Читать книгу Experimental Mechanics. A Course of Lectures Delivered at the Royal College of Science for Ireland онлайн

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79. That a pair of scales should weigh accurately, it is necessary that the weights be correct; but even with correct weights, a balance of defective construction will give an inaccurate result. The error frequently arises from some inequality in the lengths of the arms of the beam. When this is the case, the two weights which really balance are not equal. Supposing, for instance, that with an imperfect balance I endeavour to weigh a pound of shot. If I put the weight on the short side, then the quantity of shot balanced is less than 1 lb.; while if the 1 lb. weight be placed at the long side, it will require more than 1 lb. of shot to produce equilibrium. The mode of testing a pair of scales is then evident. Let weights be placed in the pans which balance each other; if the weights be interchanged and the balance still remains horizontal, it is correct.

80. Suppose, for example, that the two arms be 10 inches and 11 inches long, then, if 1 lb. weight be placed in the pan of the 10-inch end, its moment is 10; and if ¹⁰/₁₁ of 1 lb. be placed in the pan belonging to the 11-inch end, its moment is also 10: hence 1 lb. at the short end balances ¹⁰/₁₁ of 1 lb. at the long end; and therefore, if the shopkeeper placed his weight in the short arm, his customers would lose ¹/₁₁ part of each pound for which they paid; on the other hand, if the shopkeeper placed his 1 lb. weight on the long arm, then not less than ¹¹/₁₀ lb. would be required in the pan belonging to the short arm. Hence in this case the customer would get ¹/₁₀ lb. too much. It follows, that if a shopman placed his weights and his goods alternately in the one scale and in the other he would be a loser on the whole; for, though every second customer gets ¹/₁₁ lb. less than he ought, yet the others get ¹/₁₀ lb. more than they have paid for.