of planes more or less inclined to the horizon, along which the engines travel, without any further assistance, except on some of the steepest inclined planes.

The second consists of obtaining level gradients as long as possible, and, where it is necessary to change the level, it is done by the intervention of an inclined plane, with assistant engines, either stationary or locomotive. The respective merits of these two plans we shall now discuss.

It is asserted that, in a railway constructed upon the system. of variable gradients, the power necessary to convey goods between the two places will be the same as if the two places were connected by a single plane; or, supposing the two extremities of the line to be upon the same level, then the power would be the same as though the whole line were level; but this is not correct when the inclination of the plane exceeds the angle at which the carriages will roll down of themselves; as, for example:

FIGURE 1.

A

B

In figure 1, let A and B be two places between which it is desirable to form a railway, but that it is necessary to rise to the elevation of C, and then descend on the opposite side. Let AC and C B be each equal to one mile, and the rise C c equal to 95 feet, then the power necessary to carry 1 ton from

A to B will be as follows:-From A to C 1 mile =

8lbs.,

friction+4lbs., effect of gravity =12lbs. ; from C to B1 mile, 8lbs., friction-4lbs., effect of gravity + 4lbs., making + 12lbs. = 16, which is the same as though the road between A and B were level, at the rate of 8lbs. per ton per mile, because the additional resistance occasioned by the effect of gravity in ascending from A to C, 4lbs., would act as a propelling power when the goods descended from C to B, and therefore must be deducted, which would cause the whole power to be 16lbs. for the 2 miles, or 8lbs. per mile as on a level.

FIGURE 2.

D

A

=

=

d

=

Again, in figure 2, let A and B be the two places; then let A C, C D, D B, each equal 1 mile; Cc 9.5 feet, D d — 4.75 feet, and Bb 14.25, then the power necessary to convey one ton of goods from A to B will be as follows: 8lbs. per ton + 4lbs, effect of gravity 12lbs.; from C to D, 1 mile 8lbs. friction, - 2lbs., effect of gravity =6lbs; D to B, 8lbs. + 4lbs. effect of gravity= 12lbs., making 12 + 6 +12= 30lbs., at the rate of 10lbs. per mile, all same as raising from A to B in one plane, A to B being 3 miles, and

=

B

to b 14.55 feet, which would be 24lbs. friction, at the rate of 8lbs. per mile, and 6lbs. effect of gravity, at the rate of 2lbs. per mile, making 10lbs. per mile, the same as before. The effect of gravity in ascending one plane being counteracted by descending another; but this is not the case where the inclination of one plane exceeds 19 feet per mile, the inclination at which a body will descend the plane by its own gravity; because, suppose the planes AC and C B, figure 1, to be each 1 mile, and the elevation Cc to be 31 feet, then the power necessary to carry one ton of goods from A to B will be as follows:-A to C 8lbs. friction, gravity = 16lbs. = 24lbs.; but the resistance from A to C being only 8lbs. friction, we can only make use of 8lbs. out of the 16lbs. from the effect of gravity, 8lbs. of. which is consequently lost; so that we see that the compensation for the effect of gravity is lost if the inclination of a plane exceeds 19 feet per mile, when the effect of gravity exceeds the friction.

On a railway constructed with variable gradients, the resistance of the load varies according to the angle of the plane on which it happens to be travelling, and as it follows that the engine must have sufficient power to overcome the greatest resistance, it will become necessary to employ an engine of greater power and weight than on a level road, where assistance is made use of to ascend the planes: it also follows, that the rate of travelling will vary also, because when an engine of sufficient power to overcome the resistance of the steepest inclined plane, at the rate of 30 miles an hour, which would be the most rapid rate of travelling; the engines are, therefore, exposed to considerably more wear and tear than if they were kept going at a regular speed. In addition

to which, a locomotive engine is not so well adapted to raise a weight as to overcome the friction, because when an engine ascends an inclined plane, the pressure on the plane is diminished, and consequently the adhesive power between the rails and the wheels of the carriage; and if the resistance should surpass the power of adhesion, all locomotion would

Now, a railway, my young friends, constructed upon the principle of a series of level planes connected by steep inclined planes, has considerable advantages over one of variable gradients. In the first place, the engines act upon much more advantageous principles upon a level than they do

on inclined planes. Secondly, there is less loss of time in ascending to the necessary elevation at once, and then running a considerable distance upon a level, because the assistant power may be sufficient to maintain the regular speed on a level. Now, it will be seen, that on the first plane we can only obtain an average speed, whereas, on the latter, the engines travel at an uniform speed, and, therefore, admit of being made so that they will be less subject to wear; hence considerable advantages are procured by the latter over the former plan.