96 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



and with uniform velocity on the plane boundary surface between in- 

 definitely extended layers of two fluids of different densities and having 

 different progressive movements. I shall call this kind of billows 

 stationary billows, since they represent a stationary motion of two 

 fluids when they are referred to a system of coordinates which itself 

 advances with the waves. Since in the relative motion of the different 

 parts of a closed material system nothing is changed when the whole 

 receives a uniform rectilinear velocity toward any direction, therefore 

 this rearrangement of our problem is allowable. 



Moreover I propose to-day to give only the results of my mathemati- 

 cal investigations. The complete presentation of these I reserve for 

 publication in another manner. 



Before I advance to the theory of atmospheric billows, I will however 

 introduce a supplement to the considerations given in my communica- 

 tion of May, 1888, by which the region in which we have to look for 

 the conditions that give rise to atmospheric billows is better defined. 



V. THE ASCENT OF MIXED STRATA. 



In Section in of my previous communication I have shown what 

 would be the law of equilibrium, in case such a condition should be 

 attained, between atmospheric rings of different temperatures and dif- 

 ferent speeds of rotation, which however are all assumed as being com- 

 posed of mixtures that are similar to each other. I now return to equa- 

 tion (ia, page 85). Let the location of a point in the atmosphere be 

 given by the quantities 



p, the distance from the earth's axis. 



r, the distance from the center of the earth, 



Let oo be the angular velocity of the solid earth ; and /2i and il 2 be 

 the constant moments of rotation of the unit of mass of one or the 

 other layer of air : 



Let #j and 8 2 be the quantities that I have called the contained ca- 

 loric of the unit of mass of air, and that certainly may be better desig- 

 nated by the term potential temperatures, so well chosen by Bezold, 

 namely, those temperatures which the respective masses of air would 

 assume when brought adiabatioally to the normal pressure. 



Let G =s constant of gravitation. In accordance with equation (4a) 

 we now have at the boundary surfaces the relation 



^ ra vL l-i ~^P 4 J (i) 



The ratio ^ indicates also the ratio of the sines of the two angles 



which the tangent to the curve in the meridional plai e makes on the 

 one hand with the earth's axis, and on the other hand with the horizon. 

 When, as is ordinarily the case, the warmer layer has also the greater 



