862 PROF.W. H. MILLER ON THE CONSTRUCTION OF THE NEW STANDARD POUND. 
Let W be a weight of 7000 grains of the same density as U. In air (^=18’7, 
fe=755-64) U £i:T+0‘00745 grain. Therefore (T+0'00745 grain). 
(T+O-00745 gr.)=T+0-00745 gr.+^ (T+0-00745 gr.). 
T=72(R+S)H-0*00559 grain, and 4F+4G=:62(R+S) +0-01 112 grain. 
1 24 fi2 fi2 
yyg (T+0-00745 gr.) = ^[72(R+S)+0-01303 gr.]=^(R+S)+0-00281 gr. 
= F+G+0-00003 gr. 
Hence [T+0-00745 grain] =T+F+G+0-00748 grain. 
Therefore W£i:T+F+G+0-00748 grain. 
Hence in Somerset House, PSi^ W+Q— 0-01 102 gr. in air (^=18-7, 6=755-64). 
Q— 0 01102 grain =0 63407 grain. The weight of 0-63407 grain was adjusted by 
PS. This, in air (#= 18-7, 6=755-64), is equivalent to a weight of 0-63413 grain 
adjusted by W. 
The commercial standard lb. is a brass weight which in air (^=18*7, 6=755*64), 
or at the temperature 65°-66 Fahrenheit, under the pressure of 29-750 inches of mer- 
cury at 32° Fahrenheit, in Somerset House, for which log A=7-078324— 10, appears 
to weigh as much as W, or as much as PS — Q+0-01102 grain. For in air having 
the above-mentioned temperature and pressure, the apparent weight of such a lb. 
would be of that of the lost standard. This result is not affected by the uncer- 
tainty of the value of the specific gravity of the lost standard. 
In the following comparisons of the platinum copies of the pound with PS, 
I, K, L, M, N will be used to denote PS, PC No. 1, PC No. 2, PC No. 3, PC No. 4 
respectively. The zero of the scale of the barometer was 305 millimetres above the 
centre of gravity of the weights. 
Comparison of PC No. 1 with PS. 
February 16, 1846. 
100 parts =0*26222 
grain. 
February 18. 100 parts= 
= 0*27683 grain, 
K+Y, I+X. 
I+X, K+Y. 
K+X, I+Y. 
I+Y, K+X. 
20*14 
20*30 
15*32 
17*76 
20*44 
20*61 
15*29 
17*40 
21*25 
20*94 
15*51 
17*41 
20*64 
19-61 
D= 
16*05 
15*80 
17-67 
20*89 
20*94 
C = 
16*1 
16*96 
17-75 
20*01 
20*85 
F = 
766*8 
16*46 
17-24 
20*57 
19*46 
E = 
16*42 
15*35 
17-52 
20-04 
19-82 
16*24 
16*62 
20*70 
19-75 
16*60 
16*46 
19-65 
19-81 
16*27 
16*94 
204*33 
202*09 
159*80 
172*77 
20(K-|-Y):£i20(I + X)-2*24 parts. 20(K + X)£i20(I + Y) + 12*97 parts. 
40K £5: 401 + 0*03031 grain in air (<=l6*09) Z»=765*25). 
