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small as the eight-hundred-thousandth of an inch should be appre- 

 ciable by such an instrument. But can anything like this precision 

 be attained in practice ? 



When Mr. Ross was constructing his beautiful engine for dividing 

 circles, he found that he could not ascertain the position of a line 

 nearer than to the eighty-thousandth of an inch, even with achro- 

 matic glasses, and the micrometer just described : showing that such 

 a micrometer is at least ten times as delicate as can be rendered 

 available to the microscope. 



Without entering into the optical reasons why the position of a line 

 can be determined to a greater degree of accuracy than the diameter 

 of an object having sensible thickness, we will proceed to the method 

 of finding the value of the divisions of the eye-piece micrometer with 

 a particular object-glass. In the telescope this is effected by noticing 

 the number of seconds which a star occupies in passing from wire to 

 wire when the latter are placed at a certain distance apart; and 

 a better method can scarcely be desired. The diurnal motion of the 

 earth is perfectly equable, and that of the clock or chronometer by 

 which it is measured may also be considered so for short intervals of 

 time ; the errors therefore are merely those of observation ; which, by 

 sufficient repetition, may be reduced to an insensible quantity. 



In the microscope the case is widely different ; there is no such 

 perfect foundation to build on ; for we can only assign a value to 

 the eye-piece micrometer by comparing it with one on the stage ; and, 

 if the latter be accurate to the twenty-thousandth of an inch, it is the 

 utmost that can be expected. By not depending on a single division, 

 but taking an average of several, the error may possibly be diminished 

 to the half of that quantity ; and we shall then have very nearly 

 reached the limits of optical as well as mechanical accuracy; for al- 

 though the position of a line may, by very careful observation, be as- 

 certained to the eighty-thousandth of an inch, the diameter of a body 

 can hardly be measured nearer than the forty -thousandth, if so near. 

 Any means then by which this degree of accuracy can be attained 

 will be quite sufficient for our purpose, all beyond being useless. 



A slip of glass placed in the focus of the eye-glass can be used 

 with the divisions sufficiently fine to have the value of the ten- 

 thousandth of an inch with the quarter-inch object-glass, and the 

 twenty-thousandth with the eighth ; and at the same time the half, or 

 even the quarter, of a division may be estimated ; thus affording the 

 means of attaining all the accuracy that is really available. It may 

 therefore entirely supersede the more complicated and expensive 



