Mr. A. Griffiths on D if a sice Convection. 457 



Let ;? = difference of pressure between bottom and top of 

 tube, neglecting viscosity, 



-A 



L (l + tftl 



L jl + T 1 e .* { ft/, from (2). 

 / l-.-T 



Integrating 



^L+^L^-^. .... (8) 



1—e k 

 When the velocity is downwards 



^L + ^ + *f (4) 



1 — e a 



Section III. 



Determination of the magnitude of the convection-current in the 

 case of tubes of equal bore, neglecting viscosity. 



From (3) and (4), and from the expression in Section I., 

 it can be seen that the pressure tending to produce circulation 

 is given by the expression 



P«*I*+ ^+ / ^ r +<?(l + T)(L 1 -L 3 ) 

 or 1 — e & 



=,T ( L 1 -L 2 ) + 2 M + ^ fc -^L 



1— e* 1— e T 



(5) 



This pressure never can become negative in the positive 

 direction ; the limiting value of v is therefore given by the 

 equation 



, T(L] _ L2) + ^ + ^-^=0. . . (6) 

 v \-eTk 1-e fc 



In o-pneral the solution of this equation will involve con- 



