Fig. LVII.

Fig.

CHAP IX.

Concerning fuch Erect South or North Dial Plains, which, decline many degrees towards the East and Weft..

I. By the Globe..

HE Operation by the Globe is altogether the fame, as in LVIII. T the laft, Chapter, and therefore need not be here again re

peated. Wherefore, I will proceed to

II. The Trigonometrical Calculation.

This Work alfo is to be performed in like manner as the Former: And therefore I fhall not again repeat it, but give an Example ready wrought.

Suppofe an Ered Plain in the Latitude of London, 51 de 20 m. fhould decline from the South towards the Eaft 85. deg.

I. For finding the Requifite, if you work according to thofe Ca-nons for Calculation, in the laft Chapter delivered; you will find

VII

Vit 05 0

36

de. m.. 3 c6 to be 39. 22. 86 C5

Thefe Requifites thus found, you ble for the Hour-distances inall refpects, may proceed to the making of a Taas in the laft Chapter: By fetting down the Hours proper for the Diał in order, as in this Table.

Then, againft XII, fet the. Difference of Longitude, 86 d. 05 m. from which Subftract 15 deg. and there. will remain 71 d. 05 m. which fet

The Place of the Sub-file against XI and I. And from 71 d. 05

3. 550

13

VI

06

04

m. fubftract 15 de. the remainder will. be 56 d. os m. which fet against X and II. And fo by the continual Sub

fraction

fraction of 15 deg. you fhall find 11 de. 05 m. to ftand againft Fg. the Hours of VII and V; under which wrife The place of the Sub- LVIII. file: And then, fubftract 11 d. 05 m. from 15 de. there will remain 3 de. 55 m. which must be fet under the Sub-file, against the Hour of VI: And then, by the continual Addition of 15 deg. thereto; you thall have fuch Equino&tiol distances as are expreffed in the Table, against the Hours of V and VII, and IV and VIII. Then

II. For the Five Hour diftances upon the Plain: If you work by the Canon delivered in this laft 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 Diftances upon the Plain about the Sub-file (and indeed all the reft, except the extreme Hour of XII) do fall fo near together, that without a very large extention of them from the Centre, there will be no competent diftance 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 fmall 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, defcribe an obfcure Arch of a Circle C D E; and upon it fet 38 de. 23 m. the Sub-files diftance from the Meridian, from C to D, and draw the Line A D, for the Sub-file.

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

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

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

4. Affume any two points in the Sub-filar Line of the Dial AD, at fome convenient diftance from each other, as R and S: and through those two points, draw two infinite Right lines, both

Ccc 2

of

Fig. of them at Right Angles to the Sub-stilar Line A D ; as the Lines LIX. ZR Z and X S X.

5. Set one foot of your Compaffes in the Point R, and take the nearest distance to the new Augmented Stile G H; and set that diftance upon the Sub-filar Line ftom R to K.-Alfo from the Point S, take the neareft diftance to the Augmented Stile G H, and fet that diftance alfo upon the Sub-filar Line, from S to L. 6. Upon these two Points K and L, (with 60 de. of a Scale of Chords) defcribe two Semi-Circles: and in either of them set off 86 d. 05 m. (the Plains Difference of Lorgitude) from R to M, and from S to M, both of them on the fame fide of the Sub-filar Line, on which the firft Perpendicular A B was drawn.

7.

Divide either of the Semicircle into 12 equal parts (beginning at the points M) at the feveral points oo, &c.

8. Lay a Ruler to the point L, and to the feveral points OO,&c. the Ruler will crofs the Line X S X, in the points *** &c.C. Alfo, Lay a Ruler to K, and the refpective Points Oo, &c. the Ruler will cross the Line Z R Z, in the several Points*** &c.

Laftly, Lines drawn from the feveral Points*** in the Line ZRZ, to the feveral points *** in the other Line X SX each to its Correfpondent, (which the Sub-filar Line will direct you): thofe Lines fo drawn fhall be the true Hour-Lines proper for the Plain And will be at a competent diftance 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 West

Eaft

North Declining Weft

>85 Degrees."

But you muft 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 upfide downwards for the
North-decliners, fo that the Stile may point upwards to the North
Pole, and the Hours about Midnight omitted: As in the last
Chapter is directed..

CHAP..