464 The Atmospheres of the Planets. [October, 
to only half that at the surface; at the height of 15°84 
miles, only one-fourth; at 24 miles, only one-tenth ; at 44 
miles, one-hundredth; at 64 miles, only one-thousandth ; 
and at 130 miles, only one-millionth of that at the surface. 
When most favourably placed one second of arc at. the 
distance of Mars is equal to 210 miles, and for a height of 
one-fifth of a second of arc at the limb the atmosphere 
would not be distinguishable from the surface of the planet. 
This corresponding to 42 miles, it is evident that nearly the 
entire atmosphere of Mars, at the limb, is so close to the 
surface as to be, to all intents, indistinguishable from it. 
This circumstance is important, for two occultations of stars 
by Mars have been seen when no trace of any retardation or 
distortion was observed, the star disappearing sharply and 
neatly at the limb. It has been considered that this indi- 
cates that the atmosphere of Mars must be of small density, 
or else the effects of its horizontal refraction would have 
manifested themselves. From the small diameter of Mars 
a horizontal refraction of only one four-hundredth the amount 
of our own would entirely prevent the disappearance of a 
star behind Mars, but would spread the rays into a distin¢t 
circle of light around the planet. But the breadth of the 
fringe of atmosphere being thus so small, only one-hundredth 
lying beyond one-fifth of a second from the limb, it is impos- 
sible to distinguish this circle of light, so that the star seems 
to disappear sharply at the limb, though in reality vanishing 
at a fictious border to the planet. To ascertain the effect of 
this small portion of the atmosphere beyond this distance 
from the limb, as the density of the atmosphere at this 
point is barely one-hundredth of that at the surface, the 
following approximate form of the equation to the horizontal 
refraction may be employed :— 
fo = bob" 8 ye 
2 
where 7, is the horizontal refraction and 6,’ the density 
of the air at the given point as compared with that at the 
surface of the earth. 
Substituting the value of @ and putting the density of the 
atmosphere at the point in question at only one-hundredth 
of that at the surface of Mars, the horizontal refraction, at 
a distance of only one-fifth of a second of arc from the true 
limb, would be— 
Ve NOH iG 
whilst at a distance of only one-third of a second of arc 
