128 A Short History of Astronomy [Ca. V. 



than the Alfonsine^ hardly claimed, and certainly did not 

 possess, minute accuracy. Coppernicus had once told 

 Rheticus that he would be extravagantly pleased if he 

 could make his theory agree with observation to within 10' ; 

 but as a matter of fact discrepancies of a much more 

 serious character were noticed from time to time. The 

 comparatively small number of observations available and 

 their roughness made it extremely difficult, either to find 

 the most satisfactory numerical data necessary for the 

 detailed development of any theory, or to test the theory 

 properly by comparison of calculated with observed places 

 of the celestial bodies. Accordingly it became evident to 

 more than one astronomer that one of the most pressing 

 needs of the science was that observations should be taken 

 on as large a scale as possible and with the utmost 

 attainable accuracy. To meet this need two schools of 

 observational astronomy, of very unequal excellence, de- 

 veloped during the latter half of the i6th century, and 

 provided a mass of material for the use of the astronomers 

 of the next generation. Fortunately too the same period was 

 marked by rapid progress in algebra and allied branches of 

 mathematics. Of the three great inventions which have so 

 enormously diminished the labour of numerical calculations, 

 one, the so-called Arabic notation (chapter in., 64), 

 was already familiar, the other two (decimal fractions and 

 logarithms) were suggested in the i6th century and were 

 in working order early in the iyth century. 



97. The first important set of observations taken after 

 the death of Regiomontanus and Walther (chapter in., 68) 

 were due to the energy of the Landgrave William IV. of 

 Hesse (1532-1592). He was remarkable as a boy for his 

 love of study, and is reported to have had his interest in 

 astronomy created or stimulated when he was little more 

 than 20 by a copy of Apian's beautiful Astronomicum 

 Caesareum, the cardboard models in which he caused to be 

 imitated and developed in metal-work. He went on with 

 the subject seriously, and in 1561 had an observatory built 

 at Cassel, which was remarkable as being the first which had 

 a revolving roof, a device now almost universal. In this he 

 made extensive observations (chiefly of fixed stars) during 

 the next six years. The death of his father then compelled 



