

Principles of Aerodynamics. 675 
Suppose experiments to have demonstrated (a) pro- 
portionality to velocity and to linear dimensions: then it 
follows that resistance must be strictly proportional to the 
viscosity of the gas, corresponding to its temperature. On the 
contrary, if resistance increases at the rate of the squares of 
velocity and dimensions, it must be proportional to the density 
of the gas. 
It ought to be emphasized, with respect to the above- 
mentioned experimental researches, that the usual supposition 
of proportionality to density and surface is inconsistent with 
any other law than that of square of velocity. 
§ 8. A singular phenomenon, not restricting, however, the 
preceding conclusions, are the turbulent motions setting in 
when a certain limit of stability is surpassed and increasing 
with velocity of the moving body to such a degree as to pro- 
duce a whistling sound. Although no attempt even seems 
to have been made to give a theory of it, we may predict, in 
consequence of (a=@B=h=m=1: J= =), the number of 
ae ee is Ant ERPS OT ‘ 
vibrations ( of dimension ain )—for a given speed and tem- 
7 
\ 
perature—to be inversely proportional to the dimensions of 
similar moving bodies, if simultaneously pressure is changed 
in the same ratio. 
A relation of similar form, but containing additional 
empirical elements, has been found by Strouhal (Wied. Ann. 
y. p. 216, 1878) in his experiments on sounds produced by 
the motion of cylindrical bodies, for example wires, in air of 
atmospheric pressure: the number of vibrations was pro- 
portional to the ratio of velocity to diameter of the moving 
body, N= —. 
Now we may prove easily, by our method, this formula to 
imply: independence of the sound of pressure and tem- 
perature. Strouhal, on the contrary, maintains an elevation 
of sound to be produced by increase of temperature ; but his 
numbers referring to the temperatures of 9°5 C. and 37° C, 
do not seem to be very conclusive ; on the other hand, too, the 
above formula is not quite exact. The influence of pressure 
has not been investigated experimentally. 
There have not been used any other gases than air in these 
experiments; butit can be shown, by the principle of similarity, 
that the constant ¢ must have the same value for different 
gases ; the sound must be independent of their nature. 
§ 9. Experiments made by Joule and Kelvin (loc. cit. ante) 
on the heating effect aye tb thermometers and wires 
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