α The perpendicular line a 4 marks the progress of a fall during four seconds of time, divided into smaller instants. The horizontal lines across from this perpendicular to the oblique line a e represent the velocities, uniformly increasing at every instant, and which, at the end of the first second, has 2 been ascertained to be at the rate of 32 feet (and a fraction) per second, the average velocity for the whole second being 16 feet, 4 reached at the half-second. The darker triangular space or area, bounded by the lines a 4 and a e at the sides, and by one of the horizontal lines below, is a measure of the amount of fall or space passed through at the instants marked by the horizontal line of velocity. The area of the first small triangle a 1 b, belonging to the first second of time, indicates the 16 feet of fall at the end of the first second. Any point in the line of time, a 4, marks a certain instant of the fall; and any line crossing from such point to the diagonal a e, tells the velocity at that instant; while the shaded space above the line measures the amount of fall at the instant. At page 62, the reader learns 1. That the velocity of a falling body increases uniformly at every instant. 2. That the body falls 16 feet and a fraction in the first second. 3. That the extent of fall increases as the square of the units of time. If the question be put, therefore, how far a body will fall in any given time, as three seconds, the following formula, when changed into numbers, gives the answer :— S represents the space fallen through in feet. T the time in seconds. g the force of gravity, causing a velocity of 32 feet per second, and a fall of half that (g) during the first second. declaring that the body in falling freely descends 144 feet and a fraction in three seconds. GENERAL REMARKS. On Natural Science, or knowledge of the forces which produce all the changes and results going on around men on earth; and on the extent to which men have come to understand these forces, so as to be able to modify their agency for useful purposes. * 1. Children who during successive years have sported under the shade of the same great tree, are seldom aware that the tree, like themselves, has been growing all the while; so the mass of people in the world are not aware that, in the midst of very evident political fluctuations, there is going on a decided progress, on the whole, towards a higher state of well-being, of which the limit is as yet but imperfectly conceived. * 2. Within the last weeks of the year 1866, two events occurred of an importance which has strangely awakened public attention to this subject of progress. The first was, after failure of former attempts, which seemed to forbid hope of success, the final laying down of two distinct electric cables across the bed of the Atlantic Ocean, in some places more than three miles deep (forty times the height of St. Paul's Cathedral), so satisfactorily, as to remove dread of future failure. Through these precious wires, persons, thousands of miles apart, can now converse almost as readily as if they sat at opposite sides of a table. The second marvel was, that chiefly through the introduction of a simple mechanical improvement in fire-arms, the much less numerous population of Prussia overcame the vast military power of the Austrian empire. It would appear from this, that henceforth countries will be powerful, safe, and prosperous, in proportion as they attain knowledge of the laws of inanimate nature, that is, of physical science, with practical skill or arts D grounded on that, by which they may direct the energies of nature to produce results useful to them. * 3. This view is powerfully confirmed by reflecting that when many of the persons still living were born, there was not in existence a Watt's steam-engine, such as now, in thousands, are doing man's work all over the earth; nor was there a gas-light, nor a railway, nor a steam-ship, nor electric telegraphs, nor photographs, nor others of the things which, within a century, have changed entirely the condition of the human race on this globe. * 4. Persons may at first feel surprise that the great inventions referred to have been so long delayed; but the explanation is complete when a few known facts in the political history of Europe are considered. * 5. It is known that from about four thousand years ago, the Greeks first, and then the Romans, were making advances in many of the arts of civilization, far exceeding those of other nations. Their architecture, sculpture, and painting attained excellence which has not been surpassed, if equalled, in modern times; and in the horrid work of war, offensive and defensive, they seem to have accomplished all that was possible before the invention of gunpowder. In the copiousness and polish of their languages, they advanced from the rude forms of earlier times to what, as exhibited in their poetry, eloquence, and historical narratives, has appeared to modern judges to be perfection. * 6. Strangely, however, their opinions in regard to the origin of the universe, and to theology, appear to present intelligence to be almost incredibly absurd or irrational. They believed that this world had not existed very long, and that present events in it were dependent on the will, caprices, and often low animal passions of beings whom they called deities, or gods and goddesses, who were immortal, but in other respects so nearly resembled human beings that the races might occasionally mix and multiply. They spoke of Jupiter as the father of their gods, commanding obedience by launching his thunderbolts; Neptune they believed was ruling the waves, Eolus the winds; Mars was supposed to decide the event of battles, and so forth. In many situations, magnificent temples had been raised to serve in the worship of these deities under the superintendence of a venerated priesthood. Little at that time did the people dream that in future ages their descendants, although mere men, would acquire power over nature superior to that attributed then to their gods; such, for instance, as the using lightning, under the name of electricity, to carry messages to distances of thousands of miles, even across broad seas, and to bring back instantaneous answers; or the constructing of ships driven by steam, cleaving the waves more swiftly than ships with sails had ever done, and able to set at defiance the stormy winds and waves; and, lastly, constructing artillery vastly more destructive than any means ever attributed to Mars. * 7. The Greeks and Romans believing, as they did, that events on earth depended on the will of such deities as here described, of whose will they could have no foreknowledge, were prevented from thinking that by studying the ordinary course of nature they might detect, as their descendants have done, certain unchanging laws of sequence among the phenomena, the knowledge of which would enable them often to foresee what was coming, and to direct the agency of the laws to effect new results of the highest importance to their own wellbeing. * 8. Two thousand years ago the Romans had obtained dominion over nearly the whole world then known to them. It was then that Julius Cæsar, returning to Rome from successful wars in Gaul and elsewhere, subverted the government of the senate, and became absolute emperor, dictator, or despot. Afterwards, amidst strange fluctuations, corruption and confusion spread, and the decline and fall of the Roman power had commenced. At last, barbarous nations from the north and east, in overwhelming multitudes, broke in upon the empire, and, working prodigious slaughter and devastation, dismembered it. Different tribes kept possession of different portions, and, intermarrying with what remained of the former inhabitants, formed eventually the distinct kingdoms of modern Europe. * 9. The pure Latin then ceased to be the common language of the different parts of the former empire, giving place to confused mixtures of the languages of the victors and the vanquished. These were little intelligible except to the occupants of the several localities. Had it not been for the fact that Christianity was then spreading over Europe, humanizing the people, the sacred books of which religion were chiefly Greek and Latin, and that the church services everywhere were Latin, the two ancient languages of Europe, with their valuable literature, might have been lost entirely, as great part of it really was. * 10. The want of a common language in Europe, clearly understood by the people of the different nations, was powerful in delaying the advance of a new, and what was to become, a much higher civilization, arising from new discoveries in science and new inventions in art founded on these. The noble intellect of man, although at this time obstructed, did not become torpid; and striking instances of its activity were every now and then starting up during what were called the 'dark ages' between the old and the new civilization. Thus Columbus, a Genoese mariner, saw evidence which convinced him that this earth is in form a globe, and in his first voyage he fell upon, what has since been called, the new world of America lying in his way. Copernicus afterwards proved that this earth and similar globes, called planets, are all moving in orbits round the sun. Galileo, through his newly-invented telescope, then first saw the four moons of the great planet Jupiter, wheeling round it as our moon wheels round this earth. Newton discovered the great fact of Universal Gravitation which, with the simple laws of motion, regulates all the movements of the heavenly bodies. Besides these sublime facts, many subordinate novelties came, as the invention of gunpowder, the art of printing, &c., leading towards the marvels of the two last centuries already referred to. * 11. In the middle ages, the new forms of language called Italian, Spanish, French, English, German, &c., were all makng important progress, and producing admirable literatures. No one of them, however, was so generally known as to be a convenient medium for scientific intercourse between the nations. The Latin, therefore, although not deeply studied in any of the countries, was studied to a moderate degree in all, and therefore soon became the medium. The books of general interest, as those on the main branches of knowledge-of law, for instance, medicine and philosophy, were written in Latin. This practice prevailed even so late as Newton's time, who wrote his immortal Principia Philosophie Naturalis in Latin; so did Bacon his Novum Organum. And the lessons or lectures in the different universities of Europe were delivered in Latin. It became necessary, therefore, to establish schools everywhere for teaching Latin. * 12. The superiority of a polished language, like Latin, over the yet imperfect forms of the vulgar tongues in Europe, was, some centuries ago, so great that in many persons, admiration of it became a kind of idolatry; the mere words and phrases, particularly of the poets, being deemed more worthy of study than the |