Physical Structure of the Earth. 237 



of matter which, though negligible in some problems, are 

 not in others. Thus in the common hydraulic questions, 

 liquids are assumed to be incompressible ; it would be more 

 correct to say the compressibility is neglected. In small 

 problems connected with limited portions of the atmosphere, 

 the compressibility of air may be also neglected, but we could 

 not neglect it for a high column of the atmosphere. If, as 

 before remarked, the Earth were surrounded with an ocean 

 100 miles deep, the compressibility of the water could not be 

 well overlooked in tidal questions; then, a fortiori, compres- 

 sibility cannot be neglected in such a problem as the tides of 

 a liquid spheroid having a radius nearly equal to that of the 

 Earth. This is immediately made manifest by expressing the 

 compressibilities of liquids, not in terms of the amount due 

 to a single atmosphere of pressure, as is done in most tabu- 

 lated groups of results, but by some very much greater 

 standard, such as one or two thousand atmospheres. In the 

 experiments of Perkins"* the highest pressure employed was 

 two thousand atmospheres, and with this he reduced a column 

 of water by nearly ^ of its volume. The results of experi- 

 ments with great pressures such as this are highly illustrative 

 of the force by which a fluid may be compressed in the Earth's 

 interior. The actual coefficients of cubical compressibility, 

 on which calculations could be based, may be partly obtained 

 from the more exact researches of Regnault, Grassi, and 

 other recent experiments, or from special investigations on 

 fluid matter conducted with precautions such as these ob- 

 servers have employed. By then comparing the moduli of 

 compressibilities calculated from pressures of 1000 or 10,000 

 atmospheres, there could be no possibility of overlooking the 

 consequences as to the relations of liquid and solid bodies in 

 any case where they would be subjected to pressures of ab- 

 normal magnitude. 



(3) The propagation of sound in solids and liquids gives 

 further proof of the greater compressibility of liquids. 



The rate v of transmission of sound in solids and liquids is 

 a function of their compressibilities. In solids, 



P 



where E is the modulus of elasticity and p the density. In 

 liquids, 



V p Pl 



* Phil. Trans. 1826, p. 541. 



