Chapter XX: Part II (2)

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
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
the compas, iustly over the lyne meridional, than hastow est and 20
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,
whan that the sonne by moeving of the firmament cometh to his 5
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
that other toun, truste wel that thilke tounes ban diverse meridians. 10
_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
fer fro the est; and the contrarie. And in this manere they 15
chaunge nat her meridian, but sothly they chaungen her almikanteras;
for the enhausing of the pool and the distance of the
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
was northward 2 degrees fro the ecliptik lyne. I tok a subtil
compas, and cleped that oon poynt of my compas A, and that
other poynt F. Than tok I the point of A, and set it in the 10
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
seyn, in the 6 degree fro the heved of Capricorne; and thus have 15
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
I this forseide label, and leide it fix over the degree of my 20
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
over the zodiak, that is to seyn, north-ward fro the ecliptik. Than 25
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
of the 6 degree, in the heved of Capricorne. And _nota_, that in the 30
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
it may. 35

Also the degree, par aventure, of Iuppiter or of a-nother planete,
was in the first degree of Pisces in longitude, and his latitude was
3 degrees meridional; tho tok I the point of A, and sette it in
the firste degree of Pisces on the ecliptik, and thanne sette I the
point of F dounward in the same signe, by-cause that the latitude 40
was south 3 degrees, that is to seyn, fro the heved of Pisces; and
thus have I 3 degrees by-twixe bothe prikkes; thanne sette I the
degree of the longitude up-on the orisonte. Tho tok I my label,
and leide it fix upon the degree of the longitude; tho sette I the
point of A on my label, evene over the ecliptik lyne, in the ende 45
evene of the degree of the longitude, and sette the point of F
endlang in my label the space of 3 degrees of the latitude fro the
zodiak, this is to seyn, southward fro the ecliptik, toward the
bordure; and turned my riet til the prikke of F sat up-on the
orisonte; thanne saw I wel that the body of Iuppiter, in his 50
latitude of 3 degrees meridional, ascended with 14 degrees of Pisces
_in horoscopo_. And in this maner maistow wirke with any latitude
meridional, as I first seide, save in Capricorne. And yif thou wolt
pleye this craft with the arysing of the mone, loke thou rekne wel
hir cours houre by houre; for she ne dwelleth nat in a degree of 55
hir longitude but a litel whyle, as thou wel knowest; but natheles,
yif thou rekne hir verreye moeving by thy tables houre after houre,
[thou shall do wel y-now].

EXPLICIT TRACTATUS DE CONCLUSIONIBUS ASTROLABII, COMPILATUS PER GALFRIDUM
CHAUCIERS AD FILIUM SUUM LODEWICUM, SCOLAREM TUNC TEMPORIS OXONIE, AC
SUB TUTELA ILLIUS NOBILISSIMI PHILOSOPHI MAGISTRI N. STRODE, ETC.

SUPPLEMENTARY PROPOSITIONS.

41. UMBRA RECTA.

Yif it so be that thou wilt werke by _umbra recta_, and thou may
come to the bas of the toure, in this maner thou schalt werke.
Tak the altitude of the tour by bothe holes, so that thy rewle ligge
even in a poynt. Ensample as thus: I see him thorw at the
poynt of 4; than mete I the space be-tween me and the tour, and I 5
finde it 20 feet; than be-holde I how 4 is to 12, right so is the space
betwixe thee and the tour to the altitude of the tour. For 4 is the
thridde part of 12, so is the space be-tween thee and the tour the
thridde part of the altitude of the tour; than thryes 20 feet is the
heyghte of the tour, with adding of thyn owne persone to thyn 10
eye. And this rewle is so general in _umbra recta_, fro the poynt of
oon to 12. And yif thy rewle falle upon 5, than is 5 12-partyes
of the heyght the space be-tween thee and the toure; with adding
of thyn owne heyght.

42. UMBRA VERSA.

Another maner of werkinge, by _vmbra versa._ Yif so be that
thou may nat come to the bas of the tour, I see him thorw the
nombre of 1; I sette ther a prikke at my fote; than go I neer to
the tour, and I see him thorw at the poynt of 2, and there I sette
a-nother prikke; and I beholde how 1 hath him to 12, and ther 5
finde I that it hath him twelfe sythes; than beholde I how 2
hath him to 12, and thou shalt finde it sexe sythes; than thou shalt
finde that as 12 above 6 is the numbre of 6, right so is the space
between thy two prikkes the space of 6 tymes thyn altitude. And
note, that at the ferste altitude of 1, thou settest a prikke; and 10
afterward, whan thou seest him at 2, ther thou settest an-other
prikke; than thou findest between two prikkys 60 feet; than thou
shalt finde that 10 is the 6-party of 60. And then is 10 feet the
altitude of the tour. For other poyntis, yif it fille in _umbra versa_,
as thus: I sette caas it fill upon 2, and at the secunde upon 3; 15
than schalt thou finde that 2 is 6 partyes of 12; and 3 is 4 partyes
of 12; than passeth 6 4, by nombre of 2; so is the space between
two prikkes twyes the heyghte of the tour. And yif the differens
were thryes, than shulde it be three tymes; and thus mayst thou
werke fro 2 to 12; and yif it be 4, 4 tymes; or 5, 5 tymes; _et sic 20
de ceteris_.

43. UMBRA RECTA.

An-other maner of wyrking be _umbra recta_. Yif it so be that
thou mayst nat come to the baas of the tour, in this maner thou
schalt werke. Sette thy rewle upon 1 till thou see the altitude,
and sette at thy foot a prikke. Than sette thy rewle upon 2, and
beholde what is the differense be-tween 1 and 2, and thou shalt 5
finde that it is 1. Than mete the space be-tween two prikkes, and
that is the 12 partie of the altitude of the tour. And yif ther were
2, it were the 6 partye; and yif ther were 3, the 4 partye; _et sic
deinceps_. And note, yif it were 5, it were the 5 party of 12; and
7, 7 party of 12; and note, at the altitude of thy conclusioun, 10
adde the stature of thyn heyghte to thyn eye.

44. ANOTHER MANER CONCLUSION, TO KNOWE THE MENE MOTE AND THE ARGUMENTIS
OF ANY PLANETE. TO KNOW THE MENE MOTE AND THE ARGUMENTIS OF EVERY
PLANETE FRO YERE TO YERE, FROM DAY TO DAY, FROM HOURE TO HOURE, AND
FROM SMALE FRACCIONIS INFINITE.

[AD COGNOSCENDUM MEDIOS MOTUS ET ARGUMENTA DE HORA IN HORAM CUIUSLIBET
PLANETE, DE ANNO IN ANNUM, DE DIE IN DIEM.]

In this maner shall thou worche: consider thy rote first, the
whiche is made the beginning of the tables fro the yere of oure
lord 1397, and entere hit in-to thy slate for the laste meridie of
December; and than consider the yere of oure lord, what is the
date, and be-hold whether thy date be more or lasse than the yere 5
1397. And yf hit so be that hit be more, loke how many yeres
hit passeth, and with so many entere into thy tables in the first
lyne ther-as is writen _anni collecti et expansi_. And loke where the
same planet is writen in the hede of thy table, and than loke
what thou findest in directe of the same yere of oure lord whiche 10
is passid, be hit 8, or 9, or 10, or what nombre that evere it be, til
the tyme that thou come to 20, or 40, or 60. And that thou
findest in directe wryte in thy slate under thy rote, and adde hit
to-geder, and that is thy mene mote, for the laste meridian of the
December, for the same yere whiche that thou hast purposed. 15
And if hit so be that hit passe 20, consider wel that fro 1 to 20
ben _anni expansi_, and fro 20 to 3000 ben _anni collecti_; and if thy
nombere passe 20, than take that thou findest in directe of 20, and
if hit be more, as 6 or 18, than take that thou findest in directe
there-of, that is to sayen, signes, degrees, minutes, and secoundes, 20
and adde to-gedere un-to thy rote; and thus to make rotes; and
note, that if hit so be that the yere of oure lord be lasse than the
rote, whiche is the yere of oure lord 1397, than shalt thou wryte in
the same wyse furst thy rote in thy slate, and after entere in-to thy
table in the same yere that be lasse, as I taught be-fore; and 25
than consider how many signes, degrees, minutes, and secoundes
thyn entringe conteyneth. And so be that ther be 2 entrees,
than adde hem togeder, and after with-drawe hem from the
rote, the yere of oure lord 1397; and the residue that leveth
is thy mene mote fro the laste meridie of December, the whiche 30
thou hast purposed; and if hit so be that thou wolt weten thy
mene mote for any day, or for any fraccioun of day, in this
maner thou shalt worche. Make thy rote fro the laste day
of Decembere in the maner as I have taught, and afterward
behold how many monethis, dayes, and houres ben passid from 35
the meridie of Decembere, and with that entere with the laste
moneth that is ful passed, and take that thou findest in directe
of him, and wryte hit in thy slate; and entere with as mony
dayes as be more, and wryte that thou findest in directe of the
same planete that thou worchest for; and in the same wyse in 40
the table of houres, for houres that ben passed, and adde alle these
to thy rote; and the residue is the mene mote for the same day
and the same houre.

45. ANOTHER MANERE TO KNOWE THE MENE MOTE.

Whan thou wolt make the mene mote of eny planete to be by
Arsechieles tables, take thy rote, the whiche is for the yere of oure
lord 1397; and if so be that thy yere be passid the date, wryte
that date, and than wryte the nombere of the yeres. Than withdrawe
the yeres out of the yeres that ben passed that rote. 5
Ensampul as thus: the yere of oure lord 1400, I wolde witen,
precise, my rote; than wroot I furst 1400. And under that
nombere I wrote a 1397; than withdraw I the laste nombere
out of that, and than fond I the residue was 3 yere; I wiste
that 3 yere was passed fro the rote, the whiche was writen in 10
my tables. Than after-ward soghte I in my tables the _annis
collectis et expansis_, and amonge myn expanse yeres fond I
3 yeer. Than tok I alle the signes, degrees, and minutes, that
I fond directe under the same planete that I wroghte for, and
wroot so many signes, degrees, and minutes in my slate, and 15
afterward added I to signes, degrees, minutes, and secoundes,
the whiche I fond in my rote the yere of oure lord 1397;
and kepte the residue; and than had I the mene mote for
the laste day of Decembere. And if thou woldest wete the
mene mote of any planete in March, Aprile, or May, other 20
in any other tyme or moneth of the yere, loke how many
monethes and dayes ben passed from the laste day of Decembere,
the yere of oure lord 1400; and so with monethes
and dayes entere in-to thy table ther thou findest thy mene
mote y-writen in monethes and dayes, and take alle the signes, 25
degrees, minutes, and secoundes that thou findest y-write in
directe of thy monethes, and adde to signes, degrees, minutes,
and secoundes that thou findest with thy rote the yere of
oure lord 1400, and the residue that leveth is the mene mote
for that same day. And note, if hit so be that thou woldest 30
wete the mene mote in ony yere that is lasse than thy rote, withdrawe
the nombere of so many yeres as hit is lasse than the
yere of oure lord a 1397, and kepe the residue; and so many
yeres, monethes, and dayes entere in-to thy tabelis of thy mene
mote. And take alle the signes, degrees, and minutes, and 35
secoundes, that thou findest in directe of alle the yeris, monethes,
and dayes, and wryte hem in thy slate; and above thilke nombere
wryte the signes, degrees, minutes, and secoundes, the whiche
thou findest with thy rote the yere of oure lord a 1397; and
with-drawe alle the nethere signes and degrees fro the signes and 40
degrees, minutes, and secoundes of other signes with thy rote;
and thy residue that leveth is thy mene mote for that day.

46. FOR TO KNOWE AT WHAT HOURE OF THE DAY, OR OF THE NIGHT, SHAL BE FLODE
OR EBBE.

First wite thou certeinly, how that haven stondeth, that thou
list to werke for; that is to say in whiche place of the firmament
the mone being, maketh fulle see. Than awayte thou redily in
what degree of the zodiak that the mone at that tyme is inne.
Bringe furth than the labelle, and set the point therof in that 5
same cost that the mone maketh flode, and set thou there the
degree of the mone according with the egge of the label. Than
afterward awayte where is than the degree of the sonne, at that
tyme. Remeve thou than the label fro the mone, and bringe and
sette it iustly upon the degree of the sonne. And the point of 10
the label shal than declare to thee, at what houre of the day or of
the night shal be flode. And there also maist thou wite by the
same point of the label, whether it be, at that same tyme, flode or
ebbe, or half flode, or quarter flode, or ebbe, or half or quarter
ebbe; or ellis at what houre it was last, or shal be next by night or 15
by day, thou than shalt esely knowe, &c. Furthermore, if it so be
that thou happe to worke for this matere aboute the tyme of the
coniunccioun, bringe furthe the degree of the mone with the
labelle to that coste as it is before seyd. But than thou shalt
understonde that thou may not bringe furthe the label fro the 20
degree of the mone as thou dide before; for-why the sonne is
than in the same degree with the mone. And so thou may at that
tyme by the point of the labelle unremeved knowe the houre of
the flode or of the ebbe, as it is before seyd, &c. And evermore
as thou findest the mone passe fro the sonne, so remeve thou the 25
labelle than fro the degree of the mone, and bringe it to the
degree of the sonne. And worke thou than as thou dide before,
&c. Or elles knowe thou what houre it is that thou art inne, by
thyn instrument. Than bringe thou furth fro thennes the labelle
and ley it upon the degree of the mone, and therby may thou wite 30
also whan it was flode, or whan it wol be next, be it night or
day; &c.

[_The following sections are spurious; they are numbered so as to shew
what propositions they repeat._]

41_a_. UMBRA RECTA.

Yif thy rewle falle upon the 8 poynt on right schadwe, than make
thy figure of 8; than loke how moche space of feet is be-tween thee
and the tour, and multiplye that be 12, and whan thou hast multiplied
it, than divyde it be the same nombre of 8, and kepe the residue; and
adde therto up to thyn eye to the residue, and that shal be the verry 5
heyght of the tour. And thus mayst thou werke on the same wyse, fro
1 to 12.

41_b_. UMBRA RECTA.

An-other maner of werking upon the same syde. Loke upon which
poynt thy rewle falleth whan thou seest the top of the tour thorow two
litil holes; and mete than the space fro thy foot to the baas of the
tour; and right as the nombre of thy poynt hath him-self to 12, right
so the mesure be-tween thee and the tour hath him-self to the heighte 5
of the same tour. Ensample: I sette caas thy rewle falle upon 8;
than is 8 two-thrid partyes of 12; so the space is the two-thrid partyes
of the tour.

42_a_. UMBRA VERSA.

To knowe the heyghth by thy poyntes of _umbra versa_. Yif thy
rewle falle upon 3, whan thou seest the top of the tour, set a prikke
there-as thy foot stont; and go ner til thou mayst see the same top at
the poynt of 4, and sette ther another lyk prikke. Than mete how
many foot ben be-tween the two prikkes, and adde the lengthe up to 5
thyn eye ther-to; and that shal be the heyght of the tour. And note,
that 3 is [the] fourthe party of 12, and 4 is the thridde party of 12.
Now passeth 4 the nombre of 3 be the distaunce of 1; therfore the
same space, with thyn heyght to thyn eye, is the heyght of the tour.
And yif it so be that ther be 2 or 3 distaunce in the nombres, so
shulde 10
the mesures be-tween the prikkes be twyes or thryes the heyghte of
the tour.

43_a_. AD COGNOSCENDUM ALTITUDINEM ALICUIUS REI PER UMBRAM RECTAM.

To knowe the heyghte of thinges, yif thou mayst nat come to the
bas of a thing. Sette thy rewle upon what thou wilt, so that thou may
see the top of the thing thorw the two holes, and make a marke ther
thy foot standeth; and go neer or forther, til thou mayst see thorw
another poynt, and marke ther a-nother marke. And loke than what 5
is the differense be-twen the two poyntes in the scale; and right as
that difference hath him to 12, right so the space be-tween thee and
the two markes hath him to the heyghte of the thing. Ensample: I
set caas thou seest it thorw a poynt of 4; after, at the poynt of 3.
Now passeth the nombre of 4 the nombre of 3 be the difference of 1; 10
and right as this difference 1 hath him-self to 12, right so the mesure
be-tween the two markes hath him to the heyghte of the thing, putting
to the heyghte of thy-self to thyn eye; and thus mayst thou werke
fro 1 to 12.

42_b_. PER UMBRAM VERSAM.

Furthermore, yif thou wilt knowe in _umbra versa_, by the craft of
_umbra recta_, I suppose thou take the altitude at the poynt of 4, and
makest a marke; and thou goost neer til thou hast it at the poynt of
3, and than makest thou ther a-nother mark. Than muste thou
devyde 144 by eche of the poyntes be-fornseyd, as thus: yif thou 5
devyde 144 be 4, and the nombre that cometh ther-of schal be 36, and
yif thou devyde 144 be 3, and the nombre that cometh ther-of schal be
48, thanne loke what is the difference be-tween 36 and 48, and ther
shalt thou fynde 12; and right as 12 hath him to 12, right so the space
be-tween two prikkes hath him to the altitude of the thing. 10

COMMENTARY ("FOOTNOTES").

Little Lewis my son, I perceive that thou wouldst learn the Conclusions of the Astrolabe; wherefore I have given thee an instrument constructed for the latitude of Oxford, and purpose to teach thee _some_ of these conclusions. I say _some_, for three reasons; (1) because some of them are unknown in this land; (2) because some are uncertain; or else (3) are too hard. This treatise, divided into five parts, I write for thee in English, just as Greeks, Arabians, Jews, and Romans were accustomed to write such things in their own tongue. I pray all to excuse my shortcomings; and thou, Lewis, shouldst thank me if I teach thee as much in English as most common treatises can do in Latin. I have done no more than compile from old writers on the subject, and I have translated it into English solely for thine instruction; and with this sword shall I slay envy.

The _first_ part gives a description of the instrument itself.

The _second_ teaches the practical working of it.

The _third_ shall contain tables of latitudes and longitudes of fixed stars, declinations of the sun, and the longitudes of certain towns.

The _fourth_ shall shew the motions of the heavenly bodies, and especially of the moon.

The _fifth_ shall teach a great part of the general rules of astronomical theory.

Here begins the _first_ part; i.e. the description of the Astrolabe itself.

1. _The Ring._ See figs. 1 and 2. The Latin name is _Armilla suspensoria_; the Arabic name is spelt _alhahuacia_ in MS. Camb. Univ. Ii. 3. 3, but Stöffler says it is _Alanthica_, _Alphantia_, or _Abalhantica_. For the meaning of 'rewle,' see § 13.

2. _The Turet._ This answers nearly to what we call an _eye_ or a _swivel_. The metal plate, or loop, to which it is fastened, or in which it turns, is called in Latin _Ansa_ or _Armilla Reflexa_, in Arabic _Alhabos_.

3. _The Moder._ In Latin, _Mater_ or _Rotula_. This forms the body of the instrument, the back of which is shewn in fig. 1, the front in fig. 2. The 'large hole' is the wide depression sunk in the front of it, into which the various discs are dropped. In the figure, the 'Rete' is shewn fitted into it.

4. See fig. 1; Chaucer describes the 'bak-half' of the instrument first. The centre of the 'large hole amydde' is the centre of the instrument, where a smaller hole is pierced completely through. The _Southe lyne_ (marked _Meridies_ in figs. 1 and 2) is also called _Linea Meridiei;_ the _North lyne_ is also named _Linea Mediæ Noctis_.

5. The _Est lyne_ is marked with the word _Oriens;_ the _West lyne_, with _Occidens_.

6. The rule is the same as in heraldry, the _right_ or _dexter_ side being towards the spectator's left.

7. As the 360 degrees answer to 24 hours of time, 15° answer to an hour, and 5° to twenty minutes, or a _Mile-way_, as it is the average time for walking a mile. So also 1° answers to 4 minutes of time. See the two outermost circles in fig. 1, and the divisions of the 'border' in fig. 2.

8. See the third and fourth circles (reckoning inwards) in fig. 1.

9. See the fifth and sixth circles in fig. 1.

10. See the seventh, eighth, and ninth circles in fig. 1. The names of the months are all Roman. The month formerly called _Quinctilis_ was first called _Julius_ in B.C. 44; that called _Sextilis_ was named _Augustus_ in B.C. 27. It is a mistake to say that Julius and Augustus made the alterations spoken of in the text; what Julius Cæsar really did, was to add 2 days to the months of January, August (Sextilis), and December, and 1 day to April, June, September, and November. February never had more than 28 days till he introduced bissextile years.

11. See the two inmost circles in fig. 1. The names given are adopted from a comparison of the figures in the Cambridge University and Trinity MSS., neither of which are quite correct. The letters of the 'Abc.' are what we now call the Sunday letters. The festivals marked are those of St. Paul (Jan. 25), The Purification (Feb. 2), The Annunciation (Mar. 25), The Invention of the Holy Cross (May 3), St. John the Baptist (June 24), St. James (July 25), St. Lawrence (Aug. 10), The Nativity of the Blessed Virgin (Sept. 8), St. Luke (Oct. 18), St. Martin of Tours (Nov. 11), and St. Thomas (Dec. 21).

12. The 'scale' is in Latin _Quadrans_, or _Scala Altimetra_. It is certain that Chaucer has here made a slip, which cannot be fairly laid to the charge of the scribes, as the MSS. agree in transposing _versa_ and _recta_. The side-parts of the scale are called _Umbra versa_, the lower part _Umbra recta_ or _extensa_. This will appear more clearly at the end of Part II. (I here give a _corrected text_.)

13. See fig. 3, Plate III. Each plate turns on a hinge, just like the 'sights' of a gun. One is drawn flat down, the other partly elevated. Each plate (_tabella vel pinnula_) has two holes, the smaller one being the lower. This _Rewle_ is named in Arabic _Alhidada_ or _Al´id[=a]da;_ in Latin _Verticulum_, from its turning easily on the centre; in Greek _Dioptra_, as carrying the sights. The straight edge, passing through the centre, is called the _Linea Fiduciæ_. It is pierced by a hole in the centre, of the same size as that in the _Mother_.

14. See fig. 4, Plate III. The _Pin_ is also called _Axis_ or _Clavus_, in Latin-Arabic _Alchitot;_ it occupies the position of the Arctic or North Pole, passing through the centre of the plates that are required to turn round it. The _Wedge_ is called _cuneus_, or _equus restringens_, in Arabic _Alfaras_ or the horse, because it was sometimes cut into the shape of a horse, as shewn in fig. 7, Plate IV, which is copied from MS. Univ. Camb. Ii. 3. 3.

15. See fig. 2, Plate II. In the figure, the cross-lines are partly hidden by the _Rete_, which is separate and removable, and revolves within the border.

16. The _Border_ was also called _Margilabrum_, _Margolabrum_, or _Limbus_. It is marked (as explained) with hour-letters and degrees. Each degree contains 4 minutes _of time_, and each of these minutes contains 60 seconds _of time_.

17. We may place under the _Rete_ any plates we please. If only the _Mother_ be under it, without any plate, we may suppose the _Mother_ marked as in fig. 2. The plate or disc (_tympanum_) which was usually dropped in under the _Rete_ is that shewn in fig. 5, Plate III, and which Chaucer now describes. Any number of these, marked differently for different latitudes, could be provided for the Astrolabe. The greatest declination of the sun measures the obliquity of the ecliptic, the true value of which is slightly variable, but was about 23° 31' in Chaucer's time, and about 23° 40' in the time of Ptolemy, who certainly assigns to it too large a value. The value of it must be known before the three circles can be drawn. The method of finding their relative magnitudes is very simple. Let ABCD (fig. 8, Pl. IV) be the tropic of Capricorn, BO the South line, OC the West line. Make the angle EOB equal to the obliquity (say 23½°), and join EA, meeting BO in F. Then OF is the radius of the Equatorial circle, and if GH be drawn parallel to EF, OH is the radius of the Tropic of Cancer. In the phrase _angulus primi motus_, _angulus_ must be taken to mean angular motion. The 'first moving' (_primus motus_) has its name of 'moving' (_motus_) from its denoting motion due to the _primum mobile_ or 'first moveable.' This _primum mobile_ (usually considered as the _ninth_ sphere) causes the rotation of the _eighth_ sphere, or _sphæra stellarum fixarum_. See the fig. in MS. Camb. Univ. Ii. 3. 3 (copied in fig. 10, Pl. V). Some authors make 12 heavens, viz. those of the 7 planets, the _firmamentum_ (_stellarum fixarum_), the _nonum coelum_, _decimum coelum_, _primum mobile_, and _coelum empyræum_.

18. See fig. 5, Pl. III. This is made upon the alt-azimuth system, and the plates are marked according to the latitude. The circles, called in Latin _circuli progressionum_, in Arabic _Almucantar[=a]t_, are circles of altitude, the largest imperfect one representing the horizon (_horizon obliquus_), and the central dot being the zenith, or pole of the horizon. In my figure, they are 'compounded by' 5 and 5, but Chaucer's shewed every second degree, i.e. it possessed 45 such circles. For the method of drawing them, see Stöffler, leaf 5, back.

19. Some Astrolabes shew 18 of these azimuthal circles, as in my figure (fig. 5, Pl. III). See Stöffler, leaf 13, where will be found also the rules for drawing them.

20. If accurately drawn, these _embelife_ or oblique lines should divide the portions of the three circles below the _horizon obliquus_ into twelve equal parts. Thus each arc is determined by having to pass through three known points. They are called _arcus horarum inequalium_, as they shew the 'houres inequales.'

21. In fig. 2, Pl. II, the _Rete_ is shewn as it appears when dropped into the depression in the front of the instrument. The shape of it varied much, and another drawing of one (copied from Camb. Univ. MS. Ii. 3. 3, fol. 66 _b_) is given in fig. 9, Pl. IV. The positions of the stars are marked by the extreme points of the metal tongues. Fig. 2 is taken from the figures in the Cambridge MSS., but the positions of the stars have been corrected by the list of latitudes and longitudes given by Stöffler, whom I have followed, not because he is _correct_, but because he probably represents their positions as they were supposed to be in Chaucer's time very nearly indeed. There was not room to inscribe the names of all the stars on the _Rete_, and to have written them _on the plate below_ would have conveyed a false impression. A list of the stars marked in fig. 2 is given in the note to § 21, l. 4. The Ecliptic is the circle which crosses the Equinoctial at its East and West points (fig. 2). In Chaucer's description of the zodiac, carefully note the distinction between the Zodiac of the Astrolabe and the Zodiac of Heaven. The former is only _six_ degrees broad, and shews only the northern half of the heavenly zodiac, the breadth of which is _imagined_ to be 12 degrees. Chaucer's zodiac only shewed _every other_ degree in the divisions round its border. This border is divided by help of a table of right ascensions of the various degrees of the ecliptic, which is by no means easily done. See Note on l. 4 of this section. I may add that the _Rete_ is also called _Aranea_ or _Volvellum_; in Arabic, _Al´ancab[=u]t_ (the spider).

22. _The Label._ See fig. 6, Pl. III. The _label_ is more usually used on the _front_ of the instrument, where the _Rete_ and other plates revolve. The _rule_ is used on the _back_, for taking altitudes by help of the scale.

23. _The Almury_; called also _denticulus_, _ostensor_, or 'calculer.' In fig. 2, it may be seen that the edge of the _Rete_ is cut away near the head of Capricorn, leaving only a small pointed projecting tongue, which is the almury or denticle, or (as we should now say) pointer. As the _Rete_ revolves, it points to the different degrees of the border. See also fig. 9, where the almury is plainly marked.