O THE CORRECTION OF SEXTANTS FOR ERRORS 



be the mean of the values given by the different series of comparisons, 

 while the probable errors of the corrections, and of observations made 

 with the sextant in question, could be deduced from the final residuals. 

 But such a process, or even one involving only a single reading upon 

 every line of the graduation, is far too tedious and burdensome to be 

 practicable. We must be content in most cases with a comparatively 

 brief and imperfect investigation, having for its object the best result that 

 can be derived from a moderate expenditure of time and labor. With 

 this end in view the examination must be limited to a few points equally 

 distributed over the arc, but sufficiently numerous to warrant the assump- 

 tion that they collectively represent the mean arc accurately enough for 

 any kind of observation in which the sextant will be employed. In this 

 way, although the attempt to secure an exact correction for every reading 

 is abandoned, errors which similarly affect considerable portions of the arc 

 may be corrected, and the existence of large uncorrected errors can gen- 

 erally 4)e detected. The formation and solution of the normal equations 

 usually entail a rather laborious computation, but this can be greatly 

 abridged by a general solution, and by other convenient devices, if the 

 examination is always made upon a uniform system of comparisons at 

 certain invariable distances from each other. In what follows one system 

 of this kind is presented in detail, as a type of similar systems comprising 

 a greater or less number of comparisons. 



With reference to the nature of the service expected of them, sextants 

 may be divided into two classes, assigning to the first class instruments 

 used in makiug observations for latitude and time with the artificial hori- 

 zon, measuring the principal angles of surveys, etc., and to the second 

 class those emi)loyed in the ordinary routine of navigation, and other 

 operations of a similar grade. All the corrections of a sextant of the first 

 class should be determined with as much precision as the capacity of such 

 an instrument warrants, while for those of the second class it is only 

 necessary to insure the absence of errors exceeding certain limits. In 

 considering this subject with reference to the wants of the naval service, 

 it was thought to be desirable that no part of the arc should be more 

 distant in either direction from one of the points examined than the 

 space covered by the vernier. With the usual division of the limb to 

 10', reading by the vernier to 10", this condition requires an examination 

 at points not more than ten degrees apart. It was decided, therefore, to 

 make circle readings with the index set successively at 0°, 10°, 20°, etc., 

 to and including 130°. At first a comparison was also made at 140°, 

 when the range of the sextant extended so far, but after some experience 

 the practice was discontinued, for the definition of the collimator-mark 

 is frequently so much impaired by extreme obliquity of the index-mirror 



