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Full text of "Scientific Papers - Vi"

1918]             NOTE  ON  THE  THEORY  OF  THE  DOUBLE  RESONATOR                 551
If pf and j922 differ sufficiently, we may pursue an approximation from (8) founded on the smallness of S'/S. But it is of more interest to suppose that •3^ and p32 are absolutely equal, which nothing precludes. Then
)r, if S'fS be small enough,
92 differing but little from pf or p2\ Referring back to (5), we have
X,-Xi_    Sp* ._?_
A\     "    a*Cl-pf       -
yhen we introduce the value of p2 from (11).    Thus
We may now compare effects in the two component resonators, and here i certain choice presents itself. The condensations in the interiors arc X-i - XZ)/S and X2/S', and the ratio of condensations is
ipproximately. It appears that the condensation in the second resonator nay be made to exceed to any extent that in the first by making the second •esonator small enough, which sufficiently explains the advantage found in experiment to attend the combination.
In some forms of the experiment we may have to do rather with the flow through the passages than with the condensations in the interiors. In (12) ye have the ratio of the total flows already expressed. But we may be more ;oncerned with a comparison of flows reckoned per unit of area of the passages. [n the case of passages which are mere circular apertures of radii R and jR' a simple result may be stated, for then c: : C2 = R : R' ; and, since p^ = p^t ?! : c2 = S : $'. Accordingly
ind the advantage of a small S' is even more pronounced than in (13).perature upon sound is thus about 2000 times greater than upon light. If we suppose the system of temperature differences to be altered in this proportion, the course of rays of light and of sound will be the same.