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But that mathematical knowledge is not–as all Cambridge men are surely aware–the result of any special gift. It is merely the development of those conceptions of form and number which every human being possesses; and any person of average intellect can make himself a fair mathematician if he will only pay continuous attention; in plain English, think enough about the subject.

There are sciences, again, which do not involve mathematical calculation; for instance, botany, zoology, geology, which are just now passing from their old stage of classificatory sciences into the rank of organic ones. These are, without doubt, altogether within the scope of the merest common sense. Any man or woman of average intellect, if they will but observe and think for themselves, freely, boldly, patiently, accurately, may judge for themselves of the conclusions of these sciences, may add to these conclusions fresh and important discoveries; and if I am asked for a proof of what I assert, I point to “Rain and Rivers,” written by no professed scientific man, but by a colonel in the Guards, known to fame only as one of the most perfect horsemen in the world.

Let me illustrate my meaning by an example. A man–I do not say a geologist, but simply a man, squire or ploughman–sees a small valley, say one of the side-glens which open into the larger valleys in the Windsor forest district. He wishes to ascertain its age.

He has, at first sight, a very simple measure–that of denudation. He sees that the glen is now being eaten out by a little stream, the product of innumerable springs which arise along its sides, and which are fed entirely by the rain on the moors above. He finds, on observation, that this stream brings down some ten cubic yards of sand and gravel, on an average, every year. The actual quantity of earth which has been removed to make the glen may be several million cubic yards. Here is an easy sum in arithmetic. At the rate of ten cubic yards a-year, the stream has taken several hundred thousand years to make the glen.

You will observe that this result is obtained by mere common sense. He has a right to assume that the stream originally began the glen, because he finds it in the act of enlarging it; just as much right as he has to assume, if he find a hole in his pocket, and his last coin in the act of falling through it, that the rest of his money has fallen through the same hole. It is a sufficient cause, and the simplest. A number of observations as to the present rate of denudation, and a sum which any railroad contractor can do in his head, to determine the solid contents of the valley, are all that are needed. The method is that of science: but it is also that of simple common sense. You will remember, therefore, that this is no mere theory or hypothesis, but a pretty fair and simple conclusion from palpable facts; that the probability lies with the belief that the glen is some hundreds of thousands of years old; that it is not the observer’s business to prove it further, but other persons’ to disprove it, if they can.

But does the matter end here? No. And, for certain reasons, it is good that it should not end here.

The observer, if he be a cautious man, begins to see if he can disprove his own conclusions; moreover, being human, he is probably somewhat awed, if not appalled, by his own conclusion. Hundreds of thousands of years spent in making that little glen! Common sense would say that the longer it took to make, the less wonder there was in its being made at last: but the instinctive human feeling is the opposite. There is in men, and there remains in them, even after they are civilised, and all other forms of the dread of Nature have died out in them, a dread of size, of vast space, of vast time; that latter, mind, being always imagined as space, as we confess when we speak instinctively of a space of time. They will not understand that size is merely a relative, not an absolute term; that if we were a thousand times larger than we are, the universe would be a thousand times smaller than it is; that if we could think a thousand times faster than we do, time would be a thousand times longer than it is; that there is One in whom we live, and move, and have our being, to whom one day is as a thousand years, and a thousand years as one day. I believe this dread of size to be merely, like all other superstitions, a result of bodily fear; a development of the instinct which makes a little dog run away from a big dog. Be that as it may, every observer has it; and so the man’s conclusion seems to him strange, doubtful: he will reconsider it.