of Electrons in an Elastic Solid yEtlier. 141 



the south saddle. The outlet of the lake is now the north 

 saddle, and the lake is within but does not extend to the 

 limits of the north-east quadrant.] 

 We have 



at north saddle, z = w/A = 3c 3 , 1 ,„„v 



at south saddle, z = w/A = 3a/> 2 . J 



The ratio o£ the first o£ these heights to the second increases 

 very rapidly with c/b, and tends to the limit ^{c/b) z . 

 The divergence at the south saddle is 



+ 2(a-2b)=±6b 2 /(2b+c). 



This is small compared with b when c/b is large. 



For moderate as well as for large values of c/b these two 

 small quantities are of very different magnitude. For instance, 

 put c=10b, and therefore a = 76/4. We get 



height of north saddle/height of south saddle = 571^, 



divergence at south saddle/ A = ±h 



The objects of this paper can now be explained summarily 

 thus: (1) In the light of modern knowledge concerning 

 atoms and electrons we return to the old Fresnel view that 

 the aether is an isotropic elastic solid. Free aether exhibits 

 this solid in a standard state, which is stable for infinitesimal 

 strains; matter exhibits the same solid in a second state ? 

 obtained from the first by small finite straining, which is 

 rendered possible by the constitution of the solid. It is 

 assumed that the two states can permanently exist in stable 

 equilibrium for the solid as a whole (or failing that, they 

 can exist sub-permanently in an evolved state of balanced 

 motions). (2) The chief object of this paper is to recast the 

 fundamental theory of elastic solids, particularly of isotropic 

 elastic solids, in such a manner that it will be possible with 

 due development to test the validity of this assumption and 

 others; and eventually to attain such a definite form for the 

 constitution of the solid as shall lead to the known phenomena 

 of nature. (3) For precision, and to suggest other consti- 

 tutions, we postulate tentatively as simple a constitution as 

 the larger, better known, features of nature seem to permit. 



IV. Mathematical Development, initiated. 



T, the total strain, may be supposed due to a*total pure 

 strain 1 + ^, where yjr is a self-conjugate linity, followed by 

 a rotation 7 ( ) q~ l where q is a quaternion, or 



T(o = q.(l + ylr)(o.q- 1 . 



