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times in a second? or that there exist animated and regularly organised beings many thousands of whose bodies laid close together would not extend to an inch? But what are these to the astonishing truths which modern optical inquiries have disclosed, which teach us that every point of a medium through which a ray of light passes is affected with a succession of periodical movements, recurring regularly at equal intervals, no less than five hundred millions of millions of times in a second; that it is by such movements communicated to the nerves of our eyes that we see; nay, more, that it is the difference in the frequency of their recurrence which affects us with the sense of the diversity of colour; that, for instance, in acquiring the sensation of redness, our eyes are affected four hundred and eighty-two millions of millions of times ; of yellowness, five hundred and forty-two millions of millions of times; and of violet, seven hundred and seven millions of millions of times per second?1 Do not such things sound more like the ravings of madmen than the sober conclusions of people in their waking senses? They are, nevertheless, conclusions to which any one may most certainly

1 Young's Lectures on Natural Philosophy, ii. 627. See also Phil. Trans., 1801-2.

arrive who will only be at the pains of examining the chain of reasoning by which they have been obtained."

A man counting as hard as he can repeat numbers one after another, and never counting more than a hundred, so that he shall have no long words to repeat, may perhaps count ten thousand, or a hundred a hundred times over, in an hour. At this rate, counting night and day, and allowing no time for rest or refreshment, he would count one million in four days and four hours, or say four days only. To count a million a million times over, he would require four million days, or roughly ten thousand years; for five hundred millions of millions, he must have the utterly unrealisable period of five million years. Yet he actually goes through this stupendous piece of reckoning unconsciously hour after hour, day after day, it may be for eighty years, often in each second of daylight; and how much more by artificial or subdued light I do not know. He knows whether his eye is being struck five hundred millions of millions of times, or only four hundred and eighty-two millions of millions of times. He thus shows that he estimates or counts each set of vibrations, and registers them according to his results. If a man writes upon the back of a British Museum blottingpad of the common nonpareil pattern, on which there are some thousands of small spaces each differing in colour from that which is immediately next to it, his eye will, nevertheless, without an effort assign its true colour to each one of these spaces. This implies that he is all the time counting and taking tally of the difference in the numbers of the vibrations from each one of the small spaces in question. Yet the mind that is capable of such stupendous computations as these so long as it knows nothing about them, makes no little fuss about the conscious adding together of such almost inconceivably minute numbers as, we will say, 2730169 and 5790135 —or, if these be considered too large, as 27 and 19. Let the reader remember that he cannot by any effort bring before his mind the units, not in ones, but in millions of millions of the processes which his visual organs are undergoing second after second from dawn till dark, and then let him demur if he will to the possibility of the existence in a germ, of currents and undercurrents, and rhythms and counterrhythms, also by the million of millions—each one of which, on being overtaken by the rhythm from without that chimes in with and stimulates it, may be the beginning of that unsettlement of equilibrium which results in the crash of action, unless it is timely counteracted.

If another objector maintains that the vibrations within the germ as above supposed must be continually crossing and interfering with one another in such a manner as to destroy the continuity of any one series, it may be replied that the vibrations of the light proceeding from the objects that surround us traverse one another by the millions of millions every second yet in no way interfere with one another. Nevertheless, it must be admitted that the difficulties of the theory towards which I suppose Professor Hering to incline are like those of all other theories on the same subject—almost inconceivably great.

In " Life and Habit" I did not touch upon these vibrations, knowing nothing about them. Here, then, is one important point of difference, not between the conclusions arrived at, but between the aim and scope of the work that Professor Hering and I severally attempted. Another difference consists in the points at which we have left off. Professor Hering, having established his main thesis, is content. I, on the other hand, went on to maintain that if vigour was due to memory, want of vigour was due to want of memory. Thus I was led to connect memory with the phenomena of hybridism and of old age; to show that the sterility of certain animals under domestication is only a phase of, and of a piece with, the very common sterility of hybrids— phenomena which at first sight have no connection either with each other or with memory, but the connection between which will never be lost sight of by those who have once laid hold of it. I also pointed out how exactly the phenomena of development agreed with those of the abeyance and recurrence of memory, and the rationale of the fact that puberty in so many animals and plants comes about the end of development. The principle underlying longevity follows as a matter of course. I have no idea how far Professor Hering would agree with me in the position I have taken in respect of these phenomena, but there is nothing in the above at variance with his lecture.

Another matter on which Professor Hering has not touched is the bearing of his theory on that view of evolution which is now commonly accepted. It is plain he accepts evolution, but it does not appear that he sees how fatal his theory is to any view of evolution except, a teleological one—the purpose residing within the animal and not without it. There is, how

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