504 



of heliutn correspoiHling to llie teiiiperatiire and the density, as also 

 by llie value of the radius at the ends of the given portions of 

 the tube'). 



As the density de|)ends on ji as well a» on T and as j) varies 

 along the tube, Ihe liniits at the ends of the various parts will 

 depend upon the local values of [i themselves: of these only that 

 at the top of the capillary is immediately known, whereas at the 

 bottom the density is appi'oximately known, it is true, but neither 

 ji nor 7'. It is therefore necessary to proceed by successive approxi- 

 mation and starting at the top to calculate the diminution of pressure 

 assuming as a first approximation p = constant equal to the value 

 at the top of that portion of the tube, and then, using the distribution 

 of pressure which is found and the known distribution of temperature 

 to impi'ove the calcidation, etc. 



The uncertainty regarding the distribution of temperature along 

 the capillary is of course a source of error, but as a rule the errors 

 arising from this uncertainty are not of any importance, especially 

 because usually, according as this uncertainty is greater for a given 

 portion of the tube, its contribution to the total correction for the 

 molecular pressure becomes smaller. Finally for that portion which 

 reaches down to the range of temperatures which have to be detei'- 

 mined by the thermometer itself the contribution to the correction 

 can be entirely neglected. The most important contribution to the 

 coirection is due to the upper part of the capillary. 



5. Corrected temperatures. Applying the corrections on the basis 

 of the pressure-distribution along the capillary, as found by the 

 above calculation, the following results are obtained : (see tabel II 

 p. 505). 



The values between brackets ( ) refer to the calculation with the 

 more empirical values of c, and c, , introduced solely with a view 

 to the observations without taking into account the theoretical 

 limiting values. 



Calculating the correction of the helium-thermometer with mercury- 

 manometer by means of the formulae tested in the above series of 

 observations, we find (considering only the most reliable observations 

 (see table III p. 505). 



') If afterwards a changing value of n were found for helium at the lower 

 temperatures, as in oilier gases, the same formula will be applicable, for each 

 piece into which the tube is divided its own value of n being introduced. 



