Logarithm paper

Quantitation is performed by the calibration technique. Construct a new calibration curve with methomyl oxime standard solutions (0.2, 0.4, 0.6, 0.8 and 1.0 xgmL in acetone) for each set of analyses. Plot the peak area against the injected amount of methomyl oxime on logarithmic paper. As the amount of alanycarb is measured in terms of its oxime derivative, a conversion factor of 3.8 (the molecular weight ratio of alanycarb to methomyl oxime) should be applied to obtain the net amount. The injection volume should be kept constant as the peak area varies with the injection volume in flame photometric detection. Before each set of measurements, check the GC system by injecting more than one standard solution containing ca 2-10 ng of methomyl oxime. 

The character of the carbon dioxide-time curves for unsubstituted celluloses made impossible the use of simple graphical methods. It was found,22 however, that the data gave reasonably straight lines on logarithm-logarithm paper and the following scheme was employed to obtain estimates of the apparent hydrolysis. Glucose was assumed to be represented by the linear relationship... 

The t /7 of a radioisotope is determined by plotting the radioactivity (or disintegration rate) as a function of time on a semi-logarithmic paper. The slope of the resulting straight line is equal to X. The t a of the radioisotope may then be calculated from the above expression. 

FIGURE 11-4 Percentage leaf injury in pinto bean plants exposed to various ozone concentrations for various durations—concentration plotted vs. exposure duration, m, m, where m, geometric mean concentration for a particular exposure duration mgh irtf for 1 h r time, in hours and p > slope of injury line on logarithmic paper. Reprinted with permission from Larsen and Ifedc. ... 

Using logarithmic paper, plot XIM (as the ordinate) versus C (as the abscissa) for each of the three carbon dosages. Calculate the least squares fit for the three points, and plot. The iodine number is the XIM value at a residual iodine concentration (C) of 0.02 N. The regression coefficient for the least squares fit should be greater than 0.995. 

These curves, when replotted on logarithmic paper, do not give straight lines, indicating that the model cannot approximate the type of behaviour described by Cotton an Boonstra17. Nor is the approximation by one relaxation time, as in a simple Maxwell model, at all satisfactory, However, the function may, of course, be converted into a Prony6 series and the model may therefore behave in relaxation as a set of Maxwell models. 

A semi-logarithmic paper (Fig. 133) may be made with distances between say the horizontal columns in fractions of a metre, while the distances between the vertical columns are proportional to the logarithms of the numbers. Functions obeying the compound interest law will plot, on such paper, as a... 

Examples.—(1) Plot on semi-logarithmic paper Harcourt and Esson s numbers (l.c.) ... 

The laminar flow of various kinds of fluids in circular pipes can be easily compared by plotting (DI4) —dPldx) versus 32QI irD ) = SV JD, as shown in Fig, 15.3. This plot (or its equivalent on logarithmic paper) is very widely used in nonnewtonian flow calculations and publications. Its merit can be seen by rewriting Poiseuille s equation (Eq. 6.8) in the form... 

Fig. 6 shows an example of the rate of flocculation of the Chlorella cells in the agitated vessel (Fig. 1). By drawing tangents at the origin to each curve in the figure and by determining the slope, the values of the reaction-rate at f = 0 can be plotted against Nj in a logarithmic paper (see solid circles in Fig. 7). The flocculation-rate data which are obtained with the same rotation speed, n = 277 rpm of the impeller, diflerent in the metallic ion condition from Fig. 6 are rearranged similarly as are also plotted in Fig. 7.

Volume throughput over time may be recorded in a laboratory test carried out at constant pressure. Plotting the straight line (log E = log t - - Cste) on logarithmic paper gives a direct readout of the volume filtered over a given time. 

If the filter s surface area is known, the straight line giving the volume filtered during a normal industrial filtration cycle may be plotted on logarithmic paper from two or three experimental... 

When electrochemical rate data, i.e., electrode potential-current density data, are plotted, it is often done on semi-logarithmic paper. Since the logarithmic scale of this paper is usually "base 10", the Tafel slopes which are measured are related to the Tafel constants in Equation 30 by... 

The most commonly measured parameter for head injury is acceleration. It is therefore natural to express human tolerance to injury in terms of head acceleration. The first known tolerance criterion is the Wayne State Tolerance Curve, proposed by Lissner et al. [1960] and subsequently modified by Patrick etal. [1965] by the addition of animal and volunteer data to the original cadaveric data. The modified curve is shown in Figure 52.6. The head can withstand higher accelerations for shorter durations and any exposure above the curve is injurious. When this curve is plotted on logarithmic paper, it becomes a straight fine with a slope of —2.5. This slope was used as an exponent by Gadd [ 1961 ] in his proposed severity index, now... 

Plotting the concentrations on logarithmic paper would therefore yield a line whose slope indicates the number of simple molecules in the polymer [see, for example, the work of Hendrixson (23)]. Campbell (11) proposed the general use of logarithmic coordinates in this manner for various distributions, but, as has been shown (30), the method cannot be relied upon to describe data near the plait point. The simple distribution curve itself is useful for interpolating data when a relatively large number of tie lines are available but should not be used for extrapolation. 

The results of a size analysis may be represented graphically by a frequency curve or histogram. More frequently, however, they are used to draw a cumulative curve. The latter may be drawn on semi-logarithmic paper (Fig. 1.15). 

Based on the calculation methods listed above, the shape of curve vf i is nearly the same as w t in the semi-logarithmic coordinate system, except for that horizontal and vertical coordinate moves evenly. Therefore, based on different dimensionless damping coefficient, we can get the relationship between the dimensionless water level change v/ and the dimensionless time t. Draw a standard curve of v/ and t on the semi-logarithmic paper. On the coordinate paper with the same modulus, draw a curve showing the relationship between well water level displacement w and time t. Then, match the measured curve with the standard curve by moving the horizontal axis evenly. Record the value of and a in the standard curve. Select a match point in the standard curve, and record the value of nf and i, as well as the value of w and t in the measured curve. 

O. 05, 0.10 and 0.20 pg plotted against zone widths on semi-logarithmic paper... 

Example Plot the following x and y values in Table 5.2 on similar double logarithmic paper. 

Linearization of the exponential curves is similar to the case of the power function but on a single axis logarithmic paper, which is referred to as the semi-logarithmic paper. By taking the logarithms of both sides with respect to the base e, one can obtain,... 

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