I. In South Recliners. RULE I. This Fourth Tangent must be compared with the Old Latitude, and the Complement of their Difference is theNEW LATITUDE. So, In this Example, The Fourth Arch 33 de. 30 m. being fubftracted from the Old Latitude 5r de. 30 m. their difference is 18 deg. whofe Complement 72 deg. is the NEW LA TITUDE. RULE II. If the Fourth Tangent fall out to be Equal to the Old Latitude, Then the Difference will be nothing; And fo the Plain will be a Polar declining Plain: For the Pole will have no Elevation over it. So, in the Latitude of 51 de. 30 m. If a South Plain fhould Decline towards the Eaft or Weft 65 deg. 40 m. And Recline 18 de. 9 m. By the former Canon, the Fourth Tangent will be found 51 de. 30 m. Equal to the Old Latitude: So that the Difference is. Nothing. And the Hour-Lines will be Parallel one to another as in the Direct Eaft, Weff, and Polar Dials, in CH AP. VII. and CHAP. X. B RULE III. If the Fourth Tangent prove to be Greater than the Old Latitude, Then, The North Pole is Elevated in South Decliners: But if the Fourth Tangent be Leffer than the Old Latitude, Then, The South Pole is Elevated in North Decliners. II: In North Recliners.. RULE I. The Fourth Tangent found as before, is to be compared with the Complement of the Old Latitude, and: their Difference is the NEW EATITUDE. RULE I. If the Fourth Tangent prove to be Equal to the Complement of the Old Latitude: that Declining Reclining Plain will be an Equinoctial Plain Declining. So, In the Latitude of 51 de. 30 m. If a Plain fhould Decline from the North towards the Eaft or Weft 60 deg. And alfo Re-cline from the Zenith 32 deg. 11 m. The Fourth Tangent will be found to be 38 de. 30 m. Equal to the Complement of the Old Latitude: And will, therefore, be An Equinoctial Declining Plain. II. To find the New Declination. The Canon for Calculation, li As the Radius, Sine 90 d. To the Co-fine of the Reclination 54 d. 9.769218 So is the Sine of the Old Declination, 24 d. 20 m. 9.614944 9.384162 Which 41 de. min. is the NEW DECLI NATION. And now, if (according to the Precepts delivered in the VIIIth. CHA P. hereof) you do make an Upright South Dial Declining 14 deg, 1 m. in the Latitude of 72 deg. That Dial fhall ferve for A South Plain, in the Latitude of 51 de. 30 m. Declining 24 deg. 20 m, and Reclining 54 deg. And in fuch a Dial you will find the Requifites belonging thereunto, to be as the Table in the Margin. And thus much for the Making of the Dial according to its New Latitudey and New Declination. New Latiude: 72.00 New Declination 14 or Stiles heigth 17. 26 Dift. Sub.& Merid. 4, 17 41 VII But to apply this Dial to the Rest tatto clining Plain in the Old Latitude, you Hours You are not to place the Hour-line of XII perpendicular to the Horizon, as in Upright Plains, but it must make an Angle with the Horizontal Line of the Reclining Plain: And therefore the quantity of that Angle must be firft found. Therefore, III. To find the Angle made between the Meridian and the Horizon. 41VIII 4IXI XII 191 1911 The Canon for Calculation. As the Radius, Sine 90 d. Is to the Sine of the Reclination 54 d. Eq. Di. Tr.HD. VIII 45 43 17 05 10. 9.655347 So is the Tangent of the Old Declination 24 d. 20 m. 9.907957 To the Tangent of 20 deg. 6 m. Ddd 2 9.563304 Whole 1 Whole Complement 69 deg. 54 min. is the Angle that the Me ridian (or Hour-line of XII.) muft make with the Horizontal Line of the Reclining Plain. Thus for the Quantity of the Angle. But IV. To know which way (or to what Coaft) the Meridi an Line, Afcending or Defcending Above or under the Horizontal Line of the Plain, is to be drawn.. NorthRe-Equal to a Polar, the Meridian must be drawn below the Horizontal Line, at that end which is contrary to the Coast of Declination: And the Six a Clock Hour-line, is (always) the Subfilar. cliners In South In- More than a Polar the Meridian muft 1 Below And from that End of the Horizontal Line, which lies contrary to the Coaf of the Plain's Declination And, in South Incliners, is only ferviceable to help to draw the reft. Above of the Dial.. V. How the Dial (being made according to the New Latitude and New Declination) is to be transferred from the Paper Draught, upon the Reclining or Inclining Plain Having drawn an Horizontal Line upon your Dial Plain, in the moft convenient part thereof, and made choice of a Point therein for the Centre of your Dial; apply the Centre of your Paper Draught to this Centre, moving the Paper Draught about till the Meridian Eine thereof do make an Angle with the Horizontal Line drawn upon the Plain, equal to what you found it to be by the Third Section of this CHA P. And to its Proper Coat, as you' found it by the Fourth Section: Then (if you have not erred in any of your former workings) will the Stile of your Paper Draught (or rather a pattern of it cut in Paft-board) being placed upon the Sub-file of the Paper Draught, have direct refpect to the Elevated Pole And thus due refpect being had to what is here deliver'di delivered, you may eafily transfer the Stile and the reft of the Hour-lines to the Plain; putting thereon fo many as the Plain is capable to receive at any time of the Year; and leaving out fuch as are fuperfluous. ¡ CHAP. XIII. Of the Infcription of other Great and Small Circles of the Sphere upon all forts of Dial Plains, N the foregoing Chapters is fhewed how the Meridians (or. Hour-Circles) of the Sphere may be defcribed upon all forts of Plain Superficies howfoever fituate: And as thofe Hour-Circles were defcribed, fo may all other Circles of the Sphere be alfo delineated: And the manner how, I have largely treated of in my particular Treaties of Dialling already extant: So that in this place I fhall be but brief therein, and yet fufficiently Plain. And whereas the Hour of the Day on all Sm-Dials is fhewed by the whole Axis of the Stile; fo all other Circles fo defcribed, are fhewed by one fingle point taken in fome convenient place of the faid Axis, from which Point a Perpendicular let fall to the Plain upon the Sub-filar Line fhall be called the Perpendicular Stile: And the point upon the Plain, The Foot of the Perpendicular Stile; and the Point in the Axis (before affumed) the Gnodus or Apex of the Stile. Now, for the performances of the Work following (befides the Trigonometrical Calculation) the Practitioner muft be provided with a Scale (or a Sector rather) which muft have upon it Scales of Sines, Tangents, Secants, Chords, and equal parts: or if he have by him, Tables of Natural Sines, Tangents, and Secants, then a Line of equal parts only drawn from the Centre, will perform the work rather better than by the other Scales. Being thus provided; The firft business muft be How to proportion the Perpendicular Stile to the Plain. If your Dial Plain be fmall, confider whether it be Direct, or Declining; if Direct the Sub-file may be placed in the Middle: If Declining, more to the fide contrary to the Coaft of Decli nation. The Sub-ftile well made choice of, and the Perpendicular |