equator makes with the prime vertical, as well as to the height of the pole above the horizon: conSequently, when the arcs HOOE are given, the latitude EZ RP becomes known. For it is ob

Ewhen they are of the same name, and to their difference when of contrary names: except when is between the horizon and elevated pole, in which case the sum of (RO) the altitude, and (OP) the polar distance, gives the latitude.

21. Hence, it is obvious that the determination of the latitude, if we could always observe the meridian alitude of an object whose declination is known, would be an easy problem; but clouds very frequently prevent this observation. The mariner therefore requires other methods of determining the latitude; and the one which is best adapted, and has been most approved, is that which gives the latitude from the sun's declination two altitudes, and the interval of times between the observations. The requisite operation is necessarily rather long and complicated, and may at first sight appear very formidable; but, as in other instances, a little acquaintance with it causes its terrors to disappear.

To illustrate the direct method of solution, let z (Fig. 9) be the zenith, p the pole, PSPs the sun's polar distance at the middle time between the observations, and ss the places of the sun corrected for semidiameter, dip, refraction, and parallax. Then in the isosceles triangle sps, the equal sides SP. SP, and included angle SPS, which measures the interval between the observations, are given to find ss and the angle pss; and in the triangle szs, the three sides are given to find the angle zss; then zsp = Psszss; hence in the triangle zSP, the sides zs. SP, and included angle ZSP, are given to find zp, the complement of the latitude corresponding to the time to which the declination is reduced.

If the interval between the observations be considerable, it may not only be necessary to reduce the altitude at the second observation to what it would have been if the observations had been taken at the same place (vide Vince's Practical Astron. p. 50), but likewise to consider PS. PS equal to the true polar distances at the respecttive observations. (Vide Vince's Trig. art. 254).

This problem has engaged the attention of several eminent mathematicians, whose researches have been principally directed to an approximate method called Douwe's, employing as an element

This me

of calculation the latitude by account. thod, in its original form, was sometimes tedious, requiring a repetition of the operation, and when repeated not always leading to right conclusions. On this account Dr. Brinkley invented a supplementary process of computation, by which the latitude found by Douwe's method might be conveniently corrected. About the same time that this process, with its demonstration and tables, was published in the Nautical Almanac for 1797, a similar solution of the problem by M. Mendoza Rios was published in the Connoissance des Temps:

steer, a fied

which

72

λ; then

λ = log.

or log, sine of half the true distance. Whence this practical rule.

=

log.x;

(1.) Take the difference of the apparent altitudes of the moon and sun, or star, and the dif ference of their true zenith distances: a'so, half distance and difference of the apparent altitudes. the sum, and half the difference of the apparent

(2.) To the log. sines of the half sum and half difference add the log. sines of the true zenith distances, and the log. cosecants of the apparent zenith distances, and take half the sum.

(3.) From this half sum take the log. sine of the half difference of the true zenith distances,

and the remainder is the log. tangent of an are, the log. sine of which are subtracted from the said half sum of the six logarithms leaves the log, sine of half the true distance. (See Ladies' Diary for 1787, qu. 873).

108° 42' 3"

D's hor. paral. 55′ 19′′.

Having ascertained the true distance, we are next to determine the time at Greenwich corresponding thereto. To effect which, take from the Nautical Almanac the distances next less and next greater, than the true distance deduced from observation, and the difference (D) of these distances gives the moon's access to or recess from the sun or star in three hours; then take the difference (d) between the moon's distance at the beginning of that interval, and the distance deduced from observation, and say D: d:: three hours: the time the moon is acceding to, receding from the sun or star by the quantity d, admit

True distance of moon from sun at ship

-2328669

2)39-6897712

19-8448856 (a)
9.6132032

10.2316824

9-9357907 (b) 9-9090949 (a - b)

ting the moon's motion uniform for the time, which, added to the time at the beginning of the interval, gives the apparent time at Greenwich corresponding to the given true distance of the

moon from the sun or star.

Example. About 5 PM. on the 18th January, 1804, in latitude 39° 20' S. longitude, by estimation 85° E., the observed altitude of the sun's lower limb was 27° 55', that of the moon's upper limb 52° 33', and the distance of their nearest limbs 700 26' 10', height of the eye 18 feet. The time of observation and longitude of the ship are required.

D=

d ***

Hence 1° 38′ 1′′ : 52′ 8′′ :: 3h.: 1h. 35m. 44s. which, added to 21 hours, gives 22 h. 55m. 44 s. the apparent time at Greenwich.

Then, the sun's polar distance (69° 15′ 49′′),

Apparent time at ship Jan. 18th.

at Greenwich Jan. 17th.

NAVIGATION (Inland). See CANAL. NAVIGATOR. s. (navigateur, French.) Sailor; sea man; traveller by water (Brere.). NAVIGATOR'S ISLANDS, a cluster of islands in the S. Pacific ocean. The inhabitants are a strong and handsome race; scarcely a man to be seen among them less than six feet high, and well proportioned. The women are delicately beautiful; their canoes, houses, &c. well constructed; and they are much more advanced in internal policy than any of the islands in this ocean. Lon. 169. o W. Lat. 14. 19 S. See MAOUNA. NAULAGE. s. (naulum, Latin.) The freight of passengers in a ship.

NAULUM, in antiquity, was money put into the mouth of a person deceased at Rome, to pay Charon the ferryman for his passage, and this piece was to be of the current coin of the emperor that then reigned, which gave people afterwards an opportunity to know when such an one died.

NAUMACHIA, in antiquity, a show or spectacle among the ancient Romans, representing a sea-fight. These mock sea- fights are supposed to have originated at the time of the first Punic war, when the Romans first instructed their men in the knowledge of naval aflairs. Afterwards they were intended to entertain the populace, as well as to improve the seamen. They were often, like other shows, exhibited at the expence of individuals, to increase their popularity. In these spectacles they sometimes strove to excel each other in swiftness; and sometimes engaged in a warlike manner. The naumachiæ of Claudius indeed was a most savage diversion. The combatants used to destroy each other to amuse a tyrant and a cruel mob. As they passed before him they used this melancholy greeting, Ave Imperator, morituri te salutant. The emperor replied, Avete vos. This they understood as an answer of kindness, and a grant of their lives; but they soon discovered that it proceeded from wanton cruelty, and barbarous insensibility. In the time of the emperor Domitian, such a vast number of vessels engaged as would have nearly formed two regular fleets for a real fight, and the channel of water was equal in magnitude to a natural river.

NAUMBERG, a town of Germany, in Lower Hes-e, situate on the Eider, 11 miles W S.W. of Cassel.

NAUMBERG, a town of Upper Saxony, in Thuringia, capital of a bishopric, united to the house of Saxony. It has a small citadel, and the cathedral is remarkable for its fine altars, paintings, and subterranean chapels. Here are manufactures of stockings and turnery wares, and vineyards that yield an excellent red wine. It is seated on the Saale, 37 miles EN E. of Erfurt, and 60 W. of Dresden. Lon. 12.0 E. Lat. 51. 11 N.

NAUPACTUS, or NAUPACTUM, a city of Etolia, at the mouth of the Evenus. The word is derived from was, and any, because it was there that the Heraclide built the first ship, which carried them to Peloponnesus.

NAUPLIUS, a son of Neptune and Amymone, king of Euboea. He was father to Palamedes, who was sacrificed to the resentment of Ulysses by the Greeks, during the Trojan war. The death of Palamedes irritated Nauplius. When the Greeks returned from the Trojan war, Nauplius saw them with pleasure distressed in a storm on the coasts of Euboea, and to make their disaster still more universal, he lighted fires on such places as were surrounded with the most dangerous rocks, that the fleet might be shipwrecked on the coast. This succeeded; but when he saw Ulysses and Diomedes escape, he threw himself into the sea. According to some mythologists there were two persons of this name. The second was an Argonaut, remarkable for his knowledge of sea affairs and of astronomy. NAUSEA. (nausea, from VAUSER,

ναυς, a

ship; because it is a sensation similar to that which people experience upon sailing in a ship.) An inclination to vomit, without effecting it; also a disgust of food, approaching to vomiting. It is an attendant on cardialgia, and a variety of other disorders, pregnancy, &c. occasioning an aversion for food, an increase of saliva, disgusted ideas at the sight of various objects, loss of appetite, debility, &c. Lat.)

To NAUSEATE. v. n. (from nauseo. To grow squeamish; to turn away with dis gust (Watts).

To NAU'SEATE.v.a. 1. To loathe; to reject with disgust (Pope). 2. To strike with disgust (Swift).

NAUSEOUS. a. (from nausea, Latin ; nausée, French.) Loathsome; disgustful (Den.). NAU'SEOUSLY. ad (from nauseous.) Loathsomely; disgustfully (Dryden). NAUSEOUSNESS. s. (from nauseous.) Loathsomeness; quality of raising disgust (Dryden).

NAUSICA, a daughter of Alcinous, king of the Phaaceans. She met Ulysses shipwrecked on her father's coasts, and it was to her humanity that he owed the kind reception he received from the king.

NAUTES, a Trojan soothsayer, who comforted Eneas when his fleet had been burnt in Sicily. He was the progenitor of the Nautii at Rome, a family to whom the Palladium of Troy was afterwards entrusted.

NAUTIC. NAUTICAL. a. (nauticus, Lat.) Pertaining to sailors (Camden).

NAUTILUS. Pearly nautilus. In zoology, a genus of the class vermes, order testacea. Animal, a kind of sepia; shell univalve, divided into several departments communicating with each other by an aperture. Thirty-one species, often confounded with the genus argonauta, or paper-nautilus, on account of the similarity of the names. They may be thus subdivided.

A. Spiral, rounded, with contiguous whorls, comprising fifteen species, of which nine are common to our own coasts, and found chiefly on the Sandwich shore, or on Sheppy island.

B. Spiral, rounded, with separated whorls.