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the same plane with it, which may be done if yoU have but the least glimpse of the sun through A cloud; hold a string in both hands, it having first been put between the strong brass meridian and the globe; stretch it at right angles to the meridian, and apply your face near to the globe, moving your eye lower and lower, till you can but just see the sun; then bring the string held as before to this point upon the globe, that it may just obscure the sun from your sight, and the degree on the aforesaid hour circle, which the string then lies upon, will be the sun's altitude required, for his rays would shew the same point if he shone out bright.
Note. The moon's altitude may be observed by either of these methods, and the altitude of any star by the last of them.
Problem xxxv. To place the terrestrial globe in the suns rays, that It may represent the natural position of the earth, either by a meridian line, or without it.
If you have a meridian line, set the north and south points of the broad paper circle directly over it, the north pole of the globe being elevated to the latitude of the place; and standing upon a level plane, bring the place you are in under the graduated side of the strong brass meridian, then the poles and parallel circles upon the globe will, without sensible error, correspond with those in the heavens, and each point, kingdom, and state, will be turned towards the real one which it represents,
If you have no meridian line, then the day of the month being known, find the sun's declination as before instructed, which will direct you to the parallel of the day, amongst the polar parallels, reckoned from either pole towards the polar circle; which you are to remember.
Set the globe upon your horizontal plane in the sun-shine, and put it nearly north and south by the mariner's compass, it being first elevated to the latitude of the place, and the place itself brought under the graduated side of the strong brass meridian; then mova the frame and globe altogether, till the shade of extuberancy, or term of illumination, just touches the pojar parallel for the day, and the globe will be settled as before; and, if accurately performed, the variation of the magnetic needle will be shewn by the degree to which it points in the compass-box.
And here observe, if the parallel for the day should not happen to fall on any one of those drawn upon the globe, you are to estimate a proportionable part between them, and reckon that the parallel of the day. If we had drawn more, the globe would have been confused.
The reason of this operation is, that as the sun illuminates half the globe, the shade of extuberancy will constantly be 90 degrees from the point wherein the sun is vertical.
I? th,e sun be in the equator, the shade and illumination must terminate in the poles of the world; and when he is in any other diurnal parallel, the terms of illumination must fall short of, or go beyond either pole, as many degrees as the parallel which the sun describes, that day is distant from the equator; therefore, when the shade of extuberancy touches the polar parallel for the day, the artificial globe will be in the same position, with respect to the sun, as the earth really is, and will be illuminated in the same manner.
Problem xxxvi. To find naturally the suns declination, diurnal parallel, and hit place thereon.
The globe being set upon an horizontal plane, and adjusted by a meridian line or otherwise, observe upon which, or between which polar parallel the term of illumination falls ; its distance from the pole is the degree of the sun's declination; reckon the distance from the equator among the larger parallels, and you have the parallel which the sun describes that day; upon which, if you move a card, cut in the form of a double square, until its shadow falls under itself, you will obtain the very place upon that parallel over which the sun is vertical at any hour of that day, if you set the place you are in under the graduated side of the strong
Note. The moon's declination, diurnal parallel,
and place, may be found in the same manner. Likewise, when the sun does not shine bright, his declination, &c. may be found by an application in the manner of problem xxxiv.
Problem xxxvn. To Jind the sun's azimuth naturally.
If a great circle, at right angles to the horizon, passes through the zenith and nadir, and also through the sun's centre, its distance from the meridian in the morning or evening of any day, reckoned upon the degrees of the inner edge of the broad paper circle, will give the azimuth required.
Elevate either pole to the position of a parallel sphere, by bringing the north pole in north latitude, and the south pole into south latitude, into the zenith of the broad paper circle, having first placed the globe upon your meridian line, or by the other method before described; hold up a plumb-line, so that it may pass freely near the outward edge of the broad paper circle, and move it so that the shadow of the string may fall upon the elevated pole; then cast your eye immediately to its shadow on the broad paper circle, and the degree it there falls upon is the sun's azimuth at that time, which maybe reckoned from either the south or north points of the horizon.
If you have only a glimpse, or faint sight of the sun, the globe being adjusted as before, stand on the shady side, and hold the plumb-line on that side also, and move it till it cuts the sun's centre, and the elevated pole at the same time ; then cast your eye towards the broad paper circle, and the degree it there cuts is the sun's azimuth, which must be reckoned from the opposite cardinal point.
Problem xxxvin. To shew that in some places of the earths surface, the sun will be twice on the same azimuth in the morning, and twice on thesame azimuth in the afternoon: or in other words,
When the declination of the sun exceeds the latitude of any place, on either side of the equator, the sun will be on the same azimuth twice in a morning, and twice in the afternoon,
Thus, suppose the globe rectified to the latitude of Antigua, which is about 17 degrees of north latitude, and the sun to be in the beginning of Cancer, or to have the greatest north declination; set the quadrant of altitude to the 21st degree north of the east in the horizon, and turn the globe upon its axis, the sun's centre will be on that azimuth at 6h. 3O min. and also at 1O h. 3O min. in the morning. At 8 h. 30 min. the sun will be as it were stationary, with respect to its azimuth, for some time; as it