108 Mr. J. Nixon o/t the Measurement of his Horizon-Sector. 



the line of collimation of the lattei' deviated 11" in azimuth 

 from an exactly opposite direction. As the cylindrical rings 

 are of unequal diameter, they cannot both come in contact 

 with the same Y at equal heights within it; it would there- 

 fore require an almost impracticable symmetry in the sides of 

 the Ys to insure to the axis of the cylinder a precisely oppo- 

 site direction when reversed within them. With a view to 

 determine whether the deviation proceeded fiom the irregu- 

 lar figux'e of the Ys or from the excentricity of the rings, the 

 sector, containing its own and the additional object-glass, was 

 fixed between two proof-telescopes; but the experiments were 

 abandoned on discovering that the line of collimation of the 

 proof object-glass was irremediably so much out of parallel 

 with the axis of the cylinder, that neither the level of Foriin, 

 nor the longer one of Lealand, could measure the angle. 



The only consistent theory that can be suggested in expla- 

 nation is that which assigns a flexure, not to the projecting 

 tube, but solely to the cylinder of the sector. The conse- 

 quences would be an increased elevation of the lines of colli- 

 mation of both object-glasses, occasioning an augmentation of 

 the constant error with an object-glass (in its usual situation) 

 at the thicker end of the cylinder, and a diminution of the 

 error when the object-glass made use of is placed at the smaller 

 extremity. Were the cross wires fixed equidistant from the 

 ends of the cylinder, half the sum of the instrumental errors 

 by the two object-glasses (as the increment in one and the 

 decrement in the other produced by flexure would be equal 

 and opposite quantities,) should be equivalent to the error 

 arising solely from the unequal diameter of the cylindrical 

 rings. This half-sum or mean error has been found by the 

 eleventh method to amount to 14"; and the purely cylindrical 

 error comes out by the first method at 1 7". Admitting the 

 total error for the proper object-glass to be 20", its value for 



the additional one should be (14< — 20— I* =) 8"; which ex- 

 ceeds the actual measurement by only 2". The cross wires 

 are fixed nearest the smaller end of the cylinder, which would 

 make the flexure most, and the total error least, for the addi- 

 tional object-glass. But were we to confide in the results by 

 the first methods, the flexure for the proper object-glass would 

 be (20-17 =)3", and for the other (17-6 =) 11". 



[To be continued.] 



