floats from the water's surface down to their lowest immersion and up again to the surface; hence, each float is far more embarrassed in its duties and complicated in the development of its actuating force than was the frog in his retrograde movements; and what is true of each float is true of all.

But the unnatural developments are more than twofold; and the third is the radial action of the wheels upon the water and their oblique retransmitted action upon the vessel, by which we have a constant series of very unnatural developments. So unnatural, that in the Trans-Atlantic steamers at their usual or average immersion, the first or surface entering paddles would, if the vessel was as the same specific gravity as the water, raise it into the air at the angle of about 45 degrees to the surface of the water; so, too, the leaving paddles, if fully resisted and not counteracted by its buoyancy, would submerge the ship at the same angle; and thus in the dipping floats, we have an increasing series of available actions upon the vessel as the obliquities grow less and less, until parallel to the vessel's run; and a diminishing series in the rising paddles, as the obliquities in

crease.

Another unnatural development of the wheels is their excess of, or unnatural travel in the air. Each float is compelled to move about three miles in ocean steamers, and about five miles in river steamers, in order that they may aid to move the ship one mile, less the horizontal slip of the wheels. Now it is no inconsiderable development of their motive power which whirls these high wheels through the air, made very dense by the water thrown through and pervading every nook and crook of the houses. Evidently, the per centage of this power is much greater in river than in ocean steamers, and but light in slow steamers.

The last, though not least unnatural development, is in her far too diminutive resisting area.

Experiment, guided by the best judgment of men, has established that about one hundred square inches are necessary as the area of an oarblade best suited to resist, and be otherwise available to a man's power in rowing.

Now, if we may illustrate the propelling system by the published data and logs of the Collins steamer Pacific, we find that she has to each wheel of 35.6 ft. diameter, 28 floats, each 10.6 ft. by 21.5 in., of which 7 are immersed upon an average to each wheel; and that their average dip, or at half coal, is 7 ft. All immersed floats, therefore, average 263 square ft. of propelling surface, or 37,926 square inches.

For several passages each way she averaged 1,828 effective horses' power. Now, if we take each effective horse power as equal to nine men, then her motive power upon her pistons equaled an army of 16,452 laboring men.

Deducting the reactionary development through the obliquities upon the crank of 223 per cent, which, in addition to the extra friction due to the oblique actions over direct actions, equals 25 per cent, and we have an effective rotatory power upon the wheels of 12,339 men. Hence, we have to each man's power only 31 square inches of immersed propelling surface from both wheels.

Having 28 floats per wheel and 7 immersed, it is evident we have twice this area immersed per stroke, or only 61 square inches to each man's power per piston stroke, or only of that due to a rowman.

1

There is still an important consideration in these relations, in that the

oar acts steadily and effectually upon the inertia of the water parallel to its boat's run, while the float of the wheel acts from a dipping angle of 45 degrees to an equal leaving angle, so that the water is stirred to a perfect froth.

Increasing the area of the paddles does not remedy these embarrassments, for, owing to the great cycloidal slip, the water is churned by the unending series of entering and passing floats to a mere foam; and the present size, in their cycloidal movement, presents two horizontal surfaces to each wheel, and wider floats would rather shut past each other, as window blinds, and would encumber the dipping and lifting of the floats, and increase the water thrown through the wheel-houses, and consequently increase the power required to drive the returning floats against the air and wheel-house spray. In these considerations, we may not take the variable relation of the floats as if in simple circular rotation at the wharf, but in their peculiar changes due to their horizontal velocity.

The resistance, therefore, to the known power upon the wheels, under the most favorable considerations, does not equal one-fifteenth the resistance we find essential in rowing; and however signally it implicates the mechanical skill of the system, it is just as if we would give the "Whitehall" rowmen oar-blades only one-fifteenth of their present surface, or less than the flat of a man's hand; and it only equals, to each effective horsepower upon the wheels, three-fifths of an oar-blade.

THE PADDLE-WHEEL DEVELOPMENTS.

As a consequence of these very unnatural mechanical arrangements, we find a large development of the rotatory power of the wheel-1st, in producing the horizontal slip of the wheels; 2d, in producing the cycloidal slip; 3d, in producing a horizontal run from the oblique actions upon the vessel; and, 4th, the residuary development, which is only available in the run of the vessel.

To illustrate these developments by the published data and logs of the Collins steamer Pacific, we find that in several passages each way she made 214,303 double strokes of piston, or revolutions of wheels; hence the mean effective pressure of her paddles moved in rotation 3,810 geographical miles, while the ship's run was only 3,098 miles, showing a horizontal slip of the wheels of 712 miles, or 23 per cent of the ship's run.

Her cycloidal slip is, of course, much greater, as it covers the passage of each float from the surface to its deepest dip and up again to the surface. It is difficult to determine this slip actually or relatively, precisely, yet it obviously equals nearly half the run of the wheels.

The development by the oblique lifting action upon the weight of the vessel, and the depressing action upon its buoyancy by the radial floats, we can readily determine, and in the Pacific's relations equals 12 per cent of the actions which tend to produce the run of the ship.

Whatever is developed to produce the slip of her paddles cannot, of course, enter into the propelling actions upon the ship, no more than the power used in overcoming the friction of a machine can be again used.

The question arises, therefore, and it is a highly important questionWhat is that quantity of the rotatory power of the wheels developed in producing their slip?

In propelling, the water acts as a fulcrum to the motive-power, the same as if we stood in a boat and pushed against the wharf; but if the boat is

fast, and we row, the power is developed in the slow movement of the oar; and if the resistance to the oar just equals that to the boat, then the motive-power will be equally developed in the slip of the oar and the slip of the boat. The water is, therefore, a mutual restorative of equilibriums.

From the nature of the case, the horizontal resistance to the oar, or floats, into its motion, equals the horizontal resistance of the vessel into its motion, (supposing all actions parallel to her run;) and when the resistance to the oar is immovable or infinite, as when the boat is free, and we act upon the wharf, or when the boat is fast and we act upon the water, which is movable, then the immovable resistance constitutes a perfect mechanical fulerum. And it is further evident that when both resistances are movable, the resistances will be inversely as their velocities. This obviously arises from the equilibro-restorative medium, under which the actuating power is free to be diverted, in whole or in part, to the lesser resistancetherefore, the power is increased to the lesser resistance, just as the resistance is lessened.

Hence, the quantities of motive-power developed upon their respective resistances, is as their respective velocities.

[This law and its conditions should not be improperly confounded with the general law under other conditions, that the resistances to bodies in water is as the squares of their velocities, for their variable conditions harmonize them; for if the powers were independent, and not mutually, restoratively, variable inversely as the resistances, then the powers developed upon the respective resistances would be as the squares of their velocities.] These considerations present reliably the general relations of the actual motive-power developed, respectively, in the horizontal slip of the wheels and the run of the vessel, of both of which we have tangible data.

From difficulties pertaining to reliable data in relation to the cycloidal slip, and the uncertainty as to how far the horizontal slip covers the legitimate consequences of this slip, we may omit a specific computation of it, preferring to come short of the real disadvantages of the system, rather than to give any uncertain relations, or to exaggerate them. If, however, there was no horizontal slip, then the friction of the cycloidal slip to transAtlantic steamers would be an independent and not an unimportant consideration.

We may present, therefore, confidently knowing that it is below the actual, practical disadvantages, the following computation of the variable developments of the rotatory power of the paddle-wheels.

INEFFICIENCY OF STEAMER "PACIFIC'S'

WHEELS.

We have, as reliable data, of the Pacific's published log

1st. That the horizontal slip of the wheels is to the speed of the ship as 712 is to 3,098, or as 23-100ths of 1 is to 1.

2d. That the motive-power developed by the constantly variable reactions upon the vessel to produce a horizontal resultant power, equals 12-100ths of all the retransmitted actions upon the ship.

3d. That the motive-power developed in the speed of the ship equals 88-100ths of all the actions upon the vessel.

Consequently, omitting the other developments, it is evident

1st. That the development in the velocity of the ship is less than the sum of all the actions upon the ship by 12 per cent of their sum.

2d. That the sum of the actions upon the vessel is less than the rotatory

power of the wheels, by the development which produces the slip of the wheels.

If, therefore, we let a+b+c equal the rotatory power of the wheels; and a equal the power producing the slip of the wheels;

b equal the power developed by the oblique actions upon the ship, to produce the ship's velocity;

c equal the power producing the velocity of the vessel;

then a equals 23 per cent of c; and since b+c equals the action upon the vessel, b equals 12 per cent of b+c, and c equals 88 per cent of b+c. Hence these values are represented thus:

a equals 16.83 per cent of the rotatory power of the wheels;

b 66

9.98 (or 10) per ct. 73.19 (73)

Their sum equaling the full power of the wheels.

a+b, equal to 26.81 per cent of the rotatory power of the wheels, equals the unavailable power, or the mechanical loss, while c equals the available power.

It is equally evident that these unavailable developments do not cover all that are unavailable; and that the available developments given are still considerably larger than is actually, practically true.

We have, then, summarily, the steamer Pacific's developments, thus:1st. 77.25 per cent of the actuating power upon her pistons available upon her wheels;

2d. 56.54 per cent of the actuating power upon her pistons available in her speed;

3d. 43.46 per cent of the actuating power upon her pistons unavailable, or mechanically lost.

These values accrue without any regard to the known losses by extra friction due to the oblique strains over directly transmissive actions upon the crank; by the power developed in the cycloidal slip in addition to the horizontal slip of the wheels; and by the power developed in the unnatural action of so many paddles against the air and wheel-house spray.

From these reliable principles and facts, it is hardly problematical that of the actual motive-power developed in the Collins steamers, not over one-half is available in their speed. Most susceptible of positive proof is the fact, that nearly one-half of their motive-power is entirely unavailable in their speed or economy.

The simple, effectual developments of the Cornish transmission and rowboat propulsion, when properly united by mechanical or inventive skill, are to succeed these very unnatural and inefficient developments.

The losses that accrue by slip and otherwise to the wheels of the first class of light-draft river steamers, only equal from 15 to 20 per cent of their rotatory power.

The aggregate power available in their speed equals about two-thirds of their primary actuating power.

These summary considerations present in plain facts, obvious and scientific truths, the strongest and most urgent incentives to the intelligence of the age, to investigate the present, and seek of science, genius, and practical skill those improvements that shall elevate this department to that of the general enterprises of the age.

Art. 11. THE FIELD OF THE AMAZON.*

FRACTIONAL ASPECT OF THE MISSISSIPPI-RELATIONS WITH THE AMAZON—ATLANTIC THE NATURAL OUTLET OF WESTERN SOUTH AMERICA-THE PERMANENT REGION OF COMMERCIAL SUPREMACYDESCRIPTION OF THE THE AMAZON-POPULATION, PRODUCTS, AND TRADE OF ITS VALLEY—PERU, BOLIVIA, BRAZIL, upon its frEE NAVIGATION.

THE development of the great MISSISSIPPI System of the United States -with all its mighty gatherings of waters the interminable area of its drain-the measureless bulk and variety of the products borne downward by its hundred conveying tides-and the limitless expansive capacity of its harvests-overshadowing as it does all other commercial and industrial enginery combined by nature and art within the country-with all its distinctness and entirety as compared with other fluvial organizations-is not yet, in itself, either in its wonderful present, or in the magnitude of its giant prospective, a thing complete. Such is the fact now; although there has been a time within the brief period of our national existence, when a mind of unusually penetrative force, in an unusual effort of that superior foresight, was required to discern what nature had endeavored so plainly to point out to the empire-founders of middle North America: that this elongated sea with all its articulations, composed, and could compose, no more than one navigation system, essential in its wholeness to the greatness, the power, wealth, age, even the safety of the single nation here establishedthat it was but the complement of their magnificent reach of ocean-shore, and was indispensible to the full realization of these unequaled coastadvantages.

Nature, in her primeval arrangements of the territorial surface, as well as pre-ordaining the magnitude of nations, marking out with most intelligible lines the boundaries by which they should be legitimately and to a degree per force circumscribed, has also measurably indicated the extent and intimacy of their outward correspondence. Not that there are established, in these respects, unvarying limits for all states and conditions of men. We adhere with some emphasis to the modern idea that the expansion of a nation's domain, and the extension of its intercourse may safely and advantageously correspond with the force and activity of its govermental, its commercial, its social, in short, of its civilizing machinery. Barriers invincible to rude tribes, have scarcely the air of an obstacle in the way of the union or correspondence of partially civilized communities. Walls higher, thicker, stronger, are by the power of a superior enlightenment, transpierced, and riddled with intelligence-holes, until the honey-combed fabric offers no obstruction to the free passage of the sun-light, and the mutual sympathies of mutual interests find unreserved interchange. Before the progress of human improvement all fortresses of national limitation, except a few eternal barricades, designed from the first to maintain immutable separation of certain major divisions of the earth, vanish, as the endless distances and insurmountable hights of the child become trifling feasibilities to the

man.

Proportioned then to the state of the subject people, there are natural

• Exploration of the Valley of the Amazon, made under direction of the Navy Department, by W. LEWIS HERNDON and Lardner GIBBON, Lieutenants United States Navy. Part. I. By Lieutenant HERNDON.