Prof. Miller on the Imperial Standard Pound. 547 



temperature (Memorie della Societa Italiana della Scienze in Modena, 

 t. XXV. p. 1). 



The weight of air used in reducing the weighings was calculated 

 from the above expression. 



The mean rate of expansion of brass, for 1° Cent., from 0° Cent, 

 to 100° Cent., usually assumed 0-0000187 of its length at 0° Cent., 

 is considerably larger than the rate of expansion at ordinary atmo- 

 spheric temperatures, according to the observations of Mr. Sheep- 

 shanks, who found that at about 17° Cent, the coefficient of the 

 linear expansion of brass =0*00001722 for 1° Cent. This value of 

 the expansion has been accordingly adopted. 



The Hnear expansion of platinum is assumed to be 0*00000900 

 for 1° Cent., as given by Schumacher in his first table (Phil. Trans. 

 1836). The expansion of water is calculated from a mean of the 

 experiments of Despretz, I. Pierre and Kopp, corrected for the error 

 of the assumed expansion of mercury by Eegnault's observations, 

 and assuming the temperature of maximum density to be 3°' 945 

 Cent., in accordance with the result obtained by Messrs. Playfair 

 and Joule. The logarithms of the expansion to 7 places considered 

 as integers, are given with sufficient accuracy, between 4° Cent, and 

 25° Cent., by 32'72(^-3-945)2-0-215(^-3-945)l 



Though it appears that only two of the nine weights with which 

 U was compared in 1826 and 1829 are in a state of unexceptionable 

 preservation, and that the number of trustworthy comparisons is 

 reduced from 669 to 440, these are amply sufficient for the purpose 

 of ascertaining the weight of U in air ()^=65°-66 Fahr., 5 = 2975 

 inches). But in order to find the absolute weight of U, or indeed 

 its apparent weight in air of a density different from that which it 

 has when f=65°-66 Fahr., 5 = 2975 inches, a knowledge of the 

 volume of the lost standard is requisite. An indirect way of arriving 

 at it was suggested by Professor Schumacher, by an examination of 

 certain Parliamientary Reports, presented May 26, 1758, April 11, 

 1759, March 2, 1824. It appears from the first of these, that 

 Mr. Harris, then Assay Master of the Mint, presented to the Com- 

 mittee three troy pounds made under his direction, one of which was 

 the lost Imperial standard ; and from the third, that one of the two 

 remaining pounds came into the possession of Mr. VandomC, and 

 the second into the possession of Mr. Bingley of the Mint. Pro- 

 fessor Schumacher then observes that we can still either determine, 

 with the highest degree of probability, the density of the lost Im- 

 perial standard, or know with certainty that all hope to arrive at this 

 knowledge is lost. It will be only requisite to ascertain with the 

 greatest care the densities of both pounds, the one in the possession 

 of Mr. Bingley, the other in the possession of Mr. Vandome. If the 

 density of both is found the same, we might from that circumstance 

 draw the highly probable conclusion, that the three single pounds of 

 Mr. Harris, according to my hypothesis, were really made of the 

 same identical metal ; and the density of the two remaining pounds 

 might with safety be considered as that of the lost standard. If, on 

 the contrary, the two remaining pounds prove to be of </«^eren# den- 



