Conduction of Heat in Liquids. 23 



variously stated. In one place its diameter is said to be 

 *06 centim., while in another place the radius of the outer 

 surface is said to be *06 centim. and to bear to the radius of 

 the inner surface the ratio 3:2. The length is variously 

 stated as 9*8 or 8'9 centim. A layer of warmer water tended 

 to gather round the pipe, but was dispersed by means of a 

 brush driven by electricity. Graetz assumed that, through 

 the action of the brush, the outer surface of the pipe was 

 always kept at the same temperature T as the surrounding- 

 fluid. 



After some preliminary calculations of a rough nature, Graetz 

 proceeds to a complete mathematical treatment. He shows 

 that no sensible error is introduced by supposing the pipe of 

 one temperature throughout. He then assumes Poiseuiile's 

 law, that in a pipe of radius R, from which 7rR 2 a is the 

 quantity of liquid issuing in unit time, the velocity at a 



distance r from the axis is 2a( 1 — p 2 )* 



Employing this expression in his differential equation, he 

 found, by a satisfactory process, that the mean temperature of 

 the issuing liquid is given by the equation 



U = Tj^p.e e c 2V , 



where k, p, c have their usual meaning, I is the length of the 

 pipe, Y the volume of liquid issuing per minute, and ^ the 

 root of a certain equation. The two first roots are y^=- 2" 7043 

 and fi 2 =6'5Q, and the terms answering to the other roots are 

 negligible. The coefficients p x and p> 2 are a l so numerical 

 quantities, which can be calculated from the mathematical 

 theory. In his first paper, however, Graetz thought it easier 

 to deduce them from three observations on copper-sulphate 

 solution, in which the liquid traversed the pipe under three 

 different pressures. The values so deduced were p x = '91264 

 and p 2 = '01249 ; and these were employed in calculating the 

 conductivities of all the other liquids. In most cases the 

 liquid traversed the pipe under at least two different pres- 

 sures ; and the results obtained appear to agree remarkably 

 well. These results were uniformly considerably larger than 

 Weber's ; and believing them to be true, Graetz indulges in 

 a good deal of criticism, and accepts Lorberg's corrections as 

 tending in the right direction. In his second paper, how- 

 ever, he is able to determine p x and p 2 directly from hiy 

 mathematical theory ; and it turns out that p l = 'SH4:7 and 

 p 2 = -0325. 



This great divergence from the values employed of course 



