169. Light, and therefore heat so far as it depends on the Sun’s rays (§
85, towards the end) decreases in proportion to the squares of the
distances of the Planets from the Sun. This is easily demonstrated by a
Figure which, together with it’s description, I have taken from Dr.
SMITH’s Optics[37]. Let the light which flows from a point _A_, and
passes through a square hole _B_, be received upon a plane _C_, parallel
to the plane of the hole; or, if you please, let the figure _C_ be the
shadow of the plane _B_; and when the distance _C_ is double of _B_, the
length and breadth of the shadow _C_ will be each double of the length
and breadth of the plane _B_; and treble when _AD_ is treble of _AB_;
and so on: which may be easily examined by the light of a candle placed
at _A_. Therefore the surface of the shadow _C_, at the distance _AC_
double of _AB_, is divisible into four squares, and at a treble
distance, into nine squares, severally equal to the square _B_, as
represented in the Figure. The light then which falls upon the plane
_B_, being suffered to pass to double that distance, will be uniformly
spread over four times the space, and consequently will be four times
thinner in every part of that space, and at a treble distance it will be
nine times thinner, and at a quadruple distance sixteen times thinner,
than it was at first; and so on, according to the increase of the square
surfaces _B_, _C_, _D_, _E_, built upon the distances _AB_, _AC_, _AD_,
_AE_. Consequently, the quantities of this rarefied light received upon
a surface of any given size and shape whatever, removed successively to
these several distances, will be but one quarter, one ninth, one
sixteenth of the whole quantity received by it at the first distance
_AB_. Or in general words, the densities and quantities of light,
received upon any given plane, are diminished in the same proportion as
the squares of the distances of that plane, from the luminous body, are
increased: and on the contrary, are increased in the same proportion as
these squares are diminished.
[Sidenote: Why the Planets appear dimmer when viewed thro’ telescopes
than by the bare eye.]
170. The more a telescope magnifies the disks of the Moon and Planets,
they appear so much dimmer than to the bare eye; because the telescope
cannot magnify the quantity of light, as it does the surface; and, by
spreading the same quantity of light over a surface so much larger than
the naked eye beheld, just so much dimmer must it appear when viewed by
a telescope than by the bare eye.
[Sidenote: Fig. VIII.