assigned to it; it must be drawn with a definite breadth, length, and direction, about all of which the map-maker is entirely ignorant; and the position of the towns must be put at guess, not only with reference to the rest of the map, but also to one another, and to the mountain range that separates them. If the district were thoroughly known, the map would show upon its face all those geographical relations which pages of laboured description would never exhaust; but being only partially understood, the draughtsman cannot follow the method of a narrator, and be simply silent upon those things of which he is in ignorance, but he is obliged to admit of great blanks in his work, and to consent to leave unrecorded a large part of that which he really knows. Therefore, in the first infancy of geography, maps play a less prominent part than in its more advanced stages; for in attempting to show a little they are obliged to assert too much; and if they endeavour to be explicit, they seriously mislead. Nay, more, the geographer may be, and usually is, in possession of many statements that are contradictory in important points, and these may be stated in treatises, but could never be recorded in a single map; for if it were attempted, the sheet would be scrawled over in endless confusion. A map must represent the conclusion at which the maker of it has, to the best of his judgment arrived, but it does not and cannot give the evidence on which that conclusion is founded.

In all map-making two distinct crafts are required: the one is to survey and draw the outline, the other to fill it up with whatever may give life to the picture-whether it be with conventional symbols, or colouring, or those half profile views of prominent landmarks that ancient geographers so much delighted in, and to which in these present days there seems a tendency to return. Now, of these two parts, the first is thoroughly scientific; and while it requires good instruments and mathematical proficiency to be undertaken at all, it can be followed with certain success by any qualified person who chooses to engage in the labour. The other is of a totally different character; it is purely an art and not a science; it requires a union of artistic skill with great ingenuity, and there seems no assignable limit to the success it may hereafter achieve. These two branches stand to each other in somewhat the same kind of relationship that perspective does to drawing. The one being a matter of dry, accurate, and laborious science, which is the better for being kept in the background, but which can never be disregarded; while the other is a life-like portraiture, the production of which is the end and object of the whole undertaking. It is in this last branch that the great

majority of map-makers up to the present time, are so remarkably unsuccessful. There is quite sufficient accuracy of outline, for general purposes, in the maps of the civilized world; but with very rare exceptions do these maps attempt to present a picture like that which meets a traveller's eye when standing on a commanding mountain peak in a clear day. But before pursuing this question further, it will be well to consider awhile the work that lies before the geographer, for we shall be less tempted to exact too much the more clearly we perceive how vast it is.

The great features of physical geography can be recorded on a map of a very small size in itself, and quite infinitesimal with regard to that of the huge sphere it portrays. On a small sheet of paper there is room to indicate every navigable river, every spacious harbour, every great mountain chain. Lines of equal temperature may be drawn, the zones in which different groups of animal and vegetable life flourish may be sketched out, and room may be found for describing with a bold and accurate touch all other matters of a similar description, such as we find already done for us in the well-known atlases of physical geography; but when we desire to make ourselves acquainted with a particular country, and wish to learn its localities and home features, a map on a far larger scale becomes requisite, and it is a matter of some interest to determine what that scale should really be. Every geographer professes to look forward to a time-a far distant one-in which we shall be in possession of a so-called accurate map or model of the entire earth. But what is meant by the word accurate?-into what degree of detail should a reasonably perfect map be expected to enter? In fine, what should be the scale upon which it ought to be constructed? It were absurd, on the one hand, to desire that every bush and every ditch should be marked down, and on the other hand we assuredly want more than a mere indication of each woodland and each navigable river; but these are wide extremes, and where between them does that mean lie which is to be the goal of our endeavours? The principle may perhaps be accepted as follows:-that every feature which influences aspect, shelter, or means of communication should have a place on the map, that the scale should be of such a size as, generally speaking, to include every object whose magnitude and importance is sufficient to secure permanence, and to have earned for it a definite place in the recollection of its neighbours, or, what answers pretty nearly to so vague a definition, every place or thing large enough to deserve a name. The scale should therefore be sufficiently ample to include brooks, crags, and

clumps of trees. Smaller isolated objects may easily enough be represented by a dot, should they happen to be placed in a conspicuous position, and from that cause to attain importance as a landmark, which from their mere size they would not have merited. Now, as a traveller proceeds on his road, and studies the country that spreads wide away on either side, he will obtain a very accurate knowledge of all that lies within two miles of him, when the day is clear and the light such as to throw the undulations of the ground into relief. At that distance, even the minute details of the rigging of a ship will stand out clear against the sky; objects three feet across, such as distant chimneys, cease to be mere lines, and have a sensible breadth; the very trunks and boughs of trees may be visible, and their foliage seen to retain much of an individual character. Now, if the landscape, viewed at a distance of two miles, be drawn exactly as it would appear if projected upon a sheet of paper held ten inches from the eye, (which may be assumed as the distance at which a student would pore over his map), it follows as a necessary consequence that the scale of that projection would be as ten inches to two miles.

It is considered in practice that a delicately executed map of the scale of one inch to a mile, such as our ordnance surveys of England, is quite large enough to include that amount of detail which was claimed a few lines back as essential to a good map of any locality which we wish to study for general purposes. Five times that size was shown to be large enough for making a perfect picture as well as a map. Furnished with these data, let us consider what is the amount of work which has to be accomplished before geographers can become possessed of a map of the whole world, even on the first-mentioned scale. The superficies of the dry land on the globe is about fifty millions of square miles, and consequently the space over which it would have to be drawn would cover fifty million square inches of map, or a square area of five hundred feet in the side, which is a space larger than Portman-square; and a globe representing the earth, built on this same scale, would be more than two hundred yards in diameter. By dwelling awhile upon these considerations, and conceiving these acres of surface, scrawled over with countless lines and touches, each of which requires to be accurately placed to less than the breadth of a needle, we shall gain some idea of the immense variety of hill and dale, and variously configured surface on the broad expanse of this great world of which the geographer has to take cognizance, and with which he is now successfully grappling, each tiny group of which in habitable regions no larger than a wafer on the surface of the map, is capable of

forming a home neighbourhood, with, it may be, its garden, its clump of trees, its neighbouring hillock and brook; within whose narrow bounds whole families may live and die; with which all their associations of boyish days and manhood may be bound up, and in which they may read ample proofs of the presence and goodness of God in the harmony of His countless works that throng even that insignificant fraction of the earth.

The labour that is expended in accurately mapping a large tract of country is enormous. It is proverbially 'a work of ages and of nations;' for not only does it require means far beyond those at the command of a single individual, but it literally seems to take up a longer time to complete than is within the compass of a single life. We have experience of a generation passing by before the observations were made, calculated, and tested, the details filled up, the whole engraved upon plates, and the results issued to the public: for our own ordnance maps have dragged their tedious course along for more than half a century; they were begun in 1796, and a large part of them are still unissued.

The greater part of the surveyor's trouble consists in determining the position of the principal points with scrupulous nicety, for everything depends upon their accuracy. They are cardinal positions, and an error in any one of them is liable to run through the whole map, and lead to contradictions and uncertainties in some distant part of it. Hence, months of labour may be wasted if one of these proves to be incorrect; but if, on the other hand, these alone are perfectly right, and if the details of any district should have been erroneously mapped, it may be resurveyed, and the new plan will be found to fit accurately into the place of the old one. Once done, they are done for ever; but if carelessly laid down, the foundation of the map is irregular, and the whole superstructure becomes distorted and strained awry. The consequence is, that large instruments and long series of observations are brought to bear on their determination, and the work must continue until the positions assigned to them are found to agree sufficiently well with the result of more than one set of measurements and triangulation, and also with their latitudes and longitudes as learnt from the stars. Now, except in parts of Europe and North America, India and the Cape, this has never been done, and perhaps two-thirds of the globe is unmapped, with even a distant and approximative degree of accuracy, while the vast areas of Central Africa and Australia are entirely matters of guess-work.

In childhood we have perfect trust in all that our seniors

Trigonometry, Plane and Spherical.

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tell us; as boys, we consider all that is in print as infallible; and up to much later years do we put an equal and undoubted faith in our maps. But this, too, is doomed to perish utterly on the first shock of experience. There is usually as great a difference in geographical value between an ordnance map and, it may be, a beautifully engraved, popular one, as there is in poetical merit between a copy of Shakspeare and a gorgeously-bound volume of the vilest trash that was ever published by aid of titled interest and half-extorted subscriptions.

It would be quite foreign to the objects of an essay like this to enter at any length into the methods by which surveys of the highest order of accuracy are carried on, but it may be observed that while common triangulating and ordinary star observations, such as travellers depend upon, are very simple matters in theory, accurate surveying calls forth all the resources and the refinements of high mathematics, and is therefore comparatively rare. A good sextant, and a practised observer can, without much difficulty, find his latitude to nine or ten seconds, that is to say, to three hundred yards; the best instruments and most skilled observers will give the latitude to about one second, or thirty-three yards. Between these two classes of work there is all the difference in the world; the first can be managed by the rules of plane trigonometry, or without trigonometry at all, by simply protracting the angles upon the map, and marking the points of intersection made by the lines which form them; but in the second case, where the greatest possible accuracy is aimed at, a huge coil of difficulties is introduced. In the first place, the whole matter is taken out of the domain of plane mathematics, and put into the cumbrous formula of spherical trigonometry, because in accurate work, the globular form of the earth becomes far too sensible in its effects on the results to be disregarded in the calculations. Again, the instrument itself is mistrusted, and allowances have to be made for the errors of its workmanship, which must be found out by artfully contrasted observations, of such a character as to eliminate or define them. finally, the varying effect of refraction affords a serious difficulty; in fact, the matter becomes an exceedingly troublesome problem.

And

It may seem scarcely credible to some persons that, huge as is this earth, three hundred paces should take us so far round its shoulder (if such an expression be permitted) as to make a perceptible difference in the appearance of the heavens when measured by a small hand-instrument sufficiently light and simple for a traveller to take with him in the rudest