Volume 8, Issue 5 (May 2011)
Bias in the Planimetric Procedure According to ASTM E112 and Corrected Method
According to the paragraph 11.1 of ASTM E112, the sum of all the grains included completely within the known circle or rectangle area plus one half the number of the grains intersected by the circumference of the area gives the number of equivalent whole grains. It can be expressed as N=Nc+0.5Np. However it is demonstrated in this paper that there is a bias of one grain introduced by using this procedure and the formula should be changed to N=Nc+0.5Np–1. Two methods have been used in this paper to prove this conclusion. The first one is stereometric method and the second one is a handcalculation using a quadrille ruled paper and a transparence film with a circle on it. The circle of the film is randomly placed on top of the squares of the quadrille ruled paper to count the number of squares within the circle area. A computer program has been developed to allow different size of circles to be used and also to makes it possible to repeat these experiments as many times as needed.