An analytical function of the probabilities of perception and its application to the calculation of the population index in the visual observation of meteors

The probability of perception is an indispensable quantity in the visual observation of meteors. A new analytic function of the probabilities of perception is given, in which there is no uncertainty of the old fitting since any order of derivative of the function is also a single value and smooth. In virtue of the advantage that the function is convenient for the computation and analysis, several methods for calculating the population index r have also been compared with the aid of the analog calculation with a computer. It has been confirmed that the frequently used least square fitting method is not so good as thought. In addition, the best way to get a credible value of the population index is also deeply discussed.