instrtimental Error of his Horizon-Sector. 95 



siderable, some care is required in keeping the plates hori- 

 zontal in the transverse direction, and in making the proof- 

 level parallel to the cylinder; both sources of error tendintr 

 to give a measurement in defect. In some instances it was 

 attempted to place the proof- level parallel in direction to the 

 cylinder, by bringing the middle of each end of the former to 

 the highest point of the adjoining shoulder of the latter; the 

 bar being prevented from toppling by a delicate wedge of 

 mahogany gradually introduced between the sides and the arc 

 until the cross-level of the frame arrived at its mark. M^hen 

 the proof-level was placed in contact with both arcs (which 

 was more frequently the case), the deviation from parallelism 

 with the cylinder could not possibly amount to a tenth of a 

 degree, — a quantity too small to be sensible in its effect on the 

 measurements*. 



It does not appear that there were any trials of this method 

 with the plates reduced, and the results of those made pre- 

 viously were, for the reason assigned, too discordant to be 

 worth transcribing. 



Third Method. — This differs from the preceding one solely 

 in completing the measurements without reference to the levels 

 of the sector ; the proof-level being noted, both direct and 

 reversed, when in contact with the cylinder before as well as 

 after the latter is reversed within its Ys. If the angular points 

 of the Ys are level with each other, the proof-level will give 

 the inclination of the cylinder alike before and after the latter 

 is reversed ; otherwise, if the inclination be made too much 

 before, it will come out equally in defect after reversing the 

 cylinderf. 



For tin's level-tube being glued at the sockets to the Ys of 

 the frame, the inclination of the cylinder given April 16th, 

 1830, temperature 58°, by the third method, was 26"-9 with 

 the left-hand level upwards, and 29"'l with the other level 

 uppermost. On the same day, the measurements repeated at a 

 temperature of 56° were respectively 27"-3 and 29"-2 ; the mean 

 of the whole being 28"-l, or 2" less than by the first method. 



Multiplying the mean of the two methods by 0*586 (the Ys 

 opening at 'an angle of 90°), we obtain 17"-1 lor the constant 

 error of collimation of tlie sector if. 



* When we measure the inclination of a plane, if we do not place the 

 level-tube exactly at right angles to a level line drawn on the plane, we 

 obtain a measurement (in defect) equal (when the deviation and inclina- 

 tion arc both small) to the correct quantity divided by tiie secant of the 

 angle of deviation. 



t By [jrecisely the same process may be found the inclination of the 

 (mathematical) axis of rotation of a transit instrument having unequal 

 pivots. \ Sec page 429 of last volume. 



It 



