A COURSE OF

LECTURES ON NATURAL PHILOSOPHY,

BY J. LATHROP, JUN. 4. M.

LECTURE THE SECOND.

ON MECHANICS.

IN the blissful fields of Eden, ere forbidden knowledge made our first parents wise at the cost of innocence and happiness, their ingenuity was not required to procure bread for subsistence, or habitations for shelter. Ever since disobedience to the divine command, involved Adam and his posterity in a common doom, food and raiment have been attainable but by labor and industry. Life, forfeited by guilt, is prolonged only by the sweat of the brow; and from the moment, when our progenitors quitted the gates of Eden, man became obliged to toil for the indispensable necessaries of existence. No branch of the family of science therefore can boast a pedigree of higher antiquity than mechanics.

The earliest inhabitants of the globe were practical philosophers; and without knowing or examining principles, were ingenious mechanics, and successful cultivators of the soil. Scarcely had the death of Abel furnished the second article in the history of human transgression, before we find his murderer building a city, and the tuneful Jubal recorded as the father of all such as handle the harp and the organ; and this advance in music and architecture was made in the life-time of our first parent, and prior to the general worship of the Creator, by the different tribes and families of mankind.

We read of ships sailing on the waters of the Mediterranean as early as the days of Jacob; the Philistines, in the time of Saul, more than 1000 years before Christ, carried 30,000 chariots into the field of battle; and about the same period, Ammon's 's navy on the Red sea, was furnished with sails. Corn mills were of early invention, for in Deuteronomy we find it was not lawful for any man to pledge" the upper or the nether mill-stone," and Jeremiah, who went down to the pot

ter's house, and "wrought a work on the wheels," exhibited a type of God's absolute power in disposing of nations.

The works of Archimedes who flourished about 200 years before the nativity of our Savior, would alone afford materials for a volume; some of his discoveries, appear so much above the reach of men, that many of the moderns, says Adams, have found it more easy to doubt their existence than to imitate them. His name still stands foremost in the science of mathematics. By his mechanical knowledge, he alone, for three successive years, baffled the attempts of the Romans, and supported the tottering towers of Syracuse. Marcellus admired the superior skill and wisdom of Archimedes, and instructed the Roman troops to respect his safety. The impatience of a soldier proved fatal to his valuable life, and the generous victor, having found his wish to preserve it unavailing, wept over the tomb of the heroic philosopher. He even prolonged his power of preserving, after death, and consecrated his name as a talisman of safety to every person by whom it was borne.

It would be an endless task to enumerate the instances of the mechanical abilities of the ancients. Greece and Italy are filled with monuments and ruins, which assist us in estimating the resources, the inventive faculties, and the civic as well as the military virtues of those once illustrious countries.

Mechanics, is a mixed mathematical science, that treats of forces, motions, and moving powers, with their effects in machines, &c. It is distinguished by Sir Isaac Newton into practical and rational: the former treats of the mechanical powers, and of their various combinations; the latter, or rational mechanics, comprehends the whole theory and doctrine of forces, with the motions and effects of them. Of this science, Gallileo laid the best foundation, when he investigated the descent of heavy bodies; and since his time, by the assistance of new methods of computation, a great progress has been made, especially by Newton, in his Principia, which is a general treatise on rational and practical mechanics in its largest extent.

In treating of machines, we should consider the weight. that is to be raised, the power by which it is to be elevated, and the instrument or engine by which this effect is to be produced. And, in treating of these, there are two principal problems that present themselves: the first is, to determine the proportion which the power and weight ought to have to each other, that they may just be in equilibrio; the second is, to determine what ought to be the proportion between the power and weight, that a machine may produce the greatest effect in a given time.

It is manifest, that this is an enquiry of the greatest importance, though few have treated of it. When the power is only a little greater than what is sufficient to sustain the weight, the motion usually is too slow; and though a greater weight be raised in this case, it is not sufficient to compensate for the loss of time. On the other hand, when the power is much greater than what is sufficient to sustain the weight, this is raised in less time; but it may happen that this is not sufficient to compensate for the loss arising from the smallness of the load. It ought therefore to be determined when the product of the weight multiplied by its velocity, is the greatest possible; for this product measures the effect of the engine in a given time, which is always the greater in proportion both as the weight is greater, and as its velocity is greater.

The mechanical powers which are used in aid of the wants and weakness of man, are, the lever, the wheel and axle, the pulley, the inclined plane, the wedge, and the screw.

THE LEVER

Is the first and simplest of the mechanical powers. It is a straight inflexible bar, supposed to be void of all gravity when mathematically considered; but in practice, possessed of weight and flexibility.

There are three circumstances which particularly demand attention in a lever, the fulcrum or prop by which it is supported, the power to raise the weight, and the weight to be raised or sustained. It must be premised that the weights

are always supposed to act at right angles unless otherwise expressed.

There are three kinds of levers which take their names from the difference in the relative situation of the weight, power, fulcrum, or prop.

The first kind of lever is that where the fulcrum is between the power and the weight. The parts on the different sides of the prop are called the arms of the lever; and the shorter arm should be made so thick and heavy as just to balance the longer arm; the lever being thus in equilibrio with itself, may be considered without weight. We will suppose the longer arm divided into 6 equal parts, and the distance of the weight from the fulcrum of the shorter arm is exactly equal to one of these parts, so that the whole lever may be considered as divided into seven equal parts.

Now, from the proposition just explained to you, it is clear that the power gained by this lever, or added to the natural strength or force of the agent, is increased in proportion as the one arm is longer than the other.

The resistance is as much nearer to the fulcrum, as the power is lighter than the resistance. A man, therefore, who can without the help of any machine support one hundred weight, will be enabled by this lever to support six hundred. As in this lever the fulcrum may be placed exactly at an equal distance between the power and the weight, or nearer to the one than the other, it is clear that the power and the weight may counterbalance each other, when equal, or when the one exceeds or is exceeded by the other, according to the different situations of the fulcrum. For there will be an equilibrium in a straight lever of any kind, when the power is to the weight, as the distance of the weight from the fulcrum is to the distance of the power from the fulcrum. Thus the arm of a pair of scales, is supported in exact equilibrio,

and is a lever of the first kind, its fulcrum being in the middle between the weight in one scale, and the power to over

come it in the other. The steelyard is also a lever of the first kind, in which the fulcrum is placed near the weight, and the

power is applied at certain distances from it, until an equili brium is produced between the power and weight; by which means, the weight of different bodies are ascertained by the use of one weight only, of known value, and adapted to the graduations on the beam of the instrument. In the hydrostatic balance of Dearborn, the lever, with respect to theory, becomes so near nullity of weight, that the power of one hundreth part of a grain is sufficient to disturb its equilibrium, and challenge a counterpoise.

The hammer lever is also a lever of the first kind, differing from it in nothing but its form. Its name is derived from its use, that of drawing a nail out of wood by a hammer. Suppose the shaft of a hammer to be five times as long as the iron part which draws the nail, the lower part resting on the board as a fulcrum; then by pulling backwards the end of the shaft, a man will draw a nail with one fifth part of the power that he must use to pull it out with pincers; in which case the nail would move as fast as his hand, but with the hammer the hand moves five times as much as the nail, by the time that the nail is drawn out.

In the second kind of lever, the weight is between the fulcrum and the power; or the prop is at one end, the power at the other, and the weight between them. In this lever, as in the one of the first order, the nearer the weight is to the prop, or the farther the power from the prop, the greater is the effect.

In the third kind of lever, the power is between the fulcrum and the weight; it may be considered as the second kind reversed, for the power in this must exceed the weight as much as the distance of the latter from the fulcrum exceeds that of the power from the fulcrum.

If you examine the instruments in general use, you will find, that most of them are levers of one or the other denomination. Thus, a pair of pincers is made up of two levers of the first kind whose centre of motion is the rivet. The power is applied at the handles to press them together, and thereby compress the body as a weight at the opposite ends. In