In a Rutherford Memorial Lecture there are two alternative courses that might be taken. One is to describe one or other of the great developments that have later followed out from the many things which Rutherford started; the other is to describe some aspect of his own work from a historical point of view. If, as we hope and intend, the institution of these lectures should survive for many years, the first policy will probably be more useful in later times, but there still remain a number of people who lived through the wonderful experiences of those days, and while we survive it may be more interesting perhaps for us to leave some small records of what we saw. But there seems little purpose in merely giving again and again a biography recounting all the things that Rutherford did, and so I have chosen one item from among his discoveries, and I propose to give an account of this. It is the discovery of Atomic Number. I am going to try and give a picture of this whole subject; in it Rutherford of course played the leading part, but others made very important contributions, and it will be the whole history of it that I shall try to describe, and not merely his part in it. In the history of science there has been every now and then what I may call an ‘easy’ discovery, by which I do not in the least mean that it was easy to discover, but that when discovered it is so easy to understand, that it is difficult afterwards to see how people had got on without it. One example of such an ‘easy’ discovery was the discovery by Copernicus that the earth goes round the sun. After his time it was possible for anyone almost to forget what astronomy had been like before his day, and yet we have to recognize that the subject had been studied for three or four thousand years by many exceedingly intelligent men. Atomic number is another such ‘easy’ discovery. Any recent book on chemistry or physics describes the chemical elements in terms of it, and now with the development of atomic energy, even the daily press discusses quite readily the differences between uranium 238 and 235, and possibly even recalls that uranium is element number 92. In all the doubts that we may have about how future scientific discoveries will reshape our outlook on the world, we can feel sure that this one thing will never be changed; that the isotopes of the atoms of chemical elements will always have known atomic numbers and atomic weights. It now seems so simple that it is hard to believe how recently it was all discovered, and I want to show you that this ‘easy’ discovery was not at all easy to make.