Lateral line system

“ Another somewhat curious point in connection with adhesion is the slip of the driving wheels, which is naturally in the direction of causing a greater number of revolutions of the wheels than would be due to the length of rail travelled over. Occasionally, however, I have, in experimenting, noticed that fewer revolutions are made than would suffice to travel the distance as measured on a centre line between the rails. ”

“ Then move this piece of wood above the boxes until it is equidistant from the meridianal line previously found and indicated by the thread, or is the same (line) itself. This being done, according to the piece of wood so situated, draw a line on the capsules, or boxes, and it will be the perpetual meridianal line in all countries. That line, therefore, when cut at right angles by another will be divided in the centre and will be the line of the East and West. ”

“ The apical pole of the vertical main axis (principal or longitudinal axis) is different from the basal pole. The ventral pole of the horizontal sagittal axis (or dorso-ventral axis) is different from the dorsal pole. The right pole of the horizontal transverse axis (lateral or frontal axis) is equal to the left pole. ”

“ Engineers surveying for a railway lay down the line level, or as nearly level as the configuration of the surface will permit; but an engineer’s level is not a straight line; it is the segment of a circle,—that circle being the circumference of the globe. The line which practically constitutes a level bends downwards continually as it goes forward, following the form of the earth, and at every point being at right angles to the radius. ”

“ At stations and places where there are several sidings and lines connecting with the main lines, at considerable distances apart, it will be necessary to have two or more signal-cabins placed in suitable positions, not only for expediting the working of the constant shunting movements, but also to insure that there is a signal-cabin within the regulation distance of all facing points on the main line. ”

“ The example shown in Fig. 134 is of a well-hole having a riser in the center. If the radius of the plan central line of rail is made equal to one-half a tread, the pitch of tangents will be the same as of the flights adjoining, thus securing two equal tangents for the two sections of wreath. In this figure the tangents of the face-mould are developed, and also the central line of the rail, as shown over and above each quadrant and upon the pitch-line of tangents. ”

“ They are guyed at corners in order to thoroughly secure the poles so that no strain may come on the cornerwise span. It is also necessary to guy a line where it is to be deflected from a straight path, as when rounding a hill, water course or railway curve, in order to neutralize the pull of the wires, tending to incline the poles toward the center on which the arc is described ”

“ When the distant signals for a junction have to be combined with the home or starting signals for a cabin in the rear, then the starting signal post must be nearest the line with the distant arm for the right-hand junction placed under it, and the distant signal for the left-hand junction must be carried by a separate post to the left of the home or starting post. Both distant arms must be controlled by the home or starting signal. ”

“ The lateral system is best suited for well-defined channels. The description of each buoy indicates the direction of danger relative to the course which is normally followed. In principle, the positions of marks in the lateral system are determined by the general direction taken by the mariner when approaching port from seaward. These positions may also be determined with reference to the main stream of flood current. The United States Aids to Navigation System is a lateral system. ”

“ By a mechanical contrivance, the points and signals are interlocked—that is to say, supposing, for example, that the signalman has moved a lever that opens a pair of points, to enable a train to come out of a siding on to the main line, the home and distant signals must be at "danger" to stop any train from approaching on the main line, and it is physically impossible for the signalman to lower them. ”

“ Poles should be guyed or braced at all points where there are material changes in the direction of the line, and on long straight stretches about every fifth pole should be guyed or braced in both directions to prevent the poles setting back when the line wire is cut or broken at any point. ”

“ The remarks made on the interlocking of points and signals on double lines apply also to the working of single lines, with the addition that not only are the distant, home, and starting signals interlocked with each other, but with the signals and points governing the approach of a train from the opposite direction—in other words, the signals for the approach of a train to a station from one direction cannot be lowered unless those for the approach to the station of a train from the opposite direction are at danger, and the points correctly set. ”

“ When this has been done, and the needle has settled, the degrees on the compass are to be read off between the zero farthest from the quadrant, and the point of the needle nearest to that zero. This gives the magnetical bearing of the plane of the dip, that is, of a plane at right angles to the line of stretch on that side on which the plane of the stratification sinks below the plane of the horizon. ”

“ The treatment of the problems that are now coming into play is most simple, when instead of the co-ordinate system used above, we introduce another one which is rigidly connected with ponderable matter and therefore shares its displacement.
While the coordinates of a point with respect to the fixed system were called x, y, z, let those, which refer to the moving system and which I call the relative coordinates, denoted by (x) , (y) , (z) for the time being. ”

“ If there are parallel ranges, it is correct to speak of a transverse axis, running at right angles with the main axis. There is, it is apparent, a marked difference between simple chains and the accumulated parallel chains, where breadth is a prominent element, as in the Vosges, the Black Forest Mountains, the Fichtel range, the Hartz, the Ardennes. The parallel rows form a mountain system. Yet all great chains are made up of smaller ones, of groups at least, and so are mountain systems. ”

“ Thus a plane is the simplest and most symmetrical boundary by which a solid can be divided; and a straight line is the simplest and most symmetrical boundary by which a plane can be separated. These conceptions are obtained by considering the boundaries of an interminable space, capable of imaginary division in every direction. And as a limited space may be separated into two parts by a plane, and a plane again separated into two parts by a straight line, so a line is divided into two portions by a point, which is the common boundary of the two portions ”

“ Extremes meet, and so the attempt to avoid absolute horizontal lines has completely failed, because in their place we have a succession of vertical members placed side by side in such endless numbers that we really think more of the horizontal arrangement of these members, slight though they are, than we should of the simplest defined horizontal line. ”

“ The distant signal is placed at varying distances behind the home signal according to the gradient of the line and other circumstances, but on a straight and level railway it would be about 1,000 yards back, and its function is to repeat the action of the home signal, so that if the latter is at danger the driver has timely intimation of the fact, and can at once reduce the speed of his train so as to stop at the home signal. ”

“ Trees, house-tops and poles can be used in the construction of a line. When fastening a line to a tree, let your wire slack enough to swing to and fro with the tree, otherwise your line will be broken during a windstorm. Tree limbs or branches touching the wire have no bad effect on the telephone, but should be avoided if easily possible. A pole should be set no less than three feet in the earth and eighteen to thirty to the mile. Always try and keep your poles in a straight line. ”

“ The conditions of stability for a line where several surfaces of discontinuity meet, with respect to the possible formation of a new surface, are capable of a very simple expression. If the surfaces , separating the masses , meet along a line, it is necessary for equilibrium that their tensions and directions at any point of the line should be such that a quadrilateral may be formed with sides representing in direction and length the normals and tensions of the successive surfaces. ”

“ Instead of climbing the inclines by rack-work rails, there is another system which offers great advantages for economy in working, and one generally resorted to where the incline can be made in one vertical plane. This is the balanced cable, in which the gravitation force of a descending car or train is utilised to draw up, or assist to draw up, the ascending car or train. ”

“ No station to be constructed, and no siding to join a passenger line, on a steeper gradient than 1 in 260, except where it is unavoidable. When the line is double, and the gradient at a station or siding-junction is necessarily steeper than 1 in 260, and when danger is to be apprehended from vehicles running back, a catch-siding with points weighted for the siding, or a throw-off switch, to be provided to intercept runaway vehicles at a distance outside the home-signal for the ascending line, greater than the length of the longest train running upon the line. ”

“ With respect to the formation of new surfaces of discontinuity in the vicinity of the point especially considered, the system is stable, if every diagonal of the polygon is less, and practically unstable, if any diagonal is greater, than the tension which would belong to the surface of discontinuity between the corresponding masses. ”

“ It is stated, as an immediate consequence, that two lines which meet cannot make the same angle with a third line, on the same side, for they are in different directions. Parallels are knocked over in a trice. There is a covert notion of direction, which, though only defined with reference to lines which meet, is straightway transferred to lines which do not. According to the definition, direction is a relation of lines which do meet, and yet lines which have the same direction can be lines which never meet. There is a great quantity of turning wanted ”

“ Straight lines exist which have the property that any one of them may be produced both ways without limit, that through any two points in space such a line may be drawn, and that any two of them coincide throughout their indefinite extensions as soon as two points in the one coincide with two points in the other. ”

“ Rather than recognise the true state of things, the mind prefers to accept the suggestion that the upward or downward movement of the point of intersection is in part due to oppositely directed horizontal movements of the lines themselves upon the surface of the card. When the card is descending the vertical [Pg 151] line is supposed to slide a little to the right and the oblique line to the left, which would have the effect of lowering their point of intersection independently of the downward movement of the card itself. ”

“ Suppose now that we have the surveyed lines m m, and n n, fig. 27, one of which is to be finally adjusted to the ground. The shortest line is the straight one, which is generally impracticable. The most level line is the contour line, which is also impracticable. Between these two lies the right line, which is to be found by an instrumental location. The line A n n n n B, on the plan, gives the profile A n n n n B. The line A m m m m B gives the profile A m m m m B, while the finally adjusted line A 1 2 3 4 5 6 gives the profile A 1 2 3 4 5 6 B.
Fig. ”

“ Direction, as also variation, is demonstrated in a horizontal plane, when a balanced magnetick needle comes to rest at some definite point; but declination is seen to be the motion of a needle, starting from that point of the horizon, first balanced on its own axis, then excited by a loadstone, one end or pole of it tending toward the centre of the earth. And we have found that it takes place in proportion to the latitude of each region. ”

“ In others the curves may be made of easy radius, at a comparative moderate extra outlay, if the character of the line and description of traffic to be accommodated will warrant the expenditure. For main through lines, with heavy, high-speed traffic, it is advisable to have the curves of large radius, so as to avoid the necessity of reducing speed when passing round them. ”

“ For facility of carrying on the works, reliable bench marks, or reduced level stations, must be established at convenient distances along the route of the line, and from these and the fixed chain-pegs the correct line of formation level can be checked from time to time as the work proceeds. ”

“ Now, as this bisecting of the angle can go on indefinitely before the rotating line can touch the stationary line at all its points, it follows that before such contact the rotating line will have a length which cannot be stated in figures, and which defies all human computation. It can be mathematically demonstrated that a line so rotating, and increasing its length in the inverse ratio of its angle with the meridian, will have its end always receding from the meridian and approaching a line parallel to the meridian at a distance of 1.5708. ”