ON THE GRAPHICAL CONSTRUCTION OF A SOLAR ECLIPSE. 
[From the Memoirs of the Royal Astronomical Society, vol. xxxix. (1870—1871), 
pp. 1—17. Read January 13, 1871.] 
The present Memoir contains the explanation of a Graphical Construction of a 
Solar Eclipse, which (it appears to me) is at once easy, and susceptible of considerable 
accuracy: I think that if made on the suggested scale (radius =12 inches) we might 
by means of it construct a diagram such as the eclipse-diagrams of the Nautical 
Almanac, with at least as much accuracy as could be exhibited in a diagram on that 
scale. 
Article Nos. 1 to 9. General Explanation of the Construction. 
1. We may imagine the celestial sphere as seen from the centre of the Earth 
stereographically projected at each instant during the eclipse—the radius of the bounding 
circle of the projected hemisphere being a given length, say twelve inches, which is 
taken as unity—in such wise that the centre of the Moon is always at the centre of 
the projection, say M, and the pole (suppose the north pole, say N) of the Earth on 
a given radius: its position on this radius will in strictness be variable, viz. distance 
from centre = projection of Moon’s N. P. D. = tan^A. Suppose, for a moment, that the 
position at each instant of the Sun’s centre were also laid down on the projection, 
so as to obtain the projection of the Sun’s relative orbit; this will be a terminated 
short line A'B' (fig. 1), nearly straight, and lying near the centre of the projection 
(this relative orbit is not to be actually laid down, but it is replaced, as will presently 
be explained, by a relative orbit on a very enlarged scale); if at any instant the 
position of the Sun on the relative orbit be denoted by S', then the straight line 
MS' is the projection of the arc of great circle through the centres of the Moon and 
Sun, so that E being the angular distance of the centres, the length of the line 
MS' is =tan£i£, or (E being small) it is = \E.