Determination of the Surface Tensions of Liquids. 117 



direct methods. As stated above, two thiugs besides the tem- 

 perature are measured in this method : (1) fhe specific gravity 

 of the liquid taken, and (2) the vertical distance between the 

 lower ends of the two capillary tubes when air under the same 

 pressure issues in synchronous bubbles from their orifices. It 

 is not difficult to determine the specific gravity to within 

 TTTr,'oo"ir? although an accuracy of a-.-oVo" ^^ quite sufficient. 

 The distance between the ends of the two tubes can be 

 measured to about a hundredth of a millimeter, except in 

 the case of water where the degree of accuracy of measure- 

 ment is only within a tenth of the same unit of length. It is 

 now our task to pass from the data obtained from measure- 

 ments of these quantities to the capillary constants measured 

 in degrees per centimeter. 



Inasmuch as our knowledge of the form of the bubbles just 

 on the point of issuing from the orifices of the capillary tubes is 

 not at all precise, there appears to be no immediate way of find- 

 ing a relation on theoretical grounds between the data fur- 

 nished by this indirect method and those given by direct 

 methods. Jager (loc. cit.) obtained the relationship employed 

 by him in the following manner : " Wie sich unsere 

 Annahme fiir die Formulirung des Einflusses, welchen die 

 Eohrenweite auf den bewussten capillaren Druck hat, als 

 richtig erwies, so zeigt sich, wie wir spater sehen werden, dass 

 es volJstandig geniigt, wenn wir 



setzen, wohin /9 eine Constante bedeutet, die sich ebenfalls 

 leicht ermitteln lasst, wenn zwei Fliissigkeiten, deren a und s 

 bekannt sind, zu Gebot stehen. Yerwenden wir namlich zu 

 unseren Messungen stets dieselben beiden Capillarrohren, so 

 wird fill' die eine Flussigkeit die Gleichung (1) 



a (1+^s) <^{T.r') =hs, 



fiir die zweite 

 somit 



a(H-/3s') (^ (?'.r')=AV 

 a(l -f- /3s) As 



a'(l+y8s') h's' ' 



Aus dieser Gleichung kann der Werth von ^ ermittelt werden, 

 da alle iibrigen in ihr vorkommenden Grossen bekannt sind." 



In order to obtain the value of /3, he made use of Brauner'sf 

 and Wolf's J directly determined data for water and ethyl 

 ether. By transforming the equation immediately preceding 

 into 



* a = Capillary constant ; s = Specific gravity. 



f Fogg. Ann. 70, p 515. % Pogg. Ann. 70, p. 575. 



