The Earth's Beginning

by Robert S. Ball

§ 15. Collisions.

The conservation of moment of momentum remains true in a system, even though there may have been actual collisions between the several parts. This is included in the proof already given, for collisions are among the mutual actions referred to. It may, however, be instructive to give a direct proof of a particular case.

Let two particles collide when meeting in the directions A P and B P (Fig. [63]) respectively. Whether the particles be elastic or inelastic is quite immaterial, for in both cases the action and reaction must be equal and opposite, and take place along some line P Q. The action on the particle moving along A P will give to it an acceleration of moment of momentum which is equal to the moment of the action around O. The acceleration of the moment of momentum coming along B P will be equal and opposite. Thus the total acceleration of the moment of momentum is zero. Hence the collision has no effect on the total moment of momentum.

§ 16. Friction and Tides.

We have shown that such actions as collisions cannot affect the moment of momentum of the system, neither can it be affected by friction of one body on another. Here, as in the former case, the actions and reactions are equal and opposite, and consequently the accelerations of moment of momentum are zero. Nor is it possible for any tidal action to affect the total moment of momentum of the system. Every such action must be composed of the effects of one particle in the system on another, and as this must invariably produce an equal and opposite reaction the total moment of momentum is unaltered.

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INDEX.

• Acceleration of moment of momentum, [377]
• Aldebaran, [27], [28]
• Anderson, Dr., [356]
• Andromeda, Great Nebula in, [43], [204]
• Antinous, Cluster of stars in, [353]
• Apteryx, Rudimentary wing-bones of, [364], [366]
• ——, Skeleton of, [364], [366]
• ——, The, [363], [365]
• Arcturus, Spectrum of, [85]
• Argon, [265]
• Argus and surrounding stars, [103]
• Ariel, [338]
• Boring, The great, [123]
• Brooks’ comet, [89]
• Bunsen burner, The, [283]
• Butterfly and the oak-tree, The, [15]
• Calcium, [274]
• Capella, Spectrum of, [61]–[64]
• Carbon, [280]
• Ceres, [311]
• Change of moment of momentum, [375]
• Cluster, Nebulous region round a, [33]
• Clusters of stars, [53]–[60], [203]
• —— —— of 17th magnitude, [353]
• Coal-unit, [110]
• Collisions, [219], [380]
• ——, Cause of formation of nebulæ, [356]
• Comets, [37]
• Comet, Brooks’, [89]
• —— of 1882, [119]
• ——, Spectrum of, [290]
• Common, Dr. A. A., [44]
• Concord, The first, [294]–[307]
• ——, The second, [308]–[323]
• ——, The third, [324]–[336]
• Conglomerates, [159]
• Conservation of moment of momentum, [374]
• Corona of the sun, [117]
• Crab nebula, The, [19], [44]
• Crossley Reflector, The, [45], [46], [48], [49], [50], [67], [199]
• Cygnus, Nebula in, [329]
• Dark bodies in universe, [355]
• Darwin, Professor G. H., [153], [254], [332]
• Darwinian theory, [10], [268], [362]
• Dewar, Professor, [144], [272]
• Diurnal motion, The, [21]
• Dumb-bell nebula, [43], [44], [45], [46], [50], [74], [195]
• Dust from Krakatoa, [185]
• Earth, Heat in interior of, [134], [367]
• ——, ——, Cause of, [153]
• ——, History of, [122]–[157], [251]
• ——, Rigidity of, [162]
• Earth-moon system, [253], [332]
• Earthquakes, [158]–[190]
• —— in England, [175]
• ——, Routes of, [171]
• Emission of sun heat, [373]
• Energy between two attracting masses, [370]
• —— given out in contraction of nebula, [370]
• —— of a system, [216], [235]
• Equivalent of heat, [88]
• Eros, [312]
• Evaluation of sun heat given out in contraction, [371]
• Everett, Professor, [149]
• Fire-mist, The, [268]
• “Flash” spectrum, [70]
• Foot-pound, [91]
• Foraminifera, [367]
• Friction and tides, [381]
• Gas in rarefaction, [118]
• H and K lines, [70], [276]
• Heat, Cause of, [153]
• ——, Equivalent of, [88]
• —— given out in contraction of nebula, [369]
• —— in interior of the earth, [134], [367]
• ——, Unit of, [80], [89]
• Helium, [277]
• Helmholtz, [86], [96], [100]
• Hercules, Star-cluster in, [52], [53], [56], [57], [59]
• Herschel, Sir William, [4], [11], [72], [73], [74]
• Huggins, Sir W., [60], [61], [63], [65]
• Huxley, Professor, and Darwinian theory, [362]
• Huyssen, Captain, [127]
• Hydrogen in spectrum of Nova Persei, [358]
• “Inflammation” and nebular theory, [361]
• Joule’s equivalent of heat, [88]
• Jupiter, [23], [25], [26], [29], [208], [237], [310], [327]
• K and H lines, [70], [276]
• Kant, Immanuel, [4], [5], [72], [73], [74], [327]
• Keeler, Professor, [45]–[48], [67], [73], [199], [200], [202], [245]
• Kelvin, Lord, [153], [162]
• Krakatoa, [176]–[189]
• Langley, Professor, [78]
• Laplace, [4], [72], [73], [74], [206]
• Lassell, Mr., [338], [340]
• Lick Observatory, [41], [43], [44], [45]
• Lockyer, Sir Norman, [277]
• Lyra, Ring nebula in, [249]
• Mars, [25], [26], [27], [28], [29], [311], [341], [349]
• ——, Satellites of, [341]
• Mécanique Céleste, [5], [8]
• Mercury, [23], [25], [26], [29], [208]
• Meteors, [37]
• Milky Way, [205], [206], [214], [220]
• Milne, Professor, [165]
• Moment of momentum, [222], [226], [240], [352]
• —— ——, Acceleration of, [377]
• —— ——, Change of, [375]
• —— ——, Conservation of, [374]
• Momentum, Moment of, [222], [220], [240], [352]
• Monoceros, Nebulous region round a cluster in, [33]
• Moon, Origin of, [254]
• ——, Surface of, [255]
• Nautilus, The, [367]
• Nebula, Contraction of, Heat given out in, [369]
• ——, ——, Energy given out in, [370]
• —— in Orion, The great, [40], [41], [42], [44], [46], [50], [74], [195], [242]
• —— ——, ——, Spectrum of, [63], [64], [65]
• ——, The great spiral, [192], [193]
• Nebulæ, [40], [41], [43], [45], [47], [50], [57], [58], [66], [67], [71], [73], [105], [120], [157], [191]–[206], [242], [247], [249], [256], [257], [258], [259], [296], [329], [345], [348]–[360]
• ——, Development of, [242]
• ——, Discovery of, [11]
• ——, Number of, [67], [200]
• Nebular anecdote, [362]
• —— Theory, The, [2], [3], [72], [74], [157], [205], [266], [292], [307], [323], [328], [331], [337]–[347], [362], [368]
• Nebulosity, Faint diffused, in Perseus, [17]
• Neptune, [37]
• ——, Satellites of, [330], [340]
• Newcomb, Professor, [238]
• Norway, Conglomerates in, [159]
• Nova Persei, [358]
• —— ——, Spectrum of, [358], [359], [360]
• Oak-tree and the butterfly, The, [15]
• Oberon, [338]
• Orbits of the planets, [208]
• Orion, [22]
• Orion, Great nebula in, [40], [41], [42], [44], [46], [50], [74], [195], [242]
• ——, Spectrum of, [63], [64], [65]
• Pegasus, Nebula in, [47], [345]
• Perseus, A faint diffused nebulosity in, [17]
• ——, New star in, [356]
• Photosphere, The, [69]
• Pickering, Professor, [358]
• “Plane, Principal,” The, [225], [352], [379]
• Planetary system, The, [37], [208]
• Planets, [22], [26], [28]
• ——, Movement of, [35], [311]
• ——, Orbits of, [208], [298]
• ——, Rotation of, on their axes, [325]
• Platinum, [263]
• Pleiades, [22]
• ——, Nebulae in, [71]
• Potassium, [272]
• “Plane, Principal” The, [225], [352], [379]
• Probabilities, Theory of, [305]
• Radiation of sun’s heat, [82]
• Ramsay, Professor, [278]
• Ray nebulæ, [201], [211]
• Rigidity of the earth, [162]
• Ring nebula in Lyra, The, [249]
• Roberts, Dr. Isaac, [198]
• Rosse, Lord, [57], [196]–[201]
• Rowland, Prof. Henry, [273]
• Sagittarius, Nebula in, [105]
• Satellites, [37], [209]
• Saturn, [25], [26], [29], [220], [233]
• ——, Dweller in, and the Sirian, [14]
• ——, Ring of, [210], [220], [231], [232], [233], [234]
• Scheiner, Professor, [202], [204]
• Seismometer, The, [165]
• Sirian, The, and the dweller in Saturn, [14]
• Sirius, [215], [216]
• Smiths, The parable of the, [303]
• Solar system, [36], [207]
• ——, Energy of, [350]
• ——, Evolution of, [20], [246]–[260], [349]
• ——, Origin of, [351]
• Solar system, Scale of, [29], [30], [31]
• Spectra, Continuous, [68], [203]
• ——, Discontinuous, [68]
• Spectroscope, The, [60], [271]
• Spiral form in Nature, [256], [257]
• Spiral nebula, The great, [192], [193], [247]
• Spiral nebulæ, [191]–[206], [211], [212], [213], [220], [243], [247], [256], [257], [258], [259], [296], [345]
• Star-clusters, [53]–[60]
• Star, Spectrum of, [64]
• Stars distinguished from planets, [28], [29]
• Stoney, Dr. G. Johnstone, [279]
• Sun compared with the planets, [26], [29]
• ——, Corona of, [117]
• ——, Contraction of, [99], [373]
• ——, Density of, [102], [115]
• ——, Heat of, [75]–[94], [95]–[111], [371], [372], [373]
• ——, History of, [112]–[121], [251]
• ——, Nebulous part of, [121]
• ——, Spectrum of, [61], [62], [69], [70], [85], [273]
• ——, Surface of, [278]
• ——, Velocity of, [354]
• ——, Weight of, [101]
• Sun heat, given out in contraction, Evaluation of, [371], [372]
• ——, Present emission of, [373]
• Sunsets, The Krakatoa, [189]
• Système du Monde, [8]
• Thermometer for testing the heat of the earth’s interior, [129]
• Thomson, Prof. J. J., [316]
• Tides and friction, [381]
• Titania, [338]
• Umbriel, [338]
• Unit of heat, [80], [89]
• Uranus, [37], [238], [239]
• ——, Satellites of, [238], [338]
• Venus, [23], [25], [26], [29], [208], [325]
• Volcanoes, [158]–[190]
• Voltaire, Fable of, [14]
• Waves caused by Krakatoa earth quake, [179], [182], [183]

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