Mr. A. M. Worthington. 



[June 16, 



then p is tlie radius of the curvature due to revolution round the axis 

 of y, and is equal to the normal PM. 



It is possible to obtain, by inspection of the curve, some notion of 



the value of the total curvature as measured by (i + JL^ to which the 



V P ' 



pressure is proportional. 



The length of the normal p is of course capable of exact measure- 

 ment, while that of the radius of curvature p may be obtained approx- 

 imately by striking the circle of curvature. 



At a point of recurvature, -=0, and the normal alone determines 



P 



the pressure. 



If the reader will trace in this way, in one of the figures, the value 

 of the total curvature from the vertex of the drop to the base of the 

 tube at different stages of extrusion, and will, in the case of some one 

 liquid, compare the final values attained before separation, when tubes 

 of different diameters are used, he will perceive that, before the drop* 

 has attained its maximum size, the tension of the surface seems to 

 press the contained liquid against the end of the tube. But, as the drop 

 increases in size, the tension is more and more exerted in supporting 

 the additional weight of liquid, and this pressure at the end of the 

 tube diminishes ; and that this pressure at the base, when the drop 

 separates, is greater with small tubes than with wide ones, and is 

 obviously still positive in the case of water hanging from the narrower 

 tubes. 



But, with a wide tube, the final value of the total curvature that is 

 attained before rupture is obviously less than with a narrow tube ; and, 

 by the methods of measurement, which will be described in the sequel, 

 it was found that, as the diameter of the tube is increased, the final 

 value of the curvature becomes gradually smaller, zero, and then 

 increasingly negative, and here the term A in the expression for the 

 pressure 



a+t(\ + -V) 

 V pi 



gives meaning to the whole expression which would otherwise be nega- 

 tive and meaningless. 



Up to the point at which the curvature at the base is greater than 

 everything would have gone on the same, even though this term A 

 were non-existent,* the tension of the surface sufficing for the support 

 of the drop ; but, at this point, the tension ceases to be sufficient, and 

 is aided by the true internal cohesion of layer for layer of the liquid, 

 and the adhesion of each unit of area of the liquid for the solid base 



* This is only mathematically, not physically, conceivable. T is really a function 

 of A, and would cease to exist with it. 



