OBSERVATIONS FOR TIME AND LONGITUDE. 171 
Bough Determination of the Parallaxes in Declination and Bight Ascension 
of a Heavenly Body, and\ its Application to the Prediction of Occultations.* 
By Major S. C. N. Grant, r.e. 
The diagram facing p. 174 is designed for the purpose of obtaining 
rapidly, and with some degree of accuracy, the parallaxes in declination 
and right ascension of the moon, and the practical use to which the 
parallaxes, so obtained, are put is that of predicting the elements of 
occultations of stars by the moon preliminary to making observations for 
the determination of longitude. 
The generally accepted systems, both theoretical and graphic, of 
calculating the local elements of occultations are somewhat long and 
tedious; whereas the system to be described in these notes is rapid, 
simple, and sufficiently accurate for practical purposes. 
The diagram itself represents an orthographic projection of the Earth, 
showing parallels of latitude and hour circles; the line 00 represents 
the projection of the equator, and the projections of the parallels of 
latitude are drawn at intervals of 5°. The divisions on the circumference 
of the circle, however, give the positions of parallels to each degree, 
and as the intervals between these divisions can be divided into four 
parts, latitude can be plotted to 15'. 
The hour circles are drawn only on the eastern half of the circle, and a 
portion of the north-west quadrant. They are numbered in two ways— 
one from 0 at the centre to YI. at the east circumference; and the other 
from 0 at that circumference to YI. at the centre, and continued to YII. 
and YIII. beyond the centre. The use of these two systems of numbering 
will be explained hereafter. Where the space permits, the intervals 
between the hour circles have been subdivided into spaces representing 
five minutes; the hour nearest the circumference is divided only into 
spaces of fifteen minutes. Near the centre of the circle these divisions 
can be subdivided by eye into five parts, each part representing one 
* Separate copies of this paper with the diagrams mounted can be purchased 
at the Society’s rooms. 
