358 Proceedings of Boy al Society of Edinburgh. [sess. 
graduated horizon round the diagram, but any other mechanical 
means might be substituted. 
This completes the diagram as far as the calculating of azimuths 
is concerned, and, as I agree that, for practical purposes, the rising 
and setting circles could be very well dispensed with, I will not 
occupy your time with them, except to state an arbitrary rule for 
finding the centres of any of these circles. 
To find the centre of the rising or setting circle for any degree of de- 
clination : — From 90, subtract twice the declination of circle required 
and remainder will give the centre of circle required on meridian or 
line of tangents, radius being equal to distance from point as found 
to focus of ellipses. 
[The accompanying diagram has been prepared to illustrate Capt. 
Weir’s paper. It shows the ellipse for latitude 30°, the hyperbola 
for hour-angle III. o’clock, and the rising and setting circles for 
declination 30°. A complete diagram, showing the ellipses for all 
degrees of latitude from 0° to 60°, and the hour-angle hyperbolas 
for every 4 m . of time, has been accurately drawn by Mr R. Wills, 
and is to be published by Potter, mounted on cardboard for practical 
use, with Capt. Weir’s instructions, revised and to some degree 
simplified by Prof. George Darwin and Sir William Thomson.] 
As compared to Saxby’s spherograph and Burdwood’s tables, the 
two methods of computing time azimuths most in use, this diagram 
has several advantages which I shall briefly notice. 
