Liquids on the Surface of Water. 43 



tions determined by the meridional plane of the lens in the ex- 

 ternal liquid surface, and in the superior and inferior zones of 

 the floating mass. We then get, in the case of the spreading of 

 the drop, the condition 



t cos a > t' cos a' + f cos a" ; 



and in the case of equilibrium of the liquid lens, the relation 



t cos a = /' cos ot! + 1" cos a". 



But these formulae also show that / may considerably exceed t 1 

 without the extension of the drop into a film being possible, 

 and that, if the spreading does take place, it is feeble in propor- 

 tion as f becomes greater — that is to say, as the two liquids 

 brought into contact have less mutual adhesion. Unfortunately 

 the difficulties of obtaining direct measurements of a, a', a", and 

 especially of /", are opposed to the exact valuation of the limit 

 beyond which extension becomes impossible. 



25. It would be very desirable to ascertain the value of t n , or 

 the tension of the two liquids at the surface of separation — 

 whether in fact there were any, and what amount of, adhesion 

 between the two surfaces, and how far this adhesion modified 

 the tension. I have already in the former paper 17 insisted 

 somewhat on an experiment in which the motions of camphor 

 and benzoic acid on the surface of water are not interrupted by 

 the presence of a lenticular mass of a newly distilled essential 

 oil on the surface. The camphor will skate through it with 

 great vigour, cutting it up into smaller lenses, and is apparently 

 in no way impeded by its presence. Hence it may be argued 

 there can be little or no adhesion between the oil and the sur- 

 face of the water, or the motions of the camphor would be 

 arrested, as is so decidedly the case when a fixed oil spreads out 

 into a film. 



26. As this is a point of importance, I may perhaps be per- 

 mitted to refer to some results obtained during the present year as 

 to the action of oils in inducing crystallization in supersaturated 

 saline solutions, of which those of sodic sulphate may be taken as 

 the type. If we deposit on the surface of such a solution a drop 

 of oil, fixed or volatile, one of two things will happen ; it will 

 either spread out into a film, or it will form a lens. In the 

 one case, where a film is produced, this film acts as a powerful 

 nucleus, finely shaped crystals moulding themselves, as it were, 

 on its under surface, and then falling away, to make room for 

 others. In the other case, not only is there no crystallization 

 as soon as the drop is deposited and the lens formed, but it may 

 be left for weeks and months, through all the variations of atmo- 



17 Phil. Mag. for December 1869, §§ 28 & 39. 



