and as the air-pump piston is always brought down by its own weight and that of its rod, the connection of the air-pump piston-rod with the beam, by any contrivance of the kind now described, was not so necessary. Nevertheless, by a slight addition to the mechanical contrivance which has been just described, Watt obtained the means of at once preserving the true rectilinear motion of both piston-rods.

Let the lever represented by o p in fig. 36. be conceived to be prolonged to twice its length, as represented in fig. 37., so

that o p shall be twice o P.

Let the points P p be connected by a link as before. Let a link P'', equal in length to the link P p be attached to the point P', and let the extremity of this link be connected with the point p by another link, equal in length to P P', by pivots at x' and p, so that the figure PP x' P shall be a jointed parallelogram, the angles of which will be capable of altering their magnitude with every change of position of the rods op and o P. Thus, when the rod op descends, the angles of the parallelogram at P and x will be diminished in magnitude, while the angles at P' and p will be increased in magnitude. Now, let a line be conceived to be drawn from o to x. It is evident that that line will pass through the middle point of the link p P, for the triangle o P x is in all respects similar to the greater triangle OP'x' only on half the scale, so that every side of the one is

half the corresponding side of the other.

Therefore P x is half the length of p' x'; but P' x' was made equal to Pp, and therefore p x is half of P p, that is to say, x is the middle point of p p.

It has been already shown, that in the alternate motion of the rods op, op in ascending and descending, the point x is moved upwards and downwards in a true vertical line. Now since the triangle o P x is in all respects similar to o P' x', and subject to a similar motion during the ascent and descent of the rods, it is apparent that the point a must be subject to a motion in all respects similar to that which affects the points x, except that the point will move through double the space. In fact, the principle of the mechanism is precisely similar to that of the common pantograph, where two rods are so connected as that the motion of the one governs the motion of the other, so that whatever line or figure may be described by one, a similar line or figure must be described by the other. Since, then, the point x is moved upwards and downwards in a vertical straight line, the point a' will also be moved in a vertical straight line of double the length.

If such an arrangement of mechanism as has been here described can be connected with the beam of the steam engine, so that while the point a' is attached to the top of the steam piston, and the space through which it ascends and descends shall be equal to the length of the stroke of that piston, the point shall be attached to the rod of the air-pump piston, the stroke of the latter being half that of the steam piston, then the points x and x will guide the motion of the two pistons so as to preserve them in true vertical straight lines.

The manner in which these ideas are reduced to practice admits of easy explanation: let the point o be the centre of the great working beam, and let o p' be the arm of the beam on the side of the steam cylinder. Let p be a pivot upon the beam, at the middle point between its centre o and its extremity p'; and let the links PP, P' x', and P p be jointed together, as already described. Let the point or pivot o be attached to some part of the fixed framing of the engine or engine house, and let the rod o p, equal to half the arm of the beam, be attached by a pivot to the corner of the parallelogram at

p. Let the end of the steam piston-rod be attached to the corner of the parallelogram x', and let the end of the airpump be attached to the middle point x of the link Pp; by which arrangement it is evident that the rectilinear motion of the two piston-rods will be rendered compatible with the alternate circular motions of the points P' and P on the

beam.

Among the many mechanical inventions produced by the fertile genius of Watt, there is none which has excited such universal, such unqualified, and such merited admiration as that of the parallel motion. It is indeed impossible, even for an eye unaccustomed to view mechanical combinations, to behold the beam of a steam engine moving the pistons, through the instrumentality of the parallel motion, without an instinctive feeling of pleasure at the unexpected fulfilment of an end by means having so little apparent connection with it. When this feeling was expressed to Watt himself, by those who first beheld the performance of this exquisite mechanism, he exclaimed with his usual vivacity, that he himself, when he first beheld his own contrivance in action, was affected by the same sense of pleasure and surprise at its regularity and precision. He said, that he received from it the same species of enjoyment that usually accompanies the first view of the successful invention of another person.

"Among the parts composing the steam engine, you have doubtless," says M. Arago, "observed a certain articulated parallelogram. At each ascent and descent of the piston, its angles open and close with the sweetness-I had almost said with the grace-which charms you in the gestures of a consummate actor. Follow with your eye alternately the progress of its successive changes, and you will find them subject to the most curious geometrical conditions. You will see, that of the four angles of the jointed parallelogram, three describe circular arches, but the fourth which holds the piston-rod is moved nearly in a straight line. The immense utility of this result strikes mechanicians with even less force than the simplicity of the means by which Watt has attained it."

The parallel motion, of which there are several other varieties, depending, however, generally upon the same princi

ple, formed part of a patent which Mr. Watt obtained in the year 1784, another part of which patent was for a locomotive engine, by which a carriage was to be propelled on a road. In a letter to Mr. Smeaton dated 22d October, in the same year, Watt says,—

"I have lately contrived several methods of getting entirely rid of all the chains and circular arches about the great levers of steam engines, and nevertheless making the piston-rods ascend and descend perpendicularly, without any sliding motions or right-lined guides, merely by combinations of motions about centres; and with this further advantage, that they answer equally well to push upwards as to pull downwards, so that this method is applicable to our double engines which act both in the ascent and descent of their pistons.

"A rotative engine of this species with the new motion which is now at work in our manufactory (but must be sent away very soon) answers admirably. It has cost much brain work to contrive proper working gear for these double engines, but I have at last done it tolerably well, by means of the circular valves, placed in an inverted position, so as to be opened by the force of the steam; and they are kept shut by the working gear. We have erected an engine at Messrs. Goodwyne and Co.'s brewery, East Smithfield, London."

(121.) By the contrivance which has been explained above, the force of the piston in ascending and descending would be conveyed to the working end of the beam; and the next problem which Watt had to solve was, to produce by the force exerted by the working end of the beam in ascending and descending a continuous motion of rotation. In the first instance he proposed to accomplish this by a crank placed upon the axle to which rotation was to be imparted, and driven by a rod connecting it with the working end of the beam. Let K (fig. 38.) be the centre, to which motion is to be imparted by the working end H of the beam. On the axle к suppose a short lever KI to be fixed so that when KI is turned round the centre K, the axle must turn with it. Let an iron rod, the weight of which shall balance the piston and piston-rod at the other end of the beam, be connected by joints with the working end H of the beam, and the extremity 1 of the

K

I

lever KI. As the end H of the beam is moved upwards and downwards, the lever K I will be turned round the centre K,

Fig. 38.

K

H

taking successively the positions represented by faint lines in the figure; and thus a motion of continued rotation will be imparted to the axle K. This simple and effectual expedient of producing a continued rotatory motion by a crank was abandoned by Watt, as already explained, by reason of a patent having been obtained upon information of his experiments surreptitiously procured. To avoid litigation, he therefore substituted for the crank the sun and planet wheel already described; but at the expiration of the patent, which restricted the use of

the crank, the sun and planet wheel was discontinued in Watt's engine, and the crank restored.

(122.) Whether the crank or the sun and planet wheel be used, there is still a difficulty in the maintenance of a regular motion of rotation. In the various positions which the crank and connecting rod assume throughout a complete revolution, there are two in which the moving power loses all influence in impelling the crank. These positions are those which the crank assumes when the piston is at the top and bottom of the