162 $taties. 



edge, the plane surfaces with which they come in contact being 

 likewise of the hardest substances. 



257. Nevertheless, where extreme accuracy is required, the 

 best method is to place the thing to be weighed in one of the 

 scales, and to balance it by any convenient substances in the 

 other scale, till the beam takes an exact horizontal position, as 

 shown by the index FL* Then carefully remove the thing 

 whose weight is sought, and replace it by accurate weights, as 

 grains, &c., till the beam takes precisely the same position. The 

 number of grains, &c., used will be the weight required. In this 

 way, all error arising from the want of perfect equality in the 

 two arms of the balance are completely obviated. 



258. With all these precautions, the process of weighing is but 

 an approximation, strictly speaking, to perfect accuracy. (I.) The 

 best balance tends of itself with some degree of force to a hori- 

 zontal position, since the slightest inclination must cause the cen- 

 tre of gravity to rise somewhat, and consequently, if the differ- 

 ence in the two weights does not exceed this force, the balance 

 will not enable us to detect the inequality. (2.) The friction 

 both of the axis and of the points of suspension, is an obstacle to 

 motion, and the difference in the weights must be sufficient to 

 overcome this, in addition to the force just mentioned, in order 

 that the balance may show them to be unequal. 



259. Knowing, however, what weight is sufficient to produce 

 motion in any case, we know what degree of accuracy we have 

 been able to attain. This is different for different weights. A 

 small weight can be determined more exactly, other things being 

 the same, than a large one, since the friction increases with the 

 pressure. A balance constructed by Ramsden for the Royal 

 Society of London, when loaded with a weight of 10 lb , would 

 turn with a grain, or a ten-millionth part of the weight ; and 

 one made by Fortin of Paris, when charged with a weight of 

 4 lb , would turn with a 70th part of a grain. 



* Instead of an index rising perpendicularly, a pin is sometimes 

 attached to the end of the beam, and made to move over a nicely 

 graduated arc provided with a microscope ; and the whole apparatus 

 enclosed' under glass to prevent any agitation from the air. 



