808 PROF. W. H. MILLER ON THE CONSTRUCTION OF THE NEW STANDARD POUND. 
For the platinum of which T and the auxiliary weights are made log A=r32566 
by Schumacher’s Tables. For Sp and RS log A=: 1*32608, by the same tables. The 
space t^U— i^Sp contains 0*53 grain of air nearly. Therefore the weight of Sp or RS 
is nearly 5759*47 grains. The weight of A+B + C+D + F is very nearly the same. 
Hence i;(A+B + C-l-D + B) = 272*09, t;Sp = 27T84, i;RS=271’84, the unit of volume 
being the volume of a grain of water at its maximum density. Therefore 
v(A 4-BH-C-|"D + F) is larger than ^;Sp or t>RS by the volume of 0*25 grain of 
•water, or 0*00030 grain of air of ordinary density. 
Hence A + B + C-|-D + F = Sp-l-0*00157 gi‘. But Sp = U — 0*52956 gr. There- 
fore A+B + C+D-1-F=U- 0*52799 gr. Also A+B+C+D + F=RS — 0*00299 gr. 
But RS=U — 0*52441 gr. Therefore A-|-B-l-C-j-Dd-F=U — 0*52740 gr. Giving the 
former value twice the weight of the latter, 
A-|-B+C-fD-fF=U- 0*52779 = 5759*47221 grains. 
In the following comparisons of the auxiliary weights with each other the lO^-inch 
balance by Robinson was used. 
1844. 
100 parts 
= 0-3593 grain. 
A. 
F+G. 
B. 
F+G. 
1*80 
1-75 
2-70 
2-75 
2-50 
2-35 
2*65 
3-05 
2-50 
2-85 
2-55 
2-90 
2-90 
3-25 
2-60 
3-05 
3*20 
3-15 
2-80 
2-70 
3-00 
3-05 
2-50 
3-25 
3-25 
3-15 
2-70 
3-05 
3-15 
3-05 
2-50 
3*25 
2-90 
2-85 
2-80 
3-20 
3-00 
2-90 
2-95 
3*30 
2-75 
2-55 
3-00 
3-35 
2*85 
2-85 
2-75 
3-30 
33-80 
33-75 
32-50 
37-15 
12A = 12(F + G)- 
0*05 part. 
12B=12(F + G) + 4*65 parts. 
A = F + G — 0*00001 grain. 
B=F + G + 0*00138 grain. 
1844. 
100 parts 
= 0-3593 grain. 
c. 
F+G. 
D. 
F+G+ 0-004 
3-10 
3-00 
3-10 
3-20 
2-75 
3-10 
3-15 
3-15 
3-10 
2-85 
3-20 
3-00 
2-80 
3-00 
3-20 
3-15 
2-75 
2-90 
2-90 
3-10 
3-65 
3-65 
2-95 
2-95 
3-65 
3-65 
3-00 
3-05 
3-40 
2-90 
3-30 
3-55 
2-90 
2-90 
3-00 
3-30 
2-60 
3-10 
2-80 
2-90 
2*73 
2-95 
3*30 
3-20 
2-90 
3-00 
3-00 
3-15 
36-35 
37-00 
36-90 
37*70 
12C=12(F + G) + 0-65 part. 12D=12(F + G + 0°004 gr.) + 0‘8 part. 
C = F4-G + 0*00020 grain. D=F + G + 0*00424 grain. 
