152 PENETRATION PHENOMENA IN LIQUID WATER 



does not mean, of course, that binding of an atom in a molecule has no 

 effect on its stopping power. Rather, it implies that the binding of an 

 atom in different molecules has approximately the same effect on its 

 stopping power in each. Since the demands of valence lead to an ap- 

 proximate uniformity in conditions of binding, this is certainly reason- 

 able. 



If one would search for a disagreement with the Bragg rule, he should 

 investigate different compounds of an atom in which the nature of the 

 chemical binding is known to differ greatly. Furthermore, the atom 

 should be as light as possible, for binding affects only the valence elec- 

 trons, so that it is for the lightest atoms that the effect will be most pro- 

 nounced. How great the effect may be is easily estimated to order of 

 magnitude but is not known with any certainty. As mentioned above, 

 theory has thus far provided no quantitative information, and, more- 

 over, experimental stopping-power data are not yet accurate enough to 

 shed light on the question. As a rule, investigators have greatly under- 

 estimated the systematic errors in their measurements; and in inter- 

 pretations such vital factors as the velocity dependence of the relative 

 stopping power, the distinction between relative range and relative 

 stopping power, and necessary corrections to the Bethe stopping-power 

 formula have all too often been disregarded or dealt with inadequately. 

 The writer views with some skepticism the claims of many stopping- 

 power data to an accuracy of ± 1 per cent or better. Even the accepted 

 values for the stopping powers of air, surely the most carefully in- 

 vestigated of any substance, have changed as much as 5 per cent be- 

 tween 1937 (11) and 1950 (12). In perhaps the most thorough analysis 

 of the validity of the Bragg rule yet made, Gray (10) concluded that the 

 atomic Sr values are additive in molecules in almost all cases to within 

 ±1 per cent. This conclusion, based upon data for alpha particles in 

 the 5- to 9-Mev energy region, would probably be equally valid for the 

 true stopping powers. However, it is, perhaps, also an underestimate. 

 Whereas in many cases the Bragg-rule discrepancy may indeed be 1 per 

 cent or smaller, in others it may ultimately be found to be somewhat 

 greater — perhaps 2 or 3 or even 5 per cent. That it will ever be found 

 to be very much greater than the last figure for any gas (except at very 

 low particle velocities) is most unlikely. The entire problem is cer- 

 tainly ripe for refined reinvestigation. It would seem that among the 

 most promising cases are those for which large discrepancies have al- 

 ready been reported. Thus, to cite only a few: Schmieder (14) found 

 "the" stopping powers of N2O to be 92 per cent, of NO to be 109 per 

 cent, and of NO2 to be 113 per cent, of the respective Bragg-rule pre- 

 dictions; data of Gibson and Eyring (15) lead to a stopping power of 



