130 BELL SYSTEM TECHNICAL JOURNAL 



dicular rises would be observed instead of rounded-off and sloping ones, 

 if only the pencil of fragments passing through the absorbers were 

 ideally narrow and cylindrical, and were produced by bombardment 

 of atoms with particles all of the same speed; and he will attribute the 

 rounding-ofif of the steps to the facts that the fragments actually form 

 a divergent and conical beam, and the atoms from which they come 

 have been struck by impinging particles of diverse speeds. This idea 

 is strongly supported by the facts that the steps are notably steepened 

 when the divergence or "aperture" of the beam of fragments is 

 reduced, and when the diversity of speeds among the bombarding 

 particles is narrowed. 



The former of these variables is controlled by the slits and dia- 

 phragms which bound the beam, and the latter by the thickness of 

 the bombarded target whence the fragments proceed; for the bom- 

 barding particles are slowed down as they dive deeper into the target, 

 and nuclei at different depths receive impacts of different energy, and 

 thus there is a wider diversity of speeds among the particles when they 

 finally make their impacts than there is among them when they start 

 from their source. But as one cuts down either the thickness of the 

 target or the aperture of the beam of fragments, one reduces the 

 number of fragments which come to the detecting apparatus, and 

 reaches a limit when this number becomes too small to be observed 

 in any convenient time. Progress in approaching ideal conditions 

 therefore depends on progress in multiplying the number of fragments 

 by multiplying the strength of the bombarding beam. We may count 

 on a yet greater steepening of such steps as those of Fig. 8, when the 

 enormous streams of bombarding protons produced by Oliphant and 

 Rutherford are applied to very thin films and the distribution-in-range 

 of the resulting fragments is measured. A corresponding improvement 

 of the curves obtained when alpha-particles are the bombarders is 

 still in the not-immediate future. Whether under ideal conditions 

 the steps would be absolutely perpendicular, and all the fragments of 

 a group have exactly the same speeds, is not as yet to be safely inferred 

 from the data. 



There remains the great problem of converting distribution-in-range 

 curves into distribution-in-speed or distribution-in-energy curves, and 

 thus determining the energy or the speed of fragments belonging to 

 a group of which the range is known. The recent developments of 

 research in transmutation and in cosmic rays have elevated this to 

 the rank of the major problems of physics. For alpha-particles of 

 ranges of 8.6 crn. and less, it is practically solved by empirical means; 

 for such alpha-particles are supplied in such abundance by radioactive 



