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The first of these six varieties which I call an Equinoctial plane, is in the fundamen∣tal Scheme, & also in this, represented by the six of clock hour-circle EPW, wherein you may observe out of the Scheme it self
you may conclude, that the hour-lines thereof have no center to meet in, but must be parallel one to another, as they were in the East and West Dialls.
And because this Diall is no other but the very horizontall of a right Sphere, where the Equinoctial is Zenith, and the Poles of the world in the Horizon; there∣fore it is not capable of the six of clock hour (no more then the East and West are of the 12 a clock hour) which vanish upon the planes, unto which they are parallel: and the twelve a clock hour is the middle line of this Diall (because the Meridian cut∣teth the plane of six a clock at right an∣gles) which the Sun attaineth not, till he be perpendicular to the plain. And this in my opinion, besides the respect of the poles, is reason enough to call it an Equinoctiall Diall, seeing it is the Diall proper to them that live under the Equinoctiall.
This Diall is to be made in all respects as the East and West were, being indeed the very same with them, onely changing the numbers of the hours: for seeing the six of clock hour in which this plane lieth crosseth the twelve of clock hour at right angles, in which the East and West plane lieth, the rest of the hour-lines will have equall respect
unto them both: so that the fifth hour from six of the clock is equal to the fift hour from twelve; the four to the four; and so of the ••est. These analogies holding, the hour di∣stances from six are to be set off by the natu∣ral tangents in these Dials, as they were from twelve in the East and West Dials.
Draw the tangent line DSK, parallel to the line EZW in the Scheme, crosse it at right angles with MSA the Meridian line, make SA the Radius to that tangent line, on which prick down the hours; and that there may be as many hours upon the plane as it is capable of, you must proportion the stile to the plane (as in the fifth Problem) after this manner: let the length of the plane from A be given in known parts, then because the extream hours upon this plane are 5 or 7, reckoning 15 degrees to every hour from 12, the arch of the Equator will be 75 degrees: and therefore in the right angled plain triangle SA ♎, we have given the base A ♎, the length of the plane from A, and the angle AS ♎ 75 degrees, to finde the perpendicular SA; for which, as in the fifth Chapter, I say;
| As the Radius 90, | 10.000000 |
| Is to the base A ♎ 3.50. | 2.544068 |
| So is the tangent of A ♎ S 15 | 9,428052 |
| To the perpendicular AS 94 | 1.972120 |
At which height a stile being erected over the 12 a clock hour line, and the hours from
12 drawn parallel thereunto through the points made in the tangent line, by setting off the natural tangents thereon, and then the Diall is finished.
Let SA 12 be placed in the meridian, and the whole plane at S raised to the height of the pole 51 degr. 53 min. then will the stile shew the hours truly, and the Diall stand in its due position.