iS ON DIVIDING INSTRUMENTS. 



a distance of 11° 15': t:e sixth or ^. i<;ht lines, with a distance 

 of &° 37' 30": the seventh of sixteen liaes, with a distance 

 of 2" 48' 45" : and the eighth a;;d last variety, b^^ins^ the re- 

 mainder of the table, consist of thirty two lines, and was ob- 

 tained with a distance of 4° 13' 7'5". 

 Table of real The table of apparent errours, or half differences, just 

 explained, furnishes data for com;)i.tin. the tabic of real 

 errours. The rule is this; let a be he leal errour of the 

 preceding dot, and b that of the following one, and c the 

 apparent errour, taken from the table of half differences, 



of the dot under investigation ; then is 1- <• z: its real 



errour. But, as this simple expression may no', be so ge- 

 nerally understood by workmen as I wish, it may be neces- 

 sary to say the same thing less concisely. If the real errours 

 of the preceding and following dots are both +, or both — , 

 take half their sum, and prefix thereto he common sign; 

 but, if one of them is -\- , and the other — , take half their 

 difference, prefixing the sign of the gr ater quantity: again, 

 if the ap; aient errour of the dot under invesiigation has the 

 same sign of the quantity found above, give totheir sum the 

 common sign, for the real errour; but if their signs are 

 contrary, give to their difference the sign of the greater for 

 the real errour. 1 add a few examples. 



Example. I . 

 For the first point of the second quadrant. 

 Real errour of the first ; ointof the first quad- 

 rant ..t..i«.. — O'O 



Real errour of the first pdut of the third quad- 

 ra >; -_ 6-9 



Half sum or half difference • — 3*4 



Apparent errour of the dot under trial + 12'2 



Real errour -\- 8'8 



Example 2. 

 For the point 45° of the second quadrant. 

 Real errour of the first point of the quadrant + 8*8 

 Real errour of the last point of the quadrant — 6*9 



Half difference -f- 0*9 



Apparent errour of the dot under trial • — 8*9 



Real errour • * *• •• *•*****>»**,,,»,,,,,», _- 8*0 



Examph 



