488 Sir William Thomson [Jan. 29, 



surfaces A and B, that the whole interstice becomes filled with water. 

 My metrical sense of touch tells me that exactly 4J centimetre- 

 grammes of work has again been done ; this time, however, not by a 

 very great force, through a space of less than 50 micro-millimetres, 

 but by a very gentle force acting throughout the large space of the 

 turning or folding-together motion which you have seen, and now 

 see again. We know, in fact, by the elementary principle of work 

 done in a conservative system, that the work done in the first case 

 of letting the two bodies come together directly, and in the second 

 case of letting them come together by first bringing two points into 

 contact and then folding them together, must be the same, and my 

 metrical sense of touch has merely told me in this particular 

 sense what we all know theoretically must be true in every case 

 of j)roceeding by different ways to the same end from the same 

 beginning. 



Now in this second way we have, in performing the folding 

 motion, allowed the water surface to become less by 60 square 

 centimetres. It is easily seen that, provided the radius of curvature 

 in every part of the surface exceeds one or two hundred times the 

 extent of distance to which the molecular attraction is sensible, or, as 

 we may say practically, provided the radius of curvature is every- 

 where greater than 5000 micro-millimetres (that is, the two-hundredth 

 of a millimetre), we should have obtained this amount of work with 

 the same diminution of water-surface, however performed. Hence 

 our result is that we have found 4-5/60 (or 3/40) of a centimetre- 

 gramme of work per square centimetre of diminution of surface. 

 This is precisely the result we should have had if the water had been 

 absolutely deprived of the attractive force between water and water, 

 and its whole surface had been coated over with an infinitely thin 

 contractile film possessing a uniform contractile force of 3/40 of a 

 gramme weight, or 75 milligrammes, per lineal centimetre. 



It is now convenient to keep to our ideal film, and give up 

 thinking of what, according to our present capacity for imagining 

 molecular action, is the more real thing — namely, the mutual 

 attraction between the different portions of the liquid. But do not, I 

 entreat you, fall into the paradoxical habit of thinking of the surface 

 film as other than an ideal way of stating the resultant effect of 

 mutual attraction between the different portions of the fluid. Look, 

 now, at one of the pieces of water ideally rigidified, or, if you please, 

 at the two pieces put together to make one. Eemember we are at 

 the centre of the earth. What will take place if this piece of matter 

 resting in the air before you suddenly ceases to be rigid ? Imagine 

 it, as I have said, to be enclosed in a film everywhere tending to 

 contract with a force equal to 3/40 of a gramme or 75 milligrammes 

 weight per lineal centimetre. This contractile film will clearly 

 press most where the convexity is greatest. A very elementary piece 

 of mathematics tells us that on the rigid convex surface which you 

 Bee, the amount of its pressure per square centimetre will be found 



