326 Prof. W. D. Harkins on the 



one writer predicted that all pure atomic species would be 

 found to have atomic weights which are even numbers, and 

 that fluorine, for example, would be found to be a mixture 

 of isotopes of atomic weights 18 and 20, while another 

 predicted that lithium would be found to consist of isotopes 

 of atomic weights 5 and 7. The first of these predictions is 

 at variance with one of the most important of the general 

 atomic weight relations and did not need the findings of the 

 positive ray method to show its falsity. The latter violates 

 an even more general relation, but is more excusable, since 

 the lithium nuclei are the simplest of all of the complex 

 nuclei other than the basic alpha particle, so it might be 

 possible that it would not follow the general relations, which 

 indicate that the atomic weights should be 7 and 6, as pre- 

 dicted by the writer. Since the examples given above are 

 only a small fraction of the erroneous predictions, it seems 

 advisable to list below the most important general relations 

 which seem to determine the existence or non-existence of 

 atomic species. 



Before doing this it seems advisable to call attention to 

 the fact that the positive ray method, while it gives very 

 remarkable results, should not be considered to be an 

 infallible guide in determining just what isotopes exist, since 

 at its present stage of development it will err in not finding 

 those isotopes which exist in small percentages. Just what 

 its limit of detection is does not seem to be known, but it is 

 probable that percentages equal to 1 or less per cent, are 

 practically certain to be missed. It should also be kept in 

 mind that the mathematical theory of the stability of a 

 system so complicated as a complex nucleus is exceedingly 

 involved, and that small changes in the number of nuclear 

 electrons and protons may be expected to produce in some 

 cases very great changes in stability, especially when the 

 number of particles is small. Therefore all that can be 

 expected of a theory is that it will point out correctly the 

 general system, but it must not be expected that it will be 

 able to give the details in every specific instance. 



At the present time the greatest uncertainty which exists 

 in this connexion is that concerning the magnitude of the 

 "packing effect" during the formation of more complex 

 nuclei as compared with that which occurs in the formation 

 of the helium atom from hydrogen. That the packing effect 

 involved in the formation of all known complex atoms from 

 hydrogen is practically a constant and equal to 076 por 

 cent, was first stated and demonstrated by. Harkins and 

 Wilson in 1915, so this was the first definite statement of 



