The London, Edinburgh and Dublin philosophical magazine and journal of science . A nftx giving for the frictional couple:K = 2^R3[|^]e= - 4^R^ + R ± [2^Wac |^^]- (U) For an infinite time of swing, , p = 0, but with arotational velocity differing from 0, |c| = a/— becomes that case the second term on the right of (11) disappears on *™H(cR) only the first term then remains, which agrees with (2;). two grounds : first, because c=0, secondly, Lim (2) ^ =0 ; Moreover * T. H(«R) . Lim—,-tzz = —i. cTL=o Hf(cR) It appears from the accompanying graphs f of the modulus p Hf(cR) 1 \. ,. .and arg
The London, Edinburgh and Dublin philosophical magazine and journal of science . A nftx giving for the frictional couple:K = 2^R3[|^]e= - 4^R^ + R ± [2^Wac |^^]- (U) For an infinite time of swing, , p = 0, but with arotational velocity differing from 0, |c| = a/— becomes that case the second term on the right of (11) disappears on *™H(cR) only the first term then remains, which agrees with (2;). two grounds : first, because c=0, secondly, Lim (2) ^ =0 ; Moreover * T. H(«R) . Lim—,-tzz = —i. cTL=o Hf(cR) It appears from the accompanying graphs f of the modulus p Hf(cR) 1 \. ,. .and argument of —^ that this limiting value is practi-cally reached at jcRj=£.R=10, (12) where * Cf. Jahnke u. Emde, 1. c. t Tables for H^ and H^2) will be found Jahnke u. Emde, pp. 139,140. 592 Mr. D. Coster on the Rotational Oscillation, The condition c\i ^10 means that the radius of thecylinder must be about equal to or larger than the wave-length. If R is small compared with X the second part of 109 0-8 0-7 0-6 0-50-40-3 ?J mod. 0-2 0-1 iiii 10. the frictional couple is negligible. For |cR|^10 the secondterm on the right-hand side of (10) becomes : acie = — ake I since c = ke equation (11) now becomes : K= — \irfj\Vw — Itt/jl/cR-1 .-(aco=1)- Water 16° . 1 . 0-0013 . 0-0000898 00110-000171 0000085 9o Atm. air 0° Air 001 atm* 2-80-28 Air 0001 atm.* Hydrogen 1 atm. 0° .. 0091 * At these pressures /u has not become much smaller. Cf. Kundt , Pogg. Ann. 1875, Band civ. of a C
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Keywords: ., bookcentury1800, bookdecade1840, booksubjectscience, bookyear1840
