28 THE REALITIES OF MODERN SCIENCE 



of the unit weight. With these and a balance the 

 unknown weight of a body may be determined in an 

 obvious manner. The balance is merely a lever 

 supported at the center. At the ends of the equal 

 lever arms thus formed, pans are hung, in which the 

 weights to be compared are placed. With this balance 

 the ancients were familiar and Pythagoras in the sixth 

 century B.C. notes that dishonest tradesmen used to 

 shift the fulcrum slightly away from the pan containing 

 what they were selling so that a false comparison 

 resulted in their favor. Of course the check against such 

 a fraud is to interchange the contents of the two pans, 

 for then any inequality will be at once evident. In 

 general, if the arms are unequal the true weight of the 

 body may be obtained by observing the weights re- 

 quired to balance it, first in one pan and then in the 

 other. This method is called " double weighing." 

 (From these two weighings the true weight is obtainable 

 as the geometric mean.) 



Another method of obtaining the true weight of a 

 body, even though the lever arms are unequal, is known 

 as the " substitution method." The unknown body 

 is placed in one pan and balanced by the addition to 

 the other pan of lead shot, sand, or any convenient 



used for a standard and the prototype is preserved for occasional 

 comparisons. 



To obtain a weight of two units it is only necessary to make an- 

 other weight like the copy and then to make a new weight which 

 will just balance the other two. Two half units may be obtained 

 in the following manner. Weights of approximately half a unit 

 are made. These are balanced against each other and made equal. 

 They are then kept equal and worked down until together they 

 just balance the unit. In somewhat similar manner other sub- 

 multiples may be obtained. 



