buying a piece of land in a large city a difference of half an inch in the width would be a matter of importance. Now, while most of the determinations of position from which the skeleton of a map is made are done by means of the measurements of angles and not of lines, there must be, to start with, a base measured somewhere on the surface, as a necessary preliminary to the triangulation, or the angular measurement of the net-work of triangles which covers the region to be mapped, and which forms the frame, so to speak, into which all the details are to be fitted. This base line must, however, be measured with the utmost precision, even down to the smallest fraction of an inch; for any error made at this preliminary stage of the work would be many times magnified as the work was extended from its original starting-point, and the value of the whole would be destroyed. It would be hardly possible to convey to the uninitiated an idea of the skill which has been bestowed on the construction of the instruments with which this base measuring is to be done, and of the patience and care with which they must be used. With the apparatus devised by Bache and Würdemann, and used on the United States Coast Survey work, distances are measured with such precision that the probable error in one mile is only about two hundredths of an inch. And to show the accuracy with which the work may be extended from a measured base by triangulation, it may be stated that a line 5.4 miles long on Chesapeake Bay was connected in the primary triangulation of the United States Coast Survey with a measured base of 8.7 miles on Long Island, the two being 208 miles distant from each other in a straight line. Yet the measured length of the base of verification on Chesapeake Bay agreed with its calculated length, as determined by computation of thirty-two connecting triangles, within four inches. Thus the same degree of accuracy is required in the angular as in the linear measurements, the instruments required for each of them being alike delicate and ingenious in their construction and requiring the most refined skill for their handling. As a general rule, the sides of the primary triangles should be made as long as possible; that is, the two ends must be as far apart as vision aided by powerful telescopes can be extended. The object sighted at one end of

the line is a beam of the sun thrown by a mirror directly into the axis of the telescope at the other end. By this beautiful contrivance the stations may be in some cases as much as a hundred miles distant from each other, while the average length of the sides of the primary triangles in the Ordnance Survey of Ireland is fully sixty miles. This preliminary work is called the main or primary triangulation, and the points fixed in position by it are determined with all the precision that is possible by means of the most refined observations made with the largest and most perfect instruments that can be constructed. Further approaches to absolute accuracy are made by means of frequent repetitions of the observations, which are afterwards examined by the aid of mathematical analysis, so that every possible source of hidden error may be detected. It is to the points thus determined by means of the primary triangulation that the rest of the work is connected and referred; a less degree of accuracy being required for the secondary and tertiary triangulations, because these can always be checked by means of the primary stations. This more detailed work is simply a dividing up of the large triangles into smaller ones, each step in the operation having as its object the fixing of the position of more points; and this is carried on until the whole surface of the country has been cut up into triangles of suitable dimensions. In the British Ordnance Survey over districts where the scale of six inches to a mile is to be used, two points have been fixed by the triangulation on every square mile; and where the scale is five feet to a mile, sixteen points have been determined on the same area. Into the framework thus elaborately prepared the minute details are fitted, and this is done of course by the aid of comparatively small instruments, the use of which requires much less skill than is needed when the larger ones have to be employed. The plane-table is almost exclusively used on the Continent of Europe for the detailed work; and by means of this instrument the work is plotted on the field, and only needs to be inked in afterwards. By the aid of photolithography these plane-table sheets can easily be multiplied to any extent; and it is one of the greatest advances recently made in topographical surveys, that the original work can thus be

cheaply duplicated, and that all land-owners can have without delay copies, on the largest desired scale, of the original surveys of their own property.

Having thus explained as concisely as possible the nature of the operation of a topographical survey, it will be desirable to refer briefly to what is being done in Europe in the way of preparing accurate maps of the different states, before passing on to a review of our own needs. But space will not admit of our doing anything more than merely to indicate, for a few of the most prominent countries, the scope of their topographical work; the simple catalogue of the great maps in process of publication in Europe, made as concise as possible, would occupy many pages of this Review.

Let us begin with Great Britain, which, including Ireland, has an area of nearly 111,000 square miles, and where the topographical survey has been going on since about 1784. The scientific work is partly performed by officers and privates of the Royal Engineer Corps,* and it is officially known as the "Ordnance Survey." Its total cost, from 1791 to the end of 1864, including the military pay of the men employed, was £ 2,991,624, and may be estimated to have been up to the present time about £ 4,200,000. The scales adopted are numerous, and in case of some cities are as large as five and even ten feet to the mile. The principal published maps, however, are on two scales, one of six inches, and the other of one inch to the mile (1: 10,560 and 1: 63,360). Of England the map on the one-inch scale was begun in 1784 and finished in 1869; but the projection employed in it was defective, and it is in other respects not up to the present requirements of the country, hence it is now in process of working over and republication. Of the area surveyed on the six-inch scale, 24,877 square miles had been completed in England and Wales, and 27,829 in Scotland, up to the end of 1873. Ireland, on the same scale, was entirely finished in 1845, and all the sheets, 205 in number, published without, and about half with, the hill-shading. Besides the maps on the six-inch and one-inch scale, plans are furnished of any district as called for,

* 382 military, including officers, and 1,446 civil assistants were on the Ordnance Survey staff in the year 1872.

on the scale of 1: 2,500 (about 25 inches to the mile), made by photozincography; but these are not necessarily engraved or published. The map of London is on a scale of 1:1,000, and is comprised in 821 sheets. The various publications of the Ordnance Survey are sold in single sheets as wanted, at very moderate prices; but so great is their number, that the cost of a complete set, as far as already published, amounts to over £3,000. A great deal of work is prepared for the use of the government on very large scales; but it is chiefly the sixinch and one-inch maps which are of importance to the general public. At the present rate of progress it will require about ten years to complete the survey.

In Belgium the scale adopted is 1: 20,000, the area of the country being about 10,000 square miles; 450 sheets will be required, of which 137 were published up to the end of 1873 ; the contour lines are drawn at distances of one metre, every fifth one being indicated by a heavier line; the sheets are lithographed and printed in colors, the rivers and lakes being in blue, the lettering and roads in black, the meadows and forests in different shades of green, the buildings in brick-red, and the gardens in carmine.

In Prussia, since 1849, new and more perfect methods have been introduced into the topographical surveys; the planetable sheets are now published on a scale of 1: 25,000, and with contour lines at distances of 5, 121, or 25 feet, according to the nature of the country. The publication of the plane-table sheets was commenced in 1868, and in 1873 120 had been issued. There has also been, since 1841, a general map in process of publication, on a scale of 1: 100,000, which will be comprised in some 400 sheets, of which nearly all are issued. These are engraved on copper and have the topography, or hillshading, indicated according to Lehmann's system, as modified by General Müffling.

In Baden, the new map was commenced in 1874, on a scale of 1: 25,000, and with contour lines at 10 metres' distance. The work is mainly a revision and correction of older surveys, and is expected to occupy six years, at a cost of about 80,000 florins.

In Saxony, the original survey was commenced in 1780 and completed in 1806 on a scale of 1:12,000, the area of the king

dom being 5,600 square miles. A topographical map was issued in the years 1837-1860, in 22 sheets and on a scale of 1:57,600. A new map was determined on in 1860, on a scale of 1: 100,000, and it was completed in ten years; there are two editions of this, one with the line-work only and the other with the hill-shading.

Having now shown what is doing in some of those European states which are, comparatively speaking, rich, densely inhabited, and with moderate areas of territory, let us turn to the consideration of some countries which have only a thinly scattered population and a large area. Russia, for instance, with its enormous territory, just about twice the size of that of the United States, Alaska included, has been for many years actively engaged in prosecuting geographical surveys. The map of Russia in Europe, embracing about 2,100,000 square miles, has been under way since 1857, and will be embraced in about 700 sheets, of which 454 had been published in 1872. This is on a scale of 1:126,000. The military map of Poland is on the same scale, and is embraced in 57 sheets, all of which are published. Special maps of the Caucasus have also been completed; and, recently, a map of Central Asia. Norway has an area of 123,300 square miles, and a population about that of Massachusetts; that is, our own State is eighteen times more densely populated than Norway. But this comparatively poor country has set itself on having a good topographical map on a scale of 1:100,000, and which will occupy over 200 sheets. Those which have already appeared have been highly praised for their execution by competent judges; they are printed in chromolithography, like those of Belgium. Sweden also, very similar to Norway in respect to area and density of population, has her topographical maps on the same scale (1:100,000), and the work is already nearly half completed, the first sheet having been published in 1860.

We have thus given, necessarily in a very concise manner, some idea of the scope and methods of topographical surveys; and, before going on to consider what has been done in this country, it will be well to say a few words on the methods employed for mapping regions where, owing to the nature of circumstances, only imperfect work can be done, as in the first