326 THE DEBT OF THE WORLD TO PURE SCIENCE. 



in Egypt, the limits of vast periods embracing many hundreds of years. 

 Maps were made thousands of years ago showing their j)ositions; the 

 path of the sun was determined rudely; the influence of the sun and 

 moon upon the earth was recognized in some degree, and their influence 

 upon man was inferred. Beyond these matters, man, with unaided 

 vision and with knowledge of only elementary mathematics, could 

 not go. 



Mathematical investigations by Arabian students i)repared the means 

 by which, after Europe's revival of learning, one, without wealth, gave 

 a new life to astronomy. Copernicus, early trained in mathematics, 

 during the last thirty years of his life spent the hours, stolen from his 

 work as a clerk and charity physician, in mathematical and astro- 

 nomical studies, which led him to reject the complex Ptolemaic system 

 and to accept in modified form that bearing the name of Pythagoras. 

 Tycho Brahe followed. A mere star-gazer at first, he became an earn- 

 est student, improved the instruments employed, and finally secured 

 recognition from his sovereign. For twenty- five years he sought facts, 

 disregarding none, but seldom recognizing economic importance in any. 

 His associate, Kepler, profiting by his training under Brahe, carried 

 the work far beyond that of his predecessors — and this in spite of dis- 

 ease, domestic sorrows, and only too frequent experience of abject pov- 

 erty. He divested the Copernican hypothesis of many crudities, and 

 discovered the laws which have been utilized by astronomers in all 

 phases of their work. He ascertained the causes of the tides, with the 

 aid of the newly invented telescope made studies of eclipses and occu- 

 lations, and just missed discovering the law of gravitation. He laid 

 the foundation for jjractical application of astronomy to everyday life. 



In the eighteenth century astronomy was recognized by governments 

 as no longer of merely curious interest, and its students received 

 abundant aid. The improvement of the telescope, the discovery of 

 the law of gravitation, and the invention of logarithms had made pos- 

 sible the notable advances marking the close of the seventeenth 

 century. The increasing requirements of accuracy led to exactness in 

 the manufacture of instruments, to calculation and recalculation of 

 tables, to long expeditions for testing methods as well as conclusions, 

 until finally the suggestion of Copernicus, the physician, and of Kepler, 

 the ill-fed invalid, became fact, and astronomical results were utilized 

 to the advantage of mankind. The voyager on the ocean and the 

 agriculturist on land alike reap benefit from the accumulated observa- 

 tions of three centuries, though they know nothing of the principles or 

 of the laborers by whom the principles were discovered. The regula- 

 tion of chronometers as well as the fixing of boundary lines between 

 great nations is determined by methods due to slow accumulation of 

 facts, slower development in analysis and calculation, and even slower 

 improvement in instruments. 



Galvaui's observations that frogs' legs twitch when near a Motion 



