12 FERGUSON, Studies in Capillarity 



Solving this as a quadratic in 2<2 2 , we obtain 



2 1 

 



$rh + 3^1 + 1 j 



On expanding the surd, we have finally 



2a 2 = rh(i + Yl ~ °' IIir ^ + °'°74 1 ^) • • ( ix ) 



giving value of a 2 in very close numerical agreement with (vi) and (vii). 

 The equation 



2a 2 = rh(i + ~J- * 1288 ^) • • • ( x ) 



is amply accurate for experimental purposes, and may be used with com- 

 plete confidence in the determination of T for liquids having surface ten- 

 dynes 



sions of the order 10 , and tubes of 1 mm. (or less) bore. Thus, to fix 



cm. v ' 



dynes 

 our ideas, consider a liquid of surface tension 30 and density o'8 



firms. 



- — -. Such a liquid, if its contact angle were zero, would rise to a 



c.c. 



height of about 1*5 cm. in a tube of 1 mm. bore. The correcting terms 



in (x) for this liquid would then be 



1 r 1 r 2 



— - = - x '0333 = o'oiii, 0*13-70 = 0*13 x "OOIII = O'OOOI, 

 3 h 3 h 



r 3 . . . 

 and the term in -p is quite inappreciable. 



Now consider the case of a large drop of liquid sessile on a hori- 

 zontal surface, or a large bubble of air imprisoned under a sheet of glass. 

 The equations appropriate to such a system are 



2a " = ^ ~ ^(4 " x/2) (xi) 



and ' k 2 = 4a 2 sin 2 — - — ( 1 - cos 3 — ) . . fxii) 



2 3/* \ 2 / K ' 



where r, q, and k have the meanings given by Fig. 1a. It is clear that 



the correcting terms in these equations are of the order -, and that there- 



a 2 

 fore the size of the bubble or drop should be so chosen that -^ is negli- 

 gible in comparison with unity. In the case of water, for example, for 

 which a 2 is about 0-075 S( F cms., a radius of 2\ to 3 cm. is the very 

 smallest that can safely be employed. Mr. Langmuir, in some interesting 

 experiments recently carried out on the contact angles of water drops, 1 



1 Trans. Faraday Soc, XV., June, 1920, p. 62. 



