degre of Leoun, 58 degrees and 10 minutes of heyghte at noon and his declinacion is almost 20 degrees northward fro the 30 equinoxial; abate thanne thilke 20 degrees of declinacion out of the altitude at noon, than leveth thee 38 degrees and odde minutes; lo ther the heved of Aries or Libra, and thyn equinoxial in that regioun. Also yif so be that the sonnes declinacioun be southward fro the equinoxial, adde thanne thilke declinacion to the 35 altitude of the sonne at noon; and tak ther the hevedes of Aries and Libra, and thyn equinoxial. Abate thanne the heyghte of the equinoxial out of 90 degrees, and thanne leveth there the distans of the pole, 51 degrees and 50 minutes, of that regioun fro the equinoxial. Or elles, yif thee lest, take the heyest altitude 4 fro the equinoxial of any sterre fix that thou knowest, and tak his nethere elongacioun lengthing fro the same equinoxial lyne, and wirke in the maner forseid. And for more declaracion, lo here

thy figure.

26. Declaracioun of the assensioun of signes, &c.

[Declaracio de ascensione signorum.]

The excellence of the spere solide, amonges other noble conclusiouns, sheweth manifeste the diverse assenciouns of signes in diverse places, as wel in the righte cercle as in the embelif cercle. Thise auctours wryten that thilke signe is cleped of right 5 ascensioun, with which more part of the cercle equinoxial and lasse part of the zodiak ascendeth; and thilke signe assendeth embelif, with whiche lasse part of the equinoxial and more part of

altitude, and allow for his declination. Thus, if the sun's altitude be 58° 10' at noon when he is in the first degree of. Leo, subtract his declination, viz. 20°, and the result is 38° 10', the complement of the latitude. If, however, the sun's declination be south, the amount of it must be added instead of subtracted. Or else we may find TA', the highest altitude of a star A' above the equinoctial, and also YA, its nether elongation extending from the same, and take the mean of the two.

26. The 'Sphere Solid' answers nearly to what we now call a globe. By help of a globe it is easy to find the ascensions of signs for any latitude, whereas by the astrolabe we can only tell them for those latitudes for which the plates bearing the almicanteras are constructed. The signs which Chaucer calls of right (i. e. direct) ascension' are those signs of the zodiac which rise more directly, i. e. at a greater

the zodiak assendeth. Ferther-over they seyn, that in thilke cuntrey where as the senith of hem that dwellen there is in the equinoxial lyne, and her orisonte passing by the poles of this 10 worlde, thilke folke han this right cercle and the right orisonte; and evere-mo the arch of the day and the arch of the night is ther y-like long, and the sonne twyes every yeer passinge thorow the senith of her heved; and two someres and two winteres in a yeer han this forseide poeple. And the almikanteras in her Astrolabies 15 ben streighte as a lyne, so as sheweth in this figure. The utilite to knowe the assenciouns in the righte cercle is this: truste wel that by mediacioun of thilke assenciouns thise astrologiens, by hir tables and hir instrumentz, knowen verreyly the assencioun of every degree and minut in al the zodiak, as shal be shewed. And 20

angle to the horizon than the rest. In latitude 52°, Libra rises so directly that the whole sign takes more than 24 hours before it is wholly above the horizon, during which time nearly 43° of the equinoctial circle have arisen; or, in Chaucer's words, 'the more part' (i. e. a larger portion) of the equinoctial ascends with it. On the other hand, the sign of Aries ascends so obliquely that the whole of it appears above the horizon in less than an hour, so that a 'less part' (a smaller portion) of the equinoctial ascends with it. The following is a rough table of Direct and Oblique Signs, shewing approximately how long each sign takes to ascend, and how many degrees of the equinoctial ascend with it, in lat. 52°.

These numbers are sufficiently accurate for the present purpose. In ll. 8-11, there is a gap in the sense in nearly all the MSS., but the Bodley MS. 619 fortunately supplies what is wanting, to the effect that, at places situated on the equator, the poles are in the horizon. At such places, the days and nights are always equal. Chaucer's next statement is true for all places within the tropics, the peculiarity of them being that they have the sun vertical twice in a year. The statement about the 'two summer and winters' is best explained by the following. In the tropical climates, . . seasons are caused more by the effect of the winds (which are very regular, and depend mainly on the sun's position) than by changes in the direct action of the sun's light and heat. The seasons are not a summer and winter, so much

nota, that this forseid righte orisonte, that is cleped orison rectum, divydeth the equinoxial in-to right angles; and the embelif orisonte, wher-as the pol is enhaused up-on the orisonte, overkerveth the equinoxial in embelif angles, as sheweth in the figure. And for 25 the more declaracioun, lo here the figure.

27. This is the conclusioun to knowe the assenciouns of signes in the right cercle, that is, circulus directus, &c. [Ad cognoscendum ascenciones signorum in recto circulo, qui vocatur circulus directus.]

Set the heved of what signe thee liste to knowe his assending in the right cercle up-on the lyne meridional; and waite wher thyn almury toucheth the bordure, and set ther a prikke. Turne thanne thy riet westward til that the ende of the forseide signe 5 sitte up-on the meridional lyne; and eft-sones waite wher thyn almury toucheth the bordure, and set ther another prikke. Rikne thanne the nombre of degrees in the bordure by-twixe bothe prikkes, and tak the assencioun of the signe in the right cercle. And thus maystow wyrke with every porcioun of thy zodiak, &c. 10 And for the more declaracioun, lo here thy figure.

28. To knowe the assencions of signes in the embelif cercle in every regioun, I mene, in circulo obliquo. [Ad cognoscendum ascenciones signorum in circulo obliquo, in omni regione.]

Set the heved of the signe which as thee list to knowe his

as recurrences of wet and dry periods, two in each year?'-English Cyclopædia; Seasons, Change of. Lastly, Chaucer reverts to places on the equator, where the stars all seem to move in vertical circles, and the almicanteras are therefore straight lines. The line marked Horizon Rectus is shewn in fig. 5, where the Horizon Obliquus is also shewn, cutting the equinoctial circle obliquely.

27. The real object in this section is to find how many degrees of the equinoctial circle pass the meridian together with a given zodiacal sign. Without even turning the rete, it is clear that the sign Aries, for instance, extends through 28° of the equinoctial; for a line drawn from the centre, in fig. 2, through the end of Aries will (if the figure be correct) pass through the end of the 28th degree below the word Oriens.

28. To do this accurately requires a very carefully marked Astrolabe,

ascensioun up-on the est orisonte, and waite wher thyn almury toucheth the bordure, and set ther a prikke. Turne thanne thy riet upward til that the ende of the same signe sitte up-on the est orisonte, and waite eft-sones wher as thyn almury toucheth the 5 bordure, and set ther a-nother prikke. Rikne thanne the noumbre of degrees in the bordure by-twixe bothe prikkes, and tak ther the assencioun of the signe in the embelif cercle. And understond wel, that alle signes in thy zodiak, fro the heved of Aries unto the ende of Virgo, ben cleped signes of the north fro the equinoxial; 10 and these signes arysen by-twixe the verrey est and the verrey north in oure orisonte generaly for evere. And alle signes fro the heved of Libra un-to the ende of Pisces ben cleped signes of the south fro the equinoxial; and thise signes arysen ever-mo by-twixe the verrey est and the verrey south in oure orisonte. Also every 15 signe by-twixe the heved of Capricorne un-to the ende of Geminis aryseth on oure orisonte in lasse than two houres equales; and thise same signes, fro the heved of Capricorne un-to the ende of Geminis, ben cleped 'tortuos signes' or 'croked signes,' for they arisen embelif on oure orisonte; and thise crokede signes 20 ben obedient to the signes that ben of right assencioun. The signes of right assencioun ben fro the heved of Cancer to the ende of Sagittare; and thise signes arysen more upright, and they ben called eke sovereyn signes; and everich of hem aryseth in more space than in two houres. Of which signes, Gemini obeyeth 25 to Cancer; and Taurus to Leo; Aries to Virgo; Pisces to Libra ; Aquarius to Scorpioun ; and Capricorne to Sagittare. And thus

on as large a scale as is convenient. It is done by observing where the ends of the given sign, estimated along the outer rim of the zodiacal circle in fig. 2, cross the horizon obliquus as the rete is turned about. Thus, the beginning of Aries lies on the horizon obliquus, and as the rete revolves to the right, the end of it, on the outer rim, will at last lie exactly on the same curved line. When this is the case, the rete ought to have moved through an angle of about 14°, as explained in § 26. By far the best way is to tabulate the results once for all, as I have there done. It is readily seen, from fig. 2, that the signs from Aries to Virgo are northern, and from Libra to Pisces are southern signs. The signs from Capricorn to Gemini are the oblique signs, or as Chaucer calls them, 'tortuous,' and ascend in less than 2 hours; whilst the direct signs, from Cancer to Sagittarius, take more than 2 hours to ascend; as shewn in the table on p. 209. The eastern signs in fig. 2 are said to obey to the corresponding western ones.

ever-mo two signes, that ben y-lyke fer fro the heved of Capricorne, obeyen everich of hem til other. And for more declaracioun, lo 30 here the figure.

29. To knowe iustly the foure quarters of the world, as est, west, north, and sowth.

[Ad cognoscendum evidenter quatuor partes mundi, scilicet, orientem, austrum, aquilonem, et occidentem.]

Take the altitude of thy sonne whan thee list, and note wel the quarter of the world in which the sonne is for the tyme by the azimutz. Turne thanne thyn Astrolabie, and set the degree of the sonne in the almikanteras of his altitude, on thilke side that 5 the sonne stant, as is the manere in taking of houres; and ley thy label on the degree of the sonne, and rikene how many degrees of the bordure ben by-twixe the lyne meridional and the point of thy label; and note wel that noumbre. Turne thanne a-gayn thyn Astrolabie, and set the point of thy gret rewle, ther thou takest 10 thyne altitudes, up-on as many degrees in his bordure fro his meridional as was the point of thy label fro the lyne meridional on the wombe-syde. Tak thanne thyn Astrolabie with bothe handes sadly and slely, and lat the sonne shyne thorow bothe holes of thy rewle; and sleyly, in thilke shyninge, lat thyn Astrolabie couch 15 adoun evene up-on a smothe grond, and thanne wol the verrey lyne meridional of thyn Astrolabie lye evene south, and the est lyne wole lye est, and the west lyne west, and north lyne north, so that thou werke softly and avisely in the couching; and thus hastow the 4 quarters of the firmament. And for the more 20 declaracioun, lo here the figure.

29. Here both sides of the Astrolabe are used, the 'rewle' being made to revolve at the back, and the 'label' in front, as usual. First, by the back of the instrument and the 'rewle,' take the sun's altitude. Turn the Astrolabe round, and set the sun's degree at the right altitude among the almicanteras, and then observe, by help of the label, how far the sun is from the meridian. Again turn the instrument round, and set the 'rewle' as far from the meridian as the label was. Then, holding the instrument as near the ground and as horizontal as possible, let the sun shine through the holes of the 'rewle,' and immediately after lay the Astrolabe down, without altering the azimuthal direction of the meridional line. It is clear that this line will then point southwards, and the other points of the compass will also be known.