2 FERGUSON, Studies in Capillarity 



neglects the pressure-excess inside the drop due to curvature, and it would 

 be far more reasonable to define the ideal drop by the equation : — x 



M^ = irrY. 



The error is a common one, and is to be found in most manuals of 

 physical chemistry, although the correction was given a generation ago by 

 Worthington. 2 Fortunately, one is generally concerned in experimental 

 work with ratios of drop-weights, and the peccant 2 disappears on division. 



Again, Coombs and Richards, 3 in a careful determination of the sur- 

 face tension of water and of benzene, have indulged in what the late Lord 

 Rayleigh termed some " mild reflections on the inadequacy of the help 

 afforded by mathematics," in the elucidation of capillary problems. 4 Their 

 criticism takes a curious form, inasmuch as the canon of acceptance or 

 rejection of a particular approximation appears to depend on whether the 

 approximation does not, or does give impossible values when used outside 

 the range for which the approximation is valid. Such a canon would 

 make very short work of the binomial theorem for fractional indices ! 



It seems very necessary, therefore, to show exactly what problems have 

 been solved mathematically, under precisely what circumstances the ap- 

 proximations given are valid, and in what problems there is a difference 

 of opinion as to the validity of the solutions that have, from time to time, 

 been propounded. 



This apart, I desire here briefly to discuss the various known methods 

 for the measurement of capillary constants, and to consider which of them 

 may most usefully be employed in the measurement of interfacial tensions. 

 There is little need to enlarge on the importance of an accurate knowledge 

 of the tension at a liquid-liquid interface — the necessity is known — urgent, 

 and the values of the existing figures, determined as they often are by the 

 aid of stalagmometers, visco-stalagmometers, and other instruments of 

 hybrid derivation and of doubtful accuracy, are open to more than a little 

 suspicion. 



At the outset I have mentioned the lack of co-ordination of the exist- 

 ing work. The need for an ordered determination of constants is press- 

 ing, and it would seem that much of the careful work already done is in 

 measure wasted, not so much by overlapping, for within limits a certain 

 amount of overlap is all to the good, as by the use of different methods 

 whose relative accuracy has not been sufficiently well estimated, and, in 

 some cases, by lack of appreciation of the help which has undoubtedly 

 been given by mathematics. 



Without venturing to lay down cast-iron rules, I here give an out- 

 line of a systematic attack on the problem, which would have been carried 

 farther during the last year, had the work not suffered interruption by the 

 heavy demands due to the unprecedented influx of students into this, as 

 into other teaching institutions. Briefly outlined, the scheme of work stands 

 as follows : — 



1 Sec e.g. Poynting and Thomson, " Properties of Matter " (1902), p. 161. 



2 Proc. Roy. Soc, 32, 362 (1881). z Jour. Amer. Chem. Soc, 37, 1643 (1915). 



4 Proc. Roy. Soc. (A), 92, 184 (1915-16). 



