164 BELL SYSTEM TECHNICAL JOURNAL 



above? The answer presumably is 710. Millikan and Cameron, how- 

 ever, asked a slightly different question. Imagine that the cosmic 

 rays, instead of coming altogether vertically from above, are gamma- 

 rays traversing interstellar space uniformly in all directions, incident 

 therefore upon the atmosphere at all angles between zero and 90° — - 

 much the most probable assumption if they do proceed from interstellar 

 space, as it is hard to think of any possible action of the earth which 

 might constrain them all to move straight toward its centre. The 

 ionization at any depth x beneath the top of the atmosphere (continue 

 to think of x as measured in metres of w^ater) would then be due to 

 beams coming from all directions above the horizon. These beams, 

 having traversed different thicknesses of air, greater the more they are 

 inclined to the vertical, would have been absorbed to different degrees; 

 their intensities, originally (by hypothesis) the same, would be reduced 

 in different proportions. It can readily be shown that the total 

 intensity of all the beams should then vary, not as e"""", but as the 

 following function of x: 





h-^'^'dz, (2) 



Ij. standing as before for the absorption-coefficient of any cosmic-ray 

 beam coming from any one direction.'' Now the curves of Figs. 4 and 

 5, and the new curve of 1931, do not conform to this relation either. 

 It is consequently not possible to affirm that the cosmic rays behave 

 like gamma-rays of a single wave-length. 



Does the final extremity of the Millikan curve conform with formula 

 (2), so that one may assume that after a certain and feasible amount of 

 filtering, the radiation is almost altogether reduced to gamma-rays of a 

 single wave-length? To this Millikan and Cameron respond, that of 

 the curve of Fig. 5 the portion extending from abscissa 30 to abscissa 

 60 does conform, the value required for ju being .0005. Of the curve of 

 1931 they say, that from 40 to 80 metres-of- water it conforms, if for 

 the value .00028 be chosen. 



Recalling Regener's value of /x (.00018) for depths still greater, and 

 joining it with these, one is led to wonder whether at 40 and even at 

 80 metres the filtering is sensibly incomplete, and whether even at 200 

 metres the value ascribed to ^ may not be the ultimate "hardness" of 

 the rays. Further, there now arises the great question : can the curve 

 as a whole be regarded as the sum of a limited number of terms of the 



6 See R. Hellmann, Phys. ZS. 30, 357-360 (1929); E. Gold. Proc. Roy. Soc. A 82, 

 43-70 (1909). Regener used formula (1) instead of formula (2) for interpretmg his 

 data. 



