432 UNPUBLISHED FRAGMENTS. 



or, writing T for the constant 





(to 



[The terms ^f -s c y disappear in the algebraic sum since 

 a s i m il ar reason] 



The first equation makes j- 2 ^ constant throughout the tube, and 



since SoCoyo'' = 2 c y ', 2c y must be constant throughout the tube. 

 The second equation then makes -= constant throughout the tube. 



T L V 



Let -i = 



Our original equation is 



Now with ^ constant this is easily integrated. 



"0 



To determine H we have 



y "-y ' = ve - -e 



If we put the origin of coordinates in the middle of the tube 

 we have 



