378 
CAPTAIN KATER ON THE ERROR IN 
These results differ but little from those of the former comparisons, to which, 
however, I think they are to be preferred. 
It has been shown that from the present results, the value which has been 
hitherto given to Mr. Dollond’s scale requires a considerable correction. Mr. 
Dollond’s scale, by former measurements, appeared to be equal to 35.99991 
inches of Sir George Shuckburgh’s scale, and consequently to be shorter than 
that scale only .00009 of an inch ; but it now appears to be shorter than Sir 
George Shuckburgh’s scale .00116 of an inch. Sir George Shuckburgh’s 
scale, therefore, when the former comparisons were made, must have been 
curved downwards in consequence of that part of the surface of the table upon 
which it was placed being concave ; and we may remark that by consulting 
the preceding Tables, it will be seen that a curvature, the versed sine of which 
is .03 of an inch in a yard, would have been sufficient to occasion the error 
in question. 
With reference to this error in the former estimation of the value of Mr. 
Dollond’s scale, it is important to add that in the year 1828 I employed it 
(not having then access to Sir George Shuckburgh’s standard) in determining 
the value of a scale for the Government of Hanover. This scale was made by 
Mr. Dollond, according to the mode which will hereafter be described ; and 
when referred to Sir George Shuckburgh’s scale, then taken as equivalent to 
the Imperial standard yard, it appeared to be equal to 35.99973 inches : upon 
that occasion the scale for Hanover was found by numerous comparisons to be 
shorter than Mr. Dollond’s scale .00018 of an inch, which being subtracted 
from 35.99893 inches, the last determination of the value of Mr. Dollond’s 
scale, leaves for the true length of the Hanoverian scale 35.998/5 inches of the 
Imperial standard yard. 
Having now shown the nature and magnitude of the error, which is the sub- 
ject of this paper, I shall proceed to point out the means of obviating it. 
It has been seen that the error in question results from the extension and 
compression of the surfaces of the bar upon which the scale is laid off de- 
pendent upon its curvature, and that there is a neutral surface which suffers 
neither extension nor compression, and which appears from the preceding ex- 
periments to be at about one-third of the thickness of the bar from that surface 
which becomes convex. When it is the object to have two points only on the 
