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By W. E. Knowles Middleton

This background of the thermometer comprises controversy approximately its invention, the tale of other scales, Fahrenheit and centigrade, and the background of the sluggish clinical then renowned figuring out of the idea that of temperature. now not until eventually 1800 did humans drawn to thermometers start to see basically what they have been measuring, and the impetus for bettering thermometry got here principally from examine of the weather―the liquid-in-glass thermometer grew to become the meteorologist's device sooner than that of the chemist or physicist. this glorious introductory examine follows the advance of indicating and recording thermometers till contemporary occasions, emphasizing meteorological applications.

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32), this The first two lines in Eq. 33) are the FokkerPlanck equation for continuous processes, and the third line accounts for discontinuities. " W(yly') and W(y'ly) are transition probabilities for finite changes in y. 33) is formally equivalent to the Kramers-Moyal expansion, Eq. 32). We may then infer that the higher-moment terms with n :::: 3 in Eq. 32) correspond to the second line for discontinuous processes in Eq. 33). " We restrict ourselves to Gaussian distributions in all the following, except for chapter 10.

29b). The result is A PE 41 equation for the probability density function for the displacement PRD(X, t) is = oUi + Uj oUi + ~ OTij ot OXj 2 OXj OUi- Tim (OAjm UkOAjm)] + [--+ -OX j 2 ot OXk Tim OAkm] - [2 OXj (U · _U) · J J (Uj - Uj )( Uk - Uk ) . For the random displacement model, the equivalent of the well-mixed condition for the Langevin equation model is PRD(X, t) = constant. 34) The above is equivalent to Eq. (32) on p. 547 in Thomson (1987) and Eq. (9) in Sawford and Guest (1988). The form of the above two equations is like that in Sawford and Guest.

3, p. 68. 7) where the symbols have the same meaning as in Eqs. 5a,b). 1, pp. 534-535) leads to his Eqs. (9a,b) and (10), which satisfy Eqs. Bb) x and u are independent variables. 9) We differentiate Eq. 11) with respect to x, u, and t. 1, p. 3) in combination with Eq. 5a) to get the result in his Eq. Bc, pp. 329330, for the differential of a quadratic form. 2). Here Co is the universal constant associated with this structure function, and c: is the mean rate of turbulence kinetic energy dissipation with c:(x, t).

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