Pole, the Pole Star will gradually appear to rise higher and higher until when you reach the North Pole it will be directly over your head, and consequently at right angles to, or 90 degrees from, the horizon, and your latitude is then also 90 degrees. But though the Pole Star is very near the North Pole, it does not actually coincide with it, and we must find some other way of finding our latitude accurately. We get this by taking the altitude of any known star in various ways. I will explain the simplest method, of which all others are only slight modifications:

1. Measure the meridian altitude of the star-that is, its highest altitude above the horizon.

2. Deduct that altitude from 90 degrees, which gives its zenith distance, or the angular distance from a point exactly over your head.

3. Add (or subtract) the declination of the star (found in the Nautical Almanac) to the zenith distance, and the result is your latitude.

I have here a diagram showing how the latitude of Edinburgh would be found from the bright star Arcturus, which "culminates," or reaches its highest altitude, on our meridian a few minutes before twelve to-night.

I measure first its altitude, which I find is 54 degrees. Deducting that from 90 degrees gives its zenith distance=36 degrees; to that I add its declination, which I find from the almanac is 20 degrees, and the result is 56 degrees the latitude of Edinburgh.

=

Longitude is a more difficult matter, and I have no time to go into it anything like fully. You will find a beautiful description of it in Herschel's Astronomy-the best by far of all popular books on the subject. While latitude is absolute, longitude, being difference in time, is relative, for there is no such thing as absolute time; and noon at any place is merely the moment when the sun culminates on the meridian. If the observer has a clock whose going he can depend on, and he sets it to, and keeps it always at, Greenwich time, he knows from that clock or chronometer what time it is at Greenwich when any star comes to the meridian. If, then, he can observe any astronomical phenomenon, such as the meridian passage of a star, he has only to observe the difference of the times recorded on the clock set to Greenwich time and on his local clock, and the difference is the longitude in time. This is the principle on which longitudes are taken at sea, where chronometers can be kept undisturbed, but for explorers on land it is more difficult.

The moon, however, is a natural clock-very complicated, but still readable to the initiated. It is continually moving through the stars, and its angular distance from prominent stars is carefully computed for Greenwich, and recorded in the Nautical Almanac for every hour in the year. The observer, then, finding the moon's position by observation, and recording its local time, can find in the Nautical Almanac when it had the same position at Greenwich, and the difference of the times is the measure of the longitude.

In old days, when ships met, the first question was, Who are you? the next, What's your longitude? The invention of the chronometer by Harrison 120 years ago has, however, for sailors at least, vastly simplified

1 The student should read the beautiful explanation of longitude in Herschel's Astronomy, § 220 et seq.

FIG. Ia.

FIG. 2a.

FIG. 3a.

the finding of longitude at sea; and I find from inquiry among sailors, that "lunars" are practically a lost art. In illustration, I may state that I find from the Nautical Almanac that Arcturus comes to the meridian of Greenwich at 11.37 to-night. If I have a clock or chronometer marking true Greenwich time, I shall find that this star will come to our meridian at 12 minutes and 40 seconds later; the difference of longitude in time is therefore 12 minutes and 40 seconds, which, converted into angular measurement, is 3 degrees 10 minutes, the longitude (west) of Edinburgh.

Note here that at stations differing only in latitude the same star comes to the meridian at the same time, but at different altitudes. At stations differing only in longitude it comes to the meridian at the same altitude, but at different times. The instrument generally used for taking altitudes is the sextant. At sea, where we have a visible horizon -the line where the sea meets the sky-we measure altitudes from this horizon; but on land we have no true horizon, and then we use, what is more accurate, an artificial horizon, which is a cup of mercury in

1 In reading this paper the sextant, artificial horizon, theodolite, level, plane table, and other instruments were all shown and their uses described. These descriptions are omitted here, and the student is referred for detailed and illustrated descriptions of these and other instruments to Professor Rankine's Manual of Civil Engineering (Griffin, Bohn and Co.), or Mr. Usill's Practical Surveying (Crosby, Lockwood and Son, 1889).

which the heavenly body is reflected. Measure the angle between the real body in the sky and its reflection in the mercury, and half the angle is the true altitude.

PROJECTION. Having discovered our position on the surface of the globe, we come to the representation of it on a flat sheet or map.

The Latin dictionary tells us that "mappa" is a sheet or napkin. Now the surface of the globe is curved, and in a map we have only a flat surface to represent it on, and we shall for a short while study how, as it is the basis of all map-drawing. The conventional representation on a flat surface of the curved surface of the Earth is called Projection, because in its fundamental idea it is a picture of the globe projected or thrown forward from the eye on to a flat sheet; but this idea of it is so confusing to the mind unaccustomed to think out such things that, although it is the invariable way of describing it in all text-books, I have preferred to show you three forms of projection without assuming any ideal throwing of the rays on to planes.

The first I show is the modified STEREOGRAPHIC or equi-globular projection (Fig. 4), invented by Philip de la Hire about the end of the seventeenth century. A simple way of investigating this projection is to fit an iron ring over the centre of the globe, and stretch tightly, from the North Pole to the South, indiarubber bands that coincide with the meridians of longitude on the globe, fastening them firmly to the ring at the Poles. Similarly stretch indiarubber bands over the parallels of latitude, fastening them to the iron ring and to the meridians where they cross. While the ring is kept on the globe these indiarubber bands show the parallels and the meridians on the sphere. When the ring is lifted off the globe the indiarubber shrinks to a plane and shows exactly the lines of the stereographic projection. This is the projection used in all atlases for the world in hemispheres, for continents, and for large surfaces. It gives, indeed, a notion of rotundity and a general idea of proportion, but the central portions are shrunk in, and the edges are distorted.

Mercator was a

The next projection to be studied is MERCATOR'S. Fleming who lived in the sixteenth century. He was almost an exact contemporary of John Knox. He was a writer on theology and geography. His real name was Gerard Kremer, which name, meaning merchant, he Latinised, in accordance with the custom of the day, into Mercator.

His invention is very clever. The construction of it is a little complicated, and is generally shirked in text-books, but the actual idea is very simple, and I have here designed a piece of apparatus to illustrate exactly what I believe Mercator did when he evolved his system.

Though I have no direct evidence to show how Mercator argued out his system, I have not the least doubt that it was somewhat thus:

Mercator was a globe-maker, and no doubt worked from the globe. He stripped his gores off the globe, forming a map like this (Fig. 1), which was naturally very inconvenient, owing to the hiatuses between the meridians. He was obliged to join the gores along their meridians (Fig. 2). He then found that he had distorted everything, and the distortion increased in the higher latitudes owing to the gores being further apart towards the top of the map. In order to restore a balance of orientation

(or the relative positions and direction of places), as he had distorted in longitude, so he had exactly in proportion to distort in latitude, as shown in Fig. 3, a complete Mercator's Map of half the Northern Hemisphere, in which you will observe that the parallels are farther and farther apart as the latitude gets higher.

As these gores are not a familiar shape, I have a square here which will catch the eye at once (Fig. 1a). I distort it first by pulling it out horizontally as Mercator did in joining the meridians, and it ceases to be a square and the orientation is changed (Fig. 2a). I then distort it in height in the same proportion, and it becomes once more a square with the true orientation but larger than the original square (Fig. 3a). This is exactly what we did before with the gores of the globe. Every parallel, in Mercator's Projection, is a straight line, and every meridian is also a straight line. We have, then, an excellent sailing chart; sailors can now find their direction or course by drawing a straight line from point to point. As Sir George Grove puts it very neatly (though he shirks the explanation of the projection), "The most ignorant sailor can lay down his course without calculation. In fact, the invention of this map has been justly called one of the most remarkable and useful events of the sixteenth century; because it enables common, unlearned people to do easily and correctly what only clever, learned people could have done without it."

Mercator's Projection is that used in all nautical charts to this day, because to the sailor it is far more important to know his direction or course than his distance, which with ordinary nautical knowledge, or from nautical tables made for him, he can easily calculate, but he needs to see his course.

In the CONICAL PROJECTION (Fig. 5) we imagine a cone of paper to be rolled round the globe, touching it on the middle line of the map. Near their line of contact the map coincides very nearly with the globe surface, and is fairly accurate; but as it gets further away from the touching point the distortion grows, the places being shown larger than in reality. For comparatively small areas, such as for maps of England or France, it is fairly accurate, and is the projection used in atlases.

In the diagrams on pp. 424, 425, we see the same globe projected on the same scale, but with very different proportions. These three projections are typical ones and the most commonly used, but there are many others. For those desirous of studying the subject the best work on it I know is the article by Mr. Taylor, in the June number of the Scottish Geographical Magazine of last year, and to that article I refer them.

MAP-MAKING. We have now seen how the traveller finds his place on the globe's surface, and how, when found, he can project or map that information on a flat sheet. We shall now see how a map will grow. Imagine a ship sailing into unexplored seas and coming to some land, say an island. The navigator at once fixes his position in the ship in latitude and longitude. The navigator's instruments are the sextant, the chronometer, and the mariner's compass. The general idea of the mariner's compass is that it always points to the north; but accurately this is not so. The general direction of the compass, or the Magnetic Pole, is not the true north,