note * page 111 Note of February 22, 1887.—Having yesterday sent a finally revised proof of this paper for press, I have to-day received a letter from Prof. Newcomb, calling my attention to a most important paper by Mr J. Homer Lane, “On the Theoretical Temperature of the Sun,” published in the American Journal of Science for July 1870, p. 57, in which precisely the same problem as that of my article is very powerfully dealt with, mathematically and practically. It is impossible now, before going to press, for me to do more than refer to Mr Lane's paper ; but I hope to profit by it very much in the continuation of my present work which I intended, and still intend, to make.— W. T.

note * page 112 Lecture III. of Second Course of “Burnet Lectures,” Aberdeen, Dec. 1884 ; published, London, 1885 (Macmillan).

note * page 113 The notation of the text is related to temperature Centigrade on the thermodynamic principle (which is approximately temperature Centigrade by the air-thermometer), as follows :—

see my Collected Mathematical and Physical Papers, vol. i. arts, xxxix. and xlviii. part vi. §§ 99, 100; and article “Heat,” §§ 35–38 and 47–67, Encyc. Brit., and vol. iii. (soon to be published) of Collected Papers.

note † page 113 Not in molecular equilibrium of course ; and not in gross-thermal equilibrium, except in the case of t uniform throughout the gas.

note * page 114 See “On the Convective Equilibrium of Temperature in the Atmosphere,” Manchester Phil. Soc, vol. ii., 3rd series, 1861 ; and vol. iii. of Collected Papers.

note † 114 See my Collected Mathematical and Physical Papers, vol. i. art. xlviii. note 3.

note * page 115 This adjective excludes stars or nebulse rotating steadily with so great angular velocities as to be much flattened, or to be annular; also nebulæ, revolving circularly with different angular velocities at different distances from the centre, as may be approximately the case with spiral nebulæ. It would approximately enough include the sun, with his small angular velocity of once round in 25 days, were the fluid not too dense through a large part of the interior to approximately obey gaseous law. It no doubt applies very accurately to earlier times of the sun's history, when he was much less dense than he is now.

note * page 116 This method of graphically integrating a differential equation of the second order, which first occurred to me many years ago as suitable for finding the shapes of particular cases of the capillary surface of revolution, was successfully carried out for me by Prof. John Perry, when a student in my laboratory in 1874, in a series of skilfully executed drawings representing a large variety of cases of the capillary surface of revolution, which have been regularly shown in my Lectures to the Natural Philosophy Class of the University of Glasgow. These curves were recently published in the Proc. Roy. Instit. (Lecture of Jan. 29, 1886), and Nature, July 22 and 29, and Aug. 19, 1886; also to appear in a volume of Lectures now in the press, to be published in the Nature series.