367 



§ 2. Putting xa = r in eq. (10) of the previous comnnunication 

 (Siippl. N'. 42c') it reduces to 



R,=r + ^ kr' — ^ Pr* (3 log 2-2), .... (2) 

 from which R^ may be calculated, when /' is given and ^- is known 

 approximately. This value substituted in (1) gives 



/^ = ^-i'- + i^^'M2%2-l) (3) 



or 



*ï = i (f<i— /^,) (M 



(4) 



li h' 



formulae which are already known ') and by means of which the 

 sui'face tension can be calculated to a third approximation from 

 the capillary rise h in a tube of radius ?-, which is completely 

 moistened by the liquid.') 



These equations, when proper account is taken of the signs of 

 the various quantities, are applicable in every case, where the width 

 of a drop or bubble can be measured as also the pi-essure necessary 

 to form it. As an instance, when the liquid does not moist the wall 

 (mercury) the liquid may be forced up by an excess of pressure 

 from a very wide into a narrow communicating tube, until it pro- 

 trudes from the narrow tube in the form of a drop; A then is the 

 height of the liquid surface in the wide tube above the top of the 

 meniscus on the top of the capillary. ') Similarly when the capillary is 

 moistened by the liquid, the meniscus may be forced down by the 

 pressure of a gas, until a bubble is formed at the bottom of the 

 capillary. ") 



V See for instance A. Winkelmann, Handbuch der ,Physik, 2e Aufl., I, (2), 



1144 and 1159, 1908. 



') For the case, when there is an angle of contact i, the following relation is 



m 

 found by putting x = r and cp = ^ — i in eq. (9) of the previous communication 



u 



(Suppl. N". 42c) 



M- i y «''c* i (1 — .sm iy {\ + 2 sin i) -f- 



' T T^ \ -\- 8171 i 



^ — sec' i (1 — sin i)' (1 -|- sin i -(- 2 .swi' i} -I- f — sec* i log 



h* ' . V . , . .^^, - ., 2 ^'^^ 



^) In this case eq. (3) and (4) remain valid without any modification, as both 

 h and R^y^ therefore also r, change sign (see previous comm ). This simple method, 

 which is independent of the angle of contact and which allows the capillary surface 

 being refreslied by removing the drcjp, does not appear to have been ever applied 

 to mercury. 



*) Cf. A. WiNKELMANN, l.c, p. 116:2. See also furllier down in § 9. In this 

 manner, however, it is not the surface tension of the pure liquid in contact with 

 its vapuiir which is determined, but that of the binary system liquid gas. 



24* 



