If the ether is possessed of a density equal to that shown above, then the density of our original nebula must have been greater than what we have shown it to be. The density we found for it was 1/403,000,000th that of air, or 0·000000002481 of an atmosphere, and 1/5,264,800th is equal to 0·00000019 of an atmosphere; if then we add these two together we get 0·0000001925 of an atmosphere as the density of our nebula. This comes to be very slightly greater than the density of the ether, and shows that the estimate in the foregoing quotation is too high; unless it is asserted that the ether can exert no frictional action at all, which, we believe, no one has ever done; while the absolute temperature of the nebula at the new density would be 0·000053°, which would be a very small addition indeed to the 0·00000068°, we found for it at first. On the other hand, when the nebula was reduced to 29,000,000 miles in diameter the density of the ether would have increased its density from 0·1788, which we showed it then to have, only to 0·17880019 of an atmosphere, which would make no appreciable difference on its temperature, and would be so immensely greater than the 0·00000019 of an atmosphere of the ether that it could hardly be supposed to have any effect in retarding the rotation of so much heavier a body. And should it be found that the density of the ether is 1/4, 1/3, or 1/2 less, or even a great deal more, than that shown in the above quotation, it would only have proportionately less effect on our nebula, in every sense, than what we have just shown. We may, therefore, conclude that the introduction of the element ether has not vitiated our operations in any way up till now, and we shall leave it until we have acquired more knowledge of its nature and effects.

Although we have already condensed our nebula to somewhere about 4,000,000 miles in diameter, where we have shown it might begin to radiate light—radiation of heat may have begun when the diameter was ten times as great, or even before that—we propose to return to the period when it had just abandoned the ring for the formation of Mercury and was 63,232,000 miles in diameter, and became what we have called the Solar nebula; because there is a good deal to be learned from a careful study of our operations up to that period, and of what must have taken place during further condensation up till the final establishment of the sun such as it is at the present time.

When the planet Neptune was discovered, Bode's Law fell into disrepute for a time, because the new planet was found to be much nearer to the sun than, according to it, it should have been. All the other planets occupied the places assigned to them within 5 per cent. of the exact appointed distance from the sun, but Neptune turned out to be 22·54 per cent. out of his exact place, and hence the discredit thrown upon the law. It was hard treatment for a servant that had helped so unmistakably—as we know to have been the case—to the discovery of the first four asteroids, which has afterwards been followed by the discovery of a whole host of them, and that had been pressed into the service for the discovery of the very planet which was the cause of its discredit—but such is the world. However, first offences against the law are generally looked upon with merciful eyes, and the Series of Titius seems to have been so far received into favour again that, some astronomers are said to have been looking out for another planet farther off than Neptune, being convinced that there must be some reason why a law that has shown itself to be right in eight cases should be altogether wrong in the ninth. Here, we think that the most likely explanation that can be given is, that the ring out of which Neptune was formed divided itself, after breaking up, into two planets instead of one, and that this is the reason why, Bode's Law could not point out the true position of either of them. It is hard enough to believe that the ring out of which Uranus was made—which we have seen may have been 954,000,000 miles broad, and over 3,400,000,000 miles in extreme diameter—could have united its fragments, after breaking up, into one planet, and the difficulty of belief becomes greater the greater the diameter comes to be. We have, in our work, considered the breadth of Neptune's ring to have been 1,010,000,000 miles, but then we limited the diameter of the nebula to 6,600,000,000 miles—we had to draw the line somewhere—whereas it may have been a thousand million miles greater, which would very greatly increase the probability of two planets, perhaps even more, having been formed out of the ring. If it has been so, the law could not apply to the case. A new Act was required. Besides, it is not a law, never has been, but only a register of facts; and we know that truths are often discovered from similar registers. It registers, and at the same time shows, that there is a nearly fixed inter-relation, even proportion, in the distances of the planets from the centre of the sun as far out as Uranus; and were we to make a similar register, beginning at the (present) outside of the planetary system, and registering the number of revolutions, beginning with 1 for Neptune, rates of acceleration of revolution in number of days, and densities of the planets, we may draw from it some useful knowledge. But we shall first extend Bode's Law to embrace Neptune, and show the discrepancies between the actual positions of the planets and those pointed out by the law.

Here we see that, with the exception of the first step from Neptune to Uranus which is only 1·9577, we have an average gradation of acceleration of 2·5898 times, from one planet to another, from the outermost as far in as Mars; and that had Neptune had the period of revolution sought for by Leverrier in his discovery of that planet, viz. 217·387 years, or 79,399·602 days, the average rate of acceleration would have been 2·5896 times, from planet to planet, as far in as Mars. This, we think, is pretty strong evidence that one law of acceleration was in force from the beginning of the separation of rings from the nebula up to the time when the ring for Mars was separated—the departure from it in the case of Neptune, notwithstanding—and goes far to prove that part of the nebular hypothesis which implies that each of the planets is now revolving round the sun in the orbit, and with the velocity, belonging to the centre of gyration of the ring out of which it was formed. From Mars to Venus the law—the areolar law, of course—had changed to a variable decreasing law, as seen from the foregoing register, which then again changed into an increasing one, till at Mercury the rate of acceleration rose again to 2·5543 times from Venus, or very nearly the same rate of increase that existed from Uranus to Mars. The causes of these changes may or may not be able to be accounted for—we shall have to return to them hereafter, in the cases of Neptune, the earth and Venus—but there is one thing of some importance that is deducible from the register, which we shall endeavour to make clear.

Bode's Law Extended.

— —Mercury.Venus.Earth.Mars.Ateroids.Jupiter.Saturn.Uranus.Neptune.
Numbers in Progression03612244896192384

Add 4 to each for distance from sun,
Earth = 10.		4710162852100196388

Distance from the sun according to the law
(Miles)		37,186,000 |65,075,500 |92,965,000 |148,744,000 |260,300,000 |483,418,000 |929,650,000 1,782,114,000 |3,607,042,000

Actual Distance		35,987,000 |67,245,000 |92,965,000 |141,650,000 | — — |483,678,000 |886,779,000 |1,783,383,000 |2,794,000,000

Percentage of Distance beyond law.		— —3·34— —— —— —0·05— —0·07

Percentage of Distance within law.		3·22— —— —4·77— —— —4·50— —22·54

Our register as specified above will be the following:—

Planet. Rev. of Planet,
(Solar Days)		 Accel. of Revolution
(Neptune taken as 1)		 Densities of Planets
Neptune.60,180.86001.00001.132
Uranus.30,688.30001.9577
Saturn.10,759.21982.85230.736
Jupiter.4,332.58482.48331.358
Asteroids.1,714.18762.5606— —
Mars.686.97962.46294.188
Earth.365.25631.88085.660
Venus.224.70071.62554.810
Mercury.87.96922.55436.850