LXXII PHILOSOPHICAL SOCIETY OF WASHINGTON. 
troy ounces. In that case the summation of the several columns 
gives 
512 ounces = 128 x + 39 grains” 
whence 
x = 4 ounces — 0°3047 grain (2) 
and by substituting that value in the equations (1) we obtain the 
corrections to the several weights given in the second column of 
Table I. 
TABLE I.—Oorrections to the Exchequer Standard Troy Weights of 1588, 
derived from the Weighings made by Messrs. Harris and Chisholm. 
Denomination Apparent |Committee’s} Chisholm’s Loss by 
of correction | correction | correction | wear in 115 
Weight. in 1758. in 1758. in 1873. years. 
Grains. Grains. Grains. 
4 ounces divided__| — 0°30 — 0-42 — 1:27 
aigunees’. =. 55 “67 0-01 
SiOUNCES; saa === 136 0:58 0-51 
DGrounces*<="= 52202 “97 1-42 2'42 
SAOUMCRS = ee — 0-19 1:08 2:74 
64ounces' 221422225 + 0°62 — 1:17 3°87 
128 ounces -.----..-- + 12-25 + 8:67 4:39 
256,0unces === -e- — 10:50 — 17°67 — 35:91 
Sums) sees ae + 0:00 — 14°34 — 51:12 
From equations (1) and (2) we have 
4 ounces = 4-oz. weight + 0°5547 grain. 
8 ounces = 8-0z. weight + 0°3594 grain. 
whence it follows that the sum of the eight and four ounce weights, 
which constituted the Exchequer standard troy pound, was too light 
by 0°9141 of a grain. As the mean correction obtained from the 
four weights belonging respectively to the Mint and to Mr. Free- 
man agrees closely with this result, the true correction to the Ex- 
chequer standard must have been very approximately one grain; 
