THE CONSTRUCTION OF SIMPLE AND PERPETUAL CALENDARS.
In taking up the study of calendar work the first thing that the
student observes is the irregularity of motion of the various members.
Every other portion of a clock has for its main object the attainment
of the nicest regularity of motion, while the calendar must necessarily
have irregular motion. The hand of the day of the month proceeds around
its dial regularly from 1 to 28 and then jumps to 1 in February of
some years, while it continues to 29 in others; sometimes it revolves
regularly from 1 to 31 for several revolutions and then jumps from 30
to 1. What is the reason of this?
If the moon’s phases are shown they do not agree with the changes of
the month wheels, but keep gaining on them, while if an “equation of
time” is shown, we have a hand that moves irregularly back and forth
from the Figure XII at the center of its dial. What is the cause of
this gaining and losing?
In order to understand this mechanism properly we shall have to first
know what it is intended to show and this brings us to the study of the
various kinds of calendar.
The earth revolves about its axis with a circular motion; it revolves
about the sun with an elliptical motion. This means that the earth
will move through a greater angular distance, measured from the sun’s
center, in a given time at some portions of its journey than it will
do at others; at times the sun describes an arc of 57 minutes of the
ecliptic; at other times an arc of 61 minutes in a day; hence the sun
will be directly over a given meridian of the earth (noon) a little
sooner at some periods than at others. Now the time at which the sun
is directly over the given meridian is _apparent_ noon, or solar noon.
As before stated, this is irregular, while the motion of our clocks is
regular, consequently the sun crosses the meridian a little before or
a little after twelve by the clock each day, varying from 15 minutes
before twelve to 15 minutes after twelve by the clock. The best we can
do under these circumstances is to divide these differences of gaining
or losing, take the average or _mean_ of them and regulate the clock to
keep _mean_ time. Here then we have two times—the irregular _apparent_
time and the regular _mean apparent_ time. The amount to be added to or
subtracted from the mean in order to get the solar or actual apparent
time is called the _equation_ of time and this is shown by the equation
hand on an astronomical or perpetual calendar clock.
The moon revolves on its axis with a circular motion and it revolves
about the earth with an elliptical motion, the earth being at one focus
of the ellipse; as this course does not agree with that of the sun, but
is shorter, it keeps gaining so that the lunar months do not agree with
the solar.
Certain stars are so far away that they apparently have no motion of
their own and are called _fixed_; hence in observing them the only
motion we can discern is the circular motion of the earth. We can
set our clocks by watching such stars and a complete revolution of
the earth, measured by such a star, is called an _astronomical_ or
_sidereal_ day. This is the one used in computing all our time. It is
shorter than the _mean solar_ day by 3 minutes 56 seconds.
A _year_ is defined as the period of one complete revolution of the
earth about the sun, returning to the same starting point in the
heavens. By taking different starting points we are led to different
kinds of years. The point generally taken is the vernal equinoctial
point, and when measured thus it is called the _tropical_ year, which
gives us the seasons. It is 20 minutes shorter than the siderial year.
A _siderial year_ is the period of a complete revolution of the earth
about the sun. This period is very approximately 365 days, 6 hours, 9
minutes, 9.5 seconds of mean time. Here we see an important difference
between the siderial and the _civil_ year of 365 days, and it is this
difference, which must be accounted for somehow, that causes the
irregularities in our calendar work.
For ordinary and business purposes the public demands that the year
shall contain an exact number of days and that it should bear a simple
relation to the recurrence of the seasons. For this reason the _civil_
year has been introduced. The Roman emperor, Julius Caesar, ordered
that three successive years should have 365 days each and the fourth
year should have 366 days.
The fourth year, containing 366 days, is called a _leap_ year, because
it leaps over, or gains, the difference between the civil and siderial
time of the preceding three years. For convenience the leap year was
designated as any year whose number is exactly divisible by 4. This is
called the Julian calendar.
But as a siderial year is 365 days, 6 hours, 9 minutes, 9.5 seconds
of mean time, the addition of one day of twenty-four hours would not
exactly balance the two calendars; therefore Pope Gregory XIII., in
1582, ordered that every year whose number is a multiple of 100 shall
be a year of 365 days, unless the number of the year is divisible by
400, when it shall be a leap year of 366 days.
The calendar constructed in this way is called the Gregorian calendar,
and is the one in common use. Its error is very small and will amount
to only 1 day, 5 hours, 30 minutes in 4,000 years.
The revolution of the moon around the earth in relation to the _stars_,
takes place in 27 days, 7 hours and 43 minutes this is called a
_siderial_ month. But during this period the earth has advanced along
the plane of its path about the sun and the moon must make up this
distance in order to return to the same point in relation to the sun.
This period is called a _synodic_ month. Its average length is 29 days,
12 hours, 44 minutes, 2.9 seconds.
Having now understood these differences we shall be able to
intelligently examine the various calendar mechanisms on the market
and understand the reasons for their apparent departures from regular
mechanical progression, as the equation of time gives us the difference
between _real_ and _mean_ apparent, or solar time; we regulate our
clocks by means of siderial time; the irregular procession of 30 and 31
days makes the civil calendar agree with the seasons, or the tropical
year, and the remainder of the discrepancy between civil and siderial
time is made up in February at the period when it is of the least
consequence.
SIMPLE CALENDAR WORK.—Fig. 111 shows the American method of making a
simple calendar, the example shown being drawn from a movement of the
Waterbury Clock Company as a typical example. No attempt is made here
to show the day of the week or the month. The days of the month are
shown by a series of numbers from 1 to 31, arranged concentrically with
the time dial and the current day is indicated by a hand of different
color, carried on a pipe outside the pipe of the hour hand on the
center arbor.
[Illustration]
[Illustration: Fig. 111. Simple calendar on time train.]
[Illustration: Fig. 112. Calendar work for grandfather clocks.]
In order to accomplish this the motion work for the hands is mounted
inside the frames, the hour pipe and center arbor being suitably
lengthened. In the Figure A is the cannon pinion; B, the minute wheel;
C, the minute pinion; D, the hour wheel at the rear end of the hour
pipe; this pipe projects through the frame and forms a bearing in the
frame for the center arbor. Friction-tight on the hour pipe, in front
of the front plate, is the pinion E, which drives a wheel F of twice
as many teeth. This wheel F is mounted loosely on a stud and has a pin
which meshes with the teeth of a ratchet wheel G. G is carried at the
bottom end of a pipe which fits loosely on the hour pipe and carries
the calendar hand H under the hour hand and close to the dial. The
pinion on the hour pipe revolves once in twelve hours. The wheel E has
twice as many teeth and will therefore revolve once in twenty-four
hours. It moves the ratchet G one tooth at each revolution; therefore
the hand H moves one space every twenty-four hours. There are 31
teeth, so that the hand must be set forward every time it reaches the
28th and 29th of February and the 30th of April, June, September and
November. This is the simplest and cheapest of all the calendars,
occupies the least space and is frequently attached to nickel alarm
clocks for that reason.
A simple calendar work often met with in old clocks of European origin
is shown in Fig. 112. Gearing with the hour wheel is a wheel, A, having
twice its number of teeth, and turning therefore once in twenty-four
hours. A three-armed lever is planted just above this wheel; the lower
arm is slotted and the wheel carries a pin which works in this slot, so
that the lever vibrates to and fro once every twenty-four hours. The
three upper wheels, B, C and D in the drawing, represent three star
wheels. B has seven teeth, corresponding to the days of the week; C
has 31 teeth, for the days of the month; and D has 12 teeth, for the
months of the year. Each carries a hand in the center of a dial on the
other side of the plate. Every time the upper arms of the lever vibrate
they move forward the day of the week, B, and the day of the month,
C, wheels each one tooth. The extremities of the two upper levers are
jointed so as to yield on the return vibration, and are brought into
position again by a weak spring. There is a pin in the wheel, C, which,
by pressing on a lever once every revolution, actuates the month of
the year wheel, D. This last lever is also jointed, and is pressed on
by a spring so as to return to its original position. Each of the star
wheels has a click kept in contact by means of a spring. For months
with less than 31 days, the day of the month hand has to be shifted
forward.
PERPETUAL CALENDAR WORK.—Figs. 113, 114, 115, show a perpetual calendar
which gives the day of the week, day of the month and the month, making
all changes automatically at midnight, and showing the 31 days on a
dial beneath the time dial, by means of a hand, and the days of the
week and the month by means of cylinders operating behind slots in the
dial on each side of the center. This is also a Waterbury movement.
[Illustration: Fig. 113. Perpetual Calendar Movement.]
A pinion on the hour pipe engages a wheel, A, having twice the number
of teeth and mounted on an arbor which projects through both plates.
The rear end of this arbor carries a cam, B, on which rides the end of
a lever, C, which is pivoted to the rear frame. The lever is attached
to a wire, D, which operates a sliding piece, E, which is weighted at
its lower end. The cam, which, of course, revolves once in twenty-four
hours, drops its lever at midnight and the weight on E pulls it down.
E bears a spring pawl, F, which on its way down, raises the spring
actuated retaining click, H, and then moves the 31-toothed wheel G one
notch. This wheel is mounted on the arbor which carries the hand and,
of course, advances the hand.
Lying on top of the wheel, G, is a cam, I, pivoted to G near its
circumference and having an arm reaching toward the months cylinder
and another reaching towards the right leg of the pawl, H, while it is
cut away in the center, so as to clear the center arbor carrying the
hand. Trace this cam, I, carefully in Figs. 113 and 114, as its action
is vital. The lower arm of this cam is shown more clearly in Fig. 114.
It projects above the wheel and engages the long teeth, J, and the
cam, K, mounted on the year cylinder arbor; where the lower arm of I
strikes one of these teeth it shoves the upper arm outward, so that
it strikes the retaining end of the pawl, H, and holds it up, and the
descending pawl, F, may then push the wheel, G, forward for _more_ than
one tooth. The upper end of I is broad enough to cover three teeth of
the wheel, G, when pushed outward, and the slot in E is long enough so
that F may descend far enough to push G forward three teeth at once,
unless it is stopped by H falling into a tooth, so that the position of
I, when it is holding up H and the extra drop thus given to E serve to
operate the jumps of 30 to 1, 28 to 1 and 29 to 1 of the hand on the
dial. The teeth, J, Fig. 114, operate for two notches, thus making the
changes from 30 to 1. The wide tooth, M, and cam, K, acting together,
make the change for February from 28 to 31. The 29th day is added by
the movement of the cam, K, narrowing the acting surface once in four
years, as follows:
[Illustration: Fig. 114. The months change gear.]
Looking at Fig. 114 we see an ordinary stop works finger, mounted on
the months arbor and engaging a four-armed maltese cross on the wheel.
Behind the wheel is a circular cam (shown dotted in) with one-fourth of
its circumference cut away; the pivot holds the cam and cross rigidly
together while permitting them to revolve loosely in the wheel. The
cam, K, lies close to the wheel and is pressed against the cam on the
cross by a spring, so that ordinarily the full width of M and K act as
one piece on the end of the cam, I, which thus is pressed against the
retaining pawl, H, during the passage of three teeth, making the jump
from 28 to 1 each of these three years.
The fourth revolution of the maltese cross brings the cut portion of
its cam to operate on K and allows K to move behind M, thus narrowing
the acting surface so that I only covers two teeth (30 and 31) for
every fourth revolution of the month’s cylinder, thus making the leap
year every fourth year.
The months cylinder is kept in position by the two-armed pawl, N,
engaging the teeth, L, which stand at 90 degrees from the wheel, as
shown in Fig. 113. Attached to the bearing for the week cylinder (not
shown) is one revolution of a screw track, or worm, surrounding the
arbor for the hand. Attached to the arbor is a finger, O, held taut by
a spring and engaging the track, P. The revolution of the arbor raises
O on P until it slips off, when O, drawn downward by its spring, raises
the pawl, N, drops on one of the teeth, L, and revolves the cylinder
one notch.
Q is a shifter for raising the pawl, H, and allowing the hand to be
set.
[Illustration: Fig. 115. The weeks change gear.]
Fig. 115 shows the inner end of the cylinder for the days of the week.
There are two sets of these and fourteen teeth on the sprocket, R, so
as to get the two cylinders approximately the same size (there being
14 days and 12 months on the respective cylinders). S is a pawl whose
upper end is forked so as to embrace a tooth and hold the cylinder in
position. T is a hook, carried on the sliding piece, E, which swings
outward in its upward passage as E is raised and on its downward course
raises the pawl, S, and revolves the sprocket, R, one tooth, thus
changing the day of the week at the same time the hand is advanced.
To set the calendar, raise the pawl, N, and revolve the year cylinder
until M and K are at their narrowest width; that is, a leap year. Then
give the year cylinder as many additional turns as there are years
since the last leap year, stopping on the current month of the current
year. For instance, if it is two years and four months since the 29th
of February last occurred, give the cylinder 2 and ⁴/₁₂ turns which
should bring you to the current month, raise the shifter, Q, and set
the hand to the current day. Then raise the pawl, S, and set the week
cylinder to the current day. Place the hour hand on the movement so
that the cam will drop E at midnight.
Fig. 116 shows the dial of Brocot’s calendar work, which, with or
without the equation of time and the lunations, is to be met with in
many grandfather, hall and astronomical clocks. We will assume that
all of these features are present, in order to completely cover the
subject. It consists of two circular plates of which the front plate
is the dial and the rear plate carries the movement, arranged on both
sides of it. All centers are therefore concentric and we have marked
them all with the same letters for better identification in the various
views as the inner plate is turned about to show the reverse side, thus
reversing the position of right to left in one view of the inner plate.
Fig. 117 shows the wheel for the phases of the moon, which is mounted
on the outside of the inner plate immediately behind the opening in the
dial. The dark circles have the same color as the sky of the dial and
the rest is gilt, white or cream color to show the moon as in Fig. 116.
The position of this plate is also shown in Fig. 120. By the dotted
circles, about the center D.
[Illustration: Fig. 116. Dial of Brocot’s Calendar.]
The inner side containing the mechanism for indicating the days of the
week and the days of the month is shown in Fig. 118. The calendar is
actuated by means of a pin, C, fixed to a wheel of the movement which
turns once in twenty-four hours in the manner previously described
with Fig. 113. Two clicks, G and H, are pivoted to the lever, M. G,
by means of its weighted end, see Fig. 119, is kept in contact with a
ratchet wheel of 31 teeth, and H with a ratchet wheel of 7 teeth. As
a part of these clicks and wheels is concealed in Fig. 118, they are
shown separately in Fig. 119.
When the lever, M, is moved to the left as far as it will go by the
pin, e, the clicks, G and H, slip under the teeth; their beaks pass on
to the following tooth; when e has moved out of contact the lever, M,
falls quickly by its own weight, and makes each click leap a tooth of
the respective wheels, B of 7 and A of 31 teeth. The arbors of these
wheels pass through the dial (Fig. 116), and have each an index which,
at every leap of its own wheel, indicates on its special dial the
day of the week and the day of the month. A roll, or click, kept in
position by a sufficient spring, keeps each wheel in its place during
the interval of time which separates two consecutive leaps.
This motion clearly provides for the indication of the day of the week,
and would be also sufficient for the days of the month if the index
were shifted by hand at the end of the short months.
To secure the proper registration of the months of 30 days, for
February of 28 during three years, and of 29 in leap year, we have the
following provision: The arbor, A, of the day of the month wheel goes
through the circular plate, and on the other side is fixed (see Fig.
120) a pinion of 10 leaves. This pinion, by means of an intermediate
wheel, I, works another wheel (centered at C) of 120 teeth, and
consequently turning once in a year. The arbor of this last wheel bears
an index indicating the name of the month, G, Fig. 116. The arbor, C,
goes through the plate, and at the other end, C, Fig. 118, is fixed a
little wheel gearing with a wheel having four times as many teeth, and
which is centered on a stud in the plate at F. This wheel is partly
concealed in Fig. 118 by a disc V, which is fixed to it, and with
the wheel makes one turn in four years. On this disc, V, are made 20
notches, of which the 16 shallowest correspond to the months of 30
days; a deeper notch corresponds to the month of February of leap year,
and the last three deepest to the month of February common years in
each quarternary period. The uncut portions of the disc correspond to
the months of 31 days in the same period. The wheel, A, of 31 teeth,
has a pin (i) placed before the tooth which corresponds to the 28th of
the month. On the lever, M, is pivoted freely a bell-crank lever (N),
having at the extremity of the lower arm a pin (o) which leans its own
weight upon the edge of the disc, V, or upon the bottom of one of the
notches, according to the position of the month, and the upper arm of N
is therefore higher or lower according to the position of the pin, o,
upon the disc.
[Illustration: Fig. 117. Dial of Moon’s Phases.]
[Illustration: Fig. 118. Brocot’s Calendar; Rear View of Calendar Plate
showing Four Year Wheel and Change Mechanism.]
[Illustration: Fig. 119. Change Mechanism behind the Four Year Wheel in
Fig. 118]
It will be easy to see that when the pin, o, rests on the contour
of the disc the upper arm, N, of the bell-crank lever is as high as
possible, and out of contact with the pin as it is dotted in the
figure, and then the 31 teeth of the month wheel will each leap
successively one division by the action of the click, G, as the lever,
M, falls backward till the 31st day. But when the pin, o, is in one of
the shallow notches of the plate, V, corresponding to the months of
30 days, the upper arm, N, of the bell-crank lever will take a lower
position, and the inclination that it will have by the forward movement
of the lever, M, will on the 30th bring the pin, i, in contact with the
bottom of the notch, just as the lever, M, has accomplished two-thirds
of its forward movement, so the last third will be employed to make the
wheel 31 advance one tooth, and the hand of the dial by consequence
marks the 31st, the quick return of the lever, M, as it falls putting
this hand to the 1st by the action of the click, G. If we suppose the
pin, o, is placed in the shallowest of the four deep notches, that
one for February of leap year, the upper end of the arm, N, will take
a position lower still, and on the 29th the pin, i, will be met by
the bottom of the notch, just as the lever has made one-third of its
forward course, so the other two-thirds of the forward movement will
serve to make two teeth of the wheel of 31 jump. Then the hand of the
dial, A, Figs. 116 and 118, will indicate 31, and the ordinary quick
return of the lever, M, with its detent, G, will put it to the 1st.
Lastly, if, as it is represented in the figure, the pin, o, is in one
of the three deepest notches, corresponding to the months of February
in ordinary years, the pin will be in the bottom of the notch on the
28th just at the moment the lever begins its movement, and three teeth
will pass before the return of the lever makes the hand leap from the
31st to the 1st.
The pin, o, easily gets out of the shallow notches, which, as will be
seen, are sloped away to facilitate its doing so. To help it out of
the deeper notches there is a weighted finger (j) on the arbor of the
annual wheel. This finger, having an angular movement much larger than
the one of the disc, V, puts the pin, o, out of the notch before the
notch has sensibly changed its position.
PHASES OF THE MOON.—The phases of the moon are obtained by a pinion of
10, Fig. 120, on the arbor, B, which gears with the wheel of 84 teeth,
fixed on another of 75, which last gears with a wheel of 113, making
one revolution in three lunations. By this means there is an error
only of .00008 day per lunation. On the wheel of 113 is fixed a plate
on which are three discs colored blue, having between them a distance
equal to their diameter, as shown in Fig. 117, these discs slipping
under a circular aperture made in the dial, produce the successive
appearance of the phases of the moon.
EQUATION OF TIME.—On the arbor of the annual wheel, C, Figs. 116, 118,
120, is fixed a brass cam, Y, on the edge of which leans the pin, s,
fixed to a circular rack, R. This rack gears with the central wheel, K,
which carries the hand for the equation. That hand faces XII the 15th
of April, 14th of June, 1st of September and the 25th of December. At
those dates the pin, s, is in the position of the four dots marked on
the cam, Y. The shape of the cam, Y, must be such as will lead the hand
to indicate the difference between solar and mean time, as given in the
table of the Nautical almanac.
To set the calendar first see that the return of the lever, M, be made
at the moment of midnight. To adjust the hand of the days of the week,
B, look at an almanac and see what day before the actual date there
was a full or new moon. If it was new moon on Thursday, it would be
necessary, by means of a small button fixed at the back, on the arbor
of the hand of the wheel, B, of the week, to make as many returns as
requisite to obtain a new moon, this hand pointing to a Thursday;
afterward bring back the hand to the actual date, passing the number
of divisions corresponding to the days elapsed since the new moon. To
adjust the hand of the day of the month, A, see if the pin, o, is in
the proper notch. If for the leap year, it is in the month of February
in the shallowest of the four deep notches (o); if for the same month
of the first year after leap year, then the pin should be, of course,
in the notch, I, and so on.
[Illustration: Fig. 120. Brocot’s Calender: Wheels and Pinions under
the Dial with their Number of Teeth.]