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. IX.

To make Erect South Dyals, Declining Eastwards, or Westwards.

DRaw on your Plane an Horizontal line, and on it discribe a Semi-Circle, as you were taught in Prob 4.

Then Rectifie the Globe, Quadrant of Altitude Colure and Hour Index▪ as by the same Probleme: and bring the lower end of the Quadrant of Altitude to the degree of Declination from the East or West point, according is your Declination is Eastwards or Westwards; for then the Quadrant of Altitude shall represent a Plane declining from the South E••stwards, or Westwards accordingly. Then tu••n the Globe Eastwards, till the Index of the Hour-Circle points to all the Hours before Noon, and examine in what number of degrees from the Zenith the Colure cuts the Q••••drant of Altitude, when the Index points to each Hour, For a line drawn from the Center A through the

same number of degrees reckoned from the Perpendicular A B, which is the 12 a clock line towards Con the Plane, shall be the same Hour-lines the Index points at.

Example.

I would make an Erect Dyal declining from the South to∣wards the East 27. degrees: The Globe, Quadrant of Altitude, Vernal Colure, and Hour Index Rectified, as before, I bring the lower end of the Quadrant of Altitude to 27. degrees counted from the East point of the Horizon towards the North: Then

I turn the Globe East-wards till the Index points to	11	a clock, or till 15. deg. of the Equa∣tor pass through the Meridian, and find the Colure cut the Quadrant of Altitude in	9.43	counted from the Zenith.
10	19.0
9	25.57
8	35.10
7	45.56
6	60.15
5	79.45

And these are the distances of the Fore-noon Hour-lines, which I seek in the West side of the Plane, viz. from B to∣wards C; and through these distances I draw lines from the Cen∣ter, and these lines shall be the Fore-noon Hour-lines.

Now herein is a difference between Declining Dyals, and Di∣rect Dyals: For having found the distances of the Hour lines for one half of the Day, be it either for Before Noon or After Noon in a Direct Dyal, you have also found the distances for the other half Day; because, as was said Prob. 3. Equal number of Hours have equal distance from the Noon line: But in Declining Dy∣als it is not so: Because the Sun remaining longer upon that side of the Plane which it declines to, then it doth upon the contrary side, there will be a greater number of Hour lines upon it, and by consequence the distance of the Hour lines less then on the con∣trary side of the Plane.

Therefore for finding the After Noon Hour lines, I turn about the Quadrant of Altitude upon the Zenith point till the lower end of it come to the degree of the Horizon opposite to that de∣gree of Declination that the Quadrant of Altitude was placed at when I sought the Fore Noon Hour lines, viz, to 27. degrees

counted ••om the West towards the South, and bring the Ver∣••al Colure again to the Meridian, and the Index (as before) to 12. Then,

turning the Globe Westwards till the Index poin••s to	1	a clock, or till 15 degr. of the Equator pass through the Me∣ridian, I find the Colure cut the Quadrant of Altitude in	11.20	counted from the Zenith.
2	26.47
3	49.20
4	75.52

And these are the distances of the After Noon Hour lines; which dista•••••••• I seek in the East side of the Plane, viz. from B towards D (as before) and so drawing lines from the Center A through these distances, I have all the Afternoon Hour lines also drawn on my Plane.

You may note, that this Plane is capable to receive no more Hour lines After Noon then 4. for when the Colure goes off the Quadrant of Altitude, the Sun goes off these kind of Planes.

To these Hour lines I set their numbers, as you may see i•• the Figure.

Then to find both the distances of the Substilar line from the 12 a clock line, and the Elevation of the Style above the Plane, Bring the Colure to the number of degrees of the Planes Decli∣nation, counted in the Horizon from the South point towards the East point, and the Quadrant of Altitude to the degrees of the Planes Declination, counted in the Horizon from the East point to∣wards the North so shall the Quadrant of Altitude and the Co∣lure cut each other at Right Angles; and the number of degrees comprehended between the Colure and the Zenith in the Qua∣drant of Altitude, shall be the number of degrees between the Sub∣styler line and the 12. a clock line, which in this Example is 19. degrees 45. minutes: And the number of degrees comprehended between the Quadrant of Altitude and the Pole, counted in the Colure, shall be the number of degrees that the Style is to be Ele∣vated above the Plane; which in this Example is 33. degrees 40. minutes. Wherefore for the distance of the Substyler line from the 12 a clock line, I count in the Circle from the 12 a clock line in the contrary side of the Plane, viz. in the West side, because the Plane declines towards the East 19. degrees 45▪ minutes, as at D, and through that number of degrees and minutes from the Center A, I draw the line A G, which shall be the Substyl••r line: And from the Substylar line (either way) I number 33. de∣grees 40. minutes, the Elevation of the Style above the Plane, and

through those degrees and minutes I draw from the Center A, the line A F, for the Style or Gnomon; Then I let fall the Per∣pendicular F G upon the Substyle A G: So is there a Triangle

[illustration]

made, which if it be erected Perpendicularly upon the Substyle A G, the Style A F shall be Parallel to the Axis of the World, and cast a shadow upon the Hour of the Day.

Here you may see that in Declining Dyals the Style doth not stand at the same Elevation above the Plane, that it doth in Erect Direct Dyals; neither doth it stand over the 12 a clock line; but swerves from it towards the Quarter of Declination.