SECT. 3] AGE DETERMINATION IN SEDIMENTS BY NATURAL RADIOACTIVITY 827 



slant. Piggot and Urry (1939) used for age determination the hypothesis 

 proposed by Pettersson (1937) that thorium is precipitated in ocean water. 

 They assumed that the concentration of uranium-unsupported ionium is 

 constant in each type of sediment. 



The difficulties in connection with these assumptions are many. A variation 

 of the concentration of a radioactive element in the sediment can be caused by 

 decay or changes of rate of sedimentation when we assume ionium is precipi- 

 tated at a constant rate or by changes in the nature of the sediment. Further- 

 more, diffusion of radium was not considered. It was shown by Picciotto and 

 Wilgain in Picciotto (1960) that this is sometimes the case in old sediments but 

 never in recent sediments, where a diflFusion of radium is always found. The 

 difficulty arising is evident, as variations in the concentration of ionium in the 

 sediment may be caused by decay or by changes in the rate of sedimentation, 

 as outlined above. 



If the assumptions of Piggott and Urry are accepted as valid, a change in the 

 character of the sediment must be accompanied by a change in the concentra- 

 tion of ionium. Since very few deep-sea sediments are homogeneous in their 

 composition, it is impossible to know the original ionium concentration by 

 only knowing the type of sediment. Small variations in concentrations Of 

 ionium, then, may be attributed either to changes in the type of sediment or 

 to the decay of ionium. If Pettersson's assumption is adopted, variations in 

 the concentrations of ionium may be caused by the decay of ionium, thereby 

 making the determination of age possible, or by a change in the rate of sedi- 

 mentation. In the latter case, age cannot be determined, since the change in 

 the rate of sedimentation is not known. 



Both investigators encountered an additional difficulty in the fact that, at 

 that time, no attempt had been made to determine the thorium-230 directly 

 and only radium was measured. It was thereby assumed that radium was in 

 equilibrium with ^soxh. If this assumption is correct, at least for the period 

 earlier than 10,000 years ago when radium had reached secular equilibrium 

 with ionium, the following considerations are applicable. 



The ionium or the radium content is obtained as a concentration in the 

 sediment, c. It can be assumed that for the time instant when the sediment 

 settles, ionium and the sediment settle independently, having the setting rates 

 i^ and s^. The concentration of ionium is then 



cO = iojs^ gig. (15) 



After t years the concentration of ionium becomes 



c{t) = cO{t)e-^t. (16) 



The age is then given by 



t= -l/A[lnc(0 + hi.9(0-hi rO(/)]. (17) 



It is obvious that, since A is known and c{t) can be measured, assumptions 



