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DIMENSIONAL ANALYSIS AS AN AID TO MINIATURE CINEMATOGRAPHY
G. F. HUTCHINS*
At the May, 1924, convention of the Society, a paper was presented by Mr. J. A. Ball on the subject "Theory of Mechanical Miniatures in Cinematography."1 This dealt with the relation of length and time as seen from the motion picture standpoint. It is the purpose of this paper to revive this subject with the hope of making clear some points which may have been vague to many at the time.
Mr. Ball chose four fundamental quantities on which to base his discussion — force, /, mass, m, length, /, and time, t. I prefer, since these quantities are not mutually independent, to accept only three as being fundamental, namely, m, /, and /, and to regard force as a composition of the three. This may simplify the things which we must keep in mind.
Sir Isaac Newton has stated a series of laws, which, while having been recently modified by the relativity theory, may be accepted for our purposes as governing the motion of bodies in our known universe. These laws may be briefly summarized by the one equation:
/ = ma,
where a is the acceleration of the body, or its rate of change of velocity in feet per second per second. It is immediately seen that the dimensional expression for acceleration is:
We are now able to tie force in, if we choose, with our fundamental quantities of mass, length, and time, that is,
*
J t*
* General Electric Company.
1 BAI<L, J. A.: "Theory of Mechanical Miniatures in Cinematography," Trans. Soc. Mot. Pict. Eng., No. 18 (May, 1924), p. 119.
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