243 



F =iO~^ .^ .2b T\Vb'— Va') . . . . . (8) 



Ag 



Substituting the value of b, with e = 1.4.10—^^, we find 



F = 2.b2 . 10-^-'^ . T' {Vb' —Va"-) (4) 



From this result we see in the first place that the thermoelectric 

 power in approaching to T = ajiproaches to 0. As a matter of 

 fact the observations ^) for combinations of pure metals actually 

 point in this direction. 



For a combination of the metal considered in § 2 (Vb = '^0'' 

 for low temperatures) with a metal in which the density of free 

 electrons is twice as large (Fi = 1.5.10^), for 7^=4 from (4) 

 7^=rl.2.10~^ Volt is derived. For high temperatures, on the sup- 

 position that the ratio of the densities of electrons is the same there 

 as at the low temperatures, from (2) i^=fi.lO-6 is found. Hence 

 at the temperatures of liquid helium the thermoelectric power of 

 that combination w^ould on the supposition mentioned decrease to 

 V500 (^1"»^ at the lowest helium temperatures to still less) of its amount 

 at high temperatures. 



A decrease of the thermoelectric power has been deduced by 

 Neknst "') from the recent formuhition of his heat theorem. Here 

 according to (4) this decrease of the thermoelectric power is found 

 to take place finally proportionalbj to T\ This law, if it should 

 be confirmed, and if the difficulties inherent to the measurement 

 of the small thermoelectric powers at the extremely low tempera- 

 tures can be sufficiently overcome, may be of importance for 

 thermometry in the region concerned. 



§ 4. The FELTmR-e/fect. To calculate the PELTiER-efFect we consider 



1) L. HoLBORN and A. Day. Berlin Sitz. Ber. 36 (1899), p. 691. According 

 to Kamerlingh Onnes and Clay, Gomm. No. 107Ö, May 1908, the thermo- 

 element gold-silver does not yet show that decrease at liydrogen temperatures. 



Prof. Kamerlingh Onnes fmiher tells me that observations by Kamerlingh 

 Onnes and Holst, which will soon be published, show that this is still the 

 case at helium temperatures. Down to the boiling point of helium and a little 

 lower the gold-silver thermometer even indicates the temperatures fairly accura- 

 tely. Hence the importance of the further result that, when proceeding to the 

 lowest helium temperatures the thermoelectric power decreases rapidly to small 

 values. Other combinations of metals and alloys were also investigated by Kamer- 

 lingh Onnes and Holst with a view to Ihermometric determinations at the 

 lower helium temperatures. With all of tliem the same phenomenon was observed 

 of a rapid decrease of the thermoelectric powt.-. The thermoelectric power was in 

 general still considerable between hydrogen and helium temperatures. In these 

 cases the decrease mentioned took place at liquid helium temperatures. 



•2j W. Nernst. Theoretische Chemie, 7'e Autl. Stuttgart 1913. p. 753. 



16* 



