the nadir of the sonne, up-on the west orizonte, sheweth me the entring of the houre of the forseide sonne. And in this maner succedeth planete under planete, fro Saturne un-to the Mone, 30 and fro the Mone up a-gayn to Saturne, houre after houre generaly. And thus knowe I this conclusioun. And for the more declaracioun, lo here the figure. 13. To knowe the altitude of the sonne in middes of the day, that is cleped the altitude meridian. [Ad cognoscendum altitudinem solis in medio diei, que vocatur altitudo meridiana.] Set the degree of the sonne up-on the lyne meridional, and rikene how many degrees of almikanteras ben by-twixe thyn est orisonte and the degree of the sonne. And tak ther thyn altitude meridian; this is to seyne, the heyest of the sonne as for that day. 5 So maystow knowe in the same lyne, the heyest cours that any sterre fix climbeth by night; this is to seyn, that whan any sterre fix is passed the lyne meridional, than by-ginneth it to descende, and so doth the sonne. And for the more declaracioun, lo here thy figure. 14. To knowe the degree of the sonne by thy riet, for a maner curiositee, &c. [Ad cognoscendum gradum solis curiose.] Sek bysily with thy rewle the heyest of the sonne in midde of the day; turne thanne thyn Astrolabie, and with a prikke of ink marke the nombre of that same altitude in the lyne meridional. Turne thanne thy riet a-boute til thou fynde a degree of thy that he may begin with the remotest planet, Saturn, and follow the reverse order of the spheres. See fig. 10, Pl. V. Here, too, we have the obvious reason for the succession of the names of the days of the week, viz. that the planets being reckoned in this order, we find the Moon in the 25th place or hour from the Sun, and so on. 13. The reason of this is obvious from what has gone before. The sun's meridional altitude is at once seen by placing the sun's degree on the South line. 14. This is the exact converse of the preceding. It furnishes a method of testing the accuracy of the drawing of the almikanteras. zodiak acording with the prikke, this is to seyn, sittinge on the 5 prikke; and in sooth, thou shalt finde but two degrees in al the zodiak of that condicioun; and yit thilke two degrees ben in diverse signes; than maistow lightly by the sesoun of the yere knowe the signe in whiche that is the sonne. And for the more declaracioun, lo here thy figure. 15. To know which day is lyk to which day as of lengthe, &c. [Ad cognoscendum quales dies in longitudine sunt similes.] Loke whiche degrees ben y-lyke fer fro the hevedes of Cancer and Capricorn; and lok, whan the sonne is in any of thilke degrees, than ben the dayes y-lyke of lengthe. This is to seyn, that as long is that day in that monthe, as was swich a day in swich a month; ther varieth but lite. Also, yif thou take two 5 dayes naturaly in the yer y-lyke fer fro eyther pointe of the equinoxial in the opposit parties, than as long is the day artificial of that on day as is the night of that othere, and the contrarie. And for the more declaracioun, lo here thy figure. 16. This chapitre is a maner declaracioun to conclusiouns that folwen. [Illud capitulum est quedam declaracio ad certas Understond wel that thy zodiak is departid in two halfe cercles, as fro the heved of Capricorne un-to the heved of Cancer; and agaynward fro the heved of Cancer un-to the heved of Capricorne. 10 15. This is best done by help of the back of the instrument, fig. 1. Thus May 13 (old style), which lies 30° to the W. of the S. line, is nearly of the same length as July 13, which lies 30° to the E. Secondly, the day of April 2 (old style), 20° above the W. line, is nearly of the same length as the night of Oct. 2, 20° below the E. line, in the opposite point of the circle. This is but an approximation, as the divisions on the instrument are rather minute. 16. This merely expresses the same thing, with the addition, that on days of the same length, the sun has the same meridional altitude, and the same declination from the equator. The heved of Capricorne is the lowest point, wher-as the sonne 5 goth in winter; and the heved of Cancer is the heyest point, in whiche the sonne goth in somer. And ther-for understond wel, that any two degrees that ben y-lyke fer fro any of thise two hevedes, truste wel that thilke two degrees ben of y-lyke declinacioun, be it southward or northward; and the dayes of hem 10 ben y-lyke of lengthe, and the nightes also; and the shadwes y-lyke, and the altitudes y-lyke at midday for evere. And for more declaracioun, lo here thy figure. 17. To knowe the verrey degree of any maner sterre straunge or unstraunge after his longitude, though he be indeterminat in thyn Astrolabie; sothly to the trow the, thus he shal be knowe. [Ad cognoscendum verum gradum alicuius stelle aliene secundum eius longitudinem, quamvis sit indeterminata in astrolabio; veraciter isto modo.] Tak the altitude of this sterre whan he is on the est side of the lyne meridional, as ney as thou mayst gesse; and tak an assendent a-non right by som maner sterre fix which that thou knowest; and for-get nat the altitude of the firste sterre, ne thyn 5 assendent. And whan that this is don, espye diligently whan this same firste sterre passeth any-thing the south westward, and hath him a-non right in the same noumbre of altitude on the west side of this lyne meridional as he was caught on the est side; and tak a newe assendent a-non right by som maner sterre fixe which that 17. Here passeth any-thing the south westward means, passes somewhat to the westward of the South line. The problem is, to find the degree of the zodiac which is on the meridian with the star. To do this, find the altitude of the star before it souths, and by help of problem 3, find out the ascending degree of the zodiac; secondly, find the ascending degree at an equal time after it souths, when the star has the same altitude as before, and the mean between these will be the degree that ascends when the star is on the meridian. Set this degree upon the Eastern part of the horizon obliquus, and then the degree which is upon the meridional line souths together with the star. Such is the solution given, but it is but a very rough approximation, and by no means always near to the truth. An example will shew why. Let Arcturus have the same altitude at 10 P.M. as at 2 A.M. In the first case the 4th of Sagittarius is ascending, in the second (with thou knowest; and for-get nat this secounde assendent. And 10 whan that this is don, rikne thanne how manye degrees ben bytwixe the firste assendent and the seconde assendent, and rikne wel the middel degree by-twene bothe assendentes, and set thilke middel degree up-on thin est orisonte; and waite thanne what degree that sit up-on the lyne meridional, and tak ther the verrey degree 15 of the ecliptik in which the sterre stondeth for the tyme. For in the ecliptik is the longitude of a celestial body rekened, evene fro the heved of Aries un-to the ende of Pisces. And his latitude is rikned after the quantite of his declinacion, north or south to-warde the poles of this world; as thus. Yif it be of the sonne or of any 20 fix sterre, rekene his latitude or his declinacioun fro the equinoxial cercle; and yif it be of a planete, rekne than the quantitee of his latitude fro the ecliptik lyne. Al-be-it so that fro the equinoxial may the declinacion or the latitude of any body celestial be rikned, after the site north or south, and after the quantitee of his declin- 25 acion. And right so may the latitude or the declinacion of any body celestial, save only of the sonne, after his site north or south, and after the quantitee of his declinacioun, be rekned fro the sufficient accuracy for our purpose) the 2nd of Aquarius; and the mean between these is the 3rd of Capricorn. Set this on the Eastern horizon upon a globe, and it will be seen that it is 20 min. past midnight, that 10° of Scorpio is on the meridian, and that Arcturus has past the meridian by 5°. At true midnight, the ascendent is the 29° of Sagittarius. The reason of the error is that right ascension and longitude are here not sufficiently distinguished. By observing the degrees of the equinoctial, instead of the ecliptic, upon the Eastern horizon, we have at the first observation 272°, at the second 332°, and the mean of these is 302°; from this subtract 90°, and the result, 212°, gives the right ascension of Arcturus very nearly, corresponding to which is the beginning of the 5° of Scorpio, which souths along with it. This latter method is correct, because it assumes the motion to take place round the axis of the equator. The error of Chaucer's method is that it identifies the motion of the equator with that of the ecliptic. The amount of the error varies considerably, and may be rather large. But it can easily be diminished, (and no doubt was so in practice), by taking the observations as near the south line as possible. Curiously enough, the rest of the section explains the difference between the two methods of reckoning. The modern method is to call the co-ordinates right ascension and declination, if reckoned from the equator, and longitude and latitude, if from the ecliptic. Motion in longitude is not the same thing as motion in right ascension. ecliptik lyne; fro which lyne alle planetes som tyme declynen 30 north or south, save only the for-seide sonne. And for the more declaracioun, lo here thy figure. 18. To knowe the degrees of the longitudes of fixe sterres after that they ben determinat in thin Astrolabie, yif so be that they ben trewly set. [Ad cognoscendum gradus longitudinis de stellis fixis que determinantur in astrolabio, sicut in suis locis recte locentur.] Set the centre of the sterre up-on the lyne meridional, and tak keep of thy zodiak, and loke what degree of any signe that sit on the same lyne meridional at that same tyme, and tak the degree in which the sterre standeth; and with that same degree comth that 5 same sterre un-to that same lyne fro the orisonte. And for more declaracioun, lo here thy figure. 19. To knowe with which degree of the zodiak any sterre fixe in thyn Astrolabie aryseth up-on the est orisonte, althogh his dwelling be in a-nother signe. [Ad cognoscendum cum quibus gradibus zodiaci que stella fixa in astrolabio ascendit super orizontem orientalem, quamvis eius statio sit in alio signo.] Set the centre of the sterre up-on the est orisonte, and loke what degree of any signe that sit up-on the same orisonte at that same tyme. And understond wel, that with that same degree aryseth that same sterre; and this merveyllous arysing with a 18. The 'centre' of the star is the technical name for the extremity of the metal tongue representing it. The 'degree in which the star standeth' is considered to be that degree of the zodiac which souths along with it. Thus Sirius or Alhabor has its true longitude nearly equal to that of 12° of Cancer, but, as it souths with the 9th degree, it would be said to stand in that degree. This may serve for an example; but it must be remembered that its longitude was different in the time of Chaucer. 19. Also it rises with the 19th degree of Leo, as it is at some distance from the zodiac in latitude. The same 'marvellous arising in a strange sign' is hardly because of the latitude being north or |