Logarithmic graph

The Reactor Safety Study extensively used the lognormal distribution (equation 2.5-6) to represent the variability in failure rates. If plotted on logarithmic graph paper, the lopnormal distribution is normally distributed. 

For compounds the hardness-temperature curves are similar to those for the pure metals. Semi-logarithmic graphs of the data show two straight lines with the knees at about half the melting temperatures. For a dozen aluminides, Petty (1960) shows this. 

Fig. 43 Double logarithmic graph of the ultimate strength of PpPTA fibre versus the degree of polymerisation for a monodisperse distribution for various values of the diameter and for /j=0.16. Calculation for aspect ratios fr=wa(2r) 1>10... 

Figure 15 shows experimental results in a single logarithmic graph. They are compared with the theoretical predictions of a stochastic Markov process. For details see Reference 15. 

Logarithmic graphs according to equation (II-2) for several temperatures are shown in Fig. 15. It is clear that the slopes which are a measure of k increase rapidly with the temperature. 

Fig. 15.—Logarithmic graphs showing the decomposition rate of nitrogen pentoxide at several temperatures.

The rheograms can often be described over a fairly wide range by a power-law function (Figure C4-12). This means that you get a straight line in a logarithmic graph. The slope... 

Figure 8 Double logarithmic graph of relaxation data (carbon and T2) versus molecular weight (generation) for the carbon atoms 1, 2, and 3 as recorded at 75 MHz in chloroform...

A calibration curve is plotted, for each element, by plotting on a semi-logarithmic graph the number of visible grades of the element s characteristic line in linear co-ordinates and the known concentration levels in logarithmic co-ordinates. 

Appropriate information about conformational aspects of dissolved polysaccharides may be obtained by means of a double logarithmic graph of molar mass... 

Inactivation, regarding thermal treatment, is based on the assumption that death of microorganisms versus time is linear in a semi logarithmic graph. Thus, inactivation by HP usually uses the kinetic concepts of thermal treatment D (decimal reduction time time in minutes required to inactivate... 

In Figure 4.8 the ratio of the number of nuclei at any time t to the original number at time / = 0 (i.e. N/Nq) has been plotted on both a linear (left) and logarithmic (right) scale as a function of t. The linearity of the decay curve in the semi-logarithmic graph illustrates the exponential nature of radioactive decay. Since A oc N, the equation can be rewritten as... 

Figure 2.18. Sieve test data plotted on a) arithmetic probability graph paper cumulative undersize percentages) illustrating the use of the MSjCV method of analysis, b) on Rosin-Rammler-Sperling RRS) double logarithmic graph paper...

Special double logarithmic graph paper suitable for this type of plotting is available and the data from Table 2.14 are shown on such a plot in Figure 2.18b. From this plot it is possible to determine the 16, 50 and 84% cumulative percentages needed to calculate the MS/CV, as described above. Alternatively, the distribution can be characterized by the uniformity factor, n. In the example shown the median size = 870 pm (the same as determined in Figure 2.18a), the statistical mean size d = 1000 pm, and the uniformity factor n= 1.8. 

A population factor weighted over circular rings lower than 20000 with a weight given by Table A16-1 (or by an equivalent bi-logarithmic graph). 

The logarithmic graph in Fig. 9 shows accuracy results for each test 1 -5 and the average. The accuracy rises hyperbolically with growing number of iterations (in logarithmic graph it looks like the error sinks approximately linearly with order of iteration number. So if we need rehabihty with at most 1 % error, then 10 iterations will be enough. 

Disconnection times for various overcurrent devices are given in the form of a logarithmic graph. This means that each successive graduation of the axis represents a 10-times change over the previous graduation. 

Methods 2,3, and 4 just described suffer principally from the fact that the concentration of C, the distributed component, is not indicated in the coordinates. Hand (22) showed that a double logarithmic graph of XcaIXaa against Xcb/Xbb at equilibrium, which includes the concentration of C in the coordinates, is ordinarily rectilinear. This method of plotting was first proposed by Bancroft (2). As in previous cases, those systems which are not represented by straight lines are those relatively rare ( ases where the direction of the tieline slope changes with concentration. 

Calculate the A -values and draw a ln(A) to %B graph - this can also be done with semi-logarithmic graph paper, three or four decades. The more intersections that can be seen, the more complicated is the separation problem. From this graph, all isocratic chromatograms with any desired %B can be read, a calculation is more accurate. 

Results are tabulated in Table 3 1 and presented in Figure 3 2 in a linear scale rather than a logarithmic scale. Linear scales are sometimes more nseful to the mine operator who is in a remote area and has little time to waste on difficult logarithmic graphs... 

A sample of slurry is sieved for particle size. The data is collected in the laboratory (see Table 4-1). Plot the data on a logarithmic graph and determine the r/gg. 

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