587 



— I dy uv = (J 



1 

 dy(^vyz=z(\ + t)ö' ' (16) 







/ 







1 



ƒ*?• 



XÖ 



It will be easily recognized that the three quantities o, t and x 

 are all ot' them essentially positive. 



The equations fi4) and (15) now reduce to: 



and : 



y. 1 



<JT -I =- . (17) 



'^ = "4 ^ (18) 



qV' R 



Formula (17) will be denoted as the principal equation. 



§ 3. Discus.tioji of the principal equation. 



Equation (17) shows first of all that an increase of the velocitj^ 

 V of the mean motion cannot be accompanied by a proportional 

 change of the relative motion: in this case a, t and >« would remain 

 constants, whereas R increases, which would violate equation (17). 



If the value of R is given, (17) gives a condition to be fulfilled 

 by the relative motion. If a certain type of relative motion, fulfilling 

 this condition, accompanies the mean motion, the latlei' will experience 

 a resistance determined by tlie value of C, calculated from (18). 

 Now the problem arises; can we find admissible values of the 

 quantities r and x, without an exact knowledge of the true relative 

 motion? If t and x are known, (17) gives a (i.e. in some measure 

 the relative intensity of the relative motions), and (18) gives the 

 resistance coefficient. If we look at the application of statistical 

 methods in the dynamical theory of gases, we should expect that 

 for high values of R (which mean a fully developed state of tur- 

 bulence), it may be possible to calculate t and x in the following 

 manner: firstly we determine all kinds of relative motions which 

 fulfil eqq. (6) and (7); secondly we admit that all these motions may 

 be present independently of each other, their weights being governed 



