134 



Mr. A. Ferguson on the Shape of the 



effect the integrations: (1) that the radius of the tube is small 

 compared with the height to which the liquid rises in the 

 tube, and (2) that the ratio of r to a is such that any power 

 higher than its square is negligible in comparison with unity. 

 These assumptions are not independent of each other, but in 

 any given case it is simplest to test whether the conditions 

 are separately fulfilled. Thus in the case of water, the 

 approximations give very exact results in the case of a tube 

 \ mm. in diameter, and may be applied with fair accuracy 

 to a tube 1 mm. in diameter (for which r//i = *016, and 

 r 3 /a 3 = *004). This latter value represents about the limit of 

 application of the formulae in the case of water. 



§ 7. We now proceed to apply the equations of §§ 1-4 to 

 the method for the determination of surface-tension usually 

 known as Jaeger's method *. The practice of the method 

 consists in measuring the maximum pressure required to 

 liberate an air-bubble from the end of a vertical capillary 

 tube plunged below the surface of the liquid under examina- 

 tion. The apparatus needed is represented diagrammatically 

 in fig. 3 (which, for clearness of reference, is drawn out of 

 all true proportion). 



Fiff.3. 



Boyles Bottle: 























V ' 













1 



k 





r 

















i 



?' 



^ 





--_ 



V 



J 









I 



With symbols having the meaning shown, the equation of 

 equilibrium of the bubble at any stage in its formation will 

 be 



or 



where 



1_ 1 _ H+y 



R x + K 2 ~ a 2 ' " * 



H 



Pi 



Jfti-A'-^ 



(xxi.) 



* For «i different treatment see Cantor, Wied. Ann. xlii. p. 422 (1892),. 

 and Feustel, Ann. d. Phys. xvi. p. 61 (1905). 



