value. The activity due to C is proportional to λ_{3}R, and in order to represent the activity due to C to the same scale as A, it is necessary to reduce the scale of the ordinates of curve CC in Fig. 72 in the ratio λ_{3}/λ_{1}.
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Fig. 74.
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 λ_{1}P + λ_{3}R, where the values of P and R are graphically shown in Fig. 75 by the curves AA, CC. Initially after removal, λ_{1}P_{0} = λ_{3}R_{0}, 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 pro-
