594 
THE EAEL OF EOSSE ON THE EADIATION 
of the Royal Society,’ 1869, was adopted*. In accordance with this law’, if the radiant 
heat of the full moon be represented by unity, the heat ( h ) at any other phase will be 
{c ceteris paribus) 
7 {% — e) cos s + sin s 
The logarithmic factors for reducing- observations made at any elongation to a mean 
value (g 0 ) for the night were readily derived from a Table of log h for every degree of g. 
As the moon’s heating-power doubtless varies (cceter is paribus) as the square of her 
apparent semidiameter, the double of the logarithm of the apparent semidiameter 
at different times affords the simplest form of reduction for change of distance. In this 
way the logarithmic factors for correcting for changes of g and c in columns log (g) and 
log ( a ) were obtained. 
For the larger readings of the galvanometer there is a small correction required to 
reduce the readings from tangent to arcf. This correction maybe conveniently brought 
into the form of a factor if we assume, as was approximately the case, especially for the 
larger readings, that the amplitudes were equally large on each side of the zero-point J. 
For if n is the difference of two readings and r the distance of the scale from the galva- 
/X \ 
nometer, the correcting factor will be I 1 — In our case r=1440, and the log 
factor becomes 
log corr. (g)= log (l - 34 ^ 3200 ) * 
The values of log corr. ( g ) are given in column log (g) for each observation. 
The sum of log G, log (g), log (g), and log (<r) gives column log (G corr.), the logarithm 
* There is a misprint in formula (a) at the place referred to ; it should have been 
Q=100 ^1 -I'j cos . 
Since the publication of that paper it has been found that Lambert, in his ‘ Photometria,’ had already made 
o*i* ji n 2 (sin v— v . cos v) . A . sin 2 s . sin 2 n . C 
use 01 it in the lorm c=— — , 
37t . sin 2 S 
where A = mean “ albedo ” of moon’s surface, 
s = sun’s apparent semidiameter as seen at the moon, 
a — moon’s apparent semidiameter, 
C = brightness of an absolutely white plane illuminated by perpendicularly incident rays of the sun, 
c = brightness of an absolutely white plane similarly illuminated by the rays of the moon, 
v =elongation from the sun=180° — e, 
S = sun’s semidiameter as seen from the earth. 
t It appears rather doubtful whether this small correction (which only amounts at most to of the whole 
heating- effect) should have been made at all, as from subsequent experiment the deviations in different parts 
of the scale were found to he very nearly identical with the same heating-effect ; in fact the difference was less 
than the probable error of observation. 
+ Strictly speaking this correction should have been applied to each single reading, not to the mean of a set 
of readings, as was done to save labour. 
