150 Mr. A. Ferguson on the Forces acting on a 



general problem in which the position of the vertex of the 

 sphere is not restricted, and it will be seen in the sequel 

 that not only the case previously discussed, but several other 

 particular cases of special interest, can be deduced from the 

 formula? developed. 



As before, we shall, to avoid cumbersome algebra, restrict 

 the discussion to liquids having zero contact-angles. The 

 extension of the formulae to liquids having finite contact- 

 angles presents very little more difficulty, and involves no new 

 principles. 



Let fig. 1, therefore, represent a section of the spherical 

 segment having its vertex at a distance d x below the level of 



the free surface. Taking axes as shown, let M be the mass of 

 the sphere, R its radius, and let the other symbols have the 

 significance shown in the figure. Then, arguing as in the 

 previous paper *, we have for equilibrium 



M^ = M(/ + 27r/Tsin^ + 27r^[R^ 2 + (M^!!) 1 - ^J 



- 2 ^Y .... (i.) 



if we suppose that the resultant downward pull on the sphere 

 is balanced by an upward force of M^ dynes. (We may 

 suppose this to be realised by suspending the sphere from a 

 thread fixed to the pan of a balance. M ± will then be the mass 

 of the weights in the opposite pan when the balance is in 

 equilibrium.) 

 Putting 



sin( ^ 1== R 5 



a 2 = ^, r' 2 = 2Rd-d\ 

 9P 



* L. c. p. 929. 



