Instrumental Error of his Horizon-Sector. 107 



ments by the last and preceding methods should exceed by 7" 

 those derived from the eleventh method, the eye-piece of the 

 sector was taken out of its cylinder and replaced by the object- 

 glass (described page 339), which was attached to the cylinder 

 by two screws passing through a slit in the latter. By this ob- 

 ject-glass the level line of collimation of the square telescope, 

 measured twice, (precisely on the same plan as previously by 

 the proper object-glass of the sector,) appeared under an 

 elevation, not of about 20" as might have been anticipated, 

 but of only 5"'7- Although the reversing points of the great 

 levels (which were obtained with both object-glasses remain- 

 ing within the cylinder,) had not varied materially from their 

 preceding value, yet to avoid all risk of error, a set of mea- 

 surements were immediately undertaken, without the slightest 

 alteration in the state of the sector, by its own object-glass, 

 which gave 21"-9 for the error. As the average of the re- 

 sults by the two object-glasses ^= = 13"*8,^ agrees 



within the fraction of a second with that by the eleventh me- 

 thod, it is highly probable that the measurements by the ad- 

 ditional object-glass were vitiated either by the tube con- 

 taining it projecting so much beyond the cylinder as to pro- 

 duce flexure, or because the tube did not fit perfectly tight 

 within it. In fact, when the cylinder was raised carefully out 

 of, but immediately replaced within its Ys, by taking hold of 

 the two tubes containing the object-glasses, the inclination of 

 the line of collimation of the additional object-glass vai'ied se- 

 veral seconds. It should also be remarked that the error by 

 the tenth method, which differs slightly in principle from the 

 eleventh, but does not require an additional object-glass to the 

 sector, indicated the error to be 2l"'3. On the other hand, 

 it must in candour be admitted that a deflection of the pi'o- 

 jecting tube occasioned by its own weight would lower the line 

 of collimation of the (adjusted) sector, and tend to augment its 

 constant error. 



Professor Bessel states that the pivots of the axis of his 

 meridian circle are cylinders of unequal diameter, and that 

 their axes are not situated in the same straight line. The 

 formula; for the requisite corrections {all the principles of 

 which, I must confess, I do not fully comprehend,) are given 

 in the Phil. Mag. vol. Ixiii. pages 4-34 and '^35. 



It has been mentioned, (Phil. Mag. and Annals, N.S. vol. x. 

 page 344), that on reversing the cylinder of the sector when 

 fitted up with an extra object-glass placed within the eye-end, 



P2 



