1888-89.] Capt. P. Weir on a New Azimuth Diagram. 355 
I will not attempt to illustrate the correctness of my theory by 
any purely mathematical formulae, but will confine myself to stating 
as plainly as possible, and as far as I can remember, the train of 
reasoning by which I succeeded in constructing the diagram. 
Suppose that the latitude is 90° N., that is to say that the 
observer is standing on the North Pole, it is quite evident that the 
sun’s path, projected on the plane of the horizon, would be a circle, 
and also that, no matter what the declination was, the sun’s bearing 
would be the same at the same hour every day, say Greenwich 
time, its altitude only being affected by a change in declination. 
Again, suppose the observer to be on the equator and the declina- 
tion 0°, it is self-evident that the sun would rise due east, ascend 
on an azimuth circle to the zenith, and descend due west ; so that 
his path, projected on the plane of the horizon, would be a straight 
line. Suppose, again, that the observer is still on the equator, but 
the sun is in declination 20° N., by calculation his rising amplitude 
will be E. 20° N., and setting amplitude W. 20° N., while his 
meridian zenith-distance will be 20° N. 
Suppose the length of the line which represents the sun’s path to 
be fixed at any length, say about 8 inches as in diagram, then all 
that is necessary to get the bearings to fit in as by calculation is to 
shift the position of the observer, in an opposite direction to the 
declination, a distance equal to the tangent of the declination, 
taking half the length of the line as radius. 
Now, if the sun’s path may be represented on the plane of the 
horizon, by a straight line for lat. 0° and by a circle for lat. 90°, it 
is, I might say certain, that it may be represented by an ellipse for 
any intermediate latitude, on something the same principle that, 
while the crank-pin of a steam-engine describes a circle and the 
crosshead travels in a straight line, any intermediate point in the 
connecting-rod describes an ellipse. The relative lengths of the 
major and minor axes of the ellipse which will correctly represent 
the sun’s path for any particular degree of latitude may he illus- 
trated in the following simple manner : — If a disc be held so as to 
throw its shadow on a plane, with the disc edge on to the light, its 
shadow will be a straight line, corresponding to the sun’s path in 
lat. 0°; if held flat to the light, its shadow will be a circle, the 
same as the sun’s path in lat. 90°; and if canted so that it is 20° 
