116 The Rev. S. Haughton on a Classification of Elastic Media, 



to the method for bodies whose molecules act in the line joining them, that the 

 surface of wave-slowness* will be 

 (P-l)((2-l){E-l)-F'{F-l)-G'((2-l)-H'{B-l) + 2FGH=0. (18) 



(P—l,Q — l, &c.)eqviated to zero, denoting the six fixed ellipsoids used in 

 the memoir referred to ; these ellipsoids thus appear in the general theory of 

 molecular dynamics, and vnU. have the same use in interpreting the conditions 

 at the limits in the general problem, as in the particular case of attracting and 

 repelling molecules. As their use has been fully explained in my former me- 

 moir, I shall only refer to it, and pass on to other subjects. 



I shall here state the general conditions necessary, in order that the mole- 

 cular equilibrium of a body removed from the influence of external forces 

 should be stable ; this investigation will be found of use in the subsequent part 

 of this memoir. The equation of virtual velocities, in the case supposed, will 



become 



lllhVdxdydz = ; 



or, as it may be more accurately stated, 



\llhVdxdydz = 0, or < 0; 

 this sum never becoming positive for possible displacements. The equa- 

 tion of virtual velocities, as stated by M. Poisson and other writers, supposes 

 no virtual displacements but those for which equal and opposite displace- 

 ments are possible ; the correct statement of the principle is, that the sum of 

 the virtual moments of the system can never become positive for possible dis- 

 placements. For the full development of this important correction of the equation 

 of virtual velocities, as given by Lagrange, I shall refer to a memoir of M. 

 OsTEOGKADSKY, contained in the Meinoires de VAcademie de St. Petersbourg.f 



The application of the principle to the present case will be evident upon 

 the statement of the question. As the form of T^is given in terms of (n, , a,, &c.), 



we shall have 



,,^ dV^ dV^ 

 bV — —. — ctti -|- — ;— oa.j + &c. ; 

 da^ da, 



* Vide Transactions of the Eoyal Irisb Academy, vol. xxi. part ii. p. 172. 

 t Tom. iii. p. 130. 



