Conduction of Heat in Liquids. 11 



with the upper plate, a closed vessel. Two wires of different 

 metals have their one junction fused to the upper surface of the 

 upper copper plate, and their other junction kept in ice. This 

 supplies a thermoelectric current, which traverses a reflecting 

 galvanometer, whose readings supply data for the calculation 

 of the temperature of the hot junction. When the apparatus 

 has been for some time at a fixed temperature, as indicated by 

 the constancy of the galvanometer-reading, the lower plate is 

 suddenly placed on a horizontal block of ice at 0°; a screen of 

 metal, maintained at 0°, is at once put over the apparatus ; 

 and the time noted. The weight of the apparatus presses out 

 the melted water, and so keeps the surface of the ice-plate 

 horizontal and its temperature at 0°. After about two and 

 a half minutes, readings of the galvanometer are begun, and 

 repeated at regular short intervals. The law of cooling of the 

 hot junction is thus obtained ; and the dimensions and other 

 properties of the apparatus being known, the conductivity of 

 the liquid may be calculated. 



Weber's mathematical treatment is not satisfactory, as he 

 started with an unwarrantable assumption, so as to lighten 

 the work, which presents serious difficulties. He first 

 attempts to show that, practically, the upper copper plate 

 is at one temperature throughout. Let u denote the tem- 

 perature at time t, p the density, c the specific heat, k the 

 internal and h the external conductivity of the liquid layer, 

 whose thickness is A; and let the same letters, with suffix 1, 

 refer to the upper copper plate. Then, in treating the plate, 

 Weber at once assumes that at its lower surface 



, 7 dui , u 

 Ui = u and k x -=— = /; — . 

 1 dx A 



The former relation may be correct, and Lorberg considers that 

 it follows from Poisson's theory of heat. Further, most, if 

 not all, writers on the present subject have assumed that there 

 is no discontinuity in temperature in passing from any one 

 medium to another in contact with it. This is a matter 

 of great importance when the conduction takes place through 

 thin layers, and any uncertainty on the point is much to be 

 regretted. The results of direct experiments, however, have 

 been contradictory ; and several high authorities hold a con- 

 trary opinion. The second equation is, as Lorberg has shown, 

 undoubtedly erroneous ; thus, Weber's proof that the copper 

 plate is isothermal is little better than a pure assumption. 

 Granting, however, the first equation, Lorberg shows conclu- 

 sively that either copper plate is very nearly at one temperature 

 throughout. 



