Rayleigh derivation

Fig. 3. Lyman a bridhtness isophotes of Comet Kohoutek 1973 XII, intensities in Kilo-Rayleigh, derived from photographs taken with an electronic camera by Carruthers et al. (see Keller )...

In 1871 Lord Rayleigh derived the following equation that demonstrates the relationship of the intensity (/d of scattered light to the intensity (Iq) of the incident light ... 

Approximate solutions to Eq. 11-12 have been obtained in two forms. The first, given by Lord Rayleigh [13], is that of a series approximation. The derivation is not repeated here, but for the case of a nearly spherical meniscus, that is, r h, expansion around a deviation function led to the equation... 

The oscillatory behavior of cavities in an acoustic field has been well-described by a variety of mathematical models derived from Rayleigh s original approach with the inclusion of various nonideal liquid properties (28-33). Let us examine, as an example, one such equation of... 

C SOC retained SOClost SOC sSOC SOC SOC n Associated 813C value Amount of organic carbon lost Rayleigh fractionation constant of the SOC Soil organic carbon derived from com stover Total corn-derived carbon in the residue returned treatment Com derived from unharvested material in the stover harvested treatment... 

Note that Eq. (5.5) is the equation of the Rayleigh line, which can also be derived without involving any equation of state. Since (p u )2 is always a positive value, it follows that if p2 > p, P2 > Pi and vice versa. Since the sound speed c can be written as... 

Figure 8. Calcium values in vertebrate bone and soft tissue samples versus 6 Ca in dietary source (Skulan and DePaolo 1999). Bone values are systematically about 1.3%o lower than source values. Soft tissue values are more variable. All of the values are hypothesized to reflect the balance between Ca dietary intake and exchange with bone calcium (Fig. 9). The soft tissue values are variable largely because the residence time of Ca in the tissues is short. The high value of the egg white reflects Rayleigh-type distillation the egg white loses light Ca to the shell as the shell forms. The small amount of Ca left in the egg white is highly fractionated. The low 6 Ca value of the seal muscle is interpreted as a sign of distress the seal may have had a dietary Ca deficiency for several days or longer before it died, and hence was deriving most of its Ca from bone dissolution.

Dunham [5] derived these expressions Y ((t)e,Be,a0, necessarily manually, through a JBKW procedure, which he claimed to make more general [4] than what had appeared in previous literature. Dunham reported expressions F containing coefficients aj up to a, and Sandeman [19] and Woolley [20] extended manually these results according to a roughly analogous procedure. Kilpatrick [21] applied perturbation theory in successive orders to derive expressions for 1, and Bouanich [22] applied Rayleigh-Ritz perturbation theory for solution of... 

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