347 



where y is the coeiTicient of the temperature-drop at the wall. 



Using this apparatus 1 have made a few experiments to test 

 Goldschmidt's theory. 



In a set of measurements with the apparatus filled with dry |)ure 

 carbon dioxide the temperature of the bath being 0° C. the following 

 values amongst othei's were found for ti,t]c, />,'S, /a and D. 



;>=21.61cm // =5.409 /^ =1.630 ^^=5.693 



/. =413.0.10-7 ^s =485.2.10 7 />=391 .0 . 10-7 



L,„,,..=:39 1 9.10-7 Sron: =391.9.10-7 



;i>=6.28 cm 'ti =5.453 tk =4.669 <a=5.739 



L =409.7.10 7 6^ =481.1 10-7 i>— 388.5 . 10-7 

 L,„,,.=388.7 . 10 7 6V„,,. =388.2 . 10 7 



These measurements show very clearly that entirely erroneous 

 values may be arrived at for A', if the loss of heat along the ends 

 of the wire is not taken into account. 



It can now be shown by means of a simple calcidation that the 

 value found for L or 6' after having been corrected for the heat 

 carried away along the ends agrees with the value of D. The 

 quantities of heat Q^ and Q, which in the stationary condition are 

 conducted away through the surface and the ends of an electrically 

 heated wire respectively (apparatus a) are given by ^) 



- «(.r'+ï/i') , = c -^ and =c/ ?//* 4- 



<— «, t—t^ 1 , t—t^ 1 _ 



1 Tax \ 1 — Tgx 



X \ X ^ , 



4.A.y. , , 0.2388 ^.^ ,, , . ... 



where c = and in* r^ a \i\.r, ,v being an auxiliarv 



/ c 



quantity which is determined by the third equation. 



In. these equations Q is the entire quantity of heat developed in 

 the wire (app.a, Qz=z L . I . ti), t the mean temperature of the wire, 

 t^ the temperature of the glass wall, / the current and M „, /1,>j and / 

 the resistance at t^, the section, the conductivity and the length of 

 the heated wire respectively ; Tgx stands for the hyperbolic tangent of .r. 



When the values found for LI and Sk are corrected in this 

 manner, the figures given under Lrorr and Scon- are obtained; they 

 are seen to agree very well with D. In this way it appears, that 

 the application of Goldschmidt's method is allowable, if the dimen- 

 sions of the apparatus are chosen correctly. 



1) S. Weber. Ann. d. Ph. (4) 54, [1911), p. 169. 



