Other editions of book The Mathematical Theory of Electricity and Magnetism: Magnetism and Electrodynamics

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1889 Excerpt: ...we know that df dg dh dx dy dz and therefore--p =--V2. Whence it follows that y/r is the potential of the free electricity in the field. 403. Again, if there be material motion in the field we have proved, Art. 389, that „.dF.dG.dH... _ „ dF d+-F = xdx-+ + zdz--cy+bz+G-H+-dT + d' with similar expressions for Q and R. If the substance be of invariable form we know that o, o2, o3 have the same values throughout, and also that This proposition was first demonstrated by Professor Poynting, D.Sc, F.R.S., in a paper published in the Transactions of the Royal Society of London for 1884. It being proved, as above, that the time variation of the energy within a closed surface is expressible as a surface integral over that surface, Professor Poynting assumes that the flow of energy through each surface element is the argument of that surface integral. This theory, with many interesting consequences, has met with general acceptance. therefore _ d,.-.-,--... dG db whence, attending to the equations dz ay r-,in A dc da V2G =--4-itv =-5--ax dz 9 Tt-da db dy dx, dP dQ dR',, as before, and p is in this case also the potential of electrical distribution. If we adopt the shorter and more usual formulae p = c--bz----dt dx &c, where jr'=Fx+Gy+Hz. Since P, Q, i2 in the two expressions differ only by the.. djr db dlr......«,.. quantities----t1-)-51-respectively, it is indifferent which forms are employed in the case of closed currents, only it is important to remember that in the one case the yjr is the potential of free electricity, and in the other case that it differs from that potential by the quantity j/ or Fx + Gy+Hz. Note.--The field equations arriTed at in this Chapter are those principally in use, and which will be employed in subsequent pages. Many...

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This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.