four straight lines of different slopes represented by PQ, QR, RS, ST.
Such a result is to be expected, for it will be shown later that four distinct [Greek: alpha] ray products exist in radium when in radio-active equilibrium. Each of these products of radium emits an equal number of [Greek: alpha] particles per second, but the range of each is different. If a_{1} is the range of one stream, a_{2} of another, the ionization in the vessel AB, when two streams enter the vessel, should be
(nb/ρ)(a_{1} - h - b/2) + (nb/ρ)(a_{2} - h - b/2), i.e. (nb/ρ)(a_{1} + a_{2} - 2h - b).
Thus the slope of the curve should in this case be 2nb/ρ, while if only one stream enters, it should be nb/ρ. When three reach it, the slope should be 3nb/ρ and for four 4nb/ρ. These results are realized fairly closely in practice. The curve (Fig. 42) consists of four parts, whose slopes are in the proportion 16, 34, 45, 65, i.e. very nearly in the ratio 1, 2, 3, 4.
Experiments were also made with very thin layers of radium bromide, when, as we have seen (Fig. 40) a very different shape of curve is to be expected. An example of the results is shown Fig. 43, curves I., II. and III. Curve I. is obtained from radium bromide which has been heated to drive off the emanation, and curves II. and III. from the same substance several days later, when the emanation was again accumulating. The portion PQ, which is absent in the first curve, is probably due to the "excited" activity produced by the emanation. By careful examination of the successive changes in the curves after the radium has been heated to drive off the emanation, it is possible to tell the range of the [Greek: alpha] rays from each of the different products, and this has been done to some extent by Bragg and Kleeman.
It will be seen later that the results here obtained support in a novel way the theory of radio-active changes which has been advanced from data of quite a different character.
The inward slope of the curve in Fig. 43 due to the radium indicates that the [Greek: alpha] particles become more efficient ionizers as
