Conduction of Heat in Liquids. 15 



he assumes k = Jc (l + olu), where a = "00786 and prefers to 

 0° C. Lorberg, applying his own method of calculation to 

 one of Weber's observations at the higher temperature, found 

 jj? = '42877; whence a= *005. Lorberg employs his own value 

 for a to show that the divergence between his and Weber's 

 values for M//, 2 in the first experiment are much too great to 

 be due to the change in h. Employing Weber's value for a, 

 which seems fairer, I find that only about one half the 

 divergence could be accounted for. Lorberg further con- 

 siders the fluctuations in Weber's table of values for M/u, 2 to 

 be considerably beyond the limits of errors of observation, and 

 finds that they cannot be explained by supposing k, k v &c. 

 to be quadratic functions of the temperature. The following 

 is the theory he propounds to account for all the phe- 

 nomena: — 



It is, he says, very unlikely that the metal cover of the 

 apparatus remains at 0°, but, on the contrary, it will after a 

 short time assume a temperature 6. This obviously will 

 modify the temperature of the apparatus, and will, he sup- 

 poses, produce in the upper copper plate a constant excess r 

 over the temperature given by the mathematical theory. 

 Thus the temperature measured by the galvanometer is really 

 t + u ; and, the deflection varying as the temperature, we 

 should have 



x = s + A*"**, 



where s is a constant given by 



s(l — «~' t2 ) = ^ n +6 — e^ 2 a n ~g„, say. 



The formula log — — - obviously eliminates s and gives 



fj? directly. Lorberg then forms a table of values of g ny and 

 from them deduces s = 8'27. He also has a table of values of 



log — " +12 , and of a corresponding quantity <gr n \ This 



gives a value for /x 2 agreeing well with his other value, and 

 gives s = 8*24. He points out, what is unassailable, that a 

 given error in the scale-reading would produce a much smaller 

 effect on Weber's quantities than on his own. Assuming *4 

 of a scale-division as a superior limit to the error, he points 

 out that this would not account for the fluctuations in Weber's 

 table. It would, however, correspond to an error of 'Oil in 



the value of log *"-*»+« an d of '7 in the value of g n . 



Lorberg thus considers the fluctuations in his own tables 



