The semicircle on a sector in two books. Containing the description of a general and portable instrument; whereby most problems (reducible to instrumental practice) in astronomy, trigonometry, arithmetick, geometry, geography, topography, navigation, dyalling, &c. are speedily and exactly resolved. By J. T.

PROBL. 5.

To finde the declination of any Plain.

Apply the outward ledge of the fixed piece to the horizontal line of your plain, holding your instrument paralel to the hori∣zon. This done, lift up the thread and plum∣mer, until the shadow of the thread fall di∣rectly upon the pin hole on the fixed piece (where you hang the thred to take altitudes) Then observe how many degrees the shadow of the thread cuts in the limb, either from the right hand, or from the left hand 0/60. upon the loose piece; and immediately ta∣king

the altitude of the Sun. By lib. 1. cap. 2. Probl. 9, 10, 11. finde the Suns Azimuth from South. And,

When you make this observation in the morning, these Cases determine the decli∣nation of the plain.

CASE 1.

When the shadow of the thread upon the limb falls on the right hand 0/60 on the loose piece, take the difference of the sha∣dow, and Azimuth (by subtracting the lesse out of the greater) and the residue or re∣main is the plains declination. From South toward East, when the Azimuth is greater than the shadow. From South toward West, when the shadow is greater than the azi∣muth, when the shadow and azimuth are equal, its a direct South plain. When the difference is just 90. its a direct East, when above 90. subtract the difference from 180. and the remain is the declination from North toward East.

CASE 2.

When the shadow falls on the left hand 0/60. Adde the azimuth and shadow toge∣ther,

that sum is the plains declination; from South toward East, when under 90; if it be just 90, its a direct East. If above 90. subtract it from 180. the remain is the de∣clination from North toward East. When the sum is above 180. subtract 180 from it, and the remain is the declination from North toward West.

CASE 3.

When the shadow falls upon 0/60. the azimuth is the plains declination. When un∣der 90, its South-East, when equal to 90. direct East, when above 90. subtract it from 180. the remain is the declination from North toward East.

If you make the observation afternoon, the following Cases will resolve you.

CASE 4.

When the shadow falls on the left hand 0/60. the difference 'twixt the shadow and azimuth is the declination; when the shadow is more than the azimuth it declines South∣East, when less, South-West. When the sha∣dow and azimuth are equal, its a direct South plain, when their difference is equal to 90.

its a direct West; when the difference ex∣ceeds 90. subtract it from 180. the remain is the declination North-West.

CASE 5.

When the shadow falls on the right hand 0/60. take the sum of the shadow and azi∣muth, and that is the declination from South toward West, when under 90. when just 90. its a direct West plain; when more than 90. subtract it from 180. the remain is the decli∣nation North-West; when the sum is above 180. subtract 180 from it, and the remain is the declination from North toward East.

CASE 6.

When the shadow falls upon 0/60. the azimuth is the quantity of declination. From South toward West, when under 90. when equal to 90. its direct West; when more than 90. subtract it from 180. The remain is the declination from North toward West.