1888-89.] Capt. P. Weir on a New Azimuth Diagram. 359 
1. Expense . — The spherograph is rather a costly affair (about £2, 
I believe), and for that reason has not come into general use. 
Burd wood’s tables are not so expensive, but still they cost 12s. 6d. 
per set, whereas this diagram could be published in chart form at 
certainly not more than one-fifth of that price. 
2. There is very little danger of making mistakes in taking off 
the bearing from this diagram, as it is done with parallel rulers as 
from a chart, the top being north and the bottom south, while the 
bearing is of course east or west as the time is a.m. or p.m. 
3. Accuracy . — When the diagram is finely engraved the bearing 
may be taken off very accurately, as it is on a larger and more open 
scale than the spherograph. 
4. Convenience . — Being in chart form, and worked, with parallel 
rulers the same as a chart, and as the officer who uses this diagram 
will also probably be using a chart, it will come conveniently to 
his hand to use the diagram. 
Note on Capt. Weir’s Paper. By Prof. Tait. 
(Read July 15, 1889.) 
[As Sir W. Thomson was unable personally to communicate Capt. 
Weir’s paper to the Society, he asked me to add to it a Note on the 
principle of the new method.] 
Capt. Weir’s singularly elegant construction not only puts in a 
new and attractive light one of the most awkward of the formulae 
of Spherical Trigonometry, but it practically gives in a single-page 
diagram the whole contents of the two volumes of Burdwood’s 
Azimuth Tables. Further, it supplies a very interesting graphical 
plane construction of a function of three independent variables. 
In the usual notation for spherical triangles, if A be the zenith, 
C the pole, and B a heavenly body (whose declination is S), C is 
the hour-angle (h), b the colatitude 
and A the supplement 
x>f the azimuth. Hence, from the formula 
cot a sin b = cot A sin C + cos b cos C 4 
