Page:Russian Realities and Problems - ed. James Duff (1917).djvu/233

 Great Russian mathematicians, for instance, tried to give more logical unity to their science: Lobatchevsky elaborated a more comprehensive conception of space and considered the geometry of Euclid as one of the possible cases of it. Chebyshev, in one of his treatises on averages, proved that a general theorem underlies the different problems of the theory of probabilities and implies the famous theorem of Bernoulli as a special case of it.

This unifying tendency acquired a different character in the knowledge of the external World. In natural science, besides the doctrine of conservation of force or transformation of energy, this movement manifested itself particularly in the conception of matter as a system of elements, and in the doctrine of "consensus" and evolution, as a unifying process of life.

At the end of the sixties Mendeleyev published his famous treatise on the periodic system of elements, founded on the fact that, with increasing atomic or combining weights, their physical and chemical properties change; according to this regular arrangement of the elements by their weights expressed in numbers, the same properties—such as density, fusibility, optical and electric qualities, formation of oxides, etc.—recur in periods, which are, at least approximately, fixed. This theoretical scheme could not, at that time, be absolutely proved by experiment; but it was supplemented by the zero-series of indifferent gases, and the vacant places made it possible to predict the subsequent discovery of the missing numbers; some of them were really made and confirmed the unifying value of this