Suppose the distance from A to F to be ten times as great as that from A to _a_, then a force of one pound applied beneath F would balance ten pounds applied at _a_, or upon the platform. Again: let the distance from E to G be also ten times greater than the distance from the fulcrum E to F; then a force of one pound applied to raise up the end of the lever G would counterpoise a weight of ten pounds placed upon F. Now, as we gain ten times the power by the first levers, and ten times more by the lever E G, it follows, that a force of one pound tending to elevate G, would balance 100 lbs. placed on the platform; so that if the end of the lever G be attached to one arm of a balance, a weight of 10 lbs. placed in a scale suspended from the other arm, will express the value of 1000 lbs. placed upon the platform. The levers are counterpoised, when the platform is not loaded, by a weight H applied to the end of the last lever, continued beyond the fulcrum for that purpose. _Of Instruments for weighing by means of a Spring._ The spring is well adapted to the construction of a weighing machine, from the property it possesses of yielding in proportion to the force impressed, and consequently giving a scale of equal parts for equal additions of weight. It is liable, however, to suffer injury, unless the steel of which it is composed be very well tempered, from a want of perfect elasticity, and, consequently, from not returning to its original place after it has been forcibly compressed. This, however, must be considered to arise, in a great measure, from imperfection of workmanship, or of the material employed, or from its having been subjected to too great a force. _The Spring Steelyard._ The little instrument known by this name is in very general use, and is particularly convenient where great accuracy is not necessary, as a spring which will ascertain weights from one pound to fifty, is contained in a cylinder only 4 inches long and 3/4 inch diameter. This instrument is represented at _fig. 198._ It consists of a tube of iron, of the dimensions just stated, closed at the bottom, to which is attached an iron hook for supporting the substance to be weighed; a rod of iron _a b_, four tenths of an inch wide and one tenth thick, is firmly fixed in the circular plate _c d_, which slides smoothly in the iron tube. A strong steel spring is also fastened to this plate, and passed round the rod _a b_ without touching it, and without coming in contact with the interior of the cylindrical tube. The tube is closed at the top by a circular piece of iron through which the piece _a b_ passes. Upon the face of _a b_ the weight is expressed by divisions, each of which indicates one pound, and five of such divisions in the instrument now before us occupy two tenths of an inch. The divisions, notwithstanding, are of sufficient size to enable them to be subdivided by the eye.