On dividhig Instruments. 93 



be seen ihrough at proper intervals. The micrometers must 

 now be placed at a distance of 22° 3o', and the halt differences 

 ,of the parts of all the arcs of 45° measured and noted as be- 

 fore; thus descending by biseetions to 11'^ \b', 5° of 30", 

 and 2= 48' 43". HalF this last quantity is too small to allow 

 the micrometers to be brought near enough ; but it will have 

 the desired eflcct, if tliey are placed at that quantity and it's 

 half, i. e. 4^ 13' 7 "'5 ; in which case the examination, in- 

 stead of being made at the next, will take place at the next 

 division but one, to that which is the subject of trial. Du- 

 ring the whole of the time that the examination is made, all 

 the dots, except the one under examination, are for the pre- 

 sent supposed to be in their true places; and the only thing 

 in this most important part of the business, from first to last, 

 is to ascertain with the utmost care, in divisions of the mi- 

 crometer head, how much one of the parts of the interval 

 imder examination exceeds the other, and carefully to tabu- 

 late the half of their ditl'LTence. 



I will suppose that every one, who attempts to divide a 

 large astronomical instrument, will have it engraved first. 

 Dividing is a most delicate operation, and every coarser one 

 should precede it. Besides, its being num'oered is particu- 

 larly useful to distinguish one dot from another: thus, in 

 tlje two annexed tables of errors, the side columns give signi- 

 ficant names to every dot, in terms of its value to the nearest 

 tenth of a degree, and the n)istaking of one for another is 

 rendered nearly impossible. 



The I'oregoing examination furnishes materials for the 

 construction of the table of half differences, or apparent 

 errors*. The first line of this table consists of two varie- 

 ties ; i. e. the micrometers were at 180° distance for obtain- 

 ing ihc numbers ahich fill the columnsof the first and third 

 quadrant ; and at [)(}", for those of the second and fourth 

 quadrant. 'I'hc third variety makes one line, and was ob- 

 tained with a distance of 43"^: the fourth consists of two 

 lines, with a distance of 22^30': the fifth of four lines, 

 wiih a distance of H^ 15" : the sixth of eight lines, with a 

 dibtance of 5" 37' 30": the seventh of sixteen lines, with 

 a distance of 2°4S'43": and the eighth and last variety, 

 being the remainder of the tabic, consislsof thirty-two lines, 

 and was obtained with a distance of 4' 13' 7"' 5. 



The table of apparctU errors, or half differences, just cx- 



• If the table of real errors lie computed as tlie work of examination pro- 

 crcUs, tliere will be no uccaiion for tlii> tabic at all ; but, I tliiiik it be^it not 

 til lot line part interfere with aiiollier, and therefore I examine the whole 

 before ! Uvj^in tu compute. 



plained. 



