848 



tension)'); the third group contains the methods, in which <t is solely 

 derived from the shape of drop or bubble (measurement of certain 

 dimensions). This division is general and also iiolds for large drops 

 and bubbles; only in that case the pressure-method is of no impor- 

 tance practically on account of the small ness of the pressures to be 

 measured owing to the very slight curvature at the top; thus for 

 instance equation (13) which gives the ascension at the axis of a 

 wide tube of known radius is of no importance from a practical 

 point of view. 



Of greater importance in this case would seem to be the geome- 

 trical methods, which consist in measuring the coordinates of the 

 points A and B of fig. 1, Q ov /i? of fig. 3 and applying equations 

 (6), (7), (25) or (26). But the application of these methods is hindered 

 by the difficulty of an accurate measuremeut of the coordinates. 



The greatest practical importance attaches to the weight-methods. 



Gay-Lussac already derived capillary constants from measurements 



of the force which is required to lift a horizontal disk, which is 



in contact with a widely extended lic|uid '^), above the surface; this 



force, apart from the weight of the disk, is given by 



F=z:nr*(.igz — ^Jtrosinq, ...... (39) 



where z is to be replaced by its value from f22) (with l=zr). The 



3jr 

 simplest cases are those, where q^ — and ffz^.-x*)-, in the latter 



case, which can only be realized with a disk which is completely 

 moistened by the liquid, the force is a maximum *). 



^) The method of measuring the capillary rise in narrow tubes belongs both to 

 this and to the first group. 



') As mentioned by Laplace, Mécanique celeste, IV, 2e suppl. au livre X. 



*) WiNKELMANN, p. 114'S and 1156. 



*) Accurately speaking this maximum is reached a moment before the disk is 



lifted to the greatest height (ordinate of Q, fig. 3); putting v- = ^ + £, the maximum 



4 

 of P is reached, when £ = ,. But as long as s is only known to a second 



r |/ />• 



approximation, this circumstance has no influence on the equation to be used in 

 this case. 



If there is an angle of contact i, both g- and i might be found from two obser- 



3t 71 



vations, for instance one in which vC = ^ (this is impossible when />-)andano- 



ther in which the force is a maximum, in which case f = tt -\~ i. if i;>— ,asfor 



mercury, one might also determine the weight of a drop on a horizontal plate; 

 in that case (oQ) is again applicable. Or the greatest force may be measured which 

 is required to submerge a disk in a liquid (cf. A. Mayer, Sill. Journ., 4, (1897). p. 253. 



