1017] on Soap Bubbles of Long Duration 207 



curves the rate of diminution of diameter is inversely as the diameter. 

 The equation of tliis first portion of the drainage curve shown in the 

 above figure for a hydrogen bubble is y ^ 0* 1787 ^x, where y is in 

 grams, and x is in days. 



The approach to agreement between the observed and calculated 

 values thus resulting is seen in the following Table : — 



Table 11. 



In half a day * 1 gram of liquid had been collected ; in eight 

 days * 5 gram was obtained ; but a total of 1 * gram was only 

 reached on the 95th day. 



The corresponding expression in terms of mgms. from each 

 sq. cm. of the bubble surface is «/ = 0'514 aJx, The result given by 

 the bubble under similar conditions in air instead of hydrogen was 

 2/ = 0-554 V^ (See Fig. 12.) 



The final composition of the bubble is thus relatively very little 

 different from water. As a confirmation of this the original bubble 

 solution (5 per cent, of ammonium oleate, in 50 per cent, glycerine) 

 was diluted thirty-three times with carefully prepared boiled distilled 

 water. A bubble 8 cm. diameter was then blown from this 

 solution. It lasted until completely contracted after exactly four 

 weeks. During most of this time it was coloured amber to purple ; 

 on three or four of the warmer days nearer the end (temperature 

 about 10° C.) it reached a semi-black stage peculiar to these very 

 dilute bubbles. Only one drop accumulated, caused by the shrinking 

 of the bubble. This bubble has already been referrred to in connec- 

 tion with gas transference through bubbles of graded dilution (see 

 p. 24). 



By investigating the condensation on unit area of the bubble, 

 instead of on the whole bubble, a simple expression can be found that 

 is applicable to the whole of the drainage curve, instead of only to 

 the initial period of constant surface. The rate per unit area is of 

 course found by dividing the weight of total drainage by the mean 

 surface of the bubble over the period measured. This is most readily 

 done by drawing a succession of tangents, TT', to the collection curve 

 (fig. 13). The slope of these successive tangents along the curve, 

 gives the rates of collection at successive times from the whole 

 bubble surface. The surface each time is obtained from the corre- 

 sponding diameter, obtained by drawing the ordinates 00' to cut the 



