944 
partial pressure diminishes according to ifs proper molecular weight. 
The partial pressures at 10 KM. height are taken from Hann‘); 
here, however, the influence of mixture, though this influence is 
discussed, seems not to have been taken into account; this makes 
a difference in the first place for the percentage of hydrogen, which 
without mixing has increased 3'/, times already at 10 KM. The 
consequence of the convection currents; above that height every 
influence of this omission on the molecular weight in the first 
20 KM. is very small, but at great heights the differences are large 
enough. Moreover, the calculation has been largely simplified by 
considering the atmosphere as built up of two gases: hydrogen 
and an imaginary gas with a molecular weight 28.6. For the per- 
centage of hydrogen at the surface, Hann takes 0.01 °/,; from one 
of Von prem Borne’s illustrations we take: 
0 20 40 60 80 100 KM. 
0.01 0.1 3.0 37.2 94.4 98.6 °/, 
The smallest distance at which sound rays may return to the 
earth is with these assumptions 114 KM.; the sound ray becomes 
horizontal at a height of 75 KM. 
Of his method of calculation of the sound rays, Von DEM BORNE 
only says that it was tedious and was performed only in a cursory 
way. When it appeared from a preliminary control-calculation, that 
near the summit of the orbit the calculation ought to be made 
rather exactly in order to avoid great errors, we sought a mode of 
calculation, which, without taking too much time, would give results 
exact to about 1 KM. for the horizontal projection of the sound rays. 
The following general course was taken : 
Starting from different assumptions, to be mentioned afterwards, 
the composition of the atmosphere was calculated from 10 to 10 KM. 
by considering the partial pressure of each gas to decrease above 
the level of 10 KM. according to the law: 
AT, 
AT’ 
the meaning of which is sufficiently known. Above 20 KM. 7 was 
taken = 215, from 10—20 KM. 223, from O to 10 KM. 255°. *) 
From the composition thus obtained, the molecular weight was 
calculated and thence the velocity of sound by the formula: 
a Ale Ek 
ov 
log p = log p, — 
1) Lehrbuch der Meteorologie. 2te Auflage. p. 7. 1905. In the third edition 
(1914) the calculations of Humpureys, to be mentioned hereafter, are also quoted. 
2) The latter value as assumed by Hany, l.c. p. 8. 
