THE CONCEPTUAL WORLD 29 



Thus we obtain a smaller interval of duration and we 

 call this a second of time. But for many purposes 

 this interval is too long, and we can again sub-divide 

 it by making use of a tuning-fork which makes, say, 

 iooo complete vibrations in a second ; in this way 

 we obtain still smaller intervals of duration— the 

 sigmata of the physiologists. A sigma, therefore, 

 represents the interval between the beginning and end 

 of one complete vibration of a certain kind of tuning- 

 fork ; a second, that between the beginning and end 

 of one complete swing of a pendulum of a certain 

 length, placed at certain parts of the earth's surface ; 

 and a day, that between two successive transits of a 

 fixed star across a selected meridian, after all the 

 necessary corrections have been made to the obser- 

 vation. These actual occurrences, the positions of 

 the prongs of the tuning-fork, or those of the bob of 

 the pendulum, or those of the fixed star do not involve 

 duration. We consider the meridian of Greenwich 

 as an imaginary line drawn across the celestial sphere, 

 and the star as a point of light, so that the actual 

 transit is, in the limit, an occurrence which occupies 

 only an " infinitesimal" interval of duration. So also 

 with the pendulum and the tuning-fork ; the positions 

 of these things do not " use up " time, and even if the 

 intervals into which we divide astronomical time are 

 indefinitely numerous no real quantity of duration is 

 taken up by their occurrence. We know that the 

 interval between two successive transits of a fixed 

 star are not really constant, that is, the astronomical 

 day is lengthening by an incredibly small part of a 

 second each year, but how do we know this ? It is 

 not that we can feel the increments of duration, but 

 just that we assume that Newton's laws of motion are 

 true ; and hence that the tidal friction due to the 



