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.