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THE POPULAR SCIENCE MONTHLY.

knowledge, he will learn that science, in the true meaning of the term, embraces Nature and human nature, and moreover that it expresses what is known of both, whereas theology is only "the false persuasion of knowledge."

Many readers may vehemently deny the assertion just made. They will maintain the validity of theological explanations, all the more because, persisting in the old confusion of theology with religion, they refuse to acknowledge that a science of Nature and human nature, if truly expressing the facts, must be a better foundation for religion than a theology which untruly expresses those facts. The whole contest lies between the two modes of explanation and the results reached by such modes. I accept the appeal to history. This shows how, in proportion as knowledge became exact and orderly in each department of inquiry, the supernatural and metempirical explanations were silently withdrawn in favor of natural and experimental explanations. Nowadays, among the cultivated minds of Europe, it is only in the less-explored regions of research, where argument is made to do duty for observation, that the supernatural and metempirical explanations hold their ground. When science has fairly mastered the principles of moral relations as it has mastered the principles of physical relations, all knowledge will be incorporated in an homogeneous doctrine rivaling that of the old theologies in its comprehensiveness, and surpassing it in the authority of its credentials. "Christian ethics" will then no longer mean ethics founded on the principles of Christian theology, but on the principles expressing the social relations and duties of man in Christianized society. Then, and not till then, will the conflict between Theology and Science finally cease; then, and not till then, will the dread and dislike of science disappear.—Fortnightly Review.

 

CURIOUS SYSTEMS OF NOTATION.
By T. F. BROWNELL.

THERE is no example of a people without a system of numeration. The rudest savages manage to count to some extent. The attempts of many of them, however, do not succeed with numbers greater than three or four. With increasing knowledge, they learn to count larger numbers, but the process is a slow and troublesome one. It is performed in all cases by the use of the device of grouping. All systems of numeration that are known consist of this device. In the first stages, the groups are all of the first and lowest order. The savage, counting from one to five upon his fingers, closes his hand to express five; then he again begins counting upon his fingers to form a second group; and he continues to form groups of five to as great a number