ftraction of 15 deg. you shall find 11 de. 05 m. to stand against F.g. the Hours of VII and V ; under which wrise The place of the Sub- LVIII. tile: And then, substract 11 d. 05 m. from 15 de. there will remain 3 de. 55 m. which must be set under the Sub-ftile, against the Hour of VI: And then, by the continual Addition of 15 deg. thereto; you shall have fuch Equinoctiol distances as are expressed in the Table, against the Hours of V and VII, and IV and VIII. Then

II. For the Five Hour distances upon the Plain: If you work by the Canon delivered in this last Chapter, you will find them to be fuch as are exhibited in the Third Column of this Table.

By this Table, you fee that the Five Hour Distances upon the Plain about the Sub-ftile (and indeed all the rest, except the extreme Hour of XII) do fall so near together, that without a very large extention of them from the Centre, there will be no competent distance between Hour-line and Hour-line: Wherefore, laying afide your Table, proceed to make your Dial Geometrically, according to the following Precepts.

III. The Geometrical Projection, of this (or the like) Dial: when the Pole hath but small Elevation above the Plain.

1. Draw a Right Line A B, perpendicular by one fide of your Fig. Plain, and towards the Right Hand, because the Plain declineth LIX. Eastward, And with 60 deg. of a Scale of Chords, describe an obfcure Arch of a Circle CDE; and upon it set 38 de. 23 m. the Sub-ftiles distance from the Meridian, from C to D, and draw the Line AD, for the Sub-ftile.

2. Take 3 deg. 6 m. the Stiles height; and set them from D to E, drawing the Line A E for the Stile of the Dial.

3. Now (because the Stile is but of small Elevation, viz. but 3 de. 6 m.) draw another Line GH, parallel to the Line of the Stile A E, at such convenient distance as in your judgment will best fit the Dial Plain, fo that the Hours belonging to it, may come within the Limits of the Plain: So shall that Line GH, so drawn, be the Augmented Stile of the Dial.

And, by the Sub-ftile, and this Augmented Stile, the Hour-
Lines may be described (at convenient distance) without
any regard had to the Centre of the Dial. For,

4. Assume any two points in the Sub-ftilar Line of the Dial AD, at some convenient distance from each other, as Rand S: and through those two points, draw two infinite Right lines, both

Ccc 2

of

Fig. of them at Right Angles to the Sub-ftilar Line AD ; as the Lines LIX. ZRZ and X S X.

5. Set one foot of your Compasses in the Point R, and take the nearest distance to the new Augmented Stile GH; and set that distance upon the Sub-ftilar Line ftom R to K.-Alfo from : the Point S, take the nearest distance to the Augmented Stile G H, and fet that distance also upon the Sub-ftilar Line, from S to L.

6. Upon these two Points Kand L, (with 60 de. of a Scale of Chords) describe two Semi-Circles: and in either of them set off 86 d. 05 m. (the Plains Difference of Longitude) from R to M, and from S to M, both of them on the fame fide of the Sub-ftilar Line, on which the first Perpendicular A B was drawn.

7. Divide either of the Semicircle into 12 equal parts (beginning at the points M) at the several points, &c. 8. Lay a Ruler to the point L, and to the several points

,&c. the Ruler will cross the Line XS X, in the points * * *, &c. Also, Lay a Ruler to K, and the respective Points &c. the Ruler will cross the Line Z R Z, in the several

Points * * *, &c.

Lastly, Lines-drawn from the several Points * * * in the Line ZR Z, to the several points * * * in the other Line X SX each to its Correspondent, (which the Sub-tilar Line will direct you) those Lines fo drawn shall be the true Hour-Lines proper for the Plain: And will be at a competent distance one from the other, as by the Figure they do appear; the fight whereof will be more fatisfactory than many Words.

Note, that in the making of this Dial, you have made four.
Dials, viz.

Eaft

South. Declining Weft

But you must change the Names of the Hours, and place the Stile
on the contrary fide of the Line. A B for the South Declining
Weft-And by turning the Dial upside downwards for the
North-decliners, so that the Stile may point upwards to the North
Pole; and the Hours about Midnight omitted: As in the last
Chapter is directed.

CHAP.

CHAP. Χ.

Of Direct South and North Declining Plains, and how
Hour-Lines may be described upon them.

UCH Plains as do directly behold the North

SUCH

South

point of the

Horizon, but do Recline (or fall backwards) from the Zenith towards

South

the North are

North

called { South } Direct Plains Reclining : So ma

ny Dgrees as the Reclination is: And of such Plains there are Six Varieties, Three of South, and Three of North Recliners : All which may be Reduced to New Latitudes, wherein they will bee come Horizontal Plains: And consequently Dials (or Hour Lines) may be described upon them both by the Globe, Spherical Projection, and Trigonometrical Calculation, according to the Precepts delivered in the Fourth Chapter hereof.

I. Of South Recliners

Examples of all these Varieties of Reclining Plains, in the La-
titude of London, 51 deg. 30 m. To find the New Lati-
tudes.

I. Variety. Let there be a Direct South Plain in the Latitude of
London, which Reclines from the Zenith thereof 20 deg. In
what Latitude will that be an Horizontal Plain ?

The Plains Reclination 120 deg. being less then 38 de. 30 m. the Complement of the Latitude of London; Substract 20 deg. from 38 d. 30 m. the Remainder (or difference) 18 de. 30 m. is the New-Latitude. So that an Horizontal Dial made for that Lati-tude, shall be a South Recliner 20 deg. in the Latitude of London.

II. Variety. If a South Plain in the Latitude of 51 deg.
30 m. should Recline 60 deg. from the Zenith thereof:
In what Latitude will that be an Horizontal Plain ?

The Reclination of the Plain 60 deg. being Greater than 38 deg. 30 m. the Complement of the Latitude of London, Substract 38 de. 20 m. from 60 deg. and the Remainder 21 deg. 30 m. is the New-Latitude: And an Horizontal Dial made for the Latitude of

Fig. LIX.