The mariners magazine, or, Sturmy's mathematical and practical arts containing the description and use of the scale of scales, it being a mathematical ruler, that resolves most mathematical conclusions, and likewise the making and use of the crostaff, quadrant, and the quadrat, nocturnals, and other most useful instruments for all artists and navigators : the art of navigation, resolved geometrically, instrumentally, and by calculation, and by that late excellent invention of logarithms, in the three principal kinds of sailing : with new tables of the longitude and latitude of the most eminent places ... : together with a discourse of the practick part of navigation ..., a new way of surveying land ..., the art of gauging all sorts of vessels ..., the art of dialling by a gnomical scale ... : whereunto is annexed, an abridgment of the penalties and forfeitures, by acts of parliaments appointed, relating to the customs and navigation : also a compendium of fortification, both geometrically and instrumentally / by Capt. Samuel Sturmy.

CHAP. XIX. How to find the Horary Distance of a Reclining Declining Dial.

YOu have seen Chap. 17. how easily East and West Reclining Dials are to be made; and by the Figure in Chap. 18. how they fall out to be Circles of Position, as you may see by PORCQ.

I will shew you how all reclining Dials may be reduced to East or West Recliners, for some Latitude or other; and so the Hour-distance found by the Method of Chap. 17.

The Circles of Position, as have been shewed, do all cross one another in the North and South Points of the Meridian: Now therefore by the Point O, where the Plane cuts our Meridian, draw a new Horizon, as OBQC, and then shall you see your Plane in that Horizon to be a very Circle of Position.

But now we are gotten into a new Latitude OP, called before Chap. 18. the Posi∣tion Latitude; and we have here a new Reclination: for whereas this Plane reclineth in our Latitude ZFL 45 deg. his Position Reclination is O, viz. ZOL or POR 60 deg. In the making of this Dial therefore you shall forget your own Latitude, and the Planes Reclination in your Horizon; and with this new Latitude and Reclina∣tion make the Dial after the manner of the East Recliner, Chap. 17. not regarding the Declination at all: for the Base of this Plane is now fallen into the Horizontal Line of the Meridian; and his Declination being a Quadrant, he is become a Regular Plane, and neither his Declination nor Reclination shall much trouble you.

How to place your Noon-line from the Horizontal or Vertical Line of the Plane, you have found already.

Note, Your new Latitude is PO 16 d. 14 m. then you know your Plane is the 60 d. Azimuth from the Axis, because POR is 60 deg. as before 90 deg. farther from the said Azimuth you have the Pole of the Plane, and therefore is the Meridian of my Plane, and shall make the Substile of my Dial OPR 3 deg. 1 min. his Distance from the Meridian of the Place in that Aequinoctial, and is therefore the Difference of Lon∣gitude, as before.

Then have you the Side PR the Height of the Stile 14 deg. 1 min. or Elevation of the Gnomon, as before: Likewise have you OR the Declination or Substile Distance from the Meridian 8 deg. 17 min. as before, and you may proceed to draw the Dial in like manner as you have been directed in Chap. 16.

[illustration] geometrical diagram