1885.] On the Formation of Vortex Rings by Drops. 427 



naturally connected is the velocity of the drop ; it is not possible, 

 however, to alter this very much without introducing great dis- 

 turbance into the liquid. 



These results admit of very easy explanation, if our theory of the 

 formation of the rings is correct. According to this, the reason that 

 the liquids in Class I do not make rings, is because the vortex motion 

 has not penetrated sufficiently into the drop to make it break up, 

 when it becomes disk-shaped. If, however, the drops be made 

 smaller, the vortex motion has a better chance of filling it before it 

 becomes disk-shaped, and so causing it to break up into a ring. 

 When fi/p is very large, as is the case for liquids of Class IV, the 

 vortex motion is dissipated so quickly, that though the drop may 

 have been filled with vortex motion, this has all diffused away before 

 the drop reaches the disk-stage. If we make the drop larger, it will 

 take longer fco get full of vortex motion, and there may be enough left 

 in, by the time it gets disk-shaped, to cause it to break up into a ring. 

 There is another way in which the formation of rings by liquids of 

 Class IV may be promoted : suppose that, instead of letting a drop 

 fall into a column of the same liquid, we let it fall into another 

 liquid for which jx\p is smaller; then since this liquid is a worse 

 conductor of vortex motion than the drop, the vortex motion will not 

 diffuse so readily into the surrounding liquid. Thus we should 

 expect the drop to form a ring more readily than before ; and we 

 have found this to be the case. Thus, for example, drops of sul- 

 phuric acid I from Class IV, let fall into either sulphuric acid II of 

 Class III or sulphuric acid III of Class II, give rings. Similarly 

 with solutions of sugar, of caustic potash, and of glycerine. 



These effects are sometimes masked by the effects produced by 

 difference of density ; for if the drop is much heavier than the liquid 

 into which it falls, it will fall faster, and this will promote the 

 formation of the ring. If we guard against this source of error, we 

 may see that if a drop does not make rings when it falls into a column 

 of the same liquid, it will not make rings when it falls into a column 

 of another liquid of the same density, but for which fijp is greater ; 

 but it may make rings if fxjp be less than for the drop. 



On the Splitting up of the Rings. 



When a ring has travelled some little distance through the liquid, 

 its outline generally becomes irregular, and after a time takes the 

 corrugated appearance shown in fig. 1. The corrugations become 

 more and more marked as the ring falls, until the appearance is that 

 represented in fig. 8, 7 : the drops at the bottom of the bends develop 

 rings in the same way as the ring itself was originally developed. 

 This process of subdivision is repeated several times, until the ring 

 assumes the appearance shown in fig. 7. 



2 p 2 



