OF ECCENTRICITY AND GRADUATION. 



11 



the time of examination this sextant had just been repaired after its 

 return from sea service. 



The first column contains the settings, S, of the sextant, and the fourth 

 gives B, the corresponding readings of the circle, the seconds being the 

 mean of those read from the verniers, and recorded in the two preceding 

 columns. The reading at 0° is the mean of those at the beginning and end 

 of the examination. As the labor of computation is lessened by numeri- 

 cally diminishing the values of Z), especially those belonging to the larger 

 angles, Z should be either equal to the circle reading when S = 0°, or so 

 chosen as to differ a few seconds therefrom, in the direction, and to an 

 extent, indicated by the subsequent values of R. The differences D in 

 the fifth column are found by (3). Table II is serviceable in filling out 



Table II. 



the sixth and seventh columns ; it should be copied upon a slip of paper 

 in lines spaced like those of the record, and laid upon the latter beside 

 the fifth column, so that each value of D may closely follow its two co- 

 efficients. By opening the Recheutafeln at D, the two products can be 

 instantly taken out and entered in the same line. The quantities in each 

 of these three columns are next added, and the respective amounts written 

 underneath. 



No material error can be introduced by retaining only two places of deci- 

 mals in these products. At first view, indeed, even the second place might 

 seem to be superfluous, since D itself is frequently several seconds in 

 error, but in (7) the sums of the two sets of products have coefficients 

 with opposite signs, and the effect of an alteration in one of these sums is, 



