CONTEMPORARY ADVANCES IN PHYSICS 179 



At first glance this appears a simple and welcome result. Further 

 study, however, dispels the pleasant impression : this is not an instance 

 of the sort of observation which sometimes comes aptly to confirm a 

 simple theory and smooth the path for further progress; it is instead 

 a warning of dangerous complications. In introducing the curves of 

 Figs. 3 and 4 and 5, I followed the policy of speaking of them as 

 absorption-curves for rays analogous to gamma-rays descending from 

 above; assuming in effect, that any ordinate of such a curve is a meas- 

 ure of the strength of the gamma-ray beam at the corresponding level 

 of air and water. But if such rays there be, they ionize not directly, 

 but by means of fast-flying electrons (or perchance, other particles) 

 which they expel from atoms. A photon does not achieve the whole, 

 nor even the most, of its ionization at the point where it dies; the effect 

 is spread all along the path of the electron which is heir to a great part 

 of its energy; and this path may be long. Thus, the ionization at a 

 certain level of water or air may be due in part, it may even be chiefly 

 due, to electrons which were unleashed at levels much higher. It may 

 thus be chiefly due to photons which ended their careers far away 

 from the place where it is being measured. It may then be no true 

 measure of the number of photons which collide with electrons at the 

 level in question, and no true measure of the strength of the gamma- 

 ray beam at that level. Indeed it is not likely to be a true measure, 

 unless the range R of the electrons be so short that the strength of the 

 beam does not sensibly diminish as it descends through a distance 

 equal to R. (There is an exception, as I mention on the next page; 

 but in practice it may not help.) Now precisely this condition accord- 

 ing to the testimony of Bothe and Kolhorster and Rossi, is not fulfilled. 



Since the condition apparently is not fulfilled, all sorts of difificulties 

 arise. If the ionizing particles have such ranges and such powers of 

 penetration as the data suggest — not only the data just mentioned, but 

 those of the cloud-chamber method and yet others — many of those 

 which cause the ionization at any particular level of the air have 

 come from points hundreds of metres, or even kilometres, farther up. 

 Any ordinate of such a curve as that of Fig. 4 is a function of the whole 

 of the (unknown) curve representing strength-of-gamma-ray-beam as 



parison. Denote by /o the number of coincidences per unit time found with nothing 

 between the counters, by / the number found with the block of gold (or lead) between, 

 by (/ the number of grams per square cm. of gold (or lead). They equate / /o to 

 exp (— fid), and compute the value of ix\ in the first and the third of the experiments 

 just mentioned, it comes out equal to (3.5 ± 0.5) -lO'^ and (1.6 dz 0.3) -lO"'; these 

 are values of the same order of magnitude as those given by Millikan and by Regener 

 for the quantity called /x in the analysis of their curves. In view of the objections to 

 assuming exponential absorption-curves for rays which are or may be composed of 

 fast-flying electrons, I doubt whether it is expedient to use this way of stating the 

 results. 



