1^6 .Z.ECTURE xri. 



to be weighed. It is obvious that the fraud may be detected, by changing^ 

 the places of the contents of the two scales. In such a case, if a counterpoise 

 to the same weight be determined in each situation, the sum of both will be 

 greater than twice the weight; and the purchaser would be sure of having 

 even more than his due, by requesting the seller to weigh half in the one scale 

 and half in the other. For example, if one arm of the beam were only three 

 fourths as long as the other, the counterpoise, to a weight of twelve ounces, 

 would be nine ounces in one scale, and sixteen in the other, making together 

 twenty five instead of twenty four ounces. (Plate VIII. Fig. 110.) 



Supposing the beams of a balance to be accidentally unequal, either in 

 length or in weight, we may still weigh in it with accuracy, by making a 

 perfect counterpoise of any kind to a weight, and then removing the weight 

 and putting in its place as much of the substance to be weighed, as is suffi- 

 cient to restore the equilibrium. 



The weights may also be reduced, or increased, in proportion to the length 

 of the arms, if they differ from each other, care being taken to put the weights 

 always into the same scale. This is actually performed in weighing machines, 

 where a composition of levers is employed, in order to enable us to determine 

 the weight of large masses by means of weights of moderate dimensions. 

 (Plate IX. Fig. 111.) 



When the effective lengths of one or both arms of the beam are capable of 

 being varied, by changing the points of suspension according to the divisions 

 of a scale, the instrument is called a steelyard. Where one weight only is used, 

 it is not necessary that the two arms should exactly balance each other, since 

 the divisions may be so placed as to make the necessary adjustment; but it is 

 sometimes convenient to have two or three weights, of different magnitudes, 

 and fcH" this purpose the instrument should be in equilibrium without any 

 weight. In such cases, great accuracy may be obtained by applying a small 

 weight at the end, in the form of a micrometer screw. (Plate IX. Fig. 1 12.) 



The arms of a balance, though constant in length, may vary in effect with- 

 out limit, if they can sufficiently alter their inclination to the horizon ; for 

 no weight, however great, acting on the arm of a bent lever, can make it per- 



