CAPILLARY ACTION. 581 



distance between the disks is equal to TTT half the wave-length of the harmonic 

 curve, the disks will be at the points where the curve is at its mean distance 



rrt 



from the axis, and the pressure will therefore be - as before. If A C, are 



T 



the disks, so that the distance between them is less than irr, the curve must 

 be produced beyond the disks before it is at its mean distance from the axis. 

 Hence in this case the mean distance is less than r, and the pressure will be 



T 



greater than - . If, on the other hand, the disks are at 4 2 and C 2 , so that the 



distance between them is greater than TTT, the curve will reach its mean dis- 

 tance from the axis before it reaches the disks. The mean distance will there- 



7 1 



fore be greater than r, and the pressure will be less than . Hence if one 



r 



of the disks be made to approach the other, the internal pressure will be 

 increased if the distance between the disks is less than half the circumference 

 of either, and the pressure will be diminished if the distance is greater than 

 this quantity. In the same way we may shew that if the distance between 

 the disks is increased, the pressure will be diminished or increased according 

 as the distance is less or more than half the circumference of either. 



Now let us consider a cylindric film contained between two equal fixed disks 

 A and B, and let a third disk, C, be placed midway between. Let C be slightly 

 displaced towards A. If AC and OS are each less than half the circumference 

 of a disk the pressure on C will increase on the side of A and diminish on 

 the side of B. The resultant force on C will therefore tend to oppose the 

 displacement and to bring C back to its original position. The equilibrium of 

 C is therefore stable. It is easy to shew that if C had been placed in any 

 other position than the middle, its equilibrium would have been stable. Hence 

 the film is stable as regards longitudinal displacements. It is also stable as 

 regards displacements transverse to the axis, for the film is in a state of 

 tension, and any lateral displacement of its middle parts would produce a re- 

 sultant force tending to restore the film to its original position. Hence if the 

 length of the cylindric film is less than its circumference, it is in stable equi- 

 librium. But if the length of the cylindric film is greater than its circumference, 

 and if we suppose the disk C to be placed midway between A and B, and 

 to be moved towards A, the pressure on the side next A will dimmish, and 

 that on the side next B will increase, so that the resultant force will tend to 



