40 A SHORT HISTORY OF SCIENCE 



The first sun-dial of which a description is preserved belongs to 

 the time of Alexander the Great, and consisted of a hollow hemi- 

 sphere with its rim horizontal and a bead at the centre to cast the 

 shadow. Curves drawn on the concave interior divided the period 

 from sunrise to sunset into twelve parts, these lengths being thus 

 proportionate to the lengths of the daylight period. 



The use of the clepsydra, or water clock, in Greece dates from the 

 fifth century B.C. It consisted there of a spherical bottle with a 

 minute outlet for the gradual escape of water. Its use in regulat- 

 ing public speaking is illustrated by Demosthenes' demand when 

 interrupted, "You there : stop the water." 



For the sake of conformity with the sun-dial division of each 

 day and each night into twelve equal parts, the rate of flow in the 

 clepsydra required continual adjustment. Ingenious improvements 

 were made in the mechanism in course of time, but in considering 

 the work of the Greek astronomers, the impossibility of what we 

 should consider accurate time measurement must not be for- 

 gotten. 



GREEK ARITHMETIC. In Greek arithmetic the earliest known 

 numerals are merely the initials of the respective number words. 

 Two other systems came into use later. In one of these the 

 numbers from 1 to 24 are represented by the 24 letters of the 

 Ionian alphabet ; in the other the letters represent numbers, but 

 no longer in consecutive order. This use of letters for numbers 

 was not confined to Greece, but appears to have originated there. 

 The Greeks had no zero, and never discovered the immense ad- 

 vantage of a position-system, such as that by which we are able 

 to express all numbers by only ten symbols. Fractions occur not 

 infrequently. The change from the earlier notation to that with 

 24 characters was a disastrous one. There were not only more 

 characters to memorize, but computation became materially more 

 complicated. These disadvantages far more than offset the su- 

 perior compactness, the sole merit of the new system. The 

 special importance of such compactness for coins has led to the 

 suggestion that they were the medium through which this nota- 

 tion was introduced. 



