The activity due to C is thus represented by the curve CCC, Fig. 74. The total activity is thus represented by a curve A + C whose ordinates are the sum of the ordinates of A and C.
This theoretical activity curve is seen to be very similar in its general features to the experimental curve shown in Fig. 66, where the activity from a very short exposure is measured by the α rays.
Case 2. The activity curve for a long exposure to the emanation will now be considered. The activity after removal of A and C is proportional to λ1P + λ3R, where the values of P and R are graphically shown in Fig. 75 by the curves AA, CC. Initially after removal, λ1P₀ = λ3R₀, since A and C are in radio-active equilibrium, and the same number of particles of each product break up per second. The activity due to A alone is shown in curve AA, Fig. 75. The activity decreases exponentially, falling to half value in 3 minutes. The activity due to C at any time is proportional to R, and is initially equal to that of A. The activity curve due to C is thus represented by the curve CC, which is the same curve as the upper curve CC of Fig. 73. The activity of A and C together is represented by the upper curve A + C (Fig. 75), where the ordinates are equal to the sum of the ordinates of the curves A and C. This theoretical curve is seen to be very similar in shape to the experimental curve (Fig. 67) showing the decay of activity of the active deposit from a long exposure measured by the α rays.