when r is the radius of the axle, and R the radius of the wheels.

the

The engines should work expansively when moving at the ordinary rate, and upon mean inclination, with the power of working at full pressure on the steeper ascents. See Sect. V. (art. 371-380.)

The carriage is described in Plate XX; and for further information see my "Treatise on Rail Roads."

tiplied by the effective pressure on an inch in pounds, should be equal to the resistance of the carriages added to the friction of the rope and the engine.

If A be the ascending and D the descending load, and q the resistance from friction at the axis, and i the angle of inclination.

Then A (sin. + q) D (sin. i-q) i · resistance of the carriages.

sin. i (AD) + q ( A + D)

= the

The weight of the rope or chain and of the moveable parts of the engine being C, its friction and the stiffness of the rope may be represented by C S, hence, if d be the diameter of the piston, and p = the pressure on a circular inch, we have do p = sin. ¿ ( A − D) + q ( A + D) + C S.

From this the diameter of the cylinder is easily found, and in all cases

r f q= R

where R is the radius of the wheels of the carriage, r that of the axles, and ƒ the friction, when the pressure is 1.

when X is the diameter of the pulleys, and a that of the axes. level d2 p = q, ( A + D ) + C S, when it is vertical d2 p = D + C.)

In these equations the piston of the engine, and the load, are supposed to move at the same velocity; if the carriages move at n times the velocity of the piston, then it will require the square of the diameter to be increased n times.

592.—Steam carriages. The engines of steam carriages are double noncondensing engines, of the kind described in (art. 372.) They have generally two cylinders. If the mean effective pressure on the piston be p, the diameter of the cylinders d, and v the velocity in feet per minute; and if i be the angle of inclination of the rails of the road, q the friction of all the axes, W the weight of the carriages and their loads, V their velocity in feet per minute, and E the weight of the engine; then V (W + E ) ( q + sin. ¿ ) = 2 d* p v, in ascending the inclination: and V (W + E ) ( 9 — sin. i ) = 2 d2 p v, in descending the inclination. Also

=

when r is the radius of the axle, and R the radius of the wheels.

The engines should work expansively when moving at the ordinary rate, and upon the mean inclination, with the power of working at full pressure on the steeper ascents. See Sect. V. (art. 371-380.)

The carriage is described in Plate XX; and for further information see my "Treatise on Rail Roads."

SECTION X.

OF STEAM NAVIGATION.

593-On the value of the application of steam to impel vessels, it has become unnecessary to say more than that its employment is extending rapidly at almost every place on the globe where the trade is considerable; and that its use is limited only by its yet imperfect state. If we had intended to have confined our researches to the mere application of an engine to a vessel already constructed, our labour would have been short, and easily completed: but the construction of vessels is a subject which is capable of improvement; and while we think there is a power in science to indicate the steps by which it may be improved, it is our duty to submit it to the reader.

The forms of vessels for stability, speed, capacity and strength; the kinds of vessels for different purposes, the resistance, and modes of propulsion; the nature of the engines adapted for vessels, the strength of their parts, and the species of fuel, and its management to obtain the best effect; are all objects of importance, and each of these we propose to consider.

These inquiries are equally applicable to mercantile and to government purposes, but there is yet another portion of the subject to which it would be desirable to direct attention.

In the case of war, steam boats will become a means of attack, therefore it ought to be considered how far they may become a means of defence, the power of resisting being the best guard against a mode of attack, which will deprive us of many of the advantages of our insular state. Hence, the construction of gun boats for the defence of rivers, and of river navigation, and harbours, would be a proper subject for inquiry, if our limits did not forbid it.

Of the Forms of Vessels for Stability, Speed, Capacity, and Strength.

594.-In considering the properties of a vessel, the orderly arrangement of our subject requires that we should treat, First, Of stability, or the power a vessel has of resisting any change of position when in the water; Secondly, The forms having stability which have the least resistance, and are therefore best adapted for speed; Thirdly, The different methods of propelling vessels; and, Fourthly, The construction for strength.

Of the Stability of Vessels.

595.-A perfectly spherical ball floating in a fluid has no stability whatever, except that which arises from the friction of the fluid against its sides. On the addition of a small weight to any point of its surface, that point would immediately descend, and become the lowest. Such a form would be useless as a vessel. It is obvious however that when a weight has been added, and become the lowest point, the sphere possesses a degree of stability depending on the quantity of weight compared with the weight of the sphere itself. Hence, stability may be given by disposing the weight of a floating body.

Stability may also be given by the form of the floating body; a spheroid for example remains in stable equilibrium when its longer axis is horizontal, and a triangular prism resists change of position with considerable energy from its peculiar form; so does a thin rectangular prism.

596.-Stability is distinguished by its being longitudinal or lateral; these should be separately considered, and when each is the greatest possible, their joint effect will be a maximum.

597. For river navigation, the mode of obtaining stability does not appear to be of much importance, but for a sea vessel it must be obtained, so that the vessel may have the least motion possible in consequence of the action of the disturbing forces; hence, it is necessary to consider that the sea is not a level surface at rest, and that at the time when stability is most important to a vessel, the greatest degree of unevenness

occurs.

598.-Longitudinal stability. A vessel at rest would be least disturbed by the motion of the sea, if its surfaces at the water line were vertical ones; and the fore and