SCIENTIFIC AMERICAN SUPPLEMENT NO. 633
NEW YORK, FEBRUARY 18, 1888.
Scientific American Supplement. Vol. XXV., No. 633.
Scientific American established 1845
Scientific American Supplement, $5 a year.
Scientific American and Supplement, $7 a year.
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TABLE OF CONTENTS
I. ARCHITECTURE.—Elements of Architectural Design.—By H.H. STATHAM.—The commencement of a series of lectures delivered before the London Society of Arts, giving the line of development of the different styles and the aspirations of their originators. 34 illustrations. 10106
II. ASTRONOMY.—A Fivefold Comet.—A curious astronomical deduction; the probable division of one comet into five by the disturbing effects of the sun. 1 illustration. 10116
III. BIOGRAPHY.—Linnaeus.—By C.S. HALLBERG.—The life and work of the great botanist, his portrait and birthplace. 2 illustrations. 10114
IV. CHEMISTRY.—An Apparatus for Preparing Sulphurous, Carbonic, and Phosphoric Anhydrides.—By H.N. WARREN.—A simple apparatus for this purpose described and illustrated. 1 illustration. 10117
The Arrangement of Atoms in Space in Organic Molecules.—A review of Prof. JOHANNES WISLICENUS' recent theories on this abstract subject. 10117
The Isolation of Fluorine.—Note on this last isolation of an element, with the properties of the gas. 1 illustration. 10117
V. ELECTRICITY.—Observations on Atmospheric Electricity.—By Prof. L. WEBER.—Abstract of a British Association paper on this important subject. 10114
The Menges Thermo-Magnetic Generator and Motor.—The direct conversion of electricity into heat; the generator fully described. 5 illustrations. 10113
VI. ENGINEERING.—An Investigation into the Internal Stresses Occurring in Cast Iron and Steel.—By General NICHOLAS KALAKOUTZKY.—First installment of an elaborate paper, giving theoretical and experimental examination of this subject. 2 illustrations. 10105
Hargreaves' Thermo-Motor.—A new caloric engine.—Its construction, theory, and cylinder diagrams. 6 illustrations. 10104
The Compound Steam Turbine.—A description and discussion of this motor, in which a series of forty-five turbines are acted on by the current of steam. 2 illustrations. 10103
VII. MISCELLANEOUS.—Cold Storage for Potatoes.—The application of artificial cold to preserving potatoes.—Results obtained in actual experience.—A practical paper by Mr. EDWIN TAYLOR. 10115
VIII. PHYSICS.—On a Method of Making the Wave Length of Sodium Light the Actual and Practical Standard of Length.—By ALBERT A. MICHELSON and EDWARD W. MORLEY.—Description of the new standard of length and outlines of the practical method for its determination.—The question of check determinations. 1 illustration. 10115
IX. TECHNOLOGY.—Progress of the Sorghum Sugar Industry.— Elaborate report on the diffusion process as developed at the Fort Worth, Kan., station. 2 illustrations. 10110
The Lowe Incandescent Gas Burner.—The well known advanced type of gas burner described and illustrated. 1 illustration. 10110
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THE COMPOUND STEAM TURBINE.
Last year the whole of the lighting of the Newcastle Exhibition was effected by the agency of seventeen of these motors, of which four were spare, giving in the aggregate 280 electrical horse power. As the steam was provided by the authorities of the exhibition, it was good proof to the public that they had satisfied themselves that the consumption would not be extravagant, as however favorable might be the terms on which the manufacturers would be willing to lend their engines, they could scarcely be sufficiently tempting to compensate for an outrageous consumption of coal, even in Newcastle. At the time we gave an account of the result of the test, showing that the steam used was 65 lb. per electrical horse power, a very satisfactory result, and equal to 43 lb. per indicated horse power if compared with an ordinary engine driving a generator through a belt. Recently Mr. Parsons has given an account of the theory and construction of his motor before the Northeast Coast Institution, and has quoted 52 lb. of steam per electric horse power as the best result hitherto attained with a steam pressure of 90 lb. As now made there are forty-five turbines through which the steam passes in succession, expanding in each, until it is finally exhausted.
The theoretical efficiency of a motor of this kind is arrived at by Mr. Parsons in the following manner:
The efflux of steam flowing from a vessel at 15.6 lb. per square inch absolute pressure through an orifice into another vessel at 15 lb. pressure absolute is 366 ft. per second, the drop of pressure of 0.6 lb. corresponding to a diminution of volume of 4 per cent. in the opposite direction. The whole 45 turbines are so proportioned that each one, starting from the steam inlet, has 4 per cent. more blade area or capacity than that preceding it. Taking the pressure at the exhaust end to be 15 lb. absolute, that at the inlet end will be 69 lb. above the atmosphere. The steam enters from the steam pipe at 69 lb. pressure, and in passing through the first turbine it falls 2.65 lb. in pressure, its velocity due to the fall being 386 ft. per second, and its increase of volume 3.85 per cent. of its original volume. It then passes through the second turbine, losing 2.55 lb. in pressure, and gaining 3.85 per cent. in volume, and so on until it reaches the last turbine, when its pressure is 15.6 lb. before entering, and 15 lb. on leaving. The velocity due to the last drop is 366 ft. per second. The velocity of the wheels at 9,200 revolutions per minute is 150 ft. per second, or 39.9 per cent. of the mean velocity due to the head throughout the turbines. Comparing this velocity with the results of a series of experiments made by Mr. James B. Francis on a Tremont turbine at Lowell, Mass., it appears that there should be an efficiency of 72 per cent. if the blades be equally well shaped in the steam as in the water turbine, and that the clearances be kept small and the steam dry. Further, as each turbine discharges without check into the next, the residual energy after leaving the blades is not lost as it is in the case of the water turbine, but continues into the next guide blades, and is wholly utilized there. This gain should be equal to 3 to 5 per cent.
As each turbine of the set is assumed to give 72.5 per cent. efficiency, the total number may be assumed to give the same result, or, in other words, over 72 per cent. of the power derived from using the steam in a perfect engine, without losses due to condensation, clearances, friction, and such like. A perfect engine working with 90 lb. boiler pressure, and exhausting into the atmosphere, would consume 20.5 lb. of steam per hour for each horse power. A motor giving 70 per cent. efficiency would, therefore, require 29.29 lb. of steam per horse power per hour. The best results hitherto attained have been 52 lb. of steam per hour per electrical horse power, as stated above, but it is anticipated that higher results will be attained shortly. Whether that be so or not, the motor has many advantages to recommend it, and among these is the increased life of the lamps due to the uniform rotation of the dynamo. At the Phoenix Mills, Newcastle, an installation of 159 Edison-Swan lamps has been running, on an average, eleven hours a day for two years past, yet in that time only 94 lamps have failed, the remaining 65 being in good condition after 6,500 hours' service. Now, if the lamps had only lasted 1,000 hours on the average, as is commonly assumed, the renewals would have amounted to double the year's cost of fuel, as at present consumed.
The present construction of the motor and dynamo is shown in the figures.
Fig. 2 shows the arrangement of 90 complete turbines, 45 lying on each side of the central steam inlet. The guide blades, R, are cut on the internal periphery of brass rings, which are afterward cut in halves and held in the top and bottom halves of the cylinder by feathers. The moving blades, S, are cut on the periphery of brass rings, which are afterward threaded and feathered on to the steel shaft, and retained there by the end rings, which form nuts screwed on to the spindle. The whole of this spindle with its rings rotate together in bearings, shown in enlarged section, Fig. 3. Steam entering at the pipe, O, flows all round the spindle and passes along right and left, first through the guide blades, R, by which it is thrown on to the moving blades, S, then back on to the next guide blades, and so on through the whole series on each hand, and escapes by the passages, P, at each end of the cylinder connected to the exhaust pipe at the back of cylinder. The bearings, Fig. 3, consist of a brass bush, on which is threaded an arrangement of washers, each successive washer alternately fitting to the bush and the block, while being alternately 1/32 smaller than the block outside and 1/32 larger than the bush in the hole. One broad washer at the end holds the bearings central. These washers are pressed together by a spiral spring, N, and nut, and, by friction against each other, steady or damp any vibration in the spindle that may be set up by want of balance or other cause at the high rate of speed that is necessary for economical working.
The bearings are oiled by a small screw propeller, I, attached to the shaft. The oil in the drain pipes, D and F, and the oil tank, D, lies at a lower level than the screw, but the suction of the fan, K, raises it up into the stand pipe, H, over and around the screw, which gripes it and circulates it along the pipes to the bearings. The course of the oil is as follows: The oil is forced by the propeller, I, and oils the bearing, A. The greater part passes along the pipe, E, to the end bearing, C; some after oiling the bearing, C, drains back by the pipe, F, to the reservoir, D; the remaining oil passes along through the armature spindle, oils the bearings, B, and drains into the reservoir, D, from which the oil is again drawn along the pipe, G, into the stand pipe, H, by the suction of the fan, K. The suction of the fan is also connected to the diaphragm, L, and forms, with it and the spring, M, the principal part of the governor which actuates the throttle valve, V. Fig. 4 is the electrical control governor, which will be further described in connection with the dynamo. It acts directly upon the controlling diaphragm, L, by admitting or closing a large access of air to it, and thus exercises a controlling influence upon it.
The dynamo which forms the other portion of the electric generator, Fig. 1, is coupled to the motor spindle by a square tube coupling fitted on to the square spindle ends. The armature is of the drum type. The body is built up of thin iron disks threaded on to the spindle and insulated from each other by tracing paper. This iron body is turned up and grooves milled out to receive the conducting wires. For pressures of 60 to 80 volts there are fifteen convolutions of wire, or 30 grooves. The wire starting at b, Fig. 6, is led a quarter of a turn spirally, c, round the cylindrical portion, a, then passing along a groove longitudinally is again led a quarter turn spirally, d, round the cylindrical portion, a, then through the end washer, and back similarly a quarter turn, e, then led along the diametrically opposite groove, and lastly a little over a quarter turn, f, back to g, where it is coupled to the next convolution. The commutator is formed of rings of sections. Each section is formed of short lengths. Each length is dovetailed and interlocked between conical steel rings. The whole is insulated with asbestos, and, when screwed up by the end nut, forms, with the steel bush, a compact whole. There are fifteen sections in the commutator, and each coupling is connected to a section. The whole armature is bound externally from end to end with brass or pianoforte steel wire. The magnets are of soft cast iron and of the horseshoe type. They are shunt-wound only.
On the top of the magnet yoke is the electrical control governor, Fig. 4. It consists of one moving spindle on which are keyed a small soft iron bar, and also a double finger, T. There is also a spiral spring, X, attached at one end to the spindle, and at the other to an adjustable top head and clamping nut, Y. The double finger, T, covers or opens a small hole in the face, U, communicating by the pipe, W, to the diaphragm, L. The action of the magnet yoke is to attract the needle toward the poles of the magnet, while by turning the head the spiral spring, X, is brought into tension to resist and balance this force, and can be set and adjusted to any degree of tension. The double finger, T, turns with the needle, and, by more or less covering the small air inlet hole, U, it regulates the access of air to the regulating diaphragm, L. The second finger is for safety in case the brushes get thrown off, or the magnet circuit be broken, in which case the machine would otherwise gain a considerable increase of speed before the diaphragm would act. In these cases, however, the needle ceases to be attracted, falls back, and the safety finger closes the air inlet hole.
There is no resistance to the free movement of this regulator. A fraction of a volt increase or decrease of potential produces a considerable movement of the finger, sufficient to govern the steam pressure, and in ordinary work it is found possible to maintain the potential within one volt of the standard at all loads within the capacity of the machine, excepting only a slight momentary variation when a large portion of the load is switched on or off.
The resistance of the armature from brush to brush is only 0.0032 ohm, the resistance of the field magnets is only 17.7 ohms, while the normal output of the dynamo is 200 amperes at 80 volts. This, excluding other losses, gives an efficiency of 97 per cent. The other losses are due to eddy currents throughout the armature, magnetic retardation, and bearing friction. They have been carefully measured. By separately exciting the field magnets from another dynamo, and observing the increased steam pressure required to maintain the speed constant, the corresponding power was afterward calculated in watts.
The commercial efficiency of this dynamo, after allowing for all losses, is a little over 90 per cent. In the larger sizes it rises to 94 per cent. Assuming the compound steam turbine to give a return of 70 per cent. of the total mechanical energy of the steam, and the dynamos to convert 90 per cent of this into electrical output, gives a resulting efficiency of 63 per cent. As steam at 90 lb. pressure above the atmosphere will with a perfect non-condensing engine give a horse power for every 20.5 lb. of steam consumed per hour, it follows that an electrical generator of 63 per cent. efficiency will consume 32.5 lb. of steam for every electrical horse power per hour.
Again, with steam at 150 lb. pressure above the atmosphere, a generator of the same efficiency would consume only 22.2 lb. of steam per electrical horse power per hour.
The results so far actually obtained are a consumption of 52 lb. per hour of steam for each electrical horse power with a steam pressure of 90 lb. above the atmosphere.—Engineering.
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From the researches and investigations of Carnot, Joule, Rankine, Clausius, and Sir William Thomson, the science of thermo-dynamics has not only been brought into existence, but fully matured. We learn from it that whereas in the steam engine, on account of the limited range of temperature in the working cylinder and the rapid conduction of steam during condensation, no combination of cylinders can materially affect its present efficiency, internally fired engines, such as gas and caloric engines—being, as it were, less fettered—can have their already high efficiency increased by simply overcoming mechanical difficulties. To this fact is no doubt due the recent remarkable development of gas and caloric engines. The first caloric or hot air engine was invented by Sir George Cayley in 1807, and in 1827 Dr. Robert Stirling, a Scotch minister, took out his first patent for a hot air engine, which was the foundation of many subsequent machines, and by the invention of the regenerator he converted what was practically a scientific toy into an efficient machine.
One of the most ardent workers in this field at the present time is Mr. James Hargreaves, of Widnes, who, with a thorough theoretical knowledge of the subject has, after many years of patient perseverance, over come many of the mechanical difficulties, and designed the engine of which the above is an illustration.
The sectional elevation, shown in Fig. 1, is an expanded view of the machine, shown thus to enable the action of the machine to be more clearly understood; the relative position of the different parts, as actually made, is shown in the side elevation (Fig. 4). The principal working parts of the machine are the combustion chamber, D, which is of the form shown, lined with fire brick, and having an entrance, with the door screwed down like a manhole lid; the working cylinder, A, surrounded by the water casing, K; the piston, B, with a water lining, and coupled to the end of the working beam by a parallel motion, the beam being supported by two rocking columns, Z, as in engines of the "grasshopper" type; the air compressor, C, coupled directly to the piston of the working cylinder; the injection pump, F, for supplying the fuel—creosote or coal tar—to the combustion chamber; the regenerator E; the receiver and separator, V Y; the feed and exhaust valves, M.
The action of the machine is as follows: Assuming the engine to be in condition for starting, the sides of the combustion chamber, D, are red hot, the chamber charged with air, and the spray of creosote, injected by the pump, F, is ignited; the expansion of the gases produced by the combustion acts upon the bottom of the piston, B, forcing it to the top of the cylinder, and thus, by intermediate mechanism, causing the crank shaft to revolve. By the same stroke a charge of air is forced by the compressor, C, into the receiver through the pipe, R. The cylinder is, of course, single acting, and on the down stroke of the piston, B—which falls by its own weight and the momentum of the fly wheel—the exhaust gases are forced through the regenerator, E, which absorbs most of their heat; they then pass through the exhaust valve, placed immediately under the feed valve, M, along the pipe, Q, up through the pipes, T, fitted into the receiver, V, down the pipes, T, fitted into the saturator, Y, and out of the funnel fixed to the bottom of Y.
The charge of air for supplying the combustion chamber is forced by the compressor, C, through the pipe, R, outside the tubes, T, in the chambers, V and Y, along the pipe, P, through the feed valve, M, and the regenerator, E, into the combustion chamber. In its passage from the compressor, it first picks up the residual heat of the exhaust gases in the tubes, T, and finally the heat absorbed by the regenerator, E, thus entering the combustion chamber in a highly heated state. Having described generally the passage of the air from the compressor to the working cylinder, and back again to the funnel, we will now describe the details. The working cylinder, A, is fitted into the casting which forms the water casing, K, a space being left between the bottom of the cylinder and the casing, which is filled with a non-conducting mixture of asbestos to protect it from the heat of combustion; the bottom of the piston, B, has a similar protection, and the regenerator has a lining of the same mixture, to prevent any heat from escaping through the casting which holds it. The water in the casing, K, and in the piston, B, is supplied by a small pump, G, which forces the water through the pipe, P4, into the telescopic pipe, L either into the piston, B, or through the pipe, P6, into the casing, K—the bottom of the casing being connected by the pipe, P10, with the auxiliary boiler, W. The steam generated in the casing, K, is carried to the boiler, W, by the pipe, P3, and from the boiler it passes along the pipe, P2, through the valve, A2, into the chamber, V, thus giving up its heat to the incoming air, with which it mixes. The vapor gradually condenses at the bottom of the vessel, Y, and the water so formed is drawn by the pump, J, along the suction pipe, P9, and forced through the pipe, P8, back to the chamber, Y, through the valve, A1, and in the form of spray plays on the tubes, T, and absorbing any residual heat. The heat generated by compression in the cylinder, C, is absorbed by a spray of water from the pump, H, the vapor being carried along with the air through the pipe, R, to the chamber, Y, where it is separated, and falling to the bottom is circulated, as just described, by the pump, J. X is a small auxiliary air compressor, to obtain the necessary compression to start the engine, and is worked from the boiler, W. In future engines this compressor will be superseded by a specially designed injector, which will produce the necessary pressure at a considerable reduction in cost. When once the engine is started, the fire of the auxiliary boiler can, of course, be drawn, as the main engine afterward makes its own steam. The regenerator, E, has circular ends of fire clay perforated, the body being filled with fire clay spirals of the shape clearly shown in elevation in Fig. 2. The injector valve for the creosote is shown to a larger scale in Fig. 3. This valve has, however, been since considerably modified and improved. The feed and exhaust valves, M, are actuated by cams keyed to a countershaft driven by bevel wheels from the main shaft. The creosote pump, F, is also worked by a cam on the same shaft, but the pumps, G H J, are worked by eccentrics. A stop valve, N, is fixed to the supply pipe, P, under which is place a back pressure valve to retain the pressure in the combustion chamber. The engine is regulated by an ordinary Porter governor actuating the throttle valve, O. An engine, as described, has been constructed by Messrs. Adair & Co., engineers, Waterloo Road, Liverpool, and has been running most satisfactorily for several weeks, the results being clearly shown by the indicator diagrams (Figs. 5 and 6). The results obtained by this motor are very remarkable, and are a long way in advance of any previous performance, as only a little over 1/2 lb. of fuel is used per i.h.p. per hour. It may be mentioned that the temperature of the combustion chamber is calculated to be about 2,500 deg.F., and that of the exhaust gases does not exceed 180 deg.F.—Industries.
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AN INVESTIGATION INTO THE INTERNAL STRESSES OCCURRING IN CAST IRON AND STEEL.
BY GENERAL NICHOLAS KALAKOUTZKY.
_Determination of the Influence of Internal Stresses on the Strength of Materials._—We call internal stresses those which exist within the mass of any hollow cylinder or other body, when it appears to be in a state of repose, or not under the influence of external forces. When pressure is applied to a hollow cylinder, either externally or internally, the interior layers into which its walls may be conceived to be divided are subjected to a new series of stresses, the magnitude of which is independent of those already existing. These additional stresses combine with the former in such a manner that at every point of the thickness of the cylinder they have common resultants acting in various directions. Thus, if we call t the internal stress existing at a distance r_x from the axis of the cylinder, and in a direction tangential to its cross section, and T the additional stress due to pressure inside the cylinder acting at the same point and in the same direction, then the newly developed stress will be t + T.
If R and r0 be the external and internal radii of the cylinder, and if we suppose the external pressure _nil_, then, if the pressure inside the bore be P0, the stress on the radius r_x is determined by the following expression deduced from the well-known fundamental formulae of Lame:
r0 squared R squared + (rx) squared T = P0 ———- . ——————- R squared-r0 squared (rx) squared
From which we see that T is a maximum when r_x = r0, i.e., for the layer immediately next to the bore of the cylinder. Calling t0 the internal stress in this layer, and T0 the stress resulting from the action inside the bore of the pressure P0, and allowing that the sum of both these quantities must not exceed the elastic limit U of the material, we have—T0 = U - t0. And for this value of T0, the corresponding pressure inside the bore will be
R squared - r0 squared P = (U - t0) —————. R squared + r0 squared
This pressure increases with the term (U - t0). With t0 positive, i.e., when the internal stresses in the thickness of the hollow cylinder are such that the metal of the layers nearest to the bore is in a state of tension and that of the outer layers in a state of compression, then the cylinder will have the least strength when t0 has the greatest numerical value. Such stresses are termed injurious or detrimental stresses. With t0 negative, the strength of the cylinder increases with the numerical value of t0, and those stresses which cause compression in the layers nearest to the bore of the cylinder and tension in the outer layers are termed beneficial or useful stresses.
[Footnote 1: Lame holds that in a homogeneous tube subjected to the action of two pressures, external and internal, the difference between the tension and the compression developed at any point of the thickness of the tube is a constant quantity, and that the sum of these two stresses is inversely proportional to the square of the radius of the layer under consideration. Let r0, R, and r_x be the respective radii, p0, p, and p_x the corresponding pressures, and T0, T, and T_x, the tensions, then we have:
T0 - p0 = Tx - px (1) (T0 + p0) r0 squared = (Tx + px) (rx) squared (2) Tx - px = T - p (3) (Tx + px)(rx) squared = (T + P)R squared (4)
if the radii are known and p and p be given, then deducing from the above equations the values T0 and T, and also the variable pressure p_x, we determine—
p0 r0 squared(R squared + (rx) squared) - p R squared((rx) squared + r0 squared) Tx = ————————————————————— (R squared + r0 squared) (rx) squared
This is the formula of Lame, from which, making p = 0, we obtain the expression in the text.]
For these reasons, and in order to increase the power of resistance of a cylinder, it is necessary to obtain on the inner layer a state of initial compression approaching as nearly as possible to the elastic limit of the metal. This proposition is in reality no novelty, since it forms the basis of the theory of hooped guns, by means of which the useful initial stresses which should be imparted to the metal throughout the gun can be calculated, and the extent to which the gun is thereby strengthened determined. The stresses which arise in a hollow cylinder when it is formed of several layers forced on one upon another, with a definite amount of shrinkage, we call the stress of built-up cylinders, in order to distinguish them from natural stresses developed in homogeneous masses, and which vary in character according to the conditions of treatment which the metal has undergone. If we conceive a hollow cylinder made up of a great number of very thin layers—for instance, of wire wound on with a definite tension—in which case the inner layer would represent the bore of the gun, then the distribution of the internal stresses and their magnitude would very nearly approach the ideally perfect useful stresses which should exist in a homogeneous cylinder; but in hollow cylinders built up of two, three, and four layers of great thickness, there would be a considerable deviation from the conditions which should be aimed at.
The magnitude of the stresses in built-up cylinders is determined by calculation, on the presumption that initial stresses do not exist in the respective layers of the tube and of the hoops which make up the walls of the cylinder. Nevertheless, Rodman, as early as the year 1857, first drew attention to the fact that when metal is cast and then cooled, under certain conditions, internal stresses are necessarily developed; and these considerations led him, in the manufacture of cast iron guns, to cool the bore with water and to heat the outside of the moulds after casting. Although Rodman's method was adopted everywhere, yet up to the present time no experiments of importance have been made with the view of investigating the internal stresses which he had drawn attention to, and in the transition from cast iron to steel guns the question has been persistently shelved, and has only very lately attracted serious attention. With the aid of the accepted theory relating to the internal stresses in the metal of hooped guns, we can form a clear idea of the most advantageous character for them to assume both in homogeneous and in built-up hollow cylinders. In proof of this, we can adduce the labors of Colonels Pashkevitch and Duchene, the former of whom published an account of his investigations in the Artillery Journal for 1884—St. Petersburg—and the latter in a work entitled "Basis of the Theory of Hooped Guns," from which we borrow some of the following information.
The maximum resistance of a tube or hollow cylinder to external stresses will be attained when all the layers are expanded simultaneously to the elastic limit of the material employed. In that case, observing the same notation as that already adopted, we have—
R - r0 P0 = T ———— (1) r0
But since the initial internal stresses before firing, that is previous to the action of the pressure inside the bore, should not exceed the elastic limit, the value of R will depend upon this condition.
[Footnote 2: We must, however, remark that in a built-up hollow cylinder the compression of the metal at the surface of the bore may exceed the elastic limit. This cannot occur in the case of natural stresses.]
In a hollow cylinder which in a state of rest is free from initial stresses, the fiber of which, under fire, will undergo the maximum extension, will be that nearest to the internal surface, and the amount of extension of all the remaining layers will decrease with the increase of the radius. This extension is thus represented—
(r0) squared (r_x) squared + R squared (t_x) = P0 —————— . —————— R squared - (r0) squared (r_x) squared
Therefore, to obtain the maximum resistance in the cylinder, the value tx of the initial stress will be determined by the difference (T - t'x),[*need to check the prime with library or work out the equations] and since P0 is given by Equation (1), then
/ r0 (r_x) squared + R squared t_x = T ( 1 - ————— . ——————- ) (2) R0 + r0 (r_x) squared /
The greatest value t_x = t0 corresponds to the surface of the bore and must be t0 = -T, therefore
r0 squared + R squared ———————- = 2 r0 (R + r0)
whence P0 = T sqrt(2) = 1.41 T.
From the whole of the preceding, it follows that in a homogeneous cylinder under fire we can only attain simultaneous expansion of all the layers when certain relations between the radii obtain, and on the assumption that the maximum pressure admissible in the bore does not exceed 1.41 U.
Equation (2) may be written thus—
R r_x - Rr t_x = T ———— . ————— (3) R + r0 (r_x) squared
Substituting successively rx = r0 and rx = R, we obtain expressions for the stresses on the external and internal radii—
R - r0 R R - r0 tR = T ———— and tr0 = -T —— ———— R + r0 r0 R + r0
Therefore, in a homogeneous hollow cylinder, in which the internal stresses are theoretically most advantageous, the layer situated next to the bore must be in a state of compression, and the amount of compression relative to the tension in the external layer is measured by the inverse ratio of the radii of these layers. It is further evident that the internal stresses will obey a definite but very simple law, namely, there will be in the hollow cylinder a layer whose radius is sqrt(R r0), in which the stress is nil; from this layer the stresses increase toward the external and the internal radii of the cylinder, where they attain a maximum, being in compression in the internal layers and in tension in the external ones.
The internal pressures corresponding to these stresses may be found by means of very simple calculations. The expression for this purpose, reduced to its most convenient form, is as follows:
R / R / r0 p_x = T ———— ( —- - 1 ) ( 1 - ——- ) (4) R + r0 r_x / r_x /
In order to represent more clearly the distribution of stresses and pressures in the metal of a homogeneous ideally perfect hollow cylinder, let us take, as an example, the barrel of a 6 in. gun—153 mm. Let us suppose T = 3,000 atmospheres; therefore, under the most favorable conditions, P0 = 1.41 T, or 4,230 atmospheres. From Equation (1) we determine R = 184.36 mm. With these data were calculated the internal stresses and the pressures from which the curve represented in Fig. 1 is constructed. The stresses developed under fire with a pressure in the bore of 4,230 atmospheres are represented by a line parallel to the axis of the abscissae, since their value is the same throughout all the layers of metal and equal to the elastic limit, 3,000 atmospheres. If, previous to firing, the metal of the tube were free from any internal stresses, then the resistance of the tube would be
R squared - r squared0 P0 = U —————- , R squared + r squared0
or 2,115 atmospheres—that is, one-half that in the ideally perfect cylinder. From this we perceive the great advantage of developing useful initial stresses in the metal and of regulating the conditions of manufacture accordingly. Unless due attention be paid to such precautions, and injurious stresses be permitted to develop themselves in the metal, then the resistance of the cylinder will always be less than 2,115 atmospheres; besides which, when the initial stresses exceed a certain intensity, the elastic limit will be exceeded, even without the action of external pressures, so that the bore of the gun will not be in a condition to withstand any pressure because the tensile stress due to such pressure, and which acts tangentially to the circumference, will increase the stress, already excessive, in the layers of the cylinder; and this will occur, notwithstanding the circumstance that the metal, according to the indications of test pieces taken from the bore, possessed the high elastic limit of 3,000 atmospheres.
In order to understand more thoroughly the difference of the law of distribution of useful internal stresses as applied to homogeneous or to built-up cylinders, let us imagine the latter having the external and internal radii of the same length as in the first case, but as being composed of two layers—that is to say, made up of a tube with one hoop shrunk on under the most favorable conditions—when the internal radius of the hoop = sqrt(R v0) or 118.7 mm., Fig. 2, has been traced, after calculating, by means of the usual well known formulae, the amount of pressure exerted by the hoop on the tube, as well as the stresses and pressures inside the tube and the hoop, before and after firing. A comparison of these curves with those on Fig. 1 will show the difference between the internal stresses in a homogeneous and in a built-up cylinder. In the case of the hooped gun, the stresses in the layers before firing, both in the tube and in the hoop, diminish in intensity from the inside of the bore outward; but this decrease is comparatively small. In the first place, the layer in which the stresses are = 0 when the gun is in a state of rest does not exist. Secondly, under the pressure produced by the discharge, all the layers do not acquire simultaneously a strain equal to the elastic limit. Only two of them, situated on the internal radii of the tube and hoop, reach such a stress; whence it follows that a cylinder so constructed possesses less resistance than one which is homogeneous and at the same time endowed with ideally perfect useful initial stresses. The work done by the forces acting on a homogeneous cylinder is represented by the area a b c d, and in a built-up cylinder by the two areas a' b' c' d' and a" b" c" d". Calculation shows also that the resistance of the built-up cylinder is only 3,262 atmospheres, or 72 per cent. of the resistance of a homogeneous cylinder. By increasing the number of layers or rows of hoops shrunk on, while the total thickness of metal and the caliber of the gun remains the same, we also increase the number of layers participating equally in the total resistance to the pressure in the bore, and taking up strains which are not only equal throughout, but are also the greatest possible. We see an endeavor to realize this idea in the systems advocated by Longridge, Schultz, and others, either by enveloping the inner tubes in numerous coils of wire, or, as in the later imitations of this system, by constructing guns with a greater number of thin hoops shrunk on in the customary manner. But in wire guns, as well as in those with a larger number of hoops—from four to six rows and more—the increase in strength anticipated is acknowledged to be obtained in spite of a departure from one of the fundamental principles of the theory of hooping, since in the majority of guns of this type the initial compression of the metal at the surface of the bore exceeds its elastic limit. We have these examples of departure from first principles, coupled with the assumption that initial stresses do not exist in any form in the metal of the inner tube previous to the hoops having been shrunk on; but if the tube happen to be under the influence of the most advantageous initial stresses, and we proceed either to hoop it or to envelope it with wire, according to the principles at present in vogue, then, without doubt, we shall injure the metal of the tube; its powers of resistance will be diminished instead of increased, because the metal at the surface of the bore would be compressed to an amount exceeding twice its elastic limit. An example of injury inflicted in this way is to be found in the method adopted for hooping cast iron tubes cast by Rodman's process. If we take into consideration the undoubted fact of the existence to a considerable extent of useful initial stresses in these tubes, then the hoops should be put on them either with very little shrinkage or none at all, whereas ordnance authorities everywhere have applied to this case methods which are only correct for tubes which are free from initial stresses.
[Footnote 3: In certain cases this, of course, may be an advantage, as, for instance, when the inner tube is under injurious initial stresses; but then, in order to be able to apply the necessary shrinkage, we must know the magnitude of these stresses.]
During the process of hooping guns it is very important to know how to take into account the value and mode of distribution of the prejudicial stresses in the inner tube, should such exist. Knowing these stresses, it is possible, by regulating the tension of the hoops, to reduce the compression of the metal at the surface of the bore to the proper extent, thus doing away with the previously existing tension, and by that means removing a source of weakness in the tube. In precisely the same way in the shrinkage of gun hoops attention must be paid to the character and value of the stresses which arise in the course of their manufacture; otherwise it will be impossible to hoop the barrel throughout in a proper manner. If prejudicial stresses exist in the metal of a hoop before it is put in its place, then, when the gun is fired, if it had been shrunk on with the degree of tension usually allowed, the layer situated in the internal radius will be extended beyond admissible limits, thereby causing the resistance of the gun to be less than that prescribed.
[Footnote 4: When the inner tube is strengthened by means of wire, the initial or natural stresses in the latter may be neglected on account of its thinness; but when the thickness of the hoops is reduced, and the number of layers thereby increased, then the value of the initial stresses in these hoops is a very important factor with respect to the decrease or increase Of the powers of resistance of the gun.]
It is evident, from what has been said, that in order to determine precisely the resistance of hollow cylinders to internal pressures, and to make the correct calculations for hooping tubes, it is absolutely necessary to know whether internal initial stresses exist in the tube and in the hoops, and to ascertain what their nature and intensity may be—that is to say, whether they are useful or detrimental; yet it is incontestable that in the construction of modern ordnance no attention has been paid to the investigations indicated. If it be possible to ignore these considerations in the manufacture of guns of small caliber, and where the thickness of metal is not sufficiently great to admit of strongly developed internal stresses, such is by no means the case with the colossal and costly weapons of the present day. In these the thickness of metal in the tube and hoops is very great; hence the extreme probability of very considerable internal stresses developing themselves. That the strength of large guns is often far below that anticipated is demonstrated, year by year, by the repeated cases of failure. Consciousness as to the want of strength in such guns is made evident by the precautionary measures as to their use everywhere adopted. The heavy artillery produced in the gun factories of Europe is constructed with all the skill, science, and experience which engineers and artillerists can command, and therefore it would seem that instances of defective strength should not arise. Such cases, however, do occur everywhere, and irresistibly give rise to the suspicion that not only is the system of construction of guns of large caliber faulty, but also that the conditions of their manufacture must be considered as defective. Bearing in mind the enormous sums of money expended by every nation in order to secure an armament of completely trustworthy guns, this question demands speedy and searching investigation. The first step in this direction is the study of the internal stresses inherent in the metal; because, if such exist, and are capable of attaining, under certain conditions, considerable magnitudes, then it is absolutely necessary to take advantage of them in order to increase the resistance of the metal, instead of allowing them to act to its detriment.
The study of natural internal stresses is of importance, not only with reference to gun making, but also in respect of other structures where great resistance is required. All have heard of the sudden failure of crank shafts and piston rods, of the bursting of boiler shells and tubes, of the breaking of tires, etc. In the majority of cases the investigations into the causes of such sudden failures have not led to any definite results. It has usually been found that the metal possessed a satisfactory elastic resistance, and satisfied all the conditions set down in the specifications. Had attention been paid during these investigations to the state of the internal stresses in the metal, the cause of unlooked-for accidents might have been explained, and steps would consequently have been taken to avoid them in future.
We are also familiar with the development of considerable internal stresses in various kinds of steel articles which are subjected to hardening and tempering; for example, as dies, tools of various description, sword blades, and thin plates rolled at a low temperature or subjected to cold hammering. In the foundry the appearance of internal stresses is of still more frequent occurrence. The neglect of certain practical rules in casting, and during the subsequent cooling, leads to the spontaneous breakage of castings after a few hours or days, although taken out of the sand apparently perfectly sound. Projectiles for penetrating armor plate, and made of cast steel, as well as shells which have been forged and hardened, and in which the metal possessed an ultimate resistance of over twelve thousand (12,000) atmospheres, with an elastic limit of more than six or seven thousand atmospheres, will crack to a serious extent, and even break up in the lathe, while the recess for the copper ring is being turned out. In shell of this nature, as well as in chilled cast iron shell, the heads are apt to fly off spontaneously either while they are lying in store or during transport. Such phenomena, it seems to me, demonstrate the existence of internal stresses of considerable magnitude in the metal of the projectiles, and it is highly probable that the manufacture of many articles would have approached nearer to perfection had more attention been bestowed upon the study of the internal stresses which they were liable to. Having thus explained the nature and importance of the subject, I will proceed to describe the experiments which I have made with a view to its illustration.—London Engineer.
* * * * *
ELEMENTS OF ARCHITECTURAL DESIGN.
[Footnote 1: Delivered before the Society of Arts, London, November 28, 1887. From the Journal of the Society.]
BY H.H. STATHAM.
Judging from the nature of the correspondence on architecture and the duty of architects which is frequently seen in the columns of the daily papers, the Times especially, it would seem that the popular notion of architecture now is that it is a study mainly of things connected with sanitary engineering—of the best forms of drain pipes and intercepting traps. This is indeed a very important part of sound building, and it is one that has been very much neglected, and has been, in fact, in a comparatively primitive state until very recent times; and therefore it is not surprising that there should be a reaction in regard to it, and that newspapers which follow every movement of public opinion, and try to keep pace with it, should speak as if the drain pipe were the true foundation of architecture. I have a great respect for the drain pipe, and wish to see it as well laid and "intercepted" as possible; but I think, for all that, that there is something in architecture higher than sanitary engineering. I wish to consider it in these lectures as what I think it essentially is, what it has evidently been in the eyes of all those of past days who have produced what we now regard as great architectural monuments, namely, as an intellectual art, the object of which is to so treat the buildings which we are obliged to raise for shelter and convenience as to render them objects of interest and beauty, and not mere utilitarian floors, walls, and roofs to shelter a race who care nothing for beauty, and who only want to have their physical comfort provided for.
Architecture, then, from the point of view from which I am asking you to regard it—and the only point of view in which it is worth the serious regard of thoughtful people—is the art of erecting expressive and beautiful buildings. I say expressive and beautiful, and I put expressive first, because it is the characteristic which we can at least realize even when we cannot realize what can fairly be called beauty, and it is the characteristic which comes first in the order of things. A building may be expressive and thereby have interest, without rising into beauty; but it can never be, architecturally speaking, beautiful unless it has expression. And what do we mean by expression in a building? That brings us to the very pith of the matter.
We know pretty well what we mean when we say that a painted or sculptured figure is expressive. We mean that, while correctly representing the structure of the human figure, it also conveys to our minds a distinct idea of a special emotion or sentiment, such as human beings are capable of feeling and expressing by looks and actions. Expression in this sense a building cannot be said to have. It is incapable of emotion, and it has no mobility of surface or feature. Yet I think we shall see that it is capable of expression in more senses than one. It may, in the first place, express or reflect the emotion of those who designed it, or it may express the facts of its own internal structure and arrangement. The former, however, can only, I think, be said to be realized in the case of architecture of the highest class, and when taken collectively as a typical style. For instance, we can all pretty well agree that the mediaeval cathedral expresses an emotion of aspiration on the part of its builders. The age that built the cathedrals longed to soar in some way, and this was the way then open to it, and it sent up its soul in spreading vaults, and in pinnacles and spires. So also we can never look at Greek architecture without seeing in it the reflection of a nature refined, precise, and critical; loving grace and finish, but content to live with the graces and the muses without any aspirations that spurned this earth. We can hardly go further than this in attributing emotional expression to architecture. But in a more restricted sense of the word expression, a building may express very definitely its main constructive facts, its plan and arrangement, to a certain extent even its purpose, so far at least that we may be able to identify the class of structure to which it belongs. It not only may, but it ought to do this, unless the architecture is to be a mere ornamental screen for concealing the prosaic facts of the structure. There is a good deal of architecture in the world which is in fact of this kind—an ornamental screen unconnected with the constructional arrangement of the building. Nor is such architecture to be entirely scouted. It may be a very charming piece of scenery in itself, and you may even make a very good theoretical defense for it, from a certain point of view. But on the whole, architecture on that principle becomes uninteresting. You very soon tire of it. It is a mask rather than a countenance, and tends to the production of a dull uniformity of conventional design.
For we must remember that architecture, although a form of artistic expression, is not, like painting and sculpture, unfettered by practical considerations. It is an art inextricably bound up with structural conditions and practical requirements. A building is erected first for convenience and shelter; secondly only for appearance, except in the case of such works as monuments, triumphal arches, etc., which represent architectural effect pure and simple, uncontrolled by practical requirements. With such exceptions, therefore, a building ought to express in its external design its internal planning and arrangement; in other words, the architectural design should arise out of the plan and disposition of the interior, or be carried on concurrently with it, not designed as a separate problem. Then a design is dependent on structural conditions also, and if these are not observed, the building does not stand, and hence it is obvious that the architectural design must express these structural conditions. It must not appear to stand or be constructed in a way in which it could not stand (like the modern shops which are supposed to stand on sheets of plate glass), and its whole exterior appearance ought to be in accordance with, and convey the idea of, the manner and principle on which it is constructed. The most important portions of the interior must be shown as such externally by the greater elaboration and emphasis of their architectural treatment. If the general arrangement of the plan is symmetrical, on either side of a center (which, however, it cannot often be except in the largest type of monumental or public buildings), the architectural treatment must be symmetrical. If the building is necessarily arranged, in accordance with the requirements of the plan, unsymmetrically, the architectural treatment must follow suit, and the same principle must be carried out through all the details.
Now this dependence of architectural design upon plan and construction is one of the conditions which is often overlooked by amateurs in forming a judgment upon architectural design; and the overlooking of this is one reason of the uncertainty of opinion about architecture as compared with such arts as sculpture and painting. Few people know or care much about the structure and planning of buildings except those whose business it is to care about this; and consequently they do not realize what it is which they should look for in the architectural design. They like it or do not like it, and they regard this as what is called a mere question of taste, which, according to the proverb, is not to be disputed about. In fact, however, the good or bad taste of an architectural design, say, if you like, its correctness or incorrectness, is to a considerable extent a matter of logical reasoning, of which you must accurately know the premises before you can form a just conclusion. But there is another reason for this prevalent uncertainty and vagueness of opinion, arising out of the very nature of architectural art itself, as compared with the imitative arts. A painting of a figure on a landscape is primarily a direct imitation of the physical facts of nature. I do not for a moment say it is only that, for there is far more involved in painting than the imitation of nature; but the immediate reference to nature does give a standard of comparison which to a certain extent every eye can appreciate. But architecture is not an art which imitates natural forms at all, except as minor decorations, and it then does so, or should do so, only in a conventionalized manner, for reasons which we shall consider later on. Architecture is, like music, a metaphysical art. It deals with the abstract qualities of proportion, balance of form, and direction of line, but without any imitation of the concrete facts of nature. The comparison between architecture and music is an exercise of the fancy which may indeed be pushed too far, but there is really a definite similarity between them which it is useful to notice. For instance, the regular rhythm, or succession of accentuated points in equal times, which plays so important a part in musical form, is discernible in architecture as a rhythm in space. We may treat a cottage type of design, no doubt, with a playful irregularity, especially if this follows and is suggested by an irregularity, of plan. But in architecture on a grand scale, whether it be in a Greek colonnade or a Gothic arcade, we cannot tolerate irregularity of spacing except where some constructive necessity affords an obvious and higher reason for it. Then, again, we find the unwritten law running throughout all architecture that a progress of line in one direction requires to be stopped in a marked and distinct manner when it has run its course, and we find a similarly felt necessity in regard to musical form. The repetition so common at the close of a piece of music of the same chord several times in succession is exactly analogous to the repetition of cross lines at the necking of a Doric column to stop the vertical lines of the fluting, or to the strongly marked horizontal lines of a cornice which form the termination of the height or upward progress of an architectural design. The analogy is here very close. A less close analogy may also be felt between an architectural and a musical composition regarded as a whole. A fugue of Bach's is really a built-up structure of tones (as Browning has so finely put it in his poem, "Abt Vogler"), in accordance with certain ideas of relation and proportion, just as a temple or a cathedral is a built-up structure of lines and spaces in accordance with ideas of relation and proportion. Both appeal to the same sense of proportion and construction in the brain; the one through the ear, the other through the eye. Then, in regard to architecture again, we have further limiting conditions arising not only out of the principle of construction employed, but out of the physical properties of the very material we employ. A treatment that is suitable and expressive for a stone construction is quite unsuitable for a timber construction. Details which are effective and permanent in marble are ineffective and perishable in stone, and so; on and the outcome of all this is that all architectural design has to be judged, not by any easy and ready reference to exterior physical nature, with which it has nothing to do, but by a process of logical reasoning as to the relation of the design to the practical conditions, first, which are its basis, and as to the relation of the parts to each other. Of course beyond all this there is in architecture, as in music, something which defies analysis, which appeals to our sense of delight we know not how or why, and probably we do not want to know; the charm might be dissolved if we did. But up to this point architectural design and expression are based on reasoning from certain premises. The design is good or bad as it recognizes or ignores the logic of the case, and the criticism of it must rest on a similar basis. It is a matter of thought in both cases, and without thought it can neither be designed nor appreciated to any purpose, and this is the leading idea which I wish to urge and to illustrate in these lectures.
You may say: May not a design satisfy all these logical conditions, and yet be cold and uninteresting, and give one no pleasure? Certainly it may. Indeed, we referred just now to that last element of beauty which is beyond analysis. But, if we cannot analyze the result, I rather think we can express what it is which the designer must evince, beyond clear reasoning, to give the highest interest to his architecture. He must have taken an interest in it himself. That seems a little thing to say, but much lies in it. As Matthew Arnold has said of poetry:
"What poets feel not, when they make A pleasure in creating, The world, in its turn, will not take Pleasure in contemplating."
The truth runs through all art. There are, alas, so many people who do not seem to have the faculty of taking pleasure, and there is so much architecture about our streets which it is impossible to suppose any one took "pleasure in creating." When a feature is put into a design, not because the designer liked it, but because it is the usual thing and it saves trouble, it always proclaims that melancholy truth. But where something is designed because the designer liked doing it, and was trying to please his own fancy instead of copying what a hundred other men have done before, it will go hard but he will give some pleasure to the spectator. It is from this blessed faculty that a design becomes inspired with what is best described as "character." It is not the same thing as style. I have something to say in my next lecture as to what I think style means, but it is certain that a building may have style and yet want character, and it may have a good deal of character and yet be faulty or contradictory in style. We cannot define "character," but when we feel that it is present we may rely upon it that it is because the designer took interest and pleasure in his work, was not doing it merely scholastically—in short, he put something of his own character into it, which means that he had some to put.
Now, coming back to the axiom before mentioned, that architectural design should express and emphasize the practical requirements and physical conditions of the building, let us look a little more in detail into the manner in which this may be done. We will take, to begin with, the very simplest structure we can possibly build—a plain wall (Fig. 1). Here there is no expression at all; only stones piled one on another, with sufficient care in coursing and jointing to give stability to the structure. It is better for the wall, constructively, however, that it should have a wider base, to give it more solidity of foundation, and that the coping should project beyond the face of the wall, in order to throw the rain off, and these two requirements may be treated so as to give architectural expression to our work (Fig. 2). It now consists of three distinct portions—a plinth, or base, a superficies of wall, and a coping. We will mark the thickening at the base by a moulding, which will give a few horizontal lines (at B), and the coping in the same way. The moulding of the coping must also be so designed as to have a hollow throating, which will act as a drip, to keep the rain from running round the under side of the coping and down the wall. We may then break up the superficies by inserting a band of single ornament in one course of this portion of the wall—not half way, for to divide any portion of a building into mere "halves" has usually a weak and monotonous effect, but about two thirds of the distance from the base line; and this band of ornament not only breaks up the plain surface a little, but also, by carrying another horizontal line along the wall, emphasizes its horizontality. Always emphasize that which is the essential characteristic of your structure. A wall of this kind is essentially a long horizontal boundary. Emphasize its length and horizontality.
[Footnote 2: The dark shaded portion in this and the next two diagrams show the "section" of the wall as seen if we cut it through and look at it endwise.]
If we are millionaires, and can afford to spend a great deal on a wall, we may not only (Fig. 3) carry further the treatment of the coping and base, by giving them ornamental adjuncts as well as mouldings, but we might treat the whole wall superficies as a space for surface carving, not mechanically repeated, but with continual variation of every portion, so as to render our wall a matter of interest and beauty while retaining all its usefulness as a boundary, observing that such surface ornament should be designed so as to fulfill a double object: 1, to give general relief to the surface of the wall; 2, to afford matter of interest to the eye on close inspection and in detail.
That is the double function of nearly all architectural ornament. It is, in the first place, to aid the general expression and balance of the building, and give point and emphasis where needed; and, in the second place, to furnish something to the eye for study on its own account when viewed more closely.
We will take another typical and simple erection, a stone pillar to support the ends of two lintels or beams. This may be simply a long squared piece set on end (Fig. 4), and will perform its constructive functions perfectly well in that form; but it is not only absolutely expressionless, but is in one sense clumsy and inconvenient, as taking up more space than need be, presenting an unwieldy-looking mass when viewed at an angle, and shutting out a good deal of light (if that happen to be a matter of practical consequence in the case). Cutting off the angles (Fig. 5) does not weaken it much, and renders it much less unwieldy-looking, besides giving it a certain degree of verticality of expression, and rendering it more convenient as taking up less room and obstructing less light. But though the column is quite strong enough, the octagonal top does not make so good a seat or bearing for the ends of the lintels. We will therefore put a flat square stone on the top of it (Fig. 6), which will serve as a bed for the lintels to rest on securely. But the angles of this bed plate, where they project beyond the face of the column, appear rather weak, and are so actually to some extent—a double defect, for it is not enough in architecture that a thing should be strong enough, it is necessary that it should appear so, architecture having to do with expression as well as with fact. We will, therefore, strengthen this projecting angle, and correct the abruptness of transition between the column and the bed plate, by brackets (Fig. 7) projecting from the alternate faces of the column to the angles of the bed plates. As this rather emphasizes four planes of the octagon column at the expense of the other four, we will bind the whole together just under the brackets by a thin band of ornament constituting a necking, and thus we have something like a capital developed, a definitely designed finish to our column, expressive of its purpose. This treatment of the upper end, however, would make the lower end rising abruptly from the ground seem very bare. We will accordingly emphasize the base of the column, just as we emphasized the base of the wall, by a projecting moulding, not only giving expression to this connection of the column with the ground, but also giving it the appearance, and to some extent the reality, of greater stability, by giving it a wider and more spreading base to rest on. We have here still left the lines of one column vertically parallel, and there is no constructive reason why they should not remain so. There is, however, a general impression to the eye both of greater stability and more grace arising from a slight diminution upward. It is difficult to account for this on any metaphysical principle, but the fact has been felt by most nations which have used a columnar architecture, and we will accept it and diminute (so to speak) our column (Fig. 8). We have here taken a further step by treating the shaft of the column in two heights, keeping the lower portion octagonal and reducing the upper portion to a circle, and we now find it easier to treat the capital so as to have a direct and complete connection with the column, the capital being here merely a spreading out of the column into a bracket form all round, running it into the square of the bed plate. The spreading portion is emphasized by surface ornament, and the necking is again emphasized, this time more decisively, by a moulding, forming a series of parallel rings round the column. If we wish to give our column an expression of more grace and elegance, we can further reduce the thickness of it (Fig. 9), and give more spread to the capital, always taking care to be sure that the strength of the column is not reduced below what the weight which it has to carry requires. In this case a bracket is shown above the capital, projecting longitudinally only (in the direction of the lintel bearing), a method of giving a larger bearing surface for the ends of the lintels, shortening their actual bearing (in other words, widening the space which can be bridged between column and column) and giving a workmanlike appearance of stability to the construction at this point. The idea of the division of the column into two sections, suggested in Fig. 8, is kept up in Fig. 9 by treating the lower portion up to the same height with incised decorative carving. The dotted lines on each side in Fig. 9 give the outline of the original square column as shown in Fig. 4. The finished column was within that block; it is the business of the architectural designer to get it out.
[Footnote 3: This is the feature called "abacus" (i.e., "tile") in Greek architecture, but I am here considering it apart from any special style or nomenclature.]
[Footnote 4: "Bearing," in building language, is used in a double sense, for the distance between the points of support, and the extent to which the beam rests on the walls. Thus a beam which extends 20 feet between the points of support is a beam of 20 feet bearing. If the beam is 22 feet long, so that 1 foot rests on the walls at each end, it has "1 foot bearing on the wall."]
[Footnote 5: None of the forms of column sketched here have any existence in reality. They are purposely kept apart from imitation of accepted forms to get rid of the idea that architecture consists in the acceptance of any particular form sanctioned by precedent.]
Let us see if we can apply the same kind of process of evolving expression in regard to a building. We will take again the very simplest form of building (Fig. 10), a square house with a door in the center and uniform rows of windows. There cannot be said to be any architectural expression in this. There is no base or plinth at all, no treatment of the wall. The slight projection at the eaves is only what is necessary to keep the rain from running down the walls, and facilitate the emptying of the gutters, and the even spacing of the windows is essential for constructive reasons, to keep the masses of wall over each other, and keep the whole in a state of equally balanced pressure. The first thing we should do in endeavoring to give some expression to the building would be to give it a base or plinth (Fig. 11), and to mark that and the cornice a little more decidedly by mouldings and a line of paneling at the plinth.
The house being obviously in three stories, we should give it some echo externally of this division into horizontal stages by horizontal mouldings, or what are called in architectural phraseology "string courses," not necessarily exactly at the floor levels, but so as to convey the idea of horizontal division; observing here, as in the case of the wall and column, that we should take care not to divide the height into equal parts, which is very expressionless. In this case we will keep the lower string close down on the ground floor windows, and keep these rather low, thus showing that the ground floor apartments are not the most important; while the fact that the first floor ones are so is conversely made apparent by keeping these windows rather higher, putting a double string course over them, and a slight extra depth of moulding, forming a kind of cornice over each.
The space left between these and the roof, in which the attic windows are placed, is treated with a series of mullions and panelings, into which the attic windows are worked, as part of the series of openings; this gives a little richness of effect to the top story, and a continuity of treatment, which binds the whole series of windows together. To have treated the whole of the walls and windows in this way would have been merely throwing away labor; what little effect it has consists in the "character" given by the contrast of this top story treatment with the plain wall surfaces below.
The last thing is to emphasize the door, as the principal opening in the walls, and quite distinct in use and meaning from the other openings, by giving it a little architectural frame or setting, which may be done in many ways, but in this case is done by the old fashioned device (not very logical certainly) of putting a little entablature over it, and a column on either side; there is, however, this to be said for it, that the projecting tablature forms a semi-porch, protecting those at the door somewhat from rain; it must be carried in some way, and columns are the readiest and most seemly manner of doing it, and they also form, practically, something of a weather screen; the bases on which they stand also form a framework or inclosing wall for the steps, which are thus made part of the architectural design, instead of standing out as an eyesore, as on Fig. 10. We have now given the house a little general expression, but it still is vague in its design as far as regards the distribution of the interior; we do not know whether the first floor, for instance, is one large room, or two or more rooms, or how they are divided; and the little house is very square and prim in effect.
Let us try grouping the windows a little, and at the same time breaking up the flat surface of the front wall (Fig. 12). Here, as before, we have divided the building by a horizontal string, but only by one main one on the first floor level, keeping the same contrast, however, between a richer portion above and a plainer portion below; we have divided the building vertically, also, by two projecting bays finishing in gables, thus breaking also the skyline of the roof, and giving it a little picturesqueness, and we have grouped the windows, instead of leaving them as so many holes in the wall at equal distances. The contrast between the ground and first floor windows is more emphatic; and it is now the more evident that the upper floor rooms are the best apartments, from their ample windows; it is also pretty evident that the first floor is divided into two main rooms with large bay windows, and a smaller room or a staircase window, between them; the second floor windows are also shifted up higher, the two principal ones going in to the gables, showing that the rooms below them have been raised in height. Windows carried up the full height of these rooms, however, might be too large either for repose internally or for appearance externally, so the wall intervening between the top of these and the sill of the gables is a good field for some decorative treatment, confined to the bays, so as to assist in separating them from the straight wall which forms the background to them.
So far we have treated our building only as a private house. Without altering its general scale and shape we may suggest something entirely different from a private house. On Fig. 13, we have tried to give a municipal appearance to it, as if it were the guild hall of a small country town. The plain basement and the wide principal doorway, and the row of three very large equal-spaced windows above, render it unquestionable that this is a building with a low ground story, and one large room above. A certain "public building" effect is given to it by the large and enriched cornice with balustrade above and paneling below, and by the accentuation of the angles by projecting piers, and by the turrets over them, which give it quite a different character from that of a private house.
If, on the other hand, the building were the free library and reading room of the same small country town, we should have little doubt of this if we saw it as in Fig. 14, with the walls all blank (showing that they are wanted for ranging something against, and cannot be pierced for windows), and windows only in the upper portion. Similarly, if we want to build it as the country bank, we should have to put the large windows on the ground floor, bank clerks wanting plenty of light, and the ground story being always the principal one; and we might indulge the humor of giving it a grim fortress-like strength by a rusticated plinth (i.e., stones left or worked rough and rock-like) and by very massive piers between the windows, and a heavy cornice over them; the residential upper floor forming a low story subordinate to the bank story. It is true this would not satisfy a banker, who always wants classic pilasters stuck against the walls, that being his hereditary idea of bank expression in architecture.
Now if we proceed to take to pieces the idea of architectural design, and consider wherein the problem of it consists, we shall find that it falls into a fourfold shape. It consists first in arranging the plan; secondly, in carrying up the boundary lines of this plan vertically in the shape of walls; thirdly, in the method of covering in the space which we have thus defined and inclosed; and, fourthly, in the details of ornamentation which give to it the last and concluding grace and finish. All building, when it gets beyond the mere wall with which we began, is really a method of covering in a space, or, if we may put it so, a collection of spaces, marked out and arranged for certain purposes. The first thing that the architect has to do is to arrange these spaces on the ground so that they may conveniently meet the necessary requirements of the building. Convenience and practical usefulness come first; but in any building which is worth the name of architecture something more than mere convenience has to be kept in mind, even in the arrangement of the plan upon the site. It is to be a combination of convenience with effectiveness of arrangement. We shall probably find that some one compartment of the plan is of paramount importance. We have to arrange the interior so that this most important compartment shall be the climax of the plan.
The entrance and the other subsidiary compartments must be kept subordinate to it, and must lead up to it in such a manner that the spectator shall be led by a natural gradation from the subsidiary compartments up to the main one, which is the center and raison d'etre of the whole—everything in the lines of the plan should point to that. This is the great crux in the planning of complicated public buildings. A visitor to such a building, unacquainted with it previously, ought to have no difficulty in finding out from the disposition of the interior which are the main lines of route, and when he is on the line leading him up to the central feature of the plan. There are public buildings to be found arranged on what may be called the rabbit warren system, in which perhaps a great number of apartments are got upon the ground, but which the visitor is obliged laboriously to learn before he can find his way about them. That is not only inconvenient but inartistic planning, and shows a want of logic and consideration, and, in addition to this, a want of feeling for artistic effect. I saw not long ago, for instance, in a set of competitive designs for an important public building, a design exhibiting a great deal of grace and elegance in the exterior architectural embellishment, but in which the principal entrance led right up to a blank wall facing the entrance, and the spectator had to turn aside to the left and then to the right before finding himself on the principal axis of the plan. That is what I should call inartistic or unarchitectural planning. The building may be just as convenient when you once know its dodges, but it does not appear so, and it loses the great effect of direct vista and climax.
An able architect, who had given much thought to a plan of a large building of this kind, said to me, in showing me his plan, with a justifiable gratification in it, "It has cost me endless trouble, but it is a satisfaction to feel that you have got a plan with backbone in it." That is a very good expression of what is required in planning a complicated building, but few outsiders have any notion of the amount of thought and contrivance which goes to the production of a plan "with backbone;" a plan in which all the subordinate and merely practical departments shall be in the most convenient position in regard to each other, and yet shall all appear as if symmetrically and naturally subordinate to the central and leading feature; and if the public had a little more idea what is the difficulty of producing such a plan, they would perhaps do a little more justice to the labors of the man who contrives the plan, which they think such an easy business; and no doubt it may appear an easy business, because the very characteristic of a really good plan is that it should appear as if it were quite a natural and almost inevitable arrangement.
Just as it is said in regard to literature that easy writing is hard reading, so, in regard to planning, it is the complicated and rabbit warren plans that are the easiest to make, because it is just doing what you please; it is the apparently perfectly simple and natural plan which springs from thought and contrivance. Then there is the next step of raising the walls on the plan, and giving them architectural expression. This must not be thought of as an entirely separate problem, for no truly architectural intellect will ever arrange a plan without seeing generally, in his mind's eye, the superstructure which he intends to rear upon it; but the detailed treatment of this forms a separate branch of the design. Then comes the third and very important problem—the covering in of the space. Next to the plan, this is the most important. All building is the covering over of a space, and the method of covering it over must be foreseen and provided for from the outset. It largely influences the arrangement of the plan. If there were no roofing, you could arrange the walls and carry them up pretty much as you chose, but the roofing of a large space is another matter. It requires extra strength at certain points, where the weight of the roof is concentrated, and it has to be determined whether you will employ a method of roofing which exercises only a vertical pressure on the walls, like the lid of a box, or one which, like an arch, or a vault, or a dome, is abutting against the walls, and requires counterforts to resist the outward thrust of the roof. We shall come upon this subject of the influence of the roof on the design of the substructure more in detail later on. Then, if the plan is convenient and effective, the walls carried up with the architectural expression arising from the placing and grouping of the openings, and the proper emphasizing of the base and the cornice, and the horizontal stages (if any) of the structure, and the roof firmly and scientifically seated on the walls; after all these main portions of the structure are designed logically and in accordance with one another and with the leading idea of the building, then the finishing touches of expression and interest are given by well designed and effective ornamental detail. Here the designer may indulge his fancy as he pleases, as far as the nature of the design is concerned, but not, if you please, as far as its position and distribution are concerned. There the logic of architecture still pursues us.
We may not place ornament anywhere at haphazard on a building simply because it looks pretty. At least, to do so is to throw away great part of its value. For everything in architectural design is relative; it is to be considered in relation to the expression and design of the whole, and ornament is to be placed where it will emphasize certain points or certain features of the building. It must form a part of the grouping of the whole, and be all referable to a central and predominating idea. A building so planned, built, and decorated becomes, in fact, what all architecture—what every artistic design in fact should be—an organized whole, of which every part has its relation to the rest, and from which no feature can be removed without impairing the unity and consistency of the design. You may have a very good, even an expressive, building with no ornament at all if you like, but you may not have misplaced ornament. That is only an excrescence on the design, not an organic portion of it.
I have thought that it would be of use to those who are unacquainted with architectural procedure in delineating architecture by geometrical drawings if I took the opportunity of illustrating very briefly the philosophy of elevations, plans, and sections, which many non-professional people certainly do not understand.
A simple model of a building, like that in Fig. 16, will serve the purpose, as the principle is the same in the most complicated as in the simplest building. It must be remembered that the object of architectural drawings on the geometrical system is not to show a picture of the building, but to enable the designer to put together his design accurately in all its parts, according to scale, and to convey intelligible and precise information to those who have to erect the building. A perspective drawing like Fig. 16 is of no use for this purpose. It shows generally what the design is, but it is impossible to ascertain the size of any part by scale from it, except that if the length of one line were given it would be possible, by a long process of projection and calculation, to ascertain the other sizes. The rationale of the architect's geometrical drawings is that on them each plane of the building (the front, the side, the plan, etc.) is shown separately and without any distortion by perspective, and in such a manner that every portion is supposed to be opposite to the eye at once. Only the width of any object on one side can be shown in this way at one view; for the width of the return side you have to look to another drawing; you must compare the drawings in order to find out those relative proportions which the perspective view indicates to the eye at a glance; but each portion of each side can be measured by reference to a scale, and its precise size obtained, which can only be guessed at roughly from the perspective drawing. Thus the side of the model is shown in Fig. 19, the end in Fig. 17; the two together give the precise size and proportions of everything outside to scale, except the projection of the pilasters. This has to be got at from the plan and section. Everything being drawn on one plane, of course surfaces which are sloping on one elevation are represented as flat in the other. For instance, on No. 17 the raking line of the sloping roof is shown at N. So we know the slope of the roof, but we do not know to what length it extends the other way. This is shown on Fig. 19, where the portion showing the roof is also marked N, and it will be seen that the surface which is sloping in Fig. 17 is seen in the side elevation only as a space between a top and bottom line. We see the length of the roof here, and its height, but for its slope we go to the end elevation. Neither elevation tells us, however, what is inside the building; but the section (Fig. 18) shows us that it has an arched ceiling, and two stories, a lower and a higher one. The section is the building cut in half, showing the end of the walls, the height and depth of the window openings, the thickness of the floor, etc., and as all parts which are opposite the eye are shown in the drawing, the inside of the cross wall at the end of the building is shown as a part of the section drawing, between the sectional walls. In Fig. 23 the section is sketched in perspective, to show more clearly what it means. Another section is made lengthwise of the building (Fig. 20). It is customary to indicate on the plan by dotted lines the portion through which the section is supposed to be made. Thus on the plans the lines A B and C D are drawn, and the corresponding sections are labeled with the same lines. As with the elevation, one section must be compared with another to get the full information from them. Thus in Fig. 18, the ceiling, M, is shown as a semicircle; in Fig. 20, it is only a space between the top and bottom lines. It is, certainly, shaded here to give the effect of rotundity, but that is quite a superfluity. On Fig. 18 the height of the side windows is shown at F, and the thickness of the wall in which they are made. In Fig. 20 (F) their width and spacing are shown. In Fig. 18 some lines drawn across, one over the other, are shown at H. These are the stairs, of which in this section we see only the fronts, or risers, so that they appear merely as lines (showing the edge of each step) drawn one over the other. At H on the plan, Fig. 21, we again see them represented as a series of lines, but here we are looking down on the top of them, and see only the upper surfaces, or "treads," the edges again appearing as a series of lines. At H on the longitudinal section, we see the same steps in section, and consequently their actual slope, which, however, could have been calculated from Figs. 18 and 21, by putting the heights shown in section with the width shown in plan. The plan, Fig. 21, shows the thickness and position on the floor of the pillars, G G. Their height is shown in the sections. The plan of a building is merely a horizontal section, cutting off the top, and looking down on the sectional top of the walls, so as to see all their thicknesses. I have drawn (Fig. 24) a perspective sketch of one end of the plan (Fig. 22) of the building, on the same principle as was done with the section (Fig. 23), in order to show more intelligibly exactly what it is that a plan represents—the building with the upper part lifted off.