100 



into a continued fraction. The errors of these weights are 

 found by the following comparisons : Sp and RS with T ; T with 

 A + B + C + D + F; each of the weights A, B, C, D with F+G; 

 F with G+H ; G with each of the weights H + K, H + L, H + M, 

 H+N; HwithK + L+M + N + RandK + L + M+N + S;eachof 

 the weights K, L, M, N with R+S. 



Sp and RS, instead of being true troy pounds, and, consequently, 

 equal to U in a vacuum, had been adjusted so as to appear nearly as 

 heavy as U when weighed in air of ordinary density, and are there- 

 fore lighter than U by about 0'53 grain, the weight of the air con- 

 tained in the space equal to the difference between the volume of 

 U and that of Sp or RS. A space equal to the difference between 

 the volume of 7000 grains of metal of the assumed density of U, and 

 7000 grains of platinum, contains about 0'645 grain of air. Calling 

 this Q, PS may be compared with each of the weights T + A+Q, 

 T+B + Q, T + C + Q, T+D + Q. In order to determine Q with the 

 greatest precision, Mr. Barrow supplied ten weights Q of about 0*645 

 grain each, so accurately adjusted that no appreciable difference could 

 be detected between them; a weight V of 6-451 grains, and a weight W 

 of 12*901 grains, all of platinum. Then Y and Z being two platinum 

 weights of 20 grains each, the following comparisons became pos- 

 sible : each of the weights R and S with Y + Z ; each of the weights 

 Y and Z with W+ V + each of the weights Q in turn ; W with V+ 

 sum of ten weights Q ; V with the sum of the ten weights Q. In 

 comparing PS with each of the weights T + A + Q, T+B + Q, 

 T+C + Q, T+D + Q, the weight Q was changed at the end of 

 every four comparisons, and thus each of the ten weights Q used 

 in turn in a series of forty comparisons. 



By numerous weighings in air and in water the densities of the 

 several weights were found to be as follows : 



T .......... 21-1661 



PS ........ 21-1572 



PC No. 1 .. 21-1671 



PC No. 2 .. 21-1640 



PC No. 3 .. 21-1615 



PC No. 4 .. 21-1556 



By 286 comparisons of T with Sp and 122 comparisons of T with 



