42 A Short Plistory of Astronomy [Cn. It. 



are not great enough to be perceptible. It was, moreover, 

 known (probably long before the time of Hipparchus) that 

 the sun's apparent motion in the ecliptic is not quite 

 uniform, the motion at some times of the year being 

 slightly more rapid than at others. 



Supposing that we had such a complete set of observa- 

 tions of the motion of the sun, that we knew its position 

 from day to day, how should we set to work to record and 

 describe its motion ? For practical purposes nothing could 

 be more satisfactory than the method adopted in our 

 almanacks, of giving from day to day the position of the 

 sun ; after observations extending over a few years it would 

 not be difficult to verify that the motion of the sun is (after 

 allowing for the irregularities of our calendar) from year to 

 year the same, and to predict in this way the place of the 

 sun from day to day in future years. 



But it is clear that such a description would not only 

 be long, but would be felt as unsatisfactory by any one 

 who approached the question from the point of view of 

 intellectual curiosity or scientific interest. Such a person 

 would feel that these detailed facts ought to be capable 

 of being exhibited as consequences of some simpler general 

 statement. 



A modern astronomer would effect this by expressing 

 the motion of the sun by means of an algebraical formula, 

 i.e. he would represent the velocity of the sun or its 

 distance from some fixed point in its path by some 

 symbolic expression representing a quantity undergoing 

 changes with the time in a certain definite way, and 

 enabling an expert to compute with ease the required 

 position of the sun at any assigned instant.* 



,/The Greeks, however, had not the requisite algebraical 

 knowledge for such a method of representation, and Hip- 

 parchus, like his predecessors, made use of a geometrical 



* The process may be worth illustrating by means of a simpler 

 problem. A heavy body, falling freely under gravity, is found (the 

 resistance of the air being allowed for) to fall about 16 feet in 

 I second, 64 feet in 2 seconds, 144 feet in 3 seconds, 256 feet in 

 4 seconds, 400 feet in 5 seconds, and so on. This series of figures 

 carried on as far as may be required would satisfy practical re- 

 quirements, supplemented if desired by the corresponding figures 

 for fractions of seconds; but the mathematician represents the same 



