describes her whole orbit in 27 days, 7 hours, 43 minutes

A

B

E

Fig. 3.

= 39,343 minutes 2,360,580 seconds. The diameter of the orbit MA being 480,000 miles, the circumference is 3.1416 X 480,000 1,507,968 miles; SO that in one second the moon will

describe an arc =

1507968

2360580 = 63881 miles 40475 inches. Let MM represent such an arc (for clearness, made much larger than

due); draw M'B perpendicular to the diameter, and complete the parallelogram. Then B'M' or MB (which is the versed sine of the arc) represents the deflection of the moon during a minute. Now, in a circle, the chord of an arc is a mean proportional between the diameter and the versed sine. Here the arc, being small, does not differ sensibly from its chord; we may therefore assume

19. This afforded a strong confirmation of Newton's conjecture, that the force which makes a stone fall is one with the force that draws the moon. Every subsequent application of the theory of gravitation to explain the phenomena of the universe has gone to prove its truth; and thus it has been established beyond question as a universal law of nature. It is the greatest discovery of all time.

20. Effects of Gravitation. The arrangement of the matter of the universe on the great scale into globes or worlds, and these again into groups or systems, is thus due to gravitation. Were gravitation to cease acting, the whirling of the earth on its axis would scatter the matter composing it all round; and the earth and other planets, instead of revolving round the sun, would rush off in all directions into space. Every star is in all probability the centre of a group of planets, as our own sun is; and thus we have countless solar systems, each held together by this universal force.

But there are larger groups, or wholes, than solar systems. The suns themselves seem to be arranged in systems. The stars composing our firmament are thought to form a group apart, separated from other similar groups by vast blank chasms; and the several members of each group seem to hold one another in control by the mutual bond of attraction.

COHESION.

21. How distinguished from Gravitation and from Chemical Affinity.-While the great conglomerations of matter called worlds are held together by the force of gravitation, the smaller masses or bodies that make up a world owe their forms and consistency to two quite distinct forces-namely, cohesion and chemical affinity.

Cohesion (Lat. co and hæreo, to stick together) is the force that makes particles of matter cling to one another. It is best seen in solid bodies; it is in virtue of it that they keep their shape and resist being broken.

B

Were this force to cease, a stone or a piece of iron would fall asunder and become a heap of dust.

Take a

Chemical Affinity acts in a different way. piece of marble and crush it to powder; however minute the subdivision, each smallest particle retains all the properties of the whole piece. The chemist dissects a body in a different way. He takes the marble and brings out of it three substances distinct from the marble and from one another-namely, a yellow metal (calcium), a black solid substance (carbon), and a gas resembling common air (oxygen). This kind of dissection is called analysis. The chemist, moreover, can bring together again the three substances above named, and make them re-unite and form marble (synthesis). It is the force that thus binds together the particles of two or more distinct substances so as to form a new substance, that is called chemical affinity. Cohesion differs from it in this, that it only makes particles of matter stick together so as to form larger masses without changing their nature. Neither cohesion nor chemical affinity will act unless the particles are brought into close contact. In this respect they differ from gravitation, which acts at all distances.

22. Elements, Atoms, Molecules.-When the chemist, after dissecting marble with the results above described, tries to carry his analysis farther, and to resolve the carbon or the calcium into two or more constituents, he fails; no art has yet been able to bring anything out of carbon but carbon, or out of oxygen but oxygen. Substances that thus cannot be resolved into anything else are called simple substances or elements. The ultimate or smallest particles of elements that enter into chemical combination are called atoms (Gr., indivisible); the smallest particles of any substance,

whether simple or compound, that cohere together to form a mass or body, are styled molecules (little masses).

[The action of chemical affinity is resumed at page 56.]

Properties of Matter depending on Cohesion.

23. Solid, Liquid, and Gaseous States.-These three states of aggregation, as they are called, are owing to differences in the strength and manner of acting of cohesion. From various facts regarding gases, the dilatation of solid bodies by heat, and the phenomena of elasticity, it is concluded that there are two opposing forces at work—an attractive force and a repulsive force; that when attraction considerably predominates over repulsion, a solid body is the result; when there is almost a balance of the two forces, we have a liquid; and when the repulsive force has the upperhand, we have a gas. From the fact that the increase of heat increases the energy of repulsion, heat and the repulsive force may be considered as virtually one and the same thing. (See par. 80.)

Many substances are seen to assume all three forms in turn. Liquid water turns at one time into solid ice; at another, into vapour or steam. Greater extremes of heat and cold have the same effects on mercury. By applying great cold and pressure, the most elastic gases even hydrogen-have recently been rendered liquid and even solid; and it is now considered certain that all substances are capable of existing in any one of these states under certain conditions.

24. Crystallisation.-Put into a tumbler of pure water as much table-salt as it will dissolve; pour the solution (keeping back any sediment or undissolved

salt) into a flat plate, and set it aside where it will evaporate slowly and without agitation. As the water disappears, the salt forms into small cubes of the most exquisite finish and exactitude. Glauber salt (sodium sulphate), when it solidifies, takes the form of long

a, group of rock crystals; b, striation, as occasionally seen in pyrites; c, primary form of the diamond; d, calcareous spar, with truncation of edges; e, rock salt, primary form, with truncated angles; f, kitchen salt, the result of evaporation of brine (this structure consists of minute cubes piled up like courses of masonry).

four-sided oblique prisms; and in general, all inorganic substances, when becoming solid after being melted or dissolved in a fluid, have a tendency to take some regular geometrical shape, and do so when the solidification is sufficiently slow. Certain forms are characteristic of certain substances. Thus crystallised carbon (diamond) is in the shape of a solid with eight equal faces, each of which is an equilateral triangle; crystals of quartz (rock crystal) have the form of six-sided prisms, usually ending in six-sided pyramids. For the