32 Prof. W. H. Bragg on the " Elastic Medium " 



Substituting for a x this becomes 



To put this into the ordinary language we must write for Ej 



4:7T 4r7T 



and E 2 , r— and ^-respectively, and for E x & we must write 



F the " intensity of the field." 

 This gives us 



, 2(2K 1 + K 2 ) x 



This differs from the formula in Gray's ' Theory of Abso- 

 lute Measurements in Electricity and Magnetism/ in that it 



has an extra factor ^-. However, the K x has obviously 



dropped out by accident from Gray's formula, as it is 

 necessary to make the dimensions right. I cannot explain 

 the remaining difference. 



The formula used by Boltzmann involved the ratio of two 

 expressions like the above, so that even if the formula obtained 



above is the correct one the -~ would divide out. 



We may examine by this method the effect of imparting a 

 charge to an ellipsoidal conductor immersed in a uniform 

 dielectric. The proof differs but little except in language 

 from other proofs, so I will only state it briefly. 



It is easy to show that that state of strain, in which the 

 particles on every ellipsoidal surface confocal to the con- 

 ductor move normally outwards so as to lie on a new ellip- 

 soidal surface similar to the old one, is a state which produces 

 complete equilibrium everywhere. 



We must first see whether our suppositions are geometrically 

 consistent with each other : it is not at once evident that the 

 ellipsoidal confocals can expand similarly, so to speak, and at 

 the same time the displacement be always normal to them. 



x 2 II 2 z 2 

 Let -2 + Tg + 3 —1 be the equation of the ellipsoidal con- 



X 1/ ^ 



ductor. Let 2 4- - , 9 , % + , ~ ^ = 1 be one of the Con- 



or + X x b 2 + \ c 1 + \ ± 



focal ellipsoids, and let similar equations with A 2 , X 3 in place 

 of Xi represent other confocals at right angles to each other 

 and to X x . Consider the tube formed by the intersection of 

 the confocals \ 2 , X 3 , \ 2 + B\ and \ 3 + S\ 3 . If p h j9 2 ,/) 3 , be the 



