The London, Edinburgh and Dublin philosophical magazine and journal of science . face. The present note completesthe theoretical discussion there presented, by considering the * The same remark is also to be made in regard to the numbers givenby Sir E. Rutherford in Phil. Mag. xxvii. p. 868 (1914), for instancePb = 84, U = 94. t Communicated by Prof. E. Taylor Jones. \ Phil. Mag. xxvi. p. 925 (1913). 150 Mr. A. Ferguson on the Forces acting on a general problem in which the position of the vertex of thesphere is not restricted, and it will be seen in the sequelthat not only the case previously
The London, Edinburgh and Dublin philosophical magazine and journal of science . face. The present note completesthe theoretical discussion there presented, by considering the * The same remark is also to be made in regard to the numbers givenby Sir E. Rutherford in Phil. Mag. xxvii. p. 868 (1914), for instancePb = 84, U = 94. t Communicated by Prof. E. Taylor Jones. \ Phil. Mag. xxvi. p. 925 (1913). 150 Mr. A. Ferguson on the Forces acting on a general problem in which the position of the vertex of thesphere is not restricted, and it will be seen in the sequelthat not only the case previously discussed, but several otherparticular cases of special interest, can be deduced from theformula? developed. As before, we shall, to avoid cumbersome algebra, restrictthe discussion to liquids having zero contact-angles. Theextension of the formulae to liquids having finite contact-angles presents very little more difficulty, and involves no newprinciples. Let fig. 1, therefore, represent a section of the sphericalsegment having its vertex at a distance dx below the level of. the free surface. Taking axes as shown, let M be the mass ofthe sphere, R its radius, and let the other symbols have thesignificance shown in the figure. Then, arguing as in theprevious 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 sphereis balanced by an upward force of M^ dynes. (We maysuppose this to be realised by suspending the sphere from athread fixed to the pan of a balance. M± will then be the massof the weights in the opposite pan when the balance is inequilibrium.)Putting sin(^1==R5 a2= ^, r2 = 2Rd-d\9P * L. c. p. 929. Solid Sphere in contact with a Liquid Surface. 151(i.) becomesMI-M = 2^ { 2a?d-~ + M_^_ | (21W_«P) } (ii.) Equation (viii.) of the previous paper *, modified to suitthe present circumstances, becomes 2a2 1 , 8a3 vf=^ = (;/-diy-1L{M-(y-d1)*}i-2a*+ W, • (m.) which, inserting t
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