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.

By Calculation.

The Stars have little or no alteration in their Latitude; but in their Longitude they move forward about 1 degr. 25 min. in a hundred years, which is 85′.

By Noble Ticho, his Tables of Longitude and Latitude of the Stars, rectified by himself, to the beginning of the year 1601.

The Latitude of the most bright Star Sirius in the Mouth of the great Dog, is 39 deg. 30 min. and his Longitude is 8 degr. 35 min. 30″ of ♋; I desire the Stars true Longitude, or to be rectified for this present year 1667.

You must work by the Rule of Proportion, thus, if 100 give 85 m. what shall 66 the difference in years betwixt 1601, and 1667 give? Multiply, and Divide, and the Quotient will be 56 m. 6″ added to the Longitude found in the Tables of the Stars in the second Book on the back-side the Nocturnal, which 8 deg. 35 min. 30″ makes 9 d. 31′ 36″ of Cancer, the Longitude of the Star Sirius this year 1667; and so work to find the Longitude of any other Star in any other year, past, or to come.

Take 9 deg. 32′ the Longitude of the Star, out of 90 deg. there remains 80 degr. 28′, his distance from the next Equinoctial Point; which being known, the First Rule is,

As the Radius 90	10
is to the Sign of the Stars Longitude from the next Equ. Point 80 d. 28	CK 999396
So is the Co-Tangent of the Stars Latitude 39 deg. 30′ A ✶	1008389
to the Tangent of the fourth Ark 50 deg. 06 min.	1007785

Compare this fourth Ark with the Arch of Distance betwixt the Poles of the Eclip∣tick, and the Poles of the World 23 deg. 31 min. if the Longitude and Latitude of the Star be alike, as in North Signs ♈ ♉ ♊ ♋ ♌ ♍, and the Latitude is on the North-side the Ecliptick; or if the Longitude be among the Southern Signs, as ♎ ♏ ♐ ♑ ♒ ♓, and the Latitude Southward; then shall the difference between the fourth Ark found, and the distance of the Poles 23 deg. 31′ be your fifth Ark.

But if the Longitude and Latitude shall be unlike, as it is in this Example; as the Lon∣gitude in a Northern Sign, and the Latitude South; or the Longitude in a Southern Sign, and the Latitude North; then Add this fourth Ark found, to the distance of both Poles 23 deg. 31 min. the sum of both shall be the fifth Ark.

Then the Rule is,

As the Sign of the fourth Ark 50 deg. 06′	988488
is to the Sign of the Fifth Ark 73 deg. 37′	998199
So is the Tan. of the Stars Long. from the next Equin. Point 80 deg. 28 m.	4077484
to the Stars Right-Ascension from the next Equin. Point 82 deg. 21 m.	2075683
82 d. 21 m. Substracted from 90 d. or 180 leaves 7 d. 39′ which added to 90 d. the sum is 79 d. 39′ the Right-Ascen. of Sirius required.	1087195

Then the Rule to find the Declination, is,

As the Co-Sign of the fourth Ark 50 deg. 06′	980716
is to the Co-Sign of the fifth Ark 73 deg. 37′	945034
So is the Sign of the Stars Latitude 39 deg. 30′	980351
	1925385
to the Sign of the Stars Decl. required 16 d. 14′	944669

You have the proof of the Work by the foregoing Geometrical Rules; or you may take this by Calculation, if there be no former errour, the Proportion will hold.

As the Co-Sign of the Latitude 39 deg. 30 min.	988740
is to the Co-Sign of the Right-Ascen. from the next Equ. Point 82 d. 21′	912424
So is the Co-Sign of the Declination 16 deg. 14 min.	998233
	1910657
to the Compl. Sign of Longit. from the next Equinoctial 80 d. 28 m. or Sign of the Longitude 9 deg. 32 min. as was at first given.	921917

By these Rules and directions work, to find the Right-Ascension, and Declination of any Star, which you desire to know.