Conduction of Heat in Liquids. 25 



he makes on the results obtained by varying the velocity. 

 Commencing with a very rapid current, the value given for k 

 by his theory is distinctly said to increase as the velocity is 

 diminished, and this to a very decided amount*. For a con- 

 siderable diminution in the velocity the value found for k is 

 then almost constant, and this value is assumed by Graetz to 

 be the correct one. For very slow currents, again, the value 

 appears to diminish. There were also certain practical diffi- 

 culties in employing very slow currents. In these the differ- 

 ence between U and T is so small that any slight fluctuation 

 in the former has a serious effect on the results • further, the 

 difference between U and T x is so great that it is hard to say 

 to what temperature the value found for k should be assigned. 

 But the main difficulty consists in determining U correctly. 

 With moderately fast currents the liquid threads of different 

 temperature in the pipe mix on issuing into the much wider 

 tube, and the reading of a thermometer in this tube is nearly 

 independent of its position. With slow currents, however, 

 the threads do not mix properly; and even the introduction of 

 a Z-shaped tube at the end of the pipe failed to effect a 

 thorough mixture. 



Graetz points out that, in his first paper in the differential 

 equation employed, it is tacitly assumed that k is independent 

 of the temperature. He does not, however, succeed in re- 

 moving this objection unless two very doubtful points be 

 conceded. The first is that the temperature of the liquid in 

 the pipe depends only on the distance from the axis ; and the 

 second that the higher value of the conductivity in the warmer 

 layers is exactly counteracted by the increase in the velocity 

 in capillary tubes with the temperature. The effect of gravity 

 would render doubtful the first assumption, and the second 

 seems decidedly improbable. The point is of considerable 

 importance ; for, according to the theory, there must have 

 been in some of the experiments a difference of 20° C. between 

 the temperature of the entering liquid in the axis and at the 

 surface of the pipe. 



In the second series of experiments the material of the pipe 

 was platinum, which was selected as being less exposed to 

 chemical action. Graetz also takes / as the length of the pipe 

 exposed to the water in the bath ; the ends, which were fixed 

 into the corks, being excluded. Thus, in the various experi- 

 ments I is stated variously as from 6*145 to. 7*71 centim. In 

 the first series of experiments one is left to conclude that I was 

 the entire length of the pipe; and it seems highly questionable 

 what a correct use of the theory requires. In fact the 

 formula employed assumes I to be the length of the column of 

 * See pages 346 & 347 of Graetz's second paper. 



