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378 G. F. HUTCHINS [J. S. M. p. E.
For the purpose of preserving one system of nomenclature, I shall adopt the notation of the paper mentioned above; small letters will designate dimensions of the model, small prime letters dimensions in the imaginary scene or world, and capital letters the ratios of the former to the latter.
It is a well-known fact that all falling bodies are subjected to the same nearly constant acceleration on our earth, very slight changes being observed at different points on the surface. Without realizing this fact in many cases we are all conscious of it, and any attempt to show us any other behavior of falling bodies will immediately destroy our illusion as to the "earthly" qualities of the scene which we are witnessing. The acceleration must, of course, be the same as our earthly acceleration in order to establish the illusion.
Now with these facts in mind, let us write the expression, in dimensional form, for the acceleration with which we are working, calling this nearly constant acceleration which we experience on the earth g.
I
« = ?
and let us remember that
/ = LI'
m = mm' t = 7T.
Suppose for example that we wish to show a scene of a large building toppling. Let us assume that the building which we have in mind is actually 200 feet in height. Perhaps it is most convenient to build a miniature of this building ten feet in height. We have now established the ratio
In order that we may film this miniature action here on the earth we must content ourselves with the fact that the bricks in the miniature will still fall with an acceleration g, hence,
I
but