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On Growth and Form
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=== 2. On Magnitude === [[Image:Boat models by William Froude.JPG|thumb|right|Models used (by [[William Froude]]) to show that the [[Froude number|drag on a hull varies with square root of waterline length]]<ref>{{Cite book | last=Newman | first=John Nicholas | author-link=John Nicholas Newman | title=Marine hydrodynamics | url=https://archive.org/details/marinehydrodynam00newm | url-access=limited | year=1977 | publisher=[[MIT Press]] | location=Cambridge, Massachusetts | isbn=978-0-262-14026-3 | page=[https://archive.org/details/marinehydrodynam00newm/page/n43 28]}}</ref>]] (1st p. 16 β 2nd p. 22 β Bonner p. 15) :: Thompson begins by showing that an [[Surface-area-to-volume ratio|animal's surface and volume (or weight) increase with the square and cube of its length]], respectively, and deducing simple rules for how bodies will change with size. He shows in a few short equations that the [[Froude number|speed of a fish or ship rises with the square root of its length]]. He then derives the slightly more complex scaling laws for birds or aircraft in flight. He shows that an organism thousands of times smaller than a bacterium is essentially impossible.
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