60 Dr. R. T. Beatty on 



H a , H/3 .... in the capillary of the tube if the pressure were 

 so low that each atom is undisturbed by collisions while 

 radiating. Let S a , S^ . . . . be the distance travelled by an 

 atom while emitting H a , Hp .... We may call such a 

 distance the length of the luminous streak for the line in 

 question. Let F a , F^ .... be the mean free paths for an 

 atom radiating H a , H^ . . . . Let us also suppose that 

 a single collision is enough to destroy the radiating 

 properties of an atom. Then if the pressure is so high that 

 F a < S a . F^<S|3, the energies emitted will be E a . F a /S a , 

 E^ . F^/S^, and the ratio H^/H a will be constant since the 

 variables F tt , Fp are inversely as p. As the pressure is 

 lowered a stage will be reached where F a = or>S a , F / s<S i3 : 

 the energies emitted at this and lower pressures will be 

 Ea, Ej8 . F/3/S/3, so that H^/Ha will now increase with 

 diminishing pressure. Similar considerations hold for 

 Hy/H^, &c. Accordingly we may explain figs. 5 and 6 

 (PI. II.) as follows. 



If the mean free paths of two luminous atoms Ha, H/3 are 

 less than their respective luminous streaks, the intensity 

 ratio will remain constant. At lower pressures when the 

 free path of one atom is equal to or greater than its luminous 

 streak, the free path of the other remaining less than its 

 luminous streak, the intensity ratio will change. 



When the pressure is very low, so that the whole radia- 

 tion from an atom can take place between collisions, the 

 intensity ratios should again become independent of the 

 pressure. Experiments are now in progress to test this 

 deduction, a Wehnelt cathode being used to produce a bright 

 discharge in water vapour at low pressure *. 



The length of the luminous streak for H a may be cal- 

 culated from the curves shown in fig. 5 (PI. II) . The ratio 

 H/3/Ha begins to change at a pressure of about 3 mm. At 

 this pressure 



Fa= 1*25 xlO- 8 =4 . 2 x 10 _ 4 cm (See Table Y .) 



o 

 Hence S a = 4'2xl0~ 4 cm. The distance travelled by the 



luminous atom during one vibration is — , where v = velocity 



* In preliminary experiments now in progress it has been found that 

 a strongly luminous discharge can be produced if the stream of electrons 

 is concentrated by using a longitudinal magnetic field due to a powerful 

 electromagnet. 



