numerically equal to the work E Q. We get therefore Ele = q/2, that is, the two velocities are the same. By taking the more general dimensional formulas given in the table (p. 357) we find that when [9], [2] refers to the ordinary systems. Hence the product Kμ- has the dimensions of a velocity. It is in fact the velocity q/Q above referred to* Denoting this velocity by v,† we get for the various quantities the following relations. The numerator of the ratio on the left of each equation denotes the numeric of the quantity in electrostatic units, the denominator the numeric of the same quantity in electromagnetic units. Therefore if q and Q, e and E, or the numerics for any other given quantity, be determined in the two systems of units, the value of v can be at once obtained. Experiments of this kind have been made by Maxwell, Sir W. Thomson, See Maxwell, El. and Mag. chap. xx. or the author's larger treatise, vol. ii. For illustrations of the physical meaning of v see Maxwell's Electricity and Magnetism, vol. ii. chap. xix. Weber, Ayrton and Perry, J. J. Thomson, H. A. Rowland, E. B. Rosa, and others,* with the result that v = = 3 X 1010 centimetres per second approximately, or very nearly the velocity of light in air as deduced from experiments made by the methods of Foucault and Fizeau. According to Maxwell's Electromagnetic Theory of Light (Electricity and Magnetism, vol. ii., chap. xx.) this relation should hold, and thus the theory is so far confirmed. Full information regarding experiments for the determination of v will be found in Maxwell's Electricity and Magnetism, vol. ii., chap. xix., and an account of the principal determinations made down to the present time will be found in the author's larger treatise,† (vol. ii.), which contains a much more detailed and complete account of electric and magnetic measurements than it is the object of this book to give. But to Maxwell's work also we refer the reader who wishes to obtain a complete account of the mathematical theory of electricity and magnetism He may consult also portions of Sir William Thomson's Reprint of Papers on Electrostatics and Magnetism; Mascart and Joubert's Leçons sur l'Electricité et le Magnétisme;‡ and Prof. Chrystal's articles on Electricity and Magnetism,§ which contain an admirable digest of the whole mathematical theory together with much valuable information as to experimental results. measurements. * An account of the principal determinations of this quantity with the results will be found in the author's Theory and Practice of Absolute Measurements in Electricity and Magnetism, vol. ii. The Theory and Practice of Absolute Measurements in Electricity and Magnetism, vols. i. and ii. Macmillan & Co. An English translation of this work by Prof. Atkinson has lately been published. § Encyclopædia Britannica, New Edition. APPENDIX. NOTE. Recommendations of the Paris Congress and the British Association as to Practical Electrical Units. At the meeting of the Electrical Congress held in Paris in 1884, it was decided to adopt for the present, as practical unit of resistance, a resistance equal to that of a uniform column of mercury one square millimetre in section, 106 centimetres in length, and throughout at the temperature o° C. The mercury column thus specified expressed approximately and in round numbers the value of the ohm according to the latest and most accurate experiments. It was resolved to give this unit the name Legal Ohm. The Congress also arrived at certain conclusions regarding the practical units of current, electromotive force, quantity of electricity, and electrostatic capacity, as follows:: (1) That the unit of current should be called the Ampere, and be defined as of a C.G.S. electromagnetic unit of current. (2) That the Volt or practical unit of electromotive force, or difference of potentials, should be defined as the electromotive force required to maintain a current of one ampere through a resistance of one ohm. (3) That the unit quantity of electricity should be called the Coulomb, and be defined as equal to the quantity of electricity transferred by a current of one ampere in one second. (4) That the Farad or practical unit of capacity should be the capacity of a conductor which is charged to a potential of one volt by one coulomb of electricity. The British Association at its meeting in 1886 agreed that the Committee on Electrical Standards should recommend to Her Majesty's Government : (1) "To adopt for a term of ten years the Legal Ohm of the Paris Congress as a legalized standard sufficiently near to the absolute Ohm for commercial purposes. (2) "That at the end of the ten years' period the Legal Ohm should be defined to a closer approximation to the absolute Ohm. (3) "That the resolutions of the Paris Congress with respect to the Ampere, the Volt, the Coulomb, and the Farad, be adopted. (4) "That the Resistance Standards belonging to the Committee of the British Association on Electrical Standards, now deposited at the Cavendish Laboratory at Cambridge, be accepted as the English Legal Standards conformable to the accepted definition of the Paris Congress." At the meeting of the Electrical Congress held at Paris in August, 1889, resolutions were carried of which the following is an English equivalent adopted by the British Association Committee on Electrical Standards (Report, Newcastle Meeting, September, 1889):— |