Ans. D. lat. 132'0' N.; dep. 397'7' E.; course N. 72° E., dist. 418 m.; lat. in 35° 8' S.; long. in 174° 32′ W. N.B. For examination purposes it will be better to work to seconds of arc in latitude and longitude, and not to the nearest mile as in the above examples, as it might throw the answer outside the 1 miles margin allowed The latitude of a place on the earth's surface, being its distance from the equator, either north or south, is measured by an arc of a meridian contained between the zenith and the equinoctial, the zenith and the equinoctial corresponding on the celestial sphere to the position of the place and the equator upon the terrestrial sphere; hence, if the distance of any heavenly body from the zenith when on the meridian, and its declination, to the northward or southward of the equinoctial, be known, the latitude may thence be found. The latitude of a place may also be defined as the declination of the zenith, and is equal to the altitude of the pole above the horizon of the place. The best and most simple method of finding the latitude at sea is from an observed altitude of a heavenly body when on the meridian. From the altitude the zenith distance (90°—alt.) is known, and the object's declination being found from the Nautical Almanac, and corrected for Greenwich apparent time, the distance of the object both from the zenith and equinoctial is also known; consequently the distance of the zenith from the equinoctial -which is the distance of the observer from the equator-is at once determined. The way in which the latitude of the place of observation is deduced from the meridian altitude and declination of a heavenly body is readily seen as follows: In fig. I the circle is the meridian of the observer; H H' his rational horizon; and Z his zenith; E Q is the celestial equator or equinoctial; and P the elevated pole, supposed, in this case, the north pole; also E Z is the latitude of the zenith, and hence of the observer. H P. H (1) Taking S to be the place of the sun on the meridian; HS is the sun's altitude, bearing in this case south; and S Z his zenith distance; which is N., because the sun bears south; also ES is the sun's N. declination, measured from the equator at E; then, since the zenith distance and declination are of the same name, both north of the equator— Fig I EZES + S Z, or Lat. zen. dist. + decl. = (2) When S' is the place of the sun, then E S' is the sun's declination south of the equator; H S' is the altitude, and S' Z the zenith distance north; hence zenith distance and declination being of contrary names— EZ SZE S', or Lat. zenith distance - declination. = = (3) With the sun between the zenith (Z) and the pole (P), then H' S'" is the altitude, and, EZ ES""S"" Z; or Lat. = declination - zenith distance. Thus far the object observed has been taken as above the pole; but in certain cases the object may be below the pole; and now we must first show that the elevation of the pole above the horizon of any place is always equal to the latitude of that place— = EZ Lat.; also Z H' = = E P, each being a quadrant ; or, E Z Z P = ZP + PH' taking away Z P (the co-latitude) from each side of the equation, then (Lat.) E Z = P H', the elevation of the pole. Also, for latitude by the meridian altitude of an object below the pole: let S" be the object below the pole; then H' S" is its meridian altitude, and S" P is its co-declination or polar distance therefore PH'H'S" + S' P i.e. Latitude (or the elevation of the pole) = altitude + polar distance. It is here assumed that the north pole is the elevated one; hence for the southern hemisphere write south for north, and north for south, and the illustrations remain the same. The same may be illustrated in the following mannerIn fig. 2 the circle is the rational horizon, NZS the meridian, and Z the zenith of the observer and WQ E the equinoctial; then Z Q is the latitude, being the distance of the observer's zenith from the equinoctial. (1) Taking X to be the place of the sun on the meridian, S X is the sun's altitude (bearing in this case south), and Z X his zenith distance, which is N. because the sun bears south; also Q X is the sun's N. declination measured from the equinoctial at Q. Then ZQ=ZX+Q X or Lat. = zenith distance declination, 2 X Fig. 2 E the rule when zenith distance and declination have the same name (in this case both being north). The latitude is also north, because Z is north of Q. (2) When X' is the place of the sun, then Q X' is the sun's declination south, S X' the altitude also south and Z X' the zenith distance north. ZQ=ZX' Then = ZX' — QX' or latitude = zenith distance declination, the rule when zenith distance and declination have different names. The latitude is north, because Z is north of Q. (3) With the sun's place North of Z, then Z Q or latitude = declination zenith distance. When the observer's position remains stationary, the meridian altitude of a fixed star is its greatest altitude; but, as the sun, moon, and planets constantly change their declination, their greatest altitudes may be reached either before or after the meridian passage. In like manner, if the observer's position is rapidly changing in latitude, then also the greatest altitude of any heavenly body may not be the meridian altitude. Latitude by the Meridian Altitude of the Sun It is near, but rarely exactly, noon when the sun's meridian altitude is observed, because, if approaching him, you continue to raise the altitude after he has actually dipped and passed the meridian, hence it may be from I to 3 or 4 minutes past noon p.m.; on the same principle, when receding from the sun he appears to dip before he comes to the meridian, and the sight may be observed a minute or more before noon a.m. When the sun is approaching the meridian, for a quarter of an hour or so before noon continue to observe the altitude, using the tangent screw, until it is found to decrease or dip; the greatest altitude attained is the meridian altitude. In the case of a heavy sea the depression of the horizon is constantly changing, and it is therefore impossible to keep the sun's image in constant contact with the horizon. Having, then, the watch set to the time of apparent noon from the a.m. observation for time and the run of the ship in the interval, observe and read off separate altitudes in quick succession until they begin to decrease. The greatest is then taken as the meridian altitude, or, more accurately, the mean of the greatest. RULE.-I. For apparent time at Greenwich. To apparent time at ship, i.e., oh. om. os., apply the longitude in time, adding if longitude is west, but subtracting if longitude is east, putting the date back one day in east longitude. 2. Take the sun's declination (Nautical Almanac, p. I. of month) and correct it by the " Var. in 1 h." (Nautical Almanac, p. I.), always working from the nearest noon, i.e., multiplying the “Var. in 1h.” by the hours and decimal of an hour of the longitude in time. In West longitude In East longitude (Declination increasing, add the correction. Declination increasing, subtract the correction. +LL -UL' 3. Correct the observed altitude of the sun in the following order: index + error- ; dip (Table of Dip); semi-diameter (Nautical Almanac) refraction (Mean Refr. Table); and parallax + (Table of Par. in Al..); the application of these quantities gives the truc altitude of the sun's centre. |