1068

THEORY AND PRACTICE OE ENGINEERING.

Book II.

bcr of rays C D, C E, C F, &c. ; this wheel turns with the axle. Another wheel havingthe same number of spokes, Cd, Cc, Cf, turns freely on the same axle ; springs Drf, Ee,are attached to the couples of the spokes, CD, C d, C E, Ce, of the two wheels, sothat the points of attachment D and d of the extremities of the springs are in a planeperpendicular to the axis of rotation C of the axle A B, and at an equal distance fromthis axle.

Having disposed the power or mover so that it shall turn the wheel freely in the directionof the arrow X, it is evident that the extremities de,fg of the springs fixed to this wheel,would swerve from the points of attachment D, E, F, &c. ; that the equal angles Dcrf,Fee, E cf &c., whose sides pass through the extremity of the springs, considered intheir primitive position, would become other equal angles, D cd, Ece, Ec/, &c., and all theother springs would be stretched, if not equally, at least at the same angle : when the totaltension of the springs is equivalent to the resistance applied tangentially to the axle, thesystem of the two wheels will turn on the axis A B as one and the same wheel. Nowsuppose that the axis turns, and that we can measure one of the angles T>cd', at which allthe springs are stretched, we shall have in the triangle D Cd' the angle C, the equal sidesCD, Cd, and consequently the perpendicular let fall from the centre C on the side T)d, orthe radius of the circle to which the force which stretches the spring is tangential. Wemay, besides, observe the number of turns of an axis in a given time, whence we maydeduce the velocity of the point at which the force that stretches each spring is applied.Multiply this velocity by the sum of the tension of the springs, the product will be thedynamic effect of an axis in a unity of time, for example 1".

To measure the angle D cd, which moves in a plane perpendicular to the axis of rotationC of the axis A B, we fix on the lines Crf,CD, the middle of the radii, two small hammersa, b, coupled by a spring Drf', which each move in a plane perpendicular to the axis of ro-tation C, and at equal or unequal distances from this axis, but greater than the radii of thewheels. These hammers strike two bells placed beyond on circles described through a andb ; this being arranged, we can with a seconds watch measure the time which elapsesbetween the two consecutive sounds resulting from the blow of each of the hammers on thebells, and knowing besides the time of the entire* revolution of the hammers, these twoportions of time will be in the ratio of the arc which measures the angle of the right linespassing through the extremity of each spring to the entire circumference. This anglebeing known, we can easily measure the weight which stretches each spring at a knownangle, and the sum of these weights will be the total tension of the dynanometriemachine.

By this description it will be seen that simple springs without needles or scales, whoseforce of tension for the same lengthening may be sensibly unequal, gives exactly themeasurement of a tangential force applied to axes : by taking springs capable only of atension of a ton, we may place eight on a circle of 39’37 inches radius, and eight otherson a concentric circle of 8 decimetres, supposing the axle makes four turns per minute ; thedynanometrie machine, will show on this hypothesis that the dynamic effect produced by aforce applied to an axle is nearly equivalent to that obtained from 80 horses.

Portable Dynanometrie Machine _The system of two wheels which composes the

dynanometrie machine, being constructed at the same time as the axle A C B, we canonly measure the tangential force capable of overcoming the resistance applied to thisaxle: but if this first construction did not exist, or if we would avoid the expense it wouldoccasion, we might make use of the portable dynanometrie machine about to be described,and which has for its object the measurement of a tangential force applied to any axleA' C*' B', provided we suppose, which is always the case, that this axle engages or disengagesat pleasure the wheel or pinion which communicates its movement to the resistance:

Fig. 1637.

a frame of carpentry solidly bedded and fixed in the ground near the axle A'C'B', sus-tains the axle A C B by its two gudgeons; the system of two wheels, one fixed on this axle,