beard in order. About this time the clergy began to break with | following their example in the 'fifties. But for a civilian to grow the long tradition of smooth faces. A priest in 1531 is com- a moustache was long reckoned a piece of unseemly swagger. manded to abstain from wearing a beard, and Cardinal Pole, Clive Newcome, it will be remembered, wore one until the coming from the court of a bearded pope, appears bearded like a taunting question whether he was "going in the Guards "shamed Greek patriarch. The law too, the church's kinswoman, begins him into shaving clean. When in 1840 Mr George Frederick to forbid, a sign of the change, and from 1542 the society of Muntz appeared in parliament with a full beard there were those Lincoln's Inn makes rules for fining and expelling those who who felt that this tall Radical had taken his own strange method appear bearded at their mess, rules which the example of exalted of insulting English parliamentary institutions. James Ward, lawyers caused to be withdrawn in 1560. R.A. (d. 1859), painter of animals, was another breaker of the The age of Elizabeth saw lawyers, soldiers, courtiers and unwritten law, defending his beard in a pamphlet of eighteen merchants all bearded. Her Cecils, Greshams, Raleighs, Drakes, arguments as a thing pleasing at once to the artist and to his Dudleys and Walsinghams have the beard. A shaven chin such Creator. Freedom in these matters only came when the troops as that seen in the portrait of Philip Howard, earl of Arundel, is were home from the Crimea, when officers who had grown beards rare, but the beards take a hundred fashions, and satirists and and acquired the taste for tobacco during the long months in the Puritan pamphleteers were busy with them and with the men trenches showed their beards and their cigars in Piccadilly. Then who wasted hours in perfuming or starching them, in dusting came the Volunteer movement, and every man was a soldier, them with orris powder, in curling them with irons and quills. taking a soldier's licence. The dominant fashion was the Stubbs gives them a place amongst his abuses. "It is a world to moustache, worn with long and drooping whiskers. But the consider how their mowchatowes must be preserved or laid out Piccadilly weepers of the 'sixties were out of the mode for from one check to another and turned up like two horns towards the younger men when the 'eighties began, and by the end of the the forehead." Of the English variety of beards Harrison has a century whiskers were seen in the army only upon a few veteran good word: "beards of which some are shaven from the chin officers. The fashion of clean shaving had made some way, the like those of Turks, not a few cut short like to the beard of popularity of the shaven actor having a part in this. In 1909 all Marquess Otto, some made round like a rubbing brush, others modes of dealing with the hair of the face might be recognized, with a pique de vant (O! fine fashion) or now and then suffered to but the full beard had become somewhat rare in England and the grow long, the barbers being grown to be so cunning in this behalf full whiskers rarer still. The upper class showed an inclination as the tailors. And therefore if a man have a lean and straight to shave clean, although the army grudgingly recognized a rule face, a Marquess Otto's cut will make it broad and large; if it which ordered the moustache to be worn. Naval men, by be platter-like, a long slender beard will make it seem the regulation, shaved or wore both beard and moustache, but their narrower; if he be weasel-becked, then much hair left on the beards were always trimmed. Most barristers shaved the lips, cheeks will make the owner look big like a bowdled hen, and as although the last judge unable to hear an advocate whose voice a grim as a goose, if Cornelis of Chelmersford say true." ." Neverthe-moustache interrupted had left the bench. Clergymen followed less he adds that many old men do wear no beards at all." The Elizabethan fashions continued under King James, the beard trimmed to a point being common wear; but under King Charles there is a certain reaction, and the royal style of shaving the cheeks and leaving the moustache whose points sweep upward and the chin beard like a downward flame is followed by most of the gentry. With some the beard disappears altogether or remains a mere fleck below the lip. Archbishop Laud has a cavalier-like chin tuft and upturned moustache, but Abbot his predecessor wore the spade beard, the "cathedral beard" of Randle Holme, seen in all its dignity on the Chigwell brass of Samuel Harsnett, archbishop of York (died 1631), a grim figure with his angry moustache and a long and broad beard, cut square at the bottom. sca. the lay fashions as they did under the first Stuart kings, although there was still some prejudice against the moustache as an ornament military and inappropriate. A newspaper of 1857, describing the appearance of Livingstone the missionary at a Mansion House meeting, records that he came wearing a moustache, "braving the prejudices of his countrymen and thus evincing a courage only inferior to that exhibited by him amongst the savages of Central Africa." Even as late as 1884 the Pall Mall Gazette has some surprised comments on the beard of Bishop Ryle, newly consecrated to the see of Liverpool. The footman, whose full-dress livery is the court dress of a hundred years ago, must show no more than the rudimentary whisker of the early eighteen-hundreds, and butler, coachman and groom come under the same rule. The jockey and the hunt whip are shaven likewise, but the courier has the whiskers and moustache that once marked him as a foreigner in the English milor's service, and the chauffeur, a servant with no tradition behind him, is often moustached. From the Restoration year the razor comes more into use.. Young men shave clean. The restored king curls a few dark hairs of a moustache over each cheek, but his brother James is shaven. With the reign of Queen Anne the country enters the beardless age, and beards, moustaches and whiskers are no more seen. In Lastly, we may speak of the practice of the royal house since the 18th century the moustache indicated a soldier from beyond England came out of the beardless century. The regent took A Jew or a Turk was known by the beard, an appendage the new fashion, and sat "in whiskered state," but his brother loathsome as comic. Matthew Robinson, the second Lord Rokeby, and successor shaved clean and disliked even the hussar's was indeed wearing a beard in 1798, but he was reckoned a mad-moustache. The prince consort wore the moustache as a young man therefor, and Phillips's Public Character pictures him as "the only peer and perhaps the only gentleman of either Great Britain or Ireland who is thus distinguished." That George III. in his madness should have been left unshaved was a circumstance of his misery that wrung the hearts of all loyal folk. But in the very year of 1798, when Lord Rokeby's image was engraved for the curious, the Worcestershire militia officers quartered near Brighton were copying the Austrian moustache of the foreign troops, and we may note that the hair of the face, which disappeared when wigs came in, began to reappear as wigs went out. Early in the 19th century the bucks began to show a patch of whisker beside the ear, and the soldier's moustache became a common sight. Before Waterloo, guardsmen were complaining that officers of humbler regiments imitated their fashion of the moustache, and by the Waterloo year most young cavalry officers were moustached. The Horse Artillery were the next moustached corps, the rest of the, army, already whiskered, In man, adding whiskers in later years. King Edward VII. wore the gloomier and " unwholesome " sort. His treatment of most | through holes (H, H) which are slotted to allow endwise adjustsubjects was revolutionary; he deliberately ignored proportionment of the whole bearing in order to facilitate the alignment of and perspective, and the "freedom from convention" which he the shaft. Oil or other lubricant is introduced through the bole displayed caused his work to be judged with harshness. In (G), and it passes certain phases of technique he especially excelled; and his earlier through the top methods of dealing with the single line in conjunction with masses brass to grooves of black are in their way unsurpassed, except in the art of Japan, or oilways cut into the country which probably gave his ideas some assistance. He the surface of the was always an ornamentist, rather than an illustrator; and his brass for the purwork must be judged from that point of view. His frontispiece pose of distributing to Volpone is held by some to be, from this purely technical the oil uniformly to standpoint, one of the best pen-drawings of the age. His posters the journal. for the Avenue theatre and for Mr Fisher Unwin were among the first of the modern cult of that art. The following are the chief works which are illustrated with drawings by Beardsley: the Bon Mot Library, The Pall Mall Budget, and The Studio (1893), Sir Thomas Malory's Morte d'Arthur (1893-1894), Salomé (1894), The Yellow Book (1894-1895), The Savoy Magazine (1896), The Rape of the Lock (1896). See also J. Pennell, The Studio (1893); Symons, Aubrey Beardsley (1898); R. Ross, Volpone (1898); H. C. Marillier, The Early Work of Aubrey Beardsley (1899); Smithers, Reproductions of Drawings by Aubrey Beardsley, John Lane, The Later Works of Aubrey Beardsley (1901); R. Ross, Aubrey Beardsley (1908). (E., F. S.) BEARDSTOWN, a city of Cass county, Illinois, U.S.A., in the W. part of the state, on the E. bank of the Illinois river, about 111 m. N. of St Louis, Missouri. It is served by the Baltimore & Ohio South-Western, and the Burlington (Chicago, Burlington & Quincy) railways, and by steamboats plying between it and St. Louis. Pop. (1890) 4226; (1900) 4827 (444 foreign-born); (1910) 6107. The industrial establishments of the city include flour, planing and saw mills, the machine shops (of the St Louis division) of the Chicago, Burlington & Quincy railway, ice factories, pearl button factories and a shoe factory. The fishing interests are also important. Beardstown was laid out in 1827 and was incorporated as a city in 1896. It was named in honour of Thomas Beard, who settled in the vicinity in 1820. During the Black Hawk War (1832) it was a base of supplies for the Illinois troops. The old court house in which Abraham Lincoln, in 1854, won his famous "Armstrong murder case," is now used for a city hall. BEARER, strictly one who carries," a term used in India for a palanquin-bearer, and now especially for a body-servant. The term is also used in connexion with military ambulances, and "bearer" companies formed part of the Royal Army Medical Corps until amalgamated with the field-hospitals to form field-ambulances (1905). In banking and commerce the word is applied to the holder or presenter of a cheque or draft not made payable to a specific person; it has also a technical use, as in printing, of anything that supports pressure in machinery, &c. BEARINGS. In engineering a "bearing" is that particular kind of support which, besides carrying the load imposed upon it by the shaft associated with it, allows the shaft freedom to revolve. Or, put in another way, a bearing forms with the shaft a pair of elements having one degree of freedom to turn relatively to one another about their common axis. The part of the shaft in the bearing is commonly called the journal. The component parts of a small bearing, pillow block, plummer block or pedestal, as it is variously styled, are illustrated in fig. 1, and these parts, put together, are further illustrated in fig. 2 with the shaft added. Corresponding parts are similarly lettered in the two illustrations. The shaft (S) is encircled by the brasses (B1 and B2) made of gun metal, phosphor bronze or other suitable material. The lower brass fits into the main casting (A) in the semicircular seat provided for it, and is prevented from moving endways by the flanges (F, F) and from turning with the shaft by the projections (P, P), which fit into corresponding recesses in the casting (A), one of which is shown at p. After the shaft has been placed in position, the upper brass (B2) and the cap (C) are put on and both are held in place by the bolts (Q1, Q2). The brasses are bedded into the main casting (A) and the cap (C) respectively at the surfaces D, D, D, D. The complete bearing is held to the framework of the machine by bolts (R1, R2) passing Some form of lubricator is usually fitted at G in order to supply oil to the bearing continuously. A form of lubricator used for this purpose shown in place, fig. 2, and an enlarged section is shown in fig. 3. It will be seen that the lubri is F A FIG. 1. F cator consists essentially of a cup the base of which is pierced centrally by a tube which reaches to within a small distance of the lid of the cup inside, and projects into the oilway leading to the journal outside. The annular space round the tube inside is filled with oil which is transferred to the central tube and thence to the bearing by the capillary action of a cotton wick thrust down on a piece of wire. It is only necessary to withdraw the wick from the central tube to stop the supply of oil. The lubricator is fitted through a hole in the lid which is usually plugged with a piece of cane or closed by more elaborate means. A line of shafting would be supported by several bearings of the kind illustrated, themselves supported by brackets projecting from or rigidly fixed to the walls of the workshop, or on frames resting on the floor, or on hangers attached to the roof girders or principals. In bearings of modern design for supporting a line shaft the general arrangement shown in fig. 1 is modified so that the alignments of the shaft can be made both vertically or horizontally by means of adjusting screws, and the brass is jointed with the supporting main body so that it is free to follow the small deflections of the shaft which take place when the shaft is working. Another modern improvement is the formation of an oil reservoir or well in the base of the bearing itself, and the transference of the oil from this well to the shaft by means of one or two rings riding loosely on the shaft. The bottom part of the ring dips into the oil contained in the well of the bearing and, as the shaft rotates, the ring rolls on the shaft and thus carries oil up to the shaft continuously, from which it finds its way to the surfaces of the shaft and bearing in contact. It should be. understood that the upper brass is slotted crossways to allow the ring to rest on the shaft. When the direction of the load carried by the bearing is constant it is unnecessary to provide FIG. 3. pad lubrication in general use for this kind of bearing. The main casting, A, is now uppermost, and is designed so that the upper part supports and constrains the spring buckle through which the load W is transmitted to the bearing, and the lower part inside is arranged to support the brass, B. The brass is jointed freely with the main casting by means of a hemispherical hump resting in a corresponding recess in the casting. What may be called the cap, C, forms the lower part of the axle box, brush, shaped to fit the underside of the journal, whilst the lower part consists of streamers of wick resting in the oil. The oil is fed to the brush by the capillary action of the streamers. The reservoirs are filled with oil through the apertures P and O. The bottom cap is held in position by the T-headed bolts Q and Q (fig. 5). By slackening the nuts and turning the Theads fair with the slots in the cap, the cap comes right away and the axle may be examined. A leather ring L is fitted as shown to prevent dust from entering the axle box. Footsteps.-A bearing arranged to support the lower end of a vertical shaft is called a footstep, sometimes a pivot bearing. A simple form of footstep is shown in fig. 6. A casting A, designed so that it can be conveniently bolted to a foundation block, cross beam, or bracket is bored out and fitted with a brass B, which is turned inside to carry the end of the shaft S. The whole vertical load on the shaft is carried by the footstep, so that it is important to arrange efficient lubricating apparatus. Results of experiments made on a footstep, reported in Proc. Inst. Mech. Eng., 1891, show that if a diametral groove be cut in the brass, as indicated at g (fig. 6), and if the oil is led to the centre of this groove by a channel c communicating with the exterior, the rotation of the shaft draws in a plentiful supply of oil which radiates from the centre and makes its way vertically between the shaft and the brass and finally overflows at the top of the brass. The overflowing oil may be led away and may be re-introduced into the footsteps at c. The rotation of the shaft thus causes a continuous circulation of oil through the footstep. One experiment from the report mentioned above may be quoted. A 3-in. shaft, revolving 128 times per minute and supported on a manganese bronze bearing lubricated in the way explained above sustained increasing loads until, at a load of 300 pounds per square inch of the area of the end of the shaft, it seized. The FIG. 6. mechanical details of a footstep may be varied for purposes of adjustment in a variety of ways similarly to the variations of a common bearing already explained. Thrust Block Bearing.-In cases where a bearing is required to resist a longitudinal movement of the shaft through it, as for example in the case of the propeller shaft of a marine engine or a vertical shaft supporting a heavy load not carried on a footstep, the shaft is provided with one or more collars which are grooved with corresponding recesses in the brasses of the bearing. A general sketch of a thrust block for a propeller shaft is shown in fig. 7. There are seven collars turned on the shaft and into the FIG. 5. but instead of supporting a second brass it is formed into an oil reservoir in which is arranged a pad of cotton wick woven on a tin frame. The upper part of the pad is formed into a kind of FIG. 7. circumferential grooves between them fit corresponding circumferential projections on the brasses, these projections being formed in the case illustrated by means of half rings which are fitted into grooves turned in the brasses. This method of construction allows an individual ring to be replaced or adjusted if it should get hot. The total area of the rubbing surfaces should be proportioned so that the average load is not more than from 50 to 70 lb per sq. in. Arrangements are usually made for cooling a thrust block with water in case of heating. The spindles of drilling machines, boring machine spindles, turbine shafts may be cited as examples of vertical shafts supported on one collar. Experiments on the friction of a collar bearing have been made by the Research Committee of the Institution of Mechanical Engineers (Proc. Inst. Mech. Eng., 1888). Roller and Ball Bearings.-If rollers are placed between two surfaces having relative tangential motion the frictional resistance to be overcome is the small resistance to rolling. The rollers move along with a velocity equal to one half the relative velocity of the surfaces,. This way of reducing frictional resistance has been applied to all kinds of mechanical contrivances, including bearings for shafts, railway axle boxes, and axle boxes for tramcars. An example of a roller bearing for a line shaft is illustrated in figs. 8 and 9. The main casting, A, and cap, C, bolted together, form a spherical seating for the part of the bearing E corresponding to the brasses in a bearing of the usual type. Between the inside of the casting E and the journal are placed rollers held in position relatively to one another by a "squirrel cage" casting, the section of the bars of which are clearly shown in the half sectional elevation, fig. 9. This squirrel cage ensures that the several axes of the rollers keep parallel to the axis of the journal during the rolling motion. The rollers are made of hard tool steel, and the surfaces of the journal and bearing between which they roll are hardened. Two rings of balls may be used instead of a single ring of rollers, and the kind of ball bearing thus obtained is in general use principally in connexion with bicycles and motor cars (see BICYCLE). In ball bearings the load is concentrated at a few points, the points where the balls touch the race, and in the roller bearing at a few lines, the lines of contact between the rollers and the surfaces of the journal and bearing; consequently the load which bearings of this kind carry must not be great enough to cause any indentation at the points or lines of contact. Both rollers and balls, and the paths on which they roll, therefore, are made of hard material; further, balls and rollers must all be exactly the same size in an individual bearing in order to distribute the load between the points or lines of contact as uniformly as possible. The finest workmanship is required therefore to make good roller or good ball bearings. Bearings for High Speeds and Forced Lubrication.-When the shaft turns the metallic surfaces of the brass and the journal are prevented from actual contact by a film of oil which is formed and maintained by the motion of the shaft and which sustains the pressure between the journal and the brass provided the surfaces are accurately formed and the supply of oil is unlimited. This film changes what would otherwise be the friction between metallic surfaces into a viscous resistance within the film itself. When through a limited supply of oil or imperfect lubrication this film is imperfect or fails altogether and allows the journal to make metallic contact with the brass, the friction increases; and it may increase so much that the bearing rapidly becomes hot and may ultimately seize, that is to say the rubbing surfaces may become stuck together. With the object of reducing the friction at the points of metallic contact and of confining the damage of a hot bearing to the easily renewable brass, the latter is partially, sometimes wholly, lined with a soft fusible metal, technically known as white metal, which melts away before actual seizure takes place, and thus saves the journal which is more expensive because it is generally formed on a large and expensive shaft. However perfectly the film fulfils its function, the work required to overcome the viscous resistance of the film during the continuous rotation of the shaft appears as heat, and in consequence the temperature of the bearing gradually rises until the rate at which heat is produced is equal to the rate at which it is radiated from the bearing. Hence in order that a journal may revolve with a minimum resistance and without undue heating two precautions must be taken: (1) means must be taken to ensure that the film of oil is complete and never fails; and (2) arrangements must be made for controlling the temperature should it rise too high. The various lubricating devices already explained supply sufficient oil to form a partial film, since experiments have shown that the friction of bearings lubricated in this way is akin to solid friction, thus indicating at least partial metallic contact. In order to supply enough oil to form and maintain a film with certainty the journal should be run in an oil bath, or oil should be supplied to the bearing under pressure sufficient to force it in between the surfaces against the load. A bearing to which forced lubrication and water cooling are applied is illustrated in fig. 10, which represents one of the bearings of a Westinghouse turboalternator installed at the power station of the Underground Electric Railways Company of London at Lots Road, Chelsea. Oil flows under pressure from a tank on the top of a tower along a supply pipe to the oil inlet O, and after passing through the bearing and performing its duty as a film it falls away from each end of the journal into the bottom of the main casting, from which a pipe, E, conveys the oil back to the base of the tank tower where it is cooled and finally pumped back into the tank. There is thus a continuous circulation of oil through the bearing. The space C is for cooiing water, in fact the bearing is water jacketed and the jacket is connected to a supply pipe and a drain pipe so that a continuous circulation may be maintained if desired. This bearing is 12 in. in diameter and 48 in. long, and it carries a load of about 12-8 tons. The rise in temperature of the bearing under normal conditions of working without water circulating in the jacket is approximately 38° F. The speed of rotation is such that the surface velocity is about 50 ft. per second. FIG. 10. Forced lubrication in connexion with the bearings of highspeed engines was introduced in 1890 by Messrs Belliss & Morcom, Ltd., under patents taken out in the name of A. C. Pain. It should be understood that providing the film of oil in the bearing of an engine can be properly maintained a double-acting engine can be driven at a high speed without any knocking, and without perceptible wear of the rubbing surfaces. Fig. 11 shows that the general arrangement of the bearings of a Belliss & Morcom engine arranged for forced lubrication. A small force-pump F, driven from the eccentric strap X, delivers oil into the pipe P, along which it passes to A, the centre of the right-hand main bearing. There is a groove turned on the inside of the brass from which a slanting hole leads to B. The oil when it arrives at A thus has two paths open to it, one to the right and left of the groove through the bearing, the other along the slanting hole to B. At B it divides again into two streams, one stream going upwards to the eccentric sheave, and a part continuing up the pipe Q to the eccentric pin. The second stream from B follows the slanting hole in the crank shaft to C, where it is led to the big end journal through the pipe R to the crosshead pin, and through the slanting hole to D, where it finds its way into the left main bearing. The oil forced through each bearing falls away to the right and to the left of the journal and drops into the bottom of the engine framing, whence it is again fed to the pump through a strainer. The parts of an engine lubricated in this way must be entirely enclosed. F Oil Strainer Valve Load on bearings.-The distribution of pressure over the film of lubricant separating the rubbing surfaces of a bearing is variable, being greatest at a point near but not at the crown of the brass, and falling away to zero in all directions towards the boundaries of the film. It is usual in practice to ignore this variation of pressure through the film, and to indicate the severity with which the bearing is loaded by stating the load per square inch of the rubbing surfaces projected on to the diametral plane of the journal. Thus the projected area of the surfaces of a journal 6 in. in diameter Oil Relief and 8 in. long is 48 sq. in., and if the total load carried by the bearing is FIG. 11. 20,000 pounds, the bearing would be said to carry a load of 417 pounds per square inch. When a shaft rotates in a bearing continuously in one direction the load per square inch with which it is safe to load the bearing in order to avoid undue heating is much less than if the motion is intermittent. A table of a few values of the bearing loads used in practice is given in the article LUBRICANTS. Bearing Friction. If W is the total load on a bearing, and if is the coefficient of friction between the rubbing surfaces, the tangential resistance to turning is expressed by the product W. If v is the relative velocity of the rubbing surfaces, the work done per second against friction is We foot pounds. This quantity of work is converted into heat, and the heat produced per second is therefore W/778 British Thermal Units. The coefficient is a variable quantity, and bearing in mind that a properly lubricated journal is separated from its supporting brass by a film of lubricant it might be expected that would have values characteristic of the coefficient of friction between two metallic surfaces, merging into the characteristics properly belonging to fluid friction, according as the oil film varied from an imperfect to a perfect condition, that is, according as the lubrication is partial or complete, completeness being attained by the use of an oil bath or by some method of forced lubrication. This expectation is entirely borne out by experimental researches. Beauchamp Tower (" Report on Friction Experiments," Proc. Inst. Mech. Eng., November 1883) found that when oil was supplied to a bearing by means of a pad the coefficient of friction was approximately constant with the value of 1/100, thus following the law of solid friction; but when the journal was lubricated by means of an oil bath the coefficient of friction varied nearly inversely as the load on the bearing, thus making W=constant. The tangential resistance in this case is characteristic of fluid friction since it is independent of the pressure. Tower's experiments were carried out at a nearly constant temperature. The later experiments of O. Lasche (Zeilsch. Verein deutsche Ingenieure, 1902, 46, Phe's main pp. 1881 et seq.) show how u depends upon the temperature. results with regard to the variation of u are briefly:-W is a con-. stant quantity, thus confirming Tower's earlier experiments; is practically independent of the relative velocity of the rubbing surfaces within the limits of 3 to 50 ft. per second; and the product ut is constant, being the temperature of the bearing. Writing for the load per unit of projected area of the bearing, Lasche found that the result of the experiments could be expressed | by the simple formula put=constant=2, where p = the pressure in kilograms per square centimetre, and the temperature in degrees centigrade. If p is changed to pounds per square inch the constant in the expression is approximately 30. The expression is valid between limits of pressure 14 to 213 pounds per square inch, limits of temperature 30° to 100° C., and between limits of velocity 3 to 50 ft. per second. Theory of Lubrication.-After the publication of Tower's experiments on journal friction Professor Osborne Reynolds showed (Phil. Trans., 1886, p. 157) that the facts observed in connexion with a journal lubricated by means of an oil bath could be explained by a theory based upon the general principles of the motion of a viscous fluid. It is first established as an essential part of the theory that the radius of the brass must be slightly greater than the radius of the journal as indicated in fig. 12, where J is the centre of the journal and I the centre of the brass. Given this difference of curvaoil, the rotation of the journal ture and a sufficient supply of produces and maintains an oil film between the rubbing surfaces, the circumferential extent of which depends upon the rate of the oil supply and the external load. With an unlimited supply of oil, that is with oil-bath lubrication, the film extends continuously to the extremities of the brass, unless such extension would lead to negative pressures and therefore to a discontinuity, in which case the film ends film become negative. where the pressures in the The H O -R+a FIG. 12. minimum distance between the journal and the brass occurs at the point H (fig. 12), on the off side of the point O where the line of action of the load cuts the surface of the journal. To the right and left of H the thickness of the film gradually increases, this being the condition that the oil-flow to and from the film may be automatically maintained. With an unlimited supply of oil the point H moves farther from O as the load increases until it reaches a maximum distance, and then it moves back again towards O as the load is further increased until a limiting load is reached at which the pressure in the film becomes negative at the boundaries of the film, when the boundaries recede from the edges of the brass as though the supply of oil were limited. In the mathematical development of the theory it is first necessary to define the coefficient of viscosity. This is done as follows:-If two parallel surfaces AB, CD are separated by a viscous film, and if whilst CD is fixed AB moves in a tangential direction with velocity U, the surface of the film in contact with CD clings to it and remains at rest, whilst the lower surface of the film clings to and moves with the surface AB. At intermediate points in the film the tangential motion of the fluid will vary uniformly from zero to U, and the tangential resistance will be F=U/h, where is the coefficient of viscosity and h is the thickness of the film. With this definition of a viscous fluid, the following equation is established, giving the viscosity and from the general equations representing the stress in relations between p, the pressure at any point in the film, h the thickness of the film at a point x measured round the circumference of the journal in the direction of relative motion, and U the relative tangential velocity of the surfaces, (1) |