carried by the Ions produced by Rontgen Rays. 537 



If the needle is initially placed symmetrically with respect 

 to the quadrants, then 



d 9\* _Q 

 dd 



approximately when 6 is small. 



Thus if q n , q 13 denote the values of q n , q n when 6 is zero 



we have approximately, if /3= -—-, 



and 



Qi=quV, + q u V, + q M V I +/8tf(V )( -V 1 ) ; 



if V 2 = we have, since the detiexion of the needle is approxi- 

 mately proportional to the product of the potential-difference 

 between the quadrants and the potential of the needle, 



e=kY l Y s . 



Hence Q l = q 1 tf l + <i ia V g + kl3V 1 V t *-K/3V l >V 3 ; 



the fourth term on the right-hand side is small compared with 

 the third ; hence we have 



Thus the effective capacity is q n -j- &/3 Vy. 



The effective capacity was measured by connecting a 

 parallel-plate condenser with the quadrants and then observing, 

 when the system was insulated, the change in the deflexion 

 when the distance between the plates was increased by a 

 known amount. Supposing the capacity of the parallel-plate 

 condenser was C in the hrst position and C in the second, 

 then we have, if Vi and V/ are the corresponding potentials, 



Qi= (qu + C) v, + IL.V, +/s*v 1 v,» 



= (<Lu + 00 V,' + OxaVs + 0*V,' V 3 2 ; 

 thus 



V 1 _ qu+flfeV.» + Q' 

 Vi'~qn+#HY+<r 



Since Vj, Y x ' are proportional to the deflexion in the two 

 cases and 0' and C are known, this equation enables us to 

 calculate qn+ZSAfVV*, the effective capacity of the system. 



If, when the rays are on, the movement of the spot of light 

 indicates a change in the potential equal to Y per second, then 

 the quantity of electricity flowing in that time across the cross- 

 section of the vessel exposed to the rays is C V. But if n is 

 the number of ions, both positive and negative, per cubic 



