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



may move either telescope in a parallel direction to a higher 

 or lower level, or laterally ; yet its wires, whilst visible, will 

 still appear to cover at their intersecting point, that of the 

 wires of the other telescope. Rays of light falling upon an 

 object-glass from a distance within ten miles are sensibly di- 

 vergent, and form their focus within the tube at a greater di- 

 stance from the object-glass than the place of the sideral 

 focus. 



A straight line revolving about a parallel fixed line or axis 

 at a constant distance from it, describes the longitudinal sur- 

 face or sides of a cylinder. In the revolution of a cylinder 

 about its fixed axis, every point of its sides describes a circle, 

 to which that axis, passing through its centre, is perpendi- 

 cular. The longitudinal lines, formed on the surface of the 

 cylinder at any points of it, by planes passing in the direction 

 of its axis, are parallel to that axis and to each other. When 

 the sides of a cylinder press equally against a plane, the points 

 of tangence form a straight line parallel to the axis of the cy- 

 linder. Sections of the cylinder by (parallel) planes passing 

 perpendicular to its axis are circles, all of equal diameter, 

 having the axis of the cylinder in the centre ; and the in- 

 tersections by the same plane of the one in contact with the 

 cylinder, will be as many parallel straight lines, tangents to, 

 (and in the plane of) each corresponding circle of the section. 

 A circle cannot come in contact with two lines inclined to 

 each other, except at a point in each equally distant from the 

 point in which they meet (the distance varying with the an- 

 gular inclination of the lines). If we press a second plane, 

 inclined to the first in an opposite direction, equally against 

 the other side of the cylinder, transverse sections of the cylin- 

 der perpendicular to its axis, passing also through the two 

 planes, will be circles, equal in diameter, in contact with two 

 (tangential) lines inclined to each other at a constant angle, 

 and the line of junction of the two planes will be parallel to 

 the axis of the cylinder. A plane passing in the direction of 

 the axis of the cylinder and that of the line of junction of the 

 two planes will be equally inclined to both planes. The cy- 

 linder, in performing a revolution about its fixed axis, will 

 always be in contact with the same points of the two planes, 

 which points form two lines parallel to the axis of rotation or 

 that of the cylinder, and to themselves. When the cylinder is 

 taken out of the trough formed by the two planes, and re- 

 placed within it reversed in direction, its axis must be situated 

 in the same line as before, but in the opposite direction, be- 

 cause transverse sections of the cylinder and trough will still 

 be circles of the previous diameter, in contact with two lines 



inclined 



