[2] Successor of Dr. Dick, the Professor of Natural Philosophy who induced the Faculty to grant a workshop to James Watt when the Corporation of Hammermen prevented him from starting business in Glasgow, and for whom Watt was repairing the Newcomen engine when he invented the separate condenser.
[3] A model steam-engine which he made in his youth was carefully preserved by his brother in the Natural Philosophy Department. It was homely but accurate in construction: the beam was of wood, and the piston was an old thick copper penny!
[4] Proceedings on the occasion of the Presentation to the University of Glasgow of the Portrait of Emeritus Professor G.
G. Ramsay. November 6, 1907.
[5] Apparently for a short time in 1841, when Dr. Meikleham was laid aside by illness.
[6] The C.U.M.S. began as a Peterhouse society in 1843, and after a first concert, which was followed by a supper, and that by "certain operations on the chapel roof," the Master would only give permission to hold a second concert in the Red Lion at Cambridge, there being no room in College, on condition that the society called itself the University Musical Society. The new society was formed in May 1844; the first president was G.
E. Smith, of Peterhouse, the second was Blow, also of Peterhouse, a violin player and 'cellist, and the third was Thomson. [See _Cambridge Chronicle_, July 10, 1903, and _The Cambridge Review_, Feb. 20, 1908.]
[7] It is rather strange that the ninth edition of the _Encyclopaedia Britannica_ contains no biography of Green. Born in the year 1793 at Nottingham, the son of a baker, he assisted his father, who latterly acquired a miller's business at the neighbouring village of Sneinton. In 1829 his father died, and he disposed of the business in order that he might have leisure to give to mathematics, in which, though entirely self-taught, he had begun to make original researches. His famous 'Essay'
was published by subscription in 1828, and attracted but little attention. In 1833, at forty years of age, Green entered at Gonville and Caius College, and obtained the fourth place in the mathematical tripos of 1837, the year of Griffin, Sylvester, and Gregory. His university career, whatever else it may have done, apparently did not tend to make his earlier work much better known to the general scientific public, and he died in 1841 without the scientific recognition which was his due.
That came later when, as stated below, Thomson discovered him to the French mathematicians and republished his 'Essay.'
[8] January 1869, Reprint, etc., Article XV.
[9] Reprint, Article V.
[10] The geometrical idea was, however, given and applied at least as early as 1836 by Bellavitis, for a paper entitled "Teoria delle figure inversa" appears in the _Annali delle Scienze del Regno Lombardo-Veneto_ for that year. It was also described as an independent discovery by Mr. John Wm. Stubbs, in a paper in the _Philosophical Magazine_ for November 1843.
In a note on the history of the transformation in Taylor's _Geometry of Conics_ the date (without reference) of Bellavitis is given, and it is stated that the method of inversion was given afresh by Messrs. Ingram and Stubbs (Dublin, _Phil. Soc.
Trans._ I). The note also mentions that inversion was "applied by Dr. Hirst to attractions," but contains no reference to Thomson's papers!
[11] "_De Caloris distributione per Terrae Corpus_" in the Faculty minute, as stated above.
[12] _Sic._ Without doubt a mistake of the scribe for "Liouville."
[13] _North Wales Chronicle_, Report, Feb. 7, 1885.
[14] Published: _Treatise on Natural Philosophy_, vol. i in 1867; _Elements of Natural Philosophy_ in 1873.
[15] The exact date at which this was done cannot be determined from the Minutes of the Faculty, as they contain no reference to the appropriation of space for the purpose. In his _Oration on James Watt_, delivered at the Ninth Jubilee of the University of Glasgow, in 1901, Lord Kelvin referred to the Glasgow Physical Laboratory as having grown up between 1846 and 1856; and elsewhere he has referred to it as having been "incipient" in 1851.
[16] There are now in Glasgow in the winter session alone about 360 elementary students and 80 advanced students, and about 250 taking practical laboratory work.
[17] Before his death (in 1832) Carnot had obtained a clear perception of the true state of the case, and of the complete doctrine of the conservatism of energy. [See extracts from Carnot's unpublished writings appended, with a biography, to the reprinted Memoir, by his younger brother, Hippolyte Carnot.]
[18] This equation for the porous plug experiment may be established in the following manner, which forms a good example of Thomson's second definition of absolute temperature. Take pressure and volume of the gas on the supply side of the plug as p + dp and v, and on the delivery side as p and v + dv, so that dp and dv are positive. The net work done in forcing the gas through the plug = (p + dp)v - p(v + dv) = - pdv + vdp.
Let a heating effect result so that temperature is changed from T to T + ?T. Let this be annulled by abstraction of heat Cp?T at constant pressure. (Cp = sp. heat press. const.) [It is to be understood that dv is the total expansion existing, after this abstraction of heat.] The energy e of the fluid has been increased by de = - pdv + vdp - Cp?T.
Now, since the original temperature has been restored, the same expansion dv if imposed isothermally would involve the same energy change de; but in that case heat dH (dynamical) would be absorbed, and work pdv would be done by the gas.
Hence de = dH - pdv. This, with the former value of de, gives dH = vdp - Cp?T. Thomson's work-ratio is thus pdv?(vdp - Cp?T).
Now suppose dp imposed without change of volume, and dT to be the resulting temperature change. The temperature and pressure ratios are dT?T, dp?p. Thus dT?T = dp dv?(vdp - Cp?T), or
(v?T)(dT?dv) = 1?[1 - (Cp?v)(?T?dp)]
which is Thomson's equation. The minus sign on the right arises from a heating effect having been taken here as the normal case.
If the temperature T is restored by removing the heat at constant volume, a similar process gives the equation
(v?T)(dT?dv) = [1 + (?T??p)(?T?dp)]?[1 - (Cv?v)(?T?dp)]
where dp is the change of pressure before the restoration of the temperature T, and ?T??p is the rate of variation of T with p, volume constant.
[19] "On a Universal Tendency in Nature to Dissipation of Energy," _Proc. R.S.E._, 1852, and _Phil. Mag._, Oct., 1852.
[20] To this may be added the extremely useful theorem for such problems, that if any directed quantity L, say, characteristic of the motion of a body, be associated with a line or axis Ol, which is changing in direction, it causes a rate of production of the same quantity for a line or axis instantaneously at right angles to Ol, towards which Ol is turning with angular velocity ?, of amount ?L. If M be the amount of the quantity already existing for this latter line or axis, the total rate of growth of the quantity is there M + ?L. For example, a particle moving with uniform speed v in a circle of radius r, has momentum mv along the tangent. But the tangent is turning round as the particle moves with angular speed v?r, towards the radius. The rate of growth of momentum towards the centre is therefore
mv v?r = mv?r.
[21] See Gray's _Lehrbuch der Physik_, s. 278. Vieweg u. Sohn, 1904.
[22] Gray, Royal Institution, Friday Evening Discourse, February 1898.
[23] See the _Reports of the Committee on Electrical Standards_, edited by Prof. Fleeming Jenkin, F.R.S., Maxwell's _Electricity and Magnetism_, and Gray's _Theory and Practice of Absolute Measurements in Electricity and Magnetism_, Vol. II, Part II.
[24] The writer once, on a thick night, in a passenger steamer in the Race of Alderney, when the engines were stopped and soundings were being taken, saw the reel and cord go overboard, nearly taking one of the men with it. A new hank of cord had to be got and bent on a new reel; an operation that took a long time, during which the exact locality of the ship was a matter of uncertainty. Comment is needless!
[25] The tuning of a major third, in this way, is described in the paper entitled "Beats on Imperfect Harmonies," published in _Popular Lectures and Addresses_, vol. ii.
[26] The writer well remembers meeting a man of some experience in cable work who was on his way to measure the alternating currents in a Jablochkoff candle installation by the aid of an Ayrton and Perry galvanometer with steel needle!