we should hail it as better and more satisfying than any of our random imaginings. The universe is in no way limited to our conceptions: it has a reality apart from them; nevertheless, they themselves constitute a part of it, and can only take a clear and consistent character in so far as they correspond with something true and real. Whatever we can clearly and consistently conceive, that is _ipso facto_ in a sense already existent in the universe as a whole; and that, or something better, we shall find to be a dim foreshadowing of a higher reality. * * * * * EXPLANATORY NOTE ON CONSTRUCTIVE THOUGHT AND OPTIMISM. (_Partly reprinted from "Mind."_) It may be worth while to explain how it is that, to a physicist unsmitten with any taint of solipsism, a well-elaborated scheme which is consistent with already known facts necessarily seems to correspond, or have close affinity, with the truth. It is the result of experience of a mathematical theorem concerning unique distributions. For instance, it can be shown that in an electric field, however complicated, any distribution of potential which satisfies boundary conditions, and one or two other essential criteria, must be the actual distribution; for it has been rigorously proved that there cannot be two or more distributions which satisfy those conditions, hence if one is arrived at theoretically, or intuitively, or by any means, it must be the correct one; and no further proof is required. So, also, in connection with analogies and working models: although they must necessarily be imperfect, so long as they are only analogies, yet the making or imagining of models (not necessarily or usually a material model, but a conceptual model) is a recognised way of arriving at an understanding of recondite and ultra-sensual processes, occurring say in the ether or elsewhere. As an addition to evidence derived from such experiments as have been found possible, and as a supplement to the experience out of which, as out of a nucleus, every conception must grow, the mind is set to design and invent a self-coherent scheme which shall imitate as far as possible the results exhibited by nature. By then using this as a working hypothesis, and pressing it into extremes, it can be gradually amended until it shows no sign of discordance or failure anywhere, and even serves as a guide to new and previously unsuspected phenomena. When that stage is reached, it is provisionally accepted and tentatively held as a step in the direction of the truth; though the mind is always kept ready to improve and modify and enlarge it, in accordance with the needs of more thorough investigation and fresh discovery. It was so, for instance, with Maxwell's electromagnetic theory of light; and there are a multitude of other instances.