PAPER BY PROF. HELMHOLTZ. 95 



The calculations performed by me show further that for the observed 

 velocities of the wind there may be formed in the atmosphere not only 

 small waves, but also those whose wavedeugths are many kilometres 

 which, when they approach the earth's surface to within an altitude of 

 one or several kilometres, set the lower strata of air into violent motion 

 and must bring about the so-called gusty weather. The peculiarity of 

 of such weather (as I look at it) consists in this, that gusts of wind often 

 accompanied by rain are repeated at the same place, many times a day, 

 at nearly equal intervals and nearly uniform order of succession.* 



I think it may be assumed that this formation of waves in the at- 

 mosi)here most frequently gives occasion to the mixture of atmospheric 

 strata and, under fiivorable circumstances, when the ascending masses 

 form mist, give opportunity for disturbances of an equilibrium that had 

 already become nearly unstable. Under conditions, such as those 

 where we see water waves breaking and forming white caps, thorough 

 mixtures must form between the strata of air. 



In the beginning of ray previous paper I have explained how insuffi- 

 cient are the known intensities of the internal friction and the thermal 

 conductivity of gases in order to explain the equilibration of motions 

 and temperatures in the atmosphere. Since now the mechanical the- 

 ory of heat has taught us to consider friction in gases as the mixture 

 of strata having different movements, but the conduction of heat as 

 the mixture of strata having different temperatures, it is therefore in- 

 telligible that a more thorough mixture of strata in the atmosphere 

 must bring about, to a still higher degree, the effects of friction and 

 conduction, t but certainly not in a quiet, steady progress, but pro- 

 ceeding irregularly as is indeed the special character of meteorological 

 processes. 



Therefore I have considered it important to develop the theory of 

 waves at the common boundary surface of two fluids. Hitherto in 

 studies on waves of water, so far as known to me, the influence of the 

 air and its motion with the water has always been neglected, but this 

 may not be done in the present work. The problem becomes thereby 

 much more complicated and difQcult; and since even the simpler 

 problem that takes no account of the influence of the wind has at the 

 hands of many excellent mathematicians received only incomplete and 

 approximate solutions, under assumptions chosen to simplify the 

 problem, therefore I piay to be excused in that I also have at first 

 treated the simplest case of the problem, namely, the movement ot 

 rectilinear waves which propagate themselves with unchanged forms 



* This assumption of the formation of billows in the atmosphere that I recently 

 briefly expressed in my first contribution has since then also been propounded by 

 Jean Luvini {La Lumiere £lectrique. T. xxx, pp. 368, 617, 620). 



t Perhaps this would correspond to the assumptions that form the basis of the 

 theory submitted to this (Berlin) Academy by Oberbeck, March 15, 1888. [See Nos. 

 XII and XIII of this collection.— C. A.'\ 



