512 Dr. J. H. Vincent : Electrical Experiments 



fig. 2, as the volts change from 78" 5 to 364 and the external 

 resistance from 190 to 2690 ohms, the frequency changed Irom 

 77 to 63 per second. The mean current (as read by a moving- 

 coil, instrument) falls slightly from '135 to '12 ampere, the 

 root mean square volts across the arc (as read by a Kelvin 

 electrostatic voltmeter) rise from 55 to 80. The maximum 

 width of the bead changes from 1*4 to 1*7 cm. while the 

 mean voltage drop per cm. of arc-length increases from 75 

 to 91. Similar changes occur in all necklace lamps as we 

 pass from A to B. 



As one alters the volts and resistance so as to keep the 

 necklace unbroken on the lowest resistance for each voltage, 

 i. e. along lines like AC, the frequency may either decrease 

 or increase. When the internal diameter is about *35 mm., 

 tubes less than about 7 cm. in length show a rise in frequency 

 from A to C ; tubes longer than this show a fall in frequency 

 from A to C. The mean current rises from A to G when the 

 frequency rises, and falls in those cases in which the frequency 

 falls. The mean current and frequency are closely inter- 

 dependent. This is because, as will be shown later, much of 

 the electrical energy supplied to the lamp is employed in 

 overcoming the viscous resistance of the mercury. 



The arc-length affects the frequency in two ways : first, 

 when the mean arc-length increases, the mean mass of mercury 

 to be moved is lessened ; second, the arc behaves (under the 

 same mean current) as a gas having a variable pressure vshich 

 rises when the arc shortens — in fact, the pressure exerted by 

 the gas in the arc is not independent of the volume and 

 cannot be simply regarded as saturated mercury vapour. 



In spite of the complicated interactions occurring in the 

 necklace effect, some approximate rules governing the fre- 

 quency may be given. 



The frequency in the neighbourhood of the point A in the 

 different diagrams is roughly inversely as the square root of 

 the length of the mercury columns. 



On 200 volts : 



Length of 

 Tube, 



Length of 

 Arc, 



Difference, 



Frequency, 



F.v'i--A. 



L. 



A. 



L-A. 



F. 





4 



•8 



3-2 



70 



125 



4 



1-5 



2-5 



76 



120 



10 



10 



9-0 



35 



105 



10 



1-6 



8-4 



34 



98 



10 



•6 



9-4 



39 



119 



10 



1-3 



8-7 



37 



109 



20 



•5 



19 5 



275 



121 



20 



1-3 



18-7 



27 



117 



