254 FOURTH RKPORT 1834. 



universe, to the dependence of their forms on their proper gra- 

 vitation, and the motions resulting from their actions on one 

 another. The progress of science seems to tend towards the 

 sohition of another of a more comprehensive nature, regarding 

 the elementary constitution of bodies, and the forces by which 

 their constituent elements are arranged and held together. Va- 

 rious departments of science appear to be connected with each 

 other by the relation they have to this problem. The theories 

 of light, heat, electricitj-, chemistry, mineralogj^ crystallogra- 

 phy, all bear upon it. A review, therefore, of the solutions that 

 have been proposed of all such questions as cannot be handled 

 without some hypotheses respecting the physical condition of 

 the constituent elements of bodies, would probably conduce, by 

 a comparison of the hypotheses, towards reaching that generali- 

 zation to which the known connexion of the sciences seems to 

 point. This end is kept in view m the following Report. It hap- 

 pens that with respect to fluids two problems have especially en- 

 gaged the attention of mathematicians, which in a very marked 

 manner lead to the consideration of molecular forces and the 

 repulsion of heat, viz. capillary attraction, and the propagation 

 of motion as affected by the development of heat. The one 

 refers to fluid in equilibrium, the latter to fluid in motion. It 

 was my intention originally to embrace both these in one Re- 

 port, but the time required for becoming acquainted with works 

 on these subjects which have not been very long before the 

 public, and contain new trains of thought and mathematical in- 

 vestigation, did not allow of preparing the Report, such as it 

 was intended to be, in time for the present meeting ; and the 

 matter connected with capillary attraction alone \vill perhaps be 

 thought sufiicient, and of sufficient mterest, to form the subject 

 of a separate report. 



The distinction above stated as applicable to two sorts of 

 hydromechanical questions, applies equally to statical and dyna- 

 mical questions respecting solids. Some may be treated on the 

 supposition of perfect rigidity, as is the case in most of the pro- 

 blems that occur in the common elementary treatises on mecha- 

 nics : in others the solids must be supposed to be elastic ; and 

 if the elasticity he regarded not as a datum of observation, b\it 

 as a result of molecular attraction and repulsion, then, to take 

 account of it, certain hypotheses must be made respecting the 

 nature of these forces and the molecular arrangement, plainly 

 analogous and intimately related to the like hypotheses with re- 

 spect to fluids. Questions of this kind have of late largely en- 

 gaged the attention of some French mathematicians ; and the 

 nature of tlieir theories, and the results of the calculations 



