concerning the Constitution of Matter. 



193 



Another condition to be fulfilled by the motion of the strain- 

 figure is this : the acceleration must be very small compared 

 with V/T, where VT is the radius of the smallest spherical sur- 

 face within which the whole appreciable effective mass (17 a) 

 of the strain-figure may be considered to reside. 



Assuming, then, that the necessary conditions are satisfied, 

 and that the strain-figure has only six degrees of freedom, let 

 us choose three rectangular axes (those of f, ??, J, with 

 origin XI) fixed in the strain-figure, and three other rectan- 

 gular axes (those of #, y, z, with origin 0) fixed in the 

 medium and in space ; let the coordinates of X2 referred to 

 Oa*, Oy, Oz be (X, Y, Z), and let the direction-cosines of the 

 f, 7) , f axes be given by the scheme 



(i) 





«-X 



y-Y 



z-Z 



1 



h 



nil 



n x 



V 



k 



m 2 



n 2 



i 



h 



ra 3 



^3 



("For convenience 

 dimensions.) 



diagram is only drawn in two 



Let P (f, 77, f) be the undisturbed position of a certain 

 volume-element of aether (that is, the position which this 

 element would occupy if the strain-figure were non-existent), 

 and let Q (f + a, tj + /3, £ + 7) be the actual position of the 

 same element. Then, in accordance with the geometrical 

 conditions of motion, 



a, j3 } 7 are functions of £, 97, ? only ; . . . (2) 



they are the components of displacement of the element whose 

 undisturbed position would have been f, 77, f. 



If the components of P Q parallel to 0<v, Qy, Oz be called 

 /, g, h respectively, we shall have, after the manner of (1), 

 the scheme 



