SECONDARY STANDARDS. 941 
822 
G, H + M 
10 
0*000159 
0*000053 
822 
G, H + N 
10 
0*000111 
0*000037 
822 
H, K + L + M + N + R 
17 
0*000298 
0*000073 
822 
H, K-i-L + M + N+S 
17 
0*000241 
0*000060 
822 
K, R + S 
12 
0*000134 
0*000040 
822 
L, R + S 
12 
0*000178 
0*000054 
823 
M, R + S 
12 
0*000139 
0*000042 
823 
N, R + S 
12 
0*000122 
0*000037 
828 
R, Y + Z 
6 
0*000072 
0*000032 
828 
S, Y + Z 
6 
0*000063 
0*000028 
828 
Y, W + V + Q 
20 
0*000097 
0*000022 
828 
Z, W + V+Q 
20 
0*000046 
0*000034 
829 
W, V+IOQ 
6 
0*000053 
0*000024 
829 
V, lOQ 
6 
0*000119 
0*000053 
According to the 300 comparisons of U, the lost troy pound, with Sp, and the 140 
comparisons with RS, made in 1829, RS=Sp+0’00515 grain. According to the 
comparisons of T with Sp and RS in 1845, RS=Sp+0'00534 gr., a result which 
differs from the former by only 0*00019 gr. Giving to the comparisons of U and T 
with Sp twice the weight of their comparisons with RS, because the number of com- 
parisons of U and T with Sp is about twice as great as the number of comparisons 
with RS, the probable error of T, in terms of Sp and RS, will be 0*000058 gr. The 
probable error of l^(A-l-B-l-C-l-D) is 0*000026 gr., and that of Q is 0*000004 gr. 
Hence the probable error of T-f-Q+i(A-|-B-l-C-j-D) is 0*000064 gr. 
Probable errors of the comparisons of I with T and the auxiliary weights. 
Page. 
Weights compared. 
No. of comparisons («). 
Probable error of one comparison, 
gr. 
Probable error of n comparisons. 
gr* 
858 
I, T+Q+A 
40 
0*000569 
0*000091 
859 
I, T + Q + B 
40 
0*000504 
0*000081 
859 
I, T+Q+C 
40 
0*000648 
0*000104 
860 
I, T + Q+D 
50 
0*000618 
0*000083 
Hence the probable error of the comparison of I with T-|-Q+i(A-|-B-l-C-i-D) is 
0*000038 gr. But the probable error of T-l-Q-l-|^(A-f-B-l-C+D) is 0*000064 gr. 
Therefore the probable error of I is 0*000074 grain. If we substitute for A, B, C, D 
their values in terms of F-f G, the resulting values of I will be affected by the errors 
of the comparisons of A, B, C, D with F-j-G, combined with the errors of the com- 
parisons of I with T-}-Q+A, T-j-Q-j-B, T-f-Q+C, T-j-Q-l-D. The differences of 
these values of I from the mean are —0*00097 grain, -1-0*00008 grain, -)-0*0001 1 grain, 
-f-0*00078 grain respectively. 
Probable errors of the comparisons of I with K, L, M, N, the platinum lbs. Nos. 1, 
2, 3, 4, and with Sp-f-V, Professor Schumacher’s lb. 
Page. 
Weights compared. 
No. of comparisons (w). 
Probable error of one comparison. 
gr- 
Probable error of n con 
gr- 
862 
I, K 
100 
0*000514 
0*000052 
864 
I,L 
108 
0*000659 
0*000064 
866 
I, M 
102 
0 000485 
0*000048 
868 
I, N 
102 
0*000555 
0*000055 
872 
I, Sp + V 
100 
0*000495 
0*000050 
6 G 2 
