142 LAMBERT: CONSTITUTION OF THE EARTH 



To deduce the modulus of rigidity from the earthquake data 

 we must make certain assumptions, but it may be said that all 

 results point to a modulus of rigidity increasing with the depth 

 from that of rock at the surface (2.4 X 10^^ C. G. S. units), to a 

 value exceeding that of steel (8 X 10^^ C. G. S. units), and per- 

 haps three or four times as great. ^' It should be noted that 

 owing to the scantiness of data for a distance from the focus 

 greater than 13,000 kilometers, the information derived from 

 earthquake data is limited to an outer shell whose thickness is 

 about one-half the earth's radius. ^^ This scantiness beyond 

 13,000 kilometers or even smaller distances has long seemed to 

 need some explanation beyond that of mere distance and in this 

 connection attention may be drawn to Knott's recent paper 

 already referred to (footnote No. 31, p. 139), which is one of unusual 

 interest. He suggests as a possible explanation that the central 

 core of the earth, with a radius equal to perhaps 0.4 that of the 

 earth, may be non-rigid or tiearly so, but highly incompressible. 



Even this very summary and dogmatic discussion has not 

 covered even superficially the entire field. There remains the 

 further discussion of the problem of the reason for the apparent 

 fluidity of the earth for long-continued forces, and its rigidity 

 under the action of forces of short period, also the theory 

 of "firmo-viscosity" and its relation to the problem of 

 viscosity and the retardation of the rotation by tidal friction. 

 There remain also the hypotheses of various layers of fluid matter 

 interposed between other layers of solid matter to satisfy this 

 or that real or apparent result of observation. . The subject of 

 the interpretation of earthquake phenomena, extremely inter- 

 esting both from a mathematical and a physical point of view, 

 has been barely touched. Your patience and my knowledge 



^' The author has in hand some comparisons of the result of assuming the densities 

 and moduli to be as given in table i, together with similar comparisons for other 

 laws of density', but the results are not complete. So far nothing has come to light 

 to throw doubt on the general correctness of the opinion previously expressed in 

 regard to the modulus deduced from Legendre's law, at least for the outer parts of 

 the earth. 



^* One-half the; radius is the maximum depth below the surface of a chord of 120° 

 of great circle corresponding to a surface distance of about 13,000 kilometers. 



