A survey of large samples taken from mixed animal populations supports the idea that the distr. of spp. with different numbers of individuals is nearer to the log-normal than to the log-series form. The main differences in conception, apart from the increased mathematical complexity, between the log-series and the log-normal are: The former postulates no limit to the numbers either of spp. or of individuals in the population from which the samples are taken, while the log-normal implies a finite number of spp., although the number of individuals is theoretically unlimited. Three parameters are necessary to define a log-normal, whereas two are sufficient for a log-series. As a result, to the total number of individuals and of species in the sample, which is sufficient to define a log-series, must be added a third constant fixing in some way the standard deviation of the curve, before a log-normal can be fitted to given data. With increasing size of sample from a log-series population, the relation between the number of spp. and the log-number of individuals tends to a straight line, but with a log-normal population the curve is sigmoid and flattens out as it approaches the limit of the total number of spp. in the population which is being sampled. There is with the log-normal a decline in the number of spp. with one individual after the sample is large enough to include about 50% of the spp. in the population, which does not occur if the distribution is of the log-series form. There is in the log-normal distr. population the gradually increasing difference between the number of spp. with one individual and the number in the peak class as a sample size increases. This difference is limited to 10% in a log series population. It is evident that many more examples of large random samples of animal populations, with accurate counts and detn. of spp., are required before the general form or forms of distribution of the spp., and hence the pattern or balance of the populations, can be detd.