. The London, Edinburgh and Dublin philosophical magazine and journal of science. ur last expressions are obtained. The method is applicableonly when /? is integral. In a paper by Dr. Grlaisher ( Proc. London Math. 1 vol. vii.) the value of % r* + a* is determined by another method which gives the same result as the above. The physical significance of ft being integral is that in thatcase the value of on is such that the alternations at the sendingand receiving ends of the cable are in the same phase. Thecharge at the sending end being Ss=- fiir cosh fin (sin cot + cos tot) CO and at the
. The London, Edinburgh and Dublin philosophical magazine and journal of science. ur last expressions are obtained. The method is applicableonly when /? is integral. In a paper by Dr. Grlaisher ( Proc. London Math. 1 vol. vii.) the value of % r* + a* is determined by another method which gives the same result as the above. The physical significance of ft being integral is that in thatcase the value of on is such that the alternations at the sendingand receiving ends of the cable are in the same phase. Thecharge at the sending end being Ss=- fiir cosh fin (sin cot + cos tot) CO and at the receiving end Ss = - /3-7T cosech fiir (sin cot -\- cos cot), CO Fig. 3. the ratio of the amplitudesbeing cosh fiir. § 2. A cable, shown in sec-tion in fig. 3, contains twoconductors, an inner cen-tral conductor and an outerconcentric conductor, insu-lated from one another andthe water in which thewhole is immersed. Thewhole cable is supposed to • be arranged in the circular ~ZZZZZ^ZIZ^ form of fig. 2. 2irr, 2irr are the total resistances of the inner and outerconductors :. Also ^m—mr^)s + — 0, Currents in Concentric Cables. 65 27rm the total capacity of the inner dielectric measured between the two conductors ;2im the total capacity of the outer dielectric measured between the outer conductor and the water. tnn Then 2ir is the capacity of the central conductor, the m-\-n i j ?> outer one being insulated; and 2irn the capacity of the outer conductor, the inner one being insulated. u u, C C are the potentials of and the currents in the two conductors at point P and time t, and s s the density of the charges on the conductors. All these quantities being referred to a unit of length subtending unit angle at the centre, then dC (du du\ dC (du du\ , du -de^dt-w) ~To=m\-dt-dl)+n-dt; s + s=nu: and s = m(ii—u). Id1 d\ \aW-mrdt) and (§p-(m + n)tJd^S + mrJtS = 0Hence s and s satisfy the equation / cP d\/ d* d\ \»w*-dt)vw-it)s=0> where ,u, v are roots of mnrrx*—(
Size: 2348px × 1064px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1840, bookidlondon, booksubjectscience
