Eambaut — Japanese Clocks. 337 



us to suppose that this line represents the equinox, as we have 

 already seen from other considerations. 



The second part of Hoffman's remark about the twilight, 

 however, gives us a clue to the principle on which the dial is 

 constructed. 



At midwinter, in the latitude of Tokio (35° 43'), when the 

 Sun's hour angle is 90° (that is approximately at 6 a. m. and 

 6 p.m.), the Sun is about 13° below the horizon. At that time, 

 therefore, the twilight will be just becoming noticeable, though 

 for some little time before, in the morning, and after, in the 

 eveniug, there would be more or less light. 



If we assume, therefore, that the day always begins when the 

 Sun is 13° below the horizon, or when the twilight first becomes 

 bright enough to attract attention, 1 we shall have at midwinter the 

 day and night of equal duration, and all the divisions of the same 

 length. As the year advances the day increases ; at first slowly, 

 but as we approach the equinox more and more rapidly, after 

 which the change becomes slower and slower till the summer 

 solstice is reached. From this point the day diminishes again in a 

 similar manner till we arrive at the winter solstice. 



These changes are exactly what we see represented in the sixth 

 curve, which, on this hypothesis, represents the beginning of dawn. 

 At first its height increases very slowly ; at the equinox it increases 

 most rapidly, and this rate of increase falls off again as we 

 approach the solstice. The other curves are found merely by 

 dividing each vertical line, from the point at which the " dawn" 

 curve cuts it to that at which it is cut by the bottom line, into six 

 equal parts, and similarly dividing the upper portions, so that the 

 " dawn " line is the only one which concerns us. 



On this hypothesis I have traced a dial for the latitude of 

 Tokio (Fig. 3), the curves on which agree fairly well with those on 

 the clock-dial considering the nature of the problem. 



In the first place, I cannot be sure that tl^e clock was made for 

 this latitude ; and in the second, since the curves were probably, in 

 the first instance, determined by rough observations of the actual 



1 The amount of twilight then visible is almost exactly that of a midsummer's 

 midnight at Dublin, or more accurately at Rush in the same county. 



SCIEN. PR0C. R.D.S. VOL. VI *T. VI. 2 D 



