1874.] and its Influence on Lunar Questions. 495 
And lastly, for the horizontal refraction 7,, expressed in 
seconds of arc, undergone by a ray of light in passing through 
the atmosphere— 
r= GAO) /O8l 1 (fas) (Ya) Hf %)} » 
sin I 
where f is the function on which the rate of decrease of 
temperature depends. 
Were the temperature of an atmosphere constant through- 
out, the density and pressure would, in accordance with 
Mariotte’s law, diminish together in geometrical proportion 
with increase of altitude. The temperature is, however, 
not constant, but varies inversely as the altitude; so it be- 
comes necessary to assume some law for this decrease, and 
this will evidently depend primarily upon the supposed tem- 
perature of space. It has been generally assumed, by those 
who have lately written on this lunar subject, that the tem- 
perature of space is near the absolute zero of heat,—in 
contradistin¢tion to Fourier and Hopkins, who regarded it 
as but little below zero, which is preferable. Whatever 
value may be adopted, the corresponding value of the 
function f is given by the equation— 
eles 
uf Eero jae (6) 
as the temperature of space would not be reached until a 
considerable distance from the moon. 
These equations, it is seen, involve the temperature of the 
lunar surface, and from Lord Rosse’s determinations it ap- 
pears that the moon’s surface may reach 200°C. For the 
minimum value the temperature reaches during the long 
lunar night very different values have been ascribed, and it 
is evident that much may depend on the temperature of 
space assumed. It has, moreover, been generally thought 
that any lunar atmosphere would, from its extremely small 
density, exert little influence in retarding the radiation of 
heat from the moon; but it has been overlooked that the 
thickness of the envelope of atmosphere, as well as its 
density, must be considered. Now the thickness of the 
lunar atmosphere is for this purpose many times greater 
than the earth’s, and this counterbalances its tenuity; ac- 
cordingly the retardation of radiation would not be much 
less than on the earth. As during our long terrestrial polar 
nights, from six to ten times the length of the lunar night, 
the mean temperature is not usually many degrees below 
zero, it will therefore be probable that the temperature of 
