Above the plain, commanding splendid views, and is approached on the east by a funicular railway from the station.
A climate station is established on the hill of Brunate (2350 ft.) above the town to the E., reached by a funicular railway.
Below Les Avants) there is a funicular railway from Vevey up the Mont Pelerin (3557 ft.) to the north-west.
From the summit, to which there is a funicular railway, there is a magnificent view, celebrated by Byron in Childe Harold's Pilgrimage.
The river is here crossed by two iron bridges, and one stone and one timber bridge, and the upper and lower towns are connected by a funicular railway.
For longer bridges the funicular polygon affords a method of determining maximum bending moments which is perhaps more convenient.
Above Locarno is the romantically situated sanctuary of the Madonna del Sasso (now rendered easily accessible by a funicular railway) that commands a glorious view over the lake and the surrounding country.
Behind is a range of hills, the most conspicuous of which, the Monte Nero, is crowned by a frequented pilgrimage church and also by villas and hotels, to which a funicular railway runs.
A funicular railway connects the upper town with the central railway station and with Ouchy, the port of Lausanne on the lake of Geneva.
Two miles north-west of the town lies the Neroberg (800 ft.), whence a fine view of the surrounding country is obtained, and which is reached by a funicular railway from Beausite, and 6 m.
Among these are many funicular cog-wheel lines, climbing up to considerable heights, so up to Marren (5368 ft.), over the Wengern Alp (6772 ft.), up to the Schynige Platte (6463 ft.), and many others still in the state of projects.
Above sea-level, strongly fortified by the Venetians, and the new town (Citta Bassa) below, the two being connected by a funicular railway.
Three funicular railways from different points of the city give access to the highest parts of the hills behind the town.
A funicular railway runs up to the Malberg (r000 ft.), where is a sanatorium and whence extensive views are obtained over the Rhine valley.
To the north-west of Bienne two funicular railways lead up to Evilard (or Leubringen) and Macolin (or Magglingen), both situated on the slope of the Jura.
The case of the funicular polygon will be of use to us later.
And at equal horizontal intervals, the vertices of the funicular will lie on a parabola whose axis is vertical.
The funicular or link polygon has its vertices on the lines of action of the given forces, and its sides respectively parallel to the lines drawn from 0 in the force-diagram; in particular, the two sides meeting in any vertex are respectively parallel to the lines drawn from 0 to the ends of that side of the force-polygon which represents the corresponding force.
(to the right) and the funicular (to the left) are numbered similarly.
The two diagrams being supposed constructed, it is seen that each of the given systems of forces can be replaced by two components acting in the sides of the funicular which meet at the corresponding vertex, and that the magnitudes of these components will be given by the corresponding triangle of forces in the force-diagram; thus the force 1 in the figure is equivalent to two forces represented by 01 and 12.
When this process of replacement is complete, each terminated side of the funicular is the seat of two forces which neutralize one another, and there remain only two uncompensated forces, viz., those resident in the first and last sides of the funicular.
Its first and last points coincide; the first and last sides of the funicular will then be parallel (unless they coincide), and the two uncompensated forces form a couple.
If, however, the first and last sides of the funicular coincide, the two outstanding forces neutralize one another, and we have equilibrium.
Hence the necessary and sufficient conditions of equilibrium are that the force-polygon and the funicular should both be closed.
It is evident that a system of jointed bars having the shape of the funicular polygon would be in equilibrium under the action of the given forces, supposed applied to the joints; moreover any bar in which the stress is of the nature of a tension (as distinguished from a thrust) might be replaced by a string.
This theorem enables us, when one funicular has been drawn, to construct any other without further reference to the force-diagram.
As regards the funicular diagram, let LM be the line on which the pairs of corresponding sides of the two polygons meet, and through it draw any two planes w, w.
Thus ii AB, BC, CD represent the given loads, in the force-diagram, we construct the sides corresponding to OA, OB, OC, OD in the funicular; we then draw the closing line of the funicular polygon, and a parallel OE to it in the force diagram.
Draw a parallel through P to meet the sides of the funicular which correspond to OA, OB in the points H, K.
Hence if a system of vertical forces be in equilibrium, so that the funicular polygon ii closed, the length which this polygon intercepts on the vertical through any point P gives the sum of the moments about P of all the forces on one side of this vertical.
If we wish to study the effects of a movable load or system of loads, in different positions on the beam, it is only neces sary to shift the lines of action of the pressures of the support~ relatively to the funicular, keeping them at the same distanci apart; the only change is then in the position of the closing line of the funicular.
It may be noticed that if we take an arbitrary pole in the force-diagram, and draw a corresponding funicular in the skeleton diagram which represents the frame together with the lines of action of the extraneous forces, we obtain two complete reciprocal figures, in Maxwells sense.
The result might of course have been inferred from the theory of the parabolic funicular in 2.
3I) that the linear moment of each particle about the line may be found by means of a funicular polygon.
The construction of a second funicular may be dispensed with by the employment of a planimeter, as follows.
59 p is the line with respect to which moments are to be taken, and the masses of the respective particles are indicated by the ft Z a corresponding segments of a line in the force-diagram, E drawn parallel to p. The A funicular ZABCD.
It is seen that for a given direction of p this moment is least when p passes through the intersection X of the first and last sides of the funicular; i.e.
A funicular railway runs from the Korn-Markt up to the level of the castle and thence to the Molkenkur (700 ft.