hits upon a plan for knowing where to look
for the bull's-eye when he wakes. He
imagines the circle in which Mars seemed to
move, to be divided into as many equal
parts as Mars took days to go round it,
and he names these parts one, two, three,
four, &c.: beginning at the first point of
Aries in the sky where there is a light burning,
which appears (unlike the bull's-eyes) to
be stationary.

This settled, leaving the policeman in
number ten, he drops off into a pleasant fifty
days' snooze; no one need be surprised at
this, for if we have got over the difficulty of
putting Mr. Bubs into the sun, we may surely
make him sleep as long as we please.

On waking, he is careful not to look at
anything but his solar watch, which only marks
days, and he says, " Bless my soul! I have
slept forty-five days and a half; that policeman
ought to be in the middle of number
fifty-five." Mr. Bubs is not a little disgusted
to find that he is not there, but has got into
number fifty-six. Now, our watcher has one
good point about him. He does not always
think himself right, and everybody else who
differs with him, wrong. So, instead of
accusing the policeman of irregularity, he counts
the divisions over again, and looks at his
watch again, and tries to be quite certain that
he remembers the lights being in number
ten when he left it; but having done all this,
he is forced at last to conclude that the light
is not where it ought to be, and that the
solar policeman has been loitering on his beat.
So he carefully watches him all round again,
and now that Mr. Bubs's attention has been
drawn to the possibility of such a change in
speed, he notices that the man's pace does
vary, that he slackens his speed through one
half of his round, and then quickens it
through the other, and that the Apsides
where he goes quickest and slowest, are
always one hundred and eighty degrees apart,
immediately opposite one another.

Nor is this all; like most earnest searchers
after truth, an unexpected discovery rewards
his labour. Whenever the light goes fastest,
it looks brightest, and vice versâ.

Mr. Bubs has now got something to puzzle
him: his circular theory with the man walking
uniformly round will not do. For, in the
first place, the pace is not uniform, and he
must now notice the points where the speed
begins to increase and slacken, and take this
change into account when he next looks for
Mars. And, in the second place, as it seems
absurd to fancy the man turning on an extra
supply of light because he is going quicker,
how else is Mr. Bubs to account for the
change of size in the bull's-eye?

A bright idea occurs to him. The light
would, of course, look larger, the nearer it is;
and so, if Mars really does come nearer to
him at one time than another, it is plain that
he cannot be walking in a circle.

This sets Mr. Bubs observing again, and
he takes a piece of paper and makes a round
dot in the middle to represent himself, and
then, watching the light, puts down other
dots round this one for its different positions
as it goes round him, putting them the farther
away from the central dot, the dimmer the
light is.

Mr. Bubs is in ecstasies when he has done
this; for, although the plan is somewhat a
rough one, yet he finds that these little dots
look very like an oval curve, called an ellipse,
which he remembers reading about in the
Middlington Road Academy, and so he
concludes that he has completely solved every
difficulty, and that this policeman walks round
him in an ellipse, and that, the farther he is
off, the quicker he goes.

After having mentally patted himself on
the back, and said, " Clever dog, Bubs; clever
dog! " he puts on his night-cap, convinced
that when he wakes he shall know exactly
where to look for Mars.

But he is again disappointed: after allowing
for the elliptical beat, and the alteration
of speed, when he triumphantly turns to
look for the red light, it is not exactly where
it ought to be.

Another long patient watch now opens
Mr. Bubs's eyes to another freak in this eccentric
watchman. The places where his speed
is fastest and slowest (in other words the
Progression of the Apse) are not always the
same, but they keep shifting round and
round in the same direction as the man is
going; that is to say, if he is going quickest
in a certain place in one round, in the next
he is going quickest at a place a little in
front of it, but still in the same round; the
points of greatest and least speed are always
diametrically opposite.

"Well," says Mr. Bubs, as he turns in
again for a nap, " he is an odd fellow! But
I'll match him for all that; I must allow
for his going in an ellipse— I must remember
his alteration in speed—I must remember the
change in the points where he begins to alter
it. Ah! I shall know where he is the next
time I wake." However, Mr. Bubs has not
got out of his troubles yet. On looking for
Mars, he finds the light pretty nearly in
the right direction, but rather higher than
it ought to be. " The fellow has shifted his
belt," says Bubs; so he watches him round
again, and he finds that the light actually
touches the plane (the policeman's ground)
at the ascending Node, then rises higher and
higher above it, till it has got a quarter
round; then sinks through the next quarter,
or descending Node, touches the plane again,
passes through it, sinks lower and lower in
the third quarter, rises to the plane again
through the last, and again pierces it to
rise above it as it did at first. This eccenric
track is followed, Mr. Bubs knows, in
obedience to the astronomical law, that " the
orbit of a planet is in a plane inclined to that
of the Ecliptic."