THIRD COMPARISON OF AUXILIARY WEIGHTS. 
827 
The relations between G, H, K, L, M, N, R, S are given by the observations of 
1845. 
T =A + B + C + D + F 
gr- 
— 0-00029 
A =:F-fG 
— 0-00157 
B =F + G 
— 0-00174 
C =:F+G 
— 0-00182 
D=F + G 
-0-00199 
F ==G + H 
+ 0-00145 
G=H + K 
+ 0-00152 
G =H + L 
+ 0-00281 
G=H + M 
+ 0-00136 
G = H + N 
+ 0-00058 
H=K+L+M+N+R 
+ 0-00034 
H=K+L+M+N+S 
+ 0-00030 
K=R + S 
— 0-00014 
L =R + S 
— 0-00146 
M=R + S 
+ 0-00003 
N=R+S 
+ 0-00078 
A + B + C + D =4F+4G 
-0-00712 
4G =4H + K + L + M + N +0-00627 
2H =2(K + L + M+N) + R + S +0-00064 
K + L + M + N =4R + 4S 
— 0-00079 
4(K + L+M + N)= 
l6(R + S)-0-003l6 
4H =4(K + L + M + N)+ 2(R + S) + 0-00128 
4H = 
18(R + S)-0-00188 
K+L+M+N = 
4(R + S)-0-00079 
4G =4H + K + L + M + N +0-00627 
4G = 
22(R + S) + 0-00360 
4H = 
18(R + S)-0-00188 
4G + 4H = 
40(R + S) + 0-00172 
4F =4G + 4H 
+ 0-00580 
4F = 
40(R + S) + 0-00752 
4G = 
22(R + S) + 0-00360 
4F + 4G = 
62(R + S) + 0-01112 
A+B+C+D = 
62(R + S) + 0-00400 
F = 
10(R + S) + 0-00188 
A+B+C+D+F= 
72(R + S) + 0-00588 
T = 
72(R + S) + 0-00559 
grains. 
T 
= 
5759-47143 
72(R+S) 
= 
5759-46584 
18(R + S) 
= 
1439-86646 
40(R + S) 
= 
3199-70324 
10(R + S) 
799-92581 
62(R + S) 
= 
4959-54003 
22(R + S) 
1759-83678 
A+B+C+D 
4959-54403 
4F + 4G 
== 
4959-55115 
F+G 
1239-88779 
A 
1239-88622 
B 
= 
1239-88605 
C 
= 
1239-88597 
D 
1239-88580 
F 
= 
799-92769 
G 
439-96009 
H 
359-96614 
K 
79-99244 
L 
79-99112 
M 
79-99261 
N 
79-99336 
R 
= 
39-99627 
S 
= 
39-99631 
5 Q 
MDCCCLVI. 
