TIME AND SPACE 285 



came aware that it was not correct for the meridian of Rome, although 

 the latitude of Catania differs from that of the capital by more than 

 four degrees. From that time forward sun-dials came into general use ; 

 and since many have been recovered their construction is well known. 

 The most common form is that of a concave hemisphere cut in two. 

 Within one of these quarters the hours were marked. A stylus or 

 hand fastened in the top indicated the time of day, when the sun shone. 

 Pliny says the first water-clock was set up in Rome 159 B.C. These 

 water-clocks appear to have differed from the clepsydrae that had long 

 been in use in the countries farther east. They consisted of an earthen 

 vessel tapering downward to a point, in the bottom of which there was a 

 small hole through which the water flowed in a given time. It was 

 comparatively easy to ascertain when the sun was on the meridian ; but 

 not so easy to determine the exact period of midnight. This was more- 

 over, an affair of small practical importance. In the larger cities, the 

 periods or hours were announced by the sound of a trumpet; in the 

 country few persons cared how the hours of the night passed. The cus- 

 tom of proclaiming the hours of the night prevailed in some countries 

 of Europe, especially in Germany, long after clocks had come into 

 almost universal use. It is not known when the Romans began to 

 divide the day into twenty-four hours. At any rate there were two 

 kinds of days in vogue : the astronomical day, the hours of which were 

 all of the same length, and the civil or ordinary day which corresponded 

 with the former at the equinoxes only. The popular day was a matter 

 of latitude. In Rome the longest contains somewhat more than fifteen 

 hours according to mathematical calculation, but owing to the Appen- 

 nines which lie east of it the fact does not quite correspond with the 

 figures. The hour in Rome was therefore at one time of the year about 

 seventy-five minutes in length, while the hours of the night were corre- 

 spondingly shorter, and vice versa. 



Every schoolboy is taught that twelve inches make a foot, but not 

 one in a million thinks to ask what is the basis of this measurement. 

 It must at once occur to the occasional inquirer that the average human 

 foot is not twelve inches long. When, however, a unit of measurement 

 has been once fixed, the rest is easy. The metric system was the first 

 attempt to establish an invariable standard to which recourse could al- 

 ways be had in cases of doubt. A table before me gives twenty-six dif- 

 ferent lengths for the foot in the German empire, twenty-five for the 

 rest of Europe, eight for America and four for Asia. Of these the long- 

 est is that of Lombardy, which contains a little more than 435 milli- 

 meters, the shortest the foot of Siam, which is only 245.6 mm. Even 

 in Germany the foot varies from 429.5 to 250 mm. There is of course 

 the same divergence between the square and the cubic foot. The Eng- 



