60 Transactions.— Miscellaneous. 
and the valües of the hour-spaces marked on it, and tbis is the most 
troublesome part of the operation. Penrose’s method gives several ellipses 
already drawn, from which one may be selected which corresponds most nearly 
with the circumstances of the eclipse to be predicted. 
Now the method I employ is the first and simplest one. I take out 
roughly, by inspection, the moon's horizontal parallax at conjunction, and 
adopt that as a radius ; the position of the observer and of his antipodes are 
` then got out by taking the sum and difference of the declination and the sine 
of the observer's latitude into the adopted radius. These can then be laid off by 
scale on a vertical line drawn on any sheet of paper from a fixed point at its 
upper end, through which a line is drawn perpendicular to it. The moon's 
place at conjunction can then be marked on the same line'by scaling off the 
distance south in seconds, as given in the nautical almanae, and the moon's 
hourly motion in right ascension, reduced to an are of a great circle, is 
measured on the horizontal line on top, and her motion north or south on 
the perpendicular line. A line parallel to the diagonal of those co-ordinates 
drawn through the moon’s place at conjunction will give her course, and the 
distance she travels in parts of an hour may be marked off on it, the times of 
which should be marked on them. All this is just as would have to be done 
on the ordinary method, but then, instead of constructing the ellipses 
representing the parallels of latitude and computing the hour divisions, I 
keep a set of ellipses, cut out of cardboard, for every 80” of horizontal parallax, 
and for every 100” of semi-minor axis, on which the hour divisions are 
permanently marked. I see at a glance which ellipse suits the conditions 
best—that is, the one drawn to the same horizontal parallax, and of which the 
minor axis corresponds with the distance in seconds of the observer and his 
antipodes—and at once rule in the curve from the card, and also mark the 
hour divisions from it. I have then only to take off the moon’s semi-diameter, 
which, bearing a fixed proportion to the horizontal parallax, may be marked 
off on each cardboard ellipse, and it is the work of a minute to see the moment 
at which the ingress and egress occurs, and the point on the moon’s perimeter 
at which the star enters and emerges. It is obvious that the same process is 
equally applicable to solar eclipses, taking of course the differences of their 
parallaxes and motions and the sum of their semi-diameters. 
Now that binocular telescopes are so largely used, and are made to powers so 
considerable as 7 or 8 diameters, the observation of a star of fourth magnitude 
entering on the dark limb of the moon—that is before the full—may be perfectly 
well observed on board ships, and, I believe, in clear weather fifth magnitude 
stars could be seen ; and, as one observation will give a longitude thoroughly 
trustworthy within very narrow limits, it seems a pity that they should so 
seldom be used. 
