where λ is the constant of change of the emanation.
The curve of recovery of the heating effect of radium from its minimum value is identical with the curve of recovery of its activity measured by the α rays. Since the minimum heating effect is 25 per cent. of the total, the heat emission Qt at any time t after reaching a minimum is given by
where Qmax. is the maximum rate of heat emission and λ, as before, is the constant of change of the emanation.
The identity of the curves of recovery and fall of the heating effect of radium and its emanation respectively with the corresponding curves for the rise and fall of radio-activity shows that the heat emission of radium and its products is directly connected with their radio-activity. The variation in the heat emission of both radium and its emanation is approximately proportional to their activity measured by the α rays. It is not proportional to the activity measured by the β or γ rays, for the intensity of these rays falls nearly to zero some hours after removal of the emanation, while the α ray activity, like the heating effect, is 25 per cent. of the maximum value. These results are thus in accordance with the view that the heat emission of radium accompanies the expulsion of α particles, and is approximately proportional to the number expelled. Before such a conclusion can be considered established, it is necessary to show that the heating effect of the active deposit from the emanation varies in the same way as its α ray activity. Experiments made to test this point will now be considered.
246. Heat emission of the active deposit from the emanation. New radium in radio-active equilibrium contains four successive products which break up with the emission of α particles, viz. radium itself, the emanation, radium A and C. Radium B does not emit rays at all. The effect of the later products radium D, E and F may be neglected, if the radium has not been prepared for more than a year.
It is not easy to settle definitely the relative activity supplied by each of these products when in radio-active equilibrium, but it has been shown in [section 229] that the activity is not very different for the four α ray products. The α particles from radium A and C are more penetrating than those from radium itself and the emanation. The evidence at present obtained points to the conclusion that the activity supplied by the emanation is less than that supplied by the other products. This indicates that the α particles from the emanation are projected with less velocity than in the other cases.
When the emanation is suddenly released from radium by heat or solution, the products radium A, B and C are left behind. Since the parent matter is removed, the amount of the products A, B, C at once commences to diminish, and at the end of about three hours reaches a very small value. If the heating effect depends upon the α ray activity, it is thus to be expected that the heat emission of the radium should rapidly diminish to a minimum after the removal of the emanation.
When the emanation is introduced into a vessel, the products radium A, B and C at once appear and increase in quantity, reaching a practical maximum about 3 hours later. The heating effect of the emanation tube should thus increase for several hours after the introduction of the emanation.
In order to follow the rapid changes in the heating effect of radium, after removal of the emanation, Rutherford and Barnes (loc. cit.) used a pair of differential platinum thermometers. Each thermometer consisted of 35 cms. of fine platinum wire, wound carefully on the inside of a thin glass tube 5 mms. in diameter, forming a coil 3 cms. long. The glass tube containing the radium and also the tube containing the emanation were selected to slide easily into the interior of the coils, the wire thus being in direct contact with the glass envelope containing the source of heat. The change in resistance of the platinum thermometers, when the radium or emanation tube was transferred from one coil to the other, was readily measured.