where P and T are the pressure and temperature of air, and P0 and T0 are the standard values of one atmosphere of pressure and 300K. Since with mirages there is no appreciable height difference, pressure differences are negligible, and so the temperature difference dominates differences in the index of refraction. When light travels from one medium to another, the path of the light is refracted, or bent. This is what causes the “bent stick” appearance of a long object partially inserted in water, such as a pole placed into the water of a pool. This behavior is described by Snell’s law:
19) Tycho Brahe famously argued against the heliocentric theory in his time, positing that if the Earth revolved around the Sun, the change in relative position of the stars after 6 months orbital motion could not fail to be seen. He argued that the stars should seem to separate as we approach and come together as we recede. In actual fact, however, after 190,000,000 miles of supposed orbit around the Sun, not a single inch of parallax can be detected in the stars, proving we have not moved at all.
36.) If we take a journey down the Chesapeake Bay, by night, we shall see the "light" exhibited at Sharpe's Island for an hour before the steamer gets to it. We may take up a position on the deck so that the rail of the vessel's side will be in a line with the "light" and in the line of sight; and we shall find that in the whole journey the light will won't vary in the slightest degree in its apparent elevation. But, say that a distance of thirteen miles has been traversed, the astronomers' theory of "curvature" demands a difference (one way or the other!) in the apparent elevation of the light, of 112 feet 8 inches! Since, however, there is not a difference of 100 hair's breadths, we have a plain proof that the water of the Chesapeake Bay is not curved, which is a proof that the Earth is not a globe.
3) The natural physics of water is to find and maintain its level. If Earth were a giant spinning sphere tilting and hurling through space then truly flat, consistently level surfaces would not exist here. There would be a massive bulge of water in the oceans because of the curvature of the earth. If earth was curved and spinning the oceans of water would be flowing down to level and covering land. Some rivers would be impossibly flowing uphill. There would massive water chaos and flooding! What we would see and experience would be vastly different! But since Earth is in fact an extended flat plane, this fundamental physical property of fluids finding and remaining level is consistent with experience and common sense. The water remains flat because the earth is flat! 
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