ridian line drawn on the place over which you substitute this horizontal plane, it may be readily transferred from thence to the surface just levelled; this being done, we are prepared for the solution of the following problems.

It will be necessary to define a term we are obliged to make use of in the solution of these problems, namely, the shade of extuberancy: by this is meant that shade which is caused by the sphericity of the globe, and answers to what we have heretofore named the terminator, defining the boundaries of the illuminated and obscure parts of the globe; this circle was, in the solution of some of the foregoing problems, represented by the broad paper circle, but is here realized by the rays of the sun.

PROBLEM XXXIV. To observe the sun's altitude, by the terrestrial globe, when he shines bright, or when he can but just be discerned through a cloud.

Elevate the north pole of the globe to 66 degrees; bring that meridian, or hour circle, which passes through the IXth hour upon the equator, under the graduated side of the strong brass meridian; the globe being now set upon the horizontal plane, turn it about thereon, frame and all, that the shadow of the strong brass meridian may fall directly under itself; or, in other words, that the shade of its graduated face may fall exactly upon the aforesaid hour circle: at that instant the

shade of extuberancy will touch the true degree of the sun's altitude upon that meridian, which passes through the IXth hour upon the equator, reckoned from the polar circle; the most elevated part of which will then be in the zenith of the place where this operation is performed, and is the same whether it should happen to be either in north or south latitude.

Thus we may, in an easy and natural manner, obtain the altitude of the sun, at any time of the day, by the terrestrial globe; for it is very plain, when the sun rises he brushes the zenith and nadir of the globe by his rays; and as he always illuminates half of it, (or a few minutes more, as his globe is considerably larger than that of the earth) therefore, when the sun is risen a degree higher, he must necessarily illuminate a degree beyond the zenith, and so on proportionably from time to time.

But, as the illuminated part is somewhat more than half, deduct 13 minutes from the shade of extuberancy, and have the sun's altitude with toyou

tuberancy reaches, hold a pin, or your finger, on the globe, between the sun and point in dispute, and where the shade of either is lost, will be the point sought.

When the sun does not shine bright enough to cast a shadow. Turn the meridian of the globe towards the sun, as before, or direct it so that it may lie in

the same plane with it, which may be done if yott 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 sun's rays, that it may represent the natural position of the earth, either by a meridian line, or without it.

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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 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 repre

sents.

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 move the frame and globe altogether, till the shade of extuberancy, or term of illumination, just touches the polar 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.

If the sun be in the equator, the shade and illu

mination 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 sun's de-. clination, diurnal parallel, and his 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 brass meridian.

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 decli