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XL. On Liquid Vortex-Rings. By John Trowbridge, S.D., 

 Assistant Professor of Physics, Harvard College*. 



IT has often been observed by chemists that a drop of 

 coloured liquid falling from a burette or a capillary tube 

 into a liquid of different specific gravity, in which it can dif- 

 fuse, assumes the form of a ring. Yortex motion, by the 

 researches of Helmholtz, Thomson, and Maxwell, is now 

 attracting so much attention that I have thought that a study 

 of the general equations of motion of matter in connexion 

 with a study of the rings would contribute to our knowledge 

 of vortex movement. Professor W. B. Rogers published in 

 the American Journal of Arts and Sciences for 1858 an ex- 

 tended paper on smoke rings and liquid rings^ and described 

 various methods of forming them. This paper seems to have 

 been overlooked by recent investigators. It is a singular 

 coincidence that Helmholtz should have published his great 

 memoir on vortex movements in the same year that the article 

 of Professor Rogers, which details purely the experimental 

 side of the subject, appeared on the other side of the Atlantic. 

 Professor Tait's method of forming smoke rings, which is also 

 referred to by Sir William Thomson in his paper on vortex 

 atoms, is now well known. The apparatus consists merely of 

 a box closed at one end by a tightly stretched cloth, and having 

 a circular hole of 6 or 8 inches diameter at the other. Clouds 

 of sal-ammoniac vapour are generated inside the box; and 

 rings are expelled by striking the stretched cloth with the 

 hand. Sir William Thomson suggests that two such boxes, 

 placed so that the rings might impinge on each other at any 

 angle, would form a useful apparatus in studying the behaviour 

 of such rings towards each other. At the conclusion of this 

 paper several methods of studying liquid rings will be described. 

 When a drop of liquid falls from a small distance into a 

 liquid of less density, in which it cannot diffuse, the conditions 

 of its motion the instant after it strikes the surface of the 

 liquid of less density are indicated by the general equation of 

 strains f. " For each particle we have the component veloci- 

 ties u, v, w parallel to the fixed axes OX, OY, OZ. These 

 jiave the following expressions, 



da. dS dy 



u= dt' v =Ht> w =dt> 



x, y, z, t being independent variables, and «, ft, y functions of 

 them. If the disturbed condition is so related to the initial 

 condition that every particle of the body can pass from its 



* Communicated by the Author, having been presented at a Meeting 

 of the American Academy of Arts and Sciences, January 14, 1877. 

 f Thomson and Tait's 'Natural Philosophy.' 



