424 BRIDGES OVER THE THAMES. DESCRIPTIVE ACCOUNT OF THE PRINCIPAL BRIDGES ERECTED OVER THE RIVER THAMES. BY MR. C. DAVY, ARCHITECT. No. VII.- -PILE-DRIVING. (Continued from p. 388.04 Fig. 5 426 10 BRIDGES OVER THE THAMES. these, merit a notice in this place. 1st. The momentum of the stroke will be as the square root of the height from which the rammer fell. He says, that" notwithstanding the momentum or force of a body in motion is as the weight multiplied by the velocity, or simply as its velocity when the weight is given, or constant; yet the effect of the blow will be nearly as the square of that velocity, the effect being the quantity the pile is driven into the ground by the stroke. For the force of the blow transferred to the pile, being destroyed in some certain definite time by the friction of the part within the earth, which is nearly a constant quantity, and the spaces in constant forces be ing as the squares of the velocities; therefore the effects, which are those spaces sunk, are nearly as the squares of the velocities, or, which is the same thing, nearly as the height fallen by the ram to the head of the pile." The term en fiché having been used, the figs. 7 and 7* will explain the matter clearer as to what is meant by putting a pile en fiché. Let fig. 7 represent a part of the pile-engine framing, constructed with the wheel four or five feet diameter, as mentioned in paper No. VI; the cap FG projects a short distance beyond the upright posts DD; to this cap pulleys HH are fixed, the pile is suspended by ropes, and afterwards fowered to the workman, who places it in its proper position (see fig. 7*) to receive the blow. It is there held for a short time in a perpendicular DR. LARDNER'S LECTURES ON MECHANICS. is necessary in commencing the pileing in this instance; that is, by driving the first piles in the centre of the framing, and proceeding with the work outwards to prevent the earth being jammed in the centre, which would be the case were the pileing to commence at the edge of the framing. In coffer-dams the larger piles face the water, and the double or triple rows are of smaller scantling. In some situations the grating of timber, covered with thick planks, and the pier carried up upon that has been found to be sufficient without pileing. Plank or other pileing driven obliquely into the earth, is only bevelled on one side of the lower end; and such piles, if of small scantling, are charred on their extremities instead of being shod with iron. The thickness of short piles is allowed to be 1-12th of its length; but for long piles the average diameter is from 14 to 16 inches. Plank piles are in thickness from 3 to 4 inches, and from 4 to 5 according to their lengths. 427. NOTES OF DR. LARDNER'S LECTURES UNIVERSITY. (Continued from p. 409.) It is frequently required to estimate the amount of the pressure on the pivots, which is thus done :-Find the centre of gravity of the wheel and axle, and the weight of the machine will be divided between the pivots in the inverse proportion of their distances from the centre of gravity. There are two ways of increasing the mechanical advantage of the wheel and axle; viz. first by increasing the radius of the wheel on which the power acts; and, secondly, by decreasing that of the axle on which the weight acts. In theory there appears to be no limits to either of these In means, but in practice there are. the first manner, the limit is the unwieldiness of the wheel; and with regard to the second, it may be asked, what are the cases where the mechanical advantage is desired to be increased? The combination is for raising a heavy weight; and on what part of the machine will this weight press, but on its axis? The axis, therefore, ought to be increased as much as possible, since by diminishing the axis the strength is reduced. There is a very ingenious method of increasing the strength of a machine of this kind, without either of the above disadvantages. Fig. 1 is Fig. 1 428 DR. LARDNER'S LECTURES ON MECHANICS. Fig. 2 G W of the products of the half weights, multiplied by the separate radii of the two axes, will give the effective force; or, what is the same thing, the force is equal to the half weight multiplied by the difference of the two radii. A varying lever is frequently useful in machines where the work to be done, or the load to be raised (whatever be the resistance), is not uniform, while the power is so. This is done by using a leverage, which shall increase in power in the same proportion as the weight does: of which kind, one of the most beautiful instances is the fusee of a watch. Fig. 3. the other is fixed to the barrel. Now when the watch is wound up, the chain is wound on the fusee, so that when the spring is at its highest intensity, the leverage it acts at is at the smallest; and in proportion as the power (viz. strength of the spring) decreases, the leverage increases. If the elasticity be called E, and the radius R, ER will always express the whole effect. There is another way of increasing the power of the wheel and axle, without either of the disadvantages before mentioned: it is by means of what is called wheelwork-one wheel acting on another; and the series of wheels being connected either by straps, by friction, or by teeth. The first is a very common method, and is used in chines; the second is very uncommon, turning lathes and many other maacting on one another by the third indeed hardly ever used. Wheels fixed on the axle, which is called a method, have a similar toothed-wheel pinion. The teeth of the large wheels are called cogs, but those of the of one wheel act on the leaves of a pinion are called leaves. The cogs pinion, on the axle of which is placed another wheel, whose teeth act in the same manner. Fig. 4 represents three wheels acting in this way. It Fig. 4. B The spring (which is the prime mover of the watch) is a spiral piece of steel; one end of which is fastened to the fixed axis of the barrel A, and the other to the barrel itself (the spring being enclosed in the barrel). When the spring is wound up, its power is at its height; and as the watch goes down (to use a common phrase), the spring loses its elasticity, and exercises a constantly diminishing force on the fusee B, round which the chain is coiled. This fusee is of a conical figure, and the chain is fastened to the larger part of it at one end, while will be evident that this is nothing but the compound lever in another form; for if the upper and lower halves of the wheels be cut off, it will leave the system of levers as in fig. 5, Fig. 5. P the effect of which is easily calculated; viz. the power is to the weight |