CHAPTER VI. 



ON THE MOTION OF SOLIDS THROUGH A LIQUID : 

 DYNAMICAL THEORY. 



114. IN this Chapter it is proposed to study the very 

 interesting dynamical problem furnished by the motion of one 

 or more solids in a liquid. The development of this subject is due 

 mainly to Thomson and Tait* and to Kirchhofff. The cardinal 

 feature of the methods followed by these writers consists in this, 

 that the solids and the fluid are treated as forming one dynamical 

 system, and thus the troublesome calculation of the effect of the 

 fluid pressures on the surfaces of the solids is avoided. 



We begin with the case of a single solid moving through an 

 infinite mass of liquid, and we shall suppose in the first instance 

 that the motion of the fluid is entirely due to that of the solid, 

 and is therefore irrotational and acyclic. Some special cases of 

 this problem have been treated incidentally in the foregoing pages, 

 and it appeared that the whole effect of the fluid might be 

 represented by an increase in the inertia of the solid. The same 

 result will be found to hold in general, provided we use the term 

 ' inertia ' in a somewhat extended sense. 



Under the circumstances supposed, the motion of the fluid is 

 characterized by the existence of a single- valued velocity-potential 

 </> which, besides satisfying the equation of continuity 



v^ = o .............................. (i), 



* Natural Philosophy, Art. 320. 



t " Ueber die Bewegung eines Kotationskorpers in einer Fliissigkeit," Crelle t 

 t, Ixxi. (1869); Ges. Abh. t p. 376; Mechanik, c. xix. 



