I shall not refer now to the applications of these instruments in
chronography, but will rather point out first the applications in which
they are destined to produce an effective power.
For this purpose it is necessary to make them pretty massive. The number
of the vibrations depends upon such massiveness, and it is necessity to
know the relation which exists between these two quantities in order to
be able to construct an instrument under determinate conditions. I made
in former years such a research with regard to tuning forks of prismatic
form, that is to say, of a constant rectangular section continuing even
into the bent portion where the parallel branches are united by a
semicylinder, at the middle of which is the wrought iron rod as well as
the branches. The _thickness_ of the instrument is the dimension
parallel to the vibrations; its _width_ is the dimension which is
perpendicular to them, and its _length_ is reckoned from the extremity
of the branches up to the middle of the curved portion.
It is found that the number of vibrations is independent of the width,
proportional to the thickness, and very nearly inverse ratio of the
square of the length, provided the latter exceeds ten centimeters.
If we represent the length by l, the thickness by e, and the number
of vibrations by n, we shall have the following formula:
n = k x ( e / l squared )
in which k is a constant quantity whose value depends upon the nature
of the metal of which the tuning fork is made.
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