The London, Edinburgh and Dublin philosophical magazine and journal of science . lastic rigidity {cf. Appendix E and p. 124of Larmors Mther and Matter/ Also Phil. Mag. forApril 1907, p. 503). It is essential however that weknow the value of this rigidity. If it is kinetically explicablein the way originally suggested by Lord Kelvin (thoughafterwards abandoned by him) then the amount of energylocked up in the aether is something prodigious. Someday such a fact as this, when ascertained, may be foundto have a bearing on really practical problems. [ 472 ] XLIII. On a reciprocal relation between t
The London, Edinburgh and Dublin philosophical magazine and journal of science . lastic rigidity {cf. Appendix E and p. 124of Larmors Mther and Matter/ Also Phil. Mag. forApril 1907, p. 503). It is essential however that weknow the value of this rigidity. If it is kinetically explicablein the way originally suggested by Lord Kelvin (thoughafterwards abandoned by him) then the amount of energylocked up in the aether is something prodigious. Someday such a fact as this, when ascertained, may be foundto have a bearing on really practical problems. [ 472 ] XLIII. On a reciprocal relation between the ElectrostaticFields of certain Distributions of Electricity and theMagnetic Fields of corresponding Uniform Professor A. Gray, * 1. .1 uniform circular linear distribution of electricity anda uniform circular current. THE heavy circle in fig. 1 represents the circular electricaldistribution of line density p and radius a. P is apoint external to the circle and its plane, at a distance afrom its centre, and A is the intersection of CP with thecircle. Consider an element of the circle at E of length this element radially to E on the concentric circle(of radius a) described through P, and denote by ds thelength of the projection. Then ds /ds = a/a. Denote EP•by r, ^CPE by 0; we have then also AE = r, The repulsion of the charge on ds exerted on a unit chargeat P, that is the electric field intensity at P, is -_ cos 6 ds a cos 6 ds /1X V*=P—?-=P3—js- W Now the second of these forms is, by the diagram, and* Communicated by the Author. Relations of Electric and Magnetic Fields. 473 according to the so-called law of Laplace, the magnetic fieldintensity produced at A by the element ds ot a circularconductor coincident with the concentric circle drawnthrough P, and carrying a current of strength y = the whole magnetic field intensity Fm at A, due to a•current y in the concentric circle through P, is given by j cos# ; (
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