212 RADIO-ACTIVE EMANATIONS [CH. 
These effects receive a general explanation on the views already 
put forward. When the radium is placed in the closed vessel, the 
emanation is given off at a constant rate and gradually diffuses 
throughout the enclosure. Since the time taken for diffusion of 
the emanation through tubes of ordinary size is small compared 
with the time required for the activity to be appreciably reduced, 
the emanation, and also the excited activity due to it, will be 
nearly equally distributed throughout the vessel. 
The luminosity due to it should thus be equal at each end of 
the tube. Even with a capillary tube connecting the two bulbs, the 
gas continuously given off by the radium will always carry the 
emanation with it and cause a practically uniform distribution. 
The gradual increase of the amount of emanation throughout 
the tube will be given by the equation 
Ne = a 
N, > 
where JV, is the number of emanation particles present at the 
time t, V, the number present when radio-active equilibrium is 
reached, and 2 is the radio-active constant of the emanation. The 
phosphorescent action, which is due partly to the radiations from 
the emanation and partly to the excited activity on the walls, 
should thus reach half the maximum value in four days and should 
practically reach its limit after three weeks interval. 
The variation of luminosity with different distances between 
the screens is to be expected. The amount of excited activity 
deposited on the boundaries is proportional to the amount of 
emanation present. Since the emanation is equally distributed, 
the amount of excited activity deposited on the screens, due to the 
emanation between them, varies directly as the distance, provided 
the distance between the screens is small compared with their 
dimensions. Such a result would also follow if the phosphorescence 
were due to the radiation from the emanation itself, provided that 
the pressure of the gas was low enough to prevent absorption of 
the radiation from the emanation in the gas itself between the 
screens. 
