58 Transactions. — Miscellaneous. 
by which a very aceurate determination of longitude may be had from a single 
observation, for which no instrument is necessary but a hand telescope of 
moderate power. 
This excellent method was scarcely available for travellers before binocular 
telescopes came into use, but they seem to me now to be very unduly neglected, 
especially by seamen. The causes of this neglect are not far to seek. The 
first is an irreparable one: they occur very rarely—there are not, on an 
average, more than twelve each month for each latitude, of which seldom one- 
half are fairly available for good observation on shore—and with the small- 
power telescopes, wbich it would be necessary to use on board ship, the really 
available cases would hardly occur oftener than two in a month. But another 
cause of the unpopularity of these observations is, that it is necessary to make 
a preliminary investigation for each star that seems likely to be available, the 
result of which, when made, very often is simply to show that it is useless 3 80 
that out of half-a-dozen stars predicted it is rarely that more than one proves 
altogether suitable, and even that one may be lost by a passing cloud. 
It must be confessed that this is a discouraging circumstance at the best, 
and when the prediction required an elaborate caleulation, involving the 
solution of three spherical, and at least two plane, triangles, it was fatal to its 
use by practical men. I shall proceed, however, to show that the trouble may 
be reduced to very small dimensions indeed. 
The elements necessary for the prediction and computation of occultation 
are given in the nautical almanac, and more copious ones in the American 
nautical almanac ; but they could only be given without great labour for belts 
of latitude, and a special investigation has to be made for each place. Various 
plans have from time to time been published for abridging the labour of these 
predictions. The first I am acquainted with is a pamphlet by Captain, now 
Admiral, Shadwell, which was published by the Admiralty in 1847. The 
principle on which it is based, is to use essentially the same processes as those 
required for the final computations, but to shorten them by using 
approximations instead of the accurate elements ; by treating all the triangles 
as plane, and solving them by the use of the traverse-table, with which seamen 
are very familiar. 
But the most practically useful method of approximate prediction is by 
the method of graphical projection. Drawing a diagram of the earth as it 
would appear to an eye situated in the star at the moment of conjunction in 
right ascension, showing the line on it upon which the spectator would be 
carried in given intervals of time by the earth’s motion, then marking a point 
on the picture at which the moon’s centre would be at the same moment, and 
a line to indicate the direction of her movement, with the points on it which 
she will reach in given intervals; then it is clear that if the figure of the 
