160 BELL SYSTEM TECHNICAL JOURNAL 



Now, of the three known kinds of rays from radioactive substances, 

 one only is characterized by an exponential decline of its strength 

 with increase of thickness of matter traversed: to wit, the gamma-rays. 

 Regener was therefore assuming, as had many others before him, that 

 cosmic rays which have penetrated many metres of ivater behave like a 

 beam of monochromatic gamma-radiation, corpuscles of light of a single 

 frequency and energy, coming vertically from above. The value of ju — 

 .00018 in this case •'' — is many times smaller than that of any known 

 variety of gamma-rays; this is expressed by saying that the cosmic 

 rays are considerably more penetrating or "harder" than the hardest 

 of gamma-rays. 



While the expression {A + Be"'"'') fits tolerably the five experimental 

 points at the five greatest depths, it misses the two others, giving for 

 32.4 and 78.6 metres lower values of ionization than those observed. 

 One might add a second exponential term with a difi'erent, much larger 

 value of m; thus in effect assuming that the cosmic rays behave like a 

 mixture of gamma-rays of two different wave-lengths, corpuscle- 

 energies and hardnesses. This in fact is the custom, though Regener 

 did not do it in the paper whence I am quoting, being interested mainly 

 in the far end of the curve — in the range of depths at which, as is 

 commonly said, all but the hardest component of the cosmic rays have al- 

 ready been filtered out. For, if a function of x is the sum of a number of 

 terms of the form Bie"'"''', with differing values of the constants ^u,: 

 then as x is increased the various terms fall off, but in such a way that 

 eventually the one with the lowest jj. predominates more and more over 

 all the rest, however small may be its coefficient B. This is "filtering," 

 a process of great use in the science and practice of radioactivity; 

 many of the radioactive elements, or of the mixtures thereof which are 

 common, send out gamma-rays of various degrees of penetrating- 

 power, among which the hardest may be almost isolated from the rest 

 (at the price, of course, of a great cutting-down of its own intensity) 

 by a thick screen of absorbing matter. Even if the screen is not thick 

 enough to make the hardest component predominant, it may alter 

 greatly the relative proportions of harder components and softer. The 

 rays responsible for the 1.5 ions at sea-level, if of the nature of gamma- 

 rays, must have undergone a good deal of this alteration and "hard- 

 ening" in passing through the atmosphere; not nearly so much, how- 

 ever, as those deep down in Lake Constance, the whole of the atmos- 

 phere being no more powerful an absorber than a layer of ten metres 

 of water. 



We turn now to the great series of experiments made by Millikan 



'Expressed in cm."'; in (metres)"', Millikan's customary unit, it would be .018. 



