940 PROF. W. H. MILLER ON THE CONSTRUCTION OF THE NEW STANDARD POUND.
The weights (12800), (6400), (3200), (1600), (800), (400), (200), (100), and aweight of 100 grains unmarked, which accompany Barrow’s balance, are of bronze,for which log A=0 , 92260. Let them be denoted by W, V, U, T, S, R, Q, P, Orespectively. It was found that
No. of Comp. gr.
4
p =o
-0-0001
4
Q=P + 0
—0-0037
4
R =Q+P + 0
+ 0-0108
4
S =R + Q+p + 0
— 0-0009
4
T =S+R+Q+P+0
— 0-0155
4
U =T+S + R + Q+P + 0
— 0-0207
4
V =U+T + S + R + Q+P+0
— 0-0030
4
W=V+U+T+S+R+Q+P+0
— 0-0516
Hence gr .
p = o-o-oooi
Q = 20 — 0-0038
R = 40 + 0-0069S = 80 + 0-0021
T = 160 — 0-0104U = 320-0-0260V = 640—0-0343W=1280—0-1172
By a mean of 4 comparisons, the bronze weights U+T+S+P+platinum weights(32) + (16) + (8) + (4)+0'0133gr. ^ platinum troy pound Tin air ( t= 10’45,&=758-28).Hence U+T+S+P=5699 - 9724 grains.
U+T+S+P=570—(P0344 grain. Therefore 57O=5700’0068 grains. Hence
gr-
( 100 ) = 100-0000(200; = 199-9964(400) = 400-0074(800) = 800-0031
gr-
(1600) = 1599-9915(3200) = 3199-9778(6400) = 6399-9733(12800) = 12799*8981
The values assigned to these weights in computing the densities of some of the oldtroy pounds and secondary standard lbs., were obtained upon the supposition thatthe absolute weight of the platinum troy pound T was about 0-002 grain less than itafterwards appeared to be on reducing the observations with the weight of air asdetermined by Regnault . The error, which was not discovered till after going topress, is much too small to affect the last figure of the calculated densities.
Probable Errors of the Platinum Weights.
Probable errors of the comparisons of T, and of the auxiliary weights.
Page.
Weights compared.
No. of comparisons (n).
Probable error of one comparison.
Probable error of n comparisons.
815
T, Sp
168
0-000982
0-000076
818
T, RS
78
0-000727
0-000083
824
T, A + B + C + D + F
40
0-000540
0-000086
825
A, F+G
22
0-000287
0-000061
825
B, F + G
22
0-000560
0-000123
826
C, F+G
22
0-000521
0-000114
826
D, F+G
22
0-000669
0-000146
826
F, G+H
31
0-000458
0-000084
821
G, H + K
10
0-000170
0-000057
821
G, H + L
10
\
0-000154
0-000051