I might go on cataloguing in detail the many uses to which models may be put, but shall now mention only one more—perhaps the most important of all—their use in the education of the young. No method has yet been devised that is capable of giving so clear and accurate a conception of the principles of physical geography as a series of well selected models; models have, indeed, already been used for this purpose, but unfortunately their great cost has prevented their general use in schools. Since, however, the study of geography has been placed upon a new basis and a new life has been infused into it, many men have given their attention to the subject of models, and have experimented with a view to cheapen the cost of reproduction, which has hitherto prevented their wide distribution; and probably this objection will soon be remedied. The ability to read a map correctly,—to obtain from a study of the map a clear conception of the country represented,—is more uncommon than is usually supposed. Some of the recent methods of teaching geography are intended to cultivate this very faculty, but it is doubtful whether there is any better method than that which consists in the study of a series of good models in conjunction with a series of maps, all on the same scale and of the same areas. The value of a series of good models in teaching geology is so apparent that it need only be mentioned. It is often, for reasons stated above, far more valuable even, than field instruction.
For the construction of a good relief map the first requisite is a good contoured map. To this should be added, when possible, a good hachured map, upon which the elevations of the principal points are stated,—if the interval in the contoured map is a large one,—and as much material in the way of photographs and sketches as it is possible to procure. The modeler should, moreover, have some personal acquaintance with the region to be represented, or, failing that, a general knowledge of topographic forms, and at least a clear conception of the general character of the country which he seeks to represent. This is very important, for it is here that many modelers fail: the mechanical portion of the work any ordinarily intelligent person can do. A model may be as accurate as the map from which it is made, every contour may be placed exactly where it belongs, and yet the resulting model may be,—indeed, often is—"flat," expressionless, and unsatisfactory. Every topographer in drawing his map is compelled to generalize more or less, and it is fortunate for the map if this be done in the field instead of in the draughtsman's office. But topographers differ among themselves: there may be, and often is, considerable difference in two maps of the same region made by different men; in other words, the "personal equation" is a larger element in a map than is usually supposed. This being the case, there is something more required in a modeler than the mere transferring of the matter in the map,—giving it three dimensions instead of two: he must supply through his special knowledge of the region (or, failing that through his general knowledge) certain characteristics that do not appear upon the map, and undo, so far as it is necessary, certain generalizations of the topographer and draughtsman. This artistic or technical skill required correctly to represent the individuality of a given district is especially important in the modeler; it is more important, perhaps, in small-scale maps of large districts than in large-scale maps of small ones,—for in the latter the generalizing process has not been carried so far, and the smaller interval of the contour lines preserves much of the detail.
The methods by which relief maps are made have always received more attention than would, at first sight, appear to be their proper proportion. It may be due, however, to the difficulty of applying any test to determine the accuracy of the finished model, and perhaps also to the general impression that any one can make a relief map,—and so he can, though of course there will be a wide difference in the value of the results. Some, indeed, have devoted their attention to methods exclusively, letting the result take care of itself,—and the models show it. There is no more reason why a modeler should tie himself down to one method of work, than that a water-colorist, or a chemist, or anyone engaged in technical work, should do so; though in some cases he might be required, as the chemist is, to show his methods as well as his results.
One of the earliest methods, with any pretension to what we may term mechanical control, is that described by the Messrs. Harden in a paper on "The construction of maps in relief," read before the American Institute of Mining Engineers in 1887. The method was published in 1838. Upon a contoured map as a basis cross-section lines are drawn at small and regular intervals, and, if the topography be intricate, corresponding lines at right angles. The sections thus secured are transferred to thin strips of some suitable material, such as card-board or metal, and cut down to the surface line,—the strips themselves thus forming the cross-sections. These cross-sections are mounted upon a suitable base-board, and the cavities or boxes are then filled up with some easily carved material, such as plaster or wax. The top is then carved down to the form of the country or district,—the necessary guidance being obtained by the upper edges of the strips that form the cross-sections. It will be readily seen that this method is a very crude and laborious one. It necessitates in the first place a good contoured map upon which to draw the sections, but sacrifices much of the advantage thus gained because only a number of points on each contour line are used, instead of the entire line. It is no better, although actually more laborious, than the later method of driving contour pins (whose height above a base-board may be accurately measured,) along the contour lines, and then filling in. A slight modification of the latter method can be used to advantage when no contoured map is available, and when the points whose elevation is known are not numerous enough to permit the construction of one. In this case the only control that can be secured is by means of a number of pins driven into the base-board at those points whose elevation is known. The remainder of the map is then sketched in. This method is perhaps as satisfactory as any, when the material upon the map is scanty. Another method, however, growing out of the same scantiness of material, is in some cases to be preferred, especially for large models. The map is enlarged to the required size, and a tracing of it is mounted upon a frame. Another deep frame, just large enough to contain the mounted tracing, is made, and laid upon a suitable base-board upon which a copy of the map has been mounted. Upon this base-board the model is then commenced, in clay or wax. The low areas are modeled first,—horizontal control being obtained by pricking through the mounted tracing of the map with a needle point, and vertical control by measuring down from a straight edge sliding on the top of the deep frame. This system is rather crude, and only useful where the material upon the map is very scanty, but it gives excellent control.
A method used by Mr. F. H. King in the preparation of his large map of the United States is described by him in a letter to Messrs. Harden, and published by them in the place mentioned. A solid block of plaster is used,—the contoured map being transferred to it—and the plaster is carved down to produce a series of steps like those made by building up the contours. The shoulders are then carved down to produce a continuous surface. This method is one of the best of those that require carving instead of modeling.
Many other methods of producing relief maps might be mentioned, but, as most of them have been used only to make special models, they need not be described. The method that has been more used than any other still remains to be described. It is that which the writer has used almost exclusively, and consists in building up the model and modeling the detail, instead of carving it. It is a maxim of the modeler that the subject should be built up as far as possible, should be produced by adding bits of clay or wax, or other material, and not by carving away what is already on,—by addition and not by subtraction. This may be illustrated by a reference to the methods of the sculptor. The bust, or figure, or whatever the subject may be, is first modeled in clay or wax; from this model a plaster mould is made, and from this mould a plaster cast is taken. This cast is called the original, and the finished production, whether in marble, bronze, or any other hard substance, is simply a copy of this original. No one ever attempts to produce the finished bust or figure directly from the object itself. Even where the artist has for a guide a death mask, the procedure does not change. The bust is first made in clay, and this clay model, as a rule, contains all the detail which subsequently appears in the finished bust. It seems strange, therefore, that the relief map maker should use a method which the sculptor, with infinitely more skill and judgment, is afraid to use; and this on subjects that do not differ as much as might be imagined.
The contour interval to be used depends on the use to which the model is to be put. It is not always necessary to carry into the model all the contour lines upon the map: I may go further and say that it is not always desirable to do so. The number to be used depends to some extent on the skill of the modeler. As already stated, the contours are only a means of control, and one modeler requires more than another. To build into a model every contour in a contoured map of ten foot interval is a very laborious proceeding, and not worth the time it takes, as in nine out of ten maps of such interval only the fifty-foot or the one hundred-foot curves are definitely fixed, the intermediate lines being merely filled in. This filling in can be done as well, or better, by the modeler.
The question as to the proper amount of exaggeration to be given the vertical scale, as compared with the horizontal, is the question about which has raged most of the controversy connected with relief map making. This controversy has been rather bitter; some of the opponents of vertical exaggeration going to the length of saying that no exaggeration is necessary, and that "he that will distort or exaggerate the scale of anything will lie." On the other hand the great majority of those who have made relief maps insist upon the necessity of more or less exaggeration of the vertical scale—generally more than seems to me necessary, however.
An increase of angle of slope accompanies all vertical exaggeration, and this is apparent even in models in which the vertical element is only very slightly exaggerated. It produces a false effect by diminishing the proportionate width of the valleys, and by making the country seem much more rugged and mountainous than it really is. A secondary effect is to make the region represented look very small—all idea of the extent of the country being lost. This can be illustrated better than described. The King model of the United States is an example of one extreme; it is worthy of note that no examples of the other extreme—too little exaggeration—are known.
In small-scale models of large districts some exaggeration of the vertical scale is necessary in order to make the relief apparent, but the amount of this exaggeration is often increased much beyond what is essential. The proportion of scales must depend to a large extent on the character of the country represented, and on the purposes for which the model is made. It has been suggested by a writer, quoted by the Messrs. Harden, that the following exaggeration would afford a pleasing relief: "For a map, scale 6 inches to 1 mile: if mountainous, 1:3; if only hilly, 1:2; if gently undulating, 2:3. For smaller scales, except for very rugged tracts, the exaggeration should be correspondingly increased. For a tract consisting wholly of mountains no exaggeration is necessary." I know of no country of such a character that its relief, in all its detail, cannot be shown upon a scale of 6 inches to 1 mile without any exaggeration at all.