Mr. Nixon's Theory of the Telescopic Level. 427 



inclined to each other at the same angle as before. Conse- 

 quently the cylinder, although reversed, is in contact with the 

 trough at the former points, which lie in a line parallel to 

 the axis of the cylinder and to the line of junction of the sides 

 of the trough. 



Demonstration that the Line of Collimation of a perfect and 

 well-adjusted Telescopic Level is truly horizontal. 



When properly adjusted, the position of the ends of the 

 bubble relative to the level-tube being marked, the telescope 

 (cylinder) may be taken out of its Ys, and replaced, reversed 

 in direction, yet the bubble will come to rest at the mark pre- 

 viously made on the tube. Also, on making the telescope 

 perform an entire revolution within its Ys, the point of inter- 

 section of its wires will continue to intercept the same point 

 of the distant object observed. 



Now as the line of collimation remains constant in direction 

 during a revolution of the telescope within its Ys, it is evi- 

 dently situated in or parallel to the axis of the cylinder, and 

 is also parallel to either of the longitudinal lines on each side 

 of the surface of the cylinder where in contact with the in- 

 terior of the Ys, which latter are equivalent to the transverse 

 sections of the two inclined planes or trough in contact with 

 the cylinder. 



Again : as the cylinder will suffer reversing within its Ys 

 without displacing the bubble, it follows that both these lines 

 of contact are parallel to the horizon ; and being also parallel 

 to the line of collimation, the latter is perfectly horizontal. 



Or, more simply : as the cylinder when reversed in the Ys 

 has its axis in the same line as previously, and the reversing 

 does not displace the bubble, the axis, and consequently the 

 line of collimation, which is proved to be parallel to it, are 

 horizontal. 



In order to simplify the demonstration, the Ys have been 

 considered as equal in angular opening. To prove that any 

 inequality would not vitiate the instrument, we will furnish it 

 with two additional Ys, one wider, and the other narrower 

 than the pair of equal Ys, in which the telescope, adjusted for 

 observation, is supposed to rest. Our object being to place 

 each additional Y with both its sides in contact with the cy- 

 linder without disturbing the latter, we shall find it requisite 

 to lower the narrower Y, and raise the wider one ; which will 

 bring the one to touch the cylinder above, and the other be- 

 low the level of the points of contact of the adjacent original 

 Ys. Nevertheless, on reversing the cylinder, as it is of one 

 diameter throughout its length, its contact with the four Ys 



3 I 2 will 



