Septembee 28, 1906.] 



SCIENCE. 



403 



of radio-active fortunes supposedly stored in 

 the bowels of the earth. In one of the last 

 annalen, August Becker/ studying the lavas 

 of Vesuvius in the Lenard's laboratory, de- 

 tects no unusual radioactivity in the magmas 

 from deep sources, vphile Lord Kelvin has 

 lately girded his gravitational vestments anew, 

 and is thundering in the Times for a return 

 to the simple life, free from radio-active re- 

 finements. 



We may summarize, therefore, that in each 

 case specific evidence for the adequate occur- 

 rence or the localizations of volcanic heat is 

 wanting. Apart from this the manufacture 

 of volcanoes is as easy as an after-dinner dis- 

 cussion. Suppose, for instance, we all got to 

 work conjointly; let me supply the broth, as 

 I trust, thick and hot, while Elihu Thomson 

 kneads in the energy and Major Dutton bom- 

 bards the whole with a pai-ticles. Could any- 

 thing vnthstand us? True there has been 

 stuff predicted 



" Impenetrable, impaled with circling fire, 

 Yet unconsumed," 



but this need not be mentioned (at least not 

 in the summer), as it is gravely questioned 

 whether it will fit into the periodic law, and 

 it does not concern us if we are good. 



^ Cael Barus. 

 Brown Uni^teesity, 

 Peovtdence, R. I. 



THE RIGIDITY OP THE EARTH. 



To THE Editor of Science: In his discus- 

 sions of the interior condition of the earth 

 (Science, September 7, 1906, and elsewhere). 

 Professor T. J. J. See advances the proposi- 

 tion that the interior matter of the earth is at 

 the same time fluid and highly rigid. Taking 

 the words in their accepted meaning this is 

 a contradiction in terms. If the intended 

 meaning is that deep-seated material is kept 

 solid only by pressure, it is of course no new 

 hypothesis. The experimental evidence for 

 rigidity, which has been adduced by Kelvin, 

 Darwin and others, concerns, however, only 

 the actual present rigidity of the earth, and 

 has no bearing upon the question whether this 

 is or is not due to pressure. 



« Annalen der PhysiJc, XX., p. 634, 1906. 



Professor See's own supposed deduction of 

 the earth's rigidity (Astronomische Nacli- 

 ricMen, 4104) apparently rests upon a com- 

 plete misunderstanding of the meaning of 

 modulus of rigidity. He quotes from Kelvin 

 a definition of this modulus stated in a some- 

 what unusual form which seems to have mis- 

 led Professor See as to its raeaning, although 

 this is made quite clear by the context. The 

 definition quoted is from the article on Elas- 

 ticity, Encyclopedia Britannica, Vol. VII., p. 

 805, and is as follows: 



The modulus of rigidity of an isotropic sub- 

 stance is the amount of normal traction or pres- 

 sure per unit area, divided by twice the amount 

 of elongation in the direction of the traction or 

 of contraction in the direction of the pressure 

 when a piece of the substance is subjected to a 

 stress producing uniform distortion. 



The context shows that this definition refers 

 to a body subjected to a traction in one direc- 

 tion, an equal pressure in a rectangular direc- 

 tion, and zero stress in the third rectangular 

 direction. The accompanying strain is the 

 ' uniform distortion ' referred to in the defini- 

 tion. With this understanding the definition 

 is exactly equivalent to the more common 

 definition which immediately precedes the one 

 quoted, and which reads as follows: 



The ' modulus of rigidity ' of an isotropic solid 

 is the amount of tangential stress divided by the 

 deformation it produces. 



For a fluid the value of the modulus of 

 rigidity as thus defined is necessarily zero. 

 Professor See, however, apparently infers from 

 the definition quoted by him that the modulus 

 of rigidity of any body, solid or fluid, is equal 

 to the normal pressure to which it happens to 

 be subjected. At all events this is the basis 

 of the method by which he computes the rigid- 

 ity of the earth and of other planets. As- 

 suming Laplace's law of density and the re- 

 sulting distribution of interior pressure, he 

 computes the average pressure throughout the 

 earth and calls this the mean value of the 

 modulus of rigidity for the earth. Of course, 

 Kelvin's definition admits of no such inter- 

 pretation. L. M. HosKiNS. 



Palo Alto, Cal., 

 September 13, 1906. 



