324 



meter, and the half of that quantity is noted in a table + r > ac- 

 cording as its position is found forward or backward in the intended 

 order of the future divisions. The four quadrants are next examined 

 in the same manner, by removing the micrometer microscope to a 

 position 90 distant. Half the observed error is again the real dif- 

 ference of the two portions of semicircle compared ; and since the 

 sum of the quadrants (though not accurately 180) is known by the 

 previous examination, the quantities themselves are known, and the 

 real error of each quadrant is then noted. In a similar manner the 

 succeeding bisectional points, at the distances from each other of 45, 

 22 30', 11 15', 5 37' 30", 2 48' 45", and 1 24' 22", are suc- 

 cessively examined ; and the real errors of the several dots, from their 

 true places, are computed and arranged in a table, so that by means 

 of the dots themselves, together with their tabulated errors, the true 

 places for the future divisions may be correctly known. 



For the purpose of laying off these ultimate divisions, the circle is 

 again placed in a horizontal position, and the roller is again applied 

 to it. But as it would not be easy to divide the roller itself with 

 sufficient exactness, a sector is added to the apparatus, having its 

 radius four times that of the roller. This sector being fitted tight on 

 the axis of the roller, moves with an angular velocity, which is six- 

 teen times that of the circle ; so that one of the former divisions of 

 the circle is measured by an arc upon the sector of 22 30'. But 

 since the ultimate divisions are intended to be 5' each, this sectorial 

 arc must be divided into spaces of 80' each ; and of these spaces 1 6~ 

 will be equal to 22 30', and will correspond with the true 256th part 

 of the circle, or average space between the dots before laid down. 

 The sector has consequently marked upon it eighteen intervals of 80' 

 each, the first and last of which are subdivided into eight parts of 10' 

 each. The fractional parts at each extremity are for the purpose of 

 making the requisite coincidences with the former bisectional dots, 

 and the intermediate sixteen divisions are the scale by which the true 

 divisions are laid down. 



Since this sector, though very correctly divided, may be liable to 

 central error, its arc is made capable of a small adjustment, whereby 

 16-Jths of its divisions are, by trial, made to correspond accurately 

 with Trfrrth part of the circle. 



For cutting the divisions, the same apparatus is employed as was 

 used by Ramsden in his dividing engine, but originally invented by 

 Hindley, of York. These, together with the two micrometer micro- 

 scopes, constitute the whole apparatus to be employed. 



The dividing point is first placed over that part of the circle at 

 which the divisions are intended to be begun, while one of the mi- 

 croscopes is fixed accurately over the first of the 256 dots ; and at 

 the same time the first division of the sector is made to correspond 

 with the wire of the second microscope. 



The first division being now made, the circle is carried forward by 

 a slow motion till the second division of the sector comes under the 

 wire of its microscope, and the second division is now made upon 



