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PROBLEM FOR SUNSHINE.

377

is generally made larger than the rest to distinguish the 90th degree, or Pole, the shadow of this needle will shew the longitude in which the sun is vertical at the time; for it will be cast upon* the opposite semicircle of the plane of the meridian of that place; and every semicircle has for its longitude the supplement † of the opposite one: In other words, the longitude of the place which then has a vertical sun, and of all others that are having noon, is just equal to the degrees of distance at which the needle-shadow falls from the under semicircle of the brass meridian.

Thus, suppose we were making this experiment at Greenwich at 22m. before 7 in the morning of 25th April or 18th August ;--if we search for the longitude of the spot upon which the shadow of the extremity of the needle falls, we shall find it to be 99 west; and subtracting this from 180, we shall get 80 for the east meridian on which the sun then is, or where it is noon.

*** If the globe have that very inconvenient appendage, an hourcircle outside the brass meridian, a small cone of wood (very easily formed with a penknife) might, for the time, be fitted and glued on to the extremity of the axis or pivot of the index.

4. If a fine needle be now stuck perpendicularly into the globe at that spot which has latitude equal to the sun's declination, and longitude such as that just found by means of the shadow, and the place of residence be again brought to the brass meridian, it will be seen that the sun is vertical to that spot, for the needle will cast no shadow.

Thus if, as before supposed, we were attending to this at 22 min. to 7 A.M., on 25th April or 18th August, we should find that (the sun having 131° of north dec.), the place having longitude 80 east and the sun in the zenith, must be Madras.

To ensure the perpendicular insertion of the needle, it is well to bring the place so found to the brass meridian and to be guided by

If, when the place of residence is coinciding with the brass meridian, the hour circle (under the meridian) be set to 12, the shadow cast by the needle will likewise give the hour. The shadow of the brass meridian sometimes interferes with this; but, even then, the meridian on which the extremity of the needle-shadow falls may be traced up to the hour corresponding with it.

180.

The supplement of any number of degrees is what it wants of

We need solar (sun-dial) time for this :--On the two days supposed there is very little difference between the sun-dial and the clock; but the difference for any day may be found in the little table of the equation of time given a few pages onward.

the graduation in inserting it. Very fine needles may be so stuck into the globe as not to injure it.

5. If we measure 45° around this spot by means of the quadrant (or a piece of white thread marked with that length), and stick fine needles perpendicularly into several places so situated; then, whilst the needle stuck into the place having the sun vertical casts no shadow, each of these others will cast a shadow exactly equal to its length; for the sun, at each of the places represented by those spots, is 45° from the zenith, and therefore 45° high. (X, on p. 13.)

Thus Tobolsk-Pekin (nearly)—the S. E. part of Celebes-Cape St. Andrew (Madagascar)—Jerusalem-Damascus—the eastern shore of the Black Sea, &c., are all 45° distant from Madras; and needles inserted perpendicularly into the globe-surface at these places, will, at this time, cast shadows equal to their lengths; but all of course differing in their direction, and shewing, so far, the opposite bearings of the sun at those several places.

6. If a needle be stuck into each of the temperate zones,one at a spot due north, and the other at a spot due south, of the place having the sun vertical; and a third needle in the enlightened frigid zone;—it will be seen that, whilst the inhabitants of the temperate zones are Heteroscii (def. 74), and those having a vertical sun are Ascii (def. 73),—the inhabitants of the frigid zone are Periscii (def. 75), because, as the globe rotates, their shadow falls in every possible direction with regard to the North Pole.

7. If the globe could be placed even where the moon is at the time (provided that the plane on which it stood were, like that on which it now stands, parallel to our horizon, and its meridian, as now, were due north and south), then the several circumstances already mentioned-the bearings and lengths of shadows, &c.—would differ in no perceptible degree from those shewn on the globe here; for the separation of the moon from the earth being only about onefour-hundredth of the distance of either from the sun, he may be regarded as shining on both as if they were together.

DIALLING.

379

DIALLING.

THE HORIZONTAL DIAL. THE VERTICAL DIAL.

K We have just seen (note, p. 377)* that when our terrestrial globe is arranged in the sunshine, with due regard to its horizon and the plane of the meridian, the needle,† which is but a prolongation of the axis, will cast its shadow on the opposite semi-meridian to that on which the sun is shining, and that it may thus be used to mark solar time, if we refer its shadow upward to the horary circle or index when the twelves of that circle are coinciding with the brass meridian, or our own plane.

It will be equally easy to see, that, however long the needle may be, provided it be straight and well adjusted to the axis, its shadow will fall along the meridian opposite to the sun; and thus, if it were long enough, its shadow would even fall upon the horizon of the globe, exactly where the shadowed semi-circle meets that wooden circle. Hence, if we were to mark the wooden horizon where it is cut by the several meridians, with the hours, &c., to which those meridians correspond, the prolonged shadow of the needle would shew us the time on that also.

The common horizontal sun-dial is a construction upon this principle:

The whole axis of the earth, or globe, is in the plane of every meridian (G and its note, p. 9), and therefore, if we suppose the terrestrial globe, with all its meridians, to be removed from its frame, and its axis only to be left, (inclined as before, to the latitude,) the shadow cast by the axis will be identical with the shadow of any meridian that the sun may be shining opposite to, and will as faithfully shew the time on our horizon, so marked as we have supposed.

* If there have been no opportunity for performing Problem R in the sunshine, it must at least be read over very carefully before attending to what follows here.

* See n in the figure on the next page.

By rectifying the globe for several latitudes, the pupil will perceive,

1. That each different elevation of the pole causes a difference in the points at which the meridians, or their shadows, intersect the horizon:

Thus, with an elevation of the pole for 24° or 30° it will be seen, that on a dial constructed for so low a latitude the hour-arcs nearer to the north point (or XII) will be very small, and those nearer to VI, or the east and west points, will be much greater; whereas, with an elevation of the pole for 60o, or even for our own latitude (514°), those hour-arcs are more nearly equal.

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2. And hence, that the "Gnomon" or horizontal sun-dial must be placed in position with the axis of the earth, by being set in the plane of the meridian with an inclination according with the latitude, or it will not shew the time upon the face of the dial, however correctly the face may be marked.

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Let the adjoining figure represent a transparent globe with the usual meridian lines marked upon it. Let c be its centre, and ne that half of its axis which is above (or northward) of R Z Z R, the plane of the rational horizon :

Then n may represent the needle we have supposed to be attached to the north pole (3 on p. 376)-k, l, m, o, &c., meridians of the eastern hemisphere, and I, II, III, IIII, V, VI, &c., the points at which they intersect the horizon, when the pole is elevated for lat. 5140,-the numbers IIII, V, VI, VII, VIII. &c., (seen through the globe,) marking the points of similar intersection of the western horizon, by the semi-meridians opposite.

TABLE OF EQUATION OF TIME.

381

It is evident that when the sun is "on" the "first meridian," or ue south, the shadow of the axis, or of the opposite semi-circle, will De cast on XII, or the due north of the horizon; but that when the un is yet only on g, (15° eastward, or an hour earlier,) this shadow of the axis, or of the opposite semi-circle, will fall on XI; when he s only on h, (and giving noon in 30° east longitude,) this shadow vill fall on X, &c., &c.

COMPARED WITH A WELL-REGULATED CLOCK, ON THE DAYS GIVEN BELOW, THE SUN-DIAL IS

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