1895.] Conductivities of Badly Conducting Substances. 265 



the value of / by equation (6) is given approximately by the 

 equation 



r'^ 1 



it is thus greater than the value of / when the secondary circuit 

 is absent given by (7). Thus in this case the diminution in the 

 effective self-induction of the primary circuit due to the presence 

 of the secondary increases the brightness of the discharge. 



If we begin with the cylinder some way off and gradually 

 lower it into the coil A we observe that at first the approach of 

 the cylinder diminishes the brilliancy of the discbarge, but after 

 the cylinder gets within a certain distance of the coil the brilliancy 

 of the discharge increases as the cylinder is moved towards the 

 coil. Thus at first the diminution in the brilliancy due to the 

 resistance of the cylinder overpowers the increase due to the 

 diminution of the effective self-induction of the primary circuit, 

 but when the cylinder gets close to the coil the latter effect gets 

 the upper hand. This result follows from (6). In that equation 

 1/(7 is such a very large quantity that it is only when the resist- 

 ances of the secondary and primary circuits are exceedingly great 

 that the terms which do not contain 1/C are comparable with 

 those which do. When the secondary and primary circuits have 

 as in the present case only small resistances, we may omit from 

 the right-hand side of (6) all the terms which do not contain 1/0; 

 doing this we find 



^ ~ C {N'R + M'Sy 



The differential coefficient with respect to M^ of the denomi- 

 nator of the right-hand side of the equation is proportional to 



-2M'S + N(L8-NR), 



as this is positive until 



We see that until M attains this value an increase in M such 

 as that caused by the approach of the cylinder to the coil will 

 diminish /, while after M has attained this value the value of / 

 will increase as the cylinder approaches the coil. 



Resistance of Electrolytes for very rapidly alternating Electro- 

 motive forces. I determined by this method the relative resist- 

 ances of various electrolytes ; to do this bulbs of the same shape 



