Today | News | Books | Recipes Adventure | Science Fiction | Ghost stories | Poetry | Children | History Bookg 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 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 Ot' 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 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, 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 the planet is _south_, its place cannot well be found when in Capricorn for want of space at the edge of the Astrolabe. As a second example, it will be found that, when Jupiter's longitude is at the _end_ of 1° of Pisces, and his latitude 3° south, he ascends together with the 14th of Pisces, nearly. This is easily verified by a globe, which solves all such problems very readily. It is a singular fact that most of the best MSS. leave off at the word 'houre,' leaving the last sentence incomplete. I quote the last five words--'þou shalt do wel y-now'--from the MS. in St. John's College, Cambridge; they also occur in the old editions. 41. Sections 41-43 and 41_a_-42_b_ are from the MS. in St. John's College, Cambridge. For the scale of _umbra recta_, see fig. 1, Plate I. Observe that the _umbra recta_ is used where the angle of elevation of an object is greater than 45°; the _umbra versa_, where it is less. See also fig. 16, Plate VI; where, if AC be the height of the tower, BC the same height _minus_ the height of the observer's eye (supposed to be placed at E), and EB the distance of the observer from the tower, then _bc_ : E_b_ :: EB : BC. But E_b_ is reckoned as 12, and if _bc_ be 4, we find that BC is 3 EB, i.e. 60 feet, when EB is 20. Hence AC is 60 feet, _plus_ the height of the observer's eye. The last sentence is to be read thus--'And if thy "rewle" fall upon 5, then are 5-12ths of the height equivalent to the space between thee and the tower (with addition of thine own height).' The MS. reads '5 12-p_ar_tyes þe hey[gh]t of þe space,' &c.; but the word _of_ must be transposed, in order to make sense. It is clear that, if _bc_ = 5, then 5 : 12 :: EB : BC, which is the same as saying that EB = 5/12 BC. Conversely, BC is 12/5 EB = 48, if EB = 20. 42. See fig. 1, Plate I. See also fig. 17, Plate VI. Let E_b_ = 12, _bc_ = 1; also E'_b'_ = 12, _b'c'_ = 2; then EB = 12 BC, E'B = 6 BC; therefore EE' = 6 BC. If EE' = 60 feet, then BC = 1/6 EE'=10 feet. To get the whole height, add the height of the eye. The last part of the article, beginning 'For other poyntis,' is altogether corrupt in the MS. 43. Here _versa_ (in M.) is certainly miswritten for _recta_, as in L. See fig. 18, Plate VI. Here E_b_ = E'_b'_ = 12; _b'c'_ = 1, _bc_ = 2. Hence E'B = 1/12 BC, EB = 2/12 BC. whence EE' = 1/12 BC. Or again, if _bc_ become = 3, 4, 5, &c., successively, whilst _b'c'_ remains = 1, then EE' is successively = 2/12 or 1/6, 3/12 or 1/4, 5/12, &c. Afterwards, add in the height of E. 44. Sections 44 and 45 are from MS. Digby 72. This long explanation of the method of finding a planet's place depends upon the tables which were constructed for that purpose from observation. The general idea is this. The figures shewing a planet's position for the last day of December, 1397, give what is called the _root_, and afford us, in fact, a _starting-point_ from which to measure. An 'argument' is the angle upon which the tabulated quantity depends; for example, a very important 'argument' is the planet's _longitude_, upon which its _declination_ may be made to depend, so as to admit of tabulation. The planet's longitude for the given above-mentioned date being taken as the _root_, the planet's longitude at a second date can be found from the tables. If this second date be less than 20 years afterwards, the increase of motion is set down separately for each year, viz. so much in 1 year, so much in 2 years, and so on. These separate years are called _anni expansi_. But when the increase during a large round number |