Before proceeding to discuss certain aspects of modern atomic theory, I may perhaps be allowed to say a word as to the object of atomic theories in general. Most of us will, I suppose, agree that the object of physical theories is to set up a conceptual scheme which shall make it easier for us to classify and describe the experimental results in which we are interested, by providing, among other things, criteria which shall enable us to distinguish the essential from the unessential, and a scale of values which shall give us help in selecting for investigation certain problems from the infinite field before us. Every important theory is bound to bring into prominence research on certain groups of phenomena at the expense of research on other groups of phenomena: thus the general result of the electron theory is that in any physical laboratory three men out of four are working with vacua, and we see them staring intently at glass tubes with nothing, or very little, shut up in them. An immense number of beautiful results have come from these researches, exhibiting that order which is the true object and delight of the natural philosopher. A few experiments occasioned the original theory: the theory has provided the incentive for a vast number of further experiments, by suggesting for them a significance which would otherwise be lacking. The problem of the connection between radiation, matter and electricity occupies the thoughts of many of the best brains in physical science. This is a result of the electron theory; and this concentration on one problem inevitably draws attention away from other problems. Relatively little is being done, for instance, on the theory of solids, especially in the great problem of cohesion, not because it lacks interest or importance—it has intrigued natural philosophers since scientific speculation began—but because there is no simple, mentally manageable theory to guide us.

As the outcome of a short but occasionally painful experience of mathematical papers, I would suggest that such a paper, if it is to be of any interest at all to the majority of those to whom it is addressed, must necessarily be boring to some of them. It is therefore with this explanation that I am trying to put before you results which are not in any sense new, which are, indeed, the stock-in-trade of the present-day analyst, and therefore well known to many here, but which may interest some whose studies have not lain in this particular direction.