much allowance for expansion is detrimental to the rails, because where the spaces are excessively large the wheels drop into the hollow and hammer or spread the ends of the rails. The fish-bolts should not be completely tightened up until the permanent way is thoroughly set, and packed to its finished line and level. On straight line the rail-joints should be laid square and opposite to each other. Permanent-way laying with broken joints is rarely adopted, except on curves or station-yards. On curves the joints of the inner rails gain on the joints of the outer rails to the extent of-- radius + gauge -------------- × length of rail. radius The amount of this gain, or lead, is adjusted by cutting off a portion of the end of the inner rails at certain intervals. Assuming the fish-bolt holes to be spaced as shown on Fig. 342, then, when the inner rail is leading to the extent of 2 inches, a piece 4 inches long is cut off, as shown by dotted lines, leaving the original second fish-bolt hole to serve as first or end fish-bolt hole, and a new or second bolt-hole is drilled by hand at A. This method sets back the joint 2 inches from the square, and the lead is allowed to go on again until it becomes necessary to cut off another piece of 4 inches. Another mode is to have a proportion of the rails rolled 2 or 3 inches shorter for use on the curves. On curves of a 1000 feet radius and upwards, the rails should be laid to the normal gauge, but on curves of lesser radius the gauge may be slightly increased, and as much as ¾ of an inch allowed on a curve of 500 feet radius. The amount of cant, or super-elevation, to be given to the outer rail 230 on curves must be regulated by the speed of the train and the gauge of the line. Many formulæ have been compiled to determine the necessary amount of super-elevation, but experience has shown that by some of them the calculated amounts were excessive. Possibly during past years too much cant has been given in many cases. The following simple formula approaches very closely to practical experience-- (velocity in miles per hour)^2 × gauge in feet {the super-elevation ----------------------------------------------- ={ of outer rail radius in feet × 1·25 { in inches. For high-speed trains uniformity of cant is of the utmost importance, more so even than the exact amount. Any irregularity in the super-elevation of the outer rail, sometimes high and sometimes low, will produce a dangerous swaying movement in the train, which, if not promptly checked, would lead to derailment. More injury is done to curves by spreading, arising from rigid wheel-bases of engines and tenders, than from any want of counteraction to centrifugal force.