Bakerian Lecture, 1917: The Configurations of Rotating Compressible Masses . nt, but sufficientterms have not been calculated for the value of y to be determined with all terms beyond those written down, the root of equation (182), whene = 1, is found to be y = 21521, but the remaining terms appear likely to increasethis value somewhat, and we may perhaps take y = 2*2 as an approximate , we may notice, is just half-way between the two guess-values considered in § 50. When the density at the boundary is not zero, the critical value of y is less thanthis; for instan
Bakerian Lecture, 1917: The Configurations of Rotating Compressible Masses . nt, but sufficientterms have not been calculated for the value of y to be determined with all terms beyond those written down, the root of equation (182), whene = 1, is found to be y = 21521, but the remaining terms appear likely to increasethis value somewhat, and we may perhaps take y = 2*2 as an approximate , we may notice, is just half-way between the two guess-values considered in § 50. When the density at the boundary is not zero, the critical value of y is less thanthis; for instance, a critical value y = 1 corresponds to a value of e equal to aboutthree-quarters. An approximately accurate drawing of the critical figure, when e = 1, is shown infig. 4, the inner curves being strata of constant density. 51. We have considered the effect of heterogeneity in the structure of the matter,and have found that a sinking of the heavier elements to the centre of the mass willresult in an increase in the critical value of y. There is no limit to the amount of. Fig. 4. increase that can be produced in this way, although naturally the amount of increasedepends on the extent to which the Hght and heavy elements are separated and onthe ratio of their amounts. As an illustration, we considered the extreme case of acore of heavy incompressible material which we called iron, surrounded by anatmosphere of much lighter material which we called hydrogen, the two elementsbeing supposed to be completely separated. If the volume of hydrogen was initiallygreater than about one-third of that of iron, the composite mass set into rotation willfirst disintegrate through equatorial loss of matter. A drawing of the critical figure has already been shown on fig. 3 (p. 200); thismay be compared with fig. 4. 52. There is, however, a very essential difference between the failure of a uniformmass to attain the ellipsoidal form and the corresponding failure of a heterogeneousmass. Briefly s
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