82 BELL SYSTEM TECHNICAL JOURNAL 



gun which fires a shell. The speed of this "recoil atom" is calculable, 

 standing as it does to the speed of the ejected particle in the inverse 

 ratio of their masses; and it has been utilized for measuring an 

 excessively short half-period, that of RaC, which amounts to only 

 10~^ second; a tube was oriented so that some of the recoil atoms 

 flew along it, and their activity at various points of their flight was 

 measured as in the case of thoron.^^ 



Many of the half-periods, finally, are determined by analyzing the 

 curves which represent the variation in time of the rays from con- 

 tinually-changing mixtures of growing and decaying substances: 

 curves which presumably can be represented as sums of three, four or 

 even more terms like the exponential terms in equation (6), not however 

 independently known — that is to say, their coefficients and their 

 exponents must be determined by inspecting the activity-curve itself 

 and trying to build one like it. This operation sometimes requires a 

 great deal of skill and discernment and intuition. It seems little short 

 of marvelous that all the radioactive substances of the known series 

 should have been recognized and their half-periods measured. That 

 they have all been recognized there can be little doubt; for let us 

 consider what it would imply if another substance lay undetected 

 between (let us say) radon and radium A. There would have to be 

 not one such substance but three, one of them emitting alpha-rays and 

 the two others beta-rays — for otherwise the displacement-law of 

 Fajans and Soddy would be broken. But if there were an undetected 

 alpha-ray-emitting substance between radon and radium A, the atomic 

 weight of the latter would be eight units below that of the former, 

 instead of only four as we now suppose; and this difference of four 

 units would follow step by step all the way down the radium series, 

 ending in a to-be-expected value of 202 instead of 206; which would 

 vitiate the excellent agreement between the latter figure and the 

 observed atomic weight of the samples of element 82 contained in the 

 uranium ores. The same argument can be used in the thorium series; 

 in the actinium family the basis for the argument is lacking, but the 

 parallelism between this and the other two families conduces to the 

 same belief. It is all but certain, therefore, that the explorers of radio- 

 activity have done their work so thoroughly that no substance yet re- 

 mains unknown in the direct genealogical line from uranium I to radium 

 G, nor in that from thorium to thorium D, nor between radioactinium 

 and actinium D. 



^^ This experiment was first performed by J. C. Jacobsen, and later by A. W. 

 Barton, whose paper {Phil. Mag. (7) 2, pp. 1275-1282; 1926) should be consulted 

 for details. It is a very delicate one, especially as the atoms recoil because they 

 have emitted not alpha-particles but electrons, which are comparatively light and 

 are emitted with various speeds. 



