^{note * page 513} Eighth Bulletin of the Lick Observatory.

^{note * page 514} See H. Kayser, Handbuch der Spectroscopie, ii. p. 325.

^{note † page 514} Ueber die Spectren der neuen Sterne, A.N. 3917

^{note † page 514} Some estimate of the amount of heat developed by the impact may be gained from the following consideration. Suppose the materials of a cosmic cloud to fall from infinity upon our sun. The velocity V with which the cloud particles arrive at the sun's surface is hyperbolic, and therefore greater than 600 km. per second. Now we know that 1 kgr. matter moving with a velocity of V metres per second, if completely stopped, develops a quantity of heat which equals v ² calories. If, then, a quantity of cosmic matter weighing 1 kgr. at the surface of the earth would impinge upon the sun with parabolic velocity (about 600,000 metres per second), ca. 45 millions of calories would be developed by the collision. Suppose that during every second 1 kgr. matter impinges upon the area of 1 square metre, then the heat developed would be about 2400 times the amount of heat actually radiated by our sun during the same time. “Now it is easy to see that this kgr. of matter is distributed wiihin a parallelopipedou whose basis is 1 square metre and whose height is 600 km., because when the first particle of the kilogram arrives at the surface, the last particle which impinges exactly one second later will be, roughly speaking, at a distance of 600,000 metres from the surface. But the density of such a cloud is only about 1 : 800,000 of the density of air at ordinary temperature and pressure. Hence we conclude that an all round impact of cosmic matter whose density is only the 1 : 2,000,000,000th part of that of our atmosphere would still produce an amount of heat equivalent to the energy radiated into space during the same time by our sun under normal circumstances. This rough calculation appears to justify the remark in the text, that the amount of heat supplied by the collision may indeed be assumed to be practically unlimited.

^{note * page 531} Cf. Scheiner-Frost, pp. 287 and 291

^{note * page 546} See note at end of paper

^{note * page 549} (P. 126.) “It is known from the elementary principles of dynamics that the moment of momentum of a system which is subject to no external forces is constant.” Mr Moulton demonstrates, however, that when the solar nebula extended to Neptune's orbit, the moment of momentum was 32·176, while in the system at present it is only 0·151. Hence, “instead of being a constant, the moment of momentum is found to vary in a remarkable manner. It follows from these figures that if the mass of the solar system filled a spheroid extending to Neptune's orbit, aud rotated with a velocity sufficient to make its moment of momentum equal to that of the present system, and if it then contracted the centrifugal force would not equal the centripetal until it had shrunk far within Mercury's orbit. Such an enormous difference cannot be ascribed to uncertainties in the law of density, or to the approximations in the mechanical quadratures ; but it prints to a mode of development quite different from, and much more complicated than, that postulated in the nebular theory under discussion.”

^{note * page 551} See my paper, “Some Suggestions on the Nebular Hypothesis.”