200 Professor Joseph John Thomson [Jan. 19, 



Consider two different systems A and B in the same atom. Let 

 El, ai, ^1 ; E2, a2, p^ be the vahies of E, a, p for the systems A and B 

 respectively : — 



E,=^(l-e-^.') 



Pi 



Now suppose that the system A is one that does not absorb much, 

 but also does not radiate much, while B absorbs a great deal more 

 than A, but radiates still more in proportion, so that a2 > a^, but 

 tti/^i > ajp^, so that ultimately E^ is greater than E2, but at first 

 E2 is greater than Ej. The curves (1) and (2), Fig. 4, represent the 

 variations of Ei and E2 with the time. 



Suppose now that systems A and B become luminous when the 

 internal energy is equal to W. It is not necessary to assume that the 

 critical amount of energy is the same for the two systems, the assump- 

 tion is only made to simplify the diagram, the reader will see that 

 the argument would apply if the critical amounts of energy were 

 different in the two cases. 



Now consider first the case when the rate at which work is being 

 done in the tube is so small that though a-^/p^ is greater than W, 

 a.jp^ is less than W, the case represented in Fig. 4 ; here system A 

 acquires the amount of energy necessary to make it luminous, while 

 system B does not ; thus in this case the spectrum of the gas would 

 show the Hues corresponding to A but not those of B. Suppose now 



we increase the rate at which work is done in the tube, so that both 

 "■ilPi ^iid ai//?i are greater than VY, the case represented in Fig. 5. 



Here the system B attains the critical amount of energy, and it 

 reaches this value before A does, so that in this case the lines of B 



