Power with the Velocity of Cathode Rays. G55 



between an inverse first-power and an inverse second-power 

 law and is much nearer to the latter than to the former. 



Calculation of the absolute number of ions made by a 

 Cathode Ray of known velocity. 

 Hitherto the values given for the number of ions and the 

 velocity of the rays have been purely relative. It is im- 

 portant to get some definite numerical estimate of the specific 

 ionization made in air by a cathode ray of known velocity. 

 The dimensions of the solenoid were as follows : — 



Internal diameter of windings =3" 70 cm. 



External diameter of windings =4*65 „ 



Total number of turns in the three layers =231 



Total length of solenoid =13*0 cm. 



The calculated value of the field at the centre obtained by 

 summing the magnetic force at the centre due to each turn 

 over the whole length of the solenoid gives a value of 

 11 = 20*8 gauss per ampere. The field strength was tested 

 experimentally with a small search-coil and a ballistic 

 galvanometer, each of which had been previously standard- 

 ized. With 5 amperes flowing through the solenoid the 

 field strength was found to be 109 gauss at the centre and 

 105 gauss at the sides. This gives as a mean 107 gauss or 

 21*4 gauss per ampere. This differs from the calculated 

 value by less than 3 per cent., which is satisfactory in view 

 of the roughness of the winding and the degree of accuracy 

 obtainable in the rest of the measurements. We may take 

 the value of H to be 21 gauss per ampere — a mean of the 

 calculated and experimental values. 



The radius of the circle into which the rays are bent to enter 



the aperture is equal to the internal radius of the tube which 



mv 

 was 1*77 cm. From the formula p= -^we find the velocity 



of the rays is 6'Sx 10 8 x C where C is the solenoid current 



in amperes. 



The readings obtained for N are considered to be most 



accurate when the current in the solenoid was 7 amperes. 



For then the number of cathode rays was large and also the 



difference between Cj and Co was fairly great. From 



N 

 column III. of Table II. the mean value of ^ — ^-^ for 



7 amperes is -0051. Y x yUU 



AT N 



JNow a= P/. 



In all these experiments the length I was 300 cm. So that 

 « = 1-53. 



