Correction curves

M = log A - log Aq. Distance correction curves between cpiccntral distance of the seismograph versus log A (which are also sometimes referred to as attenuation curves) are used for this purpose. One standard attenuation curve is shown in Figure 14.12(a). 

Figure 14.12(a) Distance correction curve for determining the magnitude of an earthquake... 

In Steps 2 and 3, the vessel s nondimensional radius and the blast wave s nondimen-sional peak pressure at that radius were calculated. As a blast wave travels outward, its pressure decreases rapidly. The relationship between the peak pressure and the distance R depends upon initial conditions. Accordingly, Figure 6.21 contains several curves. Locate the correct curve by plotting (R, P ) in the figure, as illustrated in Figure 6.28. 

Figure32.26 Viscosity correction curves (adapted from Hydraulic Institute Standards, 12th edition, Flydraulic Institute, Cleveland, Ohio, 1969)...

Correction for the effect of the potential difference in the diffuse layer is carried out by plotting log against E - 2 rather than against E. It can be seen from Fig. 5.8 that the corrected curves are identical for both electrolytes. 

Fortunately, however, the deviations from "true dates" caused by all these factors are usually small for dates falling within the last three millennia. Correction curves are used to correct dates that fall between several millennia b.c.e. and the present day, so that the dates determined with radiocarbon are concordant with historical dates (Pearson et al. 1989 Suess 1965). 

Fig. 13 Correction curve generated with silicon powder. The silicon powder is a Standard Reference Material available from the National Institute of Standards and Technology, Gaithersburg, Md. (Reproduced with permission of the National Institute of Standards and Technology, from Ref. 71.)...

The practical application of these observations is to minimise the effect of iodate by rapidly carrying out the iodometric titration of chlorine residual in seawater at pH 4. Moreover, if desired, a titration correction curve can be generated using iodate at the specific concentration of iodide in the sample in question, as there appears to be a complete conversion of seawater iodide to iodate in the presence of excess chlorine. 

System total heads should be estimated as accurately as possible. Safety factors should never be added to these estimated total head values. This is illustrated by Figure 4.8. Suppose that OAi is the correct curve and that the centrifugal pump is required to operate at point A. Let a safety factor be added to the total head values to give a system curve OA2. On the basis of curve OA2, the manufacturer will supply a pump to operate at point A2. However, since the true system curve is OA, the pump will operate at point Ai. Not only is the capacity higher than that specified, but the pump motor may be overloaded. 

For analytical applications, when a linear relationship between fluorescence intensity and concentration is desirable, a correction curve must be built up under the same conditions as those that will be used for the actual experiment. 

Figure 5.14. Comparison of experimental activity coefficients (circles) with theoretical values using the hydration correction (curves). (From Ref. 1, with permission from the American Chemical Society.)...

Dg, Rg. and cOg for the argon dimer (van Mourik and Dunning Jr., to be published) are plotted in Figure 4. The results are similar to the corresponding He2 curves (see Figures 1 and 3), although there are now easily recognized oscillations in the uncorrected results. As in He2, the counterpoise-corrected curves are well behaved and can be used to establish the CBS limit with some confidence. 

As mentioned earlier in this section, the convergence behavior of computed properties generally becomes less exponential as the quantities become less related to energies. By way of illustration, neither the application of the counterpoise procedure nor the addition of diffuse functions to the basis set improves the convergence behavior of the computed anharmonicities co x of the HF molecule (see Figure 10). Even in this case, however, both the uncorrected and corrected curves appear to be converging to the same limits. 

Once the efficiency of normal fluorescence had been determined, the efficiencies of phosphorescence and delayed fluorescence under the same conditions were derived without reference to any other solution. The ratio of the efficiencies of delayed fluorescence (6) to that of normal fluorescence was simply caculated by comparing the intensities at one of the principal maxima in the spectra, which were, of course, identical in shape. Due correction was made for the phosphorimeter factor (assumed to be 3 for lifetimes greater than 1 msec.) and also for the different instrumental sensitivities at which the two spectra were measured. Phosphorescence efficiencies were determined in a similar manner, except that the spectra first had to be corrected and the areas under the corrected curves compared with those of the corresponding normal fluorescence spectra. The phosphorimeter and instrumental sensitivity factors were then applied as before. 

J3—ft. Strictly speaking, it depends on the intensity distribution in a line (Jones, 1938) and the ideal method of obtaining / is by a Fourier analysis of the line shape (Stokes, 1948) in practice it is doubtful whether such elaboration is worth while, and it is usually sufficient to use correction curves given by Jones (1938) for the relation between b/B and jS/JB for different line-shapes, or to use Warren s (1941) relation j32 = J52—6a which gives very similar results (King and Alexander, 1954). 

A buret is calibrated by filling with water to the zero mark, withdrawing to the 25 ml mark, and weighing the water withdrawn From the following data, compute the correction that must be applied at the 25 ml mark (similar corrections at other intervals may be used to construct a correction curve for the entire range of the buret)... 

Thermogravimetric analyses were carried out in 10°-30° temperature increments with 200-mg samples using a conventional (Mauer) TGA system. Automatic recording of weight change was used to follow reaction to equilibrium, but actual weighings were recorded only by manual operation. The sample was bathed continuously in air of controlled humidity (Pmo = 7.9 torr) flowing at 180 cc/min. Precautions were taken to minimize drafts and convective currents, and buoyancy correction curve was made to 950°C. Further details on experimental methods are available (12). 

Figure 3-1 Titration curve for histidine. The solid line represents the uncorrected titration curve for 3 mM histidine monohydrochloride titrated with 0.2 M HCL to lower pH or with 0.2 M NaOH to higher pH assuming pKa values of 1.82, 6.00, and 9.17. The dashed line represents the corrected curve showing the number of protons bound or lost per mole of histidine monohydrochloride.

Ejected electron analyzers can be calibrated at lower energies (<25 eV) using UV photoelectron spectroscopy and comparison with quantitative photoelectron spectra. The intensity ratios provide a relative transmission function (7 ) directly. Quantitative (relative) photoelectron spectra have been reported by Hotop and Niehaus79 at an ejection angle of 90°, and these results have been used by Yee et al.66 to calibrate a 127° analyzer for which the correction curve has already been shown in Fig. 3. More recently Gardner and Samson80 reported quantitative (relative) photoelectron spectra that can be used as a standard for analyzer... 

It thus appears that a judicious application of correction curves of the form of (III.l) can transform a uniform set of ab initio potential-energy curves into a set of corrected curves that are very representative of the actual system. Such curves must be of similar chemical character such as all valence states or all Rydberg states. Rydberg-valence mixing cannot be easily accounted for in ab initio calculations, and simple empirical corrections do not seem possible for such situations. 

This gives the corrected curve (dashed line) and leads to the evaluation of the oo "C" and "A" values. 

Fig. 3 Correction curve for the C02 analyzer with its expanded uncertainty band (k=2)...

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