196 ANNUAL EEPOKT SMITHSONIAN INSTITUTION, 19 32 



a moiiomolecular reaction, as first pointed out by Rutherford, and 

 if the disintegration constant is accurately known, the age of a 

 uranium-bearing mineral can be readily and accurately determined, 

 according to the fundamental equation, 



where 



7'c; = half-life period of uranium. 



Uo — nnumnt of uranium originally present. 

 Z7= amount of uranium now present. 

 In practice, however, a number of difficulties are met. Practically all 

 uranium-bearing minerals contain more or less thorium ; therefore the 

 fundamental equation must be modified to take this into account. All 

 equations heretofore used in age computations have been approxima- 

 tions. Furthermore, it can not be assumed, as has been tacitly done 

 in the past, that no common lead was originally deposited in the ura- 

 nium mineral at the time it was formed. Kovarik has developed 

 an accurate formula, which takes account of the possibility that 

 common lead may have been initially present in the mineral that is 

 being used as a geologic chronometer. 



In building up a geologic time scale in years based on atomic disin- 

 tegration, the following conditions should obtain : 



(1) The mineral must be unaltered, i. e., not changed by leaching 

 by surface waters, or by other external processes since it was origi- 

 nally formed. 



(2) The contents of U, Th, and Pb must be determined. Prefer- 

 ably these elements should be present in considerable amounts, so 

 that the analytical errors will be minimized. 



(3) The atomic weight of the lead should be determined, on lead 

 obtained from the material analyzed for U, Th, and Pb. 



(4) The geologic age of the mineral should be known. 



Very few determinations — seven at most — fulfill these requisites. 

 In fact, it has only recently been recognized that these requisites must 

 be rigorously fulfilled, and many currently accepted age determina- 

 tions rest on shaky foundations. It is probable that in the future two 

 more conditions will have to be met: (1) The material should be 

 radiographed, in order to determine its homogeneity, and (2) the 

 ratio of actinium to uranium should be determined. 



The determinations of ages in years that meet the critical re- 

 quirements are given in the subjoined table. The age deter- 

 mination based on the thorite of Brevik, Norway, should on 

 rigorous application of our criteria be excluded, because of the 

 very small amount of lead analytically found, and the possibility 

 that some of the lead was removed by leaching. The computa- 



