ANNUAL ADDRESS OF THE PRESIDENT. 
LXXVII 
R. S. troy lb. = Exch. (8 oz. + 4 oz.) — 4 grain. (5) 
R. S. troy lb. = Mint (8 oz. + 4 oz.) — 2f grains. (6) 
whence 
Exch. (8 oz. + 4 oz.) — Mint (8 oz. 4- 4 oz.) — 1|- grains. (7) 
2. The weighings by Mr. Harris, for the Parliamentary Com¬ 
mittee of 1758, give^ 
Exch. (8 oz. + 4 oz.) = Mint (8 oz. + 4 oz.) — J grain. (8) 
whence, by (6), 
R. S. troy lb. = Exch. (8 oz. + 4 oz.) — li grains. (9) 
In equations (6) and (8) the weights at the Mint were those of 
the*sixth of Queen Anne, 1707. 
3. In the Philosophical Transactions, 1742, page 187, it is stated 
that the Paris two-marc weight weighs 7560 troy grains. As the 
true weight of two marcs is 7554*22 grains, this implies that the 
Royal Society’s troy pound was too light by 5*78 (5760 7560) == 
4*40 grains. 
In the Philosophical Transactions, 1742, page 187, it is stated 
that the Royal Society’s avoirdupois pound weighed 7004 troy 
grains, while the comparisons made in 1820 show that its weight 
was then only 7000 such grains. This implies that the Royal So¬ 
ciety’s troy pound was too light by 4 00 (5760 7000) = 3*29 
grains. 
Finally, the comparisons of 1820 showed that the Royal Society’s 
troy pound was “ nearly four grains too light.” 
The mean of these three independent results shows that the Royal 
Society’s troy pound was 3*9 grains lighter than the Imperial 
standard of 1758 ; whence 
R. S. troy lb. -f 3*9 grains = Standard of 1758 (10) 
but 
Standard of 1758 = Exch. (8 oz. -f 4 oz.) -f 1? grains (11) 
and therefore 
R. S. troy lb. = Exch. (8 oz. -f 4 oz.) — 2| grains. (12) 
Considering the indefiniteness of the data respecting the weigh- 
111, p. 437. 
