192 
Proceedings of the Royal Society of Edinburgh. [Sess. 
IX. — Note on Captain Weir’s Azimuth Diagram and its anticipa- 
tion of a Spherical Triangle Nomogram. By Herbert Bell, 
M.A., B.Sc, Communicated by The General Secretary. 
(MS. received May 15, 1916. Read June 5, 1916.) 
In a paper * read before this Society in 1889, Captain Weir gave a diagram 
for solving graphically, by means of a chart and parallel ruler, the polar 
spherical triangle whose vertices are the pole, zenith, and a star, so as to 
obtain the Azimuth when the declination, hour-angle, and latitude are 
known. The purpose of this note is to show that this diagram is in reality 
equivalent to the later straight-line nomogram, and to deduce a similar 
diagram to Weir’s for another problem in spherical trigonometry. 
When three of the six parts of a spherical triangle (three sides and 
three angles) are given, and we require a fourth part, the most frequently 
recurring cases in practice are : — 
(i) The case (3.1), in which three of the 
parts concerned are consecutive, 
and the fourth — a side — stands 
alone. 
(ii) The cases (4.0), in which all the four 
parts concerned are consecutive. 
If a, b, c, A, B, C are the sides and 
angles, then the case (3.1) corresponds to 
four such parts as b, A, c, — , a, and case (4.0) to four such parts as c, 
B, a, C. 
The corresponding well-known formulae connecting the four parts 
are : — 
c 
Case (3.1) : 
Case (4.0) : 
cos a — cos b cos c + sin b sin c cos A 
cos B cos a = cot c sin a — cot C sin B 
(1) 
( 2 ) 
Captain Weir’s construction for the case (4.0) is as follows : — 
Draw the circle x = r cos C , y = —r sin C about the origin and graduate 
it in terms of C, taking r of any convenient length. Graduate the ^/-axis 
* “Theoretical Description of a new ‘Azimuth Diagram’ by Captain Patrick Weir,” 
Proc. Roy. Soc. Edin., vol. xvi, No. 129, p. 354. 
