ment, and divide the product by two. The effective space as thus determined, is always proportional to the square of the difference in velocity effected.

The nature of the difference between the two measures of force is now apparent. One shows the actual condition of a body, as to rest or motion, and is proportional in bodies of equal weight to the time in which a uniformly acting force produces the acquired velocity. The other measures the space passed over while the velocity is being acquired. Either measures the change a body is capable of producing on another body when estimated in units of its own kind.

Now it happens that the spaces which bodies or atoms traverse, while under the influence of opposing forces, form the most practical mode of determining the magnitude of all the active operations of life. Thus the products of the labor of men and animals, as well as those of machinery of all kinds, consist entirely in results equivalent to the raising of weights. Indeed, considering the atoms of bodies as minute weights, this effect or product of "work" is universal. While, therefore, the unit of this power of producing space effects is a proper one for units of its own kind, we must, to avoid confusion, distinguish carefully between the power of performing work and the moving force.

Thus the compression or extension of a spring is "work performed " upon it, and the spring is capable of performing an equal amount of work in reaction, while regaining its original freedom from tension. So with the expansion of steam or of the gases produced by exploding gunpowder, &c. Their effects are space effects, and should be measured by units of their own kind. Most of the confusion of ideas apparent in the discussions of this subject, arise from attempting to measure a quantity or magnitude of one kind by the unit of another.

As a general conclusion, we find that a small force in a moving body is capable of doing a great deal of work, if the velocity of the body is very great; while on the other hand, a great force in a body so heavy that it has but little velocity, does but comparatively little work. The converse of this is also true. In giving the same momentum to a light body and a heavy one, more coils of a spring are required for the former than for the latter, and the same amount of work will give more momentum to a heavy body than a lighter one-a principle exemplified in the employment of fly wheels to store up force.

In two bodies having equal quantities of associated force or momentum, the vis-viva or power of performing work will be in inverse proportion to the weights of the bodies. For, since the ratio of velocity increases inversely with the weight, we have the square of the inverse ratio divided by the simple ratio, which gives the simple inverse ratio of the weights for the proportion between the two living forces.

Adjourned.

ANNUAL EXHIBITIONS OF THE AMERICAN INSTITUTE.

EXTRACT FROM THE BY-LAWS OF THE AMERICAN INSTITUTE RELATING TO ANNUAL EXHIBITIONS.

ARTICLE X.

DUTIES OF THE BOARD OF MANAGERS.

SECTION 1. The board of managers shall organize by appointing a chairman and vice-chairman from their own number, and a secretary; and after such organization, if it is decided to hold a fair, they shall be entitled to the services of the corresponding secretary of the Institute in preparing circlars and conducting the preliminary correspondence relating to the exhibition, and the clerk of the Institute shall act as their principal clerk, and be in constant attendance during such exhibition.

§ 2. There shall be held in the autumn of each year, unless otherwise ordered by the Institute, a fair, in the city of New York, under the direction of the board of managers, embracing an exhibition of the products of agriculture, manufactures, commerce, and the arts of the United States. The said board may hold, in connection with the fair, a show of live stock whenever they shall deem it expedient; they shall also have the power to make, or cause to be made, a comparative test of ploughs, mowers, reapers, diggers, and other agricultural implements, by putting them into practical operation in the vicinity of the city of New York. They shall further be empowered to examine or cause to be examined any manufacturing process or heavy machinery in operation which it would be impracticable to exhibit within the limits of the fair. §3. Whenever the building and grounds occupied by the Institute for the annual exhibition are sufficiently extensive to warrant the accommodation of specimens and products of industry from all the States in the Union, the board of managers shall have

the power of appointing one of more honorary members from each State, whose especial duty it shall be to give information regarding the fair, to such of its citizens as may desire to become exhibitors thereat.

§ 4. Whenever the Institute shall authorize any special exhibition of vegetables, fruit, flowers, or of specimens of mechanical or chemical skill and ingenuity other than at autumnal fairs, the same shall be held under the direction of the board of managers.

§ 5. The first duty of the board of managers, after it has been decided to hold a fair, shall be to issue a circular inviting all inventors and proprietors of machines, manufactures, works of art, and all cultivators of agricultural and horticultural products, to exhibit the same, setting forth the advantages to be derived from such exhibitions. In order to explain the arrangements and extent of the several departments, they shall also publish in such circular the classification in section 6, which shall be adhered to as far as the room occupied by the fair will allow, in the distribution of space, and in the location of the articles received for exhibition. § 6. Classification at the annual exhibition.

I.-Department of Fine Arts and Education.

1st Group. Paintings on canvas, glass, and other surfaces; pastels, cartoons, miniatures.

2d Group. Engravings, lithographs, chemical etchings, plain and colored, enamel work, designs and drawings relating to architecture and civil engineering.

3d Group. Photographs, plain and colored, daguerreotypes, ambrotypes. All other impressions by the action of light.

4th Group. Sculpture, cameos, medals, medallions, bas relief, embossed work, fine castings in bronze, zinc, and other metals.

5th Group. Musical instruments-pianos, organs, melodeons, instruments used in bands and concerts.

6th Group. Specimens of printing and bookbinding, stationery, globes, maps, charts, and all apparatus for instructing in science, tables and machines for calculation. 7th Group. Philosophical instruments, mathematical and measuring instruments, dials, chronometers, watches and clocks, telescopes, microscopes, lenses, cameras and other optical instruments, excepting those to be carried in the pocket.

II.-Department of the Dwelling.

1st Group. Apparatus for warming, lighting, cooling and ventilating cooking-stoves, ranges and refrigerators.

2d Group. Kitchen ware and utensils, machines and implements for washing and preparing clothes.

3d Group. Carpets, oil cloths, matting, paper hangings and tapestry.

4th Group. Cabinet furniture-mirrors, upholstery and room conveniences. Writing desks, ornamental safes. 5th Group. Table furniture-cutlery, castors; glass, porcelain, silver and other ware used for holding food and condi

ments.

6th Group. Ornaments for the dwelling house, excepting those embraced in the first department. Billiard tables,

chessmen and boards, contrivances for in-door recreation and amusement.

7th Group. Building accessories and permanent attachments. Doors, window-sash, blinds, mantels, grates, stairs, encaustic tiles and other specimens of flooring, timber frames, cut and cast ornaments for the outside of dwellings, plumbers' work, water closet, apparatus and baths, bells, door-springs, locks, latches, bolts, hinges, screws, nails, and other household hardware, useful and ornamental articles for the grounds surrounding the dwelling.

III.-Department of Dress and Handicraft.

1st Group. Apparel for ladies-hats, bonnets, dresses, hose, boots and shoes, gloves, shawls, cloaks, mantillas, manufactured furs.

2d Group. Apparel for gentlemen-hats, caps, coats, vests, pantaloons, shoes, boots, gloves, overcoats, cloaks, undergarments, furs.

3d Group. Cloths of wool, cotton and silk; all other fabrics, woven, knit, or felt; ribbon, cords, tassels, thread,

buttons, pins, and other materials used in combination with cloth for dresses.

4th Group. Hand implements used by ladies in manufacturing dress-sewing machines, knitting machines, needles, thimbles, scissors, etc.