94 BELL SYSTEM TECHNICAL JOURNAL 



electrons that they Issue from their atoms with widely and irregularly 

 scattered speeds. If this is true, the presumption is that they escape 

 from the nuclei with equal speeds, the differences resulting from 

 experiences of theirs during the transit through the circumnuclear 

 electron-shells. But it must not be forgotten that a continuous 

 electronic spectrum appears together with the lines, when the gamma- 

 rays from a radioactive substance fall upon one of its stable isotopes; 

 and some allowance must certainly be made for this. 



Refreshingly in contrast with the status of this perplexing question 

 is the condition of another, for years the subject of a fervid controversy. 

 Are the gamma-rays from a self-transmuting atom emitted before or 

 after the transmutation occurs? There is only one way of settling 

 this question, and perhaps the question itself ought to be so phrased as 

 to bring this way into prominence. Granting the theory of beta-ray 

 line-spectra expounded in these pages, and granting that certain lines 

 in a certain spectrum have been recognized as being composed of 

 electrons expelled by gamma-rays of one and the same frequency from 

 various K, L, M classes in the circumnuclear electron-family, do the 

 energy-values of these lines show that the electrons come from atoms 

 as yet untransmuted, or from atoms which have already undergone 

 their transmutation — from the atoms of the parent, or those of the 

 daughter-substance? There is no forceful a priori reason for expecting 

 either of these alternatives rather than the other; the question must 

 be put to experiment. 



If one knew with all desirable accuracy the frequency of the gamma- 

 ray responsible for a particular set of lines, and the class of electrons 

 contributing each line — if one knew for instance that a certain line is 

 composed of X-electrons extracted by gamma-rays of a known fre- 

 quency V, one would measure the speed of these electrons, calculate 

 their kinetic energy, subtract it from hv, identify the difference with 

 the binding-energy Wr according to equation (11), and consult the 

 standard tables to locate the element possessing that value of the 

 extraction-energy for its iC-electrons. But there are few gamma-rays 

 of which the frequencies are independently known, and for these the 

 values are not very accurate; so that this method is not generally 

 available. 



If however two lines are composed, the one of i^-electrons and the 

 other of Li electrons ejected by gamma-rays of the same though un- 

 known frequency, then the difference between the values of kinetic 

 energy for the electrons of the two lines is equal to the difference be- 

 tween Wk and W^; and as this difference varies from element to 

 element, one can consult the tables to locate the element for which the 



