Planimeter method

As the cut and weigh method above, the planimeter method is a perimeter method that makes use of a surveyor s or draftsman s instrument called a planimeter. Using this technique the baseline is drawn as usual. The perimeter of the peak is then traced using the eyepiece containing cross-hairs of the planimeter. 

Basically, there are three approaches to peak area measurement (a) the cut and weigh method, which is accurate to within 5% (b) the planimeter method, which is accurate to within 1% (c) the integrator method, which is more accurate than method (b). It should be noted that when computer-equipped apparatus is used, enthalpy calculations are carried out automatically if the apparatus is correctly calibrated using calibration reference materials. 

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. 

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. 

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. 

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. 

Solid digital models of surface obtained by either of the methods are of individual interest for the study of geometric characteristics of microrelief and can be used for further morphological analysis in order to get solid morphological characteristics. Calculation of solid morphological characteristics is much similar to that of planimet-ric ones, except that volumes are calculated instead of areas, equivalent spheres—instead of equivalent diameters etc. 

Note 3—The use of planimeters or integrators is permissible provided their repeatability has been established and the resulting repeatability does not adversely affect the repeatability and reproducibility limits of the method given in Section 10. 

Recorder—A recording potentiometer with a full-scale response time of 2 s or less must be used. If a manual method of area measurement, such as a planimeter, is employed, the chart speed must be at least 152 cm/h (60 in./h) to minimize errors in peak area measurements. This requirement is waived if a ball-and-disc integrator or an electronic integrator is employed. 

A quick method for determining the area under a curve is to use a planimeter, an instrument designed to give the area when the planimeter is mechanically run about the boundaries of the area. Although this method is fast, it is not very accurate if the area to be determined is small. 

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