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.

PROBL. III. Having the Suns greatest Declination, and his Distance from the next Equi∣noctial-Point; to find his Right-Ascention.

IN the Foregoing Scheme, having drawn the Parallel of the Suns Declination TD, passing through the Place at ✶ the extent S ♁, is the Sign of the Suns Right-Ascen∣tion from the next nearest Equinoctial-Point, to the Radius of the Parallel TD; and therefore place the extent ST from C to X, and upon X as a Centre with the extent S ♁, describe the Arch at k, a Ruler laid from the Centre just touching the extremity of that Arch, finds the Point N in the Limb of the Meridian or Quadrant, and the Arch ON, applyed to the Line of Chords, is 59 degr. 09 min. and so much is the Suns Right-Ascension in the first quarter of the Ecliptick.

In the Triangle CK ♁ we have given as before, (1.) the Angle of the Suns grea∣test Declination KC ♁ 23 degr. 31 min. (2.) the Longitude of the Sun from the next Equinoctial-Point Aries C ♁ 61 degr. 18 min. hence to find the Suns Rght-As∣scention, the Rule is,

As the Radius	10
to the Tangent of the distance 61 degr. 18 min. C ♁	1026162
So is the Co-Sign of the Suns greatest Decl. 23 deg. 31′ KC ♁	996234
to the Tangent of the Right-Ascention CK 59 deg. 9 m.	1022396

Or in the Concave-Sphere; if you draw the Meridian from N through ♁ to S, whose Centre will be found upon the Equator, it will cut the Equinoctial in K; mea∣sure the distance GK on the Line of half-Tangents, and you have 59 d. 09′, as before.

Or extend the Compasses from 90 d. to 66 d. 29, the same distance will reach from 61 deg. 18 m. to 59 deg. 9 min. which is the Suns Right-Ascention in 61 deg. 18 ♊.

But this you are to observe, that if the Right-Ascention sought, be in the second Qua∣drant ♋ ♌ ♍, then you are to take the Complement of the Arch found to 180 deg. if in the third Quadrant ♎ ♏ ♐, adde 180 deg. to the Arch found; but in the last Quadrant, Substract the Arch found from the whole Circle 360 degr. and you shall have the Right-Ascention desired.

Example 2.

The Sun in 28 degr. 42 min. of ♋, that is, 61 degr. 18 min. from the Equinoctial Point ♎; the Rule is as before. As the Radius is to the Co-Sign of the greatest Decli∣nation, so is the Tangent of the Suns distance from the next Equinoctial-Point 61 degr. 18 min. to the Tangent of 59 degr. 09 as before, which taken from 180, is 130 deg. 51 min. which is the Suns Right-Ascention in 28 degr. 42 min. of Cancer.

Example 3.

The Sun in 1 degr. 18 min. of ♐, that is, 61 degr. 18 min. from the next Equinoctial-Point ♎, the work is the same as before; therefore to the Arch found, I add 180 degr. a Semi-Circle; so 59 deg. 09 min. and 180, makes 239 deg. 09 min. the Right-Ascention of the Sun sought in 1 deg. 18 min. of Sagitarius ♐.

Example 4.

The Sun in 28 degr. 42 min. of Capricorn, 61 deg. 18 min. from the next Equi∣noctial Point ♈, the operation is the same with the former Example; wherefore Sub∣stract the Arch found 59 deg. 09 min. from the whole Circle 360 deg. and there will remain 200 deg. 51 min. which is the Suns Right-Ascention in 28 deg. 42 min. of ♑ Capricorn.