
lard 
Principles of Aerodynamies. 679 
By similarity ( B=sab=—) aS WA it can be 
a 
shown easily that a consequence of Bunsen’s law in its 
usual form—with constant pressures—is proportionality of 
the passing volume to the cross-section of aperture, while 
proportionality to the third power of its dimensions would 
imply inverse proportionality to viscosity—this last rule being 
illustrated by the example of the transpiration formula. 
§ 12. Accerding to numerous experimental investigations 
about effusion (see § 1) the velocity of the stream of gas 
cannot be augmented, by increase of pressure, beyond a 
certain limit, not depending on the difference of internal and 
external pressure, but on their ratio si (= about, 1°69): 
1 
Now suppose two experiments with the same mouth-picce 
bf . . e P ° 
being made where this ratio has been attained P2 — = 2 
Pi 1 
Then the second experiment is similar to a third one, with 
the same velocity, with pressures p,, 2, but with dimensions 
. . e * y) . 
of the mouth-piece increased in the ratio = = mi whence it 
: 2 
follows—in accordance with the experiments alluded to— 
that this velocity must be independent of those dimensions. 
(Approximately equal to the velocity of sound, Hugoniot, 
Compt. Rend. cil. p. 1178 (1886); Lamb, Hydrod. p. 28.) 
Mach and Salcher (Wied. Ann. xlii. 1890) and Emden 
(Wied. Ann. xlix. 1899) noticed the formation of strize in 
the stream of gas, when the above critical ratio was surpassed. 
According to HKmden’s interpretation, they are a series of 
standing waves of sound, accompanied by changes of density. 
Their distances, carefully measured, were found to satisfy the 
relation 
r=0-85d4/ Ey ie! 
va 
Emden, however, might have saved part of the experimental 
work by use of our method ; for it is sufficient to know that 
A is a function of the ratio of pressures ; the proportionality 
to the dimension d follows of itself from the similarity 
p= B—hkh=n= 1) 0= “). 
nl 
Likewise, such a result being established for air, there 
follows necessarily, by (b=n=1; m= ae n= £.), its 
J wind 
