96 LECTURE XII. 



now weighs nearly half as much more. But at the mean temperature of this 

 climate, or 52, a cubic foot of distilled water weighs only 998 ounces. 

 The avoirdupois ounce appears to agree very nearly with the ancient Roman 

 ounce. Of the old French weight, 100 pounds made 108 English pounds 

 avoirdupois. The gramme of the new weights is a cubic centimetre of 

 pure water at its greatest density, that is about the temperature of 39 of 

 Fahrenheit ; it is equal to 15 English grains : hence the chiliogramme is 

 2 pounds, and five myriogrammes are nearly a hundred weight. Five 

 grammes of silver, including one tenth of alloy, make a franc, which is one 

 eightieth better than the old franc or livre, and is intrinsically worth nearly 

 ninepence three farthings English. 



The instruments usually employed for the comparison of weights are 

 either balances or steelyards. In the common balance, the weights of the 

 substances compared are equal ; in a compound weighing machine, we use 

 weights which are smaller, in a certain proportion, than those which they 

 represent: in the steelyard, a single weight acquires different values at 

 different parts of the arm, and in the bent lever balance the position of 

 the arms determines the magnitude of the counterpoise. The spring steel- 

 yard measures the weight, by the degree of flexure that it produces in a 

 spring. 



The beam of a common balance must have its arms precisely equal. 

 The scales, being freely suspended from fixed points in the beam, act on 

 them always in the direction of gravity ; and the effect is the same as 

 if the whole weight were concentrated in those points. The beam sup- 

 ports the scales, and is itself supported by means of fine edges of hard 

 steel, working on steel, agate, or garnet, in order that the motion may be 

 free, and the distances of the points precisely defined. The best beams are 

 made of two hollow cones of brass, united at their bases ; they are lifted 

 off their supports when the balance is not used, in order to avoid accidental 

 injuries ; the scales also are supported, so as not to hang from the beam, 

 until they have received their weights. According to the position of the 

 fulcrum, with respect to the points of suspension of the scales, the equili- 

 brium of the balance may be either stable, neutral, or tottering ; or if the 

 beam be too flexible, it may pass from one of these states to the other by 

 the effect of the weights. The stable equilibrium is the most usual and the 

 best, because it gives us an opportunity of determining the degree of in- 

 equality of the weights, by the position in which the centre of gravity 

 rests, or by the middle point of the vibrations of the beam, which are 

 sometimes measured by an index pointing to a graduated arc. If, how- 

 ever, the fulcrum be too much elevated above the centre of gravity, the equi- 

 librium may be too stable, and may require too great an inequality in order 

 to produce a sensible preponderance. If, on the contrary, by the elevation 

 of the points of suspension of the scales, the equilibrium be rendered tot- 

 tering the lower scale will not rise, even if it be somewhat less loaded than 

 the upper ; and steelyards of this construction have sometimes been em- 

 ployed, in order to impose on the purchaser by the appearance of an ample 

 weight. It is necessary, where great accuracy is desired, to bring the 

 equilibrium very near the state of neutrality, and to make the vibrations 



