LIST OF LATE PUBLICATIONS.

AGRICULTURE.

The American Orchardist; or a practical treatise on the culture and management of apple and other fruit trees. By James Thacher, M. D. 8vo. Boston.

CHEMISTRY-(including Geology and Botany.)

A Geological and Agricultural Survey of Rensselaer County, in the State of New-York. To which is annexed a geological profile, extending from Onondaga salt springs, across said county, to Williams College, in Mass. [By Amos Eaton.] Albany, pp. 70.

A Memoir on the geological position of a Fossil Tree, discovered in the secondary rocks of the River des Plaines. Read before the American Geological Society. By H. R. Schoolcraft. Albany, pp. 18. A Sketch of the Botany of South Carolina and Georgia. By Stephen Elliott. No. VI. Charleston.

A Dictionary of Chemistry, on the basis of Mr. Nicholson. By Andrew Ure, M. D. 1st Am. ed. with additions and notes, by Robert Hare, M. D. assisted by Franklin Bache, M. D. 2 vols. 8vo. Philad. A Manual of Chemistry. By William Thomas Brande. 1st American, from the 2d London edition; to which are added notes and emendations. By Wm. J. Macneven, M. D. Prof. &c. 8vo. Long. New-York.

A Tabular View of the modern nomenclature and system of chemistry. By W. J. Macneven. New-York.

EDUCATION.

An American Grammar, developing the principles of the English language, and impressing them upon the memory, by exercising the judgment of the learner. By James Brown. Bliss & White. N. York.

Preface to the American Grammar, designed to aid its introduction, by exposing the defects of the European system. By James Brown, New-York.

Murray's English Grammar simplified; designed to abridge and facilitate the study of the English language, by enabling the instructor to teach without the aid of his birch, and the student to learn without the drudgery of committing to memory what he does not understand. On a new plan. By Allen Fisk. Large 8vo. pp. 56. Lansingburgh.

Rudiments of Geography, on a new plan; designed to assist the memory by comparison and classification with numerous engravings of Manners, Customs and Curiosities; accompanied with an Atlas, exhibiting the prevailing religions, forms of government, degrees of civilization, &c. By William C. Woodbridge, Assistant Instructor in the American Asylum; accompanied with a system of Ancient Geography, by Mrs. E. Willard. 18mo. Hartford.

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. (Continued from page 255.)

MECHANICS.

SECTION SECOND.-DYNAMICS.

OF MOTION.

We have seen that the ideas of Space and Time, are necessarily involved in the definition of Motion.

126. Velocity is the relation between the spaces described and the times elapsed since the motion began. PISSON 179.

127. The simplest species of motion is where the direction is rectilineal, and the spaces described in equal times are themselves equal; this is called Uniform Motion, or motion with an Uniform Velocity. POISSON, 179.

Uniform motions differ from one another in their velocities.

In measuring velocities, it is convenient to take some known portion of time for the unit, in terms of which all other portions of time are to be designated. The unit in general use is the second of time.

128. A body if once set in motion will continue to move forward in a straight line with uniform velocity, until it is acted upon by some new impulse.

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Although all bodies near the Earth's surface tend to come at last to rest, however violent their original motion may have been, yet, this is no argument against the above proposition, but rather tends to confirm it; for we find the motion of all such bodies to be opposed by retarding forces; among these may be mentioned the resistance of fluid media, and friction; and we also find that by lessening the intensity of the retarding forces, the duration of the motion may be prolonged to such an extent as to show clearly, that if it were possible to remove them altogether, the motion must continue forever. The truth of this proposition is more evident in the motions of the heavenly bodies, that have for ages been known and observed, and yet, in which no diminution is perceptible. POISSON, § 182.

129. If a body, after having described a given space in a certain time shall subsequently describe a greater space in an equal time, we infer the action of some external cause, or new impulse. A motion of this sort is called Accelerated; when the velocity increases by equal increments, in equal times, the motion is said to be Uniformly or Equably Accelerated.

130. So, also, when a body, after having described a given space in a certain time, describes a less space in an equal time, we again infer the action of new impulses, but in a direction contrary to that of the original force.

A motion, where the velocity in equal times decreases, is said to be Retarded.

If the decrements in equal times be equal, it is Uniformly or Equally Retarded.

131. We measure a force by the quantity of motion it is capable of producing, and this in aggregates of matter will depend upon the velocity of the particles and their number.

The term Mass is used in Mechanics to signify the quantity of matter contained in a given body. POISSON, § 310.

132. In homogeneous bodies the mass is proportioned to the bulk; but bodies of different species often contain, under equal bulks, very different quantities of matter.

Density is the comparison between the quantities of matter of different bodies contained under equal bulks.

The difference in density, which is found in different bodies, appears to depend in a great degree upon the interstices that are known to exist between the constituent particles. These interstices are called Pores; their number and extent are so great as to render it probable that even in the densest body, the quantity of matter is small when compared with the quantity of empty space. NEWTON's Optics, Book 2d.

In applying the principles of Statics to the Dynamics of aggregates of matter, or systems of bodies, the following law, known by the name of the Principle of D'Alembert, is of great use. 133. If there be a system of bodies mutually acting in any manHer upon each other; and if at any given time we compute the

motions that these bodies would have in the succeeding instant, were their mutual action to cease; and if we also compute the motions that, in consequence of their mutual action, they actually have at that instant, the motions which must be compounded with the first of these in order to produce the second, are such as, if they acted upon the system alone, would produce no motion, or would be in equilibrio with each other. PLAYFAIR, 117. POISSON, 332. PRONY, § 382.

OF UNIFORM MOTION.

134. The relations between the velocity of a body moving uniformly, the space it describes, and the time of description, may at once be deduced from the definition of Velocity, for if v be the velocity, s the space, and t the time

A more comprehensive form may be given to this equation, so as to make it capable of comparing the motions of bodies that do not set off from the same point; thus, if s be the distance of a moving body, at some particular period, from a fixed point in the direction of its motion, b the distance of the body from the same point, at the end of the time t, v the velocity as before; then s-b will be the space described in the time t. And therefore

The variable quantities s and t may be either positive or negative, according as they represent the situation of the moving body in relation to the given point, at periods before or after that where its place coincides with the point.

=

If another body move upon the same straight line with a velocity v', if its distance from the given points', and if it move during the time t to a distance =b'; the equation of its motion will be s' =v't + b2

(2)

By combining these two equations we may solve every question in relation to the relative motion of the two bodies; if, for instance, we wish to know the instant they meet, then

135. It has been shown that the resultant of two forces, represented in magnitude and direction by the sides of a parallelogram, is represented by the diagonal; hence it is evident, that if a body be acted upon by two forces that would each impel it with

uniform velocity, it will, under their joint action, describe the diagonal of the parallelogram of which the forces are sides.

The same is true if it be acted upon by' two variable forces provided the ratio of acceleration be the same in each.

GREGORY, 217, 218. 136. If a number of bodies be moving in any manner whatever, and if an equal and parallel force act upon each of their particles o matter, the relative motions of the bodies will not be affected. On this principle we can account for several phenomena; for instance: If a fleet be manœuvring in a current, the evolutions will be performed, and the relative positions of the ships will be the same, as if in still water;

The motions and operations in a ship sailing smoothly and regularly along are performed in the same manner as if the vessel were at rest;

Relative motions upon the Earth's surface are not altered by the rapid motion both of rotation and translation with which our planet is affected in its diurnal and annual course.

OF COLLISION.

The simplest mode in which a uniform motion can be communi. cated from one body to another, is by impulse.

Their action upon one another is governed by a principle known as the third law of motion, that may be announced as follows, viz, 137. Action and Reaction are equal to each other, and in contrary directions.

This holds good not only when the bodies come into actual contact, but where they act upon one another at any distance whatever. It is nothing more than a different form of the principle of Inertia already laid down, § 12.

138. All the bodies with which we are acquainted are more or less compressible; and when they have been compressed they have a greater or less tendency to recover their primitive form. This tendency goes by the name of Elasticity. POISSON, ◊ 421.

19. A body is said to be perfectly elastic when it recovers its original form, as soon as the cause that compressed it ceases to act, with a force equal to the compressing force.

Different bodies have different degrees of elasticity, but it does not depend upon their compressibility: the gases are the most easily compressible of all bodies, and are perfectly elas tic; while there are bodies easily compressible that have little elasticity, and others that are very difficult to compress, whose elasticity is not withstanding very great.

140. Although no body is absolutely devoid of Elasticity, yet in treating of the collision of bodies we investigate the laws of the communication of motion as if the bodies under consideration were either absolutely non-elastic or perfectly elastic.