OF HEAT FEOM THE MOON. 
593 
tabular place was taken from the Nautical Almanac for every hour of sidereal time over 
which the observations extended ; then the moon’s parallax was calculated, also for every 
hour, by the following approximate formulae * : — 
a' — a— — [0-3815] P sin(0 — cc) sec o 
tan y— 
Jo- 1215 ] 
COS (© — a)’ 
y-&= 
[9-9009] sin (y — S) p 
Sill y 
■ 
J 
where a! ■= moon’s apparent right ascension, 
u — moon’s true right ascension, 
V — moon’s apparent declination, 
§ = moon’s true declination, 
P — moon’s equatorial horizontal parallax, 
©= sidereal time, 
and [0-3815] = log - ^ — , 
[0-1215] = log tan J, 
[9-9009] = log §' sin J, 
where distance from centre of the earth, 
<p'= geocentric latitude. 
From the apparent places so obtained the moon’s apparent elongation (s) from the 
point opposite the sun was derived by the equation 
cos (t— s) = sin D sin cos D cos V cos (A— a'), 
where 
D= sun’s declination, 
A = sun’s right ascension. 
It is evident that 7 r—s represents very nearly the angular amount of the moon's apparent 
illuminated phase. A slight inaccuracy arises from neglecting the angle at the sunf 
in the plane triangle earth, sun, moon. 
The moon’s tabular semidiameter and a Table of augmentations gave her apparent 
semidiameter, a. Finally, the moon’s apparent altitude was taken from a Table of 
double entry calculated for the latitude of Birr Castle, to test, by its agreement with the 
readings of the quadrant, the accuracy of the calculations mentioned above. 
In the absence of an exact knowledge of the law of variation of the moon’s radiant 
heat with her change of phase, that enunciated at page 439, No. 112 of the 4 Proceedings 
* BiitiOTrow’s ‘ Spherical Astronomy,’ page 150 (English edition, 1865); 
t This angle never exceeds 9' even at quadrature. 
