Few things are better known than that a Stage Coachman, when he approaches a rise of the road, pushes his horses to a gallop; because “the swing of the coach” (as he expresses it) “carries his cattle up the hill.” The principle is known to every one; while it is almost equally well known that the law of its operation, is according to the square of the velocity; so that the momentum of a coach which meets the hill with the horses pushed into a gallop that causes the rate of the vehicle to be 16 miles an hour, will (friction abstracted) rise four times as high as one that meets the hill when going at the rate of 8 miles an hour: the continuance of the operation of the power which overcame friction on the level, being (so far as relates to its counteractive effect) equivalent to an annihilation of friction.
This law is well known. Now let us see how this knowledge has been taken advantage of, by those who have had the expenditure of hundreds of thousands, placed at their discretion.
Rates of from 35 to 40 miles an hour, have been attained on the Liverpool and Manchester Railway for these four years. Supposing friction to be counteracted and neutralized, the momentum of a vehicle that was moving on a level at the rate of 36 miles an hour, would “swing” and cause it to rise up an inclined plane to the height of 43⅓ feet perpendicular, let the angle of ascent, or rate of rise, be what it might; while, as a velocity of 20 miles an hour, would, under similar circumstances, “swing” a carriage up 13⅓ feet perpendicular, and a velocity of 10 miles an hour, 3⅓ feet perpendicular, it needs not, nor ever has needed any thing more than a proper arrangement of levels and inclined planes, to avoid all deep cutting, high embanking, or tunnelling, in the line of a railway, except where a precipitous rise or hollow interposed itself.
It is true that it may, with reference to the deep cuttings and high embankments of the Liverpool and Manchester Railway be replied, that at the time these works were executed, it was not known that such great velocities could be attained on railways. [29a] But though it was not then known that these rates of motion could be attained, yet was it as well known as it is now, that rates of ten miles an hour could be attained by horses: while, though the first line of the railway was laid out in 1824, and the present line in 1825, it was not till October, 1828, that it became decided whether horse or elementary power should be employed: vide pages 62, 67, 68, and 69 of Mr. Treasurer Booth’s “Account of the Liverpool and Manchester Railway.”
And notwithstanding that instances of velocities equal to ten miles an hour having been attained by locomotive engines, were not very common at the time the line of the Liverpool and Manchester Railway was laid out, yet do the under-quoted extracts from various publications of the period prove, both that they had been attained, and that much higher velocities were confidently anticipated: while Mr. Treasurer Booth, at page 37 of his book, says, that “the earth work (comprising the cuttings and embankings along the whole line) was not commenced till January, 1827.” [29b]
Such statements being (as it were, officially) promulgated, and such opinions entertained relative to the velocities attainable by locomotive engines:—the question as to the employment of horses being, thus, an open one, not only during the survey for the second line, but also for two years and a half after the Act for the Liverpool and Manchester Railway was obtained; and it being equally well known as it is that the sun gives light, that for the gallop which coachmen push their horses to just before touching a hill, in order to give their vehicles the momentum which imparts the “swing that carries their horses up the hill”, rates of 15 or 16 miles an hour could be attained—it being thus known at the time the line of the Liverpool and Manchester Railway was laid out, that average velocities of 10, and occasional velocities of 15 miles an hour could be attained: and it being unquestionable that if friction be counteracted (as it is by the continuance of the operation of the moving power) the momenta imparted by those velocities will carry any vehicle up any inclined plane to the heights of 3⅓ and 7½ feet, it was necessary only to have laid out the railway in short levels, with sharp inclined planes rising a foot or two between them, to have avoided all deep cutting or high embanking.
It is true that owing to velocities of ten miles an hour, having at that time, been only occasionally attained by locomotive engines, it might have been proper to keep these ranges of levels, and inclined planes within the limit prescribed by that rate. But as this limit is not within a vertical rise of 3 feet 4 inches, it would have been perfectly possible, by arranging short levels with sharp inclined planes of three feet in height between them, to have avoided the whole of those deep cuttings and high embankments of the Liverpool and Manchester Railway, of which the under-quoted extract from Mr. Treasurer Booth’s book gives such glowing descriptions. [30]
Admitting, however, (for the question’s sake) that the “most eminent engineers” and their “assistants of undoubted talents,” by whom these “Pelion-upon-Ossa-like spoil banks, towering over the adjacent land” were ordered—and of which Mr. Booth says, in addition, “this aggregate mass has been removed to various distances, from a few furlongs to between three and four miles; and no inconsiderable portion of it has been hoisted up by machinery from a depth of 30 to 60 feet”—admitting that these gentlemen should have been warranted in expending the hundreds of thousands which were paid for making these mountains between Liverpool and Manchester, by the uncertainty then prevalent as to what velocities were attainable by locomotive engines, it cannot be said that the engineers of the London and Birmingham Railway have any similar justification to plead. That line was not, I believe, laid out till 1831, while the velocities attained on the Liverpool and Manchester Railway, and the short time within which London and Birmingham could, in consequence, be brought of each other, form the main features of the prospectus: rates of from 35 to 40 miles an hour having been (then) long attained on the Liverpool and Manchester railway.
Yet does the “Estimate” laid before Parliament shew no less a sum than 429,286l. appropriated to “Excavations, Embankments, and Tunnelling,” which, with “the increase in the number of arches in the Wolverton viaduct,” will give an estimated expenditure of nearly half a million to do that, which, taking proper advantage of the law of motion I am adverting to, would entirely have saved; except where a hill as perpendicular as a wall, or a hollow as precipitous as a well, rendered tunnelling, deep cutting, or filling up, absolutely unavoidable.
At the time the Birmingham Railway was before Parliament last session, maps of it were issued from the office of that company, which gave the “Section of the line of railway; shewing the rises and falls.”