Planimeter measurements

Since this is the energy per cm.2 in one cycle, the power per cm.2 of parellelogram area is obtained by multiplying the energy per cycle by the frequency in reciprocal seconds. The parallelogram area can be determined by planimeter measurement of a Polaroid picture, or by direct measurement. 

From a top reservoir map (Fig. 6.2) the area within a selected depth interval is measured. This is done using a planimeter, a hand operated device that measures areas. 

The stylus of the planimeter is guided around the depth to be measured and the respective area contained within this contour can then be read off. The area is now plotted for each depth as shown in Figure 6.2 and entered onto the area - depth graph. Since the structure is basically cut into slices of increasing depth the area measured for each depth will also increase. 

Planimetry. The planimeter is a mechanical device which enables the peak area to be measured by tracing the perimeter of the peak. The method is slow but can give accurate results with experience in manipulation of the planimeter. Accuracy and precision, however, decrease as peak area diminishes. 

The amount of BrOnsted sites was evaluated by measuring the surface of the characteristic band at 1540 cm . Corrections have been made to take into account the differences in weight and surface of the wafers. After each test, the wafer was weighted and its cross section was measured with a planimeter. The results were corrected to represent those of a "standard wafer" (Ag) of 5 mg and 25 units of area, according to the following expression ... 

If the area under the curve in Figure A.3 needs to be determined without access to a computer, graphical integration can be used. Once the curve has been plotted, the area under the curve can be measured with a planimeter, or by cutting out the desired area, weighing the paper, and comparing the weight to that of a sample of the same paper of known area. 

When the starting point is reached the dial reads a number proportional to the area. On some planimeters the number is proportional to area via a settable scale factor. On other instruments the factor must be determined by measuring a known area. The major advantage of the technique is the ability to handle distorted and tailing peaks to produce a true area. The major problems are the painstaking nature of tracing the peak and the use of a tool not normally found in a laboratory. 

A final point of consideration is the measurement time required. Certainly electronic integration is by far the fastest and the ball and disc integrator would also be considered fast. The manual methods in increasing slowness would be peak height, height and width, triangulation, planimeter, and finally cut and weigh technique. 

Two methods used to find the area under the photometer trace are peak-height-times-half-width approximations and actual measurements with a polar planimeter. Both methods are time consuming and offer little increase in total accuracy over the peak center method. Another method involves computer fitting an assumed scattering function, usually a Gaussian or Lorentzian (though more exotic functions have also been used) to the scan data. The integrated area under the mathematical curve is then calculated. 

The x-ray diffraction patterns were made with a Picker diffractometer, using Ni-filtered CuK radiation and glass-slide mounts. To derive accurate unit cell constants, slow-scan x-ray patterns were internally standardized with NaCl, KC1, or Si. The integrated intensities were obtained by measuring the area under each peak with a planimeter. 

Another requisite is to measure the areas of peaks accurately. In our office, areas of exothermic peaks on DSC charts have been determined for many years by weighing their cutouts. At one time,an attempt was made to use a planimeter, but this method was not used long. In recent years personal computers have come into wide use. The authors have also connected the DSC apparatus directly to a computer which collects and analyzes the data and prints out the results. This system marks a great advance in that peak areas can be measured accurately. 

The basic module for the Digiplan [92] was an electronic planimeter with a built-in microprocessor. The image structure under analysis was traced out and stored in different count channels. Measured parameters were area and lengths that could be extended to other functions such as maximum diameter, form factor, centroid and so on. 

Quantitative results were obtained using response factors determined with n-nonane internal standard. Peak areas were measured with a K and E planimeter. The low boiling fractions, i.e., methane, ethane, ethylene, isobutane, neopentane and neohexane were identified by authentic samples with a 4 x 1/8" Porapak Q Column. Preparative gas chromatography was carried out with a 6 x 1/4" Apiezon L Column. 

Area of coarse side of intersection (measured by planimeter)... 

R was determined from the area under the breakthrough curves using a planimeter. Mass eluted compared well with mass injected, indicating that mass balance was achieved. Dispersion (D) for a conservative tracer was determined by fitting the KCl breakthrough curve to the equilibrium model the fitted parameters were R and P. A nonlinear least squares method was used for parameter estimation 7. The sum of the squares of the deviation between model and data (ssq) was used as a measure of total error in the model fit. 

A typical chromatogram is presented in Fig. 7.1. The peaks are asymmetric, so the peak areas were measured with the aid of a planimeter. The hydrogen and carbon contents were calculated from the peak areas. 

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