TABLE III.-Showing the effects of a force of traction of 100 lbs. at different velocities, on canals, rail-roads, and turnpike-roads.* (From Tredgold.) This table is intended to exhibit the work that may be performed by the same mechanical power, at different velocities, on canals, rail-roads, and turnpike-roads. Ascending and descending by locks or canals, may be considered equivalent to the ascent and descent of inclinations on rail-roads and turnpikeroads. The load carried, added to the weight of the vessel or carriage which contains it, forms the total mass moved; and the useful effect is the load. To find the effect on canals at different velocities, the effect of the given power at one velocity being known, it will be as 32: 2.52::55,500: 38,542. The mass moved being very nearly inversely as the square of the velocity at least, within certain limits. : This table shows, that when the velocity is 5 miles per hour, it requires less power to obtain the same effect on a railway than on a canal; and the lower range of figures is added to show the velocity at which the effect on a canal is only equal to that on a turnpike-road. By comparing the power and tonnage of steam-vessels, it will be found that the rate of decrease of power by increase of velocity, is not very distant from the * Though the force of traction on a canal varies as the square of the velocity; the mechanical power necessary to move the boat is usually reckoned to increase as the cube of the velocity. On a rail-road or turnpike the force of traction is constant; but the mechanical power necessary to move the carriage increases as the velocity. truth; but we know that in a narrow canal the resistance increases in a more rapid ratio than as the square of the velocity that is, within certain limits; beyond them, there is a remarkable change in the circumstances of resistance. TABLE IV.-Showing the maximum quantity of labour a Horse of average strength is capable of performing, at different velocities, on canals, rail-ways, and turnpike-roads. (From Tredgold.) Where horse power is employed for the higher velocities, the animals ought to be allowed to acquire the speed as gradually as possible at the first starting. This simple expedient will save the proprietors of horses much more than they are aware of; and it deserves their attention to consider the best * According to the interesting researches of Du Buat, the resistance to the motion of boats even in canals may be regarded as proportional to the square of the velocity, or R as v2 nearly, provided R be made to depend upon the transverse sections of the vessel and the canal in which it moves, and a constant quantity K determinable by experiment. If c be the vertical section of the canal, b the vertical section of the immersed portion of the boat or barge; then R K = x ÷ ( // ・(1 + 2). The medium of Du Buat's experiments gives K = 8·46, or R 8.46 ÷ C + 2): ; but those experiments were not so numerous and varied as might be wished. See Principes d' Hydraulique, tom. ii. pp. 340, 342, &c. In cases connected with these, or kindred inquiries, where velocities in miles per hour, are to be reduced into velocities in feet per second, or the contrary; the rules at p. 102 of this work will be found useful. mode of feeding and training horses for performing the work with the least injury to their animal powers. To compare the preceding table with practice at the higher velocities, it will be necessary to have the total mass moved, which is one-third more than the useful effect in this table. Now, the actual rate at which some of the quick coaches travel is 10 miles an hour; the stages average about 9 miles; and a coach with its load of luggage and passengers amounts to about 3 tons; therefore the average day's work of 4 coach horses is 27 tons drawn one mile, or 6 tons drawn one mile by one horse. The table gives 3.6 tons, added of 3.6 = 4.8 tons drawn one mile for the extreme quantity of labour for a horse at that speed, úpon a good level road; from which should be deducted the loss of effect in ascending hills, heavy roads, &c., which will make the actual labour performed by a coach-horse average about double the maximum given by the table. The consequences are well known. According to Mr. Bevan's observations, the horses on the Grand Junction Canal draw 617 tons one mile, at the velocity of 2.45 miles per hour. According to Mr. Tredgold, if v be the maximum velocity of a horse, and v any other velocity, the immediate power of a horse is 250 v (1-2) --); and, when the weight of the vessel or carriage is to the weight of the load, as n: 1, we have 250 v (1—2-) 1 + n V = the effective power; and d being the hours the horse works in one day, the day's work will be 250 dv (1) in lbs. raised 1 mile, and 250 (1 1 + n = the force of traction in lbs. But if the force were immediately applied, the value of v would be 14.7 ✓ d ; and to find the value 1 + n when the waggons alone are moved, we have 1: 96 v3 (1 + n) we have =d. Consequently, when the velocity is given, 83 lbs. But we may assume n to be always hours; and 72 so near, as not to affect the result; and then, = d, and ༧༔ 4500 2 tons raised υ ข the day's work in lbs. or very nearly one mile. This being combined with the numbers of the preceding table, gives the effect of a horse on canals, rail-roads, and turnpike-roads. It must, however, be here added, that although the deductions from Mr. Tredgold's valuable tables, as to the effects on canals, are tolerably accurate up to rates of 4 or 5 miles per hour, yet, when boats are moved on canals at rates of from 9 to 12 or 14 miles per hour, the circumstances of the resistances undergo an essential change. The resistance, in fact, becomes so small, that passage-boats now travel at these high velocities; and it is hence probable that rail-roads and canals will admit of a competition such as the supporters of rail-roads never anticipated. I shall here briefly detail some of the facts, as they have been given in a letter widely circulated by Mr. W: Grahame of Glasgow, in the Nautical Magazine, and other places. From the traffic by canal boats, which has been actually going on during the last two years and a half, on the Paisley canal, we learn this remarkable fact, that, while a speed of ten miles per hour has been maintained by the canal boats, the banks have sustained no injury whatever. The cause of injury, in truth, has been entirely suppressed by the velocity of the boat, which passes along the water without raising a ripple. About two years ago, measures were adopted for increasing the speed of the boats on the Paisley or Ardrossan canal. This canal is by no means favourable to such experiments, being both serpentine in its course, and narrow it connects the town of Paisley with the city of Glasgow, and the village of Johnstone; the distance being about twelve miles. The boats employed on this canal are 70 feet in length, and 5.6 broad, and carry, if necessary, upwards of 120 passengers. They are formed of light iron plates, and ribs covered with wood, and light oiled cloth, at a whole cost of about 1257. They perform stages of four miles in an interval of time varying from 22 to 25 minutes, including all stoppages, and the horses run three or four of these stages alternately every day. The passengers are under cover, or not, as they please, no difference being made in this particular; and the fare is one penny per mile in the first, and three farthings per mile in the second cabin. The horses drawing the canal boat are guided by a boy, who rides one of them; and, in passing under bridges at night, a light is shown in the bow of the boat, by which he sees his way, and which light is closed when the bridge is passed. Intermediate passengers are also accommodated to distances even as small as a mile; and the facility with which the boat stops when relieved from the drawing force, is such as avoids all danger whatever. The expense of conveying a load of eight tons at a rate of nine or ten miles per hour, including all outlay, interest, and replacement of capital, is not more than 11d. per mile. It is also ascertained that one ton weight may be carried on a canal at nearly the same speed as on the railway, at about 14d. per mile, including an allowance for interest and replacement of capital. It is also believed, that if the breadth and curvature of the Paisley canal admitted boats of 90 feet length, instead of 70, they would carry more passengers by one-half without an additional expense, and a decrease of labour to the horses. The foregoing has been deduced from calculations founded on the observation of facts relating to the wear and tear of boats and horses, and the absolute resistance which these boats meet with in passing through the water. On this subject it has been observed, that, in addition to the common resistance of the water to the motion of the boat, a wave, or body of water, is also raised before it, varying in its height according to the velocity of the boat, and constantly presenting an obstacle to her progress, provided that she only moves through the water at a certain slow rate. The height of this wave will then amount to nearly two feet, often overflowing the banks of the canal, and, from the obstruction it occasions, eventually obliging the boat to be stopped. Now, if, instead of stopping the boat when this wave is raised, her velocity be increased beyond what it had then been, she advances and passes over it, and leaves it to subside in her wake, which it does, and the water becomes perfectly still. The same horses |