Steelyard

Steelyard is a balance whose arms are unequal, the same being used to Weigh different substances by placing it at different distances from the fulcrum. Let the beam be supported at the point A, while its weight W acts at C. The weight P is moved until at a point O It exact1y balances the weight of the beam above. A 1 lb. weight is now attached to the beam, and its weight acts downwards at B. P is moved till balance is obtained, and its position marked 1 lb. Points 2 3 4 etc are then marked on the beam at distances apart equal to O 1. That equal distances along the arm correspond to equal additions of weight to W is seen from the following considerations: If P at a point C just balances W, we have equilibrium, and consequently the moments of W and w about A just neutralise the moment of P about A. Hence W x A B + w x A b = A C = P x (A O + O C). But the point O is such that W x A G = P x O A, hence W x A B = P x O C. But A B and P are fixed, so that O C varies directly with W. Hence the distance from O at which P must be placed when the weight is 2 lbs. is just twice what it must be for 1 lb., and so on. The Danish steelyard consists of a beam with a heavy lump at one end and a hook for the weight at the other. The substance is weighed by altering the position of the fulcrum (F) till equilibrium obtains. The arm is graduated by hanging weights of 1, 2, 3, etc., lbs. at the end, and marking the position of F. the distances representing equal differences of weight are not equal in this form of the steelyard, so the subdivisions axe not so easily estimated.