Thermal Velocity - in Three Dimensions

In Three Dimensions

If is defined as the most probable speed, then

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If is defined as the root mean square of the total velocity (in three dimensions), then

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If is defined as the mean of the magnitude of the velocity of the atoms or molecules, then

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    The truth is that a Pigmy and a Patagonian, a Mouse and a Mammoth, derive their dimensions from the same nutritive juices.... [A]ll the manna of heaven would never raise the Mouse to the bulk of the Mammoth.
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