AFTER that portion of the Difference Engine which was completed had been for some months promoted from the workshop to my drawing-room, I met two of my friends from Ireland—Dr. Lloyd, the present Provost of Trinity College, and Dr. Robinson, of Armagh. I invited them to breakfast, that they might have a full opportunity of examining its structure. I invited also another friend to meet them—the late Professor Malthus.

After breakfast we adjourned to the drawing-room. I then proceeded to explain the mechanism of the Engine, and to cause it to calculate Tables. One of the party remarked two axes in front of the machine which had not hitherto been performing any work, and inquired for what purpose they were so placed. I informed him that these axes had been so placed in order to illustrate a series of calculations of the {388} most complicated kind, to which they contributed. I observed that the Tables thus formed were of so artificial and abstract a nature, that I could not foresee the time when they would be of any use.

This remark additionally excited their curiosity, and they requested me to set the machine at work to compute such a table.

Having taken a simple case of this kind, I set the Engine to do its work, and then told them—

That it was now prepared to count the natural numbers; but that it would obey this law only as far as the millionth term.

That after that term it would commence a series, following a different, but known law, for a very long period.

That after this new law had been fulfilled for another long period, it would then suddenly abandon it, and calculate the terms of a series following another new law, and so on throughout all time.

Of course it was impossible to verify these assertions by making the machine actually go through the calculations; but, after having made the Engine count the natural numbers for some time, I proceeded to point out the fact, that it was impossible, by its very structure, that the machine could record any but the natural numbers before it reached the number 999,990. This I made evident to my friends, by showing them the actual structure of the Engine. Having dem­on­strated this to their entire sat­is­fac­tion, I put the machine on to the number 999,990, and continued to work the Engine, when the result I had predicted soon arrived. After the millionth term a new law was taken up, and my friends were convinced that it must, from the very structure of the machine, continue for a very long time, and then {389} inevitably give place to another new law, and so on throughout all time.

When they were quite satisfied about this fact, I observed that, in a new engine which I was then contemplating, it would be possible to set it so that—

• 1st. It should calculate a Table for any given length of time, according to any given law.
• 2nd. That at the termination of that time it should cease to compute a Table according to that law; but that it should commence a new Table according to any other given law that might be desired, and should then continue this computation for any other given period.
• 3rd. That this succession of a new law, coming in and continuing during any desired time, and then giving place to other new laws, in endless but known succession, might be continued indefinitely.

I remarked that I did not conceive the time ever could arrive when the results of such calculations would be of any utility. I added, however, that they offered a striking parallel with, although at an immeasurable distance from, the successive creations of animal life, as developed by the vast epochs of geological time. The flash of in­tel­lec­tual light which illuminated the countenances of my three friends at this unexpected juxtaposition was most gratifying.

Encouraged by the quick apprehension with which these views had been accepted, I continued the subject, and pointed out the application of the same reasoning to the nature of miracles.

The same machine could be set in such a manner that these laws might exist for any assigned number of times, whether large or small; also, that it was not necessary that these laws should be different, but the same law might, when {390} the machine was set, be ordered to reappear, after any desired interval.

Thus we might suppose an observer watching the machine, to see a known law continually fulfilled, until after a lengthened period, when a new law has been appointed to come in. This new law might after a single instance cease, and the first law might again be restored, and continue for another interval, when the second new law might again govern the machine as before for a single instance, and then give place to the original law.

This property of a mere piece of mechanism may have a parallel in the laws of human life. That all men die is the result of a vast induction of instances. That one or more men at given times shall be restored to life, may be as much a consequence of the law of existence appointed for man at his creation, as the appearance and reappearance of the isolated cases of apparent exception in the arithmetical machine.

But the workings of machinery run parallel to those of intellect. The Analytical Engine might be so set, that at definite periods, known only to its maker, a certain lever might become moveable during the calculations then making. The consequence of moving it might be to cause the then existing law to be violated for one or more times, after which the original law would resume its reign. Of course the maker of the Calculating Engine might confide this fact to the person using it, who would thus be gifted with the power of prophecy if he foretold the event, or of working a miracle at the proper time, if he withheld his knowledge from those around until the moment of its taking place.

Such is the analogy between the construction of machinery to calculate and the occurrence of miracles. A further illustration may be taken from geometry. Curves are represented {391} by equations. In certain curves there are portions, such as ovals, disconnected from the rest of the curve. By properly assigning the values of the constants, these ovals may be reduced to single points. These singular points may exist upon a branch of a curve, or may be entirely isolated from it; yet these points fulfil by then positions the law of the curve as perfectly as any of those which, by their juxtaposition and continuity, form any of its branches.

Miracles, therefore, are not the breach of established laws, but they are the very circumstances that indicate the existence of far higher laws, which at the appointed time produce their pre-intended results.

In 1835, the British Association visited Dublin. I had been anxious to promote this visit, from political as well as scientific motives. I had several invitations to the residences of my friends in that hospitable country; but I thought I could be of more use by occupying apartments in Trinity College, which had kindly been placed at my disposal by the provost and fellows.

After I had enjoyed the college hospitality during three or four days, I was walking with an intimate friend, who suggested to me that I was giving great cause of offence to my learned hosts. Not having the slightest idea how this could have arisen, I anxiously inquired by what inadvertence I had done so. He observed that it arose from my dress. I looked at the various articles of my costume with a critical eye, and could discover nothing exaggerated in any portion of it. I then begged my friend to explain how I had unconsciously offended in that respect. He replied, “Your waistcoat is of a bright green.” I became still more puzzled, until he remarked that I was wearing O’Connell’s colours in the midst of the Protestant University, whose guest I was. {392}

I thanked my friend sincerely, and requested him to accompany me to my rooms, that I might change the offending waistcoat. My travelling wardrobe was not large, and, unfortunately, we found in it no entirely unobjectionable waistcoat. I therefore put on an under-waistcoat with a light-blue border, and requested him to accompany me to a tailor’s, that I might choose an inoffensive colour. As I was not to remain long in Dublin, I wished to select a waistcoat which might do double service, as not too gay for the morning, and not too dull for the evening.

On arriving at the tailor’s, he placed before me a profusion of beautiful silks, which I was assured contained all the newest and most approved patterns. Out of these I selected ten or a dozen, as best suiting my own taste. I then requested him to remove from amongst them any which might be considered as a party emblem. He took each of them rapidly up, and tossing it to another part of the counter, pronounced the whole batch to appertain to one party or the other.

Thus limited in my choice, I was compelled to adopt a waistcoat of all work, of rather gayer colours than good taste would willingly have selected for morning use. I explained to the knight of the thimble my dilemma. He swore upon the honour of his order that the finished waistcoat should be at my rooms in the college punctually as the clock struck eight the next morning.

During the rest of the day I buttoned up my coat, and the broad light-blue border of my thin under-waistcoat was alone visible. My modesty, however, was a little uneasy, lest it should be thought that I was wearing the decoration of a Guelphic knight.

I rose early the next morning: eight o’clock arrived, but no waistcoat. The college breakfast in the hall was punctual {393} at a quarter past eight; 8·20 had arrived, but still no waistcoat. At last, at half-past eight, the squire of the faithless knight of the thimble arrived with the vest.

Thus equipped, I rushed to the hall, and found that my college friends had waited for my arrival. I explained to the Dean53 that I had been detained by an unpunctual tailor, who had not brought home my waistcoat until half an hour after the appointed time. We then commenced the serious business which assembled us together. The breakfast was superb, and the society delightful. I enjoyed them both, being fortunately quite unconscious that every eye was examining the artistic and Æsthetic garment with which I had been so recently invested. I thus acquired for a time the character of a dandy of the first water. It has not unfrequently been my fate in life to have gained a character for worth or worthlessness upon grounds quite as absurd, which I have afterwards seldom taken the trouble to explain.

The Dean, however, quickly saw through the outer covering, and before the meeting was over I felt that a friendship had commenced which time could only strengthen. One day, whilst we were walking together, MacLean told me that he had heard with great interest from one of his colleagues of some views of mine relative to miracles, which he wished much to hear from my own lips.

I remarked that the explanation of them would require much more time than we could afford during the bustle of the Association; but that I should afterwards, at any quiet time, be delighted to discuss them with him.

After the meeting of the British Association terminated, I made a short tour to visit some of my friends in the North of Ireland. On my return to Dublin I again found MacLean, {394} and had the good fortune to enjoy his society in a tour which we took to Killarney.

One fine morning, as we were walking together, it being Sunday, MacLean, looking somewhat doubtfully at me, asked whether I had any objection to go to church. I replied, “None whatever,” and turned towards the church. Before we reached it an idea occurred to my mind, and I said, “MacLean, you asked me, in the midst of the bustle at Dublin, about my views respecting miracles. Have you any objection to take a walk with me by the side of the lake, and I will give you a sermon upon that subject.”—“Not the least,” replied my friend; and we turned immediately towards the banks of that beautiful lake.

I then proceeded to explain that those views of the apparently successive creations opened out to us by geology are in reality the fulfilment of one far more comprehensive law. I pointed out that a miracle, instead of being a violation of a law, is in fact the most eminent fulfilment of a vast law—that it bears the same relation to an apparent law that singular points of a curve bear to the visible form of that curve. My friend inquired whether I had published anything upon these subjects. On my answering in the negative, he strongly urged me to do so. I remarked upon the extreme difficulty of making them intelligible to the public. Reverting again to the singular points of curves, I observed that the illustration, which in a few words I had placed before him, would be quite unintelligible even to men of cultivated minds not familiar with the doctrine of curves.

We had now arrived at a bench, on which we sat. MacLean, wrapt up in the new views thus opened out to his mind, remained silent for a long interval. At last, turning towards me, he made these remarks: “How wonderful it is! Here {395} am I, bound by the duties of my profession to inquire into the attributes of the Creator; bound still more strongly by an intense desire to do so; possessing, like yourself, the same powerful science to aid my inquiries; and yet, within this last short half hour, you have opened to me views of the Creator surpassing all of which I have hitherto had any conception!”

These views had evidently made a very deep impression on his mind. Amidst the beautiful scenery in the South of Ireland he frequently reverted to the subject; and, having accompanied me to Waterford, offered to cross the Channel with me if I could spend one single day at Milford Haven.

Unfortunately, long previous arrangements prevented this delay. I parted from my friend, who, though thus recently acquired, seemed, from the coincidence of our thoughts and feelings, to have been the friend of my youth. I little thought, on parting, that one whom I so much admired, so highly esteemed, would in a few short months be separated for ever from the friends who loved him, and from the society he adorned.