CONDUCTIVITY 95 



results have been obtained by different observers ; the value of the con- 

 ductivity for a substance as given by one kind of experiment being 

 perhaps several times the conductivity as given by another kind of 

 experiment on the same substance. The chief difficulties have only 

 comparatively recently been so far surmounted that different methods 

 give fairly accordant results. We shall not attempt to give here a com- 

 plete account of the subject,* but rather seek to illustrate it by describing 

 a few typical experiments which have given good results. 



Solids Pfalet's Metlwd. Pioneer work was done in the measurement 

 of conductivities by Peclet. He used a calorimeter, the bottom of which 

 consisted of a plate of the substance to be tested, while the sides had 

 very low conductivity. The calorimeter contained a known quantity of 

 water at a known temperature, and when it was plunged into a vessel 

 of warm water at a known temperature, the rate of rise of temperature 

 of the water in the calorimeter was observed. If A was the area of the 

 plate, K its conductivity, d its thickness, Q the quantity of heat coming 

 through per second, the temperature difference of its two faces, then 

 if the heat-flow was normal to the surface 



whence Qd 



= A0 



The chief difficulty consists in measuring 6. Let us suppose that the 

 water is at rest and that the heat flows steadily, i.e. that the same quan- 

 tity flows across each cross-section of plate and water alike. Let the 

 temperature in the water on the two sides at distances d v d 2 from the 

 nearest faces differ from the temperature of the faces by 9 V # 2 , and let 

 the conductivity of water be /c 1 . We have 



KA0 

 Q " d =: d l 



If we observe the water temperatures at the distances d v d 2 from 

 the plate, and assume that these are the temperatures of the two faces 

 of the plate, we get for the conductivity 



Qd Qd 6 



or the value we find ought to be multiplied by 



to give the true value. 



Peclet was well aware of this source of error. With the cooler vessel 

 above, convection would come into play, and so reduce the difference of 

 temperature between the plate surfaces and the water round the thermo- 

 meters and virtually reduce d l + d 2 , but not sufficiently. Peclet aided 

 convection and virtually reduced d^ + d z still farther by brushing the 



surfaces all the time. He supposed that thus ~r~ was rendered 

 negligible, i.e. that the water against the plate, being continually and 

 * An account will be found in Winkelmann's Handbuck der Physik, vol. ii. 



