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 1. 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. 1. 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 1. 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 1. 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 thirtytwo. 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 1. 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 azenst us, beth noght reckned in the Climates: for thei ben azenst 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 shallexceed 45°. 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 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. 886, &c.

41a-426. 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.