38 
MR, J. J. WATERSTOR OR THE PHYSICS OF MEDIA COMPOSED OF 
specific weight of the medium that corresponds with air is taken as unity, and 
1 X v z is the value of the molecular vis viva at the surface of the planet: with any 
other medium whose specific weight is s, its mean square molecular velocity with 
the same vis viva is v 2 /s, (VII); and the absolute height of its atmosphere is 
Ry 2 
li — ~~—~r This equation gives the absolute height of an atmosphere under every 
variety of condition, and determines the limit of vis viva at the surface of a planet 
beyond which the medium cannot be retained, for when h is infinite we have 
Ftps — v 9j = 0 or v 9 /s= llg. With regard to the medium that represents the atmo¬ 
sphere of our planet, we have already determined the value of v 2 to be (2244) 2 , when 
the absolute temperature is 493° and s = 1 ; consequently, when v 2 /s = Pig, the surface 
temperature must be 65,760° Fahr. for air, and 4556° for a hydrogen atmosphere 
whose specific weight s is ty \“3 2 - At these surface temperatures such atmospheres 
would slowly evaporate into space. # 
At the surface of the Moon the limit of temperature for an atmosphere of air is 
3008° absolute or 2505° on Fahr. scale. For a hydrogen atmosphere it is 208° 
absolute or — 253° Fahr. But the proximity of the Earth reduces these limits 
respectively 100° and 7°, so that if the Moon’s surface had even a higher temperature 
than 2405°, the Earth, according to this theory, would then gradually withdraw the 
whole of any atmosphere of air that it might then have possessed. 
By employing the same equation, it appears that the temperature at the surface of 
a body like the Sun in magnitude and mass requires to be 13,400° to sustain an 
atmosphere identical in constitution and height to that of the Earth.! 
§ 38. It will not fail to be remarked that the positive evidence in favour of the 
reasoning of this section turns on one point. Does the law of vertical equilibrium of 
temperature correspond with the law of vertical equilibrium of vis viva ? We have 
seen that the correspondence is more exact than might be expected, although it is 
extremely difficult to put the question to the test of direct experiment. In a column 
of air 318 feet high the temperature at the bottom ought to be 1° higher than at the 
top in any state of the atmosphere. If air is made to circulate quickly in two tubes 
of this height lined with non-conducting material, the difference of temperature ought 
to be very distinctly shown by thermometers at the top and bottom. The quick 
motion of the air downwards and upwards may be expected to compensate for the 
disturbing effect of the sides of the tube, and even to cause then internal surface to 
assume the proper atmospherical gradient of temperature. 
The accuracy of the formula for measuring heights by the barometer, that may be 
derived from the deductions of this section depends on the integrity of the law of 
diminution of temperature, but as this varies from local causes, the theoretical rule 
does not seem to apply so well as those in common use, which are partly empirical. 
* Rote K (central heat), 
f Rote L (nebular hypothesis). 
