THE USE OF GYROSTATS.
In 1874 two famous men made a great mistake in endeavouring to prevent or diminish the rolling motion of the saloon of a vessel by using a rapidly rotating wheel. Mr. Macfarlane Gray pointed out their mistake. It is only when the wheel is allowed toprecessthat it can exercise a steadying effect; the moment which it then exerts is equal to the angular speed of the precession multiplied by the moment of momentum of the spinning wheel.
It is astonishing how many engineers who know the laws of motion of mere translation, are ignorant of angular motion, and yet the analogies between the two sets of laws are perfectly simple. I have set out these analogies in my book onApplied Mechanics. The last of them between centripetal force on a body moving in a curved path, and torque or moment on a rotating body is the simple key to all gyrostatic or top calculation. When the spin of a top is greatly reduced it is necessary to remember that the total moment of momentum is not about the spinning axis (see myApplied Mechanics, page 594); correction for this is, I suppose, what introduces the complexity which scares students from studying the vagaries of tops; but in all cases that are likely to come before an engineer it would be absurd to studysuch a small correction, and consequently calculation is exceedingly simple.
Inventors using gyrostats have succeeded in doing the following things—
(1) Keeping the platform of a gun level on board ship, however the ship may roll or pitch. Keeping a submarine vessel or a flying machine with any plane exactly horizontal or inclined in any specified way.[14]It is easy to effect such objects without the use of a gyrostat, as by means of spirit levels it is possible to command powerful electric or other motors to keep anything always level. The actual methods employed by Mr. Beauchamp Tower (an hydraulic method), and by myself (an electric method), depend upon the use of a gyrostat, which is really a pendulum, the axis being vertical.
(2) Greatly reducing the rolling (or pitching) of a ship, or the saloon of a ship. This is the problem which Mr. Schlick has solved with great success, at any rate in the case of torpedo boats.
(3) In Mr. Brennan's Mono-rail railway, keeping the resultant force due to weight, wind pressure, centrifugal force, etc., exactly in line with the rail, so that, however the load on a wagon may alter in position, and although the wagon may be going round a curve, it is quickly brought to a position such that there are no forces tending to alter its angular position. The wagon leans over towards the wind or towards the centre of the curve of the rail so as to be in equilibrium.
(4) I need not refer to such matters as the use of gyrostats for the correction of compasses on board ship, referred to in page111.
Fig. 1Fig. 1.
Problems (2) and (3) are those to which I wish to refer. For a ship of 6,000 tons Mr. Schlick would use a large wheel of 10 to 20 tons, revolving about an axis E F (fig. 1) whose mean position is vertical. Its bearings are in a frame E C F D which can move about a thwart-ship axis C D with a precessional motion. Its centre of gravity is below this axis, so that like the ship itself the frame is in stable equilibrium. Let the ship have rolled through an angle R from its upright position, and suppose the axis E F to have precessed through the angle P from a vertical position. Let the angular velocity of rolling be called R˙, and the angular velocity of precession P˙; let the moment of momentum of the wheel bem. For any vibrating body like a ship it is easy to write out the equation of motion; into this equation we have merely to introduce the momentmP˙diminishing R; into the equation for P we merely introduce the momentmR˙increasing P. As usual we introduce frictional terms; in the first place F R˙(F being a constant co-efficient) stilling the roll of the ship; in the second casefP˙a fluid friction introduced by a pair of dash pots applied at the pins A and B to still the precessional vibrations of the frame. It will be found that the angular motion P is very much greater than the roll R. Indeed, so great is P that there are stops to prevent its exceeding a certain amount. Of course so long as a stop acts, preventing precession, the roll of the ship proceeds as if the gyrostat wheel were not rotating. Mr. Schlick drives his wheels by steam; he will probably in future do as Mr. Brennan does, drive them by electromotors, and keep them in air-tight cases in good vacuums, because the loss of energy by friction against an atmosphere is proportional to the density of the atmosphere. The solution of the equations to find the nature of the R and P motions is sometimes tedious, but requires no great amount of mathematical knowledge. In a case considered by me ofa 6,000 ton ship, the period of a roll was increased from 14 to 20 seconds by the use of the gyrostat, and the roll rapidly diminished in amount. There was accompanying this slow periodic motion, one of a two seconds' period, but if it did appear it was damped out with great rapidity. Of course it is assumed that, by the use of bilge keels and rolling chambers, and as low a metacentre as is allowable, we have already lengthened the time of vibration, and damped the roll R as much as possible, before applying the gyrostat. I take it that everybody knows the importance of lengthening the period of the natural roll of a ship, although he may not know the reason. The reason why modern ships of great tonnage are so steady is because their natural periodic times of rolling vibration are so much greater than the probable periods of any waves of the sea, for if a series of waves acts upon a ship tending to make it roll, if the periodic time of each wave is not very different from the natural periodic time of vibration of the ship, the rolling motion may become dangerously great.
If we try to apply Mr. Schlick's method to Mr. Brennan's car it is easy to show that there is instability of motion, whether there is or is not friction. If there is no friction, and we make the gyrostat frame unstable by keeping its centre of gravity above the axis C D, there will be vibrations, but the smallest amount of friction will cause these vibrations to get greater and greater. Even without friction there will be instability ifm, the moment of momentum of the wheel, is less than a certain amount. We see, then, that no form of the Schlick method, or modification of it, can be applied to solve the Brennan problem.
Fig. 2Fig. 2.
Mr. Brennan's method of working is quite different from that of Mr. Schlick. Fig. 2 shows his model car (about six feet long); it is driven by electric accumulators carried by the car. His gyrostat wheels are driven by electromotors (not shown in fig. 3); as they are revolving in nearly vacuous spaces they consume but little power, and even if the current were stopped they would continue running at sufficiently high speeds to be effective for a length of time. Still it must not be forgotten that energy is wasted in friction, and work has to be done in bringing the car to a new position of equilibrium, and this energy is supplied by the electromotors. Should the gyrostats really stop, or fall to a certain low speed, two supports are automatically dropped, one on either side of the car; each of them drops till it reaches the ground; one of them dropping, perhaps, much farther than the other.
The real full-size car, which he is now constructing, may be pulled with other cars by any kind of locomotive using electricity or petrol or steam, or each of the wheels may be a driving wheel. He would prefer to generate electropower on his train, and to drive every wheel with an electric motor. His wheels are so independent of one another that they can take very quick curves and vertical inequalities of the rail. The rail is fastened to sleepers lying on ground that may have sidelong slope. The model car is supported by a mono-rail bogie at each end; each bogie has two wheels pivoted both vertically and horizontally; it runs on a round iron gas pipe, and sometimes on steel wire rope; the ground is nowhere levelled or cut, and at one place the rail is a steel wire rope spanning a gorge, as shown in fig. 2. It is interesting to stop the car in the middle of this rope and to swing the rope sideways to see the automatic balancing of the car. The car may be left here or elsewhere balancing itself with nobody in charge of it. If the load on the car—great lead weights—be dumped about into new positions, the car adjusts itself to the new conditions with greatquickness. When the car is stopped, if a person standing on the ground pushes the car sidewise, the car of course pushes in opposition, like an indignant animal, and by judicious pushing and yielding it is possible to cause a considerable tilt. Left now to itself the car rights itself very quickly.
Fig. 3Fig. 3.
Fig. 3bFig.3b(showing the ground-plan of Fig. 3).
Fig. 3 is a diagrammatic representation of Mr. Brennan's pair of gyrostats in sectional elevation and plan. The cases G and G', inside which the wheels F and F' are rotatingin vacuoat the same speed and in opposite directions (driven by electromotors not shown in the figure), are pivoted about vertical axes E J and E' J'. They are connected by spur-toothed segments J J and J' J', so that their precessional motions are equal and opposite. The whole system is pivoted about C, a longitudinal axis. Thus when precessing so that H comes out of the paper, so will H', and when H goes into the paper, so does H'. When the car is in equilibrium the axes K H and K' H' are in line N O O' N' across the car in the plane of the paper. They are also in a line which is at right angles to the total resultant (vertical or nearly vertical) force on the car. I will call N O O' N' the mid position. Let ½mbe the moment of momentum of either wheel. Let us suppose that suddenly the car finds that it is not in equilibrium because of a gust of wind, or centrifugal force, or an alteration of loading, so that the shelf D comes up against H, the spinning axis (or a roller revolving with the spinning axis) of the gyrostat. H begins to roll away from me, and if no slipping occurred (but there always is slipping, and, indeed, slipping is a necessary condition) it would roll, that is, the gyrostats would precess with a constant angular velocityα, and exert the momentmαupon the shelf D, and therefore on the car. It is to be observed that this is greater as the diameter of the rolling part is greater. This precession continues until the roller and the shelf cease to touch. At first H lifts with the shelf, and afterwards the shelf moving downwards is followed for some distance by the roller. If the tilt had been in the opposite direction the shelf D' would have acted upwards upon the roller H', and caused just the opposite kind of precession, and a moment of the opposite kind.
We now have the spindles out of their mid position; how are they brought back from O Q and O' Q' to O N and O' N',but with H permanently lowered just the right amount? It is the essence of Mr. Brennan's invention that after a restoring moment has been applied to the car the spindles shall go back to the position N O O' N' (with H permanently lowered), so as to be ready to act again. He effects this object in various ways. Some ways described in his patents are quite different from what is used on the model, and the method to be used on the full-size wagon will again be quite different. I will describe one of the methods. Mr. Brennan tells me that he considers this old method to be crude, but he is naturally unwilling to allow me to publish his latest method.
D' is a circular shelf extending from the mid position in my direction; D is a similar shelf extending from the mid position into the paper, or away from me. It is on these shelves that H' and H roll, causing precession away from N O O' N', as I have just described. When H' is inside the paper, or when H is outside the paper, they find no shelf to roll upon. There are, however, two other shelves L and L', for two other rollers M and M', which are attached to the frames concentric with the spindles; they are free to rotate, but are not rotated by the spindles. When they are pressed by their shelves L or L' this causes negative precession, and they roll towards the N O O' N' position. There is, of course, friction at their supports, retarding their rotation, and therefore the precession. The important thing to remember is that H and H', when they touch their shelves (when one is touching the other is not touching) cause a precession away from the mid position N O O' N' at a rateα, which produces a restoring momentmαof nearly constant amount (except for slipping), whereas where M or M' touches its shelf L or L' (when one is touching the other is not touching) the pressure on the shelf and friction determine the rate of the precession towards the mid position N O O' N',as well as the small vertical motion. The friction at the supports of M and M' is necessary.
Suppose that the tilt from the equilibrium position to be corrected is R, when D presses H upward. The momentmα, and its time of action (the total momental impulse) are too great, and R is over-corrected; this causes the roller M' to act on L', and the spindles return to the mid position; they go beyond the mid position, and now the roller H' acts on D', and there is a return to the mid position, and beyond it a little, and so it goes on, the swings of the gyrostats out of and into the mid position, and the vibrations of the car about its position of equilibrium getting rapidly less and less until again neither H nor H', nor M nor M' is touching a shelf. It is indeed marvellous to see how rapidly the swings decay. Friction accelerates the precession away from N O O' N'. Friction retards the precession towards the middle position.
It will be seen that by using the two gyrostats instead of one when there is a curve on the line, although the plane N O O' N' rotates, and we may say that the gyrostats precess, the tilting couples which they might exercise are equal and opposite. I do not know if Mr. Brennan has tried a single gyrostat, the mid position of the axis of the wheel being vertical, but even in this case a change of slope, or inequalities in the line, might make it necessary to have a pair.
It is evident that this method of Mr. Brennan is altogether different in character from that of Mr. Schlick. Work is here actually done which must be supplied by the electromotors.
One of the most important things to know is this: the Brennan model is wonderfully successful; the weight of the apparatus is not a large fraction of the weight of the wagon; will this also be the case with a car weighing 1,000 times asmuch? The calculation is not difficult, but I may not give it here. If we assume that suddenly the wagon finds itself at the angle R from its position of equilibrium, it may be taken that if the size of each dimension of the wagon be multiplied byn, and the size of each dimension of the apparatus be multiplied byp, then for a sudden gust of wind, or suddenly coming on a curve, or a sudden shift of position of part of the cargo, R may be taken as inversely proportional ton. I need not state the reasonable assumption which underlies this calculation, but the result is that ifnis 10,pis 7.5. That is, if the weight of the wagon is multiplied by 1,000, the weight of the apparatus is only multiplied by 420. In fact, if, in the model, the weight of the apparatus is 10 per cent. of that of the wagon, in the large wagon the weight of the apparatus is only about 4 per cent. of that of the wagon. This is a very satisfactory result.[15]
My calculations seem to show that Mr. Schlick's apparatus will form a larger fraction of the whole weight of a ship, as the ship is larger, but in the present experimental stage of the subject it is unfair to say more than that this seems probable. My own opinion is that large ships are sufficiently steady already.
In both cases it has to be remembered that if thediameterof the wheel can be increased in greater proportion than the dimensions of ship or wagon, the proportional weight of the apparatus may be diminished. A wheel of twice the diameter, but of the same weight, may have twice the moment of momentum, and may therefore be twice as effective. I assume the stresses in the material to be the same.
Page23; note at line 3. Prof. Osborne Reynolds made the interesting remark (Collected Papers, Vol. ii., p. 154), "That if solid matter had certain kinds of internal motions, such as the box has, pears differing, say, from apples, the laws of motion would not have been discovered; if discovered for pears they would not have applied toapples."
Page38; note at line 8. The motion of a rifle bullet is therefore one of precession about the tangent to the path. The mathematical solution is difficult, but Prof. Greenhill has satisfied himself mathematically that air friction damps the precession, and causes the axis of the shot to get nearer the tangential direction, so that fig. 10 illustrates what would occur in a vacuum, but not in air. It is probable that this statement applies only to certain proportions of length to diameter.
Page129; note at line 5. Many men wonder how the ether can have the enormous rigidity necessary for light transmission, and yet behave like a frictionless fluid. One way of seeing how this may occur is to imagine that when ordinary matter moves in the ether it only tends to produce motion of translation of the ether particles, and therefore no resistance. But anything such as light, which must operate in turning axes of rotating parts, may encounter enormous elastic resistance.
Richard Clay & Sons, Limited, London and Bungay.
OF THE
Small post 8vo, cloth boards.
Coal, and What We Get From It.By ProfessorR. Meldola, F.R.S., F.I.C. With several Illustrations. 2s.6d.Colour Measurement and Mixture.By SirW. de W.Abney, K.C.B., R.E., F.R.S. Numerous Illustrations. 2s.6d.Diseases of Plants.By ProfessorMarshall Ward. Numerous Illustrations. 2s.6d.Our Secret Friends and Foes.ByPercy Faraday Frankland, Ph.D., B.Sc. (Lond.), F.R.S. Illustrated. 3s.Soap-Bubbles, and the Forces which Mould Them.ByC. V. Boys, A.R.S.M., F.R.S. Illustrated. 2s.6d.Sounding the Ocean of Air.ByA. Lawrence Rotch, S.B., A.M. Numerous Illustrations. 2s.6d.Spinning Tops.By ProfessorJ. Perry, M.E. With several Illustrations. 2s.6d.The Making of Flowers.By the Rev. ProfessorGeorge Henslow, M.A., F.L.S., F.G.S. With Illustrations. 2s.6d.The Story of a Tinder-Box.By the lateCharles Meymott Tidy, M.B., M.S., F.C.S. Numerous Illustrations. 2s.Time and Tide.A Romance of the Moon. By SirRobert S. Ball, LL.D. With Illustrations. 2s.6d.The Birth and Growth of Worlds.By the late ProfessorGreen, F.R.S. With Illustrations. 1s.The Splash of a Drop.By ProfessorA. M. Worthington, F.R.S. Numerous Illustrations. 1s.6d.The Machinery of the Universe.By ProfessorA. E. Dolbear, A.B., A.M., M.E., Ph.D. Illustrated. 2s.The New State of Matter.An Address by ProfessorH. Pellat. Translated byEdmund McClure, M.A. 1s.Turbines.By Engineer-CommanderA. E. Tompkins, R.N. Illustrated. 3s.6d.
Coal, and What We Get From It.By ProfessorR. Meldola, F.R.S., F.I.C. With several Illustrations. 2s.6d.
Colour Measurement and Mixture.By SirW. de W.Abney, K.C.B., R.E., F.R.S. Numerous Illustrations. 2s.6d.
Diseases of Plants.By ProfessorMarshall Ward. Numerous Illustrations. 2s.6d.
Our Secret Friends and Foes.ByPercy Faraday Frankland, Ph.D., B.Sc. (Lond.), F.R.S. Illustrated. 3s.
Soap-Bubbles, and the Forces which Mould Them.ByC. V. Boys, A.R.S.M., F.R.S. Illustrated. 2s.6d.
Sounding the Ocean of Air.ByA. Lawrence Rotch, S.B., A.M. Numerous Illustrations. 2s.6d.
Spinning Tops.By ProfessorJ. Perry, M.E. With several Illustrations. 2s.6d.
The Making of Flowers.By the Rev. ProfessorGeorge Henslow, M.A., F.L.S., F.G.S. With Illustrations. 2s.6d.
The Story of a Tinder-Box.By the lateCharles Meymott Tidy, M.B., M.S., F.C.S. Numerous Illustrations. 2s.
Time and Tide.A Romance of the Moon. By SirRobert S. Ball, LL.D. With Illustrations. 2s.6d.
The Birth and Growth of Worlds.By the late ProfessorGreen, F.R.S. With Illustrations. 1s.
The Splash of a Drop.By ProfessorA. M. Worthington, F.R.S. Numerous Illustrations. 1s.6d.
The Machinery of the Universe.By ProfessorA. E. Dolbear, A.B., A.M., M.E., Ph.D. Illustrated. 2s.
The New State of Matter.An Address by ProfessorH. Pellat. Translated byEdmund McClure, M.A. 1s.
Turbines.By Engineer-CommanderA. E. Tompkins, R.N. Illustrated. 3s.6d.
WORKS BY MRS. RUNDLE CHARLES, AUTHOR OF"The Chronicles of the Schönberg-Cotta Family."
The Beatitudes.Thoughts for All Saints' Day. Post 8vo.Cloth boards. 1s."By the Mystery of Thy Holy Incarnation."Post 8vo.Cloth boards. 1s."By Thy Cross and Passion."Thoughts on the words spoken around and on the Cross. Post 8vo.Cloth boards. 1s."By Thy Glorious Resurrection and Ascension."Easter Thoughts. Post 8vo.Cloth boards. 1s."By the Coming of the Holy Ghost."Thoughts for Whitsuntide. Post 8vo.Cloth boards. 1s.The True Vine.Post 8vo.Cloth boards. 1s.The Great Prayer of Christendom.Thoughts on the Lord's Prayer. Post 8vo.Cloth boards. 1s.An Old Story of Bethlehem.One link in the great Pedigree. Fcap. 4to, with six plates, beautifully printed in colours.Cloth boards. 2s.Joan the Maid,Deliverer of England and France. Demy 8vo.Cloth boards. 2s. 6d.Songs, Old and New.Demy 16mo.Cloth boards. 2s. 6d.Ecce Ancilla Domini.Mary the Mother of our Lord. Studies in the Ideal of Womanhood. Post 8vo.Cloth boards. 1s. 6d.Ecce Homo, Ecce Rex.Pages from the Story of the Moral Conquests of Christianity. Crown 8vo.Cloth boards. 2s. 6d.Three Martyrs of the Nineteenth Century.Studies from the Lives of Gordon, Livingstone, and Patteson. Crown 8vo.Cloth boards. 2s. 6d.Martyrs and Saints of the First Twelve Centuries.Studies from the Lives of the Black-letter Saints of the English Calendar. Crown 8vo.Cloth boards. 2s. 6d.Against the Stream.The Story of an Heroic Age in England. With eight page woodcuts. Crown 8vo.Cloth boards. 2s. 6d.Conquering and to Conquer.A Story of Rome in the days of St. Jerome. Illustrated. Crown 8vo.Cloth boards. 2s.Attila and his Conquerors.A Story of the days of St. Patrick and St. Leo the Great. Crown 8vo.Cloth boards. 2s.Te Deum Laudamus.Christian Life in Song.Cloth 2s. 6d.Early Christian Missions of Ireland, Scotland, and England.Crown 8vo.Cloth boards. 2s. 6d.Lapsed, not Lost.A Story of Roman Carthage. Crown 8vo.Cloth boards. 2s.Within the Veil.Studies in the Epistle to the Hebrews. Post 8vo.Cloth boards. 1s.The Book of the Unveiling.Studies in the Revelation of St. John the Divine. Post 8vo.Cloth boards. 1s.Lady Augusta Stanley.Reminiscences. 18mo.Limp cloth. 6d.Sketches of the Women of Christendom.Crown 8vo.2s. 6d.
The Beatitudes.Thoughts for All Saints' Day. Post 8vo.Cloth boards. 1s.
"By the Mystery of Thy Holy Incarnation."Post 8vo.Cloth boards. 1s.
"By Thy Cross and Passion."Thoughts on the words spoken around and on the Cross. Post 8vo.Cloth boards. 1s.
"By Thy Glorious Resurrection and Ascension."Easter Thoughts. Post 8vo.Cloth boards. 1s.
"By the Coming of the Holy Ghost."Thoughts for Whitsuntide. Post 8vo.Cloth boards. 1s.
The True Vine.Post 8vo.Cloth boards. 1s.
The Great Prayer of Christendom.Thoughts on the Lord's Prayer. Post 8vo.Cloth boards. 1s.
An Old Story of Bethlehem.One link in the great Pedigree. Fcap. 4to, with six plates, beautifully printed in colours.Cloth boards. 2s.
Joan the Maid,Deliverer of England and France. Demy 8vo.Cloth boards. 2s. 6d.
Songs, Old and New.Demy 16mo.Cloth boards. 2s. 6d.
Ecce Ancilla Domini.Mary the Mother of our Lord. Studies in the Ideal of Womanhood. Post 8vo.Cloth boards. 1s. 6d.
Ecce Homo, Ecce Rex.Pages from the Story of the Moral Conquests of Christianity. Crown 8vo.Cloth boards. 2s. 6d.
Three Martyrs of the Nineteenth Century.Studies from the Lives of Gordon, Livingstone, and Patteson. Crown 8vo.Cloth boards. 2s. 6d.
Martyrs and Saints of the First Twelve Centuries.Studies from the Lives of the Black-letter Saints of the English Calendar. Crown 8vo.Cloth boards. 2s. 6d.
Against the Stream.The Story of an Heroic Age in England. With eight page woodcuts. Crown 8vo.Cloth boards. 2s. 6d.
Conquering and to Conquer.A Story of Rome in the days of St. Jerome. Illustrated. Crown 8vo.Cloth boards. 2s.
Attila and his Conquerors.A Story of the days of St. Patrick and St. Leo the Great. Crown 8vo.Cloth boards. 2s.
Te Deum Laudamus.Christian Life in Song.Cloth 2s. 6d.
Early Christian Missions of Ireland, Scotland, and England.Crown 8vo.Cloth boards. 2s. 6d.
Lapsed, not Lost.A Story of Roman Carthage. Crown 8vo.Cloth boards. 2s.
Within the Veil.Studies in the Epistle to the Hebrews. Post 8vo.Cloth boards. 1s.
The Book of the Unveiling.Studies in the Revelation of St. John the Divine. Post 8vo.Cloth boards. 1s.
Lady Augusta Stanley.Reminiscences. 18mo.Limp cloth. 6d.
Sketches of the Women of Christendom.Crown 8vo.2s. 6d.
Fcap. 8vo, with Map, cloth boards, 2s. each.
The Continental Teutons,by the late Very Rev.C. Merivale.The English,by the late Rev.G. F. MacLear, D.D.The Northmen,by the late Rev.G. F. MacLear, D.D.The Slavs,by the late Rev.G. F. MacLear, D.D.
The Continental Teutons,by the late Very Rev.C. Merivale.
The English,by the late Rev.G. F. MacLear, D.D.
The Northmen,by the late Rev.G. F. MacLear, D.D.
The Slavs,by the late Rev.G. F. MacLear, D.D.
This Series has for its aim the presentation of Early Britain at great historic periods. Each volume is the work of an accredited specialist, and the whole gives the result of recent critical examinations of our Early Records.
Anglo-Saxon Britain.By the lateGrant Allen. With Map.2s. 6d.Celtic Britain.By ProfessorRhys. With two Maps.3s.Norman Britain.By the Rev.W. Hunt. With Map.2s.Post-Norman Britain.ByHenry G. Hewlett. With Map.3s.Roman Britain.By the Rev.E. Conybeare. With Map.3s. 6d.Roman Roads in Britain.ByThomas Codrington, M. Inst. C.E., F.G.S. With Maps. Second Edition, revised.5s.Scandinavian Britain.ByW. G. Collingwood, M.A., F.S.A. With Chapters Introductory to the subject by the late ProfessorF. York Powell, M.A.3s. 6d.
Anglo-Saxon Britain.By the lateGrant Allen. With Map.2s. 6d.
Celtic Britain.By ProfessorRhys. With two Maps.3s.
Norman Britain.By the Rev.W. Hunt. With Map.2s.
Post-Norman Britain.ByHenry G. Hewlett. With Map.3s.
Roman Britain.By the Rev.E. Conybeare. With Map.3s. 6d.
Roman Roads in Britain.ByThomas Codrington, M. Inst. C.E., F.G.S. With Maps. Second Edition, revised.5s.
Scandinavian Britain.ByW. G. Collingwood, M.A., F.S.A. With Chapters Introductory to the subject by the late ProfessorF. York Powell, M.A.3s. 6d.
A set of Works designed to present the chief races of Europe as they emerge out of pre-historic darkness into the light furnished by their earliest recorded words.
Post 8vo, cloth boards, 2s. 6d. each.
Anglo-Saxon Literature.By the Rev. ProfessorEarle.French Literature.By the lateGustave Masson, B.A.Slavonic Literature.ByW. R. Morfill, M.A.The Greek Epic.ByGeorge C. W. Warr, M.A.3s.
Anglo-Saxon Literature.By the Rev. ProfessorEarle.
French Literature.By the lateGustave Masson, B.A.
Slavonic Literature.ByW. R. Morfill, M.A.
The Greek Epic.ByGeorge C. W. Warr, M.A.3s.
A Series of Monograms on the Chief Fathers of the Church, the Fathers selected being centres of influence at important periods of Church History, and in important spheres of action.
Fcap. 8vo, cloth boards, 2s. each.
Boniface.By the Rev. CanonGregory Smith.1s. 6d.Clement of Alexandria.By the Rev.F. R. MontgomeryHitchcock, B.D.3s.Leo the Great.By the Right Rev.C. Gore, D.D.Gregory the Great.By the late Rev.J. Barmby, B.D.Saint Ambrose:his Life, Times, and Teaching. By the Rev.R. Thornton, D.D.Saint Athanasius:his Life and Times. By the Rev.R. Wheler Bush.2s. 6d.Saint Augustine.By the late Rev.E. L. Cutts, D.D.Saint Basil the Great.By the Rev.R. T. Smith, B.D.Saint Bernard:Abbot of Clairvaux, A.D. 1091-1153. By Rev.S. J. Eales.2s. 6d.Saint Jerome.By the late Rev.Edward L. Cutts, D.D.Saint Hilary of Poitiers, andSaint Martin of Tours.By the Rev.J. GibsonCazenove, D.D.Saint John of Damascus.By the Rev.J. H. Lupton.Saint Patrick:his Life and Teaching. By the Rev.E. J. Newell, M.A.2s. 6d.Synesius of Cyrene,Philosopher and Bishop. ByAlice Gardner.The Apostolic Fathers.By the Rev. CanonScottHolland.The Defenders of the Faith;or, The Christian Apologists of the Second and Third Centuries. By the Rev.F. Watson, D.D.The Venerable Bede.By the Right Rev.G. F. Browne.
Boniface.By the Rev. CanonGregory Smith.1s. 6d.
Clement of Alexandria.By the Rev.F. R. MontgomeryHitchcock, B.D.3s.
Leo the Great.By the Right Rev.C. Gore, D.D.
Gregory the Great.By the late Rev.J. Barmby, B.D.
Saint Ambrose:his Life, Times, and Teaching. By the Rev.R. Thornton, D.D.
Saint Athanasius:his Life and Times. By the Rev.R. Wheler Bush.2s. 6d.
Saint Augustine.By the late Rev.E. L. Cutts, D.D.
Saint Basil the Great.By the Rev.R. T. Smith, B.D.
Saint Bernard:Abbot of Clairvaux, A.D. 1091-1153. By Rev.S. J. Eales.2s. 6d.
Saint Jerome.By the late Rev.Edward L. Cutts, D.D.
Saint Hilary of Poitiers, andSaint Martin of Tours.By the Rev.J. GibsonCazenove, D.D.
Saint John of Damascus.By the Rev.J. H. Lupton.
Saint Patrick:his Life and Teaching. By the Rev.E. J. Newell, M.A.2s. 6d.
Synesius of Cyrene,Philosopher and Bishop. ByAlice Gardner.
The Apostolic Fathers.By the Rev. CanonScottHolland.
The Defenders of the Faith;or, The Christian Apologists of the Second and Third Centuries. By the Rev.F. Watson, D.D.
The Venerable Bede.By the Right Rev.G. F. Browne.
By ProfessorMaspero. Edited by the Rev. ProfessorSayce. Translated byM. L. McClure. Each volume contains Maps, coloured Plates, and numerous other Illustrations.
Demy 4to, cloth, bevelled boards.
Volume I.The Dawn of Civilization: Egypt and Chaldaea.Fourth Edition.24s.; half-morocco,48s.Volume II.The Struggle of the Nations: Egypt, Syria, and Assyria.25s.; half-morocco,50s.Volume III.The Passing of the Empires, 850 B.C.-330 B.C.25s.; half-morocco,50s.
Volume I.The Dawn of Civilization: Egypt and Chaldaea.Fourth Edition.24s.; half-morocco,48s.
Volume II.The Struggle of the Nations: Egypt, Syria, and Assyria.25s.; half-morocco,50s.
Volume III.The Passing of the Empires, 850 B.C.-330 B.C.25s.; half-morocco,50s.
Fcap. 8vo, cloth boards, 2s. each.
Assyria, from the Earliest Times to the Fall of Nineveh.By the lateGeorge Smith, of the British Museum. A New and Revised Edition, by the Rev. ProfessorSayce.Sinai, from the Fourth Egyptian Dynasty to the PresentDay.By the lateHenry S. Palmer. A New Edition, revised throughout by the Rev. ProfessorSayce. With Map.Babylonia (The History of).By the lateGeorge Smith. Edited and brought up to date by the Rev. ProfessorSayce.Persia, from the Earliest Period to the Arab Conquest.By the lateW. S. W. Vaux, M.A. A New and Revised Edition, by the Rev.ProfessorSayce.
Assyria, from the Earliest Times to the Fall of Nineveh.By the lateGeorge Smith, of the British Museum. A New and Revised Edition, by the Rev. ProfessorSayce.
Sinai, from the Fourth Egyptian Dynasty to the PresentDay.By the lateHenry S. Palmer. A New Edition, revised throughout by the Rev. ProfessorSayce. With Map.
Babylonia (The History of).By the lateGeorge Smith. Edited and brought up to date by the Rev. ProfessorSayce.
Persia, from the Earliest Period to the Arab Conquest.By the lateW. S. W. Vaux, M.A. A New and Revised Edition, by the Rev.ProfessorSayce.
The "Higher Criticism" and the Verdict of the Monuments.By the Rev. ProfessorA. H. Sayce. Demy 8vo. Buckram, bevelled boards,5s.
The "Higher Criticism" and the Verdict of the Monuments.By the Rev. ProfessorA. H. Sayce. Demy 8vo. Buckram, bevelled boards,5s.
This Series deals with the chief systems of Ancient Thought, not merely as dry matters of History, but as having a bearing on Modern Speculation.
Fcap. 8vo, cloth boards, 2s. 6d. each.
Neoplatonism.By the Rev.C. Bigg, D.D.3s.Platonism.By the Rev.Thomas B. Strong, M.A.3s.Epicureanism.By the late ProfessorWilliam Wallace.Stoicism.By Rev.W. W. Capes, Fellow of Hertford College.Aristotelianism. The Ethics of Aristotle.By the Rev.I. Gregory Smith. The Logical Treatises, the Metaphysics, the Psychology, the Politics. By the Rev.W. Grundy.
Neoplatonism.By the Rev.C. Bigg, D.D.3s.
Platonism.By the Rev.Thomas B. Strong, M.A.3s.
Epicureanism.By the late ProfessorWilliam Wallace.
Stoicism.By Rev.W. W. Capes, Fellow of Hertford College.
Aristotelianism. The Ethics of Aristotle.By the Rev.I. Gregory Smith. The Logical Treatises, the Metaphysics, the Psychology, the Politics. By the Rev.W. Grundy.
This Series furnishes a perfect Library of English Ecclesiastical History. Each volume is complete in itself, and the possibility of repetition has been carefully guarded against.
Fcap. 8vo, with Map, cloth boards.
Bath and Wells.By the Rev.W. Hunt.2s. 6d.Canterbury.By the late Rev.R. C. Jenkins.3s. 6d.Carlisle.By the lateRichard S. Ferguson.2s. 6d.Chester.By the Rev.Rupert H. Morris. With Map.3s.Chichester.By the late Very Rev.W. R. W. Stephens. With Map and Plan.2s. 6d.Durham.By Rev.J. L. Low. With Map and Plan.2s.Hereford. By the late Rev. CanonPhillpott.3s.Lichfield.By the Rev.W. Beresford.2s. 6d.Lincoln.By the late Rev. CanonE. Venables, and the late Ven.Archdeacon Perry. With Map.4s.Llandaff.By the Rev.E. J. Newell, M.A. With Map.3s. 6d.Norwich.By the Rev.A. Jessopp, D.D.2s. 6d.Oxford.By the Rev.E. Marshall.2s. 6d.Peterborough.By the Rev.G. A. Poole, M.A.2s. 6d.Rochester.By the Rev.A. J. Pearman. With Map.4s.Salisbury.By the Rev.W. H. Jones. With Map.2s. 6d.Sodor and Man.ByA. W. Moore, M.A.3s.St. Asaph.By the Ven. ArchdeaconThomas.2s.St. David's.By the Rev. CanonBevan. With Map.2s. 6d.Winchester.By the Rev.W. Benham, B.D.3s.Worcester.By the Rev.I. Gregory Smithand Rev.Phipps Onslow.3s. 6d.York.By the Rev. CanonOrnsby, M.A., F.S.A.3s. 6d.
Bath and Wells.By the Rev.W. Hunt.2s. 6d.
Canterbury.By the late Rev.R. C. Jenkins.3s. 6d.
Carlisle.By the lateRichard S. Ferguson.2s. 6d.
Chester.By the Rev.Rupert H. Morris. With Map.3s.
Chichester.By the late Very Rev.W. R. W. Stephens. With Map and Plan.2s. 6d.
Durham.By Rev.J. L. Low. With Map and Plan.2s.
Hereford. By the late Rev. CanonPhillpott.3s.
Lichfield.By the Rev.W. Beresford.2s. 6d.
Lincoln.By the late Rev. CanonE. Venables, and the late Ven.Archdeacon Perry. With Map.4s.
Llandaff.By the Rev.E. J. Newell, M.A. With Map.3s. 6d.
Norwich.By the Rev.A. Jessopp, D.D.2s. 6d.
Oxford.By the Rev.E. Marshall.2s. 6d.
Peterborough.By the Rev.G. A. Poole, M.A.2s. 6d.
Rochester.By the Rev.A. J. Pearman. With Map.4s.
Salisbury.By the Rev.W. H. Jones. With Map.2s. 6d.
Sodor and Man.ByA. W. Moore, M.A.3s.
St. Asaph.By the Ven. ArchdeaconThomas.2s.
St. David's.By the Rev. CanonBevan. With Map.2s. 6d.
Winchester.By the Rev.W. Benham, B.D.3s.
Worcester.By the Rev.I. Gregory Smithand Rev.Phipps Onslow.3s. 6d.
York.By the Rev. CanonOrnsby, M.A., F.S.A.3s. 6d.
Small post 8vo, cloth boards.
A Homily of Clement of Alexandria,entitled, Who is the Rich Man that is Being Saved? By Rev.P. Mordaunt Barnard.1s.Bishop Sarapion's Prayer-Book:An Egyptian Pontifical dated probably about 350-356 A.D. Translated from the Edition of Dr.G. Wobbermin. With Introduction, Notes, and Indices, by the Right Rev.John Wordsworth, D.D.1s. 6d.Origen the Teacher.Being the Address of Gregory the Wonder-Worker to Origen, together with Origen's Letter to Gregory. Translated, with an Introduction and Notes, by the Rev.W. Metcalfe, D.D.1s. 6d.St. Cyprian on the Lord's Prayer.An English Translation, with Introduction by the Ven. ArchdeaconT. H. Bindley, D.D.1s. 6d.St. Polycarp, Bishop of Smyrna. By the late Rev.Blomfield Jackson, M.A.1s.The Doctrine of the Twelve Apostles.Translated into English, with Introduction and Notes, by the Rev.Charles Bigg, D.D.1s.The Epistle of St. Clement, Bishop of Rome.By the Rev.John A. F. Gregg, M.A.1s.St. Augustine's Treatise on the City of God.By Rev.F. R. M. Hitchcock, M.A., B.D.1s. 6d.St. Chrysostom on the Priesthood.By the Rev.T. Allen Moxom, M.A.2s.The Apostolical Constitutions and Cognate Documents,with special reference to their Liturgical Elements. By the Rev.De Lacy O'Leary, M.A.1s.The Epistle of Diognetus.By the Rev.L. B. Radford, M.A.1s. 6d.The Epistle of the Galilean Churches:Lugdunum and Vienne. With an Appendix containing Tertullian's Address to Martyrs and the Passion of St. Perpetua. Translated, with Introduction and Notes, by Ven. ArchdeaconT. H. Bindley, D.D.1s.The Epistles of St. Ignatius, Bishop of Antioch.By Rev.J. H. Srawley, M.A. In two volumes.1s.each.The Liturgy of the Eighth Book of "the Apostolic Constitutions,"commonly called the Clementine Liturgy. Translated into English, with Introduction and Notes, by Rev.R. H. Cresswell, M.A.1s. 6d.The Shepherd of Hermas.By the late Rev.C. Taylor, D.D. Vols. I. and II.2s.each.
A Homily of Clement of Alexandria,entitled, Who is the Rich Man that is Being Saved? By Rev.P. Mordaunt Barnard.1s.
Bishop Sarapion's Prayer-Book:An Egyptian Pontifical dated probably about 350-356 A.D. Translated from the Edition of Dr.G. Wobbermin. With Introduction, Notes, and Indices, by the Right Rev.John Wordsworth, D.D.1s. 6d.
Origen the Teacher.Being the Address of Gregory the Wonder-Worker to Origen, together with Origen's Letter to Gregory. Translated, with an Introduction and Notes, by the Rev.W. Metcalfe, D.D.1s. 6d.
St. Cyprian on the Lord's Prayer.An English Translation, with Introduction by the Ven. ArchdeaconT. H. Bindley, D.D.1s. 6d.
St. Polycarp, Bishop of Smyrna. By the late Rev.Blomfield Jackson, M.A.1s.
The Doctrine of the Twelve Apostles.Translated into English, with Introduction and Notes, by the Rev.Charles Bigg, D.D.1s.
The Epistle of St. Clement, Bishop of Rome.By the Rev.John A. F. Gregg, M.A.1s.
St. Augustine's Treatise on the City of God.By Rev.F. R. M. Hitchcock, M.A., B.D.1s. 6d.
St. Chrysostom on the Priesthood.By the Rev.T. Allen Moxom, M.A.2s.
The Apostolical Constitutions and Cognate Documents,with special reference to their Liturgical Elements. By the Rev.De Lacy O'Leary, M.A.1s.
The Epistle of Diognetus.By the Rev.L. B. Radford, M.A.1s. 6d.
The Epistle of the Galilean Churches:Lugdunum and Vienne. With an Appendix containing Tertullian's Address to Martyrs and the Passion of St. Perpetua. Translated, with Introduction and Notes, by Ven. ArchdeaconT. H. Bindley, D.D.1s.
The Epistles of St. Ignatius, Bishop of Antioch.By Rev.J. H. Srawley, M.A. In two volumes.1s.each.
The Liturgy of the Eighth Book of "the Apostolic Constitutions,"commonly called the Clementine Liturgy. Translated into English, with Introduction and Notes, by Rev.R. H. Cresswell, M.A.1s. 6d.
The Shepherd of Hermas.By the late Rev.C. Taylor, D.D. Vols. I. and II.2s.each.
Fcap. 8vo, cloth boards, 2s. 6d. each.
Buddhism:being a sketch of the Life and Teachings of Gautama, the Buddha. ByT. W. Rhys Davids, M.A. With Map.Buddhism in China.By the Rev.S. Beal. With Map.Confucianism and Taouism.By SirRobert K. Douglas, of the British Museum. With Map.Hinduism.By the late SirM. Monier-Williams, M.A., D.C.L. With Map.Islam and its Founder.ByJ. W. H. Stobart. With Map.Islam as a Missionary Religion.ByCharles R. Haines.2s.The Coran:its Composition and Teaching, and the Testimony it bears to the Holy Scriptures. BySir William Muir, K.C.S.I.The Historical Development of the Qurán.By the Rev.Edward Sell, D.D., M.R.A.S.The Religion of the Crescent, or Islam:its Strength, its Weakness, its Origin, its Influence. By the Rev.W. St. Clair Tisdall, M.A.4s.Studies of Non-Christian Religions.ByEliot Howard.
Buddhism:being a sketch of the Life and Teachings of Gautama, the Buddha. ByT. W. Rhys Davids, M.A. With Map.
Buddhism in China.By the Rev.S. Beal. With Map.
Confucianism and Taouism.By SirRobert K. Douglas, of the British Museum. With Map.
Hinduism.By the late SirM. Monier-Williams, M.A., D.C.L. With Map.
Islam and its Founder.ByJ. W. H. Stobart. With Map.
Islam as a Missionary Religion.ByCharles R. Haines.2s.
The Coran:its Composition and Teaching, and the Testimony it bears to the Holy Scriptures. BySir William Muir, K.C.S.I.
The Historical Development of the Qurán.By the Rev.Edward Sell, D.D., M.R.A.S.
The Religion of the Crescent, or Islam:its Strength, its Weakness, its Origin, its Influence. By the Rev.W. St. Clair Tisdall, M.A.4s.
Studies of Non-Christian Religions.ByEliot Howard.
Fcap. 8vo, with Map, cloth boards.
Diocese of Mackenzie River,by the Right Rev.W. C. Bompas, D.D., Bishop of the Diocese.2s.New Zealand,by the late Very Rev.Henry Jacobs, D.D., Dean of Christchurch. Containing the Dioceses of Auckland, Christchurch, Dunedin, Nelson, Waiapu, Wellington and Melanesia.5s.History of the Church in Eastern Canada and Newfoundland,by the Rev.J. Langtry.3s.The Church in the West Indies,by the Rev.A. Caldecott, B.D.3s. 6d.The Story of the Australian Church,by the Rev.E. Symonds.2s. 6d.
Diocese of Mackenzie River,by the Right Rev.W. C. Bompas, D.D., Bishop of the Diocese.2s.
New Zealand,by the late Very Rev.Henry Jacobs, D.D., Dean of Christchurch. Containing the Dioceses of Auckland, Christchurch, Dunedin, Nelson, Waiapu, Wellington and Melanesia.5s.
History of the Church in Eastern Canada and Newfoundland,by the Rev.J. Langtry.3s.
The Church in the West Indies,by the Rev.A. Caldecott, B.D.3s. 6d.
The Story of the Australian Church,by the Rev.E. Symonds.2s. 6d.
LONDON: NORTHUMBERLAND AVENUE, W.C.43 QUEEN VICTORIA STREET, E.C.
[1]TheOperatives' Lectureis always well advertised in the streets beforehand by large posters.[2]Bulwer Lytton'sComing Race.[3]The glass vessel ought to be broader in comparison with its height.[4]In 1746 Benjamin Robins taught the principles of rifling as we know them now. He showed that thespinof the round bullet was the most important thing to consider. He showed that even the bent barrel of a gun did not deflect the bullet to anything like the extent that the spin of the bullet made it deflect in the opposite direction.[5]Note.—In Fig. 16 the axis is shown inclined, but, only that it would have been more troublesome to illustrate, I should have preferred to show the precession occurring when the axis keeps horizontal.[6]When this lecture containing the above statement was in the hands of the printers, I was directed by Prof. Fitzgerald to the late Prof. Jellet'sTreatise on the Theory of Friction, published in 1872, and there at page 18 I found the mathematical explanation of the rising of a top.[7]Roughly, theInertiaorMassof a body expresses its resistance to change of mere translational velocity, whereas, theMoment of Inertiaof a body expresses its resistance to change of rotational velocity.[8]It is a very unlikely, and certainly absurd-looking, hypothesis, but it seems that it is not contradicted by any fact in spectrum analysis, or even by any probable theory of the constitution of the interstellar ether, that the stars are merely images of our own sun formed by reflection at the boundaries of the ether.[9]Sir William Thomson has performed this.[10]It must be remembered that in one case I speak of the true north, and in the other of the magnetic north.[11]Rotating a large mass of iron rapidly in one direction and then in the other in the neighbourhood of a delicately-suspended magnetic needle, well protected from air currents, ought, I think, to give rise to magnetic phenomena of very great interest in the theory of magnetism. I have hitherto failed to obtain any trace of magnetic action, but I attribute my failure to the comparatively slow speed of rotation which I have employed, and to the want of delicacy of my magnetometer.[12]I had applied for a patent for this system of signalling some time before the above words were spoken, but although it was valid I allowed it to lapse in pure shame that I should have so unblushingly patented the use of the work of Fitzgerald, Hertz, and Lodge.[13]How to see by electricity is perfectly well known, but no rich man seems willing to sacrifice the few thousands of pounds which are necessary for making the apparatus. If I could spare the money and time I would spend them in doing this thing—that is, I think so—but it is just possible that if I could afford to throw away three thousand pounds, I might feel greater pleasure in the growth of a great fortune than in any other natural process.[14]Probably first described by Mr. Brennan.[15]The weight of Mr. Brennan's loaded wagon is 313 lb., including gyrostats and storage cells. His two wheels weigh 13 lb. If made of nickel steel and run at their highest safe speed they would weigh much less.
[1]TheOperatives' Lectureis always well advertised in the streets beforehand by large posters.
[2]Bulwer Lytton'sComing Race.
[3]The glass vessel ought to be broader in comparison with its height.
[4]In 1746 Benjamin Robins taught the principles of rifling as we know them now. He showed that thespinof the round bullet was the most important thing to consider. He showed that even the bent barrel of a gun did not deflect the bullet to anything like the extent that the spin of the bullet made it deflect in the opposite direction.
[5]Note.—In Fig. 16 the axis is shown inclined, but, only that it would have been more troublesome to illustrate, I should have preferred to show the precession occurring when the axis keeps horizontal.
[6]When this lecture containing the above statement was in the hands of the printers, I was directed by Prof. Fitzgerald to the late Prof. Jellet'sTreatise on the Theory of Friction, published in 1872, and there at page 18 I found the mathematical explanation of the rising of a top.
[7]Roughly, theInertiaorMassof a body expresses its resistance to change of mere translational velocity, whereas, theMoment of Inertiaof a body expresses its resistance to change of rotational velocity.
[8]It is a very unlikely, and certainly absurd-looking, hypothesis, but it seems that it is not contradicted by any fact in spectrum analysis, or even by any probable theory of the constitution of the interstellar ether, that the stars are merely images of our own sun formed by reflection at the boundaries of the ether.
[9]Sir William Thomson has performed this.
[10]It must be remembered that in one case I speak of the true north, and in the other of the magnetic north.
[11]Rotating a large mass of iron rapidly in one direction and then in the other in the neighbourhood of a delicately-suspended magnetic needle, well protected from air currents, ought, I think, to give rise to magnetic phenomena of very great interest in the theory of magnetism. I have hitherto failed to obtain any trace of magnetic action, but I attribute my failure to the comparatively slow speed of rotation which I have employed, and to the want of delicacy of my magnetometer.
[12]I had applied for a patent for this system of signalling some time before the above words were spoken, but although it was valid I allowed it to lapse in pure shame that I should have so unblushingly patented the use of the work of Fitzgerald, Hertz, and Lodge.
[13]How to see by electricity is perfectly well known, but no rich man seems willing to sacrifice the few thousands of pounds which are necessary for making the apparatus. If I could spare the money and time I would spend them in doing this thing—that is, I think so—but it is just possible that if I could afford to throw away three thousand pounds, I might feel greater pleasure in the growth of a great fortune than in any other natural process.
[14]Probably first described by Mr. Brennan.
[15]The weight of Mr. Brennan's loaded wagon is 313 lb., including gyrostats and storage cells. His two wheels weigh 13 lb. If made of nickel steel and run at their highest safe speed they would weigh much less.