this being variable the limit itself is variable. If such values be assigned to the component quantities as to render L' the greatest possible, we shall obtain the latitude within which an eclipse is possible. If such values be assigned as will render L' the least possible, we shall obtain the latitude within which an eclipse is inevitable.

530. Greatest duration of total eclipse. The duration of a total eclipse depends on the distance over which the centre of the moon's disk moves relatively to the shadow while passing from the first to the last internal contact. This may vary from o to twice the greatest possible distance of the moon's centre from the centre of the shadow at the moment of internal contact, that is, to

and since the moon's centre moves synodically through half a minute of space in each minute of time, the interval necessary to move over 61'56" will be two hours and four minutes, which is therefore the greatest possible duration of a total lunar eclipse.

531. Relative number of solar and lunar eclipses. It will be evident, from what has been explained, that the frequency of solar is much greater than that of lunar eclipses, since two at least of the former must, and five may, take place within the year, while not one of the latter may occur. Nevertheless, the number of lunar which are exhibited at any given place on the earth is greater than that of solar eclipses, because, although the latter occur with so much greater frequency, they are seen only within particular limits on the earth's surface.

532. Effects of the earth's penumbra.- Long before the moon enters within the sides of the cone of the shadow it enters the penumbra, and is partially deprived of the sun's light, so as to render the illumination of its surface sensibly more faint. It might be inferred from this, that the obscuration of the moon is so extremely gradual, that it would be impossible to perceive the limitation of the shadow and penumbra. Nevertheless, such is the splendour of the solar light, that the thinnest crescent of the sun, to which the part of the moon's surface near the edge of the earth's shadow is exposed, produces a degree of illumination which contrasts so strongly with the shadow as to render the boundary of the latter so distinct, that the phenomenon presents one of the most striking evidences of the rotundity of the earth, the form of

the shadow being accurately that which one globe would project upon another.

533. Effects of refraction of the earth's atmosphere in total eclipses.- If the earth were not surrounded with an atmosphere capable of refracting the sun's light, the disk of the moon would be absolutely invisible after entering within the edge of the shadow. For the same reason, however, that we continue to see the sun's disk, and receive its rays after it has really descended below the horizon, an observer placed upon the moon, and therefore the surface of the moon itself, must continue to receive the sun's rays after the interposition of the edge of the earth's disk as seen from the moon. This refracted light falling upon the moon after it has entered within the limits of the shadow, produces upon it a peculiar illumination, corresponding in faintness and colour to the rays thus transmitted through the earth's atmosphere.

534. The lunar disk visible during total obscuration.— When the moon's limb first enters the shadow, the contrast and glare of the part of the disk still enlightened by the direct rays of the sun, render the eye insensible to the more feeble illumination produced upon the eclipsed part of the disk by the refracted rays. As, however, the eclipse proceeds, and the magnitude of the part of the disk directly enlightened decreases, the eye, partly relieved from the excessive glare, begins to perceive very faintly the eclipsed limb, which is nevertheless visible from the beginning in a telescope, in which it appears with a dark grey hue. When the entire disk has passed into the shadow, it becomes distinctly visible, showing a gradation of tints from a bluish or greenish on the outside to a gradually increasing red, which, further in, changes to a colour resembling that of incandescent iron when at a dull red heat. As the lunar disk approaches the centre of the shadow, this red line is spread all over it. Its illumination in this position is sometimes so strong as to throw a sensible shadow, and to render distinctly visible in the telescope the lineaments of light and shadow upon its surface.

These effects are altogether similar to the succession of tints developed in our atmosphere at sunset, and arise, in fact, from the same cause, operating, however, with a twofold intensity. The solar rays traversing twice the thickness of air, the blue and green lights are more effectually absorbed, and a still more intense red is imparted to the tints transmitted. Without pursuing these consequences further here, the reader will find no difficulty in tracing them in the effects of sunset and of sunrise, and of evening and morning twilight.

III. ECLIPSES, TRANSITS, AND OCCULTATIONS OF THE JOVIAN SYSTEM.

535. The motions of Jupiter and his satellites, as seen from the earth, exhibit from time to time all the effects of interposition. Let J J', fig. 91. represent the planet, JfJ' its conical shadow, 88' the sun, E and E' the positions of the earth when the planet is in quadrature, in which

position the shadow Jf J' is presented with least obliquity to the visual line, and therefore least foreshortened, and most distinctly seen. Let b b' d' d represent the orbit of one of the satellites the plane of which coincides nearly with that of the planet's orbit, and, for the purposes of the present illustration, the latter may be considered as coinciding with the ecliptic without producing sensible error.

From E suppose the visual lines EJ and E J' to be drawn, meeting the path of the satellite at d and g, and at a and b', and, in like manner, let the corresponding visual lines from E' meet it at d and g', and at a' and b'. Let c and c' be the points where the path of the satellite crosses the limits of the shadow, and h and h' the points where it crosses the extreme solar rays which pass along those limits.

If express the length Jf of the shadow, d the distance of the planet from the sun in semi-diameters of the planet, and r and the semi-diameters of the sun and the planet respectively, we shall have

Fig. 91.

by which formula the length of the shadow is found to be 1247 semi-diameters of the planet. Now, since the distance of the most remote satellite is not so much as 27 semi-diameters of the planet (406), and since the orbits of the satellites are almost exactly in the plane of the orbit of the planet, it is evident that

they will necessarily pass through the shadow, and almost through its axis, every revolution, and the lengths of their paths in the shadow will be very little less than the diameter of the planet.

The fourth satellite, in extremely rare cases, presents an exception to this, passing through opposition without entering the shadow. In general, however, it may be considered that all the satellites in opposition pass through the shadow.

536. Effects of interposition.-The planet and satellites exhibit, from time to time, four different effects of interposition.

537. 1st. Eclipses of the satellites. These take place when the satellites pass through the shadow behind the planet. Their entrance into the shadow, called the immersion, is marked by their nearly sudden extinction. Their passage out of the shadow, called their emersion, is manifested by their being suddenly relighted.

538. 2nd. Eclipses of the planet by the satellites. — When the satellites, at the periods of their conjunctions, pass between the lines 8 J and s'', their shadows are projected on the surface of the planet in the same manner as the shadow of the moon is projected on the earth in a solar eclipse, and in this case the shadow may be seen moving across the disk of the planet, in a direction parallel to its belts, as a small, round, and intensely black spot.

539 3rd. Occultations of the satellites by the planets. When a satellite, passing behind the planet, is between the tangents E Ja' and E J'b', drawn from the earth, it is concealed from the observer on the earth by the interposition of the body of the planet. It disappears on one side of the planet's disk, and reappears on the other side, having passed over that part of its orbit which is included between the tangents. This phenomenon is called an occultation of the satellite.

540. 4th. Transits of the satellites over the planet.When a satellite, being between the earth and planet, passes between the tangents EJ and EJ', drawn from the earth to the planet, its disk is projected on that of the planet, and it may be seen passing across, as a small brown spot, brighter or darker than the ground on which it is projected, according as it is projected on a dark or bright belt. The entrance of the satellite upon the disk, and its departure from it, are denominated its ingress and egress.

541. Phenomena predicted in Nautical Almanac. - The times of the occurrence of all these several phenomena are calculated and predicted with the greatest precision, and may be found registered in the Nautical Almanac, with the diagrams for each month to aid the observer. The mean time, at Greenwich, of the eclipses of the satellites is there accurately given, so that if the time at which any of them are observed to occur in any other place be

noted, the difference of such local time and that registered in the Almanac will give the longitude of the place east or west of the meridian of Greenwich. The observations of the other phenomena of the satellites of Jupiter cannot be made with sufficient accuracy, for the determination of differences of longitude.

542. Motion of light discovered, and its velocity measured, by means of these eclipses.-Soon after the invention of the telescope, Roemer, an eminent Danish astronomer, engaged in a series of observations, the object of which was the discovery of the exact time of the revolution of one of these bodies round Jupiter. The mode in which he proposed to investigate this was, by observing the successive eclipses of the satellite, and noticing the time between them.

Now if it were possible to observe accurately the moment at which the satellite would, after each revolution, either enter the shadow, or emerge from it, the interval of time between these events would enable us to calculate exactly the velocity and motion of the satellite. It was, then, in this manner that Roemer proposed to ascertain the motion of the satellite. But, in order to obtain this estimate with the greatest possible precision, he proposed to continue his observations for several months.

Let us, then, suppose that we have observed the time which has elapsed between two successive eclipses, and that this time is, for example, forty-three hours. We ought to expect that the eclipse would recur after the lapse of every successive period of forty-three hours.

Imagine, then, a table to be computed in which we shall calculate and register beforehand the sidereal time at which every successive eclipse of the satellite for twelve months to come shall occur, and let us conceive that the earth is at E, at the commencement of our observations: we shall then, as Roemer did, observe the times at which the eclipses occur, and compare them with the corresponding times registered in the table.

Let the earth, therefore, at the commencement of these observations, be supposed at E, fig. 65, where it is nearest to Jupiter. When the earth has moved to E", it will be found that the occurrence of the eclipse is a little later than the time registered in the table.

As the earth moves from E" towards E"", the actual occurrence of the eclipse is more and more retarded beyond the time of its computed occurrence, until at E"", in conjunction, it is found to occur about sixteen minutes later than the calculated time.

By observations such as these, Roemer was struck with the fact that his predictions of the eclipses proved in every case to be wrong. It would at first occur to him that this discrepancy might arise