Chapter VII: MISCELLANEOUS.--Turkish Baths for Horses.--With (1)

diagram.

* * * * *

FAURE'S MACHINE FOR DECORTICATING SUGAR-CANE.

The object of the apparatus shown in the accompanying engraving is to effect a separation of the tough epidermis of the sugar-cane from the internal spongy pith which is to be pressed. Its function consists in isolating and separating the cells from their cortex, and in putting them in direct contact with the rollers or cylinders of the mill. After their passage into the apparatus, which is naturally placed in a line with the endless chain that carries them to the mill, the canes arrive in less compact layers, pass through much narrower spaces, and finally undergo a more efficient pressure, which is shown by an abundant flow of juice. The first trials of the machine were made in 1879 at the Pointe Simon Works, at Martinique, with the small type that was shown at the Paris Exhibition of 1878. These experiments, which were applied to a work of 3,000 kilos of cane per hour, gave entire satisfaction, and decided the owners of three of the colonial works (Pointe Simon, Larcinty, and Marin) to adopt it for the season of 1880.

The apparatus is shown in longitudinal section in Fig. 1, and in plan in Fig. 2.

Fig. 3 gives a transverse section passing through the line 3-4, and Fig. 4 an external view on the side whence the decorticated canes make their exit from the apparatus.

The other figures relate to details that will be referred to further along.

_The Decorticating Cylinder._--The principal part of the apparatus is a hollow drum, A, of cast iron, 430 mm. in internal diameter by 1.41 m. in length, which is keyed at its two extremities to the shaft, a. Externally, this drum (which is represented apart in transverse section in Fig. 5) has the form of an octagonal prism with well dressed projections between which are fixed the eight plates, C, that constitute the decorticating cylinder. These plates, which are of tempered cast iron, and one of which is shown in transverse section in Fig. 7, when once in place form a cylindrical surface provided with 48 helicoidal, dentate channels. The length of these plates is 470 mm. There are three of them in the direction of the generatrices of the cylinder, and this makes a total of 24. All are strengthened by ribs (as shown in Fig. 8), and each is fixed by 4 bolts, _c_, 20mm. in diameter. The pitch of the helices of each tooth is very elongated, and reaches about 7.52 m. The depth of the toothing is 18 mm.

_Frame and Endless Chain._--The cylinder thus constructed rotates with a velocity of 50 revolutions per minute over a cylindrical vessel, B', cast in a piece with the frame, B. This vessel is lined with two series of tempered cast iron plates, D and D', called exit and entrance plates, which rest thereon, through the intermedium of well dressed pedicels, and which are held in place by six 20-millimeter bolts. Their length is 708 mm. The entrance plates, D, are provided with 6 spiral channels, whose pitch is equal to that of the channels of the decorticating cylinder, C, and in the same direction. The depth of the toothing is 10 mm.

The exit plates, D', are provided with 7 spiral channels of the same pitch and direction as those of the preceding, but the depth of which increases from 2 to 10 mm. The axis of the decorticating cylinder does not coincide with that of the vessel, B', so that the free interval for the passage of the cane continues to diminish from the entrance to the exit.

The passage of the cane to the decorticator gives rise to a small quantity of juice, which flows through two orifices, _b'_, into a sort of cast iron trough, G, suspended beneath the vessel. The cane, which is brought to the apparatus by an endless belt, empties in a conduit formed of an inclined bottom, E, of plate iron, and two cast iron sides provided with ribs. These sides rest upon the two ends of the vessel, B', and are cross-braced by two flat bars, _e_, to which is bolted the bottom, E. This conduit is prolonged beyond the decorticating cylinder by an inclined chute, F, the bottom of which is made of plate iron 7 mm. thick and the sides of the same material 9 mm. thick. The hollow frame, B, whose general form is like that of a saddle, carries the bearings, _b_, in which revolves the shaft, _a_. One of these bearings is represented in detail in Figs. 9 and 10. It will be seen that the cap is held by bolts with sunken heads, and that the bearing on the bushes is through horizontal surfaces only. In a piece with this frame are cast two similar brackets, B², which support the axle, _h_, of the endless chain. To this axle, whose diameter is 100 mm., are keyed, toward the extremities, the pinions, H, to which correspond the endless pitch chains, _i_. These latter are formed, as may be seen in Figs. 11 and 12, of two series of links. The shorter of these latter are only 100 mm. in length, while the longer are 210 mm., and are hollowed out so as to receive the butts of the boards, I. The chain thus formed passes over two pitch pinions, J, like the pinions, H, that are mounted at the extremities of an axle, _j_, that revolves in bearings, I', whose position with regard to the apparatus is capable of being varied so as to slacken or tauten the chain, I. This arrangement is shown in elevation in Fig. 13.

_Transmission._--The driving shaft, _k_, revolves in a pillow block, K, cast in a piece with the frame, B. It is usually actuated by a special motor, and carries a fly-wheel (not shown in the figure for want of space). It receives in addition a cog-wheel, L, which transmits its motion to the decorticating cylinder through, the intermedium of a large wooden-toothed gear wheel, L'. The shaft, _a_, whose diameter is 228 mm., actuates in its turn, through the pinions, M' and M, the pitch pinion, N, upon whose prolonged hub is keyed the pinion, M. This latter is mounted loosely upon the intermediate axle, _m_. Motion is transmitted to the driving shaft, _h_, of the endless chain, I, by an ordinary pitch chain, through a gearing which is shown in Fig. 12. The pitch pinion, N', is cast in a piece with a hollow friction cone, N², which is mounted loosely upon the shaft, _h_, and to which corresponds a second friction cone, O. This latter is connected by a key to a socket, _o_, upon which it slides, and which is itself keyed to the shaft, _h_. The hub of the cone, O, is connected by a ring with a bronze nut, _p_, mounted at the threaded end of the shaft, _h_, and carrying a hand-wheel, P. It is only necessary to turn this latter in one direction or the other in order to throw the two cones into or out of gear.

If we allow that the motor has a velocity of 70 revolutions per minute, the decorticating cylinder will run at the rate of 50, and the sugar-cane will move forward at the rate of 12 meters per minute.

This new machine is a very simple and powerful one. The decortication is effected with wonderful rapidity, and the canes, opened throughout their entire length and at all points of their circumference, leave the apparatus in a state that allows of no doubt as to what the result of the pressure will be that they have to undergo. There is no tearing, no trituration, no loss of juice, but merely a simple preparation for a rational pressure effected under most favorable conditions.

The apparatus, which is made in several sizes, has already received numerous applications in Martinique, Trinidad, Cuba, Antigua, St. Domingo, Peru, Australia, the Mauritius Islands, and Brazil.--_Publication Industrielle._

* * * * *

MOVING A BRIDGE.

An interesting piece of engineering work has recently been accomplished at Bristol, England, which consisted in the moving of a foot-bridge 134 feet in length, bodily, down the river a considerable distance. The pontoons by means of which the bridge was floated to its new position consisted of four 80-ton barges, braced together so as to form one solid structure 64 feet in width, and were placed in position soon after the tide commenced to rise. At six o'clock A.M. the top of the stages, which was 24 feet above the water, touched the under part of the bridge, and in a quarter of an hour later both ends rose from their foundations. When the tide had risen 4 ft. the stage and bridge were floated to the new position, when at 8.30 the girders dropped on to their beds.

* * * * *

THE GENERATION OF STEAM, AND THE THERMODYNAMIC PROBLEMS INVOLVED.[1]

[Footnote 1: Lecture delivered at the Institution of Civil
Engineers, session 1883-84. For the illustrations we are indebted
to the courtesy of Mr. J. Forrest, the secretary.]

By Mr. WILLIAM ANDERSON, M.I.C.E.

It will not be necessary to commence this lecture by explaining the origin of fuel; it will be sufficient if I remind you that it is to the action of the complex rays of the sun upon the foliage of plants that we mainly owe our supply of combustibles. The tree trunks and branches of our forests, as well as the subterranean deposits of coal and naphtha, at one time formed portions of the atmosphere in the form of carbonic acid gas; that gas was decomposed by the energy of the solar rays, the carbon and the oxygen were placed in positions of advantage with respect to each other--endowed with potential energy; and it is my duty this evening to show how we can best make use of these relations, and by once more combining the constituents of fuel with the oxygen of the air, reverse the action which caused the growth of the plants, that is to say, by destroying the plant reproduce the heat and light which fostered it. The energy which can be set free by this process cannot be greater than that derived originally from the sun, and which, acting through the frail mechanism of green leaves, tore asunder the strong bonds of chemical affinity wherein the carbon and oxygen were hound, converting the former into the ligneous portions of the plants and setting the latter free for other uses. The power thus silently exerted is enormous; for every ton of carbon separated in twelve hours necessitates an expenditure of energy represented by at least 1,058 horse power, but the action is spread over an enormous area of leaf surface, rendered necessary by the small proportion of carbonic acid contained in the air, by measure only 1/2000 part, and hence the action is silent and imperceptible. It is now conceded on all hands that what is termed heat is the energy of molecular motion, and that this motion is convertible into various kinds and obeys the general laws relating to motion. Two substances brought within the range of chemical affinity unite with more or less violence; the motion of transition of the particles is transformed, wholly or in part, into a vibratory or rotary motion, either of the particles themselves or the interatomic ether; and according to the quality of the motions we are as a rule, besides other effects, made conscious of heat or light, or of both. When these emanations come to be examined they are found to be complex in the extreme, intimately bound up together, and yet capable of being separated and analyzed.

As soon as the law of definite chemical combination was firmly established, the circumstance that changes of temperature accompanied most chemical combinations was noticed, and chemists were not long in suspecting that the amount of heat developed or absorbed by chemical reaction should be as much a property of the substances entering into combination as their atomic weights. Solid ground for this expectation lies in the dynamic theory of heat. A body of water at a given height is competent by its fall to produce a definite and invariable quantity of heat or work, and in the same way two substances falling together in chemical union acquire a definite amount of kinetic energy, which, if not expended in the work of molecular changes, may also by suitable arrangements be made to manifest a definite and invariable quantity of heat.

At the end of last century Lavoisier and Laplace, and after them, down to our own time, Dulong, Desprez, Favre and Silbermann, Andrews, Berthelot, Thomson, and others, devoted much time and labor to the experimental determination of the heat of combustion and the laws which governed its development. Messrs. Favre and Silbermann, in particular, between the years 1845 and 1852, carried out a splendid series of experiments by means of the apparatus partly represented in Fig. 1 (opposite), which is a drawing one-third the natural size of the calorimeter employed. It consisted essentially of a combustion chamber formed of thin copper, gilt internally. The upper part of the chamber was fitted with a cover through which the combustible could be introduced, with a pipe for a gas jet, with a peep hole closed by adiathermanous but transparent substances, alum and glass, and with a branch leading to a thin copper coil surrounding the lower part of the chamber and descending below it. The whole of this portion of the apparatus was plunged into a thin copper vessel, silvered internally and filled with water, which was kept thoroughly mixed by means of agitators. This second vessel stood inside a third one, the sides and bottom of which were covered with the skins of swans with the down on, and the whole was immersed in a fourth vessel tilled with water, kept at the average temperature of the laboratory. Suitable thermometers of great delicacy were provided, and all manner of precautions were taken to prevent loss of heat.

It is impossible not to admire the ingenuity and skill exhibited in the details of the apparatus, in the various accessories for generating and storing the gases used, and for absorbing and weighing the products of combustion; but it is a matter of regret that the experiments should have been carried out on so small a scale. For example, the little cage which held the solid fuel tested was only 5/8 inch diameter by barely 2 inches high, and held only 38 grains of charcoal, the combustion occupying about sixteen minutes. Favre and Silbermann adopted the plan of ascertaining the weight of the substances consumed by calculation from the weight of the products of combustion. Carbonic acid was absorbed by caustic potash, as also was carbonic oxide, after having been oxidized to carbonic acid by heated oxide of copper, and the vapor of water was absorbed by concentrated sulphuric acid. The adoption of this system showed that it was in any case necessary to analyze the products of combustion in order to detect imperfect action. Thus, in the case of substances containing carbon, carbonic oxide was always present to a variable extent with the carbonic acid, and corrections were necessary in order to determine the total heat due to the complete combination of the substance with oxygen. Another advantage gained was that the absorption of the products of combustion prevents any sensible alteration in the volumes during the process, so that corrections for the heat absorbed in the work of displacing the atmosphere were not required. The experiments on various substances were repeated many times. The mean results for those in which we are immediately interested are given in Table I., next column.

Comparison with later determinations have established their substantial accuracy. The general conclusion arrived at is thus stated:

"As a rule there is an equality between the heat disengaged or absorbed in the acts, respectively, of chemical combination or decomposition of the same elements, so that the heat evolved during the combination of two simple or com-pound substances is equal to the heat absorbed at the time of their chemical segregation."

TABLE I.--SUBSTANCES ENTERING INTO THE COMPOSITION OF FUEL.

-----------------------+-------------+-----------+-------------------+
| | Heat evolved in |
| Symbol and Atomic |the Combustion of |
| Weight. | 1 lb. of Fuel. |
+------------+------------+--------+----------+
| | | |In Pounds |
| | | In | of Water |
| | |British |Evaporated|
| Before | After |Thermal | from and |
| Combustion | Combustion | Units. | at 212°. |
+------------+------------+--------+----------+
Hydrogen burned | H 1 | H2O 18 | 62,032 | 64.21 |
in oxygen. | | | | |
-----------------------+------------+------------+--------+----------+
Carbon burned to | C 12 | CO 28 | 4,451 | 4.61 |
carbonic oxide. | | | | |
-----------------------+------------+------------+--------+----------+
Carbon burned to | C 12 | CO2 44 | 14,544 | 15.06 |
carbonic acid. | | | | |
-----------------------+------------+------------+--------+----------+
Carbonic oxide burned | CO 28 | CO2 44 | 4,326 | 4.48 |
to carbonic acid. | | | | |
-----------------------+------------+------------+--------+----------+
Olefiant gas (ethylene)| C2H4 28 | 2CO2 124 | 21,343 | 22.09 |
burnt in oxygen. | | 2H2O | | |
-----------------------+------------+------------+--------+----------+
Marsh gas (methane) | CH4 16 | 2CO2 80 | 23,513 | 24.34 |
burnt in oxygen. | | 2H2O | | |
-----------------------+------------+------------+--------+----------+

Composition of air--

by volume 0.788 N + 0.197 O + 0.001 CO2 + 0.014 H2O
----------------------------------------------------
by weight 0.771 N + 0.218 O + 0.009 CO2 + 0.017 H2O

This law is, however, subject to some apparent exceptions. Carbon burned in protoxide of nitrogen, or laughing gas, N_{2}O, produces about 38 per cent. more heat than the same substance burned in pure oxygen, notwithstanding that the work of decomposing the protoxide of nitrogen has to be performed. In marsh gas, or methane, CH_{4}, again, the energy of combustion is considerably less than that due to the burning of its carbon and hydrogen separately. These exceptions probably arise from the circumstance that the energy of chemical action is absorbed to a greater or less degree in effecting molecular changes, as, for example, the combustion of 1 pound of nitrogen to form protoxide of nitrogen results in the absorption of 1,157 units of heat. Berthelot states, as one of the fundamental principles of thermochemistry, "that the quantity of heat evolved is the measure of the sum of the chemical and physical work accomplished in the reaction"; and such a law will no doubt account for the phenomena above noted. The equivalent heat of combustion of the compounds we have practically to deal with has been experimentally determined, and therefore constitutes a secure basis on which to establish calculations of the caloric value of fuel; and in doing so, with respect to substances composed of carbon, hydrogen, and oxygen, it is convenient to reduce the hydrogen to its heat-producing equivalent of carbon. The heat of combustion of hydrogen being 62,032 units, that of carbon 14,544 units, it follows that 4.265 times the weight of hydrogen will represent an equivalent amount of carbon. With respect to the oxygen, it is found that it exists in combination with the hydrogen in the form of water, and, being combined already, abstracts its combining equivalent of hydrogen from the efficient ingredients of the fuel; and hence hydrogen, to the extent of 1/8 of the weight of the oxygen, must be deducted. The general formula then becomes:

Heat of combustion = 14,544 {C + 4.265 (H-(O/8))},

and water evaporated from and at 212°, taking 966 units as the heat necessary to evaporate 1 pound of water,

lb. evaporated = 15.06 {C + 4.265 (H-(O/8))},

carbon, hydrogen, and oxygen being taken at their weight per cent. in the fuel. Strictly speaking, marsh gas should be separately determined. It often happens that available energy is not in a form in which it can be applied directly to our needs. The water flowing down from the mountains in the neighborhood of the Alpine tunnels was competent to provide the power necessary for boring through them, but it was not in a form in which it could be directly applied. The kinetic energy of the water had first to be changed into the potential energy of air under pressure, then, in that form, by suitable mechanism, it was used with signal success to disintegrate and excavate the hard rock of the tunnels. The energy resulting from combustion is also incapable of being directly transformed into useful motive power; it must first be converted into potential force of steam or air at high temperature and pressure, and then applied by means of suitable heat engines to produce the motions we require. It is probably to this circumstance that we must attribute the slowness of the human race to take advantage of the energy of combustion. The history of the steam engine hardly dates back 200 years, a very small fraction of the centuries during which man has existed, even since historic times.

The apparatus by means of which the potential energy of fuel with respect to oxygen is converted into the potential energy of steam, we call a steam boiler; and although it has neither cylinder nor piston, crank nor fly wheel, I claim for it that it is a veritable heat engine, because it transmits the undulations and vibrations caused by the energy of chemical combination in the fuel to the water in the boiler; these motions expend themselves in overcoming the liquid cohesion of the water and imparting to its molecules that vigor of motion which converts them into the molecules of a gas which, impinging on the surfaces which confine it and form the steam space, declare their presence and energy in the shape of pressure and temperature. A steam pumping engine, which furnishes water under high pressure to raise loads by means of hydraulic cranes, is not more truly a heat engine than a simple boiler, for the latter converts the latent energy of fuel into the latent energy of steam, just as the pumping engine converts the latent energy of steam into the latent energy of the pumped-up accumulator or the hoisted weight.

If I am justified in taking this view, then I am justified in applying to my heat engine the general principles laid down in 1824 by Sadi Carnot, namely, that the proportion of work which can be obtained out of any substance working between two temperatures depends entirely and solely upon the difference between the temperatures at the beginning and end of the operation; that is to say, if T be the higher temperature at the beginning, and _t_ the lower temperature at the end of the action, then the maximum possible work to be got out of the substance will be a function of (T-_t_). The greatest range of temperature possible or conceivable is from the absolute temperature of the substance at the commencement of the operation down to absolute zero of temperature, and the fraction of this which can be utilized is the ratio which the range of temperature through which the substance is working bears to the absolute temperature at the commencement of the action. If W = the greatest amount of effect to be expected, T and _t_ the absolute temperatures, and H the total quantity of heat (expressed in foot pounds or in water evaporated, as the case may be) potential in the substance at the higher temperature, T, at the beginning of the operation, then Carnot's law is expressed by the equation:

/ T - t \
W = H( ------- )
\ T /

I will illustrate this important doctrine in the manner which Carnot himself suggested.

Fig. 2 represents a hillside rising from the sea. Some distance up there is a lake, L, fed by streams coming down from a still higher level. Lower down on the slope is a millpond, P, the tail race from which falls into the sea. At the millpond is established a factory, the turbine driving which is supplied with water by a pipe descending from the lake, L. Datum is the mean sea level; the level of the lake is T, and of the millpond _t_. Q is the weight of water falling through the turbine per minute. The mean sea level is the lowest level to which the water can possibly fall; hence its greatest potential energy, that of its position in the lake, = QT = H. The water is working between the absolute levels, T and _t_; hence, according to Carnot, the maximum effect, W, to be expected is--

/ T - t \
W = H( ------- )
\ T /
/ T - t \
but H = QT [therefore] W = Q T( ------- )
\ T /

W = Q (T - t),

that is to say, the greatest amount of work which can be expected is found by multiplying the weight of water into the clear fall, which is, of course, self-evident.

Now, how can the quantity of work to be got out of a given weight of water be increased without in any way improving the efficiency of the turbine? In two ways:

1. By collecting the water higher up the mountain, and by that means increasing T.

2. By placing the turbine lower down, nearer the sea, and by that means reducing _t_.

Now, the sea level corresponds to the absolute zero of temperature, and the heights T and _t_ to the maximum and minimum temperatures between which the substance is working; therefore similarly, the way to increase the efficiency of a heat engine, such as a boiler, is to raise the temperature of the furnace to the utmost, and reduce the heat of the smoke to the lowest possible point. It should be noted, in addition, that it is immaterial what liquid there may be in the lake; whether water, oil, mercury, or what not, the law will equally apply, and so in a heat engine, the nature of the working substance, provided that it does not change its physical state during a cycle, does not affect the question of efficiency with which the heat being expended is so utilized. To make this matter clearer, and give it a practical bearing, I will give the symbols a numerical value, and for this purpose I will, for the sake of simplicity, suppose that the fuel used is pure carbon, such as coke or charcoal, the heat of combustion of which is 14,544 units, that the specific heat of air, and of the products of combustion at constant pressure, is 0.238, that only sufficient air is passed through the fire to supply the quantity of oxygen theoretically required for the combustion of the carbon, and that the temperature of the air is at 60° Fahrenheit = 520° absolute. The symbol T represents the absolute temperature of the furnace, a value which is easily calculated in the following manner: 1 lb. of carbon requires 2-2/3 lb. of oxygen to convert it into carbonic acid, and this quantity is furnished by 12.2 lb. of air, the result being 13.2 lb. of gases, heated by 14,544 units of heat due to the energy of combustion; therefore:

14,544 units
T = 520° + ------------------ = 5,150° absolute.
13.2 lb. X 0.238

The lower temperature, _t_, we may take as that of the feed water, say at 100° or 560° absolute, for by means of artificial draught and sufficiently extending the heating surface, the temperature of the smoke may be reduced to very nearly that of the feed water. Under such circumstances the proportion of heat which can be realized is

5,150° - 560°
= --------------- = 0.891;
5,150°

that is to say, under the extremely favorable if not impracticable conditions assumed, there must be a loss of 11 per cent. Next, to give a numerical value to the potential energy, H, to be derived from a pound of carbon, calculating from absolute zero, the specific heat of carbon being 0.25, and absolute temperature of air 520°:

Units.
1 lb. of carbon X 0.25 X 520 = 130
12.2 of air X 0.238 X 520 = 1,485
Heat of combustion = 14,544
------
16,159
Deduct heat equivalent to work of \
displacing atmosphere by products of }
combustion raised from 60° to 100°, } 32
or from 149.8 cubic feet to 161.3 }
cubic feet, /
------
Total units of heat available 16,127

Equal to 16.69 lb. of water evaporated from and at 212°. Hence the greatest possible evaporation from and at 212° from a lb. of carbon--

16,159 u. X 0.891 - 32 u.
W = --------------------------- = 14.87 lb.
966 u.

I will now take a definite case, and compare the potential energy of a certain kind of fuel with the results actually obtained. For this purpose the boiler of the eight-horse portable engine, which gained the first prize at the Cardiff show of the Royal Agricultural Society in 1872, will serve very well, because the trials, all the details of which are set forth very fully in vol. ix. of the _Journal_ of the Society, were carried out with great care and skill by Sir Frederick Bramwell and the late Mr. Menelaus; indeed, the only fact left undetermined was the temperature of the furnace, an omission due to the want of a trustworthy pyrometer, a want which has not been satisfied to this day.[2]

[Footnote 2: In the fifty-second volume of the _Proceedings_
(1887-78), page 154, will be found a remarkable experiment on the
evaporative power of a vertical boiler with internal circulating
pipes. The experiment was conducted by Sir Frederick Bramwell and
Dr. Russell, and is remarkable in this respect, that the quantity
of air admitted to the fuel, the loss by convection and
radiation, and the composition of the smoke were determined. The
facts observed were as follows:

Steam pressure 53 lb................................... = 300.6° F.
lb.
Fuel--Water in coke and wood........................... 26.08
Ash.............................................. 10.53
Hydrogen, oxygen, nitrogen, and sulphur.......... 7.18
------
Total non-combustible..................... 43.79
Carbon, being useful combustible................. 194.46
------
Total fuel................................ 238.25

Air per pound of carbon................................ 17-1/8 lb.
Time of experiment..................................... 4 h. 12 min.
Water evaporated from 60° into steam at 53 lb. pressure 1,620 lb.
Heat lost by radiation and convection.................. 70,430 units.
Mean temperature of chimney............................ 700° F.
" " " air................................ 70° F.

No combustible gas was found in the chimney.

I will apply Carnot's doctrine to this case.

Potential energy of the fuel with respect to absolute zero:
Units.
239.25 lb. × 530° abs. × 0.238 ...................... = 30,053
194.46 lb. × 17-1/8 × 530° × 0.238,
the weight and heat of air....................... 420,660
194.46 × 14,544 units heat of combustion of carbon... 2,828,200
---------
Total energy 3,278,813
Heat absorbed in evaporating 26.08 lb. of water
in fuel............................................ -29,888
---------
Available energy.......................... 3,248,425

Temperature of furnace--

The whole of the fuel was heated up, but the heat absorbed in the
evaporation of the water lowered the temperature of the furnace,
and must be deducted from the heat of combustion.

Units.
Heat of combustion................................... 2,828,200
" " evaporation of 26.08 lb. water............... -29,888
---------
Available heat of combustion.............. 2,798,312

Dividing by 238.25 lb. gives the heat per 1 lb.
of fuel used................................... = 11,745 units.
And temperature of furnace:
11,745 units/(18.125 lb. × 0.238) + 530°......... = 3,253°
Temperature of chimney 700° + 460°............... = 1,160°
Maximum duty (3,253° - 1,160°)/3,253°............ = 0.643°

Work of displacing atmosphere by smoke at 700°:
Cubic feet.
Volumes of gases at 70°........................ = 228.3
" " " " 700°........................ = 499.8
-----
Increase of volume.................... 271.5

Units.
Work done=
(194.46 lb. × 271.5 cub. ft. × 144 sq. in. × 15 lb.)
/722 units ..................................... = 147,720
Maximum amount of work to be expected =
3,248,425 × 0.643.............................. = 2,101,700
Deduct work of displacing atmosphere............. = 147,720
---------
Available work........................ 1,953,980

Actual work done:
Units.
1,620 lb. of water raised from 60° and turned
into steam at 53 lb..... ...................... = 1,855,900
Loss by radiation and convection................. 70,430
10-1/2 lb. ashes left, say at 500°............... 1,129
---------
Total work actually done.............. 1,927,459
Unaccounted for.................................. 26,521
---------
Calculated available work........................ 1,953,980

The unaccounted-for work, therefore, amounts to only 1½ per cent.
of the calculated available work.

Sir Frederick Bramwell ingeniously arranged his data in the form
of a balance sheet, and showed 253,979 units unaccounted for; but
if from this we deduct the work lost in displacing the air, the
unaccounted-for heat falls to less than 4 per cent. of the total
heat of combustion. These results show how extremely accurate the
observations must have been, and that the loss mainly arises from
convection and radiation from the boiler.]

The data necessary for our purpose are:

Steam pressure 80 lb. temperature 324° = 784° absolute. Mean temperature of smoke 389° = 849° " Water evaporated per 1 lb of coal, from and at 212° 11.83 lb. Temperature of the air 60° = 520° absolute. " of feed water 209° = 669° " Heating surface 220 square feet. Grate surface 3.29 feet. Coal burnt per hour 41 lb.

The fuel used was a smokeless Welsh coal, from the Llangennech colleries. It was analyzed by Mr. Snelus, of the Dowlais Ironworks, and in Table II. are exhibited the details of its composition, and the weight and volume of air required for its combustion. The total heat of combustion in 1 lb of water evaporated:

= 15.06 × (0.8497 + 4.265 × (0.426 - 0.035/8))
= 15.24 lb. of water from and at 212°
= 14,727 units of heat.

TABLE II.--PROPERTIES OF LLANGENNECH COAL.

---------------------+----------+------------+---------------------+
| | | |
| | | Products of |
| | Oxygen | Combustion at 32° F.|
| Analyses | required +--------+------------+
| of 1 lb. | for | | |
| of Coal. | Combustion.| Cubic | Volume |
| | Pounds. | feet. | per cent. |
---------------------+----------+------------+--------+------------+
Carbon........... | 0.8497 | 2.266 | 25.3 | 11.1 |
Hydrogen......... | 0.0426 | 0.309 | 7.6 | 3.4 |
Oxygen........... | 0.0350 | --- | --- | --- |
Sulphur.......... | 0.0042 | --- | --- | _ --- |
Nitrogen......... | 0.1045 | --- | 0.18 | | |
Ash.............. | 0.0540 | --- | --- | | |
+----------+------------+ | | 85.5 |
| | | | | |
Total........... | 1.0000 | 2.572 | --- | | |
9-1/3.lb nitrogen | --- | --- | 118.9 | | |
6 lb. excess of air. | --- | --- | 71.4 | _| |
+----------+------------+--------+------------+
Total cubic feet of | | | | |
products per 1 lb. | | | | |
of coal........... | -- | -- | 226.4 | 100.0 |
---------------------+----------+------------+--------+------------+

The temperature of the furnace not having been determined, we must calculate it on the supposition, which will be justified later on, that 50 per cent more air was admitted than was theoretically necessary to supply the oxygen required for perfect combustion. This would make 18 lb. of air per 1 lb. of coal; consequently 19 lb. of gases would be heated by 14,727 units of heat. Hence:

14,727 u.
T = ---------------- = 3,257°
19 lb. × 0.238

above the temperatures of the air, or 3,777° absolute. The temperature of the smoke, _t_, was 849° absolute; hence the maximum duty would be

3,777° - 849°
--------------- = 0.7752.
3,777°

The specific heat of coal is very nearly that of gases at constant pressure, and may, without sensible error, be taken as such. The potential energy of 1 lb. of coal, therefore, with reference to the oxygen with which it will combine, and calculated from absolute zero, is:

Units.
19 lb. of coal and air at the temperature
of the air contained 19 lb. × 520° × 0.238 2,350
Heat of combustion 14,727
-------
17,078
Deduct heat expended in displacing atmosphere 151 cubic feet - 422
------
Total potential energy 16,656

Hence work to be expected from the boiler:

/ 3,777° - 849° \
= 17,078 units X ( --------------- ) - 422 units
\ 3,777° /
---------------------------------------------- = 13.27 lb.
966 units

of water evaporated from and at 212°, corresponding to 12,819 units. The actual result obtained was 11.83 lb.; hence the efficiency of this boiler was

11.83
------- = 0.892.
13.27

I have already claimed for a boiler that it is a veritable heat engine, and I have ventured to construct an indicator diagram to illustrate its working. The rate of transfer of heat from the furnace to the water in the boiler, at any given point, is some way proportional to the difference of temperature, and the quantity of heat in the gases is proportional to their temperatures. Draw a base line representing -460° Fahr., the absolute zero of temperature. At one end erect an ordinate, upon which set off T = 3,777°, the temperature of the furnace. At 849° = _t_, on the scale of temperature, draw a line parallel to the base, and mark on it a length proportional to the heating surface of the boiler; join T by a diagonal with the extremity of this line, and drop a perpendicular on to the zero line. The temperature of the water in the boiler being uniform, the ordinates bounded by the sloping line, and by the line, _t_, will at any point be approximately proportional to the rate of transmission of heat, and the shaded area above _t_ will be proportional to the quantity of heat imparted to the water. Join T by another diagonal with extremity of the heating surface on the zero line, then the larger triangle, standing on the zero line, will represent the whole of the heat of combustion, and the ratio of the two triangles will be as the lengths of their respective bases, that is, as (T - _t_) / T, which is the expression we have already used. The heating surface was 220 square feet, and it was competent to transmit the energy developed by 41 lb. of coal consumed per hour = 12,819 u. × 41 u. = 525,572 units, equal to an average of 2,389 units per square foot per hour; this value will correspond to the mean pressure in an ordinary diagram, for it is a measure of the energy with which molecular motion is transferred from the heated gases to the boiler-plate, and so to the water. The mean rate of transmission, multiplied by the area of heating surface, gives the area of the shaded portion of the figure, which is the total work which should have been done, that is to say, the work of evaporating 544 lb. of water per hour. The actual work done, however, was only 485 lb. To give the speculations we have indulged in a practical turn, it will be necessary to examine in detail the terms of Carnot's formula. Carnot labored under great disadvantages. He adhered to the emission theory of heat; he was unacquainted with its dynamic equivalent; he did not know the reason of the difference between the specific heat of air at constant pressure and at constant volume, the idea of an absolute zero of temperature had not been broached; but the genius of the man, while it made him lament the want of knowledge which he felt must be attainable, also enabled him to penetrate the gloom by which he was surrounded, and enunciate propositions respecting the theory of heat engines, which the knowledge we now possess enables us to admit as true. His propositions are:

1. The motive power of heat is independent of the agents employed to develop it, and its quantity is determined solely by the temperature of the bodies between which the final transfer of caloric takes place.

2. The temperature of the agent must in the first instance be raised to the highest degree possible in order to obtain a great fall of caloric, and as a consequence a large production of motive power.

3. For the same reason the cooling of the agent must be carried to as low a degree as possible.

4. Matters must be so arranged that the passage of the elastic agent from the higher to the lower temperature must be due to an increase of volume, that is to say, the cooling of the agent must be caused by its rarefaction.

This last proposition indicates the defective information which Carnot possessed. He knew that expansion of the elastic agent was accompanied by a fall of temperature, but he did not know that that fall was due to the conversion of heat into work. We should state this clause more correctly by saying that "the cooling of the agent must be caused by the external work it performs." In accordance with these propositions, it is immaterial what the heated gases or vapors in the furnace of a boiler may be, provided that they cool by doing external work and, in passing over the boiler surfaces, impart their heat energy to the water. The temperature of the furnace, it follows, must be kept as high as possible. The process of combustion is usually complex. First, in the case of coal, close to the fire-bars complete combustion of the red hot carbon takes place, and the heat so developed distills the volatile hydrocarbons and moisture in the upper layers of the fuel. The inflammable gases ignite on or near the surface of the fuel, if there be a sufficient supply of air, and burn with a bright flame for a considerable distance around the boiler. If the layer of fuel be thin, the carbonic acid formed in the first instance passes through the fuel and mixes with the other gases. If, however, the layer of fuel be thick, and the supply of air through the bars insufficient, the carbonic acid is decomposed by the red hot coke, and twice the volume of carbonic oxide is produced, and this, making its way through the fuel, burns with a pale blue flame on the surface, the result, as far as evolution of heat is concerned, being the same as if the intermediate decomposition of carbonic acid had not taken place. This property of coal has been taken advantage of by the late Sir W. Siemens in his gas producer, where the supply of air is purposely limited, in order that neither the hydrocarbons separated by distillation, nor the carbonic oxide formed in the thick layer of fuel, may be consumed in the producer, but remain in the form of crude gas, to be utilized in his regenerative furnaces.

_(To be continued.)_

* * * * *

[Continued from SUPPLEMENT No. 437, page 6970.]

PLANETARY WHEEL-TRAINS.

By Prof. C.W. MACCORD, Sc.D.

II.

It has already been shown that the rotations of all the wheels of a planetary train, relatively to the train-arm, are the same when the arm is in motion as they would be if it were fixed. Now, in Fig. 14, let A be the first and F the last wheel of an _incomplete_ train, that is, one having but one sun-wheel. As before, let these be so connected by intermediate gearing that, when T is stationary, a rotation of A through _m_ degrees shall drive F through _n_ degrees: and also as before, let T in the same time move through _a_ degrees. Then, if _m'_ represent the total motion of A, we have again,

m' = m + a, or m = m' - a.

This is, clearly, the motion of A relatively to the fixed frame of the machine; and is measured from a fixed vertical line through the center of A. Now, if we wish to express the total motion of F relatively to the same fixed frame, we must measure it from a vertical line through the center of F, wherever that maybe; which gives in this case:

n' = n + a, or n = n' - a.

but with respect to the train-arm when at rest, we have:

ang. vel. A n
------------ = ---, whence again
ang. vel. F m

n' - a n
------ = --- .
m' - a m

This is the manner in which the equation is deduced by Prof. Willis, who expressly states that it applies whether the last wheel F is or is not concentric with the first wheel A, and also that the train may be composed of any combinations which transmit rotation with both a constant velocity ratio and a constant directional relation. He designates the quantities _m'_, _n'_, _absolute revolutions_, as distinguished from the _relative revolutions_ (that is, revolutions relatively to the train-arm), indicated by the quantities _m_, _n_: adding, "Hence it appears that the absolute revolutions of the wheels of epicyclic trains are equal to the sum of their relative revolutions to the arm, and of the arm itself, when they take place in the same direction, and equal to the difference of these revolutions when in the opposite direction."

In this deduction of the formula, as in that of Prof. Rankine, all the motions are supposed to have the same direction, corresponding to that of the hands of the clock; and in its application to any given train, the signs of the terms must be changed in case of any contrary motion, as explained in the preceding article.

And both the deduction and the application, in reference to these incomplete trains in which the last wheel is carried by the train-arm, clearly involve and depend upon the resolving of a motion of revolution into the components of a circular translation and a rotation, in the manner previously discussed.

To illustrate: Take the simple case of two equal wheels, Fig. 15, of which the central one A is fixed. Supposing first A for the moment released and the arm to be fixed, we see that the two wheels will turn in opposite directions with equal velocities, which gives _n_/_m_ = -1; but when A is fixed and T revolves, we have _m'_ = 0, whence in the general formula

n' - a
------ = -1, or n' = 2 a;
-a

which means, being interpreted, that F makes two rotations about its axis during one revolution of T, and in the same direction. Again, let A and F be equal in the 3-wheel train, Fig. 16, the former being fixed as before. In this case we have:

n
--- = 1, m' = 0, which gives
m

n' - a
------- = 1, [therefore] n' = 0;
-a

that is to say, the wheel F, which now evidently has a motion of circular translation, does not rotate at all about its axis during the revolution of the train-arm.

All this is perfectly consistent, clearly, with the hypothesis that the motion of circular translation is a simple one, and the motion of revolution about a fixed axis is a compound one.

Whether the hypothesis was made to substantiate the formula, or the formula constructed to suit the hypothesis, is not a matter of consequence. In either case, no difficulty will arise so long as the equation is applied only to cases in which, as in those here mentioned, that motion of revolution _can_ be resolved into those components.

When the definition of an epicyclic train is restricted as it is by Prof. Rankine, the consideration of the hypothesis in question is entirely eliminated, and whether it be accepted or rejected, the whole matter is reduced to merely adding the motion of the train-arm to the rotation of each sun-wheel.

But in attempting to apply this formula in analyzing the action of an incomplete train, we are required to add this motion of the train-arm, not only to that of a sun-wheel, but to that of a planet-wheel. This is evidently possible in the examples shown in Figs. 15 and 16, because the motions to be added are in all respects similar: the trains are composed of spur-wheels, and the motions, whether of revolution, translation, or rotation, _take place in parallel planes perpendicular to parallel axes_. This condition, which we have emphasized, be it observed, must hold true with regard to the motions of the first and last wheels and the train-arm, in order to make this addition possible. It is not essential that spur-wheels should be used exclusively or even at all; for instance, in Fig. 16, A and F may be made bevel or screw-wheels, without affecting the action or the analysis; but the train-arm in all cases revolves around the central axis of the system, that is, about the axis of A, and to this the axis of F _must_ be parallel, in order to render the deduction of the formula, as made by Prof. Willis, and also by Prof. Goodeve, correct, or even possible.

This will be seen by an examination of Fig. 17; in which A and B are two equal spur-wheels, E and F two equal bevel wheels, B and E being secured to the same shaft, and A being fixed to the frame H. As the arm T goes round, B will also turn in its bearings in the same direction: let this direction be that of the clock, when the apparatus is viewed from above, then the motion of F will also have the same direction, when viewed from the central vertical axis, as shown at F': and let these directions be considered as positive. It is perfectly clear that F will turn in its bearings, in the direction indicated, at a rate precisely equal to that of the train-arm. Let P be a pointer carried by F, and R a dial fixed to T; and let the pointer be vertical when OO is the plane containing the axes of A, B, and E. Then, when F has gone through any angle a measured from OO, the pointer will have turned from its original vertical position through an equal angle, as shown also at F'.

Now, there is no conceivable sense in which the motion of T can be said to be added to the rotation of F about its axis, and the expression "absolute revolution," as applied to the motion of the last wheel in this train, is absolutely meaningless.

Nevertheless, Prof. Goodeve states (Elements of Mechanism, p. 165) that "We may of course apply the general formula in the case of bevel wheels just as in that of spur wheels." Let us try the experiment; when the train-arm is stationary, and A released and turned to the right, F turns to the left at the same rate, whence:

n
--- = -1; also m' = 0 when A is fixed,
m

and the equation becomes

n' - a
------ = -1, [therefore] n' = 2a:
- a

or in other words F turns _twice_ on its axis during one revolution of T: a result too palpably absurd to require any comment. We have seen that this identical result was obtained in the case of Fig. 15, and it would, of course, be the same were the formula applied to Figs. 5 and 6; whereas it has never, so far as we are aware, been pretended that a miter or a bevel wheel will make more than one rotation about its axis in rolling once around an equal fixed one.

Again, if the formula be general, it should apply equally well to a train of screw wheels: let us take, for example, the single pair shown in Fig. 8, of which, when T is fixed, the velocity ratio is unity. The directional relation, however, depends upon the direction in which the wheels are twisted: so that in applying the formula, we shall have _n/m_ = +1, if the helices of both wheels are right handed, and _n_/_m_ = -1, if they are both left handed. Thus the formula leads to the surprising conclusion, that when A is fixed and T revolves, the planet-wheel B will revolve about its axis twice as fast as T moves, in one case, while in the other it will not revolve at all.

A favorite illustration of the peculiarities of epicyclic mechanism, introduced both by Prof. Willis and Prof. Goodeve, is found in the contrivance known as Ferguson's Mechanical Paradox, shown in Fig. 18. This consists of a fixed sun-wheel A, engaging with a planet-wheel B of the same diameter. Upon the shaft of B are secured the three thin wheels E, G, I, each having 20 teeth, and in gear with the three others F, H, K, which turn freely upon a stud fixed in the train-arm, and have respectively 19, 20, and 21 teeth. In applying the general formula, we have the following results:

n 20 n' - a 1
For the wheel F, --- = ---- = ---------, [therefore] n' = - ---- a.
m 19 -a 19

n n' - a
" " " H, --- = 1 = --------, [therefore] n' = 0.
m -a

n 20 n' - a 1
" " " K, --- = ---- = ---------, [therefore] n' = + ---- a.
m 21 -a 21