“But,” said the visitor, “this is not credible. Only once in ten million times would all the seven Smiths have drawn the white beans if left solely to chance. And do you mean to tell me that what can happen only once out of ten million times did actually happen on this occasion—the only occasion in my life on which I have attempted such a thing? I don’t believe the drawing was made fairly by lot. There must have been some interference with the operation of chance. I insist on having the lots drawn again under my own inspection.” “Yes, yes,” shouted all the other boys. But all the successful Smiths roared out, “No.” They did not feel at all desirous of another trial. They knew enough of the theory of probabilities to be aware that they might wait till another ten million fortunate old boys came back to the school before they would have such luck again. The situation came to a deadlock. The Captain protested that some fraud had been perpetrated, and in spite of their assurances he would not believe them. The seven Smiths declared they had won their cakes honestly, and that they would not surrender them. The Captain was getting furious, the boys were on the point of rebellion, when the schoolmaster’s wife, alarmed by the tumult, came on the scene. She asked what was the cause of the disturbance. It was explained to her, and then Captain Smith added that by mathematical probabilities it was almost inconceivable that the only seven Smiths in the school should have been chosen. The gracious lady replied that she knew nothing, and cared as little, about the theory of probabilities, but she did care greatly that the school should not be thrown into tumult. “There is only one solution of this difficulty,” she added. “It is that you forthwith provide cakes, not only for the seven Smiths, but for every one of the boys in the school.” This resolute pronouncement was received with shouts of approval. The Captain, with a somewhat rueful countenance, acknowledged that it only remained for him to comply. He returned, shortly afterwards, to his gold-diggings in Australia, there to meditate during his leisure on this remarkable illustration of the theory of probabilities.
This parable illustrates the improbability of such arrangements as we find in the planets having originated by chance. The chances against their having thus occurred are 10,000,000 to 1. Hence we find it reasonable to come to the conclusion that the arrangement, by which the planets move round the sun in planes which are nearly coincident, cannot have originated by chance. There must have been some cause which produced this special disposition. We have, therefore, to search for some common cause which must have operated on all the planets. As the planets are at present absolutely separated from each other, it is impossible for us to conceive a common cause acting upon them in their present condition. The cause must have operated at some primæval time, before the planets assumed the separate individual existence that they now have.