Page

Prob. 9. Given the latitude of the place, the day of the month,

the moon's horizontal parallax and refraction, to find

the time of her rising

303

10. The latitude and longitude of a fixed star, or of a

planet, being given, to find its right ascension and

declination, et contra

305

11. The right ascensions and declinations of two stars,

or the latitudes and longitudes of two stars being

given, to find their distance

308

12. The places of two stars being given, and their dis-

tances from a third star, to find the place of this

third star

310

13. Given the latitude of the place, the sun's declin-

ation and altitude, to find the azimuth

313

14. Given the latitude of the place, the sun's declin.

ation and altitude, to find the hour of the day 316

14. Continued. The construction of the xvith of the

REQUISITE TABLES, used in finding the latitude by

two altitudes of the sun (Note)

317

15. Given the latitude of the place, the declination and

the altitude of a known fixed star, to find the hour

of the night when the observation was made

319

16. Given two altitudes of the sun and the time between

the observations, to find the latitude of the place 323

16. Continued. A GENERAL RULE for finding the latitude

by two altitudes of the sun, the elapsed time and the

sun's declination being given

326

17. Given the apparent distance of the moon from the

sún, or from a star, and their apparent zenith dis-

tances, to find their true distance, as seen from the

earth's centre

332

17. Continued. Investigation of a GENERAL RULE for

determining the true distance of the moon from the

sun, or from a fixed star

333

18. The latitude of a place and its longitude by account,

the distance between the sun and the moon, or the

moon and a star in the NAUTICAL ALMANAC being

given, to find the correct longitude.

337

CHAP. XIII. OF THE FLUXIONAL ANALOGIES OF SPHE-

RICAL TRIANGLES

344

Prop. 1. A preparatory proposition

344

2. To find the fluxions of the several parts of a RIGHT-

ANGLED spherical triangle, when one of its oblique

angles is 'a constant quantity

345

3. To find the fluxions of the several parts of a RICHT-