. Some Problems Illustrating the Forms of Nebulae . The general effect of the rotation is then to increase the density from whatwould obtain in the statical case, and by increasing proportion as r increasesfrom the origin, but even if it were permissible to pass to large values of rthe density would still diminish to zero. We cannot, however, extend our 418 Mr. G. W. Walker. solution to large values of z, but we may say that the tendency of the rotationis ( when n = 2) to make the density rise more steeply to its maximum. value and to move the point of maximum density further out with incr
. Some Problems Illustrating the Forms of Nebulae . The general effect of the rotation is then to increase the density from whatwould obtain in the statical case, and by increasing proportion as r increasesfrom the origin, but even if it were permissible to pass to large values of rthe density would still diminish to zero. We cannot, however, extend our 418 Mr. G. W. Walker. solution to large values of z, but we may say that the tendency of the rotationis ( when n = 2) to make the density rise more steeply to its maximum. value and to move the point of maximum density further out with increasingc» ; but there is no indication of a tendency to throw off* the outer latter result disagrees with the general conclusion stated by Jeans(loc. cit. ante). For irrotational motion / = o>a2fr2 and the particular integral we require is z co2a2 .2y (y2+i) +tan y (y*+i)J - y y where y = r2ja%. In this case z is negative and infinite when r — 0, rises to a maximumpositive value, and again declines to a negative and infinite value as r becomesindefinitely great. As before, we cannot extend our solution to great valuesof z, but we may say that the tendency of the motion is to make the distribu-tion hollow near the origin, to increase the concentration towards themaximum density at a finite value of r/a and finally to tend to throw off theouter layers when r becomes great. This latter conclusion is in agreementwith Jeans. When we pass to other cases such as Cas^s II and III, where the originaldistributi
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