Instrumental Error of his Horizofi-Seclor. $33 



measured in defect by a constant angle. On repeating the 

 observations with the object-glass placed nearest the lesser 

 ring, the measurements, it is evident, will be in excess by the 

 same quantity. 



Having substituted Dollond's eye-tube in the place of the 

 object-glass of the sector, the latter was removed to the other 

 end of the cylinder. A comparison of two observations, made 

 with the sector in its original and altered state, indicated an 

 average defect in the former of 23", or constant error of 



(f =) n*5. 



By the Third Method, 



Theory. — The surface of the fluid in which a cube or other 

 body floats, is always in contact with it, whatever its direction, 

 at the same points of its sides. A section of the cube through, 

 these points would be a horizontal plane. A line, drawn on 

 any surface of the floating cube, will be constantly parallel or 

 inclined at one angle to the horizon during a revolution in 

 azimuth of the cube. Consequently, if we fix a telescope to 

 the floating body, its line of collimation must be either level, 

 or inclined at a constant angle, whatever the (lateral) direction 

 of the telescope. Let the line of collimation lie in the line 

 drawn from the object at which it is directed to another si- 

 tuated diametrically opposite, and should it be found, on re- 

 versing the floating body, to point with equal exactness at the 

 opposite one, it must be horizontal. 



Captain Kater's floating collimator, constructed on the above 

 principle, when used to prove a telescopic-level, should be 

 placed between it and an auxiliary telescope, of which the line 

 of collimation is directed at the horizontal wire of the level. 

 Having pointed the collimator at this telescope, turn it half 

 round in azimuth, and it will be found directed either exactly 

 at the horizontal wire of the (adjusted) level, or at a small 

 angle above or below it. In the former case the instrument 

 must be perfect; in the next it measures elevations in defect 

 by half that angle; and in the latter, in excess by the same 

 quantity. 



On the Effect of Flexure in the Cylinder. 



Were the object-glass fixed within one ring, and the cross 

 wires within the other, a slight deflection of the tube could 

 not sensibly affect the parallelism of the line of sight to an 

 axis passing through the centres of both rings. When the 

 stop is fixed, as in the sector, between the rings, the effect of 

 flexure must be to depress the horizontal wire below the level 

 it would otherwise maintain. The line of sight, although still 



