VALUES OF WEIGHTS, 



411 



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

 formula : — 



Let 10 + a; be the value of the series 5 + 2 + 1 + 1' + 1", 



5 X a + jr, the value of the series 2 + 1 + 1' + 1" 

 in terms of the 5-gramme weight, 

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



then Ifl + X = 2 {5 X CI) + y, 



c 10 + a; - 2/ 

 or 5 X a = -. 



Now, temporarilj' assume that the 1-gi-arame weight is the standard, 

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

 of the 2-gramrae weight bj' 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 tenus of the 

 1-gramme weight will now Ije obtained. 



The true values are obtained as foUnus : — 



Let 1 X ?; be the true value of the 1-gramme ^^eight, 



and 2(1 X i) -I- 2, 1 x i -l- ii\ 1 x i -f u, the values of the 2, 1', and V 

 in terms of the l-gL-auiriie weight ; 



then 2( 1 X /y) -I- z -f 1 X ?> -I- 1 X /; -t- »' -)- 1 X /j -f- K = 5 X fi -I- y, 

 or 1 X /; = '— . . 



From the true value of tiie 1-grannno weight, the true vahies nf the 

 2. 1'. and 1" weiglits are olitained. 



'Xhe values of the fractions of a giaiiiiiie are olitained liy the same pinee-ss 

 aa the values of the 5, 2, 1, 1', aii(l 1" weigJLts. 



TABLE CXXVIII.— Values of Weioiits. 



