624 



MISCELLANEOUS PAPERS. 



the committee, by Mr. Freeraau aud Mr. Heed, expert scale-makers, in 

 tlie presence of Mr. Farley, deputy chamberlain. They are as follows: 



^-ounce hollow = ^-oiince solid + i giaiu. 



i-ounce weight = All smaller weiglits — i grain. 



^-ounce weight = All smaller weights — i grain. 



1-ounce weight == All smaller weights — I grain. 



2-ouuce weight = All smaller weights — ^ grain. 



4-ouuce weight = All smaller weights ^ grains. 



8-ounce weight = All smaller weights ^ grains. ' 



16-oance weight = All smaller weights ^ grains. 



32-ounce weight = All smaller weights — 2 grains. 



64-ounce weight = All smaller weights ^ grains. 



128-ouuce weight = All smaller weiglits + 15 grains. 



256-ounce weight = All smaller weights — 24 grains. 



In these equations the symbol it is used to indicate the relation 

 which the committee expressed by saying that the weights "very 

 nearly agreed." 



Regarding the entire set of weights us a standard of 512 ounces, 

 and putting x for the mass of the ^-oz. solid weight we have 



^-ounce 



^-ounce 



jounce 



^-onnce 



1-ouuce 



2-ouuce 



4-ounce 



8-ounce 



16-ounce 



32-onnce 



(>4-ounce 



128-ounce 



256-oance 



solid : 

 hollow : 

 weight : 

 weight : 

 weight : 

 weight : 

 weight : 

 weight : 

 weight : 

 weight : 

 weight ; 

 weight : 

 weight : 



Ix -{- i grain. 

 2x. 

 4x. 

 8x. 

 16x. 



32x + i grain. 



64x + 1 grain. 



128x + 2 grains. 



2.56x -j- 2 grains. 



5r2x -|- 6 grains. 



1024x -|- 27 grains. 



: 2048x -|- 15 grains. 



(3) 



Summing the various columns 



512 ounces = 4096x + 54 grains 



whence 



X = I ounce — 0.01318 grains, (4) 



and by substituting that value in the equations (3) we obtain the cor. 

 rections given for the several weights in the second column of Table II. 

 The third column contains the corrections which result upon the com- 

 mittee's assumption that the sum of the 8 and 4 ounce weights was 1^ 

 grains too light; and the fourth and fifth columns contain corrections 

 given by Mr. Chisholm in his seventh annual report.* Mr. Ohisholm 

 does not explain how he obtained the corrections quoted in the fourth 

 column of the table, but their close agreement with those in the third 

 column renders it almost certain that they were computed from the 

 comparisons made by Messrs Freeman and Reed. As the committee 

 of 1758 used Mr. Harris's weighings to the exclusion of those by Messrs. 

 Freeman and Reed, the adoption of the opposite course by Mr. Chisholm 

 is perhaps explained by the circumstance that in his report on the Ex- 

 chequer standards t he has quoted the weighings by Messrs. Freeman and 

 Meed and has attributed them to Mr. Harris. 



* 50, p. 21. 



t46,p. IL 



