322 Lord Bayleigh : Investigations in Capillarity. 



curvatures of the fluid surface at the edge of attachment. 

 If the surface could be treated as a cylindrical prolongation 

 of the tube (radius a), the pressure would be T/a, and the 

 resulting force acting downwards upon the drop would 

 amount to one-half (iraT) of the direct upward pull of the 

 tension along the circumference. At this rate the drop 

 would be but one-half of that above reckoned. But the 

 truth is that a complete solution of the statical problem for 

 all forms up to that at which instability sets in, would not 

 suffice for the present purpose. The detachment of the drop 

 is a dynamical effect, and it is influenced by collateral cir- 

 cumstances. For example, the bore of the tube is no longer 

 a matter of indifference, even though the attachment of the 

 drop occurs entirely at the outer edge. It will appear 

 presently that when the external diameter exceeds a certain 

 value, the weight of a drop of water is sensibly different in 

 the two extreme cases of a very small and of a very large 

 bore. 



But although a complete solution of the dynamical problem 

 is impracticable, much interesting information may be ob- 

 tained from the principle of dynamical similarity. The 

 argument has already been applied by Dupre (Theorie 

 Mecanigue de la Clialeur, Paris, 1869, p. 328), but his 

 presentation of it is rather obscure. We will assume that 

 when, as in most cases, viscosity may be neglected, the mass 

 (M) of a drop depends only upon the density (<r), the capillary 

 tension (T), the acceleration of gravity (g), and the linear 

 dimension of the tube («). In order to justify this 

 assumption, the formation of the drop must be sufficiently 

 slow, and certain restrictions must be imposed upon the 

 shape of the tube. For example, in the case of water de- 

 livered from a glass tube, which is cut off square and held 

 vertically, a will be the external radius ; and it will be 

 necessary to suppose that the ratio of the internal radius to 

 a is constant, the cases of a ratio infinitely small, or infinitely 

 near unity, being included. But if the fluid be mercury, the 

 flat end of the tube remains unwetted, and the formation of 

 the drop depends upon the internal diameter only. 



The " dimensions " of the quantities on which M depends 

 are : — 



sr^Mass) 1 (Length)" 3 , 



T= (Force) 1 (Length)" 1 ^ (Mass) 1 (Time)- 2 , 



g = Acceleration = (Length) 1 (Time)^ 2 , 



of which M, a mass, is to be expressed as a function. If we 

 assume 



Moc T J . ay . <r . a* 



