The following is a memorandum written by the late Richard Chace Tolman, Professor of Physical Chemistry and Mathematical Physics at the California Institute of Technology. The occasion for this investigation was an informal request from his friend of long standing, Dr. Warren Weaver of the Rockefeller Foundation, for his opinion on the current scientific status of the problem of the age of the universe. To answer this Tolman plunged, with characteristic energy and thoroughness, into a study of the relevant findings, and synthesized them in the memorandum here reproduced. We are greatly indebted to Professor H. P. Robertson who has taken care of the final preparations for publication of the manuscript reproduced here