440. The _Trajectorium Lunare_. This Machine is for delineating the
paths of the Earth and Moon, shewing what sort of Curves they make in
the etherial regions; and was just mentioned in the 266th Article. _S_
is the Sun, and _E_ the Earth, whose Centers are 81 Inches distant from
each other; every Inch answering to a Million of Miles § 47. _M_ is the
Moon, whose Center is 24/100 parts of an Inch from the Earth’s in this
Machine, this being in just proportion to the Moon’s distance from the
Earth § 52. _AA_ is a Bar of Wood, to be moved by hand round the Axis
_g_ which is fixed in the Wheel _Y_. The Circumference of this Wheel is
to the Circumference of the small Wheel _L_ (below the other end of the
Bar) as 365-1/4 days is to 29-1/2; or as a Year is to a Lunation. The
Wheels are grooved round their edges, and in the Grooves is the cat-gut
string _GG_ crossing between the Wheels at _X_. On the Axis of the Wheel
_L_ is the Index _F_, in which is fixed the Moon’s Axis _M_ for carrying
her round the Earth _E_ (fixed on the Axis of the Wheel _L_) in the time
that the Index goes round a Circle of 29-1/2 equal parts, which are the
days of the Moon’s age. The Wheel _Y_ has the Months and Days of the
year all round it’s Limb; and in the Bar _AA_ is fixed the Index _I_,
which points out the Days of the Months answering to the Days of the
Moon’s age, shewn by the Index _F_, in the Circle of 29-1/2 equal parts
at the other end of the Bar. On the Axis of the Wheel _L_ is put the
piece _D_, below the Cock _C_, in which this Axis turns round; and in
_D_ are put the Pencils _e_ and _m_, directly under the Earth _E_ and
Moon _M_; so that _m_ is carried round _e_ as _M_ is round _E_.
[Sidenote: It’s use.]
Lay the Machine on an even Floor, pressing gently on the Wheel _Y_ to
cause its spiked Feet (of which two appear at _P_ and _P_, the third
being supposed to be hid from sight by the Wheel) enter a little into
the Floor to secure the Wheel from turning. Then lay a paper about four
foot long under the Pencils _e_ and _m_, cross-wise to the Bar: which
done, move the Bar slowly round the Axis _g_ of the Wheel _Y_; and, as
the Earth _E_ goes round the Sun _S_, the Moon _M_ will go round the
Earth with a duly proportioned velocity; and the friction Wheel _W_
running on the Floor, will keep the Bar from bearing too heavily on the
Pencils _e_ and _m_, which will delineate the paths of the Earth and
Moon, as in Fig. 2d, already described at large, § 266, 267. As the
Index _I_ points out the Days of the Months, the Index _F_ shews the
Moon’s age on these Days, in the Circle of 29-1/2 equal parts. And as
this last Index points to the different Days in it’s Circle, the like
numeral Figures may be set to those parts of the Curves of the Earth’s
Path and Moon’s, where the Pencils _e_ and _m_ are at those times
respectively, to shew the places of the Earth and Moon. If the Pencil
_e_ be pushed a very little off, as if from the Pencil _m_, to about
1/40 part of their distance, and the Pencil _m_ pushed as much towards
_e_, to bring them to the same distances again, though not to the same
points of space; then as _m_ goes round _e_, _e_ will go as it were
round the Center of Gravity between the Earth _e_ and Moon _m_ § 298:
but this Motion will not sensibly alter the Figure of the Earth’s Path
or the Moon’s.
If a Pin as _p_ be put through the Pencil _m_, with its head towards
that of the Pin _q_ in the Pencil _e_, its head will always keep thereto
as _m_ goes round _e_, or as the same side of the Moon is still obverted
to the Earth. But the Pin _p_, which may be considered as an equatoreal
Diameter of the Moon, will turn quite round the Point _m_, making all
possible Angles with the Line of its progress or line of the Moon’s
Path. This is an ocular proof of the Moon’s turning round her Axis.
[Sidenote: The TIDE DIAL.
PLATE IX. Fig. VII.