the Winding of Voltmeters. Ill 



German-silver wire, and having a resistance far greater than 

 that of the voltmeter itself. By using wire of large gauge, 

 wound on a bobbin of large volume, and with as efficient an 

 arrangement for cooling as can be conveniently employed, the 

 heating-error can be rendered extremely small. Such a 

 bobbin, however, is both costly and bulky, and the employ- 

 ment of such an outside resistance-coil wastes energy, and 

 can only be used with voltmeters in electric light and power 

 installations where such a waste of energy is unimportant. 

 The following investigation has therefore been made for the 

 purpose of determining what must be the volume of this out- 

 side resistance-coil, and what must be its resistance relatively 

 to that of the voltmeter-coil, so that the heating-error may not 

 exceed any given value. 



Let R be the resistance of the coil of copper wire wound 

 on a voltmeter, let H be the rate of production of heat when 

 the maximum deflection is obtained ; then, as already shown, 

 H will be constant for a voltmeter of a given size wound ac- 

 cording to a definite law, whether it be wound with fine wire 

 for a 500-volt instrument or with thicker wire for a 50-volt 

 one. Let C be the current passing round it when this 

 maximum deflection is being produced ; then 



C 2 R = H, a constant. 

 Let the increase of resistance produced by the passage of the 

 current for some time be r ; then ^ is proportional to the pro- 

 duct of 7, the coefficient of increase of the resistance of 

 copper per degree of temperature, into H, since, as already 

 explained, the voltmeter is so wound that the rate of pro- 

 duction of heat is proportional to the increase of tempera- 

 ture. Hence 



— =a constant, A say. 



Now let there be a resistance-coil of German-silver wire of 

 uniform cross section, of volume V in series with the instru- 

 ment, and let us suppose that for any coils thus added the 

 rise of temperature is proportional to the energy wasted per 

 second per unit volume, that is to say proportional to the rate 

 of production of heat per unit volume. 



C 2 Ri 



Let Ri be the resistance of this added coil, then „ is 



proportional to its rise of temperature ; hence, if r x be the 



