[35] This cut is taken from the plate of the engine of the Red Rover, manufactured by Boulton and Watt, given in the last edition of Tredgold on the Steam Engine.
[36] Appendix I., on Marine Boilers, by J. Dinnen; Tredgold on the Steam Engine, second edition.
[37] Tredgold on the Steam Engine, Appendix, I. p. 171.
[38] Engines on a very large scale constructed upon this principle are said to be in process of construction for an iron steam-vessel of great tonnage, which is in preparation for the New York passage. It is said that the cylinders of these engines will be one hundred and twenty inches in diameter.
[39] A patent was subsequently taken out for these by Mr. Galloway. Mr. Field did not persevere in its use at the time he invented it. It has, however, been more generally adopted since the date of Galloway's patent.
AMERICAN STEAM NAVIGATION.
The circumstances which rendered these extensive tracts of inland and coast navigation eminently suited to the application of steam power, formed so many obstructions and difficulties to the application of other more ordinary means of locomotion on water. The sheltered bays and sounds which offered a smooth and undisturbed surface to the action of the infant steamer argued the absence of that element which gave effect to the sails and rigging of the wind-propelled ship, and the rapid currents of the gigantic streams formed by the drainage of this great continent, though facilitating access to the coast, rendered the oar powerless in the ascent.
At Paris, Livingstone met Fulton, who had been previously engaged in similar speculations, and being struck with his mechanical skill, and the soundness of his views, joined him in causing a series of experiments to be made, which were accordingly carried on at Plombières, and subsequently on a still more extensive scale on the Seine, near Paris. Having by this course of experiments obtained proofs of the efficiency of Fulton's projects, sufficient to satisfy the mind of Livingstone, he agreed to obtain for Fulton the funds necessary to construct a steam boat on a large scale, to be worked upon the Hudson. It was decided, in order to give the project the best chance of success, to obtain the machinery from Bolton and Watt. In 1803, Fulton accordingly made drawings of the engines intended for this first steamer, which were sent to Soho, with an order for their construction. Fulton, meanwhile, repaired to America, to superintend the construction of the boat. The delays incidental to these proceedings retarded the completion of the boat and machinery until the year 1807, when all was completed, and the first successful experiment made at New York. The vessel was placed, for regular work, to ply between New York and Albany, in the beginning of 1808; and, from that time to the present, this river has been the theatre of the most [Pg490] remarkable series of experiments on locomotion on water which has ever been presented in the history of navigation.
The speed attained by this steam boat, when it first began to ply upon the river, did not exceed four miles an hour, but by a series of improvements its rate of motion was soon increased to six miles an hour. In the steam boats subsequently constructed by Fulton a greater speed was attained; but in the latest vessels built by him he did not exceed a speed of nine miles an hour, which he considered to be the greatest that could be advantageously obtained.
While Fulton was making his plans, and engaged in the [Pg491] construction of his first boat, Mr. Stevens of Hoboken, already mentioned, was engaged in a like project, and completed a vessel, to be propelled by a steam engine, within a few weeks after the first successful voyage of Fulton. Stevens was likewise completely successful; but the exclusive privilege of navigating the Hudson by steam having been granted to Fulton by an act of Congress, Stevens was compelled to select another theatre for his operations, and he accordingly sent his steam boat by sea to Philadelphia, to navigate the Delaware, thus securing for himself the honour of having made the first sea voyage by steam.
Fulton did not long retain the monopoly of the steam navigation of the Hudson. Fortunately for the progress of steam navigation, the act conferring upon him that privilege was declared unconstitutional; and the navigation of that noble river was thrown open to the spirit and enterprise of American genius. The number of passengers conveyed upon it became enormous beyond all precedent, and inducements of the strongest kind were accordingly held out to the improvement of its navigation. The distance between New York and Albany, ascertained by a late survey to be one hundred and twenty-five geographical miles by water, had been performed by Fulton's boats occasionally in fifteen or sixteen hours, being at the rate of about eight miles an hour, including stoppages. It became a great object to increase the speed of this trip, so that it might at all times of the year be performed between sunrise and sunset. Robert L. Stevens, the son of the person of that name already mentioned, immediately after the abolition of Fulton's monopoly, placed on the river a vessel which had been built for the Delaware, which easily performed the passage in twelve hours, being at the rate of nearly ten and a half geographical miles an hour. By this increase of speed the improved boats so entirely monopolised the day work upon the river, that the former steamers were either converted into steam tugs to draw barges laden with goods, or used for night trips between New York and Albany. In the night trips the saving of one or two hours was immaterial, it being sufficient that the vessel which left the one port at night should reach the other in the morning. [Pg492]
The river Hudson rises near Lake Champlain, the easternmost of the great chain of lakes or inland seas which extend from east to west across the northern boundary of the United States. The river follows nearly a straight course southwards for two hundred and fifty miles, and empties itself into the sea at New York. The influence of the tide is felt as far as Albany, above which the stream begins to contract. Although this river in magnitude and extent is by no means equal to several others which intersect the States, it is nevertheless rendered an object of great interest by reason of the importance and extent of its trade. The produce of the state of New York and that of the banks of the great Lakes Ontario and Erie are transported by it to the capital; and one of the most extensive and populous districts of the United States is supplied with the necessary imports by its waters. A large fleet of vessels is constantly engaged in its navigation; nor is the tardy but picturesque sailing vessel as yet excluded by the more rapid steamers. The current of the Hudson is said to average nearly three miles an hour; but as the ebb and flow of the tide are felt as far as Albany, the passage of the steamers between that place and New York may be regarded as equally affected by currents in both directions, or nearly so. The passage therefore, whether in ascending or descending the river, is made nearly in the same time.
The position and form of the machinery is likewise affected by these conditions. Without the necessity of being protected from a rough sea, it is placed on the deck in an elevated position. The cylinders of large diameter and short stroke invariably used in Europe are unknown in America, and the proportions are reversed, a small diameter and stroke of great length being invariably adopted. It is rarely that two engines are used. A single engine, placed in the centre of the deck, with a cylinder from forty to sixty inches' diameter, and from eight to ten foot stroke, drives paddle-wheels from twenty-one to twenty-five feet in diameter, producing from twenty-five to thirty revolutions per minute. The great magnitude of the paddle-wheels and the velocity imparted to them enable them to perform the office of fly-wheels, and to carry the engine round its centres, not however without a perceptible inequality of motion, which gives to the American steamer an effect like that of a row boat advancing by starts with each stroke of the piston. The length of stroke adopted in these engines enables them to apply with great effect the expansive principle, which is almost universally used, the steam being generally cut off at half stroke.
The steamers which navigate the Hudson are vessels of considerable magnitude, splendidly fitted up for the accommodation of passengers; they vary from one hundred and eighty to two hundred and forty feet in length, and from twenty to thirty feet in width of beam. In the following table is given the particulars of nine steamers plying on this river, taken from [Pg494] the work of Mr. Stevenson, and from the paper of Mr. Renwick, inserted in the last edition of Tredgold:—
| Names. | Length of Deck. | Breadth of Beam. | Draft of Water. | Drain of Wheel. |
|---|---|---|---|---|
| Ft. | Ft. | Ft. | Ft. | |
| Dewit Clinton | 230 | 28 | 5·5 | 21 |
| Champlain | 180 | 27 | 5·5 | 22 |
| Erie | 180 | 27 | 5·5 | 22 |
| North America | 200 | 30 | 5 | 21 |
| Independence | 148 | 26 | -- | -- |
| Albany | 212 | 26 | -- | 24·5 |
| Swallow | 233 | 22·5 | 3·75 | 24 |
| Rochester | 200 | 25 | 3·75 | 23·5 |
| Utica | 200 | 21 | 3·5 | 22 |
| Names. | Length of Paddles. | Depth of Paddles. | Number of Engines. | Drain of Cylinder. |
|---|---|---|---|---|
| Ft. | In. | In. | ||
| Dewit Clinton | 13·7 | 36 | 1 | 65 |
| Champlain | 15 | 34 | 2 | 44 |
| Erie | 15 | 34 | 2 | 44 |
| North America | 13 | 30 | 2 | 44·5 |
| Independence | -- | -- | 1 | 44 |
| Albany | 14 | 30 | 1 | 65 |
| Swallow | 11 | 30 | 1 | 46 |
| Rochester | 10 | 24 | 1 | 43 |
| Utica | 9·5 | 24 | 1 | 39 |
| Names. | Length of Stroke. | Number of Rev. | Part of Stroke at which it is cut off. |
|---|---|---|---|
| Ft. | |||
| Dewit Clinton | 10 | 29 | 3⁄4 |
| Champlain | 10 | 27·5 | 1⁄2 |
| Erie | 10 | 27·5 | 1⁄2 |
| North America | 8 | 24 | 1⁄2 |
| Independence | 10 | ||
| Albany | -- | 19 | |
| Swallow | -- | 27 | |
| Rochester | 10 | 28 | |
| Utica | 10 |
None of these vessels have either masts or rigging, and consequently never derive any propelling power except from the engines: they are neither manned nor commanded by persons having any knowledge of navigation: the works that are visible above their decks are the beam and framing of the engine, and the chimneys.
The engines used for steamers on the Hudson, and other great rivers and bays on the eastern coast of America, are most commonly condensing engines, but they nevertheless work with steam of very high pressure, being seldom less than twenty-five pounds per square inch, and sometimes as much as fifty. By reference to the preceding table it will be seen, that the velocity of the piston greatly exceeds the limit generally observed in Europe. It is customary in European marine engines to limit the speed of the piston to about two hundred and twenty feet per minute. Even the piston of a locomotive engine does not much exceed the rate of three hundred feet per minute. In the American steamers, however, the pistons commonly move at the rate of from five to six hundred feet per minute, while the circumference of the paddle-wheels are driven at the rate of from twenty to twenty-two miles an hour. [Pg495]
The hulls of these boats are formed with a perfectly flat bottom and perpendicular sides, rounded at the angles, as represented in fig. 135. At the bow, or cutwater, they are made very sharp, and the deck projects to a great distance over the sides. The weight of the machinery is distributed over an extensive surface of the bottom of this feeble structure, by means of a frame-work of substantial carpentry to which it is attached.
At the height of from four to six feet above the water-line is placed the deck, which is a platform, having the shape of a very elongated ellipse. The extremities of its longer axis are supported by the sternpost and the cutwater, and its sides expand in gentle curves on either hand to a considerable distance beyond the limits of the hull; those parts of the deck thus overhanging the water are called the wheel guards.
Beneath the first deck is the saloon, or dining-room, which also, as is usual in European steamers, forms the gentlemen's sleeping-room. It usually extends from end to end of the vessel. The middle of the first deck is occupied by the engine, boilers, furnaces, and chimneys, of which latter there are generally two. Between the chimneys and the stern, above the first deck, is constructed the ladies' cabin, which is covered by the second deck, called the promenade deck. The great length of these boats and the elevation of the cabins render it impossible for a steersman at the stern to see ahead, and they are, consequently, steered from the bow; the wheel placed there communicating with the helm at the stern, by chains or rods carried along the sides of the boat. Until a recent period, the wheel was connected with the stern by ropes, but some fatal accidents, produced by fire, [Pg496] in which these ropes were burnt, and the steersman lost all power to guide the vessel, caused metal rods or chains to be substituted.
The spokes, which are bolted to cast-iron flanges, are of wood. These flanges, to which they are so bolted, are keyed upon the paddle shaft. The outer extremities of the spokes are attached to circular bands or hoops of iron, surrounding the wheel; and the paddle boards, which are formed of hard wood, are bolted to the spokes. The wheels thus constructed, sometimes consist of three, and not unfrequently four, independent circles of paddle boards, placed one beside the other, and so adjusted in their position, that the boards of no two divisions shall correspond.
The great magnitude of the paddle-wheels, and the circumstance of the navigation being carried on, for the most part, in smooth water, have rendered unnecessary, in America, the adoption of any of those expedients for neutralising the effects of the oblique action of the paddles, which have been tried, but hitherto with so little success, in Europe.
In the following Table is given the dimensions of five of these vessels, all plying between New York and Providence:—
| Names. | Length of Deck. | Breadth of Beam. | Draft. | Diameter of Wheel. |
|---|---|---|---|---|
| Ft. | Ft. | Ft. | Ft. | |
| Providence | 180 | 27 | 9 | -- |
| Lexington | 207 | 21 | -- | 23 |
| Narragansett | 210 | 26 | 5 | 25 |
| Massachusetts | 200 | 29·5 | 8·5 | 22 |
| Rhode Island | 210 | 26 | 6·5 | 24 |
| Names. | Length of Paddles. | Depth of Paddles. | Number of Engines. | Diameter of Cylinder. |
|---|---|---|---|---|
| Ft. | In. | In. | ||
| Providence | -- | -- | 1 | 10 |
| Lexington | 9 | 30 | 1 | 11 |
| Narragansett | 11 | 30 | 1 | 60 |
| Massachusetts | 10 | 28 | 2 | 44 |
| Rhode Island | 11 | 30 | 1 | 11 |
| Names. | Length of Stroke. | Number of Rev. | Part of stroke at which stroke is cut off. |
|---|---|---|---|
| Ft. | |||
| Providence | 65 | ||
| Lexington | 48 | 24 | |
| Narragansett | 12 | 2 | 1⁄2 |
| Massachusetts | 8 | 26 | |
| Rhode Island | 60 | 21 |
The Narragansett, the finest of these vessels, is built of oak, strengthened by diagonal straps or ties of iron, by which her timbers are connected; she is driven by a condensing engine, and has two boilers, exposing about three thousand square feet of surface to the fire. The steam is maintained at a pressure of from twenty to twenty-five lbs. per square inch: the cylinder is horizontal.
The cabins of these sea-boats are of great magnitude, and afford excellent accommodation for passengers, containing generally four hundred berths. In the Massachusetts the chief cabin is one hundred and sixty feet long, twenty-two feet wide, and twelve feet in height, its vast extent being uninterrupted by pillars or any other obstruction. "I have dined," says Mr. Stevenson, "with one hundred and seventy-five persons in this cabin, and, notwithstanding this numerous assembly, the tables, which were arranged in two parallel rows, extending from one end of the cabin to the other, were far from being fully occupied, the attendance was good, and every thing was conducted with perfect regularity and order. There are one hundred and twelve fixed berths ranged round this cabin, and one hundred temporary berths can be erected in the middle of the floor: besides these there are sixty fixed berths in the ladies' cabin, and several temporary sleeping [Pg498] places can be erected in it also. The cabin of the Massachusetts is by no means the largest in the United States. Some steamers have cabins upwards of one hundred and seventy-five feet in length. Those large saloons are lighted by Argand lamps, suspended from the ceiling, and their appearance, when brilliantly lighted up and filled with company, is very remarkable. The passengers generally arrange themselves in parties at the numerous small tables into which the large tables are converted after dinner, and engage in different amusements. The scene resembles much more the coffee-room of some great hotel than the cabin of a floating vessel."
Mr. Stevenson states, that exclusive of the time lost in stoppages, the voyage between New York and Albany is usually made in ten hours. Dr. Renwick, however, who has probably more extensive opportunities of observation, states, that the average time, exclusive of stoppages, is ten hours and a half. The distance being 125·18 geographical miles, the average rate would therefore be 119⁄10 miles per hour. If it be observed that the average rate of some of the best sea-going steamers in Europe obtained from experiments [Pg499] and observations made by myself, more than three years ago, showed a rate of steaming little less than ten geographical miles per hour, and that since that time considerable improvements in steam navigation have been made, and further, that these performances were made under exposure to all the disadvantages of an open sea, the difference between them and the performance of the American river steamers will cease to create astonishment.
Dr. Renwick states that he made, in a boat called the "New Philadelphia," one of the most remarkable passages ever performed. He left New York at five in the afternoon, with the first of the flood, and landed at Catskill, distant 95·8 geographical miles from New York, at a quarter before twelve. Passengers were landed and taken in at seven intermediate points: the rate, including stoppages, was therefore 14·2 miles per hour; and if half an hour be allowed for stoppages, the actual average rate of motion would be fifteen miles and three quarters an hour. As the current, which in this case was with the course of the vessel, did not exceed three miles and a half an hour, the absolute velocity through the water would have been somewhat under twelve miles an hour. This speed is nearly the same as the speed obtained from taking the average time of the voyages between New York and Albany at ten hours and a half; it would therefore appear that the great speed attained in this trip must have been chiefly, if not altogether, owing to the effect of the current.
The severe storms and formidable sea encountered on the lakes render necessary for the navigation, vessels in all respects as strong and powerful as those which navigate the open ocean.
The pressure of steam used in these machines is such as is never used in European engines, even when worked on railways. A pressure of one hundred pounds per inch is here considered extremely moderate. The captain of one of these boats, plying between Pittsburg and St. Louis, told Mr. Stevenson that "under ordinary circumstances his safety valves were loaded with a pressure equal to one hundred and thirty-eight pounds per square inch, but that the steam was occasionally raised as high as one hundred and fifty pounds to enable the vessel to pass parts of the river in which there is a strong current;" and he added, by way of consolation, that "this pressure was never exceeded except on extraordinary occasions!"
The dimensions and power of the Mississippi steamers may be collected from those of the St. Louis, a boat which was plying on that river in 1837. That vessel measured two hundred and fifty feet on deck, and had twenty-eight feet breadth of beam. Her draught of water was eight feet, and her measured capacity one thousand tons. She was propelled by two engines with thirty-inch cylinders, and ten feet stroke; the safety valve being loaded at one hundred pounds per square inch.
The paddle wheels of these vessels are attached to the paddle shaft, in such a manner as to be thrown into and out of gear, at discretion, by the engineer, so that the paddle shaft may revolve without driving the wheels: by this expedient the power of the engine is used to feed the boilers while the vessel stops at the several stations. The vessel is therefore stopped, not, as is usually the case, by stopping the engines, but by throwing the wheels out of connection with the paddle shaft. The engines continue to work, but their [Pg503] power is expended in forcing water into the boiler. By this expedient the activity of the engines may, within practical limits, be varied with the resistance the vessel has to encounter. In working against a strong current, the feed may be cut off from the boilers, and the production of steam, and consequently the power of the engines, thereby stimulated, while this suspension of the feed may be compensated at the next station.
The stoppages to take in goods and passengers, and for relays of fuel, are frequent. "The liberty which they take with their vessels on these occasions," says Mr. Stevenson, "is somewhat amusing: I had a good example of this on board a large vessel, called the Ontario. She was steered close in shore amongst stones and stumps of trees, where she lay for some hours to take in goods: the additional weight increased her draught of water, and caused her to heel a good deal; and when her engines were put in motion, she actually crawled into the deep water on her paddle wheels: the steam had been got up to an enormous pressure to enable her to get off, and the volume of steam discharged from the escapement pipe at every half stroke of the piston made a sharp sound almost like the discharge of fire-arms, while every timber in the vessel seemed to tremble, and the whole structure actually groaned under the shocks."
Besides the steamers used for the navigation of the Mississippi, innumerable steam tugs are constantly employed in towing vessels between the port of New Orleans and the open sea of the Gulf of Mexico. Before the invention of steam navigation, this southern capital of the United States laboured under the disadvantage of possessing almost the only bad and inconvenient harbour in the vast range of coast by which the country is bounded. New Orleans lies at a distance of about one hundred miles from the Gulf of Mexico. The force of the stream, the frequency of shoals, and the winding course of the channel rendered it scarcely possible for a sailing vessel to pass between the port and the sea with the same wind. The anchorage was every where bad, and great difficulty and risk attended the mooring of large vessels to the banks. The steam engine has, however, overcome all [Pg504] these difficulties, and rendered the most objectionable harbour of the Union a safe and good seaport, perfectly easy of approach and of egress at all times; a small steam tug will take in tow several large ships, and carry them with safety and expedition to the offing, where it will dismiss them on their voyage, and take back vessels which may have arrived.
On the Relation between the Temperature, Pressure, and Density of Common Steam.
The following formula, proposed by M. Biot, represents with great accuracy the relation between the temperature and pressure of common steam, throughout all that part of the thermometric scale to which experiments have been extended.
Let
| a = 5·96131330259 |
| log. a1 = 0·82340688193 − 1 |
| log. b1 = −·01309734295 |
| log. a2 = 0·74110951837 |
| log. b2 = −·00212510583 |
The relation between the temperature t with reference to the centesimal thermometer, and the pressure p in millimètres of mercury at the temperature of melting ice, will then be expressed by the following formula:—
| log. p = a − a1b120 + t − a2b220 + t. (1.) |
Formulæ have, however, been proposed, which, though not applicable to the whole scale of temperatures, are more manageable in their practical application than the preceding.
For pressures less than an atmosphere, Southern proposed the following formula, where the pressure is intended to be expressed [Pg506] in pounds per square inch, and the temperature in reference to Fahrenheit's thermometer,—
| p = 0·04948 + ( | 51·3 + t | ) | 5·13 | .(2.) |
| 155·7256 | ||||
| t = 155·7256 {(p − 0·04948)1⁄5·13 − 51·3} | ||||
The following formula was proposed by Tredgold, where p expresses the pressure in inches of mercury:—
| p = ( | 100 + t | ) | 6 | . |
| 177 |
This was afterwards modified by Mellet, and represents with sufficient accuracy experiments from 1 to 4 atmospheres. Let p represent pounds per square inch, and t the temperature by Fahrenheit's thermometer,—
| p = ( | 103 + t | ) | 6 | .(3.) |
| 201·18 | ||||
| t = 201·18 p 1⁄6 − 103 | ||||
M. de Pambour has proposed the following formula, also applicable through the same limits of the scale:—
| p = ( | 98·806 + t | ) | 6 | . (4.) |
| 198·562 | ||||
| t = 198·562 p 1⁄6 − 98·806 | ||||
MM. Dulong and Arago have proposed the following formula for all pressures between 4 and 50 atmospheres:—
| p = (0·26793 + 0·0067585 t)5 | . (5.) |
| t = 147·961 p1⁄5 − 39·644 |
It was about the year 1801, that Dalton, at Manchester, and Gay-Lussac, at Paris, instituted a series of experiments on gaseous bodies, which conducted them to the discovery of the law mentioned in art. (96.), p. 171. These philosophers found that all gases whatever, and all vapours raised from liquids by heat, as well as all mixtures of gases and vapours, are subject to the same quantity of expansion between the temperatures of melting ice and boiling water; and by experiments subsequently made by Dulong and Petit, this uniformity of expansion has been proved to extend to all temperatures which can come under practical inquiries.
Dalton found that 1000 cubic inches of air at the temperature of melting ice dilated to 1325 cubic inches if raised to the temperature of boiling water. According to Gay-Lussac, the increased volume was 1375 cubic inches. The latter determination has been subsequently found to be the more correct one.[40]
It appears, therefore, that for an increase of temperature from 32° to 212°, amounting to 180°, the increase of volume is 375 parts in 1000; and since the expansion is uniform, the increase of volume for 1° will be found by dividing this by 180, which will give an increase of 2081⁄3 parts in 100,000 for each degree of the common thermometer.
To reduce the expression of this important and general law to mathematical language, let v be the volume of an elastic fluid at the temperature of melting ice, and let nv be the increase which that volume would receive by being raised one degree of temperature under the same pressure. Let V be its volume at the temperature T. Then we shall have
| V = v + nv (T − 32) = v {1 + n (T − 32)}. |
If V′ be its volume at any other temperature T′, and under the same pressure, we shall have, in like manner,
| V′ = v {1 + n (T′ − 32)}. |
Hence we obtain
| V | = | 1 + n (T − 32) | ;(6.) |
| V′ | 1 + n (T′ − 32) |
which expresses the relation between the volumes of the same gas or vapour under the same pressure and at any two temperatures. The co-efficient n, as explained in the text, has the same value for the same gas or vapour throughout the whole thermometric scale. But it is still more remarkable that this constant has the same value for all gases and vapours. It is a number, therefore, which must have some essential relation to the gaseous or elastic state of fluid matter, independent of the peculiar qualities of any particular gas or vapour.
The value of n, according to the experiments of Gay-Lussac, is 0·002083, or 1⁄480.
To reduce the law of Mariotte, explained in (97.) p. 171., to mathematical language, let V, V′ be the volumes of the same gas or vapour under different pressures P, P′, but at the same temperature. We shall then have
| VP = V′P′. (7.) |
If it be required to determine the relation between the volumes of the same gas or vapour, under a change of both temperature and pressure, let V be the volume at the temperature T and under the pressure P, and let V′ be the volume at the temperature T′ and under the pressure P′. Let v be the volume at the temperature T and under the pressure P′.
By formula (7.) we have
| VP = vP′; |
and by formula (6.) we have
| V′ | = | 1 + n(T′ − 32) |
| v | 1 + n(T − 32) |
Eliminating v, we shall obtain
| V | = | P′ | · | 1 + n(T − 32) | ; |
| V′ | P | 1 + n(T′ − 32) |
or,
| VP | = | 1 + n(T − 32) | ;(8.) |
| V′P′ | 1 + n(T′ − 32) |
which is the general relation between the volumes, pressures, and temperatures of the same gas or vapour in two different states.
To apply this general formula to the case of the vapour of water, let T′ = 212°. It is known by experiment that the corresponding value of P′, expressed in pounds per square inch, is 14·706; and that V′, expressed in cubic inches, the water evaporated being taken as a cubic inch, is 1700. If, then, we take 0·002083 as the value of n, we shall have by (8.),
| VP = | 1700 × 14·706 × {1 + 0·002083 (T − 32)} | |
| 1 + 0·002083 × 180 | ||
| = 18183{1 + 0·002083 (T − 32)}. | (9.) | |
If, by means of this formula (9.), and any of the formulæ (1.), (2.), (3.), (4.), (5.), T were eliminated, we should obtain a formula between V and P, which would enable us to compute the enlargement of volume which water undergoes in passing into steam under any proposed pressure. But such a formula would not be suitable for practical computations. By the formulæ (1.) to (5.), a table of pressures and corresponding temperatures may be computed; and these being known, the formula (9.) will be sufficient for the computation of the corresponding values of V, or the enlargement of volume which water undergoes in passing into steam.
In the following table, the temperatures corresponding to pressures from 1 to 240 lbs. per square inch are given by computation from the formulæ (2.) to (5.), and the volumes of steam produced by an unit of volume of water as computed from the formula (9.).
The mechanical effect is obtained by multiplying the pressure in pounds by the expansion of a cubic inch of water in passing into steam expressed in feet, and is therefore the number of pounds which would be raised one foot by the evaporation of a cubic inch of water under the given pressure. [Pg509]
| Total pressure in Pounds per Square Inch. | Corresponding Temperature. | Volume of the Steam compared to the Volume of the Water that has produced it. | Mechanical Effect of a Cubic Inch of Water evaporated in Pounds raised One Foot. |
|---|---|---|---|
| 1 | 102·9 | 20868 | 1739 |
| 2 | 126·1 | 10874 | 1812 |
| 3 | 141·0 | 7437 | 1859 |
| 4 | 152·3 | 5685 | 1895 |
| 5 | 161·4 | 4617 | 1924 |
| 6 | 169·2 | 3897 | 1948 |
| 7 | 175·9 | 3376 | 1969 |
| 8 | 182·0 | 2983 | 1989 |
| 9 | 187·4 | 2674 | 2006 |
| 10 | 192·4 | 2426 | 2022 |
| 11 | 197·0 | 2221 | 2036 |
| 12 | 201·3 | 2050 | 2050 |
| 13 | 205·3 | 1904 | 2063 |
| 14 | 209·1 | 1778 | 2074 |
| 15 | 212·8 | 1669 | 2086 |
| 16 | 216·3 | 1573 | 2097 |
| 17 | 219·6 | 1488 | 2107 |
| 18 | 222·7 | 1411 | 2117 |
| 19 | 225·6 | 1343 | 2126 |
| 20 | 228·5 | 1281 | 2135 |
| 21 | 231·2 | 1225 | 2144 |
| 22 | 233·8 | 1174 | 2152 |
| 23 | 236·3 | 1127 | 2160 |
| 24 | 238·7 | 1084 | 2168 |
| 25 | 241·0 | 1044 | 2175 |
| 26 | 243·3 | 1007 | 2182 |
| 27 | 245·5 | 973 | 2189 |
| 28 | 247·6 | 941 | 2196 |
| 29 | 249·6 | 911 | 2202 |
| 30 | 251·6 | 883 | 2209 |
| 31 | 253·6 | 857 | 2215 |
| 32 | 255·5 | 833 | 2221 |
| 33 | 257·3 | 810 | 2226 |
| 34 | 259·1 | 788 | 2232 |
| 35 | 260·9 | 767 | 2238 |
| 36 | 262·6 | 748 | 2243 |
| 37 | 264·3 | 729 | 2248 |
| 38 | 265·9 | 712 | 2253 |
| 39 | 267·5 | 695 | 2259 |
| 40 | 269·1 | 679 | 2264 |
| 41 | 270·6 | 664 | 2268 |
| 42 | 272·1 | 649 | 2273 |
| 43 | 273·6 | 635 | 2278 |
| 44 | 275·0 | 622 | 2282 |
| 45 | 276·4 | 610 | 2287 |
| 46 | 277·8 | 598 | 2291 |
| 47 | 279·2 | 586 | 2296 |
| 48 | 280·5 | 575 | 2300 |
| 49 | 281·9 | 564 | 2304 |
| 50 | 283·2 | 554 | 2308 |
| 51 | 284·4 | 544 | 2312 |
| 52 | 285·7 | 534 | 2316 |
| 53 | 286·9 | 525 | 2320 |
| 54 | 288·1 | 516 | 2324 |
| 55 | 289·3 | 508 | 2327 |
| 56 | 290·5 | 500 | 2331 |
| 57 | 291·7 | 492 | 2335 |
| 58 | 292·9 | 484 | 2339 |
| 59 | 294·2 | 477 | 2343 |
| 60 | 295·6 | 470 | 2347 |
| 61 | 296·9 | 463 | 2351 |
| 62 | 298·1 | 456 | 2355 |
| 63 | 299·2 | 449 | 2359 |
| 64 | 300·3 | 443 | 2362 |
| 65 | 301·3 | 437 | 2365 |
| 66 | 302·4 | 431 | 2369 |
| 67 | 303·4 | 425 | 2372 |
| 68 | 304·4 | 419 | 2375 |
| 69 | 305·4 | 414 | 2378 |
| 70 | 306·4 | 408 | 2382 |
| 71 | 307·4 | 403 | 2385 |
| 72 | 308·4 | 398 | 2388 |
| 73 | 309·3 | 393 | 2391 |
| 74 | 310·3 | 388 | 2394 |
| 75 | 311·2 | 383 | 2397 |
| 76 | 312·2 | 379 | 2400 |
| 77 | 313·1 | 374 | 2403 |
| 78 | 314·0 | 370 | 2405 |
| 79 | 314·9 | 366 | 2408 |
| 80 | 315·8 | 362 | 2411 |
| 81 | 316·7 | 358 | 2414 |
| 82 | 317·6 | 354 | 2417 |
| 83 | 318·4 | 350 | 2419 |
| 84 | 319·3 | 346 | 2422 |
| 85 | 320·1 | 342 | 2425 |
| 86 | 321·0 | 339 | 2427 |
| 87 | 321·8 | 335 | 2430 |
| 88 | 322·6 | 332 | 2432 |
| 89 | 323·5 | 328 | 2435 |
| 90 | 324·3 | 325 | 2438 |
| 91 | 325·1 | 322 | 2440 |
| 92 | 325·9 | 319 | 2443 |
| 93 | 326·7 | 316 | 2445 |
| 94 | 327·5 | 313 | 2448 |
| 95 | 328·2 | 310 | 2450 |
| 96 | 329·0 | 307 | 2453 |
| 97 | 329·8 | 304 | 2455 |
| 98 | 330·5 | 301 | 2457 |
| 99 | 331·3 | 298 | 2460 |
| 100 | 332·0 | 295 | 2462 |
| 110 | 339·2 | 271 | 2486 |
| 120 | 345·8 | 251 | 2507 |
| 130 | 352·1 | 233 | 2527 |
| 140 | 357·9 | 218 | 2545 |
| 150 | 363·4 | 205 | 2561 |
| 160 | 368·7 | 193 | 2577 |
| 170 | 373·6 | 183 | 2593 |
| 180 | 378·4 | 174 | 2608 |
| 190 | 382·9 | 166 | 2622 |
| 200 | 387·3 | 158 | 2636 |
| 210 | 391·5 | 151 | 2650 |
| 220 | 395·5 | 145 | 2663 |
| 230 | 399·4 | 140 | 2675 |
| 240 | 403·1 | 134 | 2687 |
In the absence of any direct method of determining the general relation between the pressure and volume of common steam, empirical formulæ expressing it have been proposed by different mathematicians.
The late Professor Navier proposed the following:—Let S express the volume of steam into which an unit of volume of water is converted under the pressure P, this pressure being expressed in kilogrammes per square mètre. Then the relation between S and P will be
| S = | a | , |
| b + mP |
where a = 1000, b = 0·09, and m = 0·0000484.
This formula, however, does not agree with experiment at pressures less than an atmosphere. M. de Pambour, therefore, proposes the following changes in the values of its co-efficients:—Let P express the pressure in pounds per square foot; and let
a = 10000 b = 0·4227 m = 0·00258,
and the formula will be accurate for all pressures. For pressures above two atmospheres the following values give more accuracy to the calculation:—
a = 10000 b = 1·421 m = 0·0023.
In these investigations I shall adopt the following modified formula. The symbols S and P retaining their signification, we shall have
| S = | a | ,(10.) |
| b + P |
where
a = 3875969 b = 164.
These values of a and b will be sufficiently accurate for practical purposes for all pressures, and may be used in reference to low-pressure engines of every form, as well as for high-pressure engines which work expansively.
When the pressure is not less than 30 pounds per square inch, the following values of a and b will be more accurate:—
a = 4347826 b = 618.