4 20 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 be- 

 cause, 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 supernatural and metempirical explanations were silently withdrawn in 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 re- 

 search, 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 in- 

 corporated in an homogeneous doctrine rivaling that of the old theolo- 

 gies 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 so- 

 ciety. 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. BEOWNELL. 



THERE is no example of a people without a system of numeration. 

 The rudest savages manage to count to some extent. The at- 

 tempts 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 sys- 

 tems 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 



