Next in order of publication of his results stands the name of Colding, a Danish engineer, who about the year 1843 presented a series of memoirs on the steam engine to the Royal Society of Copenhagen, in which he put forth views almost identical with those of Mayer.

Last in publication order, but foremost in the importance of his experimental treatment of the subject, was our own countryman, Dr. Joule of Manchester. “Entirely independent of Mayer, with his mind firmly fixed upon a principle, and undismayed by the coolness with which his first labours appear to have been received, he persisted for years in his attempts to prove the invariability of the relation which subsists between heat and ordinary mechanical power.” (We are quoting from Professor Tyndall’s valuable work on “Heat considered as a Mode of Motion.”) “He placed water in a suitable vessel, agitated the water by paddles, and determined both the amount of heat developed by the stirring of the liquid and the amount of labour expended in its production. He did the same with mercury and sperm oil. He also caused discs of cast iron to rub against each other, and measured the heat produced by their friction, and the force expended in overcoming it. He urged water through capillary tubes, and determined the amount of heat generated by the friction of the liquid against the sides of the tubes. And the results of his experiments leave no shadow of doubt upon the mind that, under all circumstances, the quantity of heat generated by the same amount of force is fixed and invariable. A given amount of force, in causing the iron discs to rotate against each other, produced precisely the same amount of heat as when it was applied to agitate water, mercury, or sperm oil. * * * * The absolute amount of heat generated by the same expenditure of power, was in all cases the same.”

“In this way it was found that the quantity of heat which would raise one pound of water one degree Fahrenheit in temperature, is exactly equal to what would be generated if a pound weight, after having fallen through a height of 772 feet, had its moving force destroyed by collision with the earth. Conversely, the amount of heat necessary to raise a pound of water one degree in temperature, would, if all applied mechanically, be competent to raise a pound weight 772 feet high, or it would raise 772 pounds one foot high. The term ‘foot pounds’ has been introduced to express in a convenient way the lifting of one pound to the height of a foot. Thus the quantity of heat necessary to raise the temperature of a pound of water one degree Fahrenheit being taken as a standard, 772 foot-pounds constitute what is called the mechanical equivalent of heat.”

By a process entirely different, and by an independent course of reasoning, Mayer had, a few months previous to Joule, determined this equivalent to be 771·4 foot-pounds. Such a remarkable coincidence arrived at by pursuing different routes gives this value a strong claim to accuracy, and raises the Mechanical Theory of Heat to the dignity of an exact science, and its enunciators to the foremost place in the ranks of physical philosophers.

In linking together the labours of the two remarkable men above alluded to, Prof. Tyndall remarks, that “Mayer’s labours have in some measure the stamp of profound intuition, which rose however to the energy of undoubting conviction in the author’s mind. Joule’s labours, on the contrary, are an experimental demonstration. Mayer thought his theory out, and rose to its grandest applications. Joule worked his theory out, and gave it the solidity of natural truth. True to the speculative instinct of his country, Mayer drew large and mighty conclusions from slender premises; while the Englishman aimed above all things at the firm establishment of facts.... To each belongs a reputation which will not quickly fade, for the share he has had, not only in establishing the dynamical theory of heat, but also in leading the way towards a right appreciation of the general energies of the universe.”

But from these generalities we must pass to the application of the mechanical theory of heat to our special subject. We have learnt that every form of motion is convertible into heat. We know that the falling meteor or shooting star, whose motion is impeded by friction against the earth’s atmosphere, is heated thereby to a temperature of incandescence. Let us then suppose that myriads of such cosmical particles came into collision from the effect of their mutual attraction, or that the component atoms of a vast nebulous mass violently converged under the like influence. What would follow? Obviously the generation of an intense heat by the arrest of converging motion, such a heat as would result in the fusion of the whole into one mass. Mayer, in one of his most remarkable papers (“Celestial Dynamics”) remarks that the “Newtonian theory of gravitation, whilst it enables us to determine, from its present form, the earth’s state of aggregation in ages past, at the same time points out to us a source of heat powerful enough to produce such a state of aggregation—powerful enough to melt worlds: it teaches us to consider the molten state of a planet as the result of the mechanical union of cosmical masses, and to derive the radiation of the sun and the heat in the bowels of the earth from a common origin.”

And the same laws that governed the formation of the earth, governed also the formation of the moon: the variations of Nature’s operations are quantitative only and not qualitative. The Divine Will that made the earth made the moon also, and the means and mode of working were the same for both. The geological phenomena of the earth afford unmistakeable evidence of its original fluid or molten condition, and the appearance of the moon is as unmistakeably that of a body once in an igneous or molten state. The enigma of the earth’s primary formation is solved by the application of the dynamical theory of heat. By this theory the generation of cosmical heat is removed from the quicksands of conjecture and established upon the firm ground of direct calculation: for the absolute amount of heat generated by the collision of a given amount of matter is (of course, with some little uncertainty) deducible from a mathematical formula. Mayer has computed the amount of heat that the matter of the earth would have generated, if it had been formed originally of only two parts drawn into collision by their mutual attraction, and has found that it would be from 0 to 32,000 or 47,000[1] Centigrade degrees, according as one part was infinitely small as compared with the other, or as the two parts were of equal size. Professor Helmholtz, another labourer in the same field of science, has computed the amount of heat generated by the condensation of the whole of the matter composing the solar system: this he finds would be equivalent to the heat that would be required to raise the temperature of a mass of water equal to the sum of the masses of all the bodies of the system to 28,000,000 (twenty-eight million) degrees of the Centigrade scale.

These examples afford abundant evidence of sufficient heat having been generated by the aggregation of the matter of the moon to reduce it to a state of fusion, and so to produce, from a nebulous chaos of diffused cosmical matter, a molten body of definite outline and size.

It is requisite here to remark that fusion does not necessarily imply combustion. It has been frequently asked, How can a volcanic theory of the lunar phenomena be upheld consistently with the condition that it possesses no atmosphere to support Fire? To this we would reply that to produce a state of incandescence or a molten condition it is not necessary that the body be surrounded by an atmosphere. The intensely rapid motion of the particles of matter of bodies, which the dynamical theory shows to be the origin of the molten state, exists quite independently of such external matter as an atmosphere. The complex mixture of gases and vapours which we term “air,” has nothing whatever to do with the fusion of substances, whatever it may have to do with their combustion. Combustion is a chemical phenomenon, due to the combination of the oxygen of that air with the heated particles of the combustible matter: oxygen is the sole supporter of combustion, and hence combustion is to be regarded rather as a phenomenon of oxygen than as a phenomenon of the matter with which that oxygen combines. The greatest intensity of heat may exist without oxygen, and consequently without combustion. In support of this argument it will be sufficient to adduce, upon the authority of Dr. Tyndall, the fact that a platinum wire can be raised to a luminous temperature and actually fused in a perfect vacuum.

But while the mass of condensing cosmical matter was thus accumulating and forming the globe of the moon, the heat consequent upon the aggregation of its particles was suffering some diminution from the effect of radiation. So long as the radiated heat lost fell short of the dynamical heat generated, no effect of cooling would be manifest; but when the vis viva of the condensing matter was all converted into its equivalent of heat, or when the accession of heat fell short of that radiated, a necessary cooling must ensue, and this cooling would be accompanied by a solidification of that part of the mass which was most free to radiate its heat into surrounding space: that part would obviously be the outer surface.

With the solidification of this external crust began the “year one” of selenological history.

The phenomena attendant upon the cooling of the mass we will consider in the next Chapter.

CHAPTER III.
THE SUBSEQUENT COOLING OF THE IGNEOUS BODY.

In the foregoing Chapters we have endeavoured to show, by the light of modern science, first, how diffused cosmical matter was probably condensed into a planetary mass by the mutual gravitation of its particles, and secondly, how, the after destruction of the gravitative force, by the collision of the converging particles of matter, resulted in the generation of such sufficient heat as to reduce the whole mass to a molten condition. Our present task is to consider the subsequent cooling of the mass, and the phenomena attendant upon or resulting therefrom. This brief Chapter is important to our subject, as we shall have frequent occasion to refer to the leading principle we shall endeavour to illustrate in it, in subsequently treating of the causes to which the special selenological features are to be attributed.

First, then, as regards the cooling of the igneous mass that constituted the moon at the inconceivably remote period when possibly that body was really a “lesser light” shining with a luminosity of its own, due to its then incandescent state, and not simply a reflector, as it is now, of light which it receives from the sun. If we could conceive it possible that the igneous mass in the act of cooling parted with its heat from the central part first and so began to solidify from its centre, or if it had been possible for the mass to have cooled uniformly and simultaneously throughout its whole depth, or that each substratum had cooled before its superstratum, we should have had a moon whose surface would have been smooth and without any such remarkable asperities and excresences as are now presented to our view. But these suppositions are inadmissible: on the contrary we are compelled to consider that the portion of the igneous or molten body that first cooled was its exterior surface, which, radiating its heat into surrounding space, became solid and comparatively cool while the interior retained its hot and molten condition. So that at this early stage of the moon’s history it existed in the form of a solid shell inclosing a molten interior.

Now at this period of its formation, the moon’s mass, partly cooled and solidified and partly molten, would be subject to the influence of two powerful molecular forces: the first of these would consist in the diminution of bulk or contraction of volume which accompanies the cooling of solidified masses of previously molten substances; the second would arise from a phenomenon which we may here observe is by no means so generally known as from its importance it deserves to be: and as we shall have frequent occasion to refer to it as one of the chief agencies in producing the peculiar structural characteristics of the moon’s surface, it may be well here to give a few examples of its action, that our reference to it hereafter may be more clearly understood.

The broad general principle of the phenomenon here referred to is this:—that fusible substances are (with a few exceptions) specifically heavier while in their molten condition than in the solidified state, or in other words, that molten matter occupies less space, weight for weight, than the same matter after it has passed from the melted to the solid condition. It follows as an obvious corollary that such substances contract in bulk in fusing or melting, and expand in becoming solid. It is this expansion upon solidification that now concerns us.

Water, as is well known, increases in density as it cools, till it reaches the temperature of 39° Fahrenheit, after which, upon a further decrease of temperature, its density begins to decrease, or in other words its bulk expands, and hence the well-known fact of ice floating in water, and the inconvenient fact of water-pipes bursting in a frost. This action in water is of the utmost importance in the grand economy of nature, and it has been accepted as a marvellous exception to the general law of substances increasing in density (or shrinking) as they decrease in temperature. Water is, however, by no means the exceptional substance that it has been so generally considered. It is a fact perfectly familiar to iron-founders, that when a mass of solid cast-iron is dropped into a pot of molten iron of identical quality, the solid is found to float persistently upon the molten metal—so persistently that when it is intentionally thrust to the bottom of the pot, it rises again the moment the submerging agency is withdrawn. As regards the amount of buoyancy we believe it may be stated in round numbers to be at least two or three per cent. It has been suggested by some who are familiar with this phenomenon that the solid mass may be kept up by a spurious buoyancy imparted to it by a film of adhering air, or that surface impurities upon the solid metal may tend to reduce the specific gravity of the mass and thereby prevent it sinking, and that the fact of floatation is not absolutely a proof of greater specific lightness. But in controversion of these suggestions, we can state as the result of experiment that pieces of cast-iron which have had their surface roughness entirely removed, leaving the bright metal exposed, still float on the molten metal, and further that when, under the influence of the great heat of the molten mass, the solid is gradually melted away, and consequently any possible surface impurities or adhering air must necessarily have been removed, the remaining portion continues to float to the last. The inevitable inference from this is that in the case of cast-iron the solid is specifically lighter than the molten, and, therefore, that in passing from the molten to the solid condition this substance undergoes expansion in bulk.

We are able to offer a confirmation of this inference in the case of cast-iron by a remarkable phenomenon well known to iron-founders, but of which we have never met with special notice. When a ladle or pot of molten iron is drawn from the melting furnace and allowed to stand at rest, the surface presents a most remarkable and suggestive appearance. Instead of remaining calm and smooth it is the scene of a lively commotion: the thin coat of scoria or molten oxide which forms on the otherwise bright surface of the metal is seen, as fast as it forms at the circumference of the pot, to be swept by active convergent currents towards the centre, where it accumulates in a patch. While this action is proceeding, the entire upper surface of the metal appears as if it were covered with animated vermicules of scoria, springing into existence at the circumference of the pot, and from thence rapidly streaming and wriggling themselves towards the centre.

Our illustration (Fig. 1) is intended, so far as such means can do so, to convey some idea of this remarkable appearance at one instant of its continued occurrence. To interpret our illustration rightly it is necessary to imagine this vermicular freckling to be constantly and rapidly streaming from all points of the periphery of the pot towards the centre, where, as we have said, it accumulates in the form of a floating island. We may observe that the motion is most rapid when the hot metal is first put into the cool ladle: as the fluid metal parts with some of its heat and the ladle gets hot by absorbing it, this remarkable surface disturbance becomes less energetic.

Now if we carefully consider this peculiar action and seek a cause for the phenomenon, we shall be led to the conclusion that it arises from the expansion of that portion of the molten mass which is in contact with or close proximity to the comparatively cool sides of the ladle, which sides act as the chief agent in dispersing the heat of the melted metal. The motion of the scoria betrays that of the fluid metal beneath, and careful observation will show that the motion in question is the result of an upward current of the metal around the circumference of the ladle, as indicated by the arrows A, B, C in the accompanying sectional drawing of the ladle (Fig. 2). The upward current of the metal can actually be seen when specially looked for, at the rim of the pot, where it is deflected into the convergent horizontal direction and where it presents an elevatory appearance as shown in the figure. It is difficult to assign to this effect any other cause than that of an expansion and consequent reduction of the specific gravity of the fluid metal in contact with or in close proximity to the cooler sides of the pot, as, according to the generally entertained idea that contraction universally accompanies cooling, it would be impossible for the cooler to float on the hotter metal, and the curious surface-currents above referred to would be in contrary direction to that which they invariably take, i.e., they would diverge from the centre instead of converging to it. The external arrows in the figure represent the radiation of the heat from the outer sides of the pot, which is the chief cause of cooling.

Turning from cast-iron to other metals we find further manifestations of this expansive solidification. Bismuth is a notable example. In his lectures on Heat, Dr. Tyndall exhibited an experiment in which a stout iron bottle was filled with molten bismuth, and the stopper tightly closed. The whole was set aside to cool, and as the metal within approached consolidation the bottle was rent open by its expansion, just as would have been the case had the bottle been filled with water and exposed to freezing temperature. Mercury affords another example. Thermometers which have to be exposed to Arctic temperatures are generally filled with spirit instead of quicksilver, because the latter has been found to burst the bulbs when the cold reached the congealing point of the metal, the bursting being a consequence of the expansion which accompanies the act of congelation. Silver also expands in passing from the fluid to the solid state, for we are informed by a practical refiner that solid floats on molten silver as ice floats on water; it also, as likewise do gold and copper, exhibits surface converging currents in the melting-pot like those depicted above for molten iron.

It may, however, be objected that metals are too distantly related to volcanic substances to justify inferences being drawn from their behaviour in explanation of volcanic phenomena. With a view therefore of testing the question at issue with a substance admitted as closely allied to volcanic material, we appealed to the furnace slag of iron-works. The following are extracts from the letters of an iron manufacturer of great experience[2] to whom we referred the question:—

“I beg to inform you that cold slag floats in molten slag in the same way cold iron floats in molten iron.

“I filled a box with hot molten slag run quickly from a blast furnace; the box was about 5½ feet square by 2 feet deep, and I dropped into the slag a piece of cold slag weighing 16 lbs., when it came to the top in a second. I pushed it down to the bottom several times and it always made its appearance at the top: indeed a small portion of it remained above the molten slag.”

Here then we have a substance closely allied to volcanic material which manifests the expansile principle in question; but we may go still further and give evidence from the very fountain-head by instancing what appears to be a most cogent example of its operation which we observed on the occasion of a visit to the crater of Vesuvius in 1865 while a modified eruption was in progress. On this occasion we observed white-hot lava streaming down from apertures in the sides of a central cone within the crater and forming a lake of molten lava on the plateau or bottom of the crater; on the surface of this molten lake vast cakes of the same lava which had become solidified were floating, exactly in the same manner as ice floats in water. The solidified lava had cracked, and divided into cakes, in consequence of its contraction and also of the uprising of the accumulating fluid lava on which it floated, more and more space being thus afforded for it to separate, on account of the crater widening upwards, while through the joints or fissures the fluid lava could be seen beneath. But for the decrease in density and consequent expansion in volume which accompanied solidification, this floating of the solidified lava on the molten could not have occurred. Reference to Fig. 3, which represents a section of the crater of Vesuvius on the occasion above referred to, will perhaps assist the reader to a more clear idea of what we have endeavoured to describe. A A are the streams of white-hot lava issuing from openings in the sides of the central cone, and accumulating beneath the solidified crust B B in a lake of molten lava at C C; the solidified crust B B as it was floated upwards dividing into separate cakes as represented in Fig. 4. (See also Plate I.)

Let us now consider what would be the effect produced upon a spherical mass of molten matter in progress of cooling, first under the action of the above described expansion which precedes solidification, and then by the contraction which accompanies the cooling of a solidified body. The first portion of such a mass to part with its heat being its external surface, this portion would expand, but there being no obstacle to resist the expansion there would be no other result than a temporary slight enlargement of the sphere. This external portion would on cooling form a solid shell encompassing a more or less fluid molten nucleus, but as this interior has in its turn, on approaching the point of solidification, to expand also, and there being, so to speak, no room for its expansion, by reason of its confinement within its solid casing, what would be the consequence?—the shell would be rent or burst open, and a portion of the molten interior ejected with more or less violence according to circumstances, and many of the characteristic features of volcanic action would be thus produced: the thickness of the outer shell, the size of the vent made by the expanding matter for its escape, and other conditions conspiring to modify the nature and extent of the eruption. Thus there would result vast floodings of the exterior surface of the shell by the so extruded molten matter, volcanoes, extruded mountains, and other manifestations of eruptive phenomena. The sectional diagram (Fig. 5) will help to convey a clear idea of this action. Basing our reasoning on the principle we have thus enunciated, namely, that molten telluric matter expands on nearing the point of solidification, and which we have endeavoured to illustrate by reference to actual examples of its operation, we consider we are justified in assuming that such a course of volcanic phenomena has very probably occurred again and again upon the moon; that this expansion of volume which accompanies the solidification of molten matter furnishes a key to the solution of the enigma of volcanic action; and that such theories as depend upon the agency of gases, vapour, or water are at all events untenable with regard to the moon, where no gases, vapour, or water, appear to exist.

That an upheaving and ejective force has been in action with varying intensity beneath the whole of the lunar surface is manifest from the aspect of its structural details, and we are impressed with the conviction that the principle we have set forth, namely the paroxysms of expansion which successively occurred as portions of its molten interior approached solidification, supply us with a rational cause to which such vast ejective and upheaving phenomena may be assigned. Many features of terrestrial geology likewise require such an expansive force whereby to explain them; we therefore venture to recommend this source and cause of ejective action to the careful consideration of geologists.

When the molten substratum had burst its confines, ejected its superfluous matter, and produced the resulting volcanic features, it would, after final solidification, resume the normal process of contraction upon cooling, and so retreat or shrink away from the external shell. Let us now consider what would be the result of this. Evidently the external shell or crust would become relatively too large to remain at all points in close contact with the subjacent matter. The consequence of too large a solid shell having to accommodate itself to a shrunken body underneath, is that the skin, so to term the outer stratum of solid matter, becomes shrivelled up into alternate ridges and depressions, or wrinkles. In its attempt to crush down and follow the contracting substratum, it would have to displace the superabundant or superfluous material of its former larger surface by thrusting it (by the action of tangential force) into undulating ridges as in Fig. 6, or broken elevated ridges as in Fig. 7, or overlappings of the outer crust as in Fig. 8, or ridges capped by more or less fluid molten matter extruded from beneath, as indicated in Fig. 9, a class of action which might occur contemporaneously with the elevation of the ridge or subsequently to its formation.

A long-kept shrivelled apple affords an apt illustration of this wrinkle theory; another example may be observed in the human face and hand, when age has caused the flesh to shrink and so leave the comparatively unshrinking skin relatively too large as a covering for it. We illustrate both of these examples by actual photographs of the respective objects, which are reproduced on Plate II. Whenever an outer covering has to accommodate and apply itself to an interior body that has become too small for it, wrinkles are inevitably produced. The same action that shrivels the human skin into creases and wrinkles, has also shrivelled certain regions of the igneous crust of the earth. A map of a mountainous part of our globe affords abundant evidence of such a cause having been in action; such maps are pictures of wrinkles. Several parts of the lunar surface, as we shall by-and-by see, present us with the same appearances in a modified degree.

To the few primary causes we have set forth in this chapter—to the alternate expansion and contraction of successive strata of the lunar sphere, when in a state of transition from an igneous and molten to a cooled and solidified condition, we believe we shall be able to refer well nigh all the remarkable and characteristic features of the lunar surface which will come under our notice in the course of our survey.

CHAPTER IV.
THE FORM, MAGNITUDE, WEIGHT, AND DENSITY OF THE LUNAR GLOBE.

We have not hitherto had occasion to refer to what we may term the physical elements of the moon: by which we mean the various data concerning form, size, weight, density, &c. of that body, derived from observation and calculation. To this purpose, therefore, we will now devote a few pages, confining ourselves to such matters as specially bear upon the requirements of our subject, omitting such as are irrelevant to our purpose, and touching but lightly upon such as are commonly known, or are explained in ordinary elementary treatises on astronomy.

First, then, as regards the form of the moon. The form of the lunar disc, when fully illuminated, we perceive to be a perfect circle; that is to say, the measured diameters in all directions are equal; and we are therefore led to infer that the real form of the moon is that of a perfect sphere. We know that the earth and the rest of the planets of our system are spheroidal, or more or less flattened at the poles, and we also know that this flattening is a consequence of axial rotation; the extent of the flattening, or the oblateness of the spheroid, depending upon the speed of that rotation. But in the case of the moon the axial rotation is so slow that the flattening produced thereby, although it must exist, is so slight as to be imperceptible to our observation. We might therefore conclude that the moon is a perfectly spherical body, did not theory step in to show us that there is another cause by which its form is disturbed. Assuming the moon to have been once in a fluid state, it is demonstrable that the attraction of the earth would accumulate a mass of matter, like a tidal elevation, in the direction of a line joining the centres of the two bodies: and as a consequence, the real shape of the moon must be an ellipsoid, or somewhat egg-shaped body, the major axis of which is directed towards the earth. That some such phenomenon has obtained is evident from the coincidence of the times of orbital revolution and axial rotation of the lunar sphere. “It would be against all probability,” says Laplace, “to suppose that these two motions had been at their origin perfectly equal;” but it is sufficient that their primitive difference was but small, in which case the constant attraction by the earth of the protuberant part of the moon would establish the equality which at present exists.

It is, however, sufficient for all purposes with which we are concerned to regard the moon as a sphere, and the next point to be considered is its size. To determine this, two data are necessary—its apparent or angular diameter, and its distance from the earth. The first of these is obtained by measuring the angle comprised between two lines directed from the eye to two opposite “limbs” or edges of the moon. If, for instance, we were to take a pair of compasses and, placing the joint at the eye, open out the legs till the two points appear to touch two opposite edges of the moon, the two legs would be inclined at an angle which would represent the diameter of the moon, and this angle we could measure by applying a divided arc or protractor to the compasses. In practice this measurement is made by means of telescopes attached to accurately divided circles; the difference between the readings of the circle when the telescope is directed to opposite limbs of the moon giving its angular diameter at the time of the observation. But from the fact that the orbit of the moon is an ellipse, it is evident that she is at some times much nearer to us than at others, and, as a consequence, her apparent magnitude is variable: there is also a slight variation depending upon the altitude of the moon at the time of the measure; the mean diameter, however, or the diameter at mean distance from the centre of the earth has, from long course of observation, been found to be 31′ 9″.

To convert this apparent angular diameter into real linear measurement, it is necessary to know either the distance of the moon from the earth, or in astronomical language as leading to a knowledge of that distance, what is the amount of the moon’s parallax. Parallax, generally, is an apparent change of position of an object arising from change of the point of view. The parallax of a heavenly body is the angle which the earth would subtend if it were seen from that body. Supposing an observer on the moon could measure the earth’s angular diameter, just as we measure that of the moon, his measurement would represent what is called the parallax of the moon. But we cannot go to the moon to make such a measurement; nevertheless there is a simple method, explained in most treatises on astronomy, which consists in observing the moon from stations on the earth widely separated, and by which we can obtain a precisely similar result. Without detailing the process, it is sufficient for us to know that the angle which would be subtended by the earth if seen from the moon, or the moon’s parallax, is according to the latest determination, equal to 1° 54′ 5″. This value, however, varies considerably with the variations of distance due to the elliptic orbit of the moon: the number we have given represents the mean parallax, or the parallax at mean distance.

But we have to turn these angular measurements into miles. To effect this we have only to work a simple rule of three sum. It will easily be understood that, as the angular diameter of the earth seen from the moon is to the angular diameter of the moon seen from the earth, so is the diameter of the earth in miles to the diameter of the moon in miles. The diameter of the earth we know to be 7912 miles: putting this therefore in its proper place in the proportion sum, and duly working it out by the schoolboy’s rule, we get:—

1°. 54′. 5″ : 31′. 9″ :: 7912 miles. : 2160 miles.

And 2160 miles is therefore the diameter of the lunar globe.

Knowing the diameter, we can easily obtain the other elements of magnitude. According to the well-known relation of the diameter of a sphere to its area, we find the area of the moon to be 14,657,000 square miles: or half that number, 7,328,500 miles, as the area of the hemisphere at any one time presented to our view. And similarly, from the relation of the solidity of a sphere to its diameter, we find the solid contents of the moon to be 5276 millions of cubic miles of matter.

Comparing these data with corresponding dimensions of the earth, we find that the diameter of the moon is 1/3·665; the area 1/13·4245; and the volume 1/49·1865, of the respective elements of the earth. Those who prefer a graphical to a numerical comparison, may judge of the sizes of the two bodies by the accompanying illustration (Fig. 10). To gain an idea of their distance from each other it is necessary to suppose the two discs in the diagram to be 30 inches apart; the real distance of the moon from the earth being about 238,790 miles at its mean position.

Next, we come to what is technically termed the mass, but what in common language we may call the weight of the moon. It is important to know this, because the weight of a body taken in connection with its size furnishes us with a knowledge of its density, or the specific gravity of the material of which it is composed. But it is not quite so easy to determine the mass as the dimensions of the moon: to measure it, we have seen is easy enough; to weigh it is a comparatively difficult matter. To solve the problem we have to appeal to Newton’s law of universal gravitation. This law teaches us that every particle of matter in the universe attracts every other particle with a force which is directly proportional to the mass, and inversely proportional to the distance of the attracting particles. There are several methods by which this law is applied to the measurement of the mass of the moon. One of the simplest is by the agency of the Tides. We know that the moon, attracting the waters, produces a certain amount of elevation of the aqueous covering of the earth; and we know that the sun produces also a like elevation, but to a much smaller extent, by reason of its much greater distance. Now measuring accurately the heights of the solar and lunar tides, and making allowance for the difference of distance of the sun and moon from the earth, we can compare directly the effect that is due to the sun with the effect that is due to the moon: and since the masses of the two bodies are just in proportion to the effects they produce, it is evident that we have a comparison between the mass of the sun and that of the moon; and knowing what is the sun’s mass we can, by simple proportion, find that of the moon. Another method is as follows:—The moon is retained in her orbital path by the attraction of the earth; if it were not for this attraction she would fly off from her course in a tangential line. She has thus a constant tendency to quit her orbit, which the earth’s attraction as constantly overcomes. It is evident from this that the earth pulls the moon towards itself by a definite amount in every second of time. But while the earth is pulling the moon, the moon is also pulling the earth: they are pulling each other together; and moreover each is exerting a pull which is proportional to its mass. Knowing, then, the mass of the earth, which we do with considerable accuracy, we can find what share of the whole pulling force is due to it, the residue being the moon’s share: the proportion which this residue bears to the earth’s share gives us the proportion of the moon’s mass to that of the earth, and hence the mass of the moon.

There are yet two other methods: one depending upon the phenomena of nutation, or the attraction of the sun and moon upon the protruberant matter of the terrestrial spheroid; and the other upon a displacement of the centre of gravity of the earth and moon, which shows itself in observations of the sun. By each and all of these methods has the lunar mass been at various times determined, and it has been found, as the latest and best accepted value, that the mass of the moon is one-eightieth that of the earth.

From the known diameter of the earth we ascertain that its volume is 259,360 millions of cubic miles: and from the various experiments that have been made to determine the mean density of the earth, it has been found that that mean density is about 5½ times that of water; that is to say, the earth weighs 5½ times heavier than would a sphere of water of equal size. Now a cubic foot of water weighs 62·3211 pounds, and from this we can find by simple multiplication what is the weight of a cubic mile of water, and, similarly, what would be the weight of 259,360 cubic miles of water, and the last result multiplied by 5½ will give the weight of the earth in tons: The calculation, although extremely simple, involves a confusing heap of figures; but the result, which is all that concerns us, is, that the weight of the earth is 5842 trillions of tons: and since, as we have above stated, the mass of the earth is 80 times that of the moon, it follows that the weight of the moon is 73 trillions of tons.

The cubical contents of a body compared with its weight gives us its density. In the moon we have 5276 millions of cubic miles of matter, the total weight of which is 73 trillions of tons. Now, 5276 millions of cubic miles of water would weigh about 21½ trillions of tons; and as this number is to 73 as 1 is to 3·4, it is clear that the density of the lunar matter is 3·4 greater than water: and inasmuch as the earth is 5½ times denser than water, we see that the moon is about 0·62 as dense as the earth, or that the material of the moon is lighter, bulk for bulk, than the mean material of the terraqueous globe in the proportion of 62 to 100, or, nearly, 6 to 10. This specific gravity of the lunar material (3·4) we may remark is about the same as that of flint glass or the diamond: and curiously enough it nearly coincides with that of some of the aërolites that have from time to time fallen to the earth; hence support has been claimed for the theory that these bodies were originally fragments of lunar matter, probably ejected at some time from the lunar volcanoes with such force as to propel them so far within the sphere of the earth’s attraction that they have ultimately been drawn to its surface.

Reverting, now, to the mass of the moon: we must bear in mind that the mass or weight of a planetary body determines the weight of all objects on its surface. What we call a pound on the earth, would not be a pound on the moon; for the following reason:—When we say that such and such an object weighs so much, we really mean that it is attracted towards the earth with a certain force depending upon its own weight. This attraction we call gravity; and the falling of a weight to the earth is an example of the action of the law of universal gravitation. The earth and the weight fall together—or are held together if the weight is in contact with the earth—with a force which depends directly upon the mass of the two, and upon the distance between them. Newton proved that the attraction of a sphere upon external objects is precisely as if the whole of its matter were contained at its centre. So that the attractive force of the earth upon a ton weight at its surface, is the attraction which 5842 trillions of tons exert upon one ton situated 3956 miles (the radius of the earth) distant. If the weight of the earth were only half the above quantity, it is clear that the attraction would be only half what it is; and hence the ton weight, being pulled by only half the force, would only be equal to half a ton; that is to say, only half as much muscular force (or any other force but gravity) would be required to lift it. It is plain, therefore, that what weighs a pound on the earth could not weigh a pound on the moon, which is only 1/80 of the weight of the earth. What, then, is the relation between a pound on the earth and the same mass of matter on the moon? It would seem, since the moon’s mass is 1/80 of the earth, that the pound transported to the moon ought to weigh the eightieth part of a pound there; and so it would if the distance from the centre of the moon to its surface were the same as the distance of the centre of the earth from its surface. But the radius of the moon is only 1/3·665 that of the earth; and the force of gravity varies inversely as the square of the distance between the centres of the gravitating masses. So that the attraction by the moon of a body at its surface, as compared with that of the earth, is 1/80 multiplied by the square of 1/3·665; and this, worked out, is equal to 1/6. The force of gravity upon the moon is, therefore, 1/6 of that on the earth; and hence a pound upon the earth would be little more than 2½ ounces on the moon; and it follows as a consequence that any force, such as muscular exertion, or the energy of chemical, plutonic or explosive forces, would be six times more effective upon the moon than upon the earth. A man who could jump six feet from the earth, could with the same muscular effort jump thirty-six feet from the moon; the explosive energy that would project a body a mile above the earth would project a like body six miles above the surface of the moon.

It is the practice, in elementary and popular treatises on astronomy, to state merely the numerical results in giving data such as those embodied in the foregoing pages; and uninitiated readers, not knowing the means by which the figures are arrived at, are sometimes disposed to regard them with a certain amount of doubt or uncertainty. On this account we have thought it advisable to give, in as brief and concise a form as possible, the various steps by which these seemingly unattainable results are obtained.

The data explained in the foregoing text are here collected to facilitate reference.