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.
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]
[Footnote 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.
The proper way to paint a model is a matter that must rest principally
upon the judgment of the modeler, depending to some extent, also, on
the use to which the model is to be put. The plain cast is sometimes
used, drainage, lettering, etc., being put directly upon it. This has
the advantage of preserving all the detail that comes from the mould,
but it has also the disadvantage of a surface easily soiled and
impossible to clean. If the model is to be photographed, the surface
should be nearly white--in our practice we use a small amount of yellow
with the white. This yellow is hardly appreciable by the eye, but its
effect upon the photographic negative is quite marked. Yellow becomes
grey in a photograph, and, in a photograph of a model colored as
described, a grey tint is given to the whole surface. The high lights
are not pure white, and there is no harsh contrast between light and
shade. There is another point of great importance in photographing
models: the surface should have a dead finish--that is, should have no
gloss, or, at most, should have only what is known among painters as an
egg-shell gloss. It is almost impossible satisfactorily to photograph a
model that has a shiny surface. Any portion of a model that it is
desired to separate from the rest should be painted a different
color--the water, for example, should be painted a light blue; not a
blue composed of indigo, however, or any of the grey blues, as these
produce in the photograph a dead grey, and are not pleasant to the eye.
The most satisfactory color that we have used is a mixture of
cobalt--the purest of the blues--with Antwerp blue--which is quite
green--and white. This gives a color that is pleasant to the eye, has
the retreating quality to perfection, and photographs well.
Models intended for exhibition as such should be painted realistically.
There is room here for an immense improvement in the usual practice,
which is to paint the model either in some conventional scheme of light
and shade, or else to put a single flat tint upon it. If the model is
to be colored conventionally it is, in my opinion, much better to use a
flat tint, light in tone, and with a dead surface. The use of a variety
of colors upon the face of a model interferes materially with the
relief, especially if the relief is finely modeled. For this reason
models colored to indicate geologic formations should always be
accompanied by duplicates representing topography only, colored
realistically, if possible, and without lettering. Well-defined lines
other than those pertaining to the model itself, such, for example, as
those used to define the boundaries of geologic formations, should not
be allowed upon a model when it is desired to bring out all the relief.
The lettering on such models should be kept down as small as possible,
or wholly dispensed with. The latter is much the better method.