Chapter V: Prohibition (2)

Moreover, we say of all these things, or objects, that they are the causes of the sensations in question, and that the sensations are the effects of these causes. For example, if we hear a certain sound, we say it is caused by a carriage going along the road, or that it is the effect, or the consequence, of a carriage passing along. If there is a strong smell of burning, we believe it to be the effect of something on fire, and look about anxiously for the cause of the smell. If we see a tree, we believe that there is a thing, or object, which is the cause of that appearance in our field of view.

In the case of the smell of burning, when we find on looking about, that something actually is on fire, we say indifferently either that we have found out the cause of the smell, or that we know the reason why we perceive that smell; or that we have explained it. So that to know the reason why of anything, or to explain it, is to know the cause of it. But that which is the cause of one thing is the effect of another. Thus, suppose we find some smouldering straw to be the cause of the smell of burning, we immediately ask what set it on fire, or what is the cause of its burning? Perhaps we find that a lighted lucifer match has been thrown into the straw, and then we say that the lighted match was the cause of the fire. But a lucifer match would not be in that place unless some person had put it there. That is to say, the presence of the lucifer match is an effect produced by somebody as cause. So we ask, why did any one put the match there? Was it done carelessly, or did the person who put it there intend to do so? And if so, what was his motive, or the cause which led him to do such a thing? And what was the reason for his having such a motive? It is plain that there is no end to the questions, one arising out of the other, that might be asked in this fashion.

Thus we believe that everything is the effect of something which preceded it as its cause, and that this cause is the effect of something else, and so on, through a chain of causes and effects which goes back as far as we choose to follow it. Anything is said to be explained as soon as we have discovered its cause, or the reason why it exists; the explanation is fuller, if we can find out the cause of that cause; and the further we can trace the chain of causes and effects, the more satisfactory is the explanation. But no explanation of anything can be complete, because human knowledge, at its best, goes but a very little way back toward the beginning of things.

When a thing is found always to cause a particular effect, we call that effect sometimes a property, sometimes a power of the thing. Thus the odor of onions is said to be a property of onions, because onions always cause that particular sensation of smell to arise, when they are brought near the nose; lead is said to have the property of heaviness, because it always causes us to have the feeling of weight when we handle it; a stream is said to have the power to turn a waterwheel, because it causes the waterwheel to turn; and a venomous snake is said to have the power to kill a man, because its bite may cause a man to die. Properties and powers, then, are certain effects caused by the things which are said to possess them.

A great many of the things brought to our knowledge by our senses, such as houses and furniture, carriages and machines, are termed artificial things or objects, because they have been shaped by the art of man; indeed, they are generally said to be made by man. But a far greater number of things owe nothing to the hand of man, and would be just what they are if mankind did not exist—such as the sky and the clouds; the sun, moon and stars; the sea with its rocks and shingly or sandy shores; the hills and dales of the land; and all wild plants and animals. Things of this kind are termed natural objects, and to the whole of them we give the name of Nature.

Although this distinction between nature and art, between natural and artificial things, is very easily made and very convenient, it is needful to remember that, in the long run, we owe everything to nature; that even those artificial objects which we commonly say are made by men, are only natural objects shaped and moved by men; and that, in the sense of creating, that is to say, of causing something to exist which did not exist in some other shape before, man can make nothing whatever. Moreover, we must recollect that what men do in the way of shaping and bringing together or separating natural objects, is done in virtue of the powers which they themselves possess as natural objects.

Artificial things are, in fact, all produced by the action of that part of nature which we call mankind, upon the rest.

We talk of “making” a box, and rightly enough, if we mean only that we have shaped the pieces of wood and nailed them together; but the wood is a natural object and so is the iron of the nails. A watch is “made” of the natural objects gold and other metals, sand, soda, rubies, brought together, and shaped in various ways; a coat is “made” of the natural object, wool; and a frock of the natural objects, cotton or silk. Moreover, the men who make all these things are natural objects.

Carpenters, builders, shoemakers, and all other artisans and artists, are persons who have learned so much of the powers and properties of certain natural objects, and of the chain of causes and effects in nature, as enables them to shape and put together those natural objects, so as to make them useful to man.

A carpenter could not, as we say, “make” a chair unless he knew something of the properties and powers of wood; a blacksmith could not “make” a horseshoe unless he knew that it is a property of iron to become soft and easily hammered into shape when it is made red-hot; a brickmaker must know many of the properties of clay; and a plumber could not do his work unless he knew that lead has the properties of softness and flexibility, and that a moderate heat causes it to melt.

So that the practice of every art implies a certain knowledge of natural causes and effects; and the improvement of the arts depends upon our learning more and more of the properties and powers of natural objects, and discovering how to turn the properties and the powers of things and the connections of cause and effect among them to our own advantage.

Among natural objects, as we have seen, there are some that we can get hold of and turn to account. But all the greatest things in nature and the links of cause and effect which connect them, are utterly beyond our reach. The sun rises and sets; the moon and the stars move through the sky; fine weather and storms, cold and heat, alternate. The sea changes from violent disturbance to glassy calm, as the winds sweep over it with varying strength or die away; innumerable plants and animals come in being and vanish again, without our being able to exert the slightest influence on the majestic procession of the series of great natural events. Hurricanes ravage one spot; earthquakes destroy another; volcanic eruptions lay waste a third. A fine season scatters wealth and abundance here, and a long drought brings pestilence and famine there. In all such cases, the direct influence of man avails him nothing; and, so long as he is ignorant, he is the mere sport of the greater powers of nature.

But the first thing that men learned, as soon as they began to study nature carefully, was that some events take place in regular order and that some causes always give rise to the same effects. The sun always rises on one side and sets on the other side of the sky; the changes of the moon follow one another in the same order and with similar intervals; some stars never sink below the horizon of the place in which we live; the seasons are more or less regular; water always flows down-hill; fire always burns; plants grow up from seed and yield seed, from which like plants grow up again; animals are born, grow, reach maturity, and die, age after age, in the same way. Thus the notion of an order of nature and of a fixity in the relation of cause and effect between things gradually entered the minds of men. So far as such order prevailed it was felt that things were explained; while the things that could not be explained were said to have come about by chance, or to happen by accident.

But the more carefully nature has been studied, the more widely has order been found to prevail, while what seemed disorder has proved to be nothing but complexity; until, at present, no one is so foolish as to believe that anything happens by chance, or that there are any real accidents, in the sense of events which have no cause. And if we say that a thing happens by chance, everybody admits that all we really mean is, that we do not know its cause or the reason why that particular thing happens. Chance and accident are only _aliases_[1] of ignorance.

At this present moment, as I look out of my window, it is raining and blowing hard, and the branches of the trees are waving wildly to and fro. It may be that a man has taken shelter under one of these trees; perhaps, if a stronger gust than usual comes, a branch will break, fall upon the man, and seriously hurt him. If that happens it will be called an “accident,” and the man will perhaps say that by “chance” he went out, and then “chanced” to take refuge under the tree, and so the “accident” happened. But there is neither chance nor accident in the matter. The storm is the effect of causes operating upon the atmosphere, perhaps hundreds of miles away; every vibration of a leaf is the consequence of the mechanical force of the wind acting on the surface exposed to it; if the bough breaks, it will do so in consequence of the relation between its strength and the force of the wind; if it falls upon the man it will do so in consequence of the action of other definite natural causes; and the position of the man under it is only the last term in a series of causes and effects, which have followed one another in natural order, from that cause, the effect of which was his setting out, to that the effect of which was his stepping under the tree.

But, inasmuch as we are not wise enough to be able to unravel all these long and complicated series of causes and effects which lead to the falling of the branch upon the man, we call such an event an accident.

When we have made out by careful and repeated observation that something is always the cause of a certain effect, or that certain events always take place in the same order, we speak of the truth thus discovered as a law of nature. Thus it is a law of nature that anything heavy falls to the ground if it is unsupported; it is a law of nature that, under ordinary conditions, lead is soft and heavy, while flint is hard and brittle; because experience shows us that heavy things always do fall if they are unsupported, that, under ordinary conditions, lead is always soft, and that flint is always hard.

In fact, everything that we know about the powers and properties of natural objects and about the order of nature may properly be termed a law of nature. But it is desirable to remember that which is very often forgotten, that the laws of nature are not the causes of the order of nature, but only our way of stating as much as we have made out of that order. Stones do not fall to the ground in consequence of the law just stated, as people sometimes carelessly say; but the law is the way of asserting that which invariably happens when heavy bodies at the surface of the earth, stones among the rest, are free to move.

The laws of nature are, in fact, in this respect, similar to the laws which men make for the guidance of their conduct toward one another. There are laws about the payment of taxes, and there are laws against stealing or murder. But the law is not the cause of a man’s paying his taxes, nor is it the cause of his abstaining from theft and murder. The law is simply a statement of what will happen to a man if he does not pay his taxes, and if he commits theft or murder; and the cause of his paying his taxes, or abstaining from crime (in the absence of any better motive) is the fear of consequences which is the effect of his belief in that statement. A law of man tells what we may expect society will do under certain circumstances; and a law of nature tells us what we may expect natural objects will do under certain circumstances. Each contains information addressed to our intelligence, and except so far as it Influences our intelligence, it is merely so much sound or writing.

While there is this much analogy between human and natural laws, however, certain essential differences between the two must not be overlooked. Human law consists of commands addressed to voluntary agents, which they may obey or disobey; and the law is not rendered null and void by being broken. Natural laws, on the other hand, are not commands, but assertions respecting the invariable order of nature; and they remain laws only so long as they can be shown to express that order. To speak of the violation, or the suspension, of a law of nature is an absurdity. All that the phrase can really mean is that, under certain circumstances the assertion contained in the law is not true; and the just conclusion is, not that the order of nature is interrupted, but that we have made a mistake in stating that order. A true natural law is a universal rule, and, as such, admits of no exceptions.

Again, human laws have no meaning apart from the existence of human society. Natural laws express the general course of nature, of which human society forms only an insignificant fraction.

If nothing happens by chance, but everything in nature follows a definite order, and if the laws of nature embody that which we have been able to learn about the order of nature in accurate language, then it becomes very important for us to know as many as we can of these laws of nature, in order that we may guide our conduct by them.

Any man who should attempt to live in a country without reference to the laws of that country would very soon find himself in trouble. And if he were fined, imprisoned, or even hanged, sensible people would probably consider that he had earned his fate by his folly.

In like manner, any one who tries to live upon the face of this earth without attention to the laws of nature will live there for but a very short time, most of which will be passed in exceeding discomfort; a peculiarity of natural laws, as distinguished from those of human enactment, being that they take effect without summons or prosecution. In fact, nobody could live for half a day unless he attended to some of the laws of nature; and thousands of us are dying daily, or living miserably, because men have not yet been sufficiently zealous to learn the code of nature.

It has already been seen that the practice of all our arts and industries depends upon our knowing the properties of natural objects which we can get hold of and put together; and though we may be able to exert no direct control over the greater natural objects and the general succession of causes and effects in nature, yet, if we know the properties and powers of these objects, and the customary order of events, we may elude that which is injurious to us, and profit by that which is favorable.

Thus, though men can nowise alter the reasons or change the process of growth in plants, yet having learned the order of nature in these matters, they make arrangements for sowing and reaping accordingly; they can not make the wind blow, but when it does blow they take advantage of its known powers and probable direction to sail ships and turn wind-mills; they can not arrest the lightning, but they can make it harmless by means of conductors, the construction of which implies a knowledge of some of the laws of that electricity of which lightning is one of the manifestations. Forewarned is forearmed, says the proverb; and knowledge of the laws of nature is forewarning of that which we may expect to happen, when we have to deal with natural objects.

No line can be drawn between common knowledge of things and scientific knowledge; nor between common reasoning and scientific reasoning. In strictness all accurate knowledge is science; and all exact reasoning is scientific reasoning. The method of observation and experiment, by which such great results are obtained in science, is identically the same as that which is employed by every one, every day of his life, but refined and rendered precise. If a child acquires a new toy, he observes its characters and experiments upon its properties; and we are all of us constantly making observations and experiments upon one thing or another.

But those who have never tried to observe accurately will be surprised to find how difficult a business it is. There is not one person in a hundred who can describe the commonest occurrence with even an approach to accuracy. That is to say, either he will omit something which did occur, and which is of importance, or he will imply or suggest the occurrence of something which he did not actually observe, but which he unconsciously infers must have happened. When two truthful witnesses contradict one another in a court of justice, it usually turns out that one or other, or sometimes both, are confounding their inferences from what they saw with that which they actually saw. A swears that B picked his pocket. It turns out that all A really knows is that he felt a hand in his pocket when B was close to him; and that B was not the thief, but C, whom A did not observe. Untrained observers mix up together their inferences from what they see with that which they actually see in the most wonderful way; and even experienced and careful observers are in constant danger of falling into the same error.

Scientific observation is such as is at once full, precise, and free from unconscious inference.

Experiment is the observation of that which happens when we intentionally bring natural objects together, or separate them, or in any way change the conditions under which they are placed. Scientific experiment, therefore, is scientific observation, performed under accurately known artificial conditions.

It is a matter of common observation that water sometimes freezes. The observation becomes scientific when we ascertain under what exact conditions the change of water into ice takes place. The commonest experiments tell us that wood floats in water. Scientific experiment shows that, in floating, it displaces its own weight of the water.

Scientific reasoning differs from ordinary reasoning in just the same way as scientific observation and experiment differ from ordinary observation and experiment—that is to say, it strives to be accurate; and it is just as hard to reason accurately as it is to observe accurately.

In scientific reasoning general rules are collected from the observation of many particular cases; and, when these general rules are established, conclusions are deduced from them, just as in everyday life. If a boy says that “marbles are hard,” he has drawn a conclusion as to marbles in general from the marbles he happens to have seen and felt, and has reasoned in that mode which is technically termed induction. If he declines to try to break a marble with his teeth, it is because he consciously or unconsciously performs the converse operation of deduction from the general rule “marbles are too hard to break with one’s teeth.”

You will learn more about the process of reasoning when you study logic, which treats of that subject in full. At present, it is sufficient to know that the laws of nature are the general rules respecting the behavior of natural objects, which have been collected from innumerable observations and experiments; or, in other words, that they are inductions from those observations and experiments. The practical and theoretical results of science are the products of deductive reasoning from these general rules.

Thus science and common sense are not opposed, as people sometimes fancy them to be, but science is perfected common sense. Scientific reasoning is simply very careful common reasoning, and common knowledge grows into scientific knowledge as it becomes more and more exact and complete.

The way to science then lies through common knowledge; we must extend that knowledge by common observation and experiment, and learn how to state the results of our investigations accurately, in general rules or laws of nature; finally, we must learn how to reason accurately from these rules, and thus arrive at rational explanations of natural phenomena, which may suffice for our guidance in life.

FOOTNOTES

[C] From Science Primers. Introductory. By Prof. T. H. Huxley, F.R.S.

THE CIRCLE OF THE SCIENCES.

Science means classified knowledge. There may be much general knowledge that is not science. It attains to that dignity only when the particular facts known are generalized, and arranged in some order, instead of being jumbled together, and lying about loosely in the memory, to be taken up at random. Especially must the basal facts of the science be verified, not assumed.

Information that is general and assured, though as yet lacking system and a proper ordering of the elementary facts, may, and usually will in time advance to the dignity of science. History warrants this expectation. Only let not the boast be made, or the honor conferred prematurely. Geography, chemistry, and political economy are all now sciences. The first has been recognized among the sciences from an early day, though it has advanced rapidly during the present century. The last two are comparatively new members, having held their place in the “Circle” scarcely a hundred years. True, many of the facts of chemistry, and the principles of political economy had been known for ages, but the knowledge men had of them lacked either system or certainty, or both. So, also, in respect to mineralogy, botany, and zoölogy, a store of known facts had been for ages accumulating, before they could rightly be called sciences. To reach that distinction the quality and orderly arrangement of the things known are as necessary as the quantity.

In the heading of this series of articles, “Circle” does not suggest the rim of a wheel, or a curved line all the points of which are equally distant from the center around which it is drawn, but rather a group of sciences, just as “social circle,” and “circle of friends” indicate the amicable relations of the persons without saying anything of their positions in the place of their meeting. It is a goodly group, this family of the sciences, and the members now so numerous and having such distinctive characteristics will be introduced, not as a body but severally, and in five classes: The Mathematical, Physical, Mental, Moral, and Social Sciences. They hold such intimate relations with each other, mutually giving and receiving aid, that we will not attempt to keep the members of classes from mixing occasionally in our account of them, as they often do in reality.

Mathematics is the science of quantities and numbers. Its principles are of the first importance, and are of service in all the departments of science. In several of its subdivisions, of which brief mention will be made, it uses known quantities for the determination of those unknown, reasoning from certain relations existing between them. The qualities it discusses are represented by diagrams, figures, or symbols, adopted for the purpose. It is customary to speak of _pure_ and _mixed_, or _abstract_ and _applied_ mathematics; the former treating of laws, principles, and relations in the abstract, or without any special reference to anything as actual or existing. The latter discusses the principles, laws and relations in connection with existing phenomena. The operations with numbers and symbols in pure mathematics, dealing only with abstract quantities, do not necessarily imply the idea of matter. Those of the science as applied have much to do with material phenomena. The elements that enter into the calculations in both cases are axioms or self-evident truths, things that are known intuitively, or grasped by the reason soon as presented, only in applied mathematics, used more or less in all sciences, these same axiomatic, self-evident truths are employed in the discussion of natural objects, the laws, properties, and relations of which are learned mostly by experience and induction.

The sciences classed as pure mathematics are Arithmetic, Geometry, Algebra, Analytical Geometry and Calculus. Arithmetic is eminently the science of numbers, and treats of, or practically illustrates their nature and uses. It employs the nine Arabic digits or figures with the addition of the cipher, giving them various positions to express numerical values, and not the native qualities or functions of the things to which they are applied. The methods are the same, and the results obtained equally true, whatever may be the nature of the quantities about which inquiry is made. The elementary or fundamental idea in arithmetic is unity, expressed by the figure 1, from which, with the help of the other eight digits, and the individually valueless cipher, 0, expressions for all the other values, whole or fractional, are formed.

As arithmetical processes underlie, or enter into, the work of nearly all mathematical calculations, its great importance as a science is evident; though as often taught in our schools and used in business, it is simply a method of reckoning or computation.

Algebra is a kindred science, that, by the use of letters and symbols, enables us to solve more readily all difficult questions relating to numbers. It is, indeed, a kind of universal arithmetic. In the ordinary arithmetic the numbers or figures employed, taken separately, have always the same value, and the result, when, sometimes by a tedious process, obtained, is applicable only to the particular question proposed, but in solving the problem by algebra, since we employ letters to which any values may be attributed at pleasure, the result obtained is largely applicable to all questions of a particular class. Thus, having the sum and difference of two quantities given, we readily obtain an algebraic expression for the quantities themselves. By the new method the goal is reached speedily, and the cabalistic terms, that may, at his first attempts, perplex and discourage the young student, become his delight; and in many difficult processes greatly shorten the work, enabling him with ease to solve problems that to the common arithmetician are tedious, if not impossible.

Geometry, one of the oldest of sciences, measures extension, treats of order and proportion in space. Its working elements are not numbers or symbols, but points, and lines, either straight or curved, and surfaces, with volumes, or solids. The simpler problems, when successfully demonstrated, are used in solving those more complicated, making the progress easy.

Lines are made up of points, and have extension only in one direction. Surfaces have length and breadth, and are distinguished as triangles, quadrilaterals, polygons, etc., according to the number of lines that circumscribe them. Solids have length, breadth, and thickness. From a few elementary facts, much geometrical science has been deduced, by very simple, logical processes. It is intimately related to other sciences, and of much practical importance; but, if there were no other advantage derived, as a discipline of the reasoning faculty there can be nothing better. To pursue the study profitably there is little need of an instructor. Class recitations are helpful, but let any one intent on personal culture, and having only a little time for the work, get a good elementary treatise on plane and solid geometry, and study it. The exercise will become a delight, will give strength and grip to the faculties, and furnish protection against the mental dissipation caused by spending much time in the hasty, careless reading of what is fitly called light literature.

Analytical geometry is that branch which examines, discusses and develops the properties of geometrical magnitudes by the use of algebraic symbols. The questions or problems are solved, not, as in plane geometry, by diagrams or figures drawn to show certain relations of magnitudes, but by making algebraic symbols represent them, and thus solving the problems. Analysis is much used in simple algebraic processes, but more in analytical geometry, and in differential and integral calculus, which has been called the transcendental analysis. It is useful as a higher branch of the science, and without it the best achievements of the greatest mathematicians would scarcely have been possible. These last named branches are generally best pursued in our higher academies and colleges. A college course would be sadly deficient without them, but only for exceptional cases would it be advisable to put them in a course of study to be pursued privately.

If this brief mention of the higher mathematics kindles desire for further knowledge, and you hesitate to grapple with them alone, by all means go to college, and after a proper introduction, wherein the chief embarrassment is felt, even calculus will be found an agreeable acquaintance.

Under the head of “Mixed Mathematics,” applicable to both laws or abstract principles and facts, the discussion of things as actual and possible, we have first, mechanics, the science that treats of the various forces and their different effects. By _force_ is meant any power that tends to prevent, produce, or modify motion. Three are recognized—(1) gravitation, or the attraction of bodies toward each other; (2) the cause, whatever it may be, of light, heat, and electricity; (3) life, an equally mysterious power producing the actions of animals and the growth of plants. These forces, though entirely unseen and their causes unknown, are definite quantities. We readily conceive of one force as equal to, or greater than another, and know that equal forces, applied in opposite directions, balance each other. To everything that moves there is force applied greater than the resistance to be overcome. A number of forces may act on an object at the same time, accelerating, retarding, or changing the direction of the motion given to it. When the forces are so balanced as to hold the body on which they act in a state of equilibrium, their action and consequent phenomena are investigated under the head of STATICS, or the science which treats of bodies at rest. When motion is produced, DYNAMICS considers the laws that govern the moving bodies and the phenomena that result. These branches of mechanical science are of great practical importance, and a knowledge of them would save from many blunders and failures resulting from incompetence. The same laws govern in the movement of all bodies, whether solid or liquid. Hydrostatics, Hydrodynamics, Hydraulics, etc., are branches of the same science, and worthy of separate mention only because they apply the general principles of statics and dynamics to the phenomena of rest or motion in liquids. The foundation for all that is peculiar in these branches with the lengthened names, and that together may be called Hydro-mechanics, lies in the properties that distinguish the liquid from other states of material bodies, whether gaseous or solid, viz.: in the presence of cohesion, but with great mobility of parts and more or less elasticity. Some peculiarities are so noteworthy as to deserve mention even in this limited presentation. Because of the only slight cohesive attraction, and entire freedom of motion among the particles, liquid bodies possess no definite form of their own, but adapt themselves to the form of the excavations or vessels containing them. They, of course, vary much in their fluidity, the mobile liquids, as water and alcohol, flowing more readily than molasses, heavy oils, and tar. Fluids at rest press equally in all directions, upward, downward, and laterally. In this, also, they differ from solids that press only down, or in the direction of the center of gravitation. If not confined they can not be heaped up, but their particles seek a common level. An absolute water level is, of course, possible only when the area covered is so limited that lines joining all the points on the surface with the center of gravity are practically parallel, or their convergence an inappreciable quantity. In large bodies of water, as the ocean, the surface corresponds with the general rotundity of the earth.

The fact of the equal pressure of liquids in all directions, and with the same intensity, is found of great importance in practical mechanics. The strong pressure of a small column of water is finely illustrated by simple experiment with the water bellows, or hydraulic paradox, in which one pound of water in a tube lifts a hundred pounds on the top of the bellows, and the greater the disproportion between the diameter of the tube and that of the top of the bellows, the greater weight it will raise. More than two hundred years ago Pascal showed the enormous pressure exerted by a lofty column of water in a small tube. A strong cask was filled with water, and a small tube forty feet high closely fitted in its head, when a few pints of water poured into it burst the cask, and would have done so if it had been made of the strongest oaken staves and bound with hoops of iron. This is the power used in the hydraulic press, a very simple machine of much value in the industrial arts when there is a demand for great force that can be slowly and steadily applied, as in compressing cloth, oil cake, paper, gunpowder and numerous other things. Its parts are so few that it can be described without a model to represent it. A small, upright cylinder, with a closely fitting piston used as a pump to draw and force the water, and connected at the base by a tube with a much larger cylinder directly under the substance to be pressed, in which there is also a piston to be moved upward, though water tight. The whole is secured in position by powerful frame work. Beneath the piston the water is received. And knowing the principles of hydrostatics we can estimate its power. If the areas of the lower surfaces of the two pistons are to each other as one to four hundred square inches, one pound pressure on the small one will deliver to the lower surface of the large one a pressure equal to four hundred pounds weight. But let the arms of the lever used as the force pump handle be to each other as one to fifty. Then when a force of fifty pounds is applied at the end of the long arm of the lever it will descend with a force of 50×50=2,500, and there will be delivered on the lower surface of the large piston a power to raise it expressed by 50×50×400=1,000,000. Some allowance must be made for friction or other impediments, say one fourth, which is more than enough, and still a man or boy at the end of that pump handle would be able to lift at least three hundred and seventy-five tons.

The sciences we have been considering under the general name of mechanics, which is derived from a Greek word that means to contrive, invent, construct, have much to do with machinery, with the methods of construction, the propelling forces, and the phenomena produced. There were machinists and some simple machines propelled by human or brute force, by weights and springs, by falling or running water, and air in motion before the laws of motion and forces were understood, or the rude mechanic arts began to assume the character of a science. The machines were, of course, imperfect, and lacked efficiency, while many of those now in use seem nearly perfect and adapted to the work expected of them. But notwithstanding the marvelous advance that has been made in the manufacture of machinery, and the intelligent application of mechanical powers, we look for still greater things as possible in the future.

It is well, however, never to forget that whatever the seeming may be, the most perfect machine of human invention does not create force. That is as impossible for man as it is to give life or create matter. All he can do is to collect, concentrate and use, to the best advantage, the forces that exist. He may by skillful appliances gain a great mechanic advantage, and overcome very formidable resistance, but he must be content to do it very slowly; and it has been often said that “what he gains in power he loses in speed.” In many cases this seems a necessity, and he must submit to it. His simplest machine, if the fulcrum is placed very near the weight, gives a man tremendous power gained by his position at the long arm of the machine. But the point at which he applies the force must move much faster and a greater distance than the object against which it is directed. So when a man with a system of pulleys raises to the top of a tower a block of granite that four men might lift from the ground he sacrifices in speed what he gains in the new way of applying the force he has for the purpose.

You visit a large manufacturing establishment or the mechanical department of a great national or international industrial exposition and see a whole acre of machinery of all kinds, shafts, wheels, saws, lathes, and spindles in rapid motion, and, astonished at the complications, inquire for the power that carries the whole. You will possibly find it is in some remote part of the premises, and shut up in the motionless boiler where the steam is said to be generated, which only means that the water heated expands and struggles to escape from its confinement, while man understanding the laws of its action manages to liberate the force under conditions that make it his servant.

The science of numbers and magnitudes, useful in discussing the distances, measurements, and motions of terrestrial bodies, is especially so in its application to astronomy.

Astronomy as a physical science will receive consideration in the next number; here only the mathematical elements are noticed, and they are everywhere manifest. The same general laws control all material bodies, those near to us, and those seen at a distance. So the science of the stars is not now mere theory, but has all the elements of mathematical certainty. When dealing with such vast numbers and magnitudes as engage the astronomer’s attention, with a few known principles or laws, and abundant recorded telescopic observations for the basis of their work, men can calculate even more accurately than they can count or measure. Having once prepared their theorem, aided by the logarithms of Napier[1] that simplify and shorten the more difficult arithmetical calculations, they can readily determine the distance, magnitude and motions of a planet, and know that it is done with sufficient exactness. The distances of the heavenly bodies are generally determined by their parallax, that is the difference between the directions of the bodies as seen from two different points. The inclination of the lines thus drawn is the angle of parallax. By supposing the lines prolonged to the sun, and other lines drawn through the points selected to the center of the earth a quadrangle is formed, all the angles and sides of which are easily found. In measuring very minute parallaxes it may not be possible to determine the exact position of the body as projected on the celestial sphere, but in that case recourse can be had to relative parallax, or the difference between the parallaxes of two bodies lying nearly in the same direction. The best opportunity for this is afforded by the transit of Venus, and on this account great interest is felt in that phenomenon, and extensive preparations are made for taking accurate observations.

The figure, size and density of the celestial bodies have all been calculated with approximate certainty. The orbits, through which they pass in their revolutions, described, and their velocities ascertained.

There is a solar system of which the sun is the center, and in its relation to the planets stationary, though really moving on through infinite space; the orbits through which planets move are not circles, but more or less elliptic, having the sun at one focus of the ellipse.

That planets move in ellipses was announced by Kepler[2] as the first law governing their motions, and a second deduced from this and confirmed by observations, is that they do not move with equal velocity in all parts of their orbits; and that _a line drawn from the center of the earth to the center of the sun passes over equal spaces in equal times_. He also found as a third law that _the squares of the times of the revolutions of the planets are proportional to the cubes of their mean distances from the sun_.

Navigation shows how vessels are directed in their course upon the great waters. In proportion as the “paths of the seas” have become open, safe and free for all, they are found paths of knowledge and civilization. The science, small at its beginning, has grown to its present advanced state by slow degrees, helped by contributions from the most opposite sources. Practical but uneducated seamen have doubtless done much, as their ingenuity is often, in emergencies, taxed to supply means of safety and success that are wanting. More has been contributed by scholars, secluded philosophic men whose lives are spent “in communion with the skies,” in observing the motions of the heavenly bodies and studying the laws by which they are regulated. But perhaps the most valuable service has been rendered by another class who combine an experience of the sea with much knowledge of astronomical science, men acquainted with the needs of seamen and qualified to meet them. The introduction of the mariner’s compass early in the fifteenth century was an epoch in the history of navigation, as it made seamen in a measure independent of the sun and stars. This was an incalculable advantage, as soon became apparent to those who adopted the compass as their guide. Of the many improvements and helps in the science of navigation we can only name, as conspicuous, the invention of Mercator’s chart[3] in 1569, Davis’s quadrant[4] about 1600, and Hadley’s quadrant a century later. The character of the instruments and a glance at the Nautical Almanac will show how largely both mathematics and astronomy enter into the science of navigation. Nor is it quite safe to take passage with a shipmaster who has but limited knowledge of either. He should at least thoroughly understand his instruments and be a ready, accurate computer.

Geometry grew out of the practice of surveying, and now embodies many of the laws and principles of the science. There are several distinct systems of surveying, classed according to the purposes contemplated. It is astronomically employed in determining the figure of the earth by the actual measurement of arcs. A fair knowledge of mathematics and trigonometry is required in what are known as coast surveys. Land surveying is of the plainest kind, and employed in finding the contents of areas, or in dividing large tracts into lots of smaller dimensions. The chief difficulty is in getting the exact bearing of the lines and the measure of the angles when the plot is an irregular polygon.

Topographical surveying, beside the measurement of lines and angles, takes note of variations of level, that the draft may properly represent superficial inequalities. Maritime surveying is an important branch, fixing the positions of shoals, rocks and shore-lines. Mine surveying determines the location of works in the mine and decides whether the excavations conform, as required, to lines on the surface. The compass and chain are the surveyor’s most common instruments, but others are used according to the nature of the surveys to be made. Incompetency or carelessness in surveys often occasions serious trouble and loss.

Fortifications for the defense of cities and the protection of soldiers are as ancient as the existence of armies. The former, built in time of peace, of such form and materials as military science and experience suggest, are called “permanent fortifications;” and the temporary works constructed as the exigencies of a campaign require are “field fortifications.” The art and science have been practiced and studied in all ages, and there is now an immense literature on the subject.

As methods of defense must be adjusted to those of attack the earlier permanent fortifications, in the progress of society and after the introduction of artillery, became nearly worthless. High stone walls are a protection while they stand, but, however strong, they can be battered down by heavy siege guns that have less effect when directed against earth works, which seem less formidable. A place thoroughly fortified is seldom taken by a sudden assault. The United States have fortified less than most of the great European nations, but are by no means defenseless. Previous to 1860 there had been expended on our forts more than $30,000,000; and all the exposed positions have been greatly strengthened within the last twenty-five years.

_End of Required Reading for February._

THE POET’S VISION.

BY MARY A. LATHBURY.

My Lady Lily, the waters sleep,
And the winds are among the clover;
Would I could hear the tale you told
The Poet once, till with voice of gold
Singing it over and over

He came to the court and cried, “O king,
My song of thy state and glory
Is dead on my lips! I am done with strife,
And courts, and conquests. A song of life
I have learned from a water lily.”

“Carol us then thy pretty song,
Sir Poet!” the king cried, sneering;
So standing stateliest of them all
The length of the royal banquet hall,
And flinging a look unfearing,

Full on the king and his court, who sat
Smiling in fine derision,
He sang or chanted as chants a seer
When sense is fading, and draweth near
The high beatific vision.

He sang of life in the soil of death,
A seed of a heavenly sowing;
Asleep in the murk and mire of earth,
In silence waiting its wondrous birth,
Of death or of life unknowing.

He sang of the Sun of Life—His quest
In our death-deeps dark and chilly;
Of love that quickens to life the dead,
As the sun rays seek in the river-bed
The germ of the water lily.

He sang of Faith—of the eye that seeks
With a sightless aspiration
The source of Love and the fount of Light,
Till far in the folds of the utmost night,
Storm-swept with fierce temptation,

A light breaks through like a faint white star,
That grows and grows like the dawning,
Till, veiled in vapors, it hangs above
The wakened soul as the face of Love,
And Life has begun its morning.

He sang of Life in the spring o’ day,
Of patience, and truth, and duty,—
The narrow ways to the full release,
When, lapped in light and a dream of peace,
It bursts as a flower to beauty.

He sang—and his words fell thick and fast—
Of the resurrection glory;
Of good from evil, of life from death,
And then, with hesitant, bated breath,
The God-man’s marvelous story.

Then silence fell on the king and court,
And out through the open portal
The poet passed with a solemn stride
Into the midnight spaces wide,
Or into the life immortal.

My Lady Lily, you will not wake,
Wrapped in your dreams Elysian,
But this is the mystic tale you hold,
Deep in your tremulous heart of gold;
And this was the Poet’s vision.

THE HOMELIKE HOUSE.

BY SUSAN HAYES WARD.