OP ECCENTRICITY AND GRADUATION. O 



Tliese conditious having been satisfactorily established, the course of 

 procedure is as follows : Lay the sextant on the table of the apparatus 

 with the central leg, or axis guard, nearly in the middle of the small 

 circular mark, bring the clamps in opposing directions against the three 

 legs, and secure them with just sufficient pressure to prevent any subse- 

 quent displacement. Cover the horizon glass with all i4s colored screens, 

 bring the reflected image of the collimator-mark into the field of the 

 telescope, verify the focus, and see that the wire to be used in bisection is 

 perpendicular to the path described by the mark when the index-bar is 

 moved. In any position of the index-bar the mark can now be brought 

 into the field by turning the table, and vice versa within the range of 

 the sextant. By means of the table-screws make the axis of the sextant 

 parallel to (and nearly coincident with) that of the circle, which will be 

 the case when in any two, and consequently in all, positions of the index- 

 bar the image passes through the center of the field as the table rotates. 

 This is most readily accomplished by first turning either one of a pair of 

 the screws which has been brought parallel to the axis of the collimator, 

 and afterward turning the third screw when the same pair has been 

 placed at right angles to that axis. If the index-mirror is not parallel 

 to the axis of the sextant, the image cannot be made to pass through the 

 center of the field in more than two positions of the index-bar, for the 

 rotation of the axis causes that part of the ray passing through the tele- 

 scope axially which lies beyond the mirror, to describe, not a plane, but 

 a conical surface, only two elements of which can be brought parallel to 

 the plane of the circle. It is advisable, therefore, before proceeding 

 further, to see that the image passes through the field centrally when the 

 index-bar is near the middle, and also when near each end, of its range. 



The examination has usually been made by first setting the sextant at 

 0°, bisecting the collimator mark with the vertical wire by moviug the 

 tangent screw of the circle, and recording the reading of one pair of op- 

 posite verniers. After repeating this operation for each line of the gradu- 

 ation included in the inspection, a final reading is made at 0°, which ought 

 to agree closely with the first one unless some displacement has intervened. 

 With ordinary care this accident rarely happens, and if it does occur, 

 its location should be revealed by a break in the series of readings. 



The arc of a sextant, being the result of a fallible human eftbrt to ma- 

 terialize a geometrical conception, must be regarded as more or less imper- 

 fect in every detail. There is everywhere, however, a tolerably close ap- 

 proximation to a certain supposititious graduation absolutely free from 

 error, which may be called the mean arc, so situated that the algebraic 

 sum of all the distances between corresponding lines of the actual and 

 mean arcs is equal to zero. Every reading of the sextant will, therefore, 

 require a correction consisting of two parts — one due to the eccentric posi- 



