Conduction of Heat in Liquids. 19 



in diameter and '9 centim. in thickness. In the cylindrical 

 surface of each is a hole, which contains the bulb of a very 

 flat thermometer graduated to fifths of a degree. The ther- 

 mometer-stems project horizontally from the plates, which we 

 shall denote by L, II., and III. in descending order. By 

 means of small holes in I. and II., which can be closed by 

 copper plugs, liquids may be introduced between I. and II. 

 and also between II. and III. The lower plate (III.) is sup- 

 ported on a metal vessel kept at a constant low temperature ; 

 while on I. is placed a second metal vessel, through which a 

 stream of hot water is maintained. The experiment consists 

 in observing the readings T 1? T 2 , T 3 of the thermometers in 

 I., II., and III., when all have become stationary. 



Let e-i, e 2 denote the thickness of the upper and lower layers 

 of liquid, and K b K 2 the conductivities of these liquids. Also 

 let e and K denote similar quantities for the middle plate II.; 

 and suppose S the cross section, A the cylindrical surface, and 

 h the external conductivity of this same plate. Then Chris- 

 tiansen gives two approximate formulae. The first is 



K 3 ^Ti-Ta-S 



where 



a-ljcrx-T,) 



_^ T 2 -T 3 (- Afo, T,-T -t 

 - <,T 1 -T,l 1 + 8K,T,-T,J 



is a small quantity. The second is 



K 1 _«iT s -T,f 1 , Ahe 2 

 K 2 



In the first the thermometers are supposed to indicate the 

 arithmetical mean of the temperatures of the upper and lower 

 surfaces of their respective plates, which are not assumed 

 equal. Any variation with the temperature in the con- 

 ductivity of either liquid is neglected. The second formula 

 supposes the temperatures of plates I. and III. to be the same 

 throughout. It, however, allows for a variation in the con- 

 ductivity of either liquid, after the law 



K = K (1 + au), 

 where u is the temperature, and makes no assumption as to 

 the value of a. In it K x refers to a temperature ^(T 1 + T 2 ), 

 and K 2 to ^(T 2 + T 3 ). In both formulas it is assumed that 

 contiguous layers of any two materials have always the same 

 temperature, and the external conductivity of the liquids is 

 neglected. Christiansen also obtains a formula depending on 

 the cooling of the apparatus from which to obtain absolute 



C2 



