The English globe being a stabil and immobil one, performing what the ordinary globes do, and much more / invented and described by the Right Honorable, the Earl of Castlemaine ; and now publish't by Joseph Moxon ...

OPERATION XII. How to describe an East or West Dial Geometrically for the Elevation of London.

DRAW the blind Line H h and cross it from your left hand (as in Sch. 13.) with AE ae another blind-line to make an Angle at their Intersection K equal to the Complement of the Elevation, then pricking in the said Line AE ae on the right side of K, the respective Tangents of 15. 30 45. 60. and 75 De∣grees, as also on the left the Tangents of 15 and 30, Draw but Perpendiculars through the Pricks, and you have an East-Dial; whereas should you cross (as in Sch. 14.) H h with AE ae from the right hand, and pricking the aforesaid Tangents the other way, draw Perpendiculars through them, you would have a West-Dial. By these Schemes also you may know how each Dial is to be Figur'd, the East-Dial containing (as you see) all the hours from 4 in the morning 'till Noon: and the West all the hours from Noon to 8 at Night. Now for their Cocks, they are (as I said, in the last Operation) to be a Pin, or a Gal∣lowes Stile, and in height equal to the Tangent of 45. Degrees, or distance between the 9 or 3 a Clock hour Lines and that of six, which is ever their Substilar.

These Dials must be true, if their Planes lye in or Parallel to the Meridian; for since the Line H h, by being plac'd ac∣cording

to our Hypothesis horizontal, represents the intersecti∣on of the Horizon, and the line AE ae that of the Aequator, by ma∣king an Angle with the said H h equal to the complement of the Elevation, the substilar must be the Intersection of the Aequinocti∣al Colure (or 6 a Clock hour Circle) with the Plane, since that Hour-Circle falls on the Plane at right Angles. If then a Gallows Stile be set on the said Substilar and Perpendicular to it, its Shade must needs constantly cross the Aequator AE ae at right Angles. Now when the Sun is in the Plane of the 6 a clock hour Circle, his Ray makes no Angle with the said Stile, because the Sun, and the Stile are in the same Plane, and so the shade falls directly along the Substilar; but when he gets (for examples sake) into the next hour Circle, his Ray (the height of the Stile being Radius) makes an Angle of 15 Degrees with the said Stile, and conse∣quently the distance of the two shades are in the line AE a the Tangent of those Degrees. The like therefore being said of the next Hour Circle and so on, it follows (as I mention'd in the beginning) that the pricking from the intersection K, the Tangents of 15, 30, 45, 60 and 75 Degrees in the line AE ae, must give you points to draw the perpendiculars or true hour-lines of this Dial by, as also, that the Tangent of 45 Degrees gives the height of the Stile, since the Tangent of those Degrees, (which you see gives the 3 and 9 a clock lines) is equal to the Radius.

Here also we see not only why these hour-lines are so unequally distant, since they are so many Parallels mar∣shall'd according to the Divisions of a Tangent line, but why the 12 a Clock hour line can never be really express'd, for 'tis the Tangent of 90 Degrees which is infinite.

Notes

• The Constru∣ction.
• The Demon∣stration.
• The reason of the unequal distance of these hour∣lines.