^{page 259 note *} § 1 is extracted from “On Homer Lane's Problem of a Spherical Gaseous Nebula,” Nature, Feb. 14, 1907.

^{page 260 note *} The real subject of this paper is that stated in the text above. The application of the theory of gaseous convective equilibrium to sun heat and light is very largely vitiated by the greatness of the sun's mean density (1·4 times the standard density of water). Common air, oxygen, and carbonic acid gas show resistance to compression considerably in excess of the amount calculated according to Boyle's Law, when compressed to densities exceeding four, or five, or six, tenths of the standard density of water. There seems strong reason to believe that every fluid whose density exceeds a quarter of the standard density of water resists compression much more than according to Boyle's Law, whatever be the temperature of the fluid, however high, or however low. We may consider it indeed as quite certain that a large proportion of the sun's interior, if not indeed the whole of the sun's mass within the visible boundary, resists compression much more than according to Boyle's Law. It seems indeed most probable that the boundary, which we see when looking at the sun through an ordinary telescope, is in reality a surface of separation between a liquid and its vapour; and that all the fluid within this boundary resists compression so much more than according to Boyle's Law that it does not even approximately satisfy the conditions of Homer Lane's problem; and that in reality its density increases inwards to the centre vastly less than according to Homer Lane's solution (see § 56 below).

^{page 260 note †} Republished in Sir William Thomson's Math. and Phys. Papers, vol. iii. p. 255.

^{page 264 note *} If instead of taking 10⁹ tons as our unit of mass we take a gram, the numbers in this table must each be multiplied by 10⁵, and they will then be the values of S in centimetres instead of in kilometres.

^{page 265 note *} Mr Shaw informs me that much investigation in later times gives a general average mean gradient of 1° C. per 164 metres. This is very nearly the same as it would be with. no disturbance from radiation in air saturated with moisture, at 4° C.

^{page 266 note *} Quoted from the Manchester paper above referred to, Math. and Phys. Papers, vol. iii. p. 260.

^{page 266 note †} Math. and Phys. Papers

^{page 270 note *} American Journal of Science, July 1870, p. 69.

^{page 271 note *} See Appendix to the present paper, Tables I. … IV.

^{page 271 note †} Wiedemann's Annalen, Bd. xi., 1880, p. 338.

^{page 271 note ‡} Brit. Assoc. Report, 1883, p. 428.

^{page 271 note §} Mécanique Céleste, vol. v., livre xi., p. 49.

^{page 277 note *} Quoted from “On Homer Lane's Problem of a Spherical Gaseous Nebula,” Nature, Feb. 14, 1907.

^{page 278 note *} Quoted from “On Homer Lane's Problem of a Spherical Gaseous Nebula,” Nature, Feb. 14, 1907.

^{page 285 note *} Quoted from “On Homer Lane's Problem of a Spherical Gaseous Nebula,” Nature, Feb. 14, 1907.