WEIR S AZIMUTH DIAGRAM, 



293 



semi-minor axes, as I have shown, become ^= tangent latitude, and 

 a scale through which to draw the ellipses Avill be a scale of 

 tangents laid down on the meridian, but the declination scale is 

 also a scale of tangents along the meridian ; therefore both 

 declination and latitude can be measured on the same scale. 



Another advantage of this particular proportion of axes (secant 

 and tangent) is that it locates the foci of all the ellipses in the same 

 two points, which was of great assistance to me in constructing 

 my original diagrams with pins and threads. 



Having calculated the dimensions of the ellipses and laid them 

 down, the next step is to fix the position of the sun on them for 

 each particuhir period as minutely as may be required. It is evident 

 that the noon line in all latitudes, and no matter what the declina- 

 tion may be, will correspond with the meridian or minor axes of 

 the ellipses ; and it is also equally certain that the six-hour line will 

 be at right angles to the meridian 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. The ])ositions of 

 the intermediate hours, &c , will be simph' their positions on a 

 circumscribing circle projected into the ellipse, and may be arrived 

 at as follows : — Take any ellipse of latitude, and with centre O 



Fig 6 ^^^"- ^) '^"^ ^^^* 



the major axis of 



the ellipse as radius, 

 describe a circle 

 about the ellipse ; 

 divide this circle 

 into hours, &:c., as 

 minutely as may 

 be required, and 

 through these divi- 

 sions draM' lines 

 parallel to the me- 

 ridian and cutting 

 the ellipse. The 

 point where each 

 cuts the ellipse will 

 indicate the same 

 time as where it 

 cuts the circle. This 

 routine must be 

 gone through for, 

 say, every fifth or 

 tenth degree of 

 latitude, and when the points so foimd on the ellipses for each 

 particular period have been joined in a regular sweep they will 

 be found to form a curve which it can be proved is a hyperbola, 

 whose focus is also the foci of all the ellipses. 



