The Size of the Universe

Before we can discuss the size of the universe it is necessary to define exactly what we are talking about. Astronomers have in the past been somewhat loose in their use of the word universe.'' About ten years ago one of the much-discussed topics of the day was the theory of island universes in the plural ! A universe in that discussion was what we now call a galactic system, a stellar system like our own. As I am using the word tonight, there is only one universe, which contains all these systems, and everything that can be observed and that we can think of as being observable, either now or in the future. The universe is the whole of all things that exist in the physical or outer world. The next question to be considered is : has the universe any size at all? This question, whether the universe is of finite size or infinite, has occupied the minds of some of the greatest of mankind ever since science was born. exists a delightful little tract, written by Archimedes, the greatest of Greek mathematicians, about 200 b.c. It is called On the Grains of Sand and is cast in the form of a letter addressed to the king of Syracuse. It begins as follows : There are those who think, King Gelo, that the number of grains of sand is infinite ; that is, the grains of sand not only in the environs of Syracuse and the rest of Sicily, but also in all parts of the world whether inhabited or uninhabited. Others think that it is not infinite, but that no number can be named so large that it would exceed the said number of grains of sand. It appears that those who think so would still less be able to imagine