NOTE D. ART. 134. 



The dynamical equations of Art. 6 may be written, when a force- 

 potential V exists, in the form 



du_ fy ^ _ dP_ ] 

 dt dx I 



I 



&amp;lt;1&amp;gt;, 



dt 



P= (Jl +V+ L M y 



) P 



Differentiating the third of equations (1) with respect to y, the 

 second with respect to z, and subtracting, we find 



du du . /dv dw* 



Kemembering the relation (1) of Art. 127, and making use of the 

 equation of continuity [(7) of Art. 8], 



we may put (2) in the form 



r) L du du 



9 du i] du du /ox 



or ^ ~= T + ^~ + ~T~ \ 6 r 



Ct p p u p dy p az 



In the same way we obtain two similar equations, which may be 

 written down from symmetry. 



Let the projections on the co-ordinate axes of the line joining two 

 neighbouring particles on the same vortex-line be 



16 



