1888 - 89 .] Capt. P. Weir on a New Azimuth Diagram. 357 
south (according as the declination is north or south), a distance 
corresponding to tan of declination with half the distance between 
the foci as radius. (If half the major axis of any ellipse be taken 
as radius, then it would have to be shifted a distance = tan decl. x 
cos lat., which would be just the same.) It is, however, obviously 
impossible to make the ellipses shift on the paper, so the difficulty 
is very simply got over by supposing the position of the observer to 
be removed to a corresponding distance in the opposite direction, as 
illustrated in the case of lat. 0°, and as laid down in the directions 
for using the diagram. 
I have only constructed my diagram up to lat. 60°, which I con- 
sider high enough for all practical purposes, but it may be observed 
that for lat. 90° the major and minor axes would be infinity, which 
it may be said reduces the ellipse for that latitude to a circle as 
required by my first supposition. 
Having calculated the dimensions of the ellipses, the next step is 
to fix the position of the sun on them at any time, and it is evident 
that the noon line in all latitudes will correspond with the meridian 
or minor axis of the ellipses, as the sun is either due north or south 
at noon, apparent time in all latitudes. 
It is also equally certain that the six-hour line will be at right 
angles to it, and will correspond with the major axes of all the 
ellipses, as the sun will just have performed one quarter of his 
diurnal revolution at this time. 
To arrive at the position of the intermediate hours, &c., I proceed 
as follows: — Take any ellipse of latitude and with centre 0 (see 
diagram), and half the major axis of the ellipse as radius, describe a 
circle about the ellipse; divide the circle as minutely as may be 
required (say, into hours and quarters), and from these divisions 
draw lines parallel to the meridian, cutting the ellipse, and where 
they cut will be the position of the sun on it at that particular time. 
This routine has to be gone through for, say, every fifth degree of 
latitude ; and when the points on the ellipses for each particular 
period have been joined in a regular sweep, they will be found to 
form a curve very much like a hyperbola. [The hour-curves are in 
fact hyperbolas, confocal with the latitude ellipses. See Professor 
Tait’s Note below. — W.T.] 
Por convenience in measuring off the azimuth, I have put a 
