680 The Principles of Aerodynamies. 
independence of the nature of the gas—demonstrated, in 
fact, by Emden—and its independence of temperature, which 
has not yet been investigated. 
§ 13. The acoustical phenomenon accompanying the rush 
of gas through a slit has been studied experimentally by 
Kohlrausch (Wied. Ann. xiii. p. 545 (1881)) with respect to 
width of the slit and to pressure in the reservoir. The influ- 
ence of the pressure outside, of temperature, and nature of 
gas, might be inferred by our method, too, from this research; 
but we do not enter into this matter, as the results, not fitting 
easily into analytical expressions, are represented by tables, 
which would be rather cumbersome for use. 
§ 14. In the preceding investigations the effect of external 
forces has been entirely neglected—whilst there exist certain 
classes of phenomena where gravity plays a prominent part ; 
for example, motions of the earth’s atmosphere or convective 
currents produced by inequalities of temperature. By con- 
siderations analogous to those in § 5 we get three conditions 
for similarity to be fulfilled in such cases :— 
ii =n =a b=B— he; . is) 
n 
Let us examine, in this respect, Lorenz’s result concerning 
the amount of heat given off by 1 cm.’ of a vertical plane 
[height H, breadth infinite, temperature 3) above that T of 
the surrounding gas] which was evaluated approximately 
(Wied. Ann. xiii. p. 592, 1881) :— 
1 LL fooas Oneilaskea af ee. : 
Saat ra a ae 548 pH Jot. 
The form of this expression looks rather peculiar; but we 
satisfy ourselves of its dimensions fulfilling the conditions 
of similarity—as far, however, only as the coefficient ¢ 
is neglected, which points to a serious restriction of its 
validity. 
§ 15. The presence of those convection-currents gives much 
trouble in the determination of thermic conductivity of gases. 
Their influence can be diminished by rarefying the gas; but 
rarefaction below a certain limit of pressure would imply 
another source of errors in certain molecular “ discontinuities 
of temperature,’ as I have called these phenomena (Phil. 
Mag. xlvi. p. 192, 1898). 
Now it may be noticed that relative measurements of 
conductivity can be strictly performed, notwithstanding 
the unknown convective currents, by using corresponding 

