the degree that first assendeth, and set him on the ende of the 2 10 houre inequal; and thanne wol the by-ginning of the 5 hous sitte up-on the lyne of midnight; set thanne the nadir of the assendent on the ende of the 4 houre, than wol the byginning of the 6 house sitte on the midnight lyne. The byginning of the 7 hous is nadir of the assendent, and the byginning of the 8 hous is nadir of the 152; and the by-ginning of the 9 hous is nadir of the 3; and the by-ginning of the 10 hous is the nadir of the 4 ; and the byginning of the 11 hous is nadir of the 5; and the byginning of the 12 hous is nadir of the 6. And for the more declaracion, lo here the figure. 37. A-nother manere of equaciouns of houses by the Astrolabie. [De aliqua forma equacionis domorum secundum Tak thyn assendent, and thanne hastow thy 4 angles; for wel thou wost that the opposit of thyn assendent, that is to seyn, thy by-ginning of the 7 hous, sit up-on the west orizonte; and the byginning of the 10 hous sit up-on the lyne meridional; and his 5 opposit up-on the lyne of midnight. Thanne ley thy label over the degree that assendeth, and rekne fro the point of thy label alle the degrees in the bordure, til thou come to the meridional lyne; and departe alle thilke degrees in 3 evene parties, and take the evene equacion of 3; for ley thy label over everich of 3 parties, 10 and than maistow see by thy label in which degree of the zodiak is the by-ginning of everich of thise same houses fro the assendent : that is to seyn, the beginning of the 12 house next above thyn to 2 hours, so that the bringing of the 3rd house to the midnight line brings I to the 10th hour-line, and a similar placing of the 4th house brings to the 12th hour-line, which is the horizon obliquus itself. Moving onward 2 more hours, the point 7 (the nadir of 1) comes to the end of the 2nd hour, whilst the 5th house comes to the north; and lastly, when 7 is at the end of the 4th hour, the 6th house is so placed. To find the nadir of a house, we have only to add 6; so that the 7th, 8th, 9th, 10th, 11th, and 12th houses are the nadirs of the 1st, 2nd, 3rd, 4th, 5th, and 6th houses respectively. 37. Again see fig. 14, Plate VI. Here the 10th house is at once seen to be on the meridional line. In the quadrant from 1 to 10, the even division of the quadrant into 3 parts shews the 12th and 11th assendent; and thanne the beginning of the 11 house; and thanne the 10, up-on the meridional lyne; as I first seide. The same wyse wirke thou fro the assendent doun to the lyne of 15 midnight; and thanne thus hastow other 3 houses, that is to seyn, the byginning of the 2, and the 3, and the 4 houses; thanne is the nadir of thise 3 houses the by-ginning of the 3 houses that folwen. And for the more declaracioun, lo here thy figure. 38. To finde the lyne merydional to dwelle fix in any certein place. [Ad inveniendum lineam meridionalem per subtiles operaciones.] Tak a rond plate of metal; for warping, the brodere the bettre ; and make ther-upon a iust compas, a lite with-in the bordure; and ley this ronde plate up-on an evene grond, or on an evene ston, or on an evene stok fix in the gronde; and ley it even by a level. And in centre of the compas stike an evene pin or a wyr upright; 5 the smallere the betere. Set thy pin by a plom-rewle evene upright; and let this pin be no lengere than a quarter of the diametre of thy compas, fro the centre. And waite bisily, aboute 10 or 11 of the clokke and whan the sonne shyneth, whan the shadwe of the pin entreth any-thing with-in the cercle of thy plate 10 an heer-mele, and mark ther a prikke with inke. Abyde thanne stille waiting on the sonne after 1 of the clokke, til that the schadwe of the wyr or of the pin passe ony-thing out of the cercle of the compas, be it never so lyte; and set ther a-nother prikke of inke. Take than a compas, and mesure evene the middel 15 by-twixe bothe prikkes; and set ther a prikke. Take thanne a rewle, and draw a stryke, evene a-lyne fro the pin un-to the houses. Working downwards from I, we get the 2nd and 3rd houses, and the 4th house beginning with the north line. The rest are easily found from their nadirs. 38. This problem is discussed in arts. 144 and 145 of Hymes's Astronomy, 2nd ed. 1840, p. 84. The words 'for warping' mean 'to prevent the errors which may arise from the plate becoming warped.' The 'broader' of course means 'the larger.' See fig. 15, Plate VI. If the shadow of the sun be observed at a time before midday when its extremity just enters within the circle, and again at a time after midday when it is just passing beyond the circle, the altitude of the sun at these two observations must be the same, and middel prikke; and tak ther thy lyne meridional for evere-mo, as in that same place. And yif thow drawe a cros-lyne over-thwart 20 the compas, iustly over the lyne meridional, than hastow est and west and south; and, par consequence, than the nadir of the south lyne is the north lyne. And for more declaracioun, lo here thy figure. 39. Descripcion of the meridional lyne, of longitudes, and latitudes of citees and townes from on to a-nother of clymatz. This lyne meridional is but a maner descripcion of lyne imagined, that passeth upon the poles of this world and by the senith of oure heved. And hit is y-cleped the lyne meridional; for in what place that any maner man is at any tyme of the yeer, 5 whan that the sonne by moeving of the firmament cometh to his verrey meridian place, than is hit verrey midday, that we clepen oure noon, as to thilke man; and therfore is it cleped the lyne of midday. And nota, for evermo, of 2 citees or of 2 tounes, of whiche that o toun aprocheth more toward the est than doth 10 that other toun, truste wel that thilke tounes han diverse meri dians. Nota also, that the arch of the equinoxial, that is conteyned or bounded by-twixe the 2 meridians, is cleped the longitude of the toun. And yif so be that two tounes have y-lyke meridian, or oon meridian, than is the distance of hem bothe y-lyke 15 fer fro the est; and the contrarie. And in this manere they chaunge nat her meridian, but sothly they chaungen her almikanteras; for the enhausing of the pool and the distance of the the south line must lie half-way between the two shadows. In the figure, S and S' are the 2 positions of the sun, OT the rod, Ot and Oť' the shadows, and OR the direction of the south line. Ott' is the metal disc. 39. This begins with an explanation of the terms 'meridian' and 'longitude.' 'They chaungen her Almikanteras' means that they differ in latitude. But, when Chaucer speaks of the longitude and latitude of a 'climate,' he means the length and breadth of it. A 'climate' (clima) is a belt of the earth included between two fixed parallels of latitude. The ancients reckoned seven climates; in the sixteenth century there were nine. The latitude of the climate' is the breadth of this belt; the 'longitude' of it he seems to consider as measured along lines lying equidistant between the parallels of latitude sonne. The longitude of a clymat is a lyne imagined fro est to west, y-lyke distant by-twene them alle. The latitude of a clymat is a lyne imagined from north to south the space of the erthe, 20 fro the byginning of the firste clymat unto the verrey ende of the same climat, evene directe agayns the pole artik. Thus seyn some auctours; and somme of hem seyn that yif men clepen the latitude, thay mene the arch meridian that is contiened or intercept by-twixe the senith and the equinoxial. Thanne sey they that 25 the distaunce fro the equinoxial unto the ende of a clymat, evene agayns the pole artyk, is the latitude of a clymat for sothe. And for more declaracioun, lo here thy figure. 40. To knowe with which degree of the zodiak that any planete assendith on the orisonte, whether so that his latitude be north or south. Knowe by thyn almenak the degree of the ecliptik of any signe in which that the planete is rekned for to be, and that is cleped the degree of his longitude; and knowe also the degree of his latitude fro the ecliptik, north or south. And by thise samples folwinge in special, maystow wirke for sothe in every signe of the 5 zodiak. The degree of the longitude, par aventure, of Venus or of another planete, was 6 of Capricorne, and the latitude of him of the places from which the climates are named. See Stöffler, fol. 20 b; and Petri Apiani Cosmographia, per Gemmam Phrysium restituta, ed. 1574, fol. 7 b. The seven climates were as follows: 1. That whose central line passes through Meroë (lat. 17°); from nearly 13° to nearly 20°. 2. Central line, through Syene (lat. 24°); from 20° to 27°, nearly. 3. Central line through Alexandria (lat. 31°); from 27° to 34°, nearly. 4. Central line through Rhodes (lat. 36°); from 34° to 39°, nearly. 5. Central line through Rome (lat. 41°); from 39° to 43°, nearly. 6. Central line through Borysthenes (lat. 45°); from 43° to 47°. 7. Through the Riphæan mountains (lat. 48°); from 47° to 50°. But Chaucer must have included an eighth climate (called ultra Mæotides paludes) from 50° to 56°; and a ninth, from 56° to the pole. The part of the earth to the north of the 7th climate was considered by the ancients to be uninhabitable. A rough drawing of these climates is given in MS. Camb. Univ. Lib. Ii. 3. 3, fol. 33 b. 40. The longitude and latitude of a planet being ascertained from an almanac, we can find with what degree it ascends. For example, was northward 2 degrees fro the ecliptik lyne. I tok a subtil compas, and cleped that oon poynt of my compas A, and that 10 other poynt F. Than tok I the point of A, and set it in the ecliptik lyne evene in my zodiak, in the degree of the longitude of Venus, that is to seyn, in the 6 degree of Capricorne; and thanne sette I the point of F upward in the same signe, bycause that the latitude was north, up-on the latitude of Venus, that is to 15 seyn, in the 6 degree fro the heved of Capricorne ; and thus have I 2 degrees by-twixe my two prikkes. Than leide I doun softely my compas, and sette the degree of the longitude up-on the orisonte; tho tok I and wexede my label in maner of a peyre tables to resceyve distinctly the prikkes of my compas. Tho tok 20 I this forseide label, and leide it fix over the degree of my longitude; tho tok I up my compas, and sette the point of A in the wex on my label, as evene as I coude gesse over the ecliptik lyne, in the ende of the longitude; and sette the point of F endlang in my label up-on the space of the latitude, inwarde and 25 over the zodiak, that is to seyn, north-ward fro the ecliptik. Than leide I doun my compas, and lokede wel in the wey upon the prikke of A and of F; tho turned I my riet til that the prikke of F sat up-on the orisonte; than saw I wel that the body of Venus, in hir latitude of 2 degrees septentrionalis, assended, in the ende 30 of the 6 degree, in the heved of Capricorne. And nota, that in the same maner maistow wirke with any latitude septentrional in alle signes; but sothly the latitude meridional of a planete in Capricorne may not be take, by-cause of the litel space by-twixe the ecliptik and the bordure of the Astrolabie ; but sothly, in alle other signes 35 it may. given that the longitude of Venus is 6° of Capricorn, and her N. latitude 2°. Set the one leg of a compass upon the degree of longitude, and extend the other till the distance between the two legs is 2° of latitude, from that point inward, i. e. northward. The 6th degree of Capricorn is now to be set on the horizon, the label (slightly coated with wax) to be made to point to the same degree, and the north latitude is set off upon the wax by help of the compass. The spot thus marking the planet's position is, by a very slight movement of the Rete, to be brought upon the horizon, and it will be found that the planet (situated 2° N. of the 6th degree) ascends together with the head (or beginning of the sign) of Capricorn. This result, which is not quite exact, is easily tested by a globe. When the latitude of |