ANNUAL ADDRESS OF THE PRESIDENT. LXXI 
‘Mr. Freeman produced a four and eight ounce of the 6th of Queen 
Anne 1707 by which he makes weights for sale, which was heavier than 
the same weights at the Exchequer one grain and three quarters: There- 
fore, upon an average of all these weights, the pound troy should be one 
grain heavier than the weights at the Exchequer, and that added to the 
grain and a half, which, upon the former experiments, the weights at the 
Exchequer are too light a medium taken from thence makes the proper 
increase of the Exchequer pound troy to be one grain and one quarter.” 
‘« And it is to be observed, that the pound troy weight at the Mint, which 
is now used for gold, and the eight and four ounces at the Mint, marked 
with a tower, and in the time of Queen Elizabeth, are both one grain 
heavier than the eight and four ounces of the Exchequer.”’ 
‘« And considering that the Exchequer weights have been used ever since 
the 30th of Queen Hlizabeth, 1588, one hundred and seventy years to size 
other weights by, it is highly probable that the difference may have been 
occasioned by the frequent use of the standard.”’ 
‘‘ Your Committee endeavored to compare the trey weights with the 
original standard at Goldsmith’s Hall, from whence it is said, in the afore- 
said verdict of the 29th and 30th of Elizadeth, that the weights now at the 
Exchequer were made, and for that purpose sent to Goldsmith’s Hall for 
the said weights; but were informed that no such were to be found there, 
the Goldsmith’s having no weights older than those at the Exchequer; ”’ 
The Committee’s statement respecting the way in which the cor- 
rection of 1% grains was deduced from the weighings of the Ex- 
chequer weights is very obscure, and the result is not justified by 
generally accepted principles. If we put x for the sum of all the 
weights smaller than 4 ounces, then the results of the weighings 
made by the Committee may be written in the form: 
4-oz. divided = 12 
4-oz. weight = 1la— } grain. 
8-0z. weight = 22+ 4 grain. 
16-0z. weight = 42+ } grain. 
32-0z. weight = 8% + 2% grains. (1) 
64-0z. weight = 16 x + 5% grains. 
128-0z. weight = 32 2 + 22 grains. 
256-02. weight = 642+ 9 grains. 
Before proceeding further we must decide in what sense these 
weights are to be regarded as standards, and perhaps the most 
natural course will be to regard the entire set as a standard of 512 
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