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will appear by placing the quadrant of altitude to the 17th degree north of the east in the horizon. If the quadrant be set to the same degrees north of the west, the sun's centre will cross it twice as it approaches the horizon in the afternoon.
This appearance will happen more or less to all places situated in the torrid zone, whenever the sun's declination exceeds their latitude ; and from hence we may infer, that the shadow of a dial whose gnomon is erected perpendicular to an horizontal plane, must necessarily go back several degrees on the same day
But as this can only happen in the torrid zone, and as Jerusalem lies about 8 degrees to the north of the tropic of Cancer, the retrocession of the shadow on the dial of Ahaz, at Jerusalem, was, in the strictest signification of the word, miraculous.
PROBLEM XXXIX. To observe the hour of the day in the most natural manner, when the terrestrial globe is properly placed in the sun-shine.
There are many ways to perform this operation with respect to the hour, three of which are here inserted, being general to all the inhabitants of the earth ; a fourth is added, peculiar to those of London, which will answer, without sensible error, at any place not exceeding the distance of 60 miles from this capital.
By a natural Style.
Having rectified the globe as before directed, and placed it upon an horizontal plane over your meridian line, or by the other method, hold a long pin upon the illuminated pole, in the direction of the polar axis, and its shadow will shew the hour of the day amongst the polar parallels.
The axis of the globe, being the common section of the hour circles, is in the plane of each; and as we suppose the globe to be properly adjusted, they will correspond with those in the heavens; therefore the shade of a pin, which is the axis continued, must fall upon the true hour circle.
II. By an artificial Style
Tie a small string, with a noose, round the elevated pole, stretch its other end beyond the globe, and move it so that the shadow of the string may fall upon the depressed axis ; at that instant its shadow upon the equator will give the solar hour to a minute.
But remember, that either the autumnal or vernal equinoctial colure must first be placed under the graduated side of the strong brass meridian, before you observe the hour, each of these being marked upon the equator with the hour XII.
The string in this last case being moved into the
plane of the sun, corresponds with the true hour circle, and consequently gives the true hour.
III. Without any style at all.
Every thing being rectified as before, look where the shade of extuberancy cuts the equator, the colure being under the graduated side of the strong brass meridian, and.you obtain the hour in two places upon the equator, one of them going before, and the other following the sun.
Note. If this shade be dubious, apply a pin, or your finger, as before directed.
The reason is, that the shade of extuberancy being a great circle, cuts the equal in half, and the sun, in whatsoever parallel of declination he may happen to be, is always in the pole of the shade; consequently the confines of light and shade will shew the true hour of the day.
IV. Peculiar toʻthe inhabitants of London, and any place within the distance of sixty miles from it.
The globe being every way adjusted as before, and London brought under the graduated side of the strong brass meridian, hold a plumb-line, so that its shadow may fall upon the zenith point, (which, in this case, is London itself) and the shadow of the string will cut the parallel of the day upon that point to which the sun is then vertical, and that
hour circle upon which this intersection falls is the hour of the day; and as the meridians are drawn within the tropics, at 20 minutes distance from each other, the point cut by the intersection of the string upon
the parallel of the day, being so near the equator, may, by a glance of the observer's
be referred thereto, and the true time obtained to a minute.
The plumb-line thus moved is the azimuth; which, by cutting the parallel of the day, gives the sun's place, and consequently the hour circle which intersects it.
From this last operation results a corollary, that gives a second way of rectifying the globe to the
If the azimuth and shade of the illuminated axis agree in the hour when the globe is rectified, then making them thus to agree, must rectify the globe.
COROLLARY. Another method to rectify the globe
to the sun's rays.
Move the globe, till the shadow of the plumb-line, which passes through the zenith, cuts the same hout on the parallel of the day that the shade of the pin, held in the direction of the axis, falls upon amongst the polar parallels, and the globe is rectified.
The reason is, that the shadow of the axis repre , sents an hour circle; and by its agreement in the same hour, which the shadow of the azimuth string points out, by its intersection on the parallel of the day, it shews the sun to be in the plane, of the said
parallel ; which can never happen in the morning on the eastern side of the globe, nor in the evening on the western side of it, but when the globe is rectified.
This rectification of the globe is only placing it in such a manner, that the principal great circles and points may concur and fall in with those of the heavens.
The many advantages arising from these problems, relating to the placing of the globe in the sun's rays, the tutor will easily discern, and readily extend to his own, as well as to the benefit of his pupil.