Heate.—On Moon Occultations. 59 
moon covers any point on the earth at the time the spectator is there, the star 
will not be visible to him, or it will be occulted, and it is obvious that the 
moment when the moon’s image on the drawing just touches the part where 
the spectator is at the moment, on either side, will be the time at which the 
disappearance or occultation and egress will occur. 
To construct such a diagram as this does not require any considerable 
calculations, but it is tedious, and, in practice, a pretty expert computer and 
draftsman would hardly compute it in Jess than an hour, which is a good deal 
of labour to expend on a mere preliminary, which may have to be many times 
repeated before one is come to which proves to be available for observation. 
A rather large book by Mr. F. C. Penrose, containing an elaborate method 
of shortening the labour of this graphical process, was published in England 
three or four years ago. In it there are diagrams ready made, upon which the 
elements of an occultation, as taken from the nautical almanac, may be laid 
down, the reduction necessary being made by means of a slide rule. I hardly 
think that this method will be much used. It is possible that I may be so 
wedded to methods to which I am accustomed that I do not readily take to 
other ones; but, to me, it appears quite as troublesome as the ordinary plan 
as given in Loomis and many other astronomical books, to which, after giving 
every attention to Mr Penrose’s method, I have found it most convenient to 
adhere ; but, in practice, I have adopted some mechanical aids which, without 
in any degree altering or modifying the plan, assist so largely in carrying it 
out that I now find that by their use I can predict at least four in the time it 
used to take me to project one, and without any sensible diminution in 
accuracy, the result being, that when an occultation occurs while the moon is 
within an hour or two of the meridian, the prediction is true within a limit 
of about two minutes, the possible error increasing to about double that 
quantity when the moon is four hours from the meridian. 
In laying down a diagram by any process it is necessary to lay down in 
their true relative values the magnitude of the earth, or, at least, of the ellipse 
into which the observer’s latitude-parallel is projected ; of the different hour 
spaces upon it; and of the moon and her position and motions. The ready 
way of doing this is either to take the moon’s horizontal parallax in seconds, 
and to adopt that on a suitable scale as the earth's radius, in which case the 
values of the hour intervals and of the observer's distance from where the star 
is vertical must all be reduced to that radius; or an arbitrary radius, as 1,000, 
may be used, and the value of the hour intervals in the observer's latitude 
may then be laid off one for all, the same diagrams being used for an indefinite 
number of predictions ; but then all the other quantities must be reduced to 
that radius, and in either case the ellipses into which the observer's latitude- 
parallel is projected must be set out for each occultation or eclipse predicted, 
