as applied to Gases and Vapours, v't; .■ 515 



(13.) Any sucli motion of the particles of a portion of matter 

 confined in a limited space will in general give rise to a centri- 

 fugal tendency with respect to that space. In order to obtain 

 definite results with respect to that centrifugal tendency in the 

 case now under consideration^ it is necessary to define, to a cer- 

 tain extent, the general character of the supposed movement. 



In the first place, it is periodical ; secondly, it is similar with 

 respect to so large a number of radii drawn in symmetrical direc- 

 tions from the atomic centre, as to be sensibly similar in its 

 effects with respect to all directions round that centre. This 

 symmetry exists in the densities of the different particles of the 

 atomic atmosphere in a gas, and in the forces which act upon 

 them ; and we are therefore justified in assuming it to exist in 

 their motions. 



Two kinds of motion possess these characteristics. 



First. Radial oscillation, by which a portion of a spherical 

 stratum of atmosphere surrounding an atomic centre, being in 

 equilibrio at a certain distance from that centre, oscillates pe- 

 riodically to a greater and a less distance. This forms part of 

 the vis viva of the molecular movements ; but it can only affect 

 the superficial atomic elasticity by periodic small variations, 

 having no perceptible effect on the external elasticity. 



Second. Small rotations and revolutions of particles of the 

 atomic atmosphere round axes in the direction of radii from the 

 atomic centre, by which each spherical layer is made to contain 

 a great number of equal and similar vortices, or equal and similar 

 groups of vortices having their axes at right angles to the layer, 

 and similarly situated with respect to a great many symmetrical 

 directions round the atomic centre. 



Let us now consider the condition, as to elasticity, of a small 

 vortex of an atmosphere whose elasticity is proportional to its 

 density, inclosed within a cylindrical space of finite length, and 

 not affected by any force at right angles to the axis except its 

 own elasticity. Let Z denote the external radius of the cylinder, 

 /Dj its external density, p its mean density, p' the density at any 

 distance z from the axis (all the densities being measured by 

 weight), w the uniform velocity of motion of its parts. The con- 

 dition of equilibrium of any cylindrical layer is, that the differ- 

 ence of the pressures on its two sides shall balance the centri- 

 fugal force ; consequently [h being the coefficient of elasticity) 



gz dz 



The integral of this equation is jfl-«r3fl 



p'^=^ciz^g. ym^ih'^m 



