Rambaut — Japanese Clocks. 



339 



It is also worthy of remark that the curve of " dawn " as found 

 on the clock falls between the two branches of my curve, as shown 

 in accompanying diagram, where ew represents the winter and es 

 the summer half of my curve, and ec the clock curve. 



Now, assuming that these lines do denote the hours, and were 

 obtained somewhat in the manner just suggested, we are in a posi- 

 tion to make a more accurate determination of the place from which 

 they come. 



"We have the hour angle of the sun when it reaches some defi- 

 nite distance (on) from the horizon at midsummer represented by the 

 distance between the asterisks on fig. 2. The proportion this bears 

 to the whole length of the dial gives us the midsummer hour-angle 

 of the sun when at this depth (x) below the horizon, which is thus 

 found to be 126°. At midwinter, when the sun reaches the same 

 distance from the horizon, its hour angle is similarly 90°. We 

 thus obtain two equations for x and 0, viz. : — 



and 



- sin x = sin $ sin S + cos <j> cos S cos 126 c 

 sin x = sin <p sin S 



(2) 



in which 8 = 23° 27!'. 



From these equations I find 



<p = 34° 6'-5 and x = 12° 54'. 



I have traced (see fig. 4) the curve of which the ordinate (h) is 

 given by the equation (1). It is the lower of the two dotted 

 curves. The upper one is the same curve inverted, and the conti- 

 nuous curve lying between the two is found by taking the mean 



2 D 2 



