OF ARTS AND SCIENCES. 135 



shown experimentally by dropping a somewhat dense solution of one 

 of the aniline colors into a mixture of glycerine and water. The orig- 

 inal ring, after ceasing to move downward in the mixture, breaks up 

 gradually into segments, which slowly in their turn assume the ring 

 form. A mixture of water and glycerine is not necessary: jieculiar 

 cusp-like figures indiv'ating tlie first stage of vortical movement can be 

 seen whenever a thin stratum of one liquid slowly diffuses itself through 

 another liquid of different density. 



By a consideration of the equations — 



e ^ + ("1 - t^)dt = e(^ + ^i dt^ 



« C+ K - ^o)dt = e(^:+^^dt^ 



given by Helmholtz, from which he draws the conclusion that " each 



vortex line remains continually composed of the same elements of 



fluid, and swim^ forward with them in the fluid," we see, on intro- 



^> 



duciug the new expressions which we have found for --, &c., P]q. (11), 



St 



that we approach nearer and nearer to this theoretical conclusion when 

 the variations of h are smaller and smaller. Obviously, we should then 

 obtain tlie most perfect rings Tvlien the drop and the liquid in which 

 the motion takes place are composed of the same liquid. And, there- 

 fore, a drop of water falling into loater must form a more perfect ring 

 than that formed by a drop of any colored liquid of greater density 

 than water. 



The formation of these liquid rings is as fascinating and as simple 

 an occupation as blowing soap-bubbles. All liquids falling from such 

 a height that the surface of the liquid is not too much disturbed tO' 

 enable the drup to be acted upon symmetrically by the forces at the 

 free surfiice will form rings, if too great differences of density do not 

 exist, and if the drop can diffuse in the liquid. The preceding mathe- 

 matical discussion, as we have seen, shows us that a drop of pure water 

 on striking the same element under the above conditions must neces- 

 sarily assume the ring shape. This can be shown experimentally by 

 covering the free surface of the water with a fine powder, or with mat- 

 ter in a fine state of subdivision. 1 have found that an alcoholic tinct- 

 ure of ginger, whicli gives on the surface of water a milky liquid 

 consisting of particles iu a fine state of subdivision, answers the purpose 



