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



investigations which, in the case of light, must be hypothetical, are, in the case 

 of solids and fluids, essentially positive, and may be made the object of direct 

 experiment. A general inquiry into the laws of elastic media, is an interesting 

 application of rational mechanics, and although it must necessarily include cases 

 purely hj'pothetical, it is not, therefore, to be considered as unimportant. In 

 this respect it is analogous to an inquiry into the general theory of central forces, 

 the importance of which is not confined to the investigation of those laws, of 

 which examples occur in nature ; these are undoubtedly the most important, 

 but the theory of central forces, considered as a branch of mechanics, would 

 be incomplete, unless extended to all possible laws of central force. 



SECTION I. GENERAL EQUATIONS. 



The formula of virtual velocities, which contains, as shown by Lagrange, 

 the conditions necessary to be fulfilled in the interior and at the boundaries of 

 a continuous body, is the proper starting point for a deductive theory of the 

 mechanical structure of bodies. Every hypothesis which may be made, and 

 every fact which experience has discovered, respecting the molecular consti- 

 tution of bodies, may be expressed in its most simple form by the aid of this 

 formula ; which, by its flexibility, and the facility it afibrds for deducing theo- 

 retic results, becomes of more importance in questions of this nature than in 

 other mechanical problems. In order to express by means of it the condi- 

 tions of equilibrium of a continuous body, it is necessary to distinguish the 

 forces acting at each point into two classes, molecular and external forces ; in- 

 cluding among the external forces the resultants of the attractions of the other 

 points of the body, since these attractions arise from gravitation, and must not 

 be confounded with the molecular forces. The formula of vii'tual velocities 

 must also be stated in such a manner as not to involve any hypothesis as to 

 the nature of molecular forces, so as to possess the requisite degree of generahty. 

 If the problem be dynamical, we must then add accelerating forces equal and 

 opposite to those actually employed, so as to destroy the motion at each point, 

 and consider the problem as one of equihbrium of forces. These negative accele- 

 rating forces must be considered as external forces. 



