 mines the deflection of the needle. 



Suppose that the resistance of the wire of a Cardew 

 voltmeter is 300 ohms, and suppose that the voltage repre- 

 sented graphically in Fig. 4, is applied to the terminals of 

 the instrument. For the sake of convenience, however, we 

 will assume the scale to be doubled, so that the maximum 



