356 MORPHOLOGY OF THE CEREBRAL CONVOLUTIONS. 



across every transverse section of the string or rod. But in the string the point of 

 the stress is a pull, in the case of the rod it is a push, and in this way we have 

 produced tension or pressure or transferrence of energy in any form. If one body 

 presses or draws another, it is pressed or drawn by this other with an equal force 

 in the opposite direction. If anyone presses an object with his finger, his finger is 

 pressed with an equal force in the opposite direction by the object. Now, in the 

 case of partitions formed by the union of liquid films we have tension producing 

 the observed results, whilst in the case of the modelling of the cerebral surface 

 we have fissuration produced by pressures exerted by expanding central growths 

 of a plastic substance, confined in a limited space. 



The surface tension of the film of a soap bubble has been investigated by 

 Maxwell, who indicates a method of determining the tension of such films. A 

 soap bubble is simply a small quantity of soap-suds spread out so as to ex- 

 pose a large surface to the air. When by means of a tube we blow air into the 

 inside of a bubble we increase its volume, and therefore its surface, and at the same 

 time we do work in forcing air into it, and thus increase the energy of the bubble. 



That the bubble has energy may be shown by leaving the end of the tube open. 

 The bubble will contract, forcing the air out, and the current of air blown through 

 the tube may be made to deflect the flame of a candle. If the bubble is in the 

 form of a sphere of radius r, this material surface will have an area 



S = 47tr 2 . (1) 



If T be the energy corresponding to a unit of area of the film, the surface 

 energy of the whole bubble will be 



ST = 4 7tr 2 T. (2) 



The increment of this energy corresponding to an increase of the radius from 

 r to r+dr is therefore 



TdS = 87trTdr. (3) 



Now this increase of energy was obtained by forcing in air at a pressure greater 

 than the atmospheric pressure, and thus increasing the volume of the bubble. Let 

 II be the atmospheric pressure, and II + p the pressure of air within the bubble. 

 The volume of the sphere is 



V = | Ttr 3 . (4) 



and the increment of volume is 



dV = 4 7tr 2 dr. (5) 

 Now if we suppose a quantity of air already at the pressure II + p, the work 

 done in forcing it into the bubble is p d V. Hence the equation of work and 

 energy is 



pdV = Tds. (6) 

 or 47tr 2 dr = 8?iTrdr. (7) 



orp = 2Tt ( 8 ) 



This, therefore, is the excess of the pressure of the air within the bubble over 



