198 Dr. C. V. Burton on a Theory 



H) is perpendicular to the diametral plane of the acceleration 



(components X, Y, Z), taken with respect to the ellipsoid (17). 



(11), (22), (33), which are the sums of squares, are the 

 values of the effective mass in the directions of the axes of 

 reference ; while (23), (31), (12), which are the sums of pro- 

 ducts, correspond to products of inertia in Rigid Dynamics, 

 and may be called " products of mass." It may easily be 

 shown that if r is the length of any given radius of the 

 ellipsoid (17), the effective mass reckoned in the direction of 

 this radius is Me 2 /?* 2 . It may also be remarked that even 

 when the motion is one of pure translation, there will in 

 general be finite effective couples, as is immediately evident 

 from (12). 



7. Case of Symmetry, — Consider now the particular case in 

 which the strain -figure is symmetrical about a point, and let 

 this point be CI, the origin of the axes of f, 77, f. We shall 

 then have 



(11) = (22) = (33) = effective mass; 

 (23) = (31) = (12) = 0. 



; }. . (17a) 



It is also evident that a rotation of the strain-figure about 

 any axis through its centre of symmetry corresponds to no 

 physical change whatever ; there is no possibility of such 

 rotation, nor can any influence exerted on the medium have a 

 tendency to turn the strain-figure about its centre of sym- 

 metry. Hence a strain-figure symmetrical about a point is 

 dynamically equivalent to a single particle of mass 



jjj(«r + A 2 + 7i 2 )rf? d n <K = jJjW + pi + yi)di d v 3 



placed at its centre of symmetry. 



It is worth remarking that the theory now considered, 

 though differing so widely from the theory of Boscovich, 

 leads to the same dynamical results. 



8. So far we have only considered the case of a sino-le 

 strain-figure. When there are more than one, the experimental 

 properties of matter lead us to suppose : — 



(i) That the entire distribution of displacement in the 

 medium is to be found (at least very approximately ) by com- 

 pounding geometrically the distributions which the various 

 strain-figures would have produced separately. 



(ii) That the strain-figures exert forces upon one another, 

 thus changing or tending to change their motion through the 

 medium. 



