554 Prof. A. M c Aulay on 



of the intrinsic strain throughout the crystalline volumes and 

 throughout the remaining free aether there will be a misfit 

 throughout thin interface regions ; let the maximum elonga- 

 tion (of irrotational strain) necessary to account for this 

 interface misfit be not greater than *05. [For a sphere o£ 

 water, 100 metres in diameter, the interface thickness will 

 thus be of the order 10 -6 cm.] The e , / , g of (3) may be 

 looked upon as the particular free aether values of the general 

 intrinsic principal elongations e x , f\, g x . It is permissible to 

 change e x , f\, g x from positive to negative, if at the same 

 time we change (J from positive to negative, so that the 

 cubic term retains a negative value. 



Let the hydrostatic quadratic term be zero in the intrin- 

 sically strained state and have the value 



b{ez+f 2 +g 2 )\ (4) 



where b is a positive constant and e 2 , j\, g 2 are elongations 

 (either principal elongations or elongations in three given 

 rectangular coordinate directions) of the actual disturbed 

 state reckoned from the intrinsically strained state. The 

 only condition for our purposes, it is necessary to impose on 

 b, is that it is large enough to mask the effects of those 

 higher order " cubic rotational " terms which have been 

 neglected. For instance, b may be supposed practically 

 infinite. 



A medium thus endowed with two elastic moduli will 

 oscillate about the intrinsically strained stable state according 

 to MacCullagh's equations ; in other words, it is MacCullagh's 

 medium. 



To obtain a light intensity as great as at the Sun's surface 

 (2 ergs per cub. cm.) the maximum disturbed curl < 10~~ 13 . 



2. Dynamical behaviour of the solid mathematically 

 investigated. 



Without loss of generality we may divide by D and 

 assume for the future that the density is unity ; thus the 

 and b about to be used may be looked upon as our previous 

 O/D and b/J). We will consider a more general intrinsic 

 irrotational strain than that specified in § 1 ; that is to say, 

 we will suppose the intrinsic strain to be a purely arbitrary 

 continuous irrotational strain, but we continue to assume 

 that the superposed disturbed strain is small compared with 

 the intrinsic strain. 



Let p be the position vector of a point in the zero state of 



