Not so has the great Architect left his work. To supply answers entirely satisfactory to these inquiries would lead us more deeply into the mathematical branch of the subject of physical astronomy than the nature of this treatise would admit; we can only glance at a few of the more obvious proofs of the sustaining hand of Omnipotence. Many of these variations are periodic; that is, they vibrate on each side of an imaginary fixed line or plane. Thus, the position of the earth's orbit is variable; but the disturbing forces on each side counteract each other in an extended period of time, being in fact equal to that in which the planets will again have, each and all, the same position with respect to each other as they have at any given instant of time. The amount of the variation in the position of the ecliptic is at present 48" per century, and its extreme vibration on each side of its mean position 1° 21'; having attained which on one side, it will return gradually to its original position. The like holds good with respect to the orbits of the other planets. 193. Other perturbations are secular; that is, they are completed in incalculably long periods of time: as the eccentricity of the earth's orbit, which has been, since the earliest age, diminishing, and will continue so to do till it becomes a circle; when its form will resemble an oval, again attain its maximum degree of eccentricity, and then again approximate to a circle. The period required for this fluctuation is one to which the whole history of the human race is, as it were, a point. 194. Other phenomena are constant; that is, they are subject only to variations which in time are accu rately compensated. The mean length of the longest diameter of a planetary orbit, that is, its major axis, and the time of its diurnal, as well as the mean period of its annual revolution, are among these.* From these facts, and from others understood only by themselves, mathematicians have deduced the certainty of the permanence of the system, subject to those laws which now obtain throughout it. Nor will the circumstances of the bodies composing it materially vary, nor the system itself, or any individual member of it, come to destruction, even at a period indefinitely remote, unless the same Voice which at first summoned it into being shall again interfere and pronounce its doom. 195. We have alluded to the relative masses of the sun and planets. Presumptuous as it may appear that man should compare the density of those mighty and distant bodies, yet has the philosophy of Newton brought this within the reach of human intellect. In the explanation of a part of astronomy so profound, it is difficult to make the method by which this wonderful result has been attained clear to those who cannot follow his train of mathematical reasoning. We shall, however, endeavour, by following out the principles already laid down, to give some notion of the possibility, at least, of such measurement being effected, with the hope that such an attempt will be satisfactory, and render the subject in its principal outlines intelligible. 196. We have seen in § 169, that the earth causes the moon to descend from a tangent to her orbit 1612 * These subjects are most agreeably and philosophically reasoned out in Sir John Herschel's "Astronomy." feet in a minute of time, and the manner in which this may be calculated was shewn. It has also been stated (§ 161), that the force of attraction is measured by the distance through which it causes a body to move in a given time, and that this force increases directly as the mass is increased (§ 158). Now if the earth had twice its present density, i. e. if the mass under the same volume were twice as great, it follows from these premises that the moon in one minute would be drawn through 161 × 2 or 324, and if its density were increased tenfold, the moon would be drawn through 1612 × 10 or 1605 feet in one minute (refer to fig. 29, where c b is the space alluded to); but since with the increase of the attractive force the centrifugal becomes more powerful to counterbalance it, the combined effect of these two would cause the moon to revolve round the earth, on the former supposition, in half the time it now does, in the latter in one tenth of that time. Now, if it had so happened that there was a planet revolving round the sun at the same distance that the moon revolves round the earth, our task of comparing the masses of the two central bodies would be soon accomplished; for we should only have to calculate, in the manner shewn in § 169, the deflection from a tangent in a given time (viz. c b in fig. 29) of the moon and of the planet, and the proportion would give us the proportion of the masses of the two central bodies; for the amount of attraction at equal distances is in direct proportion as the masses. The relative differences in the masses of the moon and planet would introduce no error into our computation, for we have already seen (§ 162) that attraction acts equally on all bodies at equal distances. But there is no planet situated at the same distance from the sun that the moon is from the earth, and hence the calculation becomes more involved ; but may still be easily understood, if we bear in mind that the attractions are inversely as the squares of the distances. Let us first ascertain the deflection of the earth from a tangent caused by the sun's attraction. Proceeding in the same way as in that already pointed out for ascertaining the deflection of the moon produced by the earth's attraction (viz. c b in fig. 29), we shall find that the proportion between the distance through which the moon will be drawn by the earth, and that through which the earth will be drawn by the sun in the same time, will be as 1 to 22. Now, as we have already seen (§ 158), the whole amount of attraction is in a ratio compounded of the ratios of the masses directly, and of the squares of the distances inversely, that is letting F stand for the attractive force of the sun measured by the versed sine of the arc which the earth describes, in one minute of time, viz. 2.2; and ƒ for the attractive force of the earth on the moon measured by the versed sine c b, through which the moon would be drawn in a minute of time, viz. unity or 1; also the ratio of D to d for that of the distances of the earth from the sun, and of the moon from the earth, which is as 400 1; and м to m for the ratio of the masses of the sun and earth, which we desire to know; then m: M::fd2: F D2 (by the Principia, prop. 74, theor. 34), that is m : м : : 1 × 12: 2.2 × 4002 or m : м::1: 352,000; so that the mass of the earth is to that of the sun as 1 to 352,000; or it would take 352,000 earths to make a body equal in bulk to the sun. 197. In like manner, by marking the deflections of one of the satellites of those planets which are provided with them from a tangent to its orbit, and comparing it with the influence of the earth on our moon, the proportional density of that planet may be found. The mass of the planet Jupiter, which, next to the sun, is the largest body by far in our system, has lately been very accurately determined by the Astronomer Royal from a series of observations on the position of his satellites, made with the most delicate instruments, adapted to the measurement of extremely minute quantities. 198. There now remain those planets which are unaccompanied by satellites. Their densities are known by means of their perturbations, compared with what their orbits ought to be as deduced from theory; but upon this branch of the subject the plan of this treatise demands silence, inasmuch as it is too complicated to be made intelligible without more of mathematics than would accord with our design. Knowing the diameter and the mass of a heavenly body, a simple proportion will enable us to work out its mean density as compared with that of another body. See more on this subject in Part I., under the head of "The Earth;" where will be found an account of the methods adopted in measuring the density of our planet. 199. The following are the densities of the different bodies of our system, that of the Earth being 1 |
