Method of Determining Thermal Conductivity. 591 



fhe variations in temperature radially will undoubtedly be 

 small in comparison with the longitudinal variations. If the 

 radial conductivity were infinitely great, or if the diameter 

 were exceedingly small, the isothermals would be horizontal 

 and the gravity effect alluded to above would vanish and, in 

 the opinion of the author, the flow would again approximate 

 to the well known parabolic character. 



So long, however, as the isothermals are approximately 

 horizontal the nature of the flow does not affect the result: — 



For let vp = the vertical component of the product of the 

 velocity and density at a distance r from 

 the axis ; 



and let Q = quantity of heat crossing a horizontal plane 

 per sec. 



Then Q = -KA^ + ( \ R sB x 2irr . dr + I. 



•But I vpsQ X 27rr . dr — s8\ 'lirr x vp . dr 



Jo Jo 



= sQ x mass crossing section 



= sdxv'p'A [per sec. 



where v'p' may be called the average product of velocity and 

 density. This, by the law of fluid continuity, is constant 

 longitudinally, so the method will not be affected by varia- 

 tions of density in the parts of the liquid at different tem- 

 peratures. We have then : — 



Q= -KAj x +v'p'As0+I 



and hence, just as in section (2), we obtain under conditions 

 similar to those holding in equation (4) 



* = i^ (5) 



the product v'p' being equal to the mass of liquid outflowing 

 per sec. divided by the cross-section of the tube. 



(4) Apparatus. 



_ Preliminary experiments showed the importance and the 

 difficulty of maintaining the ends of the experimental tube 

 at constant temperatures in. spite of the. inflow of mercury. 



