624 MtSCELtANEOUS PAPERS. 



the committee, by Mr. Preeraau and Mr. Keed, expert scale makers, in 

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



•J-ounce liollow = ^-onnce solid -(- ^ graiu. 



J-ouuce weij^ht = All siualler weights — ^ grain. 



^-onnce weight = All smaller weights — | grain. 



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



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



4-ounce weight ^ All smaller weights ^l^ grains. 



8-ounce weight = All smaller weights ^ grains. 



16-oiince weight = All smaller weights ^ grains. 



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



64-ounce weight = All smaller weights ^ grains. 



128-ounce weight = All smaller weights + 15 grains. 



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



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

 which the committee expressed by saying that the weights "very 

 nearly agreed." 



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

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



^-ounce solid = Ix. 



4-ouuce hollow = Ix -\- i grain. 



^-onnce weight ^ 2x. 



•^-onuce weight = 4x. 



1-ounce weight =^ 8x. 



2-ounce weight = 16x. 



4-onnce weight ^ 3'2a; + i grain. V (3) 



8-onnee weight = G4ic -f- 1 grain. 



16-ounce weight = 128x -j- 2 grains. 



32-ounce weight =: 256a; + 2 grains. 



64-ounce weight =; 512jc -j- 6 grains. 



128-onnce weight = 1024j; -j~ 27 grains. 



256-ouuce weight = 2048.*; -j- 15 grains. 



Summing the various columns 



512 ounces = 4096.r + 54 grains 



whence 



X = ^ onnce — 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. Ohisholm in his seventh annual report.* Mr, Chisholm 

 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! he has quoted the weighings by Messrs. Freeman and 

 Reed and has attributed them to Mr. Harris. 



*50, p. 21. t46, p. il. 



