subject now under consideration. On this point, the data with which we are furnished is so very limited, as scarcely to render it possible to form any decisive opinion.

The engines which have been some time at work at Mr. Brandley's collieries, near Leeds, have a cogged wheel, playing in a rack, which is laid as one of the rails of the road; and those at Hetton colliery are much on the same principle. This plan is objectionable, because the whole weight of the engine, which, on the most improved construction, is not less than eight tons, is on the wheel, so that any obstacle on the rail, must of necessity shake the whole machinery. To obviate this, Mr. Gordon has contrived, and taken out a patent for a locomotive carriage with the engine on springs, which imparts the motion without any connexion with the wheels or axle-tree, and there are various other plans in progress for the same object. But le this be effected as it may, the great weight of the engine which is by far the greatest objection, is not obviated. And indeed, this appears to us only possible to be accomplished.by either diminishing the weight of the engine, as proposed by the application of Mr. Brown's pneumatic, or vacuum engine, or taking the engine entirely from the carriage, and employing stationary engines, at suitable distances, to tow or draw the carriages in regular succession. This last mode has been applied to practice in the vicinity of Newcastle, by Mr. Thompson; and the results may be seen in some very able observations annexed to the specification of his patent, and inserted in the Repertory of Arts, for March, 1822.

His method consists in dividing the line of Rail-road into any number of stages, at suitable distances apart. At the end of each stage an engine is erected for the purpose of drawing the carriages from the next stage, or engine, or either side, towards itself. This is effected by means of ropes, which, previously to commencing operation, are taken from each respective engine to the engine immediately before it by horses; but after the work has commenced, by being hooked at the end of the advancing or returning carriages.

In forming lines of rail-road upon this system, that is, where stationary engines are to be employed, it is not necessary that they incline in the direction of the loads, or be made perfectly level. For in engines of this description there is no occasion to pay that particular attention to the weight of the boiler and appurtenances, as is the case in engines

which have a locomotive principle. Indeed trifling inequalities of surface, which would be a material objection in the application of locomotive carriages, are, in the lines of road where stationary engines are employed, quite unheeded.

As many roads are traversed by night as well as by day, it becomes necessary that a signal should be given from one engine to the other as soon as the carriages have arrived and are hooked to its respective ropes, that the engine tender may not be at a loss when to throw his machinery into geer. For this purpose, Mr. Thompson recommends that the door of the fire-place of the boiler, or other strong light, be placed towards the engines on each side, so that, by opening it on that side which faces the engine, to whose ropes the carriages just arrived have been attached, the engineer may adopt such measures as will effect the desired

purpose.

It is true, locomotive engines were not at that period so well understood as at present; but it appears to us that this point still remains in a very undecided state, and that from the even now limited experience in propelling carriages on railways, at a speed any thing like that of common carriages, it is very difficult to hazard an opinion. From the data, however, that can be collected, we certainly incline to stationary engines, as the most mechanical and economical application of the requisite power.

As to the degree of danger which travellers may be exposed to by locomotive engines, it cannot, under a proper management, exceed that of a steam-boat, or a factory, where power is operating. It is true, that as the weight of the engine is of great consideration, condensing engines (if steam be the force employed,) are quite inapplicable, and what are generally called high pressures must be introduced. But though all engines which do not condense their steam, and act only by the pressure, or elastic force, are called high pressure engines, there is no necessity whatever to go to dangerous heats, and with either wroughtiron or copper boilers and valves, placed out of the reach of the operative engineer, or engine tender, may certainly be worked at 45 or 53lbs. pressure, with as much safety as at 20lbs. in condensing engines. Indeed, on investigating the cause of steam explosions, they will be found to have rarely occurred but from the grossest ignorance and neglect. Such of our readers who are desirous to have farther information on this interesting subject, we must refer to a very able report on rail-roads, by Mr. Charles Sylvester,

to the paper alluded to by Mr. Thompson, in the Repertory of Arts, for March, 1822, to a work which will shortly issue from the Press, by Mr. N. Wood of the Killingworth Colliery, of whose experiments, in conjunction with Mr. Sylvester, we have already had occasion to speak, and to Observations on a General Iron Railway, by Mr. Gray.

APPENDIX.

GEOMETRY.

GEOMETRY is that branch of mathematics which treats of the description and properties of magnitudes in general.

Definitions or Explanation of Terms.

1. A point has neither length, breadth, nor thickness. From this definition it may easily be understood that a mathematical point cannot be seen nor felt; it can only be imagined. What is commonly called a point, as a small dot made with a pencil or pen, or the point of a needle, is not in reality a mathematical point; for however small such a dot may be, yet if it be examined with a magnifying glass, it will be found to be an irregular spot, of a very sensible length and breadth; and our not being able to measure its dimensions with the naked eye, arises only from its smallness. The same reasoning may be applied to every thing that is usually called a point; even the point of the finest needle appears like that of a poker when examined with the microscope.

2. A line is length, without breadth or thickness. What was said above of a point, is also applicable to the definition of a line. What is drawn upon paper with a pencil or pen, is not in fact a line, but the representation of a line. For however fine you may make these representations, they will still have some breadth. But by the definition, a line has no breadth whatever, yet it is impossible to draw any thing so fine as to have no breadth. A line therefore, can only be imagined. The ends of a line are points.

3. A right line is what is commonly called a straight line, or that tends every where the same way.

4. A curve is a line which continually changes its direction between its extreme points.

5. Parallel lines are such as always keep at the same distance from each other, and which, if prolonged ever so far, would never meet. Fig. 1.

6. An angle is the inclination or opening of two lines meeting in a point, Fig. 2.

7. The lines AB, and BC, which form the angle, are called the legs or sides; and the point B where they meet, is called the vertex of the angle, or the angular point. An angle is sometimes expressed by a letter placed at the vertex, as the angle B, Fig. 2; but most commonly by three letters, observing to place in the middle the letter at the vertex, and the other two at the end of each leg, as the angle ABC.

8. When one line stands upon another, so as not to lean more to one side than to another, both the angles which it makes with the other are called right angles, as the angles ABC and ABD, Fig. 3, and all right-angles are equal to each other, being all equal to 90°; and the line AB is said to be perpendicular to CD.

Beginners are very apt to confound the terms perpendicular, and plumb or vertical line. A line is vertical when it is at right-angles to the plane of the horizon, or level surface of the earth, or to the surface of water, which is always level. The sides of a house art vertical. But a line may be perpendicular to another, whether it stauds upright or inclines to the ground, or even if it lies flat ups it, provided only that it makes the two angles formed by meeting with the other line equal to each other; as for instance, if the angles ABC and ABD be equal, the line AB is perpendicular to CD, what ever may be its position in other respects.

9. When one line, BE (Fig. 3,) stands upon another, CD, so to incline, the angle EBC, which is greater than a right-angle, is called an obtuse angle; and that which is less than a right-angle, called an acute angle, as the angle EBD.

10. Two angles which have one leg in common, as the angis ABC, and ABE, are called contiguous angles, or adjoining angles; those which are produced by the crossing of two lines, as the angles EBD and CBF, formed by CD and EF, crossing each other, a called opposite or vertical angles.

11. A figure is a bounded space, and is either a surface or a scli2. 12. A superficies, or surface, has length and breadth only. The extremities of a superficies are lines.

13. A plane, or plane surface, is that which is every where pe fectly flat and even, or which will touch every part of a straight line. in whatever direction it may be laid upon it. The top of a marte slab, for instance, is an example of this, which a strait edge wil touch in every point, so that you cannot see light any where between 14. A curved surface is that which will not coincide with a straight line in any part. Curved surfaces may be either convex or concave. 15 A convex surface is when the surface rises up in the middle, as, for instance, a part of the outside of a globe.

16. A concave surface is when it sinks in the middle, or is hollow, and is the contrary to convex.

A surface may be bounded either by straight lines, curved lines, of both these.

17. Every surface, bounded by straight lines only, is called polygon. If the sides are all equal, it is called a regular polygon. If they are unequal, it is called an irregular polygon. Every polyg whether equal or unequal, has the same number of sides as angles, and they are denominated sometimes according to the number of sides, and sometimes from the number of angles they contain. Thus a figure of three sides is called a triangle, and a figure of four sides a quadrangle.

A pentagon is a polygon of five sides.,