Various

“ The best we are able to do is to conceive of a polygon having an infinite number of sides, and so an infinite number of angles, the versed sines of which are infinitely small, and having, also, an infinite number of tangential directions, in which the body can successively move. Still, we have not reached the circle. We never can reach the circle. When you swing a sling around your head, and feel the uniform stress exerted on your hand through the cord, you are made aware of an action which is entirely beyond the grasp of our minds and the reach of our analysis. ”

“ As distance, through which force can act, is necessary to the impartation of velocity, so also time, during which force can act, is necessary to the same result. We do not know how motion from a state of rest begins, any more than we know how a polygon becomes a circle. But we do know that infinite force cannot impart absolutely instantaneous motion to even the smallest body, or to a body capable of opposing the least resistance. Time being an essential element or factor in the impartation of velocity, if this factor be omitted, the least resistance becomes infinite. ”

“ We come now to the reason for the fourth law, that, with a given actual velocity, the centrifugal force varies inversely as the diameter of the circle. If any of you ever revolved a weight at the end of a cord with some velocity, and let the cord wind up, suppose around your hand, without doing anything to accelerate the motion, then, while the circle of revolution was growing smaller, the actual velocity continuing nearly uniform, you have felt the continually increasing stress, and have observed the increasing angular velocity, the two obviously increasing in the same ratio. ”

“ When we see the wonderfully varied forms of plant life, and yet learn that, so to speak, each edifice is built with the same kind of brick, called a cell, modified in form and function; when we see the smallest and simplest equally with the largest and most complicated plant increasing in size subject to the laws of growth by intussusception and cell division, which are universal in the organic world ”

“ Thus it is capable of the widest variety of uses, being soft when ductility, fibrous when tenacity, and crystalline when hardness is required. Its variety of transformations is something wonderful. Meeting iron, or even iron at its best in the form of steel, in the same field, it easily vanquishes it at every point. It melts at 1,300 degrees F., or at least 600 degrees below the melting point of iron, and it neither oxidizes in the atmosphere nor tarnishes in contact with gases. The enumeration of the properties of aluminum is as enchanting as the scenes of a fairy tale. ”

“ Let us suppose a body to be moving in a circular path, around a center to which it is firmly held; and let us, moreover, suppose the impelling force, by which the body was put in motion, to have ceased; and, also, that the body encounters no resistance to its motion. It is then, by our supposition, moving in its circular path with a uniform velocity, neither accelerated nor retarded. Under these conditions, what is the force which is being exerted on this body? ”

“ I will describe as examples the reproduction of a moss, a fern, and a dicotyledon.
In such a typical moss as Funaria, we have the following cycle of developments: The sexual generation is a dioecious leafy structure, having a central elongated axis, with leaves arranged regularly around and along it. At the top of the axis in the male plant rise the antheridia, surrounded by an envelope of modified leaves called the perigonium. The antheridia are stalked sacs, with a single wall of cells, and the spiral antherozoids arise by free-cell formation from the cells of the interior. ”

“ Although in the great trees of the conifers and the dicotyledons we have apparently provision for growth for any number of years, or even centuries, yet accident or decay, or one of the many ills that plants are heirs to, will sooner or later put an end to the life of every individual plant.
Hence the most important act of a plant--not for itself perhaps, but for its race--is the act by which it, as we say, "reproduces itself," that is, the act which results in the giving of life to a second individual of the same form, structure, and nature as the original plant. ”

“ So always in practical operation that law is absolutely true which we observe to be approximated to more and more nearly as we consider smaller and smaller angles, that the versed sine of the angle is the measure of its deflection from the straight line of motion, or the measure of its fall toward the center, which takes place at every point in the motion of a revolving body. ”

“ You are taught not to accept any rule or formula on authority, but to demand the reason for it--to give yourselves no rest until you know the why and wherefore, and comprehend these fully. This is education, not cramming the mind with mere facts and rules to be memorized, but drawing out the mental powers into activity, strengthening them by use and exercise, and forming the habit, and at the same time developing the power, of penetrating to the reason of things. ”

“ If we broaden somewhat the definition of rejuvenescence and free-cell formation, and do not call the mother-cells of spores of mosses, higher cryptogams, and also the mother-cells of pollen-grains, reproductive cells, which strictly speaking they are not, but only producers of the spores or pollen-grains, then we may say that cell-division is confined to vegetative processes, rejuvenescence and free-cell formation are confined to reproductive processes. ”

“ The spores arise from special or mother-cells by a process of division, or it may be even termed free-cell formation, the protoplasm of each mother-cell dividing into four parts, each of which contracts, secretes a wall, and thus by rejuvenescence becomes a spore, and by the absorption of the mother-cells the spores lie loose in the spore sac. The spores are set free by the bursting of their chamber, and each germinates, putting out a branched thread of cells called a protonema, which may perhaps properly be termed a third generation in the cycle of the plant ”

“ There is, however, another sense in which the term "force" is employed, which, in distinction from the above, is termed a statical sense. This "statical force" is the force by the exertion of which a body keeps still. It is the force of inertia--the resistance which all matter opposes to a dynamical force exerted to put it in motion. This is the sense in which the term "force" is employed in the expression "centrifugal force." ”

“ With all its apparent potency, it has its evident weaknesses; moisture is everywhere at war with it, gases and temperature destroy its fiber and its life, continued blows or motion crystallize and rob it of its strength, and acids will devour it in a night. If it be possible to eliminate all, or even one or more, of these qualities of weakness in any metal, still preserving both quantity and quality, that metal will be the metal of the future.
The coming metal, then, to which our reference is made is aluminum, the most abundant metal in the earth's crust. ”

“ The quadruped has to support the weight of his body, and propel himself forward, with the same force. If the force be applied perpendicularly, the body is elevated, but not moved forward. If the force is applied horizontally, the body moves forward, but soon falls to the ground, because it is not supported. But when the force is applied at the proper angle, the body is moved forward and at the same time supported. Directly contrary to Capt. Giles' theory, the greater the speed of the quadruped, the nearer in a direct line with his motion does he apply the propulsive force, and vice versa. ”

“ The standard from which all computations are made of the distances passed through in given times by bodies whose motion is uniformly accelerated, and from which the velocity acquired is computed when the accelerating force is known, and the force is found when the velocity acquired or the rate of acceleration is known, is the velocity of a body falling to the earth. It has been established by experiment, that in this latitude near the level of the sea, a falling body in one second falls through a distance of 16.083 feet, and acquires a velocity of 32.166 feet per second ”

“ Dana has said, "Nearly all rocks are ore-beds of the metal." It is in every clay bank. It is particularly abundant in the coal measures and is incidental to the shales or slates and clays that underlie the coal. This under clay of the coal stratum was in all probability the soil out of which grew the vegetation of the coal deposits. It is a compound of aluminum and other matter, and, when mixed with carbon and transformed by the processes of geologic action, it becomes the shale rock which we know and which we discard as worthless slate. ”

“ Thus we see that the flowering plant is essentially the equivalent of the asexual fern, and of the sporogonium of the moss, and the pollen cell and the embryo-sac represent the two spores of the higher cryptogams, and the pollen tube and the germinal vesicles and antipodal cells are all that remain of the sexual generation, seen in the moss as a leafy plant, and in the fern as a prothallium. ”

“ We have learned the direction and the measure of the deflection, which a revolving body continually suffers, and its resistance to which is termed centrifugal force. The direction is toward the center, and the measure is the versed sine of the angle. ”

“ Forces are the realities with which, as mechanical engineers, you will have directly to deal, all through your lives. The present discussion is limited also to those forces which are developed in moving bodies, or by the motion of bodies. This limitation excludes the force of gravity, which acts on all bodies alike, whether at rest or in motion. ”

“ The water birds and animals, whose weight is supported by the water, do not exert the propulsive force in a downward direction, but in a direct line with the plane of their motion. The man who swims does not increase his motion by kicking out at an angle, but by drawing the feet together with the legs straight, thus using the water between them as a double inclined plane, on which his feet and legs slide and thus increase his motion. ”

“ It is the Archimedean lever by which the great human world has been raised. Should it for a moment forget its cunning and lose its power, earthquake shocks or the wreck of matter could not be more disastrous. However axiomatic may be everything that can be said of this wonderful metal, it is undoubtedly certain that it must give way to a metal that has still greater proportions and vaster possibilities. ”

“ Respecting writers, also, who use language with precision, and who are profound masters of this subject, it must be said that, if it had been their purpose to shroud centrifugal force in mystery, they could hardly have accomplished this purpose more effectually than they have done, to minds by whom it was not already well understood. ”

“ In the dissociation of water into its hydrogen and oxygen, with the mingled carbon in a powdered state, we undoubtedly possess the elements of combustion that are unexcelled on earth, a heat-producing combination that in both activity and power leaves little to be desired this side of the production of the electric force and heat directly from the carbon without the intermediary of boilers, engines, dynamos, and furnaces. ”

“ If instead of the whole protoplasm of the cell arranging itself into one mass, it divides into several, or if portions only of the protoplasm become marked out into new cells, in each case accompanied by rounding off and contraction, the new cells remaining free from one another, and usually each secreting a cell wall, then this process, whose relation to rejuvenescence is apparent, is called free-cell formation. ”

“ As in the general growth and the vegetative reproduction of plants cell-division is the chief method of cell formation, so in the reproduction of plants by special cells the great feature is the part played by cells which are produced not by the ordinary method of cell division, but by one or the other processes of cell formation, namely, free-cell formation or rejuvenescence. ”

“ Judging from the average congenital deaf-mute who has had special instruction in speech, it can safely be asserted that their speech is laborious, and far, very far, from being accurate enough for practical use beyond a limited number of common expressions. This being the case, it is not surprising that as an unaided means of instruction it cannot be a success, for English neither understood when spoken, nor spoken by the pupil, cannot but remain a foreign language, requiring to pass through some other form of translation before it becomes intelligible. ”

“ Motion in the radial direction is the result of these two actions, namely, leaving the first point of contact tangentially and receiving an acceleration of its motion, so that this shall be equal to that of the second point of contact. When we think about the matter a little closely, we see that at the rim of the wheel the oil has perhaps ten times the velocity of revolution which it had on leaving the journal, and that the mystery to be explained really is, How did it get that velocity, moving out on a radial line? ”