Titration of microorganisms in infectious or environmental samples is a corner stone of quantitative microbiology. A simple method is presented to estimate the microbial counts obtained with the serial dilution technique for microorganisms that can grow on bacteriological media and develop into a colony. The number (concentration) of viable microbial organisms is estimated from a single dilution plate (assay) without a need for replicate plates. Our method selects the best agar plate with which to estimate the microbial counts, and takes into account the colony size and plate area that both contribute to the likelihood of miscounting the number of colonies on a plate. The estimate of the optimal count given by our method can be used to narrow the search for the best (optimal) dilution plate and saves time. The required inputs are the plate size, the microbial colony size, and the serial dilution factors. The proposed approach shows relative accuracy well within ±0.1log10 from data produced by computer simulations. The method maintains this accuracy even in the presence of dilution errors of up to 10% (for both the aliquot and diluent volumes), microbial counts between 10(4) and 10(12) colony-forming units, dilution ratios from 2 to 100, and plate size to colony size ratios between 6.25 to 200.

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Calculations that use the Gauss-Seidel method are presented of the diffusely scattered light in a spherical atmosphere with polarization fully included. Comparisons are made between this method and the Monte Carlo calculations of other researchers for spherical geometry in a pure Rayleigh atmosphere. Comparisons with plane-parallel atmospheres are also presented. Single-scatter intensity comparisons with spherical geometry show excellent agreement. When all orders of scattering are included, comparisons of polarization parameters I, Q and U as well as the plane of polarization show good agreement when allowances are made for the statistical variability inherent in the Monte Carlo method.

A method for numerically solving the equation of radiative transfer in a spherical shell atmosphere is presented. The method uses a conical boundary and a Gauss-Seidel iteration scheme to solve for all orders of scattering along a single radial line in the atmosphere. Tests of the model indicate an accuracy better than 1% for most Earth-atmosphere situations. Results from this model are compared with flat-atmosphere model results for a scattering-only atmosphere. These comparisons indicate that excluding spherical effects for solar zenith angles greater than 85° leads to errors larger than 5% at optical depths as small as 0.10.