60 Transactions. — Miscellaneous. 



and the values of the hour-spaces marked on it, and this 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 obsei'ver'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 oflf the 

 distance south in seconds, as given in the nautical almanac, and tlie moon's 

 hourly motion in right ascension, reduced to an arc of a great circle, is 

 measured on the hoi-izontal 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 coui-se, 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 comjDuting the hour divisions, I 

 keep a set of ellipses, cut out of cardboard, for every SO" of horizontal parallax, 

 and for every 100" of semi-minor axis, on which the hour divisions are 

 permanently marked. 1 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, 

 Avhich, beaiing 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. 



