That every person in the realm who teaches mathematics should be a member of our Association is an ideal towards which we are converging non-uniformly, if at all. Were this ideal state of things a reality no apology would be needed for a paper dealing with topics which though educationally important are from a mathematical point of view very familiar. As it is, the feeling haunted me as I wrote that I was writing a sermon, and that the people whom it might benefit would not be in the room, were not even members of our Association. As, however, other writers of sermons must, I suppose, sometimes find themselves in a similar position, 1 have ventured to go on.