SIGNIFICANCE OF THE THREEFOLD STATE. 63 



The estimate of 9,100 feet for the minimum depth (where weight alone 

 acts) at which igneous quartz crystals now containing carbon dioxide, 

 liquid up to 30.9, could have been formed, 1 applies best to those cases in 

 which only carbon dioxide exists in the crystal cavities. If there are other 

 gases and liquids present in appreciable quantities, this figure becomes less 

 applicable, since the constants a (denoting an internal force or attraction) 

 and 6 (representing the sum of the spheres of influence of all the molecules 

 in the space v) used in Van der Waal's equation are not the same for 

 all gases. At how much greater depths than this the crystallization of cer- 

 tain specimens of quartz actually did take place, if rock weight alone was 

 involved, may, perhaps, be estimated by a painstaking determination of 

 the pressure under which the imprisoned carbon dioxide exists in these 

 minute cavities. This might be accomplished by piercing one of the larger 

 cavities while submerged in mercury or other liquid, and noting the expan- 

 sion of the freed bubble, as first suggested by Sir Humphry Davy. 



Though naturally subject to limitations, it is nevertheless possible to 

 throw considerable light upon the nature of cavity inclusions by the use 

 of the microscope. Some of the conditions may be stated: 



(1) If, at slightly under 30.9, the cavity is entirely filled with a liquid 

 which completely vaporizes at 30.9, it contains only carbon dioxide. 



(2) If, at slightly under 30.9, the cavity is filled with two immiscible 

 liquids, one of which passes into the gaseous state at 30.9, the liquids are 

 probably water and carbon dioxide. 



(3) If the cavity, when just below 30.9, contains a liquid and an appre- 

 ciable gas-bubble, and the liquid does not disappear when the slide is 

 warmed above 30.9, the liquid is probably water, and the bubble water- 

 vapor with perhaps some of the difficultly liquefiable gases, such as hydrogen, 

 nitrogen, or methane. 



(4) If, as is often the case, the temperature at which the liquid in a 

 cavity disappears is found to be several degrees below the critical tempera- 

 ture of carbon dioxide, two interpretations are possible: either the carbon 

 dioxide is subject to a pressure less than 73 atmospheres, or else there is a 

 small proportion of another less liquefiable gas present. If the cavity be 

 opened and only carbon dioxide be found, the pressure under which the 

 gas existed, and from that something as to the conditions under which 

 the crystal was formed, can be computed from the temperature at which 

 the liquid disappeared. If another gas, such as hydrogen or nitrogen, be 

 found and identified, it is possible, by using an equation, 2 to calculate the 

 relative proportions of the two gases from the critical temperature of the 

 mixture. Thus a cavity containing a mixture of carbon dioxide and 

 nitrogen which had a critical temperature of 29 would hold 98.7 per cent 



1 This figure is based on the assumption that the quartz crystallized at 1100; if it 

 ia desired to use other temperatures, they can be substituted in Van der Waal's equation 

 and the corresponding pressures computed. 



2 1 _ n^+(10i - n) ^ w j iere i j s the observed critical temperature of the mixture, ^ 



and t 2 are the theoretical critical temperatures of the two liquefied gases. Then n equals 

 the proportion by weight of the first liquid and 100 -n equals the proportion by weight 

 of the second liquid. 



