8 HYDROORAPHK'AL SURVEYING [chap. i. 



temperature ; and from defective graduation ; but, as it is 

 generally impossible to disentangle the errors arising from these 

 different sources, they are all included in the one correction for 

 centring. 



Centring error is to be obtained by comparing the angle 

 measured by the sextant with the true angle. 



It is to be found roughly by measuring a series of angles 

 carefully, by repetition, with a large theodolite, between well- 

 defined objects on the horizontal plane at different angular 

 distances, and then measuring the same with the sextant placed 

 on a stand. The difference will be the centring error at each 

 angle, index error being first applied. 



The most accurate method, because it employs a large 

 number of observations for the same, or nearly the same, angle, 

 is by observation of pairs of circum-meridian stars in the 

 artificial horizon, at various altitudes. Double the difference 

 between the resulting latitude by each star, and the mean lati- 

 tude, will be the centring error for an angle equal to the double 

 altitude of that star, that is the angle actually measured by 

 the sextant, index error being carefully determined and applied 

 before working out. 



The sign of the correction is easy to determine from a con- 

 sideration of whether the altitude is too little or too great. 

 Thus in north latitude, if stars south of the zenith give a latitude 

 too great, their altitudes have been too little, and the correction 

 for centring will be plus. 



It is hardly necessary to say that every precaution must be 

 taken to eliminate other errors, such as choosing stars of a 

 closely similar altitude, unless the latitude is already accurately 

 known ; determining the roof error of the horizon, or elimi- 

 nating it by reversion ; carefully correcting the refraction for 

 temperature, etc., and that it requires considerable accuracy 

 of observation, and many sets, to arrive at a good result. The 

 agreement, or otherwise, of the mean latitude by each pair 

 wiU form an excellent test of the general accuracy of observa- 

 tion, and the agreement of the resulting centring errors by 

 different observations at the same altitudes will enable the 

 observer to judge of the truth of his final errors. Thus every 

 careful set of observations for latitude affords a means of 

 testing this error. 



