The dip depends on the distance in nautical miles of the visible horizon. Thus, to the eye 30 feet above the sea the true dip is 6', or the distance of the horizon itself is about 6 miles. This is easily proved thus,

H

Let C be the centre of the earth, O the place of the observer; then the line OB drawn touching the surface at B determines B the farthest point visible to him. Draw OH perpendicular to O C, then since OB touches the circle at B, the angle CBO is a right angle (No. 138, Cor.) Hence BCA is the complement of CO B, and HOB is also the complement of COB (COH=90°), therefore ACB and HOB are equal.

The depression is given in Table 8.

C

B

206. The ALTITUDE of a terrestrial or celestial object above the sea horizon is the angle included between the line drawn from the eye to the object, and the line from the eye to the horizon. Thus, the angle M AB is the altitude of the summit M. The altitude here, in consequence of the great elevation of the spectator at A, about of the radius, or 330 miles, is less than the dip, or the summit M is really below the true horizontal line A H. This may take place when, from the small height of the object with respect to that of the observer, or its great distance, it is seen very little elevated; but in most cases A M will fall above A H.

207. The rays of light which pass from any distant object on the earth suffer a change in their direction, which is called the terrestrial refraction, by which the object appears in general higher than its true place. This effect is, on the average, about of the intercepted arc, or distance in miles, which are minutes of a degree very nearly. Thus, an object twenty-eight miles distant is raised about 2' above its true place. The sea horizon is thus raised by refraction, or the apparent dip (Table 30) is less than the true.

This proportion, however, is subject to great irregularity, and varies between and of the intercepted arc. The apparent elevations of the summits of high land are thus subject to great variations, depending on particular states of the air.

208. The apparent place of the sea horizon differs also in different temperatures of the sea and air. When the sea is warmer than the air, the horizon appears below its mean place, or that at which it appears when the air and water are of the same temperature, or the apparent dip is too small; when the sea is colder than the air, the horizon appears above its mean place,* or the apparent dip is too great.

* Admiral W. F. W. Owen informs me that he found on one occasion, in observing a star's altitude, a change of 4' in the place of the sea horizon, in the tropics, soon after sunset. Mr. Fisher observed a variation in the place of the horizon of 18′ in the arctic regions. In summer the ice horizon was elevated, not depressed; in the winter it was depressed several minutes.—(Appendix to Captain Parry's Voyage in 1821-3, p. 187.) These observations, however, do not all follow the rule above. A table for correcting the apparent place of the sea horizon for the difference of temperature of the sea and the air, according to the height of the eye, would

Colonel Sabine gives a table of depressions observed from the gangway of H. M. S. Pheasant, at 15ft. lin. above the sea, in the Gulf Stream, and after leaving it.* On Dec. 5, 1822, lat. 36° N., long. 72° W., at 10 A.M., the temperature of the sca being 70°, that of the air 60°, the dip observed by Wollaston's dip sector was 4' 57", or 1' 6" more than the table. At noon the temperature of the water had changed to 6204, the air at 60° as before, the ship having passed from the warmer water of the stream to the colder water of the rest of the ocean, and the dip observed was 3′ 37′′. From the result of his observations, Colonel Sabine considers that the navigator will be right nine times in ten in assuming that, when the sea is warmer than the air, the tabular dip is too smal. In only one case, however, did this error ever amount to so much as l′ 56′′, the sea being then at 49°, and the air at 38°, or the difference 11° and it is important to remark that the error of the table is by no means proportional to the difference of these temperatures, which in one case was no less than 29°.

Numerous instances are on record, in the accounts of modern navigation, of errors of observation arising from variation in the place of the sea horizon.

209. Besides the vertical effect of refraction above described, some instances have been recorded of a sensible change in the horizontal direction of objects. Mr. K. B. Martin observed a change in the true direction of a point of land in the Azores, towards sunset. He also mentions an extraordinary change in the direction of C. Grisnez light as seen from Ramsgate at the close of a very hot day; on which occasion, also, distant objects were elongated horizontally till tney seemed to separate into parts. ("Naut. Mag." 1847.)

Lieutenant Wilkes observed from the summit of Mowna Roa, the sun's horizontal diameter lengthened out to twice and a half the vertical one. ("Narrative of the United States Exploring Expedition," 1838-42.) In the Survey of the Isthmus of Tehuantepec, under Señor G. Moro, in 1842-3, the refractions at San Mateo on the Pacific, especially the lateral ones," produced the strangest illusions.†

66

210. The TROPICS of CANCER and CAPRICORN are the parallels of latitude 23° 28' N. and S. These are the dotted lines nearest the equator (fig. in p. 55). The sun is vertical at noon twice in the to every place between the tropics, and never to any place outside of

them.

year

be useful; but there are scarcely any data for the construction of such a table, and the theory itself appears not to be complete.

The above variation of the place of the apparent horizon, with mirage, reflected images, and other optical illusions, were first discussed, generally as questions of unequal temperature alone, by M. Biot, Mém. de l'Institut, 1809.

*Account of Experiments to determine the Figure of the Earth. London, 1825, p. 454. It is easy to conceive, that if a mass of air of different density from the rest be interposed between the spectator and the object, and if also the sides or faces which he looks through be not exactly parallel, it will have the effect of a prism, and will seem to throw the object to the right or left of its true direction. If the surfaces are curved, the effect of magnifying or diminishing will occur at the same time.

The space between the tropics is called the Torrid Zone, on account of its heat.

211. The ARCTIC CIRCLE, or North Polar Circle, and the ANTARCTIC CIRCLE, or South Polar Circle, are parallels distant 23° 28' from each pole, and are therefore in latitude 66° 32′. These are the dotted lines nearest the pole. Within these circles the sun does not set during part of the summer, nor rise during part of the winter. The spaces within these circles are called the FRIGID ZONES, on account of the cold.

The spaces between the tropics and the pola circles are called the TEMPERATE ZONES.

CHAPTER II.

INSTRUMENTS OF NAVIGATION.

I. THE COMPASS. II. THE LOG AND GLASSES.

212. THE necessary instruments of navigation are the COMFASS, which shews the direction of the ship's track; and the LoG, which, with the help of sand-glasses for measuring small intervals of time, or a watch shewing seconds, gives the velocity or rate of the ship, and thence the distance run in any interval of time.

I. THE COMPASS.

213. The Mariner's Compass consists of a circular card, of which the edge or circumference is divided into 32 points, half-points, and quarter-points, and into 360 degrees. The four principal points, or, as they are called, the cardinal points, are the North, South, East, and West; the East being towards the right when facing the North.

All the points of the compass are called by names composed of these four terms.

* In this work we employ only half and quarter points. When a more minute subdivision is required, bearings and courses are expressed in degrees.

The points half-way between two cardinal points are called after both of these points: they are the north-east (written N.E.); northwest (N.W.); south-east (S.E.); and south-west (S.W.).

A point half-way between one of these last and a cardinal point is called, in like manner, by a name composed of the nearest cardinal point and the adjacent point, N.E., N.W., S.E., or S.W. Thus the point between N. and N.E. is called north-north-east (written N.N.E.); the point between E. and N.E. is called east-north-east (written E.N.E.); and so of others.

The points next the eight principal points (namely, N., S., E., W., and N.E., N.W., S.E., and S.W.,) take the word by between the name of such point and the next cardinal point. Thus the point next to north, on the east side, is called North by East; that on the West side is called North by West. Thus, on inspecting the compass, it is easy to see the reason of the names E. by N., S.W. by W., &c.

A half-point, which is the middle division between two points, is called after that one of its adjacent points which is either a cardinal point, or is the nearest to a cardinal point. Thus the middle division between N. and N. by E. is called north-half-east (written N. E.) Half points near N.E., N.W., S.E., and S.W., take their name from these points. Thus we say N.E. N., and N.E. § E., and N.E. by E. { E.*

The same holds for a quarter and for three quarters as for a half-point.

The name of the opposite point to any proposed point is known at once, without referring to the compass, by simply reversing the names or the letters which compose it. Thus the opposite of N. being S., and that of E. being W., the opposite point to S.W. by S. is at once known to be N.E. by N. The opposite of W. S. is E. N., and so on.

214. Repeating the points in any order is called boxing the compass; to do this is, of course, one of the first things a seaman learns.

215. In becoming familiar with the points of the compass, the learner should bear in mind that their utility is far from being confined exclusively to navigation, and that in finding his way across a new country, or through the streets of a strange city, no impressions will be so distinct or so permanent as those grounded on the points of the compass.

216. As the ship's course, which is sometimes expressed in points and sometimes in degrees, is always reckoned from the north or south point, the seaman has to refer at once, in using the Tables, to the number of points, or degrees, in any course given by name.

The

* In naming the half and quarter points it is advisable in some cases to sacrifice system to simplicity. Thus, for example, seamen commonly say NNE E instead of NE by N&N; we do not, however, say ENE E, though this is simpler than E by NN, since it is at once seen to be 64 points. It would of course be more systematic, as a matter of geometry, to reckon the half points always from N or S, because the ship's course is reckoned from the meridian; but, on the other hand, as a matter of names, regard will be had to the whole points between which it falls, and to the order in which these are taken.