Capillary Surface inside a Tube of Small Radius. 131 



Also, substituting in (v.) tbe value o£ li given bj (viii.) 

 and putting x = r, we have 



v = r(l 



With a change of sign similar formulae may be applied to 

 the case of a small pendent drop such as is shown in fig. 2. 

 In which case we have 



6a . 



(X.) 



K. 



<!-£) 



and 



™.(^y ■ 



(xi.) 

 (xii.) 



Fi». 2. 







§ 4. These approximations may profitably be utilized in a 

 discussion of the ingenious method used by M. Sentis for 

 the determination of surface-tensions*. 



In these experiments a piece of capillary tubing was 



drawn out to a fine point, 

 dipped into a liquid and raised 

 therefrom, when a drop re- 

 mained clinging to the end of 

 the tube as in fig. 2 a. The 

 maximum radius (r 2 ) of the 

 drop having been measured, a 

 small beaker of the liquid, 

 standing on the head of a 

 sphero meter, was placed un- 

 derneath the drop, and was 

 raised until the liquid in the 

 beaker just touched the vertex 

 of the drop, when the sphero- 

 meter reading was taken. 

 The beaker was then farther 

 raised until the liquid in the 

 tube reached its original level 

 (fig. 2 b). The difference of 

 the spherometer readings then 

 gave directly 7^ — h. 2 . 

 By considering the forces acting on the portion of the 

 drop below CD, we see that 



• — ' 



b 



V 



__A_ 



I 

 1 



h 



B, 



9/»2 = 



(7^! — A 2 — 77)? ! 2 -l- 



(xiii.) 



where V is the volume of this portion of the drop. If this 



* Sentis, Journ. de Phys m 1887 and 1897. 

 K2 



