﻿230 DE. H. C. SOEBY ON THE APPLICATION OF [May I908, 



consideration, it seemed to me probable that the formula connecting 

 cavities and pressure may be of the form : 



, , ^.^ ^ 32-cav. 



constant quantity X o^^ 



^ "^ 32 X cav. 



In order to make the best use of the material at my disposal, I 

 adopted the following plan to learn the yalue of the constant. 

 The amount of cavities in clays of great antiquity, which have never 

 been exposed to a pressure of more than a few feet of super- 

 incumbent material, is about 32 per cent. ; and I endeavoured to 

 ascertain from known geological data the thickness of super- 

 incumbent strata corresponding to a medium amount of cavities. 

 The best cases at my disposal were from the Coal-Measures near 

 Sheffield, and the calculated cavities in the Penrhyn slate before 

 cleavage was developed. The former gave 13^ per cent, of cavities 

 for a medium thickness of 2500 feet, and the latter 11 per cent, for 

 a thickness of about 3400 feet of rock, as now compressed, of specific 

 gravity estimated at 2-85, which equals 3976 feet of rock of 

 specific gravity =2*50. Combining these together, I obtained for 

 13^ per cent, of cavities a pressure of 2700 feet of rock, instead of 

 2500, which would agree with the supposition that 200 feet of 

 the uppermost part of the Coal-Measures has been lost by denu- 

 dation. As a first attempt, I therefore worked on the supposition 

 that for no pressure the cavities are 32 per cent., and for 2700 feet 

 13J per cent. 



On the whole, it seems to me probable that the necessary force 

 may vary as the ratio between the amount of solid material and 

 that of the cavities, commencing at 32 per cent. ; something like 

 the strength of a beam of the same thickness with a long or a short 

 span. From this it would follow that, when the cavities approach 

 32 per cent., a small pressure would produce considerable effect ; 

 whereas, when the percentage is small, a great increase in pressure 

 would be necessary to produce much influence. On this supposition, 

 the law connecting cavities and pressure would have the form 



2700 feet x 



1 00 -cav. 



100-32 



cav. 



32 



100-13-5 



100-32 



13-6 32 



So far as I can see, this agrees with all the facts of the case, 

 and yet it must be looked upon as only a plausible approximation. 

 Although this and the previous formula differ much, yet, strange 

 to say, they yield so nearly the same results as to make me think 

 that they may not be far wrong. 



The Table (X) on the following page was calculated from the 

 formula just given, and shows not only the ratio between the 

 volume of the solid material and the cavities, but also the pressure 

 in feet of rock of specific gravity 2-5, and that in tons per square 

 inch. 



