1874.] and its Influence on Lunar Questions. 499 
sphere being the cause of this—arises from a very simple 
cause. From merely looking at the question in a general 
manner it has been always considered that for a similar 
surface density the refraction on the moon and earth would 
be alike ; but a mere inspection of the complete differential 
equation to the refraction of light through an atmosphere 
shows that the refraction for equal surface densities varies 
approximately for small refraction as the square root of the 
radius of the planet and the action of gravity on the surface, 
and on the moon both, are much lessthan on the earth. On 
the moon accordingly, for equal surface densities, the 
refraction is only about one-fifth of what it would be on the 
terrestrial surface, and, this circumstance having been over- 
looked, the density of the atmosphere has been greatly under- 
estimated. 
It would be useless to travel through the numerous 
methods that have been referred to as showing the non- 
existence of any lunar atmosphere, not of much greater 
tenuity than the most perfect vacuum of an air-pump, for 
they are not applicable to such an atmosphere, although it 
could hardly be called even a vacuum, much less a perfect 
air-pump vacuum, but a few general remarks will suffice. 
The effect of the atmosphere on the phenomena presented 
by the moon would be imperceptible in all except the single 
case of the retardation of occultations, for the amount of 
refraction is insufficient to in any way distort or alter the 
appearance of a star or planet seen through it, and, similarly, 
any effect it might exert upon the spe¢troscopic observations 
of our satellite would be marked by the greater action of the 
terrestrial atmosphere. The sole action it would exert 
during a solar eclipse would obviously be to simply augment 
the solar diameter to a very slight extent, but, as this latter 
is not known with accuracy, this would be undetectable; 
neither would any new lines be revealed by the spectroscope 
in observations like Mr. Stone’s,* for there would be no new 
substance to give them, as would be indeed very improbable. 
Finally, it may be observed that the rays, after refraction 
through the atmosphere, would not be convergent like after 
passing through a lens, for, the refraction diminishing with 
the height, rays from different altitudes would be divergent. 
This atmosphere, which at first sight might appear so rare 
as to be unworthy of notice, is not so in reality, for it is of 
much greater proportionate dimensions than the earth’s, 
which it even exceeds in actual volume, counterbalancing its 
* Monthly Notices of the Royal Astronomical Society, June, 1874. 
yi. 
