124 Mr. Troughton on dividing Instruments . 
Example 2. 
For the point 45 0 of the second quadrant. 
Real error of the first point of the quadrant - -j- 8,8 
Real error of the last point of the quadrant - — 6,9 
Half difference - + 0,9 
Apparent error of the dot under trial - — 8,9 
Real error ----- —8,0 
Example 3. 
Point 88°, 6, or last point, of the third quadrant. 
Real error of the point 84°, 4 of the third quadrant — 2 1 ,0 
Real error of the point 2°,8 of the fourth quadrant — 2,9 
Half sum - - - - — 1 1,9 
Apparent error of the dot under trial - — 4,0 
Real error - -- j 5,9 
Example 4. 
Point 88°, 6 , or last, of the fourth quadrant. 
Real error of the point 84°, 4 of the fourth quadrant — 21,6 
Real error of the point 2°,8 of the first quadrant — — 10,2 
Half sum - - - - — 15,9 
Apparent error of the dot under trial - -}~ 9,5 
Real error - - - - - — 6 . 4 
It is convenient, in the formation of the table of real errors, 
that they should be inserted in the order of the numbering 
of the degrees on their respective quadrants ; although their 
computation necessarily took place in the order in which the 
examination was carried on, or according to the arrangement 
in the table of apparent errors. The first dot of the first 
