Mr. Nixon's Theory of the Telescopic Level. 



will take place at points in each Y, and at perpendicular di- 

 stances below its axis, the same as before reversing. Conse- 

 quently we might remove the original Ys, subsequent to re- 

 versing the telescope, without altering the place of the bubble. 



It is also sufficiently evident, that when the Ys are not ex- 

 actly opposite to each other, (in which case they may be repre- 

 sented by sections of the trough oblique to the line of junction 

 of its sides,) the cylinder will reverse within them precisely the 

 same as though they were parallel. 



The error of collimation of a telescopic level is the angle 

 (measured on a vertical plane) expressing the inclination to 

 the horizon of the line of sight or collimation. When the 

 error is derived solely from imperfection in the instrument, it 

 is termed constant or instrumental. 



When the tube in which the telescope is placed is conical, 

 or its ends are two cylinders of unequal diameter, the line of 

 collimation, supposed level, will have a constant elevation 

 or depression, accordingly as the object-glass is situated at the 

 wider or narrower end of the tube. 



Let us trace the consequences of increasing the diameter of, 

 for instance, the object-glass end of the cylindrical tube of a 

 perfect telescopic level adjusted for observation. In the first 

 place, the thicker or object end of the tube will now come in 

 contact with its Y above its former perpendicular height, 

 without affecting the other or eye end; and the displaced 

 bubble must come to rest at a point of its scale nearer to the 

 object-glass. On reversing the tube, as the Ys are equal and 

 their angular points are level with each other, neither the ob- 

 ject nor the eye end of the tube suffer any consequent change of 

 perpendicular height ; the telescope is equally elevated after 

 as before reversing, and the bubble must settle at its new 

 mark. 



The elevation indicated by the displacement of the bubble 

 forms only a part of the error. When the tube was cylindri- 

 cal, its axis would be at a perpendicular height above the an- 

 gular point of either Y, by a quantity equal to the secant of the 

 complement of the angular opening of the Y multiplied by the 

 radius of the cylinder. But in increasing the diameter of the 

 object end of the tube, we have proportionately increased the 

 height of its axis, at a point of it exactly over the Y in which 

 it rests, whilst its height over the other Y may be considered 

 as unaltered. Our conical tube will therefore reverse in equal 

 Ys (of which the angular points are level with each other), 

 without displacing the bubble (from its new position) ; yet the 

 line of collimation (which may be adjusted to be fixed during 



a revolution 



