ON STATICS. ^97 



of the beam slow and extensive, whether the scales have weights in them 

 or not : for this purpose a small weight is sometimes inclosed within the 

 beam, which is raised or depressed at pleasure by a screw, so as to bring 

 the centre of gravity of the whole moveable apparatus as near to the ful- 

 crum as may be required for the occasion. Mr. Ramsden's balance, made 

 for the Royal Society, is capable of weighing ten pounds, and turns with 

 one ten millionth part of the weight.* (Plate VIII. Fig. 107... 109.) 



The arms of a balance have sometimes been made unequal for fraudulent 

 purposes, the weight being placed nearer to the fulcrum than the substance 

 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 counter- 

 poise 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 sufficient 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 for this purpose the instrument 

 should be in equilibrium without any weight. In such cases, great accu- 

 racy may be obtained by applying a small weight at the end, in the form 

 of a micrometer screw. (Plate IX. Fig. 112.) 



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

 without 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 perfectly vertical, since, in this position, the weight may be over- 

 powered by the minutest counterpoise acting on the other arm. The centre 

 of 1 gravity being, in the common balance, very nearly in a right line 

 between the weights, in order that it may be immediately below the 

 * Rozier's Journal, xxxiii. 144. 

 H 



