290 Lord Kayleigh on the 



attractive force on the particle m, while it is brought from an 

 infinite distance from m! to the distance / from m! ; or (2) the 

 attraction of a particle m on a narrow straight rod resolved 

 in the direction of the length of the rod, one extremity of the 

 rod being at a distance / from m, and the other at an infinite 

 distance, the mass of unit of length of the rod being w! . The 

 function II(/) is also insensible for sensible values of/, but 

 for insensible values of/ it may become sensible and even very 

 great." 



" If we next write 



I 



n(/)/rf/=fW, (r 



then 27rma-yfr(z) will represent (1) the work done by the 

 attractive force while a particle m is brought from an infinite 

 distance to a distance z from an infinitely thin stratum of the 

 substance whose mass per unit of area is a ; (2) the attraction 

 of a particle m placed at a distance z from the plane surface 

 of an infinite solid whose density is o\" 



The intrinsic pressure can now be found immediately by 

 calculating the mutual attraction of the parts of a large mass 

 which lie on opposite sides of an imaginary plane interface. 

 If the density be cr, the attraction between the whole of one 

 side and a layer upon the other distant z from the plane and 

 of thickness dz is ^ira^^^dz, reckoned per unit of area. 

 The expression for the intrinsic pressure is thus simply 



K = 2tto- 2 f f(z)dz (3) 



1 



In Laplace's investigation cr is supposed to be unity. We 

 may call the value which (3) then assumes K , so that 



K = 2ttJ f(z)dz (4) 



The expression for the superficial tension is most readily 

 found with the aid of the idea of superficial energy, intro- 

 duced into the subject by Gauss. Since the tension is con- 

 stant, the work that must be done to extend the surface by 

 one unit of area measures the tension, and the work required 

 for the generation of any surface is the product of the tension 

 and the area. From this consideration we may derive La- 

 place's expression, as has been done by Dupre* and Thomson"!". 

 For imagine a small cavity to be formed in the interior of the 



* Theorie Mecanique de la Chaleur (Paris, 1869). 

 t "Capillary Attraction," Proc. Roy. Inst. Jan. 1886. Reprinted, 

 1 Popular Lectures and Addresses/ 1889. 



