216 Profs. E. Rutherford and H. T. Barnes on the 
rod the activity decreases at first very rapidly, falling to 
about half value in about 3 minutes. After falling below 
20 per cent. of the maximum value the activity varies very 
little for a space of about 25 minutes, when there follows a 
gradual decay to zero (see Rutherford and Miss Brook, 
Phil. Mag. July 1902). 
P. Curie and Danne* have shown that the decay of 
activity of a body exposed for a long interval in the presence 
of the emanation is given by the equation 
=ae—'—(a— le, 
where I; is the activity at any time ¢, and I, the activity 
immediately after removal; A,=1/2420, »,=1/1860 where 
a second is taken as the unit of time ; the numerical constant 
a=4:20. Curie and Danne state that this equation holds 
accurately over the whole period of decay ; there is no doubt, 
however, that there is a rapid initial drop for about the first 
ten minutes after removal which is not expressed by this 
equation. The equation will, however, hold if the initial 
observations of the activity start from a period about 10 
minutes after removal, as the first change is almost com- 
pleted by that time. The equation will also hold, with the 
same limitations, for the decay of the activity of the emana- 
tion X, left behind in the radium after removal of the 
emanation. 
An analysis of the decay curves of excited activity, produced 
for different intervals of exposure in the presence of the 
emanation, shows that there are three well-marked changes 
occurring in emanation X cfradium. In the first change, half 
the matter is transformed in 3 minutes ; in the second, half 
in 34 minutes; and in the third, half in 28 minutes. A full 
account of the analysis of these changes and their peculiarities 
will be given by one of us in a later paper. The first change 
is accompanied only by a rays, the second change is not 
accompanied by @ rays at all, and the third change by a, B, 
and vy rays. 
While the curves of decrease of the rate of heat emission 
and of the activity of radium are very similar in shape, it 
is not possible to deduce directly from the result how much 
of the comparatively sudden drop of the heating effect 
observed is due to the emanation and how much to the first 
change in emanation X, on account of the rapid first change 
in the latter. The activity of the first change of emanation 
X (half value in 3 minutes) will have been reduced to about 
10 per cent. of its original value in 10 minutes. The 
* Comptes Rendus, exxxvi. p. 364 (1903). 
* 
