THE LEVER. 



93 



little friction, the axis of support must be a very little above the 

 centre of gravity, the arms must be of considerable length, and the 

 beam must be 

 light. Balances are 

 made so delicate 

 that they may be 

 turned by less than 

 a thousandth of a 

 grain. The sup- 

 porting edge of the 

 axis is made very 

 sharp and hard, 

 and rests upon two 

 supports, general- 

 ly made of agate 

 or polished steel. 

 A really good bal- 

 ance is an expen- 

 sive piece of appa- 

 ratus. 



FIG. 44. 



176. False Balances. False balances (levers of 

 the first kind with unequal arms) are sometimes 

 used by dishonest dealers. When buying, they place 

 the goods on the shorter arm ; when selling, on the longer. 

 The cheat may be exposed by changing the goods and 

 weights to the opposite sides of the balance. The true 

 weight may be found by weighing the article first on one 

 side and then on the other, and taking the geometrical 

 mean of the two false weights ; that is, by finding the 

 square-root of the product of the two false weights. 



177. Double Weighing. In another way the true 

 weight of a body may be found with a false balance. The 

 article to be weighed is placed in one pan, and a counter- 

 weight, as of shot or sand, placed in the other pan until 

 equilibrium is produced. The article is then removed, 

 and known weights placed in the pan until equilibrium is 



