WEIGHTS. 



463 



The 5-grarnme weight is now taken, temporarily, as a standard, and the 

 2+1 + r+l" weights are weighed against that, and the value of the 

 series obtained in terms of the 5-gramme weight. 



The true value of the 5-gramme weight is obtained by the following 

 formula : 



Let 



and 

 then 



or 



10 +x be the value of the series 5 + 2 + 1 + 



X a + y, the value of the series 2 + 1 + 1' + 1 

 in terms of the 5-gramme weight ; 

 5 X a the true value of the 5-gramme weight ; 

 10 + x = 2 (5 x a) + y, 



5 x a = 10 + a ~ y. 



1", 



Now, temporarily assume that the 1 -gramme weight is the standard, 

 and ascertain the values of the 1' and 1" weights ; then ascertain the value 

 of the 2-gramme weight by weighing it against 1 + 1', 1 + 1" or 1" + 1" or, 

 preferably, against all three. 



The apparent values of the 2, 1, 1', and 1" weights in terms of the 

 1 -gramme weight will now be obtained. . 



The true values are obtained as follows : 



Let 1 x b be the true value of the 1 -gramme weight, 

 and 2(1 x 6) + z, 1 X 6 + w, I X 6 + u, the values of the 2, I', and 1" 



in terms of the 1 -gramme weight ; 

 then 2(1 x& + z+lx& + lX 

 or 1x6 = 5xo 



From the true value of the 1 -gramme weight, the true values of the 

 2, 1', and 1" weights are obtained. 



The values of the fractions of a gramme are obtained by the same process 

 as the values of the 5, 2, 1, 1', and 1" weights. 



TABLE CLVIIL VALUES OF WEIGHTS. 



