232 On a Model which imitates tlie Behaviour of Dielectrics. 



figs. 2 and 4 logarithms of the velocity are plotted to 

 logarithms of the time of charge or discharge, and in each 

 case the points so obtained are very nearly on straight lines, 

 showing that the velocity of the pencil both when charging 

 and discharging is a power-function of the time. Both these 

 results have also been obtained by one of us in experiments 

 on dielectrics. The three diagrams given in fig. 1 show the 

 effect of varying the time of charge. From the equations ob- 

 tained for the velocity of the pencil (see fig. 2) it appears that 

 the exponent of t in the equations of discharge decreases as 

 the time of charge increases, a result which has been shown 

 to hold in the electrical case. The diagram in fig. 6 has been 

 given to illustrate the action of the model in imitating the pro- 

 duction of a second discharge which takes place when a charged 

 condenser, after being once short-circuited and then kept insu- 

 lated for a period, is short-circuited a second time. 



5. The production of successive sparks from a charged 

 ley den-jar is a very familiar fact. This can be imitated by the 

 model. During the earlier part of the first discharge the 

 upper springs extend to their full length, and while the lower 

 springs are still considerably compressed and if the crossbar 

 is then clamped, a state equivalent to insulation commences. 

 The extension of the lower springs, however, still continues ; 

 but as the crossbar is fixed this results in the compression of 

 the upper springs. When the crossbar is again released a 

 second discharge takes place which is weaker than the first ; 

 if the operations be repeated, further discharges can be 

 obtained until the crossbar returns to its zero position. In 

 fig. 5 a diagram is given to illustrate the effect of decreasing 

 the charging pressure of a condenser. This was obtained 

 from the model by breaking the circuit of the magnet Mi 

 only, and allowing the pencil to move under the action of M 2 . 

 It will be seen that the effect of thus lowering the pressure 

 is to cause a variation in the discharge to take place, similar 

 in form to that in the corresponding electrical cases. It is 

 interesting to consider also the effect of temperature on 

 the discharge as given by the model. Increased temperature 

 would make the mixture of oils in the cylinder become less 

 viscous. This would cause the crossbar, when moving under 

 the action of any given weight, to have a greater velocity, 

 especially at the later portions of the discharge and discharge 

 curves. This agrees with the fact that when the temperature 

 of a cable increases, the charging and discharging currents 

 as given by a galvanometer also increase. By freezing a 

 portion of the oil, the effect of very low temperatures on 

 dielectric constants could be imitated. It is evident, therefore, 



