262 Prof. Thomson, A Method of Comparing the [Feb. 11, 



where T is the periodic time of the electrical oscillations produced 

 when the jar is discharged, the secondary circuit being in position. 



Thus If -T^ I dt, and therefore the brightness of the discharge in 



the bulb will be a minimum when the time constant of the secondary 

 circuit is l/27r times the time of the electrical oscillations. In the 

 actual experiments the secondary circuit was a bulb which was 

 filled with the substance to be examined ; if the radius of the bulb 

 is a and if a is the specific resistance of the substance with which 

 it is filled, then the time constant for the most persistent distribu- 

 tion of current is ^a?lira. Thus the specific resistance of the 

 substance which has the greatest effect in diminishing the bright- 

 ness of the discharge through the bulb is equal to 8a^/T. Hence if 

 we are using oscillations whose period is one-millionth of a second 

 and if a^ = 10, then the specific resistance when the brightness of 

 the bulb is a minimum is 8 x lO''. Though the method will not 

 be sensitive for comparing resistances close to this value, yet it is 

 important to know the resistance when the dimness of the bulb is 

 a maximum, as for resistances of quite a different order the effect 

 of a change in the resistance will be too small to be appreciable. 

 As the frequency of the electrical oscillations or the size of the 

 bulb is increased the specific resistance of the substance which gives 

 the maximum effect also increases. 



The heat produced in the secondary circuit is equal to 



SJfdt; 

 the value of the integral can be calculated by the method used to 



calculate I ( ^2 ) ^i> ^^ ^^^ 



r ^ if \Sf 



" is'LR + S (nR' + ^'j + N' ^\ 



This is a maximum when 



s 



Method of making the Experiments. The method consists in 

 observing the effect produced on the currents in the primary 

 circuit by introducing a secondary circuit of standard shape made 

 of the substance to be examined. The first arrangement I tried 

 for effecting this object is shown in Fig. (1). 



The primary circuit GDEF connects the outside coatings of two 

 Ley den jars, the inside coatings of which are connected with the 

 terminals of a Wimshurst machine ; these terminals are furnished 



