•408 Mr. T. Proctor Hall on New Methods of 



This method is capable of showing a change of surface- 

 tension with almost incredible delicacy when the frame is 

 rigid. A single example is given below. The liquid was 

 common alcohol, at 20°*20 C, and each weight was found 

 with a fresh film. The increase of weight (W) due to the 

 tension is given in grams. The corresponding values of T 

 were not calculated. 





W. 



1 



•72422 

 •72420 

 •72424 

 •72422 



2 



3 



4 





Mean ... 



•72422 



Frames of this sort cannot be made with such exactness as 

 to give practical results agreeing with those calculated to 

 1 part in 70,000, nor to 1 in 7000. But if the values of the 

 surface-tension are found by either of the methods before 

 described, and compared with W//o in each case, the values 

 of r and k may be corrected for any particular frame, so that 

 reliable results may be obtained with it for other liquids with 

 much greater ease than by the former methods. 



For this purpose put n = l — 2r—7rr/2, and /3 = */2. Then 

 equation (9) becomes 



277-r* sin (3(c + 2r sin (3) + n sin /3 cos fi{c 2 — 2r q + Acr sin /3 

 + ^ 2 sin 2 y8} + r 2 <a-7r) + 7rrc 2 -27T7^-W//? = 0. . (10) 



When W is a maximum, 



16r 2 n sin 4 /3 + 12rcn sin 3 j3 + (2c 2 — 16r' 2 )n sin 2 /3 — 8rnc sin j3 

 -87rr 3 sinyScos/3-27rr 2 ccos/3-c 2 ^ = 0. . . . (11) 



These equations are almost unmanageable, however, and 

 time will be saved in most cases by disregarding them and 

 plotting a curve of experimental values to show the relation 

 between T and W/p for a given frame. 



The convenience of this method in practice will repay the 

 trouble of finding such a relation. While Michelson's method 

 has the merit of directness and simplicity, its use is limited 

 to such liquids as form a fairly stable film in air. The 

 method of thin plates is constantly open to suspicion as to the 



