r68 On dividing Instruments. 



it to return with the sector whtn the latter is set back at 

 evcrv course. Having la this manner proceeded, troui one 

 interval to another, through the whole circle, the micro- 

 meter at last will be found with its wire, at zero, on the 

 dot from which it set out ; and the sector, with its iClh 

 division, coinciding with the wires of its microscope. 



Having now given a faithful detail of every part of the 

 process of dividing this circle, I wish to remind the reader 

 that, bv verification and correction at every interval, any 

 erroneous action of the roller is prevented from extending 

 its influence to any distant uiterval. It will be further ob- 

 served, that the subdividing sector masrnifies the work ; that 

 by means of its adjustable arc, it makes the run ot the roller 

 measure its corresponding intervals upon the circle; and, 

 without foreign aid, furnishes the means of reducing the 

 bisectional intervals to the usual division of the circle. 

 Furthermore, the motion of the wire of the micrometer H, 

 according to the divisions of its head and corresponding 

 table of errors, furnishes the means of prosecuting the work, 

 with nearly the same certainty of success, as could have 

 happened, had the 256 points been (which in practice is 

 quite impossible) in their true places. 



Now, the whole of my method of dividing being per- 

 formed by taking short measures with instruments which 

 cannot themselves err in' any sensible degree, and, inas- 

 much as those measures arc taken, not by the hand, but by 

 vision, and the whole performed by only looking at the 

 work, the eye must be charged with all the errors that are 

 committed until we come to cut the divisions ; and, as in 

 this last operation the hand has no more to do than to guide 

 an apparatus so perfect in itself, that it cannot be easily 

 made to deviate from its proper course, I would wish to 

 distinguish it from the other methods by denominating it, 

 dividing ly the eye*. 



The 



* I must here rernaric, that Smeaton has represented the j^reatest degree 

 of accuracy that can be derived from vision, in judy^ing of the coincidence 

 of two lines at 5000^^ P*''' °f ^'^ inch. From this it may fairly be inferred, 

 that he had not cultivated the power of the sight, as he had done that of the 

 touch; the latter of which, with that ability which appeared in all his 

 ■works, he rendered sensible to the^J^^th part of an inch. Were materials 

 infinitely hard, no bounds could be set to the precision of contact ; but 

 taking things as they are, the different degrees of hardness in matter, may 

 be considered as a kind of magnifying power to the touch, which may not 

 unaptly be compared v.ith the assistance vvhicli the eye receives from glasses. 

 It is now quite common to divide the seaman's sextant to 10", and a good 

 eye will estimate the half of it ; v«-hich, on an eight-inch radius, is scarcely 

 -fJj^th of an inch. This quantity, small as it is, is rendered visible by 3 

 glass of one inch focal length; and such is the certainty with which these 



quaatities 



