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共 74 题- ENCYCLOPAEDIA BRITANNICA
- ELEVENTH EDITION
- VOLUME V, SLICE III
- Capefigue to Carneades
- ARTICLES IN THIS SLICE:
- FOOTNOTE:
- FOOTNOTE:
- FOOTNOTES:
- THEORY OF CAPILLARY ACTION
- M = S[sigma], (11)
- E = Se. (12)
- TdS = dE = Sde + edS. (13)
- F = mm' ([phi](f) + Cf^-2), (22)
- The element of the stratum at Q may be expressed by
- At the surface
- At a distance z within the surface
- If the liquid forms a stratum of thickness c, then
- Differentiating with respect to c, we find
- Remembering that c(0) is a finite quantity, and that
- From this we obtain
- K0 = 4[pi][beta]^(-4), T0 = 3[pi][beta]^(-5). (40)
- ON SURFACE-TENSION
- Whence
- T12 = T1 + T2 - 2T'12 (47)
- T1 = T2 = T'12;
- The value of T'12 has already been calculated (32). We may write
- As an immediate consequence of this hypothesis we have from (28)
- K = K0[sigma]^2, (49)
- T = T0[sigma]^2, (50)
- T'12 = [sigma]1[sigma]2T0; (51)
- T12 = ([sigma]1 - [sigma]2)^2 T0 (52)
- T31 = ([sigma]1 - [sigma]2 + [sigma]2 - [sigma]3)^2 T0
- We may, therefore, write for the pressure at a height y
- X = 1/2g[rho]h1^2 - T(1 - sin[alpha]1).
- For the second plate
- X = 1/2g[rho]h2^2 - T (1 - sin[alpha]2).
- Hence
- X = 1/4g[rho](h1^2 + h2^2) - T{1 - 1/2(sin[alpha]1 + sin[alpha]2)},
- The "dimensions" of the quantities on which M depends are:--
- M [approximately equals] T^{x}.g^{y}.[sigma]^{z}.a^{u},
- Accordingly
- Mg = 3.8Ta, (2)
- S = 4[pi]r^2 (1)
- ST = 4[pi]r^2T (2)
- TdS = 8[pi]rTdr (3)
- V = 4/3 [pi]r^3, (4)
- 4[pi]pr^2dr = 8[pi]r drT (7)
- Non-spherical soap bubble
- Now
- The radius of curvature of the meridian section is
- Hence dividing equation 10 by $y sin \alpha$, we find
- V being the volume of the vibrating mass.
- Substituting in the equation we find the condition
- The least root of this equation is
- The pressure due to the surface tension T is
- TABLES OF SURFACE-TENSION
- T = 1/2(K - k)^2 g[rho]
- RELATION OF SURFACE-TENSION TO TEMPERATURE
- FOOTNOTES:
- FOOTNOTE:
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- See A. Venturi, _I Caracci e la loro scuola_, 1895. (W. M. R.)
- FOOTNOTES:
- CS2 + KHO + R.OH = H2O + RO.CS.SK.
- CS2 + 2NH3 -> NH2.CSS.NH4 -> H2S + NH4CNS.
- CS2+2R.NH2 -> R.NH.CSS.NH3R -> CS(NHR)2
- The work of Cardan's, however, which ret
- Cardinals "in petto."
- _Great Britain_.--During the later 19th
- CARLOS I. (1863-1908), king of Portugal,
- FOOTNOTE:
- See _Journal asiatique_ (1877), vol. i. pp. 377-386. (G. W. T.)
- FOOTNOTES: