STANDARDS OF LINEAR MEASURE. 
373 
by the extension of the surface of the bar when it is curved upwards, and the 
error when it is curved downwards ; hut in Sir George Shuckburgh’s scale, 
when a wire is placed under the middle, the surface of the bar rests upon the 
edges of the marble slab ; the length to be considered of the bar is therefore in 
this position equal to the length of the marble 63.7 inches, and the error of the 
curvature upwards, as given in the Tables, must be increased in the proportion 
of 63.7 to 60. 
The same method must be pursued with Mr. Dollond’s scale, the bar being 
forty-two inches long. 
Lastly, these results must be reduced, but in inverse proportion, to what 
they would have been had the length of the scale been thirty-six inches. 
As the distance from 0 to 36 inches is the part of Sir George Shuckburgh’s 
scale, which has been considered upon every occasion as equal to the Imperial 
standard yard, it is this portion to which all the subsequent deductions refer. 
The following Table contains the results of the foregoing experiments, with 
each scale reduced to a bar of thirty-six inches in the manner which has 
been described, the bar being taken as equal in thickness to each scale respec- 
tively. 
Thick- 
ness of 
Bar. 
Table. 
Versed 
Sine. 
Error when 
curved 
upwards. 
Error when 
curved 
downwards. 
Sum of 
Errors. 
inches. 
inches. 
inches. 
inches. 
inches. 
Imperial Standard Yard 
1.07 
(A) 
.012 
.00028 
.00066 
.00094 
(C)* 
.01 
.00022 
.00039 
.00061 
(D) 
.02 
.00023 
.00084 
.00107 
Sir George Shuckburgh’s Scale.< 
0.42 
(E) 
.03 
.00036 
.00096 
.00132 
(F) 
.04 
.00054 
.00125 
.00179 
(H) 
.05 
.00063 
.00160 
.00223 
Mr. Dollond’s Scale 
0.17 
(L) 
.05 
.00022 
.00097 
.00119 
Captain Eater’s Scale 
0.29 
(M) 
.05 
.00071 
.00176 
.00247 
By referring to the results in this Table, derived from Sir George Shuck- 
burgh’s scale, it will be perceived that the sum of the errors increases as the 
versed sine or diameter of the wire employed. This will be more readily shown 
by dividing the sum of the errors by the corresponding diameter of the wire, 
or reducing each to a versed sine of .01 of an inch. 
* Reduced by proportion from a versed sine of .012 to that of .01 of an inch. 
