If we take ρ to be the density of platinum (21.5), we get a coal equivalent 8,300. This, therefore, seems to represent a major limit to the quantity of heat which can be obtained from the condensation of the nebula from infinity into a sun of the utmost density. § 6. ON THE PRESENT EMISSION OF SUN HEAT. According to Scheiner, “Strahlung und Temperatur der Sonne, Leipzig, 1899,” the value of the solar constant, _i.e._ the number of cubic centimetres of water which would be raised 1° Centigrade by the quantity of sun heat which, if there were no atmospheric absorption, would fall perpendicularly on a square centimetre, at the earth’s mean distance from the sun, is between 3.5 and 4.0. If we take the mean value, we have (translated into British units), the following statement:— _If at a point in space, distant from the sun by the earth’s mean distance, one square foot was exposed perpendicularly to the solar rays, then the sun heat that would fall upon it in one minute would raise one pound of water 14° Fahr._ This shows that the solar energy emitted daily amounts to 700,000,000,000 × 4 π _a_^2 foot-pounds. § 7. ON THE DAILY CONTRACTION OF THE SUN NECESSARY TO SUPPLY THE PRESENT EXPENDITURE OF HEAT. We have seen that at the radius _r_ the energy is 16 M (_a_^2/_r_). Hence for a change _dr_ it is –16 M (_a_^2/_r_^2) _dr_. At its present size, accordingly, the energy given out by a shrinkage _dr_ is 16 M _dr_. One cubic foot of the sun averages 87 pounds, so that M = 4/3 π _a_^3 × 87 16 M _dr_ = 464 × 4 π _a_^3 _dr_. We have to equate this to the expression in the last article, and we get _dr_ = 700,000,000,000/(464 _a_) = .65. This is the shrinkage of the sun’s radius expressed in feet. Hence the daily reduction of the sun’s _diameter_ is 16 inches. One coal equivalent possesses energy represented by M × 14,000 × 772. Hence we can calculate that one coal equivalent would supply the solar radiation at its present rate for about 2,800 years. II.—THE CONSERVATION OF MOMENT OF MOMENTUM. We give here an elementary investigation of the fundamental dynamical principle which has been of such importance throughout this volume. § 8. CASE WHERE THERE ARE NO FORCES. Newton’s first law of motion tells us that a particle in motion if unacted upon by force, will move continuously in a straight line without change of velocity. Let A_{0}, Fig. 60, be the position of the particle at any moment. Let A_{1} be its position after the time _t_; A_{2} be the position at the time 2_t_; A_{3} be the position at the time 3_t_, and so on. Then the first law of motion tells us that the distances A_{0} A_{1}, A_{1} A_{2}, A_{2} A_{3}, A_{3} A_{4}, must form parts of the same straight line and must be all equal.