Conduction of Heat in Liquids, 5 



upper surface of the outer cylinder, and could be fixed there 

 in such a position that the distance between the surfaces of 

 the two cylinders was everywhere the same. The tube was 

 then bent twice at right angles, and terminated in a beaker of 

 mercury. The height of the mercury in the tube varies with 

 the temperature of the air in the inner cylinder, which may 

 thus be determined. The liquid to be examined was enclosed 

 between the cylinders, and communicated with the exterior 

 only through a small funnel in the upper surface of the outer 

 cylinder, which was also originally filled with the liquid. This 

 little arrangement kept the space between the cylinders always 

 filled. 



The experiment consisted in plunging the apparatus into 

 ice-cold water and observing the height of the mercury at 

 subsequent intervals of time. Denoting the temperature of 

 the enclosed air before immersion by t , and at a time t after 

 immersion by t, Winkelmann uses the formula vt= log (t /t) } 

 where v is the " velocity of cooling." He assumes that the 

 temperature of the enclosed liquid is the same at equal dis- 

 tances from the surface of the outer cylinder ; that this outer 

 cylinder is at the same zero-temperature as the surrounding 

 ice-water; and that the inner cylinder, the liquid layer touch- 

 ing it, and the enclosed air are always of one temperature. 

 He then takes for the temperature of the liquid the formula 



u = T e~ vt (*x + fix 2 + yx 3 ); 



where x is the distance from the outer cylinder, and a, (3, y are 

 constants determined from the conditions assumed at the 

 bounding surfaces of the liquid. 



That results based on so many assumptions should not be 

 altogether satisfactory is not surprising ; and Winkelmann 

 found, from observations with three different apparatus, that 

 the value of the conductivity supplied by his formulae rose as 

 the thickness of the liquid layer was increased. 



He had previously found that the outer cylinder became 

 surrounded by a layer of water decidedly above the freezing- 

 point, and employed a stirrer to promote circulation. He 

 attributes the discrepancy in the results obtained from the 

 three double cylinders to the fact that the stirrer, while main- 

 taining the curved surface of the outer cylinder at 0°, did not 

 remove the heated water from its top or bottom. Thus, deno- 

 ting the true conductivity by K, while p stands for the ratio 

 of the top and base to the entire surface of the outer cylinder 

 of the apparatus which gave for the apparent conductivity the 

 value k, he uses the equation 



K = h + npvj 



