io8 Mr. Troughton on dividing Instruments . 
unequal to the value of half a minute or more. After having 
found the terminating point of a quadrant or circle so perma- 
nent, although I was not prepared to expect perfect equality 
throughout, yet I was much mortified to find the errors so 
great, at least ten times as much as I expected ; which fact 
indicated, beyond a doubt, that if the roller is to be trusted at 
all, it must only be trusted through a very short arc. Had 
there been any thing slippery in the action, which would have 
been indicated by measuring the same part at different times 
differently, there would have been an end of it at once ; but, 
that not being the case in any sensible degree, the roller be- 
comes an useful auxiliary to fill up- short intervals, whose 
limits have been corrected by more certain means.* 
* There are two things in the foregoing account of the action of the roller which 
have a tendency to excite surprise. The first is, that the roller should, in different 
parts of its journey round the circle, measure the latter so differently. One would not 
wonder, however, if in taking the measure across a ploughed field, it should be found 
different to a parallel measure taken upon a gravel-walk ; and, in my opinion, the cases 
are not very dissimilar. Porosity of the metal, in one part of the circle more than in 
the other, must evidently have the same effect; brass unhammered is always porous ; 
and the part, which has felt the effect of two blows, cannot be so dense as other parts 
which have felt the effect of three ; and, should the edge of the circle be indented by 
jarring -turning, it would produce a visible similitude to ploughed ground: Every 
workman must be sufficiently upon his guard against such a palpable source of error; 
yet, perhaps with our greatest care we may not be able to avoid it altogether. The 
second is, that notwithstanding the inequality above-mentioned, the roller having 
reached the point upon the circle from whence it set out, should perform a second, 
third, &c. course of revolutions, without any sensible deviation from its former track ; 
this is not perhaps so easily accounted for. It must be mentioned, that the exterior 
border of the circle should be turned rounding, presenting to the roller a convex 
edge, whose radius of curvature is not greater than one tenth of an inch. Now, were 
the materials perfectly inelastic and impenetrable, the roller could only touch the 
circle in a point, and in passing round the circle, it could only occupy a line of con- 
tact. This in practice is not the case; the citcle always marks the roller with a 
