1886.] on Capillary Attraction. 485 



at insensible distances, and, while projoosing as chief object to 

 complete the part of the theory not worked out by his predecessor, 

 treats the dynamical problem afresh in a remarkably improved 

 manner, by founding it wholly upon the principle of what we now 

 call potential energy. Thus, though the formulas in which he 

 expresses mathematically his ideas are scarcely less alarming in 

 appearance than those of Laplace, it is very easy to translate them 

 into words by which the whole theory will be made perfectly 

 intelligible to jDcrsons who imagine themselves incapable of under- 

 standing sextuple integrals. Let us place ourselves conveniently at 

 the centre of the earth so as not to be disturbed by gravity. Take 

 now two portions of water, and let them be shaped over a certain 

 area of each, call it A for the one, and B for the other, so that when 

 put together they will fit perfectly throughout these areas. To save 

 all trouble in manipulating the supposed pieces of water, let them 

 become for a time perfectly rigid, without, however, any change in 

 their mutual attraction. Bring them now together till the two 

 surfaces A and B come to be within the one-hundred-thousandth of 

 an inch apart, that is, the forty-thousandth of a centimetre, or 

 250 micro-millimetres (about half the wave-length of green light). 

 At so great a distance the attraction is quite insensible : we may feel 

 very confident that it differs, by but a small percentage, from the 

 exceedingly small force of attraction which we should calculate for it 

 according to the Newtonian law, on the supposition of perfect 

 uniformity of density in each of the attracting bodies. Well-known 

 phenomena of bubbles, and of watery films wetting solids, make it 

 quite certain that the molecular attraction does not become sensible 

 until the distance is much less than 250 micro-millimetres. From 

 the consideration of such phenomena Quincke (Pogg. Ann., 1869) 

 came to the conclusion that the molecular attraction does become 

 sensible at distances of about 50 micro-millimetres. His conclusion 

 is strikingly confirmed by the very important discovery of Eeinold 

 and Eiicker* that the black film, always formed before an undisturbed 

 soap bubble breaks, has a uniform or nearly uniform thickness of 

 about 11 or 12 micro-millimetres. The abrupt commencement, and 

 the permanent stability, of the black film demonstrate a proposition of 

 fundamental importance in the molecular theory : — The tension of the 

 film, which is sensibly constant when the thickness exceeds 50 micro- 

 millimetres, diminishes to a minimum, and begins to increase again 

 when the thickness is diminished to 10 micro-millimetres. It seems 

 not possible to explain this fact by any imaginable law of force 

 between the different portions of the film supposed homogeneous, and 

 we are forced to the conclusion that it depends upon molecular 

 heterogeneousness. When the homogeneous molar theory is thus 

 disproved by observation, and its assumption of a law of attraction 

 augmenting more rapidly than according to the Newtonian law when 



* Proc. Eoy. Soc, June 21, 1877 ; Trans. Koy. Soc, April 19, 1883. 



