98 On the Constants of Capillarity of Molten Bodies. 



culties and sources of error in these observations, that the velo- 

 city of the formation of the drop is left out of account, that for 

 a substance such as water, the values of a 2 given by different 

 experienced observers vary between 13'5 and 17*58 sq. millims., 

 we sec that the deviations from the law may very possibly be 

 due to errors of observation*. No relation such as has been sus- 

 pected to exist f between these constants of capillarity and other 

 physical or chemical properties of the substances can be deduced 

 from these Tables. 



15. According to equation (7), the constant «is the weight in 

 milligrammes of the mass of fluid which can be carried by 1 mil- 

 lim. of the contact-line of the fluid meniscus, and which is half of 

 the constant which Laplace calls H. The magnitude a measures, 

 therefore, the difference of the forces of pressure which are ex- 

 erted on the unit of a plane fluid surface, and on the unit of 

 a spherical surface, of diameter 1, in the direction of the nor- 

 mals. We may say, therefore, that a. measures the attraction 

 which the particles within the fluid exert for a given form of 

 the surface on a volume of the surface-layer, the base of which 

 is the unit of surface. 



If the surface-layer of fluid had the same density in all points 

 with the fluid inside at a finite distance from the surface, the 



quantity — , or half the quantity a?, would measure the attraction 



which is exerted on the unit mass of the surface by the particles 

 within the fluid, and the attractive functions for different sub- 

 stances would be complete multiples of the same magnitude. 



The assumption that in the surface there is the same density 

 as in the inside of the fluid appears, however, not to be admis- 

 sible. If we conceive the fluid divided into three (partial) layers 

 parallel to the fluid surface, each of these (partial) layers will 

 be attracted by the molecular forces inward, and with a force 

 so much the less the nearer it lies to the centre of the fluid. 

 But the layers overlying each individual layer press upon it, so 

 that the capillary pressure increases up to a certain value, if we 

 proceed inwards from the first external layer. Since the fluid 

 is not incompressible, the density in each separate layer will be 

 different on account of the difference of pressure, and within the 

 fluid it will be different from what it is on the outside. The 



* The constants a 2 are determined for a series of simple fluids, e. g. 

 ether (5 sq. millims.), alcohol (5"861 sq. millims.), and oil of turpentine 

 (6"/08 sq. millims.), for the usual temperature, which is much higher than 

 that of fusion of the fluid. It appears to me, therefore, very probable 

 that these fluids belong to group II., and that, could we determine their 

 capillarity-constants in the neighbourhood of the points of fusion, we should 

 have a 2 =8*6 sq. millims. 



t Conf. Dupre, Ann. der Chem. (4) vol. ix. p. 330 et seqq. 



