Chaucer's Works (ed. Skeat) Vol. III/Treatise on the Astrolabe Notes

The title 'Tractatus de Conclusionibus Astrolabii' is suggested by the wording of the colophon on p. 223. But a better title is, simply, 'Tractatus de Astrolabio,' or 'Treatise on the Astrolabe,' as the 'Conclusiones' only occupy the Second Part of the work; see p. 188. Indeed MS. F. has 'Tractatus Astrolabii'; see p. 233. MSS. B. and E. have the singular title—'Bred and mylk for childeren.'

, l. 1. Lowis was at this time (1391) ten years old (see l. 18); he was therefore born in 1381, whence it is possible that his mother was the Cecilia de Chaumpaigne who, on May 1, 1380, released the poet from all liability de raptu meo. This is, of course, a mere conjecture. Probably Lowis died young, as nothing more is known concerning him.

5. philosofre; possibly Cicero. 'Haec igitur prima lex amicitiae sanciatur, ut ... amicorum causâ honesta faciamus'; Lælius, cap. xiii.

7. suffisaunt, sufficiently good. In the best instruments, the Almicanteras, or circles of altitude, were drawn at distances of one degree only; in less-carefully made instruments, they were drawn at distances of two degrees. The one given to his son by Chaucer was one of the latter; see Part I, sect. 18, l. 8.

10. a certein, i.e. a certain number; but the word nombre need not be repeated; cf. a certein holes, Pt. I. sect. 13, l. 2, and see the very expression in the Milleres Tale, l. 7 (A 3193).

21. suffyse, let them suffice.

32. Repeated from Ho. Fame, 861-2, q.v.

62. 'Nicolaus de Lynna, i.e. of Lynn, in Norfolk, was a noted astrologer in the reign of Edward III., and was himself a writer of a treatise on the Astrolabe. See Bale—who mentions "Joannes Sombe" as the collaborateur of Nicolaus—"Istos ob eruditionem multiplicem, non vulgaribus in suo Astrolabio celebrat laudibus Galfridus Chaucer poeta lepidissimus;" (edit. 1548), p. 152.'—Note by Mr. Brae, p. 21 of his edition of the Astrolabe.

Warton says that 'John Some and Nicholas Lynne' were both Carmelite friars, and wrote calendars constructed for the meridian of Oxford. He adds that Nicholas Lynne is said to have made several voyages to the most northerly parts of the world, charts of which he presented to Edward III. These charts are, however, lost. See Hakluyt's Voyages, i. 121, ed. 1598; Warton, Hist. E. P. ii. 357; ed. 1871.

Tyrwhitt, in his Glossary to Chaucer, s.v. Somer, has the following. 'The Kalendar of John Somer is extant in MS. Cotton, Vesp. E. vii. It is calculated for 140 years from 1367, the year of the birth of Richard II., and is said, in the introduction, to have been published in 1380, at the instance of Joan, mother to the king. The Kalendar of Nicholas Lenne, or Lynne, was calculated for 76 years from 1387. Tanner in v. Nicolans Linensis. The story there quoted from Hakluit of a voyage made by this Nicholas in 1360 ad insulas septentrionales antehac Europæis incognitas, and of a book written by him to describe these countries ''a gradu .54. usque ad polum'', is a mere fable: as appears from the very authorities which Hakluit has produced in support of it.' It seems probable, therefore, that the 'charts' which Warton says are 'lost' were never in existence at all. The false spelling 'Some' no doubt arose from neglecting the curl of contraction in Somere.

§ 5, l. 5. the remenant, &c. i.e. the rest of this line (drawn, as I said,) from the foresaid cross to the border. This appears awkward, and we should have expected 'fro the forseide centre,' as Mr. Brae suggests; but there is no authority for making the alteration. As the reading stands, we must put no comma after 'this lyne,' but read right on without a pause.

8. principals. It it not unusual to find adjectives of French origin retaining s in the plural; only they commonly follow their nouns when thus spelt. Cf. lettres capitals, i. 16. 8; sterres fixes, i. 21. 4. On the other hand, we find principal cercles, i. 17. 34.

§ 7. 4. noumbres of augrim; Arabic numerals. The degrees of the border are said to contain 4 minutes of time, whilst the degrees of the signs are divided into minutes and seconds of angular measurement, the degrees in each case being the same. There is no confusion in practice between these, because the former are used in measuring time, the latter in measuring angles.

§ 8. 9. Alkabucius; i.e. (says Warton, Hist. E. P. ii. 357, ed. 1871) Abdilazi Alchabitius, whose Introductiorium ad scientiam judicialem astronomæ was printed in 1473, and afterwards. Mr. Brae quotes the very passage to which Chaucer refers, which I here quote from the edition of 1482, as described in my note to l. 119 of The Compleint of Mars (see vol. i. p. 500); viz. 'Unumquodque istorum signorum diuiditur in 30 partes equales, que gradus vocantur. Et gradus diuiditur in 60 minuta; et minutum in 60 secunda; et secundum in 60 tertia. Similiterque sequuntur quarta, scilicet et quinta, ascendendo usque ad infinita'; Alchabitii Differentia Prima.

These minute subdivisions were never used; it was a mere affectation of accuracy, the like of which was never attained.

§ 10. 5. in Arabiens, amongst the Arabians. But he goes on to speak only of the Roman names of the months. Yet I may observe that in MS. Ii. 3. 3, at fol. 97, the Arabian, Syrian, and Egyptian names of the months are given as well as the Roman.

§ 16. 12. & every minut 60 secoundes; i.e. every minute contains 60 seconds. The sentence, in fact, merely comes to this. 'Every degree of the border contains four minutes (of time), and every minute (of time) contains sixty seconds (of time).' This is consistent and intelligible. Mr. Brae proposes to read &apos;four seconds'; this would mean that 'every degree of the border contains four minutes (of time), and every minute (of the border) contains four seconds (of time).' Both statements are true; but, in the latter case, Chaucer should have repeated the words 'of the bordure.' However this may be, the proposed emendation lacks authority, although the reprint of Speght changed 'lx' into 'fourtie,' which comes near to 'four.' But the reprint of Speght is of no value at all. See Mr. Brae's preface, p. 4, for the defence of his proposed emendation, which is entirely needless.

§ 17. 6. Ptholome. The St. John's MS. has ptolomeys almagest. &apos;Almagest, a name given by the Arabs to the, or great collection, the celebrated work of Ptolemy, the astronomer of Alexandria [floruit A.D. 140-160]. It was translated into Arabic about the year A.D. 827, under the patronage of the Caliph Al Mamun, by the Jew Alhazen ben Joseph, and the Christian Sergius. The word is the Arabic article al prefixed to the Greek megistus, "greatest," a name probably derived from the title of the work itself, or, as we may judge from the superlative adjective, partly from the estimation in which it was held.'—English Cyclopædia; Arts and Sciences, i. 223. The Almagest 'was in thirteen books. Ptolemy wrote also four books of judicial astrology. He was an Egyptian astrologist, and flourished under Marcus Antoninus. He is mentioned in the Sompnour's Tale [D 2289], and the Wif of Bathes Prologue, ll. 182, 324.'—Warton, Hist. E. P. ii. 356, ed. 1871. The word almagest occurs in the Milleres Tale, near the beginning (A 3208), and twice in the Wif of Bathes Prologue (D 183, 325).

Chaucer says the obliquity of the ecliptic, according to Ptolemy, was 23° 50′. The exact value, according to Ptolemy, was 23° 51′ 20″; Almagest, lib. i. c. 13. But Chaucer did not care about the odd degree, and gives it nearly enough. See note to ii. 25. 19.

8. tropos, a turning; Chaucer gives it the sense of agaynward, i.e. in a returning direction.

14. The equinoctial was supposed to revolve, because it was the 'girdle' of the primum mobile, and turned with it. See note below to l. 28.

14, 15. 'As I have shewed thee in the solid sphere.' This is interesting, as shewing that Chaucer had already given his son some lessons on the motions of the heavenly bodies, before writing this treatise.

27. angulus. We should rather have expected the word spera or sphera; cf. 'the sper solide' above, l. 15.

28. 'And observe, that this first moving (primus motus) is so called from the first movable (primum mobile) of the eighth sphere, which moving or motion is from East to West,' &c. There is an apparent confusion in this, because the primum mobile was the ninth sphere (see Plate V, fig. 10); but it may be called the movable of the eighth, as giving motion to it. An attempt was made to explain the movements of the heavenly bodies by imagining the earth to be in the centre, surrounded by a series of concentric spheres, or rather shells, like the coats of an onion. Of these the seven innermost, all revolving with different velocities, each carried with it a planet. Beyond these was an eighth sphere, which was at first supposed to be divided into two parts, the inner part being the firmamentum, and the outer part the primum mobile; hence the primum mobile might have been called 'the first moving of the eighth sphere,' as accounting for the more important part of the motion of the said sphere. It is simpler, however, to make these distinct, in which case the eighth sphere is firmamentum or sphæra stellarum fixarum, which was supposed to have a very slow motion from West to East round the poles of the zodiac to account for the precession of the equinoxes, whilst the ninth sphere, or primum mobile, whirled round from East to West once in 24 hours, carrying all the inner spheres with it, by which means the ancients accounted for the diurnal revolution. This ninth sphere had for its poles the north and south poles of the heavens, and its 'girdle' (or great circle equidistant from the poles) was the equator itself. Hence the equator is here called the 'girdle of the first moving.' As the planetary spheres revolved in an opposite direction, thus accounting for the forward motion of the sun and planets in the ecliptic or near it, the primum mobile was considered to revolve in a backward or unnatural direction, and hence Chaucer's apostrophe to it (Man of Lawes Tale, B 295):—

'O firste moevyng cruel firmament, With thy diurnal sweigh that crowdest ay And hurlest all from Est til Occident, That naturelly wolde holde another way.'

That is—'O thou primum mobile, thou cruel firmament, that with thy diurnal revolution (or revolution once in 24 hours round the axis of the equator) continually forcest along and whirlest all the celestial bodies from East to West, which naturally would wish to follow the course of the sun in the zodiac from West to East.' This is well illustrated by a sidenote in the Ellesmere MS. to the passage in question, to this effect:—'Vnde Ptholomeus, libro i. cap. 8. Primi motus celi duo sunt, quorum vnus est qui mouet totum semper ab Oriente in Occidentem vno modo super orbes, &c. Item aliter vero motus est qui mouet orbem stellarum currencium contra motum primum, videlicet, ab Occidente in Orientum super alios duos polos .' That is, the two chief motions are that of the primum mobile, which carries everything round from East to West, and that of the fixed stars, which is a slow motion from West to East round the axis of the zodiac, to account for precession. This exactly explains the well-known passage in the Frankeleines Tale (C. T., F 1280):—

'And by his eighte spere in his werking, He knew ful wel how fer Alnath was shove Fro the heed of thilke fixe Aries above That in the ninthe spere considered is.'

Here the eight spheres are the eight inner spheres which revolve round the axis of the zodiac in an easterly direction, whilst the ninth sphere, or primum mobile, contained both the theoretical or fixed first point of Aries from which measurements were made, and also the signs of the zodiac as distinct from the constellations. But Alnath, being an actual star, viz, Arietis, was in the eighth sphere; and the distance between its position and that of the first point of Aries at any time afforded a measure of the amount of precession. Mr. Brae rightly remarks that Tyrwhitt's readings in this passage are correct (except that eighte speres should be eightespere), and those of Mr. Wright and Dr. Morris (from the Harleian MS.) are incorrect.

It may be as well to add that a later refinement was to insert a crystalline sphere, to account for the precession; so that the order stood thus: seven spheres of planets; the eighth, of fixed stars; the ninth, or crystalline; the tenth, or primum mobile; and, beyond these, an empyræan or theological heaven, so to speak, due to no astronomical wants, but used to express the place of residence of celestial beings. Hence the passage in Milton, P. L. iii. 481:—

'They pass the planets seven, and pass the fix'd, And that crystalline sphere whose balance weighs The trepidation talk'd, and that first mov'd.'

i.e. They pass the seven planetary spheres; then the sphere of fixed stars; then the crystalline or transparent one, whose swaying motion or libration measures the amount of the precession and nutation so often talked of; and then, the sphere of the primum mobile itself. But Milton clearly himself believed in the Copernican system; see Paradise Lost, viii. 121-140, where the primum mobile is described in the lines—

'that swift Nocturnal and diurnal rhomb supposed, Invisible else above all stars, the wheel Of day and night.'

§ 18. 8. compowned by 2 & 2. This means that in the best astrolabes, every almicantarath for every degree of latitude was marked; as may be seen in Metius. In others, including the one given by Chaucer to his son, they were marked only for every other degree. See Part II. sect. 5, l. 2.

§ 19. 7. cenith, as here used, has a totally different meaning from that of senith, in l. 1 above. The senith in l. 1 is what we still call the zenith; but the cenith in l. 7 means the point of the horizon denoting the sun's place in azimuth. Contrary to what one might expect, the latter is the true original meaning, as the word zenith is corrupted from the root of the word which we now spell azimuth. The Arabic as-sant is a way or path; al-samt, a point of the horizon, and, secondly, an azimuthal circle. The plural of al-samt is assumūt, whence azimuth. But zenith is a corruption of semt, from samt al-rās, the Arabic name of the vertex of heaven (rās meaning a head); and the qualifying al-rās, the most important part of the phrase, has been improperly dropped. So far from the reading cenith being wrong here, it is most entirely right, and may be found (better spelt cenit) in the same sense in Messahala. See p. 213, second footnote. For cenith, some late copies have signet, evidently taken from the Latin word signum. They make the same mistake even in l. 12 of section 18.

§ 21. 4. sterres fixes, fixed stars; here the s again appears in a plural adjective of French derivation; see note above, to § 5. 8. In MSS. Ii. 3. 3 and Ii. 1. 13 in the Cambridge University Library, is an interesting list of the 49 stars most usually placed upon the Astrolabe. The stars which are represented by the points of the tongues in Fig. 2 are the same as those in the diagram from which Fig. 2 is copied, the original of which is in MS. A. I have slightly altered the positions of the points of the tongues, to make them somewhat more correct. The following is the list of the stars there shewn; most of their names are written in the MS. Cf. footnote on p. 186.

Within the Zodiac. In Aries, Mirach, or Andromedæ, shewn by a short tongue above Aries; in Taurus, Algol, or  Persei, as marked; in Libra, Aliot or Alioth, i.e.  Ursæ Majoris (the third horse, next the cart, in Charles's Wain), as marked; also Alramech, Arcturus, or  Boötis, shewn by the tongue projecting above Libra; in Scorpio, Alpheta, Alphecca, or  Coronæ Borealis, as marked; in Sagittarius, Raz Alhagus, or  Ophiuchi, near Alpheta; in Capricornus, Altair or  Aquilæ and Vega or  Lyræ, as marked, whilst near Vega is the unmarked Arided, or  Cygni; and in Pisces, Markab or  Pegasi.

Without the Zodiac. In Aries, under Oriens, the slight projection marks Ceti or Deneb Kaitos, the Whale's Tail, and the next curiously shaped projection (with side-tongues probably referring to other stars) means Batnkaitos, the Whale's Belly, apparently  Ceti; next come the long tongue for Menkar or  Ceti, the Whale's Nose; the star Aldebaran or Bull's Eye,  Tauri; Rigel or  Orionis, Orion's Foot; Alhabor or Sirius, the Dog-star, marked by a rude drawing of a dog's head, the star itself being at the tip of his tongue; then Algomeisa, Procyon, or  Canis Minoris, marked by a tongue pointing to the left, whilst the long broad tongue pointing upwards is Regulus, Kalbalased, or  Leonis; the small tongue above the letter I in the border is Alphard or Cor Hydræ. Above Occidens, in Libra, the first tongue is Algorab or Corvi, and the next Spica Virginis or Azimech; close to the 8th degree of Scorpio is  Libræ, and close to the beginning of Sagittarius is a small head, denoting the Scorpion, at the tip of the tongue of which is the bright Kalbalacrab or Antares. The last, a projection below the letter X, is Deneb Algebi or the Goat's Tail, i.e. Capricorni.

7. That is, the little point at the end of each tongue of metal is technically called the 'centre' of the star, and denotes its exact position.

9. The stars of the North are those to the North of the zodiac, not of the equator.

12. Aldeberan, &c.; the stars Aldebaran ( Tauri) and Algomeisa ( Canis Minoris) are called stars of the south, because they are to the south of the ecliptic; but as they are meanwhile (see Fig. 2) also to the north of the equator, they of course rise to the N. of the Eastern point of the horizon. The longitude of stars was always measured along the ecliptic, which is denoted in Fig. 2 by the outermost circle of the metal ring on which the names of the signs are written.

In one of the tracts in MS. G (dated A.D. 1486), p. 30, we find 'Aldebaran, in the first gre of geminis (sic), of the nature of Mars and Venus'; and 'Algomeisa, canis minor, in the xvij gre of Cancer, of the nature of Mars and Mercury.'

29. Amiddes, &c. Observe that the Ecliptic line in the midst of the celestial zodiac, a belt 12° broad, is on the outer edge of the zodiac as shewn in the astrolabe, which is only 6° broad and shews only the northern half of that belt. The 'way of the sun' is elsewhere used of the sun's apparent diurnal path (see Part ii. sect. 30); but it here refers, as is more usual, to the annual path.

34. streitnes, narrowness, closeness, smallness of size. In Fig. 2, I have marked every degree in the southern half of the zodiac, but only every fifth degree in the northern, in order to avoid an appearance of crowding in so small a figure. In Chaucer's own Astrolabe, every other degree was marked all round.

40. Here Chaucer gives at least three reasons for the name of 'zodiac.' The true one is the second, 'for that the sterres that ben there fixed ben disposed in signes of bestes, or shape like bestes.' But these imaginary shapes are very absurd and arbitrary.

50. Not only the influences here assigned to the signs, but others due to planets, may be found in 'Porphyrii Philosophi introductio in Claudii Ptolomæi opus de affectibus astrorum,' fol. Basileæ, n.d. p. 198. I here add a few extracts from the MS. in Trinity College, Cambridge (marked R. 15. 18), to shew the nature of the old astrology. I choose them with especial reference to Aries. The other signs are spoken of in a similar manner. 'It is principally to be considered that the signes of hevyn haue theire strenght and propre significacioun vpon the membris of eny man; as, Aries hath respect to the hed, taurus to the neck, geminis (sic) the Armys, Cancer the brest, leo the hert, virgo the bowels, &c.; as it shall shew in the Chapiters folowyng. Secundarily it is to be noted that plotholomee (sic) saith, that to touche with instrument of yroun while the mone is in the signe of the same membre, is for to be dred; let the surgen beware, and the letter of blode, let hym be aferd to touche that membre with yrene, in the which the mone shal be.'—MS. G; Trad C. p. 12.

'Thenne Aries hath respect to the hed; And this signe is hote and dry, fiery & colerik. Saturne hath ij witnes in Ariete, a triplicitate and a terme. Jubiter also hath ij, a triplicitate and a terme. Mars hath iij testimonials or iij fortitudis in Ariete, A hows, A face, and A terme. The sonne hath iij fortitudis in Ariete, scilicet, an exaltacioun, a triplicite, and a face. Venus hath ij testimonials, A terme and a face. Mercury hath one testymony, that is to sey, a terme. And luna in Ariete hath no testimoniall. For the which it is to know, that the influens of the planetis may be fortyfied v maner of wayes. And these v maner be called v fortitudis of planetis, or testimonials, which be these: domus, exaltacio, triplicitas, terminus, and facies. Domus gevith to a planet v fortitudis; And a planet in his hows is lyke a kynge in his hall, And in the high trone of his glorie. A planet in his exaltacioun is lyke a kynge when he is crowned. A planet in his triplicite is like a kynge in honour, Amonge his sencible people. A planet in his terme is As a mann amonges his kynnesmenn And fryndis. Facies gyvith to a planet that thyng the which rowme gyvith to a maistre. Wherfore facies gyvith only on fortitude, Terminus ij, Triplicitas iij, Exaltacio iiij, And domus v. And for the more clere declaracioun, the dignytes of planetis in signes be comprehendid in this figure ensuynge, &c. '—Same MS., Tract C. p. 13.

'The dygnytes of planetis in the signes, most speciall they be to be noted in iudicials. When the mone is in Ariete, it is not gode, but vtterly to be exshewed, both for seke And disesid, for to shafe theire hede or to boist in the eris or in the nek; nor loke þou let no blode in the vayn of the hede. How-be-it, benyficiall it is to begynne euery worke that þou woldest bryng aboute sone. But that thynge that is stabill ought to be eschewed. In this signe it is necessary to dele with noble estatis And rich men, And for to go in-to A bayne [bath] .'—Same MS., Tract C. p. 14.

54, 5. See Prologue, l. 73. As the zodiak is here called a part of the eighth sphere, so we have been before told that the equinoctial is the girdle of the ninth sphere; see note above to sect 17. l. 28.

57. evene parties, equal parts. That is, the equinoctial bisects the zodiac. But the northern half looks much smaller than the southern on the Astrolabe, owing to the manner in which the zodiac is there represented, viz. by projection on the plane of the equator.

§ 1. Rubric, hir cours. The gender of the sun was feminine in Anglo-Saxon, and that of the moon masculine; but in Chaucer's time, the gender was very variable, owing to the influence of Latin and French.

§ 3. Between sections 2 and 3, a section is inserted in the late copies, which merely repeats section 1, and is clearly spurious. It does not appear at all in the best MSS.; though it is found in the black-letter editions. I quote it here from MS. L.

&apos;To knowe the degre of thyn sonne in thyn zodiak by the days in the baksyde off the Astrolabye.

'[T]hanne iff þou wylte wete thatt / rekyn & knowe / qwych is the day off the monyth thatt thow arte ynne, & ley thy rewle of thy astrolabye, that is to sey, the allydatha, vpon þe day in the kalendre off the Astrolabye, & he schall schewe the thy degree of the sonne.'

26, 7. After 'assendent,' the following additional paragraph occurs in MS. Bodley 619; fol. 21. It is worthy of notice, because the original of it appears in Messahala's treatise, with the title 'De noticia stellarum incognitarum positarum in astrolabio.' The paragraph runs thus:—

'Nota. þat by þis conclusion þou may knowe also where ben at þat same tyme alle oþir sterres fixed þat ben sette in thin Astrelabie, and in what place of þe firmament; And also her arising in thy orizonte, and how longe þat thei wol ben aboue þe erthe wiþ þe Arke of þe nyght / And loke euermore hov many degrees þou fynde eny sterre at þat tyme sitting vpon þin Almycanteras, and vp-on as many degrees sette þou þe reule vpon þe altitude in þe bordere; And by the mediacioun of þy eye through þe .2. smale holes shalt thou se þe same sterre by the same altitude aforseid, And so by this conclusioun may þou redely knowe whiche is oo sterre from a-noþer in the firmament / for as many as ben in the Astrelabie. For by þat same altitude shal thou se that same sterre, & non othir / for þere ne wolle non othir altitude accorde þerto.'

30. Alhabor; i.e. Sirius or the Dog-star, as is evident from the fact of its being represented by a dog's head on the Astrolabe; see also the table of stars marked on the Astrolabe (in MS. Camb. Univ. Lib. li. 3. 3, fol. 70, back), which gives the declination 15° S, the latitude 39° S, and places the star in Cancer. It is also plainly described in the same table as being 'in ore canis', so that it is difficult to resist the conclusion of the identity of Alhabor and Sirius. Mr. Brae, following later copies that have different readings of the numbers employed, identifies Alhabor with Rigel or Orionis. This is impossible, from the fact that Rigel and Alhabor both occur in the diagrams and tables; see, for instance, Fig. 2. It is true that Rigel was sometimes called Algebar, but Alhabor stands rather for the Arabic Al-’abūr. The Arabic name for the constellation Canis Major was Al-kalb al-akbar, 'greater dog,' as distinguished from Al-kalb al-asghar, or 'lesser dog'; and the star Canis Majoris was called Al-shi’ra al-’abūr, the former of which terms represented the Greek  (Sirius), whilst from the latter (al-’abūr) we have our Alhabor. See Ideler, Über den Ursprung und die Bedeutung der Sternnamen, pp. 237, 256.

§ 4. 'The houses [in astrology] have different powers. The strongest of all these is the first, which contains the part of the heaven about to rise: this is called the ascendant; and the point of the ecliptic which is just rising is called the horoscope.'—English Encyclopædia; art. Astrology.

21. In the English Cyclopædia, art. Astrology, a quotation is given from an astrological work, in reply to the question whether the 'querent' should succeed as a cattle-dealer. It contains some words very similar to Chaucer's. 'If the lord of the sixth be in quartile, or in opposition to the dispositor of the part of Fortune, or the Moon, the querent cannot thrive by dealing in small cattle. The same if the lord of the sixth be afflicted either by Saturn, Mars, or the Dragon's Tail; or be found either retrograde, combust, cadent, or peregrine. [See l. 33.] The Dragon's Tail and Mars shew much loss therein by knaves and thieves, and ill bargains, &c.; and Saturn denotes much damage by the rot or murrain.' The evil influence of the Dragon's Tail is treated of in the last chapter of 'Hermetis Philosophi de revolutionibus nativitatum', fol. Basileæ; n.d.

32. 'May seen the ascendant.' Cf. 'Cum dominator ascendens viderit, res quæ occulta est secundum ascendentis naturam erit; quod si non videt, illud erit secundum naturam loci in quo ipse est dominator'; Cl. Ptolemæi Centiloquium; sect. 90.

33. combust, said of a planet when its light is quenched by being too near the sun. Tyrwhitt, in his Glossary, says that it is used when the planet is not more than 8½ degrees distant from the sun. Cf. Troilus, iii. 717, and the note.

40. Face. See note to Part I. sect. 21. l. 50 (p. 359). The late copies are very incorrect hereabouts.

§ 6. 9. Mr. Brae well calls attention here to the absurd errors in the printed copies. Thynne has 'in the 320 signe,' and Speght 'in the xxiii signe.' The signs of the zodiac are only twelve, and the one opposite to the 1st is the 7th.

§ 8. I see no reason for supposing this proposition to be an interpolation, as Mr. Brae suggests. Though similar to § 11, it is not identical with it. Moreover, it occurs in Messahala.

§ 9. 2. the chapitre beforn, i.e. a previous chapter, viz. in sect. 6. The expression supplies no argument for altering the order of the 'conclusions.'

4. same manere, i.e. a like manner. The 'vulgar night' clearly means that the quantity of the 'crepuscules' must be subtracted from the 'arch of the night.'

§ 13. 5. cours, course; heyest cours, highest point of the path. Late copies have lyne; for which Mr. Brae suggested degre.

§ 14. 6. but 2 degrees. Suppose the sun's midday altitude is 49°, in latitude 52°. Then the co-latitude is 38°, and the sun's declination 11° North. This corresponds nearly (roughly speaking) to the 1st degrees of Taurus and Virgo. Which is right can 'lightly' be known by the time of year, for the sun cannot be in Virgo if the month be April. Compare sect. 15.

§ 17. This conclusion, as pointed out in the footnote, is not correct in theory, but can be made nearly so in practice, by taking the two altitudes very near the meridian. This is directly implied in the words 'passeth any-thing the sowth westward,' i.e. passes ever so little westward of the south line; cf. note below to 38. 10. Consequently, the first observation must also be taken very near the meridian.

25. site, situation. Late copies, sight. This proves that the word site is Chaucerian, and clears up the reading in Ho. Fame, 1114.

§ 18. Instead of reckoning a star's right ascension by referring it to the equator, it was reckoned by observing the degree of the zodiac which southed along with it. This is expressed in the first 'Table of fixed stars' in MS. Camb. Univ. Lib. Ii. 3. 3 (fol. 70, back) by the phrase 'cum gradibus, quibus celum mediant'; the other co-ordinate of position was the star's declination from the equator, as in the modern method. The ancients also used the co-ordinates of longitude and latitude of a star, the longitude being reckoned along the ecliptic, and the latitude along great circles through the poles of the ecliptic; as appears from the second Table in the same MS.

§ 19. 6. equinoxial. This, as explained in the footnote, should be 'ecliptik'; but I can find no MS. authority for the alteration, though the correction is practically made in l. 13.

§ 22. 13. place. Late copies and old editions, planet; absurdly. Latitudes of several places are given in old Latin MSS. They are frequently incorrect.

§ 23. 3. The star A is shewn by the numbers to be the Pole-star, and is obviously the one to be observed in order to find the altitude of the Pole. What the star F is, is of no consequence. The numbers used in other copies are different, and much less satisfactory. That the star A is the Pole-star or some star near the pole in this 'conclusion' is rendered probable also by the wording of the next 'conclusion'; which extends the working of it to the case of any other star, provided it be a star that never sets.

§ 25. 19. When Chaucer says that the latitude of Oxford is 'certain minutes less,' he probably means no more than that the latitude of Oxford was 51 degrees and 50 minutes, as in the text. For I suspect the original reading of the passage made the sun's altitude 38 degrees only, and the latitude 52 degrees; indeed, the passage stands so in MSS. C and P, both good authorities. But he added the statement that the latitude of Oxford was less than 52 degrees. It is probable that, on second thoughts, he put in the number of minutes, and forgot to strike out the clause 'I sey nat this,' &c., which was no longer necessary. Minutes were seldom reckoned otherwise than by tens; 'a few minutes less than 50' (say 47) is a refinement to which the ancients seldom attained. Hence the amount of 10 minutes is vaguely spoken of in l. 31 as 'odde Minutes.' Minutes were clearly not much considered. In the present case, we are assisted by Chaucer's express statement in sect. 22. l. 6. The true latitude of Oxford is between 51° 45′ and 51° 46′.

§ 26. 8-11. It is singular that this sentence, obviously wanted, should appear only in one MS., and has, accordingly, been omitted in all previous editions. There can be no doubt about the genuineness of it, as it so exactly gives the right sense, and happily supplies the words 'right orisonte' in l. 11; thus enabling the author to say, as in l. 21 he does say—'this forseid righte orisonte.'

16. this figure. Here occurs, in some of the MSS., a diagram representing a circle, i.e, a disc of the astrolabe, with straight lines drawn across it from left to right.

17. assensiouns in the righte cercle. This exactly answers to our modern 'right ascension.' We hence obtain the true origin of the phrase. 'Right ascension' was, originally, the ascension of stars at places situate on the equator, and was most conveniently measured along the equatorial circle, by observation of the times of transit of the various stars across the meridian. In other latitudes, the ascension of every degree of the zodiac could be easily tabulated by observing what degree of the equator came to the meridian with the said degree of the zodiac; see l. 20. It hence appears that, whilst persisting in using 'longitudes' and reckoning along the zodiac, the ancients were obliged, in practice, to refer the degrees of longitude to the equator. The modern method of recognizing this necessity, and registering right ascensions as of more importance than longitudes, is a great improvement. The ancients were restrained from it by their unnecessary reverence for the zodiac. Cf. Ptolemy's Almagest, lib. i. c. xiii.

§ 29. Chaucer omits to say that the experiment should be made when the sun is very nearly on the meridian. Otherwise, the confusion of the azimuth with the hour-angle might cause a considerable error.

§ 30. 3. That the phrase 'wey of the sonne' really means the sun's apparent diurnal course in this conclusion, may be further seen by consulting the Latin of Messahala. Cf. the Critical Note on p. 236.

§ 31. In my footnote, I have used the expression 'it does not mean, as it should, the zenith point.' I mean—'as, according to our modern ideas, it should';—for the derivation of zenith shews that the meaning used in this proposition is the older meaning of the two. See note above to i. 19. 7 (p. 357).

6. 24 parties. These 24 parts were suggested by the 24 hours of the day. The '32 parts' used by 'shipmen' are due to the continual halving of angles. Thus, the four cardinal points have points half-way between them, making eight points; between which, we can insert eight more, making sixteen; and between these, sixteen more, making thirty-two. Hence the 32 points of the compass.

§ 33. 5. We should probably insert or south after the word north. Such an insertion is authorised by MSS. B. and C.

§ 34. 3. That 'upon the mones syde' means nearly in the same azimuth as the moon, is apparent from l. 11 below, where Chaucer says that some treatises make no exception even if the star is not quite in the same azimuth. This was certainly a rough mode of observation.

§ 35. 9. right side, East side. See i. 6. 1 (p. 179).

18. episicle, epicycle. To account for the planetary motions, epicycles were invented. The moon, for instance, was supposed to revolve round a moving centre, which centre itself moved round the earth in a perfect circle. This came a little nearer to the true motion in some instances, but was hopelessly wrong, and nothing could be made of it, even when a second epicycle, revolving about a centre which moved in the first epicycle, was superadded. All that Chaucer says here is, that, whilst the centre of the moon's epicycle had a direct motion, the moon's motion in the epicycle itself was a reverse one, unlike that of the other planetary bodies. The subject is hardly worth further discussion, so I merely refer the reader to the Almagest, lib. iv. c. 5; and lib. ix. c. 5.

§ 36. The 'equations of houses' means the dividing of the sphere into equal portions, and the right numbering of those portions or houses. The most important house was the first, or ascendent, just rising; the next in importance was the tenth, which was just coming on the meridian; then come the seventh or descendent, just about to set, and the fourth, just coming to the line of midnight. The next in importance were the succedents, or houses immediately following these, viz. the second, the eleventh, the eighth, and the fifth. The least important were the third, twelfth, ninth, and sixth. See Fig. 14.

§ 37. 18. thise 3 howsez. That is, the nadirs of the 2nd, 3rd, and 4th houses give the houses that 'follow,' i.e. the 8th, 9th, and 10th. The word 'follow' here seems to refer, not to position, but to the order in which the houses may most conveniently be found. Chaucer omits to add that the beginnings of the 5th and 6th houses can be found in a similar way, because it is sufficiently evident. It is all from Messahala.

§ 38. 1. for warping, the brodere the bettre. This may mean, either (1) to prevent warping, the thicker the better; or (2) to prevent the errors arising from warping (for fear of warping), the larger the better. I believe the latter to be the true interpretation; for it is better thus to guard against possible errors than to make the plate very thick and, at the same time, small. Besides which, the usual meaning of brodere is wider, larger, more ample. Indeed, we find the very expression 'non sit tamen nimis parvus' in the 4th section of the Practica Chilindri of John Hoveden, published by the Chaucer Society; which see.

8. fro the centre, i.e. sticking up above the centre, the length of the wire being equal to a fourth of the diameter, or half the radius, of the circle. This proportion would do for many days in the year; but in the summer time, the pin would bear to be rather longer. Still, we need not alter the text. Cf. the Critical Note on p. 237.

10. any-thing, i.e. ever so little; so ony-thyng in l. 13; cf. § 17. 6.

§ 39. Though MS. A is rather corrupt here, there is little doubt about the corrections to be made. See the Critical Notes, p. 237.

19. That is, the latitude, or breadth, of a climate, or belt, is measured along a line which goes from North to South as far as the earth extends; so that the latitude of the first climate, for example, is measured from the beginning of it to the end of the same, in a due northerly direction. Other authors, he explains, reckoned the latitude of a climate always from the equinoxial line, instead of from the parallel of latitude which terminated the climate immediately to the south of it. Thus the latitude of the fourth climate might mean, either the breadth of that belt itself, or the whole breadth from the equator to the Northern limit of that climate. The MS. E. 2 in St. John's College, Cambridge, contains (besides Chaucer's 'Astrolabe') a Latin treatise entitled 'De septem climatibus expositio.' We find mention of the 'climates' also in MS. Camb. Ii. 3. 3, fol. 33 b, where a diagram appears representing a hemisphere, divided by parallels of latitude into 9 climates or belts, which, beginning from the equator, are as follows. 1. Inhabitabile propter Calorem. 2. Primum clima dia Meroes. 3. Secundum clima dya cienes. 4. Tertium clima di' alexandrios. 5. Quartum clima dia rodos. 6. Quintum clima dia romes. 7. Sextum clima dia boristenes. 8. Septimum clima dia rifeos. 9. Inhabitabile. This agrees with the list in the footnote on p. 221.

There is a passage in Mandeville which well illustrates Chaucer; I quote the part of it which more immediately relates to the Climates. 'For the Superficialtee of the Erthe is departed in 7 parties, for the 7 Planetes; and the parties ben clept Clymates. And oure parties be not of the 7 Clymates: for they ben descendynge toward the West. And also these yles of Ynde, which beth evene aȝenst us, beth noght reckned in the Climates: for thei ben aȝenst us, that ben in the lowe Contree. And the 7 Clymates strecchen hem, envyrounynge the World,' &c. Mandeville's Voiage, ed. Halliwell, p. 186. See also Ptolemy's Almagest, lib. ii.

As regards the longitudes of towns, it may be observed that in MS. F. 25 in St. John's College, Cambridge, the longitudes of Rome, Cordova, London, Paris, and Malta, are said to be 34° 24′, 9° 30′, 19°, 20°, and 38° respectively. These do not well agree together, but they suggest a reckoning from a meridian situated some 20° W. from that of Greenwich. Chaucer says nothing as to what meridian was used for reckoning longitudes from; and Messahala says, vaguely enough, that longitudes were reckoned 'a meridiano circulo ultime regionis habitabilis in occidente,' i.e. from the most westward habitable place, which possibly once meant Madeira.

§ 40. It is possible that this conclusion was really intended to belong to the Fourth Part of the treatise, and was written by way of instalment. See the Prologue, ll. 67-72. It is curious that in all the best MSS. (P. excepted) the last sentence should be incomplete.

13. This sentence is very awkward. It seems to mean—'and then set I the point of F upward in the same sign, because that the latitude was north, upon the latitude of Venus; that is to say, (I set it upward) keeping it in the 6th degree of Capricorn.' Upward means inward, i.e. towards the centre or towards the north; the opposite being expressed by southward, or outward, or toward the border, as in l. 48 below. Upon the latitude of Venus means that the point F of the compass was set above the second degree of latitude, so that the space between the legs of the compass became equal to 2 degrees, as said in l. 16. Lastly, the words that is to seyn, in the 6 degree, &c., are an explanation of the vaguer expression in the same signe. The repetition of the words that is to seyn, &c. (ll. 12 and 14), is intended to draw attention to the necessity of keeping both legs of the compass in the same degree of longitude (A on the zodiac, and F to the north of it).

57. Possibly Chaucer left the sentence incomplete. The words 'thou shalt do well enough' may easily have been added by another hand to bring the sentence to an apparent, though not wholly satisfactory, conclusion. The colophon is written (in a later hand) in MS. A. at the bottom of the page, a part of which, after the words 'howre after howre,' is left blank.

41-43. I have mended the text as well as I could by inserting words, and adopting different readings. Nearly all the emendations rest on authority; see the Critical Notes. The text is not a good one, but I do not see why these sections may not have been written by Chaucer. For a definition of the terms 'Umbra Extensa' and 'Umbra Versa' see sections 5 and 6 of the Practica Chilindri of John Hoveden, published by the Chaucer Society. The umbra extensa or recta is the shadow cast on a plain by any perfectly upright object; but the restriction is commonly introduced, that the altitude of the sun shall exceed 45º. The umbra versa is the shadow cast perpendicularly downwards along a wall by a style which projects from the wall at right angles to it; the restriction is commonly introduced, that the sun's altitude shall be less than 45°. The umbra versa is the one which appeared on the 'chylindre'; hence John de Hoveden explains how to calculate the altitude of an object by it.

44. This article and the next may possibly be Chaucer's. It is well known that he speaks of 'collect' and 'expans yeres' and 'rotes' in the Frankeleines Tale; Cant. Ta., F 1275, 6, the note upon which in the glossary to Urry's Chaucer may be found also in Tyrwhitt's Glossary, s.v. Expans; but it is worth while to repeat it here. 'In this and the following verses, the Poet describes the Alphonsine Astronomical Tables by the several parts of them, wherein some technical terms occur, which were used by the old astronomers, and continued by the compilers of those tables. Collect years are certain sums of years, with the motions of the heavenly bodies corresponding to them, as of 20, 40, 60, &c., disposed into tables; and Expans years are the single years, with the motions of the heavenly bodies answering to them, beginning at 1, and continued on to the smallest Collect sum, as 20. A Root, or Radix, is any certain time taken at pleasure, from which, as an era, the celestial motions are to be computed. By 'proporcionels convenientes' [C. T., F 1278] are meant the Tables of Proportional parts.' To which Moxon adds, from Chamber's Encyclopædia, with reference to C. T., F 1277, that &apos;Argument in astronomy is an arc whereby we seek another unknown arc proportional to [or rather, dependent upon] the first.'

Tables of mean motions of the Sun are given in Ptolemy's Almagest, lib. iii. c. 2; of the Moon, lib. iv. c. 3; of the Planets, lib. viii. c. 3; also in MS. Ii. 3. 3, fol. 88b, &c.

41a-42b. The fact that these articles are mere repetitions of sections 41-43 is almost conclusive against their genuineness. I do not suppose that sect 46 (at p. 229) is Chaucer's either, but it is added for the sake of completeness.