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CHAPTER X.

ON MECHANICAL NOTATION.

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376. IN complex machines of which the parts move according to different laws, and with continually varying relations of velocity and direction, it becomes exceedingly difficult to retain in the mind all the cotemporaneous movements; and a notation is in such cases of almost indispensable service. I have already shewn how in this manner the trains of machines that move with a constant velocity ratio and directional relation may be conveniently represented; and shall now proceed to explain how the more complicated connexions and motions of the last two Chapters may be reduced to notation. The only writer who has endeavoured to form a system for this purpose is Mr. Babbage. method is not a mere hypothetical device framed to meet an imaginary difficulty; but actually arose from the necessity of the case, during the construction and arrangement of one of the most involved and complicated engines that was ever devised; and having been thus applied to practice, has been found to answer its purpose perfectly. Some parts of this notation belong to mechanical combinations of which we have not yet spoken; I shall therefore, in this place, give an account of the system only so far as it applies to the contrivances hitherto explained*.

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377. Every one who has been engaged in the construction and invention of complex machinery, or who attempts

Vide "A method of expressing by signs the action of machinery," by C. Babbage, Esq., Phil. Tr. 1826, from which paper the following account of the method is derived.

to examine the various motions of an existing machine which is presented to him for the first time, must have experienced great inconvenience from the difficulty of ascertaining from drawings the state of motion or rest of any individual part at any given instant of time; and if it becomes necessary to enquire into the state of several parts at the same moment, the labour is much increased.

In the description of machinery by means of drawings, it is generally only possible to represent an engine in one particular state of its action. If indeed it is very simple in its operation, a succession of drawings may be made of it in each state of its progress, which will represent its whole course; but this rarely happens, and is attended with the inconvenience and expense of numerous drawings.

The difficulty of retaining in the mind all the cotemporaneous and successive movements of a complicated machine, and the still greater difficulty of properly timing movements which had already been provided for, led at length to the investigation of a method by which at a glance the eye might select any particular part, and find at any given time its state of motion or rest, its relation to the motion of any other part of the machine, and, if necessary, trace back the sources of its movement through all its successive stages, to the original moving power. The forms of ordinary language being far too diffuse to be employed in this case, and experience having shewn the vast power which analysis derives from the great condensation of meaning in its notation, the language of signs was resorted to for the present purpose.

378. To make the system more easily intelligible, it will be better to apply it as we go on to some machine. The example taken for this purpose in the original paper is a complete eight-day clock with going and striking parts;

but this machine is so complex as to require a large folio plate for its notation, as well as other plates to explain its construction. I shall therefore take a simpler machine, a common saw-mill. Although this machine is so easily understood as not to require the assistance of a notation, it will answer the purpose of exemplifying the method as well, and perhaps better, than a more complicated arrangement.

Fig. 197 is a diagram to explain the connexion of parts

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in the saw-mill, but is not drawn with any attention to the exact proportion or arrangement, which may be found in any encyclopædia or elementary book of machinery. A is a toothed wheel which may be supposed to be driven either by a water-wheel, or steam-engine, and its teeth are engaged with those of a second and smaller wheel B, on whose axis is fixed a crank C and an excentric E. The crank is connected by a link c with the saw-frame D; this is fitted between vertical guides, and therefore when the crank revolves receives a vertical oscillating motion.

The timber W which is submitted to the action of the saw is clamped to a carriage which moves upon rollers m, n, in a horizontal direction. While the saw is in motion as above described, the carriage and timber are made to

advance in the following manner. The excentric E communicates an oscillating motion to a lever ef, whose center of motion is f; this lever carries a click F, which acts upon the teeth of a ratchet-wheel G, to which an intermittent rotation is thus given. Upon the axis of G is a pinion H, which geering with a rack fixed to the wood-carriage, causes the latter to advance towards the saw with the same intermittent motion. This intermission is adjusted to the motion of the saw-frame, so that when the saw rises the wood shall advance, and when the saw descends, and therefore cuts, the wood shall remain at rest. The cut is made by the inclined position of the saw, the toothed edge of which is not vertical but slightly inclined forwards, so as to bring the teeth into successive action during the descent of the frame. The detent L serves to hold the ratchet-wheel, and therefore the wood-carriage, firm in its position during the cut. Now all these conditions of motion are very easily represented by the notation which we shall proceed to explain, and which is exhibited in the next page.

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