STANDARDS OF LINEAR MEASURE. 
365 
As in the preceding experiments the bar was clear of the marble when a 
wire was placed under its middle, and touched the slab when wires were 
placed under its extremities ; I next tried whether any greater errors would 
be produced by the curvature which the bar would assume by its own weight 
when clear of the marble in both cases. For this purpose I used wires of .05 
of an inch diameter, by which the bar was wholly supported. 
With wires of .05 of an inch diameter. 
Without Wires. 
A Wire under 
Wires under 
Error when curved 
Error when curved 
Sum of 
the middle. 
the ends. 
upwards. 
downwards. 
Errors. 
div. 
div. 
div. 
div. 
div. 
div. 
67.0 
60.0 
79-0 
61.0 
54.0 
78.5 
57-5 
54.0 
74.5 
60.0 
52.0 
73.0 
57-0 
55.5 
74.5 
Mean 60.5 
55.1 
75.9 
5.6 
15.2 
20.8 
0.2 Reduction to the Chord. 
60.7 
Here it may be seen that the results are very nearly the same as in the pre- 
ceding Table, and consequently that the errors of the Imperial standard yard 
are the greatest possible with a curvature, the versed sine of which is less than 
one-hundredth of an inch. 
In order to obtain accurate conclusions from the above Tables, it must be 
considered that when the bar is lying flat upon the marble it is the length of 
the scale that is taken, but when the bar is curved it is the chord of the arc 
which is measured. It therefore becomes necessary to add to the mean of the 
column headed “ without wires ” the number of divisions of the micrometer, 
which is equal to the excess of the arc above its chord. 
This correction being made, if the difference between the mean of the 
readings so corrected of the micrometer, when the bar lies flat upon the 
marble, and the mean of the readings when a wire is placed under the middle 
of the bar be taken, it will give the amount of the error arising from flexure 
independent of the chord when the bar is curved upwards. 
In like manner the difference between such corrected mean and the mean of 
