. Some Problems Illustrating the Forms of Nebulae . Some Problems Illustrating the Forms of Nebulce. 413 Boyles Law involves the possibility of an infinite density, and the lawdoes not hold physically so far. In this and In other cases where asingularity occurs we may replace it by a solid nucleus arranged so as togive the proper value of V over its surface. This case of circular symmetry for n > 1 appears to have some analogy toa ring nebula. Case II—Take 4> = h~1\ogrja, i/r = b~10) 2¥ ,2 we get p = P0^ = -^-j ± [log2 (r/a) +ffi> + &»]-». The surfaces of equal density are given by P
. Some Problems Illustrating the Forms of Nebulae . Some Problems Illustrating the Forms of Nebulce. 413 Boyles Law involves the possibility of an infinite density, and the lawdoes not hold physically so far. In this and In other cases where asingularity occurs we may replace it by a solid nucleus arranged so as togive the proper value of V over its surface. This case of circular symmetry for n > 1 appears to have some analogy toa ring nebula. Case II—Take 4> = h~1\ogrja, i/r = b~10) 2¥ ,2 we get p = P0^ = -^-j ± [log2 (r/a) +ffi> + &»]-». The surfaces of equal density are given by P = -loo-2 Z-W+ (J^Jf*. The curve, fig. 2, shows the particular surface 02 — —log2 1 + ~, a f drawn to a scale of This case is somewhat peculiar. Starting with 0 = 0 when r/a = 1, thecurve for positive values of 0 proceeds as shown, continually approaching theorigin by a succession of diminishing spirals. The locus is, however,symmetrical about 0 = 0. If now we proceed to draw another surface ofdifferent density it would be found to cross the original curve at a successionof points for which 0 > tt. This would mean that at such points twodensities are possible, and we cannot admit this. We must, therefore, stopthe curve at the nodal point 0 = ir, and then the complete series of curvesof equal density form a series of non-intersecting curves of this remarkable 414 Mr. G. W. Walker. pear shape, the density falling off to zero at infinity and increasing towardsthe origin with a singularity at the origin itself. The pear may be madesharper or blunter by taking different values of 6, which is at our disposal. This form of distribution is of some interest in connection with the-researches of Darwin,
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