with Mercury contained in Tubes. 



13 



Tims in the table above with different lengths of tube, all 

 of the same bore and external diameter, on 200 volts the 

 product of the frequency and the square root of the mean 

 reduced length of the mercury in the tube is approximately 

 constant. 



With the same tube and the same filling, the frequency 

 varies directly as the square root of the meau pressure. 



Leno-th of tube 10 cm. : 



E.M.F. 

 in circuit. 



Pressure 

 in cms. of 

 mercury. 

 P. " 



Frequency. 

 F. 



Limit of 

 Resistance. 



Nos pro- 

 portional to 

 F 



200 

 300 

 400 



1 



- 81 



162 



81 



162 



' 81 



162 



81 



162 



[ 81 



162 



81 



162 



39 1 

 55 f 



5} 



38 1 

 53/ 

 36 1 

 49 J 

 391 

 51/ 

 36 1 

 47 f 



upper 

 lower 

 upper 

 lower 

 upper 

 lower 



391 

 39/ 

 371 



37 j 



38 1 

 38 J 

 361 

 35) 

 391 

 36/ 

 361 

 33 j 



Thus in the above table if one compares the frequencies at 

 corresponding points on the two diagrams of fig. 2 ( f corre- 

 sponding to F, g to G), it is seen that this rule is obeyed at 

 low voltages, but is less closely followed at higher voltages. 



It follows that if we regard the motion as a maintained 

 harmonic motion, the corresponding inertia is proportional to 

 the length of the tube less that of the arc, and the " spring " 

 is proportional to the pressure. 



It is not necessary to have the tube straight or horizontal, 

 or to have a large mass of mercury in order to obtain the 

 necklace effect. A quartz vessel was constructed as shown in 

 fig. 8 (p. 514). The capillary portion was 6-Q cm. long, and 

 had a mean internal diameter of '38 mm. The arc occupies 

 the portion indicated in the figure. Without any auxiliary 

 heating, this lamp would start sparking w r ith a current of 

 41 amperes. The volts across the lamp just previous to 

 lighting measured about 3, so that the resistance of the thread 

 of mercury when on the point of breaking was about three- 

 quarters of an ohm. On 100 volts this lamp required a 

 resistance of about 420 ohms to produce the necklace, the 

 width of the beads being 1*3 cm. and the frequency 55*5. 

 The current was '08 ampere. On 200 volts and 1720 ohms, 



