Prof. W. Thomson on the Rigidity of the Earth. 149 



where L is the modulus of elasticity in feet. Where, from want of 

 homogeneity or shattering, &c, as found in nature, the experimental 

 value of V differs from this, we may express it by the same form of 

 equation, 



V'=aVL, 



the coefficient a having to V ' 2g the rate that the actual bears to 

 the theoretic value of V. 



He then 'determines the value of a for three of his mean experi- 

 mental transit-velocities at Holyhead, and obtains as follows : — 



Feet per side. 

 V'=10S9 a=0-637 



V'=1352 a=0-791 



V'=1220 a=±0714 



The actual velocity of wave-transmission in the slate and quartz 

 rocks, taken together, was to the theoretic velocity due to their mate- 

 rials, if perfectly solid, 



a : s/2g, or as 1*00 : 8'89; 



so that nearly eight-ninths of the full velocity of wave-transmission 

 due to the solid material is lost by reason of the heterogeneity and 

 discontinuity or shattering of the rocky mass as it is piled together 

 in nature. 



The author then shows that were the rocks quite solid, the velo- 

 city of wave-transmission would be — 



Mean of slate and quartz transverse to lamination V= 13,715 feet 

 per second. 



Mean of slate and quartz parallel to lamination V=/659 feet per 

 second. 



This difference is probably reversed in nature by reason of the 

 greater discontinuity in the former direction. The author then 

 shows that his results, which appear at first sight to conflict with 

 those of an analogous character obtained by Helmholtz and others 

 for wood, in the three principal directions of its section, are strictly in 

 accordance and analogy with the results of these experimenters. 



The author concludes by deducing some conclusions as to the 

 bearing power, safe load, and proper direction as to lamination when 

 exposed to pressure, of these rocks, of a practical character, and valu- 

 able to the civil engineer or architect. 



May 15. — Major-General Sabine, President, in the Chair. 



The following communications were read : — 



" On the Sensory, Motory, and Vaso-motory Symptoms resulting 

 from Refrigeration and Compression of the Ulnar and other Nerves 

 in Man." By Augustus Waller, M.D., F.R.S. 



" On the Rigidity of the Earth." By Professor William Thomson, 

 F.R.S. 



The author proves that unless the solid substance of the earth be 

 on the whole of extremely rigid material, more rigid for instance 

 than steel, it must yield under the tide-generating influence of sun 



