378 



NATURE 



[March 23, 1922 



of a liquid surface and a solid is constant and character- 

 istic of any given pair of liquids and solids. 



If a curved line is equally stretched^ the force 

 that it exerts along the normal at any point is directly 

 as its curvature, and the same is true of a surface of 

 simple curvature — e.g. a cylindrical surface. When the 

 curvature is double, each curvature has its appropriate 

 effect, and the normal force will vary as the sum of the 

 curvatures. As this sum is the same for all perpendi- 

 cular directions, the normal forces will be proportional 

 to the sum of the greatest and least curvatures. Since 

 the force is always directed to the centres of curvature 

 it will elevate the fluid in a capillary tube when the 

 surface is concave, and depress it when convex. When 

 the surface is cylindrical and therefore curved only in 

 one direction, as when water rises between two glass 

 plates, the curvature must be everywhere as the 

 height of the volume of fluid. When the curvature 

 is double, the sum of the curvatures must be as the 

 ordinate. This is the relation expressed by Laplace's 

 fundamental equation, and Young's essay ^ contains 

 the solution of most of the cases afterwards solved 

 by Laplace. Peacock, Lowndian professor at Cam- 

 bridge from 1836 to 1858, the editor of the Works of 

 Young, appends the following note : "In the original 

 essay the mathematical form of this investigation and 

 the figures were suppressed, the reasoning and the 

 results to which it leads being expressed in ordinary 

 language ; even in its altered form the investigation 

 is unduly concise and obscure." Clerk Maxwell 

 says of Young's methods of demonstration that, 

 " though always correct and often extremely elegant 

 [they] are sometimes rendered obscure by the scru- 

 pulous avoidance of mathematical symbols." 



The phrase " scrupulous avoidance " is quoted 

 from Challis and is appHcable only to the earlier 

 essays. In the article on cohesion of 181 6 and the 

 " Elementary Illustrations of the Celestial Mechanics of 

 Laplace," mathematical symbols are freely used, the 

 analysis being by the method of fluxions. Owing to a 

 charming devotion to Newtonian tradition, English 

 mathematics was at its lowest ebb when Young was a 

 student at Cambridge ; the reforms which Woodhouse, 

 of Caius, within a few days of the same age as Young, 

 initiated in the Cambridge School in 1803 bore fruit 

 only in 1817, through the action of Herschel, Babbage, 

 and Peacock. A poor training in antiquated methods 

 and a certain vanity in his powers of " clear and 

 simple explanation," ^ may account for the way in 

 which Young concealed his mathematics. His spirited 

 indictment of the " algebraical philosophers, who 

 have been in the habit of deducing all these quantities 

 from each ether by mathematical relations, making, 

 for example, the force a certain function or power of 

 the distance, and then imagining that its origin is 

 sufficiently explained," and of the geometricians who 

 " convert the formulae into a curve with as many 

 flexures and reflections as the labyrinth of Daedalus," 

 is of the earlier period ^ and probably traceable to his 

 personal irritation with Laplace, whom he never 

 forgave for a real or fancied appropriation of his 

 (Young's) ideas. 



» Phil. Trans., 1805. 



• Cf. the sentence, pregnant with personal character, which closes the 

 essay of 1804. 



* Lecture 49 of the " Natural Philosophy," the preface date being 1S07 ; 

 p. 471 of the edition of 1845. 



NO. 2734, VOL. 109] 



Young proceeds to consider the " Physical Founda- 

 tions of the Law of Superficial Cohesion." This he 

 finds in the nature of the forces of cohesion. Young's 

 work, and especially his " wonderful speculation," 

 as Rayleigh calls it, as to the magnitude of the pressure 

 in the interior of water due to corpuscular forces, which 

 he puts at 23,000 atmospheres, and the calculation 

 based on this estimate of the range of the cohesive 

 force and the size of molecules, are fully dealt with by 

 that writer.* 



The beginnings of Laplace's well-known theory 

 are to be foynd more than half a century earlier in 

 the work of Clairaut.^ Clairaut, like Laplace, was 

 an astronomer, and his treatise on the figure of the 

 earth consists of a mathematical analysis of the con- 

 dition of equihbrium of fluid masses. This leads to 

 the proposition that " all the particles of a mass of 

 fluid can be in equilibrium amongst themselves when 

 the force which acts on it is the sum of the attraction 

 which they exercise on one another, (namely) gravity, 

 and the attraction of any body which touches the mass." 

 Capillary phenomena are treated as a special case of the 

 proposition. Clairaut's analysis of fluid equilibrium 

 is based upon a consideration of the forces acting upon 

 an infinitely narrow canal of any figure which traverses 

 the mass. The value of the method is that it leads 

 very directly to equipotential surfaces. In the special 

 case of the rise in a capillary tube the canal starts from 

 the meniscus and ends on the general surface of the fluid. 



The force of attraction of glass for water is assumed 

 to be the same function of distance as that of water 

 for itself, and to differ only by coefficients of the 

 intensities. Since the range of the force is small (not 

 insensible), only the integrals of the attractive forces 

 about the ends of the tube need be considered. The 

 sum of these must balance the difference in the weight 

 of the limbs of the capillary tube. 



The integral of the forces acting on that end of the 

 tube which is at the general surface of the fluid will 

 clearly be equal and opposite to that of the forces on 

 the fluid below the tangent plane to the meniscus ; 

 therefore the weight of the column within the capillary 

 is supported by the whole attraction of the fluid of the 

 meniscus above the tangent plane, and of the lower end 

 of the glass tube on the parts of the canal within its 

 range. This result differs from that of Laplace because, 

 though Clairaut assumed the range of the force of 

 attraction to be small, he did not make it insensible. 

 Had he done so he would have got rid of the attraction 

 of the lower end of the capillary tube on the axial canal 

 and have arrived at substantially the same result as 

 Laplace. 



Many workers contributed to the subject in the 

 nineteenth century. The curious may find a brief 

 summary of their experiments and conclusions in the 

 papers by Charles Tomlinson which appeared, mainly 

 in the Philosophical Magazine, between the years 1870 

 and 1880. Specially interesting are the speculations 

 from those of Volta onwards as to the cause of the 

 movements of particles of camphor and of other volatile 

 solids on water. Challis's account of Gauss's important 

 memoir cannot be bettered. The. substance of it is 

 reproduced by Clerk Maxwell in the article on capillarity 

 which he wrote for the " Encyclopaedia Britannica." 



♦ Rayleigh, Phil. Mag., vol. 30, 1890, p. 285. 

 ' " Thtorie de la Figure de la Terre." (Paris, I743-) 



