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The retardation of the sun's rays in passing through a clear atmosphere obviously depends on the depth penetrated; hence neglecting the curvature of the atmospheric limit the retardation will be as the secants of the zenith distances.
The other arm of the lever describes also a triangle; and the corresponding sides of those two triangles, calculated scientifically, or measured geometrically, and also the sines, tangents, and secants generated from the angles, and geometrically measured, have the same proportions to each other as the different weights have that will balance each other on the lever, leaving the weight of the lever out of the case.
The Kansas boasted all the comforts and luxuries of a well-equipped hotel. Seated at the same table as herself was a skilful sailor, using logarithms, secants and cosecants, polar distances and hour angles, as if he were in some university class-room.
"But how much do you know of prismoidal formulae, or logarithmic secants? not to speak of segmental ordinates, or the cycloidal calculus; or even of adiabatic expansion, or torsional resistance, or the hydrostatic paradox, or the coefficient of friction? Now, these things are the very A B C of mechanics, as you'll find to your utter confusion."
At other inclinations, the interval will be the difference of the secants from the secant of the inclination, or angle of refraction of the principal beam.
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