This section is from the book "The Engineer's And Mechanic's Encyclopaedia", by Luke Hebert. Also available from Amazon: Engineer's And Mechanic's Encyclopaedia.

The height of any place or thing; one of the three dimensions of solid bodies; elevation of the celestial bodies, etc. In geometry, the altitude of a figure, or a solid, is the perpendicular distance between its vertex and base. The altitude of buildings, trees, etc. may be measured like that of geometrical solids, from the base to the vertex, but the altitude of lofty mountains or elevated plains is reckoned from the level of the ocean. There are various means for determining altitudes, such as geometrical construction; by observation of shadows; by trigonometrical calculation; and by the use of the barometer. For an account of the various instruments employed as quadrants, sextants, theodolites, barometers, etc, with the methods of applying them, consult their respective names. The altitude of terrestrial bodies may be either accessible or inaccessible. When the object viewed is accessible, and on the same horizontal plane as the observer stands, its altitude may be found in the following way: Provide two deal rods, one longer than the other; fix the shorter one vertically in the ground, and having placed your eye at its top, let an assistant move towards the tower in a direct line, till the top of the second rod is seen on a line with the summit of the object whose altitude is required.

Next measure the distance between the two rods, and also between the shorter rod and the tower. Then say, as the distance between the two rods is to the distance of the shorter rod from the tower, so is the difference in length of the rods to the difference between the height of the tower and the shorter rod. Hence, if to this difference we add the length of the shorter rod, it will give the altitude required. The result may, however, be more conveniently, as well as more accurately obtained, by means of a quadrant, or other instrument to measure angles, in the following manner. Measure the distance of the observer's place from the foot of the tower, and take the angular elevation by means of the quadrant; then say, as the cosine of the observed angle is to the measured distance, so is the sine of the observed angle to the altitude required. Altitude, in astronomy, signifies the angular distance of a celestial body from the horizon, measured on a vertical circle. The altitude is either true or apparent, accordingly as it is measured from the rational or the sensible horizon. The observed or apparent altitude varies from the true on two accounts.

First, the body is seen from the surface of the earth, instead of from the centre, which causes it to appear lower than its true place, by a quantity which is denominated the horizontal parallax. Secondly, the rays of light by which the body is perceived, are refracted by the terrestrial atmosphere, and, consequently, it appears higher than it otherwise would. To obtain the true altitude, therefore, of a celestial body, we must add the parallactic angle to the apparent altitude, and from the sum subtract the refraction. The fixed stars, from their great distances, have no sensible parallax, and hence the preceding remark applies only partially to them. But the difference between the true and apparent altitude of the moon, is, from its proximity to us, about 52°. Altitude of the eye, in perspective, is the height of that point in the perspective plane which would be made by a right line drawn from the eye and cutting the plane perpendicularly.

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