Measurement of Peak Potential of Alternating Source. 303 



Let Ci be the capacity coefficient of the anode and cathode 

 circuits of the valve ; and let at any time E x be the potential 

 difference between anode and cathode ; E 2 the potential 

 difference across the voltmeter E; E the potential given by 

 the source A. Then 



E = Ei + E 2 . 

 Since the anode of the valve is insulated, the charge on it is 

 constant, that is, 



dEi-OEjsr const. 

 The constant is determined by the condition that, when 

 E = E m , where E m is the peak voltage, E^O owing to the 

 action of the valve. Hence 



(C 1 + C)E 2 = C 1 E + (JE wl . 



The voltmeter reads the R.M.S. value of E 2 . Denoting 

 average values by a bar, we have 



(C 1 -f-C) 2 E?=0 1 2 E^ + 2C 1 CE . E OT + C 2 E W 2 . 



So that E ni is not equal to ^E 2 2 , even if E = (as is usual) , 

 unless Ci is very small compared to C ; if an accuracy of 

 1 per cent, is required, must be 200 times Cj unless a 

 correction involving a knowledge of the R.M.S. voltage of 

 the source is applied. Ci will not usually be less than 2 or 

 3 cm.; hence C 2 must be several hundred cm., which is much 

 more than the capacity of most electrostatic voltmeters, so 

 that the addition of a condenser in the position C is required. 

 A well-insulated leyden-jar will usually meet the purpose, 

 but if still higher insulation is found to be necessary, con- 

 densers for the purpose may be made readily by wrapping 

 an external conductor round rubber cable, such as is used for 

 connecting magnetos to their sparking-plugs. Such cable 

 usually has a resistance of at least 10 15 ohms per metre; the 

 7 mm. variety will stand up to 20,000 volts (direct). 



If these conditions are fulfilled — and they are easily 

 fulfilled so long as the peak potential is not greater than 

 15,000 volts — the only limit to the accuracy of the method 

 is the accuracy of the voltmeter. And here a warning may 

 be inserted. There are types of electrostatic voltmeter which 

 do not give the same reading with alternating and direct 

 current ; that is to sa} r , an alternating current of R.M.S. 

 voltage E will not give the same reading as a direct current 

 of steady voltage E. It is not safe therefore to calibrate 

 the voltmeter by alternating current ; it is best calibrated 

 by means of the valve with an alternating source of which 

 the wave-form is known. 



Dec, 1918. 



Y2 



