weir's azimuth diagram. 295 



it is just as simple with any three out of these four elements given 

 to find the fourth. Thus, given latitude, declination, and azimuth, 

 the time may be obtained, and so on. 



The diagram may be used as a sundial, which will give the 

 correct apparent time at all places on the earth's surface, tlie 

 latitude being not more than 60°, by placing it horizontally, with 

 its meridian exactly north and south, and erecting a shadow-pin 

 vertically over the declination. Where the shadow thrown by this 

 pin cuts the ellipse corresponding to the latitude of the place 

 will show the apparent time ; and, given any three of the four 

 elements mentioned, the fourth may be found by varying the 

 position of the pin, the direction of the meridian, or the ellipse of 

 latitude. 



The diagram may also be used to calculate the sun's semi-diurnal 

 arc or time of rising and setting, and, at the same time, his ompli- 

 tude or bearing when on the horizon, the latitude and declination 

 being given. 



Referring to Fig. 1 : In the triangle N A 11 we have given 

 N R=latitude, N A=polar distance, and the right angle N R A, 

 to find A 11 tlie cosine amplitude, which, it will at once be evident, 

 can be done. With the same data we can also find the angle 

 A N R, which is the semi-nocturnal arc. I may state that both 

 of these problems can be solved b}' the diagram in four different 

 •ways, but I will not encroach on the time of the meeting by 

 attempting to explain each method, and shall simply try to give an 

 idea of the general principles involved. Find the position of the 

 observer, as explained on the diagram, and, with this point as a 

 centre, describe a circle about the ellipse of latitude and just 

 touching it. This circle will represent the circle of the horizon, 

 and the point where it touches the ellipse of latitude will be the 

 position of the sun when on the horizon. Reference to the nearest 

 time curve will give the semi-diurnal arc ; and the bearing from 

 the position of the observer to the position of the sun, taken ofi' in 

 the usual way, will give us his true amplitude or bearing when 

 rising or setting. 



As each hyperbola on the diagram intersects each ellipse at 

 right angles, this point (the position of the sun when rising or 

 setting) may be found by using a pair of parallel rulers. 



Place the edge of the ruler over the position of the observer, 

 and note which time curve it just touches at the ellipse of latitude ; 

 this will be the same point as was previously found, namely, the 

 position of the sun when on the horizon. 



In some of my earlier diagrams I laid down another set of 

 lines, which, for want of a better name, I called rising and setting 

 circles. They were drawn for each degree of declination up to, say, 

 30*^, and where each curve cut each ellipse of latitiide showed the 

 position of the sun when on the horizon at the latitude of the 



