216 



eases, calling p^ and p.^ the pressures, T^ and T., the absolute tem- 

 peratures at the ends, we have 





P^ y 1^ ;. CO 



R 

 2. Pi=P^ ^01" - = 00 



For intermediate cases Knudsen deduces more complicated formulae 

 which may be applied over a wide range. As a rule the matter 

 reduces itself to the application of a correction to one of the 

 limiting cases. The application of the formulae is not allowed over 

 the range defined by 



2/^ 



When these limits are exceeded, the accuracy very soon falls below 

 1 V„. It is necessary, therefore, to avoid the above range in the 

 measurements by a suitable choice of the tubes connecting the evapo- 

 rating surface with the measuring apparatus, and by changing them, 

 when occasion arises. When this is found to be impossible, the mea- 

 suring apparatus will have to be kept at a temperature but little 

 higher than that of the liquid or the thermal molecular pressure will 

 have to be measured experimentally or a different method altogether 

 will have to be resorted to '). 



In the range where the measurements can be corrected to the 

 limiting cases by means of the more complicated formulae referred 

 to it may occur, that the corrections cannot be applied for a given 

 tube owing to the free path beiiig unknown and that this quantity 

 cannot be found with sufficient accuracy by exti'apolatiou: in that case 

 the object can be attained by means of measurements with tw^o 

 different tubes suitably chosen, so as to eliminate the pressure and 

 obtain data for the calculation of the free path, which can then be 

 introduced into the formulae. 



The pressures which we wished to measui-e lie between 0.02 baryes 

 and 1 mm. The highest of these might still have been measured 

 with a Mac Leod gauge, but for the lov/er ones this method is not 

 applicable owing to the possibility of mercury distilling over at the 

 low pressure to the cold substance. We have therefore used Knudsen's 

 heated wire gauge "] between 1 mm. and 0.01 mm. and Knudsen's 

 absolute manometer ^) between 0.001 mm. and 0.01 mm. 



1) E. g. Knupsen's method of molecular effusion through a small orifice, in 

 which the amount of vapour passing through is measured instead of the pressure, 



2) Martin Knudsen, Ann. d. Phys. Bd. 32, p. 809, 1910. 



3) Martin Knudsen, Ann. d. Phys. Bd. 35, p. 389, 1911, 



