A tutor to astronomie and geographie, or, An easie and speedy way to know the use of both the globes, coelestial and terrestrial in six books : the first teaching the rudiments of astronomy and geography, the 2. shewing by the globes the solution of astronomical & geographical probl., the 3. shewing by the globes the solution of problems in navigation, the 4. shewing by the globes the solution of astrological problemes, the 5. shewing by the globes the solution of gnomonical problemes, the 6. shewing by the globes the solution of of [sic] spherical triangles : more fully and amply then hath ever been set forth either by Gemma Frisius, Metius, Hues, Wright, Blaew, or any others that have taught the use of the globes : and that so plainly and methodically that the meanest capacity may at first reading apprehend it, and with a little practise grow expert in these divine sciences / by Joseph Moxon ; whereunto is added Antient poetical stories of the stars, shewing reasons why the several shapes and forms are pictured on the coelestial globe, collected from Dr. Hood ; as also a Discourse of the antiquity, progress and augmentation of astronomie.

PROB. XLVII.

To find in what different Places of the Earth the Sun hath the same Altitude, at the same time.

FInd by the former Probleme in what Place of the Earth the Sun is in the Zenith, and bring that Place on the

Globe to the Zenith, and on the Meridian [there] screw the Quadrant of Altitude, and turn it about the Horizon, de∣scribing degrees of Almicantars thereby, as by Prob. 23. and all those Countries in any Almicantar on the Globe shall have the Sun Elevated the same number of degrees above their Horizon. Thus those Countries in the tenth Almicantar shall have the Sun Elevated 10. degrees above their Horizon; those in the 20^th Almicantar shall have the Sun Elevated 20 degrees above their Horizon; those in the 30^th, 30. degrees &c. So that you may see, when the Sun is in the Zenith of any Place, All the Countries or Cities in any Almicantar have the Sun in one heighth at the same time above their Horizon. But to find in what different Places the Sun hath the same heighth at the same time, as well Before or After Noon, as at Full Noon; and that in Countries that have greater Latitude then the Suns greatest Declination, (and therefore cannot have the Sun in their Zenith,) requires another Operation.

Therefore, Elevate its respective Pole according to your re∣spective Latitude; and let the Degree of the Brazen Meridian which is in the Zenith represent your Habitation, and the degree of the Ecliptick the Sun is in represent the Sun: Then bring the Sun to the Meridian, and the Index of the Hour-Circle to 12, and turn the Globe Eastwards, if Before Noon, or Westwards, if After Noon, till the Index point to the Hour of the Day: Then place the lower end of the Quadrant of Altitude to the East point of the Horizon, and move the upper end (by sliding the Nut over the Meridian) till the edge of the Quadrant touch the place of the Sun: Then see at what degree of the Meridian the upper end of the Quadrant of Altitude touches the Meridian and substract that number of Degrees from the Latitude of your Place, and count the number of remaining degrees on the Meridi∣an, on the contrary side the degree of the Meridian where the up∣per end of the Quadrant of Altitude touches the Meridian, and where that number of degrees ends on the Meridian, in that La∣titude and your Habitations Longitude, hath the Sun the same heighth at the same time.

Example.

May 10. at 53. minutes past 8. a clock in the Morning I

would know in what Place the Sun shall have the same Alti∣tude it shall have at London, London's Latitude found by Prob. 1. is 51½ degrees Northwards: And because the Elevation of the Pole is equal to the Latitude of the Place (as was shewed Prob. 15.) Therefore I Elevate the North Pole 51½ degrees, so shall 51½ degrees on the Meridian be in the Zenith: This 51½ degrees on the Meridian represents London. The Suns Place found by Prob. 3. is ♉ 29. Therefore I bring ♉ 29 to the Meridian, and the Hour Index to 12. on the Hour Circle: Then I turn the Globe Eastwards (because it is before Noon) till the Index point at 8. hours 53 minutes on the Hour-Circle, and place the lower end of the Quadrant of Altitude to the East point in the Horizon, and slide the upper end either North or Southwards on the Meridian till the graduated edge cut the degree of the Ecliptick the Sun is in: Then I examine on the Meridian what degree the up∣per end of the Quadrant of Altitude touches; which in this example, I find is 38½ degrees. Therefore I substract 38½ from 51½ Londons Latitude, and there remains 13. Then counting on the Meridian 13. degrees backwards, from the Place where the Quadrant of Altitude touched the Meridian, I come to 25½ on the Meridian, Northwards. Therefore I say, In the North Latitude of 25½ degrees, and in the Longitude of Lon∣don (which is in Africa, in the Kingdom of Numidia) the Sun May 10. at 53. minutes past 8. a clock in the Morning hath the same Altitude above the Horizon it hath here at London.

The Quadrant of Altitude thus applyed to the East point of the Horizon makes right angles with all points on the Meridian, even as all the Meridians proceeding from the Pole, do with the Equator: therefore the Quadrant being applyed both to the East point, and the Suns Place, projects a line to intersect the Me∣ridian Perpendicularly in equal degrees; from which intersection the Sun hath at the same time equal Heighth, be the degrees few or many; for those 5. degrees to the Northwards of this in∣tersection, have the Sun in the same heighth that they 5 degrees to the Southwards have it: and those 10, 20, 30. degrees, more, or less, to the Northwards, have the Sun in the same heighth that they have that are 10, 20. 30. degrees more or less to the Southwards: So that this Prob. may be performed ano∣ther way more easily, with your Compasses, Thus: Having first rectified the Globe, and Hour Index, Turn about the Globe till

the Hour Index point to the Hour of the Day; Then pitch one foot of your Compasses in the Suns Place, and extend the other to the degree of Latitude on the Meridian, which in this exam∣ple is 51½ degrees North; then keeping the first foot of your Compasses on the degree of the Sun, turn about the other foot to the Meridian, and it will fall upon 25½. as before.

Blaew commenting upon this Probleme, takes notice how grosly they ere that think they can find the heighth of the Pole at any Hour of the Day, by the Suns height: because they do not consider that it is impossible to find the Hour of the Day, unless they first know the height of the Pole.