44 o SCIENCE PROGRESS 



from the fact that the pressure-excess in the drop due to its 



curvature has been neglected. If we assume that the drop is 



cylindrical round its circle of contact with the tube this pressure- 



T 

 excess will be equal to — i and the equation of equilibrium will 



become 



mg = 7rrT ..... (v). 



The error in equation (iv) was pointed out so long ago, I believe, 

 as 1 88 1 by Mr. A. M. Worthington ; nevertheless, generation 

 after generation of writers and researchers have, up to the 

 present day, repeated the erroneous statement with a persistence 

 worthy of a better cause. 



Equation (v) represents only a first approximation to the 

 truth, as in reality the phenomena attendant upon the detach- 

 ment of a falling drop are too complex to be amenable to so 

 simple a statical treatment. The equation, as given by Lord 

 Rayleigh, which best represents the results of experiment is 



mg = 3"8rT (vi), 



but this fact does not make the neglect of elementary dynamical 

 principles involved in the writing down of equation (iv) any less 

 culpable. 



In the actual practice of the method it is usually assumed 

 that with any given tube 



mg = kT, 



and the constant k is determined, once for all, from observations 

 of the drop-weight of a liquid of known surface-tension. It 

 is for this reason that an erroneously stated equation leads 

 to correct results. 



It must be confessed that the whole treatment of the prin- 

 ciples of capillarity, as given in many physico-chemical treatises, 

 is dotted with errors. Thus, in a text-book published in 191 1 

 for the use of pass and honours students in the Universities, the 

 following truly astonishing definition is to be found : " The 

 surface-tension is defined as the force which acts at right angles 

 to the surface of a liquid, along a line of unit length." Comment 

 is needless. 



In the matter of the statement of dimensions of physical 

 quantities there is much room for improvement. Surface- 

 tensions are sometimes expressed in dynes, sometimes in dynes 



