ceive, without resorting to the doctrine of probabilities, that even 137 observations will not authorize us to affirm that there will be always fewer comets near to the ecliptic than at a distance from its plane. In the above table, it may be remarked that there are six comets more between 50° and 60° than between 60° and 70°; whilst the table of Bode gave a difference of four, but in the contrary way. It must be left, therefore, to posterity to decide, whether the primordial physical circumstances, in virtue of which the principal planets are found assembled in the neighbourhood of the elliptical plane, have exercised a different influence on the movements of the comets.

Longitudes of the Ascending Nodes.-From 0° to 30°, the number of nodes is 12; 30° to 60°, 12; 60° to 90°, 20; 90° to 120°, 8; 120° to 150°, 12; 150° to 180°, 13; 180° to 210°, 14; 210° to 240°, 11; 240° to 270°, 10; 270° to 300°, 8; 300° to 330°, 11; 330° to 360°, 6.

It may perhaps be regarded as a circumstance worthy of notice, that those two regions of the ecliptic, to which only eight ascending nodes correspond, are at exactly the distance of a demicircumference from each other; but, at the same time, the space comprised between the 338th and 360th degree is still poorer in its nodes of comets; whilst the region opposite to it does not, in this respect, present any thing particular to our observation; so that probably we are not to recognize in this circumstance any thing more than one of those fortuitous numerical coincidences, which quite disappear so soon as a greater number of observations are collected.

Longitudes of the Perihelions.-From 0° to 30°, number of perihelions, 11; 30° to 60°, 13; 60° to 90°, 12; 90° to 120°, 20; 120° to 150°, 10; 150° to 180°, 8; 180° to 210°, 6; 210° to 240°, 13; 240° to 270°, 18; 270° to 300°, 10; 300° to 330°, 10; 330° to 360°, 6; total 137.

The future will shew whether, as this table would appear to indicate, the extremities of the grand axes of the orbits of comets exist in a much greater number towards the 90th and the 270th degree of the ecliptic, than at any other point; and whether it is at a right angle to each of these regions that we ought, on the contrary, to expect the fewest perihelions. Any conclu

VOL. XIX. NO. XXXVII.--JULY 1835.

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sion on this subject at present would be premature; because it is clear that 137 orbits cannot supply general results, free from accidental influences.

Distances of Perihelions.-Between the sun and the orbit of Mercury, 30; between the orbits of Mercury and that of Venus, 44; Venus and the Earth, 34; the Earth and Mars, 23; Mars and Jupiter, 6; beyond the orbit of Jupiter, 0.

It seems difficult, after perusing this table, not to consider it as demonstrated, that the perihelion distances are not all equally possible. Nevertheless, when we devote a little more attention to the several conditions of the problem, we shall probably be led to modify the deductions derived from the first glance. And here it will be expedient, in the first place, clearly to recognise the difficulty.

If the perihelions were uniformly distributed throughout the celestial spaces, the number of those which would exist in those concentric spheres, which are nearest to the sun, and having for radii the radii of the orbits of Mercury, of Venus, and of the Earth, would stand to each other in the ratio of the volumes of their spheres; or, to express it in numbers, as the cubes of 3.9, 7.2, and 10, (3.9)3, (7.2)3, and (10)3; that is to say, as 59, 373, and 1000.

Let us now write, under these last cyphers, the number of comets which are known to be included within the spheres of Mercury, Venus, and the Earth, and we shall find that they are 29, 74, and 110.

The first, 29, is very nearly the half of 59, whilst 74 is not quite a fifth of 373; and 110 is not more than between the ninth and tenth part of 1000. The number of observed comets, therefore, does not augment at all proportionably to the volumes of the spaces which include their perihelions.

But before altogether renouncing this law, it will be right to inquire if, for all the regions, more or less distant from the sun, the number of comets which are perceived may not be the same aliquot part of the total number of those stars, the perihelions of which are placed in these same regions. And all that is required to enable us to answer that it is not, is only to put the question in the precise terms which we have employed above.

The comets whose perihelions are placed between the orbits

of Mercury and the Sun, ought nearly all to be observed from the Earth: 1st, Because their angular velocity not being very great, a few cloudy days would not be sufficient to transport them from our hemisphere into the opposite one, in which the earth's curve would hide them from our view; and, 2dly, Because near the sun, and swimming, as it were, in its light, these stars, though they possessed a physical constitution the least of all favourable to it, must reflect a sufficient number of rays to be easily perceptible.

The comets which are included between the sphere of Mercury and that of Venus, as seen from the earth, appear to move more rapidly, and are conspicuously less brilliant, than those included in the former list. All other things, therefore, being equal, a smaller proportion of these ought to be seen.

As to those comets whose perihelion distance differs but little from a radius of the earth's orbit, we shall find that, besides being more feebly illuminated than those which traverse, for example, the orbit of Mercury, in a ratio which, expressed in numbers, would exceed that of 16 to 100, it will also appear that, near our globe, their apparent progress is usually extremely rapid, and that, on this account, they will generally be visible only for a few days; and if during that period the sky be at all cloudy, no signal of their passage will be at all observed.

If, then, it should now be inquired why the table last given enumerates so few comets beyond the orbit of Mars, it will be sufficient to remark, in general, that these stars, whatever their perihelion distance may be, cease to be visible from the earth so soon as their course has transported them to a distance from the sun equal to three or four radii of the earth's orbit; and, consequently, those comets whose perihelion is found situated beyond the orbit of Mars, must run their orbit without being perceived from the earth; at all events, when they are not possessed of a size and a density, and consequently a brilliancy, which is altogether extraordinary.

I shall finally remark, more especially for the benefit of those who are astonished at not finding in the table a single comet whose perihelion extends beyond the orbits of Jupiter and Saturn, that the comet of 1759, after its last appearance, sojourned for five whole years in the ellipsis which Saturn maintains,

without the slightest trace of it being perceived during this long period. It would require that the brilliancy of a comet should greatly exceed that of any of the class which have been observed for a century and a half, before we could hope to discover it, even with the strongest glasses, whenever its distance from the sun shall have become equal to a radius of Saturn's orbit.

After having thus disposed of the objections which appear to result from the numerical data which are supplied in the table just alluded to, it will be found more natural that, in endeavouring to determine the number of comets which compose a part of our solar system, we should start with the supposition that the perihelions of their orbits are uniformly distributed in space, unless some physical reason can be alleged to establish that it is not so.

The number of comets really known whose perihelion distance is less than the radius of the orbit of Mercury, amounts to 30. This radius, and that of the orbit of Uranus, are in the ratio of 1 to 49. And the volumes of two spheres are to each other as the cubes of their radii. If, therefore, we adopt the hypothesis of the equal distribution of comets in all the regions of our system, and calculate the number of those luminaries whose perihelions are included in a sphere whose radius is the distance of Uranus from the sun, the following proposition would be supplied to us :-As the cube of 3 to the cube of 49, so 30 to the number of comets sought; or thus, (1)3: (49)3 : 30: Or, in working out these numbers, as 1: 117,649::

30: 3,529,470.

Thus, within the orbit of Uranus, the solar system should be ploughed by more than three million and a half of comets; or, we should rather find the double of that the true number, when we consider that in this calculation the term which represents the number of comets contained within the sphere of Mercury is certainly much too small, and that it ought to be conceded that the light of the day, and our cloudy skies, and a too southerly declination, removes from our sight not fewer than every alternate one of these bodies.

But Lambert, from considerations borrowed from final causes, has rejected the supposition, that the number of comets aug

ments in the direct ratio of the volumes of the spheres which contain their perihelions; and he has finally substituted, in the previous proportions, the surfaces of these same spheres, instead of their volumes.* This proportion then becomes (1)2: (49)2: 30: to the number sought; or, as 1 : 2401 :: 30: 62,030.

According to this hypothesis, the sphere whose centre corresponds with the sun, and its circumference with the distance of Uranus, would include only from 60,000 to 80,000 comets.

2. On the Light of Comets; and on the means of deciding whether this light emanates from these bodies themselves, or is borrowed from the Sun.

It has often been matter of astonishment, and not, perhaps, without reason, that such questions as these should still be canvassed in that science which is regarded as of all others the most advanced. Many individuals have found a difficulty in comprehending how those methods, and those instruments which have led to the determination of the weight of the planets, should be ineffectual in determining points apparently so much more simple. To this it may be answered, that at first it was necessary to bestow an exclusive attention to the observation of the phases of these bodies, inasmuch as this was the most direct method of ascertaining the point, and because it had succeeded when tried upon Mercury, Venus, and Mars; and also that, in default of this plan, it is true, that so soon as a comet, favourably placed, shall present itself, the phenomena of polarization will decide, at least for an appreciable part of its light, whether it has been derived from the sun or not. But these more simple and direct methods having hitherto failed, I proceed now to state that there is another mode by which the question may be

Halley's Table of Comets, which was the only one which Lambert could employ at the time of the publication of his Lettres Cosmologiques, contained only twenty-one of these stars, viz. six within the sphere of Mercury, and eleven between his sphere and that of Venus. But 6+11:6 :: 3 : 1 nearly. The surfaces of the spheres of Mercury and Venus being also nearly as 1 to 3, it was possible for Lambert to demonstrate that the laws of surfaces was conformable to observation. Now-a-days, when the Table includes 137 comets, it will be evident that the law can be no longer so verified, for 30+ 44 is not equal to 3 times 30, i. e. 90.