ON DIVIDING INSTRUMENTS. }$ 



limb to be seen through at proper intervals. The miorome* 

 ters must now be placed at a distance of 22' 30', and the 

 half differences of the parts of all the arcs of 45° measured 

 and noted as before ; thus descending by bisections to 1 1' 

 J5', 5° 37' 30', and 2° 48' 45". Half this last quantity is 

 too small to allow the micrometers to be brought near 

 enough ; but it will have the desired effect, if they are placed 

 at that quar/tity and its half, i. e. 4' 13' 7*5 "; in which case 

 the examination, instead of being made at the next, will 

 take place at the next division but one, to that which is the 

 subject of trial. During the whole of the time that the 

 examination is made, all the dots, except the one under exa- 

 mination, are for the present 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 micrometer head, how much one of 

 the parts of the interval under examination exceeds the 

 other, and carefully to tabulate the half of their difference. 



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



large astronomical instrument, will have it engraved first. '"^"'^ ***°"^ 

 T-w- -J' • i 1 1 -J. i.- J be engraved 



Uividrng IS a most delicate operation, and every coarser one before it isdi- 



should precede it. Besides, its being numbered is particu- '^''^^^• 

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

 the two annexed tables of errours,|the side columns give sig- 

 nificant names to every dot, in terms of its value to the near- 

 est tenth of a degree, and the mistaking of one for another 

 is rendered nearly impossible. 



The foregoing examination furnishes materials for the con- Tables of ap- 

 struction of the table of half differences, or apparent er- parent errcu-s 

 roui"6*. The first line of this table consists of two varieties; 

 i.e. the micrometers were at 180" distance for obtaining 

 the numbers which fill the columns of the firs>t and third 

 quadrant; and at «^0°, for those of the second and fourth 

 quadrant. The third variety makes one line, and was ob- 

 tained with a distance of 45°: the fourth consists of two 

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



* If the table of real errours be computecl as the work of examination 

 proceeds, there will be no occasion for this table at all ; but I think it best 

 not to let one part interfere with another, and therefore I examine the 

 whole before I begin to compute. 



adis*" 



