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LIII. Theoi-y of the Spirit-Level. By J. Nixon, Esq.* 



Definitions\.-\.'^ I "'HAT pai't of the straight (or perpendicular) 

 -*■ hne in which the plummet hangs, and bodies 

 fall to the ground, which lies above any given point (on the earth's 

 surface) through which it passes, is termed the vertical (line) of 

 that point, and terminates upwards at another point called the 

 vertex or zenith. 2. A straight line, or plane passing through 

 the given point at right angles to its vertical, is termed a hori- 

 zontal line or plane. 3. As no one vertical is parallel to an- 

 other, the horizontal lines or planes of points situated in the 

 same vertical, although parallel to each other, are nevertheless 

 inclined to those of points lying in any other vertical, -i. Planes 

 which pass through the given point and that of its zenith (in 

 the direction of the vertical line in which they are situated), 

 cut its horizontal plane at right angles, and are called vertical 

 planes. 5. As the angle formed at the given point by the in- 

 tersection of its vertical and a straight line from any other 

 point will lie in a vertical plane, it is termed a vertical an- 

 gle, and is equal to the zenith distance of that point or line. 

 6. The vertical angle formed at the given point by the inter- 

 section of one of its horizontal lines and a straight line pro- 

 duced from any other point, is equal to the horizontal inclina- 

 tion of that line. 7. This vertical angle is also termed the ele- 

 vation or depression of the same line or point, accordingly as 

 it is situated above or below the horizontal plane (or horizon) 

 of the given point. 8. The zenith distance of a horizontal 

 line or plane, and the elevation of the zenith of any given 

 point being equal to each other and to a right angle, it follows 

 that the angle of elevation of any other point or line is equal 

 to 9QP minus its zenith distance, and that of depression to the 

 zenith distance mi?ms 90'\ 



9. Fluids gravitate in straight lines in the direction of gra- 

 vity. 10. When at rest, and subjected to the sole action of 

 gravity, their order of superposition, with curved surfaces of 

 contact, is inversely as their specific gravities. 1 1 . The hori- 

 zontal lines or plane of any given point situated on the sur- 

 face of a fluid, having other fluids superincumbent or not, are 

 tangents to that surface. 12. When the surface of the fluid 

 is of inconsiderable extent, it is sensibly a horizontal plane, 

 perpendicular to the vertical and parallel to the horizontal 

 lines and plane of any other point above or below it. 



* Communicated by the Author. 



+ The exact figure of the earth's surface is supposed to be unknown. 



If 



