125 
Mr. Troughton on dividing Instruments. 
quadrant having been assumed to be in its true place, the first 
of the third quadrant will err by just half the difference found 
by the examination ; therefore these errors are alike in both 
tables. The real error of the first dot of the second quadrant 
comes out in the first example ; that of the fourth was found 
in like manner, and completes the first line. It is convenient 
to put the error of the division 90° of each quadrant at the 
bottom of each column, although it is the same as the point 
o° on the following quadrant. The line of 45 0 is next filled 
up ; the second example shews this ; but there is no occasion 
to dwell longer upon this explanation ; for every one, who 
is at all fit for such pursuits, will think what has already 
been said fully sufficient for his purpose. However, I will 
just mention that there can be no danger, in the formation of 
this table, cf taking from a wrong line the real errors which 
are to be the criterion for finding that of the one under trial ; 
because they are in the line next to it ; the others, which in- 
tervene in the full table, not being yet inserted. The last course 
of all is, however, an exception ; for, as the examining micro- 
scopes could not be brought near enough to bisect the angle 
2 0 48' 45", recourse was had to that quantity and its half ; on 
which account the examination is prosecuted by using errors 
at two lines distance, as is shewn in the two last examples. 
When the table of real errors is constructed, the other 
table, although it is of no further use, should not be thrown 
away; for, if any material mistake has been committed, it will 
be discovered as the operation of dividing is carried on ; and, 
in that case, the table of apparent errors must be had recourse 
to ; indeed, not a figure should be destroyed until the work is 
done. 
