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Rh by wire or steel tape measurements. These measurements were taken at various times, under different conditions of temperature, and were carefully checked.

The lengths of the girders were then decided upon with a view of leaving sufficient play between them and the cantilevers, under the fullest extension by summer heat and sun heat.

At the mean temperature the end faces of the bottom booms are about 1 ft. apart from the ends of the cantilevers, and no weight-carrying connections exist between these two, all the weight of the central girders being carried by the top booms and bracings. The top booms project into the end posts of the cantilever and are there supported in a manner presently described.

The central girders—so far as longitudinal expansion is concerned—are fixed at the Queensferry and Fife ends, and to all practical purposes form parts of these two cantilevers. On the other hand, both at the Inchgarvie north and the Inchgarvie south ends, longitudinal movement is provided to the extent of 2 ft. at each end by means of an arrangement of rocking posts, slide-blocks, and expansion joints in rails.

Upon the ends of the cantilevers within the hollow end posts are placed steel castings in the shape of large cups or sockets. (See Figs. 128 and 129.) Into these are fitted knuckles or half-balls, fixed to the bottom of square posts or columns built of stout steel plates in box form. Upon the upper extremities of the posts are fixed steel castings of cup shape, the same size as those below, and into these are fitted half-balls which are fixed to the under side of the top booms of the central girders projecting into the end posts. Thus the weight of the central girders at these ends is transmitted from the top members of the central girders through these rocking posts to the bottom members of the cantilevers, and full freedom is given to the longitudinal movements.

At the Fife and Queensferry ends of the central girders there are steel castings also placed on the ends of the bottom members within end posts, but here the castings are in shape of half-bearings, to receive cylindrical pins 9 in. in diameter, and about 3 ft. long, set horizontally but at right angles to the centre line of the bridge. (See Figs. 130 and 131.) Here the girder ends are brought square down from the ends of the top members of the central girders, and are cut out to receive a casting which is placed on the top of the pin and is the exact counterpart of the one under the pin.

Longitudinal movement is therefore impossible here, but the attachments at both ends admit of a small amount of lateral deflection, which may be caused by wind pressure and by the heat of the sun's rays on either side. These are provided for in the following manner:

From the cross-girder which connects the ends of the cantilevers, both between top members and bottom members, strong plate brackets project and pass right through openings arranged in the corresponding end girders of the central girders. (See Fig. 132.) These brackets are somewhat stronger in the lower than in the upper girders. Between the two projecting brackets passes a vertical slide-block about 17 in. square, which fits exactly, and the slide-block is held in position by a vertical pin, 9 in. in diameter, the ends of which are fixed in the cross-girder of the central girder. In the top girders the slide-block is 19 in. square and the pin 6 in. in diameter.

At the Garvie ends these slide-blocks are in mean position at mean temperature, and have play at each end to the amount of 12 in. for longitudinal movement, while the vertical pins top and