I. Most of the terms at present used to describe the movements of the
heavenly bodies were used in Chaucer's time and occur very frequently in
his writings. The significance of Chaucer's references will then be
perfectly clear, if we keep in mind that the modern astronomer's
description of the _apparent_ movements of the star-sphere and of the
heavenly bodies individually would have been to Chaucer a description of
_real_ movements.
When we look up into the sky on a clear night the stars and planets appear
to be a host of bright dots on the concave surface, unimaginably distant,
of a vast hollow sphere at the canter of which we seem to be. Astronomers
call this expanse of the heavens with its myriad bright stars the
_celestial sphere_ or the _star sphere_, and have imagined upon its
surface various systems of circles. In descriptions of the earth's
relation to the celestial sphere it is customary to disregard altogether
the earth's diameter which is comparatively infinitesimal.
If we stand on a high spot in the open country and look about us in all
directions the earth seems to meet the sky in a circle which we call the
_terrestrial horizon_. Now if we imagine a plane passing through the
center of the earth and parallel to the plane in which the terrestrial
horizon lies, and if we imagine this plane through the earth's center
extended outward in all directions to an infinite distance, it would cut
the celestial sphere in a great circle which astronomers call the
_celestial horizon_. On the celestial horizon are the north, east, south
and west points. The plane of the celestial horizon is, of course,
different for different positions of the observer on the earth.
If we watch the sky for some time, or make several observations on the
same night, we notice, by observing the changing positions of the
constellations, that the stars move very slowly across the blue dome above
us. The stars that rise due east of us do not, in crossing the dome of the
sky, pass directly over our heads but, from the moment that we first see
them, curve some distance to the south, and, after passing their highest
point in the heavens, turn toward the north and set due west. A star
rising due east appears to move more rapidly than one rising some distance
to the north or south of the east point, because it crosses a higher point
in the heavens and has, therefore, a greater distance to traverse in the
same length of time. When we observe the stars in the northern sky, we
discover that many of them never set but seem to be moving around an
apparently fixed point at somewhat more than an angle of 40 deg.[194] above
the northern horizon and very near the north star. These are called
_circum-polar stars_. The whole celestial sphere, in other words, appears
to be revolving about an imaginary axis passing through this fixed point,
which is called the _north pole_ of the heavens, through the center of the
earth and through an invisible pole (the south pole of the heavens)
exactly opposite the visible one. This apparent revolution of the whole
star sphere, as we know, is caused by the earth's rotation on its axis
once every twenty-four hours from west to east. Chaucer and his
contemporaries believed it to be the actual revolution of the nine spheres
from east to west about the earth as a center.
[Illustration: Fig. 1.]
For determining accurately the position of stars on the celestial sphere
astronomers make use of various circles which can be made clear by a few
simple diagrams. In Figure 1, the observer is imagined to be at O. Then
the circle NESW is the celestial horizon, which we have described above.
Z, the point immediately above the observer is called the _zenith_, and
Z', the point immediately underneath, as indicated by a plumb line at
rest, is the _nadir_. The line POP' is the imaginary axis about which the
star-sphere appears to revolve, and P and P' are the poles of the heavens.
The north pole P is elevated, for our latitude, at an angle of
approximately 40 deg. from the north point on the horizon. PP' is called the
_polar axis_ and it is evident that the earth's axis extended infinitely
would coincide with this axis of the heavens.
In measuring positions of stars with reference to the horizon astronomers
use the following circles: Any great circle of the celestial sphere whose
plane passes through the zenith and nadir is called a _vertical circle_.
The verticle circle SPNZ', passing through the poles and meeting the
horizon in the north and south points, N and S, is called the _meridian
circle_, because the sun is on this circle at true mid-day. The _meridian_
is the plane in which this circle lies. The vertical circle, EZ'WZ, whose
plane is at right angles to the meridian, is called the _prime vertical_
and it intersects the horizon at the east and west points, E and W. These
circles, and the measurements of positions of heavenly bodies which
involve their use, were all employed in Chaucer's time and are referred to
in his writings.[195]
The distance of a star from the horizon, measured on a vertical circle,
toward the zenith is called the star's _altitude_. A star reaches its
greatest altitude when on the part of the meridional circle between the
south point of the horizon, S, and the north pole, P. A star seen between
the north pole and the north point on the horizon, that is, on the arc PN,
must obviously be a _circum-polar star_ and would have its highest
altitude when between the pole and the zenith, or on the arc PZ. When a
star reaches the meridian in its course across the celestial sphere it is
said to _culminate_ or reach its _culmination_. The highest altitude of
any star would therefore be represented by the arc of the meridional
circle between the star and the south point of the horizon. This is called
the star's _meridian altitude_.
The _azimuth_ of a star is its angular distance from the south point,
measured westward on the horizon, to a vertical circle passing through the
star. The _amplitude_ of a star is its distance from the prime vertical,
measured on the horizon, north or south.
For the other measurements used by astronomers in observations of the
stars still other circles on the celestial sphere must be imagined. We
know that the earth's surface is divided into halves, called the northern
and southern hemispheres, by an imaginary circle called the _equator_,
whose plane passes through the center of the earth and is perpendicular to
the earth's axis. If the plane of the earth's equator were infinitely
extended it would describe upon the celestial sphere a great circle which
would divide that sphere into two hemispheres, just as the plane of the
terrestrial equator divides the earth into two hemispheres. This great
circle on the celestial sphere is called the _celestial equator_, or, by
an older name, the _equatorial_, the significance of which we shall see
presently. A star rising due east would traverse this great circle of the
celestial sphere and set due west. The path of such a star is represented
in Figure 2 by the great circle EMWM', which also represents the celestial
equator. All stars rise and set following circles whose planes are
parallel to that of the celestial equator and these circles of the
celestial sphere are smaller and smaller the nearer they are to the pole,
so that stars very near the pole appear to be encircling it in very small
concentric circles. Stars in an area around the north celestial pole,
whose limits vary with the position of the observer never set for an
observer in the northern hemisphere. There is a similar group of stars
around the south pole for an observer in the southern hemisphere.
[Illustration: Fig. 2.]
The angle of elevation of the celestial equator to the horizon varies
according to the position of the observer. If, for example, the observer
were at the north pole of the earth, the north celestial pole would be
directly above him and would therefore coincide with the zenith; this
would obviously make the celestial equator and the horizon also coincide.
If the observer should pass slowly from the pole to the terrestrial
equator it is clear that the two circles would no longer coincide and that
the angle between them would gradually widen until it reached 90 deg.. Then
the zenith would be on the celestial equator and the north and south poles
of the heavens would be on the horizon.
We have still to define a great circle of the celestial sphere that is of
equal importance with the celestial equator and the celestial horizon.
This is the sun's apparent yearly path, or the _ecliptic_. We know that
the earth revolves about the sun once yearly in an orbit that is not
entirely round but somewhat eliptical. Now since the earth, the sun, and
the earth's orbit around the sun are always in one plane, it follows that
to an observer on the earth the sun would appear to be moving around the
earth instead of the earth around the sun. The sun's apparent path,
moreover, would be in the plane of the earth's orbit and when projected
against the celestial sphere, which is infinite in extent, would appear as
a great circle of that sphere. This great circle of the celestial sphere
is the ecliptic. The sun must always appear to be on this circle, not only
at all times of the year but at all hours of the day; for as the sun rises
and sets, the ecliptic rises and sets also, since the earth's rotation
causes an apparent daily revolution not only of the sun, moon, and planets
but also of the fixed stars and so of the whole celestial sphere and of
all the circles whose positions upon it do not vary. The ecliptic is
inclined to the celestial equator approximately 23-1/2 deg., an angle which
obviously measures the inclination of the plane of the earth's equator to
the plane of its orbit, since the celestial equator and the ecliptic are
great circles on the celestial sphere formed by extending the planes of
the earth's equator and its orbit to an infinite distance. Since both the
celestial equator and the ecliptic are great circles of the celestial
sphere each dividing it into equal parts, it is evident that these two
circles must intersect at points exactly opposite each other on the
celestial sphere. These points are called the vernal and the autumnal
equinoxes.
We shall next define the astronomical measurements that correspond to
terrestrial latitude and longitude. For some reason astronomers have not,
as we might expect, applied to these measurements the terms 'celestial
longitude' and 'celestial latitude.' These two terms are now practically
obsolete, having been used formerly to denote angular distance north or
south of the ecliptic and angular distance measured east and west along
circles parallel to the ecliptic. The measurements that correspond in
astronomy to terrestrial latitude and longitude are called _declination_
and _right ascension_ and are obviously made with reference to the
celestial equator, not the ecliptic. For taking these measurements
astronomers employ circles on the celestial sphere perpendicular to the
plane of the celestial equator and passing through the poles of the
heavens. These are called _hour circles_. The hour circle of any star is
the great circle passing through it and perpendicular to the plane of the
equator. The angular distance of a star from the equator measured along
its hour circle, is called the star's declination and is northern or
southern according as the star is in the northern or southern of the two
hemispheres into which the plane of the equator divides the celestial
sphere. It is evident that declination corresponds exactly to terrestrial
latitude. Right ascension, corresponding to terrestrial longitude, is the
angular distance of a heavenly body from the vernal equinox measured on
the celestial equator eastward to the hour circle passing through the
body.
The _hour angle_ of a star is the angular distance measured on the
celestial equator from the meridian to the foot of the hour circle passing
through the star.
[Illustration: Fig. 3.]
It remains to describe in greater detail the apparent movements of the sun
and the sun's effect upon the seasons. In Figure 3, the great circle MWM'E
represents the equinoctial and XVX'A the ecliptic. The point X represents
the farthest point south that the sun reaches in its apparent journey
around the earth, and this point is called the _winter solstice_, because,
for the northern hemisphere the sun reaches this point in mid-winter. When
the sun is south of the celestial equator its apparent daily path is the
same as it would be for a star so situated. Thus its daily path at the
time of the winter solstice, about December 21, can be represented by the
circle Xmn'. The arc gXh represents the part of the sun's path that would
be above the horizon, showing that night would last much longer than day
and the rays of the sun would strike the northern hemisphere of the earth
more indirectly than when the sun is north of the equator. As the sun
passes along the ecliptic from X toward V, the part of its daily path
that is above the horizon gradually increases until at V, the vernal
equinox, the sun's path would, roughly speaking, coincide with the
celestial equator so that half of it would be above the horizon and half
below and day and night would be of equal length. This explains why the
celestial equator was formerly called the equinoctial (Chaucer's term for
it). As the sun passes on toward X' its daily arc continues to increase
and the days to grow longer until at X' it reaches its greatest
declination north of the equator and we have the longest day, June 21, the
summer solstice. When the sun reaches this point, its rays strike the
northern hemisphere more directly than at any other time causing the hot
or summer season in this hemisphere. Next the sun's daily arc begins to
decrease, day and night to become more nearly equal, at A the autumnal
equinox[196] is reached and the sun again shapes its course towards the
point of maximum declination south of the equator. The two points of
maximum declination are called _solstices_.
The two small circles of the celestial sphere, parallel to the equator,
which pass through the two points where the sun's declination is greatest,
are called _Tropics_; the one in the northern hemisphere is called the
_Tropic of Cancer_, that in the southern hemisphere, the _Tropic of
Capricorn_. They correspond to circles on the earth's surface having the
same names.
II. By "artificial day" Chaucer means the time during which the sun is
above the horizon, the period from sunrise to sunset. The arc of the
artificial day may mean the extent or duration of it, as measured on the
rim of an astrolabe, or it may mean (as here), the arc extending from the
point of sunrise to that of sunset. See _Astrolabe_ ii.7.
There has been some controversy among editors as to the correctness of the
date occurring in this passage, some giving it as the 28th instead of the
18th. In discussing the accuracy of the reading "eightetethe" Skeat throws
light also upon the accuracy of the rest of the passage considered from an
astronomical point of view. He says (vol. 5, p. 133):
"The key to the whole matter is given by a passage in Chaucer's
'Astrolabe,' pt. ii, ch. 29, where it is clear that Chaucer (who, however
merely translates from Messahala) actually confuses the hour-angle with
the azimuthal arc (see Appendix I); that is, he considered it correct to
find the hour of the day by noting _the point of the horizon_ over which
the sun appears to stand, and supposing this point to advance, with a
_uniform_, not a _variable_, motion. The host's method of proceeding was
this. Wanting to know the hour, he observed how far the sun had moved
southward along the horizon since it rose, and saw that it had gone more
than half-way from the point of sunrise to the exact southern point. Now
the 18th of April in Chaucer's time answers to the 26th of April at
present. On April 26, 1874, the sun rose at 4 hr. 43 m., and set at 7 hr.
12 m., giving a day of about 14 hr. 30 m., the fourth part of which is at
8 hr. 20 m., or, with sufficient exactness, at _half past eight_. This
would leave a whole hour and a half to signify Chaucer's 'half an houre
and more', showing that further explanation is still necessary. The fact
is, however, that the host reckoned, as has been said, in another way,
viz. by observing the sun's position _with reference to the horizon_. On
April 18 the sun was in the 6th degree of Taurus at that date, as we again
learn from Chaucer's treatise. Set this 6th degree of Taurus on the east
horizon on a globe, and it is found to be 22 degrees to the north of the
east point, or 112 degrees from the south. The half of this at 56 degrees
from the south; and the sun would seem to stand above this 56th degree, as
may be seen even upon a globe, at about a quarter past nine; but Mr. Brae
has made the calculation, and shows that it was at _twenty minutes past
nine_. This makes Chaucer's 'half an houre and more' to stand for _half an
hour and ten minutes_; an extremely neat result. But this we can check
again by help of the host's _other_ observation. He _also_ took note, that
the lengths of a shadow and its object were equal, whence the sun's
altitude must have been 45 degrees. Even a globe will shew that the sun's
altitude, when in the 6th degree of Taurus, and at 10 o'clock in the
morning, is somewhere about 45 or 46 degrees. But Mr. Brae has calculated
it exactly, and his result is, that the sun attained its altitude of 45
degrees at _two minutes to ten_ exactly. This is even a closer
approximation than we might expect, and leaves no doubt about the right
date being the _eighteenth_ of April."
Thus it appears that Chaucer's method of determining the date was
incorrect but his calculations in observing the sun's position were quite
accurate. For fuller particulars see Chaucer's _Astrolabe_, ed. Skeat (E.
E. T. S.) preface, p. 1.
III. It was customary in ancient times and even as late as Chaucer's
century to determine the position of the sun, moon, or planets at any time
by reference to the signs of the zodiac. The _zodiac_ is an imaginary belt
of the celestial sphere, extending 8 deg. on each side of the ecliptic, within
which the orbits of the sun, moon, and planets appear to lie. The zodiac
is divided into twelve equal geometric divisions 30 deg. in extent called
_signs_ to each of which a fanciful name is given. The signs were once
identical with twelve constellations along the zodiac to which these
fanciful names were first applied. Since the signs are purely geometric
divisions and are counted from the spring equinox in the direction of the
sun's progress through them, and since through the precession of the
equinoxes the whole series of signs shifts westward about one degree in
seventy-two years, the signs and constellations no longer coincide.
Beginning with the sign in which the vernal equinox lies the names of the
zodiacal signs are Aries (Ram), Taurus (Bull), Gemini (Twins), Cancer
(Crab), Leo (Lion), Virgo (Virgin), Libra (Scales), Scorpio (Scorpion),
Sagittarius (Archer), Aquarius (Water-carrier), and Pisces (Fishes).
In this passage, the line "That in the Ram is four degrees up-ronne"
indicates the date March 16. This can be seen by reference to Figure 1 in
Skeat's edition of Chaucer's _Astrolabe_ (E. E. T. S.) The astrolabe was
an instrument for making observations of the heavenly bodies and
calculating time from these observations. The most important part of the
kind of astrolabe described by Chaucer was a rather heavy circular plate
of metal from four to seven inches in diameter, which could be suspended
from the thumb by a ring attached loosely enough so as to allow the
instrument to assume a perpendicular position. One side of this plate was
flat and was called the _back_, and it is this part that Figure 1
represents. The back of the astrolabe planisphere contained a series of
concentric rings representing in order beginning with the outermost ring:
the four quadrants of a circle each divided into ninety degrees; the signs
of the zodiac divided into thirty degrees each; the days of the year, the
circle being divided, for this purpose, into 365-1/4 equal parts; the
names of the months, the number of days in each, and the small divisions
which represent each day, which coincide exactly with those representing
the days of the year; and lastly the saints' days, with their
Sunday-letters. The purpose of the signs of the zodiac is to show the
position of the sun in the ecliptic at different times. Therefore, if we
find on the figure the fourth degree of Aries and the day of the month
corresponding to it, we have the date March 16 as nearly as we can
determine it by observing the intricate divisions in the figure.
The next passage "Noon hyer was he, whan she redy was" means evidently,
'he was no higher than this (i. e. four degrees) above the horizon when
she was ready'; that is, it was a little past six. The method used in
determining the time of day by observation of the sun's position is
explained in the Astrolabe ii, 2 and 3. First the sun's altitude is found
by means of the revolving rule at the back of the astrolabe. The rule, a
piece of metal fitted with sights, is moved up and down until the rays of
the sun shine directly through the sights. Then, by means of the degrees
marked on the back of the astrolabe, the angle of elevation of the rule is
determined, giving the altitude of the sun. The rest of the process
involves the use of the _front_ of the astrolabe. This side of the
circular plate, shown in Fig. 2, had a thick rim with a wide depression in
the middle. On the rim were three concentric circles, the first showing
the letters A to Z, representing the twenty-four hours of the day, and the
two innermost circles giving the degrees of the four quadrants. The
depressed central part of the front was marked with three circles, the
'Tropicus Cancri', the 'AEquinoctialis,' and the 'Tropicus Capricorni';
and with the cross-lines from North to South, and from East to West. There
were besides several thin plates or discs of metal of such a size as
exactly to drop into the depression spoken of. The principal one of these
was the 'Rete' and is shown in Fig. 2. "It consisted of a circular ring
marked with the zodiacal signs, subdivided into degrees, with narrow
branching limbs both within and without this ring, having smaller branches
or tongues terminating in points, each of which denoted the exact position
of some well-known star. * * * The 'Rete' being thus, as it were, a
skeleton plate, allows the 'Tropicus Cancri,' etc., marked upon the body
of the instrument, to be partially seen below it. * * * But it was more
usual to interpose between the 'Rete' and the body of the instrument
(called the 'Mother') another thin plate or disc, such as that in Fig. 5,
so that portions of this latter plate could be seen beneath the
skeleton-form of the 'Rete' (i. 17). These plates were called by Chaucer
'tables', and sometimes an instrument was provided with several of them,
differently marked, for use in places having different latitudes. The one
in Fig. 5 is suitable for the latitude of Oxford (nearly). The upper part,
above the Horizon Obliquus, is marked with circles of altitude (i. 18),
crossed by incomplete arcs of azimuth tending to a common centre, the
zenith (i. 19)." [Skeat, _Introduction to the Astrolabe_, pp. lxxiv-lxxv.]
Now suppose we have taken the sun's altitude by Sec.2 (Pt. ii of the
_Astrolabe_) and found it to be 25-1/2 deg.. "As the altitude was taken by the
back of the Astrolabe, turn it over, and then let the _Rete_ revolve
westward until the 1st point of Aries is just within the altitude-circle
marked 25, allowing for the 1/2 degree by guess. This will bring the
denticle near the letter C, and the first point of Aries near X, which
means 9 a.m." [Skeat's note on the _Astrolabe_ ii. 3, pp. 189-190].
IV. Chaucer would know the altitude of the sun simply by inspection of an
astrolabe, without calculation. Skeat has explained this passage in his
_Preface to Chaucer's Astrolabe_ (E. E. T. S.), p. lxiii, as follows:
"Besides saying that the sun was 29 deg. high, Chaucer says that his shadow
was to his height in the proportion of 11 to 6. Changing this proportion,
we can make it that of 12 to 6-6/11; that is, the point of the _Umbra
Versa_ (which is reckoned by twelfth parts) is 6-6/11 or 6-1/2 nearly.
(Umbra Recta and Umbra Versa were scales on the back of the astrolabe used
for computing the altitudes of heavenly bodies from the height and shadows
of objects. The _umbra recta_ was used where the angle of elevation of an
object was greater than 45 deg.; the _umbra versa_, where it was less.) This
can be verified by Fig. 1; for a straight edge, laid across from the 29th
degree above the word 'Occidens,' and passing through the center, will cut
the scale of Umbra Versa between the 6th and 7th points. The sun's
altitude is thus established as 29 deg. above the western horizon, beyond all
doubt."
V. _Herberwe_ means 'position.' Chaucer says here, then, that the sun
according to his declination causing his position to be low or high in the
heavens, brings about the seasons for all living things. In the
_Astrolabe_, i. 17, there is a very interesting passage explaining in
detail, declination, the solstices and equinoxes, and change of seasons.
Chaucer is describing the front of the astrolabe. He says: "The plate
under thy rite is descryved with 3 principal cercles; of whiche the leste
is cleped the cercle of Cancer, by-cause that the heved of Cancer turneth
evermor consentrik up-on the same cercle. (This corresponds to the Tropic
of Cancer on the celestial sphere, which marks the greatest northern
declination of the sun.) In this heved of Cancer is the grettest
declinacioun northward of the sonne. And ther-for is he cleped the
Solsticioun of Somer; whiche declinacioun, aftur Ptholome, is 23 degrees
and 50 minutes, as wel in Cancer as in Capricorne. (The greatest
declination of the sun measures the obliquity of the ecliptic, which is
slightly variable. In Chaucer's time it was about 23 deg. 31', and in the time
of Ptolemy about 23 deg. 40'. Ptolemy assigns it too high a value.) This signe
of Cancre is cleped the Tropik of Somer, of _tropos_, that is to seyn
'agaynward'; for thanne by-ginneth the sonne to passe fro us-ward. (See
Fig. 2 in Skeat's _Preface to the Astrolabe_, vol. iii, or E. E. T. S.
vol. 16.)
The middel cercle in wydnesse, of thise 3, is cleped the Cercle Equinoxial
(the celestial equator of the celestial sphere); up-on whiche turneth
evermo the hedes of Aries and Libra. (These are the two signs in which the
ecliptic crosses the equinoctial.) And understond wel, that evermo this
Cercle Equinoxial turneth iustly fro verrey est to verrey west; as I have
shewed thee in the spere solide. (As the earth rotates daily from west to
east, the celestial sphere appears to us to revolve about the earth once
every twenty-four hours from east to west. Chaucer, of course, means here
that the equinoctial actually revolves with the _primum mobile_ instead of
only appearing to revolve.) This same cercle is cleped also the Weyere,
_equator_, of the day; for whan the sonne is in the hevedes of Aries and
Libra, than ben the dayes and the nightes ilyke of lengthe in al the
world. And ther-fore ben thise two signes called Equinoxies.
The wydeste of thise three principal cercles is cleped the Cercle of
Capricorne, by-cause that the heved of Capricorne turneth evermo
consentrix up-on the same cercle. (That is to say, the Tropic of
Capricorn meets the ecliptic in the sign Capricornus, or, in other words,
the sun attains its greatest declination southward when in the sign
Capricornus.) In the heved of this for-seide Capricorne is the grettest
declinacioun southward of the sonne, and ther-for is it cleped the
Solsticioun of Winter. This signe of Capricorne is also cleped the Tropik
of Winter, for thanne byginneth the sonne to come agayn to us-ward."
VI. The moon's orbit around the earth is inclined at an angle of about 5 deg.
to the earth's orbit around the sun. The moon, therefore, appears to an
observer on the earth as if traversing a great circle of the celestial
sphere just as the sun appears to do; and the moon's real orbit projected
against the celestial sphere appears as a great circle similar to the
ecliptic. This great circle in which the moon appears to travel will,
therefore, be inclined to the ecliptic at an angle of 5 deg. and the moon will
appear in its motion never far from the ecliptic; it will always be within
the zodiac which extends eight or nine degrees on either side of the
ecliptic.
The angular velocity of the moon's motion in its projected great circle is
much greater than that of the sun in the ecliptic. Both bodies appear to
move in the same direction, from west to east; but the solar apparent
revolution takes about a year averaging 1 deg. daily, while the moon completes
a revolution from any fixed star back to the same star in about 27-1/4
days, making an average daily angular motion of about 13 deg.. The actual
daily angular motion of the moon varies considerably; hence in trying to
test out Chaucer's references to lunar angular velocity it would not be
correct to make use only of the average angular velocity since his
references apply to specific times and therefore the variation in the
moon's angular velocity must be taken into account.
VII. On the line "In two of Taur," etc., Skeat has the following note:
"Tyrwhitt unluckily altered _two_ to _ten_, on the plea that 'the time
(_four days complete_, l. 1893) is not sufficient for the moon to pass
from the second degree of Taurus into Cancer? And he then proceeds to shew
this, taking the _mean_ daily motion of the moon as being 13 degrees, 10
minutes, and 35 seconds. But, as Mr. Brae has shewn, in his edition of
Chaucer's Astrolabe, p. 93, footnote, it is a mistake to reckon here the
moon's _mean_ motion; we must rather consider her _actual_ motion. The
question is simply, can the moon move from the 2nd degree of Taurus to the
1st of Cancer (through 59 degrees) in four days? Mr. Brae says decidedly,
that examples of such motion are to be seen 'in every almanac.'
For example, in the Nautical Almanac, in June, 1886, the moon's longitude
at noon was 30 deg. 22' on the 9th, and 90 deg. 17' on the 13th; i. e., the moon
was in the _first_ of Taurus on the former day, and in the _first_ of
Cancer on the latter day, at the same hour; which gives (very nearly) a
degree more of change of longitude than we here require. The MSS all have
_two_ or _tuo_, and they are quite right. The motion of the moon is so
variable that the mean motion affords no safe guide." [Skeat, _Notes to
the Canterbury Tales_, p. 363.]
VIII. The moon's "waxing and waning" is due to the fact that the moon is
not self-luminous but receives its light from the sun and to the
additional fact that it makes a complete revolution around the earth with
reference to the sun in 29-1/2 days. When the earth is on the side of the
moon that faces the sun we see the full moon, that is, the whole
illuminated hemisphere. But when we are on the side of the moon that is
turned away from the sun we face its unilluminated hemisphere and we say
that we have a 'new moon.' Once in every 29-1/2 days the earth is in each
of these positions with reference to the moon and, of course, in the
interval of time between these two phases we are so placed as to see
larger or smaller parts of the illuminating hemisphere of the moon, giving
rise to the other visible phases.
When the moon is between the earth and the sun she is said to be in
_conjunction_, and is invisible to us for a few nights. This is the phase
called _new moon_. As she emerges from conjunction we see the moon as a
delicate crescent in the west just after sunset and she soon sets below
the horizon. Half of the moon's surface is illuminated, but we can see
only a slender edge with the horns turned away from the sun. The crescent
appears a little wider each night, and, as the moon recedes 13 deg. further
from the sun each night, she sets correspondingly later, until in her
first quarter half of the illuminated hemisphere is turned toward us. As
the moon continues her progress around the earth she gradually becomes
gibbous and finally reaches a point in the heavens directly opposite the
sun when she is said to be in _opposition_, her whole illumined hemisphere
faces us and we have _full moon_. She then rises in the east as the sun
sets in the west and is on the meridian at midnight. As the moon passes
from opposition, the portion of her illuminated hemisphere visible to us
gradually decreases, she rises nearly an hour later each evening and in
the morning is seen high in the western sky after sunrise. At her _third
quarter_ she again presents half of her illuminated surface to us and
continues to decrease until we see her in crescent form again. But now her
position with reference to the sun is exactly the reverse of her position
as a waxing crescent, so that her horns are now turned toward the west
away from the sun, and she appears in the eastern sky just before sunrise.
The moon again comes into conjunction and is lost in the sun's rays and
from this point the whole process is repeated.
IX. That the apparent motions of the sun and moon are not so complicated
as those of the planets will be clear at once if we remember that the
sun's apparent motion is caused by our seeing the sun projected against
the celestial sphere in the ecliptic, the path cut out by the plane of the
earth's orbit, while in the case of the moon, what we see is the moon's
actual motion around the earth projected against the celestial sphere in
the great circle traced by the moon's own orbital plane produced to an
indefinite extent. These motions are further complicated by the rotation
of the earth on its own axis, causing the rising and setting of the sun
and the moon. These two bodies, however, always appear to be moving
directly on in their courses, each completing a revolution around the
earth in a definite time, the sun in a year, the moon in 29-1/2 days. What
we see in the case of the planets, on the other hand, is a complex motion
compounded of the effects of the earth's daily rotation, its yearly
revolution around the sun, and the planets' own revolutions in different
periods of time in elliptical orbits around the sun. These complex
planetary motions are characterized by the peculiar oscillations known as
'direct' and 'retrograde' movements.
[Illustration: Fig. 4.]
The motion of a planet is said to be _direct_ when it moves in the
direction of the succession of the zodiacal signs; _retrograde_ when in
the contrary direction. All of the planets have periods of retrograde and
direct motion, though their usual direction is direct, from west to east.
Retrograde motion can be explained by reference to the accompanying
diagrams. In Fig. 4, the outer circle represents the path of the zodiac on
the celestial sphere. Let the two inner circles represent the orbits of
the earth and an inferior planet, Venus, around the sun, at S. (An
_inferior_ planet is one whose orbit around the sun is within that of the
earth. A _superior_ planet is one whose orbit is outside that of the
earth.) V, V' and V", and E, E', and E" are successive positions of the
two planets in their orbits, the arc VV" being longer than the arc EE"
because the nearer a planet is to the sun, the greater is its velocity.
Then when Venus is at V and the earth at E, we shall see Venus projected
on the celestial sphere at V{1}. When Venus has passed on to V' the earth
will have passed to E' and we shall see Venus on the celestial sphere at
V{2}. The apparent motion of the planet thus far will have been direct,
from west to east in the order of the signs. But when Venus is at V" and
the earth at E" Venus will be seen at V{3} having apparently moved back
about two signs in a direction the reverse of that taken at first. This is
called the planet's retrograde motion. At some point beyond V", the planet
will appear to stop moving for a very short period and then resume its
direct motion. In Fig. 5, the outer arc again represents the path of the
zodiac on the celestial sphere. The smaller arcs represent the orbits of
the superior planet, Mars, and the earth around the sun, S. At the point
of opposition of Mars (when Mars and the sun are at opposite points in the
heavens to an observer on the earth) we should see Mars projected on the
zodiac at M{1}. After a month Mars will be at M' and the earth at E', so
that in its apparent motion Mars will have retrograded to M{2}. After
three months from opposition Mars will be at M" and the earth at E",
making Mars appear at M{3} on the celestial sphere, its motion having
changed from retrograde to direct.
[Illustration: Fig. 5.]
Both Figures 4 and 5 take no account of the fact that the earth's orbit
and those of the planets are not in exactly the same planes. Remembering
this fact we see at once that the apparent oscillations of the planets are
not back and forth in a straight line but in curves and spirals. It is
easy to see why the apparent motions of the planets were accounted for by
deferents and epicycles, before the Copernican system revealed the true
nature of the solar system as heliocentric and not geocentric.