CAPILLARY ACTION. 571 



plate are T+X in the negative direction, and T sin ^ + $gph* in the positive 

 direction. Hence 



For the second plate 



Hence X = gp (h? + hf) - T (1 - 1 (sin a, + sin a,)}, 



or, substituting the values of h r and h u 



T- 



X = % j (cos c^ + cos a^f T{1 (sin 04 + sin a,) ^ (cos c^ + cos cu.) (cot a^ + cot a,)}, 



the remaining terms being negligible when a is small. The force, therefore, with 

 which the two plates are drawn together consists first of a positive part, or 

 in other words an attraction, varying inversely as the square of the distance, 

 and second, of a negative part or repulsion independent of the distance. Hence 

 in all cases except that in which the angles a t and o^ are supplementary to 

 each other, the force is attractive when a is small enough, but when cos a, 

 and cos a, are of different signs, as when the liquid is raised by one plate, 

 and depressed by the other, the first term may be so small that the repulsion 

 indicated by the second term comes into play. The fact that a pair of plates 

 which repel one another at a certain distance may attract one another at a 

 smaller distance was deduced by Laplace from theory, and verified by the 

 observations of the Abb Hauy. 



A DROP BETWEEN TWO PLATES. 



If a small quantity of a liquid which wets glass be introduced between 

 two glass plates slightly inclined to each other, it will run towards that part 

 where the glass plates are nearest together. When the liquid is in equilibrium 

 it forms a thin film, the outer edge of which is all of the same thickness. 

 If d is the distance between the plates at the edge of the film and n the 



atmospheric pressure, the pressure of the liquid in the film is II -=. , 



and if A is the area of the film between the plates and B its circumference, 

 the plates will be pressed together with a force 



ZATcosa j, . 



- + BTsma, 

 a 



722 



