772 PROF. W, H. MILLER ON THE CONSTRUCTION OF THE NEW STANDARD POUND. 
In the interval between 1829 and 1844, the difference between the two platinum 
troy pounds Sp and RS had undergone no very sensible relative change. If, as 
appears highly probable, Sp and RS have undergone no sensible absolute change, 
Sb has gained 0*0046 grain, and K has lost 0*0061 grain. 
In 1844, Sb+K=Sp4-RS+0‘0333 grain. Assuming Sp and RS to have expe- 
rienced no change since 1829, Sp-|-RS=2U— 0*01 1 1 grain; whence Sb+K=2U 
+ 0*0222 grain. 
The equations 11 ...18 give — - 
gr. gr. 
2Ex=Sb + K-0-0024=Sp + RS + 0-0309 
2L =Sb + K + 0-0080 = Sp + RS + 0-0413 
2Ed=Sb + K + 0-0191 = Sp + RS + 0-0525 
2D =Sb + K + 0-0274=Sp + RS-|-0-0607 
The first column of the following Table exhibits the errors of Ex, L, Ed, D, as 
deduced from the above equations ; the second column exhibits the errors of the 
same weights, as determined by Captain Kater, in 1824, by direct comparison with 
U ; the third shows the increase of weight of the several troy pounds in the course 
of twenty years. 
In 1844. 
In 1824. 
gr. 
Ex-U= -I- 0-0099 
L -U= + 0-0151 
Ed — U= +0-0206 
D -U= + 0-0248 
gr. gr. 
Ex-U= + 0-0010 0-0089 
L —U= +0-0005 0-0146 
Ed — U=— 0-0015 0-0221 
D —U= + 0-0022 0-0226 
In 1824, RM=U+0*0021 grain; in 1829, RM =U+ 0*0089 ; consequently RM 
gained 0*0068 grain in five years. With the single exception of K, all the new brass 
weights have become heavier since they were first compared with U, in consequence 
probably of the oxidation of their surfaces, while U, which was made in 1758, was 
preserved from further change by the coat of oxide already formed. One of these, 
Sb, appeared to have been protected by gilding, though imperfectly, as parts of its 
surface were slightly tarnished. Ex and L were brighter than Ed and D. K, though 
it had become lighter, was much tarnished, yet exhibited no traces of abrasion. The 
discordances presented by the different weighings of K previous to 1844 were highly 
perplexing, and were probably the cause of the very numerous and accurate com- 
parisons of the various troy pounds placed at the disposal of the Committee, with the 
lost standard, on which alone the possibility of restoring it with sufficient accuracy 
depends. 
Professor Schumacher received K in March 1827, accompanied by a statement 
that it had been found by Captain Kater to exceed the standard very little, not more 
tlian 0 006 grain*. In June 1828, Captain Kater compared a second weight Kn with 
each of two troy pounds in his possession, the errors of which were well determined. 
One of these was 0*0122 grain too heavy, the other 0*0267 grain too heavy. Let 
2W denote the sum of these two troy pounds. Then W=U+0*0194 grain. By a 
* Philosophical Transactions, 1836, p. 457. 
