464 PROCEEDINGS OF THE GEOLOGICAL SOCIETY. 



B and C = two constants, whose values depend on the nature and 

 strength of the saline solution in the cavity, 



Then we have 



Y=Bt + Ct 2 equation (1) 



__v+ -0000 0271^ / 2 x 



1 --00000271^ 



>y/4CV + B s 

 2C 

 / 4( f_±^0000027lp 



. >v/4CV + B 2 -B m 



' 2C W 



00000271^ ' B ' B 



2C ■••>-,• W 



v =(B^ + C^ 2 )(l--00000271i))--00000271i3 (5) 



jp=369,000^ (6) 



e=13-2{l+-007153(^-100)} 5 (7) 



lf>=0, i?==V. 



These equations can he considered strictly accurate only for 

 moderate values of t and p ; but for greater there must certainly be 

 a limit past which they would cease to give accurate results. At 

 present, however, it is impossible to say what that limit is ; and 

 therefore I think we cannot do better than adopt them provisionally. 



It will be seen from (5) that the actual relative size of the vacuities 

 depends on both the temperature and the pressure at which the 

 cavities were formed. Therefore we have single equations involving 

 two unknown quantities ; so that, unless the value of one be known, 

 that of the other cannot be determined. If the pressure were known, 

 the temperature could be calculated from (4), and thus the fluid- 

 cavities be made use of as self-registering thermometers, whilst, if 

 the temperature or the value of V were known, the pressure could 

 be calculated from (6), and thus the fluid-cavities be employed as 

 spring-balances. They are, in fact, in this respect analogous to air- 

 thermometers, which may be used as thermometers or barometers, 

 according as the real pressure or temperature is known. If the 

 actual pressure be known only approximately, but must have been the 

 same for any two or more crystals having v different, the difference 

 in the temperature could be calculated from (4) ; or, if the tempe- 

 rature were the same, and an approximation to the value of V known, 

 the difference in the pressure could be ascertained from (6). I do 

 not think there is any reason to believe that the actual size of the 

 fluid-cavities can invalidate these general principles. Is not the 

 proportion between the diameter and circumference of a circle the 

 same, whether it is visible to the naked eye or cannot be seen with- 

 out a high magnifying power ? Similarly, since there appears to be 

 no connexion between the actual quantity of fluid and the propor- 

 tionate increase in the volume by heat or decrease by pressure, we 



