FOOTNOTES
[1] A full biographical account of the Clerk and Maxwell families is given in a note by Miss Isabella Clerk in the “Life of James Clerk Maxwell,” and from this the above brief statement has been taken.
[2] “Life of J. C. Maxwell,” p. 26.
[3] “Life of J. C. Maxwell,” p. 27.
[4] “Life of J. C. Maxwell,” p. 49.
[5] “Life of J. C. Maxwell,” p. 52.
[6] “Life of J. C. Maxwell,” p. 56.
[7] “Life of J. C. Maxwell,” p. 67.
[8] “Life of J. C. Maxwell,” p. 75.
[9] Professor Garnett in Nature, November 13th, 1879.
[10] “Life of J. C. Maxwell,” p. 105.
[11] “Life of J. C. Maxwell,” p. 116.
[12] “Life of J. C. Maxwell,” pp. 123–129.
[13] “Life of J. C. Maxwell,” p. 190.
[14] Dean of Canterbury.
[15] Master of Trinity.
[16] “Life of J. C. Maxwell,” p. 174.
[17] “Life of J. C. Maxwell,” p. 195.
[18] “Life of J. C. Maxwell,” p. 207.
[19] “Life of J. C. Maxwell,” p. 208.
[20] “Life of J. C. Maxwell,” p. 210.
[21] “Life of J. C. Maxwell,” p. 211.
[22] “Life of J. C. Maxwell,” p. 216.
[23] “Life of J. C. Maxwell,” p. 256.
[24] “Life of J. C. Maxwell,” p. 267.
[25] “Life of J. C. Maxwell,” p. 269.
[26] “Life of J. C. Maxwell,” p. 278.
[27] “Life of J. C. Maxwell,” p. 292.
[28] “Life of J. C. Maxwell,” p. 303.
[29] “Life of J. C. Maxwell,” p. 259.
[30] B.A. Report, Newcastle, 1863.
[31] “Life of J. C. Maxwell,” p. 340.
[32] “Life of J. C. Maxwell,” p. 332.
[33] “Life of J. C. Maxwell,” p. 336.
[34] The Professors who were consulted were Challis, Willis, Stokes, Cayley, Adams, and Liveing.
[35] “Life of J. C. Maxwell,” p. 349.
[36] “Life of J. C. Maxwell,” p. 381.
[37] “Life of J. C. Maxwell,” p. 379.
[38] An account of the laboratory is given in Nature, vol. x., p. 139.
[39] The Chancellor continued to take to the end of his life a warm interest in the work at the laboratory. In 1887, the Jubilee year, as Proctor—at the same time I held the office of Demonstrator—it was my duty to accompany the Chancellor and other officers to Windsor to present an address from the University to Her Majesty. I was introduced to the Chancellor at Paddington, and he at once began to question me closely about the progress of the laboratory, the number of students, and the work being done there, showing himself fully acquainted with recent progress.
[40] In 1894 the list contained, in Part II., sixteen names, and in Part I., one hundred and three names.
[41] Under the new regulations Physics was removed from the first part of the Tripos and formed, with the more advanced parts of Astronomy and Pure Mathematics, a part by itself, to which only the Wranglers were admitted. Thus the number of men encouraged to read Physics was very limited. This pernicious system was altered in the regulations at present in force, which came into action in 1892. Part I. of the Mathematical Tripos now contains Heat, Elementary Hydrodynamics and Sound, and the simpler parts of Electricity and Magnetism, and candidates for this examination do come to the laboratory, though not in very large numbers. The more advanced parts both of Mathematics and Physics are included in Part II.
[42] “Life of J. C. Maxwell,” p. 383.
[43] “Statique Expérimentale et Théorique des Liquides soumis aux seules Forces Moléculaires.” Par J. Plateau, Professeur à l’Université de Gaud.
[44] The “Red Lions” are a club formed by Members of the British Association to meet for relaxation after the graver labours of the day.
[45] “Leonum arida nutrix.”—Horace.
[46] v.r., endless.
[47] “Life of J. C. Maxwell,” p. 394.
[48] “Life of J. C. Maxwell,” p. 404.
[49] In his “Hydrodynamics,” published in 1738, Daniel Bernouilli had discussed the constitution of a gas, and had proved from general considerations that the pressure, if it arose from the impact of a number of moving particles, must be proportional to the square of their velocity. (See “Pogg. Ann.,” Bd. 107, 1859, p. 490.)
[50] The proof is as follows:—
If σ be the specific heat at constant volume, σ′ at constant pressure, and consider a unit of mass of gas at pressure p and volume v, let the volume increase by an amount dv, while the temperature dy.
Thus σ′dT = σdT + pdv
But pv = ⅔T/m
Hence p being constant,
pdv = ⅔ dT/m
Therefore σ′ = σ + ⅔ 1/m
Now suppose an amount of heat, dH, is given to a single molecule and that its temperature is T. Its specific heat is σ, and
dH = σmdT
But dH = βdT
Therefore β = σm
Hence 1/m = σ/β
Thus σ′ = σ(1 + 2/(3β))
And σ′/σ = γ
Therefore γ = 1 + 2/(3β)
Or β = 2/(3(γ-1))
[51] Owing to an error of calculation the actual value obtained by Maxwell from these observations for the coefficient of viscosity is too great. More recent observers have found lower values than those given by him; the difference is thus explained.
[52] Studien über das Gleichgewicht der lebendigen Kraft zwischen bewegten materiellen Punkten Sitz d. k. Akad Wien, Band LVIII., 1868.
[53] Another supposition which might be made, and which is necessary in order to explain various actions observed in a compound gas under electric force, is that the parts of which a molecule is composed are continually changing. Thus a molecule of steam consists of two parts of hydrogen, one of oxygen, but a given molecule of oxygen is not always combined with the same two molecules of hydrogen; the particles are continually changed. In Maxwell’s paper an hypothesis of this kind is not dealt with.
[54] Nature, vol. 1., p. 152 (December 13th, 1894).
[55] See papers by Mr. Capstick, Phil. Trans., vols. 185–186.
[56] Nature, vol. x.
[57] An historical account of the development of the science of electricity will be found in the article “Electricity” in the Encyclopædia Britannica, ninth edition, by Professor Chrystal.
[58] Thomson (Lord Kelvin), “Papers on Electrostatics and Magnetism,” p. 15.
[59] J. J. Thomson, B.A., Report, 1885, pp. 109, 113, Report on Electrical Theories.
[60] Papers on “Electrostatics,” etc., p. 26.
[61] It is difficult to explain without analysis exactly what is measured by Maxwell’s Vector Potential. Its rate of change at any point of space measures the electromotive force at that point, so far as it is due to variations of the electric current in neighbouring conductors; the magnetic induction depends on the first differential coefficients of the components of the electro-tonic state; the electric current is related to their second differential coefficients in the same manner as the density of attracting matter is related to the potential it produces. In language which is now frequently used in mathematical physics, the electromotive force at a point due to magnetic induction is proportioned to the rate of change of the Vector Potential, the magnetic induction depends on the “curl” of the Vector Potential, while the electric current is measured by the “concentration” of the Vector Potential. From a knowledge of the Vector Potential these other quantities can be obtained by processes of differentiation.
[62] The 4 π is introduced because of the system of units usually employed to measure electrical quantities. If we adopted Mr. Oliver Heaviside’s “rational units,” it would disappear, as it does in (B).
[63] For an exact statement as to the relation between the directions of the lines of electric displacement and of the magnetic force, reference must be made to Professor Poynting’s paper, Phil. Trans., 1885, Part II., pp. 280, 281. The ideas are further developed in a series of articles in the Electrician, September, 1895. Reference should also be made to J. J. Thomson’s “Recent Researches in Electricity and Magnetism.”
[64] Preface to Newton’s “Principia,” 2nd edition.
[65] “Lezioni Accademiche” (Firenze, 1715), p. 25.
[66] In his sentence μ stands for the refractive index.
[67] Hertz’s papers have been translated into English by D. E. Jones, and are published under the title of Electric Waves.
[68] Some of the consequences of this electrical resonance have been very strikingly shown by Professor Oliver Lodge. See Nature, February 20th, 1890.
[69] Hertz’s original results were no doubt affected by waves reflected from the walls and floor of the room in which he worked. An iron stove also, which was near his apparatus, may have had a disturbing influence; but for all this, it is to his genius and his brilliant achievements that the complete establishment of Maxwell’s theory is due.
[70] The analogy does not consist only in the agreement between the more or less accurately measured velocities. The approximately equal velocity is only one element among many others.
[71] For a very suggestive account of some possible theories, reference should be made to the presidential address of Professor W. M. Hicks to Section A of the British Association at Ipswich in 1895.