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IX. The Stream-lines of Moving Vortex-rings. By Oliver 



Lodge D.Sc, Professor of Physics in University College^ 



Liverpool*. [Plates II., III., IV.] 



rflHE object of the present communication is to publish 

 J- drawings of vortex stream-lines, some of which I made 

 originally for my own edification. Taking the lines of a 

 stationary vortex, as given by Sir W. Thomson in his memoir 

 on Vortex Motion (Trans. Roy. Soc. Edinb. vol. xxv.), or as 

 copied into Maxwell's ' Electricity ' (plate 18, vol. ii.), I merely 

 superpose uniform motion upon them, in the shape of a series 

 of parallel lines, and join up the corners of the quadrangles 

 so formed. 



Another way of expressing the matter is to say that you 

 draw the lines of magnetic induction due to a circular ring 

 conveying a current, placed in a uniform magnetic field with 

 its lines exactly opposed to those inside the ring. 



I choose two strengths of uniform field for the sake of 

 illustration; one distinctly stronger, the other distinctly weaker, 

 than the central intensity due to the coil alone. The relative 

 intensities at centre of ring due to field and coil respectively 

 are about as 1 to 5 in fig. 1, and as 64 to 5 in fig. 2 (Plate II.). 

 Or, taking the curves as representing stream-lines : in fig. 1 

 the velocity of vortex-motion is equal to the translation- 

 velocity of the whole ring at a certain circle in its plane 

 concentric with its core and of 3*3 times the diameter of the 

 core, and also at two points on the axis ; while in fig. 2 the 

 vortex-velocity and the translation-velocity are equal at a place 

 1*5 core-radii distant from the centre of the ring outside, and 

 at another circle, say two fifths the core dimensions, inside, 

 the ring. 



In fig. 1 the ring is moving so fast that the translational 

 flow back of fluid through its centre overpowers the forward 

 vortex-motion there. In fig. 2 the vortex-motion predo- 

 minates as far as a point on the axis which I reckon as 1*38 

 core-radii distant from centre of ring, a point indicated by the 

 crossing of the partially dotted stream-line. It will be under- 

 stood that though they look so different, the two Plates repre- 

 sent the same ring moving at different speeds. The size of 

 the core or circular axis is the same in both diagrams. 



It will be observed that in fig. 2 the portion of fluid 

 permanently partitioned off from the rest by reason of its 

 vorticity is truly ring-shaped, and would become thinner or 

 more wiry if its forward motion were greater — the lines near 

 the core of the ring being prolate towards the axis ; while 

 in fig. 1 the rotational portion of fluid, which is being bodily 

 * Communicated by the Physical Society : read June 27, 1885. 



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