hif the }fotU)u of /^OS/fire lo/is in a (ras. Gil 



7. There are a numhor ot* (ronerjil properties of the con- 

 ductivity which are ilhistrated by the experiments which have 

 been ah-eady given. The experiments show that when a 

 given numbtn- of negative ions start from the negative plate 

 the number reaching the positive plate depends only on the 

 potential-diflPerence X x a and the quantity of gas ;; X a in the 

 space between the plates. Thus, in Tables I. and 11. the 

 currents obtained in air at a pressure of 2 millimetres with 

 an electric force of 700 volts per centimetre, and with dis- 

 tances of 1, 2, 3, 4, and 5 millimetres between the plates, are 

 the same as the currents in air at one millimetre pressure 

 with an electric force of 350 volts per centimetre, with distances 

 2, 4, 6, 8, and 10 millimetres ])etween the plates. Similar 

 instances of the coincidences of currents in hydrogen at 8, 4, 

 and 2 millimetres pressure are to be found in Tables IV., V., 

 and YI. Thus the currents obtained at 2 millimetres pressure 

 with a force of 262 volts per centimetre with the distances 4, 6, 

 8, and 10 millimetres between the plates are equal to those 

 at 4 millimetres pressure with a force of 525 volts per centi- 

 metre with the distances 2, 3, 4, and 5 millimetres between 

 the plates, or at 8 millimetres pressure wdth a force of 1050 

 volts per centimetre with the distances 1, 1*5, 2, 2'5 milli- 

 metres between the plates. 



This result can also be established by the theory. The 



quantity ^ is equal to — , where v is the potential-difference 



between the plates and m the mass of the gas in the space 

 between the plates. Hence 



rt X a = 711 f I — I and ax /3=m <j)l—), 



so that the ratio 



n _a(a— ^)6(«-^)« 



7^0 ~ aa — ay8e<*-^)«' 

 which is a function of ax a and a x jB, can be expressed as a 

 function of v and vi. The same conclusion follows from 

 elementary considerations. When an ion passes from one 

 plate to another the number of collisions that occur depends 

 on the quantity of gas m between the plates ; and if this 

 quantity and the potential-difference v are constant, the fall 

 of potential along the path between any two collisions will be 

 fixed. Under these conditions the velocities of the ions at 

 collision and the total number of collisions will be unchanged 

 when the distance between the plates is altered. Hence for 

 each ion starting from the negative plate the number of new 

 ions produced in the gas will be fixed w hen v and m are 

 given. 



