140 THE MECHANICS OF THE EARTH's ATMOSPHERE. 



it is not yet possible to determine the free boundaries by computation, 

 then this is only because of the analytical difficulties. In general, how- 

 ever, one can judge of the nature of these boundaries from a considera- 

 tion of the results already found. 



The mathematical investigations just referred to hold good equally 

 well for liquid jets that are bounded by quiet air as for those that are 

 bounded by similar quiet liquid. In the actual production of such liquid 

 jets it of course makes a great difference whether we allow water to 

 flow into the air or water to flow into water. In both cases disturbing 

 circumstances occur of which the mathematical theory takes no consid- 

 eration. The jets of water projected freely into the air have been most 

 thoroughly investigated.* 



In these experiments the formation of jets occurs just as would be 

 expected according to theory. On the other hand, however, it is knowu 

 that water jets are influenced to an important extent by the capillary 

 tension of the free surface, and that in consequence of this at certain 

 distances from the orifice they break up into drops. 



If we allow a liquid to flow into a similar quiet liquid then these 

 capillary effects do not occur; but in place of this another disturbing 

 cause, the viscosity, influences the phenomena. The viscosity has hith- 

 erto not been taken into consideration in the theory of the discontinu- 

 ous movements of fluids. If we attempt to consider it we stumble upou 

 a peculiar difficulty that has led the present author to experimentally 

 investigate this class of fluid motions. 



II. . 



It is well known the theory of viscosity of fluids can be developed 

 from the assumption first framed by I:^ewton,t namely, that the retard- 

 ing or accelerating influence of two portions of fluid flowing past each 

 other with different velocities is proportional to tlieir relative velocity. 

 Esi)ecially has O. E. Meyer from this hypothesis developed the general 

 difl'erential equations for the motion of linids.t 



If we assume that all parts of the moving fluid describe ])arallel ])aths,. 

 say in the direction of the axis of ^, and that the velocities v are only 

 functions of x and that finally /i is the coefficient of viscosity, then will 

 the influence of two neighboring parts upon each other be represented 

 by the expression 



^ dv 



* Besides the older experiments of Bidone aud Savart see especially Magnus, Pog- 

 geudorff J»«aZeH, vols, xcv aud cvi. 



t Matbematical Principles of Natural Philosophy : Germau translation by Wolfers,. 

 Berlin, 1872, p. 368. 



+ See Crelle, Joiirnul, vol. lix, jip. '2'29-303, and Poggeudorfif Atuialeii, vol. cxiii^ 

 pp. G8, 69. 



