193 
1915-16.] Note on Captain Weir’s Azimuth Diagram. 
according to the formula y = cot c. Construct the network consisting of 
the family of ellipses 
r 
cosec 2 a~^"cot 2 a 
- = 1 
(3) 
intersected by the family of hyperbolae 
siu 2 B cos 2 B 1 
(♦) 
The resultant diagram is reproduced in fig. 2. Since in practice we are 
concerned with positive values of x only, the other half of the plane is 
not drawn. 
An a-ellipse in the network and a B-hyperbola intersect in the point 
{cosec a sin B, cotacos B). The line joining this point to the point on the 
2 /-axis y = cot c has for equation 
cot a cos B — cot c . , 
y — x ; — — — -f cot c 
cosec a sin B 
(5) 
This line is parallel to the line y— — xcotC through the origin cutting the 
C-circle in the C-reading, since by (2) 
cot C = 
cot c sin a — cos B cos a 
sin B 
Hence the method of using : Join the C-reading to the origin by one arm 
of a parallel ruler ; make the other arm pass through the point in the net- 
work determined by a and B. This second arm then passes through the 
required value of c on the y- axis. 
As used in navigation to find the azimuth A of a star given the 
declination S, hour-angle H, and latitude <p, the four consecutive parts 
c, B, a,C (fig. 1) are replaced successively by 90° — S, H, 90° — 0, 100° — A, 
corresponding to the spherical triangle whose vertices are the star, the pole, 
and the zenith. 
The chart as used in H.M. Navy measures 30 inches x 15 inches, and 
enables one to read to an accuracy of about a quarter of a degree. 
Since two parallel lines intersect at an infinite distance, the arm of the 
parallel ruler, which always passes through the origin, and the C-reading 
on the C-circle may be regarded as pointing towards a point C at infinity, 
towards which the other arm also points. Let us then project stereo- 
graphically the x, y plane into an x , y' plane, bringing C into a finite part 
of it. We can do this by projecting some line parallel to the ^/-axis to 
infinity, e.g. the line x= — 1 ; we shall let the cc-axis become the cc'-axis, and 
VOL. xxxvi. 
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