WEIR S AZIMUTH DIAGRAM. 



289 



The sun's true azimuth or bearing may be computed from either 

 of two sets of data, which can be readily obtained at sea — 

 first, from the latitude of the ship and the declination and altitude 

 of the sun ; or, second, from the latitude, declination, and hour 

 angle of the sun, or time from noon (apparent time). In the first 

 case, when the sun's compass bearing is taken, his altitude must 

 be observed simultaneously by sextant or other means ; while, in 

 the second case, it is only necessary to note the time at which the 

 bearing was taken, as shown on the ship's clock, which is always 

 kept at apparent time, making allowance, of course, for any dif- 

 ference of longitude in the ship's position since the clock was set. 

 This second case (known amongst navigators as a time azimuth) is 

 generally employed on acciount of its convenience, and it is to 

 facilitate the computation of the sun's true azimuth by this method 

 that the diagram is especially intended, although both cases can 

 with equal ease be solved by it. 



I will now proceed to explain, as clearly and briefly as I am 

 able, the train of reasoning by which I succeeded in constructing 

 the diagram, and trust that I may succeed in making my explana- 

 tion intelligible to the members. 



In the natural projection. Fig. 1., suppose the observer to be 

 placed at C in the centre of the sphere ; then let H R represent 

 the horizon, N S a line passing through the poles, E Q the equator, 

 -p, ^ Z the zenith, and Y 



the nadir, E D the de- 

 clination, D L a small 

 circle parallel to the 

 equator, O the posi- 

 tion of a celestial ob- 

 ject, N O S a meridian, 

 and Z O Y a vertical 

 or azimuth circle. 



In computing a 

 time azimuth, we have 

 given in the spherical 

 triangle O Z N the 

 side O N=the polar 

 distance or comple- 

 ment of declination, 

 the side Z N=the 

 complement of the la- 

 titude, and the angle 

 Z N O = the hour 

 angle, to find the angle O Z N^the azimuth, which, it will be 

 evident to anyone acquainted with trigonometry, can be done. 



The general principles on which I have worked in constructing 

 a diagram to solve this problem were to project the great circle 

 E Q vertically into the plane of the horizon, and. as this is a 

 circle projected obliquely, the resulting projection will be an ellipse, 



