MEMORANDA. 



155 



By experimenting with a stage inicionieter, we next endea- 

 vour to ascertain how far the pointer must be moved, in order 

 that the crossed thread shall traverse a space in the field 

 corresponding to 1 -100th of a millimetre. By simply mani- 

 pulating on the stage of the instrument, the stage micrometer 

 can easily be put into the position shown in Fig. II., the long 

 line A B accurately coinciding with a line of the micrometric 

 scale. The eyepiece is then cautiously rotated, till the cross 

 in the field, passing along the imaginary dotted circle in 

 Fig. II., seems to touch the next line of the stage-scale, the 

 long line now assuming the position a b. The arc traversed 

 by the pointer during this rotation is then read off, — we shall 

 suppose it an arc of 8°. The sine of the corresponding arc 

 of tlie dotted circle will, of course, indicate exactly 1-lOOth 

 of a millimetre ; and froin this simple foundation any measure- 

 ment — i. e., the length of the chord of any given arc in that 

 circle — niay be calculated ; for the chord of any arc being 

 equal to twice the sine of half that arc, the value of the chord 

 of 8° is found as follows : — 



Proportion. 

 As sin. 8° : -01 Millimetre : : 2 siii. 4° : chord 8° 



Calculation. 

 Log. 2 sine 4° = 9-1446145 



Log. -01 Millim. = 2-0000000 



Subtract Log. sine 8° 



7-1446145 

 9-1435553 



Chord 8° = Num. -0100244 Millim. = 2*0010592 

 Fig. II. 



