Ach wenn-mein Herz nun bricht LAZARUS. (In broken accents.) I die! yes, it approaches, The step of death approaches! I am prepared to go the gloomy way. It is NATHANAEL. "Heiliger, verlass ihn nicht In der letzten stunde !" Holy One, forsake him not In the last hour! JEMINA. Merciful! forsake him not In the hour of death! MARY. "Ach, lasst von seinen Lippen mich Den letzten Segen küssen!" O! let me from his lips Kiss away the last benediction! MARTHA. "O lag ich schon wie du verhüllt O did I but lay like thee, enveloped CHOIR OF FRIENDS, Who have gradually assembled: "Allgnädiger, heile du Unsrer Seelen Wunde ! Barmherziger, verlass uns nicht All-gracious! heal thou We may exhibit farther specimens of this work in a future number. ARTICLE X. HEADS OF A COURSE OF LECTURES DELIVERED IN COLUMBIA COLLEGE, BY JAMES RENWICK, A. M. Professor of Natural and Experimental Philosophy and Chemistry in that Institution. DEFINITIONS AND INTRODUCTORY REMARKS. 1. Philosophy is the science which inquires into the laws that regulate the phenomena of nature, whether in the intellectual or moral world. The term Philosophy was first used by Pythagoras. CICERO, Tusculana Quæstiones, lib. 5. cap. 3. 2. Philosophy is divided into two branches, corresponding to the two great classes of substances; material and immaterial, The material world is the province of Natural Philosophy; the properties and action of the bodies which compose the universe, the objects of its investigations. 3. The essential properties of matter are Extension, Mobility, and Impenetrability. Attraction is often classed among the properties of matter, particularly that species of attraction known by the name of Gravitation; but we can conceive matter to exist which neither gravitates nor is attracted in any manner by any other portion of mat. ter, and shall yet possess extension, impenetrability, and mobility. 4. Body is a separate and determinate quantity of matter, contained under some known figure, or existing in some determinate mode. The same matter, by a change in its mode of existence, may form many different bodies. 5. Extension in three dimensions being a property of matter, it is, mathematically speaking, infinitely divisible; for geometric and arithmetic magnitude are divisible ad infinitum. 6. The actual division of matter can be carried to an almost incredible extent, as may be shown: by the great ductility of metals; by the distance at which odours affect the olfactory nerves; by the minuteness of the animalculæ discovered through the aid of the microscope, each of which is an organized being; by the colours of chemical solutions; by the smallness of the particles of light. Still it may reasonably be doubted whether matter be infinitely divisible; the more probable supposition is, that it may finally be resolved into particles perfectly hard and incapable of further division. These particles are called atoms; the theory that holds their existence the atomic theory and it seems to be supported by the strong and conclusive evidence of numerous well ascertained facts. This evidence is, however, rather the object of chemical than of physical investigation. 7. Bodies, being of that class of geometric figures called solids, are inclosed by one or more boundaries. 8. The boundaries of solids, are surfaces; the boundaries of surfaces, lines; the terminations of lines, points. Geometry has been defined by Professor Leslie to be that branch of Natural Philosophy which treats of the property of matter called extension. LESLIE'S Elements of Geometry. 9. By the term Impenetrability of Matter, it is intended to express the fact that no two particles of matter can occupy the same portion of space at one and the same time. In this sense the rarest fluid is equally impenetrable with the hardest solid. If matter were penetrable by matter, all the bodies of the universe might be united in any space, however small. MUSCHENBROCK, vol. 1, § 81. 9. The bodies that compose the universe, as regards inhabitants of our earth, are either Terrestrial or Celestial. 10. Terrestrial bodies are divided into three kingdoms; the Mineral, the Vegetable, and the Animal. 11. Bodies differ from each other in respect of the ease or difficulty with which the particles they are composed of may be separated. Those in which the particles can be moved among each other by the smallest effort, are called fluid: those, where they adhere more strongly, solid bodies. 12. Motion is continual and successive change of place. No body possesses within itself the power of changing its state, whether of motion or of rest. It cannot lose motion in any direction without communicating an equal amount to other bodies in the same direction; neither can it acquire motion in any direction, without diminishing the motion of other bodies by an equal quantity in that same direction. This is the annunciation of that principle, called by some authors Inertia, and classed by them as one of the properties of matter. PLAYFAIR'S Outlines, § 21. 13. The foundation of the principles of Natural Philosophy rests upon experiment, and a careful observation of facts. The branch of knowledge that arranges and classifies facts, is called Natural History. BACON, Novum Organum. 14. When from a comparison of a number of facts, known, from experiment or observation, to be true, the existence of a more general fact is inferred, the inference is said to be made by Induction. PLAYFAIR, 3. It is from induction that all certain knowledge of the laws of nature is derived. This method was first explained, and the rules for pursuing it laid down, by Lord Bacon, in his Novum Organum. PLAYFAIR'S Dissertation. Supplement Encyclopedia Britannica. 15. When general principles have been once established by induction, we can often, by the application of mathematical reasoning, deduce from them conclusions as clear and certain as the principles themselves. PLAYFAIR, § 4. 16. We are said to explain a phenomenon when we show it to be necessarily included in some phenomenon or fact already known, or supposed to be known; and we consider one phenomenon as the cause of another, when we conceive the existence of the latter to depend on some force or power residing in the former. PLAYFAIR, 6. 17. A fact assumed in order to explain appearances, and which has no other evidence of its reality but the explanation it is supposed to afford, is called an Hypothesis. 18. An explanation of any system of appearances or events, founded upon facts known to exist from evidence, independent of the facts themselves, is called a Theory. PLAYFAIR, 8. 19. When one system of events or appearances is similar to another; and when we infer that the causes in the two systems are also similar, we are said to reason from Analogy. PLAYFAIR, $9. 20. A theory discovered from induction, may be employed in the discovery of new facts, and to predict the result of new combinations. PLAYFAIR, 10. The order of proceeding is in this case reversed, and is called the method of Synthesis, while the inductive method is called Analysis. 21. The rules for philosophizing are as follows, viz. : there (1.) More causes of natural things are not to be assigned than are both true and sufficient to account for the phenomena. (2.) Of natural effects of the same kind, the same causes are, fore, to be assigned as far as can be done. (3.) The qualities of bodies which cannot be increased or diminished, and which are found common to all bodies on which experiments can be made, are to be considered qualities of all bodies whatsoever. (4.) In Experimental Philosophy, propositions collected from the phenomena by induction, are to be considered as either entirely or nearly true, in spite of contrary hypotheses, until other phenomena occur, by which their accuracy may be more fully pro yed, or by which they may be rendered liable to exceptions. NEWTON'S Principia. Vol. 3. p. 2. of Horsley's edition. The principle of the sufficient reason is also often of great use in philosophizing; it may be announced as follows, viz. Nothing exists in any state that is not determined by some reason to be in that state, rather than in any other. PLAYFAIR, § 12. 22. Experiment is not only valuable as the foundation of all Natural Philosophy, but is indispensable in a course of lectures upon that subject. It is not however to be expected that all the experiments made by the founders of the science, can be performed before a class. It is therefore proper to explain the purposes for which experiment is introduced. It verifies the results of our reasoning, and shows if all the circumstances have been taken into account : It exemplifies how general principles may be applied to explain particular facts: It impresses the mind more forcibly with the truth of the principles that have been laid down; and of the inferences deduced from them. PLAYFAIR, § 13. The definition of motion, which has been given above, involves the consideration of space and time: 23. Space is either absolute or relative. Absolute space is extension without limit, immoveable, but penetrable by matter. Relative space is that part of absolute space which our senses define, by its relation to bodies within it. 24. Place is also either absolute or relative. Absolute Place is the portion of absolute space occupied by a body. Relative Place is the space a body occupies, considered with relation to ather bodies. 25. Absolute Time is an abstract idea, of which no satisfactory definition can be given. Relative time is a portion of duration measured by means of motion. 26. The cause which puts a body in motion, whatever be its nature, is called a Force." The direction of a force is the straight line in which it tends to cause the point to which it is applied to move. When several forces are applied to the same body at the same instant of time, they reciprocally modify each other. If they entirely destroy each other, so that the body is kept at rest by their joint action, we say that an equilibrium takes place among them, or that the body is in equilibrio. Mathematicians have succeeded in reducing all considerations of motion to mere questions of equilibrium. Poisson, Mechanique, § 2. 27. Mechanics is the branch of Natural Philosophy which treats of the motion and equilibrium of bodies. It also treats of the construction of Machines. The first of these is called by Newton, Rational; the second, Practical Mechanics. Rational mechanics is divided into two parts; Statics, which treats of equilibrium, and Dynamics, which treats of the motion of bodies. The first principles of mechanics apply equally to solid and to fluid bodies, but are modified by the individual nature of each. Fluid bodies, however, present peculiar difficulties to the investigation of their mechanical action. We consequently treat of the sta |