178 CAPTAIN A. R. CLARKE ON THE COMPARISON OE ENGLISH AND FOREIGN 
small quantities in the first seven equations the same as in the last three, and put 
F s — C+# !? 
F* = 
N =2C-^3, 
P =2C+^ 4 , , ■ 
T 10 = C+^55 
T n = C+^6? 
T 0 = C ++, ) 
( 19 ) 
these equations, substituted in (9) . . . (18), give the following: — 
+ = 0,1 
+ + 1 - 97 = 0 , J 
Comparisons by M. Aeago. 
x 3 - 2 x- 30-81 = 0 ,) 
+— # 3 + 44 - 63 = 0 , > 
2 +-- + + 35-06 = 0,1 
+— + + 0 - 47 = 0,1 
Xq — ++ 0-49 = 0 ,] 
+— ++ 154-52 = 0 ,) 
Xq — + + 1 56 "OO = 0 , r 
+- 2 ++ 321-52 = Q.l 
M. Steuve. 
General Baeyee. 
Southampton. 
From these ten equations the values of the seven quantities x have to be determined 
by least squares. In doing so we shall not make reference to the probable errors 
attaching to them, as indeed they are not all known, but regard them as of equal weight. 
The values of + . . . x 7 being found, and substituted in the preceding equations, give 
F, = C- 0-07, j 
F b = C- 1-09, | 
N = 2C + 30-65, 
P =2C- 14-33, | • • • ( 2 °) 
- T 10 = £- 2-05, 
T n = C— 2-65, . 
T 0 = £+153-42, j 
the weight of x 7 being +f. The residual errors of the ten equations are, 
-•007) -0-03) +0-321 
+ 0*074 —0-35 1 —0-26) 
+ 0-31) 
- 0 - 95 ' 
+ 0-26 
+ 0+5 
