In effect, we have seen, from equation (a,) that after the steam has assumed in the engine the pressure R, the absolute volume of that steam, which corresponds to the volume of water S, is given by the relation

S

n + q R

On the contrary, when the steam is supposed to preserve its temperature, the volume varies in the inverse ratio of the pressure. If, then, we call m the relative volume of the steam generated at the pressure P of the boiler, a relative volume which can be known by the tables already given, it is clear that the absolute volume of the steam correspondent to the volume S of water will first be, under the pressure P, expressed by m S; and that, in passing afterwards to the pressure R, this volume will change in the inverse ratio of the pressures, that is to say, will become

Therefore to pass from one law to the other, we must write

or, what comes to the same, we must, in the formulæ already obtained, make

which. for the case of unexpansive engines, or for l'=l, reduces itself to the following:

And this is precisely the equation we made use of in the first chapter, if only we neglect in it the clearance of the cylinder c.

The quantity R contained in equation (1,) is the total resisting pressure which takes place on the unit of surface of the piston in the motion. But this resisting pressure is evidently composed of three parts, namely, the resistance arising from the motion of the load, which we will call r; that arising from the friction proper to the engine, which we will express by (f+dr.) calling fthe friction of the engine unloaded, and & the augmentation of that friction per unit of the load r; and finally the pressure which may subsist on the face of the piston opposed to the arrival of the steam, which we will represent by p; the latter quantity p expressing the atmospheric pressure, when the engine is without condensation, or only the pressure of condensation in the cylinder, when the engine is a condensing one. The quantities r, f, p and ỗ, are besides, as well as R, referred to the unit of surface of the piston.

(To be continued.)

The Menai Bridge is undergoing a complete repair, having suffered considerable damage in the storm last winter. Government has granted 8,000, but this is by no means sufficient.

The recent memorial of the Harlem Railroad Company, to the Corporation of the city of New York, praying for leave to extend a branch of their railroad through certain streets of the city, has attracted the attention of the public, and we feel certain that it will be more fairly discussed than on previous occasions, when similar propositions have been inade.

From the earliest construction of railroads in this country, there appears to have been more or less prejudice entertained against their continuation thorough large cities, and consequently, in some cases, at least, important roads were suffered to terminate at points far removed from the centre of business, and not generally accessable without the aid of carriages and omnibusses. The result of these arrangements has, in many cases undoubtedly been a serious injury to the prospects of the work.

Among the reasons given against granting permission to lay rails, or run cars in large cities are the following:-The great danger supposed to arise from using locomotive engines, both on account of the fright they are uniformly said to give to horses, and the risk of running over persons crossing the street. In the next place it was urged, that even if horses were used, too much of the public highway would be taken up by the rails, and that for general purposes, any street so occupied by a railroad, would be entirely useless to the greal injury of the property fronting upon it, or in its neighborhood. A third, and to some persons, insurmountable objection was the encouragement offered to a monopoly interfering with the free and illimitable rights of citizens.

At the time that these objections were first brought forward, they were considered, by many, as unanswerable, and although great changes have taken place in public feeling, and new light has been thrown upon such subjects, there are doubtless those who, to this day, continue in the disbe lief of the propriety of any such arrangements. We had ourselves formerly entertained an opinion unfavorable to any such imagined encroachments

upon the public comfort, safety or rights, but from an attentive examination of the subject, and from the results of the experience of several places in which city railroads have been tried, we cannot but believe that there is a great bilance in favor of this mole of transit. Philadelphia and Baltimore, as well as New York, had made the experiment some time since, and now we believe the practice has become quite general. In this city, which, from its great size, furnishes an extreme case, we have had the daily observation of the working of the Harlem railroad, and in speaking on the subject, we shall refer to the operation of the principle in this case.

Let us now consider the objections above named and then proceed to an examination of the advantages which may be adduced on the other side of the question.

The necessity for the use of a locomotive in streets exists in but few cases. It is not contemplated by any one, to introduce engines into the very heart of populous cities, but as it is proper and necessary to use them in the vicinity of towns and in their less crowded parts, we shall stop to consider the difficulties said to be inseparable from their employment. The danger to be apprehended from frightening horses, is greatly exagerated, and it is a fact worthy of notice, that they very soon become accustomed to the noise and unaccountable motion. This every one must have noticed upon a line of road which has been for some time in operation. We remember watching, with no little curiosity and amusement, the various expedients used upon the Long Island railroad, to disguise the engine in approaching Brooklyn. Among others, a sort of jacket was provided for the bright part of the works, and another for the smoke pipe; and for this or other reasons, various arrangements of the train were made, the locomotive sometimes being behind the cars. After all, it seems to us, that the horses were as little disturbed by the undisguised engine, at the head of the train, as by any other arrangement. In fact, after a while no difficulty whatever occurred, and we have seen spirited horses driven along side of the engine for some time without betraying any symptoms of fear. The noise of the exhaust steam seems to have the most effect to create terror, but we believe that various contrivances for remedying it have been made. The danger of running over passengers is also much less than is generally imagined, except in eases of wilful carelessness, we might almost say, madness. The perfect control under which a steam engine can be kept, at low velocities, renders it far superior, as a means of locomotion, to horses in ordinary wheel carriages. A locomotive under the guidance of a steady engine-man, is decidedly safer than a pair of unruly horses, driven by some dandy who is as ignorant of his art, as of managing the steam engine itself—yet who would think of excluding the latter from the highway. Moreover, the risk of accident, small as it is, is confined to a small portion of the street, which the.engine never leaves.

As to the objection that railroads are encroachments upon the public streets, we have only to appeal to experience to answer it. It is found that

when the cars are not passing, the street is, to all intents and purposes, as free and unincumbered, as without the rails-while the cars themselves take up no more room than ordinary conveyances, and not so much as a large hay wagon-no one would think of excluding hay wagons from the city, yet they not only travel through the streets, but make regular stands of certain parts of the city, to the undoubted inconvenience of many citizens. Business of all kinds seems to flourish in the neighborhood of city railroads, stores and dwellings are let for higher prices, and property is permanently improved in value, and we feel certain, that no case can be found, in which property near such rail tracks, used for constant travel, has diminished in value. The danger to passengers is extremely small, and much less than from ordinary vehicles.

In answer to the third objection, we do not intend to discuss the question of monopoly, convinced, as we are, that a corporation under suitable limitations, is far less of a monopoly than a fire engine company, who, in defiance of law, and at the peril of life and limb-to say nothing of corners of steps, and flag stone-scour not the middle of the street, but the side walks. It must be remembered, that in a large city, every means of public conveyance must be regulated by law, and the number of carts, omnibusses, porters, etc., limited. Now we have at once a monopoly, and one more onerous to the public than a railroad company could possibly be. Nothing can equal the absolute certainty with which all regulations of municipal police, can be enforced upon a railroad, while carriages and omnibusses enjoy a monopoly of lawlessness, and in fact, form the greatest nuisances in our large cities.

But a consideration of the other side of the question will open to us a view of many real advantages and permanent benefits to a city from the use of a well managed railroad. There can be no doubt that the termination of all extensive line of road, in the very centre of a large city, will be a great source of increase of wealth. But no such road should be allowed to lay its rails within the streets of a city, without opening accommodations to that part through which it passes, by running freight cars. All the disadvantages that really attach to such matters, belong as well to the least travelled, as to the most travelled road-while all the benefits belong only to the latter. Some persons entertain strange notions of public convenience, and we have heard those in the councils of our city who were for removing the various steam boat landings as far as possible from each other, in order that strangers might be compelled to traverse a larger portion of our cityfor whose benefit? why, for that of the hack driver. This sort of reasoning is not unlike that by which we suppose the good people of New York (opposed, as they are, to monopolies,) arrived at the propriety of their present custom, of giving up their residences and taking new ones on the first of May-by which cust, every one is inconvenienced except the cartmen, prters, house cleaners, and last, but not least, landlords, who enjoy the mo nopoly of having the remainder of the population at their mercy and there

fore get from them as much as they please and do as little as they can.Even to these scrupulous people a railroad is no longer a bugbear, for while it facilitates immediate access to the very centre of the city-instead of straining the population through the various streets--it likewise facilitates the egress from the centre to the outskirts and fully returns what it had carried in.

In their memorial, the Harlem railroad company mention a circumstance which to us appears worthy of very attentive consideration, viz:-that they are now carrying over one million of persons annually, entirely at their own expense, they keeping the street in order and doing their own repairs. I we only consider, what it would cost to transport one million of persons by omnibusses, (confessedly the most destructive of all vehicles to pavements,) we can imagine the gain of the city. But again, this traffic costs the people less than any other method of conveyance, the fare being at an average of about three-fourths or even one-half that of the omnibusses.

Railroads have justly been called democratic institutions, they are for the people, and rich and poor alike derive the advantage from them. In fact, the benefit to the poorer classes is one of our best arguments. How many laborers, living at a distance from their place of work, can, for a trifle, be transported thither, without loss of time or strength. We have no doubt, that calculation would show an incredible amount of labor saved in this manner to the city in each day.

We might go on to multiply arguments in favor of that view which we have taken of the question, but our design has been rather to excite the attention of others than to exhaust the subject.

In conclusion we may remark, that from the orderly and accommodating demeanor of all attached to the Harlem railroad, we feel convinced, that the design of the company, to afford every convenience to the public, will be fully carried out. By the gradual change to eight-wheel cars, a saving will arise to themselves, and increased comfort to travellers, and we have no hesitation in saying, that if the prevailing spirit is carried out in the management of the company, they will be justified by the amount of travel, before long, in resorting entirely to eight-wheel cars.

We wish the company all manner of success and prosperity in their undertaking, and hope that they will realise the reward of their public spiritedness and good management, as they certainly will at no very distant period.

NEW YORK AND HARLEM RAILROAD.

By a memorial, the publication of which was commenced in cur last, we learn that an application is to be made by this company, to the corporation of the city for permission to lay a track from the main road in Centre, through Canal street, to the Hudson river; and thereby to accommodate a greater number of citizens than they are now able to do. We were, we must confess, not a lit. tle surprised, on reading the memorial, to find that the company, which has labored so long, so perseveringly, and at such an enomous expense to con