On dividing Instruments. 95 



It is convenient, in the formation of the table of real er- 

 fors, that they should be inserted in the order of the nura- 

 beriinj; of the degrees on their respective quadrants ; although 

 their computation necessarily took place iu the order in 

 which the examination was carried on, or according to the 

 arrangement in the table of apparent errors. The tirst dot 

 of the first quadrant havina; licen ass.nmed to be in its true 

 place, the first of the third quadrant will err by just half the 

 difference found by the examination ; tlierefore 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 ihe 

 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 uf each column, although it is the 

 same as the point 0^ on the following quadrant. The line 

 of -15^ is next filled up ; the second example shows this ; but 

 there is no occasion to dwell longer upon this explanation; 

 for every one, who is at all fit for such pursuits, wid 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, of taking from a wro:iii '""£ 

 the real errors which arc to be the criterion for finding that 

 of the one under trial; because .they are in the line next to 

 it ; the others, which intervene in the full table, not being 

 yet inserted. The last course of all is, however, an execu- 

 tion ; for, as the examinin2:n>-icroscopes could not be brought 

 near enough to bisect the analc 2^ 4S' 43", recourse was had 

 to that quantity and its half; on which account the exanima- 

 tion is prosecuted by usiuir errors at two hues distance, as is 

 shown in the two last examples. 



When the table of real errors is constructed, the other 

 table, although il is of no further use, should not be thrown 

 away; for, if any material mistake has been connnitled, it 

 will be discovered as the operation of dividing is carried on ; 

 and, in that case, ilic table of apparent errors must be had 

 recourse to ; indeed, not a figure should be destroyed until 

 the work is done. 



^To be eoaiiiuiedj 



XIV, On 



