!^66 



^ 3. In dealing with a hanging di-op, (i^ — ,a, and // change sign (see 

 Suppl. N". 426') and eq. (4) becomes 



r7 = i(M,-lu,)</Ar[l-i^-i'^,(2/o,^2-l)l . . . (4') 



The practical application of this eqnation is not so simple, however, 

 as that of eq. (3), as a hanging drop formed at the end of a 

 capillary which commnnicates with a wide tube is not in stable 

 equilibrinm '). Bnt the eqnilibrinm may be made stal)ie by also 

 taking a narrow tnbe for the one with which the capillary 

 communicates, say by making the drop hang from a single capillary, 

 as in Skntis's method"); in that case, however, account must be 

 taken of the curvature of the meniscus in the narrow tnbe. If h^ 

 is the distance between the tops of the two menisci, and A, the 

 ascension of the liquid in the narrow tube (which can be obtained 

 from a sej)arate measurement), it is evident, that in e(|. (4') the 

 8ub8titution : 



h = /t, — /i,. 

 has to be made. 



^ 4. Let us return to the case of a drop, say a mercury drop, 

 forming on the top of a capillary under the influence of an excess 

 of pressure from the li(piid in a very wide communicating tube 

 (section 2). When the mercury by raising the liquid in the wide 

 tube has reached the edge of the capillary, the meniscus i)i'()tru(ling 

 above it begins to curve more and more as the liquid gets higher, 

 so that the difference in level h between the two tubes, which 

 had remained constant so far, now increases. Soon the meniscus 

 attains the maximum-curvatui'e and at the same time the difference 

 in level h reaches a maximum. 



This maximum occurs at the moment that R^ has its smallest value ') 

 which happens when R^ is all but equal to r, the radius of the 

 capillary (for simplicity A*„ is here taken as positive). Putting 



1) An imperceptible fall of the level in the wide tube is sufficient to give an 

 appreciable increase to the radius of the hanging drop, through which h becomes 

 larger, while tlie capillary counter pressure diminishes; consequently the liquid 

 flows continuous. With a lying drop on the oilier hand /; diminishes and within 

 definite limits the equilibrium is stable (see also §§ 4 and 7). 



«) Sentis, J. d. phys. 6 (1887) p 571. 



2 

 *) Seeing that between // and i^o the relation /c /?= - holds (see previous comm. 



in these proceedings). 



