At present, two different groups of scholars are working with probability laws. On the one hand, there are the mathematicians who, starting from the simple basic laws of the theory, develop complex forms of calculation, establish relations facilitating the solution of intricate problems, and also introduce new concepts, such as dispersion, mean-square error, compound probability, and so forth. On the other hand, there are the statisticians in every branch of science — physics, psychology, sociology, and so forth — who gladly take over the complex apparatus of the mathematicians, not, however, in order to carry it to completion, but in order to apply it to actual objects, in order to derive methods from it suited to the presentation of particular empirical states of affairs. This distinction between working methods corresponds to a profound and substantial difference, the same difference that separates pure mathematical research from all its applications. There can be no doubt but that the laws of probability represent a complete mathematical system, just as do the principles of the infinitesimal calculus or the principles of geometry; the strict certainty attendant upon these spheres must likewise be attributed to the principles of probability insofar as they represent closed relations, conceptual chains made up of combinations of elementary concepts. Let the reader recall Bernoulli's theorem for calculating the frequencies and the dispersion of simple repeated series, which, from the mathematical point of view, is nothing more than an enumeration of combinations.