*4© Mr. Lax on a Method of examining 
three feet radius without the risk of a greater error than 3,21 
seconds. 
To those people who are accustomed to entertain such ex- 
alted notions of the accuracy with which astronomical instru- 
ments can with a certainty be divided, this error, I dare say, 
will appear very considerable ; but for my part, lam perfectly 
satisfied that it bears but a small proportion to the accumu- 
lated error which may take place, in spite of the utmost vigi- 
lance of the artist, in an instrument divided according to any 
method which has hitherto been made public. I need not, 
however, remark upon the very great improbability that the 
error of examination should ever attain, or approach, to its 
extreme limit, as this must be sufficiently obvious to any per- 
son who is in the least degree conversant with the doctrine 
of chances ; but it may be proper to observe, that we have it 
in our power (and in this respect the examiner possesses a 
most important advantage over the divider of an instrument) 
to diminish its probable amount, as much as we please, by 
bringing the moveable wires of the micrometer and micro- 
scope several times to bisect their respective points in the 
measurement of every arc, and taking a mean of the different 
readings-ojf for the true position of the wire at the real bisec- 
tion of the point. The wire may be moved in this manner 
eight or ten times at each point ( if such a degree of caution 
should be thought necessary), and the mean taken in little 
more than a minute, so that the time of performing the work 
will not be so much increased, as might perhaps have been ap- 
prehended, and when it is completed, we may reasonably pre- 
sume that the distance of every point from zero ( whilst the 
temperature of the circle continues uniform) will have been 
