324 POPULAR SCIENCE MONTHLY. 



A page from Ptolemy's note-book may be transcribed. He was 

 seeking the position of the bright star Begulus: *'In the second year 

 of Antoninus, the ninth day of Pharmauthi, the sun being near set- 

 ting, the last division of Taurus being on the meridian (that is 5I/2 

 equinoctial hours after noon) the moon was in three degrees of Pisces 

 ■by her distance from the sun (which was 92° 8') ; and half an hour 

 rafter, the sun having set, and the quarter of Gemini on the meridian, 

 Megulu^ appeared, by the other circle of the astrolabe, 57% degrees 

 fto the eastward of the moon in longitude." The position of the sun 

 was known from the day of the year by the solar tables; the moon, at 

 53^ hours, was 92° 8' east of the sun; the moon's motion in half an 

 hour was also known from the tables, and hence her position at 6 hours 

 was determined; Begulus was at that time 571/^ degrees east of the 

 moon, and its place was thus fixed with respect to the sun. A modern 

 note-book would give the year and day, and would record that Begulus 

 crossed the meridian at a certain hour, minute, second and decimal of 

 a second by the clock. The correction of the clock would be given 

 as so many seconds and hundredths of a second. The sum of the 

 <3lock-time and the correction is the position of the star. In Ptolemy 's 

 case it was known to half a degree (two minutes of time). A modern 

 observation gives it with an error not above one tenth of a second; 

 that is with an accuracy about 1,200 times greater. 



Ptolemy's Almagest is, in essence, 'modern' in respect of the fact 

 that its theories are designed to give quantitative results and are pre- 

 sented as general bases for special calculations. With a certain set 

 of observations as data the desired results could be worked out in 

 numbers. Tables for calculating future positions of the planets were 

 also given and in Ptolemy's time the actual positions were fairly well 

 represented by the predictions. As time went on, more accurate ob- 

 servations with better instruments, were made. The observed places 

 of the planets did not agree with the predictions. The ingenuity of 

 his disciples in the middle ages was taxed to improve the theory, and 

 the tables of Ptolemy were supplanted in turn by the Hakemite tables 

 of Ibn Yunus (about A. D. 1000), the Toledan tables of Arzachel 

 (1080), the Alphonsine tables of Alphonso the Wise (1252) and others. 

 Finally, in the first half of the sixteenth century it became evident 

 that Ptolemy's theory was itself gravely at fault. It was the fortune 

 of Copernicus to open a new way to scientific thought — to lay down a 

 new theory of the world. 



The details of the long history thus sketched out are only interesting 

 to astronomers.* We are here concerned with the main outlines alone. 



* They are given in clear form in various encyclopedias and other books 

 of reference. Perhaps Berry's Short History of Astronomy (1899) will best 

 serve the purpose of the general reader. Gylden's Die Grundlehren der As- 

 tronomie (1877) develops the mathematical bases of ancient astronomy in an 

 elementary form. Delambre's Histoire de V Astronomie is still the best general 

 history. 



