30 Descriptto?i of a circular 



Is the diaphragm, anci the remaining part is a ring of nlo- 

 ther-of- pearl, having its interior circumference divided into 

 360 equal parts. The mother-of-pearl ring, which appears 

 connected with the diaphragm, is completely separate from 

 it, and is fixed at the end of a brass tube which is made 

 to move between the third eye-glass and the diaphragm, so 

 that the divided circumference may be placed exactly in the 

 focus of the glass next the eye. When the micrometer is 

 thus fitted into the telescope, the angle subtended by the 

 whole field of view, or by the diameter of the innermost 

 circle of the micrometer, must be determined either by mea- 

 suring a base or by the passage of an equatorial star, and 

 the angles subtended by any number of divisions or de- 

 grees will be found by a table coji^tructed in the following: 

 manner. 



Tuct AmpfiB, fig. 2. be the interior circumference of the 

 micrometer scale, and let mn be the object to be measured. 

 Bisect the arch mn in p, and draw Cm, Cp, Cn. The line 

 Cp will be at right angles to mn, and therefore mn will be 

 twice the sine of half the arch mn. Consequently, AB : mn 

 3= rad. sine oi ^mpn; therefore mn .x R = sin. \mpn xAB, 



sin. ^mpn x AB sin. ^-mpn , „ f t 



and mpn = ^-^jt = r~ ^ ^^'^ ^ tormula 



by which the angle subtended by the chord of any number 

 of degrees may be easily found. The first part of the for- 



sin, ^^mpn . i m * -n - -it 



mula, VIZ. ■ ' IS constant, while AB varies with the 



size of the micrometer and with the magnifying power which 

 is appHed. We have therefore computed the following^ 

 table, containing the value of the constant part of the for- 

 omla for every degree or division of the scale. 



Degreeil 



