that the firste altitude of A excedeth his seconde altitude, and tak 15 half thilke porcioun that is exceded, and adde it to his seconde altitude; and tak ther the elevacioun of thy pool, and eke the latitude of thy regioun. For thise two ben of a nombre; this is to seyn, as many degrees as thy pool is elevat, so michel is the latitude of the regioun. Ensample as thus : par aventure, the 20 altitude of A in the evening is 56 degrees of heyghte. Than wol his seconde altitude or the dawing be 48 ; that is 8 lasse than 56, that was his firste altitude at even. Take thanne the half of 8, and adde it to 48, that was his seconde altitude, and than hastow 52. Now hastow the heyghte of thy pol, and the latitude 25 of the regioun. But understond wel, that to prove this conclusioun and many a-nother fair conclusioun, thou most have a plomet hanging on a lyne heyer than thin heved on a perche ; and thilke lyne mot hange evene perpendiculer by-twixe the pool and thyn eye; and thanne shaltow seen yif A sitte evene over the pool and 30 over F at evene; and also yif F sitte evene over the pool and over A or day. And for more declaracion, lo here thy figure. 24. Another conclusioun to prove the heyghte of the pool artik fro the orisonte. (Alia conclusio ad probandum altitudinem de polo artico ab orizonte.] Tak any sterre fixe that nevere dissendeth under the orisonte in thilke regioun, and considere his heyest altitude and his lowest altitude fro the orisonte; and make a nombre of bothe thise altitudes. Tak thanne and abate half that nombre, and tak ther 5 the elevacioun of the pol artik in that same regioun. And for more declaracioun, lo here thy figure. Pole-star, then farther from the Pole than it is now. The star F is, according to Chaucer, any convenient star having a right ascension differing from that of the Pole-star by 180°; though one having the same right ascension would serve as well. If then, at the first observation, the altitude of A be 56, and at the second be 48, the altitude of the pole must be 52. See fig. 13, Plate V. 24. This comes to much the same thing. The lowest or northern altitude of Dubhe (a Ursæ Majoris) may be supposed to be observed to be 25°, and his highest or southern altitude to be 79o. Add these ; the sum is 104; 'abate' or subtract half of that number, and the result is 52°; the latitude. 25. A-nother conclusioun to prove the latitude of the regioun, &c. [Alia conclusio ad probandum latitudinem regionis.] Understond wel that the latitude of any place in a regioun is verreyly the space by-twixe the senith of hem that dwellen there and the equinoxial cerkle, north or southe, taking the mesure in the meridional lyne, as sheweth in the almikanteras of thyn Astrolabie. And thilke space is as moche as the pool artik is hey 3 in the same place fro the orisonte. And than is the depressioun of the pol antartik, that is to seyn, than is the pol antartik by-nethe the orisonte, the same quantite of space, neither more ne lasse. Thanne, yif thow desire to knowe this latitude of the regioun, tak the altitude of the sonne in the middel of the day, whan the sonne 10 is in the hevedes of Aries or of Libra ; (for thanne moeveth the sonne in the lyne equinoxial); and abate the nombre of that same sonnes altitude out of go, and thanne is the remenaunt of the noumbre that leveth the latitude of the regioun. As thus : I suppose that the sonne is thilke day at noon 38 degrees and 10 15 minutes of heyghte. Abate thanne thise degrees and minutes out of 90 ; so leveth there 51 degrees and 50 minutes, the latitude. I sey nat this but for ensample; for wel I wot the latitude of Oxenforde is certein minutes lasse, as I mighte prove. Now yif so be that thee semeth to long a taryinge, to abyde til that the 20 sonne be in the hevedes of Aries or of Libra, thanne waite whan the sonne is in any other degree of the zodiak, and considere the degree of his declinacion fro the equinoxial lyne ; and yif it so be that the sonnes declinacion be northward fro the equinoxial, abate thanne fro the sonnes altitude at noon the nombre of his de- 25 clinacion, and thanne hastow the heyghte of the hevedes of Aries and Libra. As thus : my sonne is, par aventure, in the firste 25. Here, as in $ 22, Chaucer says that the latitude can be measured by the arc Z r or PN; he adds that the depression of the Antarctic pole, viz. the arc SP' (where P' is the S. pole), is another measure of the latitude. He explains that an obvious way of finding the latitude is by finding the altitude of the sun at noon at the time of an equinox. If this altitude be 38° 10', then the latitude is the complement, or 51° 50'. But this observation can only be made on two days in the year. If then this seems to be too long a tarrying, observe his midday 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 south ward 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, anionges 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 Y A, 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 Time of Direct Time of. 160 42° 14° 43° angle to the horizon than the rest. In latitude 52°, Libra rises so Degrees of the i h. 44 m. 39° 2 h. 36 m. Aquarius I h. 4 m. 2 h. 48 m. Pisces: o h. 56 m. Virgo 2 h. 52 m. Aries 14° o h. 56 m. Libra 2 h. 52 m. Taurus 16° 2 h. 48 m. Gemini 26° 2 h. 36 m. These numbers are sufficiently accurate for the present purpose. In 11. 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 р 43° 42° 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 upon 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 upon 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, |