650 Royal Society ; — 



U and that of Sp or RS. A space equal to the diiference 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-fQ, 

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

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

 grain each, so accurately adjusted that no appreciable difference could 

 be detected between them ; a weight V of 6 -4 5 1 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. lu 

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

 X-i-C-f-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 .. 2M671 



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 



RS, assuming the density of U to have been the same as that of V, 



T=5759*47141 grains, of which U contained 5760. By numerous 



comparisons of the auxiliary weights with each other and with T, 



A= 1239*88621, B= 1239*88604, C=1239*88596,D= 1239-88579, 



Q=0*64509. 



By 80 comparisons of PS with each of the woights T + Q+A, 

 T4-Q+B, T + Q+C, and 100 of PS with T + Q+D, 



gr. t. b. 



PS52: T + Q + A--0002936 19*47 758-38 

 PSii T + Q+B-0*001731 19*19 759*31 

 PS£: T4-Q+C-0*001621 18*83 754-38 

 PS£: T4-Q+D-OOOO774 19*63 764-43 

 Mean gr. 



PS:fi: T + Q+i(A + B-hC-f-D)-0*00177 19*28 759-12 



whence, supposing U to have the same density as V, 



PS = 7000-00090 grains, of which U contained 5760. 

 Results of comparisons of PC No. 1, PC No. 2, PC No. 3, PC No. 4 

 with PS : — gr. No. of Comparisons. 



PC No. 1=PS-|-0*00051 200 



PC No. 2=PS-0*00089 216 



PC No. 3=PS-0*00178 204 



PC No. 4 = PS-0-00316 204 



' The weights Sp, Sb, K were returned to Professor Schumacher 

 accompanied by a weight V such that, by a mean of 200 compari- 

 sons, Sp-f VilP8-0-00071 gram in air (^=13-1, 6=759*09). 



