850 J. BARRELL MEASUREMENTS OF GEOLOGIC TIME 



(c) It is found that in fresh, primary, nraninm-hearing minerals of 

 the same geological age the amount of lead is closely proportional to 1;hat 

 of uranium — that is to say, the ratio Pb/U (referred to as the lead ratio) 

 is practically constant. For each gram of uranium in a mineral the 

 amount of lead generated and accumulated is the same as in any other 

 mineral of equal antiquity, always provided that no lead has been lost or 

 gained from external sources during the period concerned. 



(d) When series of minerals of different ages are compared it is found 

 that the lead ratios vary in sympathy with those ages. The older the 

 mineral the higher is the lead ratio. 



The rate at which lead is generated from uranium can easily be calcu- 

 lated. The rate of production of helium is accurately known, and the 

 mass of lead set free in the same time is roughly 6.5 times that of the 

 helium liberated. In a year one gram of uranium generates 1.25 X 10~^° 

 grams of lead, and at this rate one gram of lead would be produced in 

 8,000 million years.''® If a mineral contains a percentage of accumulated 

 lead of radioactive origin represented by Pb, and a percentage of uranium 

 represented by U, then the age of the mineral is given approximately^''' by 

 the expression: 



Pb 



-^r X 8,000 million years (or, using tlie latter value, 



Pb 



-— X 7,500 million years. — J. B.). 



Before applying this method to the actual measurement of geological 

 time, it is necessary to examine closely a number of assumptions which 

 are implied. It is clear that if any lead should have been originally 

 present in a radioactive mineral at the time of its genesis, a serious diffi- 

 culty will have arisen. In all the ordinary minerals of igneous rocks, lead 

 is a negligible quantity. The difficulty may often be overridden by an- 

 alyzing only those minerals which are much richer in uranium than the 

 main body of the rock. Within them, lead will steadily accumulate, and 

 any original lead will, as time goes on, become of less and less importance 

 in proportion to the whole. The difficulty is not, however, wholly dis- 

 pelled in this simple way. If original lead were to be present in trouble- 



"« Note by .T. B. — The nc\A'er and more accurate determinations of the half-value period 

 of radium and the ratio between the amounts of radium and uranium i-educe this 8,000 

 million years to 7,500 million, as calculated for the writer hy Professor Boltwood. This 

 is the hitherto unpublished mean of various determinations by Boltwood and others. All 

 the calculations by Holmes have been supplemented by the writer, according to this new 

 value, by the addition of a correction in parenthesis which is .9375 of the old value. 

 The results are given, however, to only two or three significant figures. 



s'^ See footnote 98. 



