ON THE COilKSION OF FLUIDS. 



661 



tion of the sine of refraction to that of incidence, in the 

 passage of a ray of light through a transparent body. It is 

 only in this case, that this kind of attraction has been sub- 

 jected to an exact analysis. I shall now submit to the con- 

 sideration of mathematicians a second case, still more re- 

 markable than the first, on account of tbe variety and sin- 

 gularity of the phenomena which depend on it, and which 

 may be analysed with equal accuracy : this case is tliat of 

 capillary action. The effects of refractive powers belong to 

 mechanics, and in particular to the theory of projectiles ; 

 those of capillary action relate to hydrostatics, or the 

 equilibrium of fluids, which are raised or depressed by its 

 means, according to certain laws, which I pro]X)se to ex- 

 plain." 



I shall here take theliberty of observing, 

 that the arguments, which I have formerly 

 advanced, in favour of the Huygenian theory 

 of light, would perhaps have occasioned some 

 little hesitation with respect to the .tciion here 

 supposed to be e.xerted by trans[>areiitbo(hes 

 on light, if liiey had ever been so fortunate 

 as to obtain Mr. Laplace's attention. Indeed 

 an " attraction insensible at all sensible dis- 

 tances," would not explain the cfTects of what 

 Newton calls inflection, which affects the 

 rays passing at a very considerable distance, 

 at least as much as the tenth or twentieth 

 of an inch, on each side of an opaque sub- 

 stance, placed in a small pencil of light in a 

 dark room. 



" Clairaut is the first, and has hitherto remained the 

 only person, that has subjected the phenomena of capillary 

 tubes to a rigorous calculation, in his treatise on the fi- 

 gure of the earth. After having shown, by arguments 

 which are equally applicable to all the theories which have 

 been advanced, the inaccuracy and iniufhciency of that of 

 Jurin, he enters into an exact analysis of all the forces 

 which can contribute to the elevation of a portion of water 

 in a tube of glass. But his theory, although explained 

 with all the elegance peculiar to the excellent work which 

 contains it, leaves undetermined the law of the height of 

 that elevation, which is found from experimenjt to be 

 inversely proportional to the diameter of the tube. 

 This great mathematician contents himself with observing, 

 that there must be an infinite variety of laws of attraction, 

 which, if substituted in his formulas, would ^ITord this con- 

 1 



elusion. The knowledge of these laws is, however, the 

 most delicate and the most important part of the theory ; 

 it is absolutely neccssary_ for connecting together the dif- 

 ferent phenomena of capillary action; and Clairaut would 

 himself have been aware of this necessity, if he had wished, 

 for example, to pass from capillary tubes to the spaces in- 

 cluded between two parallel planes, and to deduce from 

 calculation the equality, which is shown by experiment, 

 between the height of ascent of a fluid in a cylindrical 

 tube, and its height between two parallel planes, of which 

 the distance is equal to the semidiameter of the tube ; a re- 

 lation which no one has yet attempted to explain. I en- 

 deavoured, long ago, to determine the laws of attraction ort 

 which tliese phenomena depend ; some later investigations 

 have enabled me to demonstrate, that they may all be refer- 

 red to the same laws, whicB will account for the phenomena- 

 of refraction, that is, to such as limit the sensible effect of 

 the attraction to an insensible distance ; and from these 

 laws, a complete theory of capillary action may be deduced." 



It is true that Clairaut was the first that 

 attempted to lay the foundation of a theory 

 of capillary action ; but he is by no means^ 

 the only one that has made the attempt. Seg- 

 ner published, in the first volume of the 

 Transactions of the Royal Society of Gottin- 

 gen, for 1751, an essay, in which he has 

 gone much further than Clairaut : it is true 

 that he has made some mistakes in particular 

 cases: but he begins, like Mr. Laplace, from 

 the eftiscts of an attraction insensible at all 

 sensible distances ; he has demonstrated that 

 the curvature of each point of the surface of 

 a fluid is always proportional to its disttuice 

 above or below the general level, and he has 

 inferred, from earlier experiments, the trae 

 magnitude of this curvature at a given height, 

 both for water and for mercury, without ma- 

 terial error. We shall however find, that 

 the principles, which Clairaut, Segner, and 

 Litplace, have successively adopted, are insuf- 

 ficient for explaining all the phenomena ; and 

 that it is impossible to account for them with- 

 out introducing the consideration of a repul- 

 sive force ; which must ijideed inevitably be 



