Chap. XIII.

DYXA NOMETER.

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the other turning freely, is placed at the middle of its length : a factitious resistance isapplied on the length of the axle, which we may obtain in various ways : conceive forexample, that if the axle ACE. tig. 1637., is engaged between four blocks, p,rj,r,s, fixedto the beams K L, M X, and if we bring the second beam near the first by the screws Mand N, we shall increase the friction of the axle A C II on the blocks; and, by applyingother blocks and beams along the axle, we may indefinitely increase the factitious resistance•applied to the axle. Let us now explain the use of the dynanometric machine, fig. 1636.,to measure the useful resistance applied to the axle A' B' C': when the axle is subjectedto this resistance its swiftness of rotation, or the number of turns which it makes in aminute, for example, is known, in disengaging or communicating its movement to thetoothed-wheel R, or defgh of the dynanometric machine, we shall produce a factitiousresistance on the axle ACB of this machine, in the same manner as the axle ACB willhave the swiftness of rotation determined by the useful resistance. The springs, D y d> willmake known the factitious resistance applied tangentially to the toothed-wheel R, or axleACB, and consequently the useful resistance, which, by hypothesis, is equal thereto : if themeans of producing a factitious resistance equal to a real determined resistance were in-sufficient, we shall now prove that, by a very simple calculation, one may deduce from themeasurement of one part of a resistance, the total value of this resistance.

O f the tangential Force applied to an Axle , deduced from the Measurement o f one Part o f

this Force _An axle communicates ordinarily its motion to a mechanical system of the

same kind, which can move at pleasure together or separately : suppose that by the instan-taneous interruption of the communication of motion between some of these mechanicalarrangements and the axle by which the power is applied, we shall diminish the resistanceand increase the velocity of rotation of this axis: in this hypothesis, we may make itcatch the wheel It of the dynanometric machine, whose axle is submitted to a factitiousresistance, and by several trials we shall find the resistance which gives the primitivevelocity to the axle by which power is applied. Let us call X the total resistance appliedon this axle to the extremity of the radius I, and F the factitious resistance which com-municates its primitive velocity : by diminishing the machinery moved by the axle bywhich the power is applied, the total resistance X becomes of a mean value, which I callX'; now these two resistances X and X' are evidently in the known relation to thequantity of machinery turned by the axle; we shall then have X' = »X, n being a givennumber.

Further, X=X' + F; then the axle by which power is applied submitted to the resis-tance X, or the sum of the two resistances X and F, turns equally swiftly, whence it follows

that X = n X -f F, which gives for the total resistance X the following value, X= .

We comprise in the measured resistance F, the inertia and friction produced by thecommunication of motion from the axle of power to the axle of the dynanometric machine,and which adds to the factitious resistance.

The dynanometer invented by Sir David Brewster , to whom science is so considerably in-debted, deserves to be mentioned: that celebrated philosopher Inis recommended thata vesselcontaining water should have a cylinder, made of some heavier substance than the water,suspended in it by a rope passing over a pulley : when the upper surface of the cylinder ison a level with the surface of the water, the weight of the cylinder, or the force which itexerts upon the rope, will be equal to the absolute weight of the cylinder in air diminishedby the weight of a quantity of water of the same magnitude as the cylinder : a hors6or a man pulling at the rope to raise the cylinder above the fluid surface, the weight ofthe cylinder will gradually increase; and if the magnitude and specific gravity of the cy-linder are duly adjusted to the force, tiiere will be a particular position of the cylinderat which its weight will exactly balance that applied. The forces in equilibrio, or thoserequired to be measured, will be equal to the absolute weight of the cylinder, diminishedby the weight of a quantity of water equal to the magnitude of the immersed part of thecylinder: a scale attached may be so set out, that it will accurately measure the force ap-plied, and the cylinder can be increased to any length by diminishing its diameter, so thata very lengthened division may be adopted.