U23 



An Account of a Method of dividing Astronomical and other Instru- 

 ments, by ocular Inspection ; in which the usual Tools for graduating 

 are not employed ; the whole Operation being so contrived, that no 

 Error can occur but what is chargeable to Vision, ivhen assisted by 

 the best optical Means of viewing and measuring minute Quantities. 

 By Mr. Edward Troughton. Communicated by the Astronomer 

 Royal. Read February 2, 1809. [Phil. Trans. 1809, p. 105.] 



The description of the method is preceded by some account of the 

 steps by which the author acquired his present skill in the division 

 of instruments, and by observations on the comparative merits of the 

 respective methods employed by Bird, by the late Mr. John Troughton, 

 and by other artists ; after which Mr. Troughton proceeds to the ac- 

 count of his own, which, he says, was first suggested by the action 

 of the perambulator. In the first place, the circle to be divided is to 

 be turned on its inner and outer edges, to correct circles, in the most 

 exact and careful manner. A roller is then adapted to its edge, hav- 

 ing its diameter, as nearly as possible, one sixteenth that of the circle; 

 and since perfect equality could not be directly obtained, the exterior 

 surface of the roller is rendered slightly conical, by a difference of 

 -nrWth of an inch in the diameters of its upper and under surface ; so 

 that by a small motion in the direction of its axis, some one part of 

 its surface may be found perfectly adapted to its purpose. The roller 

 itself being next divided into sixteen parts, each of these will corre- 

 spond with iri-g-th of the whole circle ; a number chosen on account 

 of its being capable of continual bisection, although these divisions 

 will coincide with a very small number of the ultimate divisions of 

 the circle. 



By means of two microscopes, one over the circle, and the other 

 over the roller, the correct adaptation of the circle and roller to each 

 other is first ascertained, or duly adjusted by raising or depressing 

 the roller. An instrument for making dots, with uniformity, is next 

 to be fixed at a due distance from the edge of the circle ; and when 

 one division of the roller is brought exactly under the wire of its 

 microscope, the pointer being pressed down, makes the first dot at 

 any point which may have been previously fixed upon. When the 

 second division of the roller comes under its wire, a second dot is 

 made in a similar manner, and so on till the whole 256 are com- 

 pleted, at intervals that are nearly equal. But it is not really of any 

 consequence how erroneous they may be found by the very important 

 process of examination which is next to follow, and which constitutes 

 the intrinsic excellence of this method. 



The dividing apparatus having next been removed, the circle is to 

 be placed in the same position it is intended to have when employed 

 for observation ; and two microscopes are to be placed, at opposite 

 sides, for the examination of the point of 1 80. The dot at zero, and 

 that at 180, being first bisected, the circle is turned half round ; and 

 if when the zero point is bisected, that at 180 is found not to be bi- 

 sected, the apparent error of its position is measured by the micro- 



