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Ball — Mechanical Miniatures 121
If forces other than weights are involved in a mechanical miniature they should be scaled down in the same ratio as the weights and then the above rule still holds. For example, if it is desired to represent a rock falling from a cliff and breaking through the roof of a hut, then in the model, the strength of the hut should be scaled to correspond to the weights.
The stress or strain in a plank, or in fact any beam, can be
f shown to be proportioned to p; and where / is proportional to l^
(volume) the stress or strain becomes proportional to /. In other words the stress or strain in a beam depends directly on the scale upon which the beam (and its load) are constructed. If the hut we are considering is built on a one-tenth scale the strain in the roof due to the falling rocks will be one-tenth of what they would be in the full size hut. If the miniature planks of the roof are made of wood they will appear to be ten times as strong as they should be. Practically this means that good sized rocks which should crash through will merely bounce off. So the miniature planks should be made not out of wood but of a material having only one-tenth the strength of wood. Cardboard or papier mache would be about right. Or, the correct effect may be obtained by using wood and giving the planks a preliminary fracture so that nine tenths of their strength is gone.
It is interesting to consider the applications of these rules when human beings appear in the scene. If motion picture of a man are made with a time magnification of three, we would expect to have the representation on the screen of the motions of a man of nine times normal stature. Now the normal stature of a man is so well established in our minds that we do not immediately in this case get the impression of the magnification of dimensions. Refer
: ing again to the equation T'^ = --.-^ it will be seen that if L is not to
be greater than unity, then G must be less than unity, so we can say that the pictures above referred to represent either the motions of a man of nine times normal stature or else the motions of a normal sized man in a place (such as the moon) where the force of gravity is only one-ninth of what it is here. This latter alternative more nearly represents the impression that we get from such pictures.
If, in a scene taken with a high speed camera, there is nothing to give us a clue as to the real size of the objects as for example, no real man in the scene, or better yet, if the scene includes some customary object constructed in miniature such as a miniature house or automobile, then with this assistance our impression of the normal force of gravity is maintained and immediately we get the impression of the magnification of dimensions. Undoubtedly if pictures of a man taken with a time magnification of three were to be combined with pictures of other people taken at normal speed, and if