86 Prof. Encke on Hadley's Sextant. 



of the incidental errors of observation, are partly founded on 

 the nature of the instrument. Among these are the errors 

 of excentricity and division, which in a good instrument can be 

 ascertained only by uncommonly accurate mechanical means. 

 The remeasurement of known angles, measurement of all an- 

 gles round the horizon, if there is an opportunity of so doing, 

 are means which will in common cases enable to ascertain the 

 existence and approximate amount of such errors. Other 

 sources of error arise from the imperfect nature of the mate- 

 rials ; and although probably existing in every instrument, they 

 are in the better ones inclosed within narrow limits. To these 

 we may reckon the difficulty of producing perfectly plain glass 

 mirrors quite free from a prismatic form in their two reflecting 

 surfaces. The distinctness of the images will determine the 

 quality of the mirrors ; and although we shall suggest below a 

 method of taking into account the errors, arising from a prisma- 

 tic form of the mirrors, it would be useless to apply it, as it would 

 be impossible to obtain accurate angles by mirrors so formed. 

 The dark glasses used in observations of the sun may like- 

 wise introduce errors. If it is possible to apply them in re- 

 versed positions, and if the index error is determined with 

 and without coloured glasses, one may determine the error 

 caused by them. This error will be of no effect if the error 

 of index is determined with the same coloured glasses with 

 which the measurement is performed. In all those points it 

 will be necessary to rely on the accuracy of the artist, if the 

 deviations are not too gross. 



The errors which then remain, arise from the non-fulfil- 

 ment of the above-stated three conditions. 



Let us now assume that the sextant had all three defects, 

 that the line of collimation 

 is not pai'allel, nor either 

 of the mirrors perpendicu- 

 lar to the plane of the in- 

 strument; and let again BC 

 be the plane of the sextant, 

 and let the letters have the 

 same signification as in 

 fig. 1. If Q is the pole of 

 the plane of the sextant, the 

 line parallel to the luie of 

 collimation will not be 

 OA, but let it be O A', and 

 let A' be in the circle QA. 

 The arc A A', the inclina- 

 tion of the line of collima- 

 tion, may be = i. In the same manner let us assume that the 



pole 



