564 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1962 



Tlie 600,000 years' duration of the Paleolithic era is based on the 

 assumption that manlike types were then in existence but in very small 

 numbers. Earlier dates have been given a few species by certain 

 authorities, but some of these dates are questionable, and the earlier 

 species may have been considerably less than manlike. The 600,000- 

 year period seems a reasonable compromise between extreme 

 possibilities. 



Once the number of births at the dates indicated was determined, 

 the total number of births for each period was calculated at a constant 

 rate of increase for the period. 



The estimated rates of increase differ sharply. For the long Paleo- 

 lithic period, the average annual rate of increase was only 0.02 per 

 thousand; during 6000 B.C. to A.D. 1650, it rose to 0.6; and during 

 1650-1962, it reached 4.35. 



For the figures derived here, the following equation was used: 



r 



Bo is the number of births per year at the beginning of the period ; 

 t is the number of years in the period ; e is the base of natural loga- 

 rithms ; and r is the annual rate of increase during the period. 



The value of r is obtained by solving for r the equation ^5'=^*"' 



where Bo is the number of births the first year of the period, and Bt is 

 the number of births the final year of the period. 



SOURCES 



In the preparation of this Bulletin, the following sources were consulted. The 

 reader is referred to them for additional information. 



1. Bennett, M. K. The world's food. New York, Harper and Brothers, 1954. 



2. Braidwood, Robeet J. Near Eastern prehistory. Science, vol. 127, No. 3312, 



June 20, 195S. 



3. Brown, Harrison. The challenge of man's future. New York, The Viking 



Press, 1954. 



4. Carr-Saunders, A. M. World population, past growth and present trends. 



Oxford, Clarendon Press, 1936. 



5. Collier, John. Indians of the Americas. New York, New American Library 



of World Literature, 1947. 



6. Cook, Robert C. World population growth. Law and Contemporary Prob- 



lems (a quarterly published by the Duke University School of Law), vol. 

 25, No. 3, summer 1960. 



7. DuBAND, John. Mortality estimates from Roman tombstone inscriptions. 



Amer. Journ. Sociol., vol. 45, No. 4, January 1960. 

 S. Huxley, Julian. New bottles for new wine. New York, Harper and 



Brothers, 1957. 

 9. Kboeber, a. L. Anthropology. New York, Harcourt, Brace and Company, 



1948. 

 10. Russell, J. C. Late ancient and medieval population. Trans. Amer. Philos. 



Soc, n.s., VOL 48, pt. 3, June 1958. 



