590 



If ihev are distributed over the fluid in a certain way, with an 

 appropriate distribution of intensities, it will appear that it is possible 

 to make t very small, without making the value of x surpass tliat 

 of R. It further appears that in the choice of the dimensions of the 

 vortices an element remains arbitrarious, which element may be 

 adjusted in such a wa,j that o takes a maximum value. 



^ 4. LoRENTz' elliptic vortex. 



It has been shown by Lorentz that we can obtain a simple type 

 of motion which obeys the conditions (6) and (7), and for which 



I \ilx dy uv <^0, l)y considering a voitex in which the [larlicles of 



the fluid describe elliptic paths '). Geometrically this motion can be 



deduced from that in a circular vortex by a lateral compression. 



In the circular vortex the fluid moves in concentric orbits with the 



angular \elocity w, whicti is a function of the ladius /■ of the 



orbit. At the outer boundary of the vortex to has the value zero, 



dm 

 whereas in its centre w and ~~- have tinite values. Lorentz takes 



dr 



for to a Bessel function of /•; in order to obtain simpler formulae 



in this paper an algebraic function will be taken. 



The construction of the elliptic vortex is shown in figure 2. The 



Fig. 2. 



1) H. A. Lorentz, I.e. p. 48—62. 



I 



