The mathematical writings of the early Romist missionaries greatly improved the mathematical texts available in Chinese, and since foreigners have begun to introduce western science, the development has been rapid. But aside from the graduates from modern schools, the knowledge of mathematics even among the learned men of China is very small, and the common people study it only as far as their business requires, and that is exceedingly little. The cumbersome notation and the little aid which such studies gave in the ancient system of literary examinations (only abolished in 1905) doubtless discouraged the pursuit of what they seem to have no taste for as a people. Chinese authors acknowledge the superiority of western mathematicians, and generally ascribe their advance in the exact sciences to this power.
6. Action and Reaction of Elements.—Williams in his "Middle Kingdom" gives a table showing the leading "elementary" correspondencies in the curious speculations used by Chinese philosophers to account for any possible contingency in the changes of the visible universe, which in the hands of geomancers and fortune-tellers are the bases of considerable imposition on the people. The five elementary powers or hing are: water, fire, wood, metal and earth, and the table gives the qualities, tastes, and activities of the five hing as correlated with five points of the compass (the fifth being "center"), the five corresponding planets, five colors, five viscera, five musical notes, five early emperors, four seasons, and four quarters of the zodiac. But to consider these ideas in detail would lead too far afield into unprofitable vagaries.
7. Chemistry—Alchemy.—Chemistry and metallurgy have been unknown as sciences, but many operations in them are performed with a considerable degree of success, and bear testimony to Chinese shrewdness and ingenuity in the existing state of their knowledge. The skill which they exhibit in metallurgy, their brilliant dye-stuffs and numerous pigments; their early knowledge of gunpowder, alcohol, arsenic, Glauber's salt, calomel and corrosive sublimate; their pyrotechny; their asphyxiating and anesthetic compounds—all give evidence of no contemptible proficiency in practical chemistry. In their books of curious recipes (see section 2) are instructions for the manufacture of sympathetic inks, for removing stains, alloying metals, counterfeiting gold, whitening copper, overlaying the baser with the precious metals, etc., many of the rules in which are still in common use, and bear in their very terms the stamp of an alchemic origin. Dr. Martin in his "Lore of Cathay" presents striking evidence to show that in all probability western alchemy, from which our modern chemistry has come, had its root in the art as practised in China, where it appeared as an indigenous product, coeval with the dawn of letters.
One doctrine of Taoism which was developed six centuries before Christ regards the soul and body as identical in substance, and main-
