It is probable, moreover, that the higher regions of the atmosphere are not composed of the same air as that around us.  Sir James Dewar points out that Dalton’s law demands that every gas composing the atmosphere should have, at all heights and temperatures, the same pressure as if it were alone, the pressure decreasing the less quickly, all things being equal, as its density becomes less.  It results from this that the temperature becoming gradually lower as we rise in the atmosphere, at a certain altitude there can no longer remain any traces of oxygen or nitrogen, which no doubt liquefy, and the atmosphere must be almost exclusively composed of the most volatile gases, including hydrogen, which M.A.  Gautier has, like Lord Rayleigh and Sir William Ramsay, proved to exist in the air.  The spectrum of the Aurora borealis, in which are found the lines of those parts of the atmosphere which cannot be liquefied in liquid hydrogen, together with the lines of argon, crypton, and xenon, is quite in conformity with this point of view.  It is, however, singular that it should be the spectrum of crypton, that is to say, of the heaviest gas of the group, which appears most clearly in the upper regions of the atmosphere.

Among the gases most difficult to liquefy, hydrogen has been the object of particular research and of really quantitative experiments.  Its properties in a liquid state are now very clearly known.  Its boiling-point, measured with a helium thermometer which has been compared with thermometers of oxygen and hydrogen, is -252 deg.; its critical temperature is -241 deg.  C.; its critical pressure, 15 atmospheres.  It is four times lighter than water, it does not present any absorption spectrum, and its specific heat is the greatest known.  It is not a conductor of electricity.  Solidified at 15 deg. absolute, it is far from reminding one by its aspect of a metal; it rather resembles a piece of perfectly pure ice, and Dr Travers attributes to it a crystalline structure.  The last gas which has resisted liquefaction, helium, has recently been obtained in a liquid state; it appears to have its boiling-point in the neighbourhood of 6 deg. absolute.[11]

[Footnote 11:  M. Poincare is here in error.  Helium has never been liquefied.—­ED.]

Sec. 3.  SOLIDS AND LIQUIDS

The interest of the results to which the researches on the continuity between the liquid and the gaseous states have led is so great, that numbers of scholars have naturally been induced to inquire whether something analogous might not be found in the case of liquids and solids.  We might think that a similar continuity ought to be there met with, that the universal character of the properties of matter forbade all real discontinuity between two different states, and that, in truth, the solid was a prolongation of the liquid state.