Monday, 11 November 2013

Lecture 5: On the Moon

Lecture 5

On the Moon

Eclipseos Solis Totalis 12 Maji 1706

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Thursday April 6, 2 o'clock, Mr Babbage Astronomy Lecture V. On the appearance and phases of the Moon; its orbit. Cause of Eclipses. Theory of Tides. The Moon's Libration. On the constitution of its surface, and the appearance which would be exhibited to a spectator situated on it.

            Next in point of importance to the theory of the apparent motion of the stars and to the determination of the magnitude of the globe we inhabit are the motions of the Moon and Sun. The natural arrangement might at first seem to require our attention to be directed to this latter body, but there are other considerations which indicate the convenience of a different arrangement. The Moon is, as we shall presently discover, nearer to the Earth than any other body with which we are acquainted, and owing to its appearance above the horizon during the absence of the Sun, we can readily, by comparing it to some of the stars in its course, determine its motions.

We will suppose that our astronomer, who has constantly occupied himself in observing the positions of the stars, has not omitted to bestow his attention on this interesting luminary, and that he has remarked the various particular circumstances and appearances which attend its motion and which change daily. These different appearances which are generally termed the phases of the Moon constitute in fact its most striking characteristic and were calculated to excite the earliest attention among astronomers.

            The Sun always  presents to us a disk perfectly circular. The Moon, on the contrary, only exhibits a round appearance during a few hours. Her figure changes rapidly and in the space of 29 or 30 days, which she occupies in making the circuit of the heavens, she presents all possible variations between a circular disk perfectly illuminated and an obscure crescent almost invisible.

            This revolution, between 13 and 14 times more rapid than that of the Sun, probably in ancient times, furnished mankind with the idea of dividing time into months; and possibly into weeks, as 7 days is nearly the interval of time which elapse between each of her quarters. That this division of time is more ancient than any other is, I think, evident from this circumstance, that it is interwoven with the structure of language. It is a remarkable fact that every country where that period which we term month is made use of, the name which they give to it is always derived from that which they assign to the Moon. This clearly indicates its origin and likewise shows that the formation of the period must have been nearly that of language.

The ancients made use of these phases for the purpose of regulating time before they enquired into their causes. This cause, however, could not long escape the notice of a reflective mind. In order to follow the phenomena in the most methodical manner, although not perhaps in the most natural one, let us consider the Moon in the evening just after sunset, when she herself is near the horizon and about to disappear. The Moon then appears to us a narrow crescent [bounded] on one side by a circle and on the other by an ellipse. She sets a few minutes after the Sun and we may observe that the luminous segment is turned towards that body, that the line which joins the two points of the crescent is inclined to the horizon, and that these two points, which are called cusps, are equally distant from the Sun.

            From day to day the crescent increases, but the point or cusps still continue to terminate its diameter. The interior curve becomes [a] narrower ellipse and the Moon sets later every evening and illuminates us during a greater part of the night. The line which joins the cusps is always inclined to the horizon when the Moon sets, and its smaller diameter is always directed to the Sun. On the seventh day the Moon appears like a semicircle and is visible nearly half the night. On the following days the luminous portion continues to increase: the interior ellipse takes a contrary position.

On the 14th or 15th day the whole disk of the Moon appears illuminated and its figure is round, but the light has not a uniform tint. We may observe some points which are more luminous, others that are darker than the rest of the surface. With a telescope we may perceive large round holes, which are deep like wells, and which are luminated even to the bottom. On every part there appear places which are elevated above or depressed below the rest of the surface, and since at this time no shadow is projected by the most elevated point on the lower grounds, our observer will do well to profit by this circumstance and also of its being visible during the whole night for the purpose of making a drawing of it, and determining the relative position of the most remarkable asperities.

            The next day the western side of the Moon begins to become less distinctly terminated. On each succeeding day it becomes more and more obscure. The illuminated part is terminated by an ellipse which gradually flattens. On the 22nd day the Moon again appears an illuminated semicircle. All the phenomena which we have observed reappear in an  order. The mountains again project shadows and the enlightened part diminishes. About the 28th day the Moon rises but a short time before the Sun, and is scarcely visible for a few days, after which it reappears on the west in the form of a fine narrow crescent.

During the whole course of a revolution the enlightened part of the Moon is always nearest to the Sun, and the dark part is turned from that body. Another important remark will result from these observations. In all the phases of the Moon, the spots, and other remarkable points, always occupy the same parts of the lunar disc. The obscure part is not so completely dark, but that with a little attention the whole disc may be perceived, on which may sometimes be distinguished the most remarkable spots, which are thus found always to preserve their places. The excavations resembling wells are now not illuminated to the bottom, as they were when we observed them on the day of the full Moon, but it may be distinctly seen that the shadow of one part of their edge is projected on the opposite side. From these remarks it evidently follows that the Moon is not luminous of itself, that she only shines by a borrowed and reflected light, and it also appears that she always turns towards us the same face.

            We shall likewise easily conclude, although not quite so quickly, that the Moon is not simply a flat surface, but that it is a globe whose enlightened side is but seldom directed entirely towards us.

It was imagined by some of the ancients that the Moon was a flat surface resembling a mirror and that the appearances on its disc were owing to the reflection of the Earth's surface. This opinion however scarcely needs refutation. It is obviously incorrect. The apparently elliptic curve which terminates the enlightened surface is in fact a great circle of the lunar globe which is presented to us in [an] oblique direction. It is well known that in painting, when we wish to depict a circular object which is not quite in front of us, its perspective representation is an ellipse.

            But, if the Moon is an opaque body, it is natural to enquire whence she derives the light by which she shines. There is not much difficulty in the decision on this point. We only possess the knowledge of one body in the universe that shines with sufficient lustre to lend its splendour to the Moon. The following considerations will confirm this conjecture. At the time of the full Moon, when this luminary possesses the greatest brightness, she passes the meridian nearly at twelve o'clock at night. The Sun is then distant from her almost or about half a circle. It is consequently in the opposite side of the heavens. I say "almost" for it is evident that, if the Sun were exactly in opposition to the Moon, the interposition of the Earth would prevent the transmission of light to this latter body.

The Earth as well as the Moon receives light from the Sun, and it must also reflect part of the rays which it receives. From this circumstance it happens that in lunar eclipses the Moon is still visible, though very obscurely, for from the relative magnitudes of the two bodies the Earth will, to an inhabitant of the Moon, appear thirteen times as large and afford thirteen times as much light as we receive from that body.

            It is well known that when the solar rays are concentrated by means of a mirror or by a large convex lens the effects are very powerful. The heat produced is intense and metals and other substances presented to it are immediately melted. It is natural to suppose that if the Sun's rays produce an effect those of the Moon which are borrowed from the same source would also produce some small degree of heat: it was not expected that the heat thus generated would be very considerable but merely that it might be sufficient to be made sensible. An experiment was therefore made with a view to determine this point: a large convex glass was made use of which by the Sun's rays had melted a small piece of platina in 3 seconds. With this powerful instrument the light of the Moon was collected and condensed upon the ball of a delicate thermometer: but not the least elevation of temperature was observed. This certainly appears rather unfavourable to the opinion of the Moon receiving illumination from the Sun, but it fortunately admits of an explanation. It is found that those bodies which reflect light do not always reflect a proportionable quantity of heat. There is a striking difference in this point between a silvered looking glass and a polished plate of metal. Both reflect nearly the same quantity of light but the quantity of heat reflected is very different. The glass reflects very few of the rays which produce heat, while the metal speculum reflects almost all. The glass, on the contrary, absorbs into its substance the rays of heat, and consequently becomes warm, while the mirror of metal propelling them from its surface receives  accession of temperature.

The Moon appears to be constituted of materials which possess in an eminent degree the property we have just described as belonging to the glass. She reflects many of the rays of light but absorbs the whole of those which produce heat. This appears to be the case with our Earth and with the other planets, and we may admire the wise provisions of Nature, by which each body retains those parts which contribute to the warmth and comfort of its inhabitants, while it reflects from its surface the remainder for the illumination of distant worlds. Without this admirable contrivance we should, during the presence of the Sun, be burnt with heat and in his absence suffer the extreme of cold.

            It will now become necessary for our astronomer to determine the path of the Moon. In this enquiry he will not find much difficulty. It is easy to measure its distance from any star to which it approaches. By means of the sextant, and by repeating this a few nights he will find the number of degrees it passes over in 24 hours. And at the end of about 27 days and  he will perceive it to have arrived near the same point at which he first began to observe it.

From these observations he will conclude that the Moon revolves round the Earth, that it is nearer than any of the other celestial bodies, for in its progress it eclipsed all the stars in its path and, when we are deprived of the light of the Sun in an eclipse, the Moon is situated between us and that luminary. It will be further observed that the interval between two full Moons is about 29 days 12 hours. It seems natural to suppose that the Moon would suffer an eclipse every time she is in opposition to the Earth, for this body, being perfectly opaque, will necessarily cast a long shadow in a direction opposite to that from which [s]he is illuminated, and in consequence of the revolution of the Moon round the Earth, it might be expected that the Moon would enter this shadow once every month and suffer an eclipse. This would be the case if the three bodies were always in the same plane, but the orbit of the Moon is inclined at a small angle to the line which joins the Sun and the Earth, and in consequence of this inclination it does not at every revolution enter the Earth's shadow.

From the same cause it results that the Moon does not always pass exactly between the Earth and the Sun so as to cause an eclipse of the latter body. It should be observed that in an eclipse of the Moon the commencement is visible precisely at the same moment over all parts of the globe, provided she is above the horizon. The reason is that the Moon herself suffers a deprivation of light, but this is not the case with the Sun: an eclipse of this body being caused by the passage of the Moon between the Earth and the Sun. It will begin at different times in different parts of the globe. In some parts it will be total the whole disc being hid, or perhaps it may be annular, that is the Moon will only cover the central part, and leave a ring of light all round. The same eclipse may in other countries be partial [for example: a similar one was observed at London in 1764].

            An eclipse of the Sun always begins on the western side and ends on the Eastern one, and in this latitude it seldom happens that total darkness continues for more than four if 5 minutes. Generally in a solar eclipse the Moon's disc is covered with a faint light, which we have before observed is owing to the reflexion from the illuminated part of the Earth. Though the darkness in solar eclipses is not of long duration, it is, while it continues, very intense. The stars and planets become visible and instance[s] are related of birds going to roost. A singular appearance takes place in these eclipses: the Moon's limb is surrounded by a pale circle of light, which some astronomers have considered as an indication of a lunar atmosphere, but others as the atmosphere of the Sun, because it has been observed to move equally with the Sun and not with the Moon. And it is generally believed that the Moon has no atmosphere, or at least a very small and rare one.

With respect to the number of eclipses of both luminaries it may be observed that there cannot be fewer than two nor more than seven in one year. The most usual number is four and it is rare that more than six occur. Generally speaking there are more solar than lunar eclipses, nearly in the proportion of 4 to 3, but if we consider any particular spot its inhabitants will see more eclipses of the Moon than of the Sun, because a lunar eclipse is visible to a whole hemisphere at once, whereas a solar eclipse is confined to a small tract of country.

            Since eclipses depend on the relative situations of the Earth, the Moon and the Sun, it is evident that when these bodies arrive at the same position the eclipses will begin again to recur in the same order. It was from observing this that the ancients discovered a period of nearly 18 years at the end of which the same eclipses happened in the same order. It was called the Chaldean Saros and contains 18 Julian years 11 days 7 hours 42 minutes. This was probably the method made use of by Thales to predict the eclipses for which he was celebrated.

The doctrine of eclipses is of considerable advantage and utility. From it we may deduce a strong confirmation of the conclusions we arrived at respecting the figure of the Earth, for in all lunar eclipses the shadow of the Earth on the Moon's disc is always bounded by an arc very nearly circular, and this could not happen unless the shadow of the Earth were in all situations nearly conical, and consequently the Earth itself nearly spherical. Lunar eclipses also prove that the Sun is larger than the Earth, and the Earth larger than the Moon; that the Sun is larger than the Earth appears because the shadow of the Earth ends in a point, which it could not do if the Sun were smallest; and that the Earth is larger than the Moon because the whole of the Moon's body is sometimes involved in the Earth's shadow, and a section of this shadow at the Moon's orbit is much less than the Earth itself.

            Eclipses also that occur in similar circumstances and at distant intervals are of use in ascertaining the periods of the Moon's motions. In Geography the advantages resulting from them are great. By their means the longitudes of different places may be discovered. Those of the Moon are most serviceable for this purpose.           We have already seen what great assistance they afford to history and to the examples already adduced. I may be permitted to add another. The time of a very celebrated event in the history of our own country has been ascertained with great accuracy in considerable degree though not entirely by means of an eclipse. The invasion of Julius Caesar is stated by some historians to have [taken place] in the year 52 before Christ, by others in the year 54, and some place it as early as 56. But Dr. Halley has determined the time of this invasion to a day and says that the landing was effected on the 26th August, in the year of the world 3950, or the 55th before the usual Christian era. He was lead to this decision partly by calculating the time of the lunar eclipse, of which Drusus made such successful use to quiet the Pannonian army upon the death of Augustus, and partly by computing the time of full Moon previous to which Caesar landed his legions, and also by considering the phenomena of the tides on the Kentish coast at that particular period.

Of all the phenomena presented to us by Astronomy eclipses are certainly the most remarkable. In every age they have excited the highest interest; in early periods they were attended with the fears and terrors of the ignorant: in more modern times the accuracy with which every circumstance attending them is predicted has produced equal admiration. The theory is now so well understood that they are always mentioned in the Almanac. I shall just notice some of the most remarkable which have occurred during the last century.

            On the 12th May 1706 there was a total eclipse in the southern parts of France and Spain; at Paris about eleven digits were eclipsed. (It should be observed that the disc of the Sun or Moon is imagined to be divided into twelve parts called digits and the magnitude of an eclipse is measured by the number of these digits which are covered.) This eclipse was observed by Cassini and he made the following remarks on it. "The duration of total darkness was about five minutes. In this interval of time the stars and planets became visible. The cattle appeared terrified and returned towards their stables with evident marks of consternation. The bats and owls quitted their retreats while the birds of the day betook themselves to their places of rest. The inhabitants of the country ignorant of the cause of this wonderful phenomenon participated in the general terror. The obscurity which prevailed," observed Cassini, "could not be compared to the darkness of the night nor yet with the twilight; it had a gloom peculiar to itself. Round the obscure disc of the Moon there appeared a luminous ring which extended on all sides to about the distance of 4 degrees. The moment the least portion of the Sun's disc re-appeared the effect was instantaneous like lightning, and the superior splendour of his rays dissipated the faint gleam of this luminous ring."

In the year 1776 there was a great eclipse of the Sun; it is particularly remarkable from the observations of some Spanish astronomers. They observed a luminous point near the border of the Moon, which they explained by supposing it to be an opening in the body of the Moon through which the Sun's rays penetrated. Subsequent observations have rendered it very probable that this luminous spot was a volcano which has been discovered by Dr. Herschel and since that time been frequently observed. It must have been in a state of active eruption. This eclipse was total and annular at about the middle of the Atlantic Ocean.

            Among the remarkable eclipses of the last century may be mentioned that of 28th July 1748. It was total annular for some parts of Scotland. The French astronomer Lemonnier travelled from Paris to Edinburgh on purpose to observe this singular phenomenon and profited by making observations, which we have rarely an opportunity of repeating.

In the year 1764 there occurred another total eclipse of the Sun. It excited much attention among astronomers, who usually, on the expectation of these phenomena, calculate the time of the various appearances and draw a plan of the eclipse. One of the best of these published at this time was entitled- A Map of the Passage of the Moon's Shadow across Europe during the Total and Annular Eclipse of 1st April 1764. Its singularity, however, consisted in this, that it was the work of three ladies. The calculations were from the pen of Madame Lepante a pupil of the astronomer Lalande, the engraving was executed by another lady and the ornamental designs and embellishments were the work of a third.

            It was soon found from observation that the Moon moved round the Earth and it would perhaps be natural to conclude that the curve it describes is a circle, for this is one of the most simple in Nature. To verify this hypothesis will not be a matter of much difficulty. It is well known that, when objects of equal magnitude are viewed at the same distance, they appear of equal size: and that, if we increase our distance from an object, it appears smaller; thus a person on the top of a high tower sees the people walking below him much diminished in size, and they always appear smaller the higher he ascends. Let us apply these principles to the case of the Moon. If that body moved in a circle round the Earth she is always at the same distance and must consequently always appear of the same size. A difficulty may now arise: how shall we ascertain the apparent magnitude of a heavenly object? The eye is not a sufficiently accurate judge. For this purpose several devices have been made use of. They all go by the name of micrometers.

The description of one of them will be sufficient for my present purpose. When describing the transit instrument I mentioned that it was usual to place small wires in the field of view of the telescope. In that case the usual number is six, but for the purpose of a micrometer two are sufficient. A screw must be adapted to the instrument, by means of which these two wires may be made to approach or recede from each other at pleasure. If now any object, such as the Moon, be viewed through a telescope to which this micrometer is attached, the screw must be turned until the disc of the object be contained between the two wires; if at any subsequent period the telescope be again pointed to the same object (supposing the wires still at the same distance), it will readily be observed whether the object exceeds in breadth the distance of the wires or falls short of it. With an instrument thus prepared let us suppose our astronomer to commence his observation, and, having made the two wires coincide accurately with the edges of the Moon, let him turn the screw until the two wires touch each other. Suppose that it takes 20 revolutions of the screw to open the wires to the distance of the Moon. Then, about 14 days afterwards, let him again examine this body and he will find that its diameter is increased, for it will now require 21 turns of the screw to open the wires to such a distance as to include the disc of the Moon.

It need scarcely be observed that it is not the variable illuminated part which should be measured but the distance between its two horns or cusps. From these observations our astronomer finds that in one part of its revolution the apparent diameter of the Moon is ?th part greater than in the opposite quarter, and he will consequently conclude from the principle we have just stated that the Moon is one twentieth part nearer in one part of its course than it is in another. This immediately solves the question he had proposed. The Moon does not revolve in a circle of which the Earth is the centre, for it is evident that its distance from the Earth is variable. From observations on the Moon's apparent diameter it may be presumed that it revolves in an ellipse, and our subsequent enquiries will confirm this supposition.

            While our astronomer is measuring the diameter of the Moon his attention will naturally be attracted to the appearance of the various spots and figures on its surface. These, as they appear immovable, will furnish a ready method of ascertaining whether it has a revolution on its axis. After viewing it during several revolutions he will observe that the same spots always appear in the same place, and that the same side is constantly turned to the Earth. From this circumstance it has sometimes been erroneously inferred that the Moon does not revolve on its own axis. This, however, is not a legitimate deduction from our observations. The Moon, by keeping the same face to the Earth during a whole revolution in its orbit, must have turned once round its axis.

Thus then the general law is established that the Moon revolves round its axis in exactly the same time that it moves round the Earth. From this it would seem to follow that not more than one half the Moon's surface could ever be visible to an inhabitant of the earth, but there are some modifications by which we are enabled to see rather more than one half. This is owing to what is called the Moon's libration.

            One of the causes of this libration is the unequal motion of the Moon in her orbit, for though both the revolution round the Earth and that round her axis are completed in the same time, yet they are not both of them uniform motions. In consequence of this there is an apparent oscillation of the Moon by which we see a few degrees on each side alternately more than a hemisphere. This is called the Moon's libration in longitude.

            The Moon is also subject to a libration in latitude. It arises from the inclination of her axis to the plane of her orbit, and its effect is to render visible sometimes the parts of her surface adjacent to the north, and sometimes those situated near the south pole.

The third species of libration to which the Moon is subject was discovered by Galileo. If the two former librations did not exist, the same face of the Moon would be turned not to a spectator on the surface but to an imaginary spectator in the centre of the Earth. Now two lines drawn respectively from the centre and surface of the Earth to the centre of the Moon form an angle of some magnitude. Hence when the Moon rises parts of her surface situated towards the boundary of her upper limb are seen by a spectator which would not be seen from the Earth's centre. As the Moon rises these parts disappear, but, when the Moon having passed the meridian declines, other parts situated near that boundary, which, whilst the Moon was rising, was the lower [limb], are brought into view and which would not be seen by a spectator at the centre of the Earth. The greatest effect of this diurnal libration will be perceived by observing the Moon first at her rising and then at her setting. It should be observed that this species of libration, as well as the two preceding ones, are merely optical; they arise from the circumstances in which we are placed not from any oscillating motion in the Moon.

In considering the singular coincidence (which takes place in the equal duration of the Moon in her orbit and her rotation round her axis) we are led to enquire whether there is any physical cause to which it can be attributed, whether it is a necessary consequence of some more general law or whether it is the effect of chance. The reasoning by which these questions are answered is among the most difficult and successful efforts of human enquiry. It will be sufficient at present merely to state the results. In the first place it soon appeared that the improbability of this coincidence, being the effect of chance, is excessively great. It then remained to enquire what might be the cause, and this required a knowledge of the shape of the Moon.

            It is found from theory, as well as actual mensuration, that the Earth is a flattened spheroid. It is evident that it is on theory alone we attain a precise knowledge of the Moon's figure. From this it is found that the Moon will not be quite globular but must have a small compression at the poles. This, however, is too slight to be sensible even to our best instruments.

There is, however, another and greater deviation from a perfect sphere. Owing to the great attraction of the Earth that diameter of the Moon which passes through the Earth's centre will be larger than the other diameters. In consequence of this superior thickness of the Moon in the direction of the Earth it would happen that, if from any circumstance that diameter of the Moon were turned a little out of its direction, it would return to its original position. This effect is owing to the attraction of the Earth and is similar to a pendulum drawn a little from the perpendicular; it returns and oscillates to and fro. Another consequence of this attraction is that, if the time of the Moon's revolution on her axis had at first been nearly but not quite equal to that in her orbit, this attraction of the Earth would have rendered them quite equal.

            It appears then that the Earth causes by its attraction the Moon to assume a certain figure. In consequence of this figure, and also of the Moon having a slow rotation on its axis, it is, by the Earth's attraction, always retained with the same face directed towards us. If the Moon is thus affected by the attraction of the Earth it might probably be enquired, since the action of gravity is reciprocal, why the same part of the Earth is not always directed towards the Moon. To this it is a sufficient answer to state that the Earth possesses a quick rotatory motion, but it will be both curious and interesting to trace the different effects of the same cause modified by various circumstances.

The Earth by its attraction preserves the same face of the Moon constantly directed towards us. The effect of the Moon's attraction on our planet is to create tides in the ocean. It is well known that the more distant a body is the less will be the force of attraction exerted on it. The surface of the Earth is nearer the Moon than its centre, and this again is nearer than the opposite side. In consequence of this the waters will rise at the part immediately directed to the Moon, and also in the part diametrically opposite.

            If the Earth and the Moon were without motion and the Earth covered all over with water, the attraction of the Moon would raise it up in a heap in that part of the ocean to which the Moon is vertical, and there it would always continue, but by the rotation of the Earth on its axis each part of its surface is presented to the action of the Moon, which causing an elevation in two opposite hemispheres thus produces two floods and two ebbs every day. The effect of the Moon is not confined to the parts to which she is vertical but acts, though in a less degree, on others adjacent. If the Moon were stationery there would be exactly two tides in twenty four hours, but, as this body moves in her orbit, it takes rather more than 26 hours for the same spot on the earth to return to the same situation with respect to the Moon. From this cause it arises that two tides take place in about 24h 50m. this is the reason why the high tide/water is usually  hour later each day than it was the preceding.

That there is a great variation in the height of the tides is a fact well known to everyone. There are two causes which produce this effect. The waters of the ocean are affected by the attraction of the Sun as well as by that of the Moon, but owing to the immense distance of the former body it produces but a small effect. Sir I. Newton computed that the force of the Moon raised the waters in the great ocean 10 feet whereas that of the Sun only produced an elevation of only two feet. When the attraction of both Sun and Moon act in the same direction, that is at new and full Moon, the combined forces of both raise the tide 12 feet. But when the Moon is in her quarters the attraction of one of these bodies raises the water while the other depresses it. In this case the smaller force of the Sun must be subtracted from that of the Moon. Consequently the tides will be no more than 8 foot high. When the tides are highest they are called spring tides and are caused by the united actions of the Sun and Moon. When the tides rise least they are called neap tides and are owing to the difference of the action of these two bodies. This is the general principle on which the tides depend, but particular circumstances will considerably modify the effects. In lakes and seas of small magnitude there will be scarcely any perceptible tide for the action of the Moon will be nearly equal in every part. This is the case in the Black Sea and even in the Mediterranean. If the ocean communicates with any narrow inlet the tides will rise to a great height. At the mouth of the River Indus the elevation is above 30 ft. This is the reason of the great rise at Bristol and other places similarly situated. A question intimately connected with the theory of the tides has lately occupied the attention of one of the greatest philosophers from whose labours the science of Astronomy has derived immense improvements. I allude to the question relative to the stability of the

equilibrium of the ocean.

            There are several irregular causes such as hurricanes and earthquakes which agitate the sea, elevate it to a great height and sometimes oblige it to forsake its limits. We find from observation that it has always a tendency to return to its former state, and that the resistance it experiences would soon bring it to this state even without the action of the Sun and Moon. This tendency constitutes what is called a stable equilibrium. Amongst the infinite variety of disturbances to which it is liable from irregular causes, it might be supposed impossible that some extraordinary cause may communicate to it a shock which, though inconsiderable at its origin, may augment continually and elevate it above the highest mountains. If this were the case we should have an explanation of several phenomena in natural history and at least the possibility of such an occurrence is a subject worthy of our enquiry.

Laplace has directed his attention to this interesting question with great success. He has investigated the conditions which are necessary for the absolutely stability of the ocean and has examined whether these conditions exist in Nature. The result of this investigation is, that the equilibrium of the ocean is stable if the mean density of the Earth is greater than that of the water. And this is found to be the fact from experiments on pendulums and the attractions of mountains.

            It appears then that the equilibrium of the ocean is stable, and if as appears certain the waters have formerly covered continents which are now at present much above its level, we must search for other causes than a want of stability in the ocean. Another singular result of Laplace's analysis is that this stability would cease to exist if the mean density of the sea exceeded that of the Earth. Thus if the ocean instead of water consisted of quicksilver extraneous causes might impress on it oscillations which might continually increase in magnitude and which subverting the loftiest mountains would involve in one universal ruin this beautiful abode of Man. Such destructive revolutions are not the appointed doom of the planet we inhabit. The general deluge, which is alike certain from history and from an examination of the structure of the Earth, appears to have been arisen from the immediate will of that power which created and not from any secondary cause.

To determine the distance of the Moon from the globe round which it revolves has long been a problem with astronomers. Its solution has progressively increased in precision. We have seen that by means of micrometer the apparent diameter of the Moon may be ascertained. In order to determine her distance we must find the angle under which the Earth would appear if we were placed on the surface of the Moon. If we suppose an inhabitant of the Moon measuring the apparent diameter of the Earth, it is this angle we are in search of. By an easy calculation we may from this angle and the Earth's diameter determine the distance of the Moon. It may be stated in round numbers at 240,000 miles. This is in fact about 1200 miles too much. Astronomers, however, have not confined themselves to determining the Moon's distance they have ascertained her magnitude and weight; they have measured the height of the mountains which cover her surface and have determined her attractive force. The diameter of the Moon is about 2180 miles; this is a little greater than  of that of the Earth. If, for instance, we suppose a spring is bent 5 inches by a weight of 10 lbs and if the same spring is transported to the Moon's surface, the same weight of 10 lbs will only bend it one inch.

On directing a telescope of moderate power towards the Moon we perceive that it is a body much resembling our Earth, covered with appearances of the form of mountains, the greater part resembling those which form the craters of our volcanoes. We perceive a number of mountains in the form of  cones on whose summits are cavities resembling craters. Volcanic mountains on our globe present the same appearance. These mountains cast a shadow on the face of the Moon in a direction opposite to that of the Sun. This shadow diminishes as the mountain becomes less obliquely exposed to the Sun's rays, and when the Sun has passed its meridian the shadow falls on the opposite side.

            The mountains are, comparatively speaking, much more elevated than those of the Earth. Galileo estimated some of the at 3 miles. This, however, is considerably too great. Schroeter, who occupied himself with great success in examining the phenomena of the Moon, has found that the depths of the largest cavities are about 18,000 ft. below the Moon's surface and the elevation of the loftiest mountains are about 25,000 [ft.], that is about 3,000 ft. higher than Chimboraco [in Ecuador], which is the highest  mountain on our Earth. Schroeter has made a very curious remark on this subject. He observes that the highest mountains on the Earth, on the Moon, on Mercury and on Venus are all situated in the southern hemisphere, and that the deepest cavities in the Moon are in the same hemisphere. From this he concludes that the southern parts of these globes have undergone the greatest revolutions and been subjected to the most powerful actions.

I have mentioned that most of these mountains are volcanic. This fact is proved by an observation of Dr. Herschel. In the beginning of May 1783 he saw two mountains gradually forming on the Moon's surface. On the 4th he perceived a luminous point near the spot called Aristarchus. This light appeared still more vivid on the 19th and 20th of April following and left no doubt that it was a volcano on this part of the Moon. This new discovery was soon spread over Europe and excited the attention of astronomers. The volcano was not however recognised by foreigners -perhaps the eruption had ceased. It reappeared in March 1794 and was distinctly perceived by two people at the same instant, who were nearly 100 miles distant from each other. It appeared to the naked eye like a star on the obscure part of the Moon. This must undoubtedly have been a large eruption of lava, but we have on our own globe the remains of one issuing from Hecla in Iceland which extends 300 miles in length. This to an inhabitant of the Moon would have been very distinctly visible.

With respect to the dark spots on the Moon we are not so well informed. All that can be said of them with certainty is that they reflect less light than the rest of its surface. But whether they are seas or whether they are forests is quite undecided.

            Whether the globe we are now considering is a place of abode for rational beings or whether it is a desolate waste is a question which has been frequently disputed. I shall at present state the probability of our determining this question and the means we possess of effecting it. If an object occupying as much space as London were placed in the middle of the lunar disc, it is easy to prove that it would be visible by means of a telescope magnifying 100 times. A slight extension of this calculation will inform us that with such a telescope we might distinguish a spot of about 4,000 feet in diameter. With a telescope which magnified 50 times as much or 5,000 times we might distinguish an object of about 80 feet in diameter. Dr. Herschel's 7 foot telescopes admit of such a power. But, if we enquire what would be the magnifying power necessary to render visible an object of about 6 feet, it will be found that it must be at least 60,000 times.

From this we may judge that there is little probability of our ever seeing, on the surface of the Moon, beings of the same species with ourselves. Dr Herschel imagines he has observed changes which could only be produced by the labour of the inhabitants of the Moon. The only method of deciding the question is by examining particular districts of the Moon with telescopes of large power and making very accurate maps of them. This labour has been undertaken by Schroeter the celebrated astronomer of Liebenthal.

            The phenomena which would be observed by a spectator at the Moon are of a singular nature. Since the Moon revolves round the Earth in the space of a month and always presents the same face to it it follows that the whole surface is successively turned towards the Sun. Thus a lunar day will be nearly equal to 15 of ours and their nights will be of equal duration. Such would be the appearance in respect to the Sun. But with regard to the Earth it would be much more varied and singular. An inhabitant of the Moon situated in the centre of that hemisphere which is always directed towards [the Earth] will constantly see [it] in his zenith. It will appear to oscillate a few degrees on each side owing to the libration. But an inhabitant of the hemisphere on the opposite side to the Earth will never see it.  But the most singular spectacle will be to those inhabitants, if there are any who live on the borders of the lunar disc. They will see the Earth sometimes rise above the horizon a few degrees, and then by a retrograde motion replunge itself below and disappear during an equal time. It appears then that the two hemispheres of the Moon have a very different lot. One of them during a night equal to 15 of our days never sees the Earth. The hemisphere directed towards us enjoys more advantages: although she has a night of 15 days in length her inhabitants have always the Earth above their horizon, which affords, when full, nearly 14 times as much light as we receive from the Moon. Just such an illumination we should ... [remainder of lecture missing]