at a Curved Surface of Liquid. 45 1 



tube thoroughly wet with water, the free surface is sensibly he- 

 mispherical, and therefore r and r' are each equal to the radius 

 of the inner surface of the liquid film lining the tube above the 

 free liquid surface ; we have therefore 



A = -08x-- 

 r 



Hence, if h=. 1300 centims., r=*00012 centim., there can be 



no doubt that Laplace's theory is applicable without serious 



modification, even to a case in which the curvature is so great 



(or radius of curvature so small) as this. But in the present 



state of our knowledge we are not entitled to push it much fur- 



.ther. The molecular forces assumed in Laplace's theory to be 



" insensible at sensible distances " are certainly but little, if at 



all, sensible at distances equal to or exceeding the wave-lengths 



of ordinary light. This is directly proved by the most cursory 



observation of soap-bubbles. But the appearances presented 



by the black spot which abruptly ends the series of colours at 



places where the " bubble " is thinnest before it breaks make it 



quite certain that the action of those forces becomes sensible at 



distances not much less than a half wave-length, or An \ nn of a 



° > 40000 



centimetre. There is indeed much and multifarious evidence that, 

 in ordinary solids and liquids, not merely the distances of sen- 

 sible intermolecular action, but the linear dimensions of the 

 molecules themselves, and the average distance from centre to 

 nearest centre*, are but very moderately small in comparison 

 with the wave-lengths of light. Some approach to a definite 

 estimate of the dimensions of molecules is deducible from Clau- 

 sius's theory of ten of the average spaces travelled without colli- 

 sion by molecules of gases, and Maxwell's theory and experi- 

 ments regarding the viscosity of gases. Having perfect confi- 

 dence in the substantial reality of the views which these grand 

 investigations have opened to us, I find it scarcely possible to 

 admit that there can be as many as ten molecules in a cubic 

 centimetre of liquid carbonic acid or of water. This makes the 

 average distance from centre to nearest centre in the liquids 

 exceed a thousand-millionth of a centimetre ! 



We cannot, then, admit that the formulae which I have given 

 above are applicable to express the law of equilibrium between the 

 moisture retained by vegetable substances, such as cotton cloth or 

 oatmeal, or wheat-flour biscuits, at temperatures far above the dew- 

 point of the surounding atmosphere. But although the energy 

 of the attraction of some of these substances for vapour of water 

 (as exemplified when oatmeal, previously dried at a high tempe- 

 rature, has been used instead of sulphuric acid to produce the 



* By " average distance from centre to nearest centre," I mean the side 

 of the cube in a cubic arrangement of a number of points equal to the number 

 of real molecules in any space. 



2G£ 



