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Iceberg: Rate of Melting:
"The energy conservation of a closed local system improves twofold each time the system’s linear dimensions are doubled. This principle is demonstrated in stars and in icebergs. Icebergs can melt only as fast as they can import heat from their surrounding environment of air and ocean through the surface of the iceberg. The larger the iceberg, the lower the ratio of surface area to its volume or mass. However, as icebergs melt, their mass gets smaller at a mathematical velocity of the third power while their surface area decreases only at a velocity of the second power. This is to say the volume decreases much more rapidly than does the surface area, so, as icebergs get smaller the amount of surface area for each unit of volume of its interior mass increases at an accelerating rate.
“Therefore, icebergs melt faster and faster and when the final piece of ice dwindles to pea size it can be seen by the human eye to accelerate to extinction. Due to the principle of energy conservation improvement with size, the larger the domed-over city, the more stable its atmospheric conditions become and at ever-decreasing cost per unit of volume.”
