Prof. Potter on Hydrodynamics. 

 and 8/> involves 8(8S) the variation of (SS) ; also 



ds 

 and t?"^S 



«?/) ^ 3/c.Jw '^ 



209 



Sp: 



SS = 



Ss=. 



8*^ 



Ss- 



8 (8S)'* ' 

 with these substituted, the general equation becomes 



2>K 



"2* 



3k 



(IT 



df 



= 0, 



d^ 



dt- 



-^=0, 



as found in my last paper ; the negative sign indicating that the 

 positive variation of the pressure corresponds to a decrement of 

 the distance of the atoms. 



Proposition. To apply the expressions to the case of a diverging 

 stream of air in Roberts's experiment (often called M. Clement's 

 experiment) . 



This interesting case of a diverging stream of elastic fluid is 

 discussed experimentally, and a popular explanation of the cause 

 of the results given in a paper in the fifth volume of the new 

 series of the Transactions of the Manchester Literary and Phi- 

 losophical Society, by Mr. Hopkins. 



Mr. Hopkins shows that the rarefaction is a consequence of 

 the first law of motion, by which eveiy particle of air tends to 

 move wTith a unifonu velocity, and therefore in the divergence of 

 the stream, the density must be diminished. 



Let the figures represent the experiment, where, in fig. 1, CD 

 represents the section of the pipe through 

 M'hich the air is forced, with its circular per- 

 forated plate EF attached ; and above which, 

 at some small distance, is a plane circular 

 disc GH. Then as the air issues from the 

 pipe, the disc causes it to diverge on all sides, 

 and it immediately becomes rarefied. The 

 rarefaction increases to some distance from 

 the aperture and then diminishes again,until, 

 at the edge of the plate, the density is the 

 same as that of the atmosphere. 



Phil. Mag, S. 4. Vol. 1 . No. 3. March 1851. 



Fis. 1. 



H 



E 



B 



\ 



