In the theory of the specific heats of gases of diatomic molecules the functionplays a well-known and important part. The rotational specific heat Crot of a diatomic molecule, which is susceptible of representation as a rigid body with two equal principal moments of inertia, without spin about the other principal axis, is given bywhere R is the gram-molecular gas-constant andthe pair of equal moments of inertia being equal to A. Whether such a model is or is not an adequate representation is a matter for determination by a detailed study of the structure of the band spectrum, particularly of the nature of the normal electronic and vibrational state. It is known to be applicable to normal molecules of the halogen hydrides, to CO and other molecules which have a normal state of type 1S including (but for a certain special feature) H2.
Of. the use of the standard deviation to measure the magnitude of a random variable. See alsp an application in §4 below to the metricization of certain function-spaces. t Of . HLP, (2.11.1), p. 30. X Fox axiomatio characterizations of 9J^ and @^ c/. HLP 215 and Motzkin (4) respeotivelv.
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