92 On dividing Instrumenti. 



of the roller come? near the wire of the microscope ; then 

 clamj) it, and with the screw motion make the coincidence 

 complete; where again press iipan the fetler for the second dot: 

 proceed in this manner until the whole ronnd is completed. 



From these 256 erroneous divisior.s, by a certain course of 

 examination, and by computation, to ascertain their abso- 

 lute and individual errors, and to form these errors into con- 

 venient tables, is the next part of the proce-:s, and makes a 

 vcrv important branch of my method of dividing. 



The apparatus must now be taken off, and the circle 

 mounted in the same manner that it will be in the obser- 

 vatory. Tlie two microscopes, which have divided heads, 

 must also be firmly fixed to Ihe support of the instrument, 

 on opposite sides, and their wires brought to bisect the first 

 dot, and the one which should be 180° distant. Now, the 

 microscopes remaining fixed, turn the circle half round, or 

 until the first microscope coincides with the opposite dot ; 

 and, if the other microscope be exactly at the other dot, it 

 is obvious that these dots are 180° apart, or in the true dia- 

 meter of the circle; and if they disagree, it is obvious that 

 half the quantity by which they disagree, as measured by 

 the divisions of the micrometer head, is the error of the op- 

 posite division; for the quantity measured is that by which 

 the arealer portion of the circle exceeds the less. It is con- 

 venient to note these errors -\- or — , as the dots are found 

 too forward or too backward, according to the numbering of 

 the decrees ; and for the purpose of distinguishing the 4- 

 and — errors, the heads, as mentioned before, are num- 

 bered backwards and forwards to fitly. One of the micro- 

 scopes remaining as before, remove the other to a position 

 at right angles : and, considering for the present both the 

 former dots to be true, examine the others by them ; i. e. as 

 before, try by the micrometer how many divisions of the 

 head the greater half of the semi-circle exceeds the less, and 

 note half the quantity -|- or — , as before, and do the same 

 for the other semi-circle. One of the micrometers must now 

 be set at, an angle of 43" with the other, and the half diffe- 

 rences of the two parts of each of the four (juadrants regis- 

 tered with their respective sijjns. When the circle is a ver- 

 tical one, as in the present instance, it is much the best to 

 proceed so far in the examination with it in that position, 

 for fear of any general bending or spring of the figure ; but, 

 for the examination of smaller arcs than '15°, it will be per- 

 fectly sale, and more convenient, to have it horizontal ; be- 

 cause the dividing apparatus will theiy carry the micrometers, 

 several perforations being made in the plate B for the limb to 



be 



