STANDARDS OF LINEAR MEASURE. 
379 
bar, marking- for example the yard, it has been already shown that by cutting 
away one-half of the thickness of the bar at its ends and placing the points 
upon the new surface, the error which arises from flexure is reduced to the 
least possible quantity ; as this (the difference between one-half and one-third 
of the thickness of the bar) is the nearest approach that can be made to the 
neutral surface when the bar is curved upwards and when it is curved down- 
wards. 
When a scale of inches is required, this method is not available ; as the whole 
surface of the bar must in that case be employed. But by diminishing the 
thickness of the bar, the magnitude of the error is diminished proportionably ; 
and it is evident that the thickness of the bar might be so reduced as to render 
the error scarcely appreciable. 
Having prepared a bar, or rather a plate, of a thickness which is no more 
than sufficient to receive the divisions of the scale, and to preserve an even 
surface, the next object is to provide this plate with a proper support. For 
this purpose a bar of brass well hammered is to be employed, of a sufficient 
width, and half an inch or even an inch thick. Upon the surface of this bar 
the thin plate intended to receive the divisions is to be placed, and made to 
slide freely in a dovetailed groove, formed by two side-plates of similar thick- 
ness, screwed to the surface of the bar. Lastly, the thin plate upon which the 
scale is to be laid off is to be fixed at its middle point to the bar by a single 
screw passing through it. 
Now if the thick bar which forms the support be curved, its surfaces will 
suffer extension and compression in proportion to the thickness of the bar. 
The thin plate accommodating itself to the curvature of the bar will follow 
the same law, and the resulting error will be less in the proportion of the thick- 
ness of the plate to that of the bar. Now it has been shown that the greatest 
errors to which the Imperial standard yard (one inch thick) is liable, amount 
to nearly one-thousandth of an inch ; as a wire of one-hundredth of an inch 
diameter placed under the middle of the bar is more than sufficient to produce 
the greatest curvature of which it is susceptible ; and it follows that if such a 
bar were to form the support of a plate of one-tenth of an inch in thickness in 
the manner just described, the sum of the greatest errors, to which a scale 
