Since radium _B_ does not give out rays, the number of α particles expelled from the active deposit per second is proportional to λ₁_P_ + λ₃_R_. The activity measured by the α rays, using the electrical method, is thus proportional at any time to λ₁_P_ + _K_λ₃_R_, where _K_ is a constant which represents the ratio of the number of ions, produced in the testing vessel, by an α particle from _C_ compared with that from an α particle emitted by _A_. It will be seen later that, for this particular case, _K_ is nearly unity. Taking _K_ = 1, the activity at any time after removal is proportional to λ₁_P_ + λ₃_R_. CASE 1. We shall first consider the activity curve for a short exposure to the radium emanation. The relative values of _P_, _Q_, and _R_ at any time corresponding to this case are graphically shown in Fig. 74. The activity measured by the α rays at any time will be the sum of the activities due to _A_ and _C_ separately. Let curve _AA_ (Fig. 74) represent the activity due to _A_. This decreases exponentially, falling to half value in 3 minutes. In order to show the small activity due to _C_ clearly in the Figure, the activity due to _A_ is plotted after an interval of 6 minutes, when the activity has been reduced to 25 per cent. of its maximum value. The activity due to _C_ is proportional to λ₃_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 λ₃/λ₁. [Illustration: 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.