14 -ON DIVIDING INSTRUMENTS. 



and indiv'ulual eirours, and to form these errours into con- 

 venient tables, is the next part of tlie process, and makes a 

 very important branch of my method of dividino-. 

 Method of do- T'><' apparatus must now be taken ofF, and the circle 

 ing this. mounted in the same manner, as it will be in the observa- 



tory. The two microscopes, which have divided heads, 

 mnst also be firmly fixed to the support of the instrument, 

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

 dot, and the one wliich 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 microscojje be exactly at the other dot, it 

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

 ameter 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 errour of the 

 opposite division ; for the quantity measured is that by which 

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

 venient to note these errours -}- or ■ — , as the dots are found 

 too forward or too backward, according to the numbering of 

 - the degrees; and for the pnrpose of distinguishing the + 

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

 bered backwards and forwards to fifty. 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 other by them ; i. e. as 

 before, try by the micrometer how many divisions of the 

 head the greater half of the semicircle exceeds the less, and 

 note lialf the quantity 4- or — , as before, and do the same 

 forthe other semicircle. One of the micrometers must now 

 be set at an angle of 45° with the other, and the half-diffe- 

 rences of the two parts of each of the four quadrants regis- 

 tered with their respective signs. 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, 

 frtr fear of any general bending or spring of the figure;- 

 ^4lii*ibr tht; examination of smaller arcs than 45°, it will be 

 perfectly safe, and more convenient, to have it horizontal ; 

 because the dividing apparatus will then carrj' the microme- 

 ters, several perforations being made in the plate B for the 



limb 



