369 



// = — \~ oy , where ih bas the meaning given in ^ 2 of the previous 



communication and v) represents an intinitely small angle, ecpiation 

 (9) of the same communication, in view of (see eq. 8 and 8' i.e.) 



rp=,'/ + tp=: ^ 4 ^kR,' (2 log 2 f 1) + (o, 



takes the form: 



r = /r> -I R^ [<o + ikR,' (2 log 2 + l)]'-^ X:///-MrV ^^^^,' (6 log 2-1) . (6) 

 It follows, that the minimum of R^ is reached for 



io,=-ikR,^ {2 log 2^1) (7) 



.T 



therefore for rp =z -, that is: exactly when ,r,i =: r. The surface 

 z 



tension is thus given b}- the rehition (4), when r now represents 



the radius of tbe capillai'y and h the greatest difference in level of 



the mercury in the wide tube above the capillary ; conversely for 



given r and k the greatest difference in level is given by equation (3). 



§ 5. The mercury can still be raised to a higher level in both tubes. 



The radius of curvature R„ at the top of the drop then again 



increases, so that /t becomes smaller. All the same the mercury 



continues to rise in the wide tube, that is: the height H = h -{- i/ 



of the liquid in the wide tube above the top of the capillary (// 



represents the height of the drop and is therefore here taken with 



the positive sign) still increases. But this height also soon attains a 



maximum. 



ji 



Putting again 'V = 1- ty, we have (eq. 4 of previous comm.) 



z 



H=:h + !^=.j^-]-R, \ R,w (8) 



from which, joined to the condition .r = const =: 7', it follows that 

 H is a maximum when 



io,=.j,kR,^(\-log2),{RX--r f ^ A:r» - ^^ /.-V (12 % 2-17), (9) 

 so that 



H,n = ~ +ir-^^^kr* , (10) 



kr 



whence 



r r* \ 

 i , 



^-i(M,-M.)^^-.M I-It^ - iTTl • • ('1) 



§6. To test the use of the method sketched out in sections 4 and 5 

 a few trials were made with mercury in contact with air. The wide 

 tube was so wide (± 2 cm in radius), that the meniscus could be 



