﻿■y«=--rr-; (18) 



378 On the Coefficients of Pressure in Thermometry. 



unit volume of V e due to unit pressure per unit surface of S e , 1 



then 



1 sv' e (m 



P v e ' 



and so by (16), 



%-w=J < 19 > 



Since the result (3) may come under the notice of some 

 persons whose interest in thermometry is not accompanied by 

 a knowledge of elastic solids, it may be well to state explicitly 

 under what conditions it has been proved to hold, and wherein 

 these conditions may differ from what occurs in practice with 

 actual thermometers. 



The conditions assumed in the mathematical theory are : — 



(A) that the material is completely homogeneous, though 

 not necessarily isotropic ; 



(B) that the pressure is perfectly uniform over the surface 

 where it is applied ; 



(C) that the volume wdiose change is considered is the 

 entire volume within the inner surface. 



The fact that (3) holds when all these conditions are satisfied 

 does not of course necessarily imply that it ceases to hold if 

 one of the conditions is not satisfied. As a matter of fact it 

 certainly holds in one case when (A) is only partially satisfied, 

 viz. in the case of a spherical shell composed of concentric 

 layers of different isotropic materials, which though differing 

 in rigidity have all the same compressibility. But it is 

 obvious that in any case where the compressibility, and so 

 the bulk-modulus, is not uniform it would be meaningless. 



There is room for doubt as to how far condition (A) is 

 satisfied by thermometers. Differences of elastic quality 

 between the bulb and stem, or even between the material at 

 the outside and inside of the stem, seem not unlikely to occur. 



The condition (B) is probably never satisfied exactly; and it 

 may be very far from holding when the stem is vertical, in 

 the case either of internal pressure or external fluid pressure. 

 It may, however, be regarded as practically satisfied in the 

 case of external atmospheric pressure. 



The preceding mathematical theory gives no direct and 

 certain information as to how the change of volume is divided 

 between the bulb and stem even when the pressure is uniform. 

 If, however, we for a moment supposed the bulb and a short 



