GEODETICAL STANDARDS WITH THE ENGLISH STANDARD YARD. 
173 
Foyle Base": it is a bar similar to 0,, but rather lighter. Since 1846 it was for some 
time at St. Petersburg in custody of M. Struve, who compared it with his own standard.) 
The results of the comparisons are these : 
01,-0,= 18-38+0-26, 
I s -0,= 63-28+0-26, 
I B -0, =195-36+0-26, 
( 5 ) 
I s - I s = 86-50+0-41, 
I B - I 4 =218'58+0-22._ 
If from the seven last equations we seek by the method of least squares the most 
probable lengths of the five 10-foot standards in terms of the yard, we get, at 62°, 
OI,= 1 3 -Y 55 + 22-32,' 
I s =J^Y 55 + 69-38, 
0,=^Y 55 + 5-17, 
Ib=¥Y 65 +200-84, 
!»=¥*„- 17 - 43 . 
( 6 ) 
These values being substituted in the seven equations, the residual errors are the 
following : — 
+1-24, 
-1-24, 
-1-23, 
+0-93, 
+ 0-31, 
+ 0"31, 
-0-31. 
Now these errors are considerably larger than the directly computed probable errors 
of the different sets of comparison ; it is clear therefore that constant error has been 
influencing some or all the different series. After all, the residual errors are as small 
as could be well expected. As to I 4 , it appears that at present its relation to O, is this : 
I s -0, = -22-60. 
The difference of the same two bars, as determined in 1831, was — 22-25 ; and in 1847 
it was — 24-03 ; an agreement most satisfactory. 
It appears, then, from the above, that the Ordnance Survey Standard Bar is but very 
slightly in error, being only i,ooo,ooo fhs of its length too great ; this corresponds to 
barely 6 feet in the length of this kingdom from Scilly to Shetland ; or to 32 feet in 
the earth’s radius. 
Ordnance Toise and Metre . — In the toise, each of the yard spaces [a . b\ [# . c] were 
