The Captain sat at a table, and the seven winners were shown in to receive their prizes. “What is your name?” he said to the boy in the first class, as he shook hands with him. “Smith,” replied the boy. “Dear me,” said the Captain, “how odd that our names should be the same. Never mind, it’s a good name. Here’s your cake. Good-bye, Smith.” Then up came the boy from the second class. “What is your name?” said the Captain. “Smith, sir,” was the reply. “Dear me,” said the visitor. “This is very singular. It is indeed a very curious coincidence that two Smiths should have succeeded. Were you really chosen by drawing lots?” “Yes, sir,” said the boy. “Then are all the boys in your class named Smith?” “No, sir; I’m the only one of that name in the ten.” “Well,” said the Captain, “it really is most curious. I never heard anything so extraordinary as that two namesakes of my own should happen to be the winners. Now then for the boy from class three.” A cheerful youth advanced with a smile. “Well, at all events,” said the good-natured old boy, “your name is not Smith?” “Oh, but it is,” said the youth. The gallant Captain jumped up, and declared that there must have been some tremendous imposition. Either the whole school consisted of Smiths, or they called themselves Smiths, or they had picked out the Smiths. The four remaining boys, still expecting their cakes, here burst out laughing. “What are your names?” shouted the donor. “Smith!” “Smith!!” “Smith!!!” “Smith!!!!” were the astounding replies. The good man could stand this no longer. He sent for the schoolmaster, and said, “I particularly requested that you would choose a boy drawn by lot from each of your seven classes, but you have not done so. You have merely picked out my namesakes and sent them up for the cakes.” But the master replied, “No, I assure you, they have been honestly chosen by lot. Nine black beans and one white bean were placed in a bag; each class of ten then drew in succession, and in each class it happened that the boy named Smith drew the white bean.”
“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.
We have spoken so far of the great planets only, and we have seen how the probability stands. We should also remark that there are also nearly 500 small planets, or asteroids, as they are more generally called. Among them are, no doubt, a few whose orbits have inclinations to the ecliptic larger than those of the great planets. The great majority of the asteroids revolve, however, very close to that remarkable plane with which the orbits of the great planets so nearly coincide. Every one of these asteroids increases the improbability that the planes of the orbits could have been arranged as we find them, without some special disposing cause. It is not possible or necessary to write down the exact figures. The probability is absolutely overwhelming against such an arrangement being found if the orbits of the planets had been decided by chance, and chance alone.
We may feel confident that there must have been some particular circumstances accompanying the formation of the solar system which rendered it absolutely necessary for the orbits of the planets to possess this particular characteristic. We have pointed out in Chapter XII. that the nebular theory offers such an explanation, and we do not know of any other natural explanation which would be worthy of serious attention. Indeed, we may say that no other such explanation has ever been offered.
CHAPTER XV.
THE SECOND CONCORD.
Another Remarkable Coincidence in the Solar System—The Second Concord—The Direction of the Movements of the Great Planets—The Movement of Ceres—Yet Another Planet—Discovery of Eros—The Nearest Neighbour of the Earth—Throwing Heads and Tails—A Calculation of the Chances—The Numerical Strength of the Argument—An Illustration of the Probability of the Origin of the Solar System from the Nebula—The Explanation of the Second Concord offered by the Nebular Theory—The Relation of Energy and Moment of Momentum—Different Systems Illustrated—That all the Movements should be in the same Direction is a Consequence of Evolution from the Primæval Nebula.
WE have seen in the last chapter that there is a very remarkable concordance in the positions of the planes of the orbits of the planets, and we have shown that this concordance finds a natural historical explanation in the nebular origin of our system. We have now to consider another striking concord in the movements of the planets in their several orbits, and this also furnishes us with important evidence as to the truth of the nebular theory. The argument on which we are now to enter is one which specially appealed to Laplace, and was put forward by him as the main foundation of the nebular theory.
