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 alt.i.tude must have been 45 degrees. Even a globe will shew that the sun's alt.i.tude, 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 alt.i.tude 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 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 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 pa.s.sage, 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 a.s.sume 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 pa.s.sage "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 alt.i.tude 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 alt.i.tude 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 princ.i.p.al 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 lat.i.tudes. The one in Fig. 5 is suitable for the lat.i.tude of Oxford (nearly). The upper part, above the Horizon Obliquus, is marked with circles of alt.i.tude (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 alt.i.tude by --2 (Pt. ii of the _Astrolabe_) and found it to be 25-1/2. "As the alt.i.tude 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 alt.i.tude-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 alt.i.tude of the sun simply by inspection of an astrolabe, without calculation. Skeat has explained this pa.s.sage in his _Preface to Chaucer's Astrolabe_ (E. E. T. S.), p. lxiii, as follows:

"Besides saying that the sun was 29 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 alt.i.tudes 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; 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 pa.s.sing through the center, will cut the scale of Umbra Versa between the 6th and 7th points. The sun's alt.i.tude is thus established as 29 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 pa.s.sage 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 princ.i.p.al 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 31', and in the time of Ptolemy about 23 40'. Ptolemy a.s.signs 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 pa.s.se 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 princ.i.p.al 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...o...b..t around the earth is inclined at an angle of about 5 to the earth's...o...b..t 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 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 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. 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 pa.s.s 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 22' on the 9th, and 90 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 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 pa.s.ses 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...o...b..t, 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.

[Ill.u.s.tration: 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 pa.s.sed on to V' the earth will have pa.s.sed 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.

[Ill.u.s.tration: Fig. 5.]

Both Figures 4 and 5 take no account of the fact that the earth's...o...b..t 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.

SELECTED BIBLIOGRAPHY

BERRY, ARTHUR, _A Short History of Astronomy_. New York. 1899.

BRYANT, W. W., _A History of Astronomy_. London. 1907.

c.u.mONT, FRANZ, _Astrology and Religion among the Greeks and Romans_. New York. 1912.

CUSHMAN, H. E., _A Beginner's History of Philosophy_. Boston. 1910.

DREYER, J. L. E., _History of the Planetary Systems from Thales to Kepler_. Cambridge. 1906.

EVERSHED, M. A., _Dante and the Early Astronomers_. London. 1913.

GOMPERZ, T., _Greek Thinkers, A History of Ancient Philosophy_. New York.

1901.

GORE J. ELLARD, _Astronomical Essays, Historical and Descriptive_. London.

1907.

HINKS, A. R., _Astronomy_. London. 1911.

JACOBY, HAROLD, _Astronomy_. New York. 1913.

JASTROW, MORRIS, "Astrology," _Encyclopaedia Britannica_ ii, 795-800.

LEA, H. C., _History of the Inquisition of the Middle Ages_. New York.

1906. III. 409-549.

ORCHARD, T. N., _Milton's Astronomy_. New York. 1913.

TAYLOR, H. O., _The Mediaeval Mind_. 2 vols. New York. 1911.

TODD, MABEL L., _Steele's Popular Astronomy_. New York. 1884.