CAPTAIN KATER ON THE ERROR IN 
366 
the readings of the column headed “wires under the ends” will give the error 
proceeding from the same source when the bar is curved downwards : and the 
sum of the errors thus obtained will show the greatest error which can arise 
from a curvature, the versed sine of which is equal to the diameter of the wires 
employed. The same amount of errors may at once be obtained by taking the 
difference of the mean readings of the second and third columns. 
In the Imperial standard yard it appears that with a curvature, the versed 
sine of which is less than .012 of an inch, the amount of the errors is .000943, 
or nearly one-thousandth of an inch ; whilst the error which would result from 
the difference between the arc and its chord is absolutely insensible, not 
amounting to one hundred-thousandth of an inch. Now it must be obvious, 
that if a scale were compared at two different periods with the Imperial 
standard yard, the yard at one of such periods being placed upon a part of the 
table deviating from a plane surface .012 of an inch in a yard, and at another 
period the same quantity, but in a contrary direction, — the difference in the 
resulting values of the scale so compared would be no less than .000943 of an 
inch. This supposes the scale which is the subject of comparison either to be 
very thin, or to be placed upon a part of the table which is perfectly flat ; a 
circumstance which it is not difficult to imagine very possible, or even that 
different parts of the surface of the table may be curved in contrary directions, 
when the small amount of the curvature in question is considered. 
I may here observe, that the thickness of a single shaving which the plane 
takes off from the table is sufficient to occasion an error equal to that resulting 
from the preceding comparisons; for I found by careful measurements with a 
micrometer, that the mean thickness of such a shaving of deal was about .009 
of an inch. 
I have hitherto supposed the surface of the table not to be plane ; but if the 
table were plane and the surface of the bar were curved, the bar would by its 
weight apply itself to the plane surface of the table ; and a like error in either 
case would be the consequence. 
It has been stated that the surface of the bar of the Imperial standard yard 
is concave ; and by my present comparisons the distance from zero to thirty- 
six inches on Sir George Shuckburgh’s scale, which by former measurements 
