rotatory motion, and then to measure his power. To do this two catches A B, take into the teeth of the same wheel M, and each catch carries an arm, P, embracing somewhat stiffly the boss of the wheel. The treadles have a common centre at E, and are fastened to the same rope going over a pulley, F, so as for the depression of the one to raise the other. Again, the pulling bars C D, are connected with the treadles, and from the form of the catches, it is evident (since the levers move with some stiffness), that the first effect of an ascending motion will be to draw the rising catch out of the teeth, and keep it out until arrived at its greatest height; when the very beginning of its descending motion will bring the catch into the teeth again, and thus carry round the wheel at every downward movement of the treadle;—a method this of making a ratchet work without rattling upon the wheel.
The mechanism shewn in figure 19, is intended to produce another of our factitious resistances; and it serves likewise to make experiments on the resistance of the air. It is a fly, meeting with an equable resistance as does the fly in the striking train of a clock. The wheel W, is put on the axis of resistance of the Dynamometer; and its teeth geer in those of the vertical shaft L H. This latter is perforated from above, and has an open mortice all along its body, which a small bar penetrates, meeting at bottom the ring H, to which it is fastened by a pin going through the mortice. Again, this ring H, is moved, downward, by the rollers of the sliding bracket P, which has its motion from the wheel and rack G: and finally, the leaves I K slide in the horizontal frame; and when the machine turns would obey the centrifugal force and fly outward; but are withheld by the cords N O, which passing over the pulleys N O, and under those L M, are then fixed to the frame above L. When, now, this Machine is used, and the fly made to revolve swiftly, the leaves I K, oppose a certain resistance to the rotatory motion; and if this be too feeble, the key G must be turned backward, which will permit the ring H to rise, and the wings I K to recede from the centre. But if this resistance is already too strong, the key G must be turned forward, and the wings brought nearer: between which extremes, a point will easily be found where the resistance of the air will expend just power enough to balance that brought into the Dynamometer through the power-axis; and thus to keep the measuring weight in the position required for any given experiment.
There remains only one part to be described as belonging to this Machine. It is represented in Plate 5, fig. 15, and is a graduated bar, made to fit in the holes K, of the measuring cylinder I K Plate 1: and to carry one of the arcs A A, which thus serves to extend, virtually, the radius of that cylinder to any required dimension.
It is now time to shew something of the manner of using this Dynamometer in the measurement of forces. Let the object then be to measure the power expended by a Horse in drawing a Carriage.
To do this, we fix a Drum (see fig. 16,) of equal radius with the measuring cylinder, on the power axis A; and a similar Drum to the resisting axis H. After firmly fixing the Machine, we place the Carriage at a distance behind it in the plane of the Drum H; and carry a rope from that Drum to the Carriage: on the other hand, we fill the first Drum A, with a coil of rope, to which the Horse is harnessed; and while he travels in the plane of the Drum A, the scale P (Plate 1,) is loaded with weights, until the Carriage follows the horse’s motion without any (or with little) agitation to the scale P: at which moment the power employed is equal to one half the weight at P, multiplied by the space gone through both by the Horse and the Carriage.
If it were now desired to find the power of a man turning a crank or handle, we should take that given in the figure 12, and fix it to the power-axis A. We should also take the fly-system shewn in fig. 19, and place it on the axis-of-resistance H. Then causing the man to turn the Machine, we should put twice as much weight into the scale P, as his strength was thought able to bear. Then if he thought the work too heavy, we should draw inward the leaves of the fly, and take away part of the weight P, until the man were satisfied he could work with convenience: and when, as before, the weight P should overcome the resistance of the fly I K, without either rising or falling, (sensibly) then the power expended would be one half of the weight P, multiplied by the space described by the man’s hand in the act of turning the handle.
It may occur to some of my readers that in these experiments the whole effect is not actually measured: since the space described by the horse or the man’s hand, must be determined after the experiment. I answer that these quantities, necessarily variable, must bear an inverse proportion to the weight P: and in all cases, this weight multiplied by that space, must give the power or momentum required. Besides, it is most easy to add a piece of mechanism that shall count the number of turns, and express them in space, by the inspection of a graduated scale. Nor need we stop here. The duration, in time, of any experiment, may also be recorded by the Machine itself. These are things so naturally connected with the subject, that I cannot feel it necessary, with so much before me, to attempt exhausting them. But this I engage to do: if any serious difficulty should actually stop any reader in this career of investigation, I will obviate such difficulty at some convenient future period. And mean while those persons who have aptitude for such subjects, will find in this Machine, ample scope for extending their enquiries; and comparing many mechanical realities with the deductions of Theory, thus amending and conciliating the conclusions both of Theory and Practice.
I have said above, that the weight or spring acting on the measuring cylinder at K, must be equalized: but in reference to some applications of this Machine to real use, I would modify that precept a little. I should, indeed, always like the principal action to be of a constant nature: with a supplementary part of less intensity, prepared to add something to the former; and this, for the purpose of meeting spontaneously the case of any unexpected addition of the moving power. Thus in Plate 1, if P be a weight nearly adapted to a given resistance, I would (to prevent accident, from its being overraised by any sudden jerk of the power,) hang one or more heavy chains under the scale, which drawn from the ground to a certain length, would add a known quantity to the measuring power; and transmit with a certain softness to the work, the unequal action of the mover.
One word on the friction of this Machine. All friction must of course be avoided as much as possible; but as it will be nearly the same in every class of experiments, it is not of great importance. The same may be said of the vis inertiæ of the parts, in convulsive motions. The parts would, of course, be made as light as a proper strength would permit. My mechanical readers will easily supply these small items of foresight; to anticipate the whole of which would make this Work interminable.
OF A NEW KIND OF
BARREL SPRING,
To lengthen the going of Clocks, Jacks, &c.
Although this invention does not properly constitute a new Spring, yet it produces effects both new and important. It protracts almost indefinitely the action of a barrel Spring, and thus reduces considerably the number of wheels in a clock or other spring-driven machine. This effect is produced by setting the two ends of the spring at variance; or making them act one against another: for as these opposite tendencies can be made nearly equal, one end of the spring will be wound up almost as much as the other end runs down: thus prolonging the effect in any