253 



Report on the Theory of Capillary Attraction. By the Rev. 

 James CnAhLis, late Fellow of Trinity College, Cambridge. 



In the Report which I had the honour of drawing up last year, on 

 the analytical theory of hydrostatics and hydrodynamics, a di- 

 stinction was made between problems on the common theory of 

 fluids, and those in which molecular attraction and the repulsion 

 of heat are explicitly taken account of, and the former kind alone 

 came under review. That distinction, it was said, depended on the 

 different bases of calculation, which in the former class of pro- 

 blems are observed facts ; in the other, certain hypotheses, which 

 can be verified only by a comparison of the results of calculation 

 with experience. The latter kind of questions are of the more 

 comprehensive nature, because frequently it is proposed in them 

 to account for the facts which serve for bases of calculation in 

 the other class, and an explanation of every such fact must in- 

 clude the explanation of all those that can be mathematically 

 shovni to be dependent on it. The above distinction ought to 

 be kept in mind when we regard the part which calculation has 

 to perform in our inquiries into the nature and properties of 

 matter. It is not sufficient to say that analysis serves to classify 

 facts of observation, and to prove that several which are allied 

 to each other are consequences of some one observed fact ; for 

 we have been taught by the labours of Newton, that there are 

 facts which are not phtsnomena, the existence of which can only 

 be proved by calculation. It may now be considered an esta- 

 blished fact that all bodies attract each other proportionally to 

 their masses, with forces varying inversely as the square of the 

 distances ; but the evidence for this truth is essentially mathe- 

 matical. So, if the existing theories respecting the internal 

 constitution of bodies, and the nature of the forces which ema- 

 nate from their molecules, should be established by the progres- 

 sive advance of science, the evidence on which they will rest 

 must be mathematical. For these reasons, this, the highest de- 

 partment of physical science, may be properly denominated 

 Mathematical Physics*. The great problem of universal gra- 

 vitation, which is the only one of this class that can be looked 

 upon as satisfactorily solved, relates to the lai'ge masses of the 



• In the former Report I have inadvertently written Physical Mathematics. 

 It might perhaps be questioned whether these terms be not equally proper ; 

 but when, in addition to what is said above, the title of Newton's Principia is 

 recollected, the other would seem to be preferable. 



