March 22, 1906] 



NA TURE 



497 



The potential difference P just where the glow com- 

 mences, when the pressure is low, sometimes varies so 

 rapidly with the current i as to be roughly inversely pro- 

 portional to it. The following are some values of »' and 

 P for a gas at a constant low pressure as the temperature 

 of the platinum strip was increased ; the numbers are in 

 the order of increasing temperature : — 



(in scale divisions! P (volts) Pi 



6 60 360 



87 40 34 s 



n-2 3° 33 6 



14 2 S 35° 



Such a simple relation between P and i is, however, 

 ■exceptional. 



The fact that the potential differences at which ionisation 

 by collision or luminosity begins depend upon the current 

 density, shows that the ionisation or luminosity of an 

 atom need not, and, indeed, cannot entirely, be the result 

 of a single collision between a corpuscle and the atom. 

 For if that were the case, then since the energy of the 

 corpuscle depends only upon the electric field, and not 

 upon the current density, the effect of increasing the current 

 density would merely be to increase in the same proportion 

 the number of luminous atoms, while, as a matter of fact, 

 if the potential difference is kept constant and the current 

 increased by raising the temperature of the platinum strip 

 fhe increase in the luminosity is greater out of all pro- 

 portion than the increase in the strength of the current. 



The result, however, is easily explained if we look at 

 the question from the following point of view. Suppose 

 that for ionisation or luminosity to take place the internal 

 energy of the atom must increase by certain amounts, say 

 E,, E, respectively. Then, if the energy possessed by the 

 corpuscle were very great, the result of one collision with 

 an atom might be to give to the atom enough energy to 

 ionise it or make it luminous, or both. But even if the 

 corpuscle were less energetic, and did not in one collision 

 give enough internal energy to the atom to ionise it, it 

 would communicate some energy to it, and if the atom 

 had any power of storing up energy this would form a 

 contribution towards the critical amount of energy required 

 by the atom before it is ionised. The atom, after having 

 had this energy communicated to it, would, so long as it 

 retained any of it, not require so much energy to ionise 

 ii as before. The atom, too, might acquire energy, not 

 merely by corpuscles striking against itself, but also by 

 the collision of corpuscles with neighbouring atoms ; such 

 • ullisions generate soft Rdntgen rays, the energy of which 

 might be absorbed by the atom under consideration and 

 help to raise its energy to the critical point ; the energy 

 in the Rontgen rays might by itself raise the internal 

 energy of the atom to this value, or else raise it so 

 nearly to this value that the collision with a corpuscle 

 would give it enough energy to carry it past the critical 

 stage. The rate at which the energy, due to collisions 

 of corpuscles with itself or with neighbouring atoms, comes 

 to an atom will be proportional to the rate at which 

 energy is being communicated to the gas, i.e. to Ft, 

 where F is the electric force and i the current density, 

 and thus for a constant electric force would be proportional 

 to the current density. The atom will radiate away some 

 of its internal energy ; if the rate of this radiation is pro- 

 portional to the amount of energy, E, possessed by the 

 atom, say equal to 0E, then if q is the rate at which 

 energy is being communicated to the atom, we have 



dE/dt = q-l3E, 

 so if E vanishes with t, 



E = q/0(i-e-0/ . 



Thus q//3 is the limit to the energy acquired by the atom, 

 and this is proportional to q, while q is proportional to 

 Fi, so that the atom will acquire the critical amount of 

 energy or not according as Fi is greater or less than a 

 certain value. 



Application of these Results to Spectroscopy. — We have 

 seen that the passage from the dark to the luminous dis- 

 charge occurs with great abruptness, an increase of the 

 potential difference by i/ioo of a volt being sufficient in 

 certain circumstances to convert a discharge in which no 

 luminosity at all could be detected to one where it was 



NO. 1899, VOL. 73] 



quite bright. This suggests that the luminosity sets in 

 when the internal energy of the atom, or rather of that 

 part of it which gives rise to the particular kind of light 

 present in the luminous discharge, attains a perfectly 

 definite value. This way of regarding the origin of the 

 luminosity affords a very simple explanation of the variation 

 of the spectrum with the kind of discharge and of the 

 effect of introducing capacity or self-induction into the 

 circuit containing the discharge tube. Let us consider 

 the rise in energy of ■& vibrating system inside the atom ; 

 let E be the energy at the time t, a the rate at which it 

 is absorbing the work done in the discharge tube ; the 

 energy may be supplied to it from the Rontgen radiation 

 in the tube or from the corpuscles which come into 

 collision with the atom, a will be proportional to the 

 rate at which the electric field producing the discharge is 

 doing work in the neighbourhood of the atom we are 

 considering ; it will thus be proportional to the product 

 of the electric force and the flux of corpuscles in this 

 neighbourhood. Let us suppose that the system radiates 

 energy at a rate proportional to E, say equal to /3E, then 

 we have 



dE/dt = a-$E, 

 or 



E = a//3(i-e-0O 

 if E = o when ( = o. 



Consider two different systems, A and B, in the same 

 atom; let E,, a,, ,8, ; E, a 2 , # 2 be the values of E, a, 8 

 for the systems A and B respectively. 



E t = aJP l (i-e-/V), 



E 2 = aJP 2 (i-e-fl2/). 

 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 o,>a, but aJ0 v >a,!8 2 , then 

 ultimately E, is greater than E„, but at first E 2 is greater 

 than E,. The curves A and E, Fig. 4, represent the 

 variations of E 1 and E, with the time. 



Suppose, now, that "systems A and B become luminous 

 when the internal energy is equal to W. It is not neces- 

 sary to assume that the critical amount of energy is the 

 same for the two systems ; the assumption is only made 

 to simplify the diagram ; it will be seen that the argument 

 will apply" if the critical amounts of energy are 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 

 aJ/3, is greater than W, ct„/5, 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 lines 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 a./|3 2 and aJ8 l are 

 greater than W, 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, so that in this 

 case the lines of B will be visible. Let us now consider 

 the lines in the spectrum corresponding to the system A ; 

 these will be visible if the energy in the system reaches 

 the critical value. The conditions in this case are in some 

 respects more unfavourable for the supply of energy to 



