by the pressure of light at the sun's surface, is thus approximately μ. For a spherical drop the critical diameter may be calculated to be 1.5 μ for water. For other substances the critical value is inversely proportional to the specific gravity.
A similar effect of extreme minuteness is familiar to us as the explanation of the long time required by very small particles to settle through the atmosphere, amounting to many months in the case of the finely divided dust thrown up during the eruptions of Krakatoa. But the resistance to suspended dust particles can never exceed their weight, since it is only called forth by the motion produced by the weight itself. The pressure of light now considered may enormously exceed the weight provided the particles are small enough.
From the motions, and especially the curvature, of comets' tails the magnitude of the repulsive forces to which they are subject may be calculated. Thus Bredichin finds, in four instances, that the repulsion must have been about 18.5, 3.2, 2.0, and 1.5 times the sun's gravitational attraction. Now the vapors emitted by comets are largely hydrocarbons of specific gravity about .8. To account for these repulsions on Arrhenius' principle, the drops must have had diameters of 0.1μ, 0.59 μ, 0.94 μ, 1.25 μ respectively. In another case, where the tail curved towards the sun, Bredichin found the repulsion to be 0.3 times gravity. This would indicate particles of diameter 6 μ. Particles of this order of magnitude, and far smaller, are familiar enough to us, especially in combustion and in the early stages of condensation.
The theory suggested is then as follows: As the comet approaches the sun, the intense heat causes a violent eruption of hydrocarbon vapors on the side towards the sun. The hydrogen boils off, and the vapors condense into small drops of hydrocarbons with higher boiling-points, or ultimately solid carbon is thrown out, finely divided as in an ordinary flame. The largest of these particles fall back to the comet, or if they are not condensed till at a great distance from it, they form tails turned towards the sun. The smaller are driven rapidly from the sun by the pressure of its light, with a speed depending on their size, and form the ordinary tails pointing away from it. That particles of different sizes should be formed from the same comet is natural since the comet is likely to be formed of heterogeneous materials, and there must be great variety in the circumstances of condensation. Thus the comet of 1744 had no less than five tails of different curvature. Occasionally the calculated repulsion on the same tail is not found to follow exactly the law of the inverse square of the distance from the sun throughout its whole length. This puzzling circumstance is at once explained, if the particles should for any reason change their state of aggregation, and consequently their size, during their headlong career. In the light of this theory the following passages will be found very suggestive.