316 AEOLIAN TONES [30-4
from, the value given by (I). He further showed that with a given diameter and a given speed a rise of temperature was attended by a fall in pitch.
If, as appears probable, the compressibility of the fluid may be left out of account, we may regard N as a function of the relative velocity F, D, and v the kinematic coefficient of viscosity. In. this case N is necessarily of the form
N = VID.f(»IVD), . .......................... (2)
where / represents an arbitrary function ; and there is dynamical similarity, if v oc FT). In observations upon air at one temperature v is constant ; and if D vary inversely as V, ND/V should he constant, a result fairly in harmony with the observations of Strouhal. Again, if the temperature rises, v increases, and in order to accord with observation, we mnst suppose that the function f diminishes with increasing argument.
"An examination of the actual values in Strouhal's experiments shows that v/VD was always small; and we are thus led to represent / by a few terms of MacLaurin's series. If we take
f(x) = a-}- bay 4- coo*,
, " If the third term in (3) may be neglected, the relation between N and V is linear. This law was formulated by Strouhal, and his diagrams show that the coefficient b is negative, as is also required to express the observed effect of a rise of temperature. Further,
so that D . dNfdV is very nearly constant, a result also given by Strouhal on the basis of his measurements.
"On the whole it would appear that the phenomena are satisfactorily represented by (2) or (3)t but a dynamical theory has yet to be given. It would be of interest to extend the experiments to liquids*."
Before the above paragraphs were written I had commenced a systematic deduction of the form of / from Strouhal's observations by plotting NDj V against VD. Lately I have returned to the subject, and I find that nearly all his results are fairly well represented by two terms of (3). In C.G.S. measure
ND _ 3-02\ /K.
Although the agreement is fairly good, there are.signs that a change of wire introduces greater discrepancies than a change in V—a circumstance
* Theory of Sound, 2nd ed. Vol. ir. § 372 (1896). •e have