STANDARDS OF LINEAR MEASURE. 
375 
From the last Table it appears that the error of the scale when curved up- 
wards is scarcely more than one half of its error when curved downwards ; and 
from this it should seem that the neutral plane is not in the middle of the bar 
as I had supposed. 
If this inference be correct, the distance of the neutral plane from that sur- 
face of the bar, the curvature of which is convex, may be found by considering 
the sum of the errors in the preceding Table to represent the thickness of the 
bar, when the corresponding error resulting from the curvature upwards will 
be the distance of the neutral plane from the convex surface. This distance 
appears to be scarcely equal to one-third of the thickness of the bar. 
From the experiments which have been detailed, we are led to the following 
conclusions. 
1 . That in a standard of linear measure traced upon the surface of a bar, 
an error arises from the thickness of the bar when it is placed upon a table 
the surface of which is not plane. 
2. That this error in bars of the same material and of unequal thickness is 
within certain limits as the thickness of the bar, and depends upon the exten- 
sion of that surface of the bar which becomes convex, and the compression of 
the surface which is concave. 
3. That the error to which the same scale is liable from this cause, is directly 
as the versed sine of the curvature of the surface upon which the scale is placed. 
4. That this error very far exceeds that which would arise from the dif- 
ference of length between the arc and its chord under similar circumstances ; 
so much so, that the sum of the errors from this cause in a bar one inch thick, 
with a versed sine of not one-hundredth of an inch, is nearly one-thousandth 
of an inch ; whilst double the difference between the chord and the arc is not 
one fifty-thousandth. 
It was not until I had written thus far, that a method, with which I am per- 
fectly satisfied, occurred to me of trying a surface supposed to be plane. The 
difficulty, if not the impossibility of procuring what is called a straight edge is 
well known to workmen ; but this desideratum I supplied by the very easy 
process of stringing a bow six feet long with piano-forte wire one-hundredth of 
an inch diameter, which bears a considerable degree of tension without break- 
ing. The wire was passed over two thick wires half bedded in pieces glued 
3 c 
MDCCCXXX. 
