\ga-a f] 



(^?) • (l » 



Lord Rayleigh : Investigations in Capillarity. 323 



we have, considering in turn length, time, and mass, 



y — 3z + « = 0, 2x + 2y = 0, x + z=l \ 

 so that 



y=—<ff, ~ = 1 — x, it = o — 2x. 

 Accordingly 



M x — 

 9 



Since x is undetermined, all that we can conclude is that M 

 is of the form 



9 



where F denotes an arbitrary function. 



Dynamical similarity requires that T/gaa 12 be constant ; 

 or, if g be supposed to be so, that a 2 varies as T/cr. If this 

 condition be satisfied, the mass (or weight) of the drop is 

 proportional to T and to a. 



If Tate's law be true, that ceteris paribus M varies as a, it 

 follows from (1) that F is constant. For all fluids and for 

 all similar tubes similarly wetted, the weight of a drop would 

 then be proportional not only to the diameter of the tube but 

 also to the superficial tension, and it would be independent of 

 the density. 



In order to examine how far Tate's law can be relied upon, 

 I have thought it desirable, with the assistance of Mr. Gordon, 

 to institute fresh experiments with water, in which necessary 

 precautions were observed, especially against the presence of 

 grease. Attention has been given principally to the two 

 extreme cases, (i.) when the wall of the tube is thin, so that 

 the external and internal diameters of the tube are nearly 

 equal; (ii.) when the bore is small in comparison with the 

 external diameter. The event showed that up to an external 

 diameter of one centimetre or more, the size of the bore is of 

 little consequence, but that for larger diameters the weight of 

 the drop in (ii.) is sensibly less than in (i.). It scarcely needs 

 to be pointed out that in (i.) the diameter can only be increased 

 up to a certain limit, after wdiich the tube would not remain 

 full. In (ii.) the diameter can be increased to any extent, 

 but the drop falling from it reaches a limit. The experi- 

 ments of Tate extended also to case (ii.), but his results are, 

 I believe, erroneous. For a diameter of one-half an iuch 

 (1*27 cm.) he found for the two cases drops in the ratio of 

 1-56 :2-84. 



In mv experiments the thin-walled tubes were of glass, the 



2 A2 



