g4 On dividing Instruments. 



plained, furn-.^hes data for con.puting the table of real errors. 

 The rule is this : Let a be the real error of iheprecc/hng dot, 

 and h that of the follouina one, and c the apparent error, 

 taken from the table of half differences, of the dot under 

 investigMion ; then is -"^ + ^ = i>s ^^--^l '•'"^r. Bnt, as 

 this sim.ple expression ni1v not be so generally undersloO(i 

 bv workmen a^ I wish, it i^iav be necessary to say the same 

 thimr less concisely. If the real errors of the precedmg and 

 follawmg dots are both +, or both -, take halt their sum 

 and prefLX thereto the common sign ; but, if one o\ them is 

 + ^nd the other -, take half their difference, prefixing 

 the sion of the orealer quantity : again, if the apparent error 

 of the^'dol under invest ioation has the same sign ot thequJtii- 

 tiiv found above, give to their sum the common sign, tof 

 the real error ; but if their signs are contrary, give to their 

 difference the sign of the greater for the real error. 1 add a 



few examples. 



Kxamph I. 

 For the first point of the sce<md quadrant. 

 Real error of the first point of the first quadant - 00 

 Real errror of tlie first point of the itnrd quadrant — 6-9 

 Half sum or half difierence '. ' " — ^'^ 



Apparent error of the dot under tnal - + 12-2, 



Real error _ - - - • 



Example II. 

 For the point 45° of the second quadrant. 

 Real error of the first point )f she quach-ant - -f S'S 



Real error of the la;; ooint of the quadrant - — 6 9 



Halfdifferenot '- - . , " ''*"??» 



Apparent error of the dot under tnal - - - b-'j 



Real error - ' , ~ " " ~ ^"^ 



' Example III. 

 Point 88°- L), or last point, of the third quadrant. 

 Real error of the point 84°-4 of the third quadrant —21-0 

 Jieal error of.lhe point 2°'8 of the fourth quadrant - 2-9 



Half sum - - " " "^^'^ 



Apparent error of ll^c cjt under trial - —4-0 



Real error - - ; " -13-9 



Exawplc IV. 

 Point 8S°-6, or last, of the fourth qnad'-?.nt. 

 Real errorofUie point 84--1 of the lourlh quadrant -21-6 

 Real error of the point -J'-B of the first quadrant - 10'2 



H^lfsnm - ' , • ; ■ T^n^- 



Appai rent error of the dot unuer trial - + y'J 



Real error - - ~ " ~" . 



