# Passages from the Life of a Philosopher/Chapter IX

CHAPTER IX.
OF THE MECHANICAL NOTATION.
Soon after I had commenced the Difference Engine, my attention was strongly directed to the imperfection of all known modes of explaining and demonstrating the construction of machinery. It soon became apparent that my progress would be seriously impeded unless I could devise more rapid means of understanding and recalling the interpretation of my own drawings.
By a new system of very simple signs I ultimately succeeded in rendering the most complicated machine capable of explanation almost without the aid of words.
In order thoroughly to understand the action of any machine, we must have full information upon the following subjects, and it is of the greatest importance that this information should be acquired in the shortest possible time.
I. The actual shape and relative position of every piece of matter of which the machine is composed.
This can be accomplished by the ordinary mechanical drawings. Such drawings usually have letters upon them for the sake of reference in the description of the machine. Hitherto such letters were chosen without any principle, ​and in fact gave no indication of anything except the mere spot upon the paper on which they were written.
I then laid down rules for the selection of letters. I shall only mention one or two of them:—
1. All upright letters, as a, c, d, e, A, B, represent framing.
2. All inclined letters, as a, c, d, e, A, B, represent moveable parts.
3. All small letters represent working points. One of the most obvious advantages of these rules is that they enable the attention to be more easily confined to the immediate object sought.
By other rules it is rendered possible, when looking at a plan of any complicated machine, to perceive the relative order of super-position of any number of wheels, arms, &c., without referring to the elevation or end view.
II. The actual time and duration of every motion throughout the action of any machine can be ascertained almost instantly by a system of signs called the Notations of Periods.
It possesses equal facilities for ascertaining every contemporaneous as well as for every successive system of movements.
III. The actual connection of each moveable piece of the machine with every other on which it acts. Thus, taking from any special part of the drawing the indicating letter, and looking for it on a certain diagram, called the trains, the whole course of its movements may be traced, up to the prime mover, or down to the final result.
I have called this system of signs the Mechanical Notation. By its application to geometrical drawing it has given us a new demonstrative science, namely, that of proving that any given machine can or cannot exist; and if it can exist, that it will accomplish its desired object.
​It is singular that this addition to human knowledge should have been made just about the period when it was beginning to be felt by those most eminently skilled in analysis that the time has arrived when many of its conclusions rested only on probable evidence. This state of things arose chiefly from the enormous extent to which the developments were necessarily carried in the lunar and planetary theories.
After employing this language for several years, it was announced, in December 1825, that King William IV. had founded two medals of fifty guineas each, to be given annually by the Royal Society according to rules to be laid down by the Council.
On the 26th January 1826, it was resolved,
"That it is the opinion of the Council that the medals be awarded for the most important discoveries or series of investigations, completed and made known to the Royal Society in the year preceding the day of the award."
This rule reduced the number of competitors to a very few. Although I had had some experience as to the mode in which medals were awarded, and therefore valued them accordingly, I was simple enough to expect that the Council of the Royal Society would not venture upon a fraud on the very first occasion of exercising the royal liberality. I had also another motive for taking a ticket in this philosophical lottery of medals.
In 1824, the Astronomical Society did me the honour to award to me the first gold medal they ever bestowed. It was rendered still more grateful by the address of that eminent man, the late Henry Thomas Colebrooke, the President, who in a spirit of prophecy anticipated the results of years, at that period, long future.
​"It may not, therefore, be deemed too sanguine an anticipation, when I express the hope that an instrument which in its simpler form attains to the extraction of the roots of numbers, and approximates to the roots of equations, may, in a more advanced state of improvement, rise to the approximate solutions of algebraic equations of elevated degrees. I refer to solutions of such equations proposed by Lagrange, and more recently by other analysts, which involve operations too tedious and intricate for use, and which must remain without efficacy, unless some mode be devised of abridging the labour or facilitating the means of performance."
I felt, therefore, that the first Royal Medal might fairly become an object of ambition, whatever might be the worth of subsequent ones.
In order to qualify myself for this chance, I carefully drew up a paper, "On a Method of expressing by Signs the Action of Machinery," which I otherwise should not have published at that time.
This Memoir was read at the Royal Society on the 16th March, 1826. To the system of signs which it first expounded I afterwards gave the name of "Mechanical Notation." It had been used in England and in Ireland, although not taught in its schools. It applies to the description of a combat by sea or by land. It can assist in representing the functions of animal life; and I have had both from the Continent and from the United States, specimens of such applications. Finally, to whatever degree of simplicity I may at last have reduced the Analytical Engine, the course ​through which I arrived at it was the most entangled and perplexed which probably ever occupied the human mind. Through the aid of the Mechanical Notation I examined numberless plans and systems of computings and I am sure, from the nature of its self-necessary verifications that it is impossible I can have been deceived.
On the 16th November, 1826, that very Council of the Royal Society which had made the law took the earliest opportunity to violate it by awarding the two Royal Medals, the first to Dalton, whose great discovery had been made nearly twenty years before, and the other to Ivory, for a paper published in their "Transactions" three years before. The history of their proceedings will be found in the "Decline of Science in England," p. 115, 1830.