in Mr B.'s it did not in any case go beyond it. The answer to this is obvious, viz. the necessity of introducing, upon a line of this great acclivity, the smallest possible number of curves. The resistance produced by the curves on a level road may evidently exceed that which is effected on an inclined plane by gravity; even on a plane elevated 100 ft. to the mile. In comparing these lines, therefore, it is quite as necessary to examine the plan as the profile.

On the west side of the summit, by making the line more crooked than it now is, the grade may be kept within 80 ft. In our present line it exceeds that amount. In assuming 80 ft. per mile, the succession of curves (which it is impossible to avoid in the descent west,) will increase the resistance, quite as much, or more, than an increase of 10 ft. in the grade, together, (on both sides of the summit) say equal to an inclination of 100 ft. per mile.

In comparing Routes No. 1 by Morey Summit, and No. 14 by the Bottomly factory and Henshaw ridge, to Grout's summit, we arrive at the following results. No. 14 is 3.81 miles shorter than No. 1, and it will cost to grade it, say $161,000, (or including superstructure) $199,000 less than No. 1. It has, however, 7.72 miles exceeding 80 ft. per mile; while the line by Morey will have no grade exceeding 50 ft., and even at that inclination, it will have but 4.79 miles. No. 14 will have two grades on the east side of the summit descending to the west, of 19 ft. and 25 ft. each,-making together 44 ft. and this being equated at 18 ft. (the slope which requires double the power required on a level road,) results in a virtual increase of nearly 2.5 miles; or in other words, it adds 44 ft. to the height of the summit, and thereby diminishes the difference in the length of these two lines to 1.3 miles.

We shall now exhibit the load of an Engine upon planes of various inclinations, from 0 to 100 ft. per mile.

We will suppose an Engine weighing 10 tons to be capable of propelling a load of 260 tons (tender included) on a level; the load of this Engine upon any inclination will be thus expressed :—

1

E

=

Load on level in tons.

Engine in tons.

g= Gravity per ton on plane in lbs. f = Friction of load per ton in lbs. From the above formula we deduce the value of L, or the load in tons, with which this Engine is capable of ascending upon planes, varying in inclination, from 0 to 100 ft. per mile-the rails being in the best state, or the adhesion.

260.00 173.58 128 95 101.87 83.60 70 0460.53 52.83 46.60 41.50 37.25

When the rails are wet, or frosty, the adhesion may be diminished to; the load in this case is also diminished in the ratio of to; or upon a level, the load would be but 78 tons; on 50 ft. per mile, 16.21 tons; on 100 ft. do. 5.40

tons.

We must now consider the cost of maintaining the additional power necessary to be provided, if the shorter route should be adopted. We may safely assert, that not less than two assistant engines will, at all times, be required -one on each side of the summit. On the Liverpool and Manchester road, at the two planes of, and, equal to 59 ft. and 55 ft. respectively, the freight trains are assisted by additional engines, placed there for the purpose. On that road they have thirty engines, of this number, 10 are in daily use, an equal number in the shop undergoing repairs, and the balance laid aside, being of the older patterns, and less effective than those now made.

engines, one third Hence to have the

On the Worcester road they have 9 of which are at all times in the shop. two additional engines at the summit constantly fit for service, we must be provided with three.

The actual cost of keeping 10 engines in constant order, on the Liverpool and Manchester road, for the year ending 30th of June 1834, exclusive of the expense of running them, was £18,300, or for each, about $8,200.

On the Worcester road the actual cost of repairing and running 6 engines for the year ending 30th June, 1836, was

$30,690, or, including the interest upon the cost of the stock, $34,470; or for each, $5,745.

Cost of 3 engines of a larger size than those generally used, say 10 to 12 tons, at $9,000

Interest upon the same

$27,000 1,620

Upon a road of grades of 80 feet and upwards, the wear and tear of the engines would be far greater than upon either the Liverpool and Manchester, or the Worcester, from the necessity of using the brakes so frequently upon the descents; the effect of which, it may be incidentally remarked, is quite as injurious to the road, as to the engines. We shall therefore assume $6,500 as the cost of maintaining the engines in repair, and of running the same, and this is only about three fourths of the cost of the repairs alone, of those of the Liverpool and Manchester road. Cost of repairing and running 2 Interest upon cost of 3

Total cost of 2 (effective)

$13,000

1,620

$14,620

And this is the interest of $243,660, or upon $44,360 more than the cost of the additional 3.81 miles, by the Morey summit route. And while to the Corporation, the cost of transportation would be about the same, the sum received for tolls, on the short line, would be only of that upon the longer line.

It will be seen from what has been said, in relation to these two routes, that notwithstanding the distance gained by that through Grout's, and the consequent diminution of first cost in the construction, the total expenditure for power, on each route, will very nearly equalize the cost of construction and transportation, on each route. And when we take into consideration the practical difficulties of applying power upon steep grades, the maintaining it always with certainty, and the great danger of impairing the confidence of the public, in the safety of this mode of travel, from the greater liability to accident, and the more serious consequences resulting from accidents upon the steeper grades, we cannot but believe that your Board will coincide with us, in the preference we continue to give to the route by Morey's summit.

Computations have been made at the request of some members of the Board, to ascertain the cost of grading the

road from Worcester to Ryan summit, upon an undulating line, or upon a line with ascending and descending grades of 80 feet. The difference of cost between such a line as we are about to describe, and that upon which the first estimate was predicated, will be about $150,000. This is undoubtedly a large sum to be saved, in grading a piece of road of only 14 miles in extent. But there are so many disadvantages attending a road constructed upon this principle, that the great saving in cost becomes, comparatively, a small consideration. It is proper to remark, that the calculations of the cost of grading this line, are made upon the supposition that the fillings are to be diminished in the same manner that it is proposed to reduce the cuttings; or in other words, that the undulations are carried both above and below the uniformly ascending grade upon which the first computations were made.

If, as in the case of the route by Ryan summit, we adopt a line, say, in no instance exceeding 40 feet per mile, but generally at 35 feet, and undulating upon it in such a manner that the grade shall never fall below this line; then the height of the summit will be increased, virtually, by an amount equal to the total sum of descents, viz. 138 feet. But as the object of grading the road upon this principle is to save expense in the cost of construction, and upon this line the cuttings and fillings being nearly equal, that is to say, they are in the ratio of 1 to 1.04, we should, to derive all the benefit from it in this respect, which this mode is susceptible of yielding, extend the grade below the line before referred to, in such a manner, that the quantity of fillings may be diminished, as well as that of the cuttings, if it is carried below, the amount of the descents will be increased 231 feet, and equating these two sums, 138 feet and 231 feet at the rate of 18 feet per mile, we find them equivalent to 7.68 miles, and 12.83 miles, respectively, or enumerating them thus:

Upon the lesser, and constantly ascending grade 13.82 miles. Undulating above the uniformly ascending grade 21.47

or, in other words, the cost of transportation upon this line, by these three modes of grading, will be to each other, as 1 :: 1.55 :: 1.92, 1 being the lesser and uniformly ascending grade. This must hold true, unless the engines

were permitted to exert their whole power, uniformly as well on the descents, as on the ascents, of the undulating planes, but this could not be allowed, for in practice there are many circumstances, which limit the speed of an engine, both in reference to safety, deterioration of the machinery, and the difficulty of arranging the slides for extreme velocities; or rather of suiting them to the variable velocities, which such a system would render necessary. For these reasons, it has never been considered expedient to calculate upon a velocity, on a descending plane, greater than that which might be permitted upon a level, with safety; and upon such steep planes as 80 feet, not even so great. But in order to compensate for the loss of time in ascending, the velocity required to produce this effect on the descending planes, would be entirely inadmissible; therefore the difference of time in descending by the regulated velocity, and that which would be required to compensate for the loss of time in ascending, would be lost on the undulating line.

A very serious objection to this principle of grading, is to be found in this, viz. the route across the summit, in addition to its grade of 40 feet, is necessarily a crooked one, and in order to overcome the total resistance, it is essential that the curves be diminished to the greatest extent practicable. In doing this, we are very often obliged to encounter deep cuts, at the points of the ridges and spurs; and it is at these places that many of the deepest cuts will be found. Applying the undulating principle at these points, and thereby increasing the grades to 80 feet, they might, added to the curves, present a combined resistance, too great, in many cases, for the power of the engine to overcome.

In another view, the objection is equally serious. The practical difficulty of working an engine upon such a line would be exceedingly great. To those who have examined the subject, it is known that the engine works to very great disadvantage when the velocity has to be constantly changed; and to work effectively, it is previously regulated for a particular velocity, and the valves arranged accordingly. It is not simply the question of letting into the cylinders a greater or less quantity of steam; but it is in adapting what is technically called the lead, to the velocity which it is designed to travel with. This lead is different in