PROBLEM III.
The Sun’s Altitude being given at any time either before or after Noon, to find the Hour of the Day, and the Variation of the Compass, in any known Latitude.
With one hand hold the edge of the Quadrant right against the Sun; and, with the other hand, turn the Globe westward, if it be in the forenoon, or eastward if it be in the afternoon, until the Sun’s place at the inner edge of the Ecliptic cuts the Quadrant in the Sun’s observed Altitude; and then the Hour Index will point out the time of the day, and the Quadrant will cut the true Azimuth, or Bearing of the Sun for that time: the difference between which, and the Bearing shewn by the Azimuth Compass, shews the variation of the Compass in that place of the Earth.
The Trajectorium Lunare.
[PL. VII.] Fig. V.
440. The Trajectorium Lunare. This Machine is for delineating the paths of the Earth and Moon, shewing what sort of Curves they make in the etherial regions; and was just mentioned in the 266th Article. S is the Sun, and E the Earth, whose Centers are 81 Inches distant from each other; every Inch answering to a Million of Miles § [47]. M is the Moon, whose Center is 24⁄100 parts of an Inch from the Earth’s in this Machine, this being in just proportion to the Moon’s distance from the Earth § [52]. AA is a Bar of Wood, to be moved by hand round the Axis g which is fixed in the Wheel Y. The Circumference of this Wheel is to the Circumference of the small Wheel L (below the other end of the Bar) as 3651⁄4 days is to 291⁄2; or as a Year is to a Lunation. The Wheels are grooved round their edges, and in the Grooves is the cat-gut string GG crossing between the Wheels at X. On the Axis of the Wheel L is the Index F, in which is fixed the Moon’s Axis M for carrying her round the Earth E (fixed on the Axis of the Wheel L) in the time that the Index goes round a Circle of 291⁄2 equal parts, which are the days of the Moon’s age. The Wheel Y has the Months and Days of the year all round it’s Limb; and in the Bar AA is fixed the Index I, which points out the Days of the Months answering to the Days of the Moon’s age, shewn by the Index F, in the Circle of 291⁄2 equal parts at the other end of the Bar. On the Axis of the Wheel L is put the piece D, below the Cock C, in which this Axis turns round; and in D are put the Pencils e and m, directly under the Earth E and Moon M; so that m is carried round e as M is round E.
It’s use.
Lay the Machine on an even Floor, pressing gently on the Wheel Y to cause its spiked Feet (of which two appear at P and P, the third being supposed to be hid from sight by the Wheel) enter a little into the Floor to secure the Wheel from turning. Then lay a paper about four foot long under the Pencils e and m, cross-wise to the Bar: which done, move the Bar slowly round the Axis g of the Wheel Y; and, as the Earth E goes round the Sun S, the Moon M will go round the Earth with a duly proportioned velocity; and the friction Wheel W running on the Floor, will keep the Bar from bearing too heavily on the Pencils e and m, which will delineate the paths of the Earth and Moon, as in Fig. 2d, already described at large, § [266], [267]. As the Index I points out the Days of the Months, the Index F shews the Moon’s age on these Days, in the Circle of 291⁄2 equal parts. And as this last Index points to the different Days in it’s Circle, the like numeral Figures may be set to those parts of the Curves of the Earth’s Path and Moon’s, where the Pencils e and m are at those times respectively, to shew the places of the Earth and Moon. If the Pencil e be pushed a very little off, as if from the Pencil m, to about 1⁄40 part of their distance, and the Pencil m pushed as much towards e, to bring them to the same distances again, though not to the same points of space; then as m goes round e, e will go as it were round the Center of Gravity between the Earth e and Moon m § [298]: but this Motion will not sensibly alter the Figure of the Earth’s Path or the Moon’s.
If a Pin as p be put through the Pencil m, with its head towards that of the Pin q in the Pencil e, its head will always keep thereto as m goes round e, or as the same side of the Moon is still obverted to the Earth. But the Pin p, which may be considered as an equatoreal Diameter of the Moon, will turn quite round the Point m, making all possible Angles with the Line of its progress or line of the Moon’s Path. This is an ocular proof of the Moon’s turning round her Axis.
The Tide Dial.
[PLATE IX]. Fig. VII.
It’s use.
441. The Tide-Dial. The outside parts of this Machine consist of, 1. An eight-sided Box, on the top of which at the corner is shewn the Phases of the Moon at the Octants, Quarters, and Full. Within these is a Circle of 291⁄2 equal parts, which are the days of the Moon’s age accounted from the Sun at New Moon round to the same again. Within this Circle is one of 24 hours divided into their respective Halves and Quarters. 2. A moving elliptical Plate painted blue to represent the rising of the Tides under and opposite to the Moon; and has the words, High Water, Tide falling, Low Water, Tide rising, marked upon it. To one end of this Plate is fixed the Moon M by the Wire W, and goes along with it. 3. Above this elliptical Plate is a round one, with the Points of the Compass upon it, and also the names of above 200 places in the large Machine (but only 32 in the Figure to avoid confusion) set over those Points on which the Moon bears when she raises the Tides to the greatest heights at these Places twice in every lunar day: and to the North and South Points of this Plate are fixed two Indexes I and K, which shew the times of High Water in the Hour Circle at all these places. 4. Below the elliptical Plate are four small Plates, two of which project out from below its ends at New and Full Moon; and so, by lengthening the Ellipse shew the Spring Tides, which are then raised to the greatest heights by the united attractions of the Sun and Moon § [302]. The other two of these small Plates appear at low water when the Moon is in her Quadratures, or at the sides of the elliptic Plate, to shew the Nepe Tides; the Sun and Moon then acting cross-wise to each other. When any two of these small Plates appear, the other two are hid; and when the Moon is in her Octants they all disappear, there being neither Spring nor Nepe Tides at those times. Within the Box are a few Wheels for performing these Motions by the Handle or Winch H.
Plate XIII.