Stereological estimation of volume ratios by systematic sections

Two related problems are explored. Firstly, a single opaque solid omega 2, is considered. The problem is to estimate the minimum number of systematic sections m, necessary to estimate the volume ratio v = V (omega 2)/V (omega 1) with a coefficient of error or at most gamma 0 with a probability 1 - alpha. Secondly, we consider a population of such specimens. The second problem is to estimate the optimum number of n of specimens to be sampled and the number n of systematic sections per specimen in order to estimate the mean volume ratio v of the population with a relative error of at most epsilon 0 with a probability 1 - alpha. General guidelines for solving the two problems are presented. Practical results applicable to two populations of mouse and guinea-pid lymph nodes, exhibiting a wide variation in size and shape, are obtained.