It seems to me that the absolute and not the relative amount of relief is the desideratum, and I have always used this as my guiding principle. For small scale models I have found half an inch of relief ample. It may be worth while to state that in a model of the United States made for the Messrs. Butler, of Philadelphia, the horizontal scale was 77 miles to 1 inch, the vertical scale 40,000 feet to 1 inch, and the proportion of scales as 1 to 10. This proportion could have been brought down as low as 1:6 with advantage. One-fortieth of an inch to a thousand feet seems a very small vertical scale, but it sufficed to show all the important features of the relief. It should be stated, moreover, that the model in question was very hurriedly made—in fact, was hardly more than a sketch-model—and that more care and more minute work would have brought out many details that do not now appear. This amount of care was not considered necessary in this instance, as the model was made to be photographed and published as a photo-engraving, and was to suffer an enormous reduction—coming down to five by seven inches.2
2 See [plate] from "Butler's Complete Geography."
It has been frequently urged by the advocates of large exaggeration that the details of a country cannot be shown unless the vertical scale is exaggerated; that hills 200, 300, or even 500 feet high—depending of course upon the scale—flatten out or disappear entirely. This seems plausible, but the advantages of great exaggeration are more apparent than real. Its effect upon the model has already been mentioned; it should be added that, with the proper amount of care in finishing the model, exceedingly small relief can be so brought out as to be readily seen. With ordinary care, one-fortieth of an inch can be easily shown, and with great care and skill certainly one-eightieth and probably one-hundredth of an inch. Another plausible argument that has been advanced in favor of vertical exaggeration as a principle, is well stated by Mr. A. E. Lehman, of the Pennsylvania Geological Survey, in a paper on "Topographical Models," read before the American Institute of Mining Engineers in 1885. "A perfectly natural expression is of course desired; and to cause this the features of the topography should be distorted and exaggerated in vertical scale just enough to produce the same effect on the beholder or student of the district of country exhibited as his idea of it would be if he were on the real ground itself. Care should be taken, however, not to make the scales so disproportionate as to do violence to mental impressions. Often, indeed, prominent or important features, when they will bear it, may be still more effectively shown by additional exaggeration in the vertical scale." The fallacy of this argument is obvious. It assumes that the object of a model is to show the country as it appears to one passing through it, and not as it really is—and there is often a very wide difference between the two. The impression derived from passing through a country is, if I may use the term, a very large-scale impression, as any one who has tried it can certify; it is certainly a mistake to attempt to reproduce this impression in a small-scale model, with the help of vertical exaggeration. Even if the principle were a good one, its application would be very limited. It could only be used in large-scale models; to apply it to a model of a large area—the United States, for example—is obviously absurd.
The method referred to as being now generally in use may be briefly described as follows: requisites, a good contoured map; a hachured map in addition, if possible; a clear conception on the part of the modeler of the country to be represented; and a fair amount of skill. Materials: a base-board of wood or other suitable material; card-board or wood of the thickness required by the contour interval and the scale; and modeling wax or clay. Procedure: reproduce the contours in the wood or other material; mount these upon the base-board in their proper relationship; then fill in the intervening spaces, and the space above the topmost contour, with the modeling material.
In a series of models of the Grand Divisions of the earth, made about a year and a half ago, the contours of card-board were made as follows: the map was photographed up to the required scale, and as many prints were made as there were contour intervals to be represented—in a model of the United States of 1,000 feet contour interval there were fourteen prints. Thirteen of these were mounted upon card-board of the exact thickness required by the vertical scale, and one upon the base-board. All large paper companies use a micrometer gauge, and card-board can easily be obtained of the exact thickness required—even to less than the thousandth part of an inch. The lowest contour was then sawed out upon a scroll saw, and placed upon the corresponding line of the map mounted upon the base-board. This process was repeated with each of the succeeding contours until all were placed and glued into their proper positions. At this stage the model presents the relief in a series of steps, each step representing a rise corresponding to the contour interval. The disadvantages of the method lie in the fact that unless the greatest care is exercised in making the photographic prints there will be considerable distortion, owing to the stretching of the paper in different directions, and consequently much trouble in fitting the contours. If care be exercised in having the grain of the paper run in the same direction in all the prints, trouble in fitting the contours will be much reduced, but the distortion in one direction will remain. In our experience this distortion amounts to about two per cent.; in other words, a model that should be fifty inches long will in reality be fifty-one inches; but, as this error is distributed over the whole fifty inches, it is not too great for an ordinary model. If greater accuracy be required, it can be secured by transferring the contours to the card-board by means of tracing or transfer paper. The great advantage of the photographic method lies in the fact that when the model has been built up, with all the contours in position, it presents a copy of the map itself, with all the details, drainage, etc., in position, instead of blank intervals between the contours. Such details and drainage are a great help in the subsequent modeling.
The next step in the process is to fill in with clay or wax the intervals between the contours. I have always found wax more convenient than clay for this purpose as, unless the surface coating is a thick one, the clay is difficult to keep moist. To obviate this difficulty, some modelers have used clay mixed with glycerine instead of water; this, of course, does not become dry, but the material is, at its best, unsatisfactory. The filling-in process is the most important one in relief map making, for it is here that the modeler must show his knowledge of, and feeling for, topographic forms. Some models seem to have been constructed with the idea that when the contours have been accurately placed the work of the modeler is practically done. This is a great mistake. The card-board contours are only a means of control, occupying somewhat the same relation to the relief map that a core or base of bricks, or a frame of wood, does to other constructions as, for example, an architectural ornament or a bust. It is sometimes necessary to cut away the contour card; for, as has been already explained, a map is more or less generalized, and a contour is frequently carried across a ravine, instead of following it up, as it would do if the map were on a larger scale. Such generalizing is of course perfectly proper in a map, but, with the same scale, we expect more detail in a model. The modeler must have judgment enough and skill enough to read between the lines, and to undo the generalizing of the topographer and draughtsman, thus supplying the material omitted from the map. This can be done without materially affecting the accuracy of the model, considered even as a copy of the contoured map.
The contours of card-board or other material are, let me repeat, only a means of control. The perfect modeler—a variety, by the way, yet to be evolved—would be able to make an accurate relief map without them, in the same way that other subjects are made; as, for example, a flower panel, an architectural ornament, or any other subject in low relief, where the object sought is artistic effect and great accuracy is not a desideratum. It is the converse of this idea that has produced the numerous models that one sees; accurate enough, perhaps, but wholly expressionless and absolutely without feeling. This is the great fault of nearly all models made by building up the contours in wood and then carving down the shoulders. It is then necessary to sand-paper them, and what little character they might otherwise have had is completely obliterated by the sand-paper. Such models almost invariably look wooden. Let the modeler, then, have a clear conception of his subject and not depend wholly on the contours, and let him work out that conception in his model, "controlled" and helped by the contours, but not bound by them; the resulting model will thus be far more satisfactory and a far better representation of his subject, in other words, it will be more life-like—more nearly true to nature.
The model, provided it be not of clay, is sometimes used in the state in which it is left when finished. It is much more common, however, to make a plaster mould, and from this a plaster cast. For this purpose a moulder is usually called in; but moulders as a rule are ignorant men, accustomed to one line of work only, and the result is not always satisfactory. It is much better for the modeler himself to do this work, though to obtain good results from plaster it is necessary to know the material thoroughly, and this knowledge comes only from experience. The mould is generally made quite heavy, in order to stand the subsequent hard treatment that it may receive, and should be retouched and thoroughly dried before being prepared for the cast. The method used by some modelers of placing a frame about the model and pouring in the plaster, filling the frame to the top, is a crude and very wasteful one and not at all to be recommended. In a model of large size—say seven or eight feet square—it would require a derrick to move the mould. It is wholly unnecessary, as, with a small amount of care, a good mould can be made not more than an inch thick, or, at most, an inch and a half. The drying of the mould before use can sometimes be dispensed with, but is always desirable.
Nearly all American moulders (as distinguished from French and Italian ones) varnish the mould, and thus lose some of the finest detail and sharpness. This is unnecessary. The mould can be easily prepared with a solution of soap so as to leave nothing on the surface but a very thin coating of oil, which is taken up and replaced by the plaster of the cast. Of course, if the model has been sand-papered, no fine work in moulding or casting is necessary, as there is nothing to save. If the subject is a very intricate one, with "undercuts" (as they are called), it is customary to make a waste mould; as this is very seldom necessary in relief map work, however, the process need not be described.
To make the cast it is only necessary to repeat the processes used in making the mould. With great care and some skill a cast can be produced but little inferior in point of sharpness and detail to the original model. It is customary to make the cast very thick, and, consequently, very heavy; this is unnecessary. In our work we seldom make a cast thicker than one inch, and yet are never troubled with changes in the model after it is finished. Even in a very large cast (now in the National Museum), weighing nearly 1,500 pounds and presenting a surface of over 160 square feet, the average thickness is less than one inch, although it required over five barrels of plaster to make it. The cast, after being thoroughly dried, should be finished—all its imperfections being carefully repaired. The surface, however, should be touched as little as possible, as the slight roughness of surface that comes from the original model, through the mould, is removed by any tooling. This roughness adds much to the effect of the model; in fact, where the scale is large enough, it is sometimes desirable to emphasize it.