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XLII. Note on the Relation between the Coefficients of Pressure 

 in Thermometry. By C. Chree, M.A.* 



THE study of thermometers intended for very exact 

 physical work has been the object of much patient 

 research at the Bureau International des Poids et Mesures, 

 and an important bookf, embodying the principal results 

 obtained and giving a full account of the several corrections 

 required, has been written by Dr. Guillaume, attache to the 

 Bureau. The present paper was called into existence by 

 Dr. Guillaume's discussion on his pages 99-111 of what he 

 terms " Coefficients de Pression." 



There are two such coefficients of pressure, an " external " 

 and an "internal." Both have to do with the change in the 

 internal volume of the thermometer, i. e. the volume con- 

 tained within the inner glass surface ; but the external 

 coefficient is connected with the reduction of this volume 

 under increased pressure on the outside of the thermometer, 

 while the internal coefficient is connected with the increase of 

 volume accompanying increased pressure on the inner surface 

 itself. 



The increase of external pressure may be due to a rise in 

 the barometer or to immersion in a liquid ; while an increased 

 internal pressure follows a rise in temperature if the stem be 

 vertical, or the alteration of the thermometer from a hori- 

 zontal to a vertical position. 



As a matter of convenience, Dr. Guillaume combines the 

 correction required by the change of volume of the glass with 

 that required by the compressibility of the mercury itself. 

 Here, however, we shall have to do solely with the corrections 

 due to the compressibility of the glass. The coefficients of 

 pressure dealt with here are those which Dr. Guillaume (/. c. 

 p. 99) denotes by the letters a f and a e . They may be defined 

 as follows : — 



Let V,- denote the internal volume of the thermometer 

 when free from all pressure. Let this become increased by 

 SVi when there is a uniform internal pressure p f and no 

 external pressure, and let it become diminished by oVY' when 

 there is a uniform external pressure p" and no internal 



* Communicated by the Author. 



t TraitS Pratique de la Thermometrie de Precision. (Gauthier-Villars 

 et Fils, Paris, 1889.) 



2C2 



